4⁄6 + 2⁄4 + 3⁄5 = \(\frac{x}{y}\)

The correct responses are: "Triangle DBC is similar to triangle ABC" and "The length of side DE is 13."

Since triangle ABC is similar to triangle DBE, we know that the corresponding angles are congruent and the corresponding sides are proportional.

From the given information, we know that side BC of triangle ABC corresponds to side BE of triangle DBE, since they share vertex B. Therefore, we can use the proportion:

BC / BE = AC / DE

Substituting the given values, we have:

BC / 5 = 7.5 / 13

Solving for BC, we get:

BC = (5 x 7.5) / 13 = 2.88 (rounded to two decimal places)

Therefore, the length of side BC is 2.88.

Now we can check which of the given statements are true:

"The length of side AB is 3.75." We do not have enough information to determine the length of side AB, so this statement cannot be determined to be true or false based on the given information.

"Triangle DBC is similar to triangle ABC." This statement is true, since they share angle B and the sides BC and BE are proportional.

"Angle C in triangle ABC is congruent to angle D in triangle DBE." This statement cannot be determined to be true or false based on the given information, since we do not know which angle in triangle DBE corresponds to angle C in triangle ABC.

"The length of side AC is 4.29." This statement cannot be determined to be true or false based on the given information, since we only have information about side BC and side BE. We do not have enough information to determine the length of side AC.

"The length of side DE is 7.8." This statement is false, since the length of side DE is given as 13, not 7.8.

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Jerry's cost of going to college is $29,000.

Jerry's cost of going to college is $29,000. The cost of going to college is a major concern for many students. As a result, making a sound financial plan is essential when considering post-secondary education. It is important to weigh the costs of going to college against the benefits of obtaining a degree. Jerry has to make a choice between going to college or working in a store. If he chooses to go to college, he will have to spend $15,000 on tuition, $12,000 on room and board, and $2,000 on books. Therefore, his total cost of attending college is

$29,000 ($15,000 + $12,000 + $2,000).

If he decides not to go to college, Jerry will earn $27,000 by working in a store and spend $10,000 on room and board. By adding up his earnings and expenses, he will have a total of

$17,000 ($27,000 - $10,000)

In this case, it is less expensive for Jerry not to go to college. He will have $12,000 more in his pocket ($17,000 - $29,000) if he does not go to college. Therefore, Jerry's cost of going to college is $29,000.

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Answer:

35% off

Step-by-step explanation:

= |4 - 2.6|/((4 + 2.6)/2) = 1.4/3.3 = 0.42424242424242 = 42.424242424242%

Percentage of decrease = |4 - 2.6|/4 = 1.4/4 = 0.35 = 35%

2.6 is a 35% decrease of 4.

Answer:

Each cm cube has a surface area of 6cm, and it makes 100 mm cubes that have a 6mm surface area each.

Answer:

T = (7 * 10) + 10 + 60 + (4 * 11)

Step-by-step explanation:

The expression that can be used to determine the total cost would be the following ...

T = (7 * 10) + 10 + 60 + (4 * 11)

This expression sums up the cost of each shirt, the one-time fee, and the embroidery costs. Since 10 of the shirts cost $7 each then you need to multiply the cost by the number of shirts that cost that amount. The same goes for embroidery. Since there are a total of 11 shirts and each one costs $4 to embroider then you do 4 * 11

Answer:

The value of x = 27

Step-by-step explanation:

Given:

48x² : 64x⁴ ::: x : 36x²

Find:

The value of x

Computation:

(a)(d) = (b)(c)

(48x²)(36x²) = (64x⁴)(x)

(1,728x⁴) = (64x⁵)

x = 27

The value of x = 27

Following are the solution to the given expression:

Given:

\(\to 48x^2 : 64x^4 :: x : 36x^2\)

To Find:

x=?

Solution:  

\(\to 48x^2 : 64x^4 :: x : 36x^2\)

\(\to \frac{48x^2}{ 64x^4} =\frac{ x}{ 36x^2}\\\\\)

cross multiply:

\(\to \frac{48x^2 \times 36x^2}{ 64x^4} =x\\\\\to x= \frac{48x^2 \times 36x^2}{ 64x^4} \\\\\to x= \frac{48 \times 36}{ 64} \\\\\to x= \frac{6 \times 9}{ 2} \\\\\to x= 3 \times 9\\\\\to x=27\)

Therefore, the answer is "27".

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Answer: This has no answer

Step-by-step explanation:

The human brain cannot answer this……

The two consecutive integer numbers are 11 and 12, and the inequality is:

11 < √134  < 12

Here we just need to find two integers x and y, such that:

x^2 < 134

134 < y^2

Such that x and y are also consecutive, so y = x + 1.

Then we can write the inequality:

x < √134 < y

The numbers are:

11*11 = 121 (the smaller integer)

12*12 = 144 (the larger integer).

Then the complete inequality is:

11 < √134  < 12

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The simplification of the expression 6 + (5 + x) is 11 + x

6 + (5 + x)

Based on the associative property

= (6 + 5) + x

Add 6 and 5

= 11 + x

Associative property states that the rearranging of parenthesis in an expression will not change the result.

Commutative property on the other hand states that the numbers on which we operate can be interchanged or moved from their position without making any difference to the result.

Ultimately, the results of 6 + (5 + x) is 11 + x

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Diversity encompasses multiple dimensions such as life experiences, educational background, geographic origin, and age that is option E.

Diversity encompasses a range of factors including life experiences, educational background, geographic origin, and age. It goes beyond a single dimension and encompasses various aspects that contribute to differences among individuals. By embracing diversity in all its forms, organizations and communities can benefit from a wider range of perspectives, ideas, and talents.

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Answer:

The expression 13x - 7 is equivalent to 13x + (-7). This is because the subtraction of a negative number is the same as the addition of a positive number.

For example, if we have the expression 13x - 7, we can rewrite it as 13x + (-7) as follows:

13x - 7 = 13x + (-7)

Therefore, the expression that is equivalent to 13x - 7 is 13x + (-7).

edit: It is the same as 13x + (-7)

Answer:

A. There is no solution

Step-by-step explanation:

\(\frac{1}{3}\)(12x - 6) = 4x - 9

Evaluate.

4x - 2 = 4x - 9

Deduct 4x from both sides of the equation.

-2 = -9

Multiply both sides by (-1).

2 ≠ 9

Since 2 does not equal to 9, this equation does not make sense and thus does not have a solution.

what are the prices?

Domain would be the farthest x value to left and the farthest x value to right

Range would be lowest y value to highest y value

The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).

The volume of any cylinder can be calculated using the formula,

V = πr²h

(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)

As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:

Volume of oil = (1/5) x Total Volume

Substituting the given values, we have:

Total Volume =  π(80cm)²(200cm) = 4,031,240 cm³

Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³

Converting cm³ to litres, we have:

1 litre = 1000 cm³

Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres

Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.

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Answer:

The next number is 24

Step-by-step explanation:

The pattern is Multiply by 2, then divide by four

You didn't include a picture/ diagram

The prediction method Linear Extrapolation is the method used to estimate a point on a line when the point does not lie between the given points.

Using the equation of a line to obtain a new data point based on an existing collection of data points is known as linear interpolation in mathematics.

Now,

Since it employs a linear model to forecast the necessary point that does not reside between the given locations, this prediction technique is known as linear extrapolation.

Hence, The prediction method Linear Extrapolation is the method used to estimate a point on a line when the point does not lie between the given points.

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Answer:

7y−8

hope this helps :)

Answer:

Step-by-step explanation:

Any time you have compounding more than once a year (which is annually), unless we are talking about compounding continuously, you will use the formula

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

Here's what we have:

The amount after a certain time that she has in the bank is 4672.12; that's A(t).

The interest rate in decimal form is .18; that's r.

The number of times the interest compounds is 12; that's n

and the time that the money is invested is 3.5 years; that's t.

Filling all that into the formula:

\(4672.12=P(1+\frac{.18}{12})^{(12)(3.5)}\) Simplifying it down a bit:

\(4672.12=P(1.015)^{42}\) Raise 1.015 to the 42nd power to get

4672.12 = P(1.868847115) and divide to get P alone:

P = 2500.00

She invested $2500.00 initially.

Answer:(175, 0), (150, 25), (125, 50)

Step-by-step explanation:

The profit from selling an adult ticket is $10.00 and the profit from selling a children's ticket is $5.00, so the profit from selling one of each is $10.00 + $5.00 = $<<10+5=15.00>>15.00.

To make a profit of $2,625.00, the venue must sell at least 2,625 / 15 = <<2625/15=175>>175 tickets.

Since the venue can seat up to 350 people, we want to find combinations of adult and children's tickets that total 175 or more tickets and no more than 350 tickets.

One combination is (175, 0), which means 175 adult tickets and 0 children's tickets were sold.

Another combination is (150, 25), which means 150 adult tickets and 25 children's tickets were sold.

Yet another combination is (125, 50), which means 125 adult tickets and 50 children's tickets were sold.

Therefore, the answer is (175, 0), (150, 25), (125, 50).

The numbers which are divisible by 3 are countless. We determine it by the divisibility rules.

A number is called divisible by others whenever it is divided properly and   obtain a whole number as an outcome. As example 125 can be divided by 5 and we get the whole number 25 so 125 is said divisible by 5.

On the other hand, 225 cannot be divided by 10 and we get a decimal number. So, 225 is not divisible by 10.

A number is said to be divisible by 3 if the sum of the digits is divided by 3. Suppose we are given two number 308 and 492.

At first, we will sum the digit of each number, 3+0+8 = 11

the sum of the digit of 492 = 4+9+2 = 15

we cannot divide 11 by 3 but 15 is divided by 3. Hence, 492 is divisible by 3.

So, there are countless number which are divisible by 3.

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The relation R on the set (1, 2, 3, 4) can be represented by an arrow diagram and a matrix. The arrow diagram visually depicts the connections between the elements.

To represent the relation R on the set (1, 2, 3, 4) using an arrow diagram, we draw a directed arrow from each element in the set to the element it is related to. For example, we draw an arrow from 1 to 3 and 4, an arrow from 2 to 1, an arrow from 3 to 2 and 4, and an arrow from 4 to 2. The resulting arrow diagram shows the connections between the elements in the relation.

The matrix representation of a relation uses a table to show the presence or absence of connections between elements. For the relation R on the set (1, 2, 3, 4), we create a 4x4 matrix where the rows and columns correspond to the elements of the set. We fill in the matrix with 1s to indicate that there is a connection between the respective elements and 0s otherwise. In this case, the matrix would be:

| 0 0 1 1 |

| 1 0 0 0 |

| 0 1 0 1 |

| 0 1 0 0 |

In the matrix, a 1 in the i-th row and j-th column indicates that the element i is related to the element j. For example, the entry in the first row and third column is 1, indicating that 1 is related to 3.

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Answer:

The probability that the next person will purchase no more than one costume \(\frac{219}{239}\).

Step-by-step explanation:

The data for a single day is s follows:

The total number of customers is, N = 236 + 202 + 40 = 478.

Let X denote the number of costumes purchased by the next person.

Compute the probability that the next person will purchase no more than one costume as follows:

\(P (X\leq 1)=1-P(X>1)\)

               \(=1-\frac{40}{478}\\\\=\frac{478-40}{478}\\\\=\frac{438}{478}\\\\=\frac{219}{239}\)

Thus, the probability that the next person will purchase no more than one costume \(\frac{219}{239}\).

Answer:

9

Step-by-step explanation:

the reciprocal of 1/3 to 3 will remove the - sign. This this will make it 3² = 9

Answer:

9

Step-by-step explanation:

Given expression:

\(\left(\dfrac{1}{3}\right)^{-2}\)

\(\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:\)

\(\implies \dfrac{1}{\left(\frac{1}{3}\right)^2}\)

\(\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:\)

\(\implies \dfrac{1}{\frac{1^2}{3^2}}\)

\(\implies \dfrac{1}{\frac{1}{9}}\)

\(\textsf{Apply the fraction rule}\quad \dfrac{1}{\frac{a}{b}}=\dfrac{b}{a}:\)

\(\implies \dfrac{9}{1}\)

\(\implies 9\)

Answer:

A

Step-by-step explanation:

Answer:

Yes, it said of a mile and so that states since there are two numbers of a mile...

Step-by-step explanation:

Answer:

Water in 3 hours = 450 gallons

Step-by-step explanation:

Given that:

Water flows at a rate of 25 gallons in 10 minutes.

10 minutes = 25 gallons

1 minute = \(\frac{25}{10}\) = 2.5 gallons

Now,

Time = 3 hours

3 hours = 180 minutes

Quantity of water in 3 hours = 2.5 * 180

Quantity of water in 3 hours = 450 gallons

Hence,

Water in 3 hours = 450 gallons

a. 2600 ways different samples are possible.

b. 0.11  is the probability that all 3 of the selected students are freshmen.

total student = 26

3 students are randomly selected  on group project

a.   the possible  different sample are

\(26 C_{3}\) = \(\frac{26}{3 (26-3)}\)

      =  \(\frac{26}{3 (23)}\)

     = 2600 ways.

b.  13 students are freshmen  

Pr ( 3  selected students  is freshman)

\(\frac{13C_{3} }{26C_{3} }\) = \(\frac{286}{2600}\) = 0.11

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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