Draw your own face using the grid below and write down the coordinates of the outline

The y-intercept of the function F(x) = x⁴ + 2x - 2 is -2 and the profile is matched to the given graph thus option (B) is correct.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

As per the given graph of the function,

In option (B),

F(x) = x⁴ + 2x - 2

Put x = 0

F(0) = 0 + 0 - 2 = -2

Thus, (0,-2) will be the y-intercept which is matching in the graph.

Hence "The y-intercept of the function F(x) = x⁴ + 2x - 2 is -2 and the profile is matched to the given graph".

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The average rate of change  of the function h(x) = -x² - 9x + 23,  over the interval -8 ≤ x ≤ -2 is 1

What is average rate of change?

Let's find the average rate of change of h(x) = -x² - 9x + 23 in the interval of -8 ≤ x ≤ -2

h(-8) = -(-8)² - 9(-8) + 23

= -64 + 72 + 23

= 31

h(-2) = -(-2)² - 9(-2) + 23

= -4 + 18 + 23

= 37

Average rate of change = f(b) - f(a) / b - a

= h(-2) - h(-8)

= 37 - 31 / -2 - (-8)

= 6 / -2 +8

= 6/6

= 1

Here, the average rate of change  of the function h(x) = -x² - 9x + 23,  over the interval -8 ≤ x ≤ -2 is 1.

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Step-by-step explanation:

[tex]46064yx \times ( \frac{ { > < |x { \frac{( {))(6460 = 464}^{?} }{?} }^{?} | }^{?} }{?} [/tex]

Using the given information to complete this compounding interest question is as follows:

1. Period Used = 28 quarters

2. Rate Used = 2%

3. PV factor used = 1.14987

4. PV of the amount desired at end of the period = $15,306.04.

Compound interest adds the accumulated interest to the principal amount after each period in order to compute the period's interest.

Compound interest is the opposite of simple interest, which does not add the accumulated interest to the principal before computing another period's interest.

N (# of periods) = 28 quarters (7 x 4)

I/Y (Interest per year) = 2%

PMT (Periodic Payment) = $0

FV (Future Value) = $17,600

Results:

PV = $15,306.04

Total Interest = $2,293.96

PV factor = 1.14987

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Considering the figure the third figure  relates to first figure by reflection and not translation hence No; it is one reflection after another with respect to the two parallel lines

A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection.

The equation or the two points it passes through can be used to define the line of reflection.

In the problem, the parallel lines are the line of reflection. The parallel lines displays the mirror image of the line segment

The first image relates with the first image as a result of reflections

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The  linear equation that model the above is h = 32 -2t and the height of fire after 8 hours is 16 inches

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

Using the equation for a straight line and writing similar

h = mt + c

h = height, t = hours m and c are constants

at h = 24, t = 4

Equation becomes

24 = 4m + c--------------1

at h = 20, t = 6

20 = 6m + c---------------2

Subtract equation 2 from 1 so that the eqution reduces to

4 = -2m

m = 4/-2

m = -2

substitute m in equation 1

24 = 4( -2) + c

24 = -8 + c

c = 32

substituting m and c in he linear equation above we have

h = 32 - 2t

After 8 hours, the height h = 32 -2(8) which is 16 inches

In conclusion the linear equation is h = 32 - 2t and the height of fire after 8 hours is 16 inches

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a. The researcher should expect each person to get 17 guesses correct under the null hypothesis that the person is guessing.

b. Person A has a smaller p-value because the person's number of successes is further to the hypothesized number of successes.

At the null hypothesis, it is tested if the person is guessing, that is, if the proportion is of 0.5, hence:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the person is not guessing, that is, if the proportion is different than 0.5, hence:

[tex]H_0: p \neq 0.5[/tex]

Considering the tested proportion of 0.5, the expected number of correct guesses on the 34 trials is of:

0.5 x 34 = 17 correct guesses.

The test statistic is given by the equation presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

The parameters that are the same for each person are given as follows:

[tex]p = 0.5, n = 34[/tex]

The sample proportions are given as follows:

Then the test statistics are given as follows:

Person A is farther from the mean due to the higher test statistical, hence it has a smaller p-value.

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In scientific notation, the amount of paper used weekly by the Pittsburgh paper is approximately 5.0 x 10⁷ times more than the amount used by the Newville paper.

Scientific notation is a shorthand or approximated way to write large or small numbers.

Scientists use scientific notations to eliminate the many zeros in a number so that the number is written in a standard form.

In scientific notation, a positive integer is multiplied by another integer (positive or negative) in the power of ten.

The best way to compute the ratio of paper usage at the two newspapers is to rewrite the numbers in long form and convert the answer to scientific notation.

Location     Paper Used (square yards)

Newville     8.0 x 10³ = 8,000

Pittsburgh  4.0 x 10¹¹ = 400,000,000,000

The ratio of Pittsburgh to Newville = 8,000:400,000,000,000

= 1: 50,000,000

= 1: 5.0 x 10⁷

We can also divide 400,000,000,000 by 8,000 to get 50,000,000, which can then be written in standard form as 5.0 x 10⁷.

Thus, expressing the result in scientific notation, the Pittsburgh paper approximately uses 5.0 x 10⁷ more paper than the Newville paper.

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Location     Paper Used (square yards)

Newville     8.0 x 10³

Pittsburgh  4.0 x 10¹¹

The entire missing lengths as well as the missing angles of the given right angle triangle are as calculated below using Pythagoras theorem and trigonometric rules.

We are given a right angle triangle and as such we can use both Pythagoras theorem and even trigonometric rules such as sine rule and cosine rules.

a) W are given that A = 30°, Thus;

B = 180 - (90 + 30)

B = 60°

Using sine rule;

a/sin A = b/sin B

a/sin 30 = 6/sin 60

a = 3.464

c/sin 90 = 6/sin 60

c = 6.928

b) a = 13 and b = 13

Using Pythagoras theorem;

c = √(13² + 13²)

c = 18.385

Since a = b, it means it is an isosceles triangle and so;

A = B = 45°

c) B = 30°, c = 10

A = 180 - (30 + 90)

A = 60°

10/sin 90 = b/sin 30

b = 5

10/sin 90 = a/sin 60

a = 8.66

d) A = 45°, c = 12

B = 45°

c/sin 90 = b/sin 45 = a/sin 45

b = a = 12 * sin 45 = 8.485

e) c = 1, b = 1/√2

c/sin 90 = b/sin B

1/sin 90 = (1/√2)/ sin B

B = 45° = A

a = √(1² - (1/√2)²)

a = 0.7071

f) c = 4 and b = 4;

a = √(4² - (4)²)

a = 0

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The value of t in the equation can be express as follows:

[tex]t = \frac{V-7\pi r^{2} }{6\pi r}[/tex]

The subject of a formula is the variable that is being worked out. The subject of a formula is the variable which is expressed in terms of the other variables.

The variable to be worked out is t.

Therefore,

V = 6πrt + 7πr²

Therefore, let's make t the subject of the formula,

V = 6πrt + 7πr²

subtract 7πr² from both sides of the equation.

V = 6πrt + 7πr²

V - 7πr² = 6πrt + 7πr² -7πr²

V - 7πr² = 6πrt

divide both sides of the equation by 6πr

Hence,

[tex]\frac{V-7\pi r^{2} }{6\pi r}=t[/tex]

Therefore,

[tex]t = \frac{V-7\pi r^{2} }{6\pi r}[/tex]

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The total number of transistors in the Titan is equal to 5.950 × 10²¹ transistors.

A supercomputer simply refers to one of the most powerful computers that is designed and developed for handling, evaluating, and solving very complicated problems, calculations, or tasks, better than ordinary desktop or laptop computers.

In order to determine the total number of transistors in the Titan, we would multiply the number of transistors in its central processing unit (CPU) by the number of transistor in its graphics processing unit (GPU) as follows:

Total number of transistors = 4.485 × 10¹⁰ × 1.3268 × 10¹¹

Total number of transistors = (4.485 × 1.3268) × (10¹⁰ × 10¹¹)

Total number of transistors = 5.950 × (10⁽¹⁰ ⁺ ¹¹⁾)

Total number of transistors = 5.950 × 10²¹ transistors.

