Make c the subject in b=a\2+c

Answer:

Step-by-step explanation:

The area of the floor A = Length * Width

Given

A = 200 square meters

If the length of the floor is 32 m longed than it’s width then;

L = 32+W

A = LW

200 = (32+W)W

200 = 32W + W²

W²+32W-200 = 0

W = -32±√32²+800/2

W = -32±42.71/2

W =  -32+42.71/2

W = 10.71/2

W = 5.35 m

L = 32+5.35

L = 37.35m

Hence the dimension is  5.35ft by 37.35m

For any triangle, the three angles always add to 180

(y+10)+(2y)+(50) = 180

3y+60 = 180 ... combine like terms

3y+60-60 = 180-60 ... subtract 60 from both sides

3y = 120

3y/3 = 120/3 .... divide both sides by 3

y = 40

Answer:

four units left and one unit up

Step-by-step explanation:

this is because x is always horizontal and y is always vertical

Answer: 3/64

Step-by-step explanation:

P(Blue)=(1/8)(3/8)

P(Blue)=3/64

Also, I had this quiz :)

The work done is\(-20 (1/(2^2 + y^2 + z^2)^(1/2) - 1/2)\) Joules for the given charge.

The term "work done" describes the quantity of energy that is transmitted or expended when a task is completed or a force is applied across a distance. It is computed by dividing the amount of applied force by the distance across which it is exerted, in the force's direction. In the International System of Units (SI), the unit used to measure work is the joule (J).

Given that the force exerted by an electric charge at the origin on a charged particle at the point (2, y, z) with position Kr vector r = (x, y, z) is F(r) = 20 (x/r3) i where K is constant.

Assuming that the particle moves from point A to point B, we can find the work done.

The work done in moving a charge against an electric field is given by:W = -ΔPElectricPotential Energy is given by U = qV where q is the test charge and V is the electric potential. The electric potential at a distance r from a point charge is given by V = kq/r where k is the Coulomb constant.

The work done in moving a charge from point A to point B against an electric field is given by:W = -q (VB - VA)where q is the test charge and VB and VA are the electric potentials at points B and A respectively.

In this case, the test charge is not given, we will assume it to be +1 C.Work done = -q (VB - VA)Potential at point A (r = 2) = kQ/r = kQ/2Potential at point B \((r = √(x^2 + y^2 + z^2)) = kQ/√(x^2 + y^2 + z^2)\)

Work done = -q (kQ/\(\sqrt{(x^2 + y^2 + z^2)}\) - kQ/2)=- kQq (1/\(\sqrt{(x^2 + y^2 + z^2)}\) - 1/2)= -20 (\(1/(2^2 + y^2 + z^2)^(1/2)\) - 1/2) JoulesAnswer:

The work done is \(-20 (1/(2^2 + y^2 + z^2)^(1/2) - 1/2)\)Joules.

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Answer: 81.9 ??

Step-by-step explanation:

Step-by-step explanation:

\( {13}^{2} = {6.5}^{2} + {x}^{2} \\ {x}^{2} = 126.75 \\ x = 11.2\)

Answer:

11.3 cm

Step-by-step explanation:

since this is an equilateral triangle it's every sides are equal

side length (a) = 13 cm

formula to calculate the height of equilateral triangle is

h = \(a *\frac{\sqrt{3} }{2}\)

=\(13 * \frac{\sqrt{3} }{2}\)

=\(\frac{13\sqrt{3} }{2}\)

=11.25

=11.3

The correct interpretation of the given confidence interval is: “We are 95% confident that the population mean number of hours adults spend on formal exercise each week lies between 0.45 and 7.94.”


Option (a) is the correct interpretation because a confidence interval provides an estimate of the range within which the true population parameter (in this case, the mean number of hours spent on formal exercise) is likely to fall. The confidence level of 95% indicates that if we were to repeat the sampling process and construct confidence intervals, 95% of those intervals would contain the true population mean.

Therefore, we can say with 95% confidence that the population mean lies within the interval (0.45 hours, 7.94 hours). Option (b) is incorrect because probabilities are not associated with confidence intervals. Options (c) and € refer to the sample mean, not the population mean. Option (d) incorrectly suggests that we know the true population mean is within the interval, whereas the confidence interval provides an estimate of the likely range.

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The equation needed to find the maximum number of students is 5x + 10 ≤ 125

Inequalities is an expression used to show the non equal comparison of numbers and variables.

Let x represent the number of tickets bought.

Since the movie theater charges a $10.00 group fee and $5.50 per ticket., hence:

Money spent = 5x + 10

The teacher can spend as much as $125.00, hence:

5x + 10 ≤ 125

The equation needed to find the maximum number of students is 5x + 10 ≤ 125

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3 ( x + 1 ) = 15

Had this same question on my math test.

Step-by-step explanation:

does that mean you understand all the other questions but not 5. ?

that is strange, as this seems to be the easiest one of all the 6 questions.

to be sure, let's have a look at all 6.

1.

the distance MJ = 18 - 2 = 16

MX / XJ = 3/1

the ratio talkes about 3+1 = 4 basic units.

as the whole distance is 16, one such basic ratio unit is 16/4 = 4.

that means from M to X we have 3 of these basic ratio units, and from X to J the remaining 1 of the basic ratio units.

so, MX = 3×4 = 12

since M = 2, X = 2 + 12 = 14

2.

similar to 1.

just now

MY / YJ = 2/3

so, the ratio uses 2+3 = 5 basic units.

that means 1 basic unit is 16/5 = 3.2

2 basic units = 2 × 3.2 = 6.4

3 basic units = 3 × 3.2 = 9.6

so, MY = 6.4

since M = 2, Y = 2 + 6.4 = 8.4

3.

the distance A F = 5 - -7 = 5 + 7 = 12

AW / WF = 1/3

so, the ratio uses 1+3 = 4 basic units.

1 basic unit is 12/4 = 3

3 basic units is 3 × 3 = 9

so, AW = 3

since A = -7, W = -7 + 3 = -4

4.

the distance BF = 5 - -5 = 5 + 5 = 10

BX / XF = 3/2

so, the ratio uses 3+2 = 5 basic units.

1 basic unit = 10/5 = 2

2 basic units = 2 × 2 = 4

3 basic units = 3 × 2 = 6

so, BX = 6

since B = -5, X = -5 + 6 = 1

5.

the distance CE = 2 - -4 = 2 + 4 = 6

CY / YE = 1/1

so, the ratio uses 1+1 = 2 basic units.

1 basic unit = 6/2 = 3

so, CY = 3

since C = -4. Y = -4 + 3 = -1

6.

attention : this goes in the other direction than the other questions. all the others were looking from a point on the left to a point on the right.

but this one looks from a point on the right to a point on the left.

but the same principles apply.

the distance FD = |1 - 5| = |-4| = 4

a distance is always positive, so for this direction we need to apply the absolute value (formality we did that also for the other direction in the other questions, but there it was not necessary to use it explicitly) .

FZ / ZD = 5/3

so, the ratio uses 5+3 = 8 basic units.

1 basic unit = 4/8 = 0.5

3 basic units = 3 × 0.5 = 1.5

5 basic units = 5 × 0.5 = 2.5

so, FZ = 2.5

since F = 5, Z = 5 - 2.5 = 2.5

this is where the other direction really hits : since we have to go to the smaller side, we have to subtract the distance from the original coordinate (instead of the usual addition).

Let X and Y be two independent Poisson random variables with means λ1 and λ2. The distribution of X+Y is Poisson with mean λ1+λ2.

The distribution of X+Y can be determined using the following steps:

Step 1: Determine the probability mass function of X and Y.

Since X and Y are independent Poisson random variables, the probability mass function of X and Y are given by:

P (X = k) = (e^-λ1 λ1^k)/k! and P (Y = k) = (e^-λ2 λ2^k)/k! respectively.

Step 2: Determine the probability mass function of X+Y.

The probability mass function of X+Y is given by:

P (X+Y = n) = ΣP (X = k) * P (Y = n-k),

where Σ is taken over all values of k from 0 to n.

Substituting the values of P (X = k) and P (Y = n-k), we get:

P (X+Y = n) = Σ(e^-λ1 λ1^k/k!) * (e^-λ2 λ2^(n-k)/(n-k)!),

where Σ is taken over all values of k from 0 to n.

By simplifying the above equation, we get:

P (X+Y = n) = e^-(λ1+λ2) [(λ1+λ2) ^ n/n!].

Hence, the distribution of X+Y is Poisson with mean λ1+λ2 and the probability mass function of X+Y is given by:

P (X+Y = n) = e^-(λ1+λ2) [(λ1+λ2) ^ n/n!].

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Answer:

4/7

Step-by-step explanation:

Answer:

4/7 ounces of butter makes a pound of jello

Step-by-step explanation:

7 times 4 is 28, so 4/28 ounces of butter for 7/28 pounds of jello. so 4/28 times 4 is 16/28. 16/28 is our answer, then simplified is 4/7. Thats how we get our answer.

Answer:

44° (second option)

Step-by-step explanation:

Since the line bisects the angle, we can set them equal to each other and solve:

[Equation] 7x + 9 = 10x - 6

[Add 6 to both sides] 7x + 15 = 10x

[Subtract 7x from both sides] 15 = 3x

[Divide both sides by 3] 5 = x

Now, we will plug it into the expression for angle VXW,

[Equation] 10x - 6

[Plug-In] 10(5) - 6

[Multiply] 50 - 6

[Subtract] 44

[Answer] 44°

Have a nice day!

   I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

x ≈ 77.8°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use trig to find the missing angle.

Step 2: Identify Variables

From POV of x

Angle = x

Adjacent = 8

Opposite = 37

Step 3: Solve for x

The expression that represents the area of the figure is (b) (3 x 2) + (3 x 4)

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

Lengths = 4 ft and 2 ft

Width = 3 ft

The expression that represents the area is represented as

Area = Length1 * Width + Length2 * Width

Substitute the known values in the above equation, so, we have the following representation

Area = (3 x 2) + (3 x 4)

hence, the expression is (b)

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The equation of the table of values is y = 0.36x - 0.42

The value of x if y is about 23 is about 65

The nearest value of y when x is 10 is 3

Given the table of values of x and y

x  4  5  6  7  8

y  1.24  1.38  1.41  1.76  2.84

Next, we enter the above values in a graphing tool (desmos)

From the tool, we have the equation to be

y = 0.36x - 0.42

This means that

y ≈ 23

So, we have

0.36x - 0.42 ≈ 23

This gives

0.36x ≈ 23.42

Divide by 0.36

x ≈ 65

This means that

x = 10

So, we have

y = 0.36(10) - 0.42

Evaluate

y = 3.18

Approximate

y = 3

So, the nearest value is 3

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Answer:

3.2

Step-by-step explanation:

Answer:

pythagorean theorem !!!!!!

Step-by-step explanation:

0.8²+1.6²=3.2²

0.64+2.56=10.24

THAT means the distance is

\( \sqrt{10.24} \)

=3.2miles

The equilibrium point is (60, 2400), the consumer surplus at the equilibrium point is $48,000, and the producer surplus at the equilibrium point is $36,000.

(a) The equilibrium point occurs when the quantity demanded by consumers equals the quantity supplied by producers. To find this point, we need to set the demand function equal to the supply function and solve for x.

Demand function: D(x) = 3000 - 10x

Supply function: S(x) = 900 + 25x

Setting D(x) equal to S(x):

3000 - 10x = 900 + 25x

Simplifying the equation:

35x = 2100

x = 60

Therefore, the equilibrium point occurs at x = 60.

(b) Consumer surplus at the equilibrium point can be found by calculating the area between the demand curve and the equilibrium price. Consumer surplus represents the difference between the price consumers are willing to pay and the actual market price.

At the equilibrium point, x = 60. Plugging this value into the demand function:

D(60) = 3000 - 10(60)

D(60) = 3000 - 600

D(60) = 2400

The equilibrium price is $2400 per unit. To find the consumer surplus, we need to calculate the area of the triangle formed between the demand curve and the equilibrium price.

Consumer surplus = (1/2) * (2400 - 900) * 60

Consumer surplus = $48,000

(c) Producer surplus at the equilibrium point represents the difference between the actual market price and the minimum price at which producers are willing to sell their goods.

To find the producer surplus, we need to calculate the area between the supply curve and the equilibrium price.

At the equilibrium point, x = 60. Plugging this value into the supply function:

S(60) = 900 + 25(60)

S(60) = 900 + 1500

S(60) = 2400

The equilibrium price is $2400 per unit. To find the producer surplus, we need to calculate the area of the triangle formed between the supply curve and the equilibrium price.

Producer surplus = (1/2) * (2400 - 900) * 60

Producer surplus = $36,000

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The given statement "it is possible to have a distribution of scores where no individual has a score exactly equal to the mode" is true because the mode represents the most frequently occurring score, and it is possible for the scores to be spread out in a way that no score occurs more frequently than any other.

In a distribution of scores, the mode is the score that occurs most frequently. However, it is possible for the scores to be spread out in a way that no score occurs more frequently than any other, making it impossible for any one score to be the mode.

For example, if a group of students all score differently on a test, with no two students receiving the same score, there is no mode. In such a case, no individual would have a score exactly equal to the mode since there is no mode in the distribution. Therefore, the given statement is true.

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Answer:

(-3,-3)

the X coordinate is -3 and the Y coordinate is -3.

Answer:

x = 15.

Therefore, the width of the walkway is 15m.

Step-by-step explanation:

Let's represent the width of the walkway by "x".

We know that the total width/base of the area (including the walkway) is 300m, so we can set up the equation:

length of field + 2(width of field) + 2(width of walkway) = 300

Substituting the given values, we get:

200 + 2w + 2x = 300

Simplifying the equation, we get:

2w + 2x = 100

We also know that the area of the field is 30,000m, so we can set up the equation:

length of field x width of field = 30,000

Substituting the given values, we get:

200w = 30,000

Simplifying the equation, we get:

w = 150

Finally, we know that the total area (including the walkway) is 60,000m, so we can set up the equation:

(length of field + 2x) x (width of field + 2x) = 60,000

Substituting the values we've found so far, we get:

(200 + 2x) x (150 + 2x) = 60,000

Expanding the equation, we get:

300x^2 + 1000x - 45,000 = 0

Solving for x using the quadratic formula, we get:

x = 15 or x = -30/100

Since x can't be negative, we can discard the negative solution and conclude that x = 15.

Therefore, the width of the walkway is 15m.

Part a: The expression that represents the area of the rectangle is A = (3x + 5)(6x + 11). To calculate the area, we must multiply the two sides of the rectangle together. The length of the rectangle is 3x + 5 units and the width of the rectangle is 6x + 11 units. Therefore, the area is (3x + 5)(6x + 11).

Part b: The degree of the expression obtained in part a is 2 and the classification is a binomial.

Part c: The closure property for polynomials states that the result of combining two polynomials is also a polynomial. In part a, we combined two polynomials, 3x + 5 and 6x + 11, to form the expression (3x + 5)(6x + 11). This expression is also a polynomial, demonstrating the closure property for polynomials. The closure property for polynomials allows us to combine two polynomials and still have a polynomial as the result. This is important in mathematics because it allows us to simplify equations and solve problems more quickly and efficiently.

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Answer: r^8

Step-by-step explanation:

r to the power 16-8

r^8 , third choice

a. 405000 - 6 significant digits        b. 0.0098 - 2 significant digits

c. 39.999999 - 9 significant digits   d. 13.00 - 4 significant digits

e. 80,000,089 - 8 significant digits  f. 55,430.00 - 7 significant digits

g. 0.000033 - 2 significant digits     h. 620.03080 - 8 significant digits

a. The number 405,000 has four significant digits: 4, 0, 5, and 0.

b. The number 0.0098 has two significant digits: 9 and 8.

c. The number 39.999999 has eight significant digits: 3, 9, 9, 9, 9, 9, 9, and 9.

d. The number 13.00 has four significant digits: 1, 3, 0, and 0.

e. The number 80,000,089 has eight significant digits: 8, 0, 0, 0, 0, 0, 8, and 9.

f. The number 55,430.00 has six significant digits: 5, 5, 4, 3, 0, and 0.

g. The number 0.000033 has three significant digits: 3, 3, and 3.

h. The number 620.03080 has eight significant digits: 6, 2, 0, 0, 3, 0, 8, and 0.

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If Kim invested $11,000 in two mutual funds.  Kim invested $4,800 in one mutual fund and $6,200 in the other mutual fund.

Kim invested x amount in the fund that rose by 6%

Kim invested (11,000 - x) amount in the fund that rose by 9%.

Increase in value from the first fund = 0.06x.

Increase in value from the second fund = 0.09(11,000 - x).

Total increase in value is $846

So,

0.06x + 0.09(11,000 - x) = 846

Let's solve this equation:

0.06x + 990 - 0.09x = 846

-0.03x = -144

x = -144 / -0.03

x = 4,800

Kim invested $4,800 in the fund that rose by 6% and the remaining amount of $11,000 - $4,800 = $6,200 in the fund that rose by 9%.

Therefore Kim invested $4,800 in one mutual fund and $6,200 in the other mutual fund.

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Answer:

8? not sure tho....

Step-by-step explanation:

Answer:

Step-by-step explanation:

<1 + <2 = 180 degrees (straight angle)

<3 + <5 + <4 = 180 degrees (straight angle)

<1 = <3 (vertical angles)

<1+<2 = <3+<4+<5 (straight angles)

<2 = (<3-<1)+<4+<5 (<3 - <1 = 0)

<2 = <4 + <5

The answer for the operating cash flow (OCF) for Daniel's Market is $4612.

To calculate the operating cash flow (OCF), we need to subtract the tax payment from the earnings before interest and taxes (EBIT). The formula for OCF is:

OCF = EBIT - Tax

First, let's calculate the EBIT by subtracting the depreciation and interest expenses from the earnings before taxes (EBT):

EBIT = EBT - Depreciation Expense - Interest Expense

Given that the sales are $38952, costs are $28651, depreciation expense is $3029, and interest expense is $1962, we can calculate:

EBIT = ($38952 - $28651) - $3029 - $1962 = $7320

Next, let's calculate the tax payment by multiplying the EBIT by the tax rate of 37%:

Tax = EBIT * Tax Rate = $7320 * 0.37 = $2708.40

Now, we can calculate the OCF by subtracting the tax payment from the EBIT:

OCF = EBIT - Tax = $7320 - $2708.40 = $4611.60

Rounding this amount to the nearest whole dollar gives us an operating cash flow of $4612.

Therefore, the operating cash flow (OCF) for Daniel's Market is $4612.

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