Explain the error in this student's work and make the correction
2^2 x 2^4 x 2^3 = 2^24

Answer:

Surface area = 972 mm^2

Step-by-step explanation:

One of the formula we can use for surface area of a triangular prism is

SA = bh + L(s1 + s2 + s3), where

In the figure, the base (b) is 27 mm, the height (h) is 14 mm, the length (L) is 9 mm, and we can use 18, 27, and 21 for s1, s2, and 23:

SA = 27 * 14 + 9(18 + 27 + 21)

SA = 378 + 9(66)

SA = 378 + 594

SA = 972 mm^2

Thus, the surface area of the figure is 972 mm^2

The true mean number of pushups that can be performed, as determined by the t-distribution, is within a 95% confidence interval of (9, 21).

Since we know the sample standard deviation for this issue, the t-distribution is applied.

Given,

The sample mean, x = 15 .

The sample standard deviation, s = 9 .

The sample size, n = 10 .

As a result, df = 9. Next, we determine the number of degrees of freedom, which is one less than the sample size.

The crucial value for a 95% confidence interval is then determined by looking at the t-table or using a calculator, yielding t = 2.2622.

The margin of error;

M = t × s/n

Then,

M = 2.2622 × 9/√10 = 6

The confidence interval is:

x ± M

Then

x - M = 15 - 6 = 9

x + M = 15 + 6 = 21

Therefore,

The confidence interval is (9, 21).

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Answer:

perimeter = 28

Step-by-step explanation:

Tangents drawn to a circle from an external point are congruent, thus

AH = AB = 5

GH = GF = 2

EF = ED = 3

CB = CD = 4

Sum the 8 parts for perimeter of polygon ACEG

perimeter = 5 + 5 + 2 + 2 + 3 + 3 + 4 + 4 = 28

Answer:

a) 80 ml

b) 450 cm³

Step-by-step explanation:

A) solution

1 cm³ = 1 ml

80 cm³ = 80 ml

B) solution

1 ml = 1 cm³

450 ml = 450 cm³

Answer:

15foot

Step-by-step explanation:

The set up will give a right angled triangle.

The length of the shadow will be the hypotenuse = 16foot

The height of the tree will be the opposite = x

The angle of elevation = 70°

Using the SOH CAH TOA trig identity

Sin theta = opposite/hypotenuse

Sin 70 = x/16

x=16sin70

x = 15.04feet

Hence the height of the tree to the nearest whole foot is 15foot

Using the normal distribution, the probability that a single randomly selected value is less than 971 dollars is 0.2123.

In the given question,

CNNBC recently reported that the mean annual cost of auto insurance is 1007 dollars.

The standard deviation is 241 dollars.

We take a simple random sample of 99 auto insurance policies.

We have to find the probability that a single randomly selected value is less than 971 dollars.

From the question,

Mean = 1107 dollars

Standard Deviation = 241 dollars

So the probability that a single randomly selected value is less than 971 dollars.

Using the normal distribution

z = (x−mean)/Standard Deviation

P(x<971) = P(z<(973−1107)/241)

Simplifying

P(x<971) = P(z<(−134)/241)

P(x<971) = P(z<−0.56)

P(x<971) = 0.2123

Hence, the probability that a single randomly selected value is less than 971 dollars is 0.2123.

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Answer:

B

Step-by-step explanation:

1.5*2.5 = 3.75

15/4 = 3.75

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{3} x + 3\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{3\implies\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}\)

so we're really looking for the equation of a line whose slope is -1/3 and that is passes through (3 , 2)

\((\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y-2=- \cfrac{1}{3}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{3}x+3 \end{array}}\)

Answer:

56

Step-by-step explanation:

Answer:

b=6

Step-by-step explanation:

b-1/2(b-6)=6

b-1/2b+3=6

2b-b+6=12

b+6=12

b=12-6

b=6

Answer:

Hypotenuse = 8 cm (Approx.)

Step-by-step explanation:

Given:

Side1 = 3 cm

Side2 = 7 cm

Find:

Hypotenuse

Computation:

Hypotenuse = √Perpendicular² + base²

Hypotenuse = √side1² + side2²

Hypotenuse = √3² + 7²

Hypotenuse = √9 + 49

Hypotenuse = √58

Hypotenuse = 7.61

Hypotenuse = 8 cm (Approx.)

There are no further solutions to this initial value problem, as these two solutions cover all possible cases.To solve the initial value problem x' = |x|^(1/2), x(0) = 0, we can separate the variables and integrate.

For x ≠ 0, we can rewrite the equation as dx/|x|^(1/2) = dt. Integrating both sides gives us 2|x|^(1/2) = t + C, where C is the constant of integration.

For x > 0, we have x = (t + C/2)^2.
For x < 0, we have x = -(t + C/2)^2.

Now, considering the initial condition x(0) = 0, we have C = 0.

Thus, we have two solutions:
1) x₁(t) = 0, which satisfies the initial condition.
2) x₂(t) = t|t|/4, which satisfies the initial condition.

These solutions do not contradict Picard's theorem, as Picard's theorem guarantees the existence and uniqueness of solutions for initial value problems under certain conditions. In this case, the solutions x₁ and x₂ are both valid solutions that satisfy the given differential equation and initial condition.

There are no further solutions to this initial value problem, as these two solutions cover all possible cases.

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Answer:

-0.5x\(x^{2}\)+3x=0

Step-by-step explanation:

Answer:

y=\(\frac{9}{2\\}\) x-13

Step-by-step explanation:

first, since it's parallel the slope has to be the same and the y-intercept has to be different.

you will have y=9/2x+b

find b, by using the points you are given so you will get

-4=(9/2) times (2)+b.

then when sloving you will get b=-13 and so the full equation will be

y=9/2x-13

To compute the Legendre transform of a function, we start with the function \(f(x)\) and define a new variable \(p\) as the derivative of \(f\) with respect to \(x\), i.e., \(p = \frac{{df}}{{dx}}\). Then the Legendre transform of \(f(x)\) is given by \(g(p) = px - f(x)\).

1. Compute the Legendre transform of \(f(x) = x^2\):

  First, we need to find \(p = \frac{{df}}{{dx}}\) by differentiating \(f(x)\):

  \(\frac{{df}}{{dx}} = \frac{{d}}{{dx}}(x^2) = 2x\)

  Now, we can substitute this value of \(p\) into the Legendre transform formula:

  \(g(p) = px - f(x) = 2x \cdot x - x^2 = x^2\)

  Therefore, the Legendre transform of \(f(x) = x^2\) is \(g(p) = x^2\).

2. Compute the Legendre transform of \(g(p)\) to recover \(f(x)\):

  We'll start with the expression for \(g(p)\), which is already in the form of a Legendre transform:  \(g(p) = x^2\) .   To recover \(f(x)\), we need to find \(x\) as a function of \(p\) by inverting the derivative. Let's differentiate \(g(p)\) with respect to \(p\):  \(\frac{{dg}}{{dp}} = \frac{{d}}{{dp}}(x^2) = 0\).  Since the derivative with respect to \(p\) is zero, it implies that \(x\) is a constant with respect to \(p\). Let's call this constant \(c\). Therefore, \(x = c\) for any value of \(p\).

Hence, by the Legendre transform, \(f(x) = c^2\), where \(c\) is a constant.

The Legendre transform of \(f(x) = x^2\) is \(g(p) = x^2\), and the Legendre transform of \(g(p)\) recovers \(f(x) = c^2\), where \(c\) is a constant.

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Answer:

5/6

Step-by-step explanation:

slope = (difference in y)/(difference in x)

slope = (10 - 5)/(9 - 3) = 5/6

Answer: 5/6

Answer:

Hi! The answer to your question is \(m=5/6\)

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☁Brainliest is greatly appreciated!☁

Hope this helps!!

