Tom got 72 marks in 8 tests. How much did he get in each test on average?

The domain of the function is -5 ≤ x < 3 and the range is 0 ≤ y ≤ 2

We have the following endpoints on the graph of the function;

(x, y) = Closed (-5, 2)

(x, y) = Open (3, 2)

Minimum y = 0

Remove the y values to determine the domain

x = Closed -5

x = Open 3

The closed statement represents the inequality ≤, while the closed statement represents the inequality < or >

So, we have

Domain = -5 ≤ x < 3

Also, we have:

(x, y) = Closed (-5, 2)

(x, y) = Open (3, 2)

Minimum y = 0

Remove the x values to determine the range

x = Closed 2

x = Open 2

Minimum y = 0

The above means that the y value does not include a negative value

So, we have

Range = 0 ≤ y ≤ 2

Hence, the domain of the function is -5 ≤ x < 3 and the range is 0 ≤ y ≤ 2

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Answer:

22d

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Plug 7 in for wherever there's an "x."

f(x) = 2(7) - 6

f(x) = 14 - 6

f(x) = 8

Now subtract 9 from 8.

8 - 9 = -1

There are total 77 students in the sixth grade.

Given, there are 28 students that have braces.

out of which there are 4 students with braces for every 7 students.

Therefore, 4 ₊ 7 = 11, which means every 11 member has 4 members with braces.

Therefore, based on the given conditions, formulate:

28 × (4 ₊ 7) ÷ 4

28 × 11 / 4

now cross out the common factors.

7 × ( 11)

multiply the above terms.

77

hence we get the answer as 77 students in total in the class.

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The solution using the elimination method for the values of x, y and z are -1, 3 and 4 respectively.

To solve multiple equation in three variables using the elimination approach, we can either add or subtract the equations. To eliminate a variable, we add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are equal.

Let us classify the given equations as:

3x + 4y - 5z = -11   →→→→ (A)

4х + у- z  = -5      →→→→→(B)

x- 3y + 3z = 2      →→→→→(C)

Multiplying equation(C) by 3 and equation (A) by 1 and subtracting we get:

3x + 4y - 5z = -11

3x  - 9y + 9z=    6

13y-14z=-17→→→→→→(D)

Multiplying equation(C) by 4 and equation (B) by 1 and subtracting we get:

4x-12y+12z = 8

4x + y - z    = -5

-13y+13z=13

or, z-y=1→→→→→→→(E)

Multiplying equation(E) by 13 and equation (D) by 1 and adding we get:

-13y+13z=13

13y-14z  =-17

-z=-4

or, z = 4

Substituting the value of z in the equation (E) we get:

z-y=1

or,  4-y = 1

or, -y = -3

or,  y = 3

Substituting the value of z and y in the equation (A) we get:

3x+4y-5z=-11

or, 3x+12-20=-11

or, 3x=-11+8

or, x=-1

Hence the solution of x, y and z are -1, 3 and 4 respectively .

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Using the normal distribution, it is found that:

a) 167 students in the class can be expected to receive a score over 60.

b) 11.07% of the class is expected to receive a score between 82 and 90.

The z-score of a measure X of a normally distributed variable with mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the scores are given, respectively, by:

[tex]\mu = 72, \sigma = 9[/tex]

The proportion of students who scored over 60 is given by one subtracted by the p-value of Z when X = 60, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (60 - 72)/9

Z = -1.33.

Z = -1.33 has a p-value of 0.0918.

1 - 0.0918 = 0.9082.

Out of 184 students:

0.9082 x 184 = 167.

167 students in the class can be expected to receive a score over 60.

For item b, the proportion is the p-value of Z when X = 90 subtracted by the p-value of Z when X = 82, hence:

X = 90:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (90 - 72)/9

Z = 2.

Z = 2 has a p-value of 0.9772.

X = 82:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (82 - 72)/9

Z = 1.11

Z = 1.11 has a p-value of 0.8665.

0.9772 - 0.8665 = 0.1107.

Hence:

11.07% of the class is expected to receive a score between 82 and 90.

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We need to know about concept of work done on spring to solve the question.The natural length of the spring is 5cm.

We will need to make assumptions to solve this problem, we will assume that the natural length of the srping is [tex]x_{0}[/tex] and the work done to stretch the spring from it's natural length to a specific length is given by

W=[tex]\frac{1}{2} k(x-x_{0} )^{2}[/tex] , where W is the work done, x is the final length of the spring

We have to find out the work done to get to 7cma nd 9cm separately and then subtract one from the other to get the work done to stretch from 7cm to 9cm. We repeat the process for 9cm and 11cm and we will find the final result which is the natural length.

W=[tex]\frac{1}{2} k(7-x_{0} )^{2}[/tex]

W=[tex]\frac{1}{2} k(9-x_{0} )^{2}[/tex]

[tex]\frac{1}{2} k(9-x_{0} )^{2} -\frac{1}{2} k(7-x_{0} )^{2} =0.6\\(9-x_{0} )^{2} - (7-x_{0} )^{2} =\frac{1.2}{k}[/tex]...(i)

W=[tex]\frac{1}{2} k(9-x_{0} )^{2}[/tex]

W=[tex]\frac{1}{2} k(11-x_{0} )^{2}[/tex]

[tex]\frac{1}{2} k(11-x_{0} )^{2} -\frac{1}{2} k(9-x_{0} )^{2} =1\\(11-x_{0} )^{2} -(9-x_{0} )^{2} =\frac{2}{k}[/tex]...(ii)

Dividing equation (ii) by (i)

[tex]\frac{(11-x_{0} )^{2} -(9-x_{0} )^{2} }{(9-x_{0} )^{2} -(7-x_{0} )^{2} } =\frac{2}{1.2} \\\frac{(20-2x_{0} )2}{(16-2x_{0})2 } =\frac{1}{0.6} \\12-1.2x_{0} =16-2x_{0} \\0.8x_{0} =4\\x_{0} =5[/tex]

Thus using the concept of work done to stretch a spring we get the natural length of the spring which is 5cm.

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The square roots of 36,196,225 and 400 are ±6,±14,±15 and±20

There exits two square roots of any number one with positive sign and one with negative sign

The first number we have is 36

The square roots of 36 = ±√36 = ±6  or it can be written as 6 and -6

The second number we have is 196

The square roots of 196 = ±√196 = ±14 or it can be written as 14 and -14

The third number we have is 225

The square roots of 225 = ±√225 = ±15  or it can be written as 15 and -15

The fourth number we have is 400

The square roots of 400 = ±√400 = ±20  or it can be written as 20 and -20

Hence, the square roots of 36,196,225 and 400 are ±6,±14,±15 and±20

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Answer:10

Step-by-step explanation:

6+4=10

Answer:

2.5n - 21.5

Step-by-step explanation:

[tex]-5(4 - \frac n2) + \frac1{16}(-32 + 8) \\ \\\to -5 \times 4 + 5 \times \frac n2 - \frac1{16} \times 32 + \frac1{16} \times 8 \\ \\\to -20 + \frac{5n}2 - \frac{32}{16} + \frac{8}{16} \\ \\\to -20 + 2.5n -2 + 0.5 \\ \\\to 2.5n - 21.5[/tex]

B rents for $1.62 per sq. feet is much cheap and better as compared to A

Yard and feet are used to estimate the length. Both of the units are used in the royal and US customary system of measurements. The value of one yard is equal to three feet.

To compute Square yard to Square Feet, where Square yard is equal to 9 Square Feet, multiply the value in Square yard by 9. one can also use the Square yard to Square Feet calculator.

1 yard² = 9 feet²

A rents for $27 per yard squared

hence A rents $27 for 9 feet squared

hence A rents $3 per feet squared( $27/9) which is costlier than $1.62 per feet squared

Hence B is better as it is cost effective.

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Answer:

[tex] \sf \frac{(x^3+4x^2+21x+28)}{4}[/tex]

Step-by-step explanation:

Let's simplify step-by-step.

[tex] \sf \: \frac{ {x}^{2} + 4x - 21}{4} \times x + 7[/tex]

Distribute

[tex] \sf \frac{(x^3+4x^2+21x+28)}{4}[/tex]

Answer:

A) x + 3

      4

Step-by-step explanation:

In arithmetic, a shape is translated when it is moved up, down, left or right. The translated shapes are congruent to the original shapes because they appear to be the same size. Just one or more of their routes have been changed. No changes to the shape are made because it is simply being moved from one location to another.

By utilizing the aforementioned guidelines, we can move the provided graph to the left, right, up, or down and graph the translated graphs. The coordinates of some points on a graph can be used to translate a graph as an alternative to this. Translation f(x + k) + C for a function graph To get the new x and y coordinates of each point when the graph of the function f(x) is supplied, simply select a few key spots on the graph (where the shape is changing or turning) and proceed as follows.

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Answer:  3 answer

Step-by-step explanation:

The solution to the system of linear equations is (x, y) = (2, 3).

Graphic methods are useful to solve systems of two linear equations with two variables, as it is seen in the statement of the problem. In accordance with geometry, a line can be constructed by knowing the coordinates of two distinct points on Cartesian plane. First, rewrite each linear equation into its explicit form:

y = 2 · x - 1                      (1)

y = - 3 · x + 9                  (2)

Second, look for two points lying on each line:

y = 2 · x - 1

(0, - 1) and (1, 1)

y = - 3 · x + 9

(0, 9) and (- 3, 6)

Third, plot the points on a Cartesian plane and pass each line through corresponding pair of points. The result is presented by the image attached below.

The solution to this system is the point of intersection of the two lines. The point of intersection is (2, 3).

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Answer:

A

Step-by-step explanation:

In math, symmetry is when an object, thing, etc is identical on both ends. Split a horizontal(left to right) line through the middle of each letter.  Every letter has identical top and bottom sides except for A.

Therefore, the answer is A.

Answer:

e = 5h

$100

Step-by-step explanation:

Let e = earnings

e = 5h

For h = 20,

e = 5h = 5(20) = 100

Answer:

$ 100

Step-by-step explanation:

1 hour = $ 5

h (hours worked in a week) = 20 hrs

EXPRESSION: amount of money earned in a week = h × 5

EVALUATION: amount of money earned in a week = 20 × 5

amount of money earned in a week = $ 100 ... answer

hope that helps...

Answer:

Not 100% sure

Step-by-step explanation:

Image result for how to simplify 5(2x-8) using distributive property

The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c); where, a, b, and c are the operands. Here, the number outside the brackets is multiplied with each term inside the brackets and then the products are added.

Second blank is 6 windows for every 1 penguin

given,

there are _18_ windows for every 3 penguins.

There are _6_ windows for every 1 penguin.

its is already given that 3 penguins = 18 windows,

the first blank is 18

To get number of windows for 1 penguin, we divide 18 by 3,

18/3=6

therefore second blank is 6 windows for every 1 penguin.

Window functions—otherwise known as weighting functions, tapering functions,  functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing.

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Answer:

89.01 calariese is answer

Inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.

The various operators used in inequalities for expression are -

Given is a inequality in one variable which is → x + 3.8 > 11.3.

PART - A

The inequality that represents the coordinates that are not the solutions of this inequality is -

x + 3.8 < 11.3

or

we can simplify it to get -

Subtract 3.8 from both sides -

x + 3.8 - 3.8 < 11.3 - 3.8

x < 7.5

PART - B

In order to plot the graph of this inequality, firstly we will plot the line of equation -

x = 7.5.

Since, the inequality is strict, make a dashed line to represent the equation.

Take the coordinates of origin O(0,0), and substitute it in the inequality -

0 < 7.5

which is true. Therefore, we will shade the complete side where origin lies.

The graph of the inequality is plotted an attached with the answer.

Therefore, inequality that represents the coordinates that are not the solutions of this inequality is x < 7.5. The graph of the inequality is attached at the end.

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Answer:

A = 5

B = 9

C = 32

Step-by-step explanation:

a. if the width of the scale factor 1 is 10, then the width of the scale factor 1/2 is 1/2 of 10. so 5.

b. same thing as a. the length for scale factor of 1 is 18 so the length for scale factor of 1/2 is 9.

c. width of scale factor 1 is 10, so width of scale factor 3.2, 10 times 3.2, is 32

Answer:

A = 5

B = 9

C = 32

Step-by-step explanation:

edg 2023

The amount that Yolanda can expect to have in her account at the end of 2 years is $8,068.28.

The amount of money that Yolanda deposits twice in a year represents an annuity. An annuity is a series of payment that is made over a specified period of time. An ordinary annuity is when payment is made at the end of each period and not at the beginning of the period. Yolanda's deposit is an ordinary annuity.

When the amount deposited in an account earns interest that is compounded semi-annually, it means that both the amount that is invested and the interest that is already accrued increases in value two time in a year, every six month.

The formula that can be used to determine the future value of the amount that was deposited in the account is:

Future value = amount deposited x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

1,900 x[ {(1.04^4) - 1} / 0.04] = $8,068.28

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The slope of the line representing number of tests on the y-axis and the time in weeks on the x axis is 0.75.

As per the given question;

The total number of week is 36 weeks.

The total test conducted is 27.

As, number of tests are represented on the y-axis and the time in weeks on the x axis.

The slope is constant for the text and weeks.

Thus, slope (m) is determined  as;

m = Δy/Δx

m = number of tests/time in weeks

Put the values.

m = 27/36

m = 0.75

Therefore, the slope of the line representing number of tests on the y-axis and the time in weeks on the x axis is 0.75.

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Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part. Price Elasticity of Supply is 2.185.

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part.

Price Elasticity of Supply is buyers' responsive change in quantity supplied due to change in Price.

P Es Formula = % change in quantity supplied / % change in price.

Given : % change in supply = 59 ; % change in price = 27

So, P Es = 59 / 27 = 2.185

% change in supply > % change in price & supply is > 1 . So, Supply is Elastic.

Therefore the price elasticity of supply for Barbie's Bakery's multigrain loaf is 2.185.

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Answer Valerie can afford 21,312 car

Step-by-step explanation:

The perimeter of tr8angle DEF that is similar to triangle ABC is: 18 cm.

If two triangles are similar to each other, and the perimeter of one is A with a side length of a, and the perimeter of the other is B with a side length of b, then, the following below is the ratio of their perimeters.

Perimeter of A/perimeter of B = a/b

Given that triangles ABC and DEF are similar triangles, we have the following:

Perimeter of triangle ABC = x

One side length of triangle ABC = 4 cm

Perimeter of triangle DEF = 12 + 6 + 9 = 27 cm

One side length of triangle DEF = 6 cm

Therefore:

x/27 = 4/6

Cross multiply

6x = (27)(4)

6x = 108

6x/6 = 108/6

x = 18

Thus, the perimeter of tr8angle DEF that is similar to triangle ABC is: 18 cm.

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