plz help. this is for apex if you dont know.

Answer:

x ≈ 41.7 ° (a)

Step-by-step explanation:

b² = a² + c² - 2ac × cosβ

~~~~~~~~~~~

25² = 32² + 37² - 2(32)(37)cosx

625 = 2,393 - 2,368 cosx

cosx = \(\frac{-2393+625}{-2368}\) ≈ 0.74662162

x ≈ 41.7 ° (a)

Jennifer has 48 nickels, which means she has 144 quarters.

Let's call the number of nickels Jennifer has "n".

Since Jennifer has three more dimes than nickels, she has n + 3 dimes.

And since she has three times as many quarters as nickels, she has 3n quarters.

We can start by figuring out the total value of the nickels and dimes in terms of cents:

n * 5 cents + (n + 3) * 10 cents = 750 cents

Expanding the right side of the equation and solving for n:

5n + 10n + 30 cents = 750 cents

15n + 30 cents = 750 cents

15n = 720 cents

n = 48

So Jennifer has 48 nickels, which means she has 3 * 48 = 144 quarters.

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The 15th term of the geometric progression is 9,565,94.

A geometric progression can be expressed as an = a1rn-1 for some a1 and r. You are told that a2 * a4 = 2a5 and a1 + a2 + a3 + a4 = 80.

From the first equation, a2 = a1 r, a4 = a1 r3, and a5 = a1 r4. This tells us that

a1 r a1 r3 = 2 a1 r4

The r's and one a1 cancel leaving a1 = 2.

Now, plugging similarly into a1 + a2 + a3 + a4 = 80,

2 + 2r + 2r2 + 2r3 = 80

r3 + r2 + r + 1 = 40

In general, the easiest way to solve a cubic is by graphing, but here you know the answer will be a small integer, so just try a few. If we try r=3, we get 27 + 9 + 3 + 1 = 40 so r = 3.

So the geometric sequence here is an = 2 3n-1. The 15th term is then:

a15 = 2*3^14

a15 = 9,565,938.

Full question:

A G.P, the product of the 2nd and the 4th term is double the 5th term, and the sum of the first 4th terms is 80. find the 15th term.

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Answer:

x = 17/32

Step-by-step explanation:

Firstly, you want to simplify by combining like terms:

4x(3+5)—10 = 4 · 3 + 5 – 10

32x—10 = 7

Add ten to both sides:

32x - 10 = 7

+10             +10

32x = 17

Divide both sides by 32:

32x = 17

/32      /32

32 divided by 32x makes x

so we get x = 17/32

(we dont divide 17/32 since we would get an irrational number (0.53125))

Joan should invest  $4720 annually in her sinking fund to have $250,000 when she retires

We can use the future value formula for an annuity to solve this problem:

FV = PMT * [(1 + r)^n - 1] / r

Where:

We want to find PMT, so we can rearrange the formula:

PMT = FV * r / [(1 + r)^n - 1]

Plugging in the values we know:

FV = $250,000

r = 0.04

n = 29

PMT = $250,000 * 0.04 / [(1 + 0.04)^29 - 1]

PMT = $250,000 * 0.04 / 22.718

PMT = $4720

So Joan should invest approximately $4720 annually in her sinking fund to have $250,000 when she retires in 29 years, assuming an interest rate of 4% compounded annually.

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(a) The linear programming model to maximize the profit is written as,

Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)

(b) The optimal solution is x1 = 0, x2 = 8/3, x3 = 8, x4 = 0, and the maximum profit is $40.

(a) Linear programming model:

Let x1, x2, and x3 be the number of acres allocated to lemon, peach, and cherry trees, respectively. Then, the objective function we want to maximize is:

Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)

The first term represents the revenue from selling lemons, the second term represents the revenue from selling peaches, the third term represents the revenue from selling cherries, the fourth term represents the cost of fertilizer, and the last term represents the cost of labor.

The constraints are:

x1 + x2 + x3 ≤ 200 (total available land)

10x1 + 12x2 + 10x3 ≤ 20000 (total available labor hours)

x1, x2, x3 ≥ 0 (non-negativity constraints)

(b) Simplex algorithm:

Convert the linear programming model into standard form by introducing slack variables and expressing all variables in terms of these variables.

Maximize Z = 2(4x1)(100) + 1.5(6x2)(100) + 4(2x3)(1000) - 2(100x1 + 100x2 + 50x3) - 40(10x1 + 12x2)

Subject to:

x1 + x2 + x3 + x4 = 200

10x1 + 12x2 + 10x3 + x5 = 20000

x1, x2, x3, x4, x5 ≥ 0

In this case, the entering variable is x1, as it has the highest coefficient in the objective function.

Step 5 (continued):

1.6 0.1 0 1 -48 32 <- Z

0.4 0.9 1 1/10 0 40 <- x1

8.4 3.3 0 -1/10 1 1840 <- x5

The entering variable is x3, as it has the highest coefficient in the objective function.

The leaving variable is x1, as it has the smallest ratio of RHS to its coefficient in the x3 column.

x2 x1/12 x3 x5/120 x4 RHS

2.5 1/5 0 -1/60 0 40 <- Z

0.5 -1/5 1 1/60 0 8 <- x3

0.5 2/15 0 1/60 1/10 8/3 <- x2

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Option B is correct. 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet. This can be obtained by using the formula of density.

Given that there are 22 goldfishes,

mass of tank = 22 goldfishes

volume of tank = 56 cubic feet

                      = 22/56

                      = 0.39 goldfish per cubic feet

Hence 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet.

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Answer: 0.39 goldfish

Step-by-step explanation:

Answer:

20800000

Step-by-step explanation:

put it in a calculator

Answer:

d = mn/F

Step-by-step explanation:

F = mn/d

multiply both sides with d

d*F = mn/d*d

dF=mn

divide F from both sides

d/F = mn/F

So..

d = mn/F

Answer:

Given:

\( \boxed{ \mathsf{F = \frac{mn}{d} }}\)

Divide both sides by "mn":

\( \mathsf{ \frac{F}{mn} = \frac{mn}{d \times mn} }\)

The two mn's on the RHS gets canceled out. So we're left with:

\( \mathsf{ \frac{F}{mn} = \frac{1}{d} }\)

Invert the fractions present on either side of the "equals" sign

(In other words, flip it on its head so its numerator becomes its denominator and vice):

\( \mathsf{ \frac{mn}{F} = \frac{d}{1} }\)

Hence, we got the value of d:

\( \underline{\mathsf{ d= \frac{mn}{F} }}\)

Answer:

theres no question or answers

Step-by-step explanation:

Answer:

Where is the question? I don't see it did you forget to attach it?

Step-by-step explanation:

Answer:

x=16

Step-by-step explanation:

use the Pythagorean theorem.

\(\sqrt{a^{2}+b^2 \\)= \(c^{2}\)          Another way, you can do the problem is that you can see

\(\sqrt{12^2+b^2\)= \(20^{2}\)     that 12 divided by 4 is 3 and 20 divided by 4 is 5, which is

144+b^2=400     the two numbers from the special 3,4,5 triangle, and since

-144        -144      you have figured that much out, you can multiply 4*4 and

------------------------ get 16.

      b^2=256

\(\sqrt{256\\}\) = 16

He will have to mix 3 pounds of cashews and 7 pounds of peanuts .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Let c be denoted as cashew and p be denoted as peanuts

c + p = 10  ⇒ (1)

5.6c + 2.3p = 3.29*10 ⇒ (2)

Multiply eq(1) by 560

Multiply eq(2) by 100

560c + 560p = 5600

560c + 230p = 3290

Subtract and solve for "p":

330p = 2310

p = 7  (amt. of peanuts needed)

substitute  the value of p in eq(1)

c + 7 = 10

c = 3  (amt. of cashews needed)

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Using the long division method, it is proved that (x + 2) is a factor of (x³ + 8), because the result of the remainder is 0.

To show that (x + 2) is a factor of (x³ + 8) using long division, we can divide (x³ + 8) by (x + 2) and see if the remainder is 0. If the remainder is 0, then (x + 2) is a factor of (x³ + 8). Here's how the long division would look:

        x² - 2x + 4

x+2 | x³ + 0x² + 0x + 8

      - (x³ + 2x²)

    --------------------

         -2x² + 0x + 8

       - (-2x² - 4x)

         ---------------

              4x + 8

            - (4x + 8)

              --------

                 0

Since the remainder is 0, we can conclude that (x + 2) is a factor of (x³ + 8).

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Answer:

\(\{-20, -2 ,13\}\)

Step-by-step explanation:

The range of a function is the set of its possible output values

\(f(x) = 3x-8\\\\f(-4) = 3(-4) -8 = -12 -8 = -20\\\\f(2) = 3(2) -8 =6-8 = -2\\ \\f(7) = 3(7) -8 = 21 -8 = 13\\\\\text{Range} = \{-20, -2 ,13\}\)

Answer: 60º

Step-by-step explanation:

With respect to the line ZB, it makes an angle of 180º if measured using DZ. If the angle outside the triangle measures 140º, subtract from 180º to find the angle inside the triangle.

180º-140º=40º

So, now we have angle c=80º and angle b=40º, we can make an equation to find angles D which we'll call x.

The sum of the angles of a triangle must be equal to 180º.

80+40+x=180

120+x=180

x=180-120

x=60

Answer:

Find the measure of the angles indicated

∠CDB = 60°

Step-by-step explanation:

∠CBD + ∠CBZ = 180°

∠CBD + 140° = 180°

∠CBD = 180° - 140°

∠CBD = 40°

∠CBD + ∠BCD + ∠CDB = 180°

40° + 80° + ∠CDB = 180°

120° + ∠CDB = 180°

∠CDB = 180° - 120°

∠CDB = 60°

Answer:

3 hours

Step-by-step explanation:

The rent of the bicycle comes with a charge of:

Initial deposit = AED 80

cost per hour = AED 22

If Majid pays AED 146, then;

AED 146 - AED 80 = AED 66

Given that the charge per hour is AED 22, then to determine the number of hours that Majid can ride;

number of hours = \(\frac{AED 66}{AED 22}\)

                            = 3

Majid would be able to ride the bicycle for 3 hours when he pays AED 146.

1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799  participants were successful.

The successful  participants  can be calculate by solving a linear equation as follows

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.

Linear equations are those with one degree.

In this case, a linear equation must be resolved.

1945 for the men's total

Women are present in 2849.

Participants in total: 1945 + 2849 = 4794

Let x be the proportion of participants that were successful.

Men who failed were 5 times as numerous.

Participants in total: 5x + x = 6x

Due to the issue,

The linear formula is

6x = 4794

x = 4794/6

x = 799

799 of the participants had success.

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Answer:

The building is 86.6 m tall.

Step-by-step explanation:

Coh Cah Toa

Coh: sin(theta) = Opp/Hyp

Cah: cos(theta) = Adj/Hyp

Toa: tan(theta) = Opp/Adj

Using Toa.

tan(theta) = Opp/Adj

tan(60°) = x/50

x = 50 * tan(60°)

x = 50 * √(3)

x ≈ 86.60254038

x = 86.6 m

Answer:

30.37

Step-by-step explanation:

Answer:

\(164 \div 5.40 ={\ 30.3704{}}\)

The answer is 30.3704

Answer:

14 Serving

Step-by-step explanation:

If you multiply 1/3 14 times.

they're 13 1/3 pound servings in 4 2/3 pounds of cheese

The C. Ghost rectangle or callout shape is used to represent comments in flowcharts"

This shape is used to provide additional information or comments about a particular process or decision in a flowchart.

It is typically a rectangular shape with a dashed or dotted border, and a tail pointing to the relevant step or decision.

