The missing lengths of the sides a = 3 inches , b = 3√3 inches .
90 -60 -30 triangle .
We have given 90 -60 -30 triangle with hypotenuses = 6 in.
By the 90 -60 -30 triangle rule : The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle and the length of the longer leg is 3√ times the length of the shorter leg.
Then Shorter leg = a longer leg = b.
Hypotenuse = 2 * Shorter leg .
Plug the values.
6 = 2 * Shorter leg .
On dividing both sides by 2
Shorter leg (a) = 3 inches .
Then by the rule : longer leg is 3√ times the length of the shorter leg.
Longer leg = 3√Shorter .
Longer leg (b) = 3√3 inches .
Therefore, a = 3 inches , b = 3√3 inches .
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Find the orthogonal projection of y onto u. Y= [8 -24], u=[4 -2] A. [4 -2] B. [16 -8] C. [1 1/2] D. [16 -2]
According to the given vector, the value of the orthogonal projection of y onto u is <16, -8>
Here we have the vector values that is as follows:
Y= [8 -24],
u=[4 -2]
Now, based on the formula of the vector projection is written as,
=> [(y x u) / |u²| ] x u
Now, we have to calculate the value of the vector and it can be obtained by what we need to do is multiply the corresponding coordinates and then add up the results:
=> ⟨8,−24⟩⋅⟨4,−2⟩
=> (8)⋅(4)+(−24)⋅(−2)
When we simplify this one then we get the value as,
=>80.⟨8,−24⟩⋅⟨4,−2⟩
=> (8)⋅(4)+(−24)⋅(−2) = 80.
Similarly, now we have to calculate the value of |u²| is written as,
Here we have the sum of squares of the absolute values of the coordinates is
=> ∣4∣² + ∣−2∣² = 20.
Therefore, the magnitude of the vector is
=> √20 = 2√5
Thus the vector projection is written as,
=> [tex]\frac{8}{2\sqrt{5} }\times < 4,-2 >[/tex]
When we simplify this one then we get the resulting value of projection as <16, -8>
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Part B
The table holding Juanita's pennies gets bumped, and the stack becomes slanted.
How is the volume of the stack affected? Explain your reasoning
The volume of the stack affected will be 10,825.38 cubic millimeters.
Let r be the radius and h be the height of the cylinder.
Then the volume of the cylinder will be
V = π r²h cubic units
The table holding Juanita's pennies gets bumped, and the stack becomes slanted.
The radius of the cylinder is given as,
r = 19.05 / 2
r = 9.525 mm
Then the volume of the cylinder is calculated as,
V = π x (9.525)² x 38
V = 3.14 x 90.725 x 38
V = 10,825.38 mm³
The volume of the stack affected will be 10,825.38 cubic millimeters.
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Answer:
The volume of the stack affected will be 10,825.38 cubic millimeters.
Step-by-step explanation:
Find the area of an octagon ABCDEFGH having each side equal to 5 cm,HC=11 cm and AP⊥HC such that AP=4 cm.
The area of the octagon ABCDEFGH is 119 cm².
The figure is attached below for reference.
AP = 4 cm
HC = CD = 11 cm
Area of trapezium ABCH = Area of trapezium GDEF
Now, Area of a trapezium = [tex]\frac{1}{2} (a+b)h[/tex]
Area of trapezium ABCH = Area of trapezium GDEF = [tex]\frac{1}{2} (5+11)4 = 32[/tex] cm².
So, Area of trapezium GDEF = 32 cm².
Area of rectangle MCDG = l x b = 11 x 5 = 55 cm²
Area of the Octagon ABCDEFGH = Area of the two trapeziums + Area of the rectangle
= (2 x 32) + 55 = 119 cm².
Hence, the area of the octagon ABCDEFGH is 119 cm².
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What is the equation of a circle with a center (−3, −2) and radius of 5?
HELPPPPPPP!!!!!!
