Step-by-step explanation:
The unit circle is a circle in the form of
[tex] {x}^{2} + {y}^{2} = 1[/tex]
while x = cos t
y= sin t
, where t is an angle
So we plug in -1/7, for x to find y
[tex]( \frac{ - 1}{7} ) {}^{2} + {y}^{2} = 1[/tex]
[tex] {y}^{2} = \frac{49}{49} - \frac{1}{49} [/tex]
[tex]y = \frac{4 \sqrt{3} }{7} [/tex]
If the point is in the 2nd quadrant, your value of y is positive
If it in the third quadrant, the y value is negative
A survey of high schools offering honors classes to ninth graders reveals that 38% of the high schools offer no honors classes, 12% offer one honors class, 25% offer two honors classes, 20% offer three honors classes, and 5% offer four honors classes.
A high school is selected at random. What is the probability that it offers an even number of honors classes?
0.62
0.30
0.68
0.32
Using the discrete distribution, it is found that the probability that it offers an even number of honors classes is of 0.68.
What is the discrete probability distribution?The distribution for the number of honors classes the school offers is given by:
P(X = 0) = 0.38P(X = 1) = 0.12.P(X = 2) = 0.25.P(X = 3) = 0.2.P(X = 4) = 0.05.Hence the probability of an even number is given by:
P(even) = P(X = 0) + P(X = 2) + P(X = 4) = 0.38 + 0.25 + 0.05 = 0.68.
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Order the numbers from greatest to least?
2/9, 21%, 5/20, 8%
Answer:
5/20, 2/9, 21%, 8%
Step-by-step explanation:
2/9 = 0.22
21% = 0.21
5/20 = 0.25
8% = 0.08
0.25>0.22>0.21>0.08
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Find the area of a sector of the circle below. Express in terms of pie and as a decimal.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=18\\ \theta =40 \end{cases}\implies \begin{array}{llll} A=\cfrac{(40)\pi (18)^2}{360}\implies A=36\pi \\\\\\ A\approx 113.097 ~m^2 \end{array}[/tex]
Answer:
36π (m²) or ≈ 113.14 m²
Step-by-step explanation:
[tex]A_{circle}[/tex] = [tex]\pi r^{2}[/tex]
[tex]A_{sector}[/tex] = x
[tex]\frac{360^o}{40^o}[/tex] = [tex]\frac{18^2 \pi }{x}[/tex]
9 = [tex]\frac{18^2 \pi }{x}[/tex]
x = 36π
or
x ≈ 36 × [tex]\frac{22}{7}[/tex] ≈ 113.14 m ²
An art museum has 20 large cylindrical columns in its lobby. Each column has a height of 22 feet from
the floor to the ceiling and a diameter of 2.5 feet. If a gallon of paint covers 350 square feet, how
many gallons of paint must be purchased to paint the lateral surface area of all of the columns?
A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The amount of paint needed to paint 20 pillars is 9.874 gallons.
What is a cylinder?A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.
The curved surface area of a single-cylinder with a diameter of 2.5 feet and a height of 22 feet will be,
Curved surface area = πDh = π × 2.5 × 22 = 172.7875 ft²
The total area of 20 pillar = 20 × 172.7875 ft² = 3,455.75191 ft²
Since a gallon of paint can cover only 350 ft², therefore, the amount of paint that will be needed to paint 3,455.75191 ft² can be written as,
[tex]\text{Amount of paint needed} = \dfrac{3,455.75191\rm\ ft^2}{350\rm\ ft^2} = 9.874\rm\ gallons[/tex]
Hence, the amount of paint needed to paint 20 pillars is 9.874 gallons.
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Label the scatterplot correctly
A pot has3/10pound of soil. Rex adds some soil. Now it
has 9/10pound. How many pounds of soil did Rex add
What is the value of the expression (3/4)³
81/256
27/64
9/12
27/4
Answer:
9/12
Step-by-step explanation:
Answer:
The answer is
9 over 12
9/12
Write an equation for the translation of y =5/x
that has the asymptotes x= -7 and y= 7
The equation for the translation of y = 5/x is y = 5/(x+7) + 7 if that has the asymptotes x= -7 and y= 7
What is hyperbola?
It is a curve in two-dimensional geometry having two parts, they both are symmetric. In other words, It can be defined as the number of points in the two-dimensional geometry that have a constant difference from that point to two fixed points in the plane.
We have:
[tex]\rm y = \dfrac{5}{x}[/tex]
Vertical asymptotes x= -7 and
Horizontal asymptotes y= 7
After translation:
[tex]\rm y = \dfrac{5}{x+7}+7[/tex]
Thus, the equation for the translation of y = 5/x is y = 5/(x+7) + 7 if that has the asymptotes x= -7 and y= 7
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Which expression is equivalent to 18x+8y?
Answer
2 (9 x + 4 y)
Hope this helps :)
Which sport is required to have both male and female competitors?
A. Water polo
B. Swimming
C. Hockey
D. Mixed doubles tennis
Yesterday, Brad's Snack Shack went through 1 1/2 bottles of ketchup. If they used 1/2 as much mustard as ketchup, how many bottles of mustard did they go through? Write your answer as a fraction or as a whole or mixed number. bottles Submit
1 1/2 = 1.5
1/2 as much as 1.5 is .75 or 3/4 of a bottle of mustard.
Brad's Snack Shack used 3/4 of a bottle of mustard yesterday.
Hope this helps <3
how to find 2 square root of 3
Answer:
sqrt12
Step-by-step explanation:
being given any problem like this, let's use the form y√x, y representint 2, and x is 3, but it's generalized
in order to find the unsimplified √ we would do 2(yx). Which in this case is 12
After four years of higher education, Danielle just graduated with a Bachelor's degree in Legal Studies from Georgetown where the annual cost of tuition was $26,000. She paid for college by earning $12,000 annually through the work study program and receiving an annual scholarship. She covered the remainder of the costs by taking out $0 in student loans. If she didn't fund her education with savings or grant money, what was the amount of Danielle's annual academic scholarship?
The amount of Danielle's annual scholarship is $14,000.
What is the value of the annual scholarship?
Subtraction is an arithmetic operation that is used to determine the difference between two or more numbers. The sign used to represent subtraction is -.
annual scholarship = annual tuition - annual earning
$26,000 - $12,000 = $14,000
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Which mixed number is equivalent to
19/3
Answer:
6 1/3
Step-by-step explanation:
You just have to see how many times it goes into it
Has SETI detected any radio signals from extra-terrestrials?
A. No, they do not have proof radio signals can travel through space yet.
B. Yes, coming from the Andromeda galaxy.
C. Not yet, only interference signals from Jupiter.
D. Yes, coming from a nearby star, Alpha Centauri.
Answer:
C
Step-by-step explanation:
There are all types of radio signals traveling around us, just not the extra-terrestrial type!
The figure below shows a rectangular lawn. 23ft 14ft (a) Use the calculator to find the perimeter and area of the lawn. Make sure to include the correct units. Perimeter: Area: (b) The lawn will be mowed. Which measure would be used in finding how long it will take? Perimeter Area (c) The lawn will be surrounded by a rope. Which measure would be used in finding how much rope to buy? Perimeter Area
The area and perimeter of the lawn will be 322 square feet and 74 feet. If the lawn will be mowed. Then the area will be used. If the lawn will be surrounded by a rope. Then the perimeter will be used.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
The figure below shows a rectangular lawn.
Then the area of the rectangle will be
Area = 23 × 14
Area = 322 square feet
Then the perimeter of the rectangle will be
Perimeter = 2 (23 + 14)
Perimeter = 2 × 37
Perimeter = 74 feet
If the lawn will be mowed. Then the area will be used.
If the lawn will be surrounded by a rope. Then the perimeter will be used.
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The owner of a local movie theater keeps track of the number of tickets sold in each purchase. The owner determines the probabilities based on these records. Let X represent the number of tickets bought in one purchase. The distribution for X is given in the table. A 2-column table with 5 rows. Column 1 is labeled number of tickets with entries 1, 2, 3, 4, 5. Column 2 is labeled Probability with entries 0.17, 0.55, 0.20, 0.06, 0.02. What is the probability that a randomly selected purchase has less than two tickets? 0.17 0.55 0.72 0.83
Answer:
0.17
Step-by-step explanation:
The probability for purchasing 2 tickets at a time can be given as 0.17. The correct option is (A).
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Suppose X be the event to represent the number of tickets in purchase.
Then, as per the question distribution table can be formed as follows,
The number of tickets (X) P(X) Probability
1 0.17
2 0.55
3 0.20
4 0.06
5 0.02
Thus, the probability of selecting less than two tickets can be obtained as,
P(X < 2) = P(X = 1)
⇒ 0.17
Hence, the probability for a purchase to have less than two tickets is given as 0.17.
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Arun is caring for many yellow-spotted salamanders. He weighs each and
then counts the number of yellow spots on its back. Which trend line best fita
the data?
Answer:
The answer is B.
Step-by-step explanation:
Looking at the option, a trend line best fits the data within the plot. Seeing Answer B has the line that goes through the plot.
