Jackie Bradford has two jobs. Her full-time job pays $15 an hour. A part-time job pays $8 anhour. Last week Jackie worked 35 hours at her full-time job and 17 hours at her part-time job.a. Find the gross pay she earned at her full-time job. b. Find the gross pay she earned at herpart-time job. c. Find the total amount she earned from both jobs.

If you are adding them together, the answer would be 7^9

If you are solving the problem, the answer would be 40,353,607

Answer:

you sold fewer than 100 tickets. you only sold 50 tickets out of your 100 ticket goal.

The domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.

To find the domain of a rational expression, we need to identify any values of x that would result in division by zero. Division by zero is undefined in mathematics
In this case, we need to set the denominator, 4x+20, equal to zero and solve for x:
4x + 20 = 0
Subtract 20 from both sides:
4x = -20
Divide both sides by 4:
x = -5
Therefore, the value x = -5 makes the denominator zero.
Now, we need to consider the values of x for which the denominator is not zero. Since the denominator is a linear expression (a polynomial of degree 1), it is defined for all real numbers except x = -5.
So, the domain of the rational expression (6-x)/(4x+20) is all real numbers except x = -5.

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Answer:

Option A. A and D

Step-by-step explanation:

This answer because they are both right triangles and are near the same size

Hope this helps!

The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:

8 Months

Step-by-step explanation:

The formula in the problem (B = 100 + 75m) can be written as this:

(B-100)/75 = M

The problem gives us the balance (B=700), which we can plug into our new formula to find the number of months (m).

(700-100)/75 = M

M = 8

I hope this helps!

-TheBusinessMan

Answer:

2.5 years

Step-by-step explanation:

Answer:

x+y=30

2x+3y=80

multiplying equation one by -3 and add equation

-3x -3y=-90

2x +3y=80

2(10)+20(3)=80

80=80

Answer:

b

Step-by-step explanation:

Answer:

a) 161

Step-by-step explanation:

350 of 46%

=350 × 46/100

= 161

The correct answer is option (e): None of these answers is correct.

The statement "the mode is the most frequently occurring data value" is true. However, none of the options provided accurately describes the relationship between the mode and the mean.

The mode and the mean are different measures of central tendency and can have different values. There is no general rule or guarantee that the mode will always be larger or smaller than the mean. The relationship between the mode and the mean depends on the specific dataset and its distribution. Therefore, none of the provided options correctly describes the relationship between the mode and the mean.

The maximum and minimum points of the function are (a) (3π/2, -1) (-π/2, -1), (π/2, 3)

From the question, we have the following function that can be used in our computation:

y = –2 cos (x + π/2) + 1.

Calculating the maximum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the maximum points to be (π/2, 3)

Calculating the minimum

Here, we have

y = –2 cos (x + π/2) + 1.

Next, we plot the graph of the function

From the graph of the function, we have the minimum points to be

(3π/2, -1) (-π/2, -1)

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Answer:

we conclude that only two points (-5, 5) and (-1, 4) satisfy the system of inequalities.

Step-by-step explanation:

Given the system of inequalities

y > 2x+3

y+3x ≤ 1

Checking the point (0, 5)

Let us substittue the point (0, 5) to check if it is satisfies system of inequalities

y > 2x+3

5 > 2(0) + 3

5 > 3

True

now check for the second inequality

y+3x ≤ 1

5 + 3(0) ≤ 1

5 ≤ 1

False

Therefore, the point (0, 5) does not satisfy the system of inequalities

Checking the point (-5, 5)

Let us substittue the point (-5, 5) to check if it is satisfies system of inequalities

y > 2x+3

5 > 2(-5) + 3

5 > -10+3

5 > -7

True

now check for the second inequality

y+3x ≤ 1

5 + 3(-5) ≤ 1

5-15 ≤ 1

-10 ≤ 1

True

Therefore, the point (-5, 5) satisfies the system of inequalities.

Checking the point (-1, 4)

Let us substittue the point (-1, 4) to check if it is satisfies system of inequalities

y > 2x+3

4 > 2(-1) + 3

4 > -2+3

4 > 1

True

now check for the second inequality

y+3x ≤ 1

4 + 3(-1) ≤ 1

4-3 ≤ 1

1 ≤ 1

True

Therefore, the point (-1, 4) satisfies the system of inequalities.

Checking the point (0, -5)

Let us substitute the point (0, -5) to check if it satisfies the system of inequalities

y > 2x+3

-5 > 2(0) + 3

-5 > 0+3

-5 > 3

False

now check for the second inequality

y+3x ≤ 1

-5 + 3(0) ≤ 1

-5+0 ≤ 1

-5 ≤ 1

True

Therefore, the point (0, -5) does not satisfy the system of inequalities.

Checking the point (-3, -3)

Let us substitute the point (-3, -3) to check if it satisfies the system of inequalities

y > 2x+3

-3 > 2(-3) + 3

-3 > -6+3

-3 > -3

False

now check for the second inequality

y+3x ≤ 1

-3 + 3(-3) ≤ 1

-3 - 9 ≤ 1

-12 ≤ 1

True

Therefore, the point (-3, -3) does not satisfy the system of inequalities.

Hence, we conclude that only two points (-5, 5) and (-1, 4) satisfy the system of inequalities.

The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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The cotangent of the positive acute angle is tan(5π/12)

We can use the trigonometric identity:

cot(π - θ) = -cot(θ)

to rewrite cot(11π/12) as -cot(π/12):

cot(11π/12) = -cot(π - 11π/12) = -cot(π/12)

Now, we can use the identity:

cot(π/2 - θ) = tan(θ)

to rewrite -cot(π/12) as tan(π/12 - π/2):

-cot(π/12) = -1/tan(π/12) = tan(π/2 - π/12)

Therefore, cot(11π/12) can be written in terms of the cotangent of a positive acute angle as:

cot(11π/12) = -cot(π/12) = tan(π/2 - π/12) = tan(5π/12)

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Answer:

$638641.33

Step-by-step explanation:

Adam earns $45,000 in his first year.

His salary increases by 3% each successive year. Therefore, his salary the next year is 103% of his previous year.

This is a geometric sequence where the:

(a)

Sum of  geometric series\(=\dfrac{a(r^n-1)}{r-1}\)

Substituting the given values, Adam's total earnings over n years

\(=\dfrac{45000(1.03^n-1)}{1.03-1}\\\\$Adam's Total Earnings=\dfrac{45000(1.03^n-1)}{0,03}\)

(b)When n=12 years

\(\text{Adam's Total Earnings for the first 12 years=}\dfrac{45000(1.03^{12}-1)}{0.03}\\=\$638641.33$ (correct to the nearest cent)\)

The Corollary to the polygon is explained below and the  formula to find the measure of each interior angle is  " (n - 2)×180°/n "   .

The Corollary to the polygon Angle Sum Theorem states that : the sum of the interior angles of a regular n gon is written as :

that means , ⇒ Sum of interior angles = (n - 2) × 180° ...equation(1)

In a regular "n-gon" , all the interior angles are said to be congruent.

Let "x" be  measure of each interior angle of a regular n-gon.

So , we can write ;

⇒ Sum of interior angles = (n)×(x)  ;

Equating the above expressions with equation(1),

⇒ (n)×(x) = (n - 2) × 180°  ;

On Solving for x,

⇒ x = (n - 2)×180°/n  ;

Therefore, the measure of each interior angle of a regular "n-gon" is x = (n - 2)×180°/n  .

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Answer: the Ferris Wheel

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(A=\frac{a+b}{2}*h=\frac{4+7}{2}*3=16.5cm^2\)

\(A=\frac{ab}{2} =\frac{4*6}{2} =12in^2\)

\(A=wl=6*5=30in^2\)

\(12+30=42in^2\)

\(A=\frac{a+b}{2}h=\frac{28+40}{2}*30=1020ft^2\)

Wall = A=\(\frac{ab}{2} =\frac{6*30}{2}=90ft^2\)

Answer:

Step-by-step explanation:

Question 1:

A = (a+b/2)h

A = (4+7/2)3

A = (11/2)3

A = (5.5)3

A = 16.5cm²

Question 2:

A = bh/2 = 6*4/2 = 24/2 = 12

A = bh = 6*5 = 30

A = 12 + 30 = 42

A = 42in²

Question 3:

A = (a+b/2)h

A = (28+40/2)30

A = (68/2)30

A = (34)30

A = 1020ft²

A = bh/2

A = 30*6/2

A = 180/2

A = 90ft²

Best of Luck!

The measurement that is closest to the volume of the sphere is given as follows:

1,767.1 in³.

The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

\(V = \frac{4\pi r^3}{3}\)

From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:

r = 0.5 x 15

r = 7.5 units.

Then the volume of the sphere is given as follows:

V = 4/3 x π x 7.5³

V = 1,767.1 in³.

The sphere is given by the image presented at the end of the answer.

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Answer:

1?

Step-by-step explanation:

9 1/4 is the longest distance

2 times

According to the chart, the mile that she ran the fastest was \(9 \frac{1}{2}\) miles. 1 dot equals 1 minute so her fastest mile was \(9 \frac{1}{2}\).

I hoped this helped if not please tell me what I did wrong ૮ ˶ᵔ ᵕ ᵔ˶ ა

Answer:

The cost of membership at gym A can be written as:

c

a

=

$

10

m

+

$

15

The cost of membership at gym B can be written as:

c

b

=

$

4

m

+

$

40

Where

c

g

y

m

is the cost after

m

months.

To find when the cost is equal, equate the right side of both equations and solve for

m

:

$

10

m

+

$

15

=

$

4

m

+

$

40

Next, subtract

$

15

and

$

4

m

from each side of the equation to isolate the

m

term while keeping the equation balanced:

−

$

4

m

+

$

10

m

+

$

15

−

$

15

=

−

$

4

m

+

$

4

m

+

$

40

−

$

15

(

−

$

4

+

$

10

)

m

+

0

=

0

+

$

25

$

6

m

=

$

25

Now, divide each side of the equation by

$

6

to solve for

m

while keeping the equation balanced:

$

6

m

$

6

=

$

25

$

6

$

6

m

$

6

=

$

25

$

6

m

=

25

6

m

=

4.17

At 4 months the cost of the two gym memberships will be about the same.

Step-by-step explanation:

Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

The function is an exponential growth function

The function is given as

y=2(1.06)^9

We can begin by rewriting the given equation as:

y = 2 * 1.06t

So, we have

y = 2 * (1 + 0.06)^t

Now we can see that the equation is in the form y = a*b^t,

where a = 2 and b = 1.06^9

This equation represents exponential growth because the base of the exponent, b = 1.06, is greater than 1.

We can re-write it in the form y = a(1+r)t,

we can find the value of r by subtracting 1 from 1.06 which is 0.06 and the value of a is 2.

so we have y = 2(1+0.06)^t

So, the equation represents exponential growth with a = 2 and r = 0.06

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The volume of the composite figure is 228 ft³.

To calculate the volume of a composite figure, we need to break it down into its individual components and then sum up the volumes of each component.

From the given dimensions, it seems that the composite figure consists of multiple rectangular prisms. Let's calculate the volume of each prism and then add them together.

First prism:

Length = 8 ft, Width = 4 ft, Height = 6 ft

Volume = Length * Width * Height = 8 ft * 4 ft * 6 ft = 192 ft³

Second prism:

Length = 3 ft, Width = 2 ft, Height = 6 ft

Volume = Length * Width * Height = 3 ft * 2 ft * 6 ft = 36 ft³

Now, let's add the volumes of both prisms:

192 ft³ + 36 ft³ = 228 ft³

Therefore, the volume of the composite figure is 228 ft³.

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What is the volume of the composite figure? 8 ft 4 ft 6 ft 3 ft 2 ft

Answers 96 ft³3 76 ft³ 228 ft³ 192 ft³ ​

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match the change in the position of the minute hand with the angle made by the change.

π/3 → The minute hand moves from 4 to 6.

2π/3 → The minute hand moves from 3 to 7.

5π/6 → The minute hand moves from 5 to 10.

7π/6 → The minute hand moves from 2 to 9.

The required change in angle is given by 7π/6,  4π/6, π/2, 5π/6.

Match the change in the position of the minute hand with the angle made by the change.

Minute hand is tip in the clocks that shows the minutes of time.

Here,
60 min = 360 x π /180
1 min = π /30
A) The minute hand moves from 2 to 9 = 7 x5 x π /30 = 7π/6.
B) The minute hand moves from 3 to 7 = 4 x 5 x π /30 = 4π/6.
C) The minute hand moves from 1 to 4. = 3 x 5 x π /30 =  π/2.
D) The minute hand moves from 5 to 10 = 5 x 5 x π /30 = 5π/6.

Thus, the required change in angle is given by 7π/6,  4π/6, π/2, 5π/6.

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The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

-------------

    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

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