Answer: 0.06x
Step-by-step explanation:
An algebraic expression is an expression consist of integer constants, variables, and algebraic operations.The given statement: A number is 30% of 20% of the number x.
The required algebraic expression would be:
30% of 20% of x
[tex]=\dfrac{30}{100}\times \dfrac{20}{100}\times x[/tex] [we divide a percentage by 100 to convert it into decimal]
[tex]=\dfrac{6}{100}\times x\\\\=0.06x[/tex]
Hence, the required algebraic expression would be :
0.06x
Solve for x : 2^x+4^x+8^x=−14
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve this step by step.
[tex]2^x + 4^x + 8^x = -14[/tex]
↓
In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).
The number of times that each prime divides the original integer becomes its exponent in the final result.
Prime number 2 to the power of 2 = 4
[tex]2^x + (2^2)^x + (2^3) ^x = -14[/tex]
↓
Prime number 2 to the power of 3 = 8
[tex]2^x + 2^2x + 2^3x = -14[/tex]
↓
We need to exponentiate the power.
The following rule is applied:
[tex](A^B) ^C = A^BC[/tex]
In our example,
A is equal to 2,
B is equal to 2 and
C is equal to x.
[tex]( 2^x + 2^2x + 2^3x ) + 14 = -14 + 14[/tex]
↑
In order to solve this non-linear equation, we need to move all the terms to the left side.
In our example,
- term −14, will be moved to the left side.
Notice that a term changes sign when it 'moves' from one side of the equation to the other.
___________________
We need to get rid of expression parentheses.
If there is a negative sign in front of it, each term within the expression changes sign.
Otherwise, the expression remains unchanged.
In our example, there are no negative expressions.
↓
[tex]2^x + 2^2x + 2^3x + 14 = 0[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Which of the following lines are parallel to 2Y - 3X = 4?
A. Y = 2/3 X + 4
B. Y = 6/4 X
C. 2Y=8-3X
Answer:
B. Y = 6/4 X
Step-by-step explanation:
Well to find its parallel line we need to put,
2y - 3x = 4 into slope-intercept.
+3x to both sides
2y = 3x + 4
Now we divide everything by 2,
y = 3/2x + 2
So a line that is parallel to the given line will have the same slope but different y intercept, meaning we can cross out choices A and C.
To check look at the image below ↓
Thus,
answer choice B. Y = 6/4 X is correct.
Hope this helps :)
A 75 lb boy and a 65 lb girl play on a seesaw. The seesaw is 14 ft long and is pivoted exactly in the middle. If the girl sits on the end of her side, where must the boy sit to make the seesaw balance?
Answer: 6 feet from the pivot point
Step-by-step explanation:
Girl's weight x distance from center = Boy's weight x distance from center
65 (7) = 75x
[tex]\dfrac{65(7)}{75}=x[/tex]
6.066 = x
The boy needs to be placed 6 feet from the center (aka pivot point) which is the same as saying 1 foot from the end of the seesaw.
A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint. If a can of paint contains 75 ounces of white paint, how many ounces of blue paint are in the can?
Answer:
60 ounces
Step-by-step explanation:
A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint, that is, the white paint (w) to blue paint (b) ratio is 5:4. We can apply this ratio to different units such as ounces. This means that the mixture has 5 ounces of white paint to 4 ounces of blue paint. If a can of paint contains 75 ounces of white paint, the ounces of blue paint in the can are:
75 oz w × (4 oz b/5 oz w) = 60 oz b
Two ballpoint pens are selected at random from a box that contains3 blue pens, 2 red pensand 3 green pens. If X is the number of blue pens
Answer: 3/(28) ≈ 10.7%
Step-by-step explanation:
3 blue + 2 red + 3 green = 8 total pens
First pick and Second pick
[tex]\dfrac{3\ blue\ pens}{8\ total\ pens}\quad \times \quad \dfrac{2\ remaining\ blue\ pens}{7\ remaining\ total\ pens}\quad =\large\boxed{\dfrac{3}{28}}[/tex]
Need Help finding the process for both of these ( due today)
Similar triangles have side lengths that are proportional to each other. To find each of the missing lengths, we need to set up proportions.
The proportions will look as follows:
(length or unknown of triangle 1) / (length or unknown of triangle 2) = (length of triangle 1) / (length of triangle 2)
-On both sides, remember to be consistent with which length/unknown you put on top! If a triangle 1 length is the numerator on the left, then it also needs to be the numerator on the right! And this also works vice versa with triangle 2.
In each proportion equation, we can only have one unknown. On the left side of the equation, we choose one length or unknown of triangle 1, and the corresponding side length of unknown of triangle 2 (whichever you did not choose from triangle 1). On the right side of the equation, we use a completed proportion. This is because all of the sides of one triangle are proportional to the other triangle, but we need to know that proportion/ratio in order to find other side lengths.
Let's start with problem a, to show how this works:
Triangle 1 side lengths - 16, a, 11
Triangle 2 side lengths - 8, 3, b
As you can tell, the side lengths match up (corresponding!) on each triangle, as in they are in the same position on each triangle. Now, we will set up a proportion to find the length of side a on triangle 1.
a / 3 = 16 / 8
48 = 8a
a = 6
Next, let's find the length of side b on triangle 2.
11 / b = 16 / 8
16b = 88
b = 5.5
Moving on to problem b, we'll apply the same concept and steps from problem a in order to find the missing side lengths.
Triangle 1 side lengths: 5, 5.5, d
Triangle 2 side lengths: 15, c, 18
5 / 15 = 5.5 / c
5c = 82.5
c = 16.5
5 / 15 = d / 18
15d = 90
d = 6
Hope this helps!! :)
Answer:
On a) you can see the shapes are simular. The blue line signatures that they are equal just reduced. You can see that 8 goes into 16 two times so for the orange line 3 must times 2. Which would mean a is 6. Now on the red line all you see is 11. So divide 11 by 2 and your answer should be 5.5 for b.
On b) it is the same thing but you have to find how the blue line is divisible. 5 divided by 15 is 3. So 3 is the number you will be using to divide or multiply. For the orange line you divide 18 by 3. The answer is 6 for d. For the red line 5.5 times 3 and you should get 11 for c.
Step-by-step explanation:
Hope this helped
Based on the dot plot, which statements are correct? Check all that apply
Eleven students answered Mr. Chiu's question.
Twelve students answered Mr. Chiu's question.
Three people studied for two hours.
Three people studied for three hours.
Everyone who responded studied for at least one hour.
Four people studied for four or more hours
Answer: options 2,3and 6
Answer:
option
2-Twelve students answered Mr. Chiu’s question.
3-Three people studied for two hours.
6-Four people studied for four or more hours.
Step-by-step explanation:
hope this helps:)
Find two numbers in a given ratio such that the difference of their squares is to the sum of the numbers in a given ratio.Ratios, respectively, are 3 to 1 and 6 to 1.
According to the given situation, the computation of two number in a given ratio is shown below:-
We assume the numbers is x and y
Given that
[tex]\frac{x}{y} = \frac{3}{1}[/tex]
x = 3y
and
[tex]\frac{x^2-y^2}{x + y} = \frac{6}{1} \\\\\frac{(x + y) (x - y)}{(x + y)} = 6[/tex]
With the help of above formula we will put the value and be able to find the values of x and y
x - y = 6
3y - y = 6
2y = 6
y = 3
x = 3y = 9
x = 9, y = 3
Therefore the correct answer is x = 9 where as y = 3
HELP ASAP I NEED THIS RIGHTNOW 30 points
Answer:
Pretty sure it is c
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
She will be painting the outsides of the table, so we need to find the surface area of the table.
There is the flat part of the table, which is a rectangular prism. There are also four legs, which are rectangular prism.
So, she will paint C. the surface area of 6 rectangular prisms.
Hope this helps!
Which of the following
examples have a constant rate of change?
A : You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles.
B : The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year.
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
D : The amount bacteria double every hour.
Answer:
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
Step-by-step explanation:
If a salesperson earns $50 plus $10 for every $100 of merchandise he sells, the rate of change is 100. The linear equation is T = 50 + 100h, where T is the total amount he earns and h is the number of $100 in merchandise he sells.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Let's check all the options, then we have
A: You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles. It is an example of a linear function but the slope gets changed after 2 hours.
B: The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year. It is an example of the exponential function.
C: A salesperson earns $50 plus $10 for every $100 of merchandise he sells. It is an example of a linear function.
D: The number of bacteria doubles every hour. It is an example of the exponential function.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
More about the average rate change link is given below.
https://brainly.com/question/28744270
#SPJ5
2. Look at the figure below.
Which angle is congruent to 26?
Answer:
<4 is congruent to angle <6
Step-by-step explanation:
Assuming the lines are parallel
<2 , <4 , <6 , <8 are all equal
Congruent means they are equal.
There are 3 angles that are the same as angle 6, they are 2, 4, 8
The answer would be B. angle 4
water drips from a faucet at a rate of 41 drops/ minute. Assuming there are 15,000 drops in gallon, how many minutes would it take for the dripping faucet to fill a 1 gallon bucket? Round your answer to the nearest whole number
Answer:
366 Minutes
Step-by-step explanation:
If four times the brother's age is subtracted from three times the sister's age, the difference is 17. Give an equation that represents this statement using bbb as the age of the brother and s as the age of the sister.
Answer:
3s-4bbb=17
Step-by-step explanation:
brother=4bbb
sister=3s
3s-4bbb=17
Find the volume of the region enclosed by the cylinder x squared plus y squared equals 36 and the planes z equals 0 and y plus z equals 36.
Answer:
[tex]\mathbf{V = 1296 \pi }[/tex]
Step-by-step explanation:
Given that :
Find the volume of the region enclosed by the cylinder [tex]x^2 + y^2 =36[/tex] and the plane z = 0 and y + z = 36
From y + z = 36
z = 36 - y
The volume of the region can be represented by the equation:
[tex]V = \int\limits \int\limits_D(36-y)dA[/tex]
In this case;
D is the region given by [tex]x^2 + y^2 = 36[/tex]
Relating this to polar coordinates
x = rcosθ y = rsinθ
x² + y² = r²
x² + y² = 36
r² = 36
r = [tex]\sqrt{36}[/tex]
r = 6
dA = rdrdθ
r → 0 to 6
θ to 0 to 2π
Therefore:
[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r sin \theta ) (rdrd \theta)[/tex]
[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r^2 sin \theta ) drd \theta[/tex]
[tex]V = \int\limits^{2 \pi} _0 [\dfrac{36r^2}{2}- \dfrac{r^3}{3}sin \theta]^6_0 \ d\theta[/tex]
[tex]V = \int\limits^{2 \pi} _0 [648- \dfrac{216}{3}sin \theta]d\theta[/tex]
[tex]V = \int\limits^{2 \pi} _0 [648+\dfrac{216}{3}cos \theta]d\theta[/tex]
[tex]V = [648+\dfrac{216}{3}cos \theta]^{2 \pi}_0[/tex]
[tex]V = [648(2 \pi -0)+\dfrac{216}{3}(1-1)][/tex]
[tex]V = [648(2 \pi )+\dfrac{216}{3}(0)][/tex]
[tex]V = 648(2 \pi )[/tex]
[tex]\mathbf{V = 1296 \pi }[/tex]
For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, is the level of significance, p is the sample proportion, and n is the sample size.
Claim: p >=0.28; α:0.08. Sample statistics: p=0.20, n= 180
Required:
If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision.
Answer:
The Central Limit Theorem says that if the sample size is more than 30, the data follows a normal sampling distribution. Since the sample size is 180, and that is more than 30, a Normal sampling distribution can be used.
Since a normal sampling distribution can be used, we should FAIL TO REJECT the null hypothesis because p = 0.20, which is more than the significance level of α = 0.08. There is NOT sufficient evidence to suggest that the alternative hypothesis is true.
Hope this helps!
Help thx!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Answer E
Step-by-step explanation:
If you think about it, the origin is just (0,0). Now, think which one is the closest to that. (0,1/2), or answer E, should be your assumption.
Fine the value of x in the triangle. Then classify the triangle as acute, right,
or obtuse.
47* 45* x
Answer:
x = 88
Step-by-step explanation:
The sum of the angles in a triangle add to 180
47+45 +x = 180
Combine like terms
92+x = 180
Subtract 92 from each side
92+x-92= 180-92
x =88
1. What are foci? 2. What is the first step to take to write the equation of a hyperbola? 3. How do you represent parts of a hyperbola algebraically?
Answer: see below
Step-by-step explanation:
1) Foci is plural for Focus. Since a hyperbola has two focus points, they are referred to as foci. The foci is where the sum of the distances from any point on the curve to the foci is constant.
2) When determining the equation of a hyperbola you need the following:
a) does the hyperbola open up or to the right?
b) what is the center (h, k) of the hyperbola?
c) What is the slope of the asymptotes of the hyperbola?
3) The equation of a hyperbola is:
[tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1\qquad or\qquad \dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=1[/tex]
(h, k) is the center of the hyperbola± b/a is the slope of the line of the asymptotesThe equation starts with the "x" if it opens to the right and "y" if it opens upless than 0 but greater than (−5)
Answer:
-5 < x < 0
Step-by-step explanation:
Solve.
1/3-6<24
{s | s<6}
O {S | s < 10}
O {S | s < 54}
O {S | s < 90}
Answer:
The answer is:
The fourth option,
{s | s <90}
Step-by-step explanation:
yes
Answer:
[tex]\boxed{s|s<90}[/tex]
Step-by-step explanation:
1/3s-6<24
Add 6 on both sides.
1/3s<30
Multiply both sides by 3.
s<90
Please help. I’ll mark you as brainliest if correct
Answer:
1,-1,3,4
1,6,-2,-4
-4,6,-6,6
Step-by-step explanation:
I believe you just put in the values into the box. Watch the video to see how they did it to make sure it looks like how I did it.
How many solutions does the following equation have? 14(z+3)=14z+21
Answer:
No solutions
Step-by-step explanation:
14(z + 3) = 14z + 21
Expand brackets.
14z + 42 = 14z + 21
Subtract 14z on both sides.
42 = 21
There are no solutions.
Answer:
No solution
Step-by-step explanation:
First, We have to simplify the right side.
Distribute 14, 14z+42.
Now the equation stands as 14z+42=14z+21
Subtract 14z from both sides,
this makes it 42=21.
We know when the solution is #=#, our answer is no solution.
Of 10 girls in a class, three have blue eyes. Two of the girls are chosen at random. Find the probability that: (a) both have blue eyes; (c) at least one has blue eyes; (b) neither has blue eyes; (d) exactly one has blue eyes.
Answer:
C.
Step-by-step explanation:
It's the most reasonable answer.
What is the value of the fourth term in a geometric sequence for which a1 =
30 and r= 1/2
Answer:
3¾
Step-by-step explanation:
Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.
Formula for geometric sequence:
[tex] a^n = a ( n-1 ) * r [/tex]
Given:
First term, a1 = 30
ratio, r = ½
Required:
Find the fourth term
Where, the first term, a¹ = 30
Second term: a² = 30 * ½ = 15
Third term: a³ = 15 * ½ = 7.5
Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾
Therfore the fourth term of the geometric sequence is 3¾
Determine which type of correlation is shown in the graphed relationship
Answer:
No correlation
Step-by-step explanation:
Hey there! :)
This has no correlation because all the points are spread out throughout the graph making no correlation.
Answer:
D no correlation
Step-by-step explanation:
too many scattered dot all over the place if its some going up down its NO CORRELATION!!!
Quick!!! Urgent!!!!!!!!!
Answer:
my best answer for this is B. False.
I calculated as fast as i can.
Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows: x 0 1 2 3 p(x) 0.17 0.33 0.32 0.18 Determine the probability the student visits the gym at most twice in a month. Report your answer to two decimal places.
Answer: Probability of visiting at most twice = 0.82
Step-by-step explanation: The probability distribution is of the form:
X 0 1 2 3
P(X) 0.17 0.33 0.32 0.18
It wants the probability of visiting the gym at most twice in a month, which means the probability of never going to the gym, P(X=0), or going once, P(X=1), or going twice, P(X=2).
Using the "OR" probability:
P(visiting at most twice) = P(X=0) + P(X=1) + P(X=2)
P(visiting at most twice) = 0.17 + 0.33 + 0.32
P(visiting at most twice) = 0.82
Therefore, the probability of visiting the gym at most twice in a month is 0.82 or 82%
According to the World Health Organization (WHO) Child Growth Standards, the head circumference for boys at birth is normally distributed with a mean of 34.5cm and a standard deviation of 1.3cm. What is the probability that a boy has a head circumference greater than 36.32cm at birth
Answer:
0.081
Step-by-step explanation:
To solve this question, we would use the z score formula
z score = (x-μ)/σ, where
x is the raw score = 36.32cm
μ is the population mean = 34.5 cm
σ is the population standard deviation = 1.3cm
z score = (36.32cm - 34.5cm)/1.3cm
z = 1.4
Using the normal distribution to find the z score for 1.4
P(z = 1.4) = 0.91924
Therefore, the probability that a boy has a head circumference greater than 36.32cm at birth is
P(x>36.32) = 1 - P(z = 1.4)
= 1 - 0.91924
= 0.080757
Approximately ≈ 0.081
In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to:
Answer:
[tex]Mean = 344[/tex]
Step-by-step explanation:
Given
[tex]Population = 1013[/tex]
Let p represents the proportion of those who worry about identity theft;
[tex]p = 66\%[/tex]
Required
Mean of those who do not worry about identity theft
First, the proportion of those who do not worry, has to be calculated;
Represent this with q
In probability;
[tex]p + q = 1[/tex]
Make q the subject of formula
[tex]q = 1 - p[/tex]
Substitute [tex]p = 66\%[/tex]
[tex]q = 1 - 66\%[/tex]
Convert percentage to fraction
[tex]q = 1 - 0.66[/tex]
[tex]q = 0.34[/tex]
Now, the mean can be calculated using:
[tex]Mean = nq[/tex]
Where n represents the population
[tex]Mean = 1013 * 0.34[/tex]
[tex]Mean = 344.42[/tex]
[tex]Mean = 344[/tex] (Approximated)
The temperature is 58° F. It gets warmer by h degrees and reaches to 65° F. Find h.
Answer:
h = 7 degrees
Step-by-step explanation:
To find h, we know that it is positive because it increases in value, not decreases:
h = 65 - 58
h = 7
Answer:
h = 7°F
Step-by-step explanation:
58 + h = 65
h = 65 - 58
h = 7
Check:
68 + 7 = 65