Five marbles labeled 1 through 5 are placed in a bag. A marble is randomly pulled and the number is recorded before the marble is
placed back in the bag. The results of the simulation of 20 marble pulls are shown in a dot plot.
Which dot plot models an unfair data-generating process?
Using the dot plot concept, it is found that the left plot on the bottom row shows an unfair data-generating process.
What does a dot plot show?The dot plot shows the number of times each measure appears in the data-set.
In this problem, each trial has 5 possible outcomes and there are 20 trials, hence each number should appear 20/5 = 4 times.
On the left plot of the bottom row, outcomes 1 and 5 appear 7 times, while outcomes 2, 3 and 4 appear 2 times, which are the furthest values from 5, hence it is an unfair data-generating process.
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Answer:
Step-by-step explanation:
How is a change in the circumference of a circle related to the diameter of a circle
Answer:
let's use c as circumference, d for diameter
lets say c increases, d is related to c, d will also increase
if c decreases, d will too.
Let's put in this way.
Pretend you're at a store,
The more you spend, the more points you get in their loyalty program
C is going to be the amount you spend
D will be how many points you get
Spend more, more points
spend less, less points
P.S
C is the independent variable, D is the dependent variable. (I think that's the right way, if not ignore the postscript aka P.S)
A small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream. Find the rate of the current. (Hint: 8+x= rate going downstream and 8−x= rate going upstream.)(Round your answer to the nearest tenth.)
The rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
Let's suppose the rate of the current = r
The time it takes to go downstream + 4 hours = time to go upstream
As we know the:
[tex]\rm Time = \dfrac{Distance}{ Rate }[/tex]
Now,
[tex]\rm \dfrac{44}{ (8 + r)} + 3 = \dfrac{44}{ (8 - r)}[/tex]
After solving:
[tex]\rm \dfrac{44}{ (8 - r)}-\dfrac{44}{ (8 + r)} =3[/tex]
After cross multiplication
44(8+r) - 44(8-r) = 3(8+r)(8-r)
88r = 3(64 - r²)
3r² + 88r - 192 = 0
After solving the above quadratic equation, we get:
r = 2.03 or
r=−31.37 (reject as it is negative)
So, the r =2.03 mph
Thus, the rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.
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16) Graph g(x) = x + 3 + 2
13. What is the distance between the y-intercept of the function f(x) = 2(3)* and the y-intercept of the function g(x) represented by the table below?
Answer:
the answer is letter C.
I hope this can help you!
(21*3+8)-17+(85-12+9-45)
Answer:
91
Step-by-step explanation:
(21)(3)+8−17+85−12+9−45
=63+8−17+85−12+9−45
=71−17+85−12+9−45
=54+85−12+9−45
=54+73+9−45
=54+82−45
=54+37
=91
Factor the GCF 7x^2+21x-35
Answer:
(7)(x² + 3x - 5)
Step-by-step explanation:
To Find the GCF : Prime factorize each term
7x² = 7 × x²21x = 7 × 3 × x-35 = 7 x -5As seen above, we can conclude the GCF is 7.
Therefore, by factoring using the GCF :
(7)(x² + 3x - 5)Probability Math Question
Help would be appreciated:))
Answer:
Hi, your answer here would be based on reading this graph. For question a, there are a total of 12 people who like vanilla with sprinkles, which means that it is 12 out of 24 or 1/2 or 0.5 or 50 percent.
For b) there is a total of 9 for chocolate, so the probability is 9 out of 24 or 37.5 percent or 3/8 or 0.375
For c) there are a total of 6 with no sprinkles out of 24 so it is 1/4 or 0.25 or 25 percent.
Step-by-step explanation:
Please mark me as brainliest :)
Evaluate the expression:
-a^2 + c(a-c) - n^2 a= -3 c= -2 n= 3
Answer: -a^2+c\left(a-c\right)-n^2a=3\quad :\quad c=-\frac{-a+\sqrt{-3a^2-4an^2-12}}{2},\:c=-\frac{-a-\sqrt{-3a^2-4an^2-12}}{2}
Step-by-step explanation: YW! plese mark branlest!
only answer if you know!! no spams
Answer:
The answers would be D and C.
Hope this helps!
Use the quadratic formula to solve x^2- 5x + 3 = 0.
Answer: Heyaa! ~
Your Answer is... x = 5 ± √ 13/ 2
Step-by-step explanation:
Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.
Hopefully this helps you!
-Matthew ^^
Sand and gravel are mixed in the ratio 5:3 to form ballast.
How much sand is mixed with 750kg of gravel ?
Work Shown:
sand/gravel = 5/3
x/750 = 5/3
3x = 750*5
3x = 3750
x = 3750/3
x = 1250
