solve for "c". a(b-c)=d

The triangle on the image is a right triangle which means we can use trigonometry to untangle its mysteries.

We have a side an and angle from that we can compute anything.

We will first compute x, we do so by taking the cosine of an angle,

[tex]\cos(45)=\frac{5\sqrt{2}}{x}[/tex]

[tex]x=\frac{5\sqrt{2}}{\cos(45)}=\frac{5\sqrt{2}}{\frac{\sqrt{2}}{2}}=\frac{10\sqrt{2}}{\sqrt{2}}=\boxed{10}[/tex]

Then we can also compute y, simply by using pythagorean theorem,

[tex]10^2=y^2+(5\sqrt{2})^2[/tex]

[tex]y=\pm\sqrt{100-50}=\pm\sqrt{50}=\boxed{5\sqrt{2}}[/tex].

So triangle has sides [tex]5\sqrt{2},5\sqrt{2},10[/tex] which is also known as equilateral triangle.

Hope this helps :)

Answer: Given

room height is x feet

room length is 3x feet

room width is 3x feet

a door 3 ft wide by 7 ft tall

Find

The net area of the wall, excluding the door

Solution

The area of the wall, including the door, is the room perimeter multiplied by the height of the room. The room perimeter is the sum of the lengths of the four walls.

... gross wall area = (3x +3x +3x +3x)·x = 12x²

The area of the door is the product of its height and width.

... door area = (7 t)×(3 ft) = 21 ft²

Then the net wall area, exclusive of the door is ...

... net wall area = gross wall area - door area

... net wall area = 12x² -21 . . . . square feet

Answer:

a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.

Remember that for a cylinder of radius R and height H the volume is:

V = pi*R^2*H

And the surface will be:

S = 2*pi*R*H + pi*R^2

where pi = 3.14

Here we know that the volume is 1000cm^3, then:

1000cm^3 = pi*R^2*H

We can rewrite this as:

(1000cm^3)/pi = R^2*H

Now we can isolate H to get:

H = (1000cm^3)/(pi*R^2)

Replacing that in the surface equation, we get:

S = 2*pi*R*H + pi*R^2

S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2

S = 2*(1000cm^3)/R + pi*R^2

So we want to minimize this.

Then we need to find the zeros of S'

S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0

So we want to find R such that:

2*pi*R = (2000cm^3)/R^2

2*pi*R^3 = 2000cm^3

R^3 = (2000cm^3/2*3.14)

R = ∛(2000cm^3/2*3.14) = 6.83 cm

The radius that minimizes the surface is R = 6.83 cm

With the equation:

H = (1000cm^3)/(pi*R^2)

We can find the height:

H = (1000cm^3)/(3.14*(6.83 cm)^2) =  6.83 cm

(so the height is equal to the radius)

b) The surface equation is:

S = 2*pi*R*H + pi*R^2

replacing the values of H and R we get:

S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2

c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.

Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.

Answer:

A sample size of 752 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

If the candidate wants a 3% margin of error at a 90% confidence level, what size of sample is needed?

We have no estimate of the proportion, so we use [tex]\pi = 0.5[/tex].

The sample size is n for which M = 0.03. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645*0.5[/tex]

[tex]\sqrt{n} = \frac{1.645*0.5}{0.03}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2[/tex]

[tex]n = 751.67[/tex]

Rounding up:

A sample size of 752 is needed.

Answer:

12

Step-by-step explanation:

Find the LCM (Least Common Multiple) of the three numbers.

We could multiply 3 x 4 x 6 to get 72, but there is a smaller multiple, 12.

6 x 2 = 12

4 x 3 = 12

3 x 4 = 12

Hope this helps!

Answer: The answer is 0.182

Hope this help :)

Answer: For flour it is 360g

3 eggs

900ml of milk

Step-by-step explanation:

Answer:

First, find the amount of ingredient for one pancake:

Multiply that amount by 12 to find the amount needed for 12 pancakes:

Answer:

Avengers: Endgame ≈ 335

Black Panther ≈ 293

Mulan ≈ 126

Step-by-step explanation:

8+7+3=18

754/18 = 41.88888889

8*41.88888889 ≈ 335

7*41.88888889 ≈ 293

3*41.88888889 ≈ 126

335+293+126=764

Answer: A. If a parallelogram is not a rectangle, then it does not have congruent diagonals.

Here, we want to find the interest rate and principal

The interest rate, r = 6% and the principal, P = Rs 65,000

Compound interest:

A = P(1 + r/n)^t

Simple interest :

I = P * r * t

Simple interest for 2 years = Rs 7800

Simple interest for 1 year = Rs 7800 / 2

= Rs 3900

Compound interest for 2 years = Rs 8034

Compound interest for the second year = Rs 8034 - Rs 3900

= Rs 4134

Interest on Rs 3900 = Rs 4134 - Rs 3900

= Rs 234

Therefore,

Interest rate, r = 234/3900 × 100

= 0.06 × 100

r = 6%

Recall,

Simple interest :

I = P * r * t

Then,

P = I / r * t

= 3900 / 6% * 1

= 3900 / 0.06

= 65,000

P = Rs 65,000

https://brainly.in/question/1489411

Answer:

8 ounces of tomato paste for each cup of water.

Step-by-step explanation:

Just divide 48 / 6 to get 8 oz of tomato paste per cup of water.

Hope this helps!

Work Shown:

48 oz of tomato paste = 6 cups of water

48/6 oz of tomato paste = 6/6 cups of water

8 oz of tomato paste = 1 cup of water

In short, we divide both values by 6 so that the "6 cups" becomes "1 cup". We can say the unit rate is 8 oz of tomato paste per cup of water.

9514 1404 393

Answer:

  A. 570.69 cm³

Step-by-step explanation:

The volume is given by the formula ...

  V = πr²h

The radius is half the diameter, so is 4.35 cm. Then the volume is ...

  V = π(4.35 cm)²(9.6 cm) = 181.656π cm³ ≈ 570.69 cm³

Answer:

$7153.84

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]

Step-by-step explanation:

Step 1: Define

Identify variables

P = 5000

r = 12% = 0.12

n = 12

t = 3

Step 2: Find Interest

Answer:

C

Step-by-step explanation:

[tex] \sf {a}^{c} \times {a}^{b} = {a}^{b + c} \\ \sf = {8}^{11} \times {8}^{x} \\ \sf = {8}^{11 + x} (c)[/tex]

Answer:

firth root of 810x cubed /3x

Answer:

5 over 9

Step-by-step explanation:

multiplayer both sides of the second fraction by 3, then you have 3 over 9. So the problem becomes 8-3=5

Answer:

0.8 = 80% probability that either your aunt or your father will become a city commissioner.

Step-by-step explanation:

The candidates are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

6 candidates, which means that [tex]N = 6[/tex]

2 are the aunt and father, which means that [tex]k = 2[/tex]

3 are chosen, which means that [tex]n = 3[/tex]

What is the probability that either your aunt or your father will become a city commissioner?

Probability of at least one of them being chosen, which is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,6,3,2) = \frac{C_{2,0}*C_{4,3}}{C_{6,3}} = 0.2[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2 = 0.8[/tex]

0.8 = 80% probability that either your aunt or your father will become a city commissioner.

Answer:

B.(0.4,0.7)

Step-by-step explanation:

We are given that

Sample proportion

[tex]\hat{p}=0.55[/tex]

We have to find the range of possible values which   describes best  an estimate for the population parameter.

Estimate  for the population parameter

[tex]\hat{p}\pm Z(SE)[/tex]

A.(0.55,0.6)

Difference between 0.55 and 0.55=0

Difference between 0.55 and 0.6=0.05

Difference between 0.55 and 0.55 is not equal to difference between 0.55 and 0.6.

Hence, option A is wrong.

B.(0.4,0.7)

Difference between 0.55 and 0.4=0.15

Difference between 0.55 and 0.7=0.15

Difference between 0.55 and 0.4 is equal to difference between 0.55 and 0.7.

Hence, option B is correct.

C. (0.4,0.69)

Difference between 0.55 and 0.4=0.15

Difference between 0.55 and 0.69=0.14

Difference between 0.55 and 0.4 is not equal to difference between 0.55 and 0.69.

Hence, option C is not correct.

D.(0.5,0.59)

Difference between 0.55 and 0.5=0.05

Difference between 0.55 and 0.59=0.04

Difference between 0.55 and 0.5 is not equal to difference between 0.55 and 0.59.

Hence, option D is not  correct.

Answer:

Following are the solution to the given points:

Step-by-step explanation:

[tex]X = \text{cost of wedding}\sim \text{Normal}\ (\mu = 28732, \sigma= 1500)\\\\[/tex]

For point a:

[tex]Probability\ = 0.00000359\\\\ \text{(Using Excel function:} =NORMDIST(22000,28732,1500,1)).[/tex]

For point b:

[tex]Probability \ = 0.014678\\\\\text{(Using Excel function:} =1-NORMDIST(32000,28732,1500,1))\\\\[/tex]

For point c:

[tex]Probability\ = 0.794614436 \\\\[/tex]

[tex]\text{(Using Excel function:} \\=NORMDIST (30000,28732,1500,1)-NORMDIST(25000,28732,1500,1))\\\\[/tex]

For point d:

[tex]Q_1 = 27720.26537 \\\\\text{(Using Excel function:} =NORMINV(0.25,28732,1500)) \\\\Q_3 = 29743.73463 \\\\\text{(Using Excel function:} =NORMINV(0.75,28732,1500)).[/tex]

For point e:

[tex]IQR = Q_3 - Q_1 = 29743.73463 - 27720.26537 = 2023.469251.[/tex]

For point f:

[tex]Top\ 10\% = 30654.32735 \\\\\text{(Using Excel function:} =NORMINV(0.9,28732,1500)).[/tex]

Answer:

a) 0.3571 = 35.71% probability that the stock price will be more than $25.

b) 0.1429 = 14.29% probability that the stock price will be less than or equal to $18.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniformly distributed between $16 and $30 per share.

This means that [tex]a = 16, b = 30[/tex]

a) More than $25?

[tex]P(X > x) = \frac{30 - 25}{30 - 16} = 0.3571[/tex]

0.3571 = 35.71% probability that the stock price will be more than $25.

b) Less than or equal to $18?

[tex]P(X < 18) = \frac{18 - 16}{30 - 16} = 0.1429[/tex]

0.1429 = 14.29% probability that the stock price will be less than or equal to $18.

Answer:

D. F(x) = [tex]\frac{1}{(x+4)}^{2}[/tex]

Answer:

2 4 because I tookt the test

Answer:

The number of positive real zeros is 2 or 0

Step-by-step explanation:

Given

[tex]f(x)=x^5+3x^2-4x+2[/tex]

Required

Number of positive real zeros

Using Descartes rule of signs;

We write out the signs in front of each term;

Sign = + + - +

Count the number of times the sign alternate; i.e. from positive to negative and from negative to positive

From positive to negative, we have: 1 (i.e. + - )

From negative to positive, we have: 1 (i.e. - +)

Add up the count

[tex]count = 1+1[/tex]

[tex]count = 2[/tex]

Hence, the number of positive real zeros is 2 or 0

Answer: C

Step-by-step explanation:

There are many ways to find the linear equation that matches the table, but let's do it so that we find the slope and y-intercept.

Based on the first entry (0,-5), we know that the y-intercept is -5.

To find slope, we take any two points and plug them into this [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. We'll use the first two points.

[tex]m=\frac{0-(-5)}{2-0} =\frac{5}{2}[/tex]

Now, we know the slope is [tex]\frac{5}{2}[/tex].

The only equation that has the same slope and y-intercept that we found is C.

Answer:

Step-by-step explanation:

This is a geometric means problem where 60, the side common to both the triangles, is the geometric mean. Set it up like this:

[tex]\frac{36}{60}=\frac{60}{x}[/tex] and cross multiply to get

36x = 3600 so

x = 100

Given:

The functions are:

[tex]p(x)=\dfrac{1}{x+1}[/tex]

[tex]q(x)=\dfrac{1}{x-1}[/tex]

To find:

The rational expression for [tex]p(x)-q(x)[/tex].

Solution:

We have,

[tex]p(x)=\dfrac{1}{x+1}[/tex]

[tex]q(x)=\dfrac{1}{x-1}[/tex]

Now,

[tex]p(x)-q(x)=\dfrac{1}{x+1}-\dfrac{1}{x-1}[/tex]

[tex]p(x)-q(x)=\dfrac{(x-1)-(x+1)}{(x+1)(x-1)}[/tex]

[tex]p(x)-q(x)=\dfrac{x-1-x-1}{x^2-1^2}[/tex]             [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]p(x)-q(x)=\dfrac{-2}{x^2-1}[/tex]

Therefore, the required rational expression for [tex]p(x)-q(x)[/tex] is [tex]\dfrac{-2}{x^2-1}[/tex].

Answer:

See answers below

Step-by-step explanation:

Lateral surface area of a cone is expressed as:

L = πr√h²+r²

Given that

r = 11.5/2 = 5.75cm

h=16.6cm

L = 3.14(5.75)√16.6²+5.75²

L = 18.055√275.56+33.0625

L = 18.055*17.56

L=317.0458cm²

Volume = 1/3πr²h

Volume = 1/3π(5.75)²(16.6)

Volume = 1,723.34975/3

Volume = 574.45cm³