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Which best describes the relationship between the two triangles below?

Triangle M L N is similar to Triangle F G H because of the third angle theorem, Angle M is congruent to angle F, Angle L is congruent to angle G, and Angle N is congruent to angle H.

Triangle M L N may or may not be similar to Triangle F G H because the third angle is unknown.

Triangle M L N is similar to Triangle F G H because of the angle-angle criterion, Angle M is similar to angle F, Angle L is similar to angle G, and Angle N is similar to angle H.

Triangle M L N may or may not be similar to Triangle F G H because the side lengths are unknown.

Answer:

7.9617

Step-by-step explanation:

r=c/2pi so 50/2(3.14)

Answer: about 7.9617 !

Step-by-step explanation: you to divide 50 by 3.14 to get the diameter, then divide the diameter by 2 to get the radius, then round it!

The original value of the house when it was purchased was $450,000.

Let us assume the original value of the house was x. This means that the house has increased by 38% from x to become $621,000.

In order to find the original value therefore, you can use the formula:

Original value + (Original value x Increase) = Current price

x + (38% × x) = 621,000

1.38x = 621,000

x = 621,000 / 1.38

= $450,000

In conclusion, the original value was $450,000.

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Final answer:

The original purchase price of the house was $450,000.

Explanation:

To find the original value of the house before it increased in value, we must first understand that the current value represents 138% of the original value, since the house has increased in value by 38%. This is because the original value is 100%, and the increase is 38%, making the total 138%. Therefore, the equation to find the original purchase price (which we can call 'P') is:

P * 138% = $621,000

We can rewrite this as:

P * 1.38 = $621,000

To solve for P, we divide both sides of the equation by 1.38:

P = $621,000 / 1.38

Now, doing the division:

P = $450,000

So, the house was originally purchased for $450,000 before it increased by 38% to its current value of $621,000.

Answer:

b. g(x) only

Step-by-step explanation:

Answer:

James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a radius of 2 cm. One tray makes 6 spheres.What is the total volume of ice the tray can make at one time?

Total volume of the tray James have = 201.06 cm^3

Step-by-step explanation:

Given:

Radius of the spherical ice cube = 2 cm

No. of spheres in the ice cube = 6

We have to find the total volume of the ice tray that can make at one time.

Let the total volume be "V".

Formula to be used:

Volume of sphere =  [tex]\frac{4\pi r^3 }{3}[/tex]  cubic unit.

Total volume = [tex]n\times \frac{4\pi r^3 }{3}[/tex] cubic unit.

So,

Total volume of the ice tray (V) :

⇒ [tex]V=n\times \frac{4\pi r^3 }{3}[/tex]

⇒ Plugging n = 6 and r = 2

⇒ [tex]V=6\times \frac{4\pi (2)^3 }{3}[/tex]

⇒ [tex]V=6\times \frac{4\pi (8) }{3}[/tex]

⇒ [tex]V=6\times \frac{32\pi }{3}[/tex]

⇒ [tex]V=\frac{32\times 6\pi }{3}[/tex]

⇒ [tex]V=32\times 2\pi[/tex]

⇒ [tex]V=201.06\ cm^3[/tex]

So,

The total volume of ice the tray can make at one time = 201.06 cm^3

Answer:15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

5=1

10=2

15=3

The total number of possible New York license plates is 17,576,000.

The number of different license plates possible for a standard configuration in New York, where a license plate is composed of 3 digits followed by 3 letters, can be determined through combinatorial math.

Step-by-Step Solution:

Answer:

The median is - C

The minimum is - A

The maximum is - E

The lower quartile (Q1) is - B

The upper quartile (Q3) is - D

The median is C, the minimum is A, the maximum is E, the lower quartile (Q1) is B and the upper quartile (Q3) is D.

The value that divides the mathematical numbers or expressions in half is known as the median. The middle data point is known as the median value. Then, organize the data points in ascending order before calculating the median.

As per the given data, whiskers range from A to E.

The middle point of whisker is C.

Hence, the median is given by C.

And the whisker ranges to maximum E.

And range starts from A.

So the minimum is A.

Quartiles are three values that split sorted data into four parts, each with an equal number of observations.

The lower quartile is B and upper quartile is D.

Therefore, the answers of the median is C, the minimum is A, the maximum is E, the lower quartile (Q1) is B and the upper quartile (Q3) is D.

