Answer:
[tex]\sqrt{2^5}[/tex]
Step-by-step explanation:
The applicable rule of exponents is ...
[tex]\displaystyle a^{b/c}=\sqrt[c]{a^b}[/tex]
So, ...
[tex]2^{5/2}=\boxed{\sqrt{2^5}}[/tex]
_____
This can be simplified to ...
[tex]\sqrt{32}=4\sqrt{2}[/tex]
Find the equation of the line given
the gradient
Parrallel to the line y= - 2x+4
point ( 1-3)
Answer:
y = -2x - 1
Step-by-step explanation:
Step 1: Find the parallel line
y = -2x + b
Step 2: Solve for b
-3 = -2(1) + b
-3 = -2 + b
b = -1
Step 3: Write parallel equation
y = -2x - 1
Find the volume of this cone.
Round to the nearest tenth.
10ft
8ft
[? ] ft
Answer:
V ≈ 670.2 [tex]ft^3[/tex]
Step-by-step explanation:
Use the formula of the volume of a cone, which is [tex]V=\pi r^{2} \frac{h}{3}[/tex]
Plug in your given components and solve for V:
[tex]V=\pi (8)^2\frac{10}{3} \\V=\pi (64)\frac{10}{3} \\V=\pi (64)(3.33)\\V=\pi (213.33)\\V=670.2[/tex]
(12 points) In Africa, the Joint United Nations Programme on HIV/AIDS determined that the probability that an individual adult in Africa has the disease is 0.05. Assume for any HIV test, the probability that the test result is positive given a real HIV carrier is 0.98, and the probability that the test result is positive given a healthy individual (i.e., a person who does not carry HIV virus) is 0.05. (a) (5 pts) What is the probability that a test result will be negative
Answer:
90.35% probability that a test result will be negative
Step-by-step explanation:
We have these following probabilities:
0.05 = 5% probability that an individual adult has the disease.
If the adult has the disease, 1 - 0.98 = 0.02 = 2% probability of a negative test.
1 - 0.05 = 0.95 = 95% probability that an individual adult does not have the disease.
If the adult does not have the disease, 1 - 0.05 = 0.95 = 95% probability of a negative test.
What is the probability that a test result will be negative
2% of 5% or 95% of 95%. So
p = 0.02*0.05 + 0.95*0.95 = 0.9035
90.35% probability that a test result will be negative
What is the equivalent to 2
Answer:
There are no choices on your question
Step-by-step explanation:
Maybe 2/1 or 4/2 or 10/5.
Question 10 of 32
1 Point
The standard form of the equation of a parabola is
y=1x2 - 4x +21. What is the vertex form of the equation?
O A. y =(x+4)2 +13
O B. y=2(x+4)2 +21
C. y = 2(x-4)2 + 21
D. y = -(x-4)? +13
i thinhk is C DONT NOW
Five times the sum of a number and 13 is 20. Find the number
Answer:
x = -9
Step-by-step explanation:
Step 1: Write out expression
5(x + 13) = 20
Step 2: Distribute
5x + 65 = 20
Step 3: Isolate x
5x = -45
x = -9
And we have our answer!
Answer:
-9
Step-by-step explanation:
Let the number be x.
5(x+13) = 20
Expand.
5x+65 = 20
Subtract 26 on both sides.
5x = 20 - 65
5x = -45
Divide 5 into both sides.
x = -45/5
x = -9
The number is -9.
2.86= ? teneh + 6 hundredth
Answer:
8
Step-by-step explanation:
Answer:
8 and 6.
Step-by-step explanation:
2.86 has tenths and hundredths place.
After the decimal point is the tenths place and after the tenths place is hundredths place.
The number 8 is the tenths place and the number 6 is in the hundredths place.
The diagram shows a circle, centre O.
Work out the value of a.
