Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a standard deviation of minutes. Test the hypothesis that against the alternative that if a random sample of the test times of high school seniors has a standard deviation . Use a level of significance.

Answer:

x = 14

NP = 3.66

NL = 8.01

Step-by-step explanation:

since △NPQ ∼ △NLM

<L = <P

3x + 18 = 60

3x = 60 - 18

3x = 42

x = 42/3

x = 14

Similarly;

PN/PL = QN/QM

y/8 = 3.2/7

Cross multiply

7y = 3.2* 8

7y = 25.6

y = 25.6/7

y = 3.66

Hence NP = 3.66

Also

NP/NQ = NL/NM

3.66/3.2 = NL/7

3.2NL = 7 * 3.66

3.2NL =  25.62

NL = 25.62/3.2

NL = 8.01

Two triangle are similar if they have the same ratio of the corresponding sides and equal pair of corresponding angle. The value of the x is 14 degrees, the length of the NP is 3.7 cm (round to the nearest hundred), and the length of the NL is 8 cm ( round to the nearest hundred).

The given tingle NPQ and triangle NLM are the similar triangle.

The length of the line PL is 8 cm.

Two triangle are similar if they have the same ratio of the corresponding sides and equal pair of corresponding angle.

Value of the x-

As the two triangle are similar triangle, thus the length of the angle P is equal to the angle L. Therefore,

[tex]\angle L =\angle P\\ [/tex]

Keep the value of the angle from the diagram,

[tex]\begin{algined}\\ 3x+18&=60\\ 3x&=60-18\\\\ 3x&=42\\ x&=\dfrac{42}{3} \\ x&=14\\ \end[/tex]

Thus the value of the x is 14.

The length of the NP.

In the similar triangle the following ratios are equal,

[tex]\dfrac{PN}{PL} =\dfrac{QN}{QM} [/tex]

Put the values from the diagram,

[tex]\begin{aligned} \dfrac{y}{8}&=\dfrac{3.2}{7} \\ y&=\dfrac{3.2}{7} \times 8\\ y&=3.66\\ \end[/tex]

Value of y is equal to the length NP. Hence the length of the NP is equal to the 3.66 cm.

The length of the NL-

In the similar triangle the following ratios are equal,

[tex]\dfrac{NP}{NQ} =\dfrac{NL}{NM} [/tex]

Put the values from the diagram,

[tex]\begin{aligned} \dfrac{3.66}{3.2}&=\dfrac{NL}{7} \\ NL&=\dfrac{3.66}{3.2} \times 7\\ y&=8.01\\ \end[/tex]

Thus the length of the NL is equal to the 8.01 cm.

Hence the value of the x is 14 degrees, the length of the NP is 3.7 cm (round to the nearest hundred), and the length of the NL is 8 cm ( round to the nearest hundred).

Learn more about the similar triangle here;

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Answer:

See Annex

Step-by-step explanation:

The relaxation of any Linear Programming problem, consists of eliminating the integer constraint condition, keeping the original constraint and the objective function, solving the problem as continuous variables. If in such new condition we find that optimal solution consist of integer solution we have found optimal solution already, if not we need to go ahead with the branching procedure of making variables integer above and down of the fractional values.

In this particular case ( see GeoGebra graphic solution attached changing x₁ and x₂ by x and y respectively ), and Objective Function in red we got integer solution :

z(max)  = 11

x₁  = x  = 2

x₂ = y  = 1

Answer:

See attachment for triangle

Step-by-step explanation:

Given

Shape: Equilateral triangle

[tex]Perimeter = 10cm[/tex]

Required

Draw the triangle

First, we determine the side lengths.

The perimeter of an equilateral triangle is:

[tex]Perimeter = 3 * Length[/tex]

So, we have:

[tex]10= 3 * Length[/tex]

Solve for Length

[tex]Length = \frac{10}{3}[/tex]

[tex]Length = 3.33[/tex]

See attachment for triangle

Answer:

70  cm

Step-by-step explanation:

Answer:

70 cubic feet

Step-by-step explanation:

First step is to multiply the 2 feet deep by th 5 feet wide. which is also written as:

2*5=10

Next multiply 10 by the 7 feet tall. You can write this like:

10*7=70

70 cubic feet is the answer

Answer:

arc a = 64°

arc b = 112°

Step-by-step explanation:

inscribed angles = 1/2 their arc

arc of 102° = 204° arc

arc a = 204° - 140° = 64°

arc of 92° = 184°

arc b = 360° - 184° - 64° = 112°

you knew that it had to be a total of $60.60 and that the flat cost of the plan is $48. so you subtracted the flat cost from the total cost to get the amount that could be spent on gigabytes of data. since you knew that the gigabytes cost $3 each, you divided the remaining budget (12.60) by $3 and got the number of gigabytes that she can get.

sorry if that's confusing or wordy! hope it helps!

Answer: C and D

Step-by-step explanation:I just did it my bad for the late response.

Answer:

The mean is 6.

Step-by-step explanation:

Answer:

The number of ways to choose a cone, if order matters, is 45.

Step-by-step explanation:

Given that a certain ice cream parlor offers fifteen flavors of ice cream, and you want an ice cream cone with three scoops of ice cream, all different flavors, to determine in how many ways you can choose a cone if it matters which flavor is on. top, which is in the middle and which is on the bottom, the following calculation must be performed:

15 x 3 = X

45 = X

The number of ways to choose a cone, if order matters, is 45.

Answer:

The terai region extends from the chure range in the north to the border of India in the south.lt covers 17 percent of total land of Nepal .this terai region is mostly flat and plain with alluvial fertile deposited by the rivers . the climate of the reason is hot and wet in summer and cold and dry in winter.Terai also called the granary of Nepal as more than half percent of people of Nepal depend on the vegetation of Terai region. Terai is plain, where more cultivation is possible. Cultivation is impossible in mountain region due to difficult topography and temperate region and even in hilly region with lots of vegetation it's not possible due to slope area. Terai is only the possible region where much cultivation is possible. Different kinds of vegetation, valuable medicinal herbs, important trees, etc. are found in Terai region. So, Terai region is called the granary of Nepal.The terai region extends from the chure range in the north to the border of India in the south.lt covers 17 percent of total land of Nepal .this terai region is mostly flat and plain with alluvial fertile deposited by the rivers . the climate of the reason is hot and wet in summer and cold and dry in winter.Terai also called the granary of Nepal as more than half percent of people of Nepal depend on the vegetation of Terai region. Terai is plain, where more cultivation is possible. Cultivation is impossible in mountain region due to difficult topography and temperate region and even in hilly region with lots of vegetation it's not possible due to slope area. Terai is only the possible region where much cultivation is possible. Different kinds of vegetation, valuable medicinal herbs, important trees, etc. are found in Terai region. So, Terai region is called the granary of Nepal.The terai region extends from the chure range in the north to the border of India in the south.lt covers 17 percent of total land of Nepal .this terai region is mostly flat and plain with alluvial fertile deposited by the rivers . the climate of the reason is hot and wet in summer and cold and dry in winter.Terai also called the granary of Nepal as more than half percent of people of Nepal depend on the vegetation of Terai region. Terai is plain, where more cultivation is possible. Cultivation is impossible in mountain region due to difficult topography and temperate region and even in hilly region with lots of vegetation it's not possible due to slope area. Terai is only the possible region where much cultivation is possible. Different kinds of vegetation, valuable medicinal herbs, important trees, etc. are found in Terai region. So, Terai region is called the granary of Nepal.

Answer: V= 65.3 ft^3

Answer:

This is a trapezoid.

Step-by-step explanation:

The correct answer is A. 0.84

The value of P(X<53) is 0.84 if the Z = 1 and normal distribution has a mean of 50 and a standard deviation of 3 option (A) is correct.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We know,

[tex]\rm Z = \dfrac{X-\mu}{SD}[/tex]

X = 53, μ = 50, and SD = 3

[tex]\rm Z = \dfrac{53-50}{3}[/tex]

Z = 1

From the Z table.

The value of P(X<53) = 0.84

Thus, the value of P(X<53) is 0.84 if the Z = 1 and normal distribution has a mean of 50 and a standard deviation of 3 option (A) is correct.

Learn more about the normal distribution here:

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Answer:

D. 62 inches

Step-by-step explanation:

the object is symmetrical across z, so the lengths on the other side will be the same as x and y

the perimeter would just be 2x + 2y = 2(12) + 2(19) = 62 inches

Answer:

-9

Step-by-step explanation:

Answer:

[tex]Ship\ A = 40\ miles[/tex]

[tex]Ship\ B = 30\ miles[/tex]

Step-by-step explanation:

Given

[tex]d = 50[/tex] --- distance apart

[tex]Ship\ B = x[/tex]

[tex]Ship\ A = x + 10[/tex]

The question can be represented with the attached image.

Required

Solve for x

Using Pythagoras theorem, we have:

[tex]x^2 + (x + 10)^2 = 50^2[/tex]

Open bracket

[tex]x^2 + x^2 + 20x + 100 = 2500[/tex]

Collect like terms

[tex]x^2 + x^2 + 20x + 100 - 2500 = 0[/tex]

[tex]2x^2 + 20x -2400 = 0[/tex]

Divide through by 2

[tex]x^2 + 10x -1200 = 0[/tex]

Expand

[tex]x^2 + 40x - 30x -1200 = 0[/tex]

Factorize

[tex]x(x + 40) - 30(x +40) = 0[/tex]

Factor out x + 40

[tex](x - 30)(x +40) = 0[/tex]

Split and solve for x

[tex]x - 30 = 0\ or\ x + 40 = 0[/tex]

[tex]x = 30\ or\ x = -40[/tex]

Distance can not be negative

So:

[tex]x = 30[/tex]

Recall that:

[tex]Ship\ B = x[/tex]

[tex]Ship\ A = x + 10[/tex]

This implies that:

[tex]Ship\ B = 30\ miles[/tex]

[tex]Ship\ A = 30 + 10\ miles[/tex]

[tex]Ship\ A = 40\ miles[/tex]

Answer:

-43.6° F, -37.4° F, -17° F, 37.3° F, 51.8° F, 52° F

Step-by-step explanation:

The greater the number, the warmer the temperature.

Answer:

# of laps < 28, the number of laps will be less than 28.

1 lap = 4 minutes

28 laps = 112 minutes

Because we want less than 28 laps,

27 laps = 108 minutes

She can run any amount of laps less than 28.

Answer:

-5

Step-by-step explanation:

The number line is saying that the solution could be any number less than -2.

The value included in the solution set for the inequality graph on the number line is -5.

The number line represents an inequality graph.

Let's use the range of value on the graph as x.

Therefore, the inequality on the number line will read as follows:

x < -2

Hence,

x less than -2 includes -3, -4, -5, -6, -7, -8 ..

Therefore, the value included in the solution set for the inequality graph on the number line is -5.

learn more on inequality graph here: https://brainly.com/question/1400037

Answer:

1/12

hope this helps

have a good day :)

Step-by-step explanation:

The solution is 1/12 , is the simplest form of 1/6 divided by 2.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

1/6 divided by 2

i.e. 1/6÷ 2

=1/6* 1/2

=1/12

Hence, The solution is 1/12 , is the simplest form of 1/6 divided by 2.

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Answer:

Step-by-step explanation:

y = - x - 4 (slope-intercept form)

x + y = - 4 (standard form)

Answer:

any decimal between 3.0 and 3.45. You can,use 3.25 if u don't wanna think about it

Answer:There are mutipal answers but here’s one 3.1

Step-by-step explanation:

This means that the extra cost for using 1 gigabyte of data will be $14.99, for using 2 gigabytes of data it will be $29.98, and so on.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

The given function C(g) = 14.99g + 32 represents the cost, in dollars, for a cell phone plan that offers unlimited talk and text, with an additional charge for data usage.

The function has two parts:

The fixed cost of the plan is $32 (this is the cost you pay even if you don't use any data).

The variable cost of the data usage is $14.99 per gigabyte.

So, the cost of the plan for unlimited talk and text is the fixed cost, which is $32.

And, the additional cost for each gigabyte of data is the variable cost, which is $14.99.

This means that if you use 1 gigabyte of data, the additional cost will be $14.99, if you use 2 gigabytes of data, the additional cost will be $29.98, and so on.

Learn more about algebraic Expression here:

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Answer:

40% are girls

Step-by-step explanation:

60/150=0.4=40%

Answer:

0.4470 = 44.70% probability of a random person on the street having an IQ score of less than 98.

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.

What is the probability of a random person on the street having an IQ score of less than 98?

This is the pvalue of Z when X = 98. So

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

[tex]Z = \frac{98 - 100}{15}[/tex]

[tex]Z = -0.1333[/tex]

[tex]Z = -0.1333[/tex] has a pvalue of 0.4470

0.4470 = 44.70% probability of a random person on the street having an IQ score of less than 98.

Answer:

sorry

Step-by-step explanation:

don't know I m in 8th

I will surely help you

Answer:

Simile

Step-by-step explanation:

A simile is a figure of speech that directly compares two things. Similes differ from other metaphors by highlighting the similarities between two things using comparison words such as "like", "as", "so", or " than", while other metaphors create an implicit comparison.

Hope this helps! If you have any questions revolving around this topic,feel free to ask me and I will be happy to help!

Answer:

510

Step-by-step explanation:

Sally bank account had a beginning balance of 230

She made two deposits of 50 and 420

50+420

= 470

She made a withdrawal of 190

Therefore her balance at the end of the month can be calculated as follows

470+230

= 700

= 700-190

= 510

Hence the balance at the end of the month is 510

Answer:

B.3.2 ,3.317 ,3.606 ,3.61.

Step-by-step explanation:

i guess that is the answer,but if it isn't tell me I may try it again.good day.