The shortest racecar track is 31,680 inches long. What is the length of the track in miles?

Answer:

tan(84)=x/50

Step-by-step explanation:

The equation that  help determine the maximum height of the rocket in feet is tan(84°) = \(\frac{h}{50}\)

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios formulas are given below,

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

sec θ = Hypotenuse/Base

cosec θ = Hypotenuse/Perpendicular

cot θ = Base/Perpendicular

According to the question

Rocket builder moved 50 feet away from the base before launching his model rocket straight up in to the air.

i.e Base of right angle triangle = 50

The rocket reached its maximum height when the angle of elevation from the observer was 84 degrees

i,.e angle of elevation from the observer was = 84°

angle between hypotenuse and base =  84°

Now,

Height of the rocket from the ground = Perpendicular = h

So,

By trigonometric ratios

tan θ = \(\frac{Perpendicular}{Base}\)

tan(84°) = \(\frac{h}{50}\)

Hence, the equation that  help determine the maximum height of the rocket in feet is tan(84°) = \(\frac{h}{50}\)

To know more about trigonometric ratios here:

https://brainly.com/question/1201366

#SPJ2

Answer:

1/3 is less than 1/2

Step-by-step explanation:

1/3 = .333

1/2 = .5

Answer:

Imaoo

1/3 is less than 1/2

Step-by-step explanation:

1/3 = .333

1/2 = .5

brainliest please? :)

Answer:

r = -1/5

Step-by-step explanation:

5(r - 10) = -51

Distribute

5r - 50 = -51

Add 50 to each side

5r-50+50 = -51+50

5r = -1

Divide each side by 5

5r/5 = -1/5

r = -1/5

Answer:

V=141.3

Step-by-step explanation:

V=π*r2*h or V=B.h

V=3.14*(3*3)*5

V=3.14*9*5

V=141.3

Let's call L the length of the rectangle and W the width of the rectangle

We know the length is 3 times its width:

L = 3W

The area of a rectangle is:

A=L*W

Substituting the condition above, we have:

A = (3W)*W

Operating:

We know the area is 147 yd^2, so we equate:

Solve for W:

Taking the square root on both sides:

The width is 7 yd. Now we can easily find the length:

L=3W=3*7=21 yd

Finally, we calculate the perimeter of the rectangle. Recall the perimeter is calculated with the formula:

P=2L+2W

Thus, using the known values:

P=2*21+2*7=42 + 14 = 56 yd

The perimeter of the rectangle is 56 yd

An infinite two-dimensional figure is represented by option B, a plane.

What are two-dimensional figures?

Two-dimensional figures are shapes with two dimensions: length and width.

They are commonly called flat shapes. When they are drawn on paper, they are two-dimensional shapes.

A two-dimensional figure is classified as a polygon if it has a closed shape with straight lines.

They may have any number of sides, such as a triangle, square, pentagon, or hexagon.

However, a plane is a flat surface that extends in all directions infinitely without ending. It is also called an infinite two-dimensional figure.A line is the shortest distance between two points, so it is not an infinite two-dimensional figure.

On the other hand, a segment is a line that has a beginning and an end, making it a finite one-dimensional figure.

A point is a location that has no size or shape, making it a zero-dimensional figure.

As a result, the only option that represents an infinite two-dimensional figure is a plane.

For more questions on two-dimensional figure

https://brainly.com/question/1211190

#SPJ8

The length of the unknown sides of the triangles are as follows:

CD = 10√2

AC = 10√2

BC =  10

AB = 10

Since, Triangle ACD

ΔACD is a right angle triangle.

