Answers
Answer:
It would be 1/4
Step-by-step explanation:
Related Questions
Find the exact value for the expression under the given conditions.
cos(α+β), sin α= -8/17 for α in Quadrant lll and cosβ= -8/15 for β in Quadrant ll.
Answers
Answer:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]
Step-by-step explanation:
We are given the conditions:
[tex]\displaystyle \sin(\alpha)=-\frac{8}{17}\text{ and } \cos(\beta)=-\frac{8}{15}[/tex]
Where α is in QIII and β is in QII and we want to find the exact value of cos(α + β).
The first ratio gives us the opposite side and the hypotenuse with respect to α . Then the adjacent side is (we can ignore negatives):
[tex]a=\sqrt{(17)^2-(8)^2}=15[/tex]
The second ratio gives us the adjacent side and the hypotenuse with respect to β. Then the opposite side is:
[tex]o=\sqrt{(15)^2-(8)^2}=\sqrt{161}[/tex]
Therefore, for α, ignoring negatives, the adjacent side is 15, the opposite side is 8, and the hypotenuse is 17.
And for β, ignoring negatives, the adjacent side is 8, the opposite side is √(161), and the hypotenuse is 15.
We can rewrite our expression as:
[tex]\displaystyle \cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)[/tex]
Since α is in QIII, sin(α), cos(α) < 0, and tan(α) > 0.
And since β is in QII, cos(β), tan(β) < 0, and sin(β) > 0.
Using this information, substitute:
[tex]\displaystyle \cos(\alpha+\beta)=\left(-\frac{15}{17}\right)\left(-\frac{8}{15}\right)-\left(-\frac{8}{17}\right)\left(\frac{\sqrt{161}}{15}\right)[/tex]
Therefore:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]
What is the probability of choosing a king of hearts or a queen of spades from a deck of cards? Type your answer as a fraction
Answers
Answer:
[tex]Pr = \frac{1}{26}[/tex]
Step-by-step explanation:
Given
In a deck of card, we have:
[tex]Cards = 52[/tex]
[tex]King[Heart] = 1[/tex]
[tex]Queen[Spade] = 1[/tex]
Required
The probability of obtaining a king of heart or a queen of spade.
The probability of king of heart is:
[tex]P(King[Heart]) = \frac{n(King[Heart])}{Cards}[/tex]
[tex]P(King[Heart]) = \frac{1}{52}[/tex]
The probability of queen of spade is:
[tex]P(Queen[Spade]) = \frac{n(Queen[Spade])}{Cards}[/tex]
[tex]P(Queen[Spade]) = \frac{1}{52}[/tex]
The required probability of obtaining a king of heart or a queen of spade. is:
[tex]Pr = P(King[Heart]) + P(Queen[Spade])[/tex]
[tex]Pr = \frac{1}{52}+ \frac{1}{52}[/tex]
Take LCM
[tex]Pr = \frac{1+1}{52}[/tex]
[tex]Pr = \frac{2}{52}[/tex]
Simplify
[tex]Pr = \frac{1}{26}[/tex]
According to the data released by the Chamber of Commerce of a certain city, the weekly wages of factory workers are normally distributed with a mean of $720 and standard deviation of $40. Find the probability that a worker selected at random from the city makes the following weekly wage. (Round your answers to four decimal places.)
Answers
Complete question :
a. Of less than$720?
b. Of more than $840?
c. Between $680 and $760?
Answer:
0.500 ; 0.0013 ; 0.6827
Step-by-step explanation:
Given that :
Mean, μ = 720
Standard deviation, σ = 40
P(Z < x)
x = (x < 720)
Obtain the standardized value of x
P(x < 720) = (x - μ) / σ
P(x < 720) = (720 - 720) / 40
P(x < 720) = 0
P(Z < 0) = 0.5
B.) More than $840
P(x > 840)
P(x > 840) = (x - μ) / σ
P(x > 840) = (840 - 720) / 40
P(x > 840) = 120 / 40 = 3
P(Z > 3) = 0.0013499 (Z probability calculator)
c. Between $680 and $760?
P(760 < x < 680)
P(760 < x < 680) = ((x - μ) / σ) - ((x - μ) / σ)
P(760 < x < 680) = ((760 - 720) / 40) - (680 - 720) / 40)) = P( Z < - 1) - P(Z < - 1)
P(680 < x < 760) = 0.84134 - 0.15866 = 0.68268
What is the area of the shape below?
