Which prisms are similar to a prism with a length of 10 feet, a width of 6 feet, and a height of 12 feet?

Answer:

b=4

perimeter=12

Step-by-step explanation:

frist find b by using pythagory theorm

the a+b+c=perimeter

The value of expression is,

⇒ x ÷ 12

We have to given that;

The algebraic expression is,

⇒ x divided by 12

Hence, We can formulate;

The value of correct expression is,

⇒ x ÷ 12

⇒ x / 12

Thus, The value of expression is,

⇒ x ÷ 12

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Data:

• Monthly budget: $15

• Price of a package of ramen: $1.48

• Price of a music download: $1.15

Procedure:

Answer: 10.1

The final answer is: ∫(2x-1)÷[(x-3)(x+2)]dx = ln|x-3| + ln|x+2| + C

What is Integration ?

In calculus, integration is the inverse operation of differentiation. It is a mathematical technique used to find the integral of a function. The integral of a function f(x) is another function F(x), which gives the area under the curve of f(x) from a certain point to another.

To perform the integration of the given function:

∫(2x-1)÷(\(x^{2}\)-x-6)dx

First, we need to factor the denominator:

\(x^{2}\)- x - 6 = (x-3)(x+2)

So we can rewrite the integral as:

∫(2x-1)÷[(x-3)(x+2)]dx

Next, we need to decompose the fraction into partial fractions:

(2x-1)÷[(x-3)(x+2)] = A÷(x-3) + B÷(x+2)

Multiplying both sides by (x-3)(x+2), we get:

2x-1 = A(x+2) + B(x-3)

Substituting x=3, we get:

5A = 5

A = 1

Substituting x=-2, we get:

-5B = -5

B = 1

So we have:

(2x-1)÷[(x-3)(x+2)] = 1÷(x-3) + 1÷(x+2)

Substituting this back into the integral, we get:

∫(2x-1)÷[(x-3)(x+2)]dx = ∫[1÷(x-3) + 1÷(x+2)]dx

Using the first rule of integration, we get:

∫[1÷(x-3) + 1÷(x+2)]dx = ln|x-3| + ln|x+2| + C

where C is the constant of integration.

Therefore, the final answer is: ∫(2x-1)/[(x-3)(x+2)]dx = ln|x-3| + ln|x+2| + C

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\( \displaystyle \int \rm \: \dfrac{2x - 1}{ {x}^{2} - x - 6 } dx\)

Answer:

\( \underline{\boxed{\rm = ln |x + 2| + ln |x - 3| + C}}\)

Step-by-step explanation:

\( = \displaystyle \int \rm \: \dfrac{2x - 1}{ {x}^{2} - x - 6 } dx\)

\( = \displaystyle \int \rm \: \dfrac{2x - 1}{ {x}^{2} - 3x + 2x - 6 } dx\)

\( = \displaystyle \int \rm \: \dfrac{2x - 1}{ x(x - 3) + 2(x - 3) } dx\)

\( = \displaystyle \int \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3)} dx\)

\( \rm \: Let : \displaystyle \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3) } = \dfrac{A }{x + 2} + \dfrac{B}{x - 3} \)

\(\rm\implies\displaystyle \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3) } = \dfrac{A(x - 3) + B(x + 2) }{(x + 2)(x - 3)} \\ \)

\( \rm \implies\displaystyle \rm \: {2x - 1}{ } = {A(x - 3) + B(x + 2) } \\ \)

Put x = 3 , we get

\( \rm \implies\displaystyle \rm \: {6 - 1}{ } = {A(3- 3) + B(3 + 2) } \\ \)

\( \rm \implies\displaystyle \rm \: {5}{ } = 5 B \\ \)

\( \implies \rm \: B = 1\)

Again

put put x = -2

\( \rm \implies\displaystyle \rm \: { - 4- 1}{ } = {A( - 2- 3) + B( - 2 + 2) } \\ \)

