Three runners run along a 1.5 mile trail one Saturday morning. The graph shows the runner’s locations starting at 9:00 a.m.
Who is at the trail start at 9:00 a.m.?

The solution using laws of exponents is: [tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]

How to use laws of exponents?

Some of the laws of exponents are:

- When multiplying by like bases, keep the same bases and add exponents.

- When raising a base to a power of another, keep the same base and multiply by the exponent.

- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.  

The expression we want to solve is given as:

[tex]\frac{(x^{-\frac{3}{2} } y^{\frac{5}{3} } z^{-1})^{-1} }{zx^{\frac{3}{2} } y^{-\frac{1}{4} } * y^{-2} z^{\frac{1}{2} } }[/tex]

Using laws of exponents, we have:

[tex]x^{0} * y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]

=[tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]

Answer:

The point of intersection gives the solution set(s) of the associated system.

Step-by-step explanation:

If we have a pair of simultaneous equations in 2 variables in x and y, then the point of intersection is the ordered pair (x,y).

This could be a unique intersection, only one point or infinitely many intersection.

This gives us the solution of the simultaneous equations.

Therefore the significance of the point of intersection of a pair of simultaneous equations is that, it gives us the solution set(s) of the associated system.

Answer:

she did not make a mistake

Step-by-step explanation:

Answer:

veronica didn't make a mistake.

Step-by-step explanation:

Answer:

a=40% · 25

a=0.40 · 25

0.40 · 25= 10

a=10

Step-by-step explanation:

Answer:

Would be 25/10

Step-by-step explanation:

Answer:

To find if something is proportional you want to reduce them to there simplest form, so we want to reduce each fraction down

40/48= 5/6

56/42= 8/7

Therefore; these two fractions are not proportional because they reduce to different numbers

Hope this helps ;)

Answer:

no

Step-by-step explanation:

Cross multiply:

40 * 42 = 48 * 56

Simplifying

40 * 42 = 48 * 56

Multiply 40 * 42

1680 = 48 * 56

Multiply 48 * 56

1680 = 2688

Solving

1680 = 2688

Final answer:

To find the number of cookies Hans baked on the second day, we solve the equation x + 2x + x/2 = 224, where x is the number of cookies baked on the first day. Solving this, we find x=64, meaning he baked 128 cookies on the second day.

Explanation:

The question involves solving a problem about Hans, who spent three days baking a total of 224 cookies. On the second day, he baked twice as many cookies as on the first day, and on the third day, he baked half as many as on the first day. To find how many cookies he baked on the second day, let's denote the number of cookies baked on the first day as x.

On the second day, he baked 2x cookies.

On the third day, he baked x/2 cookies.

Adding these together: x + 2x + x/2 = 224.

Combining like terms, we get 3.5x = 224.

Dividing both sides by 3.5 gives x = 64.

Therefore, he baked 2x = 2*64 = 128 cookies on the second day.

Answer:

$2500

Step-by-step explanation:

25% is one fourth of the total monthly income.

If $625 is = x/4 then multiply both sides of the equation with 4

4 × 625 = x/4 × 4 ➡ 2500 = x

Answer:

He have 17 CDs on Monday.

Step-by-step explanation:

Given:

On Tuesday James bought seven CDs. On Wednesday half of all the CDs that he had were destroyed. On Thursday he had 12 left.

Now, to find the CDs he have on Monday.

Let the CDs he have on Monday be [tex]x.[/tex]

So, on Tuesday as James bought 7 CDs:

[tex]x+7.[/tex]

Now, on Wednesday half of all the CDs that he had were destroyed:

[tex]\frac{x+7}{2}[/tex]

As, given on Thursday he had left CDs = 12.

According to question:

[tex]\frac{x+7}{2}[/tex] [tex]=12[/tex]

Multiplying both sides by 2 we get:

[tex]x+7=24[/tex]

Subtracting both sides by 7 we get:

[tex]x=17.[/tex]

Therefore, he have 17 CDs on Monday.

To determine what percent 225 is of 150, the calculation (225 / 150) × 100% is used, resulting in 225 being 150% of 150.

To find what percent of 150 is 225, we can use the formula for calculating percents:

Percentage = (Part / Whole) × 100%

Where 'Part' is 225 and 'Whole' is 150. Now, let's calculate:

Percentage = (225 / 150) × 100%

Percentage = 1.5 × 100%

Percentage = 150%. So, 225 is 150% of 150.