Therefore, Pythagoras theorem can be used to find the sides of the triangle.

c² = a² + b²

where

c = hypotenuse side = AD = 20

a and b are the other 2 legs

lets use trigonometric ratio to find CD,

cos 45 = adjacent / hypotenuse

cos 45 = CD / 20

CD = 1 / √2 × 20

CD = 20 / √2 = 20√2 / 2 = 10√2

Hence,

20² - (10√2)² = AC²

400 - 100(2)  = AC²

AC² = 200

AC = √200 = 10√2

Triangle ABC

ΔABC is a right angle triangle too. Therefore,

AB² + BC² = AC²

Using trigonometric ratio,

cos 45 = BC / 10√2

BC = 10√2 × cos 45

BC = 10√2 × 1 / √2

BC = 10√2 / √2 =  10

Hence,

(10√2)² - 10² = AB²

200 - 100 = AB²

AB² = 100

AB = 10

Learn more on triangles here:

brainly.com/question/24304623

#SPJ1

Using the line of best fit, it is found that the prediction of the forearm length of a man whose height is of 72 in is of 19.417 in.

It states that the predicted forearm length of a person of height x is given by:

y = -0.2967 + 0.2738x.

In this problem, the height is of x = 72 in, hence:

y = -0.2967 + 0.2738(72) = 19.417 in.

More can be learned about line of best fit at https://brainly.com/question/17261411

#SPJ1

Answer:

The Median is 75

Step-by-step explanation:

median is the middle number in a set of given numbers

arranging in order will be

30,64,70,80,90,110

the middle numbers are 70 and 80

Median=80+70/2

=150/2

Median=75

Answer:

The answer is 1.99

Step-by-step explanation:

23.88 divided by 12 =1.99 and There are 12 quarts in 3 gallons.Have a nice day❤

a) There are 720 different seating arrangements if there is no restriction on the order.

b) There are 48 different seating arrangements if married couples sit together.

c) The union of sets A and B has 8 elements.

a) If there is no restriction on the order, the total number of seating arrangements can be calculated using the factorial formula. In this case, there are 6 people (3 couples) to be seated, so the number of arrangements is 6! = 720.

b) If married couples sit together, we can consider each couple as a single entity. So, we have 3 entities to be seated. The number of arrangements for these entities is 3!, which is 6. Within each couple, there are 2 possible ways to arrange the individuals. Therefore, the total number of seating arrangements is 6 * 2 * 2 * 2 = 48.

c) If there are 5 elements in set A and 3 elements in set B, the union of the two sets will have elements from both sets without any duplication. The total number of elements in the union of two disjoint sets can be calculated by adding the number of elements in each set. Therefore, the number of elements in the union of sets A and B is 5 + 3 = 8.

You can learn more about seating arrangements at

https://brainly.com/question/27935318

#SPJ11

Answer:

Step-by-step explanation:

to the rieft

Answer:

x=1 +or- √(1)-(-8)/-2

Step-by-step explanation:

-2=-x+x^2-4

-2+4= x^2-x

2=x^2-x

x^2-x-2=0

Quadratic formula

x=-b +or -√b^2-4ac/2a

from the equation

a=1

b=-1

c=-2

Insert the variables into the quadratic formula

We have

x=-(-1) +or- √(-1)^2 - 4*(1)*(-2)/-2*(1)

x=1 +or- √(1)-(-8)/-2

=1 +or- √1+8/2

=1 +or-√9/2

=1 +or- 3/2

=1+3/2 or 1-3/2

=4/2 or -2/2

x=2 or -1

The probability of drawing a seven and then a four when randomly drawing two cards without replacement is 0.0045 or approximately 0.45%.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement can be calculated using the following steps:

First, we need to determine the total number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement. This can be found using the combination formula:

C(52,2) = 52! / (2! * (52-2)!) = 1,326

Next, we need to determine the number of favorable outcomes where we draw a seven and then a four.

There are four sevens and four fours in a deck of 52 cards, so the probability of drawing a seven on the first draw is 4/52. Since we are not replacing the card, there are now 51 cards left in the deck, and three of them are fours. Therefore, the probability of drawing a four on the second draw is 3/51.

The probability of drawing a seven and then a four is the product of the probabilities of drawing a seven on the first draw and a four on the second draw:

P(seven and then four) = (4/52) * (3/51) = 0.0045 or approximately 0.45%.

Therefore, the probability of drawing a seven and then a four when without replacement is 0.0045 or approximately 0.45%.

To learn more about probability, click here:

https://brainly.com/question/30034780

#SPJ11

Answer:

Step-by-step explanation:

The x difference:

8 - 1 = 7

The y difference:

-4 - -7 = 3

Distance:

7² + 3² = 58

√58 ≅ 7.62

Please Thank and Mark as Brainliest!

9514 1404 393

Answer:

  b)  800 cm²

Step-by-step explanation:

The surface area of the figure is the sum of the areas of each of the 6 faces. Three of the faces are shown. Because the figure is presumed to be a cuboid, the three faces not shown are identical in area to those that are.

Each face is a rectangle. As such, its area is the product of its dimension (length and width).

The front face has dimensions 10 in by 10 in. Its area is (10 in)·(10 in) = 100 in².

The top face has dimensions 10 in by 15 in. Its area is (10 in)·(15 in) = 150 in².

The right-side face has the same dimensions as the top face. Its area is also 150 in².

The sum of the areas of the three faces you can see is ...

  100 in² +150 in² + 150 in² = 400 in²

The three faces you cannot see have the same area, so the total surface area of this figure is ...

  SA = 2(400 in²) = 800 in² . . . . matches choice B

___

The formula for this can be written a couple of different ways. One that matches what we did above is ...

  SA = 2(LW +WH +LH) . . . . where L, W, H are the length, width, and height

The formula is symmetrical with respect to L, W, and H, so it does not matter which number you assign to which letter. The only thing that matters is that the same letter always represents the same number.

The above formula requires 4 multiplications and 2 additions. It can be reduced to one that requires 3 multiplications and 2 additions by combining a couple of the terms. I like this formula because it is slightly less work.

  SA = 2(LW +H(L +W))

Step-by-step explanation:

i=prt

t=i÷pr

..

..

..

..

..

..

The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

To learn more about the total cost click here:

https://brainly.com/question/2433744

#SPJ1

The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

The negation of the statement "for every real number x, x is a prime number or x can be written as the sum of two prime numbers" is "there exists a real number x such that x is not a prime number and x cannot be written as the sum of two prime numbers."

Prime numbers are a type of integer that can only be divided evenly by 1 and itself. They play an important role in number theory, as they are the building blocks of the natural numbers. Prime numbers have a variety of interesting properties, such as being infinite in number and having no common factors with other numbers except 1. Understanding prime numbers is essential to many areas of mathematics, including cryptography, algorithms, and geometry.

For more information on prime numbers see:

https://brainly.com/question/30358834

#SPJ11

Answer:

Step-by-step explanation:

Jenny bought 2 pairs of dress pants and 3 pairs of jeans.

Answer:

its 1

Step-by-step explanation:

8 divided by 8 is 1

Answer:

Yes, 8 divided by 8 = 1

Answer:

volume of the prism=(1/2×(6+12)×4)×10

=36×10

=360 cm³

Answer: 5

Step-by-step explanation:

these two triangles are a dilation of each other. triangle QRS is a dilation of triangle ABC times two

To divide the test scores into five equal-width intervals, we first need to determine the range of the scores. The range is calculated by subtracting the smallest value from the largest value.

Given the scores: 45, 95, 69, 75, 90, 78, 50, 88, 89, 80, 77, 93, 30, 94, 99

The smallest value is 30 and the largest value is 99, so the range is 99 - 30 = 69.

To create five equal-width intervals, we divide the range by 5: 69 / 5 = 13.8 (approximately).

We can start by setting the lower bound of the first interval as the smallest value, which is 30. Then, we add the width (13.8) to get the upper bound of the first interval: 30 + 13.8 = 43.8 (approximately). The second interval would be from 43.8 to 57.6, the third from 57.6 to 71.4, the fourth from 71.4 to 85.2, and the fifth from 85.2 to 99.

Using these intervals, we can identify the smallest and largest values for each interval:

Interval 1: Smallest value = 30, Largest value = 43.8 (approximately)

Interval 2: Smallest value = 45, Largest value = 57.6 (approximately)

Interval 3: Smallest value = 69, Largest value = 71.4 (approximately)

Interval 4: Smallest value = 75, Largest value = 85.2 (approximately)

Interval 5: Smallest value = 88, Largest value = 99

Looking at the given statements, we can determine the true statement:

Statement a. "50 is the largest value in its interval" is false because 50 is not the largest value in any of the intervals.

