The difference between seven times a number and 9 is equal to three times the sum of the number and 2. Find the number
If x represents the number, which equation is correct for solving this problem?

The difference between seven times a number and 9 is equal to three times the sum of the number and 2. Find the number
If x represents the number, which equation is correct for solving this problem?​

Answer:

[tex]a^9 + b^ 5 + c^{13}[/tex]

Step-by-step explanation:

[tex](a^5 \times a^4)+(b^2 \times b^3) + (c^7 \times c^6)[/tex]

When bases are same and it is multiplication, then add the exponents.

[tex](a^{5+4})+(b^{2+3})+(c^{7+6})[/tex]

[tex](a^9)+(b^ 5) + (c^{13})[/tex]

Apply rule : [tex](a^b)=a^b[/tex]

[tex]a^9 + b^ 5 + c^{13}[/tex]

Answer:

[tex]a^9+b^5-c^{13[/tex]

Step-by-step explanation:

[tex](a^5*a^4) + (b^2*b^3)-(c^7*c^6)[/tex]

When bases are same, powers are to be added.

=> [tex](a^{5+4})+(b^{2+3})-(c^{7+6})[/tex]

=> [tex]a^9+b^5-c^{13[/tex]

Answer:

Step-by-step explanation:

3(−2a - 4)+3a

=-6a - 12 +3a

A: -6a - 12 +3a

[tex]hope \: this \: helps[/tex]

Answer:

the answer is A

Step-by-step explanation:

you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a

Answer:

Jason is 24 years old

Step-by-step explanation:

Lets say that Jason's age is X, and his brother's age is Y.

We know that X + Y = 55.

We also know that (X + 7) = Y.

This means (X + 7) + Y = 62 (We got the 62 by adding 55 and 7)

Anyway if X+7= Y, and X+7 + Y = 62, then X+7 = 62/2, right?

We divide the 62 by 2 and we get 31.

Alright, so X+7 = 31.

substract both sides by 7.

We get X = 24

Sorry if this seemed longer or more complicated than it should've been, I don't know how to explain it better.

The graph shows f(x) to have a y intercept at -1, which is where the diagonal line crosses the y axis. We want the y intercept to move to 3. So we must add 4 to the old y intercept to get the new y intercept.

We do this with every single point on f(x) to get g(x) = f(x)+4. This shifts the graph up 4 units.

Answer:

Option (D)

Step-by-step explanation:

Zero of any function is defined by the x-value of the function when y = 0.

Let the equation of the line given in the graph is,

y = mx + b

where m = slope of the line

b = y-intercept of the line

Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the formula,

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

If the passes through (0, -3) and (-2, 0)

m = [tex]\frac{-3-0}{0+2}[/tex]

m = [tex]-\frac{3}{2}[/tex]

Fro the graph,

y-intercept 'b' = -3

Therefore, equation of the line is,

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

For y = 0,

[tex]0=-\frac{3}{2}x-3[/tex]

[tex]\frac{3}{2}x=-3[/tex]

x = -2

Therefore, option (D) will be the answer.

Answer:

d- -2

Step-by-step explanation:

Answer:

b. the approx time it takes an investment to double in value

Answer:

T(n) = 5n + 20

Step-by-step explanation:

1 candy has a mass of 5 g.

n candies have a mass of 5n grams.

The box has a mass of 20 grams.

total mass = mass of candies + mass of box

T(n) = 5n + 20

n         T(n)

0           20

25         145

50         270

75          395

100        520

Answer:

multiplying the equation A

Step-by-step explanation:

3c=d-8 ####### *4

+ c=4d + 8

After that you will get the value of c and d.

Answer:

Multiply equation A by -4

Step-by-step explanation:

3c = d - 8

c = 4d + 8

Multiply equation A by -4.

-12c = -4d + 32

c = 4d + 8

Add the equations.

-11c = 40

Variable d is eliminated.

Answer:

29.4 degrees

Step-by-step explanation:

i divided sin by 55 degrees

Hey there! I'm happy to help!

