Two bicyclists, 44 miles apart, begin riding toward each other on a long straight avenue. One cyclist
travels 16 miles per hour and the other 17 miles per hour. At the same time, Spot (a greyhound), starting
at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 39
miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet?

Explanation

The vertical asymptote

for the given function

According to the formula

The denominator will be undefined when

The vertical asymptotes are

For the horizontal function

Since the denominator degree is higher than the numerator

Then

The horizontal asymptote is

For the oblique asymptote

Since the degree of the numerator is not one degree greater than the denominator, then there are no slant asymptotes.

There are no oblique asymptote

Answer:

(g ◦ h) (x) = 16x² + 12x -4

Step-by-step explanation:

We have

g(x) = x² − 5x

h(x)= 4x + 4

(g ◦ h) (x) = g(h(x))

h(x) = 4x + 4

g(h(x)) = g(4x + 4)

= (4x + 4)² - 5(4x+4)         //substitute 4x + 4 wherever there is an s-term in

(4x + 4)² = 16x² + 32x + 16

5(4x + 4) = 20x + 20

(4x + 4)² - 5(4x+4)  = 16x² + 32x + 16 -(20x + 20)

= 16x² + 32x + 16 - 20x - 20

= 16x² +(32x - 20x) + (16-20)

= 16x² + 12x -4

Surface Area of rectangular pyramid is lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²].

The area of ​​a rectangular pyramid is equal to the sum of the areas of the sides and faces of the rectangular pyramid. A quadrilateral pyramid is a three-dimensional shape with only a rectangular base and triangles on either side of the base.

The area of ​​the base of the rectangle is calculated by multiplying the length of the rectangle by the width of the rectangle.

The area of ​​a rectangle with a pyramidal formula is determined by observing the width, length, and height of the base,

S.A. = lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²],

where l is the length of the bottom of the rectangle, w is the width of the bottom of the rectangle, and h is the height.

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The rejection region, or area of the rejection zone, is the significance level. The test's tail determines the direction of the rejection region. When the significance threshold is unknown, it is typically considered to be 5%.

A collection of values for the test statistic for which the null hypothesis is rejected constitutes a critical zone, sometimes referred to as the rejection region. For example, if the observed test statistic is in the critical range, the null hypothesis is rejected and the alternative hypothesis is accepted.

Consider the crucial value as a cut-off point at a particular importance level. If a test statistic falls on one side of the crucial value and leads to the null hypothesis being accepted, a test statistic falling on the other side will lead to the null hypothesis being rejected.

A set of values for the test statistic for which the null hypothesis is accepted is referred to as a confidence interval and is also referred to as the acceptance area. For example, if the observed test statistic is within the confidence interval, the null hypothesis is accepted and the alternative hypothesis is rejected.

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Answer: Ima say 6

Explanation: I don't have an explanation

Answer:

8/3 square inches

Explanation:

First, we need to get the height of the triangle BAC

Area of triangle = 1/2 * base * height

6 = 1/2 * 3 * height

12 = 3 * height

Height = 12/3

The height of triangle BAC is 4inches

Next is to get the height of EDF. Since they are both similar hence;

2/3 = h/4

3h = 2 * 4

3h = 8

h = 8/3

h = 8/3in

Hence the height of triangle EDF is 8/3in

Get the area of triangle EDF

Area of triangle EDF = 1/2 * 2 * 8/3

Area of triangle EDF = 8/3 square inches

Hence the area of triangle EDF is 8/3square inches

SOLUTION

Step1:Write out the formula

Step2; write out the parameters

Step3: Substitute into the formula and simplify

Step4: simplify the expression above

Then the rate becomes

Therefore the rate is 20.49

Data:

Retail price: $4500

Pays cash: -10%

hire purshast: $675 + 24(212.50)

-----------------------------------

1. Find the 10% of 4500:

2. Substract the 10% to the retail price:

-------------------------------------

1. Add 675 and (24*212.50):

-----------------------------------------

----------------------------

As the retail price 4500 is 100% which percent is 1725:

Here, we want to writw an inequality to describe the information given.

