Answer:
[tex]x = \sqrt{-2} = 2i[/tex]
Step-by-step explanation:
[tex]5x^2-2=-12[/tex]
[tex]5x^2 =-10[/tex]
[tex]x^2 =-2[/tex]
[tex]x = \sqrt{-2} = 2i[/tex]
help me pleaseeeeeeeeeeeeeeeeee………….
Answer:
d
Step-by-step explanation:
because u did the math for you
^ means to the power, / indicationg fraction.
PLEASE IF YOU CAN ANSWER AND EXPLAIN TYVM!
1. simplify. 32^2/5. 32 raised to the power of 2 over 3(fraction)
27. the function f is definded below
f(x) = x^2+x-30/ x^2-10x+21
find all variables that are NOT in the domain of f
13. factor the following expression
16vx^3y^4+28v^5x^6
8. simplify, write answer without parentheses
(w^2/-3v^4)^2
24. solve for x 8=3/x-2
11. solve the following ewuation for R
Q=i^2Rt/J
16. solve for v
5v^2=-21v-4
Answer:
udirkkdjdjdjehdhebhgwdxddrergghg
19. In a random sample of 250 students, we found that 75 work out 4 or more times a week. Find the 95% confidence interval for the proportion of students who work out 4 or more times a week.
Answer:
The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
In a random sample of 250 students, we found that 75 work out 4 or more times a week.
This means that [tex]n = 250, \pi = \frac{75}{250} = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.2432[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.3568[/tex]
The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).
The probability that a certain hockey team will win any given game is 0.3773 based on their 13 year win history of 389 wins out of 1031 games played (as of a certain date). Their schedule for November contains 12 games. Let X = number of games won in November.
Find the probability that the hockey team wins at least 3 games in November. (Round your answer to four decimal places.)
Answer:
0.8895 = 88.95% probability that the hockey team wins at least 3 games in November.
Step-by-step explanation:
For each game, there are only two possible outcomes. Either the teams wins, or they do not win. The probability of the team winning a game is independent of any other game, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability that a certain hockey team will win any given game is 0.3773.
This means that [tex]p = 0.3773[/tex]
Their schedule for November contains 12 games.
This means that [tex]n = 12[/tex]
Find the probability that the hockey team wins at least 3 games in November.
This is:
[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]
In which:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.3773)^{0}.(0.6227)^{12} = 0.0034[/tex]
[tex]P(X = 1) = C_{12,1}.(0.3773)^{1}.(0.6227)^{11} = 0.0247[/tex]
[tex]P(X = 2) = C_{12,2}.(0.3773)^{2}.(0.6227)^{10} = 0.0824[/tex]
Then
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0034 + 0.0247 + 0.0824 = 0.1105[/tex]
[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1105 = 0.8895[/tex]
0.8895 = 88.95% probability that the hockey team wins at least 3 games in November.
A survey of high schools within a district revealed that for ninth graders, 38% 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?
0.30
O 0.32
O 0.62
O 0.68
Answer:
0.30
Step-by-step explanation:
Find the probability by adding the probabilities together for having two and four honors classes.
25% offer two honors classes and 5% offer four honors classes. Add these together:
25 + 5
= 30
So, there is a 30% probability that the school offers an even number of honors classes.
The correct answer is 0.30.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the equation below. The value of x in terms of b is . The value of x when b is 3 is .
Answer: x=-3/3=-1
Step-by-step explanation:
To solve for x in terms of b, simply treat b as a number, and solve for x as usual: first of all, we expand the left hand side:
-2bx+10=16
Subtract 10 from both sides:
-2bx=6
Divide both sides by -2b:
x=6/-2b=-3/b
This means that in particular, if we set b=3 , we have
x=-3/3=-1
help help HELP!! will give brainliest
If f(x) = x², g(x) = 5x, and h(x) = x + 4, find each value.
Find h[f(4)].