\( \rm \implies\displaystyle \rm \: { - 5}{ } = {A( - 5) } \\ \)

\( \rm \implies\displaystyle \rm A = 1 \\ \)

Thus ,

\( \displaystyle \int \rm \: \dfrac{2x - 1}{ (x + 2) (x - 3)} dx = \int\dfrac{1}{x + 2} dx + \int \dfrac{1}{x - 3} dx\)

\( \rm = ln |x + 2| + ln |x - 3| + C\)

\( \tt\int \dfrac{dx}{ {x}^{2} + {a}^{2} } = \frac{1}{a} { \tan}^{ - 1} \frac{x}{a} + c \\ \)

\( \tt\int \dfrac{dx}{ {x}^{2} - {a}^{2} } = \frac{1}{2a} log \frac{x - a}{x + a} + c \\ \)

\( \tt\int \dfrac{dx}{ {a}^{2} - {x}^{2} } = \frac{1}{2a} log \frac{a + x}{a - x} + c \\ \)

\( \tt\int \: \dfrac{dx}{ \sqrt{ {x}^{2} + {a}^{2} } } = log|x + \sqrt{ {a}^{2} + {x}^{2} } | + c \\ \)

\( \tt\int \: \dfrac{dx}{ \sqrt{ {x}^{2} - {a}^{2} } } = log|x + \sqrt{ {x}^{2} - {a}^{2} } | + c \\ \)

\( \tt \int \: \dfrac{dx}{ {a}^{2} - {x}^{2} } = { \sin }^{ - 1} \bigg(\dfrac{x}{a} \bigg) + c \\ \)

\( \tt \int \: \sqrt{ {x}^{2} + {a}^{2} } dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\= \tt \dfrac{x}{2} \sqrt{ {a}^{2} + {x}^{2} } + \dfrac{ {a}^{2} }{2} log |x + \sqrt{ {x}^{2} + {a}^{2} }| + c\)

Answers for a) $53.2, b) z = 10x+0.07y and c) y =300

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a car rental company charges $7 a day and 9 a mile to rent one of its cars, then the cost z, in dollars, to rent a car for 2 days and drive y miles can be found from the equation

z = 7x + 0.09y

a) x = 4, y = 280

z = 7*4 + 280*0.09

z = 53.2

Therefore, the cost to rent a car for 4 days and drive it for 280 miles is $53.2

b) The equation that gives the cost z

z = 10x+0.07y

c) When the costs are equal, then,

10*2+0.07y = 7*2+0.09y

20+0.07y = 14+0.09y

0.02y = 6

y = 300

Therefore, the cost of renting the cars from each of the two companies will be equal when y = 300 miles.

Hence, Answers for a) $53.2, b) z = 10x+0.07y and c) y =300

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Answer:

z

Step-by-step explanation:

Answer:

Let the three angles be 2x,9x & 4x

By the problem,2x+9x+4x=180

15x=180

x=180/15

x=12

there fore the angles are

2x= 2*12=24°

9x=108°

4x=48°

Step-by-step explanation:

The prime of the set  is  mathematically given as

A' {e,h,i,j,k}

This is further explained below.

Generally, Mathematically speaking, "set theory" refers to the study of well-defined groups, or "sets," of individual things that are collectively referred to as "members" or "elements" of the set. Because sets are the only topic of discussion in pure set theory, the only sets that may be taken into account are those that include other sets as members.

Assigned the letter A (A prime), The components that are included in the Universal set but are absent from Set A are denoted by the letter A'.

In conclusion, the prime of the set  is  mathematically given as

A' {e,h,i,j,k}

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CQ

Let U={e,f,g,h,i,j,k} and A={f,g}

find A'

Answer: 3

Step-by-step explanation:

The scale factor is the ratio of corresponding side lengths of the two triangles.

