Mathematics College

## Answers

**Answer 1**

The **opposite** of 0 is 0, the opposite of 7 is -7 and the **opposite** of 6 is -6.

If we consider a number x, then the **opposite** of the number x will be equal to -x. In a **number line** the opposite of a number lying on the **positive** side always lies on the **negative **side of number line. Also, the **opposite** of a number -x is the x that is the **number itself**. It is given in the question that we need to find opposite of 0, 7 and 6.

Let x = 0, opposite of x is -x.

=> -x = -0

=> -x = 0

Now, let x = 7, opposite of x is -x

=> -x = -7

Now, let x = 6, opposite of x is -x

=>-x = -6

Thus, the **opposite** of the **numbers** 0, 7 and 6 are 0, -7 and -6 respectively.

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## Related Questions

Peter has a tire with a diameter of 26 inches. How many inches is the radius of his tire?

### Answers

**Answer**

**The radius of Peter's tire = 13 inches**

**Explanation**

The radius of a circular figure is related to its diameter through

**Radius = ½ (Diameter)**

**Diameter = 26 inches**

**Radius = ½ (Diameter) = ½ (26) = 13 inches**

**Hope this Helps!!!**

Find the intercepts and graph each line.

a.) x – 4y =− 4

b.) 2x + 5y =-10

### Answers

**Answer:**

(1,5) I think that's what it is

graph a line with a slope of 3/4 that contains the point (2 -3)

### Answers

**Step-by-step explanation: I hope this helps.**

**Answer:**

You are testing the null hypothesis that the population proportion equals 45, using data you collected from a sample of 100 adults. You sample proportion equals .30. What does Z equal? (Round to two decimal places)

### Answers

When one is testing the null **hypothesis** that the population proportion equals 45, the. z score is -3.02.

How to illustrate the information?

The null and alternative **hypothesis** is illustrated as the population proportion equals 45,

P0 = 0.45

1 - P0 = 1 - 0.45 = 0.55

Test statistic = z

This will be illustrated as:

= 0.30 - 0.45/ [✓(0.45 * 0.55) / 100]

Test **statistic** = z = -3.02

Therefore, the **z score** is -3.02.

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what is the domain of y-x^2-1

### Answers

The** domain** of the** function** y = x² - 1 in interval notation is (-∞, + ∞).

What is defined as the domain of the function?A function is simply object that accepts input, appears to apply a rule to it, and returns the result. A** function **can be thought of as a machine that receives in a number, performs some operation(s), and then outputs the result. The essential thing regarding functions is that they consistently apply the rule. As a result, if the same value is passed through the same function, the output will remain the same. The** domain** of a function is the collection of all its inputs. Its codomain is the collection of all possible outputs. The range refers to the outputs which are actually used.

The given is y = x² - 1.

The domain of the function is;

Except when the expression is undefined, the domain of the representation is all** real numbers. **Given that there is no** **real number in this case, the expression is **undefined.**

Thus, the domain of the function in** interval notation** is (-∞, + ∞).

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Please help me with Calculus homework, Question 2 only***Answer to question 1: -3.938

### Answers

As given by the question

There are given that the function:

[tex]f(x)=x^3-6x[/tex]

Now,

According to the answer to question #1 and the graph of the function:

It is the area under the curve from x = 0 and x = 3;

So,

Some of it is below the x-axis means negative area and some of it is above the x-axis which means positive area.

Then,

Yes, they will cancel out and the integral gives the exact net result.

**Explained!**

A restaurant has two types of tables, rectangular

ones that can each seat 4 people and circular

tables that can each seat 8 people. If 144 people

are enough to fill all 30 tables at the restaurant,

how many rectangular tables does the restaurant

have?

A) 12

B) 16

C) 20

D) 24

### Answers

**Answer:**

D) 24

**Step-by-step explanation:**

c + r = 30 Eq. 1

4r + 8c = 144 Eq. 2

r = rectangular tables

c = circular tables

From Eq. 1:

c = 30 - r Eq. 3

Replacing Eq. 3 in Eq. 2:

4r + 8(30-r) = 144

4r + (8*30 + 8*-r) = 144

4r + 240 - 8r = 144

-4r = 144 - 240

-4r = -96

r = -96/-4

r = 24

from Eq. 3

c = 30 - r

c = 30 - 24

c = 6

Check:

from Eq. 2

4r + 8c = 144

4*24 + 8*6 = 144

96 + 48 = 144

The truss in the illustration is in the form of an isosceles triangle. Each of the two equal sides is 9 feet less than the third side. A truss has its outer border in the shape of an isosceles triangle. If the perimeter is 21 feet, find the length (in ft) of each side.

