URGENT Find the height of a parallelogram that has an area of 10 1/2 in² and a base of 3/4 in.

\(\huge\text{$m\angle O=\boxed{11^{\circ}}$}\)

Since we know that all angles in a triangle add up to \(180^{\circ}\), we can solve for \(x\) and substitute it back into \((x-5)^{\circ}\) to find \(m\angle O\).

\(\begin{aligned}m\angle N+m\angle O+m\angle P&=180\\(5x-8)+(x-5)+(6x+1)&=180\end{aligned}\)

Remove the parentheses and combine like terms.

\(\begin{aligned}5x-8+x-5+6x+1&=180\\(5x+x+6x)+(-8-5+1)&=180\\12x-12&=180\end{aligned}\)

Add \(12\) to both sides of the equation.

\(\begin{aligned}12x-12&=180\\12x&=192\end{aligned}\)

Divide both sides of the equation by \(12\).

\(\begin{aligned}x=16\end{aligned}\)

Now that we have the value of \(x\), we can substitute it back into \((x-5)^{\circ}\) to find \(m\angle O\).

\(\begin{aligned}m\angle O&=(x-5)\\&=16-5\\&=\boxed{11}\end{aligned}\)

Using the test statistic, at the 0.05 level of significance, we do not find sufficient evidence to support the political scientist's claim and hence reject the null hypothesis.

To determine whether there is enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65%, we can perform a hypothesis test using the given data.

Let's set up the null and alternative hypotheses:

H₀: p ≤ 0.65 (Null hypothesis: The proportion of college students interested in election results is 65% or less)

Ha: p > 0.65 (Alternative hypothesis: The proportion of college students interested in election results is more than 65%)

We are given that the sample size is 265 college students, and out of this sample, 180 students say they're interested in their district's election results.

To perform the hypothesis test, we'll calculate the test statistic, which is the z-statistic in this case, using the formula:

z = (p - p₀) / √(p₀(1-p₀)/n)

Where p is the sample proportion, p₀ is the hypothesized proportion under the null hypothesis, and n is the sample size.

Let's calculate the sample proportion:

p = 180 / 265 ≈ 0.679

Now, we can calculate the test statistic:

z = (0.679 - 0.65) / √(0.65(1-0.65)/265) ≈ 1.295

Next, we'll compare the test statistic with the critical z-value at a 0.05 level of significance (α = 0.05) for a one-tailed test.

Using a standard normal distribution table or a statistical calculator, the critical z-value at α = 0.05 is approximately 1.645.

Since the test statistic (1.295) does not exceed the critical z-value (1.645), we fail to reject the null hypothesis. In other words, we do not have enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65% based on this sample.

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Answer:

x ≈ 28.3

Step-by-step explanation:

using the cosine ratio in the right triangle

cos45°= \(\frac{adjacent}{hypotenuse}\) = \(\frac{x}{40}\) ( multiply both sides by 40 )

40 × cos45° = x , then

x ≈ 28.3 ( to the nearest tenth )

The reasonable way to test this one is to identify the validity of the hypothesis can be tested.

The hypothesis suggests that when an electric current passes through a wire, it generates a magnetic field. If this magnetic field is strong enough, it could magnetize a non-magnetic nail that is placed nearby. To test this hypothesis, an experiment can be conducted as follows:

A non-magnetic nail, a battery, a wire, and a switch.

Connect the wire to the battery and switch in series. The other end of the wire should be wrapped around the nail multiple times. Once the apparatus is set up, turn on the switch to pass an electric current through the wire.

Before running the current through the wire, test the nail for its magnetic properties by holding it close to some iron filings or other small magnetic objects. If it does not attract any of these objects, then it is non-magnetic.

Turn on the switch and run the electric current through the wire wrapped around the nail for a few minutes.

After running the current through the wire, test the nail again for its magnetic properties. Hold it close to the iron filings or other small magnetic objects and observe if it attracts them.

Compare the results obtained before and after running the current through the wire. If the nail exhibits magnetic properties after running the current, then the hypothesis that passing an electric current through a wire can magnetize a non-magnetic nail can be considered valid.

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Answer:

slope is -3/2

Step-by-step explanation:

Use the slope formula

y2-y1/x2-x1=m (rise over run)

(7,5) (5,8)

x1 y1 x2 y2

8-5/5-7=m

-(3/2)=m

Step-by-step explanation:

hope it is helpful to you

The maximum rectangular area that can be fenced can be

2499 sq meters.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know for a quadrilateral, A square has the maximum area.

We also know That the product of two numbers is maximum when the difference between them is minimum.

Given, A farmer has 2,000 meters of fencing and wants to use it to create a rectangular area for grazing.

So, 2(l + b) = 2000.

l + b = 1000.

For a square, it would be 500 and 500, But to be a rectangle it can be 49 and 51.

Therefore, The maximum area would be,

= (51×49) sq meters.

= 2499 sq meters.

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Answer:

140 db

Step-by-step explanation:

I have succesfully finished tihs

The value is closest to the sound level of the vocalizations of a blue whale is 140dB.

We have given that,

Intensity(I)= 106.8 watts/meter^2

The intensity of sound hair by the human ear is,

\(I_0=1\times10^{-12}\)

Sound intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.

We have to find which value is closest to the sound level, in decibels, of the vocalizations of a blue whale

So we have given the formula

\(B=10 log(\frac{I}{I_0} )\)

So use the given value we get

\(B=10 log(\frac{106.8}{1\times 10^{-12}} )\)

B= 140.28 dB≈140 dB

Therefore the value is closest to the sound level of the vocalizations of a blue whale is 140dB.

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To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Answer:

my fat cxck in your mouth

Step-by-step explanation:

There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

Answer:

Hello! Your Question seems to be Incomplete but if you didn't mean to make it that way. I will be Happy to answer it If you repost It. Thanks !

Step-by-step explanation:

Have a good day!

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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The approximate value of P(36 ≤ Y ≤ 48) is 0. The approximate value of P(36 ≤ Y ≤ 48) can be calculated using the normal approximation to the binomial distribution.

Since Y follows a binomial distribution with parameters n = 12 and p = 1/2, we can use the normal approximation when n is large.

1. Calculate the mean and standard deviation of Y:

The mean of Y is given by μ = np = 12 * (1/2) = 6.

The standard deviation of Y is given by σ = √(np(1-p)) = √(12 * (1/2) * (1 - 1/2)) = √(3) ≈ 1.732.

2. Standardize the values of 36 and 48:

To apply the normal approximation, we need to standardize the values of interest.

Z₁ = (36 - μ) / σ = (36 - 6) / 1.732 ≈ 17.32

Z₂ = (48 - μ) / σ = (48 - 6) / 1.732 ≈ 24.59

3. Calculate the probability using the standard normal distribution:

P(36 ≤ Y ≤ 48) = P(Z₁ ≤ Z ≤ Z₂)

Using standard normal distribution tables or a calculator, we can find the probabilities associated with Z₁ and Z₂.

P(36 ≤ Y ≤ 48) ≈ P(17.32 ≤ Z ≤ 24.59)

4. Subtract the cumulative probability associated with Z = 17.32 from the cumulative probability associated with Z = 24.59.

5. Calculate the approximate probability:

P(36 ≤ Y ≤ 48) ≈ P(17.32 ≤ Z ≤ 24.59)

≈ Φ(24.59) - Φ(17.32)

≈ 1 - Φ(17.32) (since Φ(-x) = 1 - Φ(x) for the standard normal distribution)

Looking up the value in the standard normal distribution table or using a calculator, we find that Φ(17.32) is extremely close to 1. Therefore, the probability can be approximated as:

P(36 ≤ Y ≤ 48) ≈ 1 - Φ(17.32) ≈ 1 - 1 ≈ 0

Hence, the approximate value of P(36 ≤ Y ≤ 48) is 0.

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Answer:

20 50 60 ..........

Step-by-step explanation:

205060

The speed of the fox should be greater than the rabbit's speed in other to catch up, Hence, the speed of the fox must be 35/t + 40

The distance between the rabbit and fox, d = 35 feets

The rabbit's speed = 40 feets per second

Fox's speed = F

In other to obtain a specific speed for the fox, the time at which the fox is required to catch up with the rabbit should be given.

Let the time = t

Recall :

Speed = distance / time

Distance = speed × time

Rabbit's distance from fox after time t will be :

35 + (40 × t) = 35+40t

Fox's distance after time, t = fox speed × t = F × t

In other to catch up ; both fox and rabbit must be at the same distance ;

Rabbit's distance at time t = Fox's distance at time t

35+40t = Ft

To solve for F which is the fox's speed:

Divide both sides by t

(35+40t) / t = Ft/t

35/t + 40 = F

Hence, the fox' s speed must be : 35/t + 40

To obtain the exact speed of the fox, we must be given a specific time value.

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Answer:

2 (15/28)

Step-by-step explanation:

\(5 \frac{1}{4} - 2 \frac{5}{7} \\ = \frac{21}{4} - \frac{19}{7} \\ = \frac{21\times 7}{4 \times 7} - \frac{19 \times 4}{7 \times 4} \\ = \frac{147}{28} - \frac{76}{28} \\ = \frac{(147 - 76)}{28} \\ = \frac{71}{28} \\ = 2 \frac{15}{28} \)

Approximately 3448 grams of the cereal is required to obtain 40 µg of riboflavin. This can be solved by the concept of Percentage.

To obtain 40 µg of riboflavin from the cereal, we need to calculate the amount of cereal that provides 26.5% of the RDA of riboflavin, and then use a proportion to find the amount of cereal needed to provide 40 µg.

First, we need to calculate how much riboflavin is provided by one serving of the cereal, which is 28 g. If the cereal provides 26.5% of the RDA of riboflavin per serving, we can use the following formula to find the amount of riboflavin provided by one serving:

Amount of riboflavin per serving = 26.5% of RDA for riboflavin per serving

Amount of riboflavin per serving = 0.265 x 1.22 mg/day (RDA for riboflavin)

Amount of riboflavin per serving = 0.3233 mg/serving

So, one serving of the cereal provides 0.3233 mg of riboflavin.

Next, we can use a proportion to find the amount of cereal needed to provide 40 µg of riboflavin:

Amount of riboflavin provided by x grams of cereal = 40 µg

Amount of riboflavin per gram of cereal = 0.3233 mg/28 g (from the calculation above)

Amount of riboflavin provided by x grams of cereal = (0.3233 mg/28 g) x (x g)

Amount of riboflavin provided by x grams of cereal = 0.0116 mg/g x g

x = 40 µg / 0.0116 mg/g

x ≈ 3448 g

Therefore, approximately 3448 grams of the cereal is required to obtain 40 µg of riboflavin.

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The p-value for a right-tailed test is 0.0096.so the melodic kortholt company should consider changing its current health plan.the standard error for the proportion (SE = sqrt(0.64*(1-0.64)/25) = 0.144).

1. Calculate the proportion of employees dissatisfied (16/25 = 0.64).

2. Calculate the standard error for the proportion (SE = sqrt(0.64*(1-0.64)/25) = 0.144).

3. Calculate the z-score for the test (z = (0.64 - 0.5)/SE = 1.39).

4. Calculate the p-value (p-value = 1 - cdf(z) = 0.0096).

The p-value is an indication of how likely it is that the proportion of employees dissatisfied is significantly different from the expected proportion (in this case, half). The p-value of 0.0096 means that there is only a 0.96% chance that the observed proportion of employees dissatisfied is due to chance alone, and so the melodic kortholt company should consider changing its current health plan.

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The height of Jane's shadow who is 5.9 feet tall is appoximately 6.3 feet

Given that, a tree 54 feet tall casts a shadow 58 feet long and Jane is 5.9 feet tall.

To find the height of Jane's shadow, we can use proportions and ratios.

Hence:

(Height of the tree) : (Length of the tree's shadow) = (Height of Jane) : (Length of Jane's shadow)

Plug in:

Height of the tree = 54

Length of the tree's shadow = 58

Height of Jane = 5.9

Let Length of Jane's shadow = x

54 feet : 58 feet = 5.9 feet : x

54/58 = 5.9/x

Cross multiply:

54 × x = 58 × 5.9

54x = 342.2

x = 342.2/54

x = 6.3 feet

Therefore, the measure of her shadow is approximately 6.3 feet.

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Answer:

3.64  = x

Step-by-step explanation:

Using tignometry!

As it is an right angle triangle we can use 'tan' function.

therefore:

tan(20) = x/10

tan(20) * 10 = x

3.639702343 = x

3.64  = x

Easy!

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Thanks!

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The value of x in the given triangle is 3.6 cm.

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

\(\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\)

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

Base is the adjacent smaller side of the angle θ.

The tan function for the angle which measures 20° can be written as,

\(\rm Tan(\theta)=\dfrac{Perpendicular}{Base}\\\\tan(20^o)=\dfrac{x}{10}\\\\x = 3.639\approx 3.6\ cm\)

Thus, the value of x in the given triangle is 3.6 cm.

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Answer:

D.

Step-by-step explanation:

\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies directly with "x"}}{y = k(x)}\hspace{5em}\textit{we also know that} \begin{cases} y=21\\ x=3 \end{cases} \\\\\\ 21=k(3)\implies \cfrac{21}{3}=k\implies 7=k\hspace{5em}\boxed{y=7x} \\\\\\ \textit{when x = -2, what is "y"?}\qquad y=7(-2)\implies y=-14\)

Since we know that the y-coordinate is positive, we took the positive value for sine.

a) The diagram is shown below.b) The values of six trigonometric ratios for θ are:$$\begin{aligned}\sin(\theta) &= \frac{2\sqrt{2}}{3} \\ \cos(\theta) &= -\frac{1}{3} \\ \tan(\theta) &= \frac{\sin(\theta)}{\cos(\theta)} = -2\sqrt{2} \\ \cot(\theta) &= \frac{1}{\tan(\theta)} = -\frac{\sqrt{2}}{4} \\ \sec(\theta) &= \frac{1}{\cos(\theta)} = -3\sqrt{2} \\ \csc(\theta) &= \frac{1}{\sin(\theta)} = \frac{3\sqrt{2}}{4} \end{aligned}$$We know that for an angle θ in standard position, its terminal arm intersects the unit circle at a point (x, y) where x and y are given by the values of cosine and sine functions respectively.

Hence, in our case, the coordinates of the given point are cosθ=−13cos⁡θ=−13 and sinθ=2√23sin⁡θ=23. Using these values, we can obtain other trigonometric ratios by using their respective definitions as shown above.Note: One can also use Pythagorean Identity to find sin θ when cos θ is given. Since the point is on the unit circle, we have $$\cos^2(\theta)+\sin^2(\theta)=1 \implies \sin(\theta)=\pm\sqrt{1-\cos^2(\theta)}$$Here, since we know that the y-coordinate is positive, we took the positive value for sine.

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Answer:

5+4x=25

Step-by-step explanation:

Answer:

5+4x=25

Step-by-step explanation:

Answer:

-4<n≤5

If you are using another variable just replace it in.

The information in the number line is an interval (-4,5]

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5 and it is represented as (1,5)

Given here, the line extends to -4 and ends at 5 but the it is open on the LHS and closed on the RHS and thus the interval notation is (-4,5]

Hence the interval represented in the number line is  (-4,5]

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Answer:

yeah

Step-by-step explanation:

Answer:

\( \: \: a) \: \: (49\pi - 98)ft {}^{2} \)

Answer:

The answer is $22.74

Step-by-step explanation: