Answer:
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Step-by-step explanation:
([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]
Remove the parenthesis by multiplying
[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]
This expression cannot be simplified further
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Hope this helps :)
Assume that when adults with smartphones are randomly selected, 57% use them in meetings or classes. If 8 adult smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes. The probability is
Answer:
≈ 0.2526
Step-by-step explanation:
The number of combinations of 4 out of 8:
8C4 = 8!/(4!(8-4)!)= 8*7*6*5/(1*2*3*4)= 70Success factor is:
57% = 0.57and failure factor is:
(100 - 57)%= 43%= 0.43Probability:
0.57⁴*0.43⁴*70 ≈ 0.2526Salema's score on a test was 80%. If the test was worth a total of 60 points, how many points did Salema earn?
Answer:
48
Step-by-step explanation:
Do 60*.80
60 represent the total points the test was worth
.80 represents the % number
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
100% = 60
80% = 48
The points Salema earned are 48 points.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Salema's score = 80%
Total score in the test = 60 points
Salema's score.
= 80% of 60 points
= 80/100 x 60
= 48
Thus,
The points Salema earned are 48 points.
Learn more about percentages here:
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Stephanie went to the shoe store and bought two pairs of flip-flops. One pair was $19.95, and the other was $23.55. If she has $50.00, how much will she have left after buying the shoes?
Answer:
$6.50
Step-by-step explanation:
First start by adding the prices of the pairs of shoes combined.
19.95+23.55=43.50
subtract the total price of both pairs of shoes from her total
50-43.50 = 6.50
HELP WHAT DOES THIS EVEN MEAN [CRY]
[tex]\\ \sf\longmapsto A=πr^2[/tex]
[tex]\\ \sf\longmapsto A=3.14(5)^2[/tex]
[tex]\\ \sf\longmapsto A=3.14(25)[/tex]
[tex]\\ \sf\longmapsto A=78.5cm^2[/tex]
What is the rectangular form of the polar equation?
0=-
57
y=x
V3
Oy= 32
y=-3x
Answer:
Option (1)
Step-by-step explanation:
From the picture attached,
tanθ = [tex]\frac{y}{x}[/tex]
Given : Polar equation as 'θ' = [tex]-\frac{5\pi }{6}[/tex]
Therefore, [tex]\text{tan}(-\frac{5\pi }{6} )[/tex] = [tex]\frac{y}{x}[/tex]
[tex]-\text{tan}(\frac{5\pi }{6} )[/tex] = [tex]\frac{y}{x}[/tex] [Since tan(-θ) = -tanθ]
[tex]\text{tan}(\pi -\frac{5\pi }{6} )[/tex] = [tex]\frac{y}{x}[/tex] [Since -tanθ = tan(π - θ)]
[tex]\text{tan}\frac{\pi }{6}[/tex] = [tex]\frac{y}{x}[/tex]
[tex]\frac{y}{x}=\frac{\sqrt{3}}{3}[/tex]
y = [tex]\frac{\sqrt{3} }{3}x[/tex]
Therefore, y = [tex]\frac{\sqrt{3} }{3}x[/tex] will be the rectangular form of the polar equation.
Option (1) will be the correct option.
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and the number of sit-ups a person can do (y). The results were: y = a+bx b = -0.89 a = 23.65 r2 = 0.7038 If a person watches 14 hours of television a day, predict how many sit-ups he can do. What is the value of the correlation coefficient? Round to three decimal places.
Answer:
y = 11.19 ; 0.839
Step-by-step explanation:
Given the following :
relationship between hours of TV watched per day (x) and the number of sit-ups a person can do (y)
y = a + bx ; comparing with the linear regression model function
y = predicted variable
a = intercept
b = slope or gradient
x = independent variable
b = -0.89 a = 23.65 r2 = 0.7038
Therefore, if a person watches for 14 hours per day, that is x = 14, the number of sit-ups he can do will be :
y = 23.65 + (-0.89)(14)
y = 23.65 - 12.46
y = 11.19
About 11 sit-ups.
If the r^2 value = 0.7038
Then the Coefficient of regression = r
Will be the square root of r^2
r = sqrt(r^2)
r = sqrt(0.7038)
r =0.8389278 = 0.839
evaluate -99 + 3^2•5
Answer:
= - 54
Step-by-step explanation:
- 99 + 3^2•5
- 99 + 9 × 5
- 99 + 45
= - 54
The area of a square is 36cm2. What are the dimensions of the square? You must show your work.
Answer:18
Step-by-step explanation:
because 36 is divided by 2 equals 18cm
Answer:
6cm x 6cm
Step-by-step explanation:
It's a square so the dimensions have to be the same (6x6 = 36). Even though 18 is a factor of 36, 18cm by 2cm would make a rectangle.
Robert owns two dogs. Each day, one dog eats
1/6 of a scoop of dog food and the other dog eats br
1/6 of a scoop. Together, how much dog food do
the two dogs eat each day? Write in simplest
form.
Answer:
1/3
Step-by-step explanation:
1) 1/6+1/6= 2/6
2) 2 and 6 can both be divide be 2.
2/2=1 and 6/2=3
Write the equations, after translating the graph of y = |x+2|: one unit up,
Answer:
y = |x + 2| + 1
Step-by-step explanation:
Parent Graph: f(x) = a|bx + c| + k
a is vertical stretch/shrink
b is horizontal stretch/shrink
c is horizontal movement left/right
k is vertical movement up/down
Since we are given an equation and we want to move it 1 unit up (vertical movement up), we only manipulate k:
y = |x + 2| + k
k = 1
y = |x + 2| + 1
Answer:
y = |x+2| + 1
Step-by-step explanation:
The equation will be y = |x+2| + 1.
By translating the graph one unit up, the equation will simply change by adding +1 to the graph, outside of the absolute value part.
apter 3 If a driver uses of a tank of gas every day, what fraction of a tank will he use in a) 3 days? b) 1 week? 21
You need to re copy and paste it, I can’t see the full possible answers/question.
A sound technician analyzes the audio feedback by placing a microphone at certain distances from a speaker. If the microphone is connected to the speaker, then the microphone senses 606060 decibels (\text{dB})(dB)left parenthesis, start text, d, B, end text, right parenthesis at a distance of 000 meters (\text{m})(m)left parenthesis, start text, m, end text, right parenthesis from the speaker with the decibel level decreasing by half of itself for every additional meter from the speaker. If the microphone is not connected to the speaker, then the microphone senses 30 \, \text{dB}30dB30, start text, d, B, end text at a distance of 0 \, \text{m}0m0, start text, m, end text from the speaker with the decibel level decreasing by 888 for every additional meter from the speaker. Three meters from the speaker, what is the difference between the decibel level when it is connected to the speaker versus when it is not connected to the speaker?
At three meters, the difference in the decibel level if and if not connected to the speaker is 1.5 dB
The reason for arriving at the above value is as follows:
The known parameters:
The audio sensed by the microphone when connected to the speaker are;
0 meters = 60 decibels
The level of the decibel decrease by half for each additional meter;
Therefore, when the microphone is connected to the speaker, we have;
[tex]\begin{array}{|c|cc|}\mathbf{Distance \ (m)}&&\mathbf{Sound \ (dB)}\\0&&60\\1&&30\\2&&15\\3&&7.5\end{array}\right][/tex]
If the microphone is not connected to the speaker, we have;
0 meters = 30 decibels
The level of the decibel decreasing by 8 dB for every additional meter from the speaker, therefore, when the microphone is not connected to the speaker we have;
[tex]\begin{array}{|c|cc|}\mathbf{Distance \ (m)}&&\mathbf{Sound \ (dB)}\\0&&30\\1&&22\\2&&14\\3&&6\end{array}\right][/tex]
At three meters from the speaker, the difference in the decibel level when it is connected and when it is not connected to the speaker is therefore;
Decibel level at 3 meters when connected, s₁ = 7.5 dB
Decibel level at 3 meters when not connected, s₂ = 6 dB
The difference in the decibel level = s₂ - s₁ = 7.5 dB - 6 dB = 1.5 dB
The difference in the decibel level when connected to the speaker and when not connected to the speaker is 1.5 dB
Learn more about sound level here:
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What is the perimeter of CDE?
A. 37.8 units
B. 39 units
C. 32.5 units
D. 35.6 units
This value is approximate.
=============================================================
Explanation:
To find the perimeter, we simply add up the lengths of the three external sides.
The horizontal side from D to E is 16 units long since |-10-6| = 16. I subtracted the x coordinates of the points and applied absolute value. You could also count out the spaces and you should count 16 spaces from D to E.
Unfortunately, the diagonal lengths aren't as straight forward. We have two options here: The pythagorean theorem, or the distance formula.
I'll go with the distance formula.
Let's find the distance from C to D, aka the length of side CD
[tex]C = (x1,y1) = (-1,-2)\\\\D = (x2,y2) = (-10,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-(-10))^2 + (-2-0)^2}\\\\d = \sqrt{(-1+10)^2 + (-2-0)^2}\\\\d = \sqrt{(9)^2 + (-2)^2}\\\\d = \sqrt{81 + 4}\\\\d = \sqrt{85}\\\\d \approx 9.2195\\\\[/tex]
Side CD is roughly 9.2195 units long.
