Use prime factorization to determine the greatest common factor of 180 and 504

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Answer:

Brian is 5, and Sharon is 10

Step-by-step explanation:

CURRENT AGES:

  Let   b = Brian's age

  Let 2b = Sharon's age

5 YEARS FROM NOW:

  b + 5 = Brian's age

  2b + 5 = Sharon's age

  The sum will be 25

  b + 5 + 2b + 5 = 25

  3b + 10 = 25

  3b = 15

   b = 5

So Brian is 5, and Sharon is 10

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

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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

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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The size of the car engine in cubic inches is 263.6 2 cubic inches

The given parameters are

Volume = 4320 cubic centimeters

By general conversion rule, we have

1 cubic centimeter = 0.0610237 cubic inches

Multiply both sides of 1 cubic centimeter = 0.0610237 cubic inches by 4320

4320 * 1 cubic centimeter = 0.0610237 cubic inches * 4320

Evaluate the product

4320 cubic centimeters = 263.6 2cubic inches

Substitute 4320 cubic centimeters = 263.6 2cubic inches  in Volume = 4320 cubic centimeters

Volume = 263.6 2cubic inches

Hence, the size of the car engine in cubic inches is 263.6 2cubic inches

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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:

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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Answer:

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

Step-by-step explanation:

None

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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______________________________________________________

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:

6 ft

Step-by-step explanation:

slope = [tex]\frac{rise}{run}[/tex] ( rise is vertical height and run is horizontal distance )

here vertical height = 3 and slope = [tex]\frac{1}{2}[/tex] , then

[tex]\frac{1}{2}[/tex] = [tex]\frac{3}{run}[/tex] ( cross- multiply )

run = 2 × 3 = 6 ft

Answer:

-2.5w<6.8

-2.5w/-2.5<6.8/-2.5

w>-2.72

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: 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!

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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Answer:

- p / 2

Step-by-step explanation:

4 / -8 =   - 1/2

p^3 / p^2   = p

- 1/2  * p   =  - p / 2

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 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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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 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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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

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

The general solution of the given equation is y² = 8x²Inx + cx².

A first-order linear differential equation is one that has the formula:

[tex]\frac{d y}{d x}+p(x) y=q(x)[/tex]

where p(x) and q(x) are continuous functions of x.

We begin by determining the integrating factor for the first-order linear differential equation.

I.F. = [tex]e^{\int p(x) d x}[/tex]

The solution to the first order linear differential equation is:

[tex]y \cdot e^{\int p(x) d x}=\int q(x) \cdot e^{\int p(x) d x} d x+c .[/tex]

The solution to the first order linear differential equation is:

[tex]\int \frac{1}{x} d x=\ln x+c[/tex]

So, given: [tex]y^{\prime}=\frac{\left(4 x^2+y^2\right)}{(x y)}[/tex]

The above differential equation can be written as:

[tex]\begin{aligned}&\frac{d y}{d x}=4 \frac{x}{y}+\frac{y}{x} \\&\frac{d y}{d x}-\frac{y}{x}=\frac{4 x}{y} \\&y \frac{d y}{d x}-\frac{y^2}{x}=4 x\end{aligned}[/tex]

Substitute, [tex]y^2=t, 2 y \frac{d y}{d x}=\frac{d t}{d x}[/tex].

[tex]\begin{aligned}&\frac{1}{2} \frac{d t}{d x}-\frac{t}{x}=4 x \\&\frac{d t}{d x}-\frac{2 t}{x}=8 x\end{aligned}[/tex]

Because this is a first-order linear differential equation, we must first determine the integrating factor:

[tex]\text { I. F. }=e^{-2 \int \frac{1}{x} d x}=e^{-2 \ln x}\\\text { I.F. } F=\frac{1}{x^2}[/tex]

As a result, the following is the general solution to the given IVP:

[tex]$$t \cdot(I . F .)=\int(I . F .) \cdot 8 x d x+c$$$t \cdot\left(\frac{1}{x^2}\right)=\int\left(\frac{1}{x^2}\right) \cdot 8 x d x+c$$t \cdot\left(\frac{1}{x^2}\right)=8 \int \frac{1}{x} d x+c$$t \cdot\left(\frac{1}{x^2}\right)=8 \ln x+c$$t=8 x^2 \ln x+c x^2$[/tex]

By reversing the value of t:

[tex]y^2=8 x^2 \ln x+c x^2[/tex]

We now test the solution by substituting [tex]y^2=8 x^2 \ln x+c x^2[/tex] it in the original differential equation.

[tex]\begin{aligned}&\frac{d}{d x}\left(y^2\right)=\frac{d}{d x}\left(8 x^2 \ln x+c x^2\right) \\&2 y \frac{d y}{d x}=16 x \ln x+8 x+2 c x \\&\frac{d y}{d x}=\frac{16 x \ln x+8 x+2 c x}{2 y} \\&\frac{d y}{d x}=\frac{8 x \ln x+4 x+c x}{y}\end{aligned}[/tex]

We calculated the value of [tex]y^2[/tex] and [tex]\frac{d y}{d x}[/tex] from the original differential equation:

[tex]\begin{aligned}&\frac{8 x \ln x+4 x+c x}{y}=\frac{4 x^2+8 x^2 \ln x+c x^2}{x y} \\&8 x \ln x+4 x+c x=8 x \ln x+4 x+c x .\end{aligned}[/tex]

Therefore, the general solution of the given equation is y² = 8x²Inx + cx².

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The complete question is given below:
For the following ODE, find a general solution, show the steps of derivation and check your answer by substitution.

[tex]y^{\prime}=\frac{\left(4 x^2+y^2\right)}{(x y)}[/tex]

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!

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 total amount in the bank account after 7 years will be $1490

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. The principal amount in simple interest is constant.

The formula for simple interest = (P*R*T)/100

where P = principal amount

R = rate of interest

T = time in years

As per the question,

P = 1000

R = 7%

T = 7 Years

Simple interest will be = (1000*7*7)/100 = $490

The amount of money in the savings account at the end of 7 years will be $1000 + $490 = $1490

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Answer: x = 3.6

Step-by-step explanation:

Combine multiplied terms into a single fraction

\frac{5}{8}(x+4)=0.25

\frac{5(x+4)}{8}=0.25

2 Distribute

3 Multiply all terms by the same value to eliminate fraction

4 denominators

5 Cancel multiplied terms that are in the denominator

6 Multiply the numbers

7 Subtract  20 from both sides

8 Simplify

9 Divide both sides by the same factor

10 Simplify

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