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Complete Question:

Supercomputers have been developed that are much larger and can perform many more calculations than ordinary desktop or laptop computers. One such supercomputer, the Titan, has 4.485 × 10¹⁰. transistors in its central processing unit (CPU) and another 1.3268 × 10¹¹. transistor in its graphics processing unit (GPU). Find the total number of transistors in the Titan. Show your working and give your answers in standard form.

The  slope and y-intercept of the equation of straight line y=5x+12 is 5 and 12.

What is equation of straight line?

A line that does not curl or bend is said to be straight. A line has length but no width, making it a one-dimensional figure. A line consists of points that extend infinitely in opposite directions. Two points in a 2D plane determine it. A, B, and C are real-based constants in the formula Ax + By + C = 0, A, B 0. The geometric representation of the equation is always a straight line.

Here we know that equation of straight line is y=mx +c.

Where m=slope and c=y-intercept.

Here the given equation is ,

=> y=5x+12

Compared with general form then,

=> m = 5 and c=12.

Therefore slope and y-intercept of the equation of straight line y=5x+12 is 5 and 12.

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The line has a gradient of 2 and a y -intercept of 1. So, draw the line through (0,1) and (1,3).

The frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell to total frequency.

It is given that:

24 children were asked which is their favourite colour from a choice of red, blue

green or yellow

From the data given in the question.

Red : 6

Blue: 4

Green: 8

Yellow : 1 (half of 2)

Pink: 1 (half of 2)

Thus, the frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).

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a. The finance charge on August 8 is given by: $3.69.

b. The new balance on August 8 is given by: $298.64.

A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context is needed in the problem.

A proportion is applied in this problem to find the finance charge, which is of 1.25% of 294.95, hence:

Finance charge = 0.0125 x 294.95 = $3.69.

Then the new balance on August 8 is obtained by the previous balance on July 8 added to the finance charge which we obtained above, hence it is of:

New balance = 294.95 + 3.69 = $298.64.

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Answer:

undefined

Step-by-step explanation:

to find slope it’s y2-y1/x2-x1

9-7/-2-(-2)

2/0

Undefined slope

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The intersection of two regular pentagons can be hexagon. Therefore, option D is the correct answer.

We need to find the figure formed with the intersection of two regular pentagons.

If all the polygon sides and interior angles are equal, then they are known as regular polygons. In a regular pentagon all the five sides are equal and all the angles are equal in measure.

Here, the intersection of two regular pentagons form a hexagon.

In a shape hexagon there are 7 sides.

The intersection of two regular pentagons can be hexagon. Therefore, option D is the correct answer.

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Answer:

[tex]\frac{3}{4} ft[/tex]

Step-by-step explanation:

at the first piece we can see it stops on the number line at 3/4

Also 3 divided by 4 is 3/4

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Answer:

3/4

Step-by-step explanation:

Look at 1 ft on the ruler below at left. The foot is divided into 4 equal parts, so each small part is 1/4 ft. The length of each piece of wire is 3 of these 1/4 ft lengths, so each piece of wire is 3/4 ft long.

Answer: 3/4

According to the given ratio, the hourly pay before the increase for Marta and for Khalid is 1.2

Ratio:

Ratio refers the ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

The ratio of Marta's hourly pay to Khalid's hourly pay is 6:5 Both Marta and Khalid get an increase of £1.50 in their hourly pay. The ratio of Marta's hourly pay to Khalid's hourly pay after this increase is 13:11.

Here we need to work out the hourly pay before the increase for Marta and for Khalid.

So, it can be written as,

=> 6 : 5

And the new pay after the increase is

=> 13 : 11

So, when we equate this, then we get,

=> 6/5 = 13/11

=> 1.2 = 1/2

Therefore, the hourly pay before the increase for Marta and for Khali is 1.2

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Answer:

The correct answer is: The pizza is heavier

Step-by-step explanation:

(11/5) * 10^3 = 2200 grams of pizza against 1,300 grams of cake

Using the system of linear equations, Malik sold 14 grapes and 36 oranges

In algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."

To solve this, we have to set a system of linear equations.

Let;

x + y = 50 ...eq(i)

2x + y = 64 ...eq(ii)

Solving both equations, the value of x and y are 14 and 36 respectively

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Answer: 14 and 36

Step-by-step explanation: 2023

Answer:

[tex]\huge\boxed{\sf x = 1}[/tex]

Step-by-step explanation:

g(x) = 5x + 4

Given that, g(x) = 9

So,

9 = 5x + 4

Subtract 4 to both sides

9 - 4 = 5x

5 = 5x

Divide 5 to both sides

1 = x

OR

x = 1

[tex]\rule[225]{225}{2}[/tex]

Answer:

x = 1

Step-by-step explanation:

The given information is,

→ g(x) = 5x + 4

→ g(x) = 9

Now the value of x will be,

→ 5x + 4 = g(x)

→ 5x + 4 = 9

→ 5x = 9 - 4

→ x = 5/5

→ [ x = 1 ]

Hence, the value of x is 1.

Answer:

Step-by-step explanation

Initial amount = $85

Final amount = $110

percentage error = ((Final amount - Initial amount)*100)/Final amount

= (25*100)/110

=22.7272

=22.7 (to the nearest tenth of a percent, which is 1 decimal place)

The solution is 22.7 %

The percentage error in the estimation of donations at the pet store by Jenny is 22.7 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the percentage error be represented as A

Now , the value of A is

The estimated donation amount by Jenny = $ 85

The actual donation amount collected by Jenny = $ 110

Now , the percentage error in the estimation of Jenny A is calculated by the equation ,

Percentage error in the estimation of Jenny A = ( ( | estimated donation amount - actual donation amount collected by Jenny ) | / actual donation amount collected by Jenny ) ) x 100

Substituting the values in the equation , we get

Percentage error in the estimation of Jenny A = ( | 85 - 110 | / 110 ) x 100

On simplifying the equation , we get

Percentage error in the estimation of Jenny A = ( 25/110 ) x 100

Percentage error in the estimation of Jenny A = 2500 / 110

Percentage error in the estimation of Jenny A = 22.72 %

Therefore , the value of A is 22.7 %

Hence , the percentage error in the estimation is 22.7 %

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Line e is parallel.

Line h is perpendicular.

Lines f and g are neither.

The equation that can be used  to determine the number of plates, p, that he used is 6p = 48.

Jim is a preschool teacher. While he was getting ready for his class's snack time, he put 6 carrots on each plate.

He used 48 total carrots. The equation that could be used to determine the number of plates, p, that he used can be represented as follows:

where

Therefore,

6 carrots are put on each plate.

He has 48 carrots in total. And needs to put all in a plate.

Hence, the equation that could be used to determine the number of plates, p, is  6p = 48

p = 48 / 6

p = 8

Therefore,

number of plates = 8

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The total amount the college student will have in the savings account after 5 years will be $15,095

From the question, we are to determine the amount the college student has in savings.

From the compound interest formula, we have that

A = P(1 + r/n)^nt

Where A is the amount

P is the principal

r is the interest rate

n is the number of times compounded per year

and t is the time.

From the given information,

P = $13,000

r = 3%= 0.03

n = 4

t = 5

Putting the parameters into the formula

A = P(1 + r/n)^nt

A = 13000(1 + 0.03/4)^(4×5)

A = 13000(1 + 0.03/4)^20

A = $15095.39

A ≈ $15095

Hence, the amount is $15,095

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Answer: 7,000

Step-by-step explanation: I took the test

For the given confidence interval, the correct statement is Option C. The manager can be 99% confident that the constructed interval captures the true mean number of fish in saltwater tanks.

Confidence interval:

Confidence interval refers the mean of your estimate plus and minus the variation in that estimate.

Given,

Here we need to find which of the following correctly interprets the 99% confidence interval for the true mean number of fish in saltwater tanks.

While we looking into the given question,

We know that, it states that 99% confidence interval for the true mean number of fish in saltwater tanks,

Based on these fact the correct statement is the manager can be 99% confident that the constructed interval captures the true mean number of fish in saltwater tanks.

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Answer:

58

Step-by-step explanation:

You would have to turn 7 1/4 into a whole fraction.

Do,

7 * 4 = 28

28 + 1 = 29

Your new fraction would be,

29/4

Now you have to make them equal denominators with 1/8.

Lets see,

Now multiply 4 * 2 is 8.

So multiply 29 times 2.

Which is 58.

Your new fraction is,

58/8

So therefore you would have 58 pieces.