Triangle XYZ is similar to triangle JKL.

Triangle XYZ with side XY labeled 8.7, side YZ labeled 7.8, and side ZX labeled 8.2 and triangle JKL with side JK labeled 18.27.

Determine the length of side LJ.

17.22
16.38
9.93
6.13

Answer:

Step-by-step explanation:

YES IS THE ANSWER BECAUSE X=9

AND 11+3=87

the number of solutions to an equation can be solved by either elimination method or substitution method or by factorization

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

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Answer:

a and c

Step-by-step explanation:

i just did it

Answer:

a and c

Step-by-step explanation:

Yes, $9 for 4 visitors and $18 for 8 site visitors are proportional.

To determine whether or not $9 for 4 visitors and $18 for 8 visitors are proportional, we need to test if the ratio of the value to the number of visitors is the equal for both cases.

The ratio of cost to the quantity of visitors for $9 and four visitors is:

$9/4 visitors = $2.25/ visitors

The ratio of value to the quantity of visitors for $18 and eight visitors is:

$18/8 visitors = $2.25/ visitors

We are able to see that both ratios are equal to $2.25 per visitor.

Therefore, $9 for 4 visitors and $18 for 8 site visitors are proportional.

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Answer: y=4x-2

Step-by-step explanation:

Since you are looking for y-intercept, the point has to be on the vertical line and the slope is 4 so it has to go up 4 to the right 1

A diagonal of a rectangle will intersect the same number of squares as the length of the rectangle. The rectangle has a length of 7 squares and a width of 4 squares, so the diagonal will intersect 12 squares.

A diagonal of a rectangle will always intersect the same number of squares as the length of the rectangle. In this case, the rectangle has been outlined on a grid paper with dimensions of 7x4. This means that the length of the rectangle is 7 squares and the width is 4 squares. Therefore, the diagonal of this rectangle will intersect 12 squares in total. This is because the length of the rectangle is greater than the width and so the diagonal must intersect the entire length of the rectangle and all of the squares the width intersects. As a result, the diagonal of this rectangle will intersect 12 squares.

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Answer:

I am not sure

Step-by-step explanation:

I believe if you take and break down what you paid and then it will be easier to figure out the interest

The precentile for a student in the class who studies 8 hours a week is 5.74%.

To find the percentile for a student who studies 8 hours a week, we need to first standardize the student's study time by subtracting the mean study time and dividing it by the standard deviation of study time. This will give us the student's z-score. We can then look up the student's z-score in a standard normal table to find the percentile.

The student's z-score is (8 - 9.92) / 4.54 = -1.67.

Looking up -1.67 in a standard normal table, we find that the percentile is about 5.74%. This means that about 5.74% of the students in the class studied for less than 8 hours per week.

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As per the given standard deviation, the percentile for a student in the class who studies 8 hours a week is 50.80%

The term standard deviation in math is known as a measure which shows how much variation from the mean exists.

Here we have given that in one statistics course students reported studying an average of 9.92 hours a week with a standard deviation of 4.54.

Through this details, we have identified that the value of the following are given that,

=> weekly study time = 10 hours

=> average study time = 9.92 hours

=> standard deviation = 4.54 hours

Then the formula to calculate the Test statistic is written as

=> z = (weekly study time - average study time)/standard deviation

Apply the values on it, then we get

=> z = (10 - 9.92)/4.54

=> z = 0.08/4.54 = 0.02

While we take the value of z table, then we get the Cumulative area of the test statistic is 0.5080.

And the percentile is calculated by multiply the value by 100 as,

=> 0.5080 × 100 = 50.80

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Answer:

0.248

Step-by-step explanation:

Answer:

-2x is the slope.

Step-by-step explanation:

y-9=-2(x-8)

y-9= -2x +16

y= -2x +25

m= -2

Answer: The slope is -2.

Step-by-step explanation: took the quiz.

(a) Find the dual of the LP.Primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\) subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n \leq\) \(b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n \leq b_m$ and $x_1, x_2,\)..., x_n\(\geq 0$\)

Let us find the dual of the above primal problem.

Dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq\)\(C_1$...$a_{1n}y_1+a_{2n}y_2+...+a_{mn}y_m \leq C_n$\)

and\($y_1, y_2, ..., y_m \geq 0$\)

(b) Find the standard form of the LP and dual.Standard form of the primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\)subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n +s_1 = b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n +s_m = b_m$\) and\($x_1, x_2, ..., x_n, s_1, s_2, ..., s_m \geq 0$\)

Standard form of the dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq 0$...$a_{1n}y\)

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question 9

a) 2 x 3 = 6m^2

b) diameter = 2m and radius = 1m

c) πr^2 is the equation, so 3.14 x 1^2 = 3.14m^2

and the semi circle is half of that, 1.57m^2

d) 6 + 1.57 = 7.57m^7

question 10

30 x 70 = 2,100m^2

πr^2 so 3.14 x 15^2 = 706.5m^2

2,100 + 706.5 = 2,806.5m^2

i hope this is correct :D

Each person (Tammy, John, Allison, and Henry) paid $11.25 for a movie ticket.

To determine the cost of each movie ticket, we will divide the total amount paid by the number of people who bought tickets.

Total amount paid: $45
Number of people: Tammy, John, Allison, and Henry (4 people)

Step 1: Divide the total amount paid by the number of people.
$45 ÷ 4 = $11.25

So, Allison and each of her friends paid $11.25 for a movie ticket.

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The area of the canvas can be calculated by taking the product of its length and width, which is 2w-5 and w+2, respectively, and then simplifying this expression to 5w²+3w-2, which is option D.

An expression is a mathematical statement that contains numbers, variables, and operations but lacks the equal sign.

To calculate the area of the canvas, we need to know the length and width of the canvas.

Since the length of the canvas will be 5 inches less than twice the width, the length can be expressed as:

2w-5.

The width of the canvas must include the extra 2 inches of fabric on each side to stretch and secure it around the frame, so the width is expressed as:

w+2.

The area of the canvas is then the product of the length and width,

= (2w-5)(w+2).

When this equation is simplified, it reduces to 5w²+3w-2, which is option D.

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Answer:

x+1/x-1 +1 / x+1/x-1 -1= x

Answer:

76

Step-by-step explanation:

I made a chart to simplify it

1 | -8

2| -2

3| 4

4| 10

5| 16

6| 22

7| 28

8| 34

9| 40

10| 46

11| 52

12| 58

13| 64

14| 70

15| 76

Answer:

Um...you really don't. You can convert it into fractions and percentages though.

Fraction: 83/100

Percent: 83%

You can't really simplify a decimal that has already been simplified.

Step-by-step explanation:

Answer:

The answer is three quarters, one nickel's dime, and a penny!

Step-by-step explanation:

Answer:

Dime- 4

Penny- 1

Half Dollar- 1

Step-by-step explanation:

A dollar is 100 cents and you have 91

91- 50 (half dollar)= 41

41- 1 (one penny)= 40

40- 40 (4 dimes)= 0

Therefore ,the solution to the given problem of angles comes out to be

∠K= 66 degree,LK length = 2√2 unit LK length = 2√2 unit.

In Geometrical, an angled is a structure made up of two rays, known as the angle's face, that converging at the vertex, or center, of the angle. It is feasible for two beams to form an angle within a plane depending on where they are placed. An angle is also created when two planes intersect. The nomenclature to them is diahedral angles. In plane geometry, light rays or lines with the same ending can have many different forms, or angles. The Latin word "angulus," which means "horn," is where the word "angle" in English comes from. The vertex, also known as the vertex of the angle, is the point at where the two rays meet.

Here,

Given: A right angle triangle MKL

∠M = 24 degree

and ∠K =90 degree

Thus,

=> ∠L + ∠M  +∠K =180

=> 90 + 24 + ∠K = 180

=>∠K =180-114

=> ∠K= 66 degree

and

LK length = 2√2 unit

LK length = 2√2 unit

Therefore ,the solution to the given problem of angle comes out to be

∠K= 66 degree,LK length = 2√2 unit LK length = 2√2 unit.

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46,536 is the possible number of codes if repeats are not allowed and the second letter must be 'g' and the first digit must be '3'.

If repeats are not allowed, and the second letter must be 'g', and the first digit must be '3', then we have to find the number of codes that can be possible.

Solution: Here we have to calculate the total number of possible codes if repeats are not allowed and the second letter must be 'g' and the first digit must be '3'.

The given conditions:

First digit = 3

Second letter = g

We know that a code is usually formed by combining letters, numbers or both.

Thus, for the formation of the code, the remaining 4 digits are free to choose any digit or alphabet, except the two already selected ones.

We know that the number of codes that can be formed by n objects taken k at a time, without repetition is given by:P(n, k) =n!/(n−k)!

Here, n = 25, as we have to select 25 letters, starting from A to Y.

We exclude G from these, as it has already been selected as the second letter.

k = 4 as we need to select 4 remaining characters.

We have to find the number of possible codes that can be formed without repetition, and with the conditions specified.

Here, we have 1 fixed number (3) and one fixed alphabet (g) and four spaces for the remaining digits:

Thus, the number of ways of selecting the remaining four characters = 24 × 23 × 22 × 21

Total number of codes possible = 1 × 1 × 24 × 23 × 22 × 21 = 46,536, which is our answer.

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The simplified form of radical expression is √120x is 2√(3 * 5 * x) or 2√(15x). A radical expression is a mathematical expression that contains a radical symbol (√) and a radicand, which is the number or expression under the radical symbol.

radical expression represents operations involving roots, such as square roots (√), cube roots (∛), etc.

