The expression [tex]5^{3} \times \sqrt{5}[/tex] written as a single power of 5 is [tex]5^{3\frac{1}{2} } \ OR \ 5^{\frac{7}{2} }[/tex]
To write the given expression 5^3 x √5, as a single power of 5,
First, we will write the expression properly.
[tex]5^{3} \times \sqrt{5}[/tex]
Now, to write the above expression as a single power of 5,
First, express [tex]\sqrt{5}[/tex] in index form
By law of indices [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]
∴ [tex]\sqrt{5} = 5^{\frac{1}{2} }[/tex]
Now, the expression becomes
[tex]5^{3} \times 5^{\frac{1}{2} }[/tex]
Also, by law of indices, [tex]x^{y} \times x^{z} = x^{y+z}[/tex]
∴ [tex]5^{3} \times 5^{\frac{1}{2} } = 5^{3+\frac{1}{2} }[/tex]
[tex]= 5^{3\frac{1}{2} } \ OR \ 5^{\frac{7}{2} }[/tex]
Hence, the expression [tex]5^{3} \times \sqrt{5}[/tex] written as a single power of 5 is [tex]5^{3\frac{1}{2} } \ OR \ 5^{\frac{7}{2} }[/tex]
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You need to solve a system of equations. You decide to use the elimination
method. Which of these is not allowed?
The step that is not allowed is (b) add the left side of equation 2 to the left side of equation 1
How to determine the disallowed step?The system of equations is given as:
2x - 3y = 12
-2x + y = 8
Adding the two equations would eliminate x.Multiplying the second equation by 3 and then subtracting the resulting equation from (1) would eliminate yThis means that the step that is not allowed is (b)
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If a spider can move 1/2 of a mile every hour, then how many hours would it take for a
spider to go 4 miles?
Answer:
2
Step-by-step explanation:
1/2x4=2
what is 2+2? PLEASE HELP FOR BRAINLIEST
Answer:
4
Step-by-step explanation:
simple
Decide whether the relation is a function:
{(-3, 7), (1, -8), (6, -6), (7-8), (12, 2)}
Answer:
It is a function
Step-by-step explanation:
A function is of the form:
[tex]\left[\begin{array}{c}x_1&x_2&x_3\\-&-&-\\x_n\end{array}\right][/tex] [tex]\left[\begin{array}{c}y_1&y_2&y_3\\-&-&-\\y_n\end{array}\right][/tex]
Where each of the x values must be distinct.
The x values are referred to as domain while the y values are called range.
Having said that, the given data can be represented as follows:
[tex]\left[\begin{array}{c}-3&1&6\\7&12\end{array}\right][/tex] ----------- [tex]\left[\begin{array}{c}7&-8&-6\\-8&2\end{array}\right][/tex]
From the representation above, none of the x values are repeated.
Hence, it is a function
A company ships gift baskets that contain apples and pears the distributions of weight for the apples the pears and baskets are each approximately normal with mean and standard deviation for each distribution as shown in the table below the way to the items are assumed independent let the random variable W represent the total weight for apple six pairs in one basket which of the following is closest standard deviation of W
Answer:
1.97
Step-by-step explanation:
Following are the solution to the given points:
Assume A, P, and B is the masses of apples, pears, and basket, respectively.
[tex]\to W = 4A + 6P + B[/tex]
Calculating the mean of W:
[tex]\to \bold{W = E(W) }[/tex]
[tex]\bold{= E(4A + 6P + B)} \\\\ \bold{= 4E(A) + 6E(P) + E(B)}\\\\\bold{= 4 \times 4.72 + 6 \times 5.41 + 13.52} \\\\ \bold{= 18.88 + 32.46 + 13.52} \\\\ \bold{= 64.86 }[/tex]
Calculating the variance of W:
[tex]\to \bold{W=Var(W)}\\\\[/tex]
[tex]\bold{= Var(4A + 6P + B)}\\\\ \bold{= 42 Var(A) + 62 Var(P) + Var(B)}\\\\\bold{= 16 \times 0.22 + 36 \times 0.182 + 1.882}\\\\ \bold{= 3.52 + 6.552 + 1.882}\\\\ \bold{= 5.3408}[/tex]
Calculating the standard deviation of W:
[tex]\to \bold{W= \sqrt{5.3408}= 2.311017}[/tex]
The linear combination of Normal random variables is known to follow the normal distribution.
[tex]\to \bold{W \sim N(64.86 , 2.311017)}[/tex]
Calculating the Probability of the Total Weight is more difficult.[tex]\to \bold{67 = P(W > 67)}[/tex]
[tex]\bold{= P[ Z > \frac{(67 - 64.86)}{ 2.311017}]}\\\\\bold{= P[Z > 0.93]}\\\\\bold{= 0.1762}[/tex] (Using Standard Normal distribution)
Therefore, the final answer is "64.86, 2.311017, and 0.1762".
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1/2x + 4=9
What does x equal?
Answer:
x=10
Step-by-step explanation:
1/2x+4=9
subtract 4 from both sides
1/2x=5
multiply both sides by 2 to get x by itself
x=10
Answer:
1/2x+4=9 is x=1/10
Step-by-step explanation:
theres no explanation
Simplify the expression: 2/3 (6e+9f-21g)
Answer:
4e + 6f - 14g
Step-by-step explanation:
What number is represented by point A?
Answer:
Third choice, 3/4
Step-by-step explanation:
There's 3 lines in the middle before it's the number 1, if u count 1 into the lines then there's 4, 1 divided by 4 is 0.25 or 1/4, so each small line is going up or down by 1/4. So it's 0 -> 1/4 -> 2/4 -> 3/4 which is A -> 4/4 which is 1
So A is 3/4
PLEASE HELPPPPPP. I NEED IT DONEEEEE.
Answer:
1. Couples tickets: $8
Individual tickets: $4
2. Song download cost: $2
Movie download cost: $15
Step-by-step explanation:
You can solve both of these questions by doing system of equations.
Let's start with question 1.
There are 2 variables in this equation:
- Couples tickets price: let's represent these with the letter C
- Individual tickets price: let's represent these with the letter K
Writing the two equations would look this these:
5c + 2k = 48
3c + 2k = 32
Next, isolate a variable. I am going to isolate K in the first equation.
[tex]2k = -5c + 48 \\k = -\frac{5}{2}c + 24[/tex]
Now that we isolated a variable we can plug that back in to the second equation:
[tex]3c + 2(-\frac{5}{2}c + 24) = 32\\3c - \frac{10}{2}c + 48 = 32\\3c -5c + 48 = 32\\-2c + 48 = 32\\-2c = -16\\c = 8[/tex]
We found that c is equal to 8 so we can put that back in to an equation to solve for k.
5(8) + 2k = 48
40 + 2k = 48
2k = 8
k = 4
Therefore, the price for couples tickets is $8 and the price for individual tickets is $4.
Check #1:
5(8) + 2(4) = 48
40 + 8 = 48
48 = 48
3(8) + 2(4) = 32
24 + 8 = 32
32 + 32
Now, let's go on to question 2.
There are 2 variables in this equation:
- Price of songs downloaded: let's represent these with S
- Price of movies downloaded: let's represent these with M
Writing the two equations would look like this:
15s + 11m = 195
15s + 8m = 150
There is a simple way to answer this system, however.
If you change the bottom equations signs to negative you can minus the second equation from the first equation like this:
15s + 11m = 195
-(15s +8m = 150)
Minus them to get this equation:
3m = 45
Solve
m = 15
We have found that each movie download costs $15, now let's plug this back into an equation:
15s + 11(15) = 195
15s + 165 = 195
15s = 30
s = 2
Each song costs $2 to download.
Check #2:
15(2) + 11(15) = 195
30 + 165 = 195
195 = 195
15(2) + 8(15) = 150
30 + 120 = 150
150 = 150
I hope this helps!!
- Kay :)
Which of the following angles would not be congruent to the measure of ∠7? HELPPP!!!
Answer:
6, 2, & 3
Step-by-step explanation:
I hope that this answer helps, feel free to ask questions
how many solutions does the system have 6x+3y=-12 y=-2x+4
Answer: No solutions
Step-by-step explanation: These equations, when done by substitution, end up not equaling each other.
( among us ) how many maps, most common name, best imp count 1,2,or3, best colors (top 3) you don't have all to much time so try to make it snappy
Answer:
2 maps, name noah, imp 2, color white, orange and yellow
Step-by-step explanation:
A school bought $548 in basketball equipment and uniforms costing $29.50 each. The total cost was $2,023. Write an equation you can use to find the number of uniforms the school purchased.
(a) what would the variable (x) represent in this problem?
(1) the cost of the uniforms
(2) the number of basketballs purchased
(3) The number of uniforms purchased
(b) what is the total cost of the equipment and uniforms? |____________| (no symbols)
(c) write an equation to represent this problem. use x as your variable. |___________|
Answer:
Step-by-step explanation:
Need answer asap.......
Answer: For this one, I'll use y=mx+b because that equation make the most sense in this scenario.
A) X is the number of hours, and 15, or b is the tip
B) y= 30x + 15.
Have a great day!
Stay safe and healthy!
Happy holiday seasons!
May I please have brainliest?
if someone answers this correctly I'll give em 100 points
question one pls
algebra 2
logarithms
Condense the logarithm on the right side:
[tex]3\log_b(p)-\left(2\log_b(t)+\dfrac12\log_b(r)\right)[/tex]
[tex]n\log_b(m)=\log_b(m^n) \implies \log_b(p^3)-\left(\log_b(t^2)+\log_b\left(r^{\frac12}\right)\right)[/tex]
[tex]\log_b(m)+\log(n)=\log_b(mn) \implies \log_b(p^3)-\log_b\left(t^2r^{\frac12}\right)[/tex]
[tex]\log_b(m)-\log(n)=\log_b\left(\dfrac mn\right) \implies \log_b\left(\dfrac{p^3}{t^2r^{\frac12}}\right)[/tex]
So,
[tex]x=\dfrac{p^3}{t^2r^{\frac12}}[/tex]
and [tex]r^{\frac12}=\sqrt{r}[/tex], which makes (4) the correct choice.
Need help pls help thanks
Answer:
your right
Step-by-step explanation:
May someone please show full work. How do I do this?
(Look at the image & zoom in)
! : any unnecessary comments will be reported
Answer:
9) x = 62 10) x = 61 11) x = 7
Step-by-step explanation:
9) x + 118 = 180
- 118. - 118
x = 62
10) 2x + 3 + x - 6 = 18
Add like terms
x = 61
11) x + 16 = 4x - 5
x = 7
You have 72 grams of a radioactive kind of actinium. If its half-life is 6 hours, how much will
be left after 12 hours
Answer:
There will be 18 grams left after 12 hours.
Step-by-step explanation:
Half-life is the amount of time it take for a cell to turn from one condition to another.
To find the amount of grams for the first 6 hours.
72 ÷ 2= 36
Now, since 6 x 2 = 12, we need to divide 36 by 2 to find the next half-life.
36 ÷ 2 = 18
Therefore, there will be 18 grams left after 12 hours.
Hope this helps! :D
what the answer :( can anyone tell me?
Answer:
Its B.
Step-by-step explanation:
Answer:
I belived that would be B.
Step-by-step explanation:
B. will be your answer
hope this helps! I just finished these in math:)
have an amazing day! Study hard:)
$7.49
Takis Tortilla Chips Variety Pack 18 Count
what is the unit rate of the product
Answer:
About 42 cents
Step-by-step explanation:
What we know:
An 18-count variety pack of Taki's chips costs $7.49.
To find the unit rate divide 7.49 by 18, and round to the nearest cent.
7.49/18
Before we do that, what is 749/18?
749/18 = 41 11/18
Divide that by 100 to get your answer
41.61111/100 = 0.4161111, which rounds to 42 cents.
Us
What is the mole fraction of KCl in an
aqueous solution that contains
26.3% KCI (weightweight %)?
Answer:
0.0794%
Subtract the 26.3 from 100 and get the amount for water giving you 73.7
Divide both from their molar masses
26.3/74.55=0.3528
73.7/18.016=4.0908
Add both answers, 0.3528+4.0908=4.4436
Divde the KCl total from the the total moles which gives you your final amswer
0.3528/4.4436=0.0794
Answer: 0.0794
Step-by-step explanation:
Which shows two products that both result in positive values?
(0.5)(-0.4) and (1,2)(-0,8)
(-0,5)(-0.4) and (1,2)(-0,8)
(0,5)(0.4) and (-1,2)(-0,8)
(0,5)(-0,4) and (1,2)(0,8)
Answer: A is the answer
Step-by-step explanation:
how many solutions does 10+5x/15=4 have
Answer:
3
Step-by-step explanation:
Standard form
1/3 x +6 = 0
Factorization
1/3 (x + 18) = 0
Solutions
x = -90/5 = 18
A cylinder has a base diameter of 20 meters and a height of 5 meters. What is its
volume in cubic meters, to the nearest tenths place?
Volume = PI x r^2 x h
r -s 1/2 the diameter ( 20/2 = 10)
Volume = 3.14 x 10^2 x 5
Volume = 3.14 x 100 x 5
Volume = 3.14 x 500
Volume = 1570 cubic meters
The answer is 1570.8
Ella measured the height of a in inches every week for four weeks after planting it what is the best prediction for the height of the plant after 12 weeks
Complete question is;
Elle Measured the height of a plant, in inches,Every week for four weeks after planting it.
The height of the plant, h, in inches, Can be modeled by the function h(t) = 1.5t + 3, where t represents the time in weeks.
Based on this model, what is the best prediction for the height of the plant after 12 weeks?
A 16.5 inches
B 21 inches
C 22.5 inches
D 27.3 inches
Answer:
Option B: 21 inches
Step-by-step explanation:
We are given the function h(t) = 1.5t + 3, where t represents the time in weeks.
At t = 0;
h(0): 1.5(0) + 3 = 3inches
At t = 1;
h(1): 1.5(1) + 3 = 4.5 inches
Thus, after 12 weeks, height will be;
h(12): 1.5(12) + 3 = 21 inches
Option B is correct
8 (4 x 2.3)
A 8 x 2.3
B 4 x 2.3
C 8 x 9.2
D 8 x 4
Answer:
8 x 9.2
Step-by-step explanation:
1 inch equals 2.54 cm how many inches long is 45.72 centimeters
Answer:
18 inches equals 45.72 centimeters
Step-by-step explanation:
[tex]1/2.54 = 0.39\\0.39*45.72=18[/tex]
answer here literally 5th grade math (kinda not math just logic)
Answer:
Sophia: Deep Ocean, Heather: Soft Sky, Mia: Peacock Feathers
Step-by-step explanation:
If the first statement is true:
Sophia DID choose Peacock FeathersSophia DID choose Deep OceanHeather DID choose Deep OceanHeather DID choose Soft SkyIf the second statement is true:
Sophia DID NOT choose Peacock FeathersSophia DID NOT choose Deep OceanHeather DID NOT choose Deep OceanHeather DID NOT choose Soft SkyIf the third statement is true:
Sophia DID NOT choose Peacock FeathersSophia DID choose Deep OceanHeather DID NOT choose Deep OceanHeather DID choose Soft SkyIf the fourth statement is true:
Sophia DID NOT choose Peacock FeathersSophia DID choose Deep OceanHeather DID choose Deep OceanHeather DID NOT choose Soft SkyOut of all of these, only the third statement has no doubles.
For the graph Y equals 1 find slope of a line that is perpendicular to it in the slope of a line parallel to it
Answer:
The answer is Undefined (∞).
Step-by-step explanation:
The line y = 1 has a slope of 0, and the line parallel to it, for instance, y = 3, has the same slope, m1 = 0. For the slope of the line perpendicular to that parallel line is m2 = -1/m1, which is -1/0 = ∞