Jake's solution to the equation −4(2x−3)=36 is shown below.

Step-by-step explanation:

7x + 30 = 11x - 24

30 + 24 = 11 - 7x

54 = 4x

54/4 = x

27/2 = x

13.5 = x

5y + 38 = 17y - 4

38 + 4 = 17y - 5y

42 = 12y

42/12 = y

21/6 = y

7/2 = y

3.5 = y

Answer:

C

Step-by-step explanation:

The pre-image of a reduction is always bigger. Reduction means to "get smaller," so the pre-image needs to be bigger than the ending image.

Answer:

C i think is the answer

We know at centroid medians bisect each other in the ratio 2:1.

\(\\ \sf\longmapsto TY=2x\)

\(\\ \sf\longmapsto 2x=30\)

\(\\ \sf\longmapsto x=\dfrac{30}{2}\)

\(\\ \sf\longmapsto x=15\)

Answer:

A

Step-by-step explanation:

On the median TW the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint , then

YW = \(\frac{1}{2}\) × TY = \(\frac{1}{2}\) × 30 = 15

Arc length = π r^2 (Θ/360)

There is a squared radius that can't be in the formula. The result will be an area instead of a length.

For the combination of n = 25 and p = 0.5 it is reasonable to assume that the sampling distribution of the sample proportion p will be approximately normal.

As per the given data:

A random sample is to be selected from a population

Here we have to determine for which combination of n and p is reasonable to assume that the sampling distribution of the sample proportion p will be approximately normal.

For this we have to multiply the value of n and the value of p.

Option (A):

n = 10 and p = 0.4

np = 10 × 0.4

np = 4

Option (B):

n = 25 and p = 0.5

np = 25 × 0.5

np = 12.5

Option (C):

n = 30 and p = 0.2

np = 30 × 0.2

np = 6

Option (D):

n = 40 and p = 0.1

np = 40 × 0.1

np = 4

Option (E):

n = 100 and p = 0.05

np = 100 × 0.05

np = 5

Compare all the combinations of np.

Option (B) is correct because it has the highest value of np.

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A random sample is to be selected from a population. For which combination of n and p is it reasonable to assume that the sampling distribution of the sample proportion p will be approximately normal?

(A) n = 10 and p = 0.4

(B) n = 25 and p = 0.5

(C) n = 30 and p = 0.2

(D) n = 40 and p = 0.1

(E) n = 100 and p = 0.05

If a random sample of 29 time intervals between eruptions has a mean greater than 106, it may be concluded that the average time between eruptions is longer than 106 units of time. However, it is important to note that the sample size of 29 may not be representative of the entire population of time intervals between eruptions, and therefore the conclusion drawn may not be entirely accurate.
Additionally, it is important to consider the variability of the data. If the standard deviation of the sample is high, it may indicate that there is a wide range of time intervals between eruptions, making it difficult to draw a definitive conclusion. On the other hand, if the standard deviation is low, it may indicate that the time intervals are more consistent, and the conclusion drawn may be more reliable.

Overall, it is important to consider both the mean and variability of the sample when drawing conclusions about the population of time intervals between eruptions. Further research and analysis may be necessary to validate the findings and provide a more accurate answer.

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In this given problem, we have to calculate the values of α and β for the daily consumption of electric power having gamma distribution and also have to find the probability of the given scenario.

a) The value of \(\alpha =3\) and \(\beta =6\).

b) The probability that on any given day the daily power consumption will exceed 12 million kilowatt hours is 0.10702 (approx.).

a) The gamma distribution is represented by X ∼ Γ(α, β).

We are given that the mean of gamma distribution is μ = 6 and variance is σ² = 12.

Now, we know that the mean and variance of a gamma distribution are given as follows:

Mean, μ = αβ

Variance, σ² = αβ²

By putting the values given in the question, we have

6 = αβ

12 = αβ²

Dividing the above two equations, we get:

αβ / αβ² = 1 / 2

β = 2α

Hence, substituting the value of β in the equation 6 = αβ, we get:

α = 3 and β = 6

b) We have to find the probability that on any given day the daily power consumption will exceed 12 million kilowatt hours.Since the distribution is a gamma distribution, we have X ∼ Γ(3, 6).

To find the probability of any random variable exceeding a certain value, we use the following formula:

P(X > a) = 1 - F(a)

where F(a) is the cumulative distribution function (CDF) of X.

To use this formula, we first need to find the CDF of X, which is given by:

P(X ≤ x) = F(x) = {1 / (Γ(α)β³)} ∫₀ⁿ x² e⁻(x/β) dx

We can use a computer or calculator to find this integral, or we can use tables of the gamma distribution to look up the value of F(x).

