Identify and name congruent angles

There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.

To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.

We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).

Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:

C(n + r - 1, r - 1)

where n is the sum (15) and r is the number of boxes (6).

Plugging in the values, we have:

C(15 + 6 - 1, 6 - 1) = C(20, 5)

Calculating this combination, we find:

C(20, 5) = 13,992

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Using the concepts of Probability, we got 0.2743 is the probability that he/she plays the clarinet but not the flute.

Conditional probability is called as the possibility of an event or outcome happening, based on  existence of a previous event or outcome. It is calculated by the multiplying the probability of the preceding event by the renewed probability of  succeeding, or conditional, event.

We need to find those persons  who can play clarinet but not the flute,

So, we first subtract those person from the clarinets list who are able to paly both clarinet and flute.

Suppose, Number of person who can play clarinet=172

Number of person who are able to play both clarinet and flute=47

Therefore, number of person who are only able to play clarinet but not flute=172-47=125

Probability(P)= \(\frac{Number of perople who are only able to play clarinet}{Total number of people}\)

              =>P=( 125 / 350)

               =>P=0.2743.

Hence, if a single person is selected at random,0.2743 is the probability that he/she is able to play clarinet but not flute.

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To find the measure of angle BCD, we need to determine the measure of angle BCA first.

In a regular 20-gon, the sum of the interior angles is given by the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon. So, in a 20-gon, the sum of the interior angles is (20-2) * 180 = 3240 degrees.

Since the 20-gon is regular, each interior angle has the same measure. Therefore, each interior angle of the 20-gon measures 3240 degrees / 20 = 162 degrees.

Angle BCA is one of the interior angles of the 20-gon, so it measures 162 degrees.

Now, in the heptagon BACD, the sum of the interior angles is given by the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon. So, in a heptagon, the sum of the interior angles is (7-2) * 180 = 900 degrees.

Since the heptagon is regular, each interior angle has the same measure. Therefore, each interior angle of the heptagon measures 900 degrees / 7 = 128.571 degrees (rounded to three decimal places).

Angle BCA is one of the interior angles of the heptagon, so it measures 128.571 degrees.

Finally, angle BCD is the difference between angles BCA and BCD: angle BCD = angle BCA - angle BCD = 162 degrees - 128.571 degrees = 33.429 degrees (rounded to three decimal places).

Therefore, angle BCD measures approximately 33.429 degrees.

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Let B, A, and D be three consecutive vertices of a regular 18-gon. A regular heptagon is constructed on \(ABbar\), with a vertex C next to A. Find\(\leqBCD\) ∠\(BCD\) , in degrees.

To determine the degrees of angle BCD in this problem, we must first discover the degree of each interior angle of the 20-gon and the heptagon. Calculating these values, and subtracting them from 180, we find the measure of angle BCD equals to 69.43 degrees.

In this problem, we need to find the measure of angle BCD of a heptagon formed on a side of a regular 20-gon. We have that consecutive vertices B, A, D of 20-gon and vertex C of a heptagon formed on line segment AB is our interest point.

Since A, B, D are consecutive vertices of a regular 20-gon, we first calculate the value of each interior angle using the formula (n-2)×180/n, where n is the number of sides. So the measure of each interior angle of the 20-gon is (20-2)×180/20 = 162 degrees.

The heptagon shares one of its vertices with the 20-gon (i.e., point A). Point C is a neighboring vertex of A in this heptagon. The angles of a regular heptagon are calculated in the same way, using the formula (7-2)×180/7, which gives approximately 128.57 degrees.

Therefore, to calculate the measure of angle BCD, let's note that it equals to (180 - angle BAC) + (180 - angle CAD). Since angles BAC and CAD are parts of the 20-gon and the heptagon respectively, it will be (180 - 162) + (180 - 128.57) = 18 + 51.43 = 69.43 degrees.

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Answer:

x = -2

Step-by-step explanation:

y = -3x + 2.5

if y = 8.5 then:

8.5 = -3x + 2.5

-3x = 6

x = -2

Answer:

Step-by-step explanation:

17-8=9 but if 18-7=11 then 19-8=7

Answer:

15/17

Step-by-step explanation:

Cosine is equal to adjacent/hypotenuse. Since we don't have the hypotenuse in this case, we need to solve for it.

15^2+8^2=c^2

c=17

We get 17 for the hypotonuse.

Plug it into the equation adjacent/hypotenuse and you get 15/17

No, the line passing through  (-4, 26) and (-2, 0) is  not parallel to line passing through (10, 18) and (5, 3) because slopes of both lines are different.

Line is possible in 2-d forms so, it has only x and y-co-ordinates. Z-co-ordinates is not possible.

We know very well that to prove any two lines are parallel to each other we need to prove only whether their slopes are equal or not.

Now, talking about the slopes we know that if any line is passing from point(x₁,y₁) and again passing from other point(x₂,y₂) then slope(m) of that line is given by the formula=(y₂-y₁) / (x₂-x₁)

So, for first line we have (x₁, y₁)=(-4,26)

and (x₂, y₂)=(-2,0)

So, slope(m₁) of first line is =(0-26)/(-2 - (-4))

                  =>m₁ = -26/2

                   =>m₁ = -13     ----(eq1)

Similarly, for second line, we have (x₁, y₁)=(10,18)

and (x₂, y₂)=(5,3)

So, slope(m₂) of second line is =(3-18) / (5-10)

                =>m₂ = -15/-5

                 =>m₂=     3   -------(eq2)

On comparing eq1 and eq2,we get

 =>m₁≠m₂.

Hence, the given lines are not parallel.

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(Complete question) is:

Is the line through (-4, 26) and (-2, 0) parallel to the line through (10, 18) and (5, 3)?

Here the population growth is as per the Malthusian model. As per the calculations, the bacterial population will reach 10000 after 33 days.

Here the bacterial growth is as per the exponential growth curve. So the equation is,

   \(P_{t} = P_{0} e^{rt}\)

\(P_{t}\) is the population at n

\(P_{0}\) is the initial population

r is the time

t is the rate

Population doubles after 10 days.

So,  \(2000 = 1000e^{r*10} \\\\\frac{2000}{1000} = e^{10r}\\\\ 2 = e^{10r\\}\\\\\)

Taking logarithms on both sides

\(ln(2) = lne^{10r}\\\\10r = 0.693\\ \\r = 0.0693\)

So the rate is 0.0693.

When population reaches 10000,

\(10000 =1000e^{0.0693t}\)

\(\frac{10000}{1000} =e^{0.0693n}\)

\(10 = e^{0.0693*t}\\ \\ln(10) = ln(e^{0.0693t}\\ \\2.3 = 0.0693t\\\\t = 2.3/0.0693\\= 33.18\)

So the number of days to reach population of 10000 is 33.18≈ 33 days.

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The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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Using midpoints, The length of RY is (9x - 1)/2 cm.

A midpoint is a point that is exactly halfway between two other points. In geometry, the midpoint of a line segment is the point on that line segment that is equidistant from both endpoints.

For example, in a line segment AB, the midpoint M is the point on AB that is equidistant from A and B. In other words, the distance from A to M is the same as the distance from M to B. The midpoint M is located at the exact center of line segment AB, and it divides the segment into two equal parts.

The midpoint can also be thought of as the average of the x-coordinates and y-coordinates of the endpoints. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint has coordinates:

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

Since R is the midpoint of XY, we know that RX = RY.

We are given that XR = 5x+2 cm and XY = 14x+1 cm.

Thus, RX + RY = XY

Substituting RX = RY, we get:

RY + RY = 14x + 1 - (5x + 2)

Simplifying the right side, we get:

RY + RY = 9x - 1

2RY = 9x - 1

RY = (9x - 1)/2

Therefore, the length of RY in cm is (9x - 1)/2.

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Answer:

Step-by-step explanation:

y=mx+c.... first find m(gradient/slope)

m=Y2-Y1/X2-X1

m=8-4/-6-2

m=4/-8

m=-1/2

Then find c

Take any point and fix in x and y

4=-1/2(2) +c

4=-1 +c

c=4+1=5

Therefore y=-1/2x+5

y+1/2x-5=0

Answer:

4 x^ 3 −  24 x^ 2  +  39 x  −  28

Step-by-step explanation:

This is in standard form.

Answer:

4x^{3}-24x^2+39x-28

Step-by-step explanation:

The value of 'x' in the given proportion \(\frac{14}{6}\) = \(\frac{21}{x}\) is x=9 ft . The values in the dropdown menu are:

14 x 1.5 = 21

6 x 1.5 =  9

What is proportion?

Ratio and fractions are the basis of proportion. When two ratios are equivalent, it is stated by a fraction in the form of a/b, ratio a:b, and then a proportion. Any two integers may be used here as a and b. An analysis of two numbers is a proportion.  Two sets of provided numbers are said to be directly proportional to one another if they change in two different ways, either rising or decreasing.

Given the dimensions of smaller triangle:

6 ft

14 ft

16 ft

Given the dimensions of smaller triangle:

x ft

21 ft

24 ft

Given Proportion or ratio of sides,

\(\frac{14}{6}\) = \(\frac{21}{x}\)

14 . x = 21 . 6

      x = \(\frac{21 . 6}{14}\)

      x = \(\frac{126}{14}\)

      x = 9

The missing dimensions of triangle = 9 ft

Now for the answers in dropdown menu, let's evaluate the ratios of corresponding sides:

\(\frac{9}{6}\) = \(\frac{21}{14}\)  = \(\frac{24}{16}\) = 1.5

a)14 x 1.5 = 21

b)6 x 1.5 = 9

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Refer to the attachment for the options.

The equation of the regression line is y = 4/5x - 36/5. Option (c)

Using the two points closest to the line, we can estimate the slope and intercept of the regression line. Let's use the points (20, 14) and (50, 38), since they appear to be the closest to the line.

The slope is:

m = (y2 - y1) / (x2 - x1) = (38 - 14) / (50 - 20) = 24 / 30 = 4/5

To find the y-intercept, we can use the equation y = mx + b and plug in one of the points. Let's use (20, 14):

14 = (4/5)(20) + b

14 = 16 + b

b = -2

So the equation of the regression line is:

y = 4/5x - 2

Therefore, the answer is (B) 4/5x - 36/5

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Full Question: The scatter plot and table show the number of grapes and blueberries in 10 fruit baskets. Use the two points closest to the line. Which equation is the equation of the regression line?

A. y = 1/3x - 1/3

B. y = 4/5x + 18

C. y = 4/5x - 36/5

D. y = 5/4x - 45/2

Answer:

The amount of deposit required is R37,999  for both

The percentage of purchase price for the required deposit is 20%

Therefore, deposit required=20%*R189,995

                                              =R37,999

The balance owed is the outstanding balance after payment of deposit plus the interest, bearing in mind that interest is computed using the simple interest approach

I=PRT

balance after payment of deposit=R189,995-R37,999

                                                       =R151,996

R=13.5% per year

T=48 months and 54 months

Interest on 48 month option=151,996*13.5%*48/12

                                              = R82,077.84

Interest on 54 month option=151,996*13.5%*54/12

                                              = R 92,337.57

The total payment without the initial deposit is the outstanding balance after payment of deposit plus the interest

Total payment for 48 month option=R151,996+R 92,337.57

                                                          =R  244,333.57

Total payment for 54 month option=R151,996+R82,077.84

                                                          =R 234,073.84

                                              Hope it helped!

Cutting off 1/6 of the post would be equal to cutting off 3/4 of a foot or 9 inches.

To find out how much of the wooden post would be cut off if you cut off 1/6 of it, you need to first convert the length of the post to a fraction that can be easily divided into six equal parts.

Since the post is 4 1/2 feet long, it can be represented as a mixed number:

4 1/2 = (4 x 2 + 1)/2 = 9/2

Therefore, the post is equivalent to 9/2 feet long.

To cut off 1/6 of the post, you need to divide the length of the post by 6 and then multiply the result by 1.

(1/6) x (9/2) = 9/12

To simplify this fraction, you need to find the greatest common factor (GCF) of the numerator and denominator, which is 3:

9/12 = (9/3) / (12/3) = 3/4

Therefore, if you were to cut off 1/6 of the wooden post that is 4 1/2 feet long, you would have cut off 3/4 of a foot (or 9 inches).

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The image of the point (-3, 0) under the same translation is (-2, 3).

Left/Right movement: -3 + 1 = -2 Up / Down movement: 0 + 3 = 3. The image of the point (-3, 0) under the same translation is (-2, 3).Given the point (2, 4) is translated to (1, 1) after translation. Therefore, The distance moved left/right = 2 - 1 = 1 and the distance moved up/down = 4 - 1 = 3.

Using the same distances to translate point (-3, 0), we get the new coordinates:

Left/Right movement: -3 + 1 = -2 Up / Down movement: 0 + 3 = 3

The image of the point (-3, 0) under the same translation is (-2, 3).

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Answer: Logistic regression is a very popular, statistically sound, probability-based classification algorithm that employs supervised learning.

Divisibility rule of 3:

If the sum of the digits are divisible by three, the number is divisible

Divisibility rule of 4:

If the last two digits are divisibly by four, it's divisible

Now let's apply the divisibility rule with the numbers

A) 101.444/3 = 33.1846666...

So it's clearly not divisible by three

B) 112436/3 = 37478.6666...

Not divisible by three either

C) 118754/3 = 39584.6666...

Nope.

D) 118422/3 = 39474

We found one that is divisible, so now we divide it by four

We take the last two digits and divide it with four

22/4 = 5.5

Therefore, the answer is D, because it ends with quotients that doesn't repeat

Answer:

The regular costs 11 dollars each while the deluxe cost 23 each.

Step-by-step explanation:

You need to setup two equations.I used two variable for the prices of the types of pizzas because they are unknown.I used x for the cost of regular and y for the cost of deluxe.The equation I did are 10x+y=133 and 7x+9y=284.You need to solve one equation only.I solved the first one.

Answer:

Step-by-step explanation: So the players

Answer:

Step-by-step explanation: it should be 31 two-point shots and 20 one-point shots

Answer:

- 439

Step-by-step explanation:

evaluate f(- 7) and substitute the value obtained into s(x)

f(- 7) = 3(- 7) = - 21 , then

s(- 21) = 2 - (- 21)² = 2 - 441 = - 439

Answer:

A. (s*t)(-7)=-439

Step-by-step explanation:

(s*t)(-7) is the same as s(t(-7)). First find t(-7)

t(-7)=3(-7)=-21

t(-7)=-21

Plug -21 into s(t(-7)) for t(-7).

Find s(-21).

s(-21)=2-(-21)^2=-441+2=-439

Hope this helps!

If not, I am sorry.

Answer:

Whether a net force acts on the object.

Step-by-step explanation:

Newtons first law states that an object will remain at rest unless it is acted upon by an imbalanced force.

Principal = 9000

Interest rate = 7% = 0.07

Time = 5 years

Simple interest formula:

A = P(1 + rt)

In this case:

A = 9000(1 + 0.07*5) = 9000(1 + 0.35) = 9000(1.35) = 12150

Interest = A - P = 12150 - 9000 = 3

Answer:

Step-by-step explanation:

use point-slope formula [ y- y1 = m(x - x1) ]  with the point you are given as point 1 (x1,y1) = (4,-6) and the slope m that you are also given m = -3/4

y-y1 = m(x -x1)

y-(-6) = -3/4(x -4)

y + 6 = -3/4(x-4)

you can work this toward the slope-intercept formula of y = mx +b by doing the following

y + 6 = -3/4x +3    (distribute the -3/4)

y = -3/4x + 3 -6   ( move the 6 to the other side )

y = -3/4x - 3  

there  you go  :) choice 1 looks good if you're still able to put in the answer

Step-by-step explanation:

just as the graph shows.

no trick or hidden meaning or whatever.

#1

0 seconds to 5 seconds.

0 meters to 3 meters.

traveled 3-0 = 3 meters in 5-0=5 seconds

#2

0 seconds to 8 seconds.

0 meters to 5 meters.

traveled 5-0=5 meters in 8-0=8 seconds.

The number of platters that can be made is 8.

Given that you need to make a platter which consists of 1 bagel, 2 eggs, and 3 slices of bacon. Since it is needed to calculate the maximum number of platters that can be made with 9 bagels, 17 eggs and a package of bacon containing 36 slices.

Further, If we make 1 platter then we need 1 bagels, 2 eggs and 3 slices of bacon. Therefore, for 8 platters, the material required would be 8 times of 1 platter, that is 8 bagels, 16 eggs and 24 slices of bacon.

Similarly if I have to create 9 platters , the material required would be 9 times of 1 platter, that is 9 bagels, 18 eggs and 27 slices of bacon.

So we can not make 9 platters because we need that one extra egg.

The number of platters is 8.

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Answer:

He needs to cut 3/8

Convert: needs 22/8 and has 25/8