Please help, find angle R

Answer:

  H  70 in³

Step-by-step explanation:

The volume of a pyramid is given by the formula ...

  V = (1/3)Bh

  V = (1/3)(21 in²)(10 in) = 70 in³

The volume of the pyramid is 70 cubic inches.

Answer:

[tex]= 70 {in}^{3}[/tex]

Third answer is correct.

Step-by-step explanation:

[tex]v = \frac{base \: \: \: area \times height}{3} \\ = \frac{21 \times 10}{3} \\ = 70 {in}^{3} [/tex]

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Answer:

She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.

Step-by-step explanation:

To find the experimental probability of an outcome we divide:

The number of trials in which the desired outcome happened by the total number of trials.

In this question:

Experimental probability of winning this game.

She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.

Answer:

The correct answers are B, C, D, B

Step-by-step explanation:

These answers complete the statements that show the difference between the mathematical and reasonable ranges. Good luck! :)

B) Rational Numbers

C) 30,800

D) Real Numbers

B) 800

Correct on edge2020!

Answer:

BCDB

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

9.

Property of a rhombus:

In a rhombus, the diagonals are perpendicular.

The sum of the measures of the angles of a triangle is 180 deg.

Since the diagonals are perpendicular, the angles formed by the intersection of the diagonals are right angles and measure 90 deg.

m<ABD + m<CAB + 90 = 180

50 + m<CAB + 90 = 180

m<CAB + 140 = 180

(i) m<CAB = 40

The diagonals of a rhombus divide the rhombus into 4 congruent triangles.

Call the point of intersection of the diagonals E.

Triangles CEB and AEB are congruent.

m<BCA = m<DCA = 40

m<BCD = m<BCA + m<DCA = 40 + 40

(ii) m<BCD = 80

m<CDB = m<ADB = 50

m<ADC = m<CDB + m<ADB = 50 + 50

(iii) m<ADC = 100

10.

There are two angles labeled z. One is near point E and one is near point O. One of them probably is x.

Two angles measure 60 and 80. Add them to get 140.

z (near point O) and the 140 deg angle are a linear pair. their measures add to 180 deg.

z + 140 = 180

z = 40 (This is the z near point O.)

z (near point O) and 60 deg add to an interior angle of the parallelogram.

z + 60 = 40 + 60 = 100

The interior angle at vertex O measures 100 deg.

Adjacent interior angles of a parallelogram are supplementary.

100 + y = 180

y = 80

The two angles labeled z are alternate interior angles. Since the sides of a parallelogram are parallel, the two angles labeled z are congruent and measure 40 deg.

z = 40 (This is angle z near point E)

Answer:

For this case the mean is given by:

[tex] \mu = p =0.46[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]

Step-by-step explanation:

For this case we have the following info given :

[tex] n = 215[/tex] represent the sample size

[tex]p = 0.46[/tex] represent the proportion of business graduate students from private universities had student loans

For this case we want to find the distribution for the sample proportion and we know that this distribution is given by:

[tex] \hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]

And for this case the mean is given by:

[tex] \mu = p =0.46[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]

Answer:

The mean of this distribution is 0.46 and the standard deviation is 0.034.

Step-by-step explanation:

The Central Limit Theorem estabilishes 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.

For sampling distributions of samples of size n of a proportion p, the mean is [tex]\mu = p[/tex] and the standard deviation is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]n = 215, p = 0.46[/tex]

So

[tex]\mu = 0.46, s = \sqrt{\frac{0.46*0.54}{215}} = 0.0340[/tex]

The mean of this distribution is 0.46 and the standard deviation is 0.034.

Answer:

Rhombus

Step-by-step explanation:

Answer:

Step-by-step explanation:

rhombus

Answer:

Any values that is greater than 1/2.

Step-by-step explanation:

You have to form an inequality. Given that what values is added to c will satisfy that 3 - 5c is less than 1 - c :

[tex]3 - 5c < 1 - c[/tex]

Next, you have to solve :

[tex] - 5c + c < 1 - 3[/tex]

[tex] - 4c < - 2[/tex]

[tex]c > \frac{ - 2}{ - 4} [/tex]

[tex]c > \frac{1}{2} [/tex]

Answer:

70°

Step-by-step explanation:

Since it's a trapezoid the sum of a and x would be 180°

110° + x = 180°

x = 70°

Answer:

A tangent line touches a curve at one point and has the same slope as the curve at that point. A secant line intersects at 2 or more points and has a slope equal to the average rate of change between those points.

Answer:

A Tangent of a circle is found outside of the circle but touching 2 points of the circle on the outside. But a Secant is found inside the circle and it touches 2 points in the circle. A Chord can always be Secant, but a secant can not always be a chord because it may pass through the circle.

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

In circle with center O,

[tex] chord\overline {EF} \cong chord\overline {WV}... (Given) [/tex]

Since, congruent chords are equidistant from the center of the circle.

[tex] \therefore PG = GO\\

\therefore - x +10 = - 3(x+2)\\

\therefore - x + 10 = - 3x - 6\\

\therefore 3x - x = - 6-10\\

\therefore 2x = - 16\\\\

\therefore x = \frac{-16}{2} \\\\

\huge \red {\boxed {\therefore x = - 8}} \\\\

\because \overline {PO} = \overline {PG} + \overline {GO} \\

\therefore \overline {PO} = - x + 10 + \{-3(x + 2)\}\\

\therefore \overline {PO} = - x + 10 - 3x - 6\\

\therefore \overline {PO} = - 4x + 4 \\

\therefore \overline {PO} = - 4\times (-8)+ 4 \\

\therefore \overline {PO} =32+ 4 \\

\huge \orange {\boxed {\therefore \overline {PO} =36}} \\[/tex]

Answer:

Shen has a slower heart rate than Adrian.

Shen’s unit heart rate is 64 beats per minute.

Adrian’s unit heart rate is 72 beats per minute.

Answer:

12

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

The table below contains the overall miles per gallon (MPG) of a type of vehicle. Complete parts a and b below.

28, 34, 28, 20, 21, 31, 28, 24, 34, 35 , 36, 26, 25, 20

a. Construct a 95% confidence interval estimate for the population mean MPG for this type of vehicle, assuming a normal distribution.

b. Choose the correct answer below.

A. We have 95% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval.

B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval. This is the correct answer.

C.95 % of the sample data fall between the limits of the confidence interval.Your answer is not correct.

D. The mean MPG of this type of vehicle for 95?% of all samples of the same size is contained in the interval.

Solution:

a) Mean = (28 + 34 + 28 + 20 + 21 + 31 + 28 + 24 + 34 + 35 + 36 + 26 + 25 + 20)/14 = 27.86

Standard deviation = √(summation(x - mean)²/n

n = 14

Summation(x - mean)² = (28 - 27.86)^2 + (34 - 27.86)^2 + (28 - 27.86)^2 + (20 - 27.86)^2 + (21 - 27.86)^2+ (31 - 27.86)^2 + (28 - 27.86)^2 + (24 - 27.86)^2 + (34 - 27.86)^2 + (35 - 27.86)^2 + (36 - 27.86)^2 + (26 - 27.86)^2 + (25 - 27.86)^2 + (20 - 27.86)^2 = 399.7144

Standard deviation = √(399.7144/14) = 5.34

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 5.34

n = number of samples = 14

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 14 - 1 = 13

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.16

Margin of error = 2.16 × 5.34/√14

= 3.08

The confidence interval is 27.86 ± 3.08

b) B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval.

Answer:

-$5.06

Step-by-step explanation:

Given the probability distribution of X where X is the net gain or loss

[tex]\left|\begin{array}{c|c|c}Profit(X)&\$6&-\$8\\P(X)&0.21&0.79\end{array}\right|[/tex]

The expected value of X is defined as follows:

Expected Value of X, [tex]E(X)=\sum_{i=1}^nx_iP(x_i)[/tex]

Therefore, the expected value of the player

E(X)=(6*0.21)+(-8*0.79)

=1.26-6.32

[tex]E(X)=-\$5.06[/tex]

The expected value of each player at the casino is -$5.06.

Answer:

Option (3)

Step-by-step explanation:

From the figure attached,

AB and CD are two chords intersecting at O.

m∠AOD = 37°

m∠AOC + m∠AOD = 180° [Since these angles are supplementary angles]

m∠AOC = 180° - 37°

              = 143°

By the theorem of intersecting chords,

Measure of angle formed is the half of the sum of measures of the arcs intercepted by the angle and vertical angle.

m∠AOC = [tex]\frac{1}{2}(\widehat{AC}+\widehat{BD})[/tex]

143° = [tex]\frac{1}{2}[(x+5)+(x-5)][/tex]

143° = x

Therefore, Option (3) will be the answer.

Answer:

[tex]=13x+5[/tex]

Step-by-step explanation:

[tex]\left(2x+9\right)+\left(11x-4\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=2x+9+11x-4\\\mathrm{Group\:like\:terms}\\=2x+11x+9-4\\\mathrm{Add\:similar\:elements:}\:2x+11x=13x\\=13x+9-4\\\mathrm{Add/Subtract\:the\:numbers:}\:9-4=5\\=13x+5[/tex]

Answer:

9 inches

Step-by-step explanation:

For similar problems like this, divide the area by the given length or width. In this case, your equation would be 54/6 = 9.

The width of the rectangle can be found as 9 inch.

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.

The area and length of rectangle are given as 54 inch² and 6 inches.

Suppose the width of the rectangle be x.

Since, the area of rectangle is given as the product of length and breadth, the following equation can be written as,

6x = 54

⇒ x = 54/6

⇒ x = 9

Hence, the width is given as 9 inch.

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Answer:

Step-by-step explanation:

Given that:

An epidemiologist found five cases of "big toe cancer" in the Yukon Territory.

Therefore, shoe size > 9

1) From the required data given below

                       Case       Control       Total

Yes                2(a)             3(b)            5

No                  3(c)             2(d)            5

Total               5                 5                10

∴ odds ratio = ad/bc

= 4/9

=0.444

2) From the less than 1.0 mean that the odds of cancer among case is lower than the odds of cancer among controls

Answer:

Matt ran 6 miles.

Step-by-step explanation:

Stan ran 4 and 7/10 miles, and this is 1 and 3/10 fewer miles than Matt.

this means that Matt ran the following amount of miles

4 and 7/|0 + 1 and 3/10 miles:

(4 + 1) + (7/10 + 3/10) = 5 + 10/10 = 6 miles.

This would be the correct way to solve this equation.

Answer:

Null hypothesis: H0 = 0.65

Alternative hypothesis: Ha ≠ 0.65

z = 1.172

P value = P(Z≠1.172) = 0.24

Decision we fail to reject the null hypothesis. That is, there is convincing evidence enough to reject the Null hypothesis.

Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 95% confidence interval) ---- reject Null hypothesis

Z score < Z(at 95% confidence interval) ------ accept Null hypothesis

Step-by-step explanation:

Given;

n=80 represent the random sample taken

Null hypothesis: H0 = 0.65

Alternative hypothesis: Ha ≠ 0.65

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 80

po = Null hypothesized value = 0.65

p^ = Observed proportion = 57/80 = 0.7125

Substituting the values we have

z = (0.7125-0.65)/√(0.65(1-0.65)/80)

z = 1.17201807734

z = 1.172

To determine the p value (test statistic) at 0.05 significance level, using a two tailed hypothesis.

P value = P(Z≠1.172) = 0.241197 = 0.24

Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 1.172) which falls within the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.24 which is higher than 0.05. Then we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is valid.

Answer:

D.

Step-by-step explanation:

Let's solve each choice.

A: 3 divided by 90 is 3/90 and can be simplified to 1/30. So no.

B: 1/5 divided by 6. Recall that when dividing, you multiply the 1st term by the 2nd term's reciprocal. If you do this, you get 1/30. So no.

C: 1/6 divided by 5. Again, multiply 5's reciprocal to 1/6. There you get 1/30. So no.

D: 6 divided by 1/5. Again, multiply 1/5's reciprocal to 6. 1/5's reciprocal is 5. 5*6 = 30. So this is the correct answer.

Answer:

(0, 8).

Step-by-step explanation:

The y intercept occurs when  = 0, so we have the equation:

y = -3(0) + 8

y = 0 + 8

y = 8.

The answer is (0, 8).

Answer:

Step-by-step explanation:

I remember leaving a top of ten percent (15%)

lets convert 15% into a decimal

15%=0.15

Tip=0.15x, where x is the bill price

Tip=0.15*34

Tip=5.1

So he could get  5$ and 10 cents as a tip

Answer:

1) With H1: p ≠ 3/5, the test statistic is z = 0.78

The p value for this case would be given by:

[tex] p_v = 2*P(z>0.78)=0.4354[/tex]

Best option:

A) 0.4354; fail to reject the null hypothesis

2) The test statistic in a left-tailed test is z = -1.83

The p value for this case would be given by:

[tex] p_v = P(z<-1.83)=0.0336[/tex]

Best option:

A) 0.0336; reject the null hypothesis

3) The test statistic in a right-tailed test is z = 0.52.

The p value for this case would be given by:

[tex] p_v = P(z>0.52)=0.3015[/tex]

Best option:

C) 0.3015; fail to reject the null hypothesis

Step-by-step explanation:

The significance level for all the cases is the same [tex]\alpha=0.05[/tex]

Part 1

With H1: p ≠ 3/5, the test statistic is z = 0.78

The p value for this case would be given by:

[tex] p_v = 2*P(z>0.78)=0.4354[/tex]

Best option:

A) 0.4354; fail to reject the null hypothesis

Part 2

The test statistic in a left-tailed test is z = -1.83

The p value for this case would be given by:

[tex] p_v = P(z<-1.83)=0.0336[/tex]

Best option:

A) 0.0336; reject the null hypothesis

Part 3

The test statistic in a right-tailed test is z = 0.52.

The p value for this case would be given by:

[tex] p_v = P(z>0.52)=0.3015[/tex]

Best option:

C) 0.3015; fail to reject the null hypothesis

Answer:

Endangered species

Step-by-step explanation:

An endangered species is a species that is at risk of extinction due to rapid decrease in their population .Their decrease in population might be due to loss of habitat and genetic variation. The loss of habitat might be due to natural factors like the climate change For example animals like dinosaurs during the cretaceous period that experience rapid change in the climate loss their habitat and went extinct.

Human activity can also influence loss of habitat. Development in housing , agriculture and industry can also threaten the habitats of native organisms. The loss of their habitat might cause sudden extinction of these organisms. They might find it hard to adapt to another environment or even procreate.  

Generally,  endangered species are species that are threatened by extinction. Elephants that are in danger of been wiped out is an endangered species.

Answer:

(a)77.4bpm

(b)Mean of Sample 1 = 70.3 beats per minute.  

Mean pulse of sample 2 = 70 beats per minute.

(c)

Step-by-step explanation:

(a)Population mean pulse.

The pulse of the nine students which represent the population are:

[tex]\text{Population Mean} =\dfrac{64+77+89+69+89+65+88+69+87}{9} \\=\dfrac{697}{9} \\\\=77.44[/tex]

The population mean pulse is approximately 77.4 beats per minute.

(b)Sample 1: {Janette,Clarice,Megan}

Mean of Sample 1

[tex]\text{Sample 1 Mean} =\dfrac{65+69+77}{3} \\=\dfrac{211}{3} \\\\=70.3[/tex]

Sample 2: {Janette,Clarice,Megan}

Mean of Sample 2

[tex]\text{Sample 2 Mean} =\dfrac{64+69+77}{3} \\=\dfrac{210}{3} \\\\=70[/tex]

The mean pulse of sample 1 is approximately 70.3 beats per minute.  

The mean pulse of sample 2 is approximately 70 beats per minute.

(c)

Answer:

152°

Step-by-step explanation:

Let P be any point on tangent [tex] \overleftrightarrow{YZ} [/tex] and WY is secant or chord of the [tex] \odot J[/tex] .

[tex] \therefore m\angle WYZ + m\angle WYP = 180°\\(Straight \: line \: \angle 's) \\

\therefore 104° + m\angle WYP = 180°\\

\therefore m\angle WYP = 180°- 104° \\

\red{\boxed {\bold {\therefore m\angle WYP = 76°}}} \\[/tex]

NOW, by tangent secant theorem:

[tex] m\angle WYP =\frac{1}{2}\times m(\widehat{WXY}) \\\\

76°=\frac{1}{2}\times m( \widehat{WXY}) \\\\

76°\times 2 =m( \widehat{WXY}) \\

\huge \purple {\boxed {\therefore m(\widehat{WXY}) = 152°}} [/tex]

Answer:

Jake

Step-by-step explanation:

Noah: 11 feet per second

Katie: 423 feet / 33 seconds = 12.82 ft/sec (just divide the feet / seconds)

Jake:

1 mile = 5280 feet

Adam runs 5280ft / 396 seconds = 13.34 ft/sec

Liz:

1 minute = 60 second.

Liz runs 638 feet / 60 seconds = 10.63 ft / sec

From the above results we find that Jake runs the fastest

Answer:

2.9 per hour

Step-by-step explanation:

Divide 69.9 by 24

Answer:

Step-by-step explanation:

the data is skewed left

The data in the given set is skewed towards left because the mean of the data is 7.5 and the data is not distributed symmetrically in the given set. Thus, the correct option is C.

Skewed data is the data which creates an asymmetrical, skewed curve on the graph scale. In statistics, the graph of a data set with normal distribution is symmetrical and has a bell-like shape. However, the skewed data has a tail on either side of the graph as well.

Skewness can be demonstrated on a bell curve when the data points are not distributed symmetrically to the left and right sides of the median on the curve. If the bell curve is shifted to the left or towards the right side, it is said to be skewed curve. The two halves of the distribution are not mirror images in the skewed curve because the data are not distributed equally on both sides of the distribution peak.

Therefore, the correct option is C.

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