Robert buys last year's best-selling novel, in hardcover, for $22.40. This is with a 20% discount from the original price. What was the original price of the novel?

The vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).

Herein we find the expression of a quadratic equation in vertex form, whose definition is shown below:

4 · p · (y - k) = (x - h)²      (1)

Where:

h, k - Coordinates of the vertex.

p - Distance from the vertex to the focus.

Then, the vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).

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Answer:

Step-by-step explanation:

more taking a shower you use almost 3 gallons per a shower

Answer:

x=19

Step-by-step explanation:

All of the angles add up to 180 degrees since it is a straight angle. So, the equation is:

3x+7+90+x+7=180

You combine like terms:

4x+104=180

Then you subtract on both sides:

4x=76

Then you divide by 4 on both sides:

x=19

Answer:

here is the answers

Step-by-step explanation:

sample:

1. 4x = 68

x = 68/4

x = 17

Solution :

1) x + 2x + x = 68

>> 4x = 68

>> x = 68 / 4

>> x = 17

2) x + y + 3y = 45

>> x + 4y = 45

>> 17 + 4y = 45

>> 4y = 45 - 17

>> 4y = 28

>> y = 28 / 4

>> y = 7

3) x + y - 4z = -32

>> 17 + 7 - 4z = -32

>> 24 - 4z = -32

>> -4z = -32 - 24

>> -4z = -56

>> z = 56 / 4

>> z = 14

4) x + y + z = ?

>> 17 + 7 + 14

>> 24 + 14

>> 38

5) -x + 8x = 63

>> 7x = 63

>> x = 63 / 7

>> x = 9

6) 4x + 3x - x = 42

>> 7x - x = 42

>> 6x = 42

>> x = 42 / 6

>> x = 7

Answer:

X= 1/y

Step-by-step explanation:

[tex]y = 1 - \frac{1}{ \sqrt{1} - \frac{1}{1 - x} } \\ y = 1 - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{ \frac{1 - x - 1}{1 - x} } \\ y - 1 = - \frac{1 - x}{ - x} \\ y - 1 = \frac{1 - x}{x} \\ yx - x = 1 - x \\ yx = 1 \\ x = \frac{1}{y} [/tex]

Answer:

(r+21 ) / 4

Step-by-step explanation:

as we can see DF = FM
and DF = 4R ,  FM =r+21

so,
4R = r+21
=> R= (r+21)/4

Answer:

the length of her garden will have to be 5.5ft

22÷4=5.5

Answer:

6.8%

Step-by-step explanation:

[tex]\frac{21447.20}{315400}[/tex]  When you divide this, you get 0.068.  This is in decimal form.  To change to a percent move the decimal to places to the right 6.8%

Answer: Answer choice 'B'

Step-by-step explanation:

4.00 + 0.75 + 0.40 + 0.03 = $5.18. This is Jill's amount.

3.00 + 0.40 + 0.02 = $3.42. This is Mark's amount.

To find out how much more money Jill has in comparison to how much mark has, we need to subtract Jill's money by Mark's money ($5.18 - $3.42)

if done correctly, your answer should be $1.76 (answer 'B')

Answer:

x = 84

Step-by-step explanation:

-12(x+12) + 1177 = 10 + 15

-12x - 144 + 1177 = 25

1033 = 25 + 12x

1008 = 12x

x = 84

Answer:

Mathematics shaping the modern world.

Answer:

You will translate A up until it is equal with A', then you will reflect the figure over the line of symmetry that will be half way between line segments CD and C'D'

Step-by-step explanation:

I am not sure if the polygon is drawn on a coordinate plane.  I cannot see any horizontal or vertical lines to tell you exactly how many units to move up.

The value of the function f(3) is 1

The graph represents the given parameter

The value of f(3) implies that we calculate the value of the function when x = 3

From the graph, we have

f(x) = 1, when x = 3

This means that

f(3) = 1

The above is calculated by substituting 3 for x in the equation f(x) = 1

Hence,  the value of f(3) is 1

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Answer:

At 65mph the car traveled 195 miles in 3hrs.

So divide 195 miles by 80mph to get 2.4375 hrs

Answer:

[tex]\sf p =\sqrt{\dfrac{q+3}{5}}[/tex]

Step-by-step explanation:

To find p in terms of q, we have to isolate p.

[tex]\sf \sqrt{(5p^2 - 1)^2}-2 = q\\\\[/tex]

 5p² - 1 - 2 = q

      5p² - 3 = q

Add 3 to both sides,

              5p² = q + 3

Divide both sides by 5,

                [tex]\sf p^2 = \dfrac{q+3}{5}\\\\\text{Take square root,}\\\\p =\sqrt{\dfrac{q+3}{5}}[/tex]

There is a 96.37% probability that the company will find 2 or more defective products.

There is a 2.08% probability that the company will find 4 or more defective products.

There is a 0.02% probability that the company will find 5 or more defective products. So company will give profit.

There are only two possible outcomes for each product: either it is defective or it is not. The binomial distribution is used to answer this question because each product's defect probability is independent of all other products.

Binomial probability distribution

The probability of precisely x successes on n repeated trials is known as the binomial probability.

[tex]P_x = \;^nC_r.p^x.q^{n-x}[/tex]

Where,

Px = binomial probability,

 [tex]\;^nC_r =[/tex] number of combination

p = probability of success on a single trial

q = probability of failure on a single trial = (1 - p)

n = number of trials

x = number of times for a specific outcome within n trials

So, from question,

1) The probability that, 2 or fewer defective products is;

P(X≤2) = P(X=0) +  P(X=1)+ P(X=2) -----------------(1)

So,

[tex]P_x = \;^nC_r.p^x.q^{n-x}[/tex]

P(X=0) = [tex]\;^{20}C_0.p^0.q^{20-0}[/tex] =  [tex]\; 1.(1-p)^{20-0}[/tex] = (1-0.037)²⁰ = (0.963)²⁰ =  0.4704

P(X=1) = [tex]\;^{20}C_1.p^1.q^{20-1}[/tex] =  [tex]\; 20.(0.037).(0.963)^{19}[/tex]  = 0.3614

P(X=2) = [tex]\;^{20}C_2.p^2.q^{20-2}[/tex] =  [tex]\;190\times(0.037)^2\times(0.963)^{18}[/tex] = 0.1319

Now, putting the all values in equation (1)

P(X≤2) = P(X=0) +  P(X=1)+ P(X=2) -----------------(1)

           = 0.4704 + 0.3614 + 0.1319

P(X≤2) = 0.9637 = 96.37%

There is a 96.37% probability that the company will find 2 or more defective products.

2)

1.23% are defective means p = 0.0123

The probability that find 4 or more defective products are;

 P(X≤4) = 1 - P(X< 4) -----------(2)

 P(X< 4) = P(X=0) + P(X=1)+ P(X=2) + P(X=3)-----------------(3)

So,

P(X=0) =  = [tex]\;^{20}C_0.p^0.q^{20-0}[/tex] =  [tex]\; (0.9877)^{20}[/tex] = 0.7807

P(X=1) = [tex]\;^{20}C_1.p^1.(1-p)^{20-1}[/tex] =  [tex]20\times (0.0123)\times (0.9877)^{19}[/tex] = 0.1944

P(X=2) = [tex]\;^{20}C_2.p^2.(1-p)^{20-2}[/tex] =  [tex]190\times (0.0123)^2\times (0.9877)^{18}[/tex] = 0.0024

P(X=3) = [tex]\;^{20}C_3.p^3.(1-p)^{20-3}[/tex] =  [tex]1140\times (0.0123)^3\times (0.9877)^{18}[/tex] = 0.0017

So,

P(X< 4) = 0.7807+0.1944+0.0024+0.0017 =0.9792

 P(X≤4) = 1 - P(X< 4) = 1 - 0.9792 = 0.0208 = 2.08%

There is a 2.08% probability that the company will find 4 or more defective products.

3)

1.28% are defective means p = 0.0128

The probability that find 5 or more defective products are;

 P(X≤5) = 1 - P(X< 5) -----------(4)

 P(X< 5) = P(X=0) + P(X=1)+ P(X=2) + P(X=3)+ P(X=4)-----------------(5)

So,

P(X=0) =  = [tex]\;^{20}C_0.p^0.q^{20-0}[/tex] =  [tex]\; (0.9872)^{20}[/tex] = 0.7728

P(X=1) = [tex]\;^{20}C_1.p^1.(1-p)^{20-1}[/tex] =  [tex]20\times (0.0128)\times (0.9872)^{19}[/tex] = 0.2004

P(X=2) = [tex]\;^{20}C_2.p^2.(1-p)^{20-2}[/tex] =  [tex]190\times (0.0128)^2\times (0.9872)^{18}[/tex] = 0.0246

P(X=3) = [tex]\;^{20}C_3.p^3.(1-p)^{20-3}[/tex] =  [tex]1140\times (0.0128)^3\times (0.9872)^{18}[/tex] = 0.0019

P(X=4) = [tex]\;^{20}C_4.p^4.(1-p)^{20-4}[/tex] =  [tex]4845 \times (0.0128)^3\times (0.9872)^{18}[/tex] = 0.0001

So,

  P(X< 5) = 0.7728+0.2004+0.0246+0.0019+0.0001 = 0.9998

  P(X≤5) = 1 - P(X< 5) = 1 - 0.9998 = 0.0002 = 0.02%

There is a 0.02% probability that the company will find 5 or more defective products. So company will give profit.