To simplify the radical expression √120x, we need to find the largest perfect square that divides evenly into 120 and x.

First, let's break down 120 into its prime factors: 2 * 2 * 2 * 3 * 5.

Next, we can group the prime factors into pairs. Since there are three 2's, we can pair two of them together: 2 * 2 = 4.

Now, we have 4 * 3 * 5 * x.

Taking the square root of 4 gives us 2.

Therefore, the simplified form of √120x is 2√(3 * 5 * x) or 2√(15x).

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Answer:

y = mx + b

where,

y = earning

m = slope or earning per hour = $24

x = total number of hours

b = y intercept or initial earning upon visit = $45

Hence,

y = 24x + 45

Since we are working at two separate work sites, therefore each site we must earn 810/2 = 405

So when y = 405:

405 = 24x + 45

x = 15 hours

So you must work 15 hours at each site.

Step-by-step explanation:

Answer:

7.56 hours.

Step-by-step explanation:

So my equation will be:

$45 + $24h

If we need to find out how many hours you have to work in order to earn $117 working at two separate work sites, the equation would look like this:

45 + 25h ÷ 2 = 117.

First we need to multiply both sides of th equation by 2.

\(\frac{2\left(45+25h\right)}{2}=117\cdot \:2\)

Then, I had to simplify.

\(5+25h=234\)

After simplifying, it was about time to subtract 45 from both sides of the equation.

\(45+25h-45=234-45\)

I had to simplify again, then divide both sides by 25.

\(25h=189\)

\(\frac{25h}{25}=\frac{189}{25}\)

Again, I have to simplify for a final time to get the answer of..

\(h=\frac{189}{25}\)

In decimal form, thats equal to 7.56 hours.

h = 7.56.

You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

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

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

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

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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The experimenter was most likely conducting a randomized controlled trial, also known as a randomized experiment.

In this type of experiment, participants are randomly assigned to different groups, such as an experimental group or a control group, to ensure that any observed effects can be attributed to the intervention being tested rather than other factors.

In this case, the experimenter is using a random number to assign Chris to a group with nineteen other students, which suggests that there may be multiple groups involved in the experiment. This type of design is often used in scientific research to test the effectiveness of a new treatment, intervention, or program.

Randomized controlled trials are considered the gold standard in research design because they provide strong evidence for causal relationships between variables. By randomly assigning participants to different groups, researchers can control for confounding variables and ensure that any observed differences between groups are due to the intervention being tested.

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Answer:

the answer is 1

Step-by-step explanation:

Answer:

see the attached image

Step-by-step explanation:

In this problem, we are asked to graph a line that represents the equation \(y=\dfrac{3}{4}x - 1\).

We can recognize that this equation is in slope-intercept form:

\(y = mx + b\)

where m is the line's slope, and b is its y-coordinate of the line's y-intercept (the point where it touches the y-axis).

From this information, we can deduce that the line's slope (rise over run) is 3/4, and its y-intercept is (0, -1). — notice how x is 0, since the y-axis can be represented as the line x = 0

Using this information, we can graph the following points:

(-4, -4)

(0, -1)

(4, 2)

See the attachment for an image of the graph.

The probability of selecting exactly 2 white balls and 2 red balls from the urn is 0.3 or 30%.

To find the probability of selecting exactly 2 white balls and 2 red balls from the urn, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

When drawing 4 balls from the urn without replacement, the total number of possible outcomes can be calculated using combinations. We can select 4 balls out of 10 in C(10, 4) ways:

Total outcomes = C(10, 4) = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210

Favorable outcomes:

To calculate the number of favorable outcomes, we need to determine the number of ways we can select 2 white balls out of 3 and 2 red balls out of 7. We can do this using combinations as well:

Number of ways to select 2 white balls out of 3: C(3, 2) = 3

Number of ways to select 2 red balls out of 7: C(7, 2) = 21

Number of favorable outcomes = C(3, 2) * C(7, 2) = 3 * 21 = 63

Probability:

The probability of selecting exactly 2 white balls and 2 red balls can be calculated by dividing the number of favorable outcomes by the total number of outcomes:

Probability = Number of favorable outcomes / Total outcomes = 63 / 210 = 3 / 10 = 0.3

It's important to note that since the balls are drawn without replacement, the probability of each subsequent draw depends on the outcomes of the previous draws.

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The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = \(^{52} C_{2}\)

And, the total number of ways of  getting exactly one face cards

= \(^{12} C_{1} \times ^{40} C_{1}\)  + \(^{40} C_{1} \times ^{12} C_{1}\)

= 2\(^{40} C_{1} \times ^{12} C_{1}\)

Therefore, the probability of getting exactly one face card

= \(\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }\)

\(= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }\)

\(= \frac{2(40\times 12)}{26\times 51}\)

\(=\frac{2\times 480}{1326}\)

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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