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Answer:

I believe it is

x = -3/2 (-1.5)

y = 4

Answer:

A) 4x + 3y = 6

B) -4x + 2y = 14

Add the equations

5 y = 20

y = 4

Putting y into A)

A) 4x + 3*4 = 6

A) 4x = -6

x = -1.5

Step-by-step explanation:

Answer:

6x-76

Step-by-step explanation:

If you graph it out, you'll realize it makes a line that cuts the y-intercept at -76, thus the last value. The slope also has a gradient of 6, thus the coeffecient of x.

Final answer:

The slope of the line through the points given is 6, calculated using the slope formula with the rise over run between the two points.

Explanation:

The slope of a line is calculated by finding the ratio of the vertical change (the rise) to the horizontal change (the run) between two points on the line. Using the coordinates provided (12, -4) and (15, 14), we can apply the slope formula slope (m) = (y_2 - y_1) / (x_2 - x_1). Plugging in the values gives us (14 - (-4)) / (15 - 12) = 18 / 3 = 6. Therefore, the slope of the line that contains these points is 6.

Translations of functions involve adjusting the graph horizontally by adding or subtracting values within the function's argument, and vertically by adding or subtracting values directly to the function. For the given functions, respective translations have resulted in g(x) expressions that have been adjusted according to these rules.

To answer the student's mathematics questions about translations of functions, we will apply the concepts learned from algebra to transform each given function accordingly.

In these function transformations, we've made use of horizontal and vertical translations, where adding or subtracting values within the function argument adjusts the graph horizontally, and adding or subtracting values outside the function adjusts it vertically.

Answer:

Pyramids are triangular in shape with a sided shape, whereas cones have circular bases that merely adjoin at a point.

Step-by-step explanation:

Answer:

A pyramid is a cone with a polygonal base ;)

Answer:

= 1700 :)

Step-by-step explanation:

-multiply all the sides,

-add them,

- then double the answer (or times it  by 2):

1) 30 times 20 = 600

30 times 5= 150

20 times 5 =100

2) Add them:

600+150+100 = 850

then times 850 by 2

850 times 2 = 1700

Hope that helped :)

Answer:

Guys for this one the 30, 20, 5 is 1700

Step-by-step explanation:

Step-by-step explanation:

a(n) = a ( n - 1) - 17

a(1) = 20

a(2) = a ( 2 - 1) - 17

= a (1) - 17

= 20 - 17

= 3

Now

a(3) = a ( 3 - 1 ) - 17

= a (2) - 17

= 3 - 17

= - 14

Hope it will help you.

Answer:

No, because when j = 8, the values of the expressions are different.

for a shorter answer, A

Step-by-step explanation:

No, because when j = 8, the values of the expressions are different. Therefore, option A is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 7(j-2)4j-5.

Here, j=3 ad j=8

When j=3, we have

7(3-2)4×3-5

= 7×1×4×3-5

= 84-5

= 79

When j=8, we have

7(8-2)4×8-5

= 7×5×4×8-5

= 1115

Therefore, option A is the correct answer.

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Answer: 10.2

Step-by-step explanation:

Area of a circle is

A= pixr^2

327= 3.14r^2

Divide by 3.14

= 104.14

Get the sq rat of 104.14

= 10.2

Answer:

D

Step-by-step explanation:

Answer:

1:2

 2:1

2:3

Step-by-step explanation:

3:6

Divide each side by 3

3/3: 6/3       1:2

10:5

Divide each side by 5

10/5 : 5/5      2:1

16:24

Divide each side by 8

16/8: 24/8     2:3

Answer:

I don't think it is a function

A function  is a set of ordered pairs where a x-value is paired with only one y-value.

As long if the x-value (1) is sharing only one y-value then it makes it a function.

Answer:

Step-by-step explanation:

Let x is the side of identical squares

By cutting out identical squares from each corner and bending up the resulting flaps, the dimension are:

The volume will be:

V = (10-2x) (10-2x) x

<=> V = (10x-2[tex]x^{2}[/tex]) (10-2x)

<=> V = 100x -20[tex]x^{2}[/tex] - 20[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]

<=> V = 4[tex]x^{3}[/tex]  - 40[tex]x^{2}[/tex] + 100x

To determine the dimensions of the largest box that can be made, we need to use the derivative and and set it to zero for the maximum volume

dV/dx = 12[tex]x^{2}[/tex] -80x + 100

<=>  12[tex]x^{2}[/tex] -80x + 100 =0

<=> x = 5 or x= 5/3  

You know 'x' cannot be 5 , because if  we cut 5 inch squares out of the original square, the length and the width will be 0. So we take x = 5/3

=>

To determine the dimensions of the largest box that can be made from a tin sheet, we need to find the side length of the square that will be cut out from each corner of the tin sheet. The dimensions of the largest box that can be made are approximately 6.67 inches by 6.67 inches by 1.67 inches.

To determine the dimensions of the largest box that can be made from a tin sheet, we need to find the side length of the square that will be cut out from each corner of the tin sheet. Let's assume the side length of the square to be x inches. The length and width of the resulting box will be 10 - 2x inches and 10 - 2x inches, respectively. The height of the box will be x inches. To find the dimensions of the largest box, we need to find the value of x that maximizes the volume of the box.

The volume of the box is given by V = (10 - 2x)(10 - 2x)(x). We can write this as V = 4x^3 - 40x^2 + 100x. To find the value of x that maximizes the volume, we can take the derivative of V with respect to x and set it equal to 0. Differentiating V, we get dV/dx = 12x^2 - 80x + 100. Setting this equal to 0 and solving for x, we find x = 1.67 inches (rounded to two decimal places). Therefore, the dimensions of the largest box that can be made are approximately 6.67 inches by 6.67 inches by 1.67 inches.

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In hypothesis testing for this scenario, the null hypothesis (H-0) is that the proportion of rejected screens remains 12 percent (H-0: p = 0.12). The alternative hypothesis (Ha) is that the proportion of rejected screens is less than 12 percent (Ha: p < 0.12). A sample is taken and a significance test (such as a z-test for proportion) is conducted to decide if the null hypothesis can be rejected.

The question is looking for you to conduct a hypothesis test to investigate whether a new process in manufacturing cell phone screens has led to a reduced proportion of rejected screens. When conducting such a hypothesis test, you'll need to consider a null hypothesis and an alternative hypothesis.

The null hypothesis (H-0) is often the initial claim about a population proportion. In this case, the null hypothesis would be that 12 percent of the screens (0.12) are still being rejected: H-0: p = 0.12.

The alternative hypothesis (Ha) is what you might believe to be true if the null hypothesis is proven to be incorrect. Here, the alternative hypothesis would be that less than 12 percent of screens are being rejected with the new process: Ha: p < 0.12.

To clarify, if the new process is effective, a lower proportion of screens should be rejected. Thus, the hypotheses to be tested are:

Lastly, after selecting the sample, compute the sample proportion. Here a total sample size of 100 screens with only 6 being rejected means the sample proportion (p) = 6/100 = 0.06.

From here, you would proceed to conduct a significance test (possibly a z test for proportion) and determine a p-value to make a decision regarding the null hypothesis.

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Answer:

j = 12

Step-by-step explanation:

Quotient means the answer when you divide the dividend by the divisor.

In this example, we are dividing 36 by 3, so 36 = dividend, 3 = divisor.

36 / 3 = 12. See the attachment if you need extra help on long division!

Answer:

It is 12

Step-by-step explanation:

So first you divide 36 by 3. So 3 goes into 3 once. Now 3 goes into 6 twice so there you have it

Answer:

29%

Step-by-step explanation:

If 7 is 100% correct then 5 would only be a portion of it

So you need to divide 5 by 7

So 5 divided by 7 is .714 or .71

this means the error was 29%

Answer:

The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.

Step-by-step explanation:

Conditional probability:

Let A and B any two events connected to a given random experiment E. The conditional probability of the event A on the hypothesis that the event B has occurred, denoted by P(A|B), is defined as

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

Given that,

In a city school, 70% of students have blue eyes, 45% have dark eyes and 30% have blue eyes and dark hair.

A= students have blue eyes

B= Students have dark hair.

P(A)= 70% [tex]=\frac{70}{100}[/tex] [tex]=\frac7{10}[/tex]

P(B)=45% [tex]=\frac{45}{100}[/tex] [tex]=\frac9{20}[/tex]

P(A∩B)=30%[tex]=\frac{30}{100}[/tex] [tex]=\frac3{10}[/tex]

∴P(B|A)

[tex]=\frac{P(A\cap B)}{P(A)}[/tex]

[tex]=\frac{0.3}{0.7}[/tex]

[tex]=\frac37[/tex]

=0.429

=0.429×100 %

≈43%

The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.

Answer: 24.5%

Step-by-step explanation:

Last year her stock in company A was worth $4600. If her Stock in company A has decreased by 25% since last year in stock, then the amount by which it decreased is

25/100 × 4600 = $1150

The present worth is

4600 - 1150 = $3450

Also, her stock in company B was worth $1000. If her Stock in company B has decreased by 22% since last year in stock, then the amount by which it decreased is

22/100 × 1000 = $220

The present worth is

1000 - 220 = $780

The total worth of both stocks last year was

4600 + 1000 = $5600

The total worth of both stocks this year was

3450 + 780 = $4230

The amount by which it decreased is

5600 - 4230 = 1370

the total percentage decrease in the investor stock account is

1370/5600 × 100 = 24.5%

Answer:

A) 1/2 - there are 2 sides - just as likely to occur as not to occur

B) 0% - it's never going to happen (impossible)

C) 0/0 - it's never going to happen (impossible)

D) 1/2 simplified from 2/4 - that was 2 out of the four balls. - just as likely to occur as not to occur

By proving triangle HKE and triangle GKF congruent, it is proved EG bisects HF and HF bisects EG.

Given that, parallelogram EFGH.

Prove that, EG bisects HF and HF bisects EG.

Parallelogram EFGH with diagonals EG and HF intersecting at point K.

Proof:

Consider, ΔHKE and ΔGKF

∠HKE=∠GKF (Vertically opposite angles are equal)

∠FHE=∠GFH ( Alternate angles between the parallel line EF and HG)

∠GEH=∠FGE ( Alternate angles between the parallel line EF and HG)

By AAA congruency, ΔHKE and ΔGKF are congruent

By CPCT,

KE=GK

JF=HK

So, EG bisects HF and HF bisects EG.

Hence, proved.

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Final answer:

To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH, we can use the statements and reasons provided.

Explanation:

To prove that EG¯¯¯¯¯ bisects HF¯¯¯¯¯¯ and HF¯¯¯¯¯¯ bisects EG¯¯¯¯¯ in parallelogram EFGH with diagonals EG and HF intersecting at point K, we can use the following statements and reasons:

The midpoint of a line segment is given by the formula ((x₁ + x₂) / 2, (y₁ + y₂) / 2). After applying this formula to the given options, the correct midpoint is (p, r).

The midpoint of a line segment with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Applying this formula to the given options:

After substituting the values, we find that the correct answer is Option C: (p, r).

Answer:

0.3694

Step-by-step explanation:

In this question, we are asked to calculate the probability that a golfer scored at least 74 if she played on a particular day.

Given that ,

mean = µ = 73

standard deviation = σ = 3

P(x > 74) = 1 - P(x<74 )

= 1 - P[(x -µ) / σ < (74 -73) /3 ]

= 1 - P(z <0.3333 )

Using z table

= 1 - 0.6305

= 0.3694

probability= 0.3694

To find the probability of a golfer scoring at least 74 on a course with a mean score of 73 and a standard deviation of 3, we calculate the z-score for 74, find the corresponding probability in the z-table, and subtract this from 1 to get the upper tail probability. The probability is approximately 37%.

The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. We want to find the probability that a golfer scores at least 74. This is a question of statistics and specifically involves the concept of the normal distribution and calculating z-scores.

Firstly, we need to calculate the z-score for the score of 74. The z-score is calculated as (X-μ)/σ, where X is the score we are interested, μ is the mean, and σ is the standard deviation. Substituting the given values, (74 - 73) / 3 gives a z-score of approximately 0.33.

Then, to find the probability that a score is at least 74, we need to find the proportion of data to the right of this z-score in a standard normal distribution. This is known as the 'upper tail'. We subtract the z-score from 1 because the total probability under the normal curve is 1. If we look up 0.33 in the z-table, we get a value of 0.6293. Subtracting this value from 1 gives us 0.3707.

Therefore, the probability that a golfer scores at least 74 on this course is approximately 0.37 or 37%.

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Answer:

450 square feet

Step-by-step explanation:

Think of the shape as a complete rectangular

The area of the rectangular shape would be 25×30 = 750 square feet

Now find the area of the missing space and subtract it from 750

it would be 15×20 = 300 square feet

750 - 300 = 450 square feet