Phill thinks he had merited the angles blew correctly. Triangle placed on top of a straight line, 50 * at the top left of the triangle, 90 at the bottom left of the triangle, 40* at the bottom right

Wayne's Actual ACT score is 19.2 where mean is 21, standard deviation is 5 and the Z - score is -0.6.

Standard Deviation:

Standard deviation is  a measure of the dispersion of a set of numerical values from their mean.

The general form of the standard deviation is,

\(SD=\sqrt{\frac{\sum (x_i-\bar{x})}{n} }\)

where

xi is each value in the data set,

x-bar is the mean, and

n is the number of values in the data set.

Given,

Mean = 21.

Standard deviation = 5

Wayne's standardized score on the act = −0.6 .

Here we need to find the Wayne's Actual ACT score.

Let x be the Wayne's Actual ACT score.

So,
=> z-score = (x - mean)/SD

Apply the values on it,

=> -0.6 = (x - 21) / 3

=> -1.8 = x - 21

=> x = 21 - 1.8

=> x = 19.2

Therefore, Wayne's Actual ACT score is 19.2

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The measures of the angles are 72°, and 108°.

What is Angle Sum Property?

The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°. If we have a triangle ABC, then the Sum of angles A , B, and angle C will be 180 ° and the value of the exterior angle is equal to the sum of two interior opposite angles.

We have,

two angles form a linear pair. one angle measure is 36° more than the other.

If two angles form a linear pair, then the sum of the degree measure of the angles is 180°.

Let x be the measure of the smaller angle.

Then,

36° + x is the measure of the other angle.

So,

36° + x  + x = 180°

2x = 180° - 36°

2x = 144°

x = 144°/2

x = 72°

the measure of the smaller angle is  x = 72°,

the measure of the other angle is

36° +  72° = 108°

Hence, the measures of the angles are 72°, and 108°.

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Answer:

d = \(\frac{11}{12}\)

Step-by-step explanation:

1) To solve for d, isolate it in the equation. So, to get rid of the \(-\frac{1}{2}\) with the d, add \(\frac{1}{2}\) to both sides.

\(d-\frac{1}{2} = \frac{5}{12} \\d - \frac{1}{2} +\frac{1}{2} = \frac{5}{12} + \frac{6}{12} \\d = \frac{11}{12}\)

Thus, d = \(\frac{11}{12}\).

Answer: 7½ miles

Step-by-step explanation:

15/4× 3/2 = 45/6

The value of y at x =  0, 1, 2, and 3 is -2 ,1,6,10 .

The missing options are

y = –2, 2, 6, 10

y = 2, 6, 10, 14

y = 4, 6, 8, 10

y = –4, –2, 0, 2

A function is a law that defines relation between a dependent variable and an independent variable .

A function is given

y = 4x-2

x = 0,1,2,3

y = ?

At x = 0

y = -2

x = 1

y = 2

at x =2

y = 6

at x = 3

y = 10

The value of y at x =  0, 1, 2, and 3 is -2 ,1,6,10 .

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Answer:

4x²+6x-40

2(2x²+3x-20) factor out 2

2(2x²+8x-5x-20) split the three into a difference

2(2x(x+4)-5x-20) factor the 2 out of first pair of parenthesis

2(2x(x+4)-5(x+4)) factor the 5 out of second pair of parenthesis

2(x+4)(2x-5) factor

= 2(x+4)(2x-5)

Step-by-step explanation:

i hope this helps :)

Answer:

93

Step-by-step explanation:

Given the data:

$79,$ $84,$ $86,$ $92,$ $93,$ and $97

79, 84, 86, 92, 93, 97

Highest possible score obtainable in a test = 100

Hence to calculate the highest possible score she could still attain;

We assume she obtained a score of 100 in all remaining 3 tests

Then the data becomes :

79, 84, 86, 92, 93, 97, 100, 100, 100

Median of the dataset:

Q2 = 1/2(n + 1)th term

n = sample size = 9

Q2 = 1/2(9 + 1)th term

Q2 = 1/2(10)th term

Q2 = 5th term

Q2 = 93

Answer:

cupcakes to balls

Step-by-step explanation:

The equation which describes the statement Three less than four times a number is 17 is 4x-3 = 17

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Here, it is given that Three less than four times a number is 17.

