Solve the equation 7x = 91 for x.

To stay within budget, she must use 3.9 gigabytes.

Giving the following information:

Under her cell phone plan, Sofia pays a flat cost of $54.50 per month and $5 per gigabyte. She wants to keep her bill at $ 74 per month.

First, we need to establish the total cost formula:

Total cost= 54.5 + 5*x

x= number of gigabytes

Now, we isolate x:

74= 54.5 + 5x

19.5/5= x

3.9= x

To stay within budget, she must use 3.9 gigabytes

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Let [tex]\vec K,\vec L,\vec M,\vec N[/tex] be vectors pointing the vertices K, L, M, and N, respectively.

The side KL is parallel to and has the same length as the vector

[tex]\vec L - \vec K = (2\,\vec\imath + 3\,\vec\jmath + 3\,\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = \vec\jmath + 2\,\vec k[/tex]

Similarly, the side KN is parallel and as long as

[tex]\vec N - \vec K = (6\,\vec\imath+8\,\vec\jmath+\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = 4\,\vec\imath+6\,\vec\jmath[/tex]

These vectors have magnitudes

[tex]\|\vec L - \vec K\| = \sqrt{0^2 + 1^2 + 2^2} = \sqrt5[/tex]

[tex]\|\vec N - \vec K\| = \sqrt{4^2 + 6^2 + 0^2} = 2\sqrt{13}[/tex]

and their dot product is

[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = 0\cdot4 + 1\cdot6+1\cdot0 = 6[/tex]

The parallelogram spanned by the vectors [tex]\vec L-\vec K[/tex] and [tex]\vec N-\vec K[/tex] has area equal to the magnitude of their cross product, for which we have the identity

[tex]\bigg\|(\vec L - \vec K) \times (\vec N - \vec K)\bigg\| = \|\vec L - \vec K\| \|\vec N - \vec K\| \sin(\theta) \\\\ \implies \text{area} = 2\sqrt{65} \, \sin(\theta)[/tex]

where [tex]\theta[/tex] is the angle between the sides KL and KN.

From the dot product identity, we have

[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = \|\vec L - \vec K\| \|\vec N - \vec K\| \cos(\theta) \\\\ \implies 6 = 2\sqrt{65} \cos(\theta)[/tex]

Then

[tex]\cos(\theta) = \dfrac3{\sqrt{65}} \implies \sin(\theta) = \sqrt{1-\cos^2(\theta)} = 2\sqrt{\dfrac{14}{65}} \\\\ \implies \text{area} = 2\sqrt{65} \cdot 2\sqrt{\dfrac{14}{65}} = \boxed{4\sqrt{14}}[/tex]

The number of miles covered by the student is; 54.45 miles.

The college student in discuss incurs a total cost of $144.67.

On this note, the cost incurred over the miles covered can be determined as follows;

= $144.67 - $19.95 - $65.32

= $59.4

Hence, since the cost of one mile is $59.4, it follows that the number of miles covered is;

No. of miles = 54.9/0.99

= 54.45 miles.

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Answer:

Divisible rule of 11

If the number of digits of a number is even, then add the first digit and subtract the last digit from the rest of the number

Divisible rule of 5

Divisibility by 5 is easily determined by checking the last digit in the number.  If the last number is either 0 or 5, the entire number is divisible by 5.

First of all, the number 3456 is not divisible by 11 and 5.

But if we change position of digits then the numbers divisible by 11 are-

3564 / 11= 324

3465 / 11= 315

3465 / 5= 693

4356 / 11 = 396

4653 / 11 = 423

5346 / 11 = 486

5643 / 11 = 513

6534 / 11 = 594

6435 / 11 = 585

6435 / 5=1287

But the numbers 3465 and 6435 are also divisible by 5

So the numbers divisible by 11 but not with 5 are:

3564 , 4356, 4653, 5346, 5643 and 6534

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The value of the functions are:

a. g(-4) + f(-2) = 24

b..  f(1) - g(0) = 1

A function can be defined as an expression showing the relationship between two variables.

Given the functions;

g(-4); substitute the value of x as - 4 in g(x)

g(-4) = (-4)² + 1

g(-4) = 16 + 1

g(-4)  = 17

f(-2); substitute the value of x as - 2 in f(x)

f(-2) = 3(-2) - 1

f(-2 = -7

a.  g(-4) + f(-2) = 17 -(-7)

g(-4) + f(-2) = = 24

f(1) = 3(1) - 1

f(1)  = 2

g(0) = (0)² + 1

g(0) = 1

b. f(1) - g(0) = 2 - 1

f(1) - g(0) = 1

Thus, the value of g(-4) + f(-2) and f(1) - g(0)  are 24 and 1 respectively.

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Answer:

Kelsey can buy 9 books.

Step-by-step explanation:

If Kelsey wants to buy as much books as possible with 30$, multiply 3$ by 9 (books) which is 27$.

30$-27$ is 3$ so she will have 3$ extra dollars to use for shipping.        2$ is the price for shipping so she will have an extra dollar.

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Given:

M(-1,-4) is the mid point of points a(-3, -7)

and B

To find:

Coordinates of B

Explanation:

Let (x, y) be the coordinates of B.

Since M is the midpoint of A and B,

M-A IB-EM

YM-YA-YB-YM

Substituting the values,

The x coordinate will be

-1-(-3)=-(-1)

-1+3=x+1

=2-1 x = 1

The y coordinate will beYM YAYB-YM

Substituting the values,

The x coordinate will be

- 1 - (- 3) = x - (- 1) - 1 + 3 = x + 1 x = 2 - 1 x = 1

The y coordinate will be

- 4 - (- 7) = y - (- 4) - 4 + 7 = y + 4 y = - 1

y = 7 - 8

Hence x=1, y = - 1

Final answer:

The coordinates of B are (1,-1)

The ratio of protonated/deprotonated acetic acid at the given pH is:

Therefore, the ratio of protonated/deprotonated acetic acid at the given pH is:

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Answer:

D. None Beacouse triangles are 3-sided not 2-sided.

Step-by-step explanation:

None

Answer:

-2.5w<6.8

-2.5w/-2.5<6.8/-2.5

w>-2.72

Answer:

-13y

Step-by-step explanation:

Since this expression has the same coefficient, all you have to do is solve -6-7. Just follow the keep change change rule when subtracting negative numbers so -6 + -7 = -13. Therefore, your answer will be -13y.

Let me know if you do not understand or need more explanation.

Answer:

so there is a 5% change of or ordering a large cold drink

Step-by-step explanation:

first add the total of all drinks

5+48+22+8+12+5=100

the amount of large drinks that are cold are 5

so there is a 5% change of ordering a large cold drink

Answer: 9.25

Step-by-step explanation: Round each number to the nearest place. For example, 26 would round to 30. Round each number until you get a certain number right before the hundredth place.

Answer:

- p / 2

Step-by-step explanation:

4 / -8 =   - 1/2

p^3 / p^2   = p

- 1/2  * p   =  - p / 2

The equation of the modified graph is y = (x + 6)^2

The equation of the graph is given as

y = x^2

The graph is shifted to the left by 6 units

This is represented as:

(x, y) = (x + 6, y)

So, we have

y = (x + 6)^2

Hence, the equation of the modified graph is y = (x + 6)^2

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Answer: Click on this: a=13.6cm,b=9.5cm and c=2.6cm for the triangle show it has a step by step way

Step-by-step explanation:

The sampling distribution of sample means is a mean of 79 and a standard deviation of 3.

The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.

Given that,

Population mean,  [tex]\bar{x}[/tex] = 79

Population standard deviation, σ = 18

Sample size, n = 36

We have to determine the mean and standard deviation of a sampling distribution of sample means.

Let X denotes a random variable distributed with a mean and standard deviation of 85 and 28 respectively.

Also, if a random sample of size n is drawn from the population, then the sample mean is denoted by [tex]\bar{x}[/tex].

The sampling distribution of sample means [tex]\bar{x}[/tex] is given by:

ц [tex]\bar{x}[/tex] = ц

σ [tex]\bar{x}[/tex]  = σ/√n

Therefore, for the sample size n = 36, the sampling distribution of sample means [tex]\bar{x}[/tex] is obtained as:

ц [tex]\bar{x}[/tex] = 79

σ [tex]\bar{x}[/tex]  = 18/√36 = 3

Hence, the required sampling distribution of sample means is mean of 79 and a standard deviation of 3.

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Yes, The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.

Here,

We have to find the statement,

''The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.'' is true or not.

What is Descriptive statistics?

Descriptive statistics is a means of describing features of a data set by generating summaries about data samples.

Now,

The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.

Because : Descriptive statistics refers to the summary of important aspects of a data set.

Hence, The statement ''The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.'' is true.

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The angle that the vector  [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex]  makes with the y-axis is (B) tan⁻¹ 2/3.

To find the angle of the given vector:

Given: [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex]

So,

[tex]\begin{aligned}&\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}} \\&\overrightarrow{\mathrm{A}} \cdot \hat{\mathrm{j}}=\sqrt{13} \cos \theta \\&3=\sqrt{13} \cos \theta \\&\theta=\cos ^{-1}\left(\frac{3}{\sqrt{13}}\right)\end{aligned}[/tex]

Using the formula [tex]\tan \left(\cos ^{-1} x\right)=\frac{\sqrt{1-x^2}}{x}[/tex], we obtain:

[tex]\begin{aligned}&\theta=\tan ^{-1} \frac{\sqrt{1-\frac{9}{13}}}{\frac{3}{\sqrt{13}}} \\&\theta=\tan ^{-1}\left(\frac{2}{3}\right)\end{aligned}[/tex]

Therefore, the angle that the vector  [tex]\overrightarrow{\mathrm{A}}=22_1^{\mathrm{A}}+3 \hat{\mathrm{j}}[/tex]  makes with the y-axis is (B) tan⁻¹ 2/3.

