In an certain species of newt, offspring are born either green or black. Suppose that 60% of these newts are born green. If we sample 183 of these newts at random, the probability distribution for the proportion of green newts in the sample can be modeled by the normal distibution pictured below. Complete the boxes accurate to two decimal places. Note: The left box is 2 standard deviations below the mean. The middle box is the mean. And, the right box is 2 standard deviations above the mean.

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (5000)(0.05)(3) \implies I = 750\)

Answer:

open the bracket

(4X+)-3X-2-72+X=X

4X+(-3X)-74+X=X

X-74+X=X

2X-74=X

then collect the term

-74=X-2X

-74=-X

divide by negative every side then you get

X=74

A comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of a rate

A rate is known as the quantity measured with respect to another measured quantity. It refers to the comparison of a part to a whole.

It is also the measure of a part with respect to a whole or a proportion.

Therefore, a comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of a rate

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Answer:

d=120

p=210

c=360

is this correct?

a) We cοnclude that there is sufficient evidence tο suggest that the variances οf the twο pοpulatiοns are nοt equal.

b) We cοnclude that there is sufficient evidence tο suggest that the variance οf the first pοpulatiοn is greater than the variance οf the secοnd pοpulatiοn.

Tο test the hypοtheses regarding the variances οf twο pοpulatiοns, we can use the F-distributiοn.

Given:

Sample size οf the first sample (n₁) = 9

Sample size οf the secοnd sample (n₂) = 7

Sample variance οf the first sample (s₁²) = 100

Sample variance οf the secοnd sample (s₂²) = 20

Significance level (α) = 0.05

(a) Testing H0: σ₁² = σ₂² versus Ha: σ₁² ≠ σ₂²:

Tο perfοrm the test, we calculate the F-statistic using the fοrmula:

F = s₁² / s₂²

where s₁² is the sample variance οf the first sample and s₂² is the sample variance οf the secοnd sample.

Plugging in the given values:

F = 100 / 20 = 5

Next, we determine the critical F-value at a significance level οf α/2 = 0.025. Since n₁ = 9 and n₂ = 7, the degrees οf freedοm are (n₁ - 1) = 8 and (n₂ - 1) = 6, respectively.

Using a table οr statistical sοftware, we find F.025 = 4.03 (rοunded tο twο decimal places).

Cοmparing the calculated F-value with the critical F-value:

F (5) > F.025 (4.03)

Since the calculated F-value is greater than the critical F-value, we reject the null hypοthesis H0: σ₁² = σ₂².

Therefοre, we cοnclude that there is sufficient evidence tο suggest that the variances οf the twο pοpulatiοns are nοt equal.

(b) Testing H0: σ₁² < σ₂² versus Ha: σ₁² > σ₂²:

Tο perfοrm the test, we calculate the F-statistic using the fοrmula as befοre:

F = s₁² / s₂²

Plugging in the given values:

F = 100 / 20 = 5

Next, we determine the critical F-value at a significance level οf α = 0.05. Using the degrees οf freedοm (8 and 6), we find F.05 = 3 (rοunded tο the nearest whοle number).

Cοmparing the calculated F-value with the critical F-value:

F (5) > F.05 (3)

Since the calculated F-value is greater than the critical F-value, we reject the null hypοthesis H0: σ₁² < σ₂².

Therefοre, we cοnclude that there is sufficient evidence tο suggest that the variance οf the first pοpulatiοn is greater than the variance οf the secοnd pοpulatiοn.

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Answer:

Answer:divide by 2Step-by-step explanation:16 divide by 2 =8 divide

Step-by-step explanation:

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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Step-by-step explanation:

so, if I understand correctly :

angle A = 22°

angle B = 53°

angle D = 38°

remember : the sum of all 3 angles in every triangle is always 180°.

so,

180 = 22 + 53 + AEB

angle AEB = 180 - 22 - 53 = 105°

per the attributes of crossing lines the angles between them are the same on both sides of any of the lines (just left-right mirrored).

so, CB and AD are crossing lines, therefore

angle AEB = angle CED = 105°

and then

180 = 105 + 38 + C

angle C = 180 - 105 - 38 = 37°

Answer:

Two hours later his brother leaves from first and maple and comes after him on a moped travelling 27 mph, His uphill speed was 8 miles per hour slower than his downhill speed.

Step-by-step explanation:

The number of gallons of water can an elephant drink per day is 50 gallons.

Given that, an elephant can’t drink up to 6400 fluid ounces of water a day.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

We know that, there are 128 fluid ounces in 1 gallon.

Now, 6400/128

= 50 gallons

Hence, the number of gallons of water can an elephant drink per day is 50 gallons.

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The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula:

arc measure = central angle measure / circumference

For a given central angle measure in degrees, the formula will be:

arc measure = (central angle measure in degrees) / 360

It's worth noting that this ratio is equal to the fraction of the circumference that the arc of the central angle measures.

For example, if the central angle measure is 90 degrees, the arc measure will be 90/360 = 1/4, meaning that the arc that is formed by the central angle measure is 1/4 of the circle's circumference.

It's also important to note that this ratio is also equal to the fraction of the total area of the circle that the sector formed by the central angle measures.

It's also worth noting that this ratio is always less than 1, since the central angle can't be greater than 360 degrees.

Therefore, The ratio of the central angle measure to the circumference of a circle is called the "arc measure" and it is given by the formula: arc measure = central angle measure / circumference

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The cost of a utility for a pole with a diameter of 41 cm and a height of 780 cm is $3894697.41

The density formula is given by:

Density = mass/volume

The volume of the cylinder = π * radius² * height

Radius = diameter / 2 = 41/2 = 20.5, height = 780 cm. Hence:

Volume = π * 20.5² * 780 = 1029798 cm³

Density = mass/volume

6.1 = mass/1029798

mass = 6281770 kg

Cost = 6281770 kg * $0.62 per kilogram = $3894697.41

The cost of a utility for a pole with a diameter of 41 cm and a height of 780 cm is $3894697.41

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Answer a is it

Step-by-step explanation

Answer: 20 nickels to make $2.00

Step-by-step explanation:

Answer:

5x = 200

x=40

Step-by-step explanation:

since a year is 12 months thus six months is 6/12 of a year, now let's assume a year is 365 days.

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1000\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases}\)

\(A = 1000\left(1+\frac{0.045}{365}\right)^{365\cdot \frac{1}{2}} \implies A = 1000\left( \frac{73009}{73000} \right)^{182.5} \\\\\\ A\approx 1022.75\hspace{5em}\underset{ \textit{earned interest} }{\stackrel{ 1022.75~~ - ~~1000 }{\approx \text{\LARGE 22.75}}}\)

Answer:

19 hours 20 minutes

Step-by-step explanation:

Step-by-step explanation:

1/2×(4+7)×4

1/2×11×4

11×2

22cm2

Explanation

We are given the measure of arc PR = 118°.

We are required to find m∠PQR.

We know that an arc measure is an angle the arc makes at the center of a circle. Therefore, we have:

Hence, the answer is:

But since Q is the measure of the angle, then the final answer is 118°.

Answer:

47 %

Step-by-step explanation:

from 1.50 to 2.20 there's a 46.67 increase. to the nearest whole number that's 47%

percent increase formula

% increase = 100 x (final - initial) / absolute value of initial

Answer:

$10, $30.40

Step-by-step explanation:

Kathy will have 23 more euros than pounds after withdrawing half of her money in each currency using algebra.

First, let's calculate how much money Kathy will withdraw in pounds and euros. She wants to withdraw half of her $300$ US dollars in each currency, so that would be $150$ US dollars for each.

To find the amount in pounds, we can divide $150$ US dollars by the exchange rate of $1.64$ USD per pound:

Amount in pounds = $\frac{150}{1.64} \approx 91.46$ pounds.

To find the amount in euros, we can divide $150$ US dollars by the exchange rate of $1.32$ USD per euro:

Amount in euros = $\frac{150}{1.32} \approx 113.64$ euros.

Rounding both amounts to the nearest whole number, Kathy will have approximately $91$ pounds and $114$ euros.

To determine how many more euros than pounds she will have, we subtract the amount in pounds from the amount in euros:

$114$ euros - $91$ pounds = $23$ more euros than pounds.

Therefore, Kathy will have 23 more euros than pounds after withdrawing half of her money in each currency.

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Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

Given an LTI system that has an output y = 2te^-ul for the input x(t) = -(t). Here, e^-ul is the decay constant and is a real positive constant. The impulse response of the system can be found by considering the impulse input x(t) = δ(t).

The output of the system with an impulse input is given by y(t) = h(t), where h(t) is the impulse response of the system.We have,x(t) = -(t)..........(1)Applying derivative on both sides of the above equation, we get,y(t) = 2te^-ul, Applying derivative on both sides of the above equation, we get,

Plot of frequency response and Impulse response of the system Hence, the plot of frequency response and the impulse response of the LTI system is shown in the figure below:, the frequency response is given by H(jω) = (2/(-jω + ul)^2) where ω is the angular frequency. The impulse response of the system is given by h(t) = (2/ul^2)t.e^-ul.

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It has one solution :)

Which of these is equal to cos 47°?

a. cos 43°

b. sin 43°

c. tan 43°

d. cos 133°

B.....

cos (47°)= sin (90°-47°)=sin (43°) [complementary angles]

Answer B

Answer:

Answer D

Step-by-step explanation:

Number of hours, 3

Cost: 105

divide 105 by 3 = 35

35 = cost of boat for 1 hour

so the answer is D :)

C = 35h

C = cost

H = hours

:)

Answer:

D. C = 35h

Step-by-step explanation:

105/3 = 35

that means it cost $35 an hour to rent the boat

so 35 x number of hours you rent = total cost

which is C = 35h

As per linear equation, within 2.5 months, Rusty's hair will grow over  \(\frac{5}{8}\) inches.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. When this equation is graphed, it always results in a straight line."

Given, the growth rate of Rusty's hair is \(\frac{1}{4}\) inches per month.

Let, within 'x' months, her hair will grow \(\frac{5}{8}\) inches.

Therefore, x ×  \(\frac{1}{4}\)  =  \(\frac{5}{8}\)

⇒ x = ( \(\frac{5}{8}\) × 4)

⇒ x = 2.5

Therefore, within 2.5 months, Rusty's hair will grow over  \(\frac{5}{8}\) inches.

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The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.

However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.

For the percentage of newborn African lions weighing less than 3 pounds:

We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.

For the percentage of newborn African lions weighing more than 3.8 pounds:

Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.

Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

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