Lee's family had a garden in the shape of a right triangle. The total area of the garden is 16 square feet. If they expand
the garden to form a triangle with twice the base
and twice the height, by how much will they increase the size of their
garden?
O 16 square feet
• 32 square feet
O
48 square feet
64 square
feet

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

Answer:

1. real rational decimal

2. real rational integer

3. real rational root, whole number

4. real rational

5.

6.

7. imaginary number

Step-by-step explanation:

i think this is it I'm so sorry if its wrong

i cant figure out 5 and 6 so sorry

1. real rational decimal

2. real rational integer

3. real rational root, whole number

4. real rational

5. real irrational root

6. real ration root, whole number

7. imaginary number

A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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f(x) = x² + 2x + 2

Solution:

Given vertex (1,1)

a = 1

Formula of quadratic equation  is :

y = a(x + b)² + c

where, a =1, x=x, b = x1, c = y1

Substituting  the values in the equation, we get

y = x² + 2x + 2

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A quadratic function to model the graph to the right is f(x) = x² + 2x + 2

What is a quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Solution:

Given vertex (1,1)

a = 1

Formula of quadratic equation  is :

y = a(x + b)² + c

where, a =1, x=x, b = x1, c = y1

Substituting  the values in the equation, we get

y = x² + 2x + 2

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A. inequality that compares the temperatures of the two cities is: -2 > -6. B. inequality means city R, represented by -2 on the number line greater than the temperature of city S, represented by -6 on the number line. C.  city R is warmer than city S.

In mathematics, an inequality is a statement that compares two values or expressions and indicates that one is greater than, less than, or equal to the other. Inequalities are used to describe relationships between values that are not necessarily equal, and they are written using special symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

For example, the inequality 3x + 2 < 10 means that the expression 3x + 2 is less than 10. This inequality can be solved for x by subtracting 2 from both sides and then dividing by 3, yielding x < 2. This means that any value of x that is less than 2 will satisfy the inequality.

The inequality that compares the temperatures of the two cities is: -2 > -6

This inequality means that the temperature of city R, represented by -2 on the number line, is greater than the temperature of city S, represented by -6 on the number line. In other words, city R is warmer than city S.

On the number line, the further to the right a number is, the greater it is. Since -2 is to the right of -6, this indicates that -2 is greater than -6, which represents the fact that city R is warmer than city S.

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Answer:

Unable to read entire question, but see explanation for answer

Step-by-step explanation:

First, you need to find the unit rate per dog. If it takes 3 dogs 10 days to finish 30 pounds of food, then it takes 1 dog 1 day to finish 1 pound of food. I cannot read the entirety of the question because of the cropping, but you can find how much food a single dog eats in that amount of days by just multiplying by the number of days (say, 1 pound in 1 day, or 3 pounds in 3 days). Hope this helps!

Answer:

1

Step-by-step explanation:

took test

Step-by-step explanation:

A: If there are 2 modes, x can be either 1 or 2.

B: To find the mode of the data set, we need to count how many times each number appears.

- 0 appears 2 times

- 1 appears 4 times

- 2 appears 4 times

- 3 appears 3 times

- 4 appears 1 time

Since both 1 and 2 appear 4 times in the data set, there are two modes.

For x, if we add it to the data set, then the mode must be x plus either 1 or 2.

If we choose x to be 2, then the mode would be 2, since 1 and 2 each appear 4 times, and adding another 2 would make it the mode.

So a possible value for x could be 2, and the mode would be 2.

30.2% is the necessary probability that it is a horror or comedy movie title.

Given:

There are 168 films in the horror category.

There are 118 films in the mystery category.

The following formula can be used to get the total number of movies in the video rental store:

Total number of outcomes is =  (168 + 220 + 118 + 308 + 134) =948

Let P (H) represent the likelihood that it will be a horror film, and P (M) represent the likelihood that it will be a mystery. In addition, we presumptively believe that a film can only fall into one of two categories: mystery or horror. The likelihood that a horror or mystery film will be chosen as a rental can be calculated as follows:

\(P(M or H) = P(H) + P(M)\)

                \(=\frac{168}{948} +\frac{118}{948}\)

                \(=\frac{168+118}{948}\)

                \(=\frac{286}{948}\)

                ≈\(0.302\)

Therefore, 30.2% is the necessary probability.

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Answer:

1.9 is the correct answer

Answer:

x = 5/2

Step-by-step explanation:

Solve for x:

(5 x)/2 = 25/4

Hint: | Multiply both sides by a constant to simplify the equation.

Multiply both sides of (5 x)/2 = 25/4 by 2/5:

(2×5 x)/(5×2) = 2/5×25/4

Hint: | Express 2/5×5/2 as a single fraction.

2/5×5/2 = (2×5)/(5×2):

(2×5)/(5×2) x = 2/5×25/4

Hint: | Express 2/5×25/4 as a single fraction.

2/5×25/4 = (2×25)/(5×4):

(2×5 x)/(5×2) = (2×25)/(5×4)

Hint: | Cancel common terms in the numerator and denominator of (2×5 x)/(5×2).

(2×5 x)/(5×2) = (5×2)/(5×2)×x = x:

x = (2×25)/(5×4)

Hint: | In (2×25)/(5×4), divide 25 in the numerator by 5 in the denominator.

25/5 = (5×5)/5 = 5:

x = (2×5)/4

Hint: | In (2×5)/4, divide 4 in the denominator by 2 in the numerator.

2/4 = 2/(2×2) = 1/2:

Answer:  x = 5/2

Answer:

1) x+y=-2

x=-2-y

2) x-y=-8

substitude value of x

(-2-y)-y=-8

-2-2y=-8

-2y=-6

y=3

Substitute value of y in 1

x=-2-3

x=-5

Brainliest please~

2.1 The height of the given container is \(\frac{250}{\pi r^{2} }\) cm.

2.2 The surface area in terms of r is 2πr (r + \(\frac{250}{\pi r^{2} }\) ) square cm.

2.3 The measure of radius i.e. r is 3.41 cm and the minimum surface area of the container is 221.19 square cm.

2.4 The cost of the container is not determinable as there is no data provided regarding it.

The solution has been obtained by using the formulas of cylinder.

What is a cylinder?

The cylinder, one of the most basic curvilinear geometric shapes, has traditionally been regarded as a three-dimensional solid. It is regarded as a prism with a circle as its basis in elementary geometry.

2.1 We are given that the volume of the container is 250 cubic cm.

So, using the volume of cylinder, we get the radius as

⇒ V = πr²h

⇒ 250 = πr²h

⇒ h = \(\frac{250}{\pi r^{2} }\) cm

2.2 Now, using the formula of surface area of cylinder, we get

⇒ Surface area = 2πr (r + h)

⇒ Surface area = 2πr (r + \(\frac{250}{\pi r^{2} }\))

2.3 For surface area to be minimum, we need to equate its derivative to 0.

On simplifying the surface area, we get

Area (A) = 2π\(r^{2}\) + \(\frac{500}{r}\)

Now, its derivative is

A' = 4πr - \(\frac{500}{r^{2} }\)

On equating it to 0, we get

⇒ 4πr - \(\frac{500}{r^{2} }\) = 0

⇒ 4πr = \(\frac{500}{r^{2} }\)

⇒ 4π\(r^{3}\) = 500

⇒ r = 3.41 cm

Now, on substituting this value in the area, we get

⇒ Surface area = 2π\(r^{2}\) + \(\frac{500}{r}\)

⇒ Surface area = 2π\((3.41)^{2}\) + \(\frac{500}{3.41}\)

⇒ Surface area = 221.19 square cm

2.4 The cost of the container can not be determined as no data for the same is provided.

Hence, the complete solution has been obtained.

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The Distance will be  5.

The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.

Let point (7,5) be A and point (4,9) be B

Distance formula =

Ab  = √(x1- x2) ² + (y1 -y2) ²

Then Distance AB will be

Ab  = √(7-4) ² + (5 -9) ²

= √ 3² + 4²

= √ 9 + 16

= 5

Hence the distance  will be 5.

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The points \((7,5)\)  \((4,9)\) are separated by a distance of \(5\) units.

The distance between the two points is given by the length of the segment between them.

The Distance Formula is a helpful tool for figuring out how far apart two points are when they are arbitrarily represented on a coordinate plane as points A\((x_{1},y_{1})\) and B\((x_{2},y_{2})\).

The Pythagorean Theorem is essentially the source of the Distance Formula. Calculating the right triangle's hypotenuse's length is the fundamental purpose of the distance formula.

Use the distance formula to get the distance between two places.

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

In the posted query,

\((x_{1},y_{1})=(7,5)\\\\(x_{2},y_{2})=(4,9)\)

Distance formula,

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

\(d = \sqrt{ (4-7)^{2} +(9-5)^{2} }\)

\(d = \sqrt{ (-3)^{2} +(4)^{2} }\)

\(d = \sqrt{ 9+16 }\)

\(d = \sqrt{ 25 }\)

\(d = 5\)

Therefore, the points \((7,5)\)  \((4,9)\) are at a distance of \(5\) units.

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84.27 square inch is the lateral surface area of cone.

All of an object's sides, excluding its base and top, are considered its lateral surface. The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area. A figure's lateral area consists solely of the non-base faces. The lateral surface area of several forms, such as a cuboid, cube, cylinder, cone, and sphere, is discussed in this article.

Given,

Height = 12 inches

Diameter = 4.4 inches

Radius = 2.2 inches

Lateral surface area:

πr√h² + r²

3.14 × 2.2 √(12)² + (2.2)²

3.14 × 2.2 √144 + 4.84

3.14 × 2.2 √148.84

3.14 × 2.2(12.2)

3.14 × 26.84

84.27

84.27 square inch is the lateral surface area of cone.

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Answer: 50 and 59

I divided 2950 by 25 because I knew it would somehow factor into that since it ends in 50. Then, I got 25 and 118. From there, I just divided 118 by 2 since I knew that it would end in a 9 and I multiplied 25 by 2. Not sure if this is really helpful, but you also try using a GCF calculator and look up all the factors of that number next time!

since we know the diameter is 50, then its radius is half that or 25.

\(\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=25 \end{cases}\implies \begin{array}{llll} V=\cfrac{4\pi (25)^3}{3}\implies V=\cfrac{62500\pi }{3} \\\\\\ V\approx 65449.85~cm^3 \end{array}\)

The volume of a cone is computed as follows:

where r is the radius and h is the height of the cone.

The volume of a cylinder is computed as follows:

where r is the radius and h is the height of the cylinder.

Substituting with r = 1 and h = 1, the volumes are:

And the ratio of volumes is:

Substituting with r = 2 and h = 4, the volumes are:

And the ratio of volumes is:

1/2=1/2=1/2.is the value for the given equivalent fraction, by putting the value 3.4 in the numerators respectively

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

1/2 =    /6 =   /8.

a. Multiply numerator and denominator by 3 for equivalenting the equation    /6

Therefore,

3*3/6*3

=9/18

=1/2

therefore:1/2=1/2.

b. Multiply numerator by 4

Therefore,

4/8

=1/2.

Therefore:

1/2=1/2.

1/2=1/2=1/2.

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The car gets 46 miles per gallon in the city.

Divide total miles driven in th city by miles per gallon to find total number of gallons of gas used:

10,000 miles / 46 miles per gallon = 217.3913 gallons of gas used.

Now multiply gallons used by price per gallon:

217.3913 x $1.75 = $380.43 per year

The resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively

Functions are expressions in form of variables. Given the following quadratic equation expressed as:

f(t) = 0.25t^2 − 0.5t + 3.5

We can find the equivalent value of the function when the value of t a re 2 and 6.

If the value of t is 2. hence;

f(2) =  0.25(2)^2 − 0.5(2) + 3.5

f(2) = 1 - 1 + 3.5

f(2) = 3.5

If the value of t is 6, hence;

f(6) = 0.25(6)^2 − 0.5(6) + 3.5

f(6) = 9 - 3 + 3.5

f(6) = 6.5

Hence the resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively

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Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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Answer:

I think it is 30 inches

Step-by-step explanation:

Answer: C

Step-by-step explanation: on edge 2023

Answer:

1 1/6

Step-by-step explanation:

Answer:

-1040 feet

Step-by-step explanation:

Since the altitude decreases at 40 feet per second, we can find the change in altitude by multiplying -40 by the number of seconds:

So, multiply -40 by 26:

-40(26)

= -1040

So, the change in altitude will be -1040 feet

The inequality is 30 + 7.5v ≤ 135

The number of visits Emma could make to earn her first free movie ticket is 14

From the question, we are to write and solve an inequality which can be used to determine the number of visits Emma can make to earn her first fee movie ticket

From the given information,

"She receives 30 rewards points just for signing up"

and

"She earns 7.5 points for each visit to the movie theater"

If she visits the movie theater v number of times,

Then,

She would earn

30 + 7.5v points

Also,

She needs at least 135 points for a free movie ticket.

Thus,

The inequality that could be used to determine the number of visits, v, to earn a free movies ticket is

30 + 7.5v ≤ 135

Solving the inequality

30 + 7.5v ≤ 135

Subtract 30 from both sides

30 - 30 + 7.5v ≤ 135 - 30

7.5v ≤ 105

v ≤ 105/7.5

v ≤ 14

Hence, the number of visits Emma could make to earn her first free movie ticket is 14

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The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Answer:

I think you need to add more information but this is my guess. It takes (blank) time to travel 8.42 miles

Step-by-step explanation:

Answer:

AOB = 73

BOC = 107

Step-by-step explanation:

So make an equation.

9x + 27 = 180

9x = 153

x = 17

AOB = 73

BOC = 107