When we say at most, it means the expected values may be less than or equal to but can never be more than

Mathematically;

From the question, we are told that the maximum driving time is 3 hours; the inequality here will be;

For the distance d, we have;

The B  points are  ( 8, -2 ) of Endpoint B when M is the midpoint of line AB.

What is midpoint of a segment?

M is the midpoint of line AB.

Endpoint A is (4, 2).

Midpoint M is (6, 0)

Let mid points are ( x,y) and A points are  ( x₂ , y₂ ) and B points are ( x₁ , y₁)

         x = x₁ + x₂/2     ,    y = y₁ + y₂/2

         6 = x₁ + 4/2  ,         0 = y₁ + 2/2

          12 =  x₁ + 4        ,     0 = y₁ + 2

          x₁ = 12 - 4           ,   y₁  = -2

          x₁  = 8                 ,    y₁  = -2

So, the B  points are  ( 8, -2 )

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Answer:

11/2

Explanation:

Given:

To find:

The value of y

So we have;

Let's go ahead and apply the Division property of equality by dividing both sides of the equation by 2/5;

So the value of y is 11/2

Ok, so:

Let me draw the situation here below:

Ok, let's find the angle first:

For this, we shall make use of the trigonometric functions:

In this case, the most useful function which could help us to solve this problem is tan(x). This function relations the opposite side of the angle and its adjacent side, like this:

tan(x) = opposite side / adjacent side

So, if we replace the values:

tan(x) = 15/95

tan(x) = 0,15789474

To find x, we could use the inverse function of tan(x). This one is called arctan(x).

So, arctan(tan(x)) = arctan(0,15789474)

And this is:

x = 8.97 degrees

Now, we can affirm that the angle is 8.97 degrees, which is bigger than 8.5 degrees.

Now, what should be the length of the bottom for the ramp to be safe?

Let me draw the situation:

We know that the ramp is safe if the maximum safe incline is 8.5°. So, what should be the value of x for this occurs?

We use the trigonometric function tan(x) again.

tan(8.5°) = 15/x

Remember that tan(8.5°) is a number

Then, x = 15/tan(8.5°), and this is 100.36

So, we conclude that the lenght of the bottom should be at least, 100.36

Answer:

4 mph

Explanation :

Let us call x, the woman speed as she goes uphill

Now, we know that it took the woman 2 hours to go uphill; therefore, the distance covered is

4* (x)

shortly afterwards, when the woman returns she is walking at x + 2 mph; therefore, the distance she covers is

D = 4 (x +2 )

Since the uphill and the downhill distances ar the same, we have

4x = 2 (x +2 )

4x = 2x + 4

x = 2

Hence, going to the hill, the woman speed is 2 miles per goo

Solution

For this case we have the following:

x intercept 4: (4,0)

y intercept 2: (0,2)

Then we can find the slope like this:

then the equation is given by:

y= -1/2 x+ 2

and we can use x= 1 and we have y= 3/2

x= 2 , y= 1

Then two other points could be:

(1,3/2) and (2,1)

Answer:

  (c)  40.75°

Step-by-step explanation:

Given an isosceles triangle with one angle 98.5°, you want the measures of each of the other two angles.

The sum of angles in a triangle is 180°, so we have ...

  2x + 98.5° = 180° . . . . . . x is the unknown angle measure

  x +49.25° = 90° . . . . . . divide by 2

  x = 40.75° . . . . . . . . . . subtract 49.25°

The measure of one of the congruent angles is 40.75°.