### Answers

The side lengths of the truss which is an **isosceles triangle **are 13 feet , 4 feet and 4 feet.

In geometry, an **isosceles triangle **is a **triangle **with at least two sides of identical length. It can be defined as having exactly two equal-length sides or as having at least two equal-length sides, with the **equilateral triangle **being an exception to the second definition.

The base of the **triangle **is its third side, while its two equal sides are referred to as its legs. Simple formulas can be used to calculate the **triangle's **height, area, and **perimeter **from the lengths of the **triangle's **legs and base.

Let us consider the length of the longest side of the** isosceles triangle** be x.

Therefore length of smaller sides = x - 9

The **perimeter **of the **triangle **is given as 21 meters.

Therefore :

x + (x - 9) + (x - 9) = 21

or, 3x -18 = 21

or, 3x = 39

or , x = 13 feet

Therefore length of two smaller sides of the **triangle **= x - 9 = 4 feet

Therefore the length of the three sides of the **triangle **are

4 feet , 4 feet and 13 feet.

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A frog jumped 0.7 meters. Then jumped another 0.98 meters. How many meters did he jump

### Answers

you add them together. so 0.7 + 0.98 = 1.68 so 1.68 should be your answer:)

Answer:

1.68 meters

Step-by-step explanation:

Starting Point- 0.7 meters

Adding Point- 0.98 meters

0.7+0.98= 1.68 meters

These box plots show the basketball scores for two teams.Bulldogs55708090105Wolverines355580 8596ㅏ30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110Basketball scoresCompare the shapes of the box plots.

### Answers

**Solution**

The bullfdng dataset has its median close to the center of the boxplot.

- This implies that the dataset is symmetric.

- The wolverine dataset has its median moved to the right at 80, implying that it is NOT symmetric.

- However, because there is a skew to the left of datapoints, we say that the dataset is negatively skewed

Final Answer

OPTION A

Select the three equations that pass through the points (–4, –16) and (5, 2):

y + 4 = 2(x – 16)

y – 2 = 2(x – 5)

y = 2x – 8

y + 16 = 2(x + 4)

### Answers

The **equation** of **line** passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)

What is an **equation**?

An equation is an **expression** that shows the **relationsh**ip between two or more numbers and variables.

Equations are classified based on** degre**e (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be** dependent or independent**. Dependent variables depend on other variable while an independent variable do not depend.

The standard form for linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The **equation** of **line** passing through (-4, -16) and (5, 2) is:

y - (-16) = [(2-(-16))/(5-(-4))](x - (-4))

y + 16 = 2(x + 4)

y = 2x - 8

y - 2 = 2(x - 5)

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4a + 8b/7 - a^2

if a = 3 and b = -1

### Answers

**Simplify the expression.**

**___________________**

**Solutions:****Exact Form - **[tex]\frac{13}{7}[/tex]**Decimal Form - 1.8.....****Mixed Number Form - **[tex]1\frac{6}{7}[/tex]

...^Here are all three solutions depending on what you are looking for. Hope this helps! If so, please lmk! Thanks and good luck!

A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

### Answers

**Answer:**

Let the required number be ab.

Sum of digits = a + b ........ ( 1 )

10 a + b = 4 ( a + b )

10 a + b + 18 = 10 b + a

=> 9 a + 18 = 9 b

=> a + 2 = b

10 a + a + 2 = 4 ( a + a + 2 )

=> 11 a + 2 = 8 a + 8

=> 3 a = 6

=> a = 3

=> a + 2 = 5

=>ab = 35......... [ A ]

So the number becomes 35.

ANSWER :

The original number is 35.

hope it helps you

**Given :**

• (**two-digit** number) = **3 + 4**(**sum** of its digits)

• (two-digit number) + 18 = Digit gets reverse

**To Find :**

• The number.

**Concep****t**** ****:**

-We will first assume the number on **one's** place be [tex]x[/tex] and **ten's** place be [tex]y[/tex] [why? because the **given conditions** are about the **digits** of number]

-Two-digit number then formed will be **10y + x** and its **reverse** will be **10x + y**[why? well let's take an example like a number 42. This number can be written in **expanded** form as 10×4+2×1 here 4 is number at ten's place (y) and 2 at one's place(x) It's reverse will be 24 it can be written in expanded form as 10×2+4×1 here 2 is number at ten's place (y) and 4 at one's place(x)]

-Then we will use given conditions to form the **equation** and will **solve the equations** to get the answer.

So now let's get started with our solution! :D

**Solut****ion**** ****:**

Let the one's and ten's digit of the number be [tex]x[/tex] and [tex]y[/tex] respectively.

**According to first condition,**

=> (10y + x) = 3 + 4(x + y)

=> 10y + x = 3 + 4x + 4y

=> 10y - 4y = 3 + 4x - x

=> 6y = 3 + 3x

[tex] \implies \sf \frac{6y}{3} = \frac{3}{3} + \frac{3x}{3} [/tex]

=> 2y - 1 = x ___**(equation 1)**

**According to second condition,**

=> (10y + x) + 18 = 10x + y

=> 10y - y + 18 = 10x - x

=> 9y + 18 = 9x

[tex] \implies \sf \frac{9y}{9} + \frac{18}{9} = \frac{9x}{9} [/tex]

=> y + 2 = x ___**(equation 2)**

**Solvin****g**** ****equation**** ****1**** ****and**** ****2**

y + 2 = x (equation 2)

y + 2 = 2y - 1 [From equation 1]

3 = 2y - y

3 = y (ten's place)

Now put value of **y = 3 in** equation 2

y + 2 = x (equation 2)

3 + 2 = x

5 = x (one's place)

**So, the number formed is 35****.**

I Need the answer in 2 minutes

### Answers

**Answer: **[tex]\frac{1}{1024}[/tex]

**Step-by-step explanation:**

[tex]4^{-3} = (2^{2} )^{-3} = 2^{-6}[/tex]

[tex]\frac{2^{-6} }{2^{4} } = 2^{-6-4} = 2^{-10} = \frac{1}{2^{10} } = \frac{1}{1024}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{4^{-3}}{2^4}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{2\times2\times2\times2}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{4\times4}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{16}}[/tex]

[tex]\mathsf{= \dfrac{1}{1,024}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{1,024}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

a bag contains 3 red marbles, 3 white marbles,, and 5 blue marbles. only white marbles will be added to the bag. how many white marbles should be added to the bag to make the probability of pulling a white marble 50%?

### Answers

**Step-by-step explanation:**

a probability is always

desired cases / totally possible cases

a 50% probability means 1/2 or 0.5.

that means

desired cases = 1/2 × totally possible cases

at start we have

3 red

3 white

5 blue

that makes 5 + 3 + 3 = 11 totally possible cases and 3 desired cases.

so, the starting probability to pull a white marble is

3/11.

now, we need to say

(3 + x) = 1/2 × (11 + x) (= (3+x)/(11+x) = 1/2)

to make is simpler we multiply both sides by 2 (so we get rid of the 1/2 fraction).

6 + 2x = 11 + x

6 + x = 11

x = 5

we need to add 5 white marble to give us a 50% probability to pull a white marble.

we have then

3 red

3 + 5 = 8 white

5 blue

that makes 5+8+3 = 16 totally possible cases and 8 desired cases.

so, the probability is

8/16 = 1/2

=> our calculation was correct

The number of **white marbles **should be added to the bag to make the **probability **of pulling a white marble 50% will be 5.

What is probability?

Its fundamental concept is that someone will nearly **surely** **occur**. The proportion of positive events in comparison to the **total **of occurrences.

Then the **probability **is given as,

P = (Favorable event) / (Total event)

A **bag **contains 3 red marbles, 3 white marbles, and 5 **blue marbles**. only white marbles will be **added **to the bag.

Let 'x' be the number of white marble **added**. Then the **equation **is given as,

0.50 = (x + 3) / (x + 3 + 3 + 5)

**Simplify **the equation, then we have

0.50 = (x + 3) / (x + 3 + 3 + 5)

0.50 = (x + 3) / (x + 11)

0.50x + 5.5 = x + 3

0.50x = 2.5

x = 5

The number of **white marbles **should be added to the bag to make the **probability **of pulling a white marble 50% will be 5.

