Math Is TU parallel to VW explain

Answer:

c) The Z-score = - 1.90 unusual

Step-by-step explanation:

Explanation:-

Let 'X' be the random variable in normal distribution

Given student received a score X = 50

Mean of the Population x⁻ = 69

standard deviation of the Population 'σ' = 10

now

[tex]Z = \frac{x^{-}-mean }{S.D}[/tex]

[tex]Z = \frac{x^{-}-mean }{S.D} = \frac{50 -69}{10} = - 1.90[/tex]

The Z-score = - 1.90

Conclusion:-

The Z-score = - 1.90 unusual

Answer: The Z-score = - 1.90 unusual

Step-by-step explanation:

Answer:

ED = 3.2 cm

Step-by-step explanation:

According to chord-chord power theorem,

(AE)(EB) = (CE)(ED)

2*4 = 2.5 *ED

8/2.5 = ED

ED = 3.2 cm

Answer:

3. 72.9%

Step-by-step explanation:

Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.

So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:

P(M∪C) = P(M) + P(C) - P(M∩C)

Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:

P(M) = 145/317 = 0.4574

There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:

P(C) = 167/317 = 0.5268

Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate  chip scones is:

P(M∩C) = 81/317 = 0.2555

Therefore,  P(M∪C) is equal to:

P(M∪C) = 0.4574 + 0.5268 - 0.2555

P(M∪C) = 0.7287

P(M∪C) = 72.9%

Answer:

3. 72.9%

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.

There are 172 female customers and 317-172 = 145 male customers.

150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.

81 of those are male, so 167 - 81 = 86 are female.

So the total of desired outcomes is 86 + 145 = 231

Total outcomes:

317 total customers.

Probability:

231/317 = 0.729

So the correct answer is:

3. 72.9%

Answer:

n = -1

Step-by-step explanation:

So first subtract 9 to both sides

8n = -n - 9

Now you want the n on one side and the constant on the other

so add the single n to the n side

9n = -9

Divide 9 to both sides to solve for n

n = -1

Answer:

y = 8 - 5x

Step-by-step explanation:

both equations shares the same gradient as they are parallel

from y= 9-5x, the gradient is -5

subst x = 0, y=8, and m= -5 into the y = mx + c to find the value of c

8 = (-5)(0) + c

c= 8

therefore the eqn is y = 8 - 5x

Hope this helps!

Stay safe, have a good day :D

Answer:

5-i

Step-by-step explanation:

Product=multiplication

Let the complex number=x

(3+2i)*x=17+7i

x=17+7i / 3+2i

x=(17-7i)*(3-2i)/(3+2i)*(3+2i)

=51-34i+21i+14i^2 / 9+6i+6i+4i^2

=51+13i+14i^2 / 9+12i+4i^2

= (51+14 - 13i) / 13

= (65 -13i) / 13

= 65 / 13 - 13 i / 13

= 5 - i.

Answer

About 219-220

Step-by-step explanation:

Answer: $219.047619

Step-by-step explanation: 1150.00 ÷ 5.25 = 219.047619

Answer:

Step-by-step explanation:

Hello!

An ANOVA was conducted to analyze the variable

Y: sales of "People" magazine over a 5-week period

This was studied in 4 Borders outlets in Chicago.

So this test has one factor: "Borders outlets" and four treatments: "Store 1, store 2, store 3 and store 4"

For each store you have the data for the weekly sales over a 5-week period so the sample sizes are:

n₁=n₂=n₃=n₄= 5 weeks

Store 1

∑X₁= 540; ∑X₁²= 58434

X[bar]₁= 108

S₁²= 28.50

S₁= 5.34

Store 2

∑X₂= 437; ∑X₂²= 38663

X[bar]₂= 87.40

S₂²= 117.30

S₂= 10.83

Store 3

∑X₃= 455; ∑X₃²= 41899

X[bar]₃= 91

S₃²= 123.50

S₃= 11.11

Store 4

∑X₄=505; ∑X₄²= 51429

X[bar]₄= 101

S₄²= 106

S₄= 10.30

Totals

N= n₁ + n₂ + n₃ + n₄= 4*5= 20

∑Mean= 108+87.40+91+101= 387.4

∑Variance= 28.50+117.30+123.50+106= 375.30

∑Standard deviation= 5.34+10.83+11.11+10.30= 37.58

Hypothesis test:

H₀: μ₁= μ₂= μ₃= μ₄

H₁: At least one population mean is different.

α: 0.05

The statistic for this test is

[tex]F= \frac{MS_{Treatments}}{MS_{Error}} ~~F_{k-1;N-k}[/tex]

k-1= 3 Df of the treatments, k=4 number of treatments

N-k= 16 Df of errors, N=20 total number of observations in all treatments

[tex]F_{H_0}= \frac{441.78}{93.83}= 4.71[/tex]

The critical region and p-value for this test are one-tailed to the right.

Using the critical value approach:

[tex]F_{k-1;N-k;1-\alpha }= F_{3;16;0.95}= 3.25[/tex]

The decision rule is:

If [tex]F_{H_0}[/tex] ≥ 3.25, reject the null hypothesis.

If [tex]F_{H_0}[/tex] < 3.25, do not reject the null hypothesis.

Using the p-value approach:

Little reminder: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

So under the distribution F₃,₁₆ you have to calculate the probability of the calculated  [tex]F_{H_0}[/tex]:

P(F₃,₁₆≥4.71)= 1 - P(F₃,₁₆<4.71)= 1 - 0.9847 = 0.0153

p-value= 0.0153

The decision rule for this approach is

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value is less than the level of significance, so the decision is to reject the null hypothesis.

I hope this helps!

Answer:

The volume of the crystal is [tex]V=125 \:cm^3[/tex].

Step-by-step explanation:

The volume enclosed by a cube is the number of cubic units that will exactly fill a cube.

To find the volume of a cube recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself three times. Or as a formula

                                                         [tex]V=s^3[/tex]

where:

s is the length of any edge of the cube.

From the information given we know that the crystal has edge lengths of 5 centimeters. Therefore, the volume of the crystal is

[tex]V=5^3=125 \:cm^3[/tex].

Answer 9 is in the domain of f g

Step-by-step explanation:

Answer:

-7,9

Step-by-step explanation:

x-1=-8

x=-7

x-1=8

x=9

Before Andrei adds the marbles to the glass tank, the glass tank was empty. This means that the volume of the empty tank is when n = 0 and the volume is 32 liters.

Given that:

[tex]W = 32 - 0.05n[/tex]

A linear function is represented as:

[tex]y = b + mx[/tex]

Where

[tex]b \to[/tex] y intercept

Literally, the y intercept is the initial value of the function.

In this function, the y intercept means the initial volume of the glass tank before filling it with marbles.

Compare [tex]y = b + mx[/tex] and [tex]W = 32 - 0.05n[/tex]

[tex]b = 32[/tex]

This means that the volume of the glass tank is 32 liters.

Read more about linear functions at:

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Answer:

0.05

Step-by-step explanation:

Answer:

I think it’s -4

Step-by-step explanation:

-2 plus -2 is -4

since 2 plus 2 is 4

Hope this helps ;)

Answer:

Step-by-step explanation:

It is because 2 plus 2 is 4

so -2 plus -2 is -4

hth!

Answer: 1/20

Step-by-step explanation:

Decimal Fraction Percentage

0.05 1/20          5%

Answer:

a) Q1= 144.10

Median = 150

Q3=155.90

b) The 99 percentile would be:[tex]a=150 +2.33*8.75=170.39[/tex]

And represent a value who accumulate 99% of the values below

Step-by-step explanation:

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(150,8.75)[/tex]  

Where [tex]\mu=150[/tex] and [tex]\sigma=8.75[/tex]

Part a

Lets begin with the first quartile:

[tex]P(X>a)=0.75[/tex]   (a)

[tex]P(X<a)=0.25[/tex]   (b)

We can find the quantile in the normal standard distribution and we got z=-0.674.

And we can apply the z score formula and we got:

[tex]z=-0.674<\frac{a-150}{8.75}[/tex]

And if we solve for a we got

[tex]a=150 -0.674*8.75=144.10[/tex]

The median for this case is the mean [tex]Median =150[/tex]

For the third quartile we find the quantile who accumulate 0.75 of the area below and we got z=0.674 and we got:

[tex]a=150 +0.674*8.75=155.90[/tex]

Part b

We can find the quantile in the normal standard distribution who accumulate 0.99 of the area below and we got z=2.33.

And we can apply the z score formula and we got:

[tex]z=2.33<\frac{a-150}{8.75}[/tex]

And if we solve for a we got

[tex]a=150 +2.33*8.75=170.39[/tex]

And represent a value who accumulate 99% of the values below

Answer:

A

Step-by-step explanation:

They are congruent because of the SSS theorem.  The chords are congruent because the angles are congruent (angles are congruent because they are vertical angles).  Congruent central angles have congruent chords.  The other two sides are congruent because they are all radii of the circle and radius are always congruent.

Answer:

A

Step-by-step explanation:

The triangles are isosceles and congruent  too. ( both have 2  sides congruent  as  radius and the angles between them are congruent- SAS)

Answer:

  x = 8

Step-by-step explanation:

The angle with the expression in it is complementary to the 30° angle, so is 60°. Then we have ...

  4 +7x = 60

  7x = 56 . . . . . . subtact 4

  x = 8 . . . . . . . . .divide by 7

Answer:

(0, -4)

Step-by-step explanation:

The graph that represents the function is (c) on a coordinate plane, an absolute value graph has a vertex at (0, -4)

The equation of the function is given as:

[tex]f(x) = |x| - 4[/tex]

The above function is an absolute value function shifted down by 4 units

Hence, the graph that represents the function is a graph that has its vertex at (0,-4)

Read more about absolute value graphs at:

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Answer:

As  [tex]{x \to \infty}, \,\,{f(x) \to -\infty[/tex]  and as  [tex]{x \to -\infty}, \,\,{f(x) \to \infty[/tex]

Step-by-step explanation:

Please look at the plotted points in the attached image. There we see that as x grows toward infinity (to the right), the values for f(x) seem to become more negative (so f(x) seems to go towards  minus infinity).

As we move towards the left with values of x (x going towards negative infinity, f(x) seems to become more and more positive (grow toward infinity)

Completed Question

1. OSHA is an agency responsible for workplace safety, read its rule and sketch a  diagram that shows the proper relationship between the ladder, wall and ground .

Rule: Non-self-supporting ladders, which must lean against a wall or other support, are to be positioned at such an angle  that the horizontal distance from the top support to the foot of the ladder is about the 1/4 working length of the ladder.

2. Calculate the angle that the ladder makes with the ground using a trigonometric ratio.

3. If a ladder is x feet long, how high up a wall can it safely reach?

4. Would a 51-foot ladder be long enough to climb a 50-foot wall?

Answer:

(a)See attachment

(b)75.52 degrees

(c)[tex]Height ,h=\dfrac{x\sqrt{15}}{4} $ feet[/tex]

(d) NO

Step-by-step explanation:

Part 1

Let the length of the ladder =x

Since by the given rule, Horizontal Distance =[tex]\dfrac14$ of the length of the ladder[/tex]

Horizontal Distance = [tex]\dfrac14x[/tex]

In the sketch of the problem attached below,

Part 2

From Triangle ABC

[tex]\cos C=\dfrac{BC}{AC} \\\cos C=\dfrac{x/4}{x} \\\cos C=\dfrac{1}{4}\\ C=\arccos \dfrac{1}{4}\\C \approx 75.52^\circ[/tex]

The angle that the ladder makes with the ground is 75.52 degrees.

Part 3

If the ladder is x feet long

Using Pythagoras theorem in Triangle ABC below

[tex]x^2=(x/4)^2+h^2\\h^2=x^2-\dfrac{x^2}{16}\\ h^2=\dfrac{15x^2}{16}\\h=\sqrt{\dfrac{15x^2}{16}} \\h=\dfrac{x\sqrt{15}}{4}$ feet[/tex]

Part 4

If x=51 feet

[tex]Height ,h=\dfrac{51\sqrt{15}}{4}$ = 49.38 feet[/tex]

Therefore, a 51 feet ladder would not be enough to climb a 50 feet wall as it would violate the safety rule.

Answer:

2 2/3

Step-by-step explanation:

Answer:

[tex]E_{A} =0.25*160=40[/tex]  

[tex]E_{B} =0.25*160=40[/tex]

[tex]E_{C} =0.4*160=64[/tex]

[tex]E_{D} =0.05*160=8[/tex]  

[tex]E_{F} =0.05*160=8[/tex]  

And now we can calculate the statistic:  

[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]  

The answer would be:

c. 5.25

Step-by-step explanation:

The observed values are given by:

A: 36

B: 42

C: 60

D: 14

E: 8

Total =160

We need to conduct a chi square test in order to check the following hypothesis:  

H0: There is no difference in the proportions for the final grades

H1: There is a difference in the proportions for the final grades

The level of significance assumed for this case is [tex]\alpha=0.01[/tex]  

The statistic to check the hypothesis is given by:  

[tex]\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]  

Now we just need to calculate the expected values with the following formula [tex]E_i = \% * total[/tex]  

And the calculations are given by:  

[tex]E_{A} =0.25*160=40[/tex]  

[tex]E_{B} =0.25*160=40[/tex]

[tex]E_{C} =0.4*160=64[/tex]

[tex]E_{D} =0.05*160=8[/tex]  

[tex]E_{F} =0.05*160=8[/tex]  

And now we can calculate the statistic:  

[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]  

The answer would be:

c. 5.25

Now we can calculate the degrees of freedom for the statistic given by:  

[tex]df=(categories-1)=(5-1)=4[/tex]

And we can calculate the p value given by:  

[tex]p_v = P(\chi^2_{4} >5.25)=0.263[/tex]  

The p value is higher than the significance so we have enough evidence to FAIL to reject the null hypothesis

Answer:

The number of the class containing the  largest score can be found in frequency  24 and the class is  98 - 103

For the third class 78 - 83 ; the upper limit = 83

The class width for this histogram 5

The number of students that took the exam simply refers to the frequency is  84

The percentage of students that scored higher than 95.5 is 53%

Step-by-step explanation:

The objective of this question is to use the following histogram that shows the exam scores for a Pre-algebra class to answer the question given:

NOW;

The table given in the question can be illustrated as follows:

S/N           Class                Score          Frequency

1                 68  - 73            70.5           0

2                73 - 78             75.5           4

3                78 - 83             80.5           8

4                83 - 88             85.5           12

5                88 - 93            90.5           16

6                93 - 98            95.5           20

7                98 - 103           100.5          24                            

TOTAL:                                                 84

a) The number of the class containing the  largest score can be found in frequency  24 and the class is  98 - 103

b) For the third class 78 - 83 ; the upper limit = 83  ( since the upper limit is derived by addition of  5 to the last number showing  in the highest value specified by the number in the class interval which is 78 ( i.e 78 + 5 = 83))

c)   The class width for this histogram 5 ; since it  is the difference  between the upper and lower boundaries  limit of the given class.

So , from above the difference in any of the class will definitely result into 5

d) The number of students that took the exam simply refers to the frequency ; which is (0+4+8+12+16+20+24) = 84

e) Lastly; the percentage of students that scored higher than 95.5 is ;

⇒[tex]\dfrac{20+24}{84} *100[/tex]

= 0.5238095 × 100

= 52.83

To the nearest percentage ;the percentage of students that scored higher than 95.5 is 53%

Answer:

1. 98-103 (6th class)

2. 88

3. 5

4. 84

5. 52%

Step-by-step explanation:

Find attached the frequency table.

The class of exam scores falls between (1, 2, 3, 4, 5, or 6).

The exam score ranged from 68-103

1) The largest number of exam scores = 24

The largest number of exam scores is in the 6th class = 98 -103

Step 2 of 5:

The upper class limit is the higher number in an interval. Third class interval is 83-88

The upper class limit of the third class 88.

Step 3 of 5:

Class width = upper class limit - lower class limit

We can use any of the class interval to find this as the answer will be the same. Using the interval between 73-78

Class width = 78 - 73

Class width for the histogram = 5

Step 4 of 5:

The total of students that took the test = sum of all the frequency

= 0+4+8+12+16+20+24 = 84

The total of students that took the test = 84

Step 5 of 5:Find the percentage of students that scored higher than 95.5

Number of student that scored higher than 95.5 = 20 + 24 = 44

Percentage of students that scored higher than 95.5 = [(Number of student that scored higher than 95.5)/(total number of students that took the test)] × 100

= (44/84) × 100 = 0.5238 × 100 = 52.38%

Percentage of students that scored higher than 95.5 = 52% (nearest percent)

Answer:

Option (2). 14 m

Step-by-step explanation:

Formula to get the area of a circle 'A' = [tex]\pi r^{2}[/tex]

where r = radius of the circle

Given in the question,

Area of the circle = 153.86 square meters

By putting the values in the formula,

153.86 = πr²

r = [tex]\sqrt{\frac{153.86}{\pi } }[/tex]

r = [tex]\sqrt{49}[/tex]

r = 7 meters

Diameter of circle = 2 × (radius of the circle)

                              = 2 × 7

                              = 14 meters

Therefore, diameter of the circle is 14 meters.

Option (2) is the answer.

Answer:

14m

Step-by-step explanation:

Answer:

f(x)=√x

Step-by-step explanation:

A parent function is something simple with just x

Answer:

f(x)=Square Root of x (choice B or the second one down)

Step-by-step explanation:

All the other choices have either a plus 3 or minus 3. A parent function is not going to have any type of number being added or subtracted to it.

Answer:

[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]

And if we solve this equation for x we got:

[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]

We can cancel [tex]x^2[/tex] in both sides and we have this:

[tex] 22x -6x= 256+9-121 =144[/tex]

And then we got:

[tex] 16 x= 144[/tex]

[tex] x =\frac{144}{16}= 9[/tex]

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

Step-by-step explanation:

For this case we have a right triangle and we can use the Pythagoras Theorem and using the info given by the triangle we can set up the following equation:

[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]

And if we solve this equation for x we got:

[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]

We can cancel [tex]x^2[/tex] in both sides and we have this:

[tex] 22x -6x= 256+9-121 =144[/tex]

And then we got:

[tex] 16 x= 144[/tex]

[tex] x =\frac{144}{16}= 9[/tex]

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

Answer:

The width or range of the confidence interval with sample size 200 will be about half of that of the confidence interval with sample 50.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)

- For the two random samples, of sizes 50 and 200, the Central limit theorem allows us to say that the sample mean is approximately equal to the population mean as this random sample satisfies the condition of being a simple random sample and a distribution obtained from a normal distribution.

- Making the right assumption that population standard deviation is known and z-distribution is used to find the critical value

Critical value for 95% = 1.96

The critical value for both samples are the same then.

- Standard Error of the mean = σₓ = (σ/√n)

where σ = population standard deviation

n = sample size

For the two distributions

Confidence Interval = (Sample mean) ± [(Critical value) × (Standard Error of the mean)

(Sample mean)₅₀ = (Sample mean)₂₀₀

(Critical value)₅₀ = (Critical value)₂₀₀

(Standard Error of the mean)₅₀ = (σ/√50) = 0.1414σ

(Standard Error of the mean)₂₀₀ = (σ/√200) = 0.0707σ

0.1414σ = 2 × 0.0707σ

(Standard Error of the mean)₅₀ = 2 × (Standard Error of the mean)₂₀₀

(Standard Error of the mean)₅₀ > (Standard Error of the mean)₂₀₀

Hence,

(Margin of Error)₅₀ > (Margin of Error)₂₀₀

(Margin of Error)₅₀ = 2 × (Margin of Error)₂₀₀

Confidence Interval = (Sample mean) ± (Margin of error)

Hence, the width or range of the confidence interval with sample size 50 will be about two times larger than the confidence interval with sample 200.

Hope this Helps!!!

Answer:

Graph 2

Step-by-step explanation:

You can see that all the shaded numbers are above negative 25 in that graph. Hope this helped!

Answer:

[tex] Median = \frac{60+60}{2}=60[/tex]

And we see that the closest values to 60 are 62 and 63 and then the answer would be:

The values closest to the middle are 62 inches and 63 inches.

Step-by-step explanation:

We have the following dataser given:

62 33 50 90  80 50 40 70  50 63 74 53  55 64 60 60  78 70 43 82

We can sort the values from the lowest to the highest and we got::

33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78 80 82 90

Now we see that we have n=20 values and the values closest to the middle and we can use the middle as the median and for this case the median can be calculated from position 10 and 11th and we got:

[tex] Median = \frac{60+60}{2}=60[/tex]

And we see that the closest values to 60 are 62 and 63 and then the answer would be:

The values closest to the middle are 62 inches and 63 inches.

The values closest to these middle elements are 60 and 63 inches

The dataset is given as:

62 33 50 90 80 50 40 70 50 63 74 53 55 64 60 60 78 70 43 82

Next, we sort the data elements in ascending order

33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78  80 82 90

The length of the dataset is 20.

So, the elements at the middle are the 10th and the 11 elements.

From the sorted dataset, these elements are: 60 and 62

Hence, the values closest to these middle elements are 60 and 63

Read more about median at:

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