An image of a television is shown. The depth of the television is 4 inches. The
height of the television is 39 inches with a diagonal length of 65 inches.
39 in
65 in
What is the surface area of the model?
A. 5,902 in²
B. 7,696 in²
C. 4,784 in²
D. 6,162 in²

To make more than $100 profit we must make more than 25 bobble heads and less than50. 25 < b < 50 Make between 26 to 49 bobble heads.

p(b) = -0.2b2 + 15b - 150

 -0.2b2 + 15b - 150 > 100

-0.2b2 + 15b - 250 > 0

multiply through by 10 to clear decimal

-2b2 + 150b - 2500 > 0

 To find the point where profit is exactly

$100 set the equation equal to zero

 -2b2 + 150b - 2500 = 0

b = [-150 ±√(1502 -4(-2)(-2500))]/2(-2)

 b = (-150 ±√2500)/(-4)

b = (-150 ± 50)/(-4)

 we will have 2 points that work.

b = (-150 + 50)/-4 = 25

b = (-150 - 50)/-4 = 50

To make more than $100 profit we must make more than 25 bobble heads and less than50.

 25 < b < 50

 make between 26 to 49 bobble heads.

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It'll take you 3 hours to reach your destination.

The Equation of the Line in Standard form is 4x - y = 3

What is Slope of a Line?

The slope formula is used to compute the inclination or steepness of a line. The slope of the lines is calculated using the x and y coordinates of the lines. It is the ratio of the y-axis change to the x-axis change.

Solution:

Slope of the Line passing through the points (1, 1), (2, 5)

is

m = 5-1/2-1 = 4

Equation of the line = (y - y1) = m(x - x1)

y - 1 = 4(x - 1)

y - 1 = 4x - 4

4x - y = 3

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By using determinant, it can be calculated that-

det(C) = 8

det(D) = 9

What is a determinant?

Determinant of a square matrix is equal to the product of the elements of a square matrix and their cofactors.

Here,

det(A) = -8

The matrix C is obtained from A by swapping the second and third rows

We know if the rows and columns of a matrix are swapped then the value of the determinant of the new matrix changes in sign only

So det(C) = 8

Now,

det(A) = 9

We know that the value of determinant remain unchanged on adding any combination row or column

Matrix D is obtained from A by adding 2 times the fourth row to the first

det(D) = 9

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The graph represents the situation Allison purchases lemons for $0.75 each.

The ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane is known as slope of line.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph, we can take two points (4, 3) and (8, 6) to find the slope.

Let us plug in the values in formula of slope.

m=6-3/8-4

m=3/4

m=0.75

Hence, Allison purchases lemons for $0.75 each is represented by the given graph.

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The number of different ways the club select a president, vice president, treasure, and secretary is 23751.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

The Total number of members in an archeology club = 25 members

Different position to select a member : President , Vice-president, Treasure, and Secretary

The Number of position for selecting a member = 4

Therefore, Number of different ways to select different position

= ²⁹C₄

= (25!)/ (25-4)!4!

= (25× 24×23×23×21!) / (21!) (4×3×2×1)

= 23751

Therefore, the number of different ways the club select a president, vice president, treasure, and secretary would be equal to 23751.

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The probability that all of them get the same number would be 1/36. Or probability that they will have a chance of  get the same number after 36 throws. And the probability concept that use here is theoretical probability.

        Total out comes in three dice = ( 6 × 6 × 6 = 216 ).

        Probability of getting same number = 6 × 1/6 × 1/6 × 1/6

                                                                     = 6 × 1/6 × 1 × 1/6 × 6

                                                                     = 6/6 × 1/36

                                                                     = 1 × 1/36

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Using mathematical operations, we can say that total of 69 ft of lights is needed to cover all 8 windows.

An operation is a function in mathematics that converts zero or more input values into a clearly defined output value.

The operation's arity is influenced by the number of operands.

The rules that define the order in which we should solve an expression involving many procedures are known as the operation order.

PEMDAS stands for Parentheses, Exponentiation, Multiplication, Division, and Addition and Subtraction (from left to right).

So, we know the dimensions of the window:

3 ½ feet wide and 5 feet long.

And there is a total of 8 windows.

The perimeter of the rectangle: 2(l+w)

Now, the feet of light needed will be:

2(l+w) * 8

2(3 ½+5) * 8

2(7/2+5) * 8

7+5 * 8

12 * 8

96 ft

Therefore, using mathematical operations, we can say that total of 69 ft of lights is needed to cover all 8 windows.

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Answer:

The future value of an investment is calculated by using the formula:

$FV = PV(1 + r/n)^{nt}$

where $FV$ is the future value, $PV$ is the present value (the initial investment), $r$ is the interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the number of years the investment is held.

In this case, we have $PV = 1743$, $r = 5.45% = 0.0545$, $n = 2$, and $t = 2$. Plugging these values into the formula, we get:

$FV = 1743(1 + 0.0545/2)^{2 \cdot 2} = 1743(1 + 0.0273)^{4}$

Now we can calculate the future value by raising $1 + 0.0273$ to the power of 4:

$FV = 1743(1.0273)^{4} \approx \boxed{1956}$

Note that we rounded the result to the nearest cent.

Step-by-step explanation:

Mike charged for each shirt is $2.49, each pair of slacks is $5.99 and each sports coat is $7.99.

What is system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Let

Price of shirts = x

Price of slacks = y

Price of sports = z

From the given information,

3x + y = $13.46         ..(1)

7x + 3y + z = $43.39         ..(2)

5x + 2z = $28.43        ..(3)

From equation (1), y = 13.46 - 3x

From equation (3),  z = (28.43 - 5x) / 2

Plug the value of x and z in equation (2)

7x + 3(13.46 - 3x) +(28.43 - 5x)/2 = 43.39

7x + 40.38 - 9x + 14.22 - 2.5x = 43.39

-4.5x +54.6 = 43.39

4.5x = 54.6 - 43.39

4.5x = 11.21

x = 2.49

Plug x = 2.49 in equation (1)

3(2.49) + y = 13.46

2.47 + y = 13.46

y = 5.99

Plug x = 2.49 in equation (3),

5(2.49) + 2z = 28.43

12.45 + 2z = 28.43

2z = 15.98

z = 7.99

Hence, Mike charged for each shirt is $2.49, each pair of slacks is $5.99 and each sports coat is $7.99.

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So our goal is to determine the mean test score, which we don't know, we know to raw scores, we know one raw score is 38 that's one standard deviation below the mean, which by definition of a Z score that Z equals negative one. one

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Approximately 95% of the scores should lie within the range of 79 to 91.

Approximately 95% of the scores on a standardized test with a normal distribution and a mean of 85 and a standard deviation of 3 should lie within 2 standard deviations of the mean.

Since the standard deviation is 3, 2 standard deviations is : 2 × 3 = 6.

Adding 6 to the mean of 85 gives 91, and subtracting 6 from the mean of 85 gives 79.

Therefore, approximately 95% of the scores should lie within the range of 79 to 91.

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Answer: e

Step-by-step explanation:

4+6= 10 and then divide by 50 and add 25 so 0.2+25+25.02 so then subtract 4 so about 21 or 21.02

The expression 10ax + 14ay + 15bx + 21by has a coefficient of (2a + 3b)

as a factor.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 10ax + 14ay + 15bx + 21by.

The given expression is in 4 variables namely a, b, x and y we'll combine the x and y terms in the expression.

Now, 10ax + 15bx + 14ay + 21by.

= 5x(2a + 3b) + 7y(2a + 3b).

= (2a + 3b)(5x + 7y)

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Answer:

1/9 rise 1 run 9

Step-by-step explanation:

if you graph the y coordinate as 3 and find the x value, x value should be 0. Point (0,3) and (-9,2) and do rise over run

B

Step-by-step explanation:

The value of x is 9.

The value of y is 5.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Two triangles in a composite triangle.

We see that,

m∠UST = m∠STR

This means,

x + 4 = 13

x = 13 - 4

x = 9

The sum of the angles in a triangle is 180 degrees.

One triangle is an equilateral triangle.

All three angles are equal.

This means,

The angle has to be 60°.

m∠UTR + m∠URT + m∠TUR = 180

3m = 180

m = 60

Now,

m∠URS = 180

m∠URT + m∠SRT = 180

60 + m∠SRT = 180

m∠SRT = 120

The isosceles triangle has two equal angles.

m∠RTS = m∠RST

m∠SRT + m∠RTS + m∠RST = 180

120 + 6y + 6y = 180

12y = 180 - 120

12y = 60

y = 5

Thus,

The value of x and y are 9 and 5.

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Answer: x = 52, y = 128, z = 52

Step-by-step explanation:

The polynomial we get after solving this is (x+6).

To simplify this expression, we need to use the rules of algebra. First, we can factor the numerator to get (x-6)(x+6) so the expression becomes:

(x-6)(x+6)÷ (x-6)

Now we can cancel out the (x-6) terms in the numerator and denominator to get:

(x-6)(x+6)÷(x-6) = (x+6)

This is the simplified form of the expression. Note that this result is only valid when x is not equal to 6, since division by zero is undefined.

What is a Polynomial?

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

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Answer:

1:5

Step-by-step explanation:

Answer:

2 and -5 (B & E)

Step-by-step explanation:

Factor the equation into

(x-2) (x+5)

Thus the zeros are 2 and -5

x=2 and x=-5 are the solutions of the quadratic equation x² + 3x-10 = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is x² + 3x-10 = 0

We have to find the solutions of the quadratic equation

x² + 3x-10 = 0

Let us factorize the given equation

x² +5x-2x-10=0

x(x+5)-2(x+5)=0

(x-2)(x+5)=0

Now equate both the terms with zero to find the solutions

x=2 and x=-5

Hence, x=2 and x=-5 are the solutions of the quadratic equation x² + 3x-10 = 0

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The annual percentage rate of the investment account is of:

14.1%.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The effective annual interest rate is given as follows:

[tex]E = \left(1 + \frac{r}{n}\right)^n[/tex]

In this problem we have a semi-annual compounding, hence:

n = 2.

The effective rate was of 14.6%, hence E = 1.146, and thus the interest rate is obtained as follows:

[tex]E = \left(1 + \frac{r}{n}\right)^n[/tex]

[tex]1.146 = \left(1 + \frac{r}{2}\right)^2[/tex]

1 + 0.5r = 1.0705 (applying to square root to both sides).

0.5r = 0.0705

r = 0.0705/0.5

r = 0.141 = 14.1%.

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Answer:

Step-by-step explanation:

A vending machine

The user puts in money, punches a specific button, and a specific item drops into the output slot. (The function rule is the product price. The input is the money combined with the selected button. The output is the product, sometimes delivered along with coins in change, if the user has entered more money than required by the function rule.)

Answer: it is mean to state a real world relationship that consisted a state of a input and output

Step-by-step #hopethishelps

Answer:

Step-by-step explanation:

(0,-9)

Step-by-step explanation:

10y(3/5y) = 3×10y / 5y = 3×2 = 6

since this is not one of the answer options, you must have mistyped something.

probably the real problem is

10y((3/5)y) = 2y×3 × y = 6y²

the 3rd answer option is correct.

The solution of the inequality will be;

⇒ x > 5

And, The solution is shown on number line.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ - 2/5x < - 2

Now,

Solve the inequality as;

⇒ - 2/5x < - 2

⇒ - 2x < - 2 × 5

⇒ - 2x < - 10

Multiply by - 1,

⇒ 2x > 10

⇒ x > 5

Thus, The solution of the inequality = x > 5

And, The solution is shown on number line in figure.

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To evaluate the integral, you will need to define the limits of integration and use appropriate coordinate systems for the given area.

And the area is given as   [tex]I_{xy} =\int \limits \int \limits {(y^2 - x^2)} \,dm[/tex]

What is direct integration?

Direct integration is a method of finding the moment of inertia of a body or a region about a given axis by directly integrating the product of the mass of each infinitesimal element of the body or region and the square of its distance from the axis.

To determine the product of inertia of a given area with respect to the x and y axes, you will need to first define the area and its mass distribution. Then, you can use the following formula for the product of inertia:

[tex]I_{xy} =\int \limits \int \limits {(y^2 - x^2)} \,dm[/tex]

Where Ixy is the product of inertia, y is the distance from the y-axis, x is the distance from the x-axis, and dm is the mass of an infinitesimal element of the area.

Hence, To evaluate this integral, you will need to define the limits of integration and use appropriate coordinate systems for the given area.

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The best interpretation of the slope of the linear regression equation is given as follows:

For each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

The slope represents the rate of change of the output variable relative to the input variable of a linear relation.

Hence, it can be said that the slope states by how much the output variable y changes when the input variable x is increased by 1.

The variables in this problem are given as follows:

The negative slope of -0.7 means that for each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

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Answer:

B

Step-by-step explanation:

Here is the two column proof:

     Statement                                        Reason                                              

Answer:

(12,1)

Step-by-step explanation:

Before the transformation, Point B is at (-8,1).

When it will be reflected, it will be at (8,1)

Then, it shifts 4 points to the right, and so it will be at (12,1)