Perform the following operation
and express the answer in
scientific notation.
4.0x105 x 3.0x103
[ ? ]x10!?)

Answer:

(x + 6)(x + 13)

Step-by-step explanation:

Given

x² + 19x + 78

Consider the factors of the constant term (+ 78) whuch sum to give the coefficient of the x- term (+ 19)

The factors are + 6 and + 13 , since

6 ×13 = + 78 and 6 + 13 = + 19 , then

x² + 19x + 78 = (x + 6)(x + 13) ← in factored form

[tex]\bold{ x^2+19x+78 }[/tex]

[tex]\bold{ x^2+13x+6x+78 }[/tex]

[tex]\bold{ x(x+13)+6(x+13) }[/tex]

[tex]\bold{(x+6)(x+13) }[/tex]

Complete Question

In order to test the null hypothesis of equal means (alternative hypothesis says they are unequal), two simple random samples are obtained.In sample 1, the mean and standard deviation are 10 and 6 respectively.In sample 2, the mean and standard deviation are 16 and 4 respectively.Each sample is of size 6.The data are normally distributed.The true standard deviations of the two populations may be assumed to be equal.What can you say about the P-value for the test of equal means? -->

It must be that the resulting P-value must be

A) Greater than 0.2

B) Between 0.19 and 0.10

C) Between 0.09 and .05

D) Between .049 and .02

E) Less than 0.02

Answer:

The correct option is B

Step-by-step explanation:

From the question we are told that

   The mean of sample 1 is  [tex]\= x_1 = 10[/tex]

   The standard deviation is  [tex]s_1 = 6[/tex]

   The mean of sample two is  [tex]\= x_2 = 16[/tex]

   The standard deviation is  [tex]s_2= 4[/tex]

   The sample size for both samples is  [tex]n_1 = n_2 = n = 6[/tex]

  The null hypothesis is  [tex]H_o : \mu_1 = \mu_2[/tex]

  The alternative hypothesis is  [tex]H_a : \mu_1 \ne \mu_2[/tex]

Generally the test statistics is mathematically represented as

          [tex]z = \frac{ \= x_1 - \= x_2 }{ \sqrt{ \frac{s^2_1}{n_1} +\frac{s^2_1}{n_2} } }[/tex]

=>       [tex]z = \frac{ 10 - 16 }{ \sqrt{ \frac{6^2}{6} +\frac{4^2}{6} } }[/tex]

=>       [tex]z = -1.3646[/tex]

From the z table  the area under the normal curve to the left corresponding to  -1.3646   is

    [tex]P(Z < -1.3646) = 0.086189[/tex]

Generally the p-value is mathematically represented as

     [tex]p-value = 2 P(Z < -1.3646)[/tex]

=>  [tex]p-value = 0.086189 * 2[/tex]

=>  [tex]p-value = 0.1724[/tex]

So the p-value is  Between 0.19 and 0.10

Answer:

the amount of calories depends on the minutes of exercise so c is the dependent variable and m is the independent variable

Proportional equations are of the form y = kx, for some fixed constant k. The k value is the constant of proportionality.

The +100 at the end is why we don't have a proportional equation.

Visually all proportional equations go through the origin, meaning the lines have y intercept of 0. For y = 230x+100, the y intercept is 100.

Answer:

Second one.................

Answer:

NICEE

Step-by-step explanation:

Answer:

We have two 6-sided dice.

Each one of them has 6 possible outcomes.

The total number of outcomes for the pair, will be equal to the product between the numbers of outcomes for each one of them

Then the total number of outcomes is:

C = 6*6 = 36.

The number of outcomes where the sum of the dice are 7 are:

1 and 6

6 and 1

2 and 5

5 and 2

3 and 4

4 and 3

So we have 6 outcomes where the sum of both numbers is equal to 7.

The probability of rolling a pair such that the sum is equal to 7, is equal to the quotient between the number of outcomes that meet this condition (6) and the total number of outcomes (36)

The probability is:

P = 6/36 = 1/6

Now let's do the same for 11.

The outcomes where the sum is 11 are:

5 and 6

6 and 5

So we have two outcomes.

In this case, the probability will be:

P = 2/36 = 1/18

Answer:

x = -2 ; y = -6

Step-by-step explanation:

Let y = 3x be eqn.1

So putting eqn.1 in 5x + 4y = -34 gives ,

[tex]5x + 4y = - 34[/tex]

[tex] = > 5x + 4(3x) = - 34[/tex]

[tex] = > 5x + 12x = - 34[/tex]

[tex] = > 17x = - 34[/tex]

[tex] = > x = \frac{ - 34}{17} = - 2[/tex]

Putting the value of x in eqn.1 gives :-

[tex]y = 3x = 3 \times ( - 2) = - 6[/tex]

Answer:

0.0649350649350649

Step-by-step explanation:

Answer: 0.06493506493

Step-by-step explanation:

Step-by-step explanation:

Angle EGF = 0.5(180° - 50°) = 65°.

Angle CGF = 180° - Angle EGF = 115°.

Answer: y = 0.5x - 4

Step-by-step explanation:

Answer:

y=8

Step-by-step explanation:

In functions, you should know that f(x)=y. In this problem, y is replaced by 4(0.5)^-1. So all you need to do is solve what 4(0.5)^-1 is, which is 8. This means that f(x)=8, but y is also equal to f(x). The answer is then y=8.

Hope you understand and that this helps with your question! :)

Answer:

The answer is 15=15

Step-by-step explanation:

go to math

way, which is a website

and put your question in and the answer waill come to you!

Answer:

y = sqrt x-2

or c on edge

Step-by-step explanation:

Answer:

2hours/4pages

2/4=1/2

1/2=x/12

cross multiply

12=2x

divide by 2 both sides

6=x

6 hours

Answer:

the answer is 6

Step-by-step explanation:

Step-by-step explanation:

-3x + 2y = 56

+ (-5x - 2y = 24)

=> -8x = 80, x = -10.

Therefore -3(-10) + 2y = 56, 30 + 2y = 56, y = 13.

Hence x = -10 and y = 13.

Answer:

x = -10 and y = 13.

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

I got x = 0

Step-by-step explanation:

y = (47/2)x Substitute y =0

0 = (47/2) x Multiply both side

0 = x Swap the sides

x = 0

Answer:

Step-by-step explanation:

Determine the number of solutions for each of the equations below. Be sure to

justify your conclusions. *

(z – 8)2 = -1

A. one solution

B. infinitely many solutions

C.no solution

D. x = 9

Given the expression;

(z – 8)^2 = -1

we are to find the nature of the solution;

Take the square root of both sides

(z – 8)^2 = -1

√(z – 8)^2 = √-1

z- 8 = √-1

Note that √-1 will give a complex number i to have;

z = 8 ± i

This therefore shows that the equation has no real solution.

Answer:

AEF

Step-by-step explanation:

NOT B

Answer:

It costs 19 cents or 0.19 dollars per fluid ounce.

Step-by-step explanation:

4.75 divided by 25 is 0.19. 0.19 is 19 cents.

Answer:

19

Step-by-step explanation:

Answer:

y= -9

Step-by-step explanation:

Answer:

y = -9

Step-by-step explanation:

Algebra:

3y + 11 = -16

-11 -11

3y = -27

÷ 3 ÷ 3

y = -9

Answer:

1/3

Step-by-step explanation:

Answer:

Part A. 20.7

Part B. 6.9, 6.9, 6.9

Part C. Slower. 33/5.5= 6. 6 minutes is greater than 5 minutes so Simon  ran slower than 1 mile  every 5 minutes.

Step-by-step explanation:

Answer:

-19.43

Step-by-step explanation:

You got to add 120.75 to 45.82 then you subtract it from 185.90

comment if this helps :)

Answer:

128 deg

Step-by-step explanation:

The sum of the measures of the angles of a polygon of n sides is

(n - 2)180

A trapezium has 4 sides, so the sum of the measures of the angles is

(4 - 2)180 = 2(180) = 360

m<CBE + m<C + m<D + m<DEB = 360

Angles ABC and CBE are a linear pair so the sum of their measures is 180 deg.

m<ABC + m<CBE = 180

115 + m<CBE = 180

m<CBE = 65

m<C = x

m<D = 90

Angles DEB and DEF are a linear pair so the sum of their measures is 180 deg.

m<DEB + m<DEF = 180

m<DEB + m<103 = 180

m<DEB = 77

m<CBE + m<C + m<D + m<DEB = 360

65 + x + 90 + 77 = 360

x + 232 = 360

x = 128

Answer: 128 deg

so we will get a lot of teiangles here.

90°+x+CED=180°

also CED+DEF=180°(half circle, 360/2)

CED+103°=180°

CED=180-103=77°

77°+90°+X/2=180°

x/2=180-167=13°