Answer:
C. tan K=31/24
Step-by-step explanation:
Relations in right triangles:
The sine of an angle is the length of the opposite side to the angle divided by the length of the hypotenuse.
The cosine of an angle is the length of the adjacent side of the angle divided by the length of the hypotenuse.
The tangent of an angle is the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
In this question:
Sides 24 and 31.
Side opposite to K: 31
Side adjacent to K: 24
Then
tan K=31/24
And the correct answer is given by option D.
Coefficient of y in the equation: 3(2x -1/3y) = 0 is equal to a) 3 b) 1 c)-3 d)-1
Answer:
d is the right answer because the coefficient of y is 3*(-1/3) which results -1 so d is the right answer
The coefficient of y in the given equation is 1. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 3(2x -1/3y)=0.
Now, 6x-1/y=0
A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
Here, coefficient of y is 1.
Therefore, option B is the correct answer.
To learn more about an equation visit:
https://brainly.com/question/14686792.
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Engineering
When p= 3, q. I and r. 2, the
expression 2p² q3 is equal to
Answer:
[tex]{ \tt{2 {p}^{2} {q}^{3} }} \\ = { \tt{ {2(3)}^{2} . {(1)}^{3} }} \\ = 18[/tex]
Each pizza shown is broken up into different sized slices, but they are all equivalent.
Come up with another ratio of pizza slices that is equivalent to all of these pizzas.
!!! I need help with this question !!! I tried using the standard deviation formula but my answers are wrong. Can someone please help me! Thank you for your help!
Answer:
Step-by-step explanation:
I need help with this
bing jhwwjwiwisisuwuwywywywfsfsahajai
JK=8x+6 KL=6x+20 find JL
Answer:
14x + 26
Step-by-step explanation:
JL = JK + KL
= 8x + 6 + 6x + 20
= 8x + 6x + 6 + 20
JL = 14x + 26
Solve the following equation. for x
7x - 2 < 10
Step-by-step explanation:
7x < 10+2
7x<12
x < 12/7
Hope this helps!
Answer:
[tex]7x-2<10[/tex][tex]7x-2+2<10+2[/tex][tex]7x<12[/tex][tex]\frac{7x}{7}<\frac{12}{7}[/tex][tex]x<\frac{12}{7}[/tex]OAmalOHopeO
Help ASPPP!!!
Name a point that is represented on this graph. Use an ordered pair to give your answer. (Hint:
Look at the shaded region)
Answer:
(-5, -9)
Step-by-step explanation:
From the graph shown, the perfect ordered pair represented on the graph occurs when x = -5, y = -9. Therefore the required coordinate could be (-5, -9)
Dutchess County, New York, has been experiencing a mean of 35.4 motor vehicle deaths each year. If D = the number of vehicle deaths in Dutchess County in a year, what is the distribution for D (Binomial or Poisson) Explain.
Answer:
Poisson, as we have the mean number and not a proportion.
Step-by-step explanation:
We have the mean number of vehicle deaths per year, thus, since it is a mean and not a proportion, we use the Poisson distribution.
If we were working with the proportion of accidents that end in death for example, or any other proportion, it would be a binomial random variable.
please help me its timed -H.M
Answer:
f(3) = g(3)
General Formulas and Concepts:
Algebra I
Functions
Function NotationGraphingStep-by-step explanation:
We can see from the graph that the lines intersect at (3, 6). If this is the case, then that means that when x = 3 for both functions, it outputs f(x) = 6.
Rewriting this in terms of function notation:
f(3) = 6, g(3) = 6
∴ f(3) = g(3)
The mortgage on your new house is $180,000. Your monthly mortgage payment is $839 for 30 years. How much interest will be paid if the house is kept for the full 30 years?
9514 1404 393
Answer:
$122,040
Step-by-step explanation:
The interest is the difference between the mortgage value and the total amount paid.
($839/mo)×(12 mo/yr)×(30 yr) -180,000 = $302,400 -180,000 = $122,040
$122,040 will be paid in interest.
Find the mean for the data items
Answer:
4.5
Step-by-step explanation:
Given the data :
Score, x ____: 1, 2, 3, 4, 5, 6, 7, 8
Frequency, F : 1, 5, 1, 4, 4, 1, 5, 1
This is a grouped data: The mean of a grouped data is given as :
Mean (xbar) = ΣFx / ΣF
ΣFx = (1*1)+(2*5)+(3*1)+(4*4)+(5*4)+(6*1)+(7*5)+(8*1) = 99
ΣF = (1+5+1+4+4+1+5+1) = 22
Mean (xbar) = ΣFx / ΣF = 99 / 22 = 4.5
Consider a uniform density curve defined from x = 0 to x = 8. What percent of observations fall between 1 and 5?
a) 0.20
b) 0.50
c) 0.62
d) 0.13
e) 0.63
f) None of the above
Answer: 0.50, which is choice b
Explanation:
The interval [tex]1 \le x \le 5[/tex] covers 5-1 = 4 units in the horizontal direction.
This is out of 8 units that span from x = 0 to x = 8 (we could say 8-0 = 8).
So we get the final result of 4/8 = 0.50
In other words, the interval from x = 1 to x = 5 covers exactly half of the interval from x = 0 to x = 8.
Which is the graph of the following inequality
Answer:
graph a is the correct answer
Step-by-step explanation:
The width of a rectangle measures (7k-2m)(7k−2m) centimeters, and its length measures (5k-m)(5k−m) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
[tex]P = 24k-6m[/tex]
Step-by-step explanation:
The correct expressions are:
[tex]W = 7k - 2m[/tex]
[tex]L = 5k - m[/tex]
Required
The perimeter (P)
This is calculated as:
[tex]P = 2 *(L + W)[/tex]
So, we have:
[tex]P = 2 *(5k - m + 7k -2m)[/tex]
Collect like terms
[tex]P = 2 *(5k + 7k- m -2m)[/tex]
[tex]P = 2 *(12k-3m)[/tex]
Open bracket
[tex]P = 24k-6m[/tex]
The height of Mt.Whitney is approximately 14,490 feet. What is a rounded form of this number written in scientific notation?
Which of the following is graphed below?
A runner is traveling at a constant rate of 8 meters per second. How long does it take for the runner to travel 100 meters? Now before you answer this I know it's 12.5! What I need help with is creating a equation that gives the distance, d, that the person has run if you know the amount of time, t, they have been running. Thank you! :)
Answer:
see below
Step-by-step explanation:
We know that distance = rate * time
100 meters = 8 m/s * time
100 = 8t
Divide each side by 8
100/8 = 8t/8
12.5 = t
If we know the rate and the time, we can find the distance
d = rt
Find the exact value of the logarithm without using a calculator.
Answer:
1/11
Step-by-step explanation:
We are asked to find the natural log of
[tex] \sqrt[11]{e} [/tex]
Convert to fractional exponent
[tex] ln(e {}^{ \frac{1}{11} } ) [/tex]
Apply Log of Power rule
[tex] \frac{1}{11} ln(e) [/tex]
Natural log of e is 1 so
[tex] \frac{1}{11} \times 1 = \frac{1}{11} [/tex]
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
First, remember that the ln function is just a log function with a base of e. Here's how it looks
[tex]ln(x) =log_{e}(x)[/tex]
[tex]ln(\sqrt[11]{e} ) = log_{e}(\sqrt[11]{e} )[/tex]
We can take this one step further if we realize that we can rewrite the square root as a simple power to a fraction!
[tex]log_{e}(e^{\frac{1}{11} } )[/tex]
Solving the equation above is really simple. All that function is really saying is can we raise e to some number, where the result would be e^(1/11)? In other words find x.
[tex]e^{x} = e^{\frac{1}{11} }[/tex]
Well x has to be 1/11 in that case. And that ends up being our final answer.
[tex]log_{e}(e^{\frac{1}{11} } ) = \frac{1}{11}[/tex]
Which of the following is a geometric sequence where a1 = 4 and r = 3?
A) 4, 7, 10, 13, . . .
B) 3, 7, 11, 15, . . .
C) 4, 12, 36, 108, . . .
D) 3, 12, 48, 192, . . .
Answer:
C 4,12,36 108
Step-by-step explanation:
the answer is above.
Answer:
C
Step-by-step explanation:
G.P= a,ar,ar^2,ar^3,...,
a1=4
a2=4×3=12
a3=4×9=36
a4=4×27=108
Leah is looking to take out a 30-year mortgage from a bank offering a monthly interest rate of 0.325% Using the formula below, determine the maximum amount Leah can borrow, to the nearest dollar, if the highest monthly payment she can afford is $900.
M=Pr/(1-(1+r)^-n)
M= the monthly payment
P= the amount owed
r= the interest rate per month
n= the number of payments
Answer:
[tex]P=\$276646.153[/tex]
Step-by-step explanation:
Time [tex]T=30years[/tex]
Rate [tex]r=0.325\%[/tex]
Payment per month [tex]P=\$ 900[/tex]
Generally the equation for Principle is mathematically given by
[tex]M=\frac{P r}{1-(1+r)^{-n}}[/tex]
[tex]900=\frac{P \frac{0.325}{100}}{1-(1+( \frac{0.325}{100}))^{- 30*12}}[/tex]
[tex]P=\frac{900*100*0.99}{0.325}[/tex]
[tex]P=\$276646.153[/tex]
The sum of two integers is 90 and their difference is 30. Find the larger number
Answer:
60 is the larger number
Step-by-step explanation:
Let the two numbers be a and y
x+y = 90
x-y = 30
Add the two equations together
x+y = 90
x-y = 30
-----------------
2x = 120
Divide by 2
2x/2 =120/2
x = 60
x+y =90
60+y = 90
y = 90-60
y = 30
The numbers are 60 and 30
A sofa regularly sells for $760. The sale price is $676.40. Find the percent decrease of the sale price from the regular price.
Answer: (760 - 676. 40) × 100 ÷ 760 = 11%
Step-by-step explanation:
Answer:
11% decrease
Step-by-step explanation:
Concepts:
Percent change is the change between an old value and its new value represented as a %. If a percent change is a decrease, it means that the new value is less than the old value. If a percent change is a increase, it means that the old value is less than the new value. The formula for percent change is: (NV - OV)/OV · 100 = C, where NV = New Value, OV = Old Value, and C = Percent Change.The sale price is the price at which something sells or sold after the price has been reduced by sales, discounts, etc.Solving:
Let's find the percent change by using the formula.
1. Formula for Percent Change
(NV - OV)/OV · 100 = C2. Plug in the values of NV and OV
(676.40 - 760)/760 · 100 = C3. Simplify
-83.6/760 · 100 = C-0.11 · 100 = C-11 = CTherefore, our percent decrease is 11% decrease.
What is the least common denominator that will allow you to combine the constant terms? 10 21 35 or 42
Answer:
[tex]LCM = 21[/tex]
Step-by-step explanation:
Given
[tex]-\frac{3}{5}y + \frac{1}{7}= \frac{1}{3}y -\frac{2}{3}[/tex]
Required
LCM of the constant terms
Collect like terms
[tex]\frac{1}{3}y+\frac{3}{5}y = \frac{1}{7}+\frac{2}{3}[/tex]
The constant terms are on the right-hand side
To combine them, we simply take the LCM of the denominator, i.e. 7 and 3
The prime factorization of 3 and 7 are:
[tex]3 = 3[/tex]
[tex]7 = 7[/tex]
So:
[tex]LCM = 3 * 7[/tex]
[tex]LCM = 21[/tex]
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker
Discounted price = $60
Discount = 60%
Let the usual price be x.
So, x - (60% of x) = $60
=> x - [(60/100) × x] = $60
=> x - (60x/100) = $60
=> x - (3x/5) = $60
=> (5x/5) - (3x/5) = $60
=> 2x/5 = $60
=> 2x = $60 × 5
=> 2x = $300
=> x = $300/2
=> x = $150
So, the usual price is $150.
If the length of a leg of a right triangle is 25 and the length of the hypotenuse is 35, what's the length of the other leg, to the nearest tenth?
Answer:
24.5
Step-by-step explanation:
using Pythagorean theorem
[tex]a^{2} +b^{2} =c^{2} \\[/tex]
Since we know the hypotenuse, we can change up the theorem into [tex]c^{2} -b^{2} =a^{2}[/tex]
[tex]35^{2} -25^{2} =a^{2}[/tex]
1225-625=[tex]a^{2}[/tex]
[tex]\sqrt{a^{2} } =24.5[/tex]
Find the missing side. Round your answer to the nearest
Please help me
Answer:
Step-by-step explanation:
The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,450. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 570 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time? (Round z value to 2 decimal places. Round your answer to the nearest whole number.)
Answer:
The manufacturer should advertise 11720 pages.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 12450, standard deviation of 570:
This means that [tex]\mu = 12450, \sigma = 570[/tex]
How many pages should the manufacturer advertise for each cartridge if it wants to be correct 90 percent of the time?
They should advertise the 10th percentile, which is X when Z has a p-value of 0.1, so X when Z = -1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 12450}{570}[/tex]
[tex]X - 12450 = -1.28*570[/tex]
[tex]X = 11720[/tex]
The manufacturer should advertise 11720 pages.
If two events, A and B, never occur at the same time they are _____.
complementary
compound
simple
disjoint
Answer:
Disjoint is the correct answer.
Mr. Plaggenier divided Camp Greenfield into 5 squads for an athletic scrimmages. Each squad competes against each of the other 4 squads 2 times. The scrimmage lasts 2 hours. If only one pair of teams competes at a time and all of the competitions take the same amount of time, how long is each competitions?
A)6 min.
B) 8 min.
C) 10 min.
D) 12 min.
Answer: (a)
Step-by-step explanation:
Given
There are 5 squads for an athletic scrimmages
If each team played 2 matches
Total no of matches will be
[tex]\Rightarrow \dfrac{5(5-1)}{2}\times 2=20\ \text{matches}[/tex]
So, 20 matches are played in 2 hours
Each match takes
[tex]\Rightarrow \dfrac{120}{20}=6\ \text{minute}[/tex]
Option (a) is correct.
