How do you do number 24?
If sinθ = 3/4 and is in the first quadrant, then cosθ = _____.
Answer: The answer is [tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]
Step-by-step explanation: Given that
[tex]\sin \theta=\dfrac{3}{4}[/tex] and [tex]\theta[/tex] is in Quadrant I.
We are to find the value of [tex]\cos \theta.[/tex]
We have the following trigonometric identity :
[tex]\sin^2\theta+\cos^2\theta=1\\\\\Rightarrow \cos^2\theta=1-\sin^2\theta\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\sin^2\theta}\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)^2}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\dfrac{9}{16}}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{\dfrac{7}{16}}\\\\\\\Rightarrow \cos \theta=\pm\dfrac{\sqrt{7}}{4}.[/tex]
Since [tex]\theta[/tex] lies in the first quadrant, so cosine of [tex]\theta[/tex] will be positive.
Thus,
[tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]
the top of an auto piston is a circle with a diameter measuring 8.4 centimeters . what is the area of the top piston ?
area of a circle = PI x r^2
r = 8.4/2 = 4.2
using 3.14 for PI
area = 3.14 x 4.2^2 = 55.3896 square cm
round answer as needed
Draw one card at random from a standard deck of cards. the sample space s is the collection of the 52 cards. assume that the probability set function assigns 1/52 to each of the 52 outcomes. let a = {x: x is a jack, queen, or king}, b = {x: x is a 9, 10, or jack and x is red}, c = {x: x is a club}, d = {x: x is a diamond, a heart, or a spade}.
what's the vertex and axis of symmetry of y=2x^2+8x+3 ?
(15-6)-3 = 15 - (6 -3) dose this make sense or nonsense?
find every fraction with a whole number denominator less than 50 that is equivalent to 10/15.
Sage correctly found the following quotient. 1 1/2 divided by 1/3= 4 1/2 . (a) Create a model to show the quotient. (b) Explain what the half in the quotient refers to in your model
When dividing 1 1/2 by 1/3, the quotient 4 1/2 indicates that each person receives half of a whole unit, which in our model is half of a pizza.
(a) To model the quotient 1 1/2 ÷ 1/3, imagine you have 1 1/2 units of something, like 1 1/2 pizzas. Now, if you divide each pizza into thirds, you'd have 3 halves of pizza. So, 1 1/2 pizzas divided by 1/3 pizza per person equals 4 people, each getting 1/2 of a pizza.
(b) The half in the quotient represents the portion of each whole unit (in this case, pizza) that each person receives. In our model, it signifies that each of the 4 people receives half of a pizza.
A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 238 ft2. Find the width of the walkway if the garden is 12 ft wide by 15 ft long. ft
Let us say that:
x = width of walkway
So the area is:
(12 + 2x) (15 + 2x) = 238
2x because we must add x on both sides of length and width
Expanding:
180 + 24x + 30x + 4x^2 = 238
4x^2 + 54x = 58
By completing the square:
x^2 + 13.5x + 45.5625 = 60.0625
(x + 6.75)^2 = 60.0625
x + 6.75 = ±7.75
x = -14.5, 1
Since dimension cannot be negative, therefore:
width = 1 ft
Final answer:
The width of the walkway around the garden is 3.87 ft.
Explanation:
The width of the walkway around the garden can be found by subtracting the area of the garden from the total area of the garden with the walkway.
Calculate the total area of the garden with the walkway by multiplying the length and width: 12 ft * 15 ft = 180 ft2.Subtract the area of the garden from the total area (238 ft2 - 180 ft2) to find the area of the walkway: 58 ft2.Since the walkway surrounds the garden, divide the walkway's area by the length or width of the garden to find the width of the walkway: 58 ft / 15 ft = 3.87 ft.A basketball player makes 175 out of 220 free throws. we would estimate the probability that the player makes the next free throw to be
The probability that the player will make next free throw is obtained as 0.795.
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].
The total number of free throws is 220.
And, the number of throws by the player is 175.
Now, the probability can be found as below,
P(free throws) = Throws by the Player ÷ Total throws
⇒ 175 ÷ 220 = 0.795
Hence, the probability for the next free throw can be estimated as 0.795.
To know more about probability click on,
https://brainly.com/question/11234923
#SPJ5
the lengths of the sides of a triangle are consecutive odd integers.if the perimeter of the triangle is 27 what is are the lengths of all three sides?
Please help answer this pre calc question
place the equation for g ( x^2-5) over the equation for f(4x+1)
so you get
x^2-5/4x+1
B is the answer
Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
How much water does Janine drink in a day? She normally drinks 4 bottles a day, each 16.9 ounces.
How much does a bottle of water cost? She buys 24-packs of 16.9 ounce bottles for $3.49.
How much does a reusable water bottle cost? About $10.
How long does a reusable water bottle last? Basically forever (or until you lose it).
How much does a water filter cost? How much water will they filter?
A faucet-mounted filter costs about $28 and includes one filter cartridge. Refill filters cost about $33 for a 3-pack. The box says each filter will filter up to 100 gallons (378 liters)
A water filter pitcher costs about $22 and includes one filter cartridge. Refill filters cost about $20 for a 4-pack. The box says each filter lasts for 40 gallons or 4 months
An under-sink filter costs $130 and includes one filter cartridge. Refill filters cost about $60 each. The filter lasts for 500 gallons.
The cheapest option saves her $________ over a year.
2.85 as a mixed number
I hope you got the idea
What is 1 ten thousand + 19 thousands+ 2 tens+ 9 ones in standard form
A bucket of nails contains 4.20 × 102 nails. how many dozens of nails does the bucket contain? 1 dozen=12 objects
On a backpacking trip through Europe, Troy spent 20 Swiss francs to stay one night in a youth hostel. If the foreign exchange rate between the U.S. dollar and the Swiss franc is 1:2.2, how much did Troy spend in U.S. dollars?
