Denise is planning to put a deck in her back yard. The deck will be a 10-by-7-foot rectangle with a semicircle of diameter 4 feet, as shown below. Find the area of the deck (in square feet).(round your answer to two decimal places)

Answer:

D

Step-by-step explanation:

We calculate the z-score for each

Mathematically;

z-score = (x-mean)/SD

z1 = (1.9-2.1)/0.2 = -1

z2 = (2.3-2.1)/0.2 = 1

So the proportion we want to calculate is;

P(-1<x<1)

We use the standard score table for this ;

P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%

Answer:

68

Step-by-step explanation:

Answer:

120 Hours

Step-by-step explanation:

24 hours in a day

5 days

24 x 5 = 120

Answer:

54

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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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Answer:

Hello!

________________________

5c + 16.5 = 13.5 + 10c

Exact Form:  c = 3/5

Decimal Form: c = 0.6

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you!

Answer:

3000+3d=noods

Step-by-step explanation:

Answer:

a) -8x^3 + x^2 + 6x

b)16x^2 -9

c) 24x^4 + 37x^3 +13x^2 -18x

Step-by-step explanation:

a) distribute -2x to x and 4x^2 then do the same for the other part and then add the ones w the same exponent.

b) do foil ( multiply first outside inside last) which will be 4x times 4x then 4x times 3 then -3 times 4x and 3 times -3. add like exponents

c) do the same as above

Answer:

  B)  112°

Step-by-step explanation:

After the double reflection the point is effectively rotated by an amount that is double the angle between the lines of reflection:

  2·56° = 112°

_____

In the attached, lines l and m are separated by 56°, as required by the problem statement.

Answer:

26 rows

Step-by-step explanation:

[tex]number \: of \: rows \\ = \frac{40}{ \frac{20}{13} } \\ \\ = \frac{40 \times 13}{20} \\ \\ = 2 \times 13 \\ \\ = 26 \: [/tex]

Answer:

A= 20x

B= 15n

C= 15x+ 9

D= a + 15

E= 9x + 3y

F= 10w + 10z

Step-by-step explanation:

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.

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.

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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: 4 pairs

Step-by-step explanation:

121-16=105.   However, 121 can be made by squaring -11 or 11.  16 can be made by squaring 4 or -4.  Thus, the choices are 11,4 11,-4 -11,4 -11,-4

Answer:  24

Step-by-step explanation:

Variation: y  ∞  x

y  =  kx , where k is the constant of proportionality

now to find k, we substitute for y and x in the equation above

16 = 8k

therefore,

k = ¹⁶/₈

  = 2.

Now, to find y , we move back to the equation above and substitute for x and k to get y

y =   12(2)

  =  24

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:

17+m=34

Step-by-step explanation:

Nina had 17 marbles in a bag + the x amount of marbles that her mom gives her.

so 17+x=34

(x is the variable that I chose however it could be any variable, so it would also mean the same thing as 17+m=34)

Hope this helped!

Answer:

17 + m = 34.

Step-by-step explanation:

Nina had 17 marbles;

Mother put a handful of marbles, let's say m.

Now Nina has 34 marbles.

34 marbles is [=] 17 marbles Nina had before + m from her mother.

17 + m = 34 will be the right equation.

Answer:

19cm

Step-by-step explanation:

The area  of a trapezoid [tex]=\dfrac12(a+b)h[/tex] (where a and b are the parallel sides).

Given:

Area = 189 Square cm

Height, h=14cm

a=8cm

We want to find the value of the other parallel side, b.

Substitution of the given values gives:

[tex]189=\dfrac12(8+b)14\\189=7(8+b)\\$Divide both sides by 7\\8+b=27\\Subtract 8 from both sides\\b+8-8=27-8\\b=19cm[/tex]

The length of the second parallel side is 19cm.

Answer:

Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.

The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.

The population parameter is the mean amount of mercury in the bass fish of Florida lakes.

The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.

The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.

[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]

Step-by-step explanation:

The question is incomplete.

There is no data provided.

We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.

This is a hypothesis test for the population mean.

The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]

The significance level is assumed to be 0.05.

The sample has a size n=53.

The sample mean is M=0.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.

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

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=53-1=52[/tex]

This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]

As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.

Answer:

The answer is 60cm^2.

hope it helps..

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:

The answer is below

Step-by-step explanation:

They would be written like this:

Arithmetic Progression:

Explicit formula

Tn = a + (n-1) * d

Recursive formula

Tn = Tn-1 + d

Where a is the first term, d is the common differance and n is the number of terms.

Geometric Progression:

Explicit formula

Tn = a * r ^ (n-1)

Recursive formula

Tn = Tn-1 * r

Where r is common ratio

Answer:

Step-by-step explanation:

Given the equation, 2x- y = 5, if x = 3, to get y we will simply substitute the value of x into the expression given as shown;

[tex]2x - y = 5\\\\Substituting \ x = 3\ into \ the \ equation\\\\2(3) - y = 5\\\\6 - y = 5\\\\subtracting\ 6\ from\ both\ sides\\\\6-6-y = 5- 6\\\\-y = -1\\\\multiplying\ both\ sides\ by \ -1\\-(-y) = -(-1)\\\\y = 1[/tex]

Hence, the value of y is 1

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:

B. e^x+3

Step-by-step explanation:

Y=e^x

the graph is moving 3 units up

y= y+3

y=e^x+3

answer = y=e^x+3

Answer: B

Step-by-step explanation:

Answer:

Work done = 0 J

Step-by-step explanation:

work done= ∫ F. dr

                   = [tex]\int\limits^2_0 {x} \, dx[/tex] +  [tex]\int\limits^2_2 {x} \, dx[/tex]  + [tex]\int\limits^0_2 {x} \, dx[/tex]  + [tex]\int\limits^0_0 {x} \, dx[/tex]  +  [tex]\int\limits^0_0 {y} \, dy[/tex]  + [tex]\int\limits^5_0 {y} \, dy[/tex]  + [tex]\int\limits^5_5 {y} \, dy[/tex]  + [tex]\int\limits^0_5 {y} \, dy[/tex] + [tex]\int\limits^0_0 {z} \, dz[/tex]  + [tex]\int\limits^1_0 {z} \, dz[/tex]  + [tex]\int\limits^1_1 {z} \, dz[/tex]  + [tex]\int\limits^0_1 {z} \, dz[/tex]

Work done= x²/2 + y²/2 + z²/2

Applying integral limits for entire pathway

Work done= 2 + 0 -2 + 0 + 0+ 25/2 - 25/2 + 0 + 1/2 + 0 - 1/2

Work done = 0 J

Answer:

It's written as

[tex]2.6 \times {10}^{ - 3} [/tex]

Hope this helps you

Answer:

2.6 × 10⁻³

Step-by-step explanation:

To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.

In the decimal 0.0026, the first number that is 1 or higher is 2.

0.0026 ⇒ 2.6

When trying to figure out the exponent, here are some things to keep in mind:

- when you move the decimal to the right, the exponent is negative

- when you move the decimal to the left, the exponent is positive

You moved the decimal to the right three places. So the exponent will be -3.

The result is 2.6 × 10⁻³.

Hope this helps. :)

Answer:

GOOGLE :)

equation:

y=mx+b

m= slope (how steep the line is(negative is \ positive is /))

b= y intercept (where it is on the vertical line(up and down line))

step by step

1. locate y intercept and plotthe point

2.from that point use slop to find second point and plot

Answer:

Step-by-step explanation:

Answer:

GCF - 4

Step-by-step explanation:

36 - 1, 2, 3, 4, 6, 9, 12, 18, 36

44 - 1, 2, 4, 11, 44

Hope this helps! :)

Answer:

monthly income=$900

the monthly income was multipled by 2

so, real income was, $900/2

=$ 450

so, $450×2=$900...

The real income is $400.

The term multiplication refers to the product of two or more than two numbers.

Let us assume that the real income is x.

We have to multiply the real income by 2 to get the monthly income of $900.

This implies that [tex]x\times 2=\$900[/tex],

Solving the above expression, we will get

[tex]x\times 2=\$900\\x=\dfrac{900}{2} \\x=400[/tex]

So, the real income is $400.

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