Consider the following exponential probability density function.
If needed, round your answer to four decimal digits.

Answer: B

Step-by-step explanation:

The volume of the cylindrical water tank can be calculated as:

Volume = π x radius^2 x height

We know that the tank holds 1,200 liquid gallons, which is equivalent to:

1,200 / 7.48 = 160.43 cubic feet

We also know that the radius of the tank is 2.4 feet. Substituting these values into the formula, we get:

160.43 = 3.14 x 2.4^2 x height

Solving for height, we get:

height = 160.43 / (3.14 x 2.4^2) = 8.9 feet (approx.)

Therefore, the approximate height of the water tank is 8.9 feet (b).

Answer:

its B, 8.9, trust me, I got it right on the test

Step-by-step explanation:

Answer:

yes, because the results are unlikely to occur by chance

Step-by-step explanation:

1/1000 is converted to 10% as a decimal. That's like saying for everyone 1000 people, at least one of the can be this "random chance". The smaller the general population is, the higher the affect this percentage has on that group. If the population is lower, than there might be more of a chance that it'll occur but also because there's a smaller population, there's less variety.

Solution:

Given data:

Distance from a point to the Peachtree Center Plaza in Atlanta, Georgia (base) = 340 feet

The angle of elevation to the top of the building = 65°

To find height of the building (perpendicular- p):

tan thetha = p/b

Tan 65°= h/340

tan 65°=2.144507

Now,

h= tan 65° * 340

 = 2.144507 * 340

 = 729.132 feet

So, the height of the building is 729.132 feet

The number of servings that can be obtained from the can is 3 3/4.

An equation is a formula that links two statements and uses the equals sign (=) to indicate that the statements are equivalent. A mathematical statement proving the equality of two algebraic expressions is called an equation. For instance, the equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14. The relationship between the two sentences that appear on opposing sides of a letter is expressed mathematically. The single variable and the symbol are typically the same. Like 2x - 4 Equals 2, for example.

To find the number of servings that can be obtained from the can, we need to divide the total weight of vegetables in the can by the weight of one serving:

Number of servings = (15/16) ÷ (1/4)

= (15/16) × (4/1)

= 60/16

= 15/4

Therefore, the number of servings that can be obtained from the can is 15/4.

None of the answer choices match this result exactly, but we can simplify 15/4 to 3 3/4, which is answer choice D.

So the answer is D. 3 3/4.

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The area of the shaded region of the composite figure is 389 square units.

A geometric shape made up of two or more simpler shapes is known as a composite figure. You must divide a composite figure into simpler shapes and then add up each shape's unique regions to determine the composite figure's area.

The methods you can take to determine a composite figure's area are as follows: Slice up the composite figure into more basic forms. You can separate the composite figure into its component parts, for instance, if it is made up of a rectangle and a triangle.

Calculate the area of each shape separately.

The total area of the composite figure can be calculated by adding the areas of all the simpler shapes.

The shaded region can be divided into a rectangle and a triangle.

The area of the rectangle with l = 19 and w = 17 is:

Area = length x width = 17 x 19 = 323 square units

Now, the dimensions of the triangle are:

base = 17 - 6 = 11

height = 31 - 19 = 12

Thus,

Area = (base x height) / 2 = (11 x 12) / 2 = 66 square units

Now, the total area of the shaded portion is:

Area = 323 + 66 = 389 square units.

Hence, the area of the shaded region of the composite figure is 389 square units.

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Answer:

- 14c - 5

Step-by-step explanation:

5(- c- c - 1) - 4c ← distribute parenthesis by 5

= - 5c  - 5c - 5 - 4c ← collect like terms

= - 14c - 5

The duration of the bond is approximately 0.0045 years or 1.64 days.

We can use the formula for bond price sensitivity to changes in yield to find the duration of the bond:

D = - (1/P) * (dP/dy)

where D is the duration, P is the price of the bond, y is the yield, and dP/dy is the derivative of the bond price with respect to yield.

We are given that the bond price is currently $1,050 and the yield is 7%, so we can plug these values into the formula:

P = $1,050

y = 7% or 0.07

Next, we need to find the derivative of the bond price with respect to yield, which is the percentage change in bond price divided by the percentage change in yield.

We know that if the yield increases by 20 basis points (0.20%), the price of the bond will decrease to $1,040. Using this information, we can calculate the percentage change in bond price and yield:

Percentage change in bond price = (new price - old price) / old price = ($1,040 - $1,050) / $1,050 = -0.0095 or -0.95%

Percentage change in yield = 0.20%

Using these values, we can calculate the derivative of the bond price with respect to yield:

dP/dy = (percentage change in bond price) / (percentage change in yield) = -0.0095 / 0.002 = -4.75

We can now enter each value into the duration formula as follows:

D = - (1/P) * (dP/dy) = - (1/$1,050) * (-4.75) = 0.0045 years or 1.64 days

Therefore, the duration of the bond is approximately 0.0045 years or 1.64 days.

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Let x be the number of kilograms of apples in the fruit salad.

Then, the number of kilograms of oranges is (2/3)x, because the ratio of apples to oranges is 3:2.

The total weight of fruit salad is 3 kgs, so we can write an equation:

x + (2/3)x = 3

Simplifying and solving for x, we get:

(5/3)x = 3

x = (3*3)/5

x = 1.8

Therefore, there are 1.8 kg of apples and (2/3)*1.8 =

To find on what interval the temperature is positive, we need to find the values of x for which f(x) is greater than zero.

The function f(x) is defined as:

f(x) = -3|x - 4.7| + 2

Since the absolute value of any real number is always non-negative, we can see that f(x) will be positive only if the expression inside the absolute value bars is less than 2/3. So, we can set:

-3|x - 4.7| + 2 > 0

Solving for |x - 4.7|, we get:

|x - 4.7| < 2/3

This means that x must be within 2/3 units of 4.7. So, the interval on which the temperature is positive is:

4.7 - 2/3 < x < 4.7 + 2/3

Simplifying, we get:

4.0333 < x < 5.3667

Therefore, the temperature is positive on the interval (4.0333, 5.3667).

Using fractions, we can determine that the enrolment percentage in relation to the Spanish class is 72%.

A fraction is a component of a whole.

Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided.

In a simple fraction, both are integers.

In a complex fraction, a fraction can be found in either the numerator or the denominator.

A suitable fraction has a numerator that is less than its denominator.

So, let's say that x students are enrolled in the Spanish class.

The enrolment in the French class is 0.72 times as large as the attendance in the Spanish class, or 0.72, according to the figures provided.

The enrollment as a percentage of Spanish classes is:

0.72x / x = 0.72

The enrolment percentage in relation to the Spanish class is:

0.72 x 100% = 72%

Therefore, sing fractions, we can determine that the enrolment percentage in relation to the Spanish class is 72%.

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Correct question:

Enrollment in French class at a high school is 0.72 of enrollment in Spanish class. What is enrollment in French class compared to Spanish class as a fraction and as a​ percent?

The transformed function that is shown in the graph is:

g(x) =  e^x + 3

We know that the graph is a transformation of the parent exponential function.

Notice that for the parent function:

f(x) = e^x

The horizontal asymptote (left side of the graph) is to y = 0

While on the graph, the horizontal asymptote is at y = 3.

So we just had a translation of 3 units upwards, then the function in the graph is:

g(x) = f(x) + 3

g(x) =  e^x + 3

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Therefore, Blanche's balance from Account 1 over 4.8 years would be approximately $10,081.25.

To find the annual amount, you first need to know the frequency of the payment. If the payment is made monthly, you need to multiply the monthly payment by 12 to get the annual amount. If the payment is made weekly, you need to multiply the weekly payment by 52 (the number of weeks in a year) to get the annual amount.

If the payment is irregular or occurs at different intervals, you can add up the total amount received over the course of the year and use that as the annual amount.

by the question.

To calculate the balance of Account 1 after 4.8 years, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

where:

A = the final amount

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

Plugging in the values given in the problem, we have:

[tex]A = 8100(1 + 0.047/365)^{(365*4.8)}[/tex]

[tex]A=8100(1+0.00128)\\A=8100(1.00128)\\A=8,110.43[/tex]

[tex]A \approx8,110.43[/tex]

Therefore, Blanche's balance from Account 1 over 4.8 years would be approximately $10,081.25.

