Name a pair of overlapping congruent triangles in the diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.
Given: ∠ABC ≅ ∠DCB; ∠DBC ≅ ∠ACB​

The walkway is 11 feet 6 inches long.

To find the length of the walkway, we need to add the lengths of the two boards.

The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.

The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.

Now we can add the lengths of the two boards:

6 + 11/12 feet + 5 + 7/12 feet

= 11 + 6/12 feet

=11 + 1/2 feet

Therefore, the walkway is 11 feet 6 inches long.

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The mathematical expression, for the given statement is 20g/3

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is a statement, two-thirds times g times 10.

Converting into mathematical expression,

2/3 of g = 2g/3

And,

2/3 of g of 10

= 2g/3 × 10

= 20g / 3

Hence, the mathematical expression, for the given statement is 20g/3

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Answer:

n= -17

Step-by-step explanation:

Simplifying

5 + n + (15 + -2) = 0

Combine like terms: 15 + -2 = 13

5 + n + (13) = 0

5 + n + 13 = 0

Reorder the terms:

5 + 13 + n = 0

Combine like terms: 5 + 13 = 18

18 + n = 0

Solving

18 + n = 0

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-18' to each side of the equation.

18 + -18 + n = 0 + -18

Combine like terms: 18 + -18 = 0

0 + n = 0 + -18

n = 0 + -18

Combine like terms: 0 + -18 = -18

n = -18

Simplifying

n = -18

\(\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=10\\ s=3 \end{cases} \implies 3=\cfrac{\theta \pi (10)}{180}\implies 540=10\pi \theta \\\\\\ \cfrac{540}{10\pi }=\theta \implies 17.19^o\approx \theta\)

Answer:

I believe the answer is A) In quadrant IV

Step-by-step explanation:

Answer:

x = 34

y = \(51\sqrt{3}\)

Step-by-step explanation:

\(sin30=\frac{17}{y}\)

\(y=\frac{17}{sin30} =\frac{17}{.5} =34\)

\(tan30=\frac{17}{x}\)

\(x=\frac{17}{tan30} =\frac{17}{\frac{\sqrt{3} }{3} } =(17)(3)\sqrt{3} =51\sqrt{3}\)

Hope this helps

The factored form is (5x+2)(x-4).

What is factorization?

A number, matrix, or polynomial may be broken up or decomposed into factors that, when multiplied together, produce the original number, matrix, etc. This process is known as factorization or factoring.

Here, we have

Given:  5 x squared minus 18 x minus 8

we have to find the factored form.

= 5x² - 18x - 8

= 5x² - 20x + 2x - 8

= 5x(x-4) + 2(x-4)

= (5x+2)(x-4)

Hence, the factored form is (5x+2)(x-4).

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Answer:

76 and the core of our business mam 7AM 777777 is a process in 4

Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

Answer:

x=36,y=12

Step-by-step explanation:

:D

After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.

To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:

Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)

where:

P = the initial loan amount (in this case, $219,000)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)

b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)

First, we need to calculate the monthly interest rate:

r = 4.5% / 12 = 0.00375 = 0.375%

Next, we can plug in the values to get:

Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)

= $145052.36

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Zero is the smallest amount of each paint color the store must have sold

Two or more expressions with an Equal sign is called as Equation.

Given that All yellow paint comes in 8-liter containers while blue paint is sold in containers of 12 liter.

Lets quantity of Yellow sold be x and blue sold be y

since it is given in that sold equal quantities,

we have x=y

and the number of containers of x sold will be

x/8(since each container carries 8L)

and for y it will be y/12

x/8=x/12

12x=8x

This implies that x = 0, which means that the store sold no paint at all.

Hence, zero is the smallest amount of each paint color the store must have sold

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Answer:

2/3

Step-by-step explanation:

1 and 2 are taken away, therefore you have 3, 4, 5, and 6 left as options to roll. So the answer is 4/6 since there's 4 numbers, but simplified it's 2/3.

Answer:

There are six possible outcomes when rolling a die, each of which is equally likely. Of these six outcomes, three are greater than 2 (3, 4, 5) and three are not (1, 2, 6). Therefore, the odds in favor of rolling a number greater than 2 are 3 to 3, or simply 1 to 1. Alternatively, we could express this as a probability: the probability of rolling a number greater than 2 is 3/6, or 1/2, since there are three favorable outcomes out of a total of six possible outcomes.

Step-by-step explanation:

Step-by-step explanation:

.....

Answer:

The answer is 4.