Here, we will use a calculator to find the value of F(12).F(12) = 0.89298 (approx.

)Now, using the formula for the probability of exceeding a certain value, we get:

P(X > 12) = 1 - F(12)

              = 1 - 0.89298

              = 0.10702 (approx.)

Therefore, the probability that on any given day the daily power consumption will exceed 12 million kilowatt hours is approximately 0.10702 or 10.702%.

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Answer:

Given

Step-by-step explanation:

Consider triangle ABD and triangle DCA,

AC=BD ( given that they are diameters)

Diameters of the same circle are equal

AD=AD (common side for both triangles)

<BAD= <CDA (angles in semicircles are 90°)

So since the right angle, hypotenuse and side are equal..

ABD is congruent to CDA

(Rhs congruence rule)

Hence proved..

Answer:

In year 1986 the average  cost of car is  $12,000

Step-by-step explanation:

Cost function:

C = 30.5t² + 4192

Cost = $12,000

Find:

Year

Computation:

C = 30.5t² + 4192

12,000 = 30.5t² + 4192

t = 16 year

So,

Year 1970 + 16 year

1986

So, In year 1986 the average  cost of car is  $12,000

To plot the function g(x) = cos(x) + x\(e^{-x\) in Octave, you can follow some steps.

Open Octave or GNU Octave in your preferred environment.

Define the function g(x) using an anonymous function syntax:

g = (x) cos(x) + x.*exp(-x);

Set the range of x values for the plot. In this case, we'll use x ranging from -2pi to 2pi:

x = linspace(-2*pi, 2*pi, 1000);

Plot the function using the defined range of x values:

plot(x, g(x));

Customize the plot by adding a title, labeling the axes, and displaying a grid:

title("Plot of g(x) = cos(x) + xe^{-x}");

xlabel("x");

ylabel("g(x)");

grid on;

Display the plot.

After executing these steps, you should see a plot of the function g(x) = cos(x) + x\(e^{-x\) with the specified window size, title, labeled axes, and grid.

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Answer:

Each of the inches was reduced by 3 in.

Step-by-step explanation:

This is the answer because if you divide the 24 by 3 you will get 8 and the same thing occurs if you divide the 36 by 3 and you will get 12

Answer:

-87

Step-by-step explanation:

f(x) = —x^2 + 6x + 4

Let x = -7

f(-7) = —(-7)^2 + 6(-7) + 4

Exponents first

     = -49 + 6(-7) + 4

Multiply

     = -49-42+4

Add

   = -87

-87

Answer:

Solution given:

f(x) = —x2 + 6x + 4

Substituting value of x and solve

f(-7)=-(-7)²+6*-7+4=-49-42+4=-87

There are 190 ways to select two singers for the duet from the group of 20 singers.

The number of ways to select two singers for a duet can be determined using the combination formula. Since the order of selection does not matter, we use the combination formula to calculate the number of ways.

The formula for selecting r items from a set of n items is given by:

nCr = n! / (r!(n-r)!)

In this case, we have 20 singers and we need to select 2 for the duet. Plugging the values into the formula, we get:

20C2 = 20! / (2!(20-2)!) = 20! / (2!18!) = (20 * 19) / (2 * 1) = 190.

Therefore, there are 190 ways to make the selections for the duet from the 20 singers.

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July is the seventh month of the year in the Gregorian calendar, which is the most widely used calendar system in the world.

It is considered the seventh month because it falls between June, the sixth month, and August, the eighth month. July is also the last month of the second quarter of the year, having 31 days.

July is known for many events and holidays, such as Independence Day in the United States, Canada Day, and Bastille Day in France. It's also the middle of the summer season, and people often take vacations and enjoy outdoor activities during this month.

It's important to note that in different cultures and regions the months of the year may be ordered differently.

For example, some cultures may have a lunar calendar which is based on the cycles of the moon rather than the sun, and the months may be ordered differently.

However, the Gregorian calendar is widely used around the world and it considers July as the seventh month of the year.

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Based on the information given, it can be concluded that the prediction made by Kardal using the line of best fit is specific to the dataset or population that was used to determine the line of best fit.

The line of best fit is a statistical technique used to find a line that best represents the relationship between two variables. In this case, it seems that Kardal used the line of best fit to establish a relationship between height and shoe size. However, without additional information about the dataset or the methodology used to determine the line of best fit, it is challenging to assess the accuracy or generalizability of the prediction.

It's important to note that predictions based on statistical models are subject to uncertainty and may not hold true for individuals outside the dataset used for analysis. Other factors, such as body proportions, foot structure, and personal preferences, can also influence the relationship between height and shoe size. Therefore, the prediction that a man who is 80 inches tall would wear a size 16 shoe should be taken with caution and may not be applicable in all cases.

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The degree of financial leverage for Foggy Futures Weather Forecasters

is 1.06

Degree of Financial leverage (DFL) = (EBIT) / (EBT)

Earnings Before Interest and Taxes (EBIT) = $750,000

Amount to be given as loan on $1000000

$1,000,000 x 4.5% = $1,000,000 x 4.5/100

= $45000

To find EBT ( Earnings Before Tax),

EBT = EBIT - 45000

       = 750000 - 45000

EBT = 705000

∴ DFL =  (EBIT) / (EBT)

          = 750000/705000

 DFL = 1.06

The DFL is a percentage that accountants and financial professionals use to show changes in a company's net income due to changes in its profits before interest and taxes (EBIT).

Earnings before interest and taxes (EBIT) is a measurement of a company's profit in accounting and finance that takes into account all revenues and costs (both operating and non-operating), with the exception of interest costs and income tax costs.ve

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The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.

Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:

1/4(4 + x) = 4/3

4 * 1/4(4 + x) = 4 * 4/3

Simplifying:

4 + x = 16/3

Subtract 4 from both sides of the equation:

4 + x - 4 = 16/3 - 4

Simplifying:

x = 16/3 - 12/3

x = 4/3

A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.

Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.

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The Solutions of the equation 27x² + 5 = 48x  are x = 1/9 ,  x = 5/3 .  .

In the question ,

it is given that ,

the equation is 27x² + 5 = 48x ,

we have to find the solution for it ,

27x² + 5 = 48x

rewriting it , we get ,

27x² - 48x + 5 = 0

27x² - 45x + 5 = 0

27x² - 3x - 45x + 5 = 0

Simplifying further , we get ,

3x(9x - 1) -5(9x - 1) = 0

taking (9x-1) common from both the terms ,

(9x - 1)(3x - 5) = 0

So , either (9x - 1) = 0 or (3x - 5) = 0

x = 1/9 or  x = 5/3

Therefore , the solution of the given equation are x = 1/9 ,  x = 5/3 .

The given question is incomplete , the complete question is

Solve the equation by factoring. check your solution. if there are multiple solutions, list the solutions from least to greatest separated by a comma.

27x² + 5 = 48x  .

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The probability of exactly 1 of the 4 marbles drawn being blue and at least 1 of the 4 marbles drawn being white will be 0.3535 and 0.7454 respectively.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Betty picks 4 random marbles from a bowl containing 3 white, 4 yellow, and 5 blue marbles.

The total number of the marbles will be

Total marble = 3 + 4 + 5

Total marble = 12

Then the probability of exactly 1 of the 4 marbles drawn being blue will be

\(\rm P(B) = \dfrac{^5C_1 \times ^7C_3}{^{12}C_4}\\\\P(B) = \dfrac{35}{99} = 0.353535\)

Then the probability of at least 1 of the 4 marbles drawn being white will be

\(\rm P(W) = \dfrac{^{3}C_1\times \ ^{9}C_3}{^{12}C_4} + \dfrac{^{3}C_2\times \ ^{9}C_2}{^{12}C_4} + \dfrac{^{3}C_3\times \ ^{9}C_1}{^{12}C_4} \\\\\\P(W) = \dfrac{252}{495} + \dfrac{108}{495} + \dfrac{9}{495}\\\\\\P(W) = \dfrac{369}{495}\\\\\\P(W) = 0.745454\)

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Answer:

A. 0.3535.

B. 0.7455.

Step-by-step explanation:

The probability that exactly 1 of the 4 marbles drawn is blue is 0.3535. The probability that at least 1 of the 4 marbles drawn is white is 0.7455.

Answer:

Every hexagon tessellates.

Step-by-step explanation:

Hexagons always tessellates when perfectly combined and aligned especially when the x sides and the y sides are parallel to each other.

The length of the fence in yards, using all 144 feet of material, is 12 yards. Jason will have a fence with a length of 21 yards if he uses all 144 feet of material to build the fence around his rectangular garden.

Let's denote the length of the fence as L in feet. The width of the fence is given as 9 feet. The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

In this case, we have P = 144 feet and W = 9 feet. We want to find the value of L that satisfies the equation 2L + 2W = P.

Substituting the given values, we have:

2L + 2(9) = 144

2L + 18 = 144

2L = 144 - 18

2L = 126

L = 126/2

L = 63

So the length of the fence is 63 feet.

To convert this length from feet to yards, we know that 1 yard is equal to 3 feet. Therefore, to obtain the length in yards, we divide the length in feet by 3:

63 feet / 3 = 21 yards

Therefore, the length of the fence, using all 144 feet of material, is 21 yards.

Jason will have a fence with a length of 21 yards if he uses all 144 feet of material to build the fence around his rectangular garden.

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Answer:

3x - 2y = - 28

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x - 2y = 12 ( subtract 3x from both sides )

- 2y = - 3x + 12 ( divide all terms by - 2 )

y = \(\frac{3}{2}\) x - 6 ← in slope- intercept form

with slope m = \(\frac{3}{2}\)

Parallel lines have equal slopes, thus

y = \(\frac{3}{2}\) x + c ← is the partial equation

To find c substitute (- 8, 2) into the partial equation

2 = - 12 + c ⇒ c = 2 + 12 = 14

y = \(\frac{3}{2}\) x + 14 ← equation in slope- intercept form

Multiply through by 2

2y = 3x + 28  ( subtract 2y from both sides )

0 = 3x - 2y + 28 ( subtract 28 from both sides )

- 28 = 3x - 2y , that is

3x - 2y = - 28 ← equation in standard form

Answer:

4 x 10 + 5 x 1

Step-by-step explanation:

The expanded form of a number is written as a sum where each digit of the number is multiplied by its place value. Let's understand this concept with an example. To write the number 45 in the expanded form, we split the digits into tens and ones and write it as 4 x 10 + 5 x 1.

Answer:

Step-by-step explanation:

45 in expanded form;

(4x10)+(1x5)= 45

Answer: for the question 2 I gave you the step by step explanation in the picture so you can probably better understand where you did wrong , I hope it will be helpful for you, have a nice rest of your day:)

Answer:

see explanation

Step-by-step explanation:

(f + g)(x)

= f(x + g(x)

= x² + 1 + 5 - x ← collect like terms

= x² - x + 6

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

(f - g)(x)

=f(x) - g(x)

= x² + 1 - (5 - x)

= x² + 1 - 5 + x ← collect like terms

= x² + x - 4

Answer:

Any number below 3

(2, negative infinity)

Answer:

here's the answer with steps

x + 2 < 5

-2 -2

x < 3

Focus at(7,-11)

Equation of directrix y=-3

So what can be told?

Equation of parabola

Answer:

The parabola is negative, with a vertex at (7, -7) and a line of symmetry at x = 7

Step-by-step explanation:

A parabola is set of all points in a plane which are an equal distance away from a given point (focus) and given line (directrix).

Let \((x_0,y_0)\) be any point on the parabola.

Find an equation for the distance between \((x_0,y_0)\) and the focus.  

Find an equation for the distance between \((x_0,y_0)\) and directrix. Equate these two distance equations, simplify, and the simplified equation in \(x_0\) and \(y_0\) is equation of the parabola.

Distance between \((x_0,y_0)\) and the focus (7, -11):

\(\sqrt{(x_0-7)^2+(y_0+11)^2}\)

Distance between \((x_0,y_0)\) and the directrix, y = -3:

\(|y_0+3|\)

Equate the two distance expressions and simplify, making \(y_0\) the subject:

\(\sqrt{(x_0-7)^2+(y_0+11)^2}=|y_0+3|\)

\((x_0-7)^2+(y_0+11)^2=(y_0+3)^2\)

\({x_0}^2-14x_0+49+{y_0}^2+22y_0+121={y_0}^2+6y_0+9\)

\({x_0}^2-14x_0+16y_0+161=0\)

\(y_0=-\frac{1}{16} {x_0}^2+\frac{7}{8} x_0-\frac{161}{16}\)

This equation in \((x_0,y_0)\) is true for all other values on the parabola so we can rewrite with \((x, y)\)

Therefore, the equation of the parabola with focus (7, -11) and directrix is y = -3 is:

\(y=-\frac{1}{16} {x}^2+\frac{7}{8} x-\frac{161}{16}\)

⇒ \(y=-\frac{1}{16} (x-7)^2-7\)  (in vertex form)

So the parabola is negative, with a vertex at (7, -7) and a vertical line of symmetry at x = 7

Answer: D. 1/10

Step-by-step explanation:

With there being 5 sections on the spinner and only one number wanted to be spun, the probability of that would be 1/5.

On a dice, 3 of the numbers on a cube are prime (1, 3 and 5). So the probability would be 3/6 or 1/2.

1/5 x 1/2 = 1/10, so the probability of spinning a 4 and rolling a prime number would be 1/10, or 10%

Answer:

-4

Step-by-step explanation:

2a2+5a2

2(-6)2=-24

5(2)2=20

-24+20=-4

Answer: -4

Step-by-step explanation:

(2x-6×2)(5×2×2)

-24+20

-4

Answer:

The answer is 0.