(x − 3)2 + (y − 2)2 = 25
(x − 3)2 + (y − 2)2 = 5
(x + 3)2 + (y + 2)2 = 5
(x + 3)2 + (y + 2)2 = 25
find the vector, not with determinants, but by using properties of cross products. (i × j) × k
(i × j) × k = 0, is the vector, not with determinants, but by using properties of cross products.
What is cross product?The procedure for multiplying two vectors is called the cross product of the two vectors. The sign(×) of multiplication between two vectors indicates a cross product. It is a three-dimensional system-defined binary vector operation.
A cross product in three dimensions is a binary operation on two vectors. It generates a vector that is parallel to both vectors. A and B together form a vector product, which is represented by the symbol a b. The vector that results from it is parallel to both a and b. Cross products and vector products are similar terms.
As we know,
i × j = | i | × | j | × sin 90° × k
or, i × j = 1 × 1 × 1 × k
or, i × j = k
thus, (i × j) × k = k × k
or, (i × j) × k = 0
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Sam left $4.50 as a tip for the waiter this was 18% of the bill before the tip.how much was her total bill before the tip
Answer:
.18B = 4.5
B = 4.5/.18 = 450/18 = 50/2 = $25 bill
HELP ASAP FOR BRAINLIEST
Answer:
First brand: 98 gallons
Second brand: 42 gallons
Step-by-step explanation:
x + y = 140
.4x + .9y = .55*140
x=140-y
.4(140-y) + .9y = 77
56 - .4y + .9y = 77
.5y = 21
y = 42
x + 42 = 140
x = 98
Which represents the polynomial written in standard form?
8x2y2 – 3x3y + 4x4 – 7xy3
4x4 – 3x3y + 8x2y2 – 7xy3
4x4 – 7xy3 – 3x3y + 8x2y2
4x4 + 8x2y2 – 3x3y – 7xy3
–7xy3 – 3x3y + 8x2y2 + 4x4
Answer:
Step-by-step explanation:
The correct answer is: 4x4 + 8x2y2 – 3x3y – 7xy3. This is the standard form for the polynomial, where the terms are written in descending order. The terms in this polynomial are the 4x4 term, the 8x2y2 term, the -3x3y term, and the -7xy3 term.
Pretty please someone answer this! Based on the graph shown, which of the following statements is true?
For the graph of data given option C: The median 300 is the middle number is correct.
What is median?
In mathematics, the middle number in a sorted list of numbers is referred to as the median. By arranging the numbers, the middle number can be discovered. Ascending order is used to arrange the numbers. The middle number in the ordered set of numbers is referred to as the data set's median.
Draw the median table for the graph of values given -
Number Frequency ∑f
100 14 14
200 6 20
300 18 38
400 12 50
500 2 52
600 12 64
700 8 72
The formula for median is -
Median = [n/2 + (n/2 + 1)] / 2
Median = [72/2 + (72/2 + 1)] / 2
Median = [36 + (36 + 1)] / 2
Median = 73/2
Median = 36.5
According to the table the ∑f value 36.5 corresponds to 300.
Therefore, the median 300 is the middle number.
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Given:2x-3y+z=03x+2y=354y-2z=14Which of the following is a solution to the given system?(2, 3, 5)(3, 2, 0)(1, 16, 0)(7, 7, 7)
The solution to the given system is (2, 3, 5). This can be determined by solving the system of equations using elimination.
First, add the first equation to the second equation to eliminate the y-term:
5x + z = 7
Next, add the third equation to the first equation to eliminate the x-term:
3y + z = 3
Finally, substitute the expression for z into the expression for x and solve for y:
y = 3
Now that we have the values for x and y, substitute them into one of the original equations to solve for z:
2(2) - 3(3) + z = 0
z = 5
The solution is (2, 3, 5).
Can I please get help.
The data that is considered univariate and quantitative is Shoe size, Salary, Years of experience, Height.
What is univariate quantitative data?
Univariate quantitative data refers to a type of data that consists of only one variable and the values of that variable are numerical. This means that the data represents a single measurement or characteristic, and the values can be quantified and compared using mathematical operations. Examples of univariate quantitative data include height, weight, temperature, salary, and years of experience.
Shoe size, Salary, Height, Years of experience are considered univariate and quantitative data.Shoe size is a univariate data because it only has one variable which is the size of the shoe. It is quantitative because the data can be measured in numbers.Salary is a univariate data because it only has one variable which is the amount of money earned. It is quantitative because the data can be measured in numbers.Height is a univariate data because it only has one variable which is the height of an individual. It is quantitative because the data can be measured in numbers.Years of experience is a univariate data because it only has one variable which is the amount of time an individual has worked in their profession. It is quantitative because the data can be measured in numbers.Salary and years of experience, Sports played in high school, Favorite color and age, and Favorite color are not considered univariate and quantitative data. They contain more than one variable and some of the variables are qualitative and cannot be measured in numbers.To learn more about univariate quantitative data refers to:
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triangle def was dilated according to the rule do,one-third(x,y)(one-third x, one-third y) to create similar triangle d'e'f'. on a coordinate plane, (0, 0) is the center of dilation. triangle f d e is dilated to create smaller triangle f prime d prime e prime. triangle f d e has points (negative 9, 3), (negative 9, 9), (negative 6, 6). triangle f prime d prime e prime has points (negative 3, 1), (negative 3, 3), and (negative 2, 2).which statements are true? select three opt
The statements that are true about the triangle f d e and its dilated counterpart f' d' e' are: (1) The center of dilation was (0, 0). (2) The coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). (3) f' d' e' is a similar triangle to f d e.
The triangle f d e and its dilated counterpart f' d' e' have specific properties that make them similar triangles. The center of dilation for the transformation was (0, 0). This means that the distance from the center of dilation to each point before and after the dilation was the same. The coordinates of triangle f d e were (negative 9, 3), (negative 9, 9), and (negative 6, 6). In order to obtain the coordinates of f' d' e', the dilation rule one-third(x,y) (one-third x, one-third y) was used. This means that the x and y coordinates of each point were divided by three. The result is that the new coordinates of f' d' e' are (negative 3, 1), (negative 3, 3), and (negative 2, 2). These new coordinates demonstrate that the triangle f d e and its dilated counterpart f' d' e' are similar triangles.
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Answer:
A. ∠F corresponds to ∠F'.
C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.
E. △DEF ~△D'E'F'
Step-by-step explanation:
got it right on edge 23
If you are asked to find the 85th percentile, you are being asked to find _____.
Choose the correct answer below.
A.an area corresponding to a z-score of minus 0.85
B.a data value associated with an area of 0.85 to its left
C.a data value associated with an area of 0.85 to its right
D.an area corresponding to a z-score of 0.8
If you are asked to find the 85th percentile, you are being asked to find an area corresponding to a z-score of 0.8.
The term percentile in math is defined as the area to the left of a particular data value.
According to the definition of percentile, here they are asking about the 85th percentile.
As we all know that z-score is not an area under the normal curve and the distances along the horizontal axis are represented by z-scores where as the regions under the curve are represented by areas.
Therefore, in order to find the z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution.
Then we have to convert the given percent into decimal form, then we get it as,
=> 85% = 0.85
Here we need to find the value from the z table then we get the resulting value as 0.8.
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12. Susan has 8 eggs in her fridge.
Two of the eggs have passed their sell by date and are "bad".
She selects 3 eggs at random to bake a cake.
(a) Complete the probability tree diagram.
(b) Work out the probability that Susan will select 3 "good" eggs.
(c) Work out the probability that Susan will select at least one "bad" egg.
The probability that Susan will select 3 "good" eggs are 8C3*3/4 and the probability that Susan will select at least one "bad" egg. is 8C1*1/4
How do you calculate probability?Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.
