If a is an obtuse angle in a triangle and sin a = , calculate the exact value of sin 2a.

The cost per person if number of students is 100 given the inverse variation is $46.75

C = k / n

where,

k = constant of proportionality

If n = 55 and C = $85

C = k / n

85 = k / 55

85 × 55 = k

4,675 = k

Find C if n = 100

C = k / n

= 4,675 / 100

C = $46.75

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Answer:

C = $46.75

Step-by-step explanation:

85 × 55 = k

4,675 = k

4675/100=46.75

therefore the answer is 46.75

Answer:

$13.5

Step-by-step explanation:

cost of 1 text message= $1.80÷12 =$0.15

cost of 90 messages = $0.15×90 = $13.5

Answer: $13.50 for 90 text messages

Step-by-step explanation:

$0.15×90 = $13.5

$0.15 is the unit rate for 1 text message cost.

The expected value of the number of people selected before and including the first time a woman has a turn is 1.6667 and the standard error is 0.7454.

It should be noted that the expected value will be:

1[p(x = 1)] + 2[p(x = 2)] + 3[p(x = 3)]

= 1(0.5) + 2(0.3333) + 3(0.1667)

= 1.6667

Var(X) = E(X²) - E(X)2

= 3.3335 & (1.6667)²

= 0.555611

The standard error will be:

= ✓0.555611

= 0.7454

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The area of the convex polygon is 43/2 square units

The vertices are given as:

(0,5), (-1,2), (4,4), (-3,-4) and (2,0)

The area is then calculated as:

[tex]A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )[/tex]

So, we have:

[tex]A = \frac12 * (|-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 + 2 * -4 - 0 * -3 -3 * 2 + 4 * 1|)[/tex]

Evaluate

[tex]A = \frac12 * (|-43|)[/tex]

Remove the absolute bracket

[tex]A = \frac12 * 43[/tex]

This gives

[tex]A = \frac{43}2[/tex]

Hence, the area of the convex polygon is 43/2 square units

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In [tex]15[/tex] diffret days [tex]15/4[/tex] inches of rain fell in April month if every day rained [tex]1/4[/tex] of a inch .

How to find the rain fell in [tex]15[/tex] diffret days ?

We know that rain in every day is [tex]1/4[/tex] of a inch

So for [tex]15[/tex] days

[tex]1/4+1/4+1/4+......15times\\=15/4[/tex]

So in [tex]15[/tex] diffret days in April rain fell is [tex]15/4[/tex] inches.

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Answer:

( 9, -12 )

Step-by-step explanation:

Mario's Math Tutoring

you have the midpoint

2, -5

use the midpoint formula

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

to get the endpoint

x :

(-5+x2)/2 = 2

(-5+x2) = 4

-5+x2 = 4

x2 = 9

y:

(2+y2)/2 = -5

(2+y2) = -10

2+y2 = -10

y2 = -12

Thank you Mario!

An action that would not interfere with the airflow patterns at the front opening of the biosafety cabinet is a researcher discarding waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening.

It should be noted that biosafety simply means the use of safety equipment as specifically designs tools to ensure that people are protected from hazards.

In this case, when a researcher discards waste within the biosafety cabinet to prevent the movement of their arms in and out of the front opening, it won't interfere with the airflow pattern.

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Answer:

  D. 24

Step-by-step explanation:

The 5-number summary of a data set includes ...

When the data are written in increasing order, they are ...

  23 23 24  27 27 28  30 30 30  33 34 35

The minimum is the first value on the list, 23.

The first quartile is the average of the two middle values in the lower half of the data set: (24+27)/2 = 25.5.

The median is the average of the two middle values: (28+30)/2 = 29.

The third quartile is the average of the two middle values in the upper half of the data set: (30+33)/2 = 31.5.

The maximum is the last value on the list: 35.

A. 29 is the median

B. 23 is the minimum

C. 31.5 is the 3rd quartile

D. 24 is not part of the 5-number summary

Considering the mean of a discrete distribution, you are expected to earn $0.13 by the end of the game.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

Since 71% of your rolls are successful and 29% of your rolls are unsuccessful, the distribution of your earnings is:

Hence the expected value is:

E(X) = 1 x 0.71 - 2 x 0.29 = 0.71 - 0.58 = 0.13

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Answer:

[tex]\huge\boxed{\sf 8:32\ AM}[/tex]

Step-by-step explanation:

Woke up = 7:30 AM

Time to:

Altogether:

= 14 + 9 + 39 min

(As we know that, 1 hour = 60 minutes)

So,

Time he reached the school:

7 hr 30 min + 1 hr 2 min

Combine like terms

7 hr + 1 hr + 30 min + 2 min

OR

[tex]\rule[225]{225}{2}[/tex]

Paul woke up for school at 7:30 AM. He took 14 minutes to get ready, 9 minutes to finish his breakfast and 39 minutes to commute to school. At what time did he reach the school?

In this question we are asked to calculate the time paul reach the school.

Altogether time paul took to get ready, to finish his breakfast and to commute to school.

(14 + 9 + 39) minutes

→ (23 + 39) minutes

→ 62 minutes

Now we will convert minutes into hour.

62 ÷ 60

→ 1 hr 2 min

Now we will calculate the time he reached his school.

7 hr + 30 + 1 hr 2 min

[tex]\begin{array}{cc}7 \sf{hrs} \: & \: 30 \sf{min} \\ \underline{1 \: \sf{hr}} & \underline{2 \sf{min} } \\ \pmb{8 \sf{hrs}}& \pmb{32 \sf{min}}\end{array}[/tex]

He will reach the school at 8:32 AM.

Answer: 18.6 feet

Step-by-step explanation: Horizontal distance = 17 feet and the angle

of elevation = 24°

Using the formula for the distance between two points to find the side lengths, the perimeter of the polygon is of 25 units.

The perimeter of a figure is given by the sum of the side lengths of it's outside dimensions.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

For this problem, the distances are given as follows:

Hence the perimeter is given by:

P = 3 + 2 x 5 + 2 x 6 = 25 units.

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Answer:

A= 54

B=3

Step-by-step explanation:

I hope this helps!

Answer:

784 cats      Yikes !

Step-by-step explanation:

d/c = 3/8  

              3/8 = 294/c

                        c = 294 * 8/3 = 784 cats

The change in the area is represented by the expression ΔA = 9 · x + 4, where x is the original width of the rectangle.

By geometry we know that the area of a rectangle is equal to the product of its width (x) and length (y). Based on the statement, the original rectangle is equal to:

A = x · y

A = x · (2 · x - 3)

And the change in the area is:

A + ΔA = (x + Δx) · (y + Δy)

A + ΔA = x · y + Δx · y + Δy · x + Δx · Δy

ΔA = Δx · y + Δy · x + Δx · Δy

ΔA = (2 · x - 3) · Δx + Δy · x + Δx · Δy

ΔA = 2 · (2 · x - 3) + 5 · x + 10

ΔA = 9 · x + 4

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The p-value(0.0538) is greater than the given significance level of 0.01. So, there is no sufficient evidence to show that the manufacturer needs to recalibrate the machines.

The test statistics formula for finding the z-score is,

z = (X - μ)/(σ/√n)

Where,

X = sample mean

μ = population mean

σ = population standard deviation

n = sample size

With this z-score, the p-value is calculated. If p > α, then the null hypothesis is not rejected, and if p < α, then the null hypothesis is rejected.

It is given that,

The population mean μ = 4.00

The sample size n = 81

The sample mean X = 3.97

The standard deviation σ = 0.14

and the significance level α = 0.01

So, the hypothesis is:

The null hypothesis: H0: μ = 4

The alternative hypothesis: Ha: μ ≠ 4

Thus, the test statistic value is,

z = (X - μ)/(σ/√n)

  = (3.97 - 4)/(0.14/√81)

  = - 0.03/0.015

  = -1.928

So, for z = -1.928, the p-value is 0.053855

Since p > 0.01, there is no sufficient evidence to show that the manufacturer needs to recalibrate the machines.

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Answer:The answer is A

Step-by-step explanation:

The relationship between the base of the cone and the angle of the plane that intersects the cone is that the plane must be at a 45 degree angle to the base of the cone. Thus, Option D is correct.

According to the statement

we have given that the to form a ellipse we use the base and angle of the cone, And we have to tell the relationship between them.

So, For this purpose, We know that the

An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

And to make a ellipse the relationship between the base of triangle and the angle of the cone is that the

The plane must be at a 45 degree angle to the base of the cone.

By this way we make a ellipse with the help of the cone.

So, The relationship between the base of the cone and the angle of the plane that intersects the cone is that the plane must be at a 45 degree angle to the base of the cone. Thus, Option D is correct.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone?

A. The plane is parallel to the base of the cone..

B. The plane may be perpendicular to the base of the cone..

C. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.

D. The plane must be at a  angle to the base of the cone.

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Answer:

The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.

Step-by-step explanation:

The plane doesn't need to be at an exact angle of 45 degrees. The most important thing is that the angle isn't parallel or perpendicular to the base of the cone, but it has to be non-zero without intersecting the base itself. It also only intersects one of the cones when looking at a double-cone.

The parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.

The following are the parts of the circle shown;

Thus, the parts of the circle shown in the image include, chord, diameter, radius, tangent and center point.

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Probability that the lock code consists of all even digits is [tex]1344[/tex] if we choose the [tex]4[/tex] digit lock is randomly from numbers [tex]1,2,3,4,5,6,7,8,9[/tex]

How can we find the probability that the lock code consists of all even digits?

Total numbers are [tex]1,2,3,4,5,6,7,8,9[/tex]

And we choose [tex]4[/tex] digit code

So probability of choosing [tex]4[/tex] numbers from [tex]9[/tex] numbers without reapitation is

[tex]9p_{4} =\frac{9!}{(9-4)!} \\=\frac{9*8*7*6*5!}{5!} \\=3024[/tex]

For All numbers are even , probability the last digit of number is even.

So we have [tex]4[/tex]  even number and if we fix one on last digit and can change other [tex]3[/tex] then the probability is

[tex]4*8P_{3} =4*\frac{8!}{(8-3)!} \\=4*\frac{8*7*6*5!}{5!} \\=1344[/tex]

So the total probability of code lock having all even number is [tex]1344[/tex]

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The given sample's 95% confidence interval is 11.6 ± 0.5357. I.e., from the lower bound 11.06 to the upper bound 12.14. Its margin error is 0.5357.

To find the confidence interval C.I,

It is given that,

Sample size n = 225

Sample mean μ = 11.6

Standard deviation σ = 4.1

Since 95% confidence interval, z-score is 1.96

So, the required confidence interval is calculated by,

C. I = μ ± z(σ/√n) or mean ± margin error

On substituting,

C. I = 11.6 ± 1.96(4.1/√225)

     = 11.6 ± 1.96 × 0.2733

     = 11.6 ± 0.5357

So, the lower bound = 11.6 - 0.5357 = 11.065 and

the upper bound = 11.6 + 0.5357 = 12.135.

Thus, the confidence interval is from 11.06 to 12.14, and its margin error is 0.0537 for the population mean number of unoccupied seats per flight.

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The number of teams she can make is 10.

Division is the process of putting a number into equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other basic mathematical operations include addition, subtraction, multiplication.

The number of teams that can be made can be determined by dividing the total number of friends by the total number of players in each team. The whole number that is derived from the division process is the number of teams teams that can be made given the total number of friends and the number of people that have to be in each group.

Number of teams she can make = total number of friends / number of people in each group

31 / 3 = 10 remainder 1

So, only 10 teams can be made. one person would not be on any team.

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Answer:

1/a + 1/b + 1/c = 1 , a,b,c is nonzero

Step-by-step explanation:

bc +ac +ab /abc = 1

bc + ac + ab = abc

a = b = c = 1

The length of side AC = 5 units

Missing sides of a right triangle can be solved using the Pythagoras theorem

From the given question

Length of side AB = 3 units

Length of side BC = 4 units

The length of side AC is calculated below

[tex]AC^2=AB^2+BC^2\\\\AC^2=3^2+4^2\\\\AC^2=9+16\\\\AC^2=25\\\\AC=\sqrt{25}\\\\AC=5[/tex]

Therefore, the length of side AC = 5 units

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Complete Question

The length of side ab is 3 units. the length of side bc is 4 units. the length of side ac is .......... units.

Answer: Width is 7 inches, length is 15 inches.

Step-by-step explanation:

Let the width be w. Then, the length is w+8.

[tex]2(w+w+8)=44\\\\w+w+8=22\\\\2w+8=22\\\\2w=14\\\\w=7\\\\\implies l=15[/tex]

The greatest Common factor of monomials  [tex]33c[/tex]  and  [tex]27c^4[/tex] is  [tex]3c[/tex]

How we can find the GCF of monomials ?

Monomials are [tex]33c[/tex] and [tex]27c^4[/tex]

We can write the monomials in fraction form

[tex]33c=11*3*c[/tex]

[tex]27c^4=3*9*c*c*c*c[/tex]

----------------------------------

So we can see the common factor is [tex]3c[/tex]

The Greatest Common Factor of [tex]33c ,27c^4[/tex] is [tex]3c[/tex]

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The computation shows that the amount that will be charged will be $5.00 and $9.00 respectively.

When the customer has a 6 pound Chihuahua, the amount that will be charged will be $5.00.

When a customer has a 65 pound Labrador, the amount that will be charged is $9.00.

This is illustrated as the cost is based on the weights given.

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