Answer:
Troy spent $9.09.
Step-by-step explanation:
Troy spent 20 Swiss Francs to stay one night in a youth hostel.
1 U.S. Dollar = 2.2 Swiss franc
We have to convert 20 Swiss franc to U.S. dollars.
So we divide 20 by 2.2 to convert Swiss franc to U.S. dollars.
= [tex]\frac{20}{2.2}[/tex] = 9.09090909 ≈ $9.09
Troy spent $9.09 to stay one night in a youth hostel.
Which expression represents the phrase, "one third the sum of 12 and a number"?
Use the scale factor to find the area of the enlarged figure. Explain your steps.
The area of the enlarged figure will be 327.68 square units
The scale factor will be the ratio of the similar sides of a rectangle.
For the given triangles, the required scale factors will be expressed as:
[tex]\frac{4}{8} =\frac{a}{25.6}\\\frac{1}{2} =\frac{a}{25.6}\\2a = 25.6\\a=\frac{25.6}{2} \\a=12.8[/tex]
Next is to get the area of the bigger rectangle:
[tex]Area = Length \times Width\\Area=a\times 25.6\\Area=12.8\times 25.6\\Area=327.68 units^2[/tex]
Hence the area of the enlarged figure will be 327.68 square units
Learn more here: https://brainly.com/question/21067938
A watermelon seed is 0.4cm long. How far would a line of 116 watermelon seeds stretch?
Please help with the 4 questions.
How to do lond division 0.6÷0.0024
To divide 0.6 by 0.0024 using long division, adjust the numbers to remove the decimals, becoming 6000 divided by 24. The result of this division is 250.
Explanation:To solve the problem of long division, specifically for 0.6 ÷ 0.0024, you need to adjust both numbers to remove the decimal points before division. Start by shifting the decimal point in each number. In this case, shift the decimal for both numbers 4 places to the right, resulting in 6000 divided by 24.
So, it becomes a simpler division problem: 6000 ÷ 24. When you divide 6000 by 24, the result is 250.
Therefore, the result of 0.6 ÷ 0.0024 is 250.
Learn more about Long Division here:https://brainly.com/question/28824872
Mario ordered a pizza for dinner when it arrived Mario quickly ate 1/8 of the pizza or Mario's getting napkins his pet poodle ate 1/3 of the pizza B. Write a numerical expression to show the fraction of the pizza that's left
There is 2/5 cup of cream in a nelly cream pie.How much cream would you need if you were making 3/4 of a pie
To make [tex]\frac{3}{4}[/tex] of a nelly cream pie, you would need [tex]\frac{3}{10}[/tex] cup of cream. This calculation is done by multiplying [tex]\frac{2}{5}[/tex] cup (the amount required for a whole pie) by [tex]\frac{3}{4}[/tex].
To calculate the amount of cream needed for making [tex]\frac{3}{4}[/tex] of a nelly cream pie when the full pie requires [tex]\frac{2}{5}[/tex] cup of cream, we simply multiply these two fractions. To do this, first convert the mixed number [tex]\frac{3}{4}[/tex] to an improper fraction. We already have it in the proper format, so we can directly multiply:
([tex]\frac{2}{5}[/tex]) * ([tex]\frac{3}{4}[/tex]) = (2*3)÷(5*4) = [tex]\frac{3}{10}[/tex]
Therefore, for [tex]\frac{3}{4}[/tex] of a nelly cream pie, you would need [tex]\frac{3}{10}[/tex] cup of cream.
What is the value of x in the equation 2x + 3y = 36, when y = 6?
the answer is x=9
i'm not good at showing my work, but I'm positive in my answer I'm an honors student.
Finding the area shaded figure
complete square = 100 square yards
triangle = 1/2 x base x height = 1/2 x 10 x 5 = 25 square yards
100-25 = 75 square yards
shaded area = 75 square yards
The probability that a given computer chip will fail is 0.02. find the probability that of 5 delivered chips, exactly 2 will fail.
Probability of an event is the measure of its chance of occurrence. The probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
For the given case, as failing or working of chips usually doesn't depend on other chips' working condition, so they're independent(assuming). There are two cases for each chip's working(random experiment) that it is either working or failed.
If we take Success of the considered binomial experiment(working status of chip) = Chip working fine
Then, as per given data, we have
P(chip working fine ) = 1 - P(chip not working) = 1 - 0.02 = 0.98 = Probability of success in Bernoulli experiment (chip's working status).
There are n = 5 chips, p = probability of success = 0.98, q = 1-p = 0.02
If we take X = number of chips of of 5 chips working, then:
[tex]X \sim B(n = 5, p = 0.98)[/tex]
Then, the needed probability is P(Exactly two chips fail) = P(Exactly 5-2 = 3 chips work) = P(X = 3)
And thus, the needed probability is calculated as:
[tex]P(X = 3) = \: ^5C_3(0.98)^3(0.02)^2 = \dfrac{5.4.3}{3.2.1} \times 0.941192 \times 0.0004 = 0.003764768[/tex]
(using the probability mass function of binomial distribution).
Thus, the probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004
Learn more about binomial distribution here:
https://brainly.com/question/13609688
I need help with this problem I'm not that good in math
1/5(15x-20) = 1/3(12x-9)
multiply the 15 and 20 on the left by 1/5 to get
3x-4
now multiply 12 and 9 by 1/3 to get
4x-3
now you have 3x-4 =4x-3
now solve for x
3x-4 =4x-3
subtract 3 x from each side:
-4 = x-3
add 3 to each side
-1 = x
x = -1
solve for t q=(s+t)(r/2)
You deposit $3000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 20 years?