The parallelogram shape is used to represent input or output in a flowchart, while the diamond shape is used to represent decision points. The rectangle shape is used to represent a process or action in the flowchart.

It is important to use the correct symbols and shapes in flowcharts to ensure clarity and accuracy in the representation of processes and decision-making.

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complete question:

Which of the following is used to represent comments in flowcharts?

A. Parallelogram

B. Diamond

C. Ghost rectangle or callout shape

D. Rectangle

D. y-2 cos(2x) + 4 is not a solution to the differential equation y" + 4y = 0.

The differential equation y" + 4y = 0 is a second-order, homogeneous linear differential equation with constant coefficients. The general solution to this type of differential equation is of the form y = e^(rt) where r is a root of the characteristic equation r² + 4 = 0. The roots of this equation are r = +/- √(4) = +/- 2i, which are both imaginary. Therefore, the general solution to the differential equation is y = c1cos(2x) + c2*sin(2x), where c1 and c2 are arbitrary constants.

Option D. y - 2 cos(2x) + 4 is not a solution to this differential equation because it doesn't have the same form as the general solution. It is a combination of a constant term, cosine and sine function but the general solution only contains sine and cosine function.

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Answer:

B

Step-by-step explanation:

half × base × height

height × length

Answer: B

Step-by-step explanation:

Triangle)

25 - 7 = 18

\(A=\frac{1}{2}(b)(h)\\A=\frac{1}{2}(18)(17)\\A=153cm^2\)

Rectangle)

\(A=b(h)\\A=7(17) = 119cm^2\)

Total)

\(153+119=272 cm^2\)

Answer:

350 hours

Step-by-step explanation:

Answer:

output = input - equation

y = x - 7

so 7 is your correct equation!!

Step-by-step explanation:

as u can see

When input x is subtracted from output y, we are getting answer 7

like here

imma gonna tell u how 7 is came

1-8=7

2-9=7

3-10=7

4-11=7

so 7 is our equation

its just a explanation okay

so we get our solution

•°• Y = X - 7

hope it may help you!!

mark as brainlist

Answer:

3

Step-by-step explanation:

Since we know x = -2 we can plug it into the equation

3*-2^2+5*-2+1

Solve!

3*-2^2+5*-2+1 = 3

Hope this helps!

The percentage of the total hours did Andrea work is,

⇒ 27.1%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Total number of hours to work is,

⇒ 5.8 + 8.1 + 7.3 + 8.7 hours

⇒ 29.9 hours

Here, Andre work 8.1 hours.

Hence, The percentage of the total hours did Andrea work is,

⇒ 8.1 / 29.9 × 100

⇒ 27.1%

Thus, The percentage of the total hours did Andrea work is,

⇒ 27.1%

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6.1). the rate of depreciation, r, is approximately 10.77%.

6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2).  Ncominkosi borrowed approximately R 377,510.83 from the bank.

6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.

Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.

Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.

Therefore, the rate of depreciation, r, is approximately 10.77%.

6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:

\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)

Where:

P = Monthly payment

PV = Loan principal amount

r = Monthly interest rate

n = Total number of monthly payments

Let's calculate the monthly installment amount for Ncominkosi's loan:

Loan amount = Total amount paid to the bank - Interest

Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)

Number of monthly payments = 6 years * 12 months/year = 72 months

Using the formula mentioned above:

\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)

Substituting the values:

\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)

Calculating the value:

P≈R10,505.29

Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.

Total amount paid to the bank: R 596,458.10

Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.

Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:

\(A=P(1+r/n)(n*t)\)

Where:

A = Total amount paid

P = Loan principal amount

r = Annual interest rate

n = Number of compounding periods per year

t = Number of years

We can rearrange the formula to solve for the loan principal:

\(P=\frac{A}{(1+r/n)(n*t)}\)

Substituting the values:

Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)

Calculating the value:

Loan principal (P) ≈ R 377,510.83

Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.

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