In the given triangles, the length of the corresponding sides of the triangles are:

For the first triangle:

Side A = 15 units

Side B = 15 units

For the second triangle:

Side A = 45/2 units

Side B = 45/2 units

To find the scale factor, we can divide the length of one side of the second triangle by the corresponding length of the first triangle.

For example, we can use Side A:

Scale factor = (length of Side A of the second triangle) / (length of Side A of the first triangle)

Scale factor = (45/2) / 15

Scale factor = (45/2) * (1/15)

Scale factor = 3/2

Since the two triangles are scaled copies of each other, the scale factor should be the same for all corresponding sides.

Thus, the scale factor is 3 (in simplest form).

Answer:

side = 111.274........

Explanation:

area of square = side × side

means we're finding area by finding square of side.

now, we're finding side. so, we'll do the opposite of square, which means square root.

\(side = \sqrt{area} \)

so,

\(side = \sqrt{12382} \)

side = 111.274........

please mark BRAINLIEST!

To find the area of a quadrilateral with given coordinates, you can use the Shoelace Formula.

The Shoelace Formula, also known as Gauss's area formula, provides a method to calculate the area of any polygon given its coordinates. Here's how it works for a quadrilateral:

Let's say you have the coordinates of the four vertices of the quadrilateral: (x1, y1), (x2, y2), (x3, y3), and (x4, y4).

1. Write down the coordinates in a clockwise order:

  (x1, y1), (x2, y2), (x3, y3), (x4, y4), (x1, y1).

2. Multiply each x-coordinate by the y-coordinate of the next vertex.

  For example, for the first vertex (x1, y1), multiply x1 by y2, and for the second vertex (x2, y2), multiply x2 by y3, and so on.

3. Multiply each y-coordinate by the x-coordinate of the next vertex.

  For example, for the first vertex (x1, y1), multiply y1 by x2, and for the second vertex (x2, y2), multiply y2 by x3, and so on.

4. Add up all the results from Steps 2 and 3.

5. Take the absolute value of the sum calculated in Step 4 and divide it by 2.

By following the steps of the Shoelace Formula, you can calculate the area of a quadrilateral given its coordinates. Remember to ensure that the coordinates are listed in a clockwise or counterclockwise order to obtain the correct result. This method can be applied to any quadrilateral shape and provides an efficient way to find its area without requiring complex calculations or trigonometric functions.

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The probability that the card that Olga turns over has a rose on it would be 4/5.

Since, Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Given that;

There are 5 cards with a picture of a rose and 1 card with a picture of a daisy.

Olga keeps all the cards face down on the table with the pictures hidden and mixes them up.

Then , Total number of cars after Olga removed one rose card from the table is,

4 rose cards + 1 Daisy card

= 5

Therefore, the probability divide the number of rose cards left by the total number of cards left is,

= 4/5

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Answer:

1/64

Step-by-step explanation:

Doing it by hand, I get that the number is 1/16 which is equal to 0.0625 and the previous one will be 1/8 which is 0.125.

In the formula given by others, if you apply the 12 to it you will get an=2(5-12)which is equal to 0.0078,  less than 0.100 but not the first number.

The correct value for n is 9 that will give us 2-4=1/16

253.508 is 0.01 more than 253.498.

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.

It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures.

Let the number be x

so,

x=253.498+0.01

x= 253.508

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Answer:

3 + \(\pi\) is irrational, as \(\pi\) is an irrational number in itself, not being able to change into a fraction as it is a non-terminated number.

~

(a) The probability that Y₂₀ exceeds 1000  is 3.91 × 10⁻⁶.

(b)  The professor teach in order that the probability is n = 28.09 years.

The random variable Yₙ is defined as the total numbers of dollars paid in n years.

It is provided that Yₙ can be approximated by a Gaussian distribution, also known as Normal distribution.

