Which of the following expressions could be used to represent "three less than half a number"?
• 1/2 - 3n
• 3 - 1/2n
• 3n - 1/2
• 1/2n - 3
Answer:
the answer is
[tex]3 - \frac{1}{2}n [/tex]
Pythagorean theorem
Answer:
hello
Step-by-step explanation:
a²+b²=c²
16²+b²=65²
256+b²=4225
b²=4225-256
b²=3969
[tex]b = \sqrt{3969}[/tex]
b=63
b=63 mi
have a nice day
Answer:
b = 63
Step-by-step explanation:
In a right angled triangle, hypotenuse squared is equal to the sum of the square of the other sides.
c² = a² + b² (where c is the hypotenuse, and a and b are the other two sides)
c = 65 , a = 16 b = ?
65² = 16² + b²
4225 = 256 + b²
4225 - 256 = b²
b² = 3969
b = [tex]\sqrt{3969}[/tex]
b = 63
check
c² = 16 ² + 63²
= 256 + 3969
= 4225
c = √4225
c = 65
Use trigonometric identities to verify each expression is equal. sin(x)/1-cos(x)-cot(x)=csc(x)
Answer:
See Below.
Step-by-step explanation:
We want to verify the identity:
[tex]\displaystyle \frac{\sin x}{1 - \cos x} - \cot x = \csc x[/tex]
We can multiply the fraction by 1 + cos(x):
[tex]\displaystyle \frac{\sin x(1+\cos x)}{(1 - \cos x)(1+\cos x)} - \cot x = \csc x[/tex]
Difference of Two Squares:
[tex]\displaystyle \frac{\sin x(1+\cos x)}{1-\cos^2 x} - \cot x = \csc x[/tex]
From the Pythagorean Theorem, we know that sin²(x) + cos²(x) = 1. Rearranging, we acquire that sin²(x) = 1 - cos²(x). Substitute:
[tex]\displaystyle \frac{\sin x(1+\cos x)}{\sin^2 x} - \cot x = \csc x[/tex]
Cancel:
[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\cot x = \csc x[/tex]
Let cot(x) = cos(x) / sin(x):
[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\frac{\cos x}{\sin x} = \csc x[/tex]
Combine Fractions:
[tex]\displaystyle \frac{ 1 + \cos x - \cos x}{\sin x}= \csc x[/tex]
Thus:
[tex]\displaystyle \frac{1}{\sin x}=\csc x = \csc x[/tex]
Hence proven.
write a rational number between root2 and root3
Answer:
prational number between root2
A line goes through the points (1, -19), (-4,1), (0, -15), (2, -23). What is the slope and y-
intercept of the line
Answer:
Step-by-step explanation:
The y-intercept is super easy. The y-intercept exists when x = 0; therefore, the point given where x = 0 is found in (0, -15). That means that the y-intercept is -15. Easy enough. Now, the slope.
Since all these points are on the same line, using any 2 of them in the slope formula will get us the slope. I picked the first 2 points (1, -19) and (-4, 1):
[tex]m=\frac{1-(-19)}{-4-1}=\frac{1+19}{-5}=\frac{20}{-5}= -4[/tex]
The y-intercept is -15 and the slope is -4
A fair six-sided die is rolled 54 times. Theoretically, how many times should a roll of "5" occur?
-14
-9
There is no way to tell
-5
Answer:
9 times
Step-by-step explanation:
P("5") = 1/6
n("5") = 1/6 × 54 = 9
Answer:
9
Step-by-step explanation:
(the number of different possible outcomes) 1/6 * 54 = 9
Hope that this helps!
What is the coefficient of x4 in the expansion of (3x + 1)??
O 315
O 945
O 105
35
O 2,835
At the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 6 cheeses
Answer:
Diego can choose the 15 items in 128 different ways.
Step-by-step explanation:
Since at the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads, and he wants to use the Express Lane, so he can only buy 15 items, to determine how many ways can he choose which 15 items to buy if he wants all 6 cheeses the following calculation must be performed:
4 x 4 x 8 = X
16 x 8 = X
128 = X
Therefore, Diego can choose the 15 items in 128 different ways.
Three different design configurations are being considered for a particular component. There are two possible failure modes for the component. An engineer obtained the following data on the number of failures in each mode for each of the three configurations. Is there evidence to conclude that the configuration has an effect on the type of failure?
Failure Mode
1 2 3 4
Configuration 1 20 44 17 9
2 4 17 7 12
3 10 31 14 5
Answer:
No evidence .because the configurations factors and failure mode are independent
Step-by-step explanation:
Determine if there is sufficient evidence to conclude that configuration affects the type of failure
Number of configurations = 3
Number of failures = 4
assuming Pij represents proportion of items in pop i of the category j
H0 : Pij = Pi * Pj, I = 1,2,-- I, j = 1,2,---J
Hence the expected frequencies will be
16.10 , 43.58 , 18, 12.31
7.5, 19.37, 8 , 5.47
10.73, 29.05, 12, 8.21
x^2 = 13.25
test statistic = 14.44. Hence the significance level where Null hypothesis will be acceptable will be = 2.5%
Split 294x306, which identity is used to solve it?
Answer:
identity :- ( a + b ) ( a - b ) = a² - b ²
Answer :- 89,694
Step-by-step explanation:
Given : 294 × 306
split 294 × 306
294 × 306 = ( 300 - 6 ) × ( 300 + 6 )
Using Identity, ( a + b ) ( a - b ) = a² - b ² :
= ( 300 )² - ( 6 )²
= 90000 - 36
= 89,964
Hence, 294 × 306 = 89,694
Bianca recently bought a rope that is 25 yards long. Find the length in feet
Answer:
25 yards is equal to 75 ft
Answer:
75 feet
Step-by-step explanation:
1 yard=3ft
so 25 times 3 equals 75 feet :)
Prob and stats question help
Answer:
It is C
Step-by-step explanation:
Trust me, i got it right
Answer:
C
Step-by-step explanation:
have a great rest of your day!! btw Ill view ur profile!! :)
Suppose we want to choose 5 objects,without replacement from 16 distinct objects
Answer:
4368 ways
Step-by-step explanation:
We want to choose 5 objects,without replacement from 16 distinct objects.
We can use combination in this case. The formula for the combination is given by :
[tex]_{n}C_r=\dfrac{n!}{r!(n-r)!}[/tex]
We have, n = 16 and r = 5
So,
[tex]_{16}C_5=\dfrac{16!}{5!(16-5)!}\\\\_{16}C_5=\dfrac{16!}{5!11!}\\\\=4368[/tex]
So, there are 4368 ways in which we want to choose 5 objects,without replacement from 16 distinct objects.
Please help i need it
Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high? (Round your answer to two decimal places.)
Answer:
0.42ft/mn
Step-by-step explanation:
we have the following information to answer this question
dv/dt = 40 feet
height = 11 ft
volume = 1/3πr²h
= 1/3π(h/2)²h
= 1/3πh³/4
= πh³/12
dv/dt = π3h²/12
= πh²/4
dh/dt = 4/πh²dv/dt
= 4(40)÷22/7(11)²
= 160/380.29
= 0.42 ft/min
The height of the pile is therefore increasing by 0.42ft/min at a height of 11 feets
A company that manufactures vehicle trailers estimates that the monthly profit for selling its midsize trailer is represented by function p, where t is the number of trailers sold. p(t)= -25t^3+625t^2-2500t Use the key features of function p to complete these statements. The company makes a profit when it sells _____trailers. The maximum profit of approximately $____ occurs when it sells approximately____ trailers.
Answer:
The answer is below
Step-by-step explanation:
The profit equation is given by:
p(t)= -25t³+625t²-2500t
The maximum profit is the maximum profit that can be gotten from selling t trailers. The maximum profit is at point p'(t) = 0. Hence:
p'(t) = -75t² + 1250t - 2500
-75t² + 1250t - 2500 = 0
t = 2.3 and t = 14.3
Therefore t = 3 trailers and t = 15 trailers
p(15) = -25(15³) + 625(15²) - 2500(15) = 18750
Therefore the company makes a maximum profit of approximately $18750 when it sells approximately 15 trailers.
Answer:
See below
Step-by-step explanation:
Since t is number of trailers, the domain includes only those values greater than 0.
On the relevant domain, the graph crosses the x-axis at the points (5,0) and (20,0). Between these points, the value of p(t) is positive. So the company makes a profit when it sells between 5 and 20 trailers.
On the positive interval between these points, the graph reaches a relative maximum when t roughly equals 14 and p(t) roughly equals $19,000.
So the maximum profit of approximately $19,000 occurs when it sells approximately 14 trailers.
33. Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5
b. The constant is 2
C. The power is 10
d. The constant is 5
Answer:
Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5. ( true)
b. The constant is 2
C. The power is 10
d. The constant is 5
Help me out please???
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
DE being a midsegment means that D is a midpoint. Then BD = DA, or x = 5.
Gavin was thinking of a number. Gavin doubles it and adds 6.6 to get an answer of 9. Form an equation with
x
from the information.
Answer:
(9-6.6)÷2=x
Step-by-step explanation:
Do it in reverse from 9 all the way to x.
