Write 77 as the sum of three square numbers.

Answer:

If two figures are similar, then the correspondent sides are related by a constant factor.

For example, if the base of one side of one of the figures has a length L, then the correspondent side of the other figure has a length k*L where k is the scale factor.

Let's start with the two left triangles.

In the smaller one the base is 5, and the base of the other triangle is 15.

Then we will have:

15 = k*5

15/5 = k = 3

The scale factor is 3.

Then we will have that:

a = scale factor times the correspondent side in the smaller triangle:

a = k*3 = 3*3 = 9

a = 9

For the other two triangles, the base of the smaller triangle is 12, while the base of the larger triangle is 20.

Then we will have the relation:

12*k = 20

k = (20/12) = 10/6 = 5/3

The scale factor is 5/3

This means that the unknown side b is given by:

b*(5/3) = 15

b = (3/5)*15 = 3*3 = 9

b = 9.

Given that the mean of a sample consisting of 3 observations is 34, the mode is 6, and the median is also 6. To find the values of the sample, let's arrange the given observations in ascending order. Let the three observations be x, y, and z.

Given that the mean of a sample consisting of 3 observations is 34, the mode is 6, and the median is also 6. To find the values of the sample, let's arrange the given observations in ascending order. Let the three observations be x, y, and z. The mode is the observation that occurs most frequently. As per the given data, the mode of the sample is 6. Therefore, at least two observations must be 6. Hence, the possible arrangements of x, y, and z are as follows:6 6 x6 6 y6 6 z

We know that the median is the middle observation in an ordered set of data. Thus, the observation in the middle must be 6. Therefore, we can eliminate the last arrangement:6 6 z

For the first arrangement, the mean of the sample is (6 + 6 + x)/3 = 34⇒ 12 + x = 102⇒ x = 90

Therefore, the three observations are 6, 6, and 90. For the second arrangement, the mean of the sample is (6 + 6 + y)/3 = 34⇒ 12 + y = 102⇒ y = 90

Therefore, the three observations are 6, 6, and 90. Thus, the numbers in the sample are 6, 6, and 90.

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Answer:

undefined

Step-by-step explanation:

line is straight up and down

Answer:

Undefined. It ends up being 3/0 which can't happen so it remains undefined.

Step-by-step explanation:

Answer:

x = 45/2 or 22.5

Step-by-step explanation:

Since we are given CDE ~ KLM, we know that C is similar to K, D is similar to L, and E is similar to M. The problem asks to find DE, so by comparison, it is known that DE is similar to LM.

From the two triangles, KM is similar to CE, and we can see that the ratio between the two is 8:15. We are given LM, which is 12, so we can find x using this equation to compare the smaller triangle to the bigger one:

KM/CE = LM/DE

Plug in your given values:

8/15 = 12/x

Find x:

x = 45/2 or 22.5

The measure of the smallest angle of the quadrilateral is  60° .

In the question ,

it is given that ,

the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .

So , the measure of the largest angle is = 9x

and the measure of the smallest angle is = 4x .

we know that the sum of the measure of all the angles of the quadrilateral is 360° .

that means ,

4x + 5x + 6x + 9x = 360°

24x = 360

dividing both sides by 24 ,

x = 360/24

x = 15 .

the smallest angle is = 4(15) = 60°

Therefore ,  The measure of the smallest angle of the quadrilateral is  60° .

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Answer:

Bottom left.

Step-by-step explanation:

One inequality has ≥. The other has >.

One line must be solid and the other dashed.

That eliminates the upper two choices.

The inequality with ≥ must be shaded above the solid line.

Answer: bottom left

Yes one and six tenths is to four as two and four tenths is to six

In some contexts, "is to" can mean division. For example, if you say "5 is to 10 as x is to 20," you could interpret that as a proportion, where the ratio of 5 to 10 is equal to the ratio of x to 20. This can be rewritten as:

5/10 = x/20

Now

To solve this problem, we can use proportions.

One and six tenths is equivalent to 1.6, and two and four tenths is equivalent to 2.4.

Let x be the number that corresponds to "is to" in the second part of the statement. Then, we can set up the following proportion:

1.6/4 = 2.4/x

We can cross-multiply to get:

1.6x = 9.6

And then solve for x:

x = 6

So in this case, "is to" did involve division. However, "is to" doesn't always mean division and its meaning can depend on the context in which it is used.

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The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer:

The bottom Option

Note:

Due to my sus vibes from your questions, this is the last one I am answering from you. this is basic and easy if you read it.

Answer:  th

Step-by-step explanation:

Answer: 2.6 or 2 2/3

Step-by-step explanation:

3 1/4 = 3.25

3.25/5 = 0.65

0.65 x 4 = 2.6 or 2 2/3

The proportion of the measurements lie in the interval is 0.9.

According to the given question.

Weigths of 10 young dogs.

W : 7, 5, 11, 8, 14, 19, 16, 15, 13, 27

As we know that mean si calculated by the formula

Mean = ΣW / n

Thereofre, the mean of the weights of 10 young dogs

= 7 + 5 + 11 + 8 + 14 + 19 + 16 + 15 + 13 + 27/ 10

= 13.5

And, Standard deviation (s) = 6.433

Proportion that lies in mean ± 2s

Lower = Mean - 2s

⇒ 13.5 - 2(6.433) = 0. 632

Also, Upper = Mean + 2s

⇒ 13.5 + 2(6.433) = 26.376

Mean ± 2(sd) = (0.632, 26.276)

The only digit from the data which falls outside the defined range = 27

Proportion within interval = 9 / n

Proportion which falls within interval = 9/10 = 0.9

Hence, the proportion of the measurements lie in the interval is 0.9.

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Answer:

Step-by-step explanation:

0 is the answer

Answer:

D

Step-by-step explanation:

8n = 32

32/8n

n=4

The midpoint of the midsegment of Trapezoid is   E(2m, 2n) and F (2(q+p), 2n).

According to the question,

The vertices of the trapezoid are A(4m , 4n) , B(4q , 4n) , C(4p , 0) and D(0,0).

Let mid-point of midsegment of Trapezoid be E and F

Using section formula

E (x- coordinate)= 1*4m + 0 /2

E (x- coordinate)=2m

E (Y- coordinate)= 4n/2

E  (Y- coordinate)=2n

So, the coordinates of E (2m, 2n)

similarly,

F (x- coordinate)= (1*4q + 1*4p)/2

F (x- coordinate)=2(p + q)

F (Y- coordinate)= 4n/2

F(Y- coordinate)=2n

So, the coordinates of F (2(q +p), 2n)

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Answer:

a)  See the attachment for the completed Venn diagram.

b)  The number of people who liked to watch television only is 20.

c)  The total number of people who took part in the survey was 200.

Step-by-step explanation:

Draw a Venn diagram with two overlapping circles.

Label one circle "Radio" and the other circle "TV".

Given that 50 people like to listen to the radio but not like to watch television, place the number 50 in the part of the radio circle that does not overlap the TV circle.

Given that 120 people like to listen to the radio, and 50 people like to listen to the radio but not like to watch television, then the number of people who like to listen to the radio and watch tv is:

Therefore, place the number 70 in the part where the two circles overlap.

Given that 110 people don't like to watch television, and 50 people like to listen to the radio but not like to watch television, then the number of people who don't like to listen to the radio or watch television is:

Therefore, place the number 60 in the area outside the two circles.

Given that 80 people don't like to listen to the radio, and 60 people don't like to listen to the radio or watch television, then the number of people who like to watch the television only is:

Therefore, place the number 20 in the part of the TV circle that does not overlap the radio circle.

Now the Venn diagram has been completed, we can find the total number of people who took part in the survey by adding all the numbers in the Venn diagram:

Therefore, there was a total of 200 people who took part in the survey.

We will investigate how to use ratios to determine the actual distance between cities as per defined scale.

We are given a scale conversion ( ratio ) at which distances are scaled down:

We will use the given scale ratio to determine the actual distance between two citites. The scale distance between Hawthorne and Doyelstown can be read.

Now utilize the scale conversion ratio to determine the actual distance:

Therefore, the distance between Hawthorne and Doylestown is:

Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.

We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.

The null hypothesis is that the population proportion is equal to 11.3%:

H0: p = 0.113

The alternative hypothesis is that the population proportion is greater than 11.3%:

Ha: p > 0.113

The sample proportion is P = 58/400

= 0.145

The standard error of the sample proportion is:

SE = √(p*(1-p)/n)

= √(0.113*(1-0.113)/400)

= 0.0197

The test statistic is:

z = (P - p) / SE

= (0.145 - 0.113) / 0.0197

= 1.6244

The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:

p-value = P(Z > 1.6244)

= 0.0515 (using a standard normal distribution table)

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Answer:

80° and 100°

Step-by-step explanation:

let 'x' and 'y' equal each angle

x + y = 180

now we could let y = .8x and use substitution to get this equation:

x + 0.8x = 180

1.8x = 180

x = 100

y = 80

Answer:

18 minutes

Step-by-step explanation:

It takes jose 2 minutes for 3 laps, so for 27 laps he would need 2*9 minutes.

Using the z-distribution, as we are working with a proportion, it is found that the buyers need a sample of 1505.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In this problem, we have a 98% confidence level, hence\(\alpha = 0.98\), z is the value of Z that has a p-value of \(\frac{1+0.98}{2} = 0.99\), so the critical value is z = 2.327.

There is no estimate of the percentage, hence \(\pi = 0.5\), and the margin of error is of M = 0.03, hence we solve for n to find the desired sample size.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 2.327\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.03\sqrt{n} = 2.327(0.5)\)

\(\sqrt{n} = \frac{2.327(0.5)}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{2.327(0.5)}{0.03}\right)^2\)

\(n = 1504.2\)

Rounding up, the buyers need a sample of 1505.

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The equation of the parabola in vertex form that passes through the points (-2, 4) and (1, 0):

y = -2(x + 1)^2 + 2

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex is (-1, 2), so we can write the equation as y = -2(x + 1)^2 + 2.

To find the vertex of the parabola, we can take the average of the x-coordinates of the two points, and then take the average of the y-coordinates of the two points. The average of the x-coordinates is (-2 + 1)/2 = -0.5, and the average of the y-coordinates is (4 + 0)/2 = 2. Therefore, the vertex is (-0.5, 2).

Once we know the vertex, we can find the value of a by substituting the vertex coordinates into the vertex form of the parabola. Substituting (-0.5, 2) into the equation y = a(x - h)^2 + k, we get 2 = a(-0.5 - (-1))^2 + 2. Simplifying, we get 2 = a(0.25) + 2. Solving for a, we get a = -2.

Plugging in a = -2 into the vertex form of the parabola, we get y = -2(x + 1)^2 + 2. This is the equation of the parabola in vertex form.

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The equation of the parabola in vertex form that passes through the points (-2, 4) and (1, 0):

y = -2(x + 1)^2 + 2

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex is (-1, 2), so we can write the equation as y = -2(x + 1)^2 + 2.

To find the vertex of the parabola, we can take the average of the x-coordinates of the two points, and then take the average of the y-coordinates of the two points. The average of the x-coordinates is (-2 + 1)/2 = -0.5, and the average of the y-coordinates is (4 + 0)/2 = 2. Therefore, the vertex is (-0.5, 2).

Once we know the vertex, we can find the value of a by substituting the vertex coordinates into the vertex form of the parabola. Substituting (-0.5, 2) into the equation y = a(x - h)^2 + k, we get 2 = a(-0.5 - (-1))^2 + 2. Simplifying, we get 2 = a(0.25) + 2. Solving for a, we get a = -2.

Plugging in a = -2 into the vertex form of the parabola, we get y = -2(x + 1)^2 + 2. This is the equation of the parabola in vertex form.

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The total cost of Ashley's car will be amount of $26,460.

A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.

Ashley bought a new car for $25,000. She paid a 10% down payment and financed the remaining balance for 60 months with an APR of 4.4%.

To find 10% of $25,000

⇒ down payment = $2500

The remaining balance of (25,000 - 2500) is $22,500 for 60 months with an APR of 4.4%

The total payback = P× r/100 × T + P

Here P = $22,500 , r =  4.4%, and T = 4 years

The total payback = 22,500 × 4.4/100 × 4 + 22,500

The total payback = 22,500 × 0.044 × 4 + 22,500

The total payback =3,960 + 22,500

The total payback = 26,460

Therefore, the total cost of Ashley's car will be amount of $26,460.

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Answer:

No solution

Step-by-step explanation:

3(5x+7) = 30 + 15x

DISTRIBUTE

15x+21 = 30+15x

15x-15x = 0

So no solution

Answer:

Zero solutions

Step-by-step explanation:

3(5x + 7) = 30 + 15x,            Use the distributive property

15x + 21 = 30 + 15x,             The 15x from both sides cancel each other out

21 ≠ 30                                 No matter what value of x is, 21 will never equal 30

During the current year, merchandise was sold for $662,100. Of this amount, $114,000 was cash sales and $548,100 was on account. The cost of goods sold was $423,700. Therefore, the gross profit was $238,400.

The gross profit is calculated by subtracting the cost of goods sold from the total sales. The cost of goods sold is the direct cost of producing the goods that were sold. It includes the cost of materials, labor, and overhead.

The gross profit is an important measure of a company's profitability. It shows how much money the company makes from its core business activities, before deducting other expenses.

In this case, the company's gross profit margin is 35.8%. This means that for every $100 of sales, the company makes $35.80 in gross profit. A high gross profit margin is generally considered to be a sign of a healthy business.

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The probability that emission of both CO and hydrocarbon is in excess is 0.8.

The proportion of favorable cases to all possible cases used to determine how likely an event is to occur.

Let, A be the event in which cars are emitting excess CO:

P(A) = 0.12

Let, B be the event in which cars are emitting excess hydrocarbons:

P(B) = 0.15

The cars which emit both CO and Hydrocarbons in:

P(A∩B) = 0.8

The probability that emission of both CO and hydrocarbon is in excess is 0.8.

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Answer:

Step-by-step explanation:

Candice = 25mph for 4 hours.

Candice has driven= 25 * 4= 100miles.

Liz =50mph

Liz time to catch up to candice= 50 * 2= 100miles.

Therefore, It would have taken Liz two hours to catch up with Candice

Answer:

Area = 6.25\(\pi \) ft^2

Step-by-step explanation:

Area = \(\pi \\\)\(r^{2} \)

The diameter is 5 feet.  That makes the radius 2.5 feet

Area = \(\pi \\\)\(r^{2} \)

Area = \(\pi \\\)\(2.5^{2} \)

Area = 6.25\(\pi \) ft^2