The larger number is 17

Solution:

Let "x" be the larger number

Let "y" be the smaller number

The difference between of two numbers is 9

Therefore,

larger number - smaller number = 9

x - y = 9 -------- eqn 1

The large number is one more than twice the smaller number

Larger number = 1 + 2(smaller number)

x = 1 + 2y ------ eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

1 + 2y - y = 9

1 + y = 9

y = 9 - 1

y = 8

Substitute y = 8 in eqn 1

x - 8 = 9

x = 8 + 9

x = 17

Thus the larger number is 17

Answer:

[tex]4a(x-9)-7(x-9)=(x-9)[4a-7][/tex]

Step-by-step explanation:

we have the expression

[tex]4a(x-9)-7(x-9)[/tex]

Factor the term (x-9)

so

[tex](x-9)[4a-7][/tex]

therefore

[tex]4a(x-9)-7(x-9)=(x-9)[4a-7][/tex]

Answer:

10

Step-by-step explanation

6/3.6=1.6 or 1 2/3

1.6*6=10

Answer:Start by enlarging the picture 2 inches by 3 inches up to 150%. This leads to a 3 inch by 4.5 inch picture. Eduardo wants to enlarge the picture to 4 inches by 6 inches. 4/3 = 1.33 6/4.5= 1.33 Therefore, the two whole number percents are 150% and 133%.

Answer: f(x) = |x|

Step-by-step explanation:

A function is even if for every real N, f(N) = f(-N)

As you know, the module of a function always returns the positive value of a number, so I-3I = 3 = I3I (and that for every number)

So the function f(x) = IxI is an even function.

Functions with odd powers can not be even functions, so the second and tird options are discarded.

the fourth functions seems to be:

f(x) =∛x = (x)1/3 which is not even, because if x = 1, f(1) = 1, and if x=-1, f(-1) = -1

In the given functions, an even function is [tex]f(x)=|x|[/tex]. Therefore, the correct answer is option A.

A function's even, odd, or neither properties can be expressed algebraically or graphically in a variety of ways. If a function's graph remains unchanged when reflected in the y-axis, it is said to be an even function. Consider a function f(x) that is considered an even function if f(-x) equals f(x).

1) [tex]f(x)=|x|[/tex]

Let [tex]x = -3[/tex], we get

[tex]f(-3)=|-3|[/tex]

[tex]f(-3)=3[/tex]

[tex]f(-x)= f(x)[/tex]

2) [tex]f(x)=x^3-1[/tex]

Let [tex]x = -1[/tex], we get

[tex]f(-1)=(-1)^3-1[/tex]

[tex]f(-1)=-1-1[/tex]

[tex]f(-1)=-2[/tex]

[tex]f(-x)\neq f(x)[/tex]

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

Let [tex]x = -1[/tex], we get

[tex]f(-1)=-3(-1)[/tex]

[tex]f(-1)=3[/tex]

[tex]f(-x)\neq f(x)[/tex]

4) [tex]f(x)=\sqrt[3]{x}[/tex]

Let [tex]x = -1[/tex], we get

[tex]f(-1)=\sqrt[3]{(-1)}[/tex]

[tex]f(-x)\neq f(x)[/tex]

Therefore, the correct answer is option A.

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Answer:

To find the probability that both friends randomly select a romance book one after the other, we can use the concept of conditional probability.

Let's denote the events:

- Event A: First friend selects a romance book.

- Event B: Second friend selects a romance book.

Given that there are 4 romance books left and a total of 7 books left (3 mystery + 4 romance), the probability of Event A happening for the first friend is:

\[ P(A) = \frac{4}{7} \]

After the first friend selects a romance book, there are now 3 romance books left out of a total of 6 books remaining (since one book has been chosen). So, the probability of Event B happening for the second friend, given that the first friend selected a romance book, is:

\[ P(B|A) = \frac{3}{6} = \frac{1}{2} \]

Now, to find the probability of both events happening, we multiply their probabilities:

\[ P(A \text{ and } B) = P(A) \times P(B|A) \]

\[ P(A \text{ and } B) = \frac{4}{7} \times \frac{1}{2} \]

\[ P(A \text{ and } B) = \frac{4}{14} \]

\[ P(A \text{ and } B) = \frac{2}{7} \]

So, the probability that both friends randomly select a romance book one after the other is \( \frac{2}{7} \).

Answer:

[tex]0.0749[/tex]

Step-by-step explanation:

[tex]1.498/30[/tex]

To divide the form directly in fraction divide the numerator and denominator by a common number to simplify the values.

Simplifying the value  

    Removing the decimal in the numerator makes 1000 in denominator

                                               [tex]\frac{1498}{30}*\frac{1}{1000}[/tex]

dividing by a common value i.e 2                            

                                         [tex]\frac{749}{10}*\frac{1}{1000}[/tex]

Now, removing the decimals from denominator puts the decimal in the numerator gives   [tex]0.0749[/tex]

Answer:

1.498 divided by 30 equals 749/15000 OR 0.04993

Step-by-step explanation:

Simply divide as you would a whole number, but place the decimal point above in your answer. So, your first step would be to calculate how many times 30 goes into 149. Your answer will go two places AFTER your decimal point. Then you continue to solve, as you would a whole number!

Will has 24 quarters from 2005, which means the total value of these quarters equals to $6.

Will has 40 state quarters in total. If 3/5 of them are from 2005, this simply means that you need to find 3/5 of 40. So, we multiply 40 by 3/5:
40 * 3/5 = 24.

So, Will has 24 quarters from the year 2005.

Next, to find the value of these quarters, remember that each quarter is worth 25 cents (or $0.25 in dollar form). Therefore, we multiply the number of quarters (24) by the value of each quarter (.25):
24 * 0.25 = $6.

So, the total value of the quarters from 2005 is $6.

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Answer:

you just have to add or divide

Answer:

y = x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 1 and c = - 7, thus

y = x - 7 ← equation of line

Answer:

The system has no solution

Step-by-step explanation:

we have

[tex]y=\frac{2}{3}x+7[/tex] ----> equation A

[tex]3y=2x-3[/tex]

Isolate the variable y

Divide by 3 both sides

[tex]y=\frac{2}{3}x-1[/tex] ------> equation B

Compare equation A and equation B

Both lines have the same slope and different y-intercept

so

Line A and Line B are parallel lines

The lines do not intersect

therefore

The system has no solution, because both lines are parallel

see the attached figure to better understand the problem

The equation 0.15 x + 150 ≥ 450 will help Teagan determine how much he has to sell today ⇒ A

Step-by-step explanation:

The given is:

We need to find which equation will help Teagan to determine how much he has to sell today

Assume that he has to sell by $x today

∵ The store pays $150 per day plus a commission of 15%

   of their sales

∵ Teagan's total sales = x

- Multiply 15% by x, then add the product by 150

∴ Teagan makes = 15% × x + 150

∵ 15% × x = [tex]\frac{15}{100}[/tex] × x = 0.15 x

∴ Teagan makes = 0.15 x + 150

∵ Teagan wants to make at least $450 today

- At least means ≥

∴ Teagan makes ≥ 450

- Substitute Teagan makes by 0.15 x + 150

∴ 0.15 x + 150 ≥ 450

The equation 0.15 x + 150 ≥ 450 will help Teagan determine how much he has to sell today

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Answer:

you mean A

Step-by-step explanation:

Answer:

U'(-5, -2), V'(-3, -1), W'(-3, 3), Z'(-5, 6).

Plot these points. Then connect them to form trapezoid U'V'W'Z'.

Answer:

[tex]2 \frac{1}{3} [/tex]

Step-by-step explanation:

Assuming the question is

[tex]7 \times \frac{9}{27} [/tex]

reduced to the lowest term.

We proceed as follows:

[tex]7 \times \frac{9}{3 \times 9} [/tex]

We cancel the common factors to get:

[tex]7 \times \frac{1}{3} [/tex]

This simplifies to

[tex] \frac{7}{3} = 2 \frac{1}{3} [/tex]

Answer:

[tex]Total\ sales\ should\ be=\$ 300000[/tex]

Step-by-step explanation:

[tex]Let\ her\ total\ sale=x[/tex]

Total Earning:

[tex]The\ offer=\$ 42500\\\\Income\ from\ the\ sales=8\%\ of\ total\ sale\\\\Income\ from\ the\ sales=8\%\ of\ x\\\\Income\ from\ the\ sales=\frac{8}{100}\times x\\\\Income\ from\ the\ sales==0.08x\\\\Total\ earning=Offer+Income\ from\ the\ sales\\\\Total\ earning=42500+0.08x[/tex]