Answer:
(9-6.6)÷2=x
Step-by-step explanation: since you had 9 as the answer, start there. Then subtract 6.6. You then divide that number by 2 to get x
Find the median of the following data 9,15,17,18,6,20,8,5,18,18,10,5,14,12,10,7
Answer:
11
Step-by-step explanation:
first, sort the numbers from lowest to highest.
5,5,6,7,8,9,10,*10,12*,14,15,17,18,18,18,20
the median is the number in the middle of the data
average if you need to (10+12 and divide by 2)
The average car depreciates at a rate of 14% per year.
Mr. Wixted wants to buy a new sports car for $30,048.
At this rate of depreciation, what will the car be worth in 5 years?
Round your answer to the nearest hundredth.
A company's sales force makes 400 sales calls, with + 0.25 probability that a sale will be made on a call. What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made? Enter your answer as a decimal value, rounded to 4 decimal places.
Answer:
0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.
Step-by-step explanation:
We use the normal approximation to the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
A company's sales force makes 400 sales calls, with 0.25 probability that a sale will be made on a call.
This means that [tex]n = 400, p = 0.25[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 400*0.25 = 100[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.25*0.75} = \sqrt{75}[/tex]
What is the probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made?
Using continuity correction, this is [tex]P(55+0.5 \leq X \leq 75-0.5) = P(55.5 \leq X \leq 74.5)[/tex], which is the p-value of Z when X = 74.5 subtracted by the p-value of Z when X = 55.5.
X = 74.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{74.5 - 100}{\sqrt{25}}[/tex]
[tex]Z = -2.94[/tex]
[tex]Z = -2.94[/tex] has a p-value of 0.0016
X = 55.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.5 - 100}{\sqrt{25}}[/tex]
[tex]Z = -5.14[/tex]
[tex]Z = -5.14[/tex] has a p-value of 0
0.0016 - 0 = 0.0016
0.0016 probability that greater than 55 (exclusive) but less than 75 (exclusive) sales will be made.
Mark is hosting a "Who Dunnit?" party at his house. He plans on taping off a triangular section of his backyard to represent the crime scene. If the sides measure 23 feet, 15 feet, and 32 feet, how much tape will be needed? DO NOT ANSWER JUST TO STEAL MY POINTS!! AND NO CHICKEN NUGGETS!!!!
Answer:
70 feet
Step-by-step explanation:
as perimeter of triangle =
23+15+32= 70 feet
Answer:
Solution given:
side 1=23ft.
side 2=15ft
side 3=32ft
we have
perimeter=sum of all sides
=23+15+32=70ft
70ft tape will be needed.
If ∠1 = 3x, ∠2 = 5x + 18, and s ⊥ r, find m∠1.
I hope it will help you.
Answer:
x = 9
Step-by-step explanation:
angle <1 and angle <2 is complementary and their sum is 90 degrees
3x + 5x + 18 = 90 add like terms
8x + 18 = 90 subtract 18 from both sides
8x = 72 divide both sides by 8
x = 9 to find the measure of angle <1 replace x with the value we found
Express 0.1 as a percent.
HELPPP PLSSSSSSSSSSS
Answer:
45 + m<DBC = 180
Step-by-step explanation:
m<ABD + m<DBC = 180
45 + m<DBC = 180
Which statement is true about the function f(x) = negative StartRoot x EndRoot?
Answer:
It has the same domain and range as the function f(x) = StartRoot x EndRoot. It has the same range but not the same domain as the function f(x) = StartRoot x EndRoot. It has the same domain and range as the function f(x) = negative StartRoot negative x EndRoot.
Step-by-step explanation:
In the school chorus,
5/25 of the students are fourth-graders.
In simplest form, what fraction of the students in the school chorus are fourth graders?
Answer:
1/5 of the students are 4th graders
The probability that a person has blue eyes is 16%. Three unrelated people are selected at random. a. Find the probability that all three have blue eyes b. Find the probability that none of the three have blue eyes c. Find the probability that one of the three has blue eyes
Answer:
Step-by-step explanation:
All three have blue eyes.
P(1 has blue eyes) = 16/100 = 4/25
P(3 have blue eyes) = 4/25 * 4/25 * 4/25
P(3 have blue eyes ) = 64/15625
If you need the decimal answer, it is .004096
No one has blue eyes out of three
The probability for this is very large.
P(no blues) = 1 - 64/15625
P(no blues) = 15561/15625
If you need the decimal answer, it is 0.996
One has blue eyes (the other two do not).
P(1 has blue eyes) = 16/100 * 84/100*84/100
P(1 has blue eyes) = 112896/1000000
P(1 has blue eyes) = 0.112896
Help pls I need help
Answer:
From the origin , move 3 units to the right and 2 units up. B