Let assume the number be x ,

then 4 times the number will be = 4x

and, 3 less then the number means  = 4x-3

which is equals to 17 that is :

4x-3 = 17

Therefore, the equation which describes the statement Three less than four times a number is 17 is 4x-3 = 17

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The function f(x, y) = 5x^2 + 4y^2 + 6xy + 30x - 5 has no solutions where both fx(x, y) = 0 and fy(x, y) = 0. Therefore, the correct choice is:

D. There are no solutions where fx(x, y) = 0 and fy(x, y) = 0.

To find the solutions where fx(x, y) = 0 and fy(x, y) = 0, we need to calculate the partial derivatives of f(x, y) with respect to x and y, respectively, and solve the resulting equations simultaneously.

The partial derivative of f(x, y) with respect to x, denoted as fx(x, y), is obtained by differentiating f(x, y) with respect to x while treating y as a constant:

fx(x, y) = 10x + 6y + 30.

The partial derivative of f(x, y) with respect to y, denoted as fy(x, y), is obtained by differentiating f(x, y) with respect to y while treating x as a constant:

fy(x, y) = 8y + 6x.

To find the values of x and y where both fx(x, y) = 0 and fy(x, y) = 0, we can set each partial derivative equal to zero and solve the resulting equations:

10x + 6y + 30 = 0    ...(1)

8y + 6x = 0         ...(2)

From equation (2), we can rearrange it as:

6x = -8y

x = (-8y) / 6

x = -4y/3       ...(3)

Substituting equation (3) into equation (1), we have:

10(-4y/3) + 6y + 30 = 0

-40y/3 + 6y + 30 = 0

-40y + 18y + 90 = 0

-22y + 90 = 0

-22y = -90

y = 90/22

y = 45/11

However, when we substitute the value of y back into equation (3), we get:

x = -4(45/11) / 3

x = -180/33

Therefore, there are no values of x and y that satisfy both fx(x, y) = 0 and fy(x, y) = 0.

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The percent error of the measurement, to the nearest tenth of a percent is: 1.4%.

Percent error can be described as the disparity between the value of what was estimated and the actual value, which is compared to the actual value as expressed in percentage.

The formula for calculating the percent error is:

Percent error = |measured value - actual value| / actual value × 100%.

We have the following given:

Actual length = 7.4 inches

Measured length = 7.3 inches

Therefore:

Percent error = |7.3 - 7.4| / 7.4 × 100%.

= 0.1/7.4 × 100

= 1.4%

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Answer:

Let's have x be his age.

He said that 400:

400 reduced by 3 times my age:

400 − 3x

is 190:

=> 400 − 3x = 190

=> 3x = 400−190

=> x= 210

=> 210÷3

=> 70

The correct interpretations are:

90% of the mean closing stock prices are in the 90% confidence interval, and 99% of the mean closing stock prices are in the 99% confidence interval.

The 90% confidence interval contains the mean closing stock price 90% of the time, and the 99% confidence interval contains the mean closing stock price 99% of the time.

There is 90% confidence that the mean closing stock price is in the 90% confidence interval, and 99% confidence that the mean closing stock price is in the 99% confidence interval.

The 99% confidence interval is wider than the 90% confidence interval.

To construct confidence intervals for the population mean, we will use the formula: Confidence Interval = Sample Mean ± (Z * (Standard Deviation / √n))

Where:

Sample Mean is the mean of the sample data.

Z is the Z-score corresponding to the desired confidence level.

Standard Deviation is the known population standard deviation.

n is the sample size.

Given the sample data and the known population standard deviation (σ = $2.31), we can calculate the confidence intervals.

