A professor had students keep track of their social interactions for a week. The
number of social interactions over the week is shown in the following grouped
frequency distribution. What is the class width?
Number of Social
Interactions
35-42
43-50
51-58
59-66
67-74
75-82
83-90
91-98
99-106
107-114
Frequencies
5
15
15
20
12
10
8
6
1
2

Answer: 6

Step-by-step explanation:

Answer:

Refer to step-by-step

Step-by-step explanation:

Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]

Plug in the value of 2 into the limit.

[tex](2)^{2}=4[/tex]

Thus we proved the limit.

Answer:

Find the difference between two integers by adding the additive inverse. The distance is the absolute value of the difference. Check the distance by plotting the original two integers on a number line and counting the units between them

Answer:

Find the difference between two integers by adding the additive inverse. The distance is the absolute value of the difference. Check the distance by plotting the original two integers on a number line and counting the units between them.

Step-by-step explanation:

sample answer

Answer:

vertices in total will coincide = 1174/2 = 587

Step-by-step explanation:

1st polygon: 1174 sides, 1174 vertex, arc for between 2 vertex= 360°/1174 (arc1)

2nd polygon: 2935 sides, 2935 vertex, arc for between 2 vertex= 360°/2935 (arc2)

360°/1174 = (360°/2935) x (5/2)  (every 2.5 arc2 = 1 arc1)

It means every 5 arc2 = 2 arc1, this is the 2nd vertex coincide

vertices in total will coincide = 1174/2 = 587

check: 2935/5 = 587

Answer:

12/30, if you reduce then it would be 2/5 because you divided by 6 hope this helps! :D

Step-by-step explanation:

The fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]

Given the following data:

To find the fraction that represents the eaten portion of the cake;

In this exercise, you're required to find what fraction represents the eaten portion of the wedding cake.

[tex]Fraction = \frac{E}{W}[/tex]

Substituting the values into the equation, we have;

[tex]Fraction = \frac{12}{30}[/tex]

Dividing both sides by 6, we have;

[tex]Fraction = \frac{2}{5}[/tex]

Therefore, the fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]

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The z-score for the 0.75 proportion is -1.95.

The Z-score calculates the deviation of the measure from the mean in standard deviations. We seek for the p-value linked with this Z-score after locating the Z-score in the z-score database.

The likelihood that the value of the measure will be less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.

In a set with mean X and standard deviation μ, the z score of a measure X is given by:

Z=(X-μ)/σ

In this problem, we have that:

n=100,p=0.82

So,μ=E(X)=np=100×0.82=82

Therefore, √V(X)=√np×(1-p)=√100×0.82×0.18=3.841

For Finding the probability that less than 75 in the sample keypads pass inspection.

Using continuity correction, this is (P(75-0.5)<=P(74.5)), which is the p-value of Z when X = 74.5.

=>z= (74.5-82)/3.841

=>z= - 7.5/3.841

=>z= - 1.95 has a p-value to 0.

Hence, if a random sample of 100 keypads is analyzed and 75 pass inspection, then the z-score for 0.75 proportion is -1.95

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Answer:

The appropriate answer is option b (0.0228).

Step-by-step explanation:

The given values are:

Random sample,

[tex]n=100[/tex]

Average length of time,

[tex]\bar{x}=3.1 \ minutes[/tex]

Waiting time,

[tex]\mu=3 \ minutes[/tex]

Standard deviation,

[tex]\sigma=0.5[/tex]

Now,

The test statistics will be:

⇒  [tex]z=\frac{(\bar{x}-\mu)}{\frac{\sigma}{\sqrt{n} } }[/tex]

On substituting the values, we get

⇒     [tex]=\frac{(3.1-3)}{\frac{0.5}{\sqrt{100} } }[/tex]

⇒     [tex]=\frac{0.1}{0.05}[/tex]

⇒     [tex]=2[/tex]

hence,

⇒  [tex]P(z >2 ) = 1 - P(z <2 )[/tex]

By using the table,

⇒                 [tex]=1-0.9772[/tex]

⇒                 [tex]=0.0228[/tex]

The marginal average cost is -1 and The marginal average cost for 200 is  $699.

The price to manufacture a second unit of output is known as the marginal cost. Since marginal cost aids in determining the level of production that is the most effective for a manufacturing process, it is a crucial topic in cost accounting. It is estimated by estimating the costs incurred even if just one more unit is produced.

Given The total cost​ (in dollars) of manufacturing x auto body frames is ​C(x)=40,000+500x.

Average cost = Cx / x

Average cost = (40,000 + 500x)/ x

For x = 200

Average cost = (40,000 + 500 * 200)/200

Average cost = 700$ per frame

Marginal average cost = d(Cx/x)/dx

d(Cx/x)/dx = -40,000/ x^2

at x = 200

Marginal average cost = -40,000/ 200^2  = -1

Marginal average cost = -1 tells us the average cost

decrease at the rate of -1 for every x

Average cost for 200 = 700$ per frame

Average cost for 200 = 700 + 1 (-1)

The average cost for 200 = 700 -1 = 699$

therefore, the Marginal average cost for 200 is $699.

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4x - 2 (-x + 12) = 36

4x + 2x - 24 = 36

6x = 60

x= 10

Answer:

its A

Step-by-step explanation:

just took the test

Answer:

The first graph on edge 2021

The unit rate for 4543.08 km in 52.4 hours is 86.7 km.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

4543.08 km = 52.4 hours

Divide 52.4 into both sides.