Statement b. "77 is the largest value in its interval" is true because 77 is the largest value in Interval 4 (75 to 85.2).

Statement c. "93 is the smallest value in its interval" is false because 93 is not the smallest value in any of the intervals.

Statement d. "89 is the smallest value in its interval" is false because 89 is not the smallest value in any of the intervals.

Therefore, the true statement is b. "77 is the largest value in its interval."

Learn more about stastistics here:

https://brainly.com/question/30915447

#SPJ11

With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.

Given that:

Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.

We need to know how many servings of 3/4 cup can be obtained from 13 cups.

now we need to divide 13 by 3/4

=13 ÷ 3/4  

= 13 × 4/3

= 52/3

= 17\(\frac{1}{3}\)

With one third of a serving remaining, there are 17 servings total.

To learn more about divide:

https://brainly.com/question/15381501

#SPJ4

The expected number of cards Henry needs to turn up to get the third ace is 31.8

Given: We need to find what is the expected number of cards Harry needs to turn up to get the third ace and Harry has a standard deck of 52 cards.

Now, we know there are 4 ace cards. Let’s consider the ace cards and non-ace cards separately.

There are (52-4) = 48 non-ace cards.

Let us consider that the non-ace cards will be cut by an ace card.

So, there are 5 possible ways in which the ace cards can cut the division, provided

We are having an equal number of non-ace cards in between the appearance of each ace card which means the setup is symmetric among the non-ace cards.

So let us name the spaces between ace cards as s1, s2, s3, s4, and s5.

Therefore, the position of the third ace card is equal to s1 + s2 + s3 + 3.

The expected value of this position is E[s1 + s2 + s3 + 3].

By linearity of expectation, E[s1 + s2 + s3 + s4] is E[s1] + E[s2] + E[s3] + 3.

As the setup is symmetric between the five places, E[s1] = E[s2] = E[s3] = E[s4] = E[s5]

And since E[s1 + s2 + s3 + s4 + s5] = E[s1] + E[s2] + E[s3] + E[s4] + E[s5] = 48

Therefore, E[s1] = E[s2] = E[s3] = E[s4] = E[s5] = 48 / 5

The expected value of position is E[s1] + E[s2] + E[s3] + 3

   = 48 / 5 + 48 / 5 + 48 / 5 + 3

   = 3 * 48 / 5 + 3

   = 31.8

Hence, the expected number of cards Henry needs to turn up to get the third ace is 31.8

Know more about “statistical probability” here: https://brainly.com/question/15006619

#SPJ4

If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.

We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

From the given information, we have:

cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)

tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5

Now, we can use the definitions of sine and cosine to find tan A:

tan A = sin A / cos A = (7/25)/(24/25) = 7/24

Substituting the values we have found into the formula for tan(A - B), we get:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]

= (-13/72)/(25/72)

= -13/25

Therefore, tan(A - B) = -13/25.

Learn more about tan(A - B) here:https://brainly.com/question/24305408

#SPJ1

Answer:

Angle(APR) = 43

x = 21.5

Step-by-step explanation:

The given angles are complementary :

So APR + RPW = 90

APR = 43

2x = 43

x = 21.5

Answer:Hope this helps!

APR=43 degrees

x=21.5

Step-by-step explanation:

To find the surface area of the triangular prism, we need to find the area of each face and add them up.

The triangular face has a base of 32 feet and a height of 30 feet, so its area is:

(1/2) * base * height = (1/2) * 32 * 30 = 480 square feet.

There are two identical rectangular faces, each with a length of 37 feet and a width equal to the height of the triangular face, which is 30 feet. So, the area of each rectangular face is:

length * width = 37 * 30 = 1110 square feet.

Therefore, the total surface area of the triangular prism is:

2 * area of rectangular face + area of triangular face

= 2 * 1110 + 480

= 2700 square feet.

So, the surface area of the triangular prism is 2700 square feet.

To learn more about area click here: brainly.com/question/30307509

#SPJ11