The probability is [(X - μ) < 1.1] = 0.6046.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given: σ² = 64

Mean μ = 34

To find: Probability[(X - μ) < 1.1]

Computation:  Standard deviation σ = √σ²

Standard deviation σ = √64

Standard deviation σ = 8

Probability[(X - μ) < 1.1] = Probability[-1.1 < (X - μ) < 1.1]

Probability[(X - μ) < 1.1] = Probability[-1.1/(8/√38) < (X - μ) < 1.1/(8/√38)]

Using z table

The probability =  [(X - μ) < 1.1] = 0.6046.

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Given:

5 red marbles

4 blue marbles

1 green marble

Upon choosing green marble, we win $10

Upon choosing blue marble, we win $2

Upon choosing red marble, we win $0

It costs $3 to play each game.

To find:

The expected value of playing the game

Step by step solution:

Firstly we need to calculate the probablity of occuring of each event:

P (Choosing a red marble) = 5/10 = 1/2

P (Choosing a blue marble) = 4/10 = 2/5

P (Choosing a green marble) = 1/10 = 1/10

We will now associate the money related to each case:

= 1/2 × $0 + 2/5 × $2 + 1/10 × $10

= 0 + $ 4/5 + $1

= $ 1.8

The initial speed to the waterpark is 40 miles/hr.

The return speed is 60 miles/hr.

Given,

t = 3hr

Return speed = s +20m

Return time = 3 -1 = 2hrs

Solution:

s = d/t

s = d/3

d = 3s----1

s + 20 = d/t - 1

s + 20 = d/3-1

s + 20 = d/2

2s + 40 = d------2

Equating equations 1 and 2,

3s = 2s + 40

s = 40 miles/hr

The initial speed to the waterpark is 40 miles/hr.

Return speed = s +20

= 40+20

= 60 miles/hr

The return speed is 60 miles/hr.

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The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.

A parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given that parallelogram ABCD, has m∠ABC = 135° and the length of diagonal AC is 41 units.

The measure of length of side AD is 35 units and length of side AB is 7 units.

WE know that the opposite side of a parallelogram are same. Thus,

The length of segment CD = AB = 7 units.

Also, the length of diagonal AC =  41 units. Then;

The length of segment AE = 1/2 AC = 41/2 = 20.5 units.

Therefore, m∠BCD + m∠ABC  = 180

m∠BCD + 135  = 180

m∠BCD  = 180 - 135

m∠BCD = 45 degrees.

Hence, The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.

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Answer:

45

7

20.5

Step-by-step explanation:

You have a cone with surface area of 628.32 m². In order to find the volume of the cone you use the following formula:

V= 1/3 π r² h

r: radius of the base of the cone = 15m/2 = 7.5m

h: heigth of the cone

Then, you have to calculate first the height of the cone. To do that, you use the information about the surface area. You use the following formula:

S = πr² + πrl

l: diagonal of the cone

Then, you have to find l, and then you can calculate hYou solve for l from the surface area formula:

l = (S - πr²)/πr = (628.32 - π(7.5)²)/(π(7.5))

l = 19.16

To calculate the heigth of the cone you use the Pythagoras theorem, just as follow:

h = √(l²-r²) = √((19.16)²-(7.5)²) = 17.63m

Next, you can replace the values of h and r into the formula for the Volume:

V= 1/3 π r² h = (1/3)π (7.5m)²(17.63m) = 1038.5m³

Hence, the volume of the given cone is 1038.49 m3

a) The opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.

b) The sum of the given number and its opposite will be 7.928.

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

The given number is as,

3, 7.5, and -2(2/3)

a)

The opposite number is obtained as 1 by dividing the given number,

⇒ 1 / 3 = 0.33

⇒ 1 / 7.5 = 0.133

⇒ 1 / -2(2/3) = -0.375

b)

The sum of the given number and its opposite is,

= 3+0.33 + 7.5 + 0.133+ (-2(2/3) ) + (-0.375)

= 7.928

Thus, the opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.and the sum of the given number and its opposite will be 7.928.

