G(x) = 5x + 3
Find G(2b)

[tex]|\Omega|=2\cdot6\cdot52=624\\|A|=1\cdot3\cdot16=48\\\\P(A)=\dfrac{48}{624}=\dfrac{1}{13}[/tex]

Answer:

1/13

Step-by-step explanation:

Answer:

B) –3x – 6 = 21

Step-by-step explanation:

Well the distributive property is the multiplying of a number by more numbers in parenthesis.

For example  -3(x + 2) by using the distributive property we get,

-3x - 6

Thus,

the answer is B) -3x - 6 = 21 because it shows the aftermath of the distributive property.

Hope this helps :)

When distributive property applies on 3(x + 2) = 21 expression than it changes as 3x + 6 = 21.

Distributive property explains us how to solve expressions in the form of a(b + c).

After apply distributive property this term convert as ab+ac.

The given expression is,

3(x + 2) = 21

To solve the expression, use distributive property,

According to distributive property,

a(b + c) changes in the form of ab+ac.

Solve for the given expression,

3x + 2×3 = 21

3x + 6 = 21

Solve for the value of x,

3x = 21 - 6

3x = 15

x = 5

Hence, option (C) is correct.

To know more about Distributive property on:

https://brainly.com/question/5637942

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Step-by-step explanation:

5) a. x/2 = 7-5

x/2 = 2

x = 2×2

x=4

b.4x - 2 = 3x +7

4x - 3x = 7 + 2

x = 9

c. x+2 = 42 × 3

x+2 = 126

x = 124

d. 13x + 260 = 39

13x = 39 - 260

13x = -221

x = -17

6) a. 6x / 7 = 4 +2

6x = 6 × 7

6x = 42

x = 7

b. -49 = 7x + 7

-49 - 7 = 7x

7x = - 56

x = -8

c. -7 + 7x - 21 = 0

7x - 28 = 0

7x = 28

x = 4

d. 8x - 32 + 2 = 42

8x - 30 = 42

8x = 42 + 30

8x = 72

x = 9

e. 5x + 7 = 18

5x = 11

x = 2.5

Answer:

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]

  = [tex]-\frac{36}{7}[/tex]

y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]

  = [tex]\frac{40}{7}[/tex]

Therefore, coordinates of pint B will be,

[tex](-\frac{36}{7},\frac{40}{7})[/tex]

Answer:

The answer is below

Step-by-step explanation:

Given that mean (μ) = 266 days, standard deviation (σ) = 16 days, sample size (n) = 16 women.

a) The mean of the sampling distribution of Xbar ([tex]\mu_x[/tex]) is given as:

[tex]\mu_x=\mu=266\ days[/tex]

The standard deviation of the sampling distribution of Xbar ([tex]\sigma_x[/tex]) is given as:

[tex]\sigma_x=\frac{\sigma}{\sqrt{n} } =\frac{16}{\sqrt{16} }=4[/tex]

b) The z score is a measure in statistics used to determine by how much the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

For x > 270 days:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{270-266}{\frac{16}{\sqrt{4} } }=1[/tex]

The probability the average pregnancy length exceed 270 days = P(x > 270) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587 = 15.87%

Answer:

R4 ≤ 0.00008

R4 = 0.00001

Step-by-step explanation:

Given: sinh( 0.4 ) ≈ [tex]1 - \frac{(0.4)^2}{2!} + \frac{(0.4)^2}{4!}[/tex]

using Taylor's Theorem

R4 ≤ 0.00008

R4 = 0.00001

attached is the detailed solution

Hey there! I'm happy to help!

If you reflect a point across the x-axis, you have (x,y)⇒(x,-y). If you reflect across the y-axis, you have (x,y)⇒(-x,y). A 180° rotation is the same thing as reflecting across both the x and y axes. This means that the rule for rotating the point with coordinates (x,y) 180° clockwise about the origin is D. (x,y)⇒      (-x,-y).

Have a wonderful day! :D

Answer:  x = ¹/₂ ± √⁸¹

                     ------------

                            2

Step-by-step explanation:

First write out the equation

x² - x - 20

Now we now write the equation by equating to 0

x² - x - 20 = 0

We now move 20 to the other side of the equation. So

x² - x    =  20,

We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes

x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²

x² - ( ¹/₂ )²       = 20 + ¹/₄

( x - ¹/₂ )²       = 20  + ¹/₄, we now resolve the right hand side expression into fraction

( x - ¹/₂ )²          =  ⁸¹/₄ when the LCM is made 4

Taking the square root of both side to remove the square,we now have

x - ¹/₂               =  √⁸¹/₄

x - ¹/₂               =     √⁸¹/₂

Therefore,

                    x = ¹/₂ ± √⁸¹

                          -----------

                               2

Answer:

In this question it is given that:

The cash account of a company had an ending balance of $6750. During the last month, the account was debited for a total of $11,350 and credited for a total of $10,500.

And we have to use the formula

Substituting the values , we will get

Therefore beginning cash balance is

Answer:

The distribution of scores would not have the same mean and standard deviation

Step-by-step explanation:

According to the given data we have the following:

mean=456

Standard deviation=100

mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed

Therefore, we can conclude that a subgroup of these high school seniors would not to be a perfect representation, hence, the distribution of scores would not have the same mean and standard deviation.

Answer:

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Step-by-step explanation:

To express the given product (108 X 125) as a product of prime factors

Step 1: Express each of the numbers as a product of its prime factors.

[tex]108=2^2 \times 3^3\\125=5^3[/tex]

Step 2: Write the product together, and combine any like terms if any

Therefore,

[tex]108 \times 125=2^2 \times 3^3 \times 5^3[/tex]

Answer:

-4.30

Step-by-step explanation:

The computation of the test statistic is shown below:

Data are given in the question

Sample = 55 night students

Sample mean = 2.3

Standard deviation = 0.02

Sample = 50 day students

Sample mean = 2.35

Standard deviation = 0.08

Based on the above information, the test statistic is

[tex]z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma _1^2}{n_1} + {\sqrt{\frac{\sigma _2^2}{n_2}}}}}[/tex]

[tex]z = \frac{2.3 - 2.35}{\sqrt{\frac{(0.02)^2}{55} + {\sqrt{\frac{(0.08)^2}{50}}}}}[/tex]

= -4.30

Hence, the test statistic is -4.30

Answer:

x = 25°

Step-by-step explanation:

From the picture attached,

Since AE║BC and AC is a transverse,

Therefore, ∠EAC ≅ ∠BCA [Alternate interior angles]

m∠EAC = m∠BCA = x°

∠BCD = ∠DCB + ∠DBC [Since ∠BCD is an exterior angle of ΔBDC]

m∠BCD = m∠DCB + m∠DBC

50° = x° + x°

2x = 50

x = 25°

Therefore, value of x is 25°.

Answer: 25 degrees

Step-by-step explanation:

Answer:

The answer is missing.

I think there is something wrong with the equation on its own

Step-by-step explanation:

Equation for the hovercraft

F(x)= X²+6x+2

Olivia catapult equation

F(x)= √2x

Differential of the both equation will give the velocity at x time

F(x)= X²+6x+2

DF(x)/Dx= 2x +6

F(x)= √2x

F(x)= (2x)^½

DF(x)/Dx= (2x)^-½

So the differential is the velocity of the both equation.

Let's equate both equation to find the value of x at which they have same velocity.

(2x)^-½=- 2x+6

(2x)^-1= (-2x+6)²

(2x)^-1= 4x² -24x +36

0= 8x³ - 48x² +72x -1

Answer:

Total amount to be paid back = $29971

Step-by-step explanation:

Formula used to calculate the final amount of the loan to be paid,

Total amount to be paid = [tex]P(1+\frac{r}{n})^{nt}[/tex]

Where P = Principal amount of loan taken

r = rate of interest

n = Number of compounding in a year

t = duration of investment

By substituting the values in the formula,

Total amount to be paid after loan maturity = [tex]18000(1+\frac{0.04}{1})^{13\times 1}[/tex]

= [tex]18000(1.04)^{13}[/tex]

= 18000(1.66507)

= $29971.32

≈ $29971

Total amount to be paid after loan maturity will be $29971.

Answer:

h(6) = 8

Step-by-step explanation:

h(6) is find the value of the function when x=6

What is the y value  ( the value of the blue line) when x=6

Go to x=6 and go up to the blue line

y =8

h(6) = 8

Answer:

At X = 6 , h(X) = 8

plug the value of x

h (6) = 8

please see the attached picture..

Hope this helps...

Good luck on your assignment...

Answer:

x = 50°

Step-by-step explanation:

Step 1.

180° - 80° (because there are 180 degrees in a triangle) = 100°

Step 2.

100° ÷ 2 = 50° (because the two angles on the bottom are identical, as this is an isosceles triangle - which we know because the two sides on the left and right are both the same length, 7 units)

Step 3.

Answer: x = 50°

Answer:

2 11/12

Step-by-step explanation:

3/4 + 2 1/6

Add the fractions.

35/12

= 2 11/12

Answer:

[tex]2\frac{11}{12}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}+2\frac{1}{6}=\\\\\frac{18}{24}+2\frac{4}{24}=\\\\2\frac{22}{24}=\\\\2\frac{11}{12}[/tex]

Answer:

99.5% Confidence interval = (-0.025, 0.547)

= -0.025 < p < 0.547

Step-by-step explanation:

             | A | B | C | Total

Male      | 5 | 4 | 17 | 26

Female | 6 | 2 | 15 | 23

Total     | 11 | 6 | 32 | 49

If p represent the proportion of all female students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.

All female students = 23

Female students that score an A = 6

p = (6/23) = 0.2608695652 = 0.261

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = (6/23) = 0.261

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 99.5% confidence interval for sample size of 23 is obtained from the t-tables since information on the population standard deviation is not known.

we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 23 - 1 = 22.

Significance level for 99.5% confidence interval

(100% - 99.5%)/2 = 0.25% = 0.0025

t (0.0025, 22) = 3.119 (from the t-tables)

Standard error of the mean = σₓ = √[p(1-p)/N]

p = 0.261

N = sample size = 23

σₓ = √(0.261×0.739/23) = 0.091575

99.5% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.261 ± (3.119 × 0.091575)

CI = 0.261 ± 0.2856

99.5% CI = (-0.0246, 0.5466)

99.5% Confidence interval = (-0.025, 0.547)

= -0.025 < p < 0.547

Hope this Helps!!!

Answer:

XY ≈ 14.87 units

Step-by-step explanation:

Calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = X(- 6, 3) and (x₂, y₂ ) = Y(8, - 2)

d = [tex]\sqrt{(8+6)^2+(-2-3)^2}[/tex]

   = [tex]\sqrt{14^2+(-5)^2}[/tex]

   = [tex]\sqrt{196+25}[/tex]

   = [tex]\sqrt{221}[/tex]

   ≈ 14.87 ( to 2 dec. places )

Answer:

15

Step-by-step explanation:

4! +3! /2

4!=4*3*2*1=24

3!=3*2*1=6

24+6/2=30/2=15

Correct Question:

5 (u + 1) - 7  = 3 (u - 1) + 2u.

Solve for u

Answer:

See explanation below

Step-by-step explanation:

In this given question, we are required to find u.

Given the equation:

5 (u + 1) - 7 = 3 (u - 1) + 2u​

Required:

Solve for u

To find u, first simplify both sides individually.

Simply 5 (u + 1) - 7:

Expand the parenthesis:

5u + 5 - 7

Collect like terms:

5u - 2

Simplify 3 (u - 1) + 2u​:

Expand the parenthesis:

3u - 3 + 2u

Collect like terms:

3u + 2u - 3

5u - 3

Bring both simplified equations together:

5u - 2 = 5u - 3

5u - 5u - 2 = -3

-2 = -3

Since -2 ≠ -3, there is no solution.

Therefore, we can say the equation is invalid.

[tex]\dfrac{3}{x^3y} +\dfrac{7}{xy^4}\\\\\\\dfrac{1}{xy}(\dfrac{3}{x^2} +\dfrac{7}{y^3})[/tex]

It's xy.

Answer:

6y +2x +7

Step-by-step explanation:

10 + 6y + 2x - 3​

The only like terms are the constant

6y+2x +10-3

6y +2x +7

Answer:

2x + 6y + 7.

Step-by-step explanation:

10 + 6y + 2x - 3

= 2x + 6y - 3 + 10

= 2x + 6y + 7.

Hope this helps!

Answer:

0.8390

Step-by-step explanation:

From the question,

Z score = (Value-mean)/standard deviation

Z score = (150.2-160.5)/10.4

Z score = -0.9904.

P(x>Z) = 1- P(x<Z)

From the Z table,

P(x<Z) = 0.16099

Therefore,

P(x>Z) = 1-0.16099

P(x>Z) = 0.8390

Hence the probability that a person weighs more than 150.2 pounds = 0.8390

Answer:

[tex]f(x)=((x-9)^2+16)x^2[/tex]

[tex]f(x)=x^4-18x^3+97x^2[/tex]

Step-by-step explanation:

If you want to, I could add the explanation as well. Just notify me.

Something really important I want to note is that since 9-4i is a zero, then 9+4i must must also be a zero.

Answer:

15

Step-by-step explanation:

Answer: [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.

We assume that repetition is not allowed

Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex]  [By permuattaions]

[tex]=\dfrac{4\times3\times2}{2}=12[/tex]

Favourable outcome = First green then red  (only one way)

So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{12}[/tex]

hence, the required probability =[tex]\dfrac{1}{12}[/tex]

Answer:

18+18 as point XYZ is in centroid of Q

Step-by-step explanation:

so it's equal.

36.which is option A.

Answer:

the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.

Step-by-step explanation:

Given that :

The mean value [tex]\mu[/tex] = 12

The standard deviation [tex]\sigma[/tex] = 3.5

Let Consider Q to be the weight of the parcel that is normally distributed .

Then;

Q [tex]\sim[/tex] Norm(12,3.5)

The objective is to determine thewight  value of c under which there is a surcharge

Also, let's not that 99% of all the parcels are below the surcharge

However ;

From the Percentiles table of Standard Normal Distribution;

At 99th percentile; the value for Z = 2.33

The formula for the Z-score is:

[tex]Z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]2.33 = \dfrac{X - 12}{3.5}[/tex]

2.33 × 3.5 = X - 12

8.155 = X - 12

- X = - 12 - 8.155

- X = -20.155

 X = 20.155

the weight  value of c under which there is a surcharge = X + 1 (0) since all the  pounds are below the surcharge

c = 20.155 + 1(0)

c = 20.155

Thus ; the value of c is  20.155 such that 99% of all parcels are under the surcharge weight.