a) The possible pairs of mutually exclusive outcomes are given below:
A and B
A and C
A and D
B and C
B and D
C and D
b) The Three of the outcomes that are said to be all mutually exclusive are:
A (The contestant is a woman over 25)B ( The contestant is a man.)C (The contestant is 21 years old )c) The probability of having B and D is written as P(B or D) = P(B) + P(D)
What is the probability?Mutually exclusive events cannot happen at the same time, like rolling a kick the bucket and getting a 1 and a 2. In this case, there are four conceivable results: A, B, C, and D, a few of which we commonly select.
For example, If A is the outcome, C or D cannot be. To find mutually exclusive pairs, we check which outcomes cannot occur together. A and B are mutually exclusive because they cannot both be true.
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What is the area of DEF? D to F is 7.65, d to e is 2.12 and e to f is 6
What is the value of x?
The value of x in the circle is,
⇒ x = 25.6
We have to given that;
An angle is, 23 degree
Hence, We can formulate;
(14x - 22) + 23 = 360
14x + 1 = 360
14x = 359
x = 25.6
Thus, The value of x in the circle is,
⇒ x = 25.6\
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Please hurry!!
A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The
100
function f(x)= -5
X represents the remaining time in minutes needed to fill the tank. How is the graph of the
parent function (x)-
-
100
transformed to create the graph of the function (x)=
X
O It is a vertical stretch with a factor of 100 and a translation 5 units right.
O It is a vertical stretch with a factor of 95.
O
It is a vertical stretch with a factor of 100 and a translation 5 units down.
It is a vertical stretch with a factor of 500.
-5?
The function is transformed and it is a vertical stretch with a factor of 100 and a translation 5 units down
Given data ,
Let the transformed function be represented as f' ( x )
Now , The pace of filling a 100-gallon fish tank is x gallons per minute. The tank has been filling for five minutes already.
The parent function's graph is f (x) = x.
Consequently, the function's graph is provided as
f ( x ) = ( 100/x ) - 5
The graph is now 100 times longer vertically, giving us f (x) = 100/x.
By translating by 5 units down, we obtain f (x) = (100/x) - 5.
Hence , it is a translation of 5 units down and a vertical stretch of 100.
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Kristin and deshawn are selling flower bulbs for a school fundraiser customers can buy bags of windflower bulbs and packages of crocus bulbs Kristen sold 4 bags of windflower bulbs and 9 packages of crocus for a total of 200 deshawn sold 2 bags of windflower bulbs and 6 packages of crocus bulbs for a total of 124 find the cost each of one of the bag of windflower bulbs and one package of crocus bulbs ?
The cost each of one of the bag of windflower bulbs and one package of crocus bulbs is $14 and $16 respectively.
What is the cost of each of bag of windflower bulbs and a package of crocus bulbs?Let
cost each of one of the bag of windflower bulbs = x
Cost of each one package of crocus bulbs = y
4x + 9y = 200
2x + 6y = 124
Multiply (2) by 2
4x + 12y = 148
So,
4x + 9y = 200
4x + 12y = 248
Subtract to eliminate x
12y - 9y = 248 - 200
3y = 48
divide both sides by 3
y = 48/3
y = 16
Substitute y = 16 into (1)
4x + 9y = 200
4x + 9(16) = 200
4x + 144 = 200
4x = 200 - 144
4x = 56
x = 56/4
x = 14
Therefore, each one bag of windflower bulbs and one package of crocus bulbs is $14 and $16 respectively.
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Which statement about the following equations is correct?
y = 2x + 5
y
O The equations are independent because the lines intersect in one point.
The equations are dependent because the lines are the same line.
O The equations are independent because the equations represent parallel lines.
O The equations are dependent because the lines do not intersect.
= -2x+5
Answer:
Step-by-step explanation:
The correct statement about the given equations is: "The equations are dependent because the lines are the same line."
In the equation y = 2x + 5, the slope is 2, which means the line has a positive slope and is upward sloping.
The y-intercept is 5, indicating that the line intersects the y-axis at the point (0, 5).
The equation y = -2x + 5 is equivalent to y = 2(-x) + 5, which has the same form as the first equation but with a negative slope.
However, the equations are still dependent because when you simplify the second equation, you obtain the first equation.
These two equations represent the same line with a different slope. Therefore, they are dependent, and any point that satisfies one equation will satisfy the other equation as well.
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1) Given a sample of lifetime of the light bulbs X1, X2, X3,. X36) with LX =1800 hours, ›X2-90560 and level of confidence c = 95%. Find the Point Estimate X =
Step-by-step explanation:
if the length of a Square Garden is 49 feet than what it is area
The difference of a number and 4/3 is 11/3. What is the number?
Answer:
n = 5
Step-by-step explanation:
Let n represent the unknown the numberSince we know the difference of n and 4/3 is 11/3, we can use the following equation to solve for n: n - 4/3 = 11/3Step 1: Multiply both sides by 3 (i.e., the least common multiple of 3) to clear the fractions:
3(n - 4/3 = 11/3)
3n -12/3 = 33/3
3n - 4 = 11
Step 2: Add 4 to both sides:
(3n - 4 = 11) + 4
3n = 15
Step 3: Divide both sides by 3 to solve for n:
(3n = 15) / 3
n = 5
Type the correct answer in the box.
Rewrite the quadratic equation in the form y = a(x - h)² + k
The quadratic equation can be written as follows:
y = 5(x - 3)² + 50.
How to rewrite the quadratic function?The quadratic function in the context of this problem is defined as follows:
y = 5x² - 30x + 95
The coefficients of the quadratic function are given as follows:
a = 5, b = -30 and c = 95.
Then the x-coordinate of the vertex is given as follows:
h = -b/2a
h = 30/10
h = 3.
The y-coordinate of the vertex is given as follows:
h = 5(3)² - 30(3) + 95
h = 50.
Hence the equation is:
y = 5(x - 3)² + 50.
Missing InformationThe quadratic function in the context of this problem is defined as follows:
y = 5x² - 30x + 95
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can we express 1,012 as the sum of two consecutive number?
Answer:
Step-by-step explanation:
Let's check if we can express it or not ;
Let the two consecutive number be x and x + 1 .
x + x + 1 = 1012
2x + 1 = 1012
2x = 1011
x = 505.5
Then two consecutive numbers are 505.5 and 506.5
It isn't said that number should be integer ? It can be anything . That is why " yes " would be the correct answer .
2. Write each of the following in algebraic notation:
: 2.1 Three times the difference between k and the square of p
The expression in algebraic notation is 3 * (k - p²)
Writing the expressions in algebraic notationFrom the question, we have the following parameters that can be used in our computation:
Three times the difference between k and the square of p
Three times means 3*
So, we have
3 * the difference between k and the square of p
the difference between k and the square of p means
k - p²
So, we have
3 * (k - p²)
So, we can conclude that
The expression"Three times the difference between k and the square of p" in algebraic notation is 3 * (k - p²)
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If a family borrows 43,008 for an addition to their home and the loan is to be paid off in monthly payments over 9 years how much should each payment be?
The family's monthly payment should be $504.70.
To calculate the monthly payment for a loanWe can use the following formula:
[tex]P = (r * A) / (1 - (1 + r)^(-n))[/tex]
where
P = a recurring paymentr is the ongoing interest rate.A = loan amountn = total number of paymentsIn this instance, the total loan amount is $43,008, the total number of payments is 9 years * 12 months/year = 108 months . The yearly interest rate must first be divided by 12 to determine the monthly interest rate. Assume that there is a 5% yearly interest rate.
[tex]r = 0.05 / 12 = 0.00417[/tex]
Now we can substitute the values into the formula and solve for P:
[tex]P = (0.00417 * $43,008) / (1 - (1 + 0.00417)^(-108))[/tex]
= $504.70
Therefore, the family's monthly payment should be $504.70.
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a mother is 33 years older than her twin children. in 3 years, her age will be twice the amount of both her childrens combined. how old are the twins now?
Answer:
8 years old--------------
Let the age of the mother be x and twins be y.
Set up two equations as per information given:
1) x - y = 33, (age relation now)2) x + 3 = 2(y + 3 + y + 3) (relation in 3 years time)Simplify the second equation and substitute x = y + 33:
x + 3 = 2(2y + 6)x + 3 = 4y + 12y + 33 + 3 = 4y + 12y + 36 = 4y + 124y - y = 36 - 123y = 24y = 8The twins are 8 now.
need answer please.
The area is 96 square inches.
Answer:
64[tex]ft^{2}[/tex]
Step-by-step explanation:
Calculate the (lateral) faces that need to be stained.
[tex]a = lw[/tex]
Assuming that you have to stain all four sides and not just the facade, find the surface area of each face and then find the sum. That sum will be your answer.
Apply the formula given above.
4*4 = 16
the area of one face is 16[tex]ft^{2}[/tex]
multiply 16 by 4 = 64
Fill the boxes to show the numbers marked with arrows on the number line. 1 +TH++
The inequality that of the number line is x < 8
Stating the inequality that represents the number lineFrom the question, we have the following parameters that can be used in our computation:
The number line (see attachment)
On the number line, we have the following
Open circle on 8Arrow points to the left of 8The above means that we make use of the less than symbol
This is because the open circle uses < or > while arrows pointing left means <
So, we have
x < 8
Hence. the inequality that best describes the included values of x is x < 8
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31. Find the area of the shape below: 15m 3m (a) 87m² (b) 102m2 (c) 152m² (d) 18m² (e) 207m2 4m 6m 6m 3m
Hello!
see attachment
A1 = green
A2 = yellow
A3 = red
A1 = 15m * 3m = 45m²
A2 = (15m - (6m + 6m)) * 4m = 3m * 4m = 12m²
A3 = 15m * 3m = 45m²
A = A1 + A2 + A3
= 45m² + 12m² + 45m²
= 102m²Answer:
b. 102 m²
Step-by-step explanation:
In order to find the area of shape.
Let's separate it into three rectangle.
We know that
Area of rectangle: Length*breadth
Using this
Area of left rectangle=15*3=45 m²
Area of middle rectangle=4*(15-6-6)=12 m²
Area of right rectangle= 15*3=45m²
Now
Total Area of shape= 45m²+12m²+45m²=102m²
A company bought a photocopier for R150 00 on 1 july 2022,they will use the old photocopier as a trader in when they replace it with the a similar new photocopier in 5 years time on 2027.
calculate the trade in value of the old photocopier after 5 years,if it depreciates at a rate of 9% p.a on straight line method.
Answer:
do it yourself what do you do while teacher is teaching
Dr. Salaam orders 39 grams of marijuana for a patient. Each bud is about 0.07 grams of marijuana.
How many buds will each patient need and If the dispensary charges $530 an ounce for the strain the patient likes, how much will the patient have to pay in total? (28.4 grams = 1 ounce)
The patient will have to pay approximately $727.74 in total.
How to solve for the dispensary chargesTotal grams of marijuana: 39 grams
Weight of each bud: 0.07 grams
Number of buds = Total grams of marijuana / Weight of each bud
Number of buds = 39 / 0.07 ≈ 557.14
Since the patient can't purchase a fraction of a bud, they will need 558 buds (rounding up).
Now, let's calculate the total cost.
Dispensary cost: $530 per ounce (28.4 grams)
First, we need to find the cost per gram:
Cost per gram = $530 / 28.4 ≈ $18.66
Total grams of marijuana: 39 grams
Total cost = Cost per gram * Total grams of marijuana
Total cost = $18.66 * 39 ≈ $727.74
The patient will have to pay approximately $727.74 in total.
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100 Points! Graph the function. State the domain and range of the function. Photo attached. Thank you!
Answer:
Domain: [tex]x\geq -2[/tex]
Range: [tex]y\geq 0[/tex]
Step-by-step explanation:
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
have a great day and thx for your inquiry :)
An economy's consumer price index (CPI) is described by the function f(t)=-0.1t^3+3t^2+500 where t=0 corresponds to the year 1995. Find the point of inflection of the function.
There are 12 people on a basketball team. The coach chooses 3 players to play
three different positions. How many ways can the players be chosen?
Answer:
There are 12 ways to choose the first player, 11 ways to choose the second player, and 10 ways to choose the third player. However, this counts each group of 3 players 3 times, since the order in which the players are chosen doesn't matter. Therefore, the number of ways to choose 3 players from 12 is
3×2×1
12×11×10
=220.
Step-by-step explanation:
Okay so this is for my portfolio. I have two figures; a rectangular prism (think cereal box) and a cylinder. Is it possible for the cylinder to have a larger VOLUME than the prism, but a smaller measurement of cubic inches?? (Please say yes )
Step-by-step explanation:
No, it is not possible. Cubic inches are a measurement of volume. If the cylinder has a larger volume, then it also has more cubic inches.
Answer:
no TWT
Step-by-step explanation:
Because these solids have the same height and the same cross-sectional areas at every level, the solids have the same volume due to Cavalieri's principle. The volume of the prism is: V = A B a s e ⋅ h = π r 2 h Therefore, the volume of the cylinder is: V = π r 2 h This should make sense because a cylinder is essentially a circular prism. Also Its cool that we both go to Connexus, i saw it from an old post of yours <3
Select ALL the correct answers. Which of the following statements are true about the equation below? The graph of the quadratic equation has a maximum value. The extreme value is at the point (7,-3). The graph of the quadratic equation has a minimum value. The solutions are . The extreme value is at the point (3,-7). The solutions are .
The correct statements regarding the quadratic function x² - 6x + 2 are given as follows:
The graph of the quadratic equation has a minimum value.The solutions are: x = 0.35 and x = 5.64.The extreme value is at the point (3,-7).How to analyze the quadratic function?The quadratic function in the context of this problem is given as follows:
y = x² - 6x + 2.
The coefficients are given as follows:
a = 1, b = -6, c = 2.
As a > 0, the function is a concave up quadratic function, hence it has a minimum value.
Using a calculator with the given coefficients, we have that:
The solutions are: x = 0.35 and x = 5.64.The vertex is: (3, -7).Missing InformationThe function is:
y = x² - 6x + 2.
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Find the x-coordinate of the critical point for the function
guys pls help me thank you sm
Step-by-step explanation:
You have to study the f'(x)
f'(x)= (e^x - 2)÷(e^x-2x)
it has to be = 0
(c.e.: e^x > 2x)
e^x - 2=0
e^x = 2
x= ln 2
In the figure below, m3=133°. Find mZ1, mZ2, and m 2 4.
4
1
3
2
m 21 =
m 22 =
m 24 =
The measure of the angles ∠1, ∠2, and ∠4 will be 133°, 47°, and 47°, respectively.
Given that:
Angle, ∠3 = 133°
Two angles are said to be supplementary angles if their sum is 180 degrees. Then we have
∠3 + ∠4 = 180°
133° + ∠4 = 180°
∠4 = 47°
When two lines intersect, then their opposite angles are equal. Then we have
∠4 = ∠2
∠2 = 47°
∠1 = ∠3
∠1 = 133°
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In a class of 30 students, 12 have a cat and 19 have a dog. There are 6 students who
do not have a cat or a dog. What is the probability that a student chosen randomly
from the class has a dog?
Answer:
P(dog) = 12/30 = 0.4 or 40%
Step-by-step explanation:
We can use the formula for probability:
P(dog) = number of students with a dog / total number of students
To find the number of students with a dog, we can use the fact that 19 students have a dog and 6 students have neither a cat nor a dog:
number of students with a dog = total number of students - number of students with no pets - number of students with only a cat
number of students with a dog = 30 - 6 - 12 = 12
So the probability that a student chosen randomly from the class has a dog is:
P(dog) = 12/30 = 0.4 or 40%
Select the correct answer. What is 12% of 50? A. 6 B. 7 C. 10 D. 12
Answer:
A. 6
Step-by-step explanation:
We know that 12% can be written in fraction form as [tex]\frac{12}{100}[/tex]. So, 12% of 100 is [tex]100\cdot\frac{12}{100} = 12[/tex].
