if 15% of x is 12. what is x?

By means of trigonometric functions, the length of side BC is approximately equal to 11.6 centimeters.

In this problem we find a geometric system formed by two right triangles, from which we need to determine the exact measure of side BC. This can be done by means of trigonometric functions, that represents relationships between two sides of a right triangle:

sin θ = y / r

cos θ = x / r

tan θ = y / x

cot θ = x / y

sec θ = r / x

csc θ = r / y

Where:

First, obtain the length of side BD:

cos θ = BD / AB

BD = AB · cos θ

BD = 5 · cos 30°

BD = 5√3 / 2 cm

Second, calculate the length of side BC:

sin θ = BD / BC

BC = BD / sin θ

BC = 5√3 / 2 / sin 22°

BC ≈ 11.6 cm

To learn more on trigonometric functions: https://brainly.com/question/14434745

#SPJ1

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

[tex]2^{2x}-2^2 2^x-12=0 \\ \\ (2^x)^2-4(2^x)-12=0[/tex]

Factoring the quadratic in [tex]2^x[/tex],

[tex](2^x+6)(2^x-2)=0 \\ \\ 2^x=-6,2 \\ \\ 2^x=2 \implies x=1 \\ \\ 2^x=-6 \implies x \notin \mathbb{R} \\ \\ \therefore x=\log_{2} (6)[/tex]

Answer:

C

Step-by-step explanation:

Multiply z times itself. Then multiply z times that first answer, to get z^3.

There's a formula for cubing a binomial but even if you don't remember it (like me) you can still find z^3.

But remember that i^2 = -1

This is related to sqrt(-1)= i, a definition for the imaginary number.

On the graph, go left or right for the real part and up or down for the imaginary part.

see image.

In the aforementioned scenario, the choice you must include in your response is to find a common denominator.

One can refer to a fraction as being in its lowest term or in its simple form when the numerator and denominator are known to have no common factors besides 1. In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in daily speech.

The common denominator will be between 10 and 20, and there is a common numerator as well. The common denominator will be 20 because both can divide it and 10 is less than 20.

Finding a common denominator is the solution you should choose in the scenario mentioned above.

To know more about fraction, visit:

https://brainly.com/question/10354322

#SPJ1

The equation that matches the graph is 7x-30y=-275

We should know that an equation is a mathematical expression in which two sides are equal.

The equation of a line is the equation formed with the slope of the straight line

The slope of the of the is determined taking the points

[tex]M=\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]

Slope=(7-1)÷(35-5)

m=1/5

The equation of the line is

1/5 = (y-1)÷(x-35)

Cross multiplying the equation

7x-245=30y-30

Rearrange,

7x-30y=-30-245

7x-30y=-275

In conclusion the equation to match the graph is 7x-30y=-275

Learn more about equation of a line on https://brainly.com/question/21511618

#SPJ1

The expression that represents the volume of the prism is

2 × 3 × 9 units³. That is option C.

Prism is defined as the type of polyhedron that has two polygonal faces lying in parallel planes and with the other faces parallelograms.

A prism can be of a regular shape or of an irregular shape. The volume of a regular shapes prism can be calculated using the formula stated below

volume of a prism = l × b × h

Length (l) = 9 units

Breath = 2 units

Height (h) = 3 units.

Therefore, the volume of the given prism can be calculated as 2 × 3 × 9 units³.

Learn more about volume here:

https://brainly.com/question/28795033

#SPJ1

Therefore, the length of a rectangle is 13m and width is 8m

A region's size on a planar or curved surface is described mathematically as its area. In contrast to a plane region or plane's area, which refers to a form or planar lamina, a surface area is the size of an open surface or the edge of a three-dimensional object.

Here,

width=x

length=2x-3

Area =l x w

104=(2x-3)(x)

104=2x^2-3x

52=x^2-3/2(x)

52+9/16=x^2-3/2(x)+9/16

841/16=(x-3/4)^2

29/4=x-3/4

x=32/4

x= 8m

Thus width = 8m

length =  2(8)-3  = 13m

Therefore the length of a rectangle is 13m and width is 8m

To know more about area, visit

https://brainly.com/question/27683633

#SPJ1

Answer:

the price of one gallon of milk has increased by 25%.

Step-by-step explanation:

The price of one gallon of milk has increased from $3.24 to $4.05, which is an increase of $4.05 - $3.24 = $0.81. To find the percentage increase, we can divide the amount of the increase by the original price and multiply by 100%. This gives us:

(0.81 / 3.24) * 100% = 25%

Therefore, the price of one gallon of milk has increased by 25%.

The solution is 25 %

The percentage increase in the price of one gallon of milk is given by the equation P = 25 %

What is Percentage Error?

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage error is the difference between the measured value and the true value , as a percentage of the true value

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Given data ,

Let the original price of the milk be A = $ 3.24

Let the increased price of the milk be B = $ 4.05

Let the percentage increase in the price be = P

Now , the equation will be

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100

Substituting the values in the equation , we get

Percentage increase P = [ ( 4.05 - 3.24 ) / 3.24 ] x 100

On simplifying the equation , we get

Percentage increase P = ( 0.81 / 3.24 ) x 100

Percentage increase P = 0.25 x 100

Percentage increase P = 25 %

Therefore , the value of P is 25 %

Hence , the percentage increase is 25 %

To learn more about percentage error click :

https://brainly.com/question/28746643

#SPJ2

Answer: 1.0017805194 ounces

Step-by-step explanation:

To change 28.4 g to oz divide the mass in grams by 28.349523125. The 28.4 grams to ounces formula is [oz] = [28.4] / 28.349523125. Thus, we get (all results rounded to 2 decimals):

28.4 g to oz = about 1 oz

28.4 g to ounces =  about 1 ounces

28.4 grams to ounces = about  1 oz

Twenty-eight point four grams to ounces equal 1 international avoirdupois ounces, the unit used to measure grocery products (mass) in retail stores in the United States for example.

The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

Learn more about linear equations at:

brainly.com/question/13763238

#SPJ1

Answer:

  see below for the chart

  64 pages in 1 hour

Step-by-step explanation:

You want to fill in the chart showing the analysis of the problem statement saying HP can read 16 pages in 1/4 hour. The problem statement is requesting the number of pages he can read in 1 hour.

See below for a filled-in chart.

Analysis of the bottom line tells you that the right column is 4 times the middle column.

  1 = 4 × 1/4

  ?? = 4 × 16 = 64

Harry Potter can read 64 pages in one hour.

The volume of the first and second designs are  2.7 m³ and 2.64 m³ so, the second design will hold more sand.

The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.

Given:

One design is 3 m by 3 m by 30 cm,

A second design is 3.25 m by 3.25 m by 25 cm,

Calculate the volume for the first design as shown below,

Volume of first design = 3 × 3  × 30/ 100   (1 m = 100 cm),

The volume of the first design = 270 / 100

The volume of the first design = 2.7 m³

Calculate the volume of the second design as shown below,

The volume of the second design = 3.25 × 3.25 × 25 / 100

The volume of the second design = 264.06 / 100

The volume of the second design = 2.64 m³

The difference in the volume of both designs = The volume of the first design - The volume of the second design

The difference in the volume of both designs = 2.7 - 2.64

The difference in the volume of both designs =0.06 m³

Thus, the first design will hold more volume of sand.

To know more about volume:

brainly.com/question/13807002

#SPJ1

The function plotted in the graph is given by - g(x) = 3.5 sin(x)

        [tex]$\sin \theta=\frac{a}{h}[/tex]

      {θ} = angle theta

      {a} = length of opposite side a

      {h} = length of hypotenuse h

        [tex]${\displaystyle {\begin{aligned}\sin(x)&=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \;= \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}}[/tex]

        {sin(A) / a = sin(B) / b = sin(C) / c}

Given is a graph as shown in the image.

A sine function has its maximum value of [1] and the minimum value of [-1]. The given graph g(x), is a amplitude scaled version of the function f(x) given by -

f(x) = sin(x)

and

g(x) = Asin(x)

Here, [A] is equal to 3.5. So, the function g(x) is equal to -

g(x) = 3.5 sin(x)

Therefore, the function plotted in the graph is given by -

g(x) = 3.5 sin(x)

To solve more questions on sine function, visit the link below -

https://brainly.com/question/11881676

#SPJ1

You would need to deposit $2,500 in order to have $5,000.00 in the account in 1633 days.

1st method: This can be found by using the simple interest formula I=PRT. In this case, I=5000, P=2500, R=.42, and T=1633. Solving for I gives you the answer.

2nd Method: If you deposit $2,500 in an account now, you will have $5,000 in the account in 1633 days. $2,500 * 1.42 = $3,550 $3,550 + $2,500 = $6,050 $6,050 / 2 = $3,025

To know about simple interest, click here

https://brainly.com/question/25845758

Answer:

[tex]\frac{x}{x+2}+\frac1x=1\\\rightarrow \frac{x^2+(x+2)}{(x^2+2x}=1\\\rightarrowx^2+x+2=x^2+2x\\\rightarrowx+2=2x\\\rightarrow x=\boxed2[/tex]

Only one solution, which is two. The answer should be C. You could obviously see that if there is no squaring then there will be no extraneous solutions.

We need to use Right Angled Triangle Properties.

PR≈15 and QR≈12 is the length of the sides.

What is a Right Angled Triangle?

According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of its angles is a right angle (90o). Triangle PQR is a right triangle in the illustration, and its components are its base, height, and hypotenuse. Here, QR is the base, PQ is the height, and PR is the hypotenuse. The essential side of a right triangle is its hypotenuse, which is also its largest side and sits across from the triangle's right angle.

In a right triangle we have: (Hypotenuse)2 = (Base)2 + (Altitude)2

Area of a right triangle = (1/2 × base × height) square units.

PR is the Hypotenuse of the Triangle.

PQ=9

Angle ∡PQR=37° and Angle ∡RPQ=53°

So Sin(theta)=opposite side/Hypotenuse

⇒Sin(37°)=9/Hypotenuse

⇒Hypotenuse=9/0.6018

⇒Hypotenuse=14.955

PR⇒14.955

We know that (Hypotenuse)2 = (Base)2 + (Altitude)2

⇒(14.955)2=(9)2+(QR)2

QR=11.9438

PR≈15 and QR≈12

We need to use Right Angled Triangle Properties.

PR≈15 and QR≈12 is the length of the sides.

To refer more about Right Angled Triangle, visit:

https://brainly.com/question/1248322

#SPJ1

Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor.

To determine the total increase recorded in the Work in Process account related to direct labor, we need to first calculate the total standard cost of direct labor for the period and then compare it to the actual cost of direct labor.

According to the standard cost card, each unit of the product requires 2 hours of direct labor at a rate of $16.00 per hour.

This means that the total standard cost of direct labor for the period is 2 * $16.00 * 7,800 = $248,000.

Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor. Therefore, the total increase recorded in the Work in Process account related to direct labor would be $0.

To learn more about direct labor costs refer :

https://brainly.com/question/26527325

#SPJ1

Answer:

no melissa isn't correct she has made 3 mistakes

Step-by-step explanation:

The formula to find the arc length of a circle = θ/360 ×2××r

The formula to find the area of a sector= θ/360××r²

The only thing missing is "θ"

The arc length is given to be 15cm so basically θ/360×2×3.14×12 = 15

θ= 360×15 ÷ 2×3.14×12 = 5400÷ 75.36= 71.65

now that we found "θ" we just continue with the formula to find the area of a sector (θ/360×r²)

=71.65×3.14×12²= 90cm

(it's a bit complicated but i hope this helped i tried to simplify it as much as i could)

The journal entry is given in answer part b

A discount coupon is defined as a certificate that entitles the customer to avail of a reduction in the invoice price if the terms mentioned on it are met. It is a technique applied by the sellers to expand sales.

Given that, Clarks Inc., a shoe retailer, sells boots in different styles. In early November, the company starts selling “SunBoots” to customers for $70 per pair. When a customer purchases a pair of SunBoots, Clarks also gives the customer a 30% discount coupon for any additional future purchases made in the next 30 days. Customers can’t obtain the discount coupon otherwise. Clarks anticipates that approximately 20% of customers will utilize the coupon, and that on average those customers will purchase additional goods that normally sell for $100.

a) Two performance obligations are associated with contract. The first one is related to the sun boots, and the other one is associated with discount coupon provided. The discount coupon would be considered a separate obligation because it gives a certain right to the customers that they would not have received if the sale was not made to them.

b) Journal entry =

Account title and explanation            Debit ($)                    Credit ($)

Cash (1000×$70)                                    $70000                  

Sales Revenue ($70,000-$6000)                                           $64000

Deferred Revenue                                                                    $6000

Now,

Computation of the deferred revenue:

Deferred revenue = pairs sold × Average purchase price × Discount × Redemption of coupon

= 1000 × 100 × 30% × 20%

= $6000

For more references on discount coupon, click;

https://brainly.com/question/18917474

#SPJ1

Final conclusion would be that the difference between the means of the two samples is not statistically significant.

What is Null Hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

It is not possible to test the claim that the two samples come from populations with the same mean without more information about the samples themselves. In order to test this claim, you need to have the sample data, the sample sizes, and the standard deviations of the samples. You can then use a t-test for independent samples to determine whether the difference between the means of the two samples is statistically significant.

The t-test is a statistical test that is used to compare the means of two samples. The test statistic for the t-test is the difference between the means of the two samples divided by the standard error of the difference. The degree of freedom for the t-test is the sum of the sample sizes minus 2. The significance level, alpha, is the probability of making a type I error, which is the probability of rejecting the null hypothesis when it is true. The rejection region for the t-test is the set of values of the test statistic for which the null hypothesis is rejected.

If the test statistic does not fall in the rejection region, you cannot reject the null hypothesis, and you must conclude that the difference between the means of the two samples is not statistically significant.

Final conclusion would be that the difference between the means of the two samples is not statistically significant.

To know more about Null Hypothesis visit,

https://brainly.com/question/25263462

#SPJ4

The expected number of students that pick soda is 80

From the bar graph, we have the following parameters that can be used in our computation:

Ice cream = 40

Soda = 20

popsicle = 10

This means that the proportion of soda is

Soda = 20/(40 + 20 + 10)

Evaluate the sum

Soda = 20/70

So, we have

Soda = 2/7

For a group of 280 students, we have

Soda = 2/7 *280

Evaluate

Soda = 80

Hence, the number of students is 80

Read more about probability at

https://brainly.com/question/251701

#SPJ1

The required butter she needed is given as 1.67 cups of butter.

As given in the question, Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels,

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

here,
Let the nutter need be x cups,
now,
Taking the ratio o butter to kernels
[1 / 2] / 3 = x / 10
x = 10 / 6
x = 1.67

Thus, As of the given proportion, she requires 1.67 cups of butter.

Learn more about ratios here:

brainly.com/question/13419413

#SPJ1

Answer:

My sister is

18

years old.

Step-by-step explanation:

s = m + 8        Eq. 1

s + m = 28      Eq. 2

s = my sister age

m = my age

Replacing Eq. 1 in Eq. 2:

(m+8) + m = 28

2m + 8 = 28

2m = 28 - 8

2m = 20

m = 20/2

m = 10

From Eq. 1:

s = m + 8

s = 10 + 8

s = 18

Check:

from Eq. 2:

s + m = 28

18 + 10 = 28

The true statement regarding the probabilities on the spinner is given as follows:

The probability that the spinner will point to yellow is less than 1/4.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

Hence, for the spinner given in this problem, the probabilities are given by the fraction occupied by each area, as shown by the image given at the end of the answer.

From the text, these fractions, representing the probabilities, are given as follows:

The problem is given by the image shown at the end of the answer.

More can be learned about probabilities at https://brainly.com/question/24372153

#SPJ1

The number or visits that Jim must make to make Plan A the cheaper option is more than 5 visits

An equation is the statement that illustrates the variables given. Jim has to choose between two gym membership plans.

For Plan A: $50 monthly membership fee and $10 per visit. This will be:

50 + 10v

Plan B: $25 one time membership fee and $15 per visit. This will be:

= 25 + 15v

Let v = number of visit

This will be illustrated as:

50 + 10v = 25 + 15v

Collect like terms

15v - 10v = 50 - 25

5v = 25

Divide

v = 25 / 5

v = 5

There will be more than 5 visits for a cheaper option.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:Printmaking is the process of creating artworks by the process of printing. It can be done on paper, brick, wood, and even metal.A lithographic is a planetographic process where the design is drawn into a flat stone and is prepared by use of metal. As per the paintings shows the artwork shows us the rhinosaruers. The painting is made from water and oil.Hence the painting B shows us the use of lithography.

The remainder term Rn is equal to (-2) raised to the power of n multiplied by e raised to the power of -2c, divided by n+1 factorial, multiplied by (x-2) raised to the power of n, for some c between x and 2.

The remainder term Rn in the nth order Taylor polynomial centered at a for the given function f(x)=e^-2x, a=2 is equal to (-2) raised to the power of n multiplied by e raised to the power of -2c, divided by n+1 factorial, multiplied by (x-2) raised to the power of n, for some c between x and 2. This remainder term represents the difference between the approximate value of the function given by the Taylor polynomial and the actual value of the function. By taking the limit as n approaches infinity, the remainder term can be used to determine the exact value of the function. The remainder term is an important concept in calculus as it is used to determine the accuracy of a given approximation.

For n=5, R5(x) = (-2)^5 e^-2c/(5+1)! (x-2)^5 for some c between x and 2.

Substituting n=5, x=7 and c=4, we have:

R5(7) = (-2)^5 e^-8/(6)! (7-2)^5

R5(7) = (-2)^5 e^-8/(720) (25)

R5(7) = (-2)^5 e^-8/18000

R5(7) = (-2)^5 e^-8/18000

R5(7) = -1.388888888 x 10^-9

Learn more about factorial here

https://brainly.com/question/15689921

#SPJ4

Using confidence interval concepts, it is found that the correct options are:A. With 99% confidence, the mean width of all widgets is between 14.3 and 30.4.

There is a 99% chance that the mean of the population is between 14.3 and 30.4.

The interpretation of a x% confidence interval is that we are x% sure that the population mean is in the interval.

In this problem, 99% confidence interval for widget width is between 14.3 and 30.4, hence we are 99% sure that the population mean, that is, the mean width of all widgets is between 14.3 and 30.4, hence options A and C are correct.

To learn more about confidence interval refer

https://brainly.com/question/15712887

#SPJ1