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The slope of the equation is -7. Then the slope of the perpendicular line will be 1/7.

Let the equation of the line be y = mx + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx + c is given as y = -(1/m) + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given as,

y = - 7x

The slope of the equation is -7. Then the slope of the perpendicular line will be

⇒ -(1/(-7))

⇒ 1/7

The slope of the equation is -7. Then the slope of the perpendicular line will be 1/7.

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The answer is (2) 2f-5=86; I hope- :\

The median is a better measure of center for the male's data, while the mean is a better for the female's data.

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

(a) The IQR of the male's data

From the given male's boxplot, we have the following data elements;

Upper quartile (Q3) = 14

Lower quartile (Q1) = 2

Then the IQR is calculated as:

IQR = Q3 - Q1

So, we have:

IQR = 14 - 2

IQR = 12

Hence, the IQR for the given males' data is 12

(b) The difference between the median values can be calculated as;

Median of male's data = 14

Median of female's data = 9

The difference (d) between the median values is;

d = 14 - 9

d = 5

Hence, the difference between the median values of each data set is 5

(c) The distribution of data

It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.

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The median is a better measure of center for the male's data, while the mean is a better for the female's data.

What are quartiles?

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

(a) The IQR of the male's data

From the given male's boxplot, we have the following data elements;

Upper quartile (Q3) = 14

Lower quartile (Q1) = 2

Then the IQR is calculated as:

IQR = Q3 - Q1

So, we have:

IQR = 14 - 2

IQR = 12

Hence, the IQR for the given males' data is 12

(b) The difference between the median values can be calculated as;

Median of male's data = 14

Median of female's data = 9

The difference (d) between the median values is;

d = 14 - 9

d = 5

Hence, the difference between the median values of each data set is 5

(c) The distribution of data

It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.

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There is a real number whose product with every real number equals zero

a. Some real number has the property that its product with every real number equals 0.

b. There is a real number a such that the product of á and any real equals zero.

c. There is a real number á with the property that for every real number b, the product of a and b equals zero.

Answer: (-1.5, 0)

Step-by-step explanation:

Use the midpoint formula, [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]. Plug in the points into the equation to get [tex](\frac{-5+2}{2},\frac{5-5}{2})[/tex] = (-1.5, 0)

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=10\\ \theta =85 \end{cases}\implies \begin{array}{llll} A=\cfrac{(85)\pi (10)^2}{360} \\\\\\ A=\cfrac{425\pi }{18}\implies A\approx 74.18~cm^2 \end{array}[/tex]

The slope of  P=(-4,-1) Q=(-3,-3) is -2.

Given,

 P=(-4,-1)

Q=(-3,-3)

The  slope  between two points   P=(x₁, y₁)

Q=(x₂ ,y₂)

slope = (y₂-y₁)/(x₂-x₁)

So slope between  P=(-4,-1)   Q=(-3,-3) is

 [(-3)-(-1) ]/ [(-3)-(-4)]

=-2/1

=-2

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

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The interval in which the function has positive average rate of change is x > √3

The function is given as

f(x) = x^3 - 9x

Differentiate the above function to determine the average rate of change

So, we have

f'(x) = 3x^2 - 9

Set the function to greater than 0

So, we have

3x^2 - 9 > 0

Add 9 to both sides

3x^2 > 9

Divide by 3

x^2 > 3

Take the square root of both sides

x > √3

Hence, the interval in which the function has positive average rate of change is x > √3

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The cutoff score is  mathematically given as

x_n=70.32 (cutoff)

This is further explained below.

Generally, the equation for is  mathematically given as

[tex]&P\left(X > x_0\right)=0.15 \Rightarrow P\left(X < x_0\right)=0.85 \\[/tex]

[tex]&\Rightarrow P\left(\frac{X-\mu}{\sigma} < \frac{x_0-\mu}{\sigma}\right)=0.85 \\[/tex]

[tex]&\Rightarrow P\left(Z < \frac{x_0-\mu}{\sigma}\right)=0.85 \\\\&\Rightarrow \frac{x_0-\mu}{\sigma}=\text { invNorm }(0.85) \\\\&\Rightarrow x_0=\mu+\sigma \times \text { invNorm }(0.85)[/tex]

Use z-table to get inv Norm() = 1.04

x_0=62+8 *(1.04)=70.32

In conclusion, Top 15% are above x_n=70.32 (cutoff)

Clearly this is 85th percentile

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Answer:

Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.