We also know that 50 is half of 100. Therefore, 12% of 50 is exactly half of 12% of 100:
[tex]12\% \cdot 50[/tex]
[tex]= \frac{1}{2}(12\% \cdot 100)[/tex]
[tex]= \frac{1}{2}(12)[/tex]
[tex]\boxed{=6}[/tex]
Find the areas of the sectors formed by \angle ACB .
A circle is shown. The measure of central angle A C B is 131 degrees. The radius is 3 centimeters. Point D is on the circle but not on arc A B.
Give the exact answers in terms of \pi . Do not approximate the answers.
Area of small sector =
cm2
Area of large sector =
cm2
Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° clockwise.
U′(1, −1), V′(0, 4), W′(4, 1)
U′(−1, −1), V′(−4, 0), W′(1, 4)
U′(1, 1), V′(−4, 0), W′(−1, 4)
U′(−1, 1), V′(0, −4), W′(−4, −1)
The coordinates of the vertices for the image of the triangle U′V′W′ is
U′(1, 1), V′(−4, 0), W′(−1, 4)
How to find the coordinates after transformationTo rotate a point 90 ° clockwise about the origin, we can apply the transformation (x, y) → (y, -x)
So applying this transformation to each vertex of triangle UVW we get
U(−1, 1) → U' = (1, 1)
V(0, −4) → V' = ( -4, 0)
W(−4, −1) → W' = (-1, 4)
Therefore the coordinates of the vertices for the image triangle U'V'W' are U′(1, 1), V′(−4, 0), W′(−1, 4)
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I need the answer and work for these please
Answer:
Step-by-step explanation:
Hello!
Start With Plugging the numbers in (5) Now use your units to divide and multiply to get your answer
2. The base of a solid is a region bounded by the curve x^2/8^2+y^2/4^2=1(an ellipse with the major and minor axes of lengths 16 and 8 respectively). Find the volume of the solid if every cross section by a plane perpendicular to the major axis (x-axis) has the shape of an isosceles triangle with height equal to 1/4 the length of the base
Answer:
85 1/3 cubic units
Step-by-step explanation:
You want the volume of a solid whose base is the ellipse in the x-y plane with axes 16 and 8 units and whose cross sections perpendicular to the major axis are isosceles triangles with height equal to 1/4 of the cross section dimension parallel to the minor axis.
AreaThe isosceles triangle cross section has base 2y and height (2y)/4, so area of ...
A = 1/2bh
A = (1/2)(2y)(2y/4) = y²/2
VolumeA differential of volume is the product of the area of a slice and its thickness:
dV = A·dx = (1/2)y²·dx
The total volume is the integral of this differential of volume over the interval x ∈ [-8, 8]. That integral will be twice the integral on the interval [0, 8}, so we have ...
[tex]\displaystyle V=2\int_0^8{\dfrac{y^2}{2}}\,dx=16\int_0^8{\left(1-\dfrac{x^2}{64}\right)}\,dx=16\left((8-0)-\dfrac{8^3-0^3}{3\cdot64}\right)\\\\\boxed{V=85\dfrac{1}{3}\text{ cubic units}}[/tex]
__
Alternate computation
The volume of half an ellipsoid with semi-axes 2, 4, and 8 is ...
V = (1/2)(4/3)π(abc)
V = (1/2)(4/3)π(2)(4)(8) = 128π/3
The area of half an ellipse with semi-axes 2 and 4 is ...
A = (1/2)π(ab)
A = (1/2)π(2)(4) = 4π
The area of a triangle with the same semi-axes is ...
A = 1/2bh = (1/2)(2)(2·4) = 8
Then the ratio of triangle area to ellipse area at each cross section is ...
triangle / ellipse = 8/(4π) = 2/π
The volume of the solid of interest is estimated to be this factor multiplied by the volume of the half-ellipsoid:
(2/π)(128π/3) = 256/3 = 85 1/3 . . . . same as above