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Suppose that 20% of the residents of Illinois have the flu and that 75% of the patients going to a doctor for testing have the flu. If a practioneer in Illinois uses a test that is 60% accurate...

a. What is the probability that a patient receives a false-negative result?

b. What is the probability that a patient receives a true-negative result?

c. What is the probability of a false-negative result given that the result is negative?

### Answers

The **probabilities **in this problem are given as follows:

**A. **False - negative: 0.08 = 8%.

**B. **True - negative: 0.48 = 48%.

**C.** False-negative given that the result is negative: 0.1429 = 14.29%.

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a **previous **event. The **formula **is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which the **parameters **of the formula are given as follows:

P(B|A) is the probability of event B happening, given that event A happened.[tex]P(A \cap B)[/tex] is the probability of both events A and B happening.P(A) is the probability of event A happening.

The probability of a **false negative** is composed as follows:

20% have the flu.Of those, 40% have negative results.

Hence:

P(FN) = 0.2 x 0.4 = 0.08 = 8%.

The probability of a **true negative** is composed as follows:

80% do not have the flu.Of those, 60% have negative results.

Hence:

P(TN) = 0.8 x 0.6 = 0.48 = 48%.

The probability of **negative **results is:

P(N) = P(FN) + P(TN) = 0.08 + 0.48 = 0.56.

Hence the **conditional probability** is given by:

P(FN|N) = 0.08/0.56 = 0.1429 = 14.29%.

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Point M is the midpoint of AB . AM=2x+9, and AB=8x−50.

What is the length of AM?

### Answers

Using the midpoint theorem, the **length **of AM is 43

Calculating Length of a line

From the question, we are to determine the **length **of AM

From the given information,

Point M is the midpoint of AB

Thus,

From the **midpoint theorem**

We can write that

AM + MB = AB

AM = MB

AM + AM = AB

2AM = AB

Also, from the given information,

AM = 2x + 9

and

AB = 8x - 50

Therefore,

From 2AM = AB

2(2x + 9) = 8x - 50

Solve for x

2(2x + 9) = 8x - 50

4x + 18 = 8x - 50

18 + 50 = 8x - 4x

68 = 4x

x = 68/4

x = 17

But,

AM = 2x + 9

Substituting the value of x

Thus,

AM = 2(17) + 9

AM = 34 + 9

AM = 43

This means the **length **of AM is 43

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(5^3)^9 divided by 5^12

### Answers

Exact Form:

11920928955078128/390625

Decimal Form:

30517578125

30517578125

I looked it up

solve for x. round to the nearrest hundredth if necessary

### Answers

**Answer:**

(b) 5.69

**Step-by-step explanation:**

You want the side opposite a **24° angle** in a **right triangle** with a **hypotenuse of 14** units.

Sine

The sine relation is ...

Sin = Opposite/Hypotenuse

sin(24°) = x/14

Solving for x, we get ...

** x =** 14·sin(24°) **≈ 5.69**

what is −2 1 4 + (−1 3 4 )

### Answers

Using **subtraction **we get the value as -3 4 8 .

**Subtraction **is a mathematical operation that mimics the removal of elements from a collection.

**Subtraction **involves several important patterns. Because it is anticommutative, changing the **sequence **also changes the **sign **of the solution. Additionally, it is not **associative**, so the technique employed affects when removing more than two numbers. Since 0 is the **additive identity**, removing it from a number has no impact. **Subtraction **follows the same ideas as related operations like **addition **and **multiplication**. Each of these principles may be proved, starting with **integer subtraction **and progressing to real numbers and beyond.The study of these patterns of **subtraction **in common binary operations is done in abstract algebra.

The given expression is −2 1 4 + (−1 3 4 )

Simplifying we get : -2 1 4 - 3 1 4

now using **subtraction **we get : - 3 4 8

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Find the derivative of the function. F(x) = (5x² + 2x³)^4

### Answers

**Answer:**

Derivative of y=(x⁴-2x³+5x²-4)³

**Step-by-step explanation:**

A journalist believes that, in reality, these components have a shorter lifespan than what the company is reporting.

He tests a random group of 35 of these components and finds a mean lifespan of 4.05 years.

a. What is the mean of the sampling distribution of sample means when 35 random components are tested?

