Find the common difference of the arithmetic sequence. 4, 10, 16, 22, . . .

Answer:

0.8413

Step-by-step explanation:

Find the z score.

z = (x − μ) / σ

z = (992 − 999) / 7

z = -1

Use a chart or calculator to find the probability.

P(Z > -1)

= 1 − P(Z < -1)

= 1 − 0.1587

= 0.8413

The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct

Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined

Probability can be defined as the ratio of favorable outcomes to the total number of events.

We use Z-statistic to find out the probability,

z = (x − μ) / σ

x = raw score = 992 mL
μ = population mean = 999 mL
σ = standard deviation
z = [992 − 999]/7
z = -1

P-value from Z-Table:

P(x<992) = 0.15866

P(x>992) = 1 - P(x<992) = 0.84134

Thus, the required probability that a bottle has a volume greater than 992 mL is 0.84134

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Answer:

z = 70°

y = 103°

Step-by-step explanation:

From the picture attached,

110° + z° = 180° [Supplementary angles]

z = 180 - 110

z = 70°

Since sum of interior angles of a polygon = (n - 2)×180°

where n = number of sides of the polygon

For a quadrilateral (n = 4),

Sum of interior angles = (4 - 2) × 180°

                                     = 360°

z° + y° + 100° + 87° = 360°

70° + y° + 187° = 360°

y = 103°

Therefore, measure of the angles x = 70° and y = 103°.

Answer:

the answer is c

Step-by-step explanation:

because if the surgery has a 92% success rate and the splints have a 72% success rate then surgery would be recommended because it has a higher success rate

Answer:

78.

Step-by-step explanation:

12 / (48-12) = 26 / x

12/36 = 26/x

1/3 = 26/x

x = 26*3 = 78.

Answer:

5 ≥ c

Step-by-step explanation:

-15≤-3c

Divide each side by -3, remembering to flip the inequality

-15/-3 ≤ -3c/-3

5 ≥ c

Answer:

c ≤ 5

Step-by-step explanation:

Since you have to divide both sides of the equation by a negative number, you have to flip the equality sign.

-15 ≤ -3c

(-15)/(-3) ≤ (-3c)/-3

5 ≥ c

c ≤ 5

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

A) 3x²c² + 5xc² - 2c²

Factor c² from all terms in the expression.

c²(3x² + 5x - 2)

Factor 3x² + 5x - 2

c²(3x-1)(x+2)

B) x² + 6x + 9

x² + 3x + 3x + 9

Factor common terms.

x(x+3)+3(x+3)

Take x+3 common.

(x+3)(x+3)

C) x² - 9

x² -3²

Apply formula : a² - b² = (a+b)(a-b)

(x+3)(x-3)

Answer:

A) [tex]c^2(3x-1)(x+2)[/tex]

B) [tex](x+3)(x+3)[/tex]

C) [tex](x+3)(x-3)[/tex]

Step-by-step explanation:

Part A:

[tex]3x^2c^2+5xc^2-2c^2[/tex]

Taking [tex]c^2[/tex] common

[tex]c^2(3x^2+5x-2)[/tex]

Using mid term break formula

[tex]c^2 (3x^2+6x-x-2)[/tex]

[tex]c^2[3x(x+2)-1(x+2)][/tex]

[tex]c^2(3x-1)(x+2)[/tex]

Part B:

[tex]x^2 + 6x + 9.[/tex]

[tex](x)^2+2(x)(3)+(3)^2[/tex]

[tex](x+3)^2[/tex]

[tex](x+3)(x+3)[/tex]

Part C:

[tex]x^2-9[/tex]

[tex](x)^2-(3)^2[/tex]

[tex](x+3)(x-3)[/tex]

Answer:

120

Step-by-step explanation:

Answer: 120

Hope that helped!(:

Answer:

to be honest I'm not sure how to do this question plz answer my question plz

Step-by-step explanation:

to be honest I'm not sure how to do this question plz answer my question plz I'm so much home workout

Answer: 23, 25, 27

Step-by-step explanation:

Let the 3 consecutive odd numbers be x, x+2 and x+4.

So

2x+(x+2)+3(x+4)=152

2x + x + 2 + 3x + 12 = 152

6x+14=152

6x = 152 - 14

x=138/6

x=23

So, the numbers are 23, 25 and 27.

Answer:

The painting is [tex]t = 10911.1 \ years \ old[/tex]

Step-by-step explanation:

From the question we are told that

    The amount of carbon present after t year is

           [tex]y(t) = y_o * e ^{-0.00012t}[/tex]    {Note ; This is the function }

Here  [tex]y(t)[/tex] is the amount of carbon-14 after time t

        [tex]y_o[/tex] the original amount of carbon-14

Now given that the paint as at now contain 27% of the original carbon-14

  Then it mean that

            [tex]y(t) = 0.27 y_o[/tex]

So the equation is represented as

       [tex]0.27 y_o = y_o * e ^{-0.00012t}[/tex]

=>    [tex]0.27 = * e ^{-0.00012t}[/tex]

=>    [tex]ln(0.27) = -0.00012t[/tex]

=>  [tex]- 1.30933 = -0.00012t[/tex]

=>  [tex]t = \frac{-1.30933}{-0.00012}[/tex]

=>   [tex]t = 10911.1 \ years[/tex]

Answer:

The last set.

Step-by-step explanation:

The first 3 sets  contain  'one-to-many' relations , for example (1, 3) and (1, 5) in set 1 and (0, 0) and (0, 2) in set  3 , so they are not functions.

The last set does not have any of these and is a function.

Answer:

For 3^-6 = 1/3^6 = 726 and for 3^-4 = 1/3^4 = 81

Step-by-step explanation:

ARE THE NUMBERS SEPARATED OR THEY ARE TO BE JOIN TOGETHER,IF THERE ARE SEPARATED THE SOLUTION IS GOING TO BE...

3^-6

using law of indices x^-a = 1/x^a

So 3^-6 = 1/3^6

Now find the power of 3^6

which is the same as 3×3×3×3×3×3 = 729

therefore 1/3^6 = 729

For 3^-4

using the above method

3^-4 is same as 1/3^4

which is equal to

finding the nominator

3×3×3×3 = 81

so the answer is 81

Answer:

[tex] \sqrt{392 {x}^{7} } [/tex]

Simplify

that's

[tex] \sqrt{392} \times \sqrt{ {x}^{7} } \\ \\ = \sqrt{196 \times 2} \: \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2} \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2x ^{7} } [/tex]

Hope this helps you

Answer:

the answer is x = sqrt 48

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.

for labor. Joni paid $85 less per hour for labor. explanation:

The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.

It refers to the total amount of the expenditure done on a product in manufacturing or procuring.

It refers to the expenditure done on procuring labor for the work.

In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,

labor cost Shannon Paid=339.50-112

=$227.50

labor cost per hour=227.50/3.5

=$6.5 per hour

Joni paid total $455 in which the cost of spare parts is $310 and rest is labor

labor cost paid by Joni=455-310

=$145

labor cost per hour=145/2.5

=$58 per hour

So by doing comparing we found that Shannon had paid $6 per hour extra for labor.

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Answer:

C

Step-by-step explanation:

So you can use the 30, 60, 90 degree triangle ratio of x: 2x: x√3

The 3 is the x, and the hypotenuse is the 2x, so it's 6

Answer:

C. 6

Step-by-step explanation:

I just finished the test and I got 100 percent

Answer:

The interest is

Step-by-step explanation:

Simple interest is given by

[tex]I = \frac{P \times R \times T}{100} [/tex]

where

P is the principal

R is the rate

T is the time given

From the question

The principal / P = $ 5700

The rate / R = 4.5%

The time given / T = 3 years

So the interest is

[tex]I = \frac{5700 \times 4.5 \times 3}{100} [/tex]

[tex]I = \frac{76950}{100} [/tex]

We have the final answer as

I = $ 769.50

Hope this helps you

sine(X) = opposite side / hypotenuse

sine(X) = (2√11) / (4√11)

sine(X) = (2/4)

sine(X) = 0.5

X = arcsine(0.5)

X = 30°  

Answer: m∠x = 30°

Step-by-step explanation:

In a right triangle, if the short side of the right angle is Half the length of the hypotenuse, the triangle has angles of 30°, 60° and 90°

∠x is the smallest one, so  m∠x = 30°

It is possible to figure the sine and get the angle from that, but in this case it might not be necessary.  ;-)

Answer:

second option

Step-by-step explanation:

x / x - 1 + 3x / x + 2

= x(x + 2) / (x - 1)(x + 2) + 3x(x - 1) / (x - 1)(x + 2)

= (x² + 2x) / (x² + x - 2) + (3x² - 3x) / (x² + x - 2)

= (4x² - x) / (x² + x - 2)

Answer:

9

Step-by-step explanation:

Extend every other side of the hexagon so that a triangle is formed.  Since the hexagon is equiangular, the overall triangle is an equilateral triangle, as well as the smaller triangles in the corners.

The length of the sides of the overall triangle is 7 + 2 + 4 = 13.

Therefore, the other two sides of the hexagon are 5 and 4.

The sum is 5 + 4 = 9.

Answer:

[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]

[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]

Step-by-step explanation:

Part a

We want to find:

[tex] P(X<6.4)[/tex]

And we just need to find the area below the curve until x=6.4, since we have a triangle we can do this:

[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]

Part b

For this case we want to find this probability:

[tex] P(X>4.8)[/tex]

And we can use the complement rule and we got:

[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]

Answer:

c

Step-by-step explanation:

Answer:

The height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].      

Step-by-step explanation:

It is given that,

Distance between a person and an elephant is 15 ft

The angle of elevation of the elephant is 30 degrees.

We need to find the height of the elephant. For this let us consider that height is h. So,

[tex]\tan\theta=\dfrac{P}{B}\\\\\tan(30)=\dfrac{h}{15}\\\\h=15\times \tan(30)\\\\h=\dfrac{15}{\sqrt3}\ ft[/tex]

So, the height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].      

Answer:

The answer is B.

Step-by-step explanation:

You have to substitute x = 2, into the equation of y :

[tex]y = 6 {x}^{3} - 5 {x}^{2} + 4x - 3[/tex]

[tex]let \: x = 2[/tex]

[tex]y = 6 {( 2)}^{3} - 5 {(2)}^{2} + 4(2) - 3[/tex]

[tex]y = 48 - 20 + 8 - 3[/tex]

[tex]y = 33[/tex]

They left off the equation but we can know it's

y(t) =  h₀ - g t² / 2

That's

y(t) = 144 - 16 t²

It hits the ground when

0 = 144 - 16 t²

16 t² = 144

t² = 144 / 16 = 9

t = 3 seconds

Answer: 3 seconds

Answer:

1,114.6 kPa

Step-by-step explanation:

P(t) = 1300 (0.95)^t

P(3) = 1300 (0.95)^3

P(3) = 1114.6

Answer:

a) How long will it take to repay the loan?

20 years

b) What amount of interest does the purchase pay?

$134,896

Step-by-step explanation:

a) How long will it take to repay the loan?

In the above question, they are asking you for the Loan duration

The Formula for Loan duration(T) =

ln (- m/(r÷n) × C - m)/In (1 + r/n)

Where:

m = monthly payments = $1395.40

C = Amount of mortgage =$200,000

r = Interest rate = 5.7% = 0.57

n = compounded quarterly = 4

T = ln (- 1395.40/(0.57÷4) × 200,000 - 1395.40)/In (1 + 0.57/4)

T = 20 years.

Therefore, it will take 20 years to repay the Loan.

b) What amount of interest does the purchase pay?

The total number of payments =

Loan duration × Number of months

Number of months = 12 months( because it is monthly payment)

Loan duration = 20 years

Total number of payments = 240 payments.

In the question, we are given the amount paid monthly payment as

$1,395.40

Total amount paid = Monthly payments × Total number of payments

= $1,395.40 × 240

= $334,896

The amount of Interest the purchase pay = $334,896 - $200,000

= $134,896

Answer:

hope this is right y=74

Step-by-step explanation:

have not done this since two years ago so...

but anyway 148-180 = 32

32 is that angle

if this were a right triangle my answer would be different but 148/2 still completes this triangle and somewhat makes sense.

The correct answer is 90.