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Explanation:
We have something of the form [M*N]^2 where M = 3 and N = (2a)^(3/2)
Squaring the M leads to M^2 = 3^2 = 9
Squaring the N leads to N^2 = (2a)^3 = 8a^3
Notice how the fractional exponent goes away. The denominator '2' cancels with the '2' from the squaring operation
In other words, the rule is [tex]\left(x^{1/2}\right)^2 = x[/tex] where x is nonnegative.
A more general form of the rule is [tex]\left(x^{p/2}\right)^2 = x^p[/tex]
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After squaring M and N, we then get to
[MN]^2 = M^2*N^2 = 9*8a^3 = 72a^3
So that shows why choice B is the answer.
A salesperson at a jewelry store earns 4% commission each week. Last week, Heidi sold $680 worth of jewelry. How much did make in commission? How much did the jewelry store make from sales?
Answer:
$27.2
Step-by-step explanation:
680x0.04=. 27.2
She made $27.2 last week
A 35 foot ladder is set against the side of the house so it reaches up 21 feet if the ladder at its base and pulls it 4 feet farther from the house how far up the side of the house will the ladder reach now
Answer:
=14.2
Step-by-step explanation:
a^2 + b^2 = c^2
21 ^2 + x ^2 = 35^2
= 28
28 + 4 = 32
The side with 21 then becomes the new x
x/a =
=14.2
The height of the house that can be ladder reached now will be 14.18 feet.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
A 35-foot ladder is set against the side of the house so it reaches up 21 feet.
Then the base length will be
35² = 21² + b²
1225 = 441 + b²
b² = 784
b = 28 feet
If the ladder is at its base and pulls it 4 feet farther from the house.
Then the height of the house that can be ladder reach now will be
35² = 32² + h²
1225 = 1024+ h²
h² = 201
h = 14.18 feet
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
#SPJ2
which choices is equivalent to the product below ? 2.3.6
Answer:
What product
Step-by-step explanation:
Write the percent of the figure that is shaded.
PLEASE HELP ILL GIVE EXTRA POINTS!!!
Answer:
so the total is 20 and its at ten so
10/20=5/10=1/2
so 50 percent
plzzz brainlest
Please help with 15, 17 and 19
Given:
15. [tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)[/tex]
17. [tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)[/tex]
19. [tex]2^{\log_2100}[/tex]
To find:
The values of the given logarithms by using the properties of logarithms.
Solution:
15. We have,
[tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)[/tex]
Using property of logarithms, we get
[tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)=1[/tex] [tex][\because \log_aa=1][/tex]
Therefore, the value of [tex]\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)[/tex] is 1.
17. We have,
[tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)[/tex]
Using properties of logarithms, we get
[tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-\log_{\frac{3}{4}}\left(\dfrac{3}{4}\right)[/tex] [tex][\because \log_a\dfrac{m}{n}=-\log_a\dfrac{n}{m}][/tex]
[tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-1[/tex] [tex][\because \log_aa=1][/tex]
Therefore, the value of [tex]\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)[/tex] is -1.
19. We have,
[tex]2^{\log_2100}[/tex]
Using property of logarithms, we get
[tex]2^{\log_2100}=100[/tex] [tex][\because a^{\log_ax}=x][/tex]
Therefore, the value of [tex]2^{\log_2100}[/tex] is 100.
What is the value of the upper quartile?
Which figure has at least one line of symmetry?
Answer:
the second green shape because the first one is a rectangle which has 2 equal sides
Answer:
the third orange one
Step-by-step explanation:
i have the same question and these 2 show up as answers on both so it has to be this one
Please help me with my math answer
Step-by-step explanation:
20 ml is your answer
i hope it helps u
Answer:
If I'm reading it correctly the answer should be 20.
To get that answer all you do is 4x5.
If using the method of completing the square to solve the quadratic equation x^2+8x+11=0, which number would have to be added to "complete the square"?
Answer:
4
Step-by-step explanation:
x²+8x+11=0
x²+8x+(+4)²-(+4)²+11=0
Answer:
16
Step-by-step explanation:
x2+8x= −11−11
28=4→(4)2=16
x2+8x+16=x2+8x+16= −11+16−11+16
(x+4)2= 55
16
A submarine sits at –300 meters in relation to sea level. Then it descends 115 meters. What is its new position in relation to sea level?
Answer:
-415 meters
Step-by-step explanation:
As it was already -300 and it decended even more
so:
-300-`115=-415
Answer:
The answer is A, -415 meters.
Step-by-step explanation:
All right, so the key words we need here are -300, descends, and 115.
Descends means go lower, or in this case, subtract.
We are already at -300 and we descend 115, so we are going to subtract.
Subtracting a number is the same as adding the negative of that number.
-300 + -115 = -415
The answer is A, -415 meters.
Hope this helps, please mark brainliest if possible. :)
In ΔVWX, the measure of ∠X=90°, XW = 65, WV = 97, and VX = 72. What is the value of the cosine of ∠V to the nearest hundredth?
Answer:
The cosine of ∠V is of 0.74.
Step-by-step explanation:
Relations in a right triangle:
The cosine of an angle is given by the length of the adjacent side divided by the length of the hypotenuse.
XW = 65, WV = 97, and VX = 72.
[tex]\sqrt{65^2+72^2} = 97[/tex], and thus, this is a right triangle.
What is the value of the cosine of ∠V to the nearest hundredth?
The hypotenuse is the largest side, that is, WV = 97.
The adjacent side of angle V is VX = 72. So
[tex]\cos{B} = \frac{72}{97} = 0.74[/tex]
The cosine of ∠V is of 0.74.
hey besties, I need help
Answer:
C
Step-by-step explanation:
[tex]\frac{2}{3} (x + 2) - \frac{1}{3} (x - 2)[/tex]
First, multiply [tex]\frac{2}{3}[/tex] to [tex](x + 2)[/tex] , then [tex]\frac{1}{3}[/tex] to [tex](x - 2)[/tex], after you have done that, you would get an equation looking like this[tex]\\[/tex]:
[tex]\frac{2}{3} x + \frac{4}{3} - \frac{1}{3}x - \frac{2}{3}[/tex]
Next, add and/or subtract the fractions with the variables together and the ones without together, and that is how you get to your final answer
[tex]\frac{1}{3}x + \frac{2}{3}[/tex]
At the movie theatre, they give out a free drink to every 75th customer and a free bag of popcorn to every 30th customer. On Monday 3,000 customers came to the theatre. How many people received both free item
Answer:
20 people
Step-by-step explanation:
At the movie theater, they give out a free drink to every 75th customer and a free bag of popcorn to every 30th customer.
On Monday, 3,000 customers came to the theater.
To find the number of people who got both free items, we will calculate the Least Common Multiple (LCM) of 30 and 75.
LCM of 30, 75
= 5 × 3 × 5 × 2
= 150
Each 150th customer will receive both free items.
Total number of people who receive both free items = 3000 ÷ 150
= 20 people
On Monday 20 people will receive both free items.
The point (3,−4) lies on the graph of y=(x−5)2+k where k is some constant. Which other point must also lie on the same graph?
Answer:
The other point lies on the graph is (0, - 8).
Step-by-step explanation:
Point (3, - 4) lies on the graph [tex]y = (x -5)^2 + K[/tex]
So, put x = 3 and y = - 4 in the equation.
[tex]- 4 = ( 3 -5)^2 + K\\\\- 4 = 4 + K \\\\K= - 8[/tex]
So, the equation of graph is
[tex]y = (x - 5)^2 -8[/tex]
Let x = 5 lies on the graph so
[tex]y = (5 -5)^2 -8 \\\\y = -8[/tex]
So, the other point lies on the graph is (0, - 8).
The mean salary offered to students who are graduating from Coastal State University this year is , with a standard deviation of . A random sample of Coastal State students graduating this year has been selected. What is the probability that the mean salary offer for these students is or less
Answer:
The probability that the mean salary offer is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean salary for the population, [tex]\sigma[/tex] is the standard deviation for the population and n is the size of the sample.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Z-score with the Central Limit Theorem:
Z-is given by:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
What is the probability that the mean salary offer for these students is X or less?
The probability that the mean salary offer is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean salary for the population, [tex]\sigma[/tex] is the standard deviation for the population and n is the size of the sample.
Consider a test of H 0: μ = 85 performed with the computer. SPSS reports a two-tailed p-value of 0.2714. Make the appropriate conclusion for the given situation: H a: μ > 85, z = 1.10, α = 0.10
Answer:
p-value of 0.1357 > 0.1, which means that we do not reject the null hypothesis, that is, there is not sufficient evidence to conclude that the population mean is above 85.
Step-by-step explanation:
Decision:
If the p-value is greater than the significance level, we accept the null hypothesis. Otherwise, we reject the null hypothesis.
In this question:
Null hypothesis:
μ = 85
Alternate hypothesis:
a: μ > 85
SPSS reports a two-tailed p-value of 0.2714.
We are testing if the mean is greater than a value, which is a one-tailed test, so the p-value is of 0.2714/2 = 0.1357
Decision:
p-value of 0.1357 > 0.1, which means that we do not reject the null hypothesis, that is, there is not sufficient evidence to conclude that the population mean is above 85.
Write the recurring decimal 0.48 a
as a fraction.
Show all your working.
Answer:
[tex] \frac{16}{33} [/tex]
Step-by-step explanation:
[tex]x = 0.48... \\ 100 \times x = 0.48 \times 100 \\ 100x - x = 48.48.. - 0.48 \\ 99x = 48 \\ \frac{99x}{99} = \frac{48}{99} \\ x = \frac{16}{33} [/tex]
The total cost
of an $82 meal
with a 20% tip
Answer:
$16.40
Step-by-step explanation:
Answer:
98.40
Step-by-step explanation:
First find the tip
82* 20%
82* .20
16.40
Add the tip to the cost of the mean
82+16.40
98.40
Solve the following system of equations using matrices (row operations).
x-y=3
6x-5z=36
6y+2z=18
Answer:
(6,3,0)
Step-by-step explanation:
Given,
x - y + 0z = 3
6x - 0y - 2z = 36
0x + 6y + 2z = 18
You have the following augmented matrix:
(1) 1 -1 0 3
(2) 6 0 -2 36
(3) 0 6 2 18
Let's (3) add to (2) and divide by 6
(1) 1 -1 0 3
(2) 1 1 0 9
(3) 0 6 2 18
Now, let's (2) add to (1) and divide by 2
(1) 1 0 0 6
(2) 1 1 0 9
(3) 0 6 2 18
Let's (3) ÷ 2
(1) 1 0 0 6
(2) 1 1 0 9
(3) 0 3 1 9
Let's (1) subtract from (2)
(1) 1 0 0 6
(2) 0 1 0 3
(3) 0 3 1 9
Finally, let's (2) multiply by 3 and subtract from (3)
(1) 1 0 0 6
(2) 0 1 0 3
(3) 0 0 1 0
Thus,
x = 6, y = 3 and z = 0
The answer is (6, 3, 0)
We have to verify the answer
6 - 3 = 3 ⇒⇒ 3 = 3
6*6 - 5*0 = 36 ⇒⇒ 36 = 36
6*3 + 2*0 = 18 ⇒⇒ 18 = 18
Please please help need today
Answer:
you need to zoom in i cant see plz :)
Step-by-step explanation:
Given f(x) = x − 7 and g(x) = x2 .
Find g(f(4)).
Answer:
9
Step-by-step explanation:
f(x) = x − 7 and g(x) = x^2
g(f(4))
First find f(4)
f(4) = 4-7 = -3
Then put this result in g(x)
g(-3) = (-3) ^2 = 9
g(f(4) = 9
g(f(4)) =9.
Answer:
Solution given;
(x) = x − 7 and g(x) = x2 .
now
g(f(4))=g(4-7)=g(-3)=(-3)²=9
The graph shown below expresses a radical function that can be written in
the form f(x) = a(x+k)1/*+c
value of k in this function?
What does the
graph tell you about the value of k in this function
Each book weighs 6 ounces. Which Ordered pair is a visible solution if X represents the number of books he orders NY represents the total weight of the books in ounces
⚠️ I NEED HELP ASAP!
What is the zero of the linear function graphed below?
Answer:
(1,0)
Step-by-step explanation:
The zero of the function is where it crosses the x axis ( where y=0)
x=1 where y=0
(1,0)
PLEASE HELP! I REALLY NEED IT
Answer:
i think its like this:
Step-by-step explanation:
Savannah hike 1 mile every day after Hiking on Monday she has height 102 miles after hiking on Friday how many miles will she have hike
Answer:
106
Step-by-step explanation: ts 6 9 21 30
After Monday
102 + Tuesday + Wednesday + Thursday + Friday After
102 + 1 + 1 + 1 + 1 = 106
I need the answer plzzzzzz
Answer:
D
Step-by-step explanation:
compare the numbers
Ms. Snyder is giving a 28-question test that is made up of multiple choice questions worth 2 points each and open response questions worth 4 points each. The entire test is worth 100 points. Let x represent the number of multiple choice questions, and let y represent the number of open response questions.
Write a system of linear equations to represent each situation.
Answer:
x *2 + (28-x)*4 = 100
Step-by-step explanation:
Given
Total number of questions in the paper = 28
Out of these 28 questions let us say that x number of questions are of 2 points and 28-x questions are of 4 points.
Also, the complete test is of 100 marks
Thus, the linear equation representing the
x *2 + (28-x)*4 = 100
Josh buys candy that costs $8 per pound. He will spend at most $88 on candy. What are the possible numbers of pounds he will buy?
Answer:
11 pounds
Step-by-step explanation:
You would do 88 divided by 8 to get 11
Write the slope-intercept form of the equation for the line.
Answer:
its 4/2 or simplified to 2/1
Step-by-step explanation:
mark me brainliest pls
