Consider the probability that no less than 37 out of 295 cell phone calls will be disconnected. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.

a. Area to the right of 36.5
b. Area to the right of 37.5
c. Area to the left of 36.5
d. Area to the left of 37.5
e. Area between 36.5 and 37.5

Answer: See the graph below.

It is a straight line segment with endpoints (-2,-3) and (4,9).

===============================================================

Explanation:

We're told that x is between -2 and 4, including both endpoints.

Let's see what y is when we plug in x = -2

y-2x-1 = 0

y-2(-2)-1 = 0

y+4-1 = 0

y+3 = 0

y = -3

So x = -2 pairs up with y = -3. The point (x,y) = (-2,-3) is on the line. This is the left most endpoint.

Repeat for x = 4 to find what y must be

y-2x-1 = 0

y-2(4)-1 = 0

y-8-1 = 0

y-9 = 0

y = 9

Therefore the point (x,y) = (4,9) is also on the line. It's the right most endpoint

Once we have the two points, we can form the straight line. Simply connect the endpoints mentioned as shown below. We don't extend the line infinitely outwards in both directions because [tex]-2 \le x \le 4[/tex] meaning x cannot be smaller than -2, and x cannot be greater than 4 either.

Side note: The given equation is the same as y = 2x+1. It has slope 2 and y intercept 1.

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

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

Given:

[tex]4x+x-3-9+4x=6[/tex]

---------->>>>

Combine like terms.

[tex]9x-12=6[/tex]

---------->>>>

Add 12 to both sides.

[tex]9x=18[/tex]

---------->>>>

Divide both sides by 9.

[tex]x=2[/tex]

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

Hope this is helpful.

Answer:

Equation: f(x) = 2(x + 5)^2 + 2

Vertex: (-5, 2)

Step-by-step explanation:

The form the question wants us to write the quadratic function in is called "vertex form":

f(x) = a (x - h)^2 + k

a = the a in a standard quadratic equation (y = ax^2 + bx + c) or the coefficient of the x^2

h = x coordinate of the vertex

k = y coordinate of the vertex

To find the vertex, we are going to use the quadratic equation given:

2x^2 + 20x + 52

Comparing it to the standard quadratic equation (y = ax^2 + bx + c),

a = 2

b = 20

c = 52

Now we can start finding our vertex.

To find h, we are going to use this formula:

-b / 2a

We already know b = 20 & a = 2, so we can just substitute that into our formula:

- (20) / 2*2

Which equals:

-20/4 = -5

So h (or the x coordinate of the vertex) is equal to -5

Next we will find k, or the y coordinate of the vertex.

To do that, we are going to plug in -5 into 2x^2 + 20x + 52:

2(-5)^2 + 20(-5) + 52

2(25) -100 + 52

50 - 100 + 52

-50 + 52

2

k (or the y coordinate of the vertex) is equal to 2

The vertex is (-5, 2)

However, we still need to find our equation in vertex form.

We know a = 2, h = -5, & k = 2. Now we substitute these into our vertex form equation:

a(x - h)^2 + k

(2)(x - (-5))^2 + (2)

2(x + 5)^2 + 2

(Remember that the -5 cancels with the - in front of it, making it a positive 5)

The equation is f(x) = 2(x + 5)^2 + 2

Hope it helps (●'◡'●)

Answer:   6.1% decrease

Note: It appears that your teacher doesn't want you to type in the percent sign, as that's already covered for you.

=========================================================

Explanation:

The salary decreased by 51500-48355 = 3145

Divide this over the initial salary to get 3145/51500 = 0.0611 which is approximate.

This converts to the percentage 6.11% and that rounds to 6.1%

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

As an alternative, you can use the formula method below

A = old value = 51500

B = new value = 48355

C = percent change when going from A to B

C = [ (B-A)/A ] * 100%

C = [ (48355-51500)/51500 ] * 100%

C = (-3145/51500)*100%

C = -0.0611*100%

C = -6.11%

C = -6.1%

The negative C value indicates a percent decrease.

Answer:

335%

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Histogram shows the range of data on the x-axis while the frequency of occurrence is on the y-axis.