Required Earning=$66500

[tex]To\ move\ that\ city\\\\Total\ earning=required\ earning\\\\42500+0.08x=66500\\\\0.08x=66500-42500\\\\0.08x=24000\\\\x=\frac{24500}{0.08}\\\\x=300000\\\\Total\ sales\ should\ be=\$ 300000[/tex]

Her total sales would need to be at least $300,000 for her to move

Step-by-step explanation:

Briana has been offered a sales job in another city

We need to find what would her total sales need to be for her to move

Assume that her total sales is x

∵ The offer was for $42,500 plus 8% of her total sales

∵ Her total sales = x

- To find her annual salary multiply x by 8% and add the

  product to $42,500

∴ Her annual salary = 8% × x + 42,500

∵ 8% × x = [tex]\frac{8}{100}[/tex] × x = 0.08 x

∴ Her annual salary = 0.08 x + 42,500

∵ Briana needs to have an annual salary of at least $66,500

- At least means ≥

∴ Her annual salary ≥ 66,500

- Substitute her annual salary by the expression above

∴ 0.08 x + 42,500 ≥ 66,500

- Subtract 42,500 from both sides of inequality

∴ 0.08 x ≥ 24,000

- Divide both sides by 0.08

∴ x ≥ 300,000

∴ Her total sales ≥ $300,000

Her total sales would need to be at least $300,000 for her to move

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Answer:

Option B

see the attached figure

Step-by-step explanation:

we know that

Opposite number or additive inverse of any number (n) is a number which, if added to n, results in 0

so

In this problem

The opposite of -1/2 is 1/2

so

point M is 1/2 ----> point M is located in the interval (0,1)

The opposite of 5/2 is -5/2

so

point N is -5/2 ----> point M is located in the interval (-3,-2)

therefore

The correct answer is the option B

A fishermen can save gas by implementing the strategies Plan Efficient Routes, Maintain Proper Boat Speed, Reduce Idle Time, Optimize Load and Equipment and Regular Maintenance

Fishermen can save gas by implementing the following strategies:

Plan Efficient Routes: By planning their fishing trips in advance and mapping out efficient routes, fishermen can minimize the distance traveled and save on gas consumption.

Maintain Proper Boat Speed: Operating the boat at an appropriate speed can significantly impact fuel efficiency.

Reduce Idle Time: Minimizing idle time while on the water can help save gas.

Optimize Load and Equipment: Carrying excessive weight on the boat can increase fuel consumption.

Regular Maintenance: Keeping the boat and engine properly maintained is essential for fuel efficiency.

Utilize Wind and Tides: When feasible, fishermen can take advantage of wind and tidal currents to reduce reliance on the engine.

Share Resources: Collaborating with other fishermen or joining fishing cooperatives can help share resources and reduce individual fuel consumption.

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Answer:

y = 9

Step-by-step explanation:

Substitute the x- coordinate of the point into the equation and solve for y, that is

y = 2(5) - 1 = 10 - 1 = 9

Thus point is (5, 9 )

Answer:

1. B) Figure B.

2. C) Figure C.

3. D) Figure D.

4. C) Figure C.

Step-by-step explanation:

Given: Radius of Circle A= 4

           Radius of Circle B= 5

           Radius of circle C= 6

           Radius of circle D= 7

Now, finding circumference and area of all the circle.

We know, circumference of circle= [tex]2\pi r[/tex]

Area of circle= [tex]\pi r^{2}[/tex]

Where, r= radius of circle and π = 3.14

First, solving for figure A

Circumference= [tex]2\times 3.14\times 4= 25.12\ cm[/tex]

Area= [tex]3.14\times 4^{2} = 50.24\ cm^{2}[/tex]

Solving for Figure B

Circumference= [tex]2\times 3.14\times 6= 31.4\ cm[/tex]

Area= [tex]3.14\times 5^{2} = 78.5\ cm^{2}[/tex]

Solving for Figure C

Circumference= [tex]2\times 3.14\times 6= 37.68\ cm[/tex]

Area= [tex]3.14\times 6^{2} = 113.04\ cm^{2}[/tex]

Solving for Figure D

Circumference= [tex]2\times 3.14\times 7= 43.96\ cm[/tex]

Area= [tex]3.14\times 7^{2} = 153.86\ cm^{2}[/tex]

∴ 1. Answer is Figure B.

   2. Answer is figure C.

   3. Answer is Figure D

   4. Answer is Figure C.