Answers
Answer:
31 1/2 yd 2
Step-by-step explanation:
4*6=24
3*5= 15 15/2 = 7 1/2
24+7 1/2 = 31 1/2
Help with number 10! Step by step please!
Answers
9514 1404 393
Answer:
x = -9 (as you know)
Step-by-step explanation:
[tex]\log_6\dfrac{1}{6}=\dfrac{x}{9}\\\\\log_6{(6^{-1})}=\dfrac{x}{9}\\\\-1=\dfrac{x}{9}\\\\x=(-1)(9)=\boxed{-9}[/tex]
_____
I find it helpful to remember that a logarithm is an exponent.
[tex]\log_a(a^b)=b[/tex]
4^?=1024? i know the answer is 5 but is there an easier way to find that out instead of guessing?
Answers
Answer:
here you go............
Step-by-step explanation:
I hope it helped
Amit Almor, a psychology researcher at the University of South Carolina, conducted a series of experiments on conversation and attention level. He found that subjects were four times more distracted while preparing to speak or speaking than when they were listening. This research has many implications, including those for the issue of using cell phones while driving.
You decide to explore this issue by having three different groups try tracking a fast-moving target on a computer screen. The first group is preparing to speak, the second group is speaking, and the third group is listening to a conversation.
The sample mean and sum of squares of the scores for each of the three groups are presented in the following table.
Group Sample Mean Sum of Squares
Preparing to speak 98.3 7,2810.0900
Speaking 101.5 6,6156.8100
Listening 103.2 70,277.7600
After collecting the data, you analyze the data using an ANOVA. The results of your analysis are presented in the following ANOVA table.
Source of Variation SS df MS F
Between Treatments 3,095.00 2 1,547.50 5.52
Within Treatments 209,244.66 747 280.11
Total 212,339.66 749
These findings are significant at α = 0.05, which tells you that the difference is very unlikely to have occurred just by chance, but it does not tell you the size of the effect. A simple measure of the effect size is given by: ________
Required:
What is the formula for this measure of the effect size?
Answers
Answer:
η²
SSbetween / SStotal
η² = 0.0145757
Step-by-step explanation:
Effect size, η² = SSbetween / SStotal
SSbetween is the sum of square between the groups in the experiment. It is sometimes denoted as SSb.
The sum of square Total, SStotal measures the entire variability in these dataset.
SSbetween = 3,095.00 ; SStotal = 212,339.66
η² = SSbetween / SStotal
Effect size η²= 3,095.00 / 212,339.66
Effect size = 0.0145757
Melanie invested $9,800 in an account paying an interest rate of 4 1 2 4 2 1 % compounded quarterly. Amelia invested $9,800 in an account paying an interest rate of 4 3 4 4 4 3 % compounded continuously. After 20 years, how much more money would Amelia have in her account than Melanie, to the nearest dollar?
Answers
After 20 years, the amount of Money Amelia would have more than Melanie would be $181,551.37.
What is the future value of Melanie's account?The formula for calculating future value:
FV = P (1 + r) nm
FV = Future value P = Present value R = interest rate = 4 1/2 ÷ 4 = 1.125%m = number of compounding = 4N = number of years9800(1 + 0.0125)^80 = 23,983.29
What is the future value of the amount in Amelia's account?the formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate9800 e^0.0475 x 20 = 205,534.66
Difference = 205,534.66 - 23,983.29 = $181,551.37
To learn more about future value, please check: https://brainly.com/question/18760477
What is the solution to the system of equations?
y = 2/3x+ 3
x=-2
{-2, -15/2}
{-2, 5/3}
{-2, 11/6}
{-2, 13/3}
Answers
Answer:
(-2,5/3)
Step-by-step explanation:
How do you know if alternate interior angles and alternate exterior angles have the same measure?
Plz be specific..Will give BRAINLIEST!!!!!!!
Answers
Answer:
If the transversal cuts across parallel lines (the usual case) then alternate exterior angles have the same measure. So in the figure above, as you move points A or B, the two alternate angles shown always have the same measure.
Step-by-step explanation:
Hope this helps
It's Pythagorean theorem
Answers
Answer:
6root3
Step-by-step explanation:
Answer:
6 radical 3
Step-by-step explanation:
A company produces remote-controlled helicopters. The company’s profit, in thousands of dollars, as a function of the number of helicopters produced per week can be modeled by a quadratic function. When 1 helicopter is produced per week, the company’s profit is 4 thousand dollars. The maximum profit, 22 thousand dollars, occurs when 4 helicopters are produced per week.