We have the following ranges from the Histogram ;

0 to 11

11 to 22

22 to 33

33 to 44

44 to 55

55 to 66

66 to 77

77 to 88

88 to 99

99 to 110

From the given set of data, the frequency according to the range is as follows;

0 to 11; 4

11 to 22; 8

22 to 33; 7

33 to 44; 6

44 to 55; 4

55 to 66; 2

66 to 77; 2

77 to 88; 1

88 to 99; 0

99 to 110; 1

The only Histogram that corresponds to these frequency is option A

Answer:

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number.

Step-by-step explanation:

I hope it helps

Answer:

[tex]\displaystyle V = \frac{6561 \pi}{2}[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Shell Method:                                                                                                         [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 9

Step 2: Identify

Find other information from graph.

See attachment.

Bounds of Integration: [0, 9]

Step 3: Find Volume

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

Answer:

2 1/8

Step-by-step explanation:

7/8 is the same as 0.875 and therefore you need 0.125 also known as 1/8 to make it a whole number. When you add it to the already existing whole 2 you get three. Subtract three from five to make two which is what you need to add on top to finally get 5.

Answer:

You: Your welcome❤

Answer:

[tex]y=-\frac{3}{2}x+1[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope (m)

[tex]3x+2y = 10[/tex]

First, we must organize this given equation in slope-intercept form. This will help us identify its slope.

[tex]3x+2y = 10[/tex]

Subtract 3x from both sides

[tex]2y = -3x+10[/tex]

Divide both sides by 2

[tex]y = -\frac{3}{2} x+5[/tex]

Now, we can identify clearly that [tex]-\frac{3}{2}[/tex] is in the place of m in [tex]y=mx+b[/tex], making it the slope. Because parallel lines have the same slope, this makes the slope of the line we're currently solving for [tex]-\frac{3}{2}[/tex] as well. Plug this number into [tex]y=mx+b[/tex]:

[tex]y=-\frac{3}{2}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=-\frac{3}{2}x+b[/tex]

Plug in the given point (8,-11) and solve for b

[tex]-11=-\frac{3}{2}(8)+b\\-11=-\frac{24}{2}+b\\-11=-12+b[/tex]

Add 12 to both sides

[tex]1=b[/tex]

Therefore, the y-intercept of the line is 1. Plug this back into [tex]y=-\frac{3}{2}x+b[/tex]:

[tex]y=-\frac{3}{2}x+1[/tex]

I hope this helps!

Given:

The graph that shows the ennoblement for college R between 1950 and 2000.

To find:

The two decades that has the greatest change in enrollment.

Solution:

From the given graph, it is clear that the change in the enrollment is:

From 1950 to 1960 is [tex]4-3.5=0.5[/tex] thousand.

From 1960 to 1970 is [tex]5-4.5=1.5[/tex] thousand.

From 1970 to 1980 is [tex]5.5-5=0.5[/tex] thousand.

From 1980 to 1990 is [tex]6.5-5.5=1[/tex] thousand.

From 1990 to 2000 is [tex]7-6.5=0.5[/tex] thousand.

The two decades 1960-1970 and 1980-1990 have the greatest change in enrollment.

Answer:1980 to 1990

Step-by-step explanation:

Answer:

you just gave your self the answer because you just need to multiply

Step-by-step explanation:

15080 is the answer

Answer:

a) The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

b) We have to find X when Z has a p-value of [tex]\frac{a}{100}[/tex], and X is given by: [tex]X = \mu - Z\sigma[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]

a. Find the probability of a pregnancy lasting X days or longer.

The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of [tex]Z = \frac{X - \mu}{\sigma}[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

b. If the length of pregnancy is in the lowest a​%, then the baby is premature. Find the length that separates premature babies from those who are not premature.

We have to find X when Z has a p-value of [tex]\frac{a}{100}[/tex], and X is given by: [tex]X = \mu - Z\sigma[/tex], in which [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

Answer:

0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean per capita consumption of milk per year is 131 liters with a variance of 841.

This means that [tex]\mu = 131, \sigma = \sqrt{841} = 29[/tex]

Sample of 132 people

This means that [tex]n = 132, s = \frac{29}{\sqrt{132}}[/tex]

What is the probability that the sample mean would be less than 133.5 liters?

This is the p-value of Z when X = 133.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{133.5 - 131}{\frac{29}{\sqrt{132}}}[/tex]

[tex]Z = 0.99[/tex]

[tex]Z = 0.99[/tex] has a p-value of 0.8389

0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.

Answer:

6

Step-by-step explanation:

You can apply the proportion of 9/6 to 4 to get 6:

6*(9/6)= 9

So

4*(9/6) = Length LA

6= Length LA

Answer:

Option C, or [tex]2\frac{2}{3}[/tex]

Explanation:

We can see that the Line FM in the smaller triangle dialates to Line LK in the bigger triangle by the scale factor of:

FM/LK

6/9 or 2/3

So we would know that to find out the value of LA in the bigger triangle we would have to dialate it’s corresponding side FI in the smaller triangle by the same scale factor:

4 * 2/3

=> [tex]2\frac{2}{3}[/tex] = LA

Hope this helps!

Answer:

Take a look of the image below, we can think on this problem as a problem of two triangle rectangles.

We can see that both triangles share the adjacent cathetus, then the height of the flagpole is just the difference between the opposite cathetus.

Remember the relation:

Tan(a) = (opposite cathetus)/(adjacent cathetus)

So, if we define H as the height of the cliff

X as the distance between the observer and the cliff

and h as the height of the flagopole

we can write:

tan(40°) = H/X

tan(45°) = (H + h)/X

Notice that we have two equations and 3 variables (we should have the same number of equations than variables) then here is missing information, and we can't get an exact solution for the height of the flagpole.

But we can write it in terms of the height of the cliff H, or in terms of the distance between the observer and the cliff.

We want to find the value of h.

If we take the quotient between both equations, we get:

Tan(45°)/Tan(40°) = (H + h)/H

1.192 = (H + h)/H

1.192*H = H + h

1.192*H - H = h

0.192*H = h

So the height of the flagpole is 0.192 times the height of the cliff.

Answer:

7sin

2

x+3cos

2

x=4

4sin

2

x+3sin

2

x+3cos

2

x=4

4sin

2

x+3=4

4sin

2

x=1

sin

2

x=

4

1

sinx=

2

1

or sinx=−

2

1

Step-by-step explanation:

TAKING THE POSITIVE ROOT x=

6

π

tan(

6

π

)=

3

1

Answer:

1822

Step-by-step explanation:

The fraction 1822 is equal to 911 when reduced to lowest terms.

18

22

is equivalent to 9

11

because 9 x 2 = 18 and 11 x 2 = 22

27

33

is equivalent to 9

11

because 9 x 3 = 27 and 11 x 3 = 33

36

44

is equivalent to 9

11

because 9 x 4 = 36 and 11 x 4 = 44

Answer:

18/22

Step-by-step explanation:

You can choose any number and if you multiply the top number (numerator) and the bottom number (denominator) by that same number, the fractions are equivalent.

If you choose the number 2, then multiply 9 x 2 = 18, and 11 x 2 = 22

Or multiply by 7. Then you would get an equivalent fraction of 63/77  

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

180-90=2b+b

90=3b

90/3=b

30=b

2b=2*30

   =60

180-90=a+a

90=2a

a=90/2

a=45

the answer is 45 degrees

hope it helps!!let me know if it does

Answer:

a= 15°

Step-by-step explanation:

> use the fact that the sum of angles in a triangle is 180°

> based on the picture in the small right triangle we have b° +2b° +90° =180°

b +2b +90 =180° , combine like terms

3b +90 = 180, subtract 90 from both sides of the equation

3b = 90, divide by 3 both sides of the equation

b = 30°

> angle b has a ray that continues as a line so it makes an 180° angle and we have the acute triangle so we can write that

a + a+ (180-b) =180, substitute b

2a + 180-30 =180, subtract 180 from both sides, and add 30 to both sides

2a=30, divide by 2 both sides

a= 15°

Answer:

AB

Step-by-step explanation:

From the question given above, we were told that triangle ABC is similar to triangle PTG.

Since both triangles are similar, the following assumptions hold:

PG / AC = PT / AB = TG / BC

Comparing the equation above with those given in the question, the missing part of the equation is AB

Answer:

1/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability that the ticket drawn has a number which is a multiple of 5 =

Number of tickets that are a multiple of 5 / total number of tickets

Multiple of 5 = 5, 10, 15, 20

there would be 4 tickets that would be a multiple of 5

= 4/20

To transform to the simplest form. divide both the numerator and the denominator by 4

= 1/5

9514 1404 393

Answer:

  ∠CAB = 86°

  ∠ABC = 43°

  ∠BCA = 51°

Step-by-step explanation:

This can be done a couple of different ways (as with most math problems). We can use the distance formula to find the side lengths, then the law of cosines to find the angles. Or, we could use the dot product. In the end, the math is about the same.

The lengths of the sides are given by the distance formula.

  AB² = (4-1)² +(-3-0)² +(0-(-1)) = 16 +9 +1 = 26

  BC² = (1-4)² +(2-(-3))³ +(3-0)² = 9 +25 +9 = 43

  CA² = (1-1)² +(0-2)² +(-1-3)² = 4 +16 = 20

From the law of cosines, ...

  ∠A = arccos((AB² +CA² -BC²)/(2·AB·CA)) = arccos((26 +20 -43)/(2√(26·20)))

  ∠A = arccos(3/(4√130)) ≈ 86°

  ∠B = arccos((AB² +BC² -AC²)/(2·AB·BC)) = arccos((26 +43 -20)/(2√(26·43)))

  ∠B = arccos(49/(2√1118)) ≈ 43°

  ∠C = arccos((BC² +CA² -AB²)/(2·BC·CA)) = arccos((43 +20 -26)/(2√(43·20)))

  ∠C = arccos(37/(4√215)) ≈ 51°

The three angles are ...

  ∠CAB = 86°

  ∠ABC = 43°

  ∠BCA = 51°

_____

Additional comment

This sort of repetitive arithmetic is nicely done by a spreadsheet.

Answer:

D

Step-by-step explanation:

There 2 ways to interpret this problem.

From the info given:

These two triangles are congruent by SSS and congruent triangles have congruent or equal side lengths so the answer have to be 1.

If the triangles are similar, the side lengths form a proportion of that

[tex] \frac{3}{3} = \frac{3}{3} [/tex]

So the ratio or scale factor is 1.

The scale factor in the figure is 1.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Given that two triangles, LMN and OPQ, we need to find the scale factor,

We can see triangles are congruent, and we know that

Two triangles are congruent, by the SSS congruence criterion, if they are similar and the scale factor happens to be 1,

Hence, the scale factor in the figure is 1.

Learn more about scale factors, click;

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Answer: The first number is 2, the second number is 3 and the third number is -2

Step-by-step explanation:

Let the first number be 'x', the second number be 'y' and the third number be 'z'

The equations according to the question becomes:

⇒ x + y + z = 3              ....(1)

⇒ x - y + z = -3              ....(2)

⇒ x - z = 1 + y              ....(3)

Rearranging equation 3:

⇒ x - y = 1 + z                .....(4)

Putting in equation 2:

⇒ 1 + z + z = -3

⇒ 1 + 2z = -3

⇒ z = -2

Putting this value in equation 4 and equation 1, we get:

⇒ x - y = -1

⇒ x + y = 5

Cancelling 'y' by eliminiation method and equation becomes:

⇒ 2x = 4

⇒ x = 2

Putting value of 'x' and 'z' in equation 1:

⇒ 2 + y - 2 = 3

⇒ y = 3

Hence, the first number is 2, the second number is 3 and the third number is -2

It is the graph of y= x translated 7 units up.

+7 in the function means it crosses the y axis at +7

The statement correctly describes the graph of y= x + 7 is y= x translated 7 units up.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

We have a function y = x.

and, a translated function y= x + 7

Here, The plus 7 at the end will shift the graph 7 units up.

It also means the the function cut the y axis at +7.

Thus, It is the graph of y= x translated 7 units up.

Learn more about Transformation here:

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Answer:

d=35000Km

Step-by-step explanation:

After 20h I traveled for

s1=1250*20=25000Km

My friend

s2=500*20=10000Km

Therefore d=25000+10000=35000Km