determine the equation of the circle graphed below.

( please help me )

Answer: x=4

               x=12

Step-by-step explanation:

7x=28

divide 7 on both sides

28/7=4

x=4

4x=48

divide 4 on both sides

48/4=12

x=12

Answer: $9886.22

Step-by-step explanation:

To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

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Answer:

Remove any grouping symbol such as brackets and parentheses by multiplying factors.

Use the exponent rule to remove grouping if the terms are containing exponents.

Combine the like terms by addition or subtraction.

Combine the constants.

Answer:

54i - 8

Step-by-step explanation:

6*9i + 4i*2i

=54i + 8i^2

= 54i - 8

In linear equation, the no of points which are lost at both end of the original series in 2.

What in mathematics is a linear equation?

When calculating centered moving average using 4 - period moving average .

the no of points which are lost at both end of the original series in 2..

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Answer:

32

Step-by-step explanation:

Answer:

95 cm^2

Step-by-step explanation:

perimeter(p)=39cm

L=3x-1

B=2x+3

Now,

p=2(l+b)

39=2(3x-1+2x+3)

39=6x-2+4x+6

39=10x+4

39-4=10x

x=35/10

x=3.5

Putting the value of x

L=3x-1; =3×3.5-1; =10.5-1; =9.5cm

B =2x+3; =2×3.5+3; =7+3; =10cm

Again,

A= L×B

=9.5×10

=95cm^2

Answer:

The graph should sort of look like the image bellow

Step-by-step explanation:

Since it is a cubic function, the graph would curve up on into the shape of a palabora, come back down, and go up again.

    Graph crossing the x-axis at (-2, 0), (2, 0) and (3, 0) will be the correct choice.

         f(x) = (x - a)(x - b)(x - c)

         Roots (where the graph crosses or touches the x-axis) of the

         equation will be x = a, b, c

Given in the question,

Equation of the graph → f(x) = (x + 2)(x -2)(x - 3)

For zeros of the equation, equate the equation with zero.

f(x) = (x + 2)(x -2)(x - 3) = 0

x = -2, 2, 3

    Therefore, graph having zeros at (-2, 0), (2, 0) and (3, 0) will be correct graph.

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Step-by-step explanation:

we know that,

《opposite angle are equal in a rhombus 》

HERE,

one angle =2x

Opposite angle =3x-40

According to the question,

\(\tt{ 2x=3x-40 }\)

\(\tt{3x=2x+40 }\)

\(\tt{3x-2x=40 }\)

\(\tt{ x=40 }\)

#quality answer

\(\boxed{\large{\bold{\blue{ANSWER~:) }}}}\)

In this given rhombus,

we know that

\(\boxed{\sf{opposite~ angle~ are~ equal ~in~ a~ rhombus }}\)

According to the question,

Therefore.

The value of x In the given rhombus is 40°

I have added the complete question. That is in the attachment

Answer:

$13.2

Step-by-step explanation:

Cost of 1 inch = $0.4

Perimeter of painting is same as perimeter of a rectangle since painting is a rectangle

Perimeter = 2(l+b)

L = 10¼

B = 6¼

P = 2(10¼ + 6¼)

P = 2(41/4 + 25/4)

P = 2(10.25 + 6.25)

P = 2(16.5)

P = 33

Total cost of framing

= 0.4 x 33

= $13.2

Answer: YES, Its correct.

\(M_x=\frac{-6+2}{2}=2\\\\M_y=\frac{-3+7}{2}=2\\\\M=(2,2)\)

Answer:

(-2,2)

Step-by-step explanation:

The midpoint is the middle of the line. So, you can take it step-by-step and look at the individual numbers.

Between -6 and 2, that is 8 spaces. So, the middle would be four spaces from one of those numbers. Therefore, X-COORDINATE = -2

Between -3 and 7, that is 10 spaces. So the middle would be 5 spaces from one of those numbers, Therefore, Y-COORDINATE = 2

So, the midpoint would be (-2,2)

Answer:

9x - 13y

Step-by-step explanation:

2(3x - 2y) + 3(x - 3y)

Use distributive law a(b + c) = ab + ac

⇒ 2·3x - 2·2y + 3·x - 3·3y

⇒ 6x - 4y + 3x - 9y

Gather like terms:

⇒ 6x + 3x - 4y - 9y

Combine like terms:

⇒ 9x - 13y

Answer:

blue

Step-by-step explanation:

It is shown that: (a) The function f+g is convex.