### Answers

The **mean** of the sampling distribution of sample means when 35 **random** components are tested will be 4.05 years.

How to illustrate the information?

From the information, it should be noted that the journalist believes that, in reality, these components have a shorter **lifespan** than what the company is reporting.

He the tests a **random** group of 35 of these components and finds a mean lifespan of 4.05 years.

Therefore from the information, we acne see that the. **mean** lifespan has already been given.

Therefore, the **mean** lifespan is 4.05 years.

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The perimeter of the rectangle below is 104 units. Find the length of side RS

Write your answer without variables

### Answers

**Answer:**

24

**Step-by-step explanation:**

Opposite sides on a rectangle are equal

So 2(3x+3)+2(4x)=104

Now expand, so 6x+6+8x=104

Simplify like terms, 14x+6=104

14x+6-6=104-6

14x=98

14x/14=98/14

x=7

Now just substitute the 7 in for the 3x+3 as thats what we are looking for.

3×7+3=24

write an algebraic expression that represent the purchase. Baseball= $7, Sweat socks = $6, Soccer ball = $30. Mr. Mishra bought x number of soccer balls and 5 baseballs. Write an expression for the cost of Mr. Mishra's purchase.

### Answers

**Answer:**

[tex]\text{Total cost=30x+35}[/tex]

**Step by step explanation:**

The total cost of a purchase is represented by:

[tex]\text{ cost of the unit}\cdot\text{ number purchased=total cost}[/tex]

Then, since Mr. Mishra bought:

x number of soccer balls and each soccer ball is $30.

5 baseballs and each baseball is $7

Then, the algebraic expression of the purchase is given by:

[tex]\begin{gathered} \text{Total cost=30x+7}\cdot5 \\ \text{Total cost=30x+35} \end{gathered}[/tex]

If [tex]h(x)=\frac{sinx}{sin2x}[/tex], then [tex]lim_{x-\pi }h(x)[/tex] is equivalent to which of the following?

a. [tex]-\frac{1}{2}[/tex]

b. 0

c. 1

d. Does not exist

### Answers

**Answer: -1/2**

**Step-by-step explanation:**

[tex]\lim_{x \to \pi} \frac{\sin x}{2\sin x \cos x}\\\\=\lim_{x \to \pi} \frac{1}{2\cos x}\\\\=\frac{1}{2\cos \pi}\\\\=-\frac{1}{2}[/tex]

**Answer:**

[tex]-\frac{1}{2}[/tex]

**Step-by-step explanation:**

If we try direct substitution we get: [tex]lim_{x\to\pi}h(x)=\frac{sin(\pi)}{sin(2\pi)}[/tex]

The radian [tex]2\pi[/tex] is a full rotation from 0 radians, in other words it's equivalent to 0 radians.

Using the unit circle as a reference you'll remember when the angle is 0 radians, the y-value is zero, so: [tex]sin(2\pi)=0[/tex]

When the angle is: [tex]\pi[/tex] it's at a half rotation where the y-value is still zero on the unit circle.

So you get the **indeterminate form of**: [tex]\frac{0}{0}[/tex]

We can use **L'Hôpital's rule** which states: [tex]lim_{x\to c}\frac{f(x)}{g(x)}=lim_{x\to c}\frac{f'(x)}{g'(x)}[/tex] if the original limit is in **indeterminate form** such as the one above.

Taking the derivative of sin(x) we simply use the property that: [tex]\frac{d}{dx}[sin(x)]=cos(x)[/tex]

For the sin(2x) we can use the chain rule which essentially states: [tex]h(x)=f(g(x))\\h(x)=f'(g(x))*g'(x)[/tex]

It deals with composite equations, and in this case we can represent the composite function as:

[tex]f(x)=sin(g(x))\\g(x)=2x[/tex]

Using the chain rule we get: [tex]cos(2x)*2[/tex]

So now we have the limit: [tex]lim_{x\to \pi}\frac{cos(x)}{2cos(2x)}[/tex]

at pi radians the unit circle is at a half rotation where the x/y coordinates are: [tex](-1, 0)[/tex]

so cos(pi) = -1

at 2 * pi radians were basically back at 0 radians where the x/y coordinates are: [tex](1, 0)[/tex]

so cos(2 * pi) = 1

Now plugging in these values we get the fraction: [tex]\frac{-1}{2*1}[/tex] which just simplifies to: [tex]-\frac{1}{2}[/tex] which turns out to be the limit!

HELP ASAP 100 POINTS

A group of seniors decide to spend their spring break away from home, attending at least one major event. The following table summarizes their preferences.

Attend a concert Attend a festival

Stay in state 214 186

Travel out of state 391 59

What percent want to attend a festival, given that they want to travel out of state?

6.94%

13.11%

24.08%

31.72%

### Answers

**Answer:**

I think 31.72 because it 39156+214186 is 253342 it would be to low

A percentage isa number or ratio that represents a fraction of 100.

The **percentage** who want to attend a **festival**, given that they want to travel **out **of** **state** **is 6.94%.

What is a percentage?

A percentage isa number or ratio that represents a fraction of 100.

We have,

Attend a concert Attend a festival

Stay in state 214 186

Travel out of state 391 59

The number of **groups** who wants to attend a **concert** while **staying** in a state:

= 214

The number of **groups** who wants to attend a **concert** while traveling **out** of the state:

= 391

The number of **groups** who wants to attend a **festival** while **staying** in a state:

= 186

The number of **groups** who wants to attend a **festival** while traveling **out** of the state:

= 59

The **percentage** who want to attend a **festival**, given that they want to travel **out** of state:

= The number of groups who wants to attend a festival while staying out of the state/ Total number of groups from all four conditions

= 59 / ( 214 + 391 + 186 + 59 ) x 100

= 59 / 850 x 100

= 6.94%

Thus,

The **percentage** who want to attend a **festival**, given that they want to travel **out **of** **state** **is 6.94%.

Option A is the correct answer.

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7.

A coach travels from the station to the beach, a distance of 576km away in 6hrs.

The coach is only allowed to travel at a maximum speed of 90km/h. Did the coach

break the speed limit?

### Answers

**Answer:**

Yes.

**Step-by-step explanation:**

distance = rate x time

Let r = rate

567 = r6 Divide both sides by 6

94.5 = r If he was driving at a constant rate the whole time then he was driving at 94.5 miles per hour which is faster than 90

Rewrite the expression 26 + 8 as the product of the GCF (greatest common factor) and a sum. Then, simplify the expression. Show all of your steps. pls help due today

### Answers

The expression 26+8 as the product of the **GCF** and a sum is:

2(13+4).

Given we have the** expression** as 26+8

We need to find the greatest common factor of the numbers 26 and 8.

26 = 2 × 13

8 = 2 × 2 × 2

Multiply all the** prime factors** that both numbers share in order to determine the GCF:

Therefore, GCF = 2

Now we can write the expression as:

26 + 8

=2(13 + 4)

=2×17

=34

Hence we get the** required **expression as 2(13 + 4).

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A person is standing 18 feet away from a street light that is 20.2 feet tall. How long is his shadow if he is 5.2 feet tall? Enter the exact value of the answer.

### Answers

The **shadow** of the person is **6.24 feet long**.

The **height** of the street light is 20.2 feet.The height of the person is 5.2 feet.The person is standing at a distance of 18 feet from the street light.Let the length of the shadow be "x".The above configuration of the street light, the person, and the shadow creates a situation of **similar triangles**.Using the properties of the similar triangles, we know that the **ratio** of the **corresponding sides** of the similar triangles is the **same**.The height of the street light divided by the sum of the length of the shadow of the person plus the distance of the person from the street light is equal to the height of the person divided by the length of the shadow.20.2/(x+18) = 5.2/x20.2x = 5.2x + 18*5.215x = 18*5.2x = (18*5.2)/15x = 6.24Thus, the length of the shadow is 6.24 feet.

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How can I find the slope of the line and what can the slope mean?

### Answers

If we take two ordered pairs from the table, we can find the slope with the following equation:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

in this case, we can take the points (1,1/2) and (2,1) to get the following using the formula above:

[tex]\begin{gathered} m=\frac{1-\frac{1}{2}}{2-1}=\frac{\frac{1}{2}}{1}=\frac{1}{2} \\ \Rightarrow m=\frac{1}{2} \end{gathered}[/tex]

**we have that the slope is m = 1/2, and this means that for each 2 gallons of distilled water, Rodnika will add 1 gallon of sea salt**