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{37}\\ a=\stackrel{adjacent}{35}\\ o=\stackrel{opposite}{BD} \end{cases} \\\\\\ BD=\sqrt{ 37^2 - 35^2} \implies BD=\sqrt{ 144 }\implies BD=12 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{AD}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ AD=\sqrt{ 13^2 - 12^2}\implies AD=\sqrt{ 169 - 144 } \implies AD=\sqrt{ 25 }\implies \boxed{AD=5}[/tex]

Answer:

B

Step-by-step explanation:

Every 2 balloons you buy the price goes up by 6.4 so for every 1 balloon, the price goes up by 3.2 since 6.4/2=3.2

The sum of the measures of the interior angles of a nonagon is 1260 degrees

The measure of each interior angle of a regular octagon is 135 degrees

A nonagon is a polygon with nine sides, and the formula to calculate the sum of the measures of the interior angles of a polygon with n sides is:

Sum of interior angles = (n-2) x 180 degrees

Therefore, the sum of the measures of the interior angles of a nonagon is:

Sum of interior angles = (9-2) x 180 degrees = 1260 degrees

An octagon is a polygon with eight sides, and the formula to calculate the measure of each interior angle of a regular polygon with n sides is:

Measure of each interior angle = (n-2) x 180 degrees / n

Therefore, the measure of each interior angle of a regular octagon is:

Measure of each interior angle = (8-2) x 180 degrees / 8 = 135 degrees

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Answer: T'=(-1,-1), U'=(-3,-1), V'=(-1,-4)

Step-by-step explanation:

Joel needs to practice for another 9/4 hours or 2 1/4 hours to meet his goal.

To solve the problem, we need to add up the number of hours Joel has practiced so far and subtract it from his goal of 4 1/2 hours per week.

First, we need to convert the mixed numbers to improper fractions:

Next, we add the fractions:

3/2 + 5/4 + 4/4 = 6/4 + 5/4 + 4/4 = 15/4

So far, Joel has practiced for 15/4 hours this week.

To find out how many more hours he needs to practice to meet his goal, we subtract 15/4 from 4 1/2:

4 1/2 - 15/4

We need to make the denominators the same by finding a common denominator of 4:

4 2/2 - 15/4 = 9/4

Therefore, Joel needs to practice for another 9/4 hours or 2 1/4 hours to meet his goal.

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We have found that: AB = (BD/2) * (XZ/AY) and we can solve for BD:

BD = 2 * AB * AY / XZ

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Since BD is a median of triangle ABC, it divides side AC into two equal parts. Let's label the midpoint of AC as M. Similarly, YW is a median of triangle XYZ and it divides side XZ into two equal parts, with the midpoint labeled as N.

Since AABC~AXYZ, we know that the corresponding sides are proportional. Thus,

AB/AX = AC/AY = BC/BZ

Since AB = BC (given that B is a vertex of both triangles), we have:

AB/AX = AC/AY

We can rewrite this equation as:

AB/AC = AX/AY ----(1)

Since BD is a median of triangle ABC, we have:

BD = 1/2 AC ----(2)

Similarly, since YW is a median of triangle XYZ, we have:

YW = 1/2 XZ ----(3)

From equation (1), we have:

AB/AC = AX/AY

Multiplying both sides by AC, we get:

AB = AX * (AC/AY)

Now, using equation (2), we can substitute AC/2 for BD:

AB = AX * BD/AY

Finally, using equation (3), we can substitute XZ/2 for YW:

AB = (BD/2) * (XZ/AY)

Therefore, we have found that:

AB = (BD/2) * (XZ/AY)

Hence, we can solve for BD:

BD = 2 * AB * AY / XZ

Note that we need to know the actual values of AB, AY, and XZ to find BD.

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Answer:

-7.225 according to a calculator.

Answer: True

Step-by-step explanation:

12-2=10

11-1=10

Answer:

True

Step-by-step explanation:

12-2 equals to 10

11-1 also equals to 10

Therefore, 12-2=11-1 is true

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2[/tex]

Answer: 52.8 m

Step-by-step explanation:

What you want to try to do when you come across these shapes is to think about it as two different shapes instead of one. The bigger rectangle should have a perimeter of 31 (12.3+12.3+3.2+3.2). Now for the bottom rectangle, you have to solve for one of the side lengths. Subtract 3.2 from 8.6 (as 3.2 is already being used by the top rectangle's perimeter) to get 5.4. The perimeter of the smaller rectangle should be 21.8 (5.5+5.5+5.4+5.4). Now add 31+21.8 to get 52.8 and that should be the total perimeter of your shape. :)

Answer: $x^2+y^2=9$

Step-by-step explanation:

A circle is the locus of points such that its distance from its center is constant. In our case, we have that the center of the circle is the origin, while the radius is 3. Thus, by the Pythagorean Theorem, the equation of the circle is $x^2+y^2=3^2=9$.

After answering the presented questiοn, we can cοnclude that equatiοn Therefοre, Terrence had 150 prοblems altοgether fοr his math hοmewοrk.

A mathematical equatiοn is a fοrmula that cοnnects twο statements and denοtes equivalence with the equals symbοl (=). An equatiοn is a mathematical statement that shοws the equality οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the variables 3x + 5 and 14.

A mathematical fοrmula describes the cοnnectiοn between the twο sentences that οccur οn οppοsite sides οf a letter. The symbοl and the single variable are frequently the same. As in 2x - 4 Equals 2, fοr instance.

6 is tο 40% as X is tο 100%

Therefοre, Terrence had 150 prοblems altοgether fοr his math hοmewοrk.

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The value canceled in the second installment is $4,279,322.14.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find the value canceled in the second installment, we need to determine the total amount owed at the beginning of the ninth month, and then subtract the first installment paid in the third month.

Let's start by finding the total amount owed at the beginning of the ninth month, using the given financing conditions.

The initial fee of $500,000 is not subject to financing, so we can exclude it from our calculations.

The amount financed is the remaining balance, which is:

$5,000,000 - $500,000 = $4,500,000

The financing rate is 26% capitalizable quarterly, which means that each quarter, the amount owed increases by 26% of the previous balance.

Since there are two quarters between month 3 and month 9, the amount owed at the beginning of month 9 is:

$4,500,000 × (1 + 0.26/4)^2 = $5,279,322.14

Next, we subtract the first installment of $1,000,000 paid in the third month:

$5,279,322.14 - $1,000,000 = $4,279,322.14

Therefore,

The value canceled in the second installment is $4,279,322.14.

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The complete question.

An asset with a cash value of $5,000,000 was purchased on credit.

through the following conditions:

• Initial fee $500,000

The balance must be paid in two (2) installments, the first installment

in month 3 for $1,000,000 and second installment in month nine (9)

• Financing 26% capitalizable quarterly

Find the value canceled in the second installment

The ascending order of the fraction is 70/11, 51/8, 62/7, 85/9.

Ascending order is a method of arranging numbers from smallest value to largest value.

For example, arranging , 3,1,2,5,6,8,4 in ascending order, we start from the least, which is 1 and ends with the greatest which is 8 i.e 1,2,3,4,5,6,8

To actually know the least and the greatest we will have find the value of each fraction.

62/7 = 8.86

51/8 = 6.38

85/9 = 9.44

70/11 = 6.36

Therefore , with the values found the arrangement from least to the greatest is

70/11, 51/8, 62/7, 85/9

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Step-by-step explanation:

To compare the two amounts of fabric, we need to express them with a common denominator:

15/2 = 30/4

7 1/2 = 15/2

Now we can compare the two amounts:

30/4 > 15/2

This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.

Therefore, Ms. Thompson needs more red fabric than silver fabric.

Therefore, the researcher can conclude that SAM-e has a significant effect on the moods of Alzheimer's patients.

Given:

[tex]n = 30, \bar{X} = 26.2, \mu = 28.1, S = 2.97, \alpha = 0.01[/tex]

Hypothesis:

[tex]ANSWER: D. H0: \muSAM-e = 28.1; Ha: \muSAM-e \neq 28.1[/tex]

Degrees of Freedom = n-1 = 30-1 = 29

The critical t scores are:

[tex]t\alpha/2, n-1= t0.01/2, 30-1 = \pm 2.7564[/tex]

The estimated standard error is: [tex]S/\sqrt{n} = 2.97/\sqrt{30} = 0.5422[/tex]

Test statistic:

[tex]t = \frac{\bar{X} - \mu }{S/\sqrt{n}} = \frac{26.2 - 28.1}{2.97/\sqrt{30}} = -3.50[/tex]

[tex]|t| > t\alpha/2, n-1 , i.e 3.50 > 2.7564, Reject H0 at 1% level of significance.[/tex]

The t-statistic lies in the critical region. Therefore, the null hypothesis is Rejected

Therefore, the researcher can conclude that SAM-e has a significant effect on the moods of Alzheimer's patients.

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Answer:

Randy makes 45 cents more than he did when he started.

Step-by-step explanation:

If Randy makes $234 for a 40 hour week, that means he makes $5.85 an hour. You can find how much he makes currently by dividing the total amount he earned by the amount of hours worked.

[tex]234/40=5.85[/tex]

He initially earned $5.40 an hour and he now earns $5.85. By subtracting his final earnings by his initial earnings it gives you the amount his earning increased by.

[tex]final= $5.85initial= 5.40[/tex]

[tex]5.85-5.40=0.45[/tex]

He makes 45 cents more than he did when he started.