What are probability and examples?The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). Writing P(heads) = 12
Hence,
The probability that Susan will select 3 "good" eggs are 8C3*3/4 and the probability that Susan will select at least one "bad" egg. is 8C1*1/4
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1) Rustam has three times as many carrots as Pio. Rustam has 5 fewer carrots that Claudine.
Form an equation relating the number of carrots that Pio has compared to Claudine.
b. Use your equation to find out how many carrots Pio has, if Claudine has 20?
C. Use your equation to find out how many carrots Claudine has, if Pio has 10?
3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and if pio has 10 then the number of carrots with Claudine are 35
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Rustam has three times as many carrots as Pio
R=3P
Where is Rustam, P is Pio and C is Claudine.
Rustam has 5 fewer carrots that Claudine.
R=C-5
3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine.
Now let us find the number of carrots Pio has when Claudine has 20
3P=20-5
3P=15
Divide both sides by 3
P=5
Pio has 5 carrots when Claudine has 20.
Now if pio has 10 then the number of carrots with Claudine
3(10)=C-5
30+5=C
35=C
Hence, 3P=C-5 is the equation relating the number of carrots that Pio has compared to Claudine, Pio has 5 carrots when Claudine has 20 and if pio has 10 then the number of carrots with Claudine are 35
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A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1 and X2 as given in the table. Consequently, .
If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage
X1: Gas mileage before using octane booster
X2: Gas mileage after using octane booster
The researcher is comparing X1 and X2, to determine if using an octane booster increases gasoline mileage.
1. The researcher selected a random sample of seven cars and drove them for two weeks without using the octane booster (X1).
2. The researcher then drove the same seven cars for two weeks with the octane booster (X2).
3. The researcher then compared the data from X1 and X2 to see if there was an increase in gasoline mileage.
4. If the data from X2 is higher than the data from X1, then the researcher can conclude that using an octane booster increases gasoline mileage.
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Find the margin of error for the given values of c, s, and n. c = 0.98, s = 3.3, n = 22 Click the icon to view the t-distribution table. The margin of error is . (Round to one decimal place as needed.)
The margin of error is 1.6393 for the supplied values of c, s, and n, which are 0.98, 3.3 and 22respectively.
what is margin ?
Margin is the term used to describe the equity that a trader has in their account. Using funds borrowed from a broker to buy stocks is referred to as "marging" or "buying on margin." Instead of a typical brokerage account, you must have a margin account to execute this. Beginning with your gross profit, which is the distinction between revenue and COGS, you may compute profit margin. Find the percentage of revenue that represents gross profit next. Calculate it by dividing your gross profit by your revenue. You can calculate your margin % by multiplying the sum by 100.
Given that,
standard deviation = s = 3.3
z is the 98% = z score = 2.33
Sample size = n =22
Margin of error is expressed using the formula;
M = z * √s²/n
M = 2.33* √3.3²/22
M = 2.33* 0.7035
M = 1.6393
Therefore, the margin of error is 1.6393 for the supplied values of c, s, and n, which are 0.98, 3.3 and 22respectively.
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Why is 1 A common factor of every number?
A number multiplied by 1 is the number itself. So,1 is a factor of every number.
1 is the factor of every number as one divides every number exactly, without leaving any remainder behind, and gives the quotient as the number itself.
1 is the greatest factor of itself and the smallest factor of any other number.
There are some properties of factors one:
Every whole number is the product of 1 and itself so, each number is a factor of itself. Every number is a factor of zero and 1 is the smallest factor of every number, and multiple and the greatest factor of a multiple is the multiple itself.Every number other than 1 has at least two factors, namely the number itself and 1.To know more about common factors:
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please help me answer this ty :)
work out the value of r in the equation below
5.8/r=tan 19
give your answer in 1d.p.
Answer: 16.8
Step-by-step explanation:
[tex]\frac{5.8}{r}=\tan 19^{\circ}\\\\\frac{r}{5.8}=\frac{1}{\tan 19^{\circ}}\\\\r=\frac{5.8}{\tan 19^{\circ}}}\\\\r \approx 16.8[/tex]
Please, help me! I need help in this solve
Answer:
Step-by-step explanation:
15x² - 2x - 1 = 0
15x² - 5x + 3x - 1 = 0
5x(3x - 1) + 3x - 1 = 0
(5x + 1)(3x - 1) = 0
x = -1/5, 1/3
8x² - 10x - 3 = 0
8x² - 12x + 2x - 3 = 0
4x(2x - 3) + 2x - 3 = 0
(4x+1)(2x-3) = 0
x = -1/4 , 3/2
16x² - 8x + 3 = 0
This question has complex answers as the D = 64 - 192 < 0
So, ignore this question. It is wrong or it has complex answers.
Use the quadratic formula for it.
9x² - 6x - 2 = 0
This also needs the quadratic formula as the answer is in roots.
8x² - 2x - 3 = 0
8x² - 6x + 4x - 3 = 0
2x ( 4x - 3) + 4x - 3 = 0
(2x + 1)(4x-3) = 0
x = -1/2 , 3/4
select all the examples of exponential function
a) y=3x-2
b) y=3^x
c) y=(1/2)^3x
d) y=3x^2
E) y=(1/2)^x
Answer:
Select all the examples of the exponential function
a) y=3x-2
b) y=3^x
c) y=(1/2)^3x
d) y=3x^2
E) y=(1/2)^x
Write an equation relating the total amount in a in Terry’s account to the number of years,t. Is the relationship proportional?Explain
An equation relating the total amount in a in Terry’s account to the number of years, t is A = P + P*(r/100)*t. Yes, the relationship is proportional.
what is an equation?An equation is a well-formed formula that connects two expressions with the equals sign to express the equality of those two expressions. For example, in French, an equation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions connected with the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
An equation relating the total amount in a in Terry’s account to the number of years, t is A = P + P*(r/100)*t.
Where, A is total amount,
P is amount which Terry deposit,
r is rate of interest,
and t is number of years.
Yes, the relationship is proportional.
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a map of the town that hannah lives in can be represented by the cartesian plane. hannah starts off at $(-4, 9)$ and walks $10$ units to the left and $7$ units down to get to her new location. along what line could she have walked to get to the new location directly from her old location? express your answer in the form $ax by
The answer in the form of x,y is -7x + 10y = 118.
A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.
from given conditions, we get,
(-4, 9) and 10 left 7 down puts her at ( -4 - 10 , 9 - 7) = ( -14, 2)
So, the points ( -4, 9) and (-14,2) are on the line
Slope of this line = [ 2 - 9] / [ -14 - -4 ] = [ -7] / [ -10] = 7/10
Equation of the line
y = (7/10)(x - - 4) + 9
y = (7/10) ( x + 4) + 9 multiply through by 10
10y = 7 (x + 4) + 90
10y = 7x + 28 + 90
-7x + 10y = 118
Therefore, the answer in the form of (x , y) is -7x + 10y = 118
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Bonjour je suis entrain de faire la distributivité et je bloque sur ce calcul quelqu'un pourrait m'aider svp.
4x+[3-(7-x)]-[4x-(x-2)]
Merci
Answer:
Step-by-step explanation:
beaucoup pour votre aide !
Pour résoudre cette expression, nous allons appliquer la distributivité, c'est-à-dire multiplier chaque terme entre parenthèses par le nombre devant les parenthèses.
On commence par 4x + [3 - (7-x)], ce qui donne:
4x + (3 - 7 + x)
Ensuite, nous pouvons appliquer la distributivité à 4x-(x-2):
4x + (3 - 7 + x) - (4x - x + 2)
Enfin, nous pouvons réorganiser les termes pour simplifier l'expression:
4x + 3 - 7 + x - 4x + x - 2
En réarrangeant, nous obtenons:
-2 - 4 + 5x
Donc, l'expression complète est: -2 - 4 + 5x.
What are the values of the constants in the vertex form of the quadratic equation that models the bird's path? with answers.
h = 0
k = 20
a = -0.12
next question
which system of equations could you use to determine where the paths intersect? b.
y = 0.8x and y = -0.12x2 + 20
The point of intersection of the bird's paths can be found by setting up a system of equations consisting of y = 0.8x and y = -0.12x2 + 20 and solving for x. The x-coordinate of the point of intersection is approximately 3.33.
y = 0.8x
and
y = -0.12x2 + 20
First, set the two equations equal to each other:
0.8x = -0.12x2 + 20
Next, subtract 20 from both sides of the equation:
0.8x = -0.12x2
Then, divide both sides by 0.8:
x = -0.15x2
Finally, solve for x by dividing both sides by -0.15:
x = 10/3 or x ≈ 3.33
To find the point of intersection of the bird's paths, we can set up a system of equations consisting of y = 0.8x and y = -0.12x2 + 20. We then set the two equations equal to each other and solve for x. Subtracting 20 from both sides of the equation, we get 0.8x = -0.12x2. We then divide both sides of the equation by 0.8, giving us x = -0.15x2. Finally, by dividing both sides of the equation by -0.15, we can solve for x to find the point of intersection, which turns out to be x = 10/3 or approximately 3.33. In other words, the paths intersect at a point with a x-coordinate of approximately 3.33.
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Find the complex conjugates for each of the following numbers: a. - 19 = Preview b. -25i = Preview c. - 11 - 92i = Preview d. 413i - 37 Preview
The complex conjugates for each of the following numbers
a. - 19 = -19
b. -25i = +25i
c. - 11 - 92i = 11 + 92i
d. 413i - 37 = -413i - 37
The term complex number in math is defined as the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number.
Here we have given that the list of complex number and here we need to find the complex conjugates for each of the following numbers:
As we all know that conjugate in Mathematics is formed by changing the sign of one of the terms in a binomial.
Based on the definition, here we have the general form a + bi as the conjugate as a - bi.
From this one we have identified that here we have only changed the sign of imaginary pat.
So, the complex conjugate of the given complex numbers are written as
=> a. - 19 = -19
Here we have only the number part so the sign remains constant
b. -25i = +25i
Here we have only the imaginary part so we have changed it to positive.
c. - 11 - 92i = 11 + 92i
Based on the complex conjugate rule the term must be changed.
d. 413i - 37 = -413i - 37
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The average of the first 3 weights was 20 pounds. the average of the next twelve was 25 pounds. what was the overall average of the weights
The requried average weight of 15 weights is given as 24 pounds.
What is average?The average of the values is the ratio of the total sum of values to the number of values.
Here,
The average of the first 3 weights was 20 pounds. the average of the next twelve was 25 pounds.
overall average = total weight of 3 + total weight of 12 / [3 + 12]
overall average = 360 / 15 = 24 pounds
Thus, the requried average weight of 15 weights is given as 24 pounds.
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Two questions, see attachment
Answer:
12. <4 = 100°
Step-by-step explanation:
For number 12. angle m<2 is a corresponding angle to angle m<6 . So the equations, (3x+20) and (5x-20) are equal to each other.
So lets set them equal to each other:
(3x+20) = (5x-20)
40 = 2x
x = 20
Now we need to plug in the value of x into the equation of angle m<2, to find its angle.
(3x+20) = ?
(3(20)+20) = ?
= 80 degrees
m<2 = 80 degrees
We need to find <4
Since <4 and <2 share the same line and are supplementary angles (they add up to 180) we can subtract the value of <2 from 180 to find <4
180 - 80 = 100
So <4 is 100 degrees.
11 is 25% of what number?
Answer:
44 is your answer
Step-by-step explanation:
