Consider the following trigonometric function. h(x) = 3 sin (2x - pi) + 2. Graph h(x) in the interactive widget.

Answer:

[tex]258 in^2[/tex]

Step-by-step explanation:

Given the dimensions

L = 9 in

W = 6 in

H = 5 in

we can see that the craft is a cuboid/rectangular prism

the expression for the surface area is given as

[tex]Surface -area=2lw+2lh+2hw[/tex]

substituting we have

[tex]Surface- area=(2*9*6)+(2*9*5)+(2*5*6)[/tex]

[tex]Surface -area=108+90+60= 258[/tex]

[tex]Surface -area=258 in^2[/tex]

Answer: The volume of the​ sculpture is 141.84 cubic-feet

Step-by-step explanation: Please see the attachments below

Answer:

q<16

Step-by-step explanation:

Multiply four quarts by four gallons. This gives us 16. Now, since it says less than, and not less than or equal to, we use < symbol. q<16

Answer:

q<16

Step-by-step explanation:

Answer:

5.94% of customers carries a balance of GH¢100 or lower.

82.64% of customers carries a balance of GH¢500 or lower.

0% of current account customers carries average daily balances exactly equal to GH¢500.

76.7% of customers maintains account balance between GH¢100 and GH¢500

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 350, \sigma = 160[/tex]

What percentage of customers carries a balance of GH¢100 or lower?

This is the pvalue of Z when X = 100. So

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

[tex]Z = \frac{100 - 350}{160}[/tex]

[tex]Z = -1.56[/tex]

[tex]Z = -1.56[/tex] has a pvalue of 0.0594

5.94% of customers carries a balance of GH¢100 or lower.

What percentage of customers carries a balance of GH¢500 or lower?

This is the pvalue of Z when X = 500.

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

[tex]Z = \frac{500 - 350}{160}[/tex]

[tex]Z = 0.94[/tex]

[tex]Z = 0.94[/tex] has a pvalue of 0.8264

82.64% of customers carries a balance of GH¢500 or lower.

What percentage of current account customers carries average daily balances exactly equal to GH¢500?

In the normal distribution, the probability of finding a value exactly equal to X is 0. So

0% of current account customers carries average daily balances exactly equal to GH¢500.

What percentage of customers maintains account balance between GH¢100 and GH¢500?

This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 100.

From b), when X = 500, Z = 0.94 has a pvalue of 0.8264

From a), when X = 100, Z = -1.56 has a pvalue of 0.0594

0.8264 - 0.0594 = 0.767

76.7% of customers maintains account balance between GH¢100 and GH¢500

Answer:

EG and GF

Step-by-step explanation:

when a perpendicular bisector bisects a segment it creates a right angle. It also divides the segment in half. So EG≅GF

Answer:

Hey mate, here's ur answer:

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

(4a - 3b + 4c) + (8a - 2b + 3c)

=4a+−3b+4c+8a+−2b+3c

=(4a+8a)+(−3b+−2b)+(4c+3c)

=12a−5b+7c

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

Hope it helps

#stayhomestaysafemate

:D

Answer:

a. The qualifying time in seconds is approximately 297 sec.

b. The proportion of boys from the western region who qualify to run in this event is about 1.88% (0.0188).

Step-by-step explanation:

Part a

In this question, the key concept to take into account is the normal distribution. This distribution is completely characterized when we have the population's mean, [tex] \\ \mu[/tex], and the population standard deviation, [tex] \\ \sigma[/tex].

In this case:

[tex] \\ \mu = 5\;min\;17\;sec[/tex]

[tex] \\ \sigma = 12\;sec[/tex]

Because we are asked to finding the qualifying time in seconds, let us to convert [tex] \\ \mu[/tex] from minutes to seconds:

[tex] \\ 5\;min*\frac{60\;sec}{1\;min}[/tex]

[tex] \\ 5 * 60 \;sec*\frac{min}{min}[/tex]

[tex] \\ 300 \;sec*1[/tex]

[tex] \\ 300 \;sec[/tex]

We still need to sum 17 sec:

Then, [tex] \\ \mu = (300 + 17)\;sec[/tex]

[tex] \\ \mu = 317\;sec[/tex]

Time in seconds of the fastest 5% runners

They are those that in the normal distribution are below 5% (0.05) in the cumulative normal distribution, that is, [tex] \\ P(x<0.05)[/tex]. Those above it, spend more time in the track event.

For this cumulative value, we can use the standardized score, or z-score, for solving the value in seconds that corresponds to it. The formula for the z-score is  

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where x is the raw value or, in this case, the time in seconds in question. Then, for a cumulative probability of 5%, the corresponding z-score is (consulting a cumulative normal standard table, available on the Internet or in any Statistic book):

 [tex] \\ z \approx -1.65[/tex]

For this, we need to find a cumulative probability in the cumulative standard normal table equal or approximately to 0.05, and this value is about z = -1.65.

With this value at hand, we can solve [1] for x.

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ -1.65 = \frac{x - 317\;sec}{12\;sec}[/tex]

[tex] \\ -1.65 * 12\;sec = x - 317\;sec[/tex]

[tex] \\ (-1.65 * 12\;sec) + 317\;sec = x[/tex]

[tex] \\ -19.80\;sec + 317\;sec = x[/tex]

[tex] \\ x = -19.80\;sec + 317\;sec[/tex]

[tex] \\ x = 297.20\;sec[/tex]

Thus, rounding it to the nearest second, we have that "the qualifying time in seconds" is, approximately, 297 sec. This is the time that the 5% fastest high school boys have to meet the state competition requirement. They spend less time to run the same distance than others.  

Part b

In this part, we have to take into account the previously obtained time (297 sec) to find "the proportion of boys from this region who qualify to run in this event in the state meet." In other words, how many, in percent, can qualify, knowing that, in this part of the state (western region), the population's mean is different (5min 22sec or 300sec + 22sec = 322sec, considering that we already have the value in seconds for 5min from the previous answer).

Then, for this region, the proportion of boys that can qualify to run in this event in the state meet can be calculated using the formula [1] for z-scores:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

Where, in this case, the value for x = 297 sec, for the reasons already explained. With the resulting value for z, we can consult the cumulative standard normal distribution to find the probability in question. Then

[tex] \\ z = \frac{(297 - 322)\;sec}{12\;sec}[/tex]

[tex] \\ z = \frac{-25\;sec}{12\;sec}[/tex]

[tex] \\ z = -2.08333... \approx -2.08[/tex]

For a z = -2.08, the corresponding probability, consulting a cumulative standard normal distribution is, approximately, 0.0188 or about 1.88% of the boys for western region of the state.

Then, in other words, "the proportion of boys from this region who qualify to run in this event in the state meet" is about 1.88%.

We can see the results in the graphs below. The first graph is for western region.

Answer:

b. 0.02

Step-by-step explanation:

The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. In this case, this will mean rejecting that the proportions are not significantly different.

Usually, a p-value is considered to be statistically significant when p ≤ 0.05.

From the answer options provided, alternative b. 0.02 is the only one that represents the difference in proportions to be statistically significant (there is only a 2% chance that the proportions are not significantly different).

Therefore, the answer is b. 0.02

Answer:

A.g(x)= 4x^2 because the parabola is a compression and the higher the coefficient, the skinnier the parabola

Answer:

L ⊥ N

Step-by-step explanation:

Since M and N are perpendicular, and L is parallel to M, anything that's perpendicular to M is also perpendicular to L. In fact, since we have parallel lines, we now have many sets of congruent angles, but the only ones we know the actual measurements of are the right angles from the perpendicular lines.

Answer:

x = 4 ± √13

Step-by-step explanation:

x² − 8x + 3 = 0

Complete the square.  (-8/2)² = 16.

x² − 8x + 16 − 13 = 0

(x − 4)² − 13 = 0

(x − 4)² = 13

x − 4 = ±√13

x = 4 ± √13

Answer:

0.58 +/- 0.115

(0.465, 0.695)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 29/50 = 0.58

Number of samples n = 50

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

0.58 +/- 1.645√(0.58(1-0.58)/50)

0.58 +/- 1.645(0.069799713466)

0.58 +/- 0.114820528652

0.58 +/- 0.115

(0.465, 0.695)

The 90% confidence interval estimate of the true population proportion of account customers who have a visa card with the bank is;

0.58 +/- 0.115

(0.465, 0.695)

Answer:

(A) For this research we made use of the paired t test.

(B) For the t test, we conclude that in the null Hypothesis H₀, there was no difference between the average labor force participation rate for women between the years of 1968 and​ 1972 as against the alternate Hypothesis Hₐ.

From the output data we have, since the P value is 0.024 and  is lesser than the alpha value of 0.05, we will accept the alternate Hypothesis instead of the null Hypothesis.

Note:Kindly find an attached copy of the complete question below.

Step-by-step explanation:

Solution

Recall that:

The U.S of Bureau of Labor Statistics have published Values for the labor force participation rate of women​ (LFPR).

We are more interested in if there was a difference between female participation 1968 and​ 1972, a rapid change in women.

so we will check values for 19 randomly selected cities for 1968 and​ 1972,

Now,

(a) Which of this test is most appropriate for this data

The test which will be more suitable for these data will be paired to test t.

Because the data is for labor force participation for two different years, we apply the t test. now that we are making a comparison of two different year times, we will apply the t test in this research.

In this case, the sample size for both the years evaluated should be same, since we need to pair each and all the data.

(b)By using the test you selected, explain your conclusion

Now, to test the data paired t test, we have already the null Hypothesis  H₀: In this case there  is no difference between the average labor force participation rate for women between the years of 1968 and​ 1972 as compared with the alternate Hypothesis Hₐ: there was a significant difference between the average labor force participation rate for women between the years of 1968 and​ 1972.

However, from the output, we have that the P value is 0.024 which is lower than the alpha value of 0.05.

In conclusion, the alternate Hypothesis accepted while the null Hypothesis is rejected.

Note: kindly find an attached copy of the complete question to this solution

below.

Answer:

im going to say a wallaby because they are smaller and lighter and if you think of the weight then less power is needed for a wallaby

idk lol XD

Step-by-step explanation:

Answer:

[tex] y = 5x[/tex]

And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:

[tex] y_f = 5(2x) = 10x[/tex]

And if we find the ratio between the two equations we got:

[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]

So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2

Step-by-step explanation:

For this case we have this equation given:

[tex] y = 5x[/tex]

And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:

[tex] y_f = 5(2x) = 10x[/tex]

And if we find the ratio between the two equations we got:

[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]

So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2

Answer:

Step-by-step explanation:

When we use the distributive property for expanding polynomial products, we often use it in the form ...

  (a +b)c = ac +bc

Here, we have ...

  (a +b) = (x -1)   ⇒   a=x, b=-1

  c = (4x+2)

So, the proper application of the distributive property looks like ...

  (a +b)c = ac +bc

  (x -1)(4x +2) = x(4x+2) -1(4x+2) . . . . . different from the work shown

We must conclude ...

  The distributive property was not applied correctly in the first step.

Answer:

Therefore, the mean and the standard deviation for the number of electrical outages (respectively) are 0.26 and 0.5765 respectively.

Step-by-step explanation:

Given the probability distribution table below:

[tex]\left|\begin{array}{c|cccc}x&0&1&2&3\\P(x)&0.8&0.15&0.04&0.01\end{array}\right|[/tex]

(a)Mean

Expected Value, [tex]\mu =\sum x_iP(x_i)[/tex]

=(0*0.8)+(1*0.15)+(2*0.04)+(3*0.01)

=0+0.15+0.08+0.03

Mean=0.26

(b)Standard Deviation

[tex](x-\mu)^2\\(0-0.26)^2=0.0676\\(1-0.26)^2=0.5476\\(2-0.26)^2=3.0276\\(3-0.26)^2=7.5076[/tex]

Standard Deviation [tex]=\sqrt{\sum (x-\mu)^2P(x)}[/tex]

[tex]=\sqrt{0.0676*0.8+0.5476*0.15+3.0276*0.04+7.5076*0.01}\\=\sqrt{0.3324}\\=0.5765[/tex]

Therefore, the mean and the standard deviation for the number of electrical outages (respectively) are 0.26 and 0.5765 respectively.

Answer:

A

Step-by-step explanation:

Calculate the products in the multiple choice and see if any equal the product in the problem.

Hence as the products calculated in choice A equal that in the problem;the answer is A

Answer:

a. x<3

b. 3,4,5,6

c.x>6

Answer:

It’s E

Step-by-step explanation:

The length of the diagonal of the figure considered is given by: Option E: 5√2

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Consider the figure attached below.

The triangle ABC is a right angled triangle as one of its angle is of 90 degrees.

Thus, we can use Pythagoras theorem here to find the length of the diagonal line AC.

Since it is given that:
|AB| = 5 units = |BC|, thus, we get:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|AC| = \sqrt{5^2 + 5^2} = \sqrt{2 \times 5^2} = \sqrt{5^2} \times \sqrt{2} = 5\sqrt{2} \: \rm units[/tex]

We didn't took negative of root as length cannot be negative.

Thus, the length of the diagonal of the figure considered is given by: Option E: 5√2

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

Answer:

Explained below.

Step-by-step explanation:

A compound event is an event in which has possible outcomes more than one.  

To determine the probability of compound events on has to compute the sum of the probabilities of all the individual events and, if required, remove any coinciding probabilities.

Examples of compound events are:

The number of favorable outcome is rolling a 5, is 1.

The total number of outcomes of rolling a die is 6.

Then the probability of rolling a 5 is 1/6.

The number of favorable outcome of pulling a heart is 13.  

The total number of outcomes is 52.

The probability of pulling a heart from a standard deck is 13/52 or 1/4.

Thus, the procedure is to compute the sum of the probabilities of all the individual events and, if required, remove any coinciding probabilities.

[tex]the \: right \: answer \: is \: of \: option \: d \\ please \: see \: the \: attached \: picture \\ hope \: it \: helps[/tex]

Answer:

7.5 in

Step-by-step explanation:

Step one

This problem bothers on the mensuration of solid shapes, a sphere.

We know that the volume of a sphere is expresses as

V= (4/3) πr³

Given that the volume of the sphere is

1767.1459 in³

To solve for the radius r we need to substitute the value of the volume in the expression for the volume we have

Step two

1767.1459= (4/3) πr³

1767.1459*3= 4πr³

5301.4377/4*3.142=r³

421.82031=r³

Step three

To get r we need to cube both sides we have

r= ³√421.82031

r= 7.49967589711

To the nearest tenth

r= 7.5 in

The probability that more than half of the 8 randomly chosen blood donors have Type A blood is approximately 0.2533 or 25.33%.

To calculate the probability that more than half of the 8 randomly chosen blood donors have Type A blood, we can use the binomial probability formula:

[tex]\mathrm{P(X > n/2) = \sum [ P(X = k) ]}[/tex]

where the sum is taken from k = (n/2 + 1) to k = n

In this case, n represents the number of trials (8 blood donors) and p is the probability that a single blood donor has Type A blood (0.40).

P(X = k) is the probability of getting exactly k donors with Type A blood, and it is given by the binomial probability formula:

[tex]\mathrm {P(X = k) = (n, k) \times p^k \times (1 - p)^{(n - k)}}[/tex]

where (n choose k) represents the number of combinations of n items taken k at a time, and it is given by:

[tex]\mathrm {(n, k) = \frac{n!}{(k! \times (n - k)!)}}[/tex]

Now, let's calculate the probability that more than half (i.e., 5 or more) of the donors have Type A blood:

[tex]\mathrm{P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)}[/tex]

[tex]\mathrm {P(X = k) = (8, k) \times 0.40^k \times (1 - 0.40)^{(8 - k)}}[/tex]

[tex]\mathrm{P(X = 5)} = (8, 5) \times 0.40^5 \times (1 - 0.40)^{(8 - 5)}\\\\= 56 \times 0.01024 \times 0.343\\\\= 0.1961984[/tex]

[tex]\mathrm{P(X = 6)} = (8, 6) \times 0.40^6 \times (1 - 0.40)^{(8 - 6)}\\\\= 28 \times 0.004096 \times 0.36\\\\= 0.0516608[/tex]

[tex]\mathrm {P(X = 7)} = (8, 7) \times 0.40^7 \times (1 - 0.40)^{(8 - 7)}\\\\= 8 \times 0.0016384 \times 0.4\\\\= 0.0052224[/tex]

[tex]\mathrm {P(X = 8)} = (8, 8) \times 0.40^8 \times (1 - 0.40)^{(8 - 8)}\\\\= 1 \times 0.00065536 \times 0.4\\\\= 0.000262144[/tex]

Now, add all these probabilities together to get the final result:

[tex]\mathrm {P(X > 4)} = 0.1961984 + 0.0516608 + 0.0052224 + 0.000262144\\\\= 0.253343344[/tex]

Therefore, the probability that more than half of the 8 randomly chosen blood donors have Type A blood is approximately 0.2533 or 25.33%.

Learn more about probability click;

https://brainly.com/question/32117953

#SPJ4

Answer:

2.5% of adults are intellectually disabled by this criterion

Step-by-step explanation:

The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 105

Standard deviation = 16

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

What percent of adults are intellectually disabled by this criterion

Below 73

73 = 105 - 2*16

So 73 is 2 standard deviations below the mean.

Of the 50% of the measures that are below the mean, 95% are within 2 standard deviations of the mean, that is, between 73 and 105. The other 100 - 95% = 5% are below 73. So

0.05*0.5 = 0.025

0.025*100 = 2.5%

2.5% of adults are intellectually disabled by this criterion

Answer:

<BAR ≅<CAR

Step-by-step explanation:

Just took the test

Answer:

A edg 2020

Step-by-step explanation:

Answer:

The sum of the arithmetic sequence is [tex]S_{8}=-324[/tex].

Step-by-step explanation:

A sequence is a set of numbers that are in order.

In an arithmetic sequence the difference between one term and the next is a constant.  In other words, we just add the same value each time infinitely.

If the first term of an arithmetic sequence is [tex]a_1[/tex] and the common difference is d, then the nth term of the sequence is given by:

                                                  [tex]a_{n}=a_{1}+(n-1)d[/tex]

For the sequence

                                                [tex]-2,-13,-24,-35,...[/tex]

The pattern is continued by adding -11 to the last number each time.

An arithmetic series is the sum of an arithmetic sequence.  We find the sum by adding the first, [tex]a_1[/tex] and last term, [tex]a_n[/tex], divide by 2 in order to get the mean of the two values and then multiply by the number of values, n

                                                    [tex]S_{n}=\frac{n}{2}(a_{1}+a_{n})[/tex]

The sum of the arithmetic sequence is

[tex]a_{8}=-2+(8-1)(-11)=-2-77=-79[/tex]

[tex]S_{8}=\frac{8}{2}(-2-79})=4\left(-2-79\right)=4\left(-81\right)=-324[/tex]

I can't solve it because it didn't have enough information

Answer:

3136

Step-by-step explanation:

Thats the answer please I don't have time to write the explanation

Answer: x=70°

Step-by-step explanation:

These are supplementary angles, meaning they add up to 180°

45+(2x-5)=180°

45+2x-5=180

40+2x=180

2x=140

x=70°