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H=16.4

Step-by-step explanation:

1.2x4=4.8

3.9x4=15.6

so

4.1x4=16.4

Answer:

Step-by-step explanation:

Set up a proportion. x stands for hours that we need to find out.

[tex]\frac{6hrs}{74score} = \frac{xhrs}{98score}\\ 6(98)=74(x)\\588= 74x\\588/74=x\\8=x[/tex]

**the answer was 7.9 BUT I rounded it to 8.

Lisa would need to study for 8 hours to get a score of 98.

Option B is the graph of the given function.

The height of the parallelogram is 6.97m.

It is important to kite that the aea of a parallelogram is calculated as:

= Base × Height

In this case, the base is given as 8.6m. Therefore, the height will be:

Area = Base × Height

59.9 = 8.6 × Height

Now, we will find the height

Height = 59.9 / 8.6

Height = 6.97m

The complete question is written below.

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The area of the parallelogram is 59.9m² and.the vase is 8.6m,What is the height

Start making the graph of the situation

from this, we can understand that x is Coreys' initial distance, z is Coreys' final distance, and y will be how many feet had Corey to step back in order to gain a better view.

Using the red triangle we find x through the tan of the given angle

Using the blue triangle we find z through the tan of the given angle the same way as before

finally, find y as the difference between z and x

Corey had to go back 59.71 ft to gain a better view.

we have

S= 4*(pi)*r^2​

solve for r

That means ------> isolate the variable r

step 1

Divide by 4*(pi) both sides

so

S/(4*pi)=r^2

step 2

Square root both sides

so

1110800. Equity Account will be after stock dividends

Similar to a cash dividend, however instead of cash, stocks are given out. A stock dividend will increase the number of shares outstanding while lowering the stock price.

In this issue, there are 460000 shares outstanding at a price of $30, which equals 13800000

Equity's total market value is $13800000.

Each shareholder will get a 20% increase in stock, and the number of existing shares will increase as a result of the 20% stock dividend.

Shares outstanding after dividend announcement total 460000 + 46000 ×20% =552000.

The number of outstanding common shares will rise to 552000 as a result of the issuance of 92000 more shares.

Common stock only contains the par value; for example, if the market price of a share is $30 and the par value is $1, the excess amount of $29×92000:2668000 is added to the capital surplus account. It will total 861000 + 2668000=3529000.

Due to the absence of any monetary transactions, the total owners' equity is unaltered.

The retained earnings will be decreased by 92000 × 30 = 2760000, resulting in 3870800 – 2760000=1110800.

Equity Account will be after stock dividends.

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Using division, If you have 7/8 of a cup of tomato sauce and you must fill small containers with exactly 1/4 of a cup of tomato sauce, then number of containers can fill completely is 3 containers

The total  quantity of tomato sauce that you have = 7/8 of a cup

The quantity of tomato sauce with you must fill small containers = 1/4 of a cup

To find the number of containers that you can fill completely, you have to use division

Number of containers can fill completely = The total  quantity of tomato sauce that you have / The quantity of tomato sauce with you must fill small containers

= 7/8 ÷ 1/4

= 7/8 × 1/4

= 7/2

= 3.5

≈ 3 containers

Hence, using division, if you have 7/8 of a cup of tomato sauce and you must fill small containers with exactly 1/4 of a cup of tomato sauce, then number of containers can fill completely is 3 containers

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The area of a sector of a circumference is given by the following formula:

Where r is the radius of the circumference, and θ is the angle of the sector in radians.

The radius is already known: 15cm.

We need to estimate the angle of the shaded region. The shaded region and the sector whose angle is 72° form together a 180° angle. (This is according to the figure. That is not said in an explicit way but we will need to assume that since there is not enough information to calculate the area if it is otherwise.)

Then, the angle of the shaded area, plus 72° is 180°:

Now, before applying the formula we need to express the angle in radians. Recalling that 180° is equal to π radians:

Now, we have the angle in radians. We can use the equation: