Question
Francie rode her bike for 2.5
hours at 12 miles per hour. How far did she ride?

Answer: y=-1/8x-2

Step-by-step explanation:

Given the slope, we can start to fill out the slot-intercept form equation.

y=-1/8x+b

We don't know the value of b, but we can plug in the given point to solve for b.

-3=-1/8(8)+b

-3=-1+b

b=-2

Now that we know b, we can finish our slope-intercept equation.

y=-1/8x-2

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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The function that represents the dotted line of the graph using transformation rules is; f(x - 1) - 4.

For the function f(x) of the given graph,  when we look at the solid line, we see that it has a root at x = -1 which means it has a zero at x = -1.

However, when observing the dashed line, we see that it has a root at x = 0 which means it has a zero at x = 0.

Thus, we can  deduce from transformation rules that the function was moved by 1 unit to the right to get the new function.

Secondly, we observe that the dashed line is also below the function f(x), and we observe further that 4 was subtracted. Therefore, when we use the transformation rules again for subtracting from a function, we get the final function as; f(x - 1) - 4.

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The equation of this parallel line using point slope is  y = 4x - 31.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis may be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

Given that the equation of a line is y = 4x - 2.

Here, we observe that the slope m = 4

Parallel lines have the same slope. So, the slope of the new line is:

m = 4

Given that points (x1, y1) = (5, -11) are also in the new parallel line.

Using the Point-Slope form we can write:

y - y1 = m (x - x1)

Substitute the value of x and y coordinates in the above equation:

y - (-11) = 4 (x - 5)

y + 11 = 4x - 20

y = 4x - 20 -11

y = 4x - 31

Hence, the equation of this parallel line using point slope is  y = 4x - 31.

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Answer:

There are 40 apples in the basket.

This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.

I hope this helped you, have an amazing day! :)

Answer:

Anna had $125 in her account before the deposit. Here's the math:

$150 (current balance) - $25 (deposit) = $125 (previous balance)

Answer:

See below.

Step-by-step explanation:

I assume the fraction 3/5 is raised to the 3rd power.

I assume this is the given expression.

\( (\dfrac{3}{5})^3 \)

The base is 3/5    True

The base is 3     False

The exponent is 3    True

The expanded form is \( \dfrac{3}{5} \times \dfrac{3}{5} \times \dfrac{3}{5} \)       True

The expanded form is \( \dfrac{3 \times 3 \times 3}{5} \)     False

\( (\dfrac{3}{5})^3 = \dfrac{9}{15} \)      False

\( (\dfrac{3}{5})^3 = \dfrac{27}{125} \)      True

The Domain of the function are the set of x values of the graph. So, assuming this is the whole graph (that it doesn't continueof screen), the Domain will be the set from the lowest "x" value to the highest. The lowest is the leftmost, which is, in this case, 0, and the highest is the rightmost, which is in the 8th tick, and, since the graph is counting by two on "x", this is x = 16.

These poinst are included, so the domain is:

The range is similar, but for the "y" values. So, the lowest is y = 0 and the highest is on the 4th tick, since it is counting by 20 on "y", this is y = 80. So, the Range is:

To check if it is a function, we need to check if each x values correspond to a single y value. We can do it by checking if there is any vertical line that passes through the graph 2 or more times. But, since it is a line, this won't happen, which means each "x" have only one corresponding "y" so this it a function.

A discrete function don't complete every point of "x", it "jumps" and in at least one part of the graph. But this graph don't have any "jumps", it continue from start to end without undefined values, so it is continuous.

Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)

- Therefore, the equation is;

\({ \boxed{ \tt{y = - 2x}}}\)

- What is x when y is 15

\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = \(\frac{-15}{3}\)

                        x = -5

Therefore, when y = 15, x = -5.

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Answer:

- 16

Step-by-step explanation:

The way this is given, you have to find the second term before you can fine the third.

a2 = d(n - 1) * (-2)^2

a2 = 2 * (-2)^2

a2 = 2 * 4

a2 = 8

a3 = d(3 - 1) * (-2)^3

a3 = 2 * (-2)^3

a3 = 2 * - 8

a3 = - 16

All of the statements are true.

Here is a breakdown of the set operations:

A U B (the union of A and B) is the set of all elements that belong to either A or B or both. In this case, the elements that belong to

A ∩ B (the intersection of A and B) is the set of all elements that belong to both A and B. In this case, the elements that belong to

A - B (the difference between A and B) is the set of all elements that belong to A but not to B. In this case, the elements that belong to

B - A (the difference between B and A) is the set of all elements that belong to B but not to A. In this case, the elements that belong to

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Answer:

-1 ,-1/2 , -3/4 , -1 /4, -5 / 8 , -7 / 8 , -13 / 16, 0.

Step-by-step explanation:

Answer:

She would have $1 left in her account.

Step-by-step explanation:

43 + 50 = 93

93 - 92 = 1

Hope this helps..?

Answer:

$1

Step-by-step explanation:

We start off with $43.

Tanya deposits $50 to her account.

50+43=93.

She has $93 now.

She writes a check for $92.

93-92=1.

Man, Tanya is broke no cap.

Answer:

315 inches long

Step-by-step explanation:

180 x .75= 135 <--- that is 75% of 180

then add the two numbers

180 + 135

you add them because the original length of the car is 180 inches and the truck is 75% longer.

180 + 135= 315

Answer:

A = $17,238.65

I (interest) = $8,838.65

Step-by-step explanation:

Using the formula A = P(1 + r/n)^nt

A = $17,238.65

A = P + I where

P (principal) = $8,400.00

I (interest) = $8,838.65

First, convert R as a percent to r as a decimal

r = R/100

r = 3.6/100

r = 0.036 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 8,400.00(1 + 0.036/12)^(12)(20)

A = 8,400.00(1 + 0.003)^(240)

A = $17,238.65

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $8,400.00 at a rate of 3.6% per year compounded 12 times per year over 20 years is $17,238.65

The expression arcctg(tg(x)) simplifies to arcctg(tan(x)).

To simplify the expression arcctg(tg(x)), we can apply trigonometric identities and properties.

The function arcctg(x) is the inverse cotangent function, which is the angle whose cotangent is x. Similarly, tg(x) represents the tangent function.

First, let's simplify the expression inside the arcctg function, which is tg(x):

tg(x) = sin(x) / cos(x)

Now, we can substitute this value into the original expression:

arcctg(tg(x)) = arcctg(sin(x) / cos(x))

Using the property of inverse trigonometric functions, we can rewrite this as:

arcctg(sin(x) / cos(x)) = arcctg(1 / tan(x))

Now, we can simplify further using the identity:

1 / tan(x) = cot(x)

Therefore:

arcctg(1 / tan(x)) = arcctg(cot(x))

Using another identity, we know that the cotangent function is the reciprocal of the tangent function:

cot(x) = 1 / tan(x)

Therefore, we can simplify the expression to:

arcctg(cot(x)) = arcctg(1 / tan(x)) = arcctg(tan(x))

Finally, we arrive at the simplified expression:

arcctg(tg(x)) = arcctg(tan(x))

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Answer:

less than

Step-by-step explanation:

314+175= 489 round that it would be 500 so it would be less than 600

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Hello there!

The sum of 314 and 175 = 489.

If we round it, we will get 500.

500 is less than 600.

So the sum of 314+175 is less than 600.

Hope this helps you!

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\(GraceRosalia\)

Solution

To find the probability that exactly 2 don't grow?

This is a binomial probability question. The "success" here is that the seed doesn't grow, so

p = 1 - 0.95 = 0.05 q=0.95 n=8 (number of repetitions) r =2 (number of success)

where

P = success

q = failure

Therefore the probability that exactly 2 don't grow = 0.052 (3d.p)

We get that the cost of the battery is $ 8.24 per battery.

We are given that the cost of 88 batteries = $ 724.72

We need to find the cost of one battery.

We will do this by diving the cost of 88 batteries by 88.

Using division, we get that:

cost of one battery = $ 724.72 ÷ 88

Simplifying the expression, we get that:

cost of one battery = $ 8.24 per battery.

Therefore, we get that the cost of the battery is $ 8.24 per battery.

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The length of the hypotenuse of the right triangle is 4.1in

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

In trigonometry, if θ is the angle opposite the 4 in line, then sinθ= opp/hyp

cosθ=adj/hyp

tanθ= opp/adj

to find the hypotenuse

sin80= 4/hyp

hyp= 4/sin80

hyp = 4/0.985

therefore the hypotenuse = 4.1 in

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The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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Answer:

12

Step-by-step explanation:

36 / (x - 3) = 4

multiply both sides by (x - 3):

(x - 3)(36 / (x - 3)) = 4(x - 3)

36 = 4(x - 3)

expand right side:

36 = 4x - 12

add 12 to both sides:

36 + 12 = 4x - 12 + 12

48 = 4x

divide both sides by 4:

48/4 = 4x/4

x = 12

Without more information or a diagram, it's not possible to definitively determine which side-angle relationship (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of sides and angles known in a triangle.

Given the question, it's clear that we are discussing a concept in Geometry - the side-angle relationships in a triangle. However, without more information or an accompanying diagram, it isn't possible to definitively determine which of the side-angle relationships (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of side and angle information known about a triangle. For example, ASA means that we know two Angles and the Side between them. SAS relates to knowledge of two Sides and the Angle between them, and so forth. More information or a visual representation would allow a more conclusive answer.

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Answer:

6

Step-by-step explanation:

-36/-6 = 6

Answer:

The answer is positive 6.

Step-by-step explanation:

Hope this helps!

The line or points has a slope value of -1

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

The slope of -3 up to positive 3

For a start, we represent the above parameters using an ordered pair

The ordered pair is represented as

(x, y) = (-3, 3)

The slope of the point is then calculated using the following slope formula

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3, 3) and (0, 0)

The coordinate (0, 0) represents the origin

Substitute the known values in the above equation

So, we have the following equation

Slope = (3 - 0)/(-3 - 0)

Evaluate the difference

So, we have the following equation

Slope = (3)/(-3)

Evaluate the quotient

So, we have the following equation

Slope = -1

Hence, the slope is -1

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Answer:

y=2.6x+49

Step-by-step explanation:

The temperature on the first day of the spring was about _49_F.

The average rate of change in 10 it’s about _2.6_ F per week

Answer:

1 and 2

Step-by-step explanation:

If x is 1: 2 x 1 + 7 = 2 + 7

= 9  This works.

If x is 2: 2 x 2 + 7 = 4 + 7

= 11  This works

If x is 3: 2 x 3 + 7 = 6 + 7

= 13  This does not work since 2x + 7 has to be less than 13.

Answer:

I belive the equation would be...

Step-by-step explanation:

8x+$35=$167.00

Hope it helps??

Answer

they worked 16.5 hours that week.

Step-by-step explanation:

You first subtract the tip by the total cost and that gives you $132.00. and from that cost you divide by $8 which they get paid by the hour... and then you get the 16.5 and that means they worked 16.5 hours that week.

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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Answer:

a

Step-by-step explanation:

there are not two points on the same line.