Answer:
[tex]h(f(4))=20[/tex]
Step-by-step explanation:
We are given the functions:
[tex]f(x)=x^2,\, g(x)=5x\text{, and } h(x)=x+4[/tex]
And we want to find
[tex]h(f(4))[/tex]
Find f(4) first:
[tex]f(4)=(4)^2=16[/tex]
Thus:
[tex]h(f(4))=h(16)[/tex]
Now, evaluate h(16):
[tex]h(16)=(16)+4=20[/tex]
Hence:
[tex]h(f(4))=20[/tex]
Help please
The cost, c(x), for parking in a hospital lot is given by c(x) = 5x + 3.00, where x is the number of hours. What does the slope mean in this situation?
Answer:
The slope is the cost per hour.
$5 per hour
match the description in column a to its corresponding word in column b.
help me plsssss
Answer:
1-a
2-h
3-g
4-d
5-c
6-j
7-f
8-k
9-b
10-i
numbers are column A and alphabets are column B!
Using the digits 2 through 8, find the number of different 5-digit numbers such that, digits can be used more than once.
Answer:
7 digits can be used for each position
There are a total of 5 positions
N = 7^5 = 16,807 numbers
You have 7 choices for the first position, second position, etc.
Find the areas in that unit square PQRS, P(4,3), Q(4,1), S(-1,3), R(-1,1)
Answer:
Step-by-step explanation:
P(4,3), Q(4,1), S(-1,3), R(-1,1)
[tex]Distance =\sqrt{(x_{2}-x_{1})^{2}+(y_{2} -y_{1})^{2}}\\\\PQ= \sqrt{(4-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-2)^{2}}\\\\\=\sqrt{4}\\\\=2 \ units\\\\\\QS=\sqrt{(-1-4)^{2}+(3-1)^{2}}\\\\=\sqrt{(-5)^{2}+(2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\ units\\\\\\SR =\sqrt{(-1-[-1])^{2}+(1-3)^{2}}\\\\=\sqrt{(-1+1)^{2}+(-2)^{2}}\\\\=\sqrt{0+4}\\\\= \sqrt{4}\\\\= 2 \\\\\\PR = \sqrt{(-1-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-5)^{2}+(-2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\\\\[/tex]
PQRS is a rectangle
Area= length *breadth
= 2 * √29
= 2√29 sq.units
A right rectangular prism has a length of 2 1/4 cm, width of 8 cm, and height of 20 1/2 cm.
What is the volume of the prism?
Enter the answer in the box.
cm³
Answer:
369 cm^3
Step-by-step explanation:
you just multiply all the numbers together
Answer:
369 cm³.
Step-by-step explanation:
Volume of a rectangular prism is just length × width × height. So:
2.25 × 8 = 18
18 × 20.5 = 369
So, the volume is 369 cm³.
Quadrilateral A'B'C'D'A
′
B
′
C
′
D
′
A, prime, B, prime, C, prime, D, prime is the result of dilating quadrilateral ABCDABCDA, B, C, D about point AAA by a scale factor of \dfrac{1}{2}
2
1
start fraction, 1, divided by, 2, end fraction.
Answer:
[tex]A' = (2,0)[/tex]
Step-by-step explanation:
Given
See attachment for ABCD
[tex]k = \frac{1}{2}[/tex] --- the scale factor
Required
The coordinates of A'
From the attachment, we have:
[tex]A = (4,0)[/tex]
So:
[tex]A' = k * A[/tex]
[tex]A' = \frac{1}{2} * (4,0)[/tex]
[tex]A' = (2,0)[/tex]
Answer:
on khan, both are false
Step-by-step explanation:
The lifespan, in years, of a certain computer is exponentially distributed. The probability that its lifespan exceeds four years is 0.30. Let f(x) represent the density function of the computer's lifespan, in years, for x>0. Determine an expression for f(x).
Answer:
The correct answer is "[tex]0.300993e^{-0.300993x}[/tex]".
Step-by-step explanation:
According to the question,
⇒ [tex]P(x>4)=0.3[/tex]
We know that,
⇒ [tex]P(X > x) = e^{(-\lambda\times x)}[/tex]
⇒ [tex]e^{(-\lambda\times 4)} = 0.3[/tex]
∵ [tex]\lambda = 0.300993[/tex]
Now,
⇒ [tex]f(x) = \lambda e^{-\lambda x}[/tex]
By putting the value, we get
[tex]=0.300993e^{-0.300993x}[/tex]
Find the value of x in each case:
A screw manufacturer makes specialized tiny screws that are 15mm long. The manufacturing process does not make every screw exactly 15mm long. The lengths of the screws are normally distributed with mean 15mm and standard deviation 0.04mm. To test for quality control, 36 screws are to be measured. What is the probability that a sample mean is less than 14.99mm?
Answer:
The probability that a sample mean is less than 14.99mm=0.066808
Step-by-step explanation:
We are given that
Mean,[tex]\mu=15 mm[/tex]
Standard deviation,[tex]\sigma=0.04 mm[/tex]
n=36
We have to find the probability that a sample mean is less than 14.99mm.
We know that
[tex]P(\bar{x}<a)=P(Z<\frac{\bar{x}-a}{\frac{\sigma}{\sqrt{n}}})[/tex]
Using the formula
[tex]P(\bar{x}<14.99)=P(Z<\frac{14.99-15}{\frac{0.04}{\sqrt{36}}})[/tex]
[tex]P(\bar{x}<14.99)=P(Z<-1.5)[/tex]
=[tex]1-P(Z\geq -1.5)[/tex]
[tex]=1-0.93319[/tex]
=0.066808
Hence, the probability that a sample mean is less than 14.99mm=0.066808
How would I simplify the expressions on the picture?
Answer:
7. [tex]x^{11}[/tex] 8. [tex]y^{2}\\[/tex] 9. [tex]p^{12}[/tex] 10.[tex]a^{3} b^{2}[/tex] 11.[tex]g^{16}[/tex] 12.[tex]r^{9} h^{3}[/tex] 13.[tex]m^{15} p^{6}[/tex] 14.[tex]k^{6} y[/tex] 15.[tex]x^6 z^4[/tex]
Step-by-step explanation:
7. [tex]x^3[/tex] × [tex]x^8[/tex] = [tex]x^{11}[/tex] when multiplying with exponents you add
8. [tex]\frac{y^{6} }{y^{4} }[/tex] = [tex]y^{2}[/tex] when dividing with exponents you subtract
9. [tex](p^{3})^4[/tex] = [tex]p^{12}\\[/tex] when it's power to power, you multiply
10. [tex]\frac{a^{9} b^{4}}{a^{6} b^{2}}[/tex] = [tex]a^{3} b^{2}[/tex] (subtract exponents)
11. [tex](g^{8})^2[/tex] = [tex]g^{16}[/tex] (multiply exponents)
12. [tex]r^{4} h^{2} r^{5} h[/tex] = [tex]r^{9} h^{3}[/tex] (add exponents [tex]r^4 + r^5\\[/tex] and [tex]h^2 +h^1\\[/tex] )
13. [tex](m^{5} p^{2})^3[/tex] = [tex]m^{15} p^{6}[/tex] (multiply exponents)
14. [tex]\frac{k^{7} y^{4}}{y^{3}k}[/tex] = [tex]k^{6} y[/tex] (subtract exponents [tex]k^7-k^1[/tex] and [tex]y^4-y^3\\[/tex] )
15. [tex]x^3 z^2 x^3 z^2[/tex] = [tex]x^6 z^4[/tex] (add exponents same as #12)
Assume that $4,000 I deposited into an investment account doubled in value over a six year period. What annual interest rate must I have earned over this period? Is the initial amount of the deposit relevant to the calculation of the annual interest rate? Why or why not?
