Kristin left the movie theater and traveled
toward the lake at an average speed of 33
km/h. Jennifer left sometime later
traveling in the opposite direction with an
average speed of 45 km/h. After Kristin
had traveled for two hours they were 156
km apart. How long did Jennifer travel?

Answer:

?

Step-by-step explanation:

??????

Multiply total yards by 3

6.2 yards x 3 = 18.6 feet

Answer:

18.6 , if wrong correct me

Step-by-step explanation:

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Then 1 - 3/5 = 2/5. This means that 2/5 of the frogs in that particular part of the rainforest are not poisonous. This fraction can also be expressed as 40/100 or 0.4 in decimal form.

In the given scenario, we know that 3/5 of the frogs in a particular part of the rainforest are poisonous. This means that the remaining fraction of the frogs are not poisonous.

To find this fraction, we need to subtract 3/5 from 1 (since the sum of the fractions of poisonous and non-poisonous frogs is equal to 1).

It's important to note that just because a frog is not poisonous, it doesn't mean it's safe to touch or handle them. It's always best to admire these beautiful creatures from a safe distance and leave them alone in their natural habitat.

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Answer:

a. \(\mathbf{P(\overline x < 68) = 0.9998}\)

b. \(\mathbf{P(68 < \overline x < 69 ) =0}\)

c. \(\mathbf{P ( \overline x > 66 ) =0.02275}\)

Step-by-step explanation:

Given that ;

Let Y be a random variable In a​ population, where:

mean \(\mu_y\) = 65

\(\sigma^2_y\) = 49

standard deviation σ  = \(\sqrt{49}\) = 7

The objective is to determine the following :

In a random sample of size n​ = 69​, find Pr(Y <68) =

Using the Central limit theorem

\(P(\overline x < 68) = \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{68 - \mu }{\dfrac{\sigma}{\sqrt{n}}} } \end {pmatrix}\)

\(P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{68 - 65 }{\dfrac{7}{\sqrt{69}}} } \end {pmatrix}\)

\(P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{3 }{\dfrac{7}{8.3066}} } \end {pmatrix}\)

\(P(\overline x < 68) = (Z < 3.5599 )\)

From the z tables:

\(\mathbf{P(\overline x < 68) = 0.9998}\)

In a random sample of size n​ = 124​, find Pr (68< Y <69)=

\(P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{ 69 - \mu}{\dfrac{\sigma}{\sqrt{n}}} \end {pmatrix}\)

\(P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- 65}{\dfrac{7}{\sqrt{124}}} < Z < \dfrac{ 69 - 65}{\dfrac{7}{\sqrt{124}}} \end {pmatrix}\)

\(P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{3}{\dfrac{7}{11.1355}} < Z < \dfrac{ 4}{\dfrac{7}{11.1355}} \end {pmatrix}\)

\(P(68 < \overline x < 69 ) = P \begin {pmatrix} 4.7724 < Z < 6.3631 \end {pmatrix}\)

\(P(68 < \overline x < 69 ) = P( Z < 6.3631 ) - P ( Z < 4.7724 )\)

From z tables

\(P(68 < \overline x < 69 ) = 0.9999 - 0.9999\)

\(\mathbf{P(68 < \overline x < 69 ) =0}\)

In a random sample of size n​ = 196​, find Pr (Y >66)=

\(P ( \overline x > 66 ) = P ( \dfrac{\overline x -\mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{66 -\mu }{\dfrac{\sigma}{\sqrt{n}}})\)

\(P ( \overline x > 66 ) = P ( Z> \dfrac{66 - 65 }{\dfrac{7}{\sqrt{196}}})\)

\(P ( \overline x > 66 ) = P ( Z> \dfrac{1 }{\dfrac{7}{14}})\)

\(P ( \overline x > 66 ) = P ( Z> \dfrac{14 }{7})\)

\(P ( \overline x > 66 ) = P ( Z>2)\)

\(P ( \overline x > 66 ) = 1 - P ( Z<2)\)

from z tables

\(P ( \overline x > 66 ) = 1 - 0.9773\)

\(\mathbf{P ( \overline x > 66 ) =0.02275}\)

\({\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=7 \end{cases}\implies 7=ab^5 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\[1em] y=\frac{1}{4} \end{cases}\implies \cfrac{1}{4}=ab^0\implies \cfrac{1}{4}=a(1)\implies \cfrac{1}{4}=a \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{7=\left( \cfrac{1}{4} \right)b^5\implies 28=b^5}\implies \sqrt[5]{28}=b~\hfill \boxed{y\approx \cfrac{1}{4}(1.9473)^x}\)

Parent function f(x) = 1/2ˣ will be translated Vertically compress by a factor of 1/3, which gives a function f(x) = 1/2ˣ - 1/3.

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point. Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation. For instance, this transformation shifts the parallelogram 3 units upward and 5 units to the right. The formula is (x, y) (x + 5, y + 3).

Given

Parent function

f(x) = 1/2ˣ

Vertically compress by a factor of 1/3

Translation

f(x) = x - k

f(x) = 1/2ˣ - 1/3

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Answer:

y = 36

Step-by-step explanation:

given y varies directly  with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition when x = 5 , y = 15

15 = 5k ( divide both sides by 5 )

3 = k

y = 3x ← equation of variation

when x = 12 , then

y = 3 × 12 = 36

Answer:

be more pacific

Step-by-step explanation:

The amount of the tv in 3 years which depreciates at a rate of 4% per year is £708 .

We have given principal amount =  £800 , rate = 4% and time = 3 years .

Putting above values in equation (1) , we get

        \(A=800(1-\frac{4}{100} )^3\\A= 800(1 -0.04)^3\\A=800(0.96)^3\\A=800\times 0.88\\A= \£707.78\)

Note that the minus sign is due to depreciation .

On rounding off , amount will be £708 .

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Answer:

the answer is 6 because the first triangle is =90 degree but since it is represented as numbers it is 6

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Answer:

Hey Mate...

Step-by-step explanation:

All that the slope-intercept form (the equation to describe linear equations) is, is an equation (y=mx+b) where m (the number that multiples x) is the slope and b (the number that is not multiplying a variable on the right-hand side of the equation) is the y-intercept.

Answer: third equation (x - 4 = 9)

Step-by-step explanation:

I don't think the one is supposed to be there but, x + 9 = 14, 6 x = 30, and x - 4 = 9 solves to x = 5, x = 5, and x = 13, respectively. So the first two equations have the same solution, while the third equation does not.

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

the approximate area of corcle is 3848

\(diameter = 70in \\ radius = \frac{70}{2} \\ = 35in \\ area = \pi \: r {}^{2} \\ = \pi \: 35 {}^{2} \\ = 3848.45in {}^{2} \)

Answer: y=3x+5

Step-by-step explanation:

9x^3 + 4x^2 + 5

Explanation:

Let's simplify step-by-step.

6x^2−3−5x^3−(4x^3+2x^2−8)

Distribute the Negative Sign:

=6x^2−3−5x^3+−1(4x^3+2x^2−8)

=6x^2+−3+−5x^3+−1(4x^3)+−1(2x^2)+(−1)(−8)

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

Combine Like Terms:

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

=(−5x^3+−4x^3)+(6x^2+−2x^2)+(−3+8)

=−9x^3+4x^2+5

The value of p is 781.25.

What is a population growth?

Population Growth is defined as the increase in the number of individuals in a population is called population growth.

What is a common growth factor?

The growth factor is the ratio between the old price and the new price, once sales tax is included.

We want to know the population when y = 0, or when the number of years is zero.

Substitute the same in the equation

p = (400).\((\frac{5}{4} )^{y}\)

When y = 1 or at the 1st year, the population will be p = (400)(\(\frac{5}{4}\) ) = 500

This means that the population is increasing by a common growth factor of \((\frac{5}{4})\) .

When y = 3, or at year 3 we get the population as p = 400  \((\frac{5}{4} )^{3}\)

                                                                                      = 781.25

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Answer:

some ppl got summer school

Step-by-step explanation:

Answer: Angle 1 corresponds with Angle 7.

Using arrangements with repetitions, it is found that they can be grouped in 46,200 ways.

The number of possible arrangements of n elements is given by the factorial of n, that is:

\(A_n = n!\)

When elements are repeated \(n_1, n_2, \cdots, n_n\) times, the formula is as follows:

\(A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}\)

In this problem:

Then, the number of ways they can be grouped is:

\(A_{11}^{4,3,3,1} = \frac{11!}{4!3!3!1!} = 46200\)

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Answer:

a) \(6x^2 + 17x + 31 + \frac{70}{x-2}\)

Step-by-step explanation:

(see attachments for explanation)

To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.

The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.

Therefore, the fraction of pocket money left can be written as 17/35.

Answer:

810 m

Step-by-step explanation:

Split the polygon into two parts

(Small and Big rectangle)

SR : 18(18+3) = 378

BR : 18(3+3+18) = 432

378+432 = 810

Hope this helps :)

The domain is {-8, -12, 1, -2} and the range is {5, -11, -1, -4}

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

The graph

On the graph, we have

(-8,5) (-12,-11)  (1-1) (-2,-4)

The domian is the set of the input values

Using the ordered pairs as a guide, we have

Domain = {-8, -12, 1, -2}

For the range, we have

The range is the set of the output values

So, we have

Range = {5, -11, -1, -4}

Hence, the range is  {5, -11, -1, -4}

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Answer:

Craig has £13.40

He sees this offer in a restaurant:

Main courses £8.90 each. Buy one main course and get the 2nd HALF PRICE!

Can he afford to buy two main courses? Show your working.

Answer:$1.50

Step-by-step explanation: