6. Erin leaves home at 11am. She cycles at a speed of 16 miles per hour for 90 minutes. She
stops for half an hour. Erin then cycles home and arrives at 3pm.
(a) Draw a distance-time graph to show Erin's journey.
(b) What is Erin's average speed on the return part of her cycle?

The sequence of transformations applied to function f(x) to produce function r(x) is a reflection across the y-axis and dilation by a scale factor of 1/4.

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) of a graph is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, function f(x) = -x would be transformed to function r as follows:

f(x) = -(-x)

r(x) = x

By applying a dilation with a scale factor of 1/4 to function r, we have:

r(x) = (1/4 × x)    → r(x) = f(1/4x)

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Answer:

larger number = 3

smaller number = -1

Step-by-step explanation:

x = larger number

y = smaller number

x+y=2

8-2y=4x-2 ---> 10 = 4x+2y

10 = 4x+2y

5=2x+y

y = 5-2x

2x=5-y

x+5-2x = 2

-x+5=2

-x=-3

x=3

3+y=2

y=-1

Frank equation is : 0.25x + 1.95 = y

Alice equation is : 0.4x + 1.5 = y

This question is incomplete and actual question is

Frank and Alice are penguins. At birth, Frank’s beak was 1.95 inches long, while Alice’s was 1.50 inches long. Frank’s beak grows by 0.25 inches per year and Alice’s grows by 0.40 inches per year. Write an equation to represent the length of each penguin’s beak in x years.

Given that

Frank’s beak was 1.95 inches long and Frank’s beak grows by 0.25 inches per year

let y be the total long

equation is 0.25x + 1.95 = y

while Alice’s was 1.50 inches long and Alice’s grows by 0.40 inches per year

equation is 0.4x + 1.5 = y

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The simple interest would be $84.

What is simple interest?

Calculating the interest on a loan using simple interest is quick and simple. Simple interest is calculated by dividing the principle by the daily interest rate and the number of days between installments.

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest.

Interest = (Principle x Rate x Time in years)/100

            = (1200 x 3.5 x 2)/100

            = 84

The simple interest would be $84.

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Answer:

Step-by-step explanation:

F 3/8x 3/8y

To solve for v, isolate the variable by dividing each side by factors that don't contain the variable.

Solve for v.

Hope this helps!

The interest rate on loan is 5.25%.

What is principal amount?

The loan amount that the lender gives to the borrower is referred to as the primary amount. Additionally, it is the factor the lender uses to calculate interest.

What is simple interest?

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. The formula to calculate simple interest is  I=P.r.t

Given, Principal amount=$125,000, time=10years, Interest=$65,625.

Let r be the rate of interest, on applying simplest interest formula

                                               I=P.r.t

Where P=principal amount, r=rate, t=time.

I=125,000 x r x10

65,625=125,000 x r x10

r=[tex]\frac{65,625}{125,000(10)}[/tex]

r=0.0525

r=5.25%

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Answer: 1.1

Step-by-step explanation:

10 * .11 is 1.1

When multiplying decimals by ten you move the decimal place once to the right.

Answer:

1.1

Step-by-step explanation:

0.11 x 10 = 1.1

You are moving the decimal point over once (x 10).

Using the corresponding angle theorem, the value of m∠E is 155.

In the given question we have to find the value of m∠E.

As we know that,

According to the corresponding angle theorem, if a transversal meets two parallel lines, the corresponding angles must be congruent.

So from the figure

4x−35=x+10

Add 35 on both side we get

4x=x+10+35

4x=x+45

Subtract  on both side

4x−x=x+45−x

3x=45

Divide by 3 on both side we get

x=15

So the value of x+10

=15+10

=25

As we know that value the angle of straight line is 180.

So m∠E+25=180

Subtract 25 on both side we get

m∠E=180−25

m∠E=155

Hence, the value of m∠E is 155.

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Answer:

25

Step-by-step explanation:

6.3= 1 blanket

to find 4 blankets you multiply 6.3 by 4

6.3x4=25.2

to the nearest whole number

25

56.78% of the penguins in the population have a weight between 13.0 kg and 16.5 kg, according to the usual distribution.

Given,

The mean of the population, μ = 15.1 kg

Standard deviation, σ = 2.2 kg

We have to find the percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg;

Here,

z score = x - μ / σ

The ratio of the p-value of Z when X = 16.5 minus the p-value of Z when X = 13 indicates the percentage of penguins in the population whose weight is between 13.0 kg and 16.5 kg.

x = 16.5

z score = x - μ / σ

z = (16.5 - 15.1) / 2.2  = 0.64

Z = 0.64 has a p-value of 0.7389.

x = 13

z score = x - μ / σ

z = (13 - 15.1) / 2.2 = -0.95

Z = -0.95 has a p-value of 0.1711.

0.7389 - 0.1711 = 0.5678.

0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

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The length of the equal sides is 11.1cm

From the question, we have

perimeter = 30 cm

base = 7.8 cm

perimeter =  sum of all sides

30=7.8+x+x

30-7.8=2x

x = 22.2/2 =11.1cm

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

Complete question: An isosceles triangle has a perimeter of 30 cm. If the base is 7.8 cm long, find the length of the equal sides. ​

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Answer:

Point form:

(18/11 , -8/11)

Equation form:

x=18/11 , y=-18/11

In the game where average score was 40 , then Jim's score was 100 .

In the question ,

it is given that ,

the average score in the game was 40  .

and also given that the Jim's score was 5/2 of the average .

So ,  the Jim's score can be calculated using the equation .

Jim's score = (5/2) × (Average score of the game)

Substituting the value of average in the equation ,

we get,

Jim's Score = (5/2) × 40

= 5 × 20

= 100

Jim's score is 100 .

Therefore , The Jim's score in the game where average score was 40 is 100   .

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Answer: Yes

Step-by-step explanation: Can this help , 81 ÷ 3 is 27 which is one of the factors in the 3 multiplications

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{7}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so for the parallel line we're really lookikng for the equation of aline whose slope is 5/7 and that it passes through (-5 , 6)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{5}{7}}(x-\stackrel{x_1}{(-5)}) \implies y -6= \cfrac{5}{7} (x +5) \\\\\\ y-6=\cfrac{5}{7}x+\cfrac{25}{7}\implies y=\cfrac{5}{7}x+\cfrac{25}{7}+6\implies {\Large \begin{array}{llll} y=\cfrac{5}{7}x+\cfrac{67}{7} \end{array}}[/tex]

now, keeping in mind that perpendicular lines have negative reciprocal slopes

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{5}}}[/tex]

so for the perpendicular line we're really looking for the equation of a line whose slope is -7/5 and that it passes through (-5 , 6)

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{7}{5}}(x-\stackrel{x_1}{(-5)}) \implies y -6= -\cfrac{7}{5} (x +5) \\\\\\ y-6=-\cfrac{7}{5}x-7\implies {\Large \begin{array}{llll} y=-\cfrac{7}{5}x-1 \end{array}}[/tex]

The coterminal angle is 299°, lies in the IV quadrant and the reference angle is 61°.

Coterminal angles: are angles in standard position (angles with the initial side on the

positive x-axis) that have a common terminal side. For example, the angles 30°, –330°

and 390° are all coterminal.

For angle 659°,

coterminal angle = 659 - 360

                            = 299°

For quadrant,

299/90 = 3.32

After truncating it's equal to 3.

Therefore, it lies in the IV quadrant.

A reference angle is the size of the smallest acute angle, t, formed by the terminal side of the angle t and the horizontal axis.

659 = 2*360-61

Therefore, the reference angle is 61°.

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Answer:

Step-by-step explanation:

The set of ordered pairs that represent dilation factor of 2 is

a. A' (2, 12) B' (12, 12) C' (2, 4)

Dilation is a method of transformation which uses a scale factor. The scale factor determines if the dilation is magnification or shrinking

|0 < r < 1| is shrinking

|r > 1| is magnification

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

From the graph the coordinates are read and following the given transformation rule we have

preimage                           image

A (1, 6)   → (1 * 2, 6 * 2) →   A' (2, 12)

B (6, 6)  → (6 * 2, 6 * 2) →    B' (12, 12)  

C (1, 2)  → (1 * 2, 2 * 2) →    C' (2, 4)

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The power of a test is measured by its capability of rejecting a null hypothesis that is false, so option C is the correct answer

what is power with respect to probability?

Power is defined as the probability of correctly rejecting the false null hypothesis. It is the measure of the capability of rejecting a null hypothesis that is false.

Power = P[ rejecting a null hypothesis that is false.]

So, option C is correct, the power of a test is measured by its capability of rejecting a null hypothesis that is false

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The changes in his account is that (d) The balance of the account increases by 6% each year.

The function of the account balance is given as

f(x) = 4,000 (1.06)*

The above function is an exponential growth function

Such that the growth factor (b) is the number in bracket

This is represented as

b = 1.06

The percentage growth rate (r) is calculated as:

r = b - 1

Substitute known values

r = 1.06 - 1

Evaluate the difference

r = 0.06

Express as percentage

r = 6%

This implies that the balance increases by 6% each year.

So, the true statement is (d)

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The value of  the function (f + g)(x) = [tex]x^{2}[/tex] -5x + 9

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

f(x) = - 2x + 4, g(x) = [tex]x^{2}[/tex] -3x + 5

(f+g)(x) = f(x) + g(x)

So by adding the two functions

(f + g)(x) = -2x + 4 + [tex]x^{2}[/tex] -3x + 5

(f + g)(x)  = [tex]x^{2}[/tex] -5x + 9

In conclusion, the value of [tex]x^{2}[/tex] -5x + 9

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Answer:

Step-by-step explanation:

B

Answer 0,4

Answer:

(-5,-1)

Step-by-step explanation:

Start at the orginal.  This is (0,0), the middle of the graph.  From that point you move 5 spaces left.  That is the -5 in the answer.  Then from that point, you move one space down.  That is the -1 in the answer.

After Ann start to translate the document in 2 days, they need more 4.4 days to complete the work.

A unit work would take Ann 10 days to complete, means each day Ann completes 1/10 work

She works for 2 days, hence the work done = 2 x 1/20 = 2/10

The remaining work = 1 - 2/10 = 8/10

Then Ben joins.

A unit work would take Ben 12 days to complete, means each day Ben completes 1/12 work.

Each day, both Ann and Ben will complete:

1/10 + 1/12 = 11/60 unit work

The remaining work = 8/10

Hence, if each day 11/60 work can be completed, to complete 8/10 work, they need:

8/10 : 11/60 = 48/11 = 4.4 days

Therefore we can conclude, after Ann works for 2 days, they need more 4.4 days to complete the work.

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Answer:

2 : 5 or 2/5

Step-by-step explanation:

The ratio is 40 : 100, which can simplify into 2 : 5.

Answer:

Step-by-step explanation:

We can tell that an equation has multiple/ infinitely many solutions if we try to solve it and get a variable or a number equal to itself.

Let's solve the given equation and see what we'll get :-

[tex]\sf 15-10b-6=-10b+9[/tex]

Add 10b to both sides:-

[tex]\sf 15-10b-6+10b=-10b+9+10b[/tex]

Simplify:-

[tex]\sf 15-6=9[/tex]

Subtract:-

[tex]\sf 15-6=9[/tex]

[tex]\sf 9=9[/tex]

As we can see, both sides ended up equal, therefore, this equation has infinitely many solutions!

Hope this helps!

Have a great day!

The expression [tex]s(n) = 2 + \sum\limits_{i = 2}^{n} [5 + 2 \cdot (i - 2)][/tex] represents the n-th element of the series.

In this question we find a sequence with a progressive difference between any two consecutive terms, whose definition is shown below:

s(1) = a

[tex]s(n) = a + \sum\limits_{i = 2}^{n} [b + r \cdot (i - 2)][/tex]

Where:

First, determine value of the first element of the sequence:

a = 2

Second, find the difference between the first and second elements of the sequence:

b = 7 - 2

b = 5

Third, determine the increase for the difference between two consecutive elements of the sequence:

r = 2

The formula for the n-th term is [tex]s(n) = 2 + \sum\limits_{i = 2}^{n} [5 + 2 \cdot (i - 2)][/tex].

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The positive value of Z is 2.17.

What do you mean by normal distribution?

A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction. Because of its flared appearance, a normal distribution's graphic representation is occasionally referred to as a bell curve. The specific shape may change depending on how the population is distributed, but the peak and curve are always symmetrical and in the centre.

The information can be represented in the standard normal curve below:

It is given that 97% of the standard normal curve lies between −z and z.

The area in between is 0.97 meaning that one side is (0.97)/2 = 0.485

In addition, the region not shaded is the level of significance represented by (1-0.97)/2 = 0.03/2 = 0.015

From the Z-Score table (0 to Z table), this probability corresponds to the Z value of Z= 2.17 and -2.17

Thus the positive value of Z is 2.17.

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