What is the first speed at which the ratio of stopping distance to speed is greater than 3 to 1

50 mph
40 mph
20 mph

Answer:

The first option is the correct one, the area of the shaded portion of the circle is

[/tex](5 \pi -11.6)ft^2[/tex]

Step-by-step explanation:

Let us first consider the triangle + the shadow.

The full area of the circle is the radius squared times pi, so

A=[tex](5 ft)^2 \cdot \pi \\25 ft^2 \cdot \pi[/tex]

Since [tex]\frac{72^{\circ}}{360^{\circ}}=\frac{1}{5}[/tex], the area of the triangle + the shaded area is one fifth of the area of the whole circle, thus

[tex]A_1=\frac{1}{5}25 ft^2 \cdot \pi\\ =5 ft^2 \cdot \pi[/tex]

If we want to know the area of the shaded part of the circle, we must subtract the area of the triangle from [tex]A_1[/tex].

The area of the triangle is given by

[tex]A_{triangle}=\frac{1}{2}\cdot (2.9+2.9)ft \cdot 4 ft\\= 11.6 ft^2[/tex]

Thus the area of the shaded portion of the circle is

[tex]A_1-A_{triangle}=5 \pi ft^2-11.6ft^2\\= (5 \pi -11.6)ft^2[/tex]

Answer:

A

Step-by-step explanation: i did the test and review

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The correct option would be A. an = 3 + 4n

You may test my substituting values in:

3 + 4(1) = 7

3 + 4(2) = 11

etc

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- Ally ✧  

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Answer:

a

Step-by-step explanation:

Answer:

Number of week day hours purchased  is 5

Step-by-step explanation:

Total number of Parking hours purchased = 26 parking hours

Parking cost on weekdays = $2 per hour

Parking costs on weekends = $10 per hour

Total amount spent on parking =  $220.

To Find:

Number of week days purchased = ?

Solution:

Let  

The number of week days purchased be x

The number of weekends purchased be  y

We know that the total hours purchased is 26

So,

x+y = 26

y = 26-x------------------------------------------------------(1)

Now the total cost is 220

(Total number of weekdays X cost per weekday ) +(Total number of weekends + cost per weekend) =220

Substituting the values

=>[tex]x\times 2 + y \times 10[/tex] = 220

=>[tex]x \times 2 + (26-x) \times 10 =220[/tex]

=>2x + 260 -10x =220

=>260 -8x = 220

=>260 -220 =8x

=>40 = 8x

=>x=[tex]\frac{40}{8}[/tex]

x= 5-------------------------------------------(2)

Now substituting (2) in (1) we get

y= 26-5

y= 21

Answer:

x=4.8473 cups

Step-by-step explanation:

Concentration of Liquids

It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by

[tex]\displaystyle C=\frac{x}{y}[/tex]

It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.

Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is

x-1 cups of juice.

The new concentration is

[tex]\displaystyle \frac{x-1}{x}[/tex]

The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is

[tex]\displaystyle x-1-\frac{x-1}{x}[/tex] cups of juice.

Simplifying, the cups of juice are

[tex]\displaystyle \frac{\left (x-1\right)^2}{x}[/tex]

The new concentration is

[tex]\displaystyle \frac{\left (x-1\right)^2}{x^2}[/tex]

For the third time, we now have

[tex]\displaystyle \frac{\left (x-1\right)^2}{x}-\frac{\left (x-1\right)^2}{x^2}[/tex] cups of juice.

Simplifying, the final amount of juice is

[tex]\displaystyle \frac{\left (x-1\right)^3}{x^2}[/tex]

And the final concentration is

[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}[/tex]

According to the conditions of the question, this must be equal to 50% (0.5)

[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}=0.5[/tex]

Taking cubic roots

[tex]\displaystyle \sqrt[3]{\frac{\left (x-1\right)^3}{x^3}}=\sqrt[3]{0.5}[/tex]

[tex]\displaystyle \frac{\left (x-1\right)}{x}=\sqrt[3]{0.5}[/tex]

Operating and joining like terms

[tex]\displaystyle x-\sqrt[3]{0.5}\ x=1[/tex]

Solving for x

[tex]\displaystyle x=\frac{1}{1-\sqrt[3]{0.5}}[/tex]

[tex]x=4.8473\ cups[/tex]

Let's test our result

Final concentration:

[tex]\displaystyle \frac{\left (4.8473-1\right)^3}{4.8473^3}=0.5[/tex]

After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa. Thus mom gave $ 320 to each girl

Solution:

Given that Lily and Elsa are both college students

Before mom gave them this months allowance lily had $750 and Elsa had &215

Amount (in dollars) with Lily and Elsa already is given as:

amount with Lily = $ 750

amount with Elsa = $ 215

After mom gave each girl an equal amount of money for this months allowance, lily had twice as much money as Elsa

Let "x" be the equal amount of money which mom gave to Lily and Elsa

Now amount with Lily and Elsa after mom gave equal amount is:

amount with Lily = amount with Lily already + x

amount with Lily = 750 + x

amount with Elsa = amount with Elsa already + x

amount with Elsa = 215 + x

Given that lily had twice as much money as Elsa

Amount with lily = 2(amount with elsa)

750 + x = 2(215 + x)

750 + x = 430 + 2ax

2x - x = 750 - 430

x = 320

Therefore mom gave $ 320 to each girl

Answer:

89.6%

Step-by-step explanation:

The probability a random person shares your birthday is 1/365, or 0.27%.  That means the probability that they don't share your birthday is 364/365, or 99.73%.

So the probability that you meet 40 people who don't share your birthday is:

P = (364/365)^40

P = 89.6%

The probability that it takes meeting more than 40 people before you meet someone who shares the same birthday as you is roughly 10.13% given that the probability of meeting a random person who has the same birthday as you is approximately 0.27%. This is calculated as the complement of the probability that we don't encounter a matching birthday in 40 people.

The probability of meeting a random person who shares the same birthday as us is 1/365, approximately a 0.27% chance. Now, to calculate the probability that it requires meeting more than 40 people before finding someone who has the same birthday is essentially the complement of the probability that we find someone with the same birthday in 40 people or less.

We can start by calculating the probability of not meeting someone with the same birthday in one encounter which is 364/365 (approximately 0.9973). The probability that we don’t encounter a matching birthday in 40 people is (364/365)^40 (approximately 0.8987). Subsequently, The probability that it takes meeting more than 40 people before you meet someone who has the same birthday is the complement of this probability, which is 1 - 0.8987 = 0.1013 or approximately a 10.13% chance.

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Answer: The outbound trip is 18 miles per hour

Step-by-step explanation:

Let x represent the speed of the plane.

An aircraft carrier made a trip. Let us assume that this trip was outbound. The trip there took 5 hours.

Distance = speed × time. Therefore

Distance = 5x

The trip back took 6 hours. It averaged 3 mph faster on the trip there then on the return trip. This means that the speed on the trip back is x - 3 mph.

Distance = 6(x-3) = 6x - 18

Since the distance is the same,

5x = 6x - 18

6x - 5x = 18

x = 18

The speed on return or inbound trip would be 18 - 3 = 15 mph

Answer:

Bakery will sell  [tex]4w+6[/tex] loaves of bread next year.

Step-by-step explanation:

Given:

Number of loaves of bread sold last year = 'w'

Now Given:

This year, the bakery sold three more than twice the number of loaves of bread sold last year.

Framing in equation form we get

Number of loaves of bread sold this year = [tex]2w+3[/tex]

Also Given:

next year the bakery plans on selling twice the number of loaves of bread sold this year.

framing in equation form we get;

Number of loaves of bread bakery will sell next year = [tex]2(2w+3) = 4w+6[/tex]

Hence Bakery will sell  [tex]4w+6[/tex] loaves of bread next year.

The bakery expects to sell  4w + 6  loaves of bread next year.

Let's break down the problem step by step:

1. Number of loaves sold this year:

  - Last year, the bakery sold  w  loaves of bread.

  - This year, the bakery sold three more than twice the number of loaves sold last year.

  - Therefore, the number of loaves sold this year is:

   [tex]\[ 2w + 3 \][/tex]

2. Number of loaves expected to be sold next year:

  - Next year, the bakery plans to sell twice the number of loaves sold this year.

  - Therefore, the number of loaves expected to be sold next year is:

   [tex]\[ 2 \times (2w + 3) \][/tex]

3. Simplify the expression:

  - Distribute the 2 in the expression:

  [tex]\[ 2 \times (2w + 3) = 2 \times 2w + 2 \times 3 = 4w + 6 \][/tex]

Therefore, the bakery expects to sell  4w + 6  loaves of bread next year.

Answer:

[tex]10|y|[/tex]

Step-by-step explanation:

We have been given that the vertices of a triangle are A (5, 0), B (x, y) and C (25, 0). We are asked to find the area of the given triangle.

We will use area formula for triangle with vertices A, B and C as given below:

[tex]|\frac{A_x(B_y-C_y)+B_x(C_y-A_y)+C_x(A_y-B_y)}{2}|[/tex]

Upon substituting the given coordinates of points A, B and C in above formula, we will get:

[tex]|\frac{5(y-0)+x(0-0)+25(0-y)}{2}|[/tex]

[tex]|\frac{5(y)+x(0)+25(-y)}{2}|[/tex]

[tex]|\frac{5y+0-25y}{2}|[/tex]

[tex]|\frac{-20y}{2}|[/tex]

[tex]|-10y|[/tex]

[tex]10|y|[/tex]

Therefore, the area of the given triangle would be [tex]10|y|[/tex].

Answer:

12

Step-by-step explanation:

3x + 7 = 5x - 17

5x - 3x = 7 + 17

2x = 24

x = 12

Answer: [tex]\$1.99[/tex]

Step-by-step explanation:

The missing figure is attached.

For this exercise you need to analize the information provided.

You can observe in the picture attached that the cost of a package of wrapping paper is $3.76 and each bow costs $1.05.

Since Inez bought 1 package of wrapping paper and 4 bows, you get that the total amount of money she spent was:

[tex]Total=\$3.76+4(\$1.05)\\\\Total=\$7.96[/tex]

According to the data given in the exercise, Inez wrapped 4 identical gifts.  So, let be "x" the cost for wrapping each gift.

This is:

[tex]x=\frac{\$7.96}{4}\\\\x=\$1.99[/tex]

1.99

Step-by-step explanation:

Answer:

  no

Step-by-step explanation:

The ratio is ...

  boys : girls = 42 : 56 = (14·3) : (14·4) = 3 : 4 . . . . not 5:6

Emma is not correct.

Answer:

Step-by-step explanation:

[tex]E=\frac{1}{2}mv^2[/tex]

All the variables on the right are being multiplied together then the whole mess is being divided by 2.  Let's get rid of the 2 first.  The undoing of division is multiplication, so we will begin by multiplying both sides by 2 to get

[tex]2E=mv^2[/tex]

Next we will move the m. The undoing of multiplication is division.  So we divide both sides by m to get

[tex]\frac{2E}{m}=v^2[/tex]

The undoing of a square is to take the square root, so we will do that to both sides giving us, finally

[tex]\sqrt{\frac{2E}{m} }=v[/tex]

Answer:

d

Step-by-step explanation:

Answer:

-6 and -7 are the roots

Step-by-step explanation:

The quadratic equation given is:

[tex]x^{2}+13x=-42\\Taking\ -42\ to\ left\ hand\ side\ we\ get\\x^{2} +13x+42=0[/tex]

We can factorise the equation as:

[tex]x^{2}+6x+7x+42=0\\(x^{2}+6x)+(7x+42)=0\\[/tex]

Taking x common from the first bracket and 7 common from the second bracket we get:

[tex]x(x+6)+7(x+6)[/tex]

Taking (x+6) common from both terms we get:

[tex](x+6)(x+7)=0[/tex]

x= -6 or x=-7

Hence -6 and -7 are the roots of the given quadratic equation.

Answer:

Step-by-step explanation:

All the masses here are based on the main mass of the sand.  So we will call sand "x".  If there is two times as much cement as sand, then cement is 2x; if there is three times as much stone as sand, then stone is 3x.  All of these added together equal a mass of 600 kg:

x + 2x + 3x = 600 so

6x = 600 and

x = 100 kg

There are 100 kg of sand.  That means that there is 200 kg of cement and 300 kg of stone

Answer:

200 kg

Step-by-step explanation:

Total weight of the mixture = 600kg

Let the weight of the cement in the mixture be x kg.

According to the problem statement, there is twice as much cement as sand, therefore the weight of sand relative to cement will be 1/2, i.e.

sand weight = 1/2x =0.5x

Similarly, weight of stone will be three times as much as sand.

Meaning, stone weight = 3*0.5x=1.5x

Total weight of all the components will be

cement weight + sand weight  + stone weight  =

x + 0.5x + 1.5x = 3x

But 3x = 600,

x = 600/3= 200 kg

Answer:

The store must sell 35 bikes to break even.

Step-by-step explanation:

115-65 = 50. 1750 divided by 50 = 35.

Answer:you must sell 35 bikes each month to break even

Step-by-step explanation:

The point at which you break even is the point when there is neither profit nor loss. It mean that

Revenue - cost = 0

Revenue = cost

The cost of operating the bicycle per month is ​$1750

The store pays an average of ​$65 per bike. Let x represent the number of bikes that the store gets in a month. The total cost of x bikes would be

1750 + 65x

The average selling price of each bicycle is ​$115. Total revenue from x bikes would be

115 × x = 115x

Therefore, to break even,

1750 + 65x = 115x

115x - 65x = 1750

50x = 1750

x = 1750/50 = 35

Answer:

Step-by-step explanation:

1. ∠PQR is an alternate interior angle with the one marked 40°, so it has the measure 40°.

∠PRQ is an alternate interior angle with the one marked 60°, so it has the measure 60°.

Among the answer choices, the one describing ∠PQR as 40° is the only correct one.

__

2. ∠BAD = 2×∠BAE

  130 = 2(9x + 2) . . . substitute the given expressions

  65 = 9x + 2 . . . . . divide by 2

  63 = 9x . . . . . . . . .subtract 2

  7 = x . . . . . . . . . . . .divide by 9

__

3. Think again. Anything being rotated follows a circular path. Circular paths with different radii and the same center are concentric circles.

Straight lines connecting the pre-image and image points will be parallel (and different lengths), but the question is concerned with paths, not endpoints.

Why the path is described as "concentric circles," we're not sure. The path for a 90° rotation will be a 90° arc. It is perfectly reasonable to describe the paths of the two points as concentric arcs, rather than concentric circles. See the attachment.

__

4. Correct. The triangle inequality requires the sum of the two shortest side lengths exceed the longest side length. Here, that means 2+5 > 5 (true). The "toothpicks" meet the requirements of the triangle inequality, so will make a triangle.

The "triangle sum theorem" has to do with angles, not side lengths.

Answer:

It takes 16 days to quadruple its population.

Step-by-step explanation:

The population of the virus can be represented by the following exponential function.

[tex]A(t) = A_{0}e^{rt}[/tex]

In which A(t) is the population after t days, [tex]A_{0}[/tex] is the initial population and r is the growth rate.

In this problem, we have that:

[tex]A(8) = 2A_{0}[/tex]

So, we use this to find the value of r.

[tex]A(t) = A_{0}e^{rt}[/tex]

[tex]2A_{0} = A_{0}e^{8r}[/tex]

[tex]e^{8r} = 2[/tex]

Applying ln to both sides

[tex]8r = 0.6931[/tex]

[tex]r = 0.0867[/tex]

How long will it take to quadruple its population?

This is t when [tex]A(t) = 4A_{0}[/tex]

[tex]A(t) = A_{0}e^{rt}[/tex]

[tex]4A_{0} = A_{0}e^{0.0867t}[/tex]

[tex]e^{0.0867t} = 4[/tex]

Again we apply ln to both sides.

[tex]0.0867t = 1.39[/tex]

[tex]t = 16[/tex]

It takes 16 days to quadruple its population.

The number of days it takes to quadruple it's population is; 16days

According to the question;

Therefore;

8days = 2A.

We are required to determine how long it will take to quadruple it's population;

Let no. of days required = x days.

By cross multiplication; we have;

By dividing through by 2A; we have;

Read more:

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Answer:

9.692%

Step-by-step explanation:

We have been given that a manufacturing process produces a critical part of average length 120 ​millimeters, with a standard deviation of 3 millimeters. All parts deviating by more than 5 millimeters from the mean must be rejected.

5 millimeters below mean would be [tex]115[/tex] and 5 millimeters above mean would be [tex]125[/tex].

Corresponding z values for 115 and 125 would be:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{115-120}{3}[/tex]

[tex]z=\frac{-5}{3}[/tex]

[tex]z=-\frac{5}{3}[/tex]

[tex]z=\frac{125-120}{3}[/tex]

[tex]z=\frac{5}{3}[/tex]

Now, we need to find [tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})[/tex] using normal distribution table.

[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=P(z<-1.66)+P(z>1.66)[/tex]

We know that [tex]P(z>1.66)=1-P(z<1.66)[/tex].

[tex]P(z>1.66)=1-0.95154 [/tex]

[tex]P(z>1.66)=0.04846[/tex]

[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=0.04846+0.04846[/tex]

[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=0.09692[/tex]

Now, we need to convert 0.09692 into percentage as:

[tex]0.09692\times 100\%=9.692\%[/tex]

Therefore, 9.692% of parts must be​ rejected on​ average.

About 0% of the parts would be​ rejected, on​ average.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

where μ is the mean, x = raw score and σ is the standard deviation.

Given μ = 120, σ = 3. For z > 5:

P(z > 5) = 1 - P(z < -38.3) = 1 - 1 = 1 = 0%

About 0% of the parts would be​ rejected, on​ average.

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Answer: Averages less than 2litres per day

Step-by-step explanation:

The normal range of urine excreted per day is between 1 to 2 litres, but the kidney must produce a minimum urine volume of 500mL per day, to get rid of body waste, anything below that is abnormal, and not good for the body

Answer:

187 eggs

Step-by-step explanation:

Correct Question:

After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has 7 eggs left over. Each carton holds 12 eggs. How many eggs did Dale collect?

Dale filled up each carton with 12 eggs (that's the full capacity.

Dale filled up 15 full cartons.

So, the eggs he collected in carton:

15 * 12 = 180 eggs

He still had 7 left over, so total number of eggs that Dale collected is:

180 + 7 = 187 eggs

Answer:

The answer to your question is letter A

Step-by-step explanation:

Process

1.- Find two points of the line

A (1, 4)    B ( -1, 5)

2.- Find the slope of the line

     [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

     [tex]m = \frac{-5 - 4}{-1 - 1}[/tex]

     [tex]m = \frac{-9}{-2} = \frac{9}{2}[/tex]

3.- Find the equation of the line

     y - y1 = m(x - x1)

    y - 4 = 9/2(x - 1)

    2y - 8 = 9x - 9

    9x - 2y = - 9 + 8

    9x - 2y = - 1

4.- Convert the equation to a inequality,

    9x - 2y ≤ -1

Answer:

  14.5 m

Step-by-step explanation:

Let x represent the length of the diagonal. Then the length of the rectangle is (x-3) and its width is (x-8). The area is the product of these, so is ...

  (x -3)(x -8) = 74

  x^2 -11x +24 = 74 . . . . eliminate parentheses

  x^2 -11x = 50 . . . . . . . .subtract 24

  x^2 -11x +30.25 = 80.25 . . . . add 30.25 to complete the square

  (x -5.5)^2 = 80.25 . . . . . . write as square

  x - 5.5 = √80.25 ≈ 8.958 . . . . take the square root

  x = 8.958 + 5.5 = 14.458 . . . . .add 5.5

The length of the diagonal is about 14.5 meters.

Answer:

Step-by-step explanation:

The diagram of the rectangle, ABCD is shown in the attached photo. The diagonal of the rectangle forms a triangle, ABC

Applying Pythagoras theorem,

d^2 = (d - 8)^2 + (d - 3 )^2

d^2 = d^2 - 16d + 64 + d^2 - 6d + 9

d^2 = 2d^2 - 22d + 73

d^2 - 22d + 73 = 0

d^2 = 22d - 73 - - - - - - 1

If the area is 74 m^2, it means that

(d- 8)(d- 3) = 74

d^2 - 11d + 24 = 74

d^2 = 74 - 24 + 11d

d^2 = 50 + 11d - - - - - - - -2

Equating equation 1 and 2, it becomes

22d - 73 = 50 + 11d

22d - 11d = 50 + 73

11d = 123

d = 123/11 = 11.182

diagonal = 11.2 m to the nearest tenth.

Answer:

2 + (13/4)x = 1/2 + (11/2)y

Step-by-step explanation:

Let each jar of paint used by Liam be x

Let each jar of paint used by Evan be y.

Liam uses 2 quarts of yellow paints and adds 3 1/4 jars of blue paint. so we have

2 + 3 1/4x

= 2 + (13/4)x

Since Evan also uses 1/2 quarts of yellow paints and add 5 1/2 jar of red paint, we have

1/2 + 5 1/2y

= 1/2 + (11/2)y

Since they end up with the same volume of paint, we have

2 + (13/4)x = 1/2 + (11/2)y

Final answer:

The equation to show that Liam and Evan end up with the same volume of paint, considering all quantities are in quarts, is 2 + 3.25 = 0.5 + 5.5.

Explanation:

To solve the problem where Liam and Evan end up with the same volume of paint, we can write an equation that sets the total volume of paint used by each person equal to each other. Since Liam uses 2 quarts of yellow paint and adds 3 1/4 (which is equivalent to 3.25) jars of blue paint and Evan uses 1/2 quart of yellow paint and adds 5 1/2 (equal to 5.5) jars of red paint, the equation comparing their total amounts of paint in quarts can be written as:

2 + 3.25 = 0.5 + 5.5

Before writing this equation, we need to ensure that both expressions represent quantities in the same unit. We confirm that all the amounts are given in quarts, so there is no need to convert units in this case. The equation illustrates that the total volume of paint used by Liam and Evan is equal.

Answer:

(c) [tex]\left\ ({{4} \atop {1}} )\right.[/tex] [tex]0.25^{1} 0.75^{3}[/tex]

Step-by-step explanation:

As given in the statement, we have:

Out of 4 games pieces, 1 is winner.

Probability to win =p= [tex]\frac{1}{4}[/tex]

Jeff has game pieces = n = sample size = 4

As we need to find the probability that he wins exactly 1 prize, we will use binomial probability here :

[tex]P (X = k) = \left\ ({{n} \atop {k}} )\right. p^{k} (1-p)^{n-k} \\[/tex]

Evaluating at k=1, (k=1 as we need to find probability for exactly 1 prize won)

put n = 4, p =[tex]\frac{1}{4}[/tex]

P (X = 1) =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (1-0.25)^{4-1}[/tex]

P =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (0.75)^{3}[/tex]

Which is the probability that he wins exactly 1 prize and is option c.

Probability (Jeff wins 1 price in 4 game pieces) = C] [tex](4 c 1)(0.25)^1(0.75)^3[/tex]

Important Information : Probability (Winning a price) = 1 / 4 = 0.25

Probability (Not winning price) = 1 - Pr (Winning Price) = 1 - 0.25 = 0.75

Using Binomial Probability : Pr (X = r) = [tex]N c r . P^r . Q^(n-r)[/tex] .

Here N = number of trials (4 game pieces here) , P = Probability of Success (of winning price = 0.25) , R = Number of Success (1 price) , Q = Probability of failure (of not winning price = 0.75) ,

So, Probability = [tex]4 c 1 (0.25)^1 (0.75)^3[/tex]

To learn more about Probability, refer https://brainly.com/question/13609688?referrer=searchResults

Answer:

The real roots are

[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]

The sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]

Step-by-step explanation:

The given quadratic equation is [tex]8x^2+12x-14[/tex] has two real roots.

To find the roots .

[tex]8x^2+12x-14=0[/tex]

Dividing the above equation by 2

[tex]\frac{1}{2}(8x^2+12x-14)=\frac{0}{2}[/tex]

[tex]4x^2+6x-7=0[/tex]

For quadratic equation [tex]ax^2+bx+c=0[/tex] the solution is [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Where a and b are coefficents of [tex]x^2[/tex] and x respectively, c is a constant.

For given quadratic equation

a=4, b=6, c=-7

[tex]x=\frac{-6\pm\sqrt{6^2-4(4)(-7)}}{2(4)}[/tex]

[tex]=\frac{-6\pm\sqrt{36+112}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{148}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{37\times 4}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{37}\times\sqrt{4}}{8}[/tex]

[tex]=\frac{-6\pm\sqrt{37}\times 2}{8}[/tex]

[tex]=2\frac{(-3\pm\sqrt{37})}{8}[/tex]

[tex]=\frac{-3\pm\sqrt{37}}{4}[/tex]

[tex]x=\frac{(-3\pm\sqrt{37})}{4}[/tex]

The real roots are

[tex]x=\frac{(-3+\sqrt{37})}{4}[/tex] and [tex]x=\frac{(-3-\sqrt{37})}{4}[/tex]

Now to find the sum of the squares of these roots

[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3+\sqrt{37}-3-\sqrt{37}}{4}[/tex]

[tex]=\frac{-6}{4}[/tex]

[tex]=\frac{-3}{2}[/tex]

[tex]\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3}{2}[/tex]

Therefore the sum of the squares of these roots is [tex]\frac{-3}{2}[/tex]

Answer:

B. $337.50

Step-by-step explanation:

1.5% of $22,500 is 337.5

Answer:

B. $337.50

Step-by-step explanation:

Answer:

Each DVD cost for Hector at $17.80.

Step-by-step explanation:

Total Money Spent = $36.75

Number of DVD to buy = 2

Sales tax = $2.15

Amount of Coupon to be used = $1.00

We need to find the cost of each DVD.

Let the Cost of each DVD be 'x'.

Now We can say that Total Money spent on DVD's is equal to Number of DVD to buy multiplied by Cost of each DVD plus Sales Tax minus Amount Coupon used.

Framing in equation form we get;

[tex]2x+2.15-1=36.75[/tex]

Solving the equation to find the value of x we get;

[tex]2x+1.15=36.75\\\\2x=36.75-1.15\\\\2x= 35.6\\\\x=\frac{35.6}{2}= \$17.8[/tex]

Hence Each DVD cost for Hector at $17.80.

Answer:

Only one.

Step-by-step explanation:

Given that there are 25 cookie of the same type in a cookie jar.

We have to select 4 cookies from these 25.

Since they are all the same type, they are identical.

The question is

How many ways can you choose 4 cookies from a cookie jar containing 25 cookies of all the same type?

There is no difference if we take any four cookies from these 25.

Hence no of different ways = 1

Only one is the answer.

Answer:

Step-by-step explanation:

25 P4=25×24×23×22=303600

Answer:

The answer is option is (4) y ≤ 14

Step-by-step explanation:

The given function, y = - 0.5[tex](x + 10)^{2} + 14[/tex]

We have to find the range of this function. If we take the first part of the function alone we can see that it is always negative or zero. So the maximum value of the function is 14.

This happens when we make the first part zero and for that we put x = -10.

So the maximum value of the function occurs at x = -10 and that value is y = 14.

Hence the range is y ≤ 14.

The answer is option is (4) y ≤ 14