The words at most means that there is a maximum point that is included as a probability. This means that we will use the less than or equal sign (≤) in our inequality.

Let's write this all out as an inequality now. We will use i to represent how much the baby ate.

1,800≤2i+250  

This inequality shows that Alexandria's 1,800 calories is at most 250 more than twice those of her baby sister. Therefore, the correct option is A. 1,800≤250+2i .

Have a wonderful day!

Answer:

The correct option is A. 1,800≤250+2i.

Answer:

The answer is below

Step-by-step explanation:

Given that mean (μ) of 32.9 seconds and a standard deviation (σ) of 6.4 seconds.

The z score is used to measure by how many standard deviation the raw score is above or below the mean. It is given by:

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

a) For x < 33.2 seconds

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{33.2-32.9}{6.4} =0.05[/tex]

From the normal distribution table, the probability that a randomly chosen student completes the activity in less than 33.2 seconds = P(x < 33.2) = P(z < 0.05) = 0.5199 = 51.99%

b) For x > 46.6 seconds

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{46.6-32.9}{6.4} =2.14[/tex]

From the normal distribution table,  the probability that a randomly chosen student completes the activity in more than 46.6 seconds = P(x > 46.6) = P(z > 2.14) = 1 - P(z < 2.14) = 1 - 0.9927 = 0.0073 = 0.73%

c) For x = 35.5 seconds

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{35.5-32.9}{6.4} =0.41[/tex]

For x = 42.8 seconds

[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{42.8-32.9}{6.4} =1.55[/tex]

From the normal distribution table, the proportion of students take between 35.5 and 42.8 seconds to complete the activity = P(35.5 < x < 42.8) = P(0.41< z< 1.55) = P(z < 1.55) - P(z < 0.41) = 0.9332 - 0.6591 = 0.2741 = 27.41%

d) A probability of 75% = 0.75 corresponds to a z score of 0.68

[tex]z=\frac{x-\mu}{\sigma}\\\\0.68=\frac{x-32.9}{6.4} \\\\x-32.9=4.4\\x=4.4+32.9\\x=37.3[/tex]

75% of all students finish the activity in less than 37.3 seconds

Answer:

a=6

b=5.5

Step-by-step explanation:

not very sure but..

since 8X2=16,

a=3X2

b=11/2

Answer:

D. x^2 - 6x + 7.

Step-by-step explanation:

The roots are 3 plus or minus sqrt(2). That means the equation is...

(x - [3 + sqrt(2)]) * (x - [3 - sqrt(2)])

= [x - 3 - sqrt(2)] * [x - 3 + sqrt(2)]

= x^2 - 3x - xsqrt(2) - 3x + 9 + 3sqrt(2) + xsqrt(2) - 3sqrt(2) - (sqrt(2))^2

= x^2 - 3x - 3x + 9 - 2 - xsqrt(2) + xsqrt(2) + 3sqrt(2) - 3sqrt(2)

= x^2 - 6x + 7.

Hope this helps!

Answer:

g(x)

Step-by-step explanation:

The vertex of g(x) as shwon in the graph is located in the point wich coordinates are (3.5,6.25) approximatively

We need to khow the coordinates of f(x) vertex

f(x) = -x² + 4x -5

let a be the leading factor, b the factor of x and c the constant:

The coordinates of a vertex are: ([tex]\frac{-b}{2a}[/tex] , f([tex]\frac{-b}{2a}[/tex]) )

-b/2a = -4/ (-1*2) = 4/2 = 2

f(2)= -2²+4*2-4 = -4+4-4 = -4

obviosly f(x) has a minimum wich less than g(x)'s maximum

Answer:

Step-by-step explanation:

g(x) i think

Answer: The answer is two

Step-by-step explanation: If you look for opposites of a number its either negative or positive. So when the answer is negative, the opposite is positive and if the answer is positive, the opposite is negative.

Answer:

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

Step-by-step explanation:

The opposite of a number is the number that is the same distance from 0 on the number line.

-2 opposite is 2.

Answer:

Step-by-step explanation:

Let x represent the number of pounds of chocolate in the mix. Then the total price of 10 pounds of mix is ...

  10x +5(10 -x) = 80

  5x +50 = 80

  5x = 30

  x = 6 . . . . . . . . pounds of chocolate

  10 -x = 4 . . . . . pounds of jelly candy

6 pounds of chocolate and 4 pounds of jelly should be used to make the mixture.

Answer:

Option d: The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

The data are continuous if they can take on any value within a range. In this case study, there are different elephants including small/young ones and big ones/old ones.

Thus, their heights will vary and can take on any value within a particular range.

Answer: 9.0876544e+58

Step-by-step explanation:

Answer:

90876543579645968765443223456789009876543212345678909876544

Step-by-step explanation:

90876543579645968765443223456789009876543212345678909876543

+

1

=

90876543579645968765443223456789009876543212345678909876544

Answer:

y + 2 = (-1/2)(x - 4)

Step-by-step explanation:

Let's move from (2, -1) to (4, -2) and measure the changes in x and y.  x increases by 2 units from 2 to 4, and y decreases by 1 unit from -1 to -2.  Thus, the slope of the line connecting the two points is m = rise / run =

-1

--- = (-1/2).

2

Using the point-slope formula, we get:

y + 2 = (-1/2)(x - 4)

Answer:

5:1

Step-by-step explanation:

20/4= 5

1*5 = 5

5:1 ratio

Hope this helps!

Answer:

55%

Step-by-step explanation:

Because 11/20= 0.55

0.55=55%

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial  probability distribution because:

A binomial distribution is a probability of a success or failures outcomes in an  repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

b = binomial probability  also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

[tex]C_{n,x}[/tex] is calculated as:

[tex]C_{n,x}[/tex] = n! / x!(n – x)!

        = 10!  / 10!(10-10)!

        = 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

           = C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

           =  1 * 0.0282 * (0.3) ⁰

           = 1 * 0.0282 * 1

  P(X=x)        = 0.0282

Answer:

The null hypothesis is ;

H0 ≥ 12

While the alternative hypothesis H1 is ;

H1 < 12

Step-by-step explanation:

Here, we want to correctly identify the null hypothesis H0 and the alternative hypothesis H1

The null hypothesis is as follows ;

H0 ≥ 12

While the alternative hypothesis H1 is ;

H1 < 12

Answer:

[tex]\dfrac{15}{16}[/tex]

Step-by-step explanation:

When a six sided die is rolled, the possible outcomes can be:

{1, 2, 3, 4, 5, 6}

Even numbers are {2, 4, 6}

Odd Numbers are {1, 3, 5}

Probability of even numbers:

[tex]\dfrac{\text{Favorable cases}}{\text{Total cases }} = \dfrac{3}{6} = \dfrac{1}{2}[/tex]

This is binomial distribution.

where probability of even numbers,  [tex]p =\frac{1}{2}[/tex]

Probability of not getting even numbers (Getting odd numbers) [tex]q =\frac{1}{2}[/tex]

Probability of getting r successes out of n trials:

[tex]P(r) = _nC_r\times p^r q^{n-r}[/tex]

Probability of getting even numbers at most 5 times out of 7 is given as:

P(0) + P(1) +P(2) + P(3) +P(4) + P(5)

[tex]\Rightarrow _7C_0\times \frac{1}{2}^0 \frac{1}{2}^{7}+_7C_1\times \frac{1}{2}^1 \frac{1}{2}^{6}+_7C_2\times \frac{1}{2}^2 \frac{1}{2}^{5}+_7C_3\times \frac{1}{2}^3 \frac{1}{2}^{4}+_7C_4\times \frac{1}{2}^4 \frac{1}{2}^{3}+_7C_5\times \frac{1}{2}^5 \frac{1}{2}^{2}[/tex]

[tex]\Rightarrow (\dfrac{1}{2})^7 (_7C_0+_7C_1+_7C_2+_7C_3+_7C_4+_7C_5)\\[/tex]

[tex]\Rightarrow (\dfrac{1}{2})^7 (1+7+\dfrac{7 \times 6}{2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6}{2})\\\Rightarrow \dfrac{120}{128} \\\Rightarrow \dfrac{15}{16}[/tex]

Answer:

Step-by-step explanation:

Volume of a cylinder = πr²h

where r is the radius

h is the height

The height of a right cylinder is 3 times the radius of the base is written as

h = 3r

Volume = 249cubic units

So we have

249 = π r²(3r)

249 = π3r³

Divide both sides by 3π

r³ = 249/3π

r = 2

h = 3(2)

h = 6 units

Hope this helps you

Answer:

2n + 10.

Step-by-step explanation:

2(n + 5)

= 2 * n + 2 * 5

= 2n + 10.

Hope this helps!

Answer: 2n + 10

Explanation: In this problem, the 2 "distributes" through the parenthses which means that it multiplies by each of the terms inside.

So we have 2(n) + 2(5) which simplifies to 2n + 10.

Answer:

170.67

Step-by-step explanation:

Answer:

171

Step-by-step explanation:

Modeling the situation

If we fill the pyramid mold 2\text{ cm}2 cm2, start text, space, c, m, end text from the top, we have a smaller pyramid that's similar to the original pyramid.

Since the pyramids are similar, we can set up a proportional equation to find the side lengths and height of the smaller pyramid, and then find its volume.

Hint #22 / 4

Base and height of smaller pyramid

The height of the smaller pyramid is 10-2=8\text{ cm}10−2=8 cm10, minus, 2, equals, 8, start text, space, c, m, end text.

We can solve for the length \blueE{\ell}ℓstart color #0c7f99, ell, end color #0c7f99 in the smaller pyramid using a proportional equation.

\begin{aligned} \dfrac{\blueE{\ell}}{10} &= \dfrac{8}{10} \\\\ \blueE{\ell} &= \blueE{8} \end{aligned}  

10

ℓ

​  

ℓ

​  

=  

10

8

​  

=8

​  

Hint #33 / 4

Volume of smaller pyramid

\begin{aligned} \text{volume}_{\text{pyramid}} &= \dfrac13(\text{base area})(\text{height}) \\\\ &= \dfrac13 \cdot (\blueE{\ell})^2\cdot (\text{height}) \\\\ &= \dfrac13 \cdot \blueE{8}^2\cdot(8)\\\\ &= \dfrac{512}{3}=170.\overline{6}\\\\ &\approx \purpleD{170.67} \end{aligned}  

volume  

pyramid

​  

​  

=  

3

1

​  

(base area)(height)

=  

3

1

​  

⋅(ℓ)  

2

⋅(height)

=  

3

1

​  

⋅8  

2

⋅(8)

=  

3

512

​  

=170.  

6

≈170.67

​  

Hint #44 / 4

To the nearest cubic centimeter, the volume of the smaller pyramid is about 171\text{ cm}^3171 cm  

3

171, start text, space, c, m, end text, cubed.

The true statement about the given transformation is; B: It is a dilation because the transformation is not isometric.

An isometric transformation is a shape-preserving transformation in the plane or in space. They include reflection, rotation and translation.

Now, from the given attachment showing the two figures, we can see that there is a dilation which means that it can't be isometric as the definition of Isometric transformation does not include Dilation.

Read more about Transformation at; https://brainly.com/question/4289712

#SPJ5

Answer:

b

Step-by-step explanation:

just took the test

Answer:

90º

Step-by-step explanation:

just look at where 31º on the right lines up with the value on the left (aka around 90º)

Answer:

87.8 °F ≈ 90°F

Step-by-step explanation:

[tex]x \ degrees \ F = 31 \ degree \ Celsius *\frac{9}{5} + 32\\x \ degrees \ F = 55.8 + 32\\\\x \ degrees \ Fahrenheit = 87.8 \ degrees \ Farenheit[/tex]