an instructor flips a coin and divides her class into two groups: those who got heads and those who got tails. by doing this, the instructor has created

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:

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

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

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:

W'(-6,4)

Step-by-step explanation:

W (6,4)  When it is reflective over the y axis it is now not six to the right of the y axis, it is now 6 to the left.

W' ( -6,4)

W' (-6 4) is now reflected over the x axis.  Instead of being 4 units above the x axis, it is now 4 unit below

W" (-6,-4)

 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:

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

Congruence theorem used here are;-

1. HL theorem

2. SAS theorem

3. SSS theorem

Given,

Triangles ACR and ABR have a common side (hypotenuse of two right triiangles).

ABR and ACR form a right angle.

The AB and AC sides line up.

The BR and CR sides line up.

1. The HL theorem can be used since two triangles have congruent hypotenuses and pairs of legs.

2. Because two triangles contain two pairs of congruent legs and a pair of included right angles between these legs, you can utilize the SAS theorem.

3. Because two triangles have two pairs of congruent legs and congruent hypotenuses, you can utilize the SSS theorem.

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Question is incomplete. Completed question is given below;-

Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.

Triangles A B R and A C R share side A R. Angles A B R and A C R are right angles. Sides A B and A C are congruent. Sides B R and C R are congruent.

HL

SAS

SSS

ASA

AAS

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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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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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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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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Answer:

426 cm^2

Step-by-step explanation:

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]

The probability mode for the given value is created. The expected value and standard deviation of prospective winnings are -$0.28 and $18.33. The expected value and standard deviation if the game is played five times are -$1.40 and $40.99. The probability that the person running the game makes a profit is 0.561.

Probability is a way to determine how likely something is to happen. It is computed by dividing the frequency of the event by the total number of outcomes. The formula then becomes P(X) = frequency of the event÷total number of outcomes.

The product of the probabilities determines the likelihood that two or more occurrences will coincide. This is given by, P(A and B) = P(A)P(B).

a) To create a probability model follow the steps. Let X is an occurrence of an event.  The table is attached here.

b)  The expected value is calculated using the formula, E(X) = μ = ∑ x P(x).

[tex]\begin{aligned}E(X)=\mu&=x_1p_1+x_2p_2+x_3p_3\\&=40\left(\frac{1}{6}\right)+0\left(\frac{5}{36}\right)+(-10)\left(\frac{25}{36}\right)\\&=-\$ 0.28\end{aligned}[/tex]

Also,

[tex]\begin{aligned}E(X^2)&={x_1}^{2}p_{1}+{x_2}^{2}p_{2}+{x_3}^{2}p_{3}\\&=(40)^2\frac{1}{6}+(0)\frac{5}{36}+(-10)^2\frac{25}{36}\\&=(1600)\frac{1}{6}+(0)\frac{5}{36}+(100)\frac{25}{36}\\&=266.67+69.44\\&=336.11\end{aligned}[/tex]

And the standard deviation is calculated using the formula, σ=√Var[X].

[tex]\begin{aligned}\sigma=\sqrt{\text{Var}(X)}&=\sqrt{E(X^2)-E(X)^2}\\&=\sqrt{336.11-0.08}\\&=\sqrt{336.03}\\&=\$18.33\end{aligned}[/tex]

c) The expected value and standard deviation for playing the game 5 times are calculated as follows.

The expected value is,

[tex]\begin{aligned}5\times E(X)&=5(-\$0.28)\\&=-\$1.40\\\end{aligned}[/tex]

The standard deviation is,

[tex]\begin{aligned}\sigma&=\sqrt{5\times\tex{Var}(X)\\&=\sqrt{5\times336.03\\&=\sqrt{1680.15}\\&=\$40.99\end{aligned}[/tex]

d) The dice rolling is random and the winning chance is independent. The probability the person running the game makes a profit (P(x<0)) is given by,

The population mean, μ(Y) = -$0.28

The standard deviation for a population of 100 is,

[tex]\begin{aligned}\sigma&=\sqrt{\frac{\text{Var}(X)}{n}}\\&=\frac{18.33}{\sqrt{100}}\\&=1.83\end{aligned}[/tex]

The z-score for mean winning is,

[tex]\begin{aligned}z&=\frac{x-\mu}{\sigma}\\&=\frac{0-(-0.28)}{1.83}\\&=0.153\end{aligned}[/tex]

For a person to make a profit, the mean winning of the player should be less than the z-score. Then,

The P-value from the z-table, P(z<0.153)=0.5608

The answer is 0.561.

The complete question is -

You pay $10 and roll a die. If you get a 6, you win$50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What’s the probability the person running the game makes a profit?

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Answer: its 4

Step-by-step explanation: trust me bro i had this question too

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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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

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 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 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?

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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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

In 3rd step Henry made a mistake by taking the division operator rather than taking subtraction.

A number system is defined as a system of writing to express numbers.

The given problem is 5⁴5⁶/5²

We know that when bases are same then powers will be added

5⁴⁺⁶/5²

5¹⁰/5²

When denominator is taken up then the sign of denominator power value changes to negative.

5¹⁰⁻²

5⁸

Hence, in 3rd step Henry made a mistake by taking the division operator than subtraction.

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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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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: 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 final two equations which represent the given situation are:

2x - y = -6 and 3x - y = -5.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a linear equation of two variables.

Suppose,

The larger number is 'y' and the smaller number is 'x'.

First relation,

'y' is equal to twice the sum of a smaller number (x) and 3. So we represent this as:

y = 2(x+3)

y = 2x + 6

2x - y = -6                     ............(1)

Second relation,

The larger number (y) is equal to 5 more than 3 times the smaller number (x). So we represent this as:

y = 5 + 3x

3x - y = -5                     .............(2)

Hence, the final two equations which represent the given situation are:

2x - y = -6 and 3x - y = -5.

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