BCO=41 degrees
Answer:
a = 49°
Step-by-step explanation:
OB = OC ( both radii of the circle ), thus
Δ BOC is isosceles and the base angles are congruent, that is
∠ OBC = ∠ OCB = 41° , so
∠ BOC = 180° - (2 × 41)° = 180° - 82° = 98°
The angle on the circumference BAC is half the angle at the centre for angles subtended on the same arc , thus
a = 0.5 × 98° = 49°
If the measure of the angle ∠BOC will be 98°. Then the measure of the angle ∠BAC will be 49°.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The central angle is double the angle at the periphery that was subtended by the same chords.
The measure of the angle ∠BCO is 41°.
The angle ∠BCO and angle ∠CBO will be congruent. Because they are angles of an isosceles triangle.
We know that the sum of all the interior angles of the triangle will be 180°. Then the measure of the angle ∠BOC will be given as,
∠BOC + ∠CBO + ∠BCO = 180°
∠BOC + 41° + 41° = 180°
∠BOC = 98°
Then the measure of the angle ∠BAC will be
∠BAC = (1/2) ∠BOC
∠BAC = 1/2 x 98°
∠BAC = 49°
If the measure of the angle ∠BOC will be 98°. Then the measure of the angle ∠BAC will be 49°.
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ2
Please heeeelllllllpppppp
Answer:
point A90°CCWStep-by-step explanation:
a) All of the arcs show point A is the center of rotation.
__
b) The angle marked at point A is 90°.
__
c) The arrows indicate the direction of rotation is counterclockwise.
Use the end behavior of the graph to solve 3x^3+9x^2-12x < 0
Answer:
1. x = 4
2. x = -1
3. x = 0
Answer:
Step-by-step explanation:
If AD=BD, which of the following relationships can be proved and why?
B
o
A. A ACD= A BCD, because of ASA.
B. XACD N BOD because of SAS
C. There is not enough information to prove a relationship.
(D. A ACD S ABCD, because of AS
SUBMIT
< PREVIOUS
Answer: SAS
Step-by-step explanation:
There are 7 times as many female students as male students at a university. What fraction of the university are female
Let’s give total students a number. Let’s say there are 800 total students
Men = x
Women = 7x. ( 7 times more)
Together there are 8x students.( 7x + x)
We have 8 x = 800
Divide both sides by 8
X = 100
100 men
700 women
Now find the fraction which is number of women / total students = 700/800 = 7/8
7/8 of the students are women.
The remainder when 2x^2-x-5 divided by (x-3) is
Answer:
10
Step-by-step explanation:
2x^2-x-5= 2x^2-6x + 5x -15 +10= 2x(x-3) +5(x-3) + 10= (2x+5)(x-3) + 10
(2x^2-x-5)/(x-3)= 2x+5 + 10/(x-3)
So the remainder is 10
Write an equation in standard form for a line that passes through (2, 2) and (0, -3).
Answer:
y=(5/2)x-3
Step-by-step explanation:
slope of the line=(y2-y1)/(x2-x1)=(-3-2)/(0-2)=5/2
use any point to get the line:
y-(-3)=(5/2)(x-0)
y=(5/2)x-3
25x^4 +120x^2y +144y^2
Answer:
We can factor this into (5x+12y)^2
Step-by-step explanation:
The selection of a password of a computer account has the followingrestrictions: The password must be 6, 7, or 8 characters long. A charactercan be lower case letter or a decimal digit. The first character must be alowercase letter. Determine the total number of possible passwords with thegiven restrictions
Answer:
2,095,636,800,000 possible passwords.
Step-by-step explanation:
There are:
26 lower case characters.
10 decimal digits.
Passwords with 6 characters:
The first character must be a lower case letter, so 26 possible outcomes.
Any of the other 6 - 1 = 5, there are 36 possible options. So
[tex]T_{6} = 26*36^{5} = 1572120576[/tex]
Passwords with 7 characters:
Same logic as above, just the last 6 with 36 possible options. So
[tex]T_{7} = 26*36^{6} = 56596340736[/tex]
Passwords with 8 characters:
7 with 36 possible options
[tex]T_{8} = 26*36^{7} = 2037468300000[/tex]
Total:
[tex]T = T_{6} + T_{7} + T_{8} = 1572120576 + 56596340736 + 2037468300000 = 2095636800000[/tex]
2,095,636,800,000 possible passwords.
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. 2 4 6 8 10 12 14 amount of sugar (mg) 60 80 100 120 140 160 180 200 Frequency What is the sample size for this data set
Answer:
The sample size for the data set = 56
Step-by-step explanation:
The sample size or number of individuals (n) is gotten from a histogram by summing up the total frequencies of occurrences.
In this example, the frequencies are: 2 4 6 8 10 12 14
Therefore, the sample size (n) is calculated as follows:
n = 2 + 4 + 6 + 8 + 10 + 12 + 14 = 56
Therefore the sample size for the data set = 56
The sample size for the data set = 56
Given that,
Data was collected for a sample of organic snacks.The calculation is as follows:
= 2 + 4 + 6 + 8 + 10 + 12 + 14
= 56
Learn more: https://brainly.com/question/15622851?referrer=searchResults
Suppose the time it takes a barber to complete a haircuts is uniformly distributed between 8 and 22 minutes, inclusive. Let X = the time, in minutes, it takes a barber to complete a haircut. Then X ~ U (8, 22). Find the probability that a randomly selected barber needs at least 14 minutes to complete the haircut, P(x > 14) (round answer to 4 decimal places) Answer:
Answer:
[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]
And replacing we got:
[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]
The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714
Step-by-step explanation:
We define the random variable of interest as x " time it takes a barber to complete a haircuts" and we know that the distribution for X is given by:
[tex] X \sim Unif (a= 8, b=22)[/tex]
And for this case we want to find the following probability:
[tex] P(X>14)[/tex]
We can find this probability using the complement rule and the cumulative distribution function given by:
[tex] P(X<x) = \frac{x-a}{b-a} ,a \leq x \leq b[/tex]
Using this formula we got:
[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]
And replacing we got:
[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]
The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714
Two clinical trials were designed to test the effectiveness of laser treatment for acne. Seaton et al. (2003) randomly divided participants into two groups. One group received the laser treatment, whereas the other group received a sham treatment. Orringer et al. (2004) used an alternative design in which laser treatment was applied to one side of the face, randomly chosen, and the sham treatment was applied to the other side. The number of facial lesions was the response variable.
Orringer et al. used _______________ in a ___________ design.
Seaton et al. used a completely _____________design.
Answer:
Blocking in a paired design
Completed randomized design
Step-by-step explanation:
Orringer et. al used blocking in a paired design. He use the special type of randomized block design; a matched pair design wherein there is just two treatment conditions (laser treatment and the sham treatment) and the subjects are then group the subjects in pairs using the blocking variable which is a treatment applied to one side of face randomly chosen.
While Seaton et. al. used a completely randomized design. Here the subjects/participants are just merely assigned albeit randomly to either the laser or the sham treatment.
What is the slope-intercept form of the equation 6x-3y=18
Answer:
Step-by-step explanation:
Saying "put an equation into slope-intercept form" is another way of saying, "solve this equation for y". Not 6y or -3y...just plain old ordinary positive y. In order to begin that process, we need to first isolate the term that has the y in it. We do that by subtracting 6x from both sides to get
-3y = -6x + 18
Now, again, we are not solving for -3y, just y. We do that by dividing both sides by -3 to get
[tex]y=\frac{-6x}{-3}+\frac{18}{-3}[/tex]
Simplifying that gives us
y = 2x - 6
The is it mean, range, mode, or median of the following set of data is 6. 13, 7, 9, 5, 2, 3, 5, 4, 10, 12
the way you have laid this question out is strange but im assuming you want me to find the mean, range, medium and mode of the numbers provided?
Answer:median=order them and find the middle= 6
mean=add them all up and divide by the amount of numbers=(6+13+7+9+5+3+2+5+4+10+12)/11=6.9
range= the difference between the smallest and largest number=13-2=11
mode= the one that appears the most= 5
Assume that 1700 births are randomly selected and 4 of the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
Answer: Significantly low.
Step-by-step explanation:
Ok, we know that out of 1700 randomly selected, only 4 of them are girls.
Then the frequency is:
p = 4/1700
Now, using the subjective judgement (meaning that it is based on the opinion only, there is no real math involved)
I can conclude that the number of girls is significantly low, meaning that out of 1700 births we have 4 girls, then the other 1694 must be boys.
A student is given data that follows a normal distribution. According to the data, the mean amount of time that students spent reading outside of school each month was 10 hours, and the standard deviation was 2 hours. The student creates a normal distribution curve to model the situation and labels the curve so that 34% of the students fall in the range between 10 and 12 hours. Select the information that justifies the student's labeling.
a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.
b. Only 95% of the students will fall in the range of 10-2 and 10+2 hours
c. Only 68% of the students will fall in the range of 10-6 and 10+6 hours
d. Only 95%of the students will fall in the range of 10 -8 and 10 + 8 hours.
Answer:
a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.
Step-by-step explanation:
He appies the empirical 68-95-99.7 rule, where 68% of the data is expected to be within ne standard deviation from the mean, to the right and to the left.
Half of this (68%/2=34%) will be between the mean and one deviation standard to the right. This is between 10 hours and 10+2=12 hours.
The right answer is:
a. Only 68% of the students will fall in the range of 10- 2 and 10 + 2 hours.
Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Hey there! :)
Answer:
a. 3
b. -22
c. -2
d. -2
e. 5a + 8
f. a² + 6a + 3
Step-by-step explanation:
Calculate the answers by substituting the values inside of the parenthesis for 'x':
a. f(1) = 5(1) - 2 = 3
b. f(-4) = 5(-4) - 2 = -22
c. g(-3) = (-3)² + 2(-3) - 5 = 9 - 6 - 5 = -2
d. g(1) = 1² + 2(1) - 5 = 1 + 2 -5 = -2
e. f(a+ 2) = 5(a+2) - 2 = 5a + 10 - 2 = 5a + 8
f. g(a + 2) = (a + 2)² + 2(a + 2) - 5 = a² + 4a + 4 + 2a + 4 - 5 =
a² + 6a + 3
Two random samples were drawn from two employers to obtain information about hourly wages. Use the following information and the PopMeanDiff template to determine if there is a significant difference in wages across the two employers.
Kroger Wal-Mart
Sample size 80 60
Sample mean $6.75 $6.25
Population standard deviation $1.00 $0.95
The p-value is _____.
a. 0.0026
b. 0.0013
c. 0.0084
d. 0.0042
Answer:
a) 0.0026
P- value is 0.0026
Step-by-step explanation:
Step(i):-
Given data
first sample size n₁= 80
mean of the first sample x⁻₁= $6.75
Standard deviation of the first sample (σ₁) = $1.00
second sample size (n₂) = 60
mean of the second sample( x₂⁻) = $6.25
Standard deviation of the second sample (σ₂) = $0.95
step(ii):-
Test statistic
[tex]Z = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{\frac{(S.D)_{1} ^{2} }{n_{1} } +\frac{(S.D)_{2} ^{2} }{n_{2} } } }[/tex]
Null Hypothesis :H₀: There is no significant difference in wages across the two employers.
x⁻₁= x₂⁻
Alternative Hypothesis :H₁: There is significant difference in wages across the two employers.
