Simplify the expression. Write the answer using scientific notation.
(5x107)(6x104)
A) 1.1 x 1012
B) 3.0x 1029
C) 3.0 x 1012
D) 1.1 x 1029

Answer:

C) 100 cm²

Step-by-step explanation:

(14*6)/2*10

20/2*10

10*10

100

The area of the given shaded part of the rectangle is 100 square meters as shown.

The entire space filled by a triangle's three sides in a two-dimensional plane is defined as its area.

The fundamental formula for calculating the area of a triangle is A = 1/2 b h.

The area of the shaded part = area of the rectangle -  area of the triangle

The area of the shaded part = 14 × 10 - (1/2) × 8 × 10

The area of the shaded part = 140 - 80/2

The area of the shaded part = 140 - 40

Apply the subtraction operation, and we get

The area of the shaded part = 100 meters²

Thus, the area of the given shaded part of the rectangle is 100 square meters.

Learn more about the triangles here:

https://brainly.com/question/17997149

#SPJ3

One way to write this polar coordinate is to say (2.5, pi/2) meaning we move 2.5 units away from the origin toward the pi/2 direction

pi/2 radians = 90 degrees

An alternative is to write (-2.5, 3pi/2) which is where we aim at the 3pi/2 direction (270 degrees) and walk backward while still facing directly south, and we'll arrive at the same location.

Answer:

The correct option is B.

Step-by-step explanation:

The hypothesis to determine whether the vending machines are properly dispensing 12 ounces of coffee is:

H₀: [tex]\mu_{A}=\mu_{B}=\mu_{C}[/tex]

Hₐ: Not all means are equal.

The ANOVA output is as follows:

One-way ANOVA: Machine A, Machine B, Machine C

Source           DF              SS                MS              F              P

Factor              2            8.363           4.182         31.73       0.000

Error               15             1.977            0.132

Total               17           10.340

The significance level is α = 0.05.

The p-value of the model is:

p-value = 0.000

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.000 < α = 0.05

The null hypothesis will be rejected.

Conclusion:

There is a significant difference between the means.

Thus, the correct option is B.

Answer: A. $16.13

Step-by-step explanation:

Total students = 82+74+96+99 =351

Sum of earnings of 82 seniors  = $26.75  x 82= $2193.5

Sum of earnings of 74 juniors  = $12.25 x 74 = $906.5

Sum of earnings of 96 sophomores  = $15.50  x 96 = $1488

Sum of earnings of 99 freshmen  =  $10.85 x 99 = $1074.15

Total earnings =  $2193.5  + $906.5+  $1488 +$1074.15

= $5662.15

(Total earnings) ÷ (Total students )

= $5662.15÷ 351

= $16.13

Answer:

The measure of each side of the cube is

Step-by-step explanation:

Since it's a cube all it's sides are equal

To find the length of each side we use the formula

Volume of a cube = l³

where l is the measure of one side

From the question

Volume = 3375 cubic inches

Substitute this value into the formula and solve for l

That's

Find the cube root of both sides

That's

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Area of a square is expressed as A = L² where L is the length of one side of the square.

The rate of change of area will be expressed  using chain rule as;

dA/dt = dA/dL * dL/dt where;

dL/dt is the rate at which the side length of the square is decreasing.

Given L = 7cm, dL/dt = 8cm/sec and dA/dL = 2L

dA/dL = 2(7)

dA/dL = 14cm

Substituting the given value into the chain rule expression above to get the rate of change of the area of the square, we will have;

dA/dt = dA/dL * dL/dt

dA/dt = 14cm * 8cm/sec

dA/dt = 112cm²/sec

Hence, the rate of change of the area of the square when the side length is 7 cm is 112cm²/sec

Answer:

False.

Step-by-step explanation:

In a data where two variables are observed simultaneously, such data is termed to be Bivariate Data. When this data are represented graphically, such a diagrammatic representation is called scatter diagram. In a scatter diagram, all the points lie on or near one particular line. This line is called the regression line.

Recall that the equation for a straight line in the gradient intercept form is y = ax+b .

As an approximation , one can fit the regression line by first computing x and y. The regression line should pass through (x,y) in such a way that the remaining scatter points are evenly distributed on both sides of the line. Therefore, Simple linear regression methods can be used for studying relationship among maximum five variables is a false statement.

Answer:

Step-by-step explanation:

xy = 2y + xy = 0

Hence, 2y + xy = 0 ---------(1)

Differentiating equation (1) n times by Leibnitz theorem, gives:

2y(n) + xy(n) + ny(n - 1) = 0

Let x = 0: 2y(n) + ny(n - 1) = 0

2y(n) = -ny(n - 1)

∴ y(n) = -ny(n - 1)/2 for n ≥ 1

For n = 1: y = 0

For n = 2: y(1) = -y

For n = 3: -3y(2)/2

For n = 4: -2y(3)

Answer:

The  confidence interval is  [tex]0.304 < p < 0.324[/tex]

Step-by-step explanation:

From the question we are told

      The sample proportion [tex]\r p = 0.314[/tex]

      The margin of error  is [tex]E = 0.01[/tex]

The confidence interval for  p is mathematically represented as

       [tex]\r p - E < p < \r p + E[/tex]

=>    [tex]0.314 - 0.01 < p < 0.314 + 0.01[/tex]

=>   [tex]0.304 < p < 0.324[/tex]

Answer:

7x^2 -5x-2

Step-by-step explanation:

(7x+2)(x−1)

FOIL

first 7x*x = 7x^2

outer 7x*-1 = -7x

inner 2x

last 2*-1 = -2

Add them together

7x^2 -7x+2x -2

7x^2 -5x-2

Answer:

[tex] \boxed{\red{7 {x}^{2} - 5x - 2}}[/tex]

Answer C is correct

Step-by-step explanation:

[tex](7x + 2)(x - 1) \\ 7x(x - 1) + 2(x -1 ) \\ 7 {x}^{2} - 7x + 2x - 2 \\ = 7 {x}^{2} - 5x - 2[/tex]

Answer:

3x - 4

Step-by-step explanation:

As Tina's age is 3 into x ( 3 x x= 3x)but 4years less (-4)

Therefore Tina's age is 3x - 4

Answer:

3x - 4

Step-by-step explanation:

Use these representations:  niece's age: x

We triple x and then subract 4 years from the result, obtaining:

Tina's age:  3x - 4

Answer: First a horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.

Step-by-step explanation:

Let's construct g(x) in baby steps.

Ok, we start with f(x) = x^2

The first thing we have is a horizontal translation of A units (where A is not known)

A vertical translation of N units to the right, is written as:

g(x) = f(x - N)

Then we have:

g(x) = (x - A)^2 = x^2 - 2*A*x + A^2

Now, you can see that actually g(x) has a negative leading coefficient, which means that we also have an inversion over the x-axis.

Remember that if we have a point (x, y), a reflection over the x-axis transforms our point into (x, -y)

Then if we apply also a reflection over the x-axis, we have:

g(x) = -f(x - A) = -x^2 + 2*A*x - A^2 = -x^2 + 16*x - 44

Then:

2*A = 16

A*A = 44.

The first equation says that A = 16/2 = 8

But 8^2 is not equal to 44.

Then we need another constant coefficient, which is related to a vertical translation.

If we have a relation y = f(x), a vertical translation of N units up, will be

y = f(x) + N.

Then:

g(x) = -f(x - A) + B

-x^2 + 2*A*x - A^2 + B = x^2 + 16*x - 44

Now we have:

2*A = 16

-A^2 + B = - 44

From the first equation we have A = 8, now we replace it in the second equation and get:

-8^2 + B = -44

B = -44 + 64 = 20

Then we have:

The transformation is:

First an horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.

Answer:

Perimeter = 42 cm

Step-by-step explanation:

A square has all equal sides so you would just add 10.5 + 10.5 + 10.5 + 10.5 to get 42 cm.

Answer:

42 cm

Step-by-step explanation:

Side of square = 10.5 cm (given)

Perimeter of square = Side X 4

                                  = 10.5 X 4

                                  = 42 cm

HOPE THIS HELPED YOU !

:)

Answer:

Lori will pay $12 more if she makes monthly payments

Step-by-step explanation:

to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72

subtracting the amount she would pay as a down payment

$72 - $60 is $12

Lori will pay $12 more if she makes monthly payments

Weight of man and paint = 160 + 5 = 165 total pounds.

Gravitational force is independent of the path taken so we can ignore the radius of the silo.

Work done = total weight x height

The problem says he climbs to the top so overall height is 90 feet

Work = 165 lbs x 90 ft = 14,850 ft-lbs

Answer:

the answer to the question is "C"

Answer:

Step-by-step explanation:

When you add the left side of the equation, you get 33.2 because 70-30 is 40, 40+2 is 42, 42-9 is 33, 33+0.3 is 33.03, 33.3-0.1 is 33.2.

When you add the right side of the equation, you get 33.2, because they are the same problem but on side has brackets.

Hope this helps you.

Answer:

x = - 11

Step-by-step explanation:

Given

5x + 2 = 4x - 9 ( subtract 4x from both sides )

x + 2 = - 9 ( subtract 2 from both sides )

x = - 11

Answer: x = -11

Step-by-step explanation:

Move all terms containing  x  to the left side of the equation.

A mathematical statement that says two expressions have the same value; any number sentence with an  = .

Answer:

Measure number 2 of the tape is for the pinus  

Step-by-step explanation:

To measure, kindly place pinus next to ruler and pinus will be in line with measurement #2

Call and ask for pinus step by step

Answer:

7 and one sixteenths of an inch.

Answer:

Sara studies longer by 15 minutes.

Step-by-step explanation:

Let's calculate how long Sebastian studies for. From 3:15 - 4:15, there is 1 hour and from 4:15 to 4:45, there are 30 minutes so Sebastian studies for 1 hour and 30 minutes. Now, let's calculate how long Sara studies for. From 4:30 - 5:30, there is 1 hour, from 5:30 - 6:00, there are 30 minutes and from 6:00 - 6:15, there are 15 minutes so Sara studies for 1 hour 45 minutes. This means that Sara studies longer by 45 - 30 = 15 minutes.

Answer:

6 1/6 pounds

Step-by-step explanation:

since 2/3 coverted into sixths is 4/6, and 14-6 is 8, and 1/2 into sixths is 3/6, 4/6-3/6 is 1/6. You put the whole in the front and you have 6 1/6

Answer:

0.16

Step-by-step explanation:

See the picture attached for reference.

As you see the best points are the green areas which covers 2 out of 5 zones.

Since it is same for both broken points, the probability of  this is:

Answer is 0.16

Complete Question

The option to the blank space are shown on the first uploaded image

Answer:

Neal's decision is to fail to reject the null hypothesis   (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all  Ledee household is greater than , 854.28 kWh

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 854.11[/tex]

   The sample size is  [tex]n = 65[/tex]

    The sample mean is  [tex]\= x = 879.28 \ kWh[/tex]

    The standard deviation is  [tex]\sigma = 133.29 \ kWh[/tex]

    The level of significance is  [tex]\alpha = 0.05[/tex]

     The  null hypothesis is  [tex]H_o: \mu = 854.11[/tex]

     The  alternative hypothesis is  [tex]H_a : \mu > 854.11[/tex]

     The  t-statistics is  [tex]t = 1.522[/tex]

      The  p-value is [tex]p-value = 0.066[/tex]

Now from the given data we can see that

         [tex]p-value < \alpha[/tex]

Generally when this is the case , we fail to reject the null hypothesis

   So

Neal's decision is to fail to reject the null hypothesis   (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all  Ledee household is greater than , 854.28 kWh            

Answer:

see below

Step-by-step explanation:

n < 2^n

First let n=1

1 < 2^1

1 <2  This is true

Next, assume that

(k) < 2^(k)

as we attempt to prove that

(k+1) < 2^(k+1)

.

.

.

Therefore we can conclude that

k+1 < 2^(k+1)

Answer:

Step-by-step explanation:

Hello, please consider the following.

First, assume that n equals [tex]\boxed{1}[/tex]. Therefore, [tex]\boxed{1<2^1}[/tex] is [tex]\boxed{\text{True}}[/tex]

Next, assume that [tex]\boxed{k<2^k}[/tex], as we attempt to prove [tex]\boxed{k+1<2^{k+1}}[/tex]

Since .... Therefore, we can conclude that [tex]\boxed{k+1<2^{k+1}}[/tex]

The choice for the last box is confusing. Based on your feedback, we can assume that we are still in the step 2 though.

And the last step which is not included in your question is the conclusion where we can say that we prove that for any integer [tex]n\geq 1[/tex], we have [tex]n<2^n[/tex].

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

[tex]\displaystyle y=\frac{1}{2}x-2[/tex]

The point-slope form is represented with the formula:

[tex]y-y_1=m(x-x_1)[/tex]

We are given a point [tex](x_1, y_1)[/tex] and a slope: [tex]\displaystyle \frac{1}{2}[/tex].

We are asked to solve this equation in slope-intercept form, which is:

[tex]y=mx+b[/tex]

Givens

[tex]x_1: 10\\\\y_1: 3\\\\\displaystyle m: \frac{1}{2}[/tex]

To solve:

1. Substitute the givens into the point-slope form equation:

[tex]y-y_1=m(x-x_1)\\\\\displaystyle y-3=\frac{1}{2}(x-10)[/tex]

2. Simplify by using the distributive property, which states:

[tex]a(b+c)=ab+ac[/tex]

[tex]\displaystyle y-3=\frac{1}{2}x-5[/tex]

3. Simplify further by combining like terms:

[tex]\displaystyle y-3+3=\frac{1}{2}x-5+3\\\\\displaystyle y=\frac{1}{2}x-2[/tex]

The final answer in slope-intercept form is:

[tex]\large \boxed{\displaystyle y=\frac{1}{2}x-2}[/tex]

Answer:

y = 1/2x - 2

Step-by-step explanation:

Step 1:

y = mx + b      Slope Intercept Form

Step 2:

y = 1/2x + b          Equation

Step 3:

3 = 1/2 ( 10 ) + b         Input x and y

Step 4:

3 = 5 + b         Multiply

Step 5:

3 - 5 = b      Subtract 5 on both sides

Step 6:

b = - 2

Answer:

y = 1/2x - 2

Hope This Helps :)

Answer:

22,880 yard

Step-by-step explanation:

1 mile - 1760 yard

therefore 13 miles x 1760 yard/mile = 22,880 yard

Answer:

Discarding the influential outlying cases when detected  is also known as flagging outliers in a data set, and this is because outliers do not follow the rest of the dataset's pattern. if this outliers are not discarded they would have a negative effect on any model attached to the dataset

Step-by-step explanation:

In a regression class ; If extremely influential outlying cases are detected in a Data set, discarding this influential outlying cases is the right way to go about it

Discarding the influential outlying cases when detected  is also known as flagging outliers in a data set, and this is because outliers do not follow the rest of the dataset's pattern. if this outliers are not discarded they would have a negative effect on any model attached to the dataset

Answer:

simply convert first feets into miles

Given is 5280 feets=1 miles

63756 /5280=12.075 miles

70 minutes  = 1.16666= 1.17 hrs

rate is 12.075 miles/1.17 hrs

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  lower bound is  [tex]0.0234[/tex]

The  upper bound is  [tex]0.100[/tex]

So from the value obtained the solution to the question are

  1  Does not include

  2 sufficient

 3  not different  

Step-by-step explanation:

From the question we are told that

The  sample size of  individuals who earned in excess of​ $100,000 per​ year is   [tex]n_ 1 = 1205[/tex]

The  number of  individuals who earned in excess of​ $100,000 per​ year  that said yes is

    [tex]w = 712[/tex]

The  sample size  individuals who earned less than​ $100,000 per​ year is [tex]n_2 = 1310[/tex]

The  number of  individuals who earned less than​ $100,000 per​ year that said yes is

       [tex]v= 693[/tex]

The sample proportion of  individuals who earned in excess of​ $100,000 per​ year  that said yes is

           [tex]\r p _ 1 = \frac{w}{n_1 }[/tex]

substituting values

          [tex]\r p _ 1 = \frac{712}{1205}[/tex]

          [tex]\r p _ 1 =0.5909[/tex]

The sample proportion of  individuals who earned less than​ $100,000 per​ year that said yes is

          [tex]\r p _ 1 = \frac{v}{n_2 }[/tex]

substituting values

         [tex]\r p _ 1 = \frac{693 }{1310}[/tex]

        [tex]\r p _ 1 = 0.529[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

           [tex]\alpha = 1 -0.95[/tex]

           [tex]\alpha = 0.05[/tex]

 Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table the value is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

    Generally the margin of error is  

   [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p _1 (1- \r p_1 )}{n_1} + \frac{ \r p _2 (1- \r p_2 )}{n_2} } }[/tex]

substituting values

   [tex]E = 1.96 * \sqrt{ \frac{ 0.5909 (1- 0.5909 )}{1205} + \frac{ 0.592 (1- 0.6592 )}{1310} } }[/tex]

    [tex]E =0.03846[/tex]

Generally the 95% confidence interval is  

        [tex](\r p_1 - \r p_2) - E < p_1 - p_2 <( \r p_1 - \r p_2 ) + E[/tex]

substituting values

        [tex](0.5909 - 0.529 ) - 0.03846 < p_1 - p_2 < (0.5909 - 0.529 ) + 0.03846[/tex]

         [tex]0.02344 < p_1 - p_2 < 0.10036[/tex]

The  lower bound is  [tex]0.0234[/tex]

The  upper bound is  [tex]0.100[/tex]

So from the value obtained the solution to the question are

  1  Does not include

  2 sufficient

 3  not different  

The lower bound is 0.0234 and the upper bound is 0.100. Then the 95% confidence interval is (0.0234, 0.100)

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

The research group asked the following question of individuals who earned in excess of​ $100,000 per year and those who earned less than​ $100,000 per​ year.

The sample size of individuals who earned in excess of $100,000 per year will be

[tex]\rm n_1 =1205[/tex]

The sample size of individuals who earned less than $100,000 per year will be

[tex]\rm n_1 =1205[/tex]

The number of individuals who earn an excess of $100,000 per year that said yes will be

[tex]\rm w = 712[/tex]

The number of individuals who earn less than $100,000 per year that said yes will be

[tex]\rm v= 693[/tex]

Then the sample proportion of individuals who earned in excess of $100,000 per year that said yes will be

[tex]\rm \hat{p}_1=\dfrac{w}{n_1}\\\\\hat{p}_1=\dfrac{712}{1205}\\\\\hat{p}_1= 0.5909[/tex]

Then the sample proportion of individuals who earned less than $100,000 per year that said yes will be

[tex]\rm \hat{p}_2=\dfrac{v}{n_2}\\\\\hat{p}_2=\dfrac{693}{1310}\\\\\hat{p}_2= 0.529[/tex]

The confidence level is 95% then the level of significance is mathematically represented as

[tex]\alpha =1-0.95\\\\\alpha =0.05[/tex]

Then the critical value of α/2 from the normal distribution table. Then the value of z is 1.96, then the error of margin will be

[tex]E = z_{\alpha /2} \times \sqrt{\dfrac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \dfrac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\E = 1.96 \times \sqrt{\dfrac{05909(1-0.5909)}{1205} + \dfrac{0.529(1-0529)}{1310}}\\\\E = 0.03846[/tex]

The 95% confidence interval will be

[tex]\begin{aligned} (\hat{p}_1-\hat{p}_2)-E & < p_1-p_2 < (\hat{p}_1-\hat{p}_2) + E\\\\(0.5909 - 0.529) - 0.03846 & < p_1-p_2 < (0.5909 - 0.529) + 0.03846\\\\0.02344 & < p_1-p_2 < 0.10036 \end{aligned}[/tex]

More about the margin of error link is given below.

https://brainly.com/question/6979326

Answer:

A. 5:4

Step-by-step explanation:

Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.