Area of composite shapes ?

Answer:

the domain of given f is (-2,4)

Answer:

The  percentage of adults in the USA have stage 2 high blood pressure=98.679%

Step-by-step explanation:

We are given that

Mean, [tex]\mu=120[/tex]

Standard deviation, [tex]\sigma=18[/tex]

We have to find percentage of adults in the USA have stage 2 high blood pressure.

[tex]P(x\geq 160)=P(Z\geq \frac{160-120}{18})[/tex]

[tex]P(x\geq 160)=P(Z\geq \frac{40}{18})[/tex]

[tex]P(x\geq 160)=P(Z\geq 2.22)[/tex]

[tex]P(x\geq 160)=1-P(Z\leq 2.22[/tex]

[tex]P(x\geq 160)=0.98679[/tex]

[tex]P(x\geq 160)=98.679[/tex]%

Hence,  the  percentage of adults in the USA have stage 2 high blood pressure=98.679%

Answer:

80 ft

Step-by-step explanation:

The formula for finding the surface area of a rectangular prism is:

A = 2(wl + hl + hw)

A = 2({4x3} + {4x3} + {4x4})

A = 2 (12 + 12 + 16)

A= 2 ( 40)

A = 80 feet

Hello,

P(A)=0.4

P(B)=0.3

P(AUB)+P(A∩B)=P(A)+P(B)

P(AUB)=0.4+0.3-0.1=0.6

Answer C

The correct answer is option (C).

P(A ∪ B) = 0.6

If A, B are two different events then P(A U B) = P(A) + P(B) - P(A ∩ B)

We have been given, P(A) = 0.4, P(B) = 0.3

From given Venn diagram,

P(A ∩ B) = 0.10

Now, P(A U B) = P(A) + P(B) - P(A ∩ B)

⇒ P(A U B) = 0.4 + 0.3 - 0.10

⇒ P(A ∪ B) = 0.6

Therefore, the correct answer is option (C) .6

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Answer:

The 98% confidence interval for the probability of flipping a head with this coin is (0.4756, 0.7044).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

An experimenter flips a coin 100 times and gets 59 heads.

This means that [tex]n = 100, \pi = \frac{59}{100} = 0.59[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.59 - 2.327\sqrt{\frac{0.59*0.41}{100}} = 0.4756[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.59 + 2.327\sqrt{\frac{0.59*0.41}{100}} = 0.7044[/tex]

The 98% confidence interval for the probability of flipping a head with this coin is (0.4756, 0.7044).

Answer:

Problem 7) C

Problem 8) B

Step-by-step explanation:

Recall that inverse variation has the form:

[tex]\displaystyle y=\frac{k}{x}[/tex]

Where k is the constant of variation.

Problem 7)

We are given that y = 39 when x = 1/3. Thus:

[tex]\displaystyle 39=\frac{k}{{}^{1}\!/ \!{}_{3}}[/tex]

Solve for k:

[tex]\displaystyle k=\frac{1}{3}(39)=13[/tex]

Hence, our equation is:

[tex]\displaystyle y=\frac{13}{x}[/tex]

Then when x = 26, y equals:

[tex]\displaystyle y=\frac{13}{(26)}=\frac{1}{2}[/tex]

Problem 8)

We are given that y = 25 when x = -1/5. Thus:

[tex]\displaystyle 25=\frac{k}{-{}^{1}\!/ \!{}_{5}}[/tex]

Solve for k:

[tex]\displaystyle k=-\frac{1}{5}(25)=-5[/tex]

Hence, our equation is:

[tex]\displaystyle y=-\frac{5}{x}[/tex]

Step-by-step explanation:

there is the answer. good luck

Given: The series ∑cₙ[tex]9^n[/tex] is convergent

To find: The series ∑cₙ[tex](-3)^n[/tex] is convergent or not.

Solution: If the radius of convergence R the we can conclude that R≥4

So, the series will converge as -3<9.

Answer:

x = -4   or   x = 5

Step-by-step explanation:

To solve the absolute value equation

|X| = k

where X is an expression in x, and k is a non-negative number,

solve the compound equation

X = k or X = -k

Here we have |2 - 4x| = 18

In this problem, the expression, X, is 2 - 4x, and the number, k, is 18.

We set the expression equal to the number, 2 - 4x = 18, and we set the expression equal to the negative of the number, 2 - 4x = -18. Then we solve both equations.

2 - 4x = 18  or  2 - 4x = -18

-4x = 16   or   -4x = -20

x = -4   or   x = 5

Answer:

x = -5 . x= 4

Step-by-step explanation:

because |4| = 4 and |-4| = 4

you can see that TWO inputs can get an output of (lets say) 4

The absolute value function can be seen as a function that ignores negative signs

so to get an OUTPUT of "18" using the absolute value function

there are really two ways of getting there

"2-4x = 18"  AND "2-4x = -18"

if you solve both of those you will find that -5 and 4 will

produce the 18 and -18

Answer:

a. 0.2

b. 0.42

c. 0.7

d. the solution is in the explanation

e. x and y are not independent

Step-by-step explanation:

a. from the joint probability mass function table,

p(x=1) and p(Y= 1)

= p(1,1) = 0.2

b. prob(0,0)+prob(0,1)+prob(1,0)+prob(1,1)

= 0.10 + 0.04 + 0.08 + 0.20

= 0.42

P(X ≤ 1 and Y ≤ 1) = 0.42

c. prob {X ≠ 0 and Y ≠ 0}

= prob(1,1) + prob(1,2) + prob(2,1) + prob(2,2)

= 0.20 + 0.06 + 0.14 + 0.30

= 0.7

d. we have to calculate the marginal pmf of x and y here.

we have the x values as 0,1,2

prob(x=0) = 0.1 + 0.04 + 0.02

= 0.16

prob(x=1) = 0.08 + 0.2 + 0.06

= 0.34

prob(x=2) = 0.06+0.14+0.3

= 0.50

we have y values as 0,1,2

prob(y=0) = .1+.08+.06

= 0.24

prob(y=1) = .04+.2+.14

= 0.38

prob(y = 2) = 0.02+0.06+0.3

= 0.38

P(X ≤ 1) = prob(x=0)+prob(x=1)

= 0.34+0.16

= 0.50

e. from the joint table we have this,

prob(1,1) = 0.2

prob(x=1) = 0.34

prob(y=1) = 0.38

then prob(x=1)*prob(y=1)

= 0.34*0.38

= 0.1292

therefore prob(1,1) is not equal to prob(x=1)*prob(y=1)

0.2≠0.1292

x and y are not independent

Answer:

[tex]{ \bf{A=(P + \frac{r}{100} ) {}^{n} }} \\ { \tt{ = (4000 + \frac{5.5}{100} ) {}^{15} }} \\ \\ { \tt{ = \: 1.074 \times {10}^{54} \: dollars}}[/tex]

Answer: y= -3/7x + 3

Step-by-step explanation:

I used some graph paper for this, mark the two points and use a ruler to connect the lines. y=-3/7x is slope, and 3 is the y intercept.

Answer:

3x + 7y -2=0

Step-by-step explanation:

Two points are given to us and we need to find the Equation of the line passing through the two points . The points are (0,3) and (7,0) . We can use here two point form of the line as ,

[tex]\implies y-y_1 = \dfrac{y_2-y_1 }{x_2-x_1} ( x - x_1) \\\\\implies y - 3 =\dfrac{3-0}{0-7}(x - 0 ) \\\\\implies y - 3 =\dfrac{-3}{7}x \\\\\implies 7y - 2 = -3x \\\\\implies \underline{\underline{3x + 7y -2 = 0 }}[/tex]

Answer:

I got u, it is litearly 16540/83.8 = $19737.5

Step-by-step explanation:

its very simple sincen 100-16.2=83.8

Step-by-step explanation:

we know that 1m=100cm

so 1m:5m(final)

1:5

Answer:

1/5

Step-by-step explanation:

Since 100cm = 1m

then

100cm:5m becomes 1m:5m

which in fraction is 1/5

Answer:

[tex] \large{ \tt{❀ \: m \: \angle \: NML= m \: \angle \:QML + m \: \angle \: NMQ}}[/tex]

[tex] \large{ \tt{⤇m \: \angle \:NML= 115 \degree + 28 \degree }}[/tex]

[tex] \boxed{ \large{ \tt{⤇ \: m \: \angle \:NML = 143 \degree }}}[/tex]

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

15×115+3{0÷3}5-3×(-6)

15×115+3of 0 of 5-3×(-6)

15×115+0 of 5-3×(-6)

15×115+0+18

1725+0+18

1743

Answer: hello your question is incomplete attached below is the complete question

answer :

a)   [tex]\int\limits^3_0 {(10-x)-(x+4)} \, dx[/tex]     ( option D )

b) A =  1/2 (6)(3)   ( option B )

c) Area of shaded region = 9

Step-by-step explanation:

a) Using integration with respect to x

Area =   [tex]\int\limits^7_4 {(y-4)} \, dy + \int\limits^a_7 {(10-y)} \, dy[/tex]         ( note a = 10 )

          = y^2/2 - 4y |⁷₄  + 10y - y^2/2 |¹⁰₇

          = 33/2 - 12 + 30 - 51/2   = 9

hence the best integral from the options attached is option D

[tex]\int\limits^3_0 {(10-x)-(x+4)} \, dx[/tex]

= [ 10x - x^2 /2 - x^2/2 - 9x ] ³₀

= 30 - 9/2 - 9/2 - 12  = 9

b) Using Geometry

Area = 1/2 * base * height

        = 1/2 * 6 * 3

        = 9

Answer:

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

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

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A statistician calculates that 7% of Americans are vegetarians.

This means that [tex]p = 0.07[/tex]

Sample of 403 Americans

This means that [tex]n = 403[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.07[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.07*0.93}{403}} = 0.0127[/tex]

What is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%?

Proportion below 7 - 3 = 4% or above 7 + 3 = 10%. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them, and multiply by 2.

Probability the proportion is below 4%

p-value of Z when X = 0.04.

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.04 - 0.07}{0.0127}[/tex]

[tex]Z = -2.36[/tex]

[tex]Z = -2.36[/tex] has a p-value of 0.0091

2*0.0091 = 0.0182

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

Answer:  [tex]37.5\sqrt{3}[/tex]

This value is exact. We can write this as 37.5*sqrt(3)

This approximates to roughly 64.9519

The units for the area are in square feet.

==========================================

Explanation:

Split the regular hexagon into 6 identical equilateral triangles.

Each equilateral triangle has side length x = 5 ft.

The exact area of one of the equilateral triangles is

A = 0.25*sqrt(3)*x^2

A = 0.25*sqrt(3)*5^2

A = 0.25*sqrt(3)*25

A = 0.25*25*sqrt(3)

A = 6.25*sqrt(3)

Multiply this by 6 to get the exact area of the regular hexagon.

6*A = 6*6.25*sqrt(3) = 37.5*sqrt(3) which is the exact area in terms of radicals or square roots.

If your teacher meant to say choice B is 37.5*sqrt(3), then that would be the final answer. If your teacher only said 37.5 without the sqrt(3) term, then there's a typo.

Answer:

Quadrants

Step-by-step explanation:

When two lines intersect such that they are perpendicular to each other, then  quadrants are said to be formed. So that a given space would be divided into four quadrants when two perpendicular lines are drawn on it.

Each section which is called quadrant is at right angle to one another. So that the addition of their angles at the meeting point is the sum of four right angles i.e [tex]360^{o}[/tex]. Thus each of the four sections created by the intersecting lines is called a quadrant.

Answer:

Amazon

Step-by-step explanation:

Hi there!

[tex]\large\boxed{40x^{6}}[/tex]

Begin by simplifying (2x²)²

2² · (x²)² <-- Power rule for exponents, multiply them together:

4 · x⁴ = 4x⁴

Multiply by 10x². ADD exponents when multiplying.

10x² · 4x⁴ = 40 · x²⁺⁴

40x⁶

Answer:

First term=1

Second term=-x

Third term=[tex]2x^2[/tex]

Fourth term =[tex]-\frac{28}{3!}x^3[/tex]

Step-by-step explanation:

We are given that function

[tex]f(x)=(1+3x)^{-1/3}[/tex]

We have to find the  first four non zero terms of the Maclaurin series for the binomial.

Maclaurin series of function f(x) is given by

[tex]f(x)=f(0)+f'(0)x+\frac{1}{2!}f''(0)x^2+\frac{1}{3!}f'''(0)x^3+....[/tex]

[tex]f(0)=(1+3x)^{\frac{-1}{3}}=1[/tex]

[tex]f'(x)=-\frac{1}{3}(1+3x)^{-\frac{4}{3}}(3)=-(1+3x)^{-\frac{4}{3}}[/tex]

[tex]f'(0)=-1[/tex]

[tex]f''(x)=\frac{4}{3}\times 3 (1+3x)^{-\frac{7}{3}}[/tex]

[tex]f''(0)=4[/tex]

[tex]f'''(x)=-4\times \frac{7}{3}\times 3(1+3x)^{-\frac{10}{3}}[/tex]

[tex]f'''(0)=-28[/tex]

Substitute the values we get

[tex](1+3x)^{-\frac{1}{3}}=1-x+\frac{4}{2!}x^2+\frac{-28}{3!}x^3+...[/tex]

[tex](1+3x)^{-\frac{1}{3}}=1-x+2x^2+\frac{-28}{3!}x^3+...[/tex]

First term=1

Second term=-x

Third term=[tex]2x^2[/tex]

Fourth term =[tex]-\frac{28}{3!}x^3[/tex]

Answer:

$191

Step-by-step explanation:

Find how much she will be paying over the 24 months:

34(24)

= 816

Add the down payment to this:

816 + 70

= 886

Find the difference between this and 695:

886 - 695

= 191

So, the difference will be $191 more

Answer:

root(250)

answer choice C

Step-by-step explanation:

explanation in the pic above.

Answer:

x is 10.66

Step-by-step explanation:

What are complementary angles?

They are angles that up to 90

So we have Sin A and Cos B

4x + 10+ 2x + 16= 90

collect like terms

6x+ 26= 90

6x= 90-26

6x= 64

x= 64/6

x= 10.66

Hence the value of x is 10.66

Answer:

not 10.66

Step-by-step explanation:

Answer:

soln,

x=63°

Step-by-step explanation:

yea , 63° is the answer you asked

Answer:

x = 5 and y = 1.5

Step-by-step explanation:

hope this helps please like and mark as brainliest

Answer:

Step-by-step explanation:

> the equation given is x-y =0

> three points that will solve the equation could be

if x= -2 , y = -2 then x-y = 0 is -2 -(-2) =0 so it works point (-2,-2)

if x=1, y = 1 then x-y = 0 is 1-1 =0 is true so we have point (1, 1)

if x=2 ,y= 2 then x-y = 0 is 2-2 =0 is true so we have point (2, 2)