The function that models the scenario, where h is the number of helicopters produced per week, is
f(h) = –2(h – 4)2 + 22.
When 6 helicopters are produced weekly, the company’s profit is (blank)
thousand dollars.
Answers
Explanation:
I took this in 9th grade so I know how to do this kind of stuff
Answer:
the answer is B
Step-by-step explanation:
En una caja hay 10 monedas de $50, 20 monedas de $20 y $20 de 10. La probabilidad de sacar una moneda de $10 es:
A 20/20
B 1/2
C 4/10
D 2/5
DOY CORONITA SI RESPONDEN BIEN PLIS
Answers
Answer:
tha answer is c
Step-by-step explanation:
A new pair of shoes is advertised for $110. The sales tax is 7.5%. What is the total cost of the shoes?
Answers
Answer:
118.25
Step-by-step explanation
If the tax is in percent, divide the tax rate by 100. You do this by moving the decimal point two spaces to the left. In this, there's 7.5/100 = 0.0
Find the tax value by multiplying tax rate by the item value:
tax = 110 × 0.075
tax = 8.25
Which of the following points satisfies the linear inequality below? Select all correct answers.
5x + 2y 26
Select all that apply:
(0,5)
(3,1)
(3,-4)
(-4,1)
Answers
Answer:
All points satisfy the inequality
Step-by-step explanation:
Given
[tex]5x + 2y \le 26[/tex]
Required
Select all points that satisfy the above inequality
[tex](a)\ (0,5)[/tex]
This implies that
[tex]x = 0; y = 5[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 0 + 2 * 5 \le 26[/tex]
[tex]0 + 10 \le 26[/tex]
[tex]10 \le 26[/tex]
This satisfy the inequality
[tex](b)\ (3,1)[/tex]
This implies that
[tex]x = 3;\ y =1[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 3 + 2 * 1 \le 26[/tex]
[tex]15 + 2 \le 26[/tex]
[tex]17 \le 26[/tex]
This satisfy the inequality
[tex](c)\ (3,-4)[/tex]
This implies that:
[tex]x = 3; y-4[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 3 + 2 * -4 \le 26[/tex]
[tex]15 -8 \le 26[/tex]
[tex]7 \le 26[/tex]
This satisfy the inequality
[tex](d)\ (-4,1)[/tex]
This implies that:
[tex]x = -4; y =1[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * -4 + 2 *1 \le 26[/tex]
[tex]-20 + 2 \le 26[/tex]
[tex]-18 \le 26[/tex]
This satisfy the inequality
What is the length of line segment FE?
Enter your answer, as a decimal rounded to the nearest tenth, in the box.
FE =
units
Answers
Answer:
(7,-1)because it is problem of vector lesson so that we have to use formula of vector
F (-3,4)
E (4,3)
distance formula: √(4-(-3))^2 + (3-4)^2 = √49+1 = √50 = 7.07 or 7.1
Question 10 of 10
Which is not a characteristic of an exponential parent function?
A. It passes through (0,1).
B. It goes through the origin.
C. The domain is all real numbers.
D. The range is positive real numbers (y > 0).
SUBMIT
Answers
It does not pass through origin.
12. The product of 0.08 and 0.7 is 5.6
A) True
B) False
Answers
Answer:
B (false)
Step-by-step explanation:
it is 0.056
The mark up on an item is $3.75. If the mark up is 35%, what was the original price? Round
your answer to the nearest hundredth. (Show all work)
Answers
Answer:
$10.71
Step-by-step explanation:
[tex]\frac{3.75}{y} =\frac{35}{100}[/tex]
y × 35 = 3.75 × 100
35y = 375
35y ÷ 35 = 375 ÷ 35
[tex]y=10\frac{5}{7}[/tex]
y = 10.7142857143
10.7142857143 round to 10.71
Gina will pay $14 for fabric at a crafting store. The tax rate is 8.5%. How much will she pay for her fabric including tax?
Answers
Answer:
$15.19
Step-by-step explanation:
8.5% = 0.085
0.085 x 14 = $1.19
1.19+14= $15.19
who was the first Democratic elected president of Nigeria
Answers
Answer:
Alhaji Shehu Shagari
Step-by-step explanation:
Alhaji Shehu Shagari the first Democratic elected president of Nigeria, He was elected in October 1979. He contested under the The National Party of Nigeria. Prior to that time, Nigeria had been under military rule for more than 13 years.
In December 1983, there was a military coup and he was overthrown.
What formula can be used to find circumference? Choose all that what formula can be used to find circumference?choose all that apply apply.
Сл
2πr
πd
2πd
Answers
Answer:
2
Step-by-step explanation:
because it can find the circumference
How many cities could have an annual rainfall of 28.5 in 32.5 in
Answers
Answer:
A) 6
Step-by-step explanation:
Answer:
2. A) 6
Step-by-step explanation:
#CarryOnLearning
Natasha goes bowling she pays $5.75 for an admission ticket and $9.25 for each round of bowling she plays the total amount of Tasha pays for admission and the number of rounds who plays is $33.50 which equation can be used to determine the number of rounds X that Natasha bowled
a.) 5.75 x + 9.25=33.50
b.) 9.25 X - 5.75= 33.50
c.) 5.75 + 9.25 X= 33.50
d.) 5.75 x - 9.25=33.50.
Answers
What is the measure of ∠B?
Triangle A B C with ray A G through point C and angle measures A = 3x, B = 4x, and exterior angle B C G = 10x minus 45.
60∘60 degrees
15∘15 degrees
45∘45 degrees
105∘
Answers
Answer:
Solution given:
4x+3x=10x-45[exterior angle is equal to the sum of two opposite interior angle]
45=10x-7x
x=45/3
x=15
now.
<B=4x=4×15=60° is your answer
The required measure of ∠B is 60° for the given triangle.
What is the Exterior Angle?An exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.
According to the shown figure, we have:
The external angle is ∠BCG = 10x - 45.
And, two interior angles as ∠A = 3x, and ∠B = 4x.
As we know that the sum of two opposite interior angles equals the exterior angle.
So, we can be written as follows:
4x + 3x = 10x - 45
45 = 10x - 7x
x = 45/3
x = 15
So, the measure of ∠B is:
∠B = 4x
∠B = 4 × 15
∠B = 60°
Thus, the required measure of ∠B is 60°.
Learn more about the exterior angles here :
https://brainly.com/question/28835566
#SPJ2
if a questions asks to find the area of half of the circle would you do 3.14(pie) times r2(radius squared) times 1/2? and if no then what would you do?
Answers
Answer:
[tex]A=\dfrac{3.14r^2}{2}[/tex]
Step-by-step explanation:
The area of a circle is given by :
[tex]A=\pi r^2[/tex]
Where
r is the radius of the circle.
If we talk about the area of half of the circle, it means we have to half the area such that,
[tex]A=\dfrac{\pi r^2}{2}\\\\or\\\\A=\dfrac{3.14r^2}{2}[/tex]
Hence, this is the required solution.
what is -5/3 as an equivalent fraction
Answers
Answer:
-20/12 as an example there are many others
1. -1 2/3
2. -10/6
3. - 15/9
To find an equivalent fraction you need to multiply the denominator and the numerator by the same number. For example:
1/3 — 1*3/3*3 — which equals 3/9
Hope this helps!!
Plsssss help me with this angle circle problem what is x
Answers
Answer:
x = 3
Step-by-step explanation:
Once again we want to use the relationship stated earlier
Where A * B = C * D
Once again imagine that the segments in the given problem have letters
A = x
B = 12
C = x + 1
D = 9
Now we create an equation using the relationship
12 * x = 9(x+1)
now we solve using basic algebra
step 1 distribute the 9 to the x and the 1
9 * x = 9x
9 * 1 = 9
now we have 12x = 9x + 9
step 2 subtract 9x from each side
12x - 9x = 3x
9x - 9x cancels out
now we have 3x = 9
step 3 divide each side by 3
3x/3=x
9/3=3
we're left with x = 3
Answer:
x = 3 / C. 3
Step-by-step explanation:
Hope this helps
If one side of a cube measures x cm what is the volume
Answers
Answer:
The volume is x times x times x which is x^3 :)
2=n over 3 what does n equal?
Answers
Answer:
n = 6
Step-by-step explanation:
2 = [tex]\frac{n}{3}[/tex]
multiply both sides by 3
=> n = 6
Answer:
n = 6
Step-by-step explanation:
If 2 = n/3, then n = 6, because 3 times 2 is 6 (2 of 3 is 6)
(side note, this might not be what you are looking for soo)