two people share some money in the ratio 3:5. one person gets $75, find out two possible values with the amount of money the other person gets​

The cross sectional area of the cargo trailer floor, which is a composite figure consisting of a square and an isosceles triangle, indicates that the volume of the inside of the trailer is about 3,952 ft³.

A composite figure is a figure comprising of two or more regular figures.

The possible cross section of the trailer, obtained from a similar question on the internet, includes a composite figure, which includes a rectangle and an isosceles triangle.

Please find attached the cross section of the Cargo Trailer Floor created with MS Word.

The dimensions of the rectangle are; Width = 6 ft, length = 10 ft

The dimensions of the triangle are; Base length 6 ft, leg length = 4 ft

Height of the triangular cross section = √(4² - (6/2)²) = √(7)

The cross sectional area of the trailer, A = 6 × 10 + (1/2) × 6 × √(7)

A = 60 + 3·√7

Volume of the trailer, V = Cross sectional area × Height

V = (60 + 3·√7) × 6.5 = 3900 + 19.5·√7

Volume of the trailer = (3,900 + 19.5·√(7)) ft³ ≈ 3952 ft³

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Answer:

B.) 3√15

Step-by-step explanation:

a^2 + b^2 = c^2

x^2 + 11^2 = 16^2

x^2 + 121 = 256

x^2 = 256 - 121

x^2 = 135

√x^2 = √135

√135 = √9 • √15

√9 = 3

√15 = √15

3√15

An increase in the real interest rate will most likely lower the reward to savings. The correct answer is D.

When the real interest rate increases, it means that the return on savings and investments is higher in real terms, adjusted for inflation. As a result, individuals are incentivized to save more as they can earn a higher return on their savings.

When the reward to savings is lower, it becomes less attractive for individuals to save. Higher interest rates can discourage borrowing and encourage saving, which reduces consumer spending on durable goods and other discretionary purchases.

Option A is incorrect because an increase in the real interest rate would likely lead to a decrease in consumer's purchases of durable goods, as higher interest rates increase the cost of borrowing, making it more expensive to finance large purchases.

Option B is incorrect because an increase in the real interest rate generally makes borrowing more expensive, as it increases the cost of borrowing for individuals and businesses.

Option C is incorrect because an increase in the real interest rate usually encourages individuals to save more and spend less, as the potential return on savings is higher.

The correct answer is D.

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Answer: 85

Step-by-step explanation:

\(100-3(3y-4x)\\\\=100-3(3 \cdot 7-4 \cdot 4)\\\\=100-3(21-16)\\\\=100-3(5)\\\\=100-15\\\\=85\)

Answer:

148

Step-by-step explanation:

use bidmas to get final solution

100-3(12-28)

100-3 × (-16)

=148

Answer:3/4 is the answer

Step-by-step explanation:

Answer:(s)

1/4  -  7/1  =  - 27/4  

Decimal:   - 6.75

Mixed number:  - 6 3/4

Step-by-step explanation:

1/4  -  7/1  =  - 27/4  or - 6.75 or  - 6 3/4

LCM:   4, 1  = 4

Adjust Fraction Based On LCM:

1/4 - 28/4

Apply The Fraction Rule:

a/c - b/c  =  a - b/c

1 - 28/4

Subtract the numbers:

1  -  28   =  - 27

             =  -27/4

Apply Fraction Rule:

- a/b  =  - a/b

Thus:

1/4 - 7/1  =  - 27/4  

Decimal:   - 6.75

Mixed Number Form  - 6 3/4

I hope that helps you!!!

Step-by-step explanation:

\(cd + db = a \\ b(c + d) = a \\ \frac{b(c + a)}{a + b} \\ b = \frac{a}{c + d} \)

Answer:

The other answer is correct

Step-by-step explanation:

In a hypothesis testing context, before examining the data, one should establish a null hypothesis and an alternative hypothesis.

Before conducting any analysis or collecting data, it is crucial to define the null hypothesis and the alternative hypothesis. The null hypothesis (H₀) represents the assumption of no effect or no difference between groups or variables, while the alternative hypothesis (H₁) represents the claim or hypothesis being tested. These hypotheses help define the question or statement that the researcher wants to investigate.

Formulating the null and alternative hypotheses before examining the data is important to ensure the hypothesis testing process is objective and guided by clear expectations. It helps to establish a framework for statistical analysis and allows for making informed decisions based on the evidence provided by the data.

Additionally, this initial step ensures that the hypothesis testing process remains rigorous and avoids potential biases that may arise from post hoc analyses.

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The unit rate of the linear equation y = 8x is 8.

A linear equation of a function illustrates the straight line on a coordinate plane. It can be expressed in a slope intercept form y = mx + b, where:

The slope shows steep the gradient is and it is the change in the rise over the run. For a unit rate which is usually the ratio between two different quantities. We can say in the linear equation, the unit rate represents the slope of the function.

Given that:
y = 8x

To find the unit rate(slope) which is the change in the y-axis(rise) over the change in the x-axis(run) by using slope-intercept form. Then, we can conclude that the unit rate is 8.

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Answer:

120 bottles of water are needed. 3 cases are needed.

Step-by-step explanation:

If there are 60 people and they each have 2 bottles of water, we know that there are 120 bottles in total, 60x2 = 120.

There are 40 bottles in one case. Knowing this, we divide 120 by 40 to get that 3 cases are needed.

\(V = πr^2h = πr^2 * (4/π) = 4r^2.\) The volume of the cylinder with a radius r and a cross-section perpendicular squares. To determine the volume of a solid with a circular base and cross sections that are perpendicular squares, we need to use the formula for the volume of a cylindrical shell.

Radius can r according to the formula that is given the volume is already mentioned.

\(V = πr^2hh\) is the height of the cylinder. Squares are the cross section of cylinders,  side length can be equal to 2r. So, the area of each cross-section is \((2r)^2 = 4r^2.\)

The h in consideration of the area of cross-section h = Area of the cross section \(/ πr^2h = (4r^2) / πr^2 = 4/π\)The volume of the shell of the cylinder is \(V = πr^2h = πr^2 * (4/π) = 4r^2\)The volume of the cylinder with a radius r and a cross-section perpendicular squares.

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Answer:-

first take the angle sum property in triangle CAB

45+30+∠B=180

75+∠B=180

∠B=180-75

∠B=105

In a parallelogram, opposite angles are equal

therefore,

∠D=105(opposite angles are equal)

hope you find it helpful

The center of the circle can be found using a ruler-and-compass construction by drawing two arcs that intersect at the center of the circle. The radius of the circle can also be found using a ruler by measuring the distance from the center of the circle to any point on the circumference of the circle.

To make a ruler-and-compass construction of the center of a given circle, follow these steps:

Draw a line segment through the center of the circle using a ruler. This line segment should intersect the circle at two points.

Using a compass, draw an arc with the center at one of the intersection points and the radius equal to the length of the line segment.

Draw another arc with the center at the other intersection point and the same radius.

The point where the two arcs intersect is the center of the circle.

Use a ruler to draw a line from the center of the circle to any point on the circumference of the circle. This line is the radius of the circle.

The center of the circle can be found using a ruler-and-compass construction by drawing two arcs that intersect at the center of the circle. The radius of the circle can also be found using a ruler by measuring the distance from the center of the circle to any point on the circumference of the circle.

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The area of square four is a² + b² + 2ab

The area of a square = l²

The Area so the two square = a² + b²

Area of the  triangles = 4(0.5ab) = 2ab

Add the area together

Area of the square four = area of square + area of 4 triangles

Area of the square four = a² + b² + 2ab

Hence the area of the square four is a² + b² + 2ab

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Answer:

4.578? hope this helps

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

x-8=-2

x=-2+8

x=6

Answer:

x = 6

Step-by-step explanation:

x - 8 = -2

x - 8 + 8 = -2 + 8

x + 0 = 6

x = 6

Check:

6 - 8 = -2

The equation which represents the relationship between 'h' the number of hours, and c, the total cost is y = 250x+850.

A straight line equation is a mathematical equation that describes the relationship between the coordinate points on that straight line. It can be written in several ways and indicates the slope, x-intercept, & y-intercept of a line.

Now, as per the given question;

The attorney charges price for an initial meeting = $850.

And, the charges for each hour is = $250.

Thus, the equation which shows the given situation is-

y = 250x + 850.

In which, 250 is the value of the slope 'm'.

The y- intercept is shown by 850.

Thus, the total cost will be found out by equation  y = 250x+850.

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The Value of x is approximately -1.841 (rounded to 3 decimal places).

To solve for x in the equation x = (1 - bc - b)/(da) - 1, we substitute the given values for a, b, c, and d.

Given: a = 7, b = 6, c = 8, d = 9

Substituting these values into the equation, we have:

x = (1 - 6*8 - 6)/(7*9) - 1

Simplifying further, we have:

x = (1 - 48 - 6)/(63) - 1

x = (-53)/63 - 1

To find the value of x, we perform the division and subtraction:

x = -0.841 - 1

x = -1.841

Therefore, the value of x is approximately -1.841 (rounded to 3 decimal places).

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The stem-and-leaf display of the data is

Stem | Leaves

1 | 2

2 | 2

3 | 3

4 | 5, 8

To start, let's assume we have a set of data values, such as 12, 22, 33, 45, 48, 53, 61, 62, 72, 83, 91, 96, 99.

The stem-and-leaf display consists of two parts: the "stem" and the "leaf." The stem represents the leading digit(s) of the data values, and the leaf represents the trailing digit(s). For example, the number 12 has a stem of 1 and a leaf of 2.

Now, let's organize the data values into their corresponding stems:

Stem 1: 12

Stem 2: 22

Stem 3: 33

Stem 4: 45, 48

Next, we list the leaves corresponding to each stem. The leaves are listed in ascending order next to their respective stems:

Stem 1: 2

Stem 2: 2

Stem 3: 3

Stem 4: 5, 8

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Answer:

D: (1,2)

Step-by-step explanation:

To find the translation vector, we need to determine the difference between corresponding coordinates of the original triangle and the translated triangle.

Let's denote the original triangle's vertices as A(0, 0), B(3, 0), and C(0, 4). The corresponding vertices of the translated triangle are A'(1, 2), B'(4, 2), and C'(1, 6).

To find the translation vector, we subtract the coordinates of each vertex in the original triangle from the coordinates of the corresponding vertex in the translated triangle.

Translation vector for point A:

x-component: 1 - 0 = 1

y-component: 2 - 0 = 2

Translation vector for point B:

x-component: 4 - 3 = 1

y-component: 2 - 0 = 2

Translation vector for point C:

x-component: 1 - 0 = 1

y-component: 6 - 4 = 2

Therefore, the translation vector is (1, 2).

Answer:

Yes its D

Step-by-step explanation:

Correct on edg. 2021

The question that points out his most serious omission from the monthly budget preparation is d. What if you need to replace the furnace?

A monthly budget is an outline of the cash inflows and cash outflows from a person's or firm's account during a month's period.  It tracks cash inflows based on income and the outflows in expenses.

The preparation of a monthly budget helps in financial planning and control by tracking expenses and income.

Thus, the most relevant question that deals with a budget overlook is not about losing stock income, going to the doctor, increased electric bill but Option D.

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Answer:

length of rope = 51 inches

Step-by-step explanation:

Let the length of the rope = x inches

\(\dfrac{1}{3}*x=17\\\\\\Multiply \ both \ sides \ by \ 3 \\\\x = 17*3\\\)

x = 51

Answer:

17 inches 0-0 dang

Step-by-step explanation:

Answer:

The Original point is (1, -8)

The Final point in my graph of A is (1, -3)

Step-by-step explanation:

translate the figure 5 units up means to move the points up by 5. In my graph I've shown all the points translated 5 units up

Answer: c

Step-by-step explanation:

Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

What is transformation ?

A transformation is a function that changes the position, size, or shape of an object or a graph. In mathematics, transformations are often used to map a function from one coordinate space to another. There are several types of transformations, including translations, rotations, reflections, and scalings.

Part A: Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

Part B:

Horizontal stretching/shrinking: k is the horizontal scale factor.

Vertical stretching/shrinking: k is the vertical scale factor.

Part C:

Horizontal stretching/shrinking: g(x) = f(kx)

Vertical stretching/shrinking: g(x) = kf(x)

Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

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Theorem 4.4.1, also known as the positive divisor theorem, states that for all positive integers a and b, if a divides b, then a is less than or equal to b. In other words, if a is a factor of b, then a is smaller than or equal to b.

To prove this theorem, we can use the definition of divisibility, which states that if a divides b, then there exists an integer k such that b = ak. Since a and b are both positive, k must also be positive.

Multiplying both sides of the equation b = ak by the positive integer 1/a, we get b/a = k, which means that k is a positive integer. Therefore, a ≤ b/a, or equivalently,\(a^2 ≤ ab\). Since a is positive, we can divide both sides of this inequality by a to get a ≤ b.

Thus, we have shown that if a divides b, then a is less than or equal to b, which proves Theorem 4.4.1. This theorem is a fundamental property of divisibility and is often used in number theory and other mathematical areas.

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The measure of the mid  segment is 53 .

Given :

the measures of the bases of a trapezoid are 35 and 71.

What is trapezoid ?

A trapezoid is a four-sided shape which has one pair of sides as parallel. It is basically a two-dimensional shape or figure similar to a square etc .

Mid segment :

A mid segment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

A trapezoid mid segment is parallel to the set of parallel lines in a trapezoid and is equal to the average of the lengths of the bases.

Measure of mid segment = sum of two bases / 2

= 35 + 71 / 2

= 106 / 2

= 53

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If an nxn matrix A are linearly independent when A is invertible, because option (C) If A is invertible, then the equation Ax = 0 has the unique solution x=0. Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent.

When a matrix A is invertible, it means that there exists a matrix A^-1 such that AA^-1 = A^-1A = I, where I is the identity matrix.

Now suppose that the columns of A are linearly dependent. This means that there exist scalars c1, c2, ..., cn, not all zero, such that

c1A[:,1] + c2A[:,2] + ... + cn×A[:,n] = 0

where A[:,i] represents the i-th column of the matrix A.

In other words, there exists a non-zero vector x = [c1; c2; ...; cn] such that Ax = 0.

Multiplying both sides by A^-1, we get:

A^-1(Ax) = A^-1(0)

x = 0

But this contradicts our assumption that x is non-zero. Therefore, the columns of A must be linearly independent

Therefore, the correct option is (C) If A is invertible, then the equation Ax = 0 has the unique solution x=0. Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent.

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The given question is incomplete, the complete question is:

Explain why the columns of an nxn matrix A are linearly independent when A is invertible. Choose the correct answer below.

A) -1 If A is invertible, then A has an inverse matrix A Since AA = I, A must have linearly independent columns.

B) If A is invertible, then for all x there is a b such that Ax = b. Since x = 0 is a solution of Ax = 0, the columns of A must be linearly independent.

C) If A is invertible, then the equation Ax = 0 has the unique solution x=0. Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent.

D) If A is invertible, then A has an inverse matrix A-1. Since AA-1 =A-1A, A must have linearly independent columns.

The mean and standard deviation for the number of correct answers for such students is; μ = 6.5 and σ = 1.802776

Given there is a surprise​ true/false test with 13​ questions.

Thus, the probability of correctly guessing the answer is; p=0.5

Let "X' be the answers correctly guess by a student.

The formula for the binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

A) The mean of the binomial distribution is given by the formula;

μ = np

μ = 13 * 0.5

μ = 6.5

The formula for standard deviation is:

σ = √(np(1 - p))

σ = √(13 * 0.5(1 - 0.5))

σ = 1.802776

B) The probability that the student getting at least 11 correct​answers is given by:

P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13)

Using online binomial probability calculator, we have;

P(X ≥ 11) = 0.01123

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Complete question is;

Several psychology students are unprepared for a surprise​true/false test with 13 ​questions, and all of their answers are guesses.

a. Find the mean and standard deviation for the number of correct answers for such students.

b. Would it be unusual for a student to pass by guessing​ (which requires getting at least 11 correct​ answers)? Why or why​not?

Answer:

24/12 = 2/1 = 2

Step-by-step explanation:

Answer:

\(\huge\boxed{Answer\hookleftarrow}\)

\( \frac{12}{24 } \\ = \frac{24}{12} \)

\( \frac{24}{12} \\ = \frac{2}{1} \\ = 2\)

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