For the 90% confidence interval:

Sample Mean = $18.946

Z-score for a 90% confidence level = 1.645 (obtained from the standard normal distribution table)

Sample Size (n) = 16

Plugging these values into the formula, we get:

90% Confidence Interval = $18.946 ± (1.645 * ($2.31 / √16))

= $18.946 ± $0.9297

= ($18.0163, $19.8757)

Interpretation: We can say with 90% confidence that the population mean closing stock price falls within the range of $18.0163 to $19.8757.

For the 99% confidence interval:

Sample Mean = $18.946

Z-score for a 99% confidence level = 2.576 (obtained from the standard normal distribution table)

Sample Size (n) = 16

Plugging these values into the formula, we get:

99% Confidence Interval = $18.946 ± (2.576 * ($2.31 / √16))

= $18.946 ± $1.2091

= ($17.7369, $20.1551)

Interpretation: We can say with 99% confidence that the population mean closing stock price falls within the range of $17.7369 to $20.1551.

From the calculations, we can see that the 99% confidence interval is wider than the 90% confidence interval. This is expected because as we increase the confidence level, we need to account for a larger range of possible values, resulting in a wider interval.

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In the column space of each matrices A = [1 2 0 0 0 0 ] B = [ 1 0 0 2 0 0 ] C = [ 1 0 2 0 0 0] ,matrix A and B are lines and  the column space of matrix C is a plane.

To classify the column space of each matrix as either a line or a plane, we need to find the dimension of the column space.

For matrix A, the column space is spanned by the first two columns since the remaining columns are all zero. These two columns are linearly independent, so the column space is a line in R².

For matrix B, the column space is spanned by the first and fourth columns since the remaining columns are all zero. These two columns are also linearly independent, so the column space is a line in R².

For matrix C, the column space is spanned by the first, third, and fourth columns since the remaining columns are all zero. These three columns are linearly independent, so the column space is a plane in R³.

Therefore, the column space of matrix A and B are lines in R², while the column space of matrix C is a plane in R³.

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Answer:

y=ex-4

Step-by-step explanation:

Hope i helped:))

The correct equation which represented by the graph is,

⇒ y = eˣ - 4

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The graph of function is shown in figure.

Since we are given two types of functions, exponential and logarithmic, we need to remember that there is just an option that matches with the graph.

So, By the graph we can see that we are looking for an exponential function which intercepts are located at the point (0,-3) and a point which y-coordinate is equal to 0 and its x-coordinate is located at the x-axis between the number 1 and 2.

Hence, From the given options we can see that the only exponential function that intercepts the function at y equal to -3 is the fourth option, so, let's prove that:

Option D,

⇒ y = eˣ - 4

Finding the y-intercept, we need to make "x" equal to 0, so:

⇒ y = eˣ - 4

⇒ y = e⁰ - 4

⇒ y = 1 - 4

⇒ y = - 3

So, we know that the y-intercept point is located at (0,-3)

Finding the x-intercept, we need to make "y" equal to 0, so:

⇒ y = eˣ - 4

⇒ 0 = eˣ - 4

⇒ eˣ = 4

⇒ x = ln 4

⇒ x = 1.386

So, we know that the x-intercept point is located at (1.386,0)

Hence, we have that the axis interception points are (0,-3) and (1.386,0), so, the function that matches with the shown graph is the function from the option D.

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Answer:

3 is the answer pls like me it is the correct one ty

Step-by-step explanation:

The dimensions of the page that will minimize the amount of rectangle paper used are 16 inches (height) by 8 inches (width).

Area of the rectangle:

The amount of area occupied by a rectangle within its boundary is known as the area of the rectangle.

The formula to find the area of the rectangle is

A = L x W

where

L refers the length

W refers the width

Given,

A rectangular page is to contain 72 square inches of print. The margins at the top and bottom of the page are to be 2 inches wide. The margins on each side are to be 1 inch wide.

Here we need to find the  dimensions of the page that will minimize the amount of paper used.

Let us consider H and W denote the height and the width of the printed matter area respectively.

Then here we know that the value of HW = 72 and

the area of the sheet of paper is calculated as

A = (H + 4)(W + 2)

Here the value of height of the paper is calculated by H plus the top and bottom margins and

Similarly,  the value of width of the paper is W plus the side margins.

Now, to minimize A, we have to rewrite A in terms of W.

Then we get the value of

A = (72/W + 4) (W + 2)

Which is equal to,

A = 72 + 144/w + 4w + 8

By taking the derivative, then we get,

A' = -144W⁻² + 4

Apply the value of A' = 0, then we get,

144W² = 4

W² = 144/4

W =√36

W = 36.

If the value of W is 6, then the value of H is,

H (6) = 72

H = 72/6

H = 12

Now, we have to add 4 to the height and the 2 to the width in order to find the full paper dimensions.

Then we get the desired dimensions are 16 inches (height) by 8 inches (width).

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Answer:

To find out which cake is the most expensive per serving, we need to calculate the cost per serving for each cake.

The first cake serves 2 people and costs $4.50. So the cost per serving is:

$4.50 ÷ 2 = $2.25 per serving

The second cake serves 8 people and costs $10.00. So the cost per serving is:

$10.00 ÷ 8 = $1.25 per serving

The third cake serves 10 people and costs $20.00. So the cost per serving is:

$20.00 ÷ 10 = $2.00 per serving

Therefore, the first cake is the most expensive per serving, at $2.25 per serving.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

5/64

Step-by-step explanation:

5/8 : 8 = 5/8 * 1/8 = 5/64

Answer:

12 4/5

Step-by-step explanation:

simplified

Answer:

9100x < 28000

Step-by-step explanation:

Hope this helps! :D

Answer:

4=q+13

or, 4 - 13 = q

or, -9=q

q = -9

The total wage bill for hiring 3 students to deliver the catalogues and leaflets will be 3 x £51.30 = £153.90.

Number is an abstract concept used to count, measure and identify a quantity. It is a fundamental part of mathematics, and is also used in many other fields, such as physics and computing. Numbers can represent both discrete, such as the number of people in a room, and continuous, such as the temperature outside. Numbers are also used to represent abstract ideas, such as the amount of money in a bank account.

In order to calculate the minimum number of students needed to deliver the catalogues and leaflets, we need to calculate how many catalogues and leaflets can be delivered in 8 hours by one student.

16 catalogues and 90 leaflets can be delivered in 1 hour by one student. Therefore, 128 catalogues and 720 leaflets can be delivered in 8 hours by one student.

Therefore, the total number of catalogues and leaflets that can be delivered in 8 hours by one student is 848 (128 + 720).

Since the total number of catalogues and leaflets to be delivered is 384 + 1890 = 2274, the minimum number of students required to deliver all the catalogues and leaflets is 3 (2274 / 848 = 2.67).

Therefore, the total wage bill for hiring 3 students to deliver the catalogues and leaflets will be 3 x £51.30 = £153.90.

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Answer:

0.08 divided by 13.56 = 0.00589970501.

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer: 0.00589970501

It is better to choose to toss the coin 50 times regardless of the game.

Let's first calculate the expected value of winning in each game by tossing the coin 20 times:

Game A: The probability of getting exactly 10 heads out of 20 is \($\binom{20}{10}0.5^{20}\approx0.176$\). Therefore, the expected value of winning in Game A is \($0.176\times1000=176$\).

Game B: The probability of getting between 9 and 11 heads out of 20 is \($\sum_{k=9}^{11}\binom{20}{k}0.5^{20}\approx0.263$\). Therefore, the expected value of winning in Game B is \($0.263\times1000=263$\).

Now, let's calculate the expected value of winning in each game by tossing the coin 50 times:

Game A: The probability of getting exactly 25 heads out of 50 is \($\binom{50}{25}0.5^{50}\approx0.112$\). Therefore, the expected value of winning in Game A is \($0.112\times1000=112$\).

Game B: The probability of getting between 22 and 28 heads out of 50 is \($\sum_{k=22}^{28}\binom{50}{k}0.5^{50}\approx0.298$\). Therefore, the expected value of winning in Game B is \($0.298\times1000=298$\).

As we can see, the expected value of winning is higher in both games when tossing the coin 50 times compared to 20 times. Therefore, it is better to choose to toss the coin 50 times regardless of the game.

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