(b) If c ≥ 0, then cf is convex. (c) If c ≤ 0, then cf is concave. The proposition is proven.

To prove the proposition, we'll need to show that each part (a), (b), and (c) holds true. Let's start with part (a).

(a) The function f+g is convex:

To prove that the sum of two convex functions is convex, we'll use the definition of convexity. Let's consider two points, x and y, in the interval I, and a scalar λ ∈ [0, 1]. We need to show that:

\((f+g)(λx + (1-λ)y) ≤ λ(f+g)(x) + (1-λ)(f+g)(y)\)

Now, since f and g are both convex, we have:

\(f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) \: (1) \\

g(λx + (1-λ)y) ≤ λg(x) + (1-λ)g(y) \: (2)\)

Adding equations (1) and (2), we get:

\(f(λx + (1-λ)y) + g(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y) + λg(x) + (1-λ)g(y) \\

(f+g)(λx + (1-λ)y) ≤ λ(f+g)(x) + (1-λ)(f+g)(y)\)

This shows that

\((f+g)(λx + (1-λ)y) ≤ λ(f+g)(x) + (1-λ)(f+g)(y),\)

which means that f+g is convex.

(b) If c ≥ 0, then cf is convex:

To prove this, let's consider a scalar λ ∈ [0, 1] and two points x, y ∈ I. We need to show that:

\((cf)(λx + (1-λ)y) ≤ λ(cf)(x) + (1-λ)(cf)(y)\)

Since f is convex, we know that:

\(f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y)\)

Now, since c ≥ 0, multiplying both sides of the above inequality by c gives us:

\(cf(λx + (1-λ)y) ≤ c(λf(x) + (1-λ)f(y))

\\ (cf)(λx + (1-λ)y) ≤ λ(cf)(x) + (1-λ)(cf)(y)

\)

This shows that cf is convex when c ≥ 0.

(c) If c ≤ 0, then cf is concave:

To prove this, we'll consider the negative of the function cf, which is (-cf). From part (b), we know that (-cf) is convex when c ≥ 0. However, if c ≤ 0, then (-c) ≥ 0, so (-cf) is convex. Since the negative of a convex function is concave, we conclude that cf is concave when c ≤ 0.

In summary, we have shown that:

(a) The function f+g is convex.

(b) If c ≥ 0, then cf is convex.

(c) If c ≤ 0, then cf is concave.

Therefore, the proposition is proven.

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a) This implies that (f + g)(λx + (1 - λ)y) ≤ λ(f(x) + g(x)) + (1 - λ)(f(y) + g(y)), which proves that f + g is convex, b) This implies that (cf)(λx + (1 - λ)y) ≤ λ(cf(x)) + (1 - λ)(cf(y)), proving that cf is conve, c) Therefore, Proposition 1 is proven, demonstrating that the function f + g is convex, cf is convex when c ≥ 0, and cf is concave when c ≤ 0.

To prove Proposition 1, we will demonstrate each part individually:

(a) To prove that the function f + g is convex, we need to show that for any x, y in the interval I and any λ ∈ [0, 1], the following inequality holds:

(f + g)(λx + (1 - λ)y) ≤ λ(f(x) + g(x)) + (1 - λ)(f(y) + g(y))

Since f and g are convex functions, we know that for any x, y in I and λ ∈ [0, 1], we have:

f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y)

g(λx + (1 - λ)y) ≤ λg(x) + (1 - λ)g(y)

By adding these two inequalities together, we obtain:

f(λx + (1 - λ)y) + g(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y) + λg(x) + (1 - λ)g(y)

This implies that (f + g)(λx + (1 - λ)y) ≤ λ(f(x) + g(x)) + (1 - λ)(f(y) + g(y)), which proves that f + g is convex.

(b) To prove that cf is convex when c ≥ 0, we need to show that for any x, y in I and any λ ∈ [0, 1], the following inequality holds:

(cf)(λx + (1 - λ)y) ≤ λ(cf(x)) + (1 - λ)(cf(y))

Since f is a convex function, we have:

f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y)

By multiplying both sides of this inequality by c (which is non-negative), we obtain:

cf(λx + (1 - λ)y) ≤ c(λf(x)) + c((1 - λ)f(y))

This implies that (cf)(λx + (1 - λ)y) ≤ λ(cf(x)) + (1 - λ)(cf(y)), proving that cf is convex when c ≥ 0.

(c) To prove that cf is concave when c ≤ 0, we can use a similar approach as in part (b). By multiplying both sides of the inequality f(λx + (1 - λ)y) ≤ λf(x) + (1 - λ)f(y) by c (which is non-positive), we obtain the inequality (cf)(λx + (1 - λ)y) ≥ λ(cf(x)) + (1 - λ)(cf(y)), showing that cf is concave when c ≤ 0.

Therefore, Proposition 1 is proven, demonstrating that the function f + g is convex, cf is convex when c ≥ 0, and cf is concave when c ≤ 0.

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The slope of the line tangent to the graph of \(y = x^2 - 2x + 1\) when \(x = 1\) is 2.



1. Take the derivative of the given function: \(y' = 2x - 2\).

2. Substitute \(x = 1\) into the derivative: \(y' = 2(1) - 2 = 2\).



To find the slope of the tangent line, we need to differentiate the given function with respect to \(x\). The derivative of \(x^2\) is \(2x\), and the derivative of \(-2x\) is \(-2\). Therefore, the derivative of \(y = x^2 - 2x + 1\) is \(y' = 2x - 2\).

Next, we substitute \(x = 1\) into the derivative to find the slope at that point. By plugging in \(x = 1\) into the derivative, we get \(y' = 2(1) - 2 = 2\). Thus, the slope of the tangent line at \(x = 1\) is 2.

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(a) The margin of error for a 95% confidence interval for μ ≈ 2.034

(b) If the sample size were increased to n = 89, the margin of error would be smaller.

(a) To calculate the margin of error for a 95% confidence interval for μ, we can use the formula:

Margin of Error = z * (σ / sqrt(n))

Where:

- z is the z-score corresponding to the desired confidence level (95% confidence level corresponds to z = 1.96)

- σ is the population standard deviation

- n is the sample size

Provided:

- σ = 9

- n = 79

- z = 1.96

Substituting the values into the formula:

Margin of Error = 1.96 * (9 / sqrt(79))

Margin of Error ≈ 2.034

So, the margin of error for a 95% confidence interval for μ is approximately 2.034 (rounded to at least three decimal places).

(b) As the sample size increases, the standard error decreases, resulting in a smaller margin of error.

This is because the margin of error is inversely proportional to the square root of the sample size.

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The two triangles n = (75 + 3) / 5 = 18. The measure of angle q is 18 degrees.

1. First, find the value of n by using the equation 5(n - 3) = 75 + 3

2. Next, add 75 and 3 together and divide by 5. This gives us a value of 18 for n.

3. Finally, use the equation 5(n - 3) to determine the measure of angle q in triangle qrs. This equals 5(18 - 3) = 5(15) = 75 degrees.

The two triangles qrs and xyz are similar, meaning they have the same angle measures. In order to find the measure of angle q in triangle qrs, we must first find the value of n. The measure of angle x in triangle xyz is 75 degrees and the measure of angle q in triangle qrs is equal to 5(n - 3) degrees. We can use this equation to solve for the value of n. To do this, we add 75 and 3, then divide by 5. This gives us a value of 18 for n. Therefore, the measure of angle q in triangle qrs is 18 degrees.

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2400cm³

             \(=300\times 8\\ =2400cm^3\)

\((Analyze\ the\ information\ carefully)\)

I hope this helps you

:)

The correct answer is (b) The central limit theorem is applicable for the sample mean.

The condition that the population size be at least 10 times the sample size is necessary to ensure that the sample mean follows a normal distribution, as required by the central limit theorem. The central limit theorem states that the sample mean will be approximately normally distributed, regardless of the underlying population distribution, as long as the sample size is large enough. In this case, the condition is necessary to ensure that the sample size is sufficiently large for the central limit theorem to be applicable. Options (a), (c), (d), and (e) are not the correct answers because they do not directly relate to the condition that the population size be at least 10 times the sample size.

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The value of Kb will be  1.83 × 10⁻¹¹.

The given problem states that Ka is equal to 5.47×10⁻⁴, and the task is to find Kb. Ka and Kb are related to each other through the equation Kw = Ka × Kb. Kw represents the ion product of water, which is equal to the concentration of H₃O⁺ ions multiplied by the concentration of OH⁻ ions. It has a value of 1.0 × 10⁻¹⁴.

Using the fact that pKw = pH + pOH = 14.00, we can determine the relationship between pKa and pKb. By rearranging the equation, we get pKa + pKb = 14.00. This equation relates the logarithms of the acid dissociation constant (pKa) and the base dissociation constant (pKb).

To find Kb, we can use the formula Kb = Kw/Ka. Substituting the given values, we have Kb = (1.0 × 10⁻¹⁴)/(5.47 × 10⁻⁴). Simplifying this expression, we find Kb = 1.83 × 10⁻¹¹.

Therefore, the value of Kb is determined to be 1.83 × 10⁻¹¹.

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Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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Dot plots are better suited for maintaining the identity of individual observations, especially in smaller data sets, while histograms are useful for visualizing the distribution of larger data sets, even though they lose the identity of each specific data point.

Regarding dot plots and histograms, the true statement is that dot plots do not lose the identity of individual observations. Dot plots display each data point as a dot on a number line or axis, preserving information about individual data points. This is especially useful when dealing with small to moderate-sized data sets, as it allows for easy identification of patterns, clusters, or outliers.

On the other hand, histograms are a graphical representation that organizes data into intervals or bins, which can provide an overview of the distribution of a larger data set. While histograms are often easier to construct and can help visualize patterns and trends for large data sets, they lose the identity of individual observations, as the data points are grouped together in bins.

In summary, dot plots are better suited for maintaining the identity of individual observations, especially in smaller data sets, while histograms are useful for visualizing the distribution of larger data sets, even though they lose the identity of each specific data point.

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Answer:

Buying 5 packs of bread rolls and 3 packs of burger meat

Step-by-step explanation:

Sara needs to find the least common multiple between 6 bread rolls and 10  pieces of burger meat:

\(LCM:\\10\ 6\ |2\\5\ \ 3\ |3\\5\ \ 1\ |5\\1\ \ 1\ |1\\\\LCM = 2*3*5=30\)

Sara will get the same amount of burger to bread rolls when she buys 30 units of each. The numbers of packs of each product that she must buy are:

\(B=\frac{30}{6}=5\ packs\\ M=\frac{30}{10}=3\ packs\)

Sara should buy 5 packs of bread rolls and 3 packs of burger meat.

Answer:

16 years

Step-by-step explanation:

1.7% of 2000 is $34

$544 divided by $34 = 16 years, that is if the interest is yearly and not monthly though

It will take  16 years for a $2,000 investment to earn $544 in interest at a 1.7% interest rate.

percentage, a relative value indicating hundredth parts of any quantity.

Given that  it take a $2 000 investment to earn $544 in interest at a 1.7 interest rate.

We have to find the time.

We can use the simple interest formula to solve this problem:

I = Prt

where I is the interest earned,

P is the principal,

r is the interest rate per time period, and

t is the time period.

Given that Principle amount = $2,000,

Interest I = $544, and

Interest rate r = 1.7% per year.

Percentage value is converted to decimal by dividing with 100.

1.7/100=0.017

We need to find t in years.

Substituting the given values into the formula, we get:

544 = 2,000 × 0.017t

544=34t

Divide both sides by 34

t = 544 /34

t = 16

Therefore, it will take  16 years for a $2,000 investment to earn $544 in interest at a 1.7% interest rate.

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Answer: C

Step-by-step explanation: