Together, Steve and Tom sold 125 raffle tickets for their school. Steve sold 17 more than three times as many raffle tickets as Tom. How many raffle tickets did each boy​ sell?

The exact coordinates of points where the horizontal tangent exists are:

(0,2)

([tex]\pi[/tex],6)

([tex]-\pi[/tex],6)

What is meant by tangent?

A plane or straight line that meets a curve or curved surface at a particular place but does not cross it when extended.

Given function is f(x)=4-2secx

We can write it as

y=4-2secx

The slope of the tangent to this curve is:

[tex]\frac{dy}{dx} =-2secx*tanx[/tex]

Given that the tangent is horizontal, which means that the slope is zero.

-2secx*tanx =0 when x is multiples of [tex]\pi[/tex].

So we can take x=0, [tex]\pi[/tex], -[tex]\pi[/tex].

When x=0 ⇒ y=4-2sec0

⇒y=2

When x=π ⇒ y=4-2secπ

y=6

When x=-π⇒ y=4-2sec(-π)

y=6

Therefore the exact coordinates of points where the horizontal tangent exists are:

(0,2)

([tex]\pi[/tex],6)

([tex]-\pi[/tex],6)

The graph is attached below.

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Answer:

Step-by-step explanation:

4.

first, you broke the 2 eggs, and then cooked the eggs. after cooking them, you ate the two eggs that you cracked and cooked.

An equation of the circle that satisfies the given condition is (x+3))^2 + (y - 2)^2 = 73

The formula for finding the equation of a circle is expressed as:

(x-a)^2 + (y - b)^2 = r^2

Determine the value of r^2 using the distance between two points

r^2 = (-6-2)^2 + (-6+3)^2
r^2 = 64 + 9

r^2 = 73

Given the centre (a, b) as (-3, 2), the equatio of the circle will be;

(x-(-3))^2 + (y - 2)^2 = 73

(x+3))^2 + (y - 2)^2 = 73

Hence the equation of the circle is (x+3))^2 + (y - 2)^2 = 73

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A. Obtuse Triangle

B. Acute Triangle

C. Right Triangle

D. Right Triangle

What is meant by an obtuse triangle?

Obtuse-angled triangles or obtuse triangles are triangles with any one of its angles being an obtuse angle or greater than 90°. Only 180° is equal to the internal angles of an acute triangle.

Given triangles are A. 15,16,17. B 20,18,7. C 17,144,145. D 24,32,40.

If the sum of squares of least two sides is greater than the square of the largest side then it is an obtuse triangle.

If the sum of squares of least two sides is less than the square of the largest side then it is an acute triangle.

If the sum of squares of least two sides is equal to the square of the largest side then it is a right triangle.

A. side lengths are 15,16,17

[tex]15^{2}+16^{2} =481\\17^{2} =289\\481 > 289[/tex]

Therefore this triangle is an obtuse triangle.

B. side lengths are 7,18,20

[tex]7^{2} +18^{2} =373\\20^{2}=400 \\373 < 400[/tex]

Therefore this triangle is an acute triangle.

C. side lengths are  17,144,145

[tex]17^{2} +144^{2} =21025\\145^{2}=21025 \\21025=21025[/tex]

Therefore this triangle is a right triangle.

D. side lengths are  24,32,40

[tex]24^{2} +32^{2} =1600\\40^{2}=1600 \\1600=1600[/tex]

Therefore this triangle is a right triangle.

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Answer:

Step-by-step explanation:

All it's saying is that the 12% of the people are 35 and the 82% of people who did not submitted data is 175 people

The calculated test statistic (2.08) is greater than the critical value (1.96), we reject the null hypothesis and conclude that there is evidence to suggest that the contest has increased participation in the box tops for education program.

To determine if the contest has increased participation in the box tops for the education program, we need to conduct a hypothesis test.

We will use a significance level of 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Null Hypothesis: The proportion of students submitting box tops for education is still 12% (or has decreased) after the contest.

Alternative Hypothesis: The proportion of students submitting box tops for education has increased after the contest.

To test this hypothesis, we will use a one-sample proportion test. We will use the sample proportion, p' = 35/210 = 0.1667, as an estimate of the population proportion, p. The test statistic is calculated as:

z = (p' - p) / √(p x (1-p)/n)

where n is the sample size.

Under the null hypothesis, the expected value of the test statistic is 0, and the standard deviation of the test statistic is sqrt(p*(1-p)/n).

Using p = 0.12 and n = 210, we have:

z = (0.1667 - 0.12) / √(0.12 x 0.88/210) ≈ 2.08

The critical value for a significance level of 0.05 and a two-tailed test is ±1.96.

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Answer:

3/50

Step-by-step explanation:

3 g, 5 r, 2 o

3 + 5 + 2 = 10

Orange = 2 jelly beans

Probability of selecting an orange jelly bean: 2/10 or 1/5

If you put the jelly bean back in, there is still 10 jelly beans.

Green = 3 jelly beans

Probability of selecting a green jelly bean: 3/10\

Multiply the probabilities:

1/5 x 3/10

= 3/50

Answer:

To find the value of b_n in an arithmetic sequence given by the recursive definition b_1 = 8 and b_n = b_{n-1} - 3, we can use the formula for the nth term in an arithmetic sequence:

b_n = b_1 + (n-1)d

where d is the common difference. In this case, d = -3.

So, we can plug in the values for b_1 and d to find b_n:

b_n = 8 + (n-1)(-3)

b_n = 8 - 3(n-1)

Now, to find the value of b_n for a specific n, we just need to substitute the value of n into the equation for b_n. For example, if we want to find b_14, we would substitute n = 14:

b_14 = 8 - 3(14-1)

b_14 = 8 - 3(13)

b_14 = 8 - 39

b_14 = -31

So, the value of b_14 is -31, and the answer is (1) 14.

Answer:

Step-by-step explanation:

This is a standard quadratic equation in the form ax^2 + bx + c = 0, where a = 1, b = -5 and c = 6. To solve for x, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where ± represents the positive and negative square root, and the expression under the square root is called the discriminant (b^2 - 4ac).

So, substituting the values for a, b, and c, we have:

x = (-(-5) ± √((-5)^2 - 4 * 1 * 6)) / 2 * 1

x = (5 ± √(25 - 24)) / 2

x = (5 ± √1) / 2

Since the square root of 1 is 1, the two solutions are:

x = (5 + 1) / 2 = 3

x = (5 - 1) / 2 = 2

So, the solutions to the equation x^2 - 5x + 6 = 0 are x = 2 and x = 3.

Velocity of rock when it hits the ground is -22.9955152 ft/s

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time

Its position function is s(t) = –25t² + 1.86t

When it reaches back ground s(t) = 25 m/s

Substituting

               s(t) = –25t² + 1.86t = 25

Using the quadratic formula (-b±√b²-4ac)/2a

(-1.86 ±√1.86-4*25*-25)2*25

(-1.86 ±√1.7298+625)50

(-1.86 ±√626.7298)/50

(-1.86÷25)50

(-1.86+25)50 or( -1.86 -25)50

48.14/50 = 0.9628

This figure is taken because its positive

Time = 0.9628 seconds

Now we need to find velocity when it reaches ground, that is velocity after 0.9628 seconds.

Differentiating s(t) equation

   Substituting t = 0.9628 seconds

               v(t) = –25(0.9628)² + 1.86(0.9628)

v(t) = -23.174596 + 0.1790808

Velocity of rock when it hits the ground is -22.9955152 ft/s

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Answer:

There are approximately 38 cows in the herd.

Step-by-step explanation:

In this problem, we are asked to find the number of cows in a herd, given that 16% of the cows have already given birth to calves and 32 have not yet done so.

Assuming there are no other types of cows in the herd, we can determine that the 32 cows that have not had calves make up 84% of the herd, since they are what is left over when 16% is subtracted from 100% (the whole herd).

[tex]100\%-16\% = 84\%[/tex]

We can now create a equation that shows that 84% of the herd is 32 cows, representing the total number of cows in the herd as x.

[tex]32 \text{ cows} = 84\% \cdot x[/tex]

Finally, to solve for the number of cows in the herd, we can multiply both sides by 100/84.

[tex]\dfrac{100}{84}(32 \text{ cows}) = (84\% \cdot x)\dfrac{100}{84}[/tex]

[tex]x \approx 38 \text{ cows}[/tex]

So, there are approximately 38 cows in the herd.

Part A: We are 99% confident that the mean age of all instructors in College A is between 42.79128 and 51.2088 years old.

Part B: We are 99% confident that the mean age of all instructors in College A is College C by between 37.36368 and 54.63632 years old.

Part C: We are 99% confident that the mean age of all instructors in College B is College C by between 46.24672 and 57.75328 years old.

In this question, they are asking to calculate the 99% confidence intervals for the mean age of instructors in three different colleges (A, B, and C). They want to compare the mean age of instructors in College A to College B, College A to College C, and College B to College C. The numeric answers should be rounded to 5 decimal places.

To calculate these confidence intervals, you need to find the sample mean and standard deviation of the data for each college. Then, you can use the formula for a two-sample t-test to calculate the confidence intervals. The formula is (sample mean A - sample mean B) ± t-critical value * (standard deviation of A/√nA + standard deviation of B/√nB), where nA and nB are the sample sizes for Colleges A and B, respectively.

Part A: We are 99% confident that the mean age of all instructors in College A is College B by between 20.81733 and 23.72867.

To calculate the 99% confidence interval, we must first calculate the mean and standard deviation of the sample data. The mean age of all instructors in College A is 22.273 and the standard deviation is 1.936.

Next, we must use the t-distribution to calculate the 99% confidence interval. The critical value is 2.228. The confidence interval is calculated as follows:

Lower Bound = 22.273 - (2.228 x 1.936) = 20.81733

Upper Bound = 22.273 + (2.228 x 1.936) = 23.72867

Therefore, we are 99% confident that the mean age of all instructors in College A is College B by between 20.81733 and 23.72867.

Part B: We are 99% confident that the mean age of all instructors in College A is College C by between 17.73173 and 25.71367.

To calculate the 99% confidence interval, we must first calculate the mean and standard deviation

Part C: We are 99% confident that the mean age of all instructors in College B is College C by between 46.24672 and 57.75328 years old.

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Answer:

[tex]\textsf{C.} \quad \sin x[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}[/tex]

Rewrite the numerator and denominator of the given rational expression using the following trigonometric identities:

[tex]\boxed{\boxed{\begin{array}{c}\underline{\sf Trigonometric\;Identities}\\\\\boxed{\sec^2 x=\dfrac{1}{\cos^2x}} \qquad \boxed{\csc^2 x=\dfrac{1}{\sin^2 x}}\qquad \boxed{\csc x=\dfrac{1}{\sin x}}\\\\\end{array}}}[/tex]

Therefore:

[tex]=\dfrac{\dfrac{1}{\cos^2x} \cdot \dfrac{1}{\sin x}}{\dfrac{1}{\cos^2x}+\dfrac{1}{\sin^2x}}[/tex]

Multiply the fractions in the numerator, and make the denominators of the fractions in the denominator the same:

[tex]=\dfrac{\dfrac{1}{\sin x\cos^2x}}{\dfrac{\sin^2x}{\sin^2x\cos^2x}+\dfrac{\cos^2x}{\sin^2x\cos^2x}}[/tex]

[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}\right)}[/tex]

[tex]\textsf{Apply the trigonometric identity}\;\;\boxed{\sin^2x + \cos^2 x = 1}:[/tex]

[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{1}{\sin^2x\cos^2x}\right)}[/tex]

[tex]\textsf{Apply\:the\:fraction\:rule}\;\;\boxed{\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{ad}{bc}}:[/tex]

[tex]=\dfrac{\sin^2x\cos^2x}{\sin x\cos^2x}[/tex]

Cancel the common factor cos²x:

[tex]=\dfrac{\sin^2x}{\sin x}[/tex]

Simplify:

[tex]= \sin x[/tex]

Therefore:

[tex]\large\textsf{$\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}=$}\;\boxed{\boxed{\sin x}}[/tex]

The equation of inverse of f is f-1(x) = √(x/2)

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x^2

Express as an equation

so, we have the following representation

y = 2x^2

Swap x and y

so, we have the following representation

x = 2y^2

Divide by 2

y^2 = x/2

Take the square roots

y = √(x/2)

Hence, the inverse is f-1(x) = √(x/2)

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26 is the value of a from the given figure.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We need to find the value of a from the figure.

∠D is 46 degrees.

AD is 28, AT is 37

CosD=Adjacent side/ Hypotenuse

Cos46=a/37

0.695=a/37

a=0.697×37

a=26

Hence, the value of a is 26

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Answer:

Step-by-step explanation:

38.06

Solving a quadratic equation, we will see that the object will hit the ground after 5.9 seconds.

The equation for the vertical movement of an object will be:

H(t) = -16*t^2 + v0*t + h0

Where v0 is the initial velicity, in this case 85ft/s, and h0 is the initial height,  55ft.

Then the height equation is:

H(t) = -16*t^2 + 85*t + 55

The object will hit the ground when the height is equal to zero, then we need to solve:

-16*t^2 + 85*t + 55 = 0

Using the quadratic formula we will get:

[tex]t = \frac{-85 \pm \sqrt{(85)^2 - 4*(-16)*55} }{2*-16} \\\\t = \frac{-85 \pm 103.7 }{-32}[/tex]

We only care for the positive solution, which is:

t = (-85 - 103.7)/-32 = 5.9

So it will take 5.9 seconds for the object to hit the ground.

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Answer:

see image

Step-by-step explanation:

First of all, the problem might be that we need to set this up differently than how it is written.

"Subtract THIS from THAT" means that you have to put the second thing first and minus the first thing:

THAT - THIS



Next, the minus in the middle has to go to all three of the terms in the second part. This is going to change the sign of all three parts. See image.

Last, hopefully fraction addition with positive and negative signs isn't too terribly confusing.

1/5 - 2/5 is -1/5.

And -1/4 - 1/4 is -2/4, which is -1/2.

see image.

Make sure the y^2 and the y look like they are next to the whole fraction and are not on the bottom of the fraction.

Answer:

To perform a dilation with a scale factor of 2 centered at the origin, we need to multiply each coordinate of the original points A and B by the scale factor of 2.

The coordinates of point A after dilation are:

A′(2 * 3, 2 * 7) = A′(6, 14)

Similarly, the coordinates of point B after dilation are:

B′(2 * 4, 2 * 9) = B′(8, 18)

So, the endpoints of the dilated line segment are A′(6, 14) and B′(8, 18).

The statement that describes the point of intersection on the graph is  Calvin will plant lily bulbs and iris bulbs. Option C

The point of intersection on the graph represents the values of x and y where both conditions are satisfied.

In this case, the point of intersection represents the number of lily bulbs (x) and the number of iris bulbs (y) that Calvin will plant such that the number of iris bulbs is equal to the number of lily bulbs.

So, the correct statement that describes the point of intersection on the graph is "Calvin will plant lily bulbs and iris bulbs".

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Answer: X= -66

Step-by-step explanation:

If m angle UYV=56

Then WYX= -x-10=56

then X=-66

Using sine law and cosine law, s is 13.6 units and T is 37.7 degrees while U is 59.3 degrees

The Law of Cosines, also known as the Cosine Formula, is a fundamental mathematical relationship between the sides and angles of a triangle. It states that the dot product of two sides of a triangle is equal to the product of the third side and the cosine of the angle between the two sides.

The general form of the Law of Cosines is:

C^2 = A^2 + B^2 - 2ABcos(C)

where C is the angle between sides A and B, and A, B, and C are the lengths of the sides of the triangle. The formula can be rearranged to solve for any one of the sides or angles given the other two.

In this problem, we can easily solve for s.

s² = 8² + 12² - 2(8)(12)cos83

s² = 184.601

s = √184.601

s = 13.6 units

The value of angle T is calculated using sine law;

13.6 / sin 83 = 8 / sin T

sin T = 8(sin 83) / 13.6

sin T = 0.58385

T = sin⁻¹(0.58385)

T = 37.7°

Using sum of angle in a triangle;

T + S + U = 180°

83 + 37.7 + U = 180

U = 180 - 120.7

U = 59.3°

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thank you and have a good day :)

Answer:

20

Step-by-step explanation:

1/5(3+2+5)^2

3+2+5 = 10

10^2 = 100

100/5 = 20

The height of each elevator at this time is, -2.5 m, negative means below ground level.

The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.

Distance = Time × Speed

To find how long it would take each elevator to reach ground level, we can set h = 0 in the given expressions for their travel times:

Elevator A:  

= 0.8h + 16

= 0.8(0) + 16

= 16 seconds

Elevator B:  

= -0.8h + 12

= -0.8(0) + 12
= 12 seconds

Therefore, elevator A would take 16 seconds and elevator B would take 12 seconds to reach ground level at this time.

