Enter equations one at a time in order to send a line
through the coins to "capture" them.

The total area of the shaded portion is (x² - 16)(x²- 1) square meters.

Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.

The area of the outer square is (x² - 8)², and the area of the inner square is x². Therefore, the area of the shaded region can be found by subtracting the area of the inner square from the area of the outer square:

Area of shaded region = Area of outer square - Area of inner square

= (x² - 8)² - x²

Expanding the first term using the formula for the square of a binomial, we get:

Area of shaded region = (x⁴ - 16x² + 64) - x²

= x⁴ - 17x² + 64

Therefore, the expression that represents the total area of the shaded figure is x⁴ - 17x² + 64, which can be simplified by factoring:

x⁴ - 17x² + 64 = (x² - 16)(x² - 1)

So the simplified expression for the total area of the shaded figure is (x² - 16)(x²- 1).

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Answer:

x = 35

Step-by-step explanation:

since the figures are similar then the ratios of corresponding parts are in proportion, that is

\(\frac{x}{10}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) ( cross- multiply )

2x = 7 × 10 = 70 ( divide both sides by 2 )

x = 35

The unit rate of 24t = 98 is A. 24 feet per year.

Unit rate is the rate of increase or decrease of a unit of item

Now, since a 984-foot tree has grown at a constant rate each year. Since we have the equation 24t = 984, wheret is the age of the tree in years.

To determine the unit rate, we compare it with the function y = mx where m = gradient

Now, the gradient is the rate of change of y per unit of x.

Now, comparing y = mx with 24t = 984,

Since m = 24 which is the gradient which is also the unit rate.

So, the unit rate of 24t = 98 is A. 24 feet per year.

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Answer:

\(\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx = \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

Antiderivatives - Integrals

Integration Constant C

U-Substitution

Integration Rule [Reverse Power Rule]:                                                               \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Property [Multiplied Constant]:                                                         \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:                                                       \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Step-by-step explanation:

Step 1: Define

\(\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx\)

Step 2: Identify Variables

Find the variables u-solve using u-substitution.

U-Substitution

\(\displaystyle u = 1 + \sqrt{x}\)

\(\displaystyle du = \frac{1}{2\sqrt{x}}dx\)

U-Solve

\(\displaystyle x = (u - 1)^2\)

\(\displaystyle dx = 2\sqrt{x}du\)

Step 3: Integration

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

Answer:

8

Step-by-step explanation:

x /2 -1 = 3

add 1 to both sides

x/2 = 4

multiply by 2

x = 8

The signal, (a) x(t) = 3cos(4t) is periodic with period T = pi/2. To see this, we can compute:

x (t + T) = 3cos (4(t + pi/2)) = 3cos (4t + 2pi) = 3cos(4t)

which shows that the signal repeats itself every T = pi/2 seconds.

\((b) \times (t) = e^{( - t)} \)

This signal is not periodic.

\(e^{(-t)} = e^{(-(t+T))} \)

for all t.

However, this is not possible since e^(-t) approaches 0 as t approaches infinity. Therefore, the signal is not periodic.

\((c) \times (t) = [cos (2t - \frac{\pi}{3}] ^2\)

This signal is periodic with period T = pi. To see this, we can compute:

\(x (t + T) = [cos (2(t + \pi) - \pi/3)] ^2 = [cos (2t + 5\pi/3)] ^2 = [cos (2t - pi/3)] ^2 = x(t) \\

(d) x(t) = cos(4t) u(t) + sin(4t) u(-t)\)

This signal is not periodic. To see this, suppose that there exists a period T such that x(t) = x (t + T) for all t. Then we must have:

cos(4t) u(t) + sin(4t) u(-t) = cos(4(t+T)) u(t+T) + sin(4(t+T)) u(-(t+T)) for all t.

However, this is not possible since the two terms on the left-hand side have different signs for t < 0, whereas the two terms on the right-hand side have the same sign for t < -T.

Therefore, the signal is not periodic.

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Answer:

13/15

Step-by-step explanation:

i took the test :)

Answer:

  2

Step-by-step explanation:

You want the slope of segment DC given points A, B, C, D are collinear and the rise between B and A is 2 units, while the run is 1 unit.

The slope of a line is the same everywhere on the line. It is the same for segment DC as for segment BA on the same line.

  slope = rise/run = 2/1 = 2

The slope of DC is 2.

<95141404393>

        Thanks for reposting the pertinent question:

        Therefore the SLOPE of DC:

         DC  =   2

        POINTS:  D, C, B, and A  are COLLINEAR

       SLOPE of:  DC  is  Equal (=)  To the SLOPE  of: AB

       AB  =   2/1   =  2

       Therefore the SLOPE of DC:

       DC  =   2

I hope this helps you!

Answer:

x = -3

Step-by-step explanation:

Notice that the addition of angle <CDH plus angle <HDE have to give the measure of angle <CDE (which is 144 degrees as stated in the problem)

Then, we can say in equation form:

<CDH + <HDE = 144

replacing with their expressions in terms of x:

x + 93 + 57 + x = 144

solving for x:

2 x + 150 = 144

2 x = 144 - 150

2 x = - 6

x = -3

Answer:

Step-by-step explanation:

|x+a|=b

x+a=±b

x=a±b

x=a+b

and x=a-b

Answer:

58.79 mL of juice

Step-by-step explanation:

To do this, let's gather the data first:

In 1 cup of orange juice we have 500 mg of potassium. A patient weights 135 lb, and he needs to take care of it's potassium intake and not exceed 2 mg of K / kg per day.

So obviously he cannot drink a whole cup of orange juice. It has to be less. In order to know this, we need to know first the weight in kg. 1 lb equals 0.4536 kg so in 135 lb:

W = 135 lb * 0.4536 kg/lb = 61.24 kg

Now, we need to know with this weight, how much potassium it can takes:

Intake = 61.24 kg * 2 mg/kg = 122.48 mg of K

So, the maximum amount of potassium per day is 122.48 mg. This means that the quantity of orange juice this person can take is:

Juice = 122.48 mg * 240 mL / 500 mg

Juice = 58.79 mL of juice or simply 59 mL

The confidence interval is 0.559 < p < 0.641 and expected value is 0.600

To construct a confidence interval for the true population proportion, we can use the formula:

p ± Z * √((p × (1 - p)) / n)

Where:

p = sample proportion (336/560)

Z = critical value for the desired confidence level

95% confidence = Z-value of approximately 1.96

n = 560

Let's calculate the confidence interval:

p = 336/560 ≈ 0.600

Z ≈ 1.96 (for a 95% confidence level)

n = 560

Plugging these values into the formula:

p ± Z × √((p × (1 - p)) / n)

0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)

0.600 ± 1.96 × √((0.240) / 560)

0.600 ± 1.96 × √(0.0004285714)

0.600 ± 1.96 × 0.020709611

0.600 ± 0.040564459

The confidence interval is:

0.559 < p < 0.641

Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.

For proportions, the expected value is simply the sample proportion, which is approximately 0.600.

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Answer:

a.35

Step-by-step explanation:

10 + 20/2 equals 20

20/2+5 equals 15

20+15 equals 35

Answer: no one cares

Step-by-step explanation:

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

The expanded and simplified form of the expression (x + 5)(x - 1) is  x² - x + 5x - 5.

Given the expression in the question;

(x + 5)(x - 1)

To expand and simplify the expression (x+5)(x-1),

we use the distributive property:

(x + 5)(x - 1)

x(x - 1) + 5(x - 1)

Now we can simplify each term by using the distributive property again:

x(x - 1) = x² - x

5(x - 1) = 5x - 5

Putting these terms back together, we have:

(x+5)(x-1) = x² - x + 5x - 5

Combining like terms, we get:

(x+5)(x-1) = x² + 4x - 5

Therefore, (x+5)(x-1) simplifies to the quadratic expression x² + 4x - 5.

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a. Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b.   the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

To estimate the probability that a randomly selected house  has a value less than $500,000:

P( x < 500,000)=P(x=0)+P(x=500)

=0.34+0.37+

=0.71

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume a normal distribution.

-The probability can therefore be calculated as:

P(x')=P( z < (x' -u)/σ.sqrt(n)))

P(z< (500-403)/(578sqrt(40)))

=P(z<2.2068)

=0.986336

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

The complete question is -

a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.

(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.

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a. The monthly contribution from a friend's company is $120 minus 0.5, or $60.

b. The total monthly contribution to the fund is $180.

The computation of FV in Excel is shown in the attachment below:

Using the current number as a starting point, subtract the prior value to determine the growth rate. To calculate the growth rate in percentage terms, divide the difference by the previous amount and multiply the result by 100. Growth Rate equals (Ending Value - Beginning Value) - 1. The year-over-year (YoY) growth rate of a business, for instance, would be 20% if its revenue increased from $100 million in 2020 to $120 million in 2021.

GDP, turnover, wages, etc., all have growth rates that reflect how much they have changed over time (month, quarter, year). Percentages are a pretty common way to communicate it.

20 years is the age.

20 times 12 periods equals 240.

3% growth rate

The computation of FV in Excel is shown in the attachment below:

So, FV= $7,223,115.77

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Answer:

z/17

Step-by-step explanation:

ratio means divide

z/17

Step-by-step explanation:

\(4(a + b) - {x}^{2} (a + b)\)

\(a + b(4 - {x}^{2} )\)

\((a + b)(2 - x)(2 + x)\)

The proof is given as follows:

The transitive property argues that "if two quantities are equal to the third quantity, then we may claim that all the quantities are equal to one other".

The term transitive refers to a transfer. If there are three quantities a, b, and c, and if an is connected to b by some rule and b is related to c by the same method, then a and c are related to each other by the same rule; this property is known as the transitive property of equality.

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Answer:

625

Step-by-step explanation:

0.76x=475

x=625

Hope I helped!

Answer:

15 degrees

Step-by-step explanation:

90-75= 15

........

Answer:

C :)

Step-by-step explanation:

No, the two triangles are similar. Option D is correct.

While having the same size is not required, it is required by law to demonstrate that the two triangles have the same form. The angles that correspond to those sides have the same congruence and the same ratio of sides.

It is given in ΔVWX and ΔYZX

WX=8,ZX=2

VX=9,YX=3

When two triangles have an equal number of corresponding sides and corresponding angles, they are said to be similar.

It is obtained that,

ZX/WX=1:4

YX/VX=1:3

ZX/WX≠YX/VX

Since their ratio is not equal there is no possibility for the triangles to be similar. As a result, the triangle is not similar.

Thus, option D is correct.

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the surface area of the cylinder is approximately 471 dm².

Now, For the surface area of the cylinder, we need to find the lateral area  and the area of the two circular bases.

Since, The formula for the lateral area of a cylinder is

L = 2πrh,

where r is the radius of the cylinder and h is the height.

In this case, the diameter is 10 dm,

So the radius is 5 dm.

And the height is also 10 dm.

Therefore, the lateral area is:

L = 2πrh

L = 2π(5 dm)(10 dm)

L = 100π dm²

The formula for the area of a circle is

A = πr²,

where r is the radius.

In this case, the radius is 5 dm,

So the area of each base is:

A = πr²

A = π(5 dm)²

A = 25π dm²

To find the total surface area, we add the lateral area and the area of the two bases:

SA = 2(Area of Base) + Lateral Area

SA = 2(25π dm²) + 100π dm²

SA = 50π dm² + 100π dm²

SA = 150π dm²

Substitute pi as 3.14, we can calculate:

SA ≈ 150(3.14) dm²

SA ≈ 471 dm²

Therefore, the surface area of the cylinder is approximately 471 dm².

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Answer:

65 mil in 6.5 centimeters

Step-by-step explanation:

Answer:

There are 65 millimeters in 6.5 cm.

Step-by-step explanation:

For every 1 centimeter, there are 10 millimeters.

The true statement is B.

The function will have at least one zero on the interval -5 < x < 4

Here we have a polynomial function g(x), and we know that it passes through two known points (-5, 6) and (4, -3).

Remember that a relation is only a function if each point on its domain is mapped into a single point in the range.

Also, this is a polynomial function, so it is continuous, then there are no jumps.

So, at some point in that interval x ∈ (-5, 4), we must have a zero for our function, where a zero is a value of x such that:

g(x)=  0

Then the correct statement is B, g(x) has at least one zero i the given interval.

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