Answers
Answer:
(B) m∠BCD = 108°
Step-by-step explanation:
The measure of an arc is equal to the measure of its corresponding central angle. The corresponding central angle of arc AB is angle ACB.
Therefore, if the measure of arc AB is 72°, then m∠ACB = 72°.
Angles on a straight line sum to 180°.
Assuming that AD is a straight line, then:
m∠BCD + m∠ACB = 180°
m∠BCD + 72° = 180°
m∠BCD + 72° - 72° = 180° - 72°
m∠BCD = 108°
Therefore, the measure of angle BCD is 108°.
Related Questions
A teaching hospital in South-West Part of Nigeria receives on the average 5 pregnant women with high blood pressure per week. What is the probability that on a particular week, the teaching hospital will receive:
1.) No high BP pregnant woman
Answers
Answer:
The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Step-by-step explanation:
We use the Exponential distribution,
Since we are given that on average, 5 pregnant women with high blood pressure come per week,
So, average = m = 5
Now, on average, 5 people come every week, so,
5 women per week,
so, we get 1 woman per (1/5)th week,
Hence, the mean is m = 1/5 for a woman arriving
and λ = 1/m = 5 = λ
we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,
P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,
Now,
P(X>1) = 1 - P(X<1),
Now, the probability density function is,
[tex]f(x) = \lambda e^{-\lambda x}[/tex]
And the cumulative distribution function (CDF) is,
[tex]CDF = 1 - e^{-\lambda x}[/tex]
Now, CDF gives the probability of an event occuring within a given time,
so, for 1 week, we have x = 1, and λ = 5, which gives,
P(X<1) = CDF,
so,
[tex]P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068[/tex]
So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
16
Find X.
25
X
Pythagorean Theorem
Answers
Answer:
3√41
Step-by-step explanation:
a^2+b^2=c^2
rearrange this to make x (a or b it doesn't matter) the subject
√b=c^2-a^2
now substitute this in:
√b=25^2-16^2
=369
then simple do the square root
√369
=3√41
Hope this helps!
Sample Answer: The activity type would be the input and the cost would be the output. Because there are two different costs for the same activity, this would not be a function.
Select any items on the list that you included in your response:
The activity type would be the input and the cost would be the output.
Because the rec center charges different prices for the same activity on different days, one input does not result in exactly one output.
No, the situation does not represent a function.
Answers
Due to the variation in costs for the same activity on different days, the situation does not represent a function.
Based on the information provided, it is clear that the situation does not represent a function. A function is a mathematical relationship where each input (or element from the domain) corresponds to exactly one output (or element from the range). In this case, the activity type serves as the input, and the cost represents the output.
However, since the rec center charges different prices for the same activity on different days, it violates the fundamental principle of a function, which states that one input cannot result in multiple outputs. The fact that there are two different costs associated with the same activity contradicts the definition of a function.
For example, let's consider the activity type "swimming." On Monday, the cost might be $10, but on Tuesday, the cost could be $15. This inconsistency demonstrates that one input, "swimming," leads to different outputs ($10 and $15). Therefore, it fails the criterion of a function.
To clarify, if each activity type had a consistent, unique cost associated with it, the relationship between the activity type and cost could be considered a function. However, since multiple costs exist for the same activity type, we cannot establish a definitive mapping between the inputs and outputs, rendering it non-functional.
In conclusion, due to the variation in costs for the same activity on different days, the situation does not represent a function.
for more such question on function visit
https://brainly.com/question/11624077
#SPJ8
Find each value given the following function:
Answers
Answer:
Step-by-step explanation:
1) f(-4) --> if x < or equal to 3
2) 1/(-4)-4
3) The answer is - 1/8
Mamá compra una caja de cubitos de azúcar. María se come la capa superior (S), que tiene 77 cubitos; después se come la cara lateral (L), que consta de 55 cubitos; y finalmente se come la cara frontal (F) también. ¿Cuántos cubitos quedan en la caja
Answers
Si mamá compra una caja de cubitos de azúcar y María se come la capa superior (S) de 77 cubitos, luego se come la cara lateral (L) de 55 cubitos y finalmente se come la cara frontal (F) también, podemos determinar cuántos cubitos quedan en la caja sumando todas las partes que María ha consumido.
En total, María se ha comido 77 cubitos de la capa superior, 55 cubitos de la cara lateral y otros cubitos de la cara frontal. Como no se proporciona el número exacto de cubitos de la cara frontal, no podemos calcular el número total de cubitos que quedan en la caja.
Para obtener la cantidad final de cubitos que quedan en la caja, necesitaríamos saber cuántos cubitos hay en la cara frontal y luego restar la suma de los cubitos que María se ha comido. Sin esa información adicional, no podemos determinar cuántos cubitos quedan en la caja.
For such more question on María
https://brainly.com/question/27824731
#SPJ8
HELP ME PLEASE.
The figure below shows a rectangle ABCD having diagonals AC and DB:
Jimmy wrote the following proof to show that the diagonals of rectangle ABCD are congruent:
Jimmy's proof:
Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent).
Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°
Statement 3:
Statement 4: Triangle ADC and BCD are congruent (by SAS postulate)
Statement 5: AC = BD (by CPCTC)
Which statement below completes Jimmy's proof? (1 point)
• AB=AB (reflexive property of equality)
• AB=AB (transitive property of equality)
O DC=DC (reflexive property of equality)
O DC=DC (transitive property of equality)
Answers
Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent).
Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°).
Statement 3: DC = DC (reflexive property of equality).
Statement 4: Triangle ADC and BCD are congruent (by SAS postulate).
Statement 5: AC = BD (by CPCTC).
The statement that completes Jimmy's proof is:
DC = DC (reflexive property of equality)
The reflexive property of equality states that any quantity is equal to itself. In this case, statement 3 is stating that the diagonal DC is equal to itself, which is true by the reflexive property of equality.
Therefore, the completed proof is:
Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent).
Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°).
Statement 3: DC = DC (reflexive property of equality).
Statement 4: Triangle ADC and BCD are congruent (by SAS postulate).
Statement 5: AC = BD (by CPCTC).
for such more question on triangle
https://brainly.com/question/17335144
#SPJ8
Factor using the GCMF.
6x4 + 12x³ + 15x²
2x^3 + 4x^2 + 5x
3(2x^4 +4x³+5x²)
3x² (2x² + 4x + 5)
3x^2
Answers
Answer:
3x² (2x² + 4x + 5)
Step-by-step explanation:
Step 1: Identify the coefficients.
In the given expression, the coefficients are 6, 12, and 15.
Step 2: Find the GCMF of the coefficients.
The GCMF is the largest number that can divide each coefficient evenly. In this case, the GCMF of 6, 12, and 15 is 3.
Step 3: Identify the variables.
The variables in the expression are x^4, x^3, and x^2.
Step 4: Find the GCMF of the variables.
The GCMF of the variables is the highest power of x that appears in each term. Here, it is x^2.
Step 5: Combine the GCMF of the coefficients and variables.
The GCMF of the coefficients (3) and the GCMF of the variables (x^2) can be multiplied together to get the overall GCMF: 3x^2.
Step 6: Factor out the GCMF from the expression.
To factor out the GCMF 3x^2, divide each term of the expression by 3x^2:
(6x^4 + 12x^3 + 15x^2) / (3x^2) = 2x^2 + 4x + 5
Step 7: Write the factored form.
The factored form of 6x^4 + 12x^3 + 15x^2 is 3x^2(2x^2 + 4x + 5).
What did Amy do wrong
Answers
What Amy did wrong was not moving the pointer to the arc intersection with the horizontal side
What is an angle bisector?An angle bisector is defined in geometry as a line that splits an angle into two equal angles.
The steps involved in constructing an angle bisector are;
Draw an angle on your paper. Make sure one side is horizontal.Place the pointer on the vertex. Draw an arc that intersects both sides.Move the pointer to the arc intersection with the horizontal side.Connect the arc intersections from with the vertex of the angle.Learn more about angle bisectors at: https://brainly.com/question/24334771
#SPJ1
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The value of x is equal to 15 units.
What is the triangle midpoint theorem?In Mathematics and Geometry, the Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.
In Mathematics and Geometry, a midsegment is a type of line segment that is used for connecting the midpoints of two sides of a triangle.
By applying the triangle midpoint theorem, we can determine the value of x as follows:
JH = 1/2(LM)
JH = 1/2 × 30
JH = x = 15 units.
Read more on midsegment here: https://brainly.com/question/14981061
#SPJ1
Markshisand
Which steps should be used to compare the fractions and
O Find a common numerator.
O Add the numerators and denominators to determine which sum is larger.
O Use the "greater than" symbol to show which denominator is larger.
O Multiply the first fraction by 2 and the second fraction by 3
Answers
1. Find a common denominator: Make sure both fractions have the same denominator by finding a common multiple of the two denominators.
2. Compare the numerators: Once the fractions have a common denominator, compare the numerators to determine which numerator is larger.
3. Use the "greater than" or "less than" symbol: Based on the comparison of the numerators, use the appropriate symbol (> or <) to indicate which fraction is larger.
4. Simplify or convert: If necessary, simplify the fractions or convert them to mixed numbers for a clearer comparison.
Therefore, the steps mentioned in the given options are not entirely accurate. The correct steps to compare fractions are as described above.
35
The cost of packing a box of chocolates is given by x2, where x is the number of chocolates (a box can never have fewer than 3 chocolates). If the
weight of a box of chocolates is given by x + 2, what is the cost of packaging per weight unit?
OA.
B.
O c.
OD.
O
++2
2² +1
²+1
--
Reset
Next
Answers
The cost of packaging per weight unit is x + 1.
To derive this answer, we first need to understand the given information. The cost of packing a box of chocolates is given by [tex]x^2[/tex], where x is the number of chocolates. However, we also know that a box can never have fewer than 3 chocolates.
Now, let's calculate the weight of a box of chocolates. It is given by x + 2.
To find the cost of packaging per weight unit, we need to divide the cost of packing by the weight of the box. Therefore, the cost of packaging per weight unit can be calculated as ([tex]x^2[/tex]) / (x + 2).
Simplifying this expression, we can rewrite it as ([tex]x^2[/tex]) / (x + 2) = (x + 1) - 1 / (x + 2).
Hence, the cost of packaging per weight unit is x + 1, which means that for every unit of weight, the cost of packaging is x + 1.
For more such questions on weight, click on:
https://brainly.com/question/29892643
#SPJ8
Two cars start moving from the same point. One travels south at 50 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing 2 hours later? Round the result to the nearest hundredth.
Answers
The rate at which the distance between the cars is increasing 2 hours later is 0 mi/h, by using the Pythagorean theorem.
To find the rate at which the distance between the cars is increasing, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Let's assume that after 2 hours, the distance traveled by the southbound car is d_south and the distance traveled by the westbound car is d_west.
Since the southbound car travels at a speed of 50 mi/h for 2 hours, we have d_south = 50 mi/h [tex]\times[/tex] 2 h = 100 mi.
Similarly, the westbound car travels at a speed of 20 mi/h for 2 hours, so d_west = 20 mi/h [tex]\times[/tex] 2 h = 40 mi.
Now, we can use the Pythagorean theorem to find the distance between the two cars:
[tex]distance^2 = d_south^2 + d_west^2distance^2 = 100^2 + 40^2distance^2 = 10000 + 1600distance^2 = 11600[/tex]
distance ≈ sqrt(11600) ≈ 107.68 mi
To find the rate at which the distance between the cars is increasing, we differentiate the equation with respect to time:
2 [tex]\times[/tex] distance [tex]\times[/tex] [tex]\(\frac{{d(\text{{distance}})}}{{dt}}\)[/tex] = 2 [tex]\times[/tex] d_south [tex]\times[/tex] [tex]\(\frac{{d(d_{\text{{south}}})}}{{dt}}\)[/tex] + 2 [tex]\times[/tex] d_west [tex]\times[/tex] (d(d_west)/dt)
Since d_south and d_west are constant (no mention of their rates of change), we can simplify the equation to:
2 [tex]\times[/tex] distance [tex]\times[/tex] [tex]\(\frac{{d(\text{{distance}})}}{{dt}}\)[/tex] = 0
Therefore, the rate at which the distance between the cars is increasing 2 hours later is 0 mi/h.
For more questions on Pythagorean theorem:
https://brainly.com/question/27997683
#SPJ8
21 20 15 22 19 23 17 what is the median and range
Answers
The median would be 22:
Step-by-step explanation: The median is the number that is in the middle
Simply defined, the median is the number right in the middle of a set.
But before I get down to finding the median, I will order the numbers from least to greatest:
15, 17, 19, 20, 21, 22, 23
Now, the middle number is 20. So that's the median.
As for the range, it's the difference between the largest number and the smallest one:
Range = Greatest number - Smallest number
= 23 - 15
= 6
In summary, the median, the number in the middle, is 20, and the range, the difference between the largest number and the smallest one, is 6.
The slope of a parabola
�
=
3
�
2
−
11
�
+
10
y=3x
2
−11x+10 at a point
�
P is 7. Find the
�
−
y− coordinate of the point
�
P
Answers
The y-coordinate of point P is 1.To find the y-coordinate of the point P on the parabola y = 3x^2 - 11x + 10 where the slope is 7, we can differentiate the equation to find the derivative. The derivative of y = 3x^2 - 11x + 10 is y' = 6x - 11.
To find the x-coordinate of point P, we can set the derivative equal to the given slope: 6x - 11 = 7. Solving for x, we get x = 3.
To find the y-coordinate of point P, we substitute the x-coordinate back into the original equation: y = 3(3^2) - 11(3) + 10. Simplifying, we find y = 1.
Therefore, the y-coordinate of point P is 1.
For more question on coordinate
https://brainly.com/question/25383910
#SPJ8
A deposit of $2,580 is placed into a retirement fund at the beginning of every 6 months for 15 years. The fund earns 3% annual interest, compounded biannually and paid at the end of the 6 months. How much is in the account right after the last deposit?
Round your answer to the nearest dollar.
Answers
The amount in the account right after the last deposit, rounded to the nearest dollar, is approximately $3,982.
To calculate the amount in the account right after the last deposit, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the principal is $2,580, the annual interest rate is 3% (0.03 in decimal form), the interest is compounded biannually (twice per year), and the total duration is 15 years.
First, let's calculate the number of compounding periods:
Since interest is compounded twice a year, and there are 15 years, the total number of compounding periods is 15 * 2 = 30.
Now, we can plug the values into the formula:
A = $2,580(1 + 0.03/2)^(2*30)
A = $2,580(1 + 0.015)^60
A = $2,580(1.015)^60
Using a calculator, we find that (1.015)^60 ≈ 1.545.
A = $2,580 * 1.545
A ≈ $3,982.10
Therefore, the amount in the account right after the last deposit, rounded to the nearest dollar, is approximately $3,982.
for such more question on compound interest
https://brainly.com/question/28020457
#SPJ8
if a(x) = 3x+1 and b(x) = [tex]square root of x-4[/tex], what is the domain of (boa)(x)
Answers
The domain of (boa)(x) is [1, ∞].
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.
Based on the information provided above, we have the following functions:
a(x) = 3x+1
[tex]b(x) = \sqrt{x-4}[/tex]
Therefore, the composite function (boa)(x) is given by;
[tex]b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}[/tex]
By critically observing the graph shown in the image attached below, we can logically deduce the following domain:
Domain = [1, ∞] or {x|x ≥ 1}.
Read more on domain here: brainly.com/question/9765637
#SPJ1
How are triangleABC and triangle ADE related? How do you know pls explain.
Answers
Triangle ABC and ADE are similar triangles
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.
It has been shown that angles in ABC and ADE are equal.
To show that the ratio of corresponding sides are equal
6/12 = 8/16 = 10/20
The ratios all give a value of 1/2
Therefore we can say that the triangles ABC and ADE are similar.
learn more about similar triangles from
https://brainly.com/question/14285697
#SPJ1
What is the area of this rectangle? Rectangle with width 5.1 cm and height 11.2 cm. Responses 16.3 cm2 16.3 cm, 2 32.6 cm2 32.6 cm, 2 57.12 cm2 57.12 cm, 2 571.2 cm2
Answers
The area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².
To find the area of a rectangle, we multiply its length by its width. In this case, the width is given as 5.1 cm and the height (or length) is given as 11.2 cm.
Area = length × width
Area = 11.2 cm × 5.1 cm
Calculating the product, we get:
Area = 57.12 cm²
Therefore, the area of the rectangle is 57.12 cm².
The correct answer is: 57.12 cm².
It is important to note that when calculating the area of a rectangle, we should always include the appropriate unit of measurement (in this case, cm²) to indicate that we are dealing with a two-dimensional measurement. The area represents the amount of space covered by the rectangle's surface.
So, the area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².
for more such question on rectangle visit
https://brainly.com/question/2607596
#SPJ8
a) angle of line of From a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three figure bearings? A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point. (b) How far is the boy now from the start- ing point? A boy runs 200 m on a bearing of 230°.
Answers
a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$
\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}
100 sin 35° = 80 sin 55°=57.73 mT
herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.
Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.
To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.
Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.
Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.
To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.
(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus
:$$c^2 = a^2 + b^2$$
where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$
c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$
Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.
Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$
Therefore, the bearing of the boy's current position from the starting point is N51°E.
For such more question on triangle
https://brainly.com/question/1058720
#SPJ8
The table represents a linear relationship
X—2 0 4
Y-4 3 1
Which equation represents the table
Y=1/2x+5
y=-1/2x+3
Y=2x-3
Y=-4x+2
Answers
The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.
To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.
Given the table:
X: 2 0 4
Y: -4 3 1
We can plot these points on a graph and see that they form a straight line.
Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.
Based on the given options, we can now evaluate each equation to see which one represents the line:
Y = 1/2x + 5
When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.
Y = -1/2x + 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.
Y = 2x - 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.
Y = -4x + 2
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.
In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.
For more question on equation visit:
https://brainly.com/question/29174899
#SPJ8
Let f(x)
f'(x) =
-
=
1
v2x2+5x+3
Question Help:
(Use sqrt(N) to write √N)
Video Written Example
Answers
The derivative of the function [tex]f(x) = \frac{1}{\sqrt{2x^2 + 5x + 3}}[/tex] is [tex]f'(x) = -\frac{4x + 5}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
How to calculate the derivative of the functionFrom the question, we have the following parameters that can be used in our computation:
[tex]f(x) = \frac{1}{\sqrt{2x^2 + 5x + 3}}[/tex]
Factor the expression
So, we ave
[tex]f(x) = \frac{1}{\sqrt{(x + 1)(2x + 3)}}[/tex]
The derivative of the function can be calculated using as follows:
[tex]f'(x) = (-\frac{1}{2})((x + 1)(2x + 3))^{-\frac{1}{2} - 1} \cdot \frac{d}{dx}[(x + 1)(2x + 3)][/tex]
Next, we have
[tex]f'(x) = -\frac{\frac{d}{dx}(x + 1) \cdot (2x + 3) + (x + 1) \cdot \frac{d}{dx}(2x + 3)}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
Differentiate
[tex]f'(x) = -\frac{1 \cdot (2x + 3) + (x + 1) \cdot 2}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
This gives
[tex]f'(x) = -\frac{2x + 3 + 2x + 2}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
Evaluate the like terms
[tex]f'(x) = -\frac{4x + 5}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
Hence, the derivative of the function is [tex]f'(x) = -\frac{4x + 5}{2((x + 1)(2x + 3))^\frac{3}{2}}[/tex]
Read more about derivative at
https://brainly.com/question/33109674
#SPJ1
two dice are thrown simultaneously.find the probability of getting a) A sum less than 5
Answers
The probability of getting a sum less than 5 is 6/36, which can be simplified to 1/6.
When two dice are thrown simultaneously, the total number of outcomes is 36 (6 faces on each die, giving 6*6 = 36 possible outcomes).
To find the probability of getting a sum less than 5, we need to determine the favorable outcomes.
The possible favorable outcomes are:
1 + 1 = 2
1 + 2 = 3
1 + 3 = 4
2 + 1 = 3
2 + 2 = 4
3 + 1 = 4
There are a total of 6 favorable outcomes.
Thus, there is a 1 in 6 chance of getting a sum less than 5 when throwing two dice simultaneously.
For more such questions on sum less
https://brainly.com/question/19182918
#SPJ8
What is the solution to this system of equations? 10 y = x - 2; y = - 0.5x + 7 10 (3, 2); (6, 4); (4, 6); (2, 3)
Answers
Answer:x=bx2 is the answer
Step-by-step explanation:
X
45°
X =
Find x.
17
X
45°
AVC
Answers
The value of the length labelled x is 17√2/2
How to determine the valueTo determine the value of the variable, we need to know the six different trigonometric identities.
These identities are listed as;
cosinesinetangentcotangentsecantcosecantFrom the information given, we have that;
Using the sine identity
sin theta = opposite/hypotenuse
But we have from the image that;
Theta = 45 degrees
Opposite side of the triangle = x
Hypotenuse side = 17
Now, substitute the values, we get;
sin 45 = x/17
find the value, we have;
1/√2 = x/17
cross multiply and rationalize
x = 17√2/2
Learn more about trigonometric identities at: https://brainly.com/question/7331447
#SPJ1
Please awnser asap I will brainlist
Answers
Using substitution method, the solution to the system of linear equations
x = 26667 and y = 533
What is the solution to the system of linear equation?Let's set up the system of equations based on the given information.
Let:
x = number of currency A
y = number of currency B
Equation 1: x + y = 3200 (Total budgeted spending money)
Equation 2: 1.30x + 1.50y = Total cost of purchasing currency (to be determined)
Based on the information provided, Abigail wants to have five times as much currency A as currency B:
Equation 3: x = 5y
Now, let's solve the system of equations using substitution method
Substitute Equation 3 into Equation 1:
5y + y = 3200
6y = 3200
y = 3200 / 6
y = 533.33 (approximately)
Substitute the value of y back into Equation 3 to find x:
x = 5(533.33)
x = 2666.67 (approximately)
Now, let's calculate the total cost of purchasing currency using Equation 2:
Total cost of purchasing currency = 1.30x + 1.50y
Total cost of purchasing currency = 1.30(2666.67) + 1.50(533.33)
Total cost of purchasing currency = 3466.67 + 800
Total cost of purchasing currency = 4266.67 (approximately)
Therefore, the system of equations has a solution where:
x ≈ 2667 (number of currency A)
y ≈ 533 (number of currency B)
This means that Abigail should exchange approximately 2667 units of currency A and 533 units of currency B. The total cost of purchasing the currency would be approximately $4266.67.
In practical terms, this means that Abigail will have a budgeted spending money of $3200, and she plans to allocate it between currency A and currency B based on the given exchange rates and her preference of having five times as much currency A as currency B.
Learn more on system of linear equation here;
https://brainly.com/question/13729904
#SPJ1
Please awnser asap I will brainlist
Answers
Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.
How many tickets of each kind has been sold?Let's solve the problem step by step.
Let:
x = number of $10 tickets sold
y = number of $20 tickets sold
z = number of $30 tickets sold
From the given information, we can form the following equations:
Equation 1: x + y + z = 3318 (Total number of tickets sold)
Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)
Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)
We can use these three equations to solve for the values of x, y, and z.
First, let's substitute Equation 2 into Equation 1:
x + (x + 109) + z = 3318
2x + 109 + z = 3318
2x + z = 3209 (Equation 4)
Now, let's substitute the value of y from Equation 2 into Equation 3:
10x + 20(x + 109) + 30z = 61760
10x + 20x + 2180 + 30z = 61760
30x + 30z = 59580
x + z = 1986 (Equation 5)
We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.
Multiplying Equation 4 by 30, and Equation 5 by 2, we get:
60x + 30z = 96270 (Equation 6)
2x + 2z = 3972 (Equation 7)
Now, subtract Equation 7 from Equation 6:
(60x + 30z) - (2x + 2z) = 96270 - 3972
58x + 28z = 92298
Simplifying, we have:
29x + 14z = 46149 (Equation 8)
Now, we can solve Equations 5 and 8 simultaneously:
x + z = 1986 (Equation 5)
29x + 14z = 46149 (Equation 8)
Multiplying Equation 5 by 14, and Equation 8 by 1, we get:
14x + 14z = 27804 (Equation 9)
29x + 14z = 46149 (Equation 8)
Now, subtract Equation 9 from Equation 8:
(29x + 14z) - (14x + 14z) = 46149 - 27804
15x = 18345
Divide both sides of the equation by 15:
x = 18345 / 15
x = 1223
Substituting the value of x into Equation 5, we can find z:
1223 + z = 1986
z = 1986 - 1223
z = 763
Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:
1223 + y + 763 = 3318
y + 1986 = 3318
y = 3318 - 1986
y = 1332
Therefore, the solution to the problem is:
x = 1223 (number of $10 tickets sold)
y = 1332 (number of $20 tickets sold)
z = 763 (number of $30 tickets sold)
Learn more on system of linear equation here;
https://brainly.com/question/13729904
#SPJ1
Use the chain rule to find the derivative of
f(x) = 4√/8x³ + 2x4
Type your answer without fractional or negative exponents. Use sqrt(x) for √√x.
X.
f'(x) =
Answers
Using chain rule, the derivative of f(x) = 4√(8x³ + 2x⁴) is
f'(x) = (2/√(8x³ + 2x⁴)) * (24x² + 8x³)
What is the derivative of the function?To find the derivative of the function f(x) = 4√(8x³ + 2x⁴), we can use the chain rule.
Let's break down the function into its components:
u(x) = 8x³ + 2x⁴ (inside function)
v(u) = 4√u (outer function)
To find the derivative, we apply the chain rule, which states:
(f(g(x)))' = f'(g(x)) * g'(x)
In this case, f(g(x)) = v(u(x)), and g(x) = u(x).
First, let's find the derivative of the inner function u(x):
u'(x) = 24x² + 8x³ (using the power rule for differentiation)
Next, let's find the derivative of the outer function v(u):
v'(u) = 4 * (1/2) * 1/√u = 1/√2u = 2/√u
Now, we can apply the chain rule:
f'(x) = v'(u(x)) * u'(x)
f'(x) = (2/√u) * (24x² + 8x³)
f'(x) = (2/√(8x³ + 2x⁴)) * (24x² + 8x³)
The derivative of the function is (2/√(8x³ + 2x⁴)) * (24x² + 8x³)
Learn more on chain rule here;
https://brainly.com/question/30895266
#SPJ1
Heather is making chocolate biscuits
she has:
2kg of flour
1kg of butter
340g of icing sugar
200g of chocolate
here is the list of ingredients for making 20 biscuits.
100g of flour
120g of butter
80g of icing sugar
25g of chocolate
work out how mnany bisuits she can make
Answers
Therefore, Heather can make a maximum of 4 biscuits with the given ingredient quantities.
To determine how many biscuits Heather can make, we need to compare the amount of each ingredient required for a single biscuit to the total amount of ingredients she has.
Let's calculate the number of biscuits she can make based on the ingredient quantities provided:
First, we need to find the ratio of each ingredient required per biscuit:
Flour: 100g per biscuit
Butter: 120g per biscuit
Icing sugar: 80g per biscuit
Chocolate: 25g per biscuit
Next, we divide the total amount of each ingredient by the respective ratio to find the maximum number of biscuits she can make:
Flour: 2kg / 100g = 20 biscuits
Butter: 1kg / 120g = 8.33 biscuits (approximately)
Icing sugar: 340g / 80g = 4.25 biscuits (approximately)
Chocolate: 200g / 25g = 8 biscuits
Since we can only make a whole number of biscuits, the limiting factor is the icing sugar. Heather can only make 4 biscuits since she has 4.25 times the required amount of icing sugar.
For such more question on ingredient
https://brainly.com/question/28301963
#SPJ8
For the following equations find 1) the general form for all solutions 2) the solutions on the interval (pi/2)<=θ<3pi in terms of pi.
cscθ=2
Answers
For the following equations:
1) In general, the solutions can be expressed as θ = π/6 + 2πn or θ = 5π/6 + 2πn, where n is an integer.
2) The solutions within the interval (π/2) ≤ θ < 3π can be represented as θ = 7π/6 or θ = 11π/6, both in terms of π.
To solve the equation cscθ = 2, we need to find the values of θ that satisfy the equation.
1) General Form for All Solutions:
The reciprocal of sine is cosecant (csc), so we can rewrite the equation as 1/sinθ = 2. To solve for θ, we can take the reciprocal of both sides:
sinθ = 1/2
Now, we need to determine the values of θ where the sine function equals 1/2. The sine function is positive in the first and second quadrants, so we'll focus on those quadrants.
In the first quadrant (0 ≤ θ < π), the reference angle with a sine of 1/2 is π/6.
In the second quadrant (π < θ < 2π), the reference angle with a sine of 1/2 is also π/6.
To account for all solutions, we can add multiples of the period of sine (2π) to the reference angles. Therefore, the general form for all solutions is:
θ = π/6 + 2πn or θ = 5π/6 + 2πn
where n is an integer representing the number of periods of sine added.
2) Solutions on the Interval (π/2) ≤ θ < 3π in Terms of π:
For the given interval, we need to find the values of θ that satisfy the equation and lie within the interval (π/2) ≤ θ < 3π.
From the general form, we can see that the solutions that satisfy the interval are:
θ = π/6 + 2π or θ = 5π/6 + 2π
Simplifying these expressions gives us:
θ = 7π/6 or θ = 11π/6
Therefore, the solutions on the interval (π/2) ≤ θ < 3π in terms of π are:
θ = 7π/6π or θ = 11π/6π.
For more such information on: equations
https://brainly.com/question/17145398
#SPJ8
A university is interested in determining the average statistics anxiety score for all undergraduate students in the U.S. For a random sample of 33 undergraduate students, it is found that the average average statistics anxiety score is 39.4 with a standard deviation of 0.9. Assume that the statistics anxiety scores for all undergraduate students in the U.S is normally distributed. A 98% confidence interval for the true mean statistics anxiety score μ is closest to.
Answers
The 98% confidence interval for the true mean statistics anxiety score (μ) is approximately (39.037, 39.763).
To calculate the 98% confidence interval for the true mean statistics anxiety score (μ) for all undergraduate students in the U.S., we can use the formula:
Confidence interval = sample mean ± (critical value * standard error)
First, we need to find the critical value associated with a 98% confidence level. Since we are assuming a normal distribution, we can use the Z-table or a statistical software to find this value. For a 98% confidence level, the critical value is approximately 2.33.
Next, we calculate the standard error (SE) using the formula:
SE = standard deviation / √sample size
In this case, the standard deviation is 0.9 and the sample size is 33. Plugging these values into the formula, we get: SE = 0.9 / √33 ≈ 0.156
Now, we can calculate the confidence interval:Confidence interval = 39.4 ± (2.33 * 0.156)
Simplifying the expression:Confidence interval ≈ 39.4 ± 0.363
This gives us the interval (39.037, 39.763). This means we are 98% confident that the true mean statistics anxiety score for all undergraduate students in the U.S. falls within this interval.
for more search question interval
https://brainly.com/question/20309162
#SPJ8
