The doctor tells Emily that she needs to exercise enough to burn at least 200 calories each day. She prefers kickboxing or swimming. While kickboxing she burns 10 calories per minute, and while swimming she burns 7 calories per minute.

The composition of the fuctions g(x) and f(x) evaluated in x = 4 is equal to:

g( f(4)) = 45

Here we have two functions f(x) and g(x), such that:

g(x) = 3.25*x + 6

And f(x) is defined by the table:

x            f(x)

-2            -1

0             3

 4            12

7              9

19             6

And we want to find the composition of g(x) and f(x) evaluated in x = 4.

g( f(4))

By using the table of f(x), we can see that f(4) = 12

Then:

g( f(4)) = g(12)

Evaluating g(x) in x = 12 we get:

g(12) = 3.25*12 + 6 = 45

Then we conclude that g( f(4)) = 45

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Answer:

The surface area of the prism is 386m²

Step-by-step explanation:

The surface area of a box is equal to the sum of the areas of each side of the box.

\(2 \times (lenght) \times (widht) + 2 \times (lenght) \times (height) + 2 \times (width) \times (height)\)

Substitute the values of the length l=15, the width w=7, and the height h=4 into the formula.

\(2 \times 15 \times 7 + 2 \times 15 \times 4 + 2 \times 7 \times 4\)

Simplify each term.

\(210 + 120 + 56\)

Simplify by adding numbers.

\(386m ^{2} \)

Hence, the Surface area of this prism is 386m².

Answer:

After calculating values from test statics we come to know that value of if null hypothesis is true then it will rejected

As critical values of z is ±1.96 after apply the test statics formula , we get the value of z that is - 4.50 As we consider the equation that

H₀ > z

Apply test statistic we fine the true value . So there is sufficient evidence to reject the claim.

Step-by-step explanation:

critical values z₀ = ±1.96; standardized test statistic z ≅ -4.50;

reject H₀

There is sufficient evidence to reject the claim.

Answer:

Step-by-step explanation:

3: x=9, y=15

4:n=12, m=5

5: a=55

6: p=60

7:z=28, d=126

8: h=9, g=61

9:Angle B=129

10:Angle L=85

11: Angle Y= 61

Cost of a bottle of juice is $ 1.62

Equation for determining the cost of juice is 1.56 + 20x = 33.96

Given,

The cost of a bag of chips = $ 1.56

Number of juice bottles bought by Sarah = 20 pack

Total cost before tax = $ 33.96

Cost of one bottle of juice = x

We have to find x:

Then the equation will be:

1.56 + 20x = 33.96

Add -1.56 to both sides:

1.56 + 20x - 1.56 = 33.96 - 1.56

We get,

20x = 32.4

Now find x,

x = 32.4 / 20

Then,

x = 1.62

That is, the equation for finding the cost of a bottle of juice is 1.56 + 20x = 33.96.

The cost of one bottle of juice is $1,62

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Given that there exist undefinable restrictions, the domain for the function f(x)=23x + 4 is (-∞,∞).

In mathematics, a function is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Four main categories may be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.

Here,

f(x)=−23x+4

as there are undefined constraints,

domain=(-∞,∞)

The domain for function f(x)=−23x + 4 is (-∞,∞) as there are undefined constraints.

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Answer:

-24

Step-by-step explanation:

The standard from of equation of a line is expressed as g(x) = mx+c where;

m is the slope

c is the y-intercept of the line.

Given the expression g(x)= (- 8)(x +3), rewriting in standard form first we have;

g(x)= (- 8)(x +3)

gx)= -8x - 24

On Comparing with g(x) mx+ c, we will see that;

c = -24

Hence the y-intercept of the quadratic function is -24

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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Answer:

(4x - 3)(3x + 2)

Step-by-step explanation:

(4x - 3)(3x + 2)

The quadratic regression function which models the data in the form ax² + bx + c is written thus ;f(x) = -147.30x² + 3231.00x - 8213.66.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

According to our question-

A polynomial of degree two, the quadratic regression function. where y is the entire profit made, and x is the selling price of the widget.

f(10.25) = -147.30(10.25)² + 3231.00(10.25) - 8213.66

f(10.25) = 9428.38

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Step-by-step explanation:

i)Initial School population,

given 15 units = 1200

1 unit =

\(1200 \div 15 \\ = 80\)

Number of teachers (initial) = 1 unit = 80.

ii)take j = number of teachers joining the school.

New teacher population = 80+j

\( \frac{3}{43} (1280 + j) = 80 + j \\ \frac{3840}{43} + \frac{3}{43} j = 80 + j \\ j - \frac{3}{43} j = \frac{3840}{43} - 80 \\ \frac{40}{43} j = \frac{400}{43} \\ 40j = 400 \\ j = 400 \div 40 \\ = 10\)

The area of the trapezoid is equal to 139.5 in² and the correct option is B.

area of the trapezoid is calculated using the formula: 1/2 × (AB + CD) × height (EB)

AB = 12 in

CD = 2 in + 12 in + 5 in = 19 in

height = 9 in

area of trapezoid ABDE = 1/2 × (12 + 19) × 9 in²

area of trapezoid ABDE = 1/2 × 31 × 9 in²

area of trapezoid ABDE = 1/2 × 279 in²

area of trapezoid ABDE = 139.5 in²

Therefore, the area of the trapezoid is equal to 139.5 in².

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Hence Proved N to N is uncountable set by using a diagonalization argument

What is Diagonalization Argument?

Georg Cantor published the Cantor's diagonal argument in 1891 as a mathematical demonstration that there are infinite sets that cannot be put into one-to-one correspondence with the infinite set of natural numbers. It is also known as the diagonalization argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof.

Proof:

We write f as the sequence of value it generates

that is, say f:N-N is defined as f(x) =x then

we write f as : 1,2,3,4........

similarly if f:N-N were f(x) = 2x then we write it as :2,4,6,8.......

now assume on the contrary that the set of functions from N to N is countable

then,

\(f_{1}\)   :     \(f_{11}\)        \(f_{12}\)       \(f_{13}\) , ...........

\(f_{2}\)   :     \(f_{21}\)        \(f_{22}\)       \(f_{23}\) , ...........

\(f_{3}\)   :     \(f_{31}\)        \(f_{32}\)       \(f_{33}\) , ........... and so on

Here \(f_{ij}\) =\(f_{i}(j)\)

consider the function f as :

f : (\({f11}\) +1 ) , (\({f22}\) +1) , (\({f33}\) +1),.........

Then f wouldn't appear in the list of the function we had above since any \(f_{i}\) would disagree with f at the i th place

Therefore the set of the function from N to N is an uncountable set

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Its formed  an obtuse triangle  with side lengths 4 in, 5 in, and 8 in.

What is obtuse triangle?

When given 3 sides of a triangle, the longest side must be less than the sum of the other 2 sides.

8 < 4 + 5 so a triangle can be formed.

In fact it will be an obtuse triangle.

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The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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Anica has 13 stuffed animals, and each box holds 5 animals.

How many boxes does Anica completely fill?

We can completely fill 2 boxes of 5 stuffed animals

A total of 10 stuffed animals are packed

How many animals are left?

The remaining animals would then be the subtraction of 13 - 10

13 animals in total and 10 packed

There are 3 animals left outside

Answer:

first one, put value of x= -3 and y = 0

second one, pit vale of x=7 and y= -7

Step-by-step explanation:

first one,

-14(-3) -20(0) =42

or, 42-0 = 42

or, 42 = 42

proved

second one,

-14(7) -20(-7) = 42

or, -98 + 140=42

or, 42 = 42

proved

Answer:

QUESTION:

If you throw a six-sided number cube. then how many times will I get a 7

ANSWER:

This is a tricked question. You will never roll a 7 on a six-sided numbered cube unless you have 2 dice.

Step-by-step explanation:

Hope that this helps you out! :)      

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Hey!

For any graphing calculator problems I would recommend using desmos if your teacher allows it or getting a graphing calculator such as a ti-nspire :)

This way, it will be able to graph and get the answers quicker!

The answers to this question is (37.5,15) and (0,60). To find your answers when you graph always look for where the lines intersect. If the lines do not intersect then it is not one of your answer choices. (examples are below).

Answer:

11

Step-by-step explanation:

yeah-ya............ right?

Check the picture below.

Step-by-step explanation:

(3x-15)°= 105°

3x=120

x=40°

(y+25)°=180-105

(y+25)°=75°

y=75-25

y=50°

Answer:

x = 40°

y = 50°

23.731 g rounded to three significant figures is 23.7 g.

Rule for significant figures:

All non-zero numbers are significant.

In 23.731, there are 5 non-zero numbers. So, there are 5 significant figures. To get number in 3 significant figures round the number at the first decimal place.

Now, the 23.731 g can be expressed in 3 significant figures as 23.7 g.

The y-intercept of the graph is: 3,000

The slope is: -2.75

The linear equation of the graph is: y = -2.75x + 3,000.

The linear equation that represents a linear graph shows the slope (m) and y-intercept (b) of the graph and is expressed in slope-intercept form as, y = mx + b.

In the given graph:

The y-intercept (b) is the starting value, which is the point on the y-axis where the line intercepts, and it is equal to: 3,000.

Using two points on the graph, (0, 3,000) and (2, 2,450), the slope of the graph = change in y / change in x = (3,000 - 2,450)/(0 - 2) = 550/-2 = -2.75.

To write the linear equation, substitute m = -2.75 and b = 3,000 into y = mx + b:

y = -2.75x + 3,000.

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A sine function that has an amplitude of 2, a midline of 4 and a period of 2/3 is write as:

The sine function is written considering the general formula in the form

sine function, y = A sin wx + b

where

A = amplitude

w = 2π / period

b  = midline

In the problem the values available are

A = 2

b = 4

period = 2/3

substituting the known values

sine function, y = A sin wx + b

sine function, y = 2 sin (2π / 2/3) x + 4

sine function, y = 2 sin (3π) x + 4

sine function, y = 2 sin 3πx + 4

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