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The correct question is given below:

The angle that the vector  [tex]\overrightarrow{\mathrm{A}}=2 \hat{i}+3 \hat{\mathrm{j}}[/tex]  makes with the y-axis is:

(A) tan⁻¹ 3/2

(B) tan⁻¹ 2/3

(C) sin⁻¹ 2/3

(D) cos⁻¹ 3/2

The function which represents the jeepney fare in terms of the distance(d) in kilometers is F = 2x ₊ 3.

Given a bus ride costs 11 pesos for first 4 kilometers.

2.00 pesos for each succeeding kilometer.

Function of Fare (F) in terms of distance (d).

Let F represent the total fare and d represent the distance in kilometers.

F = rate of fare × distance

rate = 11 for 4 km, and 2 for each km

rate = 11, if x ≤ 4,

rate = 2, if (x₋4), and x > 4

hence the equation is:

F = 11 pesos, if x ≤ 4,

F = 11 ₊ 2(x₋4), if x > 4

Simplify the above equation.

F = 11 ₊ 2x ₋ 8

F = 2x ₊ 3

Hence we derived the function in terms of distance as F = 2x ₊ 3

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In the given triangle ABC right angled at C and [tex]AC = b[/tex] and [tex]CB = a[/tex], the equation using value of b used for solving for a will be [tex]tan(22.6degrees) = \frac{a}{12}[/tex].

According to the question statement, Triangle A B C is shown. Angle A C B is [tex]90[/tex] degrees and angle C A B is [tex]22.6[/tex] degrees. The length of hypotenuse A B is [tex]13[/tex] centimeters, the length of A C is b, and the length of C B is a.

We are supposed to find the equation using value of b used for solving for a.

Solution: Given,

  [tex]AB = 13cm\\AC = b\\BC = a\\Angle BAC = 22.6degrees[/tex]

If hypotenuse is 13cm then value of b is either 5 or 12 as per Pythagorean Triplet. As there is no value such as 5 in the given options we take the value of [tex]b=12 cm[/tex].

[tex]cos(22.6degrees) = \frac{b}{13} =\frac{12}{13} \\sin(22.6degrees) = \frac{a}{13}\\[/tex]

Using the above two equations,

[tex]tan(22.6degrees)=\frac{a}{b} \\b=12\\tan(22.6degrees)=\frac{a}{12}[/tex]

Therefore option three "tan(22.6o) = StartFraction a Over 12 EndFraction" is the correct answer.

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Answer: C tan (22.6)=a/12

Step-by-step explanation: edge 2023

The scientific results to 5.97 x [tex]10^{24}[/tex] kg is the Earth's mass.

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The base case for which the inductive proof for p(n) is defined, is the smallest value of n for which p(n) is defined.

Mathematical induction refers to a strategy for demonstrating a theorem's correctness by first demonstrating that, if it holds true in one particular situation, it will also hold true in all subsequent cases in the series.

Now,

Hence, the base case for which the inductive proof for p(n) is defined, is the smallest value of n for which p(n) is defined.

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Answer:15,000

Step-by-step explanation: 3500 divided by 7 because there are 7 days in a week= 500 and then 500 times 30 because of the thirty days

Answer:

Given the salary of Ram in 7days is rs.3500

Ram earns in a day = 3500 Divided By 7
                                = rs.500

Ram earns in 30 days = 500 Multiplied by 30
                                   = rs.15,000

All Done!

The range of the function is x∈[(-8 ,16)]

It is required to find the  range.

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

Since f(x) = -2x + 4  is linear, its limit values correspond to the limits imposed by the domain (in this case x∈[(-6 ,6)]

By put the value of x in the given function we get,

f(-6) = -2(-6) + 4

        =12+4

         =16

f(6) = -2*6 + 4

       =-12+4

        =-8

So the range is -8<x<16.

Therefore, the range of the function is x∈[(-8 ,16)]

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Answer: 710

Step-by-step explanation:

260 + 450 = 710

Answer:

We are looking for a new number which is 260 more than 450.

We will get the new number by adding 260 to 450.

We write it down as:

450+260=710

And finally the solution for: What number is 260 more than 450?

is 710

All Done!

Answer:

1 cookie

Step-by-step explanation:

75% = 75/100

75 and 100 are both divisible by 25, therfore the simplified verision is 3/4

[tex]\frac{75}{100} /\frac{25}{25} =\frac{3}{4}[/tex]

in order to get 100% we would need to:

3/4 + num of cookies = 4/4

re-arranged by subtracting 3/4 on bith sides:

num of cookie = 4/4 - 3/4

num of cookie = 1/4

meaning 1/4 of her orders is cookies

______________________________________________________

Five percent is considered a half of 10 percent. So, to find 5% of a number, all you need to do is divide 10 percent of the number by 2.

________________________________________________________

Hope this helps! If so, lmk! Thanks and good luck!

Answer:

Find the rate of change for each set of ordered pairs. What is

the average rate of change of all three sets?

(1, 15), (2, 12)

(-1,14), (3, 10)

(3,11), (5, 15)

Write your answer to the average rate of change as a fraction,

a/b.

Step-by-step explanation: