Type the correct answer in the box. Use numerals instead of words. What is the missing value in the inverse variation given in the table?

Answer:

[tex]\boxed{\mathrm{864 \: in^2}}[/tex]

Step-by-step explanation:

The shape is a cube.

Apply formula for total surface area of cube.

[tex]SA=6a^2[/tex]

[tex]SA=\mathrm{total \: surface \: area}\\ a =\mathrm{side \: length}[/tex]

[tex]SA=6(12)^2[/tex]

[tex]SA=6(144)[/tex]

[tex]SA=864[/tex]

Answer:

[tex]\boxed{Area = 144 inches^2}[/tex]

Step-by-step explanation:

Area of a cube = Volume/Length

Where Length = 12 inches, Volume = 1728

Area = 1728/12

Area = 144 inches^2

Answer:

(A) With 99% confidence, the proportion that favours the Green initiative is between 418.895 and 423.105 (no approximation; answers were gotten exactly in 3 decimal places).

(B) If many groups of 593 (greater than the initial sample size of 556) randomly selected Americans were surveyed then a different confidence interval would be used or produced from each group.

About 90% of these confidence intervals will contain the true population proportion of Americans who favour the Green initiative and about 10% will not contain the true population proportion.

Step-by-step explanation:

(A) 99% of 421 = 416.79

421 - 416.79 = 4.21

4.21 ÷ 2 = 2.105

(421-2.105), (421+2.105)

The lower and upper limits are:

[418.895 , 423.105]

(B) A wider confidence interval such as 90% will be better suited in a case of multiple samples like this.

Answer:

H0:μ=18, Ha:μ<18

H0:μ=11.3, Ha:μ<11.3

H0:μ=3.7, Ha:μ<3.7

Step-by-step explanation:

A left tailed test is a type of test usually taken from the alternative hypothesis that includes only one of either the less than or greater than options and not both.

A left tailed test corresponds with the less than option and in this case study, the left tailed test are:

H0:μ=18, Ha:μ<18

H0:μ=11.3, Ha:μ<11.3

H0:μ=3.7, Ha:μ<3.7

Answer:

i think is 7

Step-by-step explanation:

Answer:

A=82°

a= 67.4

c = 60.1

Step-by-step explanation:

For A

A+B+C =180°

A= 180-(B+C)

A= 180-(36+62)

A= 189-(98)

A= 82°

For a

a/sinA= b/sinB

a/sin82= 40/sin36

a= (40*sin82)/sin36

a=( 40*0.9903)/0.5878

a=67.39

Approximately = 67.4

For c

c/sinC= b/sinB

c= (sinC*b)/sinB

c= (sin62*40)/sin36

c =(0.8829*40)/0.5878

c = 60.08

Approximately = 60.1

Answer:

Step-by-step explanation:

shape D

Answer:

D.

Step-by-step explanation:

Well congruent means same size and same shape.

a) rectangle

This shape is a rectangle where as the given shape is a parallelogram.

This is not congruent to the given shape.

b) Parallelogram

This may be a parallelogram but it is too wide,

Hence, it is not congruent.

c) Rectangle

This is not a parallelogram,

Hence, this s not congruent

d) Parallelogram

This is a parallelogram with the same size just not in the same place but it is still congruent.

Thus, answer choices D. is the correct answer.

Answer:

Subtract c from each side, using the subtraction property of equality

Step-by-step explanation:

0 = ax^2 + bx + c

Subtract c from each side, using the subtraction property of equality

-c = ax^2 + bx + c-c

-c = ax^2 + bx

Answer:

subtract c from each side, so the answer would be D

Answer:

[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points

[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]

Substitute:

[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

We can use the slope formula since we have 2 points

m = ( y2-y1)/(x2-x1)

    = (9-3)/( 7 - -5)

    = (9-3) /( 7+5)

   = 6/ 12

  = 1/2

Answer:

$57

Since $71.25 was paid for working 7.5 hours.

That means he was being paid $9.5 per hour.

Which is 71.25÷7.5.

And on tuesday that's 9.5×6 which is $57

Answer:

x= 1.75

Step-by-step explanation:

Answer:

1.75 = x?

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

To find 20% of 50 you need to times 20 with 50 and divide by 100.

20×50÷100

=10

Answer:

The value of Chi-square test statistic is χ² = 5.75.

Step-by-step explanation:

The Chi-square Goodness of fit test will be used to determine whether the die is fair or not.

The hypothesis can be defined as follows:

H₀: The die is fair.

Hₐ: The die is not fair.

The Chi-square test statistic is given by:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]

Consider the table attached below.

The value of Chi-square test statistic is χ² = 5.75.

Answer:

The probability that Pat will pass the exam is 0.02775.

Step-by-step explanation:

We are given that exam consists of 100 true-false questions. Pat plans to guess the answer to each question without reading it.

If a grade on the exam is 60% or more, Pat will pass the exam.

Let X = grade on the exam by Pat

The above situation can be represented through binomial distribution such that X ~ Binom(n = 100, p = 0.50).

Here the probability of success is 50% because there is a true-false question and there is a 50-50 chance of both being the correct answer.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]100 \times 0.50[/tex] = 50

and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]

                                                                  = [tex]\sqrt{100 \times 0.50 \times (1-0.50)}[/tex]

                                                                  = 5

So, X ~ Normal([tex]\mu=50, \sigma^{2} = 5^{2}[/tex])

Now, the probability that Pat will pass the exam is given by = P(X [tex]\geq[/tex] 60)

         P(X [tex]\geq[/tex] 60) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{60-50}{5}[/tex] ) = P(Z [tex]\geq[/tex] 2) = 1 - P(Z < 2)

                                                       = 1 - 0.97725 = 0.02275

Hence, the probability that Pat will pass the exam is 0.02775.

Answer:

  181.8 yd

Step-by-step explanation:

The law of cosines is good for this. It tells you for triangle sides 'a' and 'b' and included angle C, the length of 'c' is given by ...

  c^2 = a^2 +b^2 -2ab·cos(C)

For the given geometry, this is ...

  c^2 = 400^2 +240^2 -2(400)(240)cos(16°) ≈ 33,037.75

  c ≈ √33037.75 ≈ 181.8 . . . yards

Marsha's ball is about 181.8 yards from the hole.

Answer:

181.8 yds

Step-by-step explanation:

I got it correct on founders edtell

Answer:

The probability that the average length of rods in a randomly selected bundle of steel rods is greater than 259 cm is 0.65173.

Step-by-step explanation:

We are given that a company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 259.2 cm and a standard deviation of 2.1 cm. For shipment, 17 steel rods are bundled together.

Let [tex]\bar X[/tex] = the average length of rods in a randomly selected bundle of steel rods

The z-score probability distribution for the sample mean is given by;

                            Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean length of rods = 259.2 cm

           [tex]\sigma[/tex] = standard deviaton = 2.1 cm

           n = sample of steel rods = 17

Now, the probability that the average length of rods in a randomly selected bundle of steel rods is greater than 259 cm is given by = P([tex]\bar X[/tex] > 259 cm)

     P([tex]\bar X[/tex] > 259 cm) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{259-259.2}{\frac{2.1}{\sqrt{17} } }[/tex] ) = P(Z > -0.39) = P(Z < 0.39)

                                                                = 0.65173

The above probability is calculated by looking at the value of x = 0.39 in the z table which has an area of 0.65173.

Hello!

Answer:

Table B.

Step-by-step explanation:

An inverse of a function means that the x and y values are swapped in comparison to the original function. For example:

We can use points on the table:

[tex]f(x)[/tex] = (7, 21)

The inverse of this function would 7 as its y value, and 21 as its x value:

[tex]f^{-1} (x)[/tex] = (21, 7)

The only table shown that correctly shows this relationship is table B.

Answer:

New height= 41.4 inches

Second new height= 36inches

Step-by-step explanation:

Height is assumed to be 36 inches

If it increases by 15%.

15%= 0.15

It's new height =( 36*0.15) +36

New height= 5.4+36

New height = 41.4 inches

This expression (36*0.15) is the expression of adding 15% to the height.

So if the 15% is taken away again , height= 41.4-(36*0.15)

Height= 41.4-5.4

Height= 36 inches

Answer:

d.

Step-by-step explanation:

[tex]f(g(x))=3(g(x))^2-12=3(5x+3)^2-12=3(25x^2+30x+9)-12=75x^2+90x+27-12=75x^2+90x+15[/tex]

Answer:

sin⁴x - sin²x = cos⁴x - cos²x

Solve the right hand side of the equation

That's

sin⁴x - sin²x

From trigonometric identities

So we have

sin⁴x - ( 1 - cos²x)

sin⁴x - 1 + cos²x

sin⁴x = ( sin²x)(sin²x)

That is

( sin²x)(sin²x)

So we have

( 1 - cos²x)(1 - cos²x) - 1 + cos²x

Expand

1 - cos²x - cos²x + cos⁴x - 1 + cos²x

1 - 2cos²x + cos⁴x - 1 + cos²x

Group like terms

That's

cos⁴x - 2cos²x + cos²x + 1 - 1

Simplify

We have the final answer as

So we have

Since the right hand side is equal to the left hand side the identity is true

Hope this helps you

Answer:

9 miles

Step-by-step explanation:

Let's say that the speed that Jeremy's father drives Jeremy through traffic is x. When there is no traffic, Jeremy's father drives 18 miles per hour faster than his speed in traffic, x. This would make the speed that Jeremy's father drives Jeremy to school without traffic, 18 / 60 + x. This is as it is 18 miles per hour faster, not 18 miles per minute faster.

Now recall the formula Speed = Distance / Time, or S = D / T. We want the distance here ( How far (in miles) from Jeremy's home to school ) so let's isolate D here in this formula,

S = D / T ⇒ D = S [tex]*[/tex] T - and as you know, the distance from Jeremy's home to school is the same, with or without traffic. So, we can consider case 1 : Jeremy's " distance traveled " in traffic, and case 2 : Jeremy's " distance traveled " without traffic, and make them equal to one another.

20 [tex]*[/tex] x = 12 [tex]*[/tex] ( 18 / 60 + x ),

20x = 3.6 + 12x,

8x = 3.6,

x = 0.45 - Now the distance is 20 [tex]*[/tex] x, and hence 20 [tex]*[/tex] 0.45 = 9 miles

Triangle DAC is congruent to triangle BCA by SAS congruence theorem.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, AD = BC and AD || BC.

AD = BC (Given)

AD || BC (Given)

AC = AC (Reflexive property)

∠DAC=∠BCA (Interior alternate angles)

By SAS congruence theorem, ΔDAC≅ΔBCA

By CPCT, AB=CD

Therefore, triangle DAC is congruent to triangle BCA by SAS congruence theorem.

To learn more about the congruent theorem visit:

https://brainly.com/question/24033497.

#SPJ5

Answer:

8

Step-by-step explanation:

To find the answer to these problems you can work backwards

12-4=8

Answer:

Fibonacci numbers is a series of numbers in which each number is sum of two preceding numbers.

Step-by-step explanation:

It is a sequence in mathematics denoted F. Fibonacci numbers have important contribution to western mathematics. The first two Fibonacci numbers are 0 and 1, all the numbers are then sum of previous two numbers. Fibonacci sequence is widely used in engineering applications for data algorithms. Fibonacci sequence is basis for golden ratio which is used in architecture and design. It can be seen in petals of flower and snail's shell.

Answer: 0.045 is the growth rate.

Step-by-step explanation:

A generic exponential growth function can be written as:

f(t) = A*(1 + r)^t

where A is the initial amount.

t is the unit of time.

r is the rate of growth.

For example if we have an increase of 10% per year, with an initial population of 100 we have that:

A = 100, r = 10%/100% = 0.10, t = number of years.

the equation will be:

f(t) = 100*(1 + 0.10)^t

Now, in this case the equation is:

S(t) = 152*(1.045)^t

We can write this as:

S(t) = 152*(1 + 0.045)^t

Then 152 is the initial amount and 0.045 is the growth rate.

Answer:

[tex]\boxed{ x = 2}[/tex]

Step-by-step explanation:

=> [tex]2x = 4[/tex]

Dividing both sides by 2

=> [tex]\frac{2x}{2} = \frac{4}{2}[/tex]

=> x = 2

2x=4

x=4/2=2

.............

Answer:

-0.5

Step-by-step explanation:

σM=σ/√N

=9/√36

=9/6

=3/2=1.5

Z=(x-μ)/σ/√N

=(19.5-24)/9/√36

=-4.5/1.5=-3

The probability that the sample mean will be larger than 19.5 = -0.5

P(>19.5)=P(Z>-3)= -0.5

Answer:

201 miles

Step-by-step explanation:

Base fee =  $15.95

Mileage fee = $ 0.95  per/mile

Paid = $206.90

Distance= ?

--------------

Equation to calculate miles:

Answer: Choice C.  an = 8 + 9(n-1)

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

Work Shown:

a1 = 8 is the first term

a7 = 62 is the seventh term

an = a1+d(n-1) = nth term of arithmetic sequence

a7 = a1+d(7-1) ... plug in n = 7; solve for d

62 = 8+d(6)

62 = 6d+8

6d+8 = 62

6d = 62-8

6d = 54

d = 54/6

d = 9 is the common difference

an = a1 + d(n-1)

an = 8 + 9(n-1) is the nth term of this arithmetic sequence

Answer:

Choice C.  an = 8 + 9(n-1)

Step-by-step explanation:

I just took the test

Answer:

x = 4/3

Step-by-step explanation:

Direct variation:

y = kx

We use the given x-y point to find k.

6 = k * 2/3

k = 6 * 3/2

k = 9

The equation is

y = 9x

For y = 12,

12 = 9x

x = 12/9

x = 4/3

Answer:

Margin of Error = ME =± 5.2592

Step-by-step explanation:

In the given question n= 20 < 30

Then according to the central limit theorem z test will be applied in which the standard error will be  σ/√n.

Sample Mean = μ = 64

Standard Deviation= S= σ = 12

Confidence Interval = 95 %

α= 0.05

Critical Value for two tailed test for ∝= 0.05 = ±1.96

Margin of Error = ME = Standard Error *Critical Value

ME = 12/√20( ±1.96)=

ME    = 2.6833*( ±1.96)= ± 5.2592

The standard error for this test is σ/√n

=12/√20

=2.6833