Answer:
Interest rate is about 12.246%
The initial deposit doesn't matter because when you divide both sides by the initial deposit you're always left with (1+i)ⁿ=2
Step-by-step explanation:
[tex]4000(1+i)^6=8000\\(1+i)^6=2\\1+i=\sqrt[6]{2} \\1+i=1.122462048\\i=.12246[/tex]
Divide the following complex numbers:
[tex](2 + i) \div (1 - 4i)[/tex]
Answer:
[tex]-\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
Step-by-step explanation:
[tex] (2 + i) \div (1 - 4i) = [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} [/tex]
[tex] = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i} [/tex]
[tex] = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)} [/tex]
[tex] = \dfrac{2 + 8i + i + 4i^2}{1 + 16} [/tex]
[tex] = \dfrac{2 + 9i - 4}{17} [/tex]
[tex] = \dfrac{-2 + 9i}{17} [/tex]
[tex]= -\dfrac{2}{17} + \dfrac{9}{17}i[/tex]
find the first three common multiplies
6 and 8
Answer:
24,48,72
Step-by-step explanation:
multiples of 6- 6,12,18,24,30,36,42,48,54,60,66,72
multiples of 8- 8,16,24,32,40,48,56,64,74,80
Use quadratic regression to find the
equation for the parabola going
through these 3 points.
(-4, 7) (6, -33) (10, -105)
HELP PLZ
Answer:
[tex]y= -x^{2} -2x+15[/tex]
Step-by-step explanation:
[tex]y= -x^{2} -2x+15[/tex]
Solve the expression using the correct order of operations.
0.75x3.2+ (9.1)2-((-2.3)-(-0.9))2
Answer:
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]
Step-by-step explanation:
Given
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2[/tex]
Required
Solve
Start with the bracket
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ (9.1)^2-(-1.4)^2[/tex]
Evaluate all exponents
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ 82.81-1.96[/tex]
Evaluate all products
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 2.4+ 82.81-1.96[/tex]
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]
Lightbulbs. A company produces lightbulbs. We know that the lifetimes (in hours) of lightbulbs follow a bell-shaped (symmetric and unimodal) distribution with a mean of 7,161 hours and a standard deviation of 564 hours. Use the Empirical Rule (68-95-99.7 rule) to answer the following question: The shortest lived 2.5% of the lightbulbs burn out before how many hours
Answer:
Please find the complete question and its solution in the attached file.
Step-by-step explanation:
Shortest had survived after 6741 hours [tex]2.5\%[/tex] of the lights burnt.
[tex]\to 0.15\% + 2.35\% = 2.50\%[/tex]
What is the mean?
7.9.10.12.15.16
Answer:
11.5
Step-by-step explanation:
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Answer:
11.5
Step-by-step explanation:
Add all them all together.
7+9+10+12+15+16=69
Divide by the amount of numbers there are
69/6=11.5
11.5
You are charged $9.33 total for a meal, assume the 7% sales tax, how much was the menu price of this item?
I have already tried
$8.68
$8.71
$8.67
all were wrong
Answer:
$8.71.
Step-by-step explanation:
Given that you are charged $ 9.33 total for a meal, assuming the 7% sales tax, to determine how much was the menu price of this item, the following calculation must be performed:
100 + 7 = 107
107 = 9.33
100 = X
100 x 9.33 / 107 = X
933/107 = X
8.71 = X
Therefore, the menu price of this item was $ 8.71.
If a seed is planted, it has a 90% chance of growing into a healthy plant. If 12 seeds are planted, what is the probability that exactly 2 don't grow
Answer:
0.2301 = 23.01% probability that exactly 2 don't grow.
Step-by-step explanation:
For each seed planted, there are only two possible outcomes. Either it grows into a healthy plant, or it does not. The probability of a seed growing into a healthy plant is independent of any other seed, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
90% chance of growing into a healthy plant.
This means that [tex]p = 0.9[/tex]
12 seeds are planted
This means that [tex]n = 12[/tex]
What is the probability that exactly 2 don't grow?
So 12 - 2 = 10 grow, which is [tex]P(X = 10)[/tex]. Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{12,10}.(0.9)^{10}.(0.1)^{2} = 0.2301[/tex]
0.2301 = 23.01% probability that exactly 2 don't grow.
is there a formula for this?
help asap!!
Answer:
yes
Step-by-step explanation:
the answer is c well thats what my teacher said
Answer:
B
Step-by-step explanation:
using sine rule
[tex] \frac{y}{sin \: 45} = \frac{5}{sin \: 45} \\ y = 5[/tex]
using sin rule
[tex] \frac{x}{sin \: 90} = \frac{5}{sin \: 45} \\ \\ 5sin90 = xsin45 \\ \\ x = \frac{5 \: sin \: 90}{sin \: 45} \\ x = \frac{5}{0.7071} \\ x = 7.071[/tex]
x=5√2
A student-faculty government committee of 4 people is to be formed from 20 student
volunteers and 5 faculty volunteers.
a. If one person from the group of volunteers is chosen at random to draw the names
out of a hat, what is the probability that the person drawing the names is a student?
b. How many ways can the committee of four be formed if there are no restrictions on
composition.
C. How many ways can two of the students be chosen?
d. How many ways can 2 faculty be chosen?
e. What is the probability that the random selection of the four-person committee will
result in two students and two faculty?
the answer is c i just had this question your welcome
Finding the Coordinates of the Image On a coordinate plane, the center of dilation is at (0, 0). Triangle A B C is dilated to create triangle A prime A C prime. The points of A B C are (negative 3, 3), (negative 1, 1), and (negative 3, 1). The points of A prime A C prime are (negative 9, 9), (negative 3, 3), and (negative 9, 3). The dilation DO,3 (x, y) → (3x, 3y) is performed on the pre-image △ABC to make a similar triangle. Which statements are true? Check all that apply. ∠A corresponds to ∠A'. ∠A'AC' corresponds to ∠B. CB corresponds to C'A. Segment A'A is parallel to segment C'C. △ABC ~ △A'AC'.
Answer:
- A corresponds to A’
- A’AC’ corresponds to B
- CB corresponds to C’A
- ABC ~ A’AC’
Step-by-step explanation:
the old building at the back of the school is badly in need of repair. the company Hsa and the executive are planning to renovate the building to accommodate a new music room. There are 15 rooms in the building and the dimension of the rooms to be redone with tiles are 6m long and 4 m wide. ted the tile man has 500 one meter square tiles.
Explain how you would estimate whether Ted has enough tiles to cover all the kitchen floors in the entire apartment building?
How many tiles, each measuring 1 square meter, are needed to cover one room floor?
How many tiles are needed to cover all the floors in the entire building? Show your work?
Answer:
a. If the area of the tiles is greater than or equal to the area of all the rooms.
b. 24
c. 360
Step-by-step explanation:
a. Explain how you would estimate whether Ted has enough tiles to cover all the kitchen floors in the entire apartment building?
Ted would have enough tiles if the area of the tiles is greater than or equal to the area of all the rooms. Since we have 500 one meter square tiles, we have 500 m² of tiles.
Since the rooms are 6 m long and 4 m wide, the area of each room is 6 m × 4 m = 24 m². Since there are 15 rooms, the area of all the rooms is 15 × 24 m² = 360 m².
Since the area of the tiles = 500 m² is greater than the area of the rooms = 360 m², Ted would have enough tiles to cover all kitchen floors in the entire apartment building.
b. How many tiles, each measuring 1 square meter, are needed to cover one room floor?
Since the area of each room floor is 24 m² and the area of each tile is 1 m², so the number of 1 square meter tiles needed to cover each floor is n = area of floor/area of tile = 24 m²/1 m² = 24.
c. How many tiles are needed to cover all the floors in the entire building?
Since 24 tiles are needed to cover each floor and there are 15 rooms in the building, we would require 24 tiles/room × 15 rooms/building = 360 tiles.
So we require 360 tiles.
