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Surface area of the box measuring 5 inches by 3 inches by 7 inches is 142 square inches.

The surface area of the object that refers to the overall space that is filled by its surfaces. Different 3D shapes in the geometry have various surface areas, which can be quickly estimated using the formulas. Two categories are used to classify the surface area:

Curved surface area or Lateral surface area

Surface area in total

Surface area of rectangle = 2 ( lb + bh + hl )

Dimensions of box = 5 inches by 3 inches by 7 inches

Hence,

Length = 5 inches

Breadth = 3 inches

Height = 7 inches

By putting it in formula of surface area of rectangle

= 2 ( lb + bh + hl )

= 2 ( 5*3 + 3*7 + 7*5 )

= 2 ( 15 + 21 + 35 )

= 2 * 71

 = 142 square inches

Hence, the total surface area of the box is 142 square inches.

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Answer:

50π feet^2

Step-by-step explanation:

area of the circle = 10^2 π = 100π feet^2

A of the sector = 100π/2 = 50π feet^2

The correct option is option C i.e. the amount of cut (C) to be marked on the stake is equivalent to 3.75 Ft.

Given that:

It is required to set a stake to mark a grade of 45.49 ft.

i.e. required grade = 45.49 ft

The Hl of the level is 53.56 ft

i.e. HI =  53.56 ft

the rod on the stake reads 4.32 ft.

i.e. Stake reading =  4.32 ft

We know that,

The formula for cut/fill is:

Cut/Fill = HI – Stake reading – required grade

Cut/Fill = 53.56 ft - 4.32 ft - 45.49 ft

Cut/Fill = 53.56 ft - 49.81 ft

Cut/Fill = 3.75 ft

As the value is positive therefore this amount is for cut and not the amount of fill.

The amount of cut (C) to be marked on the stake is 3.75 Ft.

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The probability that the sample mean diameter surpasses 71 when n = 30 is 0.5 if the distribution is normal (the quoted article makes this assumption and even gives the related normal density curve).

The likelihood that the sample mean diameter exceeds 71 when n = 30 is 0.5, since the normal distribution is symmetric around the mean. This means that there is a 50% probability of the sample mean diameter being above the mean, and a 50% probability that it is below the mean.

The correct question is : suppose the distribution is normal (the cited article makes that assumption and even includes the corresponding normal density curve). a. how likely is it that the sample mean diameter exceeds 71 when n = 30

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4. a. The graph of the system is attached below.

b. The solution is: (-1, 3).

5. a. (2, 40) is the solution as shown by the graph.

b. (2, 40) means that both will complete 40 cranes after 2 days

On a graph, when two lines are plotted for different equations, the solution is the coordinates of the point where both lines intersect.

4. a. The graph of y = -3x is the red line in the image attached below, while that of y = x + 4 is the blue line. They both intersect each other at (-1. 3).

b. The solution of the system is therefore, (-1, 3).

5. a. Using the graph given that shows the lines of the equations of DeAndre and Leah, both lines intersect at (2, 40).

We can therefore state that the solution to the system as shown in the graph is: (2, 40).

b. In the context of the scenario given, the solution (2, 40) means that both will have completed equal amounts of 40 cranes after 2 days.

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Answer:

∠BEC is supplementary to ∠AEB

∠AED and ∠BEC are a pair of vertical angles

 The factors in the word problem for the amount of fat in the ice cream

combination are given by the fat in each constituent.

The amount of fat in Cherry ice-cream is 11 grams.

The amount of fat in the Mint Chocolate Chunk ice-cream is 16 grams.

Reasons:

The given parameters are;

Let C represent the amount of fat in Cherry ice-cream, and let M represent

the amount of fat in Mint Chocolate Chunk ice-cream, we get;

4·C + M = 60...(1)

C + 4·M = 75...(2)

Multiplying equation (1) by 4 and then subtracting equation (2) from the

result gives;

4 × (4·C + M) = 4 × 60

16·C + 4·M = 240...(3)

(16·C + 4·M) - (C + 4·M) = 240 - 75

15·C = 165

The amount of fat in Cherry ice-cream C = 11 grams

4 × 11 + M = 60

M = 60 - 4 × 11 = 16

The amount of fat in the Mint Chocolate Chunk ice-cream, M = 16 grams

Answer:

Perimeter is 12+2√26

Step-by-step explanation:

Question:

The perimeter of quadrilateral PQRS with the vertices

P(-2, -2), Q(-1, 3), R(5, 3), and S(4, -2)​

Find distances PS and QR:

Notice the y-coordinates are the same for 2 pairs of points

P(-2, -2), S(4, -2)​ and Q(-1, 3), R(5, 3)

So the distance PS = |-2|+4= 6 and QR = |-1|+5 = 6

Find the distances PQ and SR:

Use the distance formula:

[tex]d= \sqrt{(x_{2}-x_{1} ) ^{2} + (y_{2}-y_{1} ) ^{2} }[/tex]

P([tex]x_{1}[/tex] = -2, [tex]y_{1}[/tex] = -2), Q( [tex]x_{2}[/tex] = -1, [tex]y_{2}[/tex] = 3)

PQ = [tex]\sqrt{(-1--2)^{2} +(3- -2)^{2} } = \sqrt{1^{2} +5^{2} } = \sqrt{26}[/tex]

SR = [tex]\sqrt{26}[/tex], because of PQ and SR are equal.

Find the perimeter of quadrilateral PQRS:

The perimeter is equal to the sum of all sides of the quadrilateral.

P= PS + QR + PQ + SR = 6+6+ √26 +√26 = 12+2√26

The p-value is 0.0388 at 9% significance, so (a) Yes, she has enough evidence with assumptions used in the test is (c) all the sampled data come from a normal distribution and (d) the populations are independent and therefore their covariances are zero.

All data in attached table

First, we must calculate the grand mean. So,

Grand mean ([tex]\bar{\bar{g}}[/tex]) = [tex]\frac{\bar{g_{1}} + \bar{g_{2}} + \bar{g_{3}} + \bar{g_{4}}}{k}[/tex]

= (67.5 + 67.17 + 67.28 + 66.77) / 4

= 67.18

Next, we calculate SSTr

SSTr = [tex]\sum n_i(\bar{g_{i}} - \bar{\bar{g}})^2[/tex]

= 9360(67.5-67.18)^2 + 9870(67.17-67.18)^2 + 7020(67.28-67.18)^2 + 5040(66.77-67.18)^2

= 1,876.875

Then, we calculate SSE

SSE = [tex]\sum(n_i-1)Sg_i^2[/tex]

= (9360-1)(14.85^2) + (9870-1)(15.1^2) + (7020-1)(14.79^2) + (5040-1)(15.16^2)

= 7,007,556.804

Before we calculate F test, we first calculate the N value with this formula,

N = [tex]\sum n_i[/tex]

= 9360 + 9870 + 7020 + 5040

= 31,290

Then, for F test use this formula,

F = [tex]\frac{SSTr/(k-1)}{SSE/(N-k)}[/tex]

= [tex]\frac{1876.875/(4-1)}{7007556.804/(31290-4)}[/tex]

= 2.793

Next, for p-value we use p value calculator for f test with following data,

F-ratio value = 2.793

DF-numerator = k - 1 = 4 - 1 = 3

DF-denominator = N - k = 31290 - 4 = 31286

and we get the p-value is 0.0388

Since, 0.0388 < 9% of significance, so she has enough evidence to initiate a deeper investigation.

Thus, assumptions used in the test is all the sampled data is normal distribution and the population are independent with covariances are zero and the result is yes, she has sufficient evidence.

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Answer:

he would have a 50% chance of getting one of the 10 prizes

The inequality that can be used to find the values for p is p + 7 ≤ 50.

Given the information,

Mr. Smith can only spend up to $50 at a museum. The museum admission ticket is $7. He can use his P dollars to purchase other items from the museum.

The total budget is $50.

The cost per ticket is $7

⇒ Total spent ≤  Total Budget

⇒ p + 7 ≤ 50

⇒ p ≤ 43

Therefore, p + 7 ≤ 50 will be the inequality that aids in determining the range of values for p.

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The probability is 0.25.

What is probability?

Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To determine how likely an event is to occur, mathematics has created the concept of probability.

Given there are 2 coins flipped 4 times, we get the following sample space

S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

Now, A = event of having at least 3 heads.

A= {HHHH, HHHT, HHTH, HTHH, THHH}

The number of events having the first flip heads is 4.

Therefore, the probability is:

P(A) =

[tex]=\frac{successful \space\ events}{total\space\ sample\space\ events}\\=\frac{4}{16}\\=0.25[/tex]

Therefore, the probability of flipping at least 3 heads in 4 flips of 2 fair coins given that the first flip is heads is 0.25.

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The required numbers for the given case are 3 and 7 respectively.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

As per the given data the problem can be solved as follows,

Suppose the first number be x and the second be y.

Now, the equations can be formed as,

x + 3y = 24             (1)

5x + 3y = 36           (2)

Solve these equations by multiplying equation (1) by 5 and then subtract from (2) as below,

5x + 3y - 5(x + 3y) = 36 - 5 × 24

3y - 15y = -84

=> -12y = -84

=> y = 7

Substitute y = 7 in equation (1) to get,

x + 3 × 7 = 24

=> x = 3

Hence, the numbers for the given problem are 3 and 7 respectively.

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The probability of randomly getting the red marbles from both Jar A and Jar B is 8/25.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, the probability that both marbles will be red is:

Probability formula: P(E) = Favourable events/Total events

We know that:

Jar A: 4 red marbles and 6 blue marbles

The probability of randomly choosing red marble is:

P(E) = Favourable events/Total events

P(E) = 4/10

P(E) = 2/5

Jar B: 8 red marbles and 2 blue marbles

The probability of randomly choosing red marble is:

P(E) = Favourable events/Total events

P(E) = 8/10

P(E) = 4/5

So, the total probability will be:

2/5 * 4/5

8/25

Therefore, the probability of randomly getting the red marbles from both Jar A and Jar B is 8/25.

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Correct question:

Jar A contains 4 red marbles and 6 blue marbles. Jar B contains 8 red marbles and 2 blue marbles. (20 points) If you choose marbles from Jar A and Jar B at random, what is the probability that they are both red?

Answer:

[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]

Step-by-step explanation:

Division of fractions can be represented as multiplication by one of the fractions' reciprocal. (Skip, Flip, and Multiply)

So,

[tex]\dfrac{11}{3} \div \dfrac{2}{3} = \dfrac{11}{3} \times \dfrac{3}{2}[/tex]

And we can simplify this to:

[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]

95% of the associations we would anticipate to see by chance are weaker than the statistical relationship between the two variables.

Statistical connection:

A statistical relationship states that if one variable (X) changes, another will systematically rise (Y).

Given,

Statistical significance is the degree to which a statistical link exists between two variables.

Here, we must determine whether it is stronger than the proportion of associations we would anticipate to occur by chance.

While researching the posed question, we discovered that the statistical correlation is more than the 95% chance correlation rate.

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Answer:

-4/3

Step-by-step explanation:

We can find the slope of the line using

m = ( y2-y1)/(x2-x1)

m = ( -9 -3)/( 8 - -1)

   = ( -9-3)/( 8+1)

   = -12 / 9

  = -4/3

Answer:

[tex]\sf m=-\frac{4}{3}[/tex]

Step-by-step explanation:

First, select any two coordinates of the line.

( -1, 3 ) ⇒ ( x₁ , y₁ )

( 2, -1 ) ⇒ ( x₂ , y₂ )

And now let us use the below formula to find the slope of the line.

[tex]\sf m= \frac{y_1-y_2}{x_1-x_2} \\[/tex]

Let us find the slope now.

[tex]\sf m= \frac{y_1-y_2}{x_1-x_2} \\\\\sf m= \frac{3-(-1)}{-1-2} \\\\\sf m= \frac{4}{-3}\\\\\sf m=-\frac{4}{3}[/tex]

The horse was worth it for $1800.

What is proportion?

A mathematical comparison of two numbers is called a proportion. Ratios and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers.

Based on the given question condition, where, 'h' denotes the amount for the horse in dollars,  the proportion can be defined as:

or,  [tex]\frac{19200 + h}{12} = \frac{10450+h}{7}[/tex]

or, (19200 + h)7 = (10450 + h)12

or, 134400 + 7h = 125400 + 12h

or, 12h - 7h = 134400 - 125400

or, 5h = 9000

or, h = 9000/5 = 1800

Hence, the horse was worth $1800.

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Answer:

Figure B.

Step-by-step explanation:

Figure A uses what is visually similar in size cylinders to give a detailed image of the amount of money (assumingly as profit). Each given cylinder that is in similar size represents $200, and so it is easy to figure out how the amount of money per store.

In the case of Figure A,

Save Store = $400

Leff's Store = $800

Low Pricer = $1200

In the case of Figure B, however, while it gives a legend for price per cylinder of that proportion, it does not make use of the legend, and does not give a adequate legend to decipher the Figure. In essence, the data given in Figure B is useless as it makes no use of its legend.

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Slope is "change in y over change in x".

    [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using those two points, you'd have

    [tex]m=\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{0-6}{3-0}=\dfrac{-6}{3}=-2[/tex]

Notice that doesn't match any of the listed answers.  The reason is that two of those answers aren't reduced.

If you reduce the first answer of [tex]\dfrac{6}{-3}[/tex], you have  [tex]\dfrac{6}{-3}=-2[/tex].  So that first answer is equivalent to the calculation above.

The answer from your list is the first one.

The given expression of trigonometry is equivalent to cos(2θ).

trigonometry capability, in math, one of six capabilities (sine [sin], cosine [cos], digression [tan], cotangent [cot], secant [sec], and co-secant [csc]) that address proportions of sides of right triangles. These six geometrical capabilities comparable to a right triangle.

We have,

1 - tan^2(θ)/1 +  tan^2(θ)

Use 1 + tan^2(θ) = sec^2(θ)

1 - tan^2(θ)/ sec^2(θ)

1/ sec^2(θ) - tan^2(θ)/sec^2(θ)

Use tan(θ) = sin(θ)/cos(θ)

cos^2(θ) - sin^2(θ)×cos^2(θ)/cos^2(θ)

cos^2(θ) - sin^2(θ)

Using sin^(θ) + cos^2(θ) = 1

cos^2(θ) - (1 - cos^2(θ))

2cos^2(θ) - 1

Here we have 2cos^2(θ) - 1 = cos(2θ)

Then, simplification of given expression is cos(2θ).

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Correct question:

which expression is equivalent to 1 - tan^2(θ)/1 +  tan^2(θ) for all values of θ for which 1 - tan^2(θ)/1 +  tan^2(θ) is defined?

Testing the hypothesis "Americans express executives hypothesize that 40% of college students own an Americans express credit card." is an example of generalizing.

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge. A straightforward hypothesis only hypothesizes the relationship between two independent and dependent variables.

An example of testing a generalization is "American Express executives' hypothesis that 40% of college students own an American Express credit card."

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Answer: 20 cards.

Step-by-step explanation: If Sarah can make 4 cards in 60 minutes, then she can make 1 card in 60/4 = 15 minutes.

Therefore, in 300 minutes, she can make 300/15 = <<300/15=20>>20 cards.

The side length of the original cube is, 8.60 feet.

What is volume?

The amount of three-dimensional space that is occupied is measured by volume. It is frequently expressed quantitatively using SI-derived units, other imperial units, or US customary units. Volume and the notion of length are connected.

Given:

A 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft^3.

Let x = the side of the cube then

x^3 = original volume of the cube and

8x^2 = volume of the 8 feet slice

Therefore,

x^3 - 8x^2 = 44

Subtract 44 on both sides,

x^3 - 8x^2 - 44 = 44 - 44

x^3 - 8x^2 - 44 = 0

After solving x ≈ 8.59553

⇒ x = 8.60

Hence, the side length of the original cube is 8.60 feet.

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Answer: 256

Step-by-step explanation:

8^8/3 is the same as an 8 square root! We have to factor out and I get 2^8 after finish factor the smallest number and get 256!

Answer:

x=6

Step-by-step explanation:

i assume these are similar triangles so we can set them up as fractions

x/9=4/x

cross multiply

9(4)=x(x)

36=x^2

√.    √

6=x

and now we can check if each have the same ratio

6/9= 4/6

2/3=2/3

hopes this helps please mark brainliest

Answer:

16

Step-by-step explanation:

Let us assume the square is (m-a)²
We have to find a

(m-a)² = m² -2am + a²

We are given
m² -8m

Comparing terms
2a = 8

a = 4

so the square is (m-4)²

which is m² - 8m + 16