86.7 km = 1 hour

Thus,

The unit rate is 86.7 km.

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Answer:

190.625 ft^2

Step-by-step explanation:

A = bh = (15.25) * (12.5) = 190.625 ft^2

Answer:

190

Step-by-step explanation:

All you have to do is multiply the dimensions(...that's what the formula states)

So, 15.2 × 12.5 = 190ft^2

NEVER FORGET YOUR UNIT, in this case it's ft^2(always 2/square when it's area)

You're very welcome and good luck :)

Answer:

(1, 1)

Step-by-step explanation:

in the order pair you have (x, y) so if is ( 3, 0) it means is ( x=3, y=0)

substitute in the inequality those x, and y values and see if it checks

y ≥ 4x-5

for ( 3, 0) is 0 ≥ 4*3-5 false

for ( 3,4)  is 4 ≥ 4*3-5 false

for (1,1) is 1 ≥ 4*1-5 true because 1 ≥ -1

for (2, 1) is 1 ≥ 4*2-5 false

Answer:

Deal A was the better deal.

Step-by-step explanation:

20*.10= 2 dollar discount for a total of 20-2= $18 total

22*.16= 3.52 dollar discount for a total of 22-3.52 =$18.48

Even though deal B had the larger discount you will still be paying a bit more compared to deal A

Answer:

n=15/4c

Step-by-step explanation:

y=mx+b

b=0 as it does not state any initial value

y=n

x=c

m=3 3/4 or 15/4

combining these together you get:

n=15/4c+0

The equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Darien uses [tex]3\frac{3}{4}[/tex] cups of flour to make one loaf of bread, we need to establish an equation, that will represent the number of cups of flower Darien uses, c, to bake n loaves of bread,

So,

Since, she uses [tex]3\frac{3}{4}[/tex] cups for one loaf of bread so for n loaf =

(We will multiply the amount used in one loaf to the number of loafs needed)

Therefore,

To make n number of loafs = [tex]3\frac{3}{4} c[/tex]

Hence, the equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]

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Answer:

x ≈ 8.5 cm

Step-by-step explanation:

Law of Sines

a/sinA = b/sinB

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

x/sin89 = 8/sin70

multiply both sides by sin89

x = 8/sin70 * sin89

Breakout the calculator

x = 8.512125544373626

x ≈ 8.5 cm

The function f(x) = -x-3.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given function:

f(x)+3f(-x) = 2x+6.

Let the function is an even function.

So, f(-x) = f(x)

To solve for f(x):

Substituting the property of an even function,

f(x) - 3f(x) = 2x + 6

-2f(x) = 2x + 6

f(x) = -x-3

Therefore, f(x) = -x-3 is the function.

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The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12) which forms an ellipsoid.

Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.

Given the function as f(x, y, z) = ln(144 − 9x² − 16y² − z²)

For f(x, y, z) to be real, the function 144 − 9x² − 16y² − z² should be greater than 0. So,

144 − 9x² − 16y² − z² > 0

9x² + 16y² + z² < 144

x²/ 4² + y²/ 3² + z²/ 12² < 1

Therefore, the domain is an ellipsoid.

Therefore x ∈ (-4, 4)

y ∈ (-3, 3)

z ∈ (-12, 12)

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Answer:

5/14 * 5/14

Step-by-step explanation:

Answer:

triangle

Step-by-step explanation:

It looks like a traingle

Therefore , the solution of he given problem of linear equation comes out to be x = 5.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Given : 2x-4=6

To prove x =5

Thus,

We have to find the value of x

[tex]= > 2x =10\\= > x =10/2\\= > x =5[/tex]

Therefore , the solution of he given problem of linear equation comes out to be x = 5.

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Answer:

Step-by-step explanation:

he needs 10 inches of each color to make the wreath

10

+ 10

+ 10

+ 10

= 40

40 inches of ribbon

9514 1404 393

Answer:

  72°

Step-by-step explanation:

The external angle E is half the difference of subtended arcs CG and DF.

  E = (CG -DF)/2

  2E = CG -DF . . . . . . multiply by 2

  DF = CG -2E = 160° -2(44°) . . . . . add DF-2E to both sides; substitute values

  arc DF = 72°

Answer:

A is linear

Step-by-step explanation:

check the delta y  (y2 - y1)  and or the delat x (x2 - x1)   and see if the differences are the same from each neighboring ordered pairs

answer A has a slope (m) of  (y2 - y1) / (x2 - x1) = 2/2 = 1

Answer:

5x+4

Step-by-step explanation:

5x + 6 - 2

5x + 4

Given:

A 7-sides regular polygon.

To find:

The sum of the interior angles of the given regular polygon.

Solution:

The formula for the sum of the interior angles of a regular polygon is:

[tex]Sum=180^\circ(n-2)[/tex]

Where, n is the number of sides of the regular polygon.

The given regular polygon has 7 sides. Putting [tex]n=7[/tex] in the above formula, we get

[tex]Sum=180^\circ(7-2)[/tex]

[tex]Sum=180^\circ(5)[/tex]

[tex]Sum=900^\circ[/tex]

Therefore, the sum of the interior angles of the given regular polygon is 900 degrees.

Answer:

The answer is 0.30.

I wish you luck in your assignments.

Answer:

0.3

Step-by-step explanation:

Since 5 rounds up, that would cause the 0.09 to become a 0.1, so it would be 0.3

Answer:

Yes, 1/4 and 4/16 are equivalent

Step-by-step explanation:

1/4 = 0.25

4/16 = 0.25