Hervenson is working two summer jobs, making $12 per hour at Mcdonald's and making $8 per hour washing cars. In a given week, he can work at most 20 totalhours and must eam a minimum of $200. If Hervenson works 15 hours at McDonalds, determine the minimum number of whole hours washing cars that he mustwork to meet his requirements. Write a system of inequalities to describe Hervenson's situation.

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

15 years old

Step-by-step explanation:

Start by defining the variables that we are going to use throughout our working:

Let the current age of Wei Ling and Wei Xuan be L and X years old respectively.

Next, form equations using the given information.

5 years ago

Wei Ling: (L -5) years old

Wei Xuan: (X -5) years old

Given that the ratio of Wei Ling's age to that of Wei Xuan's is 2: 5,

\( \frac{ L - 5}{X - 5} = \frac{2}{5} \)

Cross multiply:

2(X -5)= 5(L -5)

Expand:

2X -10= 5L -25

2X= 5L -25 +10

2X= 5L -15 -----(1)

9 years time

Wei Ling: (L +9) years old

Wei Xuan: (X +9) years old

Given that the ratio of Wei Ling's age to that of Wei Xuan is 3: 4,

\( \frac{L + 9}{X + 9} = \frac{3}{4} \)

Cross multiply:

3(X +9)= 4(L +9)

Expand:

3X +27= 4L +36

3X= 4L +36 -27

3X= 4L +9 -----(2)

Let's solve using the elimination method.

(1) ×3:

6X= 15L -45 -----(3)

(2) ×2:

6X= 8L +18 -----(4)

(3) -(4):

6X -6X= 15L -45 -(8L +18)

0= 15L -45 -8L -18

0= 7L -63

7L= 63

L= 63 ÷7

L= 9

Substitute L= 9 into (1):

2X= 5(9) -15

2X= 45 -15

2X= 30

X= 30 ÷2

X= 15

Thus, Wei Xuan is 15 years old now.

Answer:

The slope is -2 and y-intercept is (0, 5/4).

Step-by-step explanation:

-8x-4y=-5

4y=-8x-(-5)

4y=-8x+5

y=-8/4x+5/4

y=-2x+5/4

y=mx+b where m=slope and b=y-intercept.

Thus, m=-2 and b=5/4.

The average allowance for each student is $9.25.

To find the average allowance for each student, we need to add up all the allowances and divide by the total number of students.

Adding up the allowances:

$7 + $12 + $8.50 + $10 + $7 + $8 + $10.50 + $11 = $74

There are 8 students, so we divide the total allowance by 8 to get:

$74 / 8 = $9.25

Therefore, the average allowance for each student is $9.25.

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√9 × √16 and 5√2 × √2 simplify to a rational answer

A rational number is a number that can be written in the form of a/b, where a and b are integers, and b is not equal to 0. e.g 1/3, 2/3, √4 = 4/1, etc.

The opposite of a rational number is called an irrational or non-rational number. They are mostly in the form of square roots, which when evaluated can be expressed in the form a/b e.g √7, π, 2/√5, 3√11, etc.

Given:

For √9 × √16:

√9 × √16 = 3× 4 = 12

This is a rational answer

For √3 × √2:

√3 × √2 = √(3×2) = √6

This is not a  rational answer

For √11 × √5:

√11 × √5 = √(11×5) = √55

This is not a  rational answer

For 5√2 × √2:

5√2 × √2 = 5√(2×2) = 5√4 = 5×2 = 10

This is a rational answer

Therefore, √9 × √16 and 5√2 × √2 simplify to a rational answer. Select the 1st and 4th options

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The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

A.)  \(\frac{500}{3} \pi units^3\)

Step-by-step explanation:

To find the volume of the sphere, you need to use the following equation:

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

In this equation, "V" represents the volume (units³) and "r" represents the radius (units). Since you have been given the value of the radius (r = 5 units), you can use it to solve the equation.

\(V= \frac{4}{3} \pi r^3\)                              <----- Volume equation

\(V= \frac{4}{3} \pi (5)^3\)                           <----- Plug 5 into "r"

\(V= \frac{4}{3} \pi (125)\)                         <----- Solve 5³

\(V= \frac{500}{3} \pi\)                              <----- Multiply \(\frac{4}{3}\) and 125

Answer:

\(\sf A. \quad \dfrac{500}{3} \pi \:\:units^2\)

Step-by-step explanation:

Volume of a sphere

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

(where r is the radius)

From inspection of the given diagram:

Substitute the value of r into the equation and solve for V:

\(\begin{aligned}\sf V & = \sf \dfrac{4}{3} \pi r^3\\\\\implies \sf V & = \sf \dfrac{4}{3} \pi (5)^3\\\\& = \sf \dfrac{4}{3} \pi (125)\\\\ & = \sf \dfrac{4 \cdot 125}{3} \pi\\\\& = \sf \dfrac{500}{3} \pi \:\:units^2\end{aligned}\)

Answer:

Step-by-step explanation:

Multiply the amount of tablets by 1/4 to find the answer

The earned interest on given principal amount of $1000 is $1587.

Compound interest is defined as the interest on the both initial principal amount and interest amount of previous period.

We have initial saving of $1000 in bank which gives 8% interest compounded annually.

Formula to find interest , P(1 + r/100)^n

p is principal, r is rate of interest , n is time period.

Interest for 6 years = $1000(1 + 8/100)^6

⇒$1000(108/100)

⇒ $1000×1.59

⇒ $1587 approx

Thus, required answer is $1587 approx.

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Answer:

I plotted it out on the graph and here it is:

Answer:

1.5

Step-by-step explanation:

To find the common ratio of a geometric sequence, you divide two consecutive terms together. You can start by dividing 9/6, or 1.5. To confirm this is the common ratio, you can divide 27/2 ÷ 9, which is indeed 1.5. The common ratio is the multiplier of the sequence, so it is consecutive and does not change throughout the function.

Answer:

r = 3/2

Step-by-step explanation:

1.5 written as a fraction is 3/2

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

The prices from 5 gas stations surveyed are given as:

$2.79, $2.99, $2.69, $2.89, and $2.69.

There are no outliers in the dataset

So, the dataset can be summarized by the mean

The mean is

Mean = Sum/Count

So, we have

Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5

Evaluate

Mean = 2.81

The article quoted $2.69 as the typical price

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

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Answer:

  30 gallons

Step-by-step explanation:

Let c represent the capacity of the container in gallons.

  2/5c +8 = 2/3c . . . . adding 8 gallons to 2/5 full gives 2/3 full

  8 = (2/3-2/5)c = 4/15c . . . . subtract 2/5c

  8(15/4) = c = 30 . . . . . . . . . multiply by 15/4

The container can hold 30 gallons.

Answer: 7

Step-by-step explanation:

15 + 5x = 50

    5x = 35

     x = 7

Answer:

10 years old is the answer

The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

In the given question,

We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.

Since we have to find the image after a dilation.

So we learn about it now,

Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.

So the given point is (-9,12).

Scale factor is 1/3.

So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as

=(-9×1/3,12×1/3)

Simplifying

=(-3,4)

Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

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Answer:

8x^{12}yx^{3}  

Step-by-step explanation:

Simplify the expression.

Hopefully this helps you

- Matthew

Answer:  5/8 inch represents 1 mile

Step-by-step explanation:

to get 1, multiply 4/5 by its reciprocal, 5/4

Then multiply 1/2 by 5/4

1/2 × 5/4 = 5/8

Answer: The correct answer is 5/8

Step-by-step explanation: Answer verified as correct on test

A unit vector has a module of 1.

We can calculate the coordinates of a unit vector in the direction of an specific vector by dividing the coordinates of that vector by the module.

Then, first we will calculate the module of the vector:

We then can write the unit vector as:

Answer: (-2√5/5, -√5/5)

Answer:

a=13 - 4b/5

b=65/4-5a/4

Step-by-step explanation:

Step-by-step explanation:

X+x+1+x+2=225

3x+3=225

3x+3-3=225-3

3x=222

3x÷3=222÷3

X=74

Which means the first number is 74, the second number is 74+1 and the third number is 74+2. Therfore the consecutive integers that add up to 225 are 74, 75,and 76

Check answer

74+75+76=225

225=225

The smallest positive integer which when divided by 5 leaves a remainder of 3 is 8

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

Divisor = 5

Remainder = 3

Using the above as a guide, we have the following:

Smallest integer = Divisor + Remainder

So, we have

Smallest integer = 5 + 3

Evaluate

Smallest integer = 8

Hence, the smallest is 8

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Hello!

This is a question about an arithmetic sequence. We can solve it using the formula:

Let's replace them with the values mentioned in the exercise:

86 seats in row 20.

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

V=6280cm²

Step-by-step explanation:

V=pi r²h

V=3.14 x 10²cm×20cm

V=6280cm²

In statistics, the risk of making an error is referred to as a significance level. A significance level represents the probability of making a Type I error, which occurs when a null hypothesis is rejected even though it is true.

The most common significance level used in statistical analyses is 0.05 or 5%. This means that there is a 5% chance of rejecting a true null hypothesis.

In general, the choice of significance level depends on the specific application and context of the statistical analysis.

The 5% significance level is commonly used in scientific research, particularly in the fields of medicine and psychology.

The choice of this level is based on a balance between the risk of making a Type I error and the risk of making a Type II error, which occurs when a null hypothesis is not rejected even though it is false.

A Type II error is often more serious than a Type I error since it may lead to incorrect conclusions about the relationship between variables or the effectiveness of a treatment or intervention.

A 5% significance level provides a reasonable balance between these two types of errors. However, in some situations, a higher or lower significance level may be more appropriate.

For example, in a clinical trial where the consequences of a Type II error are severe, a lower significance level may be used to reduce the risk of this type of error.

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Answer:

Move it 2 places to the right.

Step-by-step explanation:

The magnitude of the exponent of 10 tell you how many places to move

The sign of the exponent of 10 tells you the direction.

Positive, decimal moves right.

Negative, decimal moves left.

Answer:

1/14

Step-by-step explanation:

The ratio is 5:70. The fraction form of that is 5/70. To get the lowest terms, I divided both numbers by 5. So it is 1/14

Answer:

[1;1;1]

Step-by-step explanation:

try this option; all the details are in the attachment.

Answer: 22

Step-by-step explanation:

Two dozen equals 24, divide it in half leaves 12 vanilla sprinkle doughnuts

the remaining 12 minus the 2 strawberry cream equals 10 chocolate sprinkles

add the 10 chocolate plus 12 vanilla to get 22

Answer:

x = 35 degrees

x + 5 = 40 degrees

3x = 15 degrees

Explanation:

Given that the angle measures of a triangle is 180 degrees, we have

3x + (x + 5) + x = 180

3x + x + 5 + x = 180

5x + 5 = 180

Subtract 5 from both sides

5x + 5 - 5 = 180 - 5

5x = 175

Divide both sides by 5

5x/5 = 175/5

x = 35 degrees

x + 5 = 35 + 5 = 40 degrees

3x = 3(5) = 15 degrees