To find at what height the elevators pass each other, we can set their travel times equal to each other and solve for h:

0.8h + 16 = -0.8h + 12

1.6h = -4

h = -2.5

Now, we can substitute value of h in the expression

Elevator A:

= 0.8(-2.5) + 16

= 14 seconds

Elevator B:

= -0.8(-2.5) + 12

= 14 seconds

Therefore, the elevators would pass each other 14 seconds after they both start moving towards each other.

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The complete question:

Elevators A building has two elevators that both go above and below ground.

At a certain time of day, the travel time it takes elevator A to reach height h in meters is 0.8h+16 seconds.

The travel time it takes elevator B to reach height h in meters is -0.8h+12 seconds.

How long would it take each elevator to reach ground level at this time? If the two elevators travel toward one another, at what height do they pass each other? How long would it take?

133 days saw either rain or high winds.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Example: If an experiment has 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event will be as follows:

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

P(r) = 66 days

P(w) = 98 days

P(both) = 31 days

P(r or w) = P(r) + P(w) - P(both)

P(r or w) = 66 + 98 - 31

P(r or w) = 133 days

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Answer:

11/3

Step-by-step explanation:

-4(r-2/3)+4<-8

-4r+8/3+4<-8

8/3+4<-8+4r

8/3+4+8<4r

44/3<4r

44/12=r

11/3=r

WXYZ must be a square, all the sides must have a length of 5.

The vertices of the quadrilateral are:

W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3)

Distance can be calculated using the formula derived from Pythagoras theorem. In coordinate geometry, the distance formula is:

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

We have to prove that WXYZ is a square.

Using the distance formula :

[tex]WX = \sqrt{(-1-3)^2+(1-4)^2}\\ \\WX = \sqrt{16 + 9}\\ \\WX = \sqrt{25}\\ \\WX = 5[/tex]

Since WXYZ must be a square, all the sides must have a length of 5.

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The given question is incomplete, complete question is:

Select the correct answer from each drop-down menu.

Given: W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3) are the vertices of quadrilateral WXYZ.

Prove: WXYZ is a square.

Using the distance formula, I found that

…

A. all four sides have a length of 5

B. all four sides have different lengths

C. only 2 sides have the same length

D. all four sides have a length of 10

The area of the running track, given the parallel sections and the semicircle sections, is https://brainly.com/question/30584763

To find the area of the running track, you first need to find the area of the whole shape and then the area of just the inner section.

Area of whole shape :

= Area of both semicircles + Area of the rectangle

= ( π x 46. 41 ²) + ( 85 x ( 46. 41 x 2 ))

= 14, 659.06 m ²

Then, find the area of the inner section :

=  ( π x 36. 41 ²) + ( 85 x ( 36. 41 x 2 ))

= 10, 356. 45 m ²

The area of the running track is :

= 14, 659.06 - 10, 356. 45

= 4, 302. 61 m ²

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The probability of Rosh winning the tournament is 50%, which means the probability of one of the other three players winning is 50% divided by 3, or approximately 16.67% each. Therefore, the probability that Craig wins the tournament is 16.67%.

Answer:

4x + y = 2

Step-by-step explanation:

y + 2 = - 4(x - 1) ← distribute parenthesis by - 4

y + 2 = - 4x + 4 ( add 4x to both sides )

4x + y + 2 = 4 ( subtract 2 from both sides )

4x + y = 2 ← in standard form

Answer:

[tex]\boxed{\mathrm\bold {4\dfrac{43}{72}}}[/tex]

Step-by-step explanation:

Let the unknown fraction be x

We are given sum of the fractions = 5 3/8 and one of the fractions is 7/9

First convert 5 3/8 to an improper fraction for easier calculation

[tex]5 \dfrac{3}{8} = \dfrac{5\times 8 + 3}{8} = \dfrac{43}{8}[/tex]

Therefore we get:
[tex]\dfrac{7}{9} + x = 5\dfrac{3}{8}\\\\\dfrac{7}{9} + x = \dfrac{43}{8}\\\\[/tex]

Subtract  [tex]\dfrac{7}{9}[/tex]  on both sides to isolate x:

[tex]\dfrac{7}{9} - \dfrac{7}{9} + x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]

[tex]x = \dfrac{43}{8} - \dfrac{7}{9}[/tex]

To compute the right side