Step-by-step explanation:

All you have to do is count the dots between the library and Gabes house.

To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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Answer:

a

  \(E = 0.4850 \)  

b

 \(E = 0.8689\)  

Step-by-step explanation:

From the question we are told that

   The sample size is  n  =  108

    The sample mean is  \(\= x = 8.8 \ years\)  

     The standard deviation is  \(\sigma = 3.5\)

From the question we are told the confidence level is  85% , hence the level of significance is    

      \(\alpha = (100 - 85 ) \%\)

=>   \(\alpha = 0.15\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } = 1.44 \)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>    \(E = 1.44 *  \frac{ 3.5 }{\sqrt{108} }\)

=>    \(E = 0.4850 \)  

From the question we are told the confidence level is  99% , hence the level of significance is    

      \(\alpha = (100 - 99 ) \%\)

=>   \(\alpha = 0.01\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } = 2.58 \)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>    \(E = 2.58 *  \frac{ 3.5 }{\sqrt{108} }\)

=>    \(E = 0.8689\)  

Answer:

Since 5 9/16 is closest to 6, and 4 1/8 is closest to the benchmark 4. The total of the benchmark is 10. So, Parker's estimate is (I'm assuming the dropdown had "wrong" as an option)

Step-by-step explanation:

Parker assumed that Mr.Thompson used about nine pounds of pancake mix. Parker was fairly close but just one off. If you were to solve this without having to use a whole number for an estimate. The answer would be 9 11/16, instead of 10. Anyways, I should explain why 5 9/16 is round to 6. It's rounded to six as a whole number because 9/16 is over half of 16. Half of 16 is "8".So anything that is 8/16 and up is automatically round to the number ahead (that's whole).

I hope this helps!!!

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Answer:

4:5 or 0.8

Step-by-step explanation:

if the correspond sides are 24 (smaller figure) and 30 (larger figure), then the requred scale factor is:

24:30=4:5 (or 0,8).

Answer:

Step-byHow do I calculate the mean?

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of value

-step explanation:

46+57+66+63+49+52+61+68= 462/8 the total number of observation

the answer 57

The correct statement is that for each hour, the earnings go up by $7. Option A

If we have the equation of the line, we can substitute the value of 7 for the number of hours into the equation and solve for the earnings. The equation would typically be in the form of "earnings = slope * hours + y-intercept," where the slope represents the rate of earnings per hour and the y-intercept represents the earnings when no hours are worked.

We can find the slope of the graph to know as said above;

m = y2 - y1/x2 - x1

m = 14 - 0/2 - 0

m = 7

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Answer:

1 and 20    or   2 and 10   or   4 and 5

Step-by-step explanation:

the divisors of 20 are 1 , 2 , 4 , 5 , 10 , 20

Then

20 = 1 × 20

     = 2 × 10

     = 4 × 5

11 MPH

10% of 10 can be calculated or known as 1. Therefore, 10+1 = 11 MPH on Tuesday.

Answer:

y = 3x - 1

Step-by-step explanation:

y = mx + b

y = 3x -2

m = slope   Parallel line have the same slope

(3,8)

y = 3x + b

8 = 3(3) + b

8 = 9 + b

-9  -9

-1 = b

y = 3x - 1

Hope this helps!

Answer:

Frequency: 244

relative frequency: 0.61

Step-by-step explanation:

check: 60:244 = 0.15:x

x = 0.61

8/21 of the lawn still needs to be mowed.

To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Miss Lianto's fraction: (2/7) x (3/3) = 6/21

Son's fraction: (1/3) x (7/7) = 7/21

To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:

Combined fractions mowed: 6/21 + 7/21 = 13/21

So, Remaining fraction: 1 - 13/21 = 8/21

Therefore, 8/21 of the lawn still needs to be mowed.

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We can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability.

What is probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The theoretical probability of rolling a 5 on a fair die is 1/6, which means that if the die is rolled many times, we would expect to see a 5 about 1/6 of the time.

For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 25/100

experimental probability = 0.25

So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.

For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 30/200

experimental probability = 0.15

So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.

Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.

On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.

Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.

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We might say that Maya's experimental probabilities oscillate about the theoretical probability, but after more trials, the experimental probabilities ought to converge to the theoretical probability.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

A fair die has a theoretical probability of rolling a 5 of 1/6, therefore if the die is rolled several times, we can anticipate seeing a 5 roughly 1/6 of the time.

For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 25/100

experimental probability = 0.25

So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.

For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 30/200

experimental probability = 0.15

So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.

Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.

On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.

Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.

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