Repeat this idea to find the length of CE
[tex]C = (x1,y1) = (-1,-2)\\\\E = (x2,y2) = (6,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-6)^2 + (-2-0)^2}\\\\d = \sqrt{(-7)^2 + (-2)^2}\\\\d = \sqrt{49 + 4}\\\\d = \sqrt{53}\\\\d \approx 7.2801\\\\[/tex]
Side CE is roughly 7.2801 units long
The perimeter of triangle CDE is approximately...
P = DE+CD+CE
P = 16 + 9.2195 + 7.2801
P = 32.4996
This then rounds to 32.5 units. The answer is choice C.
Find the slope of the line containing the points (2, 7) and (-5, -4).
the answer is 11/7.you can see the image
Answer:
[tex]\boxed {\boxed {\sf \frac{11}{7}}}[/tex]
Step-by-step explanation:
The slope describes the direction and steepness of a line. The formula is:
[tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]
Where (x₁, y₁) and (x₂, y₂) are the points the line contains. For this problem, the line contains the points (2,7) and (-5, -4). Therefore:
x₁= 2 y₁ = 7 x₂ = -5 y₂ = -4Substitute these values into the formula.
[tex]m= \frac{ -4 -7}{-5-2}[/tex]
Solve the numerator (-4 -7 = -11).
[tex]m= \frac{ -11}{-5-2}[/tex]
Solve the denominator (-5-2 = -7).
[tex]m= \frac{ -11}{-7}[/tex]
Simplify the fraction. The 2 negative signs cancel each other out.
[tex]m= \frac{11}{7}[/tex]
The slope of the line is 11/7
write each equation explicitly in terms of x. then indicate whether the equation is a function. y^2-x^2+1=50
Step-by-step explanation:
y² - x² + 1 = 50
y² = x² - 1 + 50 = x² + 49
y = ±sqrt(x² + 49)
this is not a function in that sense, as for every x there are not one but 2 y (result) values.
coefficient of 8x+7y
Answer:
8
Step-by-step explanation:
Identify the exponents on the variables in each term, and add them together to find the degree of each term.
8x→1
7y→1
The largest exponent is the degree of the polynomial.
1
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient of a polynomial is the coefficient of the leading term.
____________________________________________________________
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient in a polynomial is the coefficient of the leading term.
8
List the results.
Polynomial Degree: 1
Leading Term: 8x
Leading Coefficient: 8
Hope This Helps!!!
The function fix) = (x - 4)(x - 2) is shown.
What is the range of the function?
8
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
all real numbers greater than or equal to - 1
6
2
16
2
14
COL
40
8
G D
Answer:
The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1
Step-by-step explanation:
A cell phone company charges a monthly fee of $18 plus five cents for each call. A
customer's total cell phone bill this month is $50.50. Use n to represent the number of
calls.
Answer:
650 calls
Step-by-step explanation:
so since you have 18$ per month plus 5 cents per call you would do
18+0.5n(n represent the number of calls)= the total fee of $50.50 cents.
thus,now you need to figure out how much the phone calls were without the monthly fee so you would do:
50.50-18=32.50
so 32.50 is the price of all the phone calls
then you divide 32.50 by 0.05 which equals to 650
meaning that n=650
hope I helped!
Complete the function table.
Input (n) Output (n-2)
Answer: Choice C
This is because the input n = 2 leads to the output n-2 = 2-2 = 0
As another example: the input n = 4 leads to the output n-2 = 4-2 = 2
Whatever the input is, subtract 2 from it to get the output.
30 points!!!!!!
There are 6 red marbles, 9 blue marbles, and 10 green marbles in a bag.
What is the theoretical probability of randomly drawing a red marble and then a green marble?
10%
9.6%
64%
16%
Answer:
A or B depending on whether replacement takes place
Step-by-step explanation:
Without replacementprobability of getting a red marble=6/25
probability of getting a green marble (considering no replacement of marble drawn has taken place)=10/24
probability of randomly drawing a red marble and then a green marble=(6/25)*(10/24)=0.1=10%
With replacementprobability of getting a red marble=6/25
probability of getting a green marble (considering replacement of marble drawn has taken place)=10/25
probability of randomly drawing a red marble and then a green marble=(6/25)*(10/25)=0.096=9.6%
A research worker gave a scholastic aptitude test to a sample of eighth graders. Then he correlated the aptitude test scores with the chronological ages of the subjects. He found a correlation of - .42. How should this result be interpreted?
Answer: There is an moderate relationship between the aptitude test scores with the chronological ages of the subjects.
Step-by-step explanation:
The correlation coefficient tells about the strength and direction of the relation ship between any 2 variables. When the value of correlation coefficient lies between -0.5 to -0.3 or 0.3 to 0.5, then it indicates that there is moderate association between variables.Here , variables → aptitude test scores and chronological ages of the subjects.
Since correlation coefficient (-0.42) lies between -0.5 and -0.3 .
[-0.5< -0.42< -0.3]
That means there is an moderate relationship between the aptitude test scores with the chronological ages of the subjects.
Gerbils were used to assess the effect of Natural Neutral, a drug designed to reduce emotionality in high-drive people. Each of 20 gerbils spent 10 solitary minutes in an open field. The investigator recorded the number of fecal boluses for each animal. Then each animal was given an injection of Natural Neutral and the open field task was repeated.
No Drug Drug
mean number of boluse 6 8
standard deviation of boluses 2 2
The design of this study is:______
a. paired samples;
b. independent samples;
c. testing the significance of a correlation;
d. none of the other alternatives are correct.
Answer: a. paired samples;
Step-by-step explanation:
Paired samples are samples in which each data point in one sample is uniquely paired to a data point in the other sample.
Here, we have a paired sample of fecal boluses for gerbils by characterizing then as "No Drug" and "Drug".
hence, the design of this study is paired samples.
So, option A is correct.
NOTE : Independent samples are opposite of paired samples.
Testing the significance of a correlation require to check relation between two variables.
Simplify the expression (6^4)^2
When raising a power inside parentheses to another power, multiply the numbers:
(6^4)^2 = 6^(4x2) = 6^8
Simplified = 6^8
6^8 = 1679616
Answer:
[tex] \boxed{ \purple{ {6}^{8} }}[/tex]Step-by-step explanation:
[tex] \mathsf{ ( { {6}^{4}) }^{2} }[/tex]
It is the example of Power to power law of indices.
Multiply the exponents
⇒[tex] \mathsf{ {6}^{4 \times 2} }[/tex]
Multiply the numbers
⇒[tex] \mathsf{ {6}^{8} }[/tex]
-------------------------------------------------------
[tex] \mathsf{\orange{ \underline{ power \: to \: power \: law \: of \: indices}}}[/tex]
If [tex] \mathsf{ ({x}^{a} )^{b}} [/tex] is an algebraic term then [tex] \mathsf{( {x}^{a} ) ^{b} = {x}^{a \times b} }[/tex]
i.e When an algebraic term in the index form is raised to another index , the base is raised to the power of two indices.
Hope I helped!
Best regards!!
Week 4 Assignment: Solving Systems of Linear Equations by Eliminatio
Due Aug 2 by 11:59pm
Points 10
Submitting an external tool
Solve applications of systems of equations by elimination
Question
The sum of two numbers is -17. Their difference is 41. Find the numbers.
Sorry, that's incorrect. Try again?
I
10
-5
FEEDBACK
VIEW ANSWER
SUI
Content attribution
Answer:
The two numbers are 12 and -29
Step-by-step explanation:
Let x and y be the two numbers
x+y = -17
x - y = 41
Add the two equations together
x+y = -17
x - y = 41
----------------
2x = 24
Divide by 2
x = 12
Now find y
x+y = -17
12 +y = -17
Subtract 12 from each side
y = -17-12
y = -29
Nasa is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before the launch and has a diameter of 4.7 feet. What is the total weight in pounds?
Answer:
Step-by-step explanation:
How long will it take $3800 to grow into $5700 if it’s invested at 6% interest compounded continuously?
Answer: 25 years
Step-by-step explanation:
t = I / Pr
t = 5700 / ( 3800 × 0.06 ) = 25
t = 25 years
Nghiệm riêng của phương trình
y′′−y′=x2+x
có dạng
Answer:
i don't understand the question
Find the distance given the coordinates (-2, -1) & (-8, 7) in the simplest form
O 72
072
O 10
O 100
Find the product of all solutions of the equation (10x + 33) · (11x + 60) = 0
Answer:
18
Step-by-step explanation:
Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:
10x + 33 = 0 or 11x + 60 = 0
10x = -33 or 11x = -60
x = -33/10 or x = -60/11
Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.
A jet travels 500 kilometers in 40 minutes with a tail wind. Returning, the jet takes 50 minutes to cover the same distance. What is the rate of the plan and the speed of the wind?
Answer:
675 km/hr and 75 km/hr
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*(40/60)=500 and (x-y)*(50/60)=500. Solving it, we get x=675 and y=75