- Brooklynn Deka

Number of students included  in the sample to estimate the proportion with confidence interval 95% is equal to 9604.

As given in the question,

Confidence interval = 95%

z -critical value for 95% confidence interval = 1.96

Estimate proportion is in the limit 0f 0.07

Let us assume value of

sample proportion 'p' = 0.5

Margin of error  = 0.01

level of significance = 0.05

let 'n' be the sample size to represent number of students included for the hypothesis.

n = p ( 1 - p ) ( z- critical value / margin of error )²

⇒ n = 0.5 ( 1 - 0.5 )( 1.96 / 0.01 )²

⇒ n = 0.5 (0.5 ) (3.8416/ 0.0001)

⇒ n = 0.25 × 38416

⇒ n = 9604

Therefore, the number of students included for the hypothesis to estimate the proportion with confidence interval 95% is equal to 9604.

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Answer:

7 times x = t

Step-by-step explanation:

if your buying 3 dozen of donuts, the total cost would be by doing 7x3

Solution:

It should be noted:

Let's reread the sentence carefully.

Eric sells donuts for $7    per dozen.

                                   ↥           ↥

                                  $7     1 dozen

The equation created: $7 = 1 dozen

If x dozen doughnuts were sold, equation: $7x = t = x dozen

Thus, the equation that can determine the total cost, t, for x dozen of donuts is $7x = t.

The question is asking which months had bills under $40.

To answer the question, we need to look at the bar chart and identify the bars that are below the $40 mark. Based on the given options, we can select all the months that meet this criterion.

It is essential to note that the answer options provided are the only ones we can choose from. Therefore, we need to be careful and check all the options that apply. In this case, we need to look for bars that are lower than $40 and select all the corresponding months.

In conclusion, to answer the question, we need to check the bar chart and select all the months that had energy bills under $40. The answer options are March, October, May, September, April, and November.

Upon examination, we can see that the months with energy bills under $40 are as follows:

A. March
C. May
E. April

These months had lower energy consumption, resulting in a reduced monthly energy bill. Various factors may contribute to such fluctuations in energy usage, such as seasonal changes, the shop's operational hours, or the efficiency of the equipment used.

In summary, the months of March, May, and April had energy bills under $40 for Wally's tackle shop. It's essential to monitor energy usage regularly to identify patterns and potential opportunities for cost savings and efficiency improvements.

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The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

To find the extreme values of V, we need to take the derivative of V and set it equal to zero. So, let's begin:

\(V(x) = x(10-2x)(16-2x)\)
Taking the derivative with respect to x:
\(V'(x) = 10x - 4x^2 - 32x + 12x^2 + 320 - 48x\)
Setting V'(x) = 0 and solving for x:
\(10x - 4x^2 - 32x + 12x^2 + 320 - 48x = 0\\8x^2 - 30x + 320 = 0\)
Solving for x using the quadratic formula:
\(x = (30 ± \sqrt{(30^2 - 4(8)(320))) / (2(8))\\x = (30 ± \sqrt{(1680)) / 16\\x = 0.93 or x =5.07\)
So, the extreme values of V occur at x ≈ 0.93 and x ≈ 5.07. To determine whether these are maximum or minimum values, we need to examine the second derivative of V. If the second derivative is positive, then the function has a minimum at that point. If the second derivative is negative, then the function has a maximum at that point. If the second derivative is zero, then we need to use a different method to determine whether it's a maximum or minimum.

Taking the second derivative of V:
V''(x) = 10 - 8x - 24x + 24x + 96
V''(x) = -8x + 106

Plugging in x = 0.93 and x = 5.07:
V''(0.93) ≈ 98.36 > 0, so V has a minimum at x ≈ 0.93.
V''(5.07) ≈ -56.56 < 0, so V has a maximum at x ≈ 5.07.

Now, to interpret these values in terms of the volume of the box, we need to remember that V(x) represents the volume of a box with length 2x, width 2x, and height x. So, the maximum value of V occurs at x ≈ 5.07, which means that the volume of the box is greatest when the height is about 5.07 units. The minimum value of V occurs at x ≈ 0.93, which means that the volume of the box is smallest when the height is about 0.93 units.

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a) The extreme values of V are:

Minimum value: V(0) = 0

Relative maximum value: V(3) = 216

Absolute maximum value: V(4) = 128

b) The absolute maximum value of V at x = 4 represents the case where the box has a square base of side length 4 units, height 2 units, and width 8 units, which has a volume of 128 cubic units.

a) To find the extreme values of V, we first need to find the critical points of the function. This means we need to find where the derivative of the function equals zero or is undefined.

Taking the derivative of V(x), we get:

\(V'(x) = 48x - 36x^2 - 4x^3\)

Setting this equal to zero and solving for x, we get:

\(48x - 36x^2 - 4x^3 = 0\)
4x(4-x)(3-x) = 0

So the critical points are x = 0, x = 4, and x = 3.

We now need to test these critical points to see which ones correspond to maximum or minimum values of V.

We can use the second derivative test to do this. Taking the derivative of V'(x), we get:

\(V''(x) = 48 - 72x - 12x^2\)

Plugging in the critical points, we get:

V''(0) = 48 > 0 (so x = 0 corresponds to a minimum value of V)
V''(4) = -48 < 0 (so x = 4 corresponds to a maximum value of V)
V''(3) = 0 (so we need to do further testing to see what this critical point corresponds to)

To test the critical point x = 3, we can simply plug it into V(x) and compare it to the values at x = 0 and x = 4:

V(0) = 0
V(3) = 216
V(4) = 128

So x = 3 corresponds to a relative maximum value of V.
b) In terms of the volume of the box, the function V(x) represents the volume of a rectangular box with a square base of side length x and height (10-2x) and width (16-2x).
The minimum value of V at x = 0 represents the case where the box has no dimensions (i.e. it's a point), so the volume is zero.
The relative maximum value of V at x = 3 represents the case where the box is a cube with side length 3 units, which has a volume of 216 cubic units.
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The assumption that the population standard deviations are unknown but assumed unequal is not necessary for performing a one-way ANOVA. In fact, the one-way ANOVA assumes that the population standard deviations are equal.

The other assumptions - that the samples are selected independently and that the populations are normally distributed - are necessary for performing a one-way ANOVA. It is important to note that violating these assumptions can lead to inaccurate results and conclusions. Therefore, it is crucial to assess the validity of these assumptions before performing a one-way ANOVA.

This can be done through statistical tests and graphical analysis. Overall, understanding the assumptions of a one-way ANOVA is important in order to interpret and apply its results correctly.

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Answer:

where's the picture. to the nearest mile...

Step-by-step explanation:

;-;

The probability of drawing a seven and then a four when randomly drawing two cards without replacement is 0.0045 or approximately 0.45%.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement can be calculated using the following steps:

First, we need to determine the total number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement. This can be found using the combination formula:

C(52,2) = 52! / (2! * (52-2)!) = 1,326

Next, we need to determine the number of favorable outcomes where we draw a seven and then a four.

There are four sevens and four fours in a deck of 52 cards, so the probability of drawing a seven on the first draw is 4/52. Since we are not replacing the card, there are now 51 cards left in the deck, and three of them are fours. Therefore, the probability of drawing a four on the second draw is 3/51.

The probability of drawing a seven and then a four is the product of the probabilities of drawing a seven on the first draw and a four on the second draw:

P(seven and then four) = (4/52) * (3/51) = 0.0045 or approximately 0.45%.

Therefore, the probability of drawing a seven and then a four when without replacement is 0.0045 or approximately 0.45%.

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F(x) = x^2 + 8x^3 + k

End behavior: As x approaches positive or negative infinity, F(x) approaches positive infinity.

Maximum/minimum: There is no global maximum or minimum without more information about k.

x-intercepts: There are no x-intercepts for this function.

Restrictions on domain and range: No restrictions specified.

F(x) = x^6 + kx^4 - 9x^2 - 27

End behavior: As x approaches positive or negative infinity, F(x) approaches positive infinity.

Maximum/minimum: There is no global maximum or minimum without more information about k.

x-intercepts: There are no x-intercepts for this function.

Restrictions on domain and range: No restrictions specified.

f(x) = -1/2x^7 - 441x^3 + k

End behavior: As x approaches positive or negative infinity, f(x) approaches negative infinity.

Maximum/minimum: There is no global maximum or minimum without more information about k.

x-intercepts: There are no x-intercepts for this function.

Restrictions on domain and range: No restrictions specified.

The number of turns and the maximum and minimum number of x-intercepts for this type of function can't be determined without a graph.

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Answer:

7.13 each

Step-by-step explanation:

70 - 13 = 57. Divide 57/8 and get your answer

(7.125 rounded is 7.13)

Answer:

-4 degrees

Step-by-step explanation:

You subtract 14-18

The steps to construct an equilateral triangle inscribed in a circle are as shown above.

A polygon is a plane figure that is bound by three or more line segments that join at the vertices. Polygons can be constructed through a series of steps using various tools such as a compass, a straight edge, and a protector. Given the problem in step 2 to construct regular polygons inscribed in a circle, let us construct an equilateral triangle inscribed in a circle as follows:Step-by-step construction of an equilateral triangle inscribed in a circle by hand using a compass and straightedge:Step 1: Draw a circle of radius r and label the center O. Step 2: Construct a line segment that passes through the center O of the circle, and let the line segment be labeled AB. Step 3: Place the compass on point A and draw an arc that intersects circle O at point C. Without adjusting the compass, place the compass on point B and draw another arc that intersects circle O at point D. Step 4: With the same radius from Step 3, place the compass on point C and draw an arc that intersects line AB at point E. Step 5: Place the compass on point D and draw another arc with the same radius from Step 3 that intersects line AB at point F. Step 6: Draw a line segment from point C to point F and another line segment from point D to point E. The line segments CF and DE should intersect at point G.Step 7: Draw a line segment from point G to point O.

Finally, triangle CEF is the desired equilateral triangle inscribed in the circle O.A screenshot of the construction is as follows:Answer: The steps to construct an equilateral triangle inscribed in a circle are as shown above.

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Answer:

The solution is in the image

Answer:

\(y = - 3x {}^{ - 12x - 1} \)

Step-by-step explanation:

Hope that's help your answer

In a hypothesis, when the t value is 7.14 and the critical value is 6.10, the decision that should be made is to reject the null hypothesis.

It should be noted that a hypothesis is simply used to get information about a certain thing.

In this case, in a hypothesis, when the t value is 7.14 and the critical value is 6.10, the decision that should be made is to reject the null hypothesis.

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a) The probability that at least 879 actually did vote is given as follows:

P(X≥879​) = 0.0244.

b) The result suggests that there is enough evidence to consider that the proportion is greater than 69%, as the probability is less than 0.05.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \(\mu = np, \sigma = \sqrt{np(1-p)}\).

The parameters of the binomial distribution for this problem are given as follows:

n = 1227, p = 0.69.

Hence the mean and the standard deviation are given as follows:

The probability that at least 879 people voted, using continuity correction, is one subtracted by the p-value of Z when X = 878.5, hence:

Z = (878.5 - 846.63)/16.2

Z = 1.97

Z = 1.97 has a p-value of 0.9756.

1 - 9756 = 0.0244 = 2.44%.

(continuity correction is used because the binomial distribution is discrete, while the normal distribution is continuous).

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