Plzz look at this problem first person with correct answer will get branliest

If a group of friends wanted to rent a cabin for the fourth of July. The number of  friends that were originally in the group is 8.

Let x represent the number of friends in the group

Cost per person =960/x

After   the 4 friends dropped out the remaining number of friends was = x - 4

New cost per person =960/x + 120

New total cost of the cabin rental = (x - 4) * (960/x + 120)

Set the two expressions equal to each other

960 = (x - 4) * (960/x + 120)

960 = 960 - (3840/x) + 120(x - 4)

Simplifying

3840/x = 120x - 480

Multiplying both sides by x

3840 = 120x^2 - 480x

Rearranging

120x^2 - 480x - 3840 = 0

Dividing both sides by 120

x^2 - 4x - 32 = 0

Quadratic equation

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where:

a = 1, b = -4, and c = -32.

Plugin the formula

x = (4 ± √(16 + 128)) / 2

x = (4 ± √(144)) / 2

x = (4 ± 12) / 2

x = 8 or x = -4

Therefore the number of friends  is 8.

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value of angle in the triangle is 19.5°

A triangle is a closed, 2-dimensional geometric shape that consists of three line segments connected end-to-end to form three sides. The three sides of a triangle enclose a region of space, and the interior angles between these sides sum to 180 degrees. The side opposite to the largest angle is the longest side and is called the hypotenuse in a right-angled triangle.  

In the given triangle,

Hypotenuse, h=18

Base, p=6

To find value of angle x

Using trigonometric function

Sinx=p/h

Sinx=6/18

x=Sin⁻¹1/3

x=19.47≈19.5°

Hence, value of angle in the triangle is 19.5°

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The value of the range of each data set are,

1) 15

2) 20

3) 16

4) 12

We have to given that;

Data set are,

Science: 86, 85, 90, 75, 56, 80

Math: 75, 73, 93, 84, 93, 70

Freshmen: 64, 62, 56, 63, 72

Seniors: 72, 68, 67, 60, 70

Since, Range is difference between the highest and smallest number of data set.

Hence, We get;

Science: 86, 85, 90, 75, 56, 80

Range = 90 - 75 = 15

Math: 75, 73, 93, 84, 93, 70

Range = 83 - 73 = 20

Freshmen: 64, 62, 56, 63, 72

Range = 72 - 56 = 16

Seniors: 72, 68, 67, 60, 70

Range = 72 - 60 = 12

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In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.

The components of a whole or group of objects are represented by fractions. A fraction consists of two parts. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the whole or collection. The denominator is the figure that appears below the line.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the fundamentals of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, and division.

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The statement that describes when the plans are based on the same number of aerobic exercise sessions is:

The number of strength-training exercises and aerobic exercises per week is calculated as follows:

Let a be the number of strength-training exercises and b be the number of aerobic exercises per week respectively.

For the beginner plan:

15a + 20b = 90  eqn. (1)

For the advanced plan:

20a + 30b = 130 eqn. (2)

Solving the simultaneous equation by elimination method:

Multiply eqn. (1) by 3 and eqn. (2) by 2

45a + 60b = 270 eqn. (3)

40a + 60b = 260 eqn. (4)

Subtract eqn. (4) from eqn. (3)

5a = 10

a = 2

Substitute a = 2 in eqn (2)

b = 3

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Complete question:

A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week.

Which statement describes when the plans are based on the same number of aerobic exercise sessions?

Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.

Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.

Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

You should deposit approximately $340.84 monthly to reach $293,000 in 28 years at a 4.4% annual interest rate compounded monthly.

To calculate the monthly deposit required for an investment plan paying 4.4% interest compounded monthly to reach $293,000 in 28 years, we use the future value of an annuity formula:

FV = P * (((1 + r)^n - 1) / r)

Here, FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of payments. First, convert the annual interest rate (4.4%) to a monthly rate by dividing by 12, which gives 0.0367 (4.4%/12) or 0.00367 as a decimal. The number of payments (n) is 28 years * 12 months/year = 336.

We want to find P, so rearrange the formula:

P = FV / (((1 + r)^n - 1) / r)

Substitute the values:

P = $293,000 / (((1 + 0.00367)^336 - 1) / 0.00367)

P ≈ $340.84

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The interpretation of OA in the linear multiple regression model with two independent variables, where E(Y|X1=x1,X2=x2) = β0 + β1x1 + β2x2, is the same as in the simple regression model when X1 was the only regressor. OA represents the intercept or the predicted value of Y when both independent variables are equal to zero.

OB: OB represents the predicted difference in Y between two observations for a one-unit increase in X1, holding X2 constant. In other words, it shows the change in the predicted value of Y for a unit increase in X1, while controlling for the effect of X2.

OC: OC represents the predicted difference in Y between two observations for a one-unit increase in X2, holding X1 constant. It shows the change in the predicted value of Y for a unit increase in X2, while controlling for the effect of X1.

OD: OD represents the predicted difference in Y between two observations for a one-unit increase in both X1 and X2. It shows the change in the predicted value of Y for a unit increase in both X1 and X2, while holding the other variable constant.

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Answer:

ans= 36.72 /1- 15/100

= 36.72 * 20/17

= 36.72 * 1.17647 = 43.2

the original price = £43.2

The correct expression is, (9 - 2/x)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

''9 minus the quotient of 2 and x.''

Now, The mathematical expression is written as;

⇒ 9 - 2/x

Thus, The correct expression is, (9 - 2/x)

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P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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The annual property tax for the Joseph family is $8749.8.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

The Joseph family took out a $175,000,

25-year mortgage at an APR of 4%.

The assessed value of their house is $9,000.

The annual property tax rate is 97.22% of assessed value.

The annual property tax = 9000 x 97.22/100

The annual property tax = $8749.8

Therefore, the annual property tax = $8749.8

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Answer:

-3

Step-by-step explanation:

16/4=4, so seven less than that is -3

The slope of equation  y = -5/6 x + 4 is -5/6 and the slope-intercept form of -5/6x+4 is y = -5/6 x + 4

The slope of a function y = f(x) is given by a formula

slope = y2-y1 / x2- x1

where ( x1 , y1) and (x2, y2) are coordinates of any two points on the line of graph representing y = f(x)

Or we can simply use the slope-intercept form

y = mx+ c

where m is the slope of the given equation and c is the constant

so, in  the given equation y = -5/6 x + 4

slope of the equation is -5/6

Hence, The slope of equation  y = -5/6 x + 4 simply is -5/6 and the slope intercept form of -5/6x+4 is y = -5/6 x + 4

When you know the slope of the line to be investigated and the point given is also the y intercept, you can utilize the slope intercept formula y = mx + b. (0, b). The y value of the y intercept point is represented by b in the formula.

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Answer:

-9

Step-by-step explanation:

-3 - 6

-3 + -6

-9

hope this helps!

The height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

The volume of the cylinder can = 1000 cubic cm

Consider the height of the cylinder as h and the radius of the base is r

Volume of the cylinder = π\(r^2\)h = 1000

h = 1000 / π\(r^2\)

The surface area of the cylinder

A = 2π\(r^2\) + 2πrh

A = 2π\(r^2\) + 2πr(1000 / π\(r^2\) )

A = 2π ( \(r^2\) + 1000 / π\(r^2\))

Differentiate the terms

A' =  2π (2r + 1000 / π\(r^3\))

When the minimum surface area

2π (2r + 1000 / π\(r^3\)) = 0

r = \((1000/2\pi )^\frac{1}{3}\)

r = 5.41 cm

Then,

h =  1000 / π\(r^2\)

= 1000 / (π × 5.41 × 5.41)

= 1000 / 91.94

= 10.87 cm

Hence, the height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

Shape 2 and 3

Step-by-step explanation:

shape 1 is not enclosed so it cannot have area

A ratio describes a relationship between two or more quantities. When mixing colors, ratios are often used to determine the ratio of different colors required to achieve a desired hue. Ratios can be expressed in 1:, 2:3,.. etc.

Ratios affect the appearance of paint colors. In this scenario, Can A has a higher percentage of red than can B. This means that the shade of pink you get with Can A is likely to be darker and more red due to the higher concentration of red.

Can B, on the other hand, has a lower percentage of red, suggesting that the resulting pink hue is lighter and less red than can A.  

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Answer:

The Sandbox must be 19x19 for the area to be 361.

Step-by-step explanation:

(19x19=361)

The length of the sandbox will be 19 feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.

Given that Mr. Drew wants to build a square sandbox with an area of 361 square feet.

The length will be calculated by using the area formula for square;

Area of square = Length x width

Then the area of the square can be written as;

Area of square = ( Length )²

361=  ( Length )²

( Length ) = √361

( Length ) = 19feet

Therefore, the length of the sandbox will be 19feet.

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................b = 17...............

Answer:

2/3

Step-by-step explanation:

dy/dx equals derivative of y by x

dy/dx=20t/30t=2/3

Answer:

C. 3.5

Step-by-step explanation:

Math

Way

Answer:

Step-by-step explanation:

13/40 it can not be simplified any further.

The solution to the given equation which is log₃(1/9) = 2x - 1 is equal to x = -1/2.

To solve the equation log₃(1/9) = 2x - 1, we need to isolate the variable x on one side of the equation. We can start by using the logarithm property that states that the logarithm of a number to a base is equal to the exponent to which the base must be raised to obtain that number. In other words, log₃(1/9) = x if and only if \(3^x\) = 1/9.

So, let's rewrite the given equation using this property as follows:

\(3^{(log(1/9))\) = \(3^{2x-1\)

Simplifying the left-hand side using the logarithm property, we get:

1/9 = \(3^{(2x - 1)\)

Now, we can solve for x by taking the logarithm of both sides to base 3:

log₃(1/9) = log₃(\(3^{(2x - 1)\))

-2 = (2x - 1) * log₃(3)

-2 = 2x - 1

2x = -1

x = -1/2

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Answer: Where is the triangle?

Step-by-step explanation: Brainliest pls:)

The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

The graph of quadratic functions is a technique to study the nature of the quadratic functions graphically. The shape of the parabola is determined by the coefficient 'a' of the quadratic function f(x) = ax2 + bx + c, where a, b, c are real numbers and a ≠ 0.

the vertex of a quadratic function is. \(f(x)=a(x-h)^2+k, where (h,k)\) is the vertex of parabola. When a>0 then function will be open upward if a<0 then function will be opens downward.

Steps to plot graph of quadratic function.

a\(x^2\) is imply a vertical scaling of the parabola, if a<0 the parabola will also flip its mouth from the positive to negative side.

\(a(x+\frac{b}{2a} )^2\) This is a horizontal shift of magnitude |\(\frac{b}{2a}\)| units. The direction of the shift will be decided by the sign of b/2a. The new vertex of the parabola will be at (-b/2a,0).

This transformation is a vertical shift of magnitude |\(\frac{D}{4a}\)| units. The direction of the shift will be decided by the sign of \(\frac{D}{4a}\). The final vertex of the parabola will be at (\(\frac{-b}{2a} ,\frac{-D}{4a}\)).

So, The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

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Porosity calculated as ratio of pore to total vol. Plot of porosity vs averaging length scale (edge of square used for averaging). Rep. elemental vol = vol of square used for averaging.

The porosity as a function of the averaging length scale can be calculated as follows:

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