Which expression is equivalent to 3/ x^5y
[tex] \sqrt[3]{ {x}^{5}y } [/tex]
Answer:
[tex]\sqrt[3]{x^5 \ y } = (x^5 y)^\frac{1}{3} = x^{ \frac{5}{3}} \ y^ { \frac{1}{3}}[/tex]
Answer:
[tex] {x}^{ \frac{5}{3} } {y}^{ \frac{1}{3} } [/tex]
Step-by-step explanation:
A cube root is equivalent to the power of 1/3, so by taking the powers of the exponents and multiplying them by 1/3, you get your answer.
Gloria received a 4 percent raise and is now making $24,960 a year, what was her salary before the raise?
She gets a 4% raise so her new pay is 100% + 4% of her previous pay.
104% = 1.04 as a decimal.
Divide her new pay by 1.04:
24,960 / 1.04 = 24,000
Her previous pay was $24,000
Solve the quadratic equation 12x^2 - 288 = 0 using the square root method.
Answer:
C) x = ± 4
Step-by-step explanation:
12x² - 288 = 0
Add 288 on both sides. Anything plus zero gives itself.12x ² = 288
Divide both side by 12[tex] \small \sf \: x {}^{2} = \frac{288}{12} \\ [/tex]
Divide 288 by 12 to get 24[tex]\small \sf x {}^{2} = \frac{ \cancel{288 }}{ \cancel{12}} \\ [/tex]
x² = 24
Taking square root of each side and remember to use positive and negative roots[tex] \small \sf \: \sqrt{x {}^{2} } = ± \sqrt{ 24} [/tex]
[tex] \small \sf \: x_1, _2 = ