No need of a answer anymore.

Answer:

I didn't know which one you wanted...

Step-by-step explanation:

1. Finding the x an y-intercepts

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (2,0)

y-intercept(s): (0,−24)

2. Finding the slope and y-intercept

Use the slope-intercept form to find the slope and y-intercept.

Slope: 12

y-intercept: −24

Answer:

61,925 miles

Step-by-step explanation:

Given :

The p-value of the tires to outlast the were warranty were given in the the question as = 0.96

Checking the normal distribution table, The probability that corresponds to 0.96

from the Normal distribution table is 1.75.

Mean : 'μ'= 60000 miles

Standard deviation : σ=1100

The formula for z-score is given by

: z= (x-μ)/σ

1.75=(x-60000)/1100

1925=x-60000

x=61925

Therefore, the tread life of tire should be 61,925 miles if they want 96% of the tires to outlast the warranty.

Answer:

D. *6F

Step-by-step explanation:

C=(F-32)*5/9

30=(F-32)*5/9

F = (30*9)/5+32

F = 86

Answer:

5 [tex]\frac{1}{3}[/tex], 10 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

[tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = 1 [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex] ÷ 1 [tex]\frac{1}{3}[/tex] = 2

Thus to obtain a term in the sequence multiply the previous term by 2, thus

a₅ = [tex]\frac{8}{3}[/tex] × 2 = [tex]\frac{16}{3}[/tex] = 5 [tex]\frac{1}{3}[/tex]

a₆ = [tex]\frac{16}{3}[/tex] × 2 = [tex]\frac{32}{3}[/tex] = 10 [tex]\frac{2}{3}[/tex]

Answer:

Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.

The domain is all of the x values. Therefore the domain is {-1, 2}.

The range is all of the y values. Therefore the range is {-4, -3, 2}.

We don't use ( ) or [ ] because T is a discrete relation.

First find the distance it is reflected:

D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.

Now calculate the magnification: -20/ 20 = -1

Now calculate the height:

-1 x 2.50 = -2.50

The negative sign means the image is inverted.

The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.

Answer:

y=2x+6

Step-by-step explanation:

The slope is 2x and the y-intercept is 6. It is shown how to graph it in the attachment.

Answer:

HL (try HL, I believe that's the right answer)

Answer:

HL

Step-by-step explanation:

BRO TRUST ME

Answer:

15 49-cent stamps

Step-by-step explanation:

We can solve this problem with the equations 0.49(x) + 0.21(y) = 9.45 and x - 5 = y. Well, 0.49(15) + 0.21(10) = 9.45, so we know that there are 15 49-cent stamps and 10 21-cent stamps. The question is asking for the number of 49-cent stamps, so we can tell Travis bought 15 49-cent stamps.

Hope this helps! Plz give me brainliest, it will help me achieve my next rank.

The number of 49-cent stamps that Travis bought given the equation is 15.

Given this equation: 0.49s+0.21(s−5)=9.45 take the following steps to determine the value of s

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Answer:

A) Null hypothesis; H0: μ1 − μ2 ≤ 0

Alternative hypothesis; Ha: μ1 − μ2 > 0

B) Test statistic = t = 1.878

C) p-value is 0.038823.

D) Reject the Null hypothesis H0

Step-by-step explanation:

We are given;

α = 0.05

n1 = 16

n2 = 10

bar x1 = 6.82

bar x2 = 6.28

s1 = 0.65

s2 = 0.75

A) The hypothesis is as follows;

Null hypothesis; H0: μ1 − μ2 ≤ 0

Alternative hypothesis; Ha: μ1 − μ2 > 0

B) Formula yo determine the test statistic is;

t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))

Plugging in the relevant values, we have;

t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))

t = 0.54/√(0.02640625 + 0.05625)

t = 0.54/0.2875

t = 1.878

C) The formula for the degree of freedom is;

Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))  

Plugging in the relevant values, we have;

Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))  

Δ = 0.00683205566/(0.000046486 + 0.0003515625)

Δ ≈ 17

Thus, the P-value;

From online p-value calculator from t-score and DF which i attached, we have the p-value as;

The p-value is 0.038823.

D) The p-value result is significant at p < 0.05

Thus, we reject the Null hypothesis H0

A) Null hypothesis: μ1 − μ2 ≤ 0

B) Test statistic = t = 1.878

C) The p-value is 0.038823.

D) Reject the Null hypothesis H0.

What all information we have ?

α = 0.05

n1 = 16

n2 = 10

bar x1 = 6.82

bar x2 = 6.28

s1 = 0.65

s2 = 0.75

Part A)

The hypothesis is as follows;

Null hypothesis; H0: μ1 − μ2 ≤ 0

Alternative hypothesis; Ha: μ1 − μ2 > 0

Part B)

The formula to determine the test statistic is :

t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))

t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))

t = 0.54/√(0.02640625 + 0.05625)

t = 0.54/0.2875

t = 1.878

The formula to determine the test statistic is t = 1.878.

Part C)

The formula for the degree of freedom is;

Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))  

Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))  

Δ = 0.00683205566/(0.000046486 + 0.0003515625)

Δ ≈ 17

Thus, the P-value is 0.038823.

Part D)

The p-value result is significant at p < 0.05 is :

Thus, we reject the Null hypothesis H0.

Learn more about "Hypothesis":

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Answer:

At a significance level of 0.05, there is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0

The significance level is 0.05.

The sample 1 (Pernod 5), of size n1=400 has a proportion of p1=0.06.

[tex]p_1=X_1/n_1=24/400=0.06[/tex]

The sample 2, of size n2=400 has a proportion of p2=0.1.

[tex]p_2=X_2/n_2=40/400=0.1[/tex]

The difference between proportions is (p1-p2)=-0.04.

[tex]p_d=p_1-p_2=0.06-0.1=-0.04[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{24+40}{400+400}=\dfrac{64}{800}=0.08[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.08*0.92}{400}+\dfrac{0.08*0.92}{400}}\\\\\\s_{p1-p2}=\sqrt{0.000184+0.000184}=\sqrt{0.000368}=0.019[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.04-0}{0.019}=\dfrac{-0.04}{0.019}=-2.085[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=2\cdot P(z<-2.085)=0.037[/tex]

As the P-value (0.037) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Hey there! :)

Answer:

y = 1/4x - 3.

Step-by-step explanation:

Use the slope-formula to find the slope of the line:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in two points from the line. Use the points (-4, -4) and (0, 3):

[tex]m = \frac{-3 - (-4)}{0 - (-4)}[/tex]

Simplify:

m = 1/4.

Slope-intercept form is y = mx + b.

Find the 'b' value by finding the y-value at which the graph intersects the y-axis. This is at y = -3. Therefore, the equation is:

y = 1/4x - 3.

Answer:

35 students

Step-by-step explanation:

Take the number of students in the class and multiply by 60% and see if you get an integer number

28 * .60 =16.8  not an integer

32 * .6 =19.2

35 * .6 =21  yes

39*.6 =23.4

Answer:

19/9 because it equals to 2.111..  Which is greater than 1

Step-by-step explanation:

By the way if it's right can i get brainliest.

Answer:

1 < 19/9

Step-by-step explanation:

1  vs 19/9

Rewriting 19/9 as 9/9 + 9/9+ 1/9

1 vs 1+1 +1/9

1 vs 2 1/9

1 < 19/9

Answer:

A) Null and alternative hypothesis

[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]

B) M = 2.2 hours

C) s = 0.52 hours

D) P-value = 0.255

E) At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean tree-planting time significantly differs from two hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=2\\\\H_a:\mu\neq 2[/tex]

The significance level is 0.05.

The sample has a size n=10.

The sample mean is M=2.2.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.52.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.52}{\sqrt{10}}=0.1644[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2.2-2}{0.1644}=\dfrac{0.2}{0.1644}=1.216[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=10-1=9[/tex]

This test is a two-tailed test, with 9 degrees of freedom and t=1.216, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>1.216)=0.255[/tex]

As the P-value (0.255) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean tree-planting time significantly differs from two hours.

Sample mean and standard deviation:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(1.7+1.5+2.6+. . .+2.3)\\\\\\M=\dfrac{22}{10}\\\\\\M=2.2\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((1.7-2.2)^2+(1.5-2.2)^2+(2.6-2.2)^2+. . . +(2.3-2.2)^2)}\\\\\\s=\sqrt{\dfrac{2.4}{9}}\\\\\\s=\sqrt{0.27}=0.52\\\\\\[/tex]

Answer:

[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]

Step-by-step explanation:

Given

[tex]f(b) = b^2 - 75[/tex]

Required

Determine the roots

To get the root of the function, then f(b) must be 0;

i.e. f(b) = 0

So, the expression becomes

[tex]0 = b^2 - 75[/tex]

Add 75 to both sides

[tex]75 + 0 = b^2 - 75 + 75[/tex]

[tex]75 = b^2[/tex]

Take square roots of both sides

[tex]\sqrt{75} = \sqrt{b^2}[/tex]

[tex]\sqrt{75} = b[/tex]

Reorder

[tex]b = \sqrt{75}[/tex]

Expand 75 as a product of 25 and 3

[tex]b = \sqrt{25*3}[/tex]

Split the expression

[tex]b = \sqrt{25} *\sqrt{3}[/tex]

[tex]b = \±5 *\sqrt{3}[/tex]

[tex]b = \±5 \sqrt{3}[/tex]

[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]

The options are not clear enough; however the roots of the equation are [tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]

Answer: 57769.8 in²

Let A be the area of the shaded region

We have a relation that can help us calculate its area

A= 0.5*(θ-sin(θ))*r² where r is the radius and θ the angle

A= 0.5*(150-sin(150°))* 27.8² =57769.79≈57769.8 in²

Answer:

818.4

Step-by-step explanation:

Answer:

a) E(X) = 16.09 ft³

E(X²) = 262.22 ft⁶

Var(X) = 3.27 ft⁶

b) E(22X) = 354 dollars

c) Var(22X) = 1,581 dollars

d) E(X - 0.01X²) = 13.470 ft³

Step-by-step explanation:

The complete Correct Question is presented in the attached image to this solution.

a) Compute E(X), E(X2), and V(X).

The expected value of a probability distribution is given as

E(X) = Σxᵢpᵢ

xᵢ = Each variable in the distribution

pᵢ = Probability of each distribution

Σxᵢpᵢ = (13.5×0.20) + (15.9×0.59) + (19.1×0.21)

= 2.70 + 9.381 + 4.011

= 16.092 = 16.09 ft³

E(X²) = Σxᵢ²pᵢ

Σxᵢ²pᵢ = (13.5²×0.20) + (15.9²×0.59) + (19.1²×0.21)

= 36.45 + 149.1579 + 76.6101

= 262.218 = 262.22 ft⁶

Var(X) = Σxᵢ²pᵢ - μ²

where μ = E(X) = 16.092

Σxᵢ²pᵢ = E(X²) = 262.218

Var(X) = 262.218 - 16.092²

= 3.265536 = 3.27 ft⁶

b) E(22X) = 22E(X) = 22 × 16.092 = 354.024 = 354 dollars to the nearest whole number.

c) Var(22X) = 22² × Var(X) = 22² × 3.265536 = 1,580.519424 = 1,581 dollars

d) E(X - 0.01X²) = E(X) - 0.01E(X²)

= 16.092 - (0.01×262.218)

= 16.0926- 2.62218

= 13.46982 = 13.470 ft³

Hope this helps!!!

Answer:

54

give me brainliest please please please and follow my page

Step-by-step explanation:

To find length of KC...we need to find the length of HM and MU first ...

so....HM= 96- 78 = 14

JU = 96 + HM = 96 + 14 = 110

....

KU = 110 - JK = 110 - 82 = 28

....

UN = 105+ 82 -( 96 + 14 )

187 - 110

= 77

UC = 77 - 51 = 26

KC = UC + KU = 26 + 28 = 54

The length of [tex]\overline{KC}[/tex] along line [tex]\overline{JN}[/tex] is given as 54 (Option A) See the computation below.

To determine the length of [tex]\overline{KC}[/tex], the length of [tex]\overline{HM}[/tex] and [tex]\overline{MU}[/tex]must first be derived.

[tex]\overline{HM}[/tex] = 96 - 78

[tex]\overline{HM}[/tex] = 14

[tex]\overline{JU}[/tex] = 96 + [tex]\overline{HM}[/tex]

= 96 + 14

[tex]\overline{JU}[/tex]= 110

[tex]\overline{KU}[/tex] = 110 - [tex]\overline{JK}[/tex]

= 110 - 82

[tex]\overline{KU}[/tex]= 28

[tex]\overline{UN}[/tex] = 105+ 82 -( 96 + 14 )

=187 - 110

[tex]\overline{UN}[/tex]= 77

[tex]\overline{UC}[/tex] = 77 - 51

[tex]\overline{UC}[/tex]= 26

Thus,

[tex]\overline{KC}[/tex] = [tex]\overline{UC}[/tex] + [tex]\overline{KU}[/tex]

[tex]\overline{KC}[/tex]= 26 + 28

[tex]\overline{KC}[/tex]= 54

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This is a great question!

When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -

[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]

____

Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,

[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]

Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,

( 1. The new store will have a profit of $3400 after its third month in business.  

( ​​2. The new store will have a profit of $2400 after its third month in business.

( 3. ​The new store will sell 2400 items in its third month in business.

( 4. The new store will sell 3400 items in its third month in business.

The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

The substitution method is the algebraic method to solve simultaneous linear equations.

Given function is,

[tex]r(x) = x^2+5x+14[/tex]...(1)

And [tex]c(x) = x^2-4x+5[/tex]...(2)

Now, substituting the value into the equation (1) and (2).

[tex]r(5) = (5)^2+5(5)+14=64[/tex]

[tex]c(5) = (5)^2-4(5)+5=10[/tex]

Therefore,

[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]

Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

Learn more about the topic Substitution:

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Answer:

Y=1/4x-4

Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25

Answer:

This equation displays the distributive property which states that a(b + c) = a(b) + a(c).

Answer:

Distributive property

Step-by-step explanation:

4(x+3)=4x+12

This example shows distributive property because 4 is distributed (multiplied) to x +3. When 4 is distributed, it will equal 4x+12!!

Hope it helps!!!!

Answer:

20 years old.

Step-by-step explanation:

Let us say that the man's age is represented by x and the son's age is represented by y.

As of now, x = 2y.

In 20 years, both ages will increase by 20. We can have an equation where the son's age increased by 20 equals 2/3 of the man's age plus 20.

(y + 20) = 2/3(x + 20)

Since x = 2y...

y + 20 = 2/3(2y + 20)

3/2y + 30 = 2y + 20

2y + 20 = 3/2y + 30

1/2y = 10

y = 20

To check our work, the man's age is currently double his son's, so the man is 40 and the son is 20. In 20 years, the man will be 60 and the son will be 40. 40 / 60 = 2/3, so the son's age is 2/3 of his father's.

So, the son's present age is 20 years old.

Hope this helps!

Answer:

x = 2, y = 5

Step-by-step explanation:

Hello,

   y=6x-7

   9x-2y=8

can be written as

   (1) 6x - y = 7

   (2) 9x -2y = 8

(2)-2*(1) gives

   9x -2y -12x +2y = 8 - 2*7 = 8 - 14 = -6

   <=> -3x=-6

   <=> x = 6/3=2

and we replace it in (1)

  y = 6*2-7=12-7=5

hope this helps

Answer:

[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's follow the advise and proceed with the substitution

first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t

[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]

Now we can substitute in the equation

[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]

so the new equation is

[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]

the auxiliary equation is

[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]

so the solutions of the new equation are

[tex]y(t)=ae^{2t}+be^{-10t}[/tex]

with a and b real

as

[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]

[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]

hope this helps

do not hesitate if you have any questions

Answer:

3.26%

Step-by-step explanation:

The computation of the probability that she is a student is shown below:

Percentage of student developers = 25.8% = SD

The Percentage of the developer is student = 7.4% = DS

The percentage of the developer is not student = 76.4% = ND

Based on this, the probability is

[tex]= \frac{SD \times DS}{SD \times DS + DS \times ND}[/tex]

[tex]= \frac{25.8\% \times 7.4\%}{25.8\% \times 7.4\% + 7.4\% \times 76.4\%}[/tex]

=3.26%

we simply considered all the elements

Answer:

  a) 207 mph

  b) x = (1260-w)/1.17

  c) 1000 mb

Step-by-step explanation:

a) Put the pressure in the equation and solve.

  w(900) = -1.17(900) +1260 = 207

The wind speed for a hurricane with a pressure of 900 mb is 207 mph.

__

b) Solving for x, we have ...

  w = -1.17x +1260

  w -1260 = -1.17x

  x = (1260 -w)/1.17 . . . . inverse function

__

c) Evaluating the inverse function for w=90 gives ...

  x = (1260 -90)/1.17 = 1170/1.17 = 1000 . . . millibars

The approximate barometric pressure for a hurricane with a wind speed of 90 mph is 1000 millibars.

Answer:

  2 1/4

Step-by-step explanation:

The volume of soil needed is ...

  (14/3 yd)(26/3 yd)(2/36 yd) = 728/324 yd³ = 2.247 yd³

The nearest higher quarter-yard is 2.250 yd³. That's how much you need to order.

  You need to order 2 1/4 cubic yards.

___

There are 3 ft or 36 inches to a yard.

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

[tex]y=z=0\implies x=2\implies (2,0,0)[/tex]

[tex]x=z=0\implies y=2\implies(0,2,0)[/tex]

[tex]x=y=0\implies 2z=2\implies z=1\implies(0,0,1)[/tex]

Plane 2, 4x + 4y + z = 8:

[tex]y=z=0\implies4x=8\implies x=2\implies(2,0,0)[/tex]

[tex]x=z=0\implies4y=8\impliesy=2\implies(0,2,0)[/tex]

[tex]x=y=0\implies z=8\implies(0,0,8)[/tex]

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

[tex]\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx[/tex]

[tex]=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx[/tex]

[tex]=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}[/tex]