x⁻₁≠ x₂⁻
[tex]Z = \frac{6.75 -6.25 }{\sqrt{\frac{(1^{2} }{80 } +\frac{((0.95)^{2} }{60} } }[/tex]
Z = 3.01
P- value:-
Given data is two tailed test
The test statistic Z = 3.01
First we have to find the Probability of z-statistic
P(Z>3.01) = 1- P( z <3.01)
= 1- (0.5 + A(3.01)
= 0.5 - A(3.01)
= 0.5 - 0.49865 ( from normal table)
= 0.0013
P(Z>3.125) = 0.0013
Given two tailed test
P- value = 2 × P( Z > 3.01)
= 2 × 0.0013
= 0.0026
Final answer:-
The calculated value Z = 3.125 > 1.96 at 0.05 level of significance
null hypothesis is rejected
Conclusion:-
P- value is 0.0026
Find the value of each variable
Answer:
To find a we use sine
sin 60° = a / 4√3
a = 4√3sin60°
a = 6
To find b we use sine
sin 45° = a / b
a = 6
b = 6 / sin 45°
b = 6√2
To find c we use cosine
cos 60° = c / 4√3
c = 4√3 cos 60°
c = 2√3
To find d we use tan
tan 45° = a / d
a = 6
d = 6 / tan 45°
d = 6
Therefore a = 6 b = 6√2 c = 2√3
d = 6
That's option A.
Hope this helps
F(x)=(x+1)(x-3)(x-4)
Answer :
x1 = -1
x2= +3
x3 = +4
I hope it helps
If you are doing it by roots how ever it would be 3
a particular city had a population of 24,000 in 1900 and a population of 29,000 in 1920. Assuming that its population continues to grow exponentially at a constant rate, what population will it have in 2000
Answer:
It will have a population of 61,779 in 2000.
Step-by-step explanation:
The population for the city, in t years after 1900, can be modeled by a exponential function with constant growth rate in the following format:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the population in 1900 and r is the growth rate.
Population of 24,000 in 1900
This means that [tex]P(0) = 24000[/tex]
Population of 29,000 in 1920.
1920 is 1920 - 1900 = 20 years after 1900.
This means that P(20) = 29000. So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]29000 = 24000(1+r)^{20}[/tex]
[tex](1+r)^{20} = \frac{29000}{24000}[/tex]
[tex]\sqrt[20]{(1+r)^{20}} = \sqrt[20]{\frac{29000}{24000}}[/tex]
[tex]1 + r = 1.0095[/tex]
So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]P(t) = 24000(1.0095)^{t}[/tex]
What population will it have in 2000
2000 is 2000 - 1900 = 100 years after 1900. So this is P(100).
[tex]P(t) = 24000(1.0095)^{t}[/tex]
[tex]P(100) = 24000(1.0095)^{100} = 61779[/tex]
It will have a population of 61,779 in 2000.
Which of the following equations describes the line shown below? Check all
that apply.
Answer:
Correct options are F and D.
Step-by-step explanation:
First, the slope. 5-(-5)/-4-1
This can be simplified to 10/-5, or -2.
Y intercept: (0, -3).
Slope intercept form: y=-2x-3
Point slope: y-5=-2(x+4) or y+5=-2(x-1)
PLEASE ANSWER, URGENT!!! In a math exam, Zach, Wendy, and Lee have an average score 91. Wendy, Lee and Chen have an average score 89. Zach and Chen have an average score 95. What is Zach's score?
Answer:
98
Step-by-step explanation:
Z as Zach; W as Wendy; L as Lee; C as Chen
We know that average score of Z,W, and L is 91, so:
(z + w + l)/3 = 91
z + w + l = 273
Average score W, L, C = 89, so:
(w + l + c)/3 = 89
w + l + c = 267
We take both:
(z + w + l) – (w + l + c) = 273 – 267
z – c = 6
Average score Z and C = 95
(z + c)/2 = 95
z + c = 190
(z + c) – (z – c) = 184
2c = 184
c = 92
z + c = 190
z + 92 = 190
z = 98
So, Zachs score is 98