The mean and standard deviation of Yₙ are:

μYₙ=40n

σYₙ =√100n

(a) For n = 20 the mean and standard deviation of Y₂₀ are:

μYₙ= 40n = 40×20 = 800

σYₙ = √100n = √100× 20 = 44.72

Compute the probability that Y₂₀ exceeds 1000 as follows:

P(Yₙ >100) = P( Yₙ - μYₙ/σYₙ > 1000 - 800/44.72)

                 = P(Z > 44.72)

                 = 1 - P(Z > 44.72)

                 = 0.00000391

By Using a z table for probability.

Thus, the probability that Y₂₀ exceeds 1000  is 3.91 × 10⁻⁶.

(b) It is provided that P (Yₙ > 1000) > 0.99.

   P(Yₙ >1000) = 0.99

⇒ 1 - P(Yₙ < 1000) = 0.99

⇒  P(Yₙ <1000) = 0.01

⇒ P(Z < z) = 0.01

The value of z for which P (Z < z) = 0.01 is 2.33.

Compute the value of n as follows:

    Z = Yₙ - μYₙ/σYₙ

⇒ 2.33   =  1000 - 40n/√100 n

⇒ 2.33 = 100/√n - 4√n

⇒ 5.4289 = (100 - 4n)²/n

⇒ 5.4289 = 10000 + 16n² - 800n/ n

⇒ 5.4289n = 10000 + 16n² -800n

⇒ 16n² - 805.4289n + 1000 = 0

The last equation is a quadratic equation.

The roots of a quadratic equation are:

n = -b ± √b-4ac/ 2a

a = 16

b = -805.4289

c = 10000

On solving the last equation the value of n = 28.09.

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Answer:

36 Degrees

Step-by-step explanation:

First the entire angle of BAC is 71 degrees, so all you have to do is subtract the known angle (2) by the entire angle. 71-35= 36. So that means the measure of angle 1 is 36 degrees.

Answer:

2

Step-by-step explanation:

slope=y1-y2/x1-x2

3-(-5)/2-(-2)=8/4

=2

To find the slope, subtract the y values over the x values.

3 -  - 5 / 2 - - 2 > Remember subtracting a negative is the sam as adding positives, so this can be rewritten as 3 + 5 / 2 + 2 .

3 + 5 / 2 + 2 > 8 / 4 > 2.

This means the slope between the two points is 2!

Answer:

Step-by-step explanation:

The function is nonlinear.  Note that each new x value is obtained by adding 2 to the previous x value (spacing is 2), and that the y values don't follow such a pattern, but follow:

1 = 0 + 1

3 = 1 + 2

9 = 3 + 6

Answer:

a

Step-by-step explanation:

anything less than 18 is wrong

The correct option is C. It is safe to apply the central limit theorem, even if the sample size for each sample is 15, if the sample population is normally distributed.

The central limit theorem states that, if you take repeated samples of a population and calculate the mean of each sample, the distribution of the means of those samples will tend to be normally distributed, provided that the sample size is large enough. This means that, even if the original population is not normally distributed, the distribution of the means of the samples will tend towards a normal distribution as the sample size increases.

However, if the original population is already normally distributed, then you can apply the central limit theorem with a smaller sample size and still expect the distribution of the means of the samples to be normally distributed. Therefore, in order for it to be safe to apply the central limit theorem with a sample size of 15, the sample population must be normally distributed.

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the missing value of the equation A = -2(x – 9) ² +? can be found by substituting x = 9, giving us A = -2(9 – 9) ² + 36(9) = 36(9) = 324. The process of completing the square is an algebraic technique which allows one to solve equations with a quadratic term.

The missing value can be found by solving the equation. To do this, we must first add 2(x – 9) ² to both sides of the equation, giving us -2x² + 36x + 2(x – 9) ² = 0. We can then factorise this equation to give (x – 9) ² = 0. This equation can be rearranged to give x = 9. This means that the value of A is 324 when x = 9, and therefore, the width of the storage bin in feet is 9, which gives a maximum area.

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Answer:

c = 11

Step-by-step explanation:

-8 = -19 + 11

Answer:

Step-by-step explanation:

\(7\times 8\times 3\\\\Multiply\\\\7\times \:8=56\\\\=56\times \:3\\\\=168\)

Answer:

hope you can understand

The rank of a matrix is equal to the dimension of its column space, and the null space of a matrix is trivial if and only if the matrix is invertible.

A matrix is a collection of data in a well-organized format in rectangular form. Matrices can be used to represent and solve systems of linear equations.

They are used to represent data sets and can be used for various purposes, including linear transformations and eigenvalue computations.

Matrices can be used to solve problems in physics, economics, statistics, and computer science.

Matrices are row equivalent if they have the same rank. A matrix has a rank equal to the number of nonzero rows in its reduced row echelon form.
Matrices A and B are row equivalent if there is a sequence of elementary row operations that transform A into B. If matrices A and B are row equivalent, then rank A = rank B is true.If v₁ and v₂ are linearly independent eigenvectors of matrix A, then v₁ and v₂ must correspond to different eigenvalues is true.

Eigenvectors are special types of vectors that remain parallel to their original direction when a transformation is applied to them. Linear independence is a condition where one vector can not be expressed as a linear combination of another.

Two vectors that are eigenvectors of a matrix A are said to be linearly independent if they correspond to different eigenvalues.If A is a 5 × 8 matrix whose columns span R5, then rank A = 5 is false. The rank of a matrix is the dimension of its column space.

The columns of a matrix span Rn if and only if the rank of the matrix is n. Since the columns of matrix A span R5, its rank cannot be equal to 5 because there are only 5 columns in the matrix.

For every m x n matrix, Nul A = 0 if and only if the linear transformation xAx is one-to-one is false. Nul A is the null space of matrix A, which is the set of all vectors that map to the zero vector when multiplied by A.

A linear transformation xAx is one-to-one if it maps distinct elements in the domain to distinct elements in the range. The null space of A is trivial (Nul A = 0) if and only if A is invertible.

Thus, Nul A = 0 does not imply that the linear transformation xAx is one-to-one.If matrices A and B are similar, then A and B have the same eigenvalues is true. Two matrices A and B are similar if there is an invertible matrix P such that A = PBP-1.

Two matrices that are similar have the same eigenvalues, which are the solutions of the characteristic equation det(A - λI) = 0.

The eigenvectors, however, may be different because they are related to the matrix A, not the matrix P.

Matrices are a powerful tool for solving linear algebra problems. Row equivalent matrices have the same rank, eigenvectors correspond to different eigenvalues, and similar matrices have the same eigenvalues. The rank of a matrix is equal to the dimension of its column space, and the null space of a matrix is trivial if and only if the matrix is invertible.

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the equation of the circle in standard form is equal to

(x-h)^2+(y-k)^2=r^2

where

(h,k) is the center and r is the radius

In this problem

(h,k)=(0,0)

r=√3

substitute

(x-0)^2+(y-0)^2=(√3)^2

Answer:

In D

Step-by-step explanation:

in d you can place the lamp there

Answer:

A

Step-by-step explanation:

- \(\frac{1}{2}\) (x + 3) > x - 3 ( multiply both sides by 2 to clear the fraction )

- (x + 3) > 2x - 6 ← distribute parenthesis on left side by - 1

- x - 3 > 2x - 6 ( subtract 2x from both sides )

- 3x - 3 > - 6 ( add 3 to both sides )

- 3x > - 3

divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity

x < 1

Answer:

A. x<1

Step-by-step explanation:

-1/2 (x+3) > x - 3

(-1/2)x-3/2>x-3

Multiply both sides by 2:

-x-3>2x-6

add both sides by 3:

-x-3+3>2x-6+3

-x>2x-3

minus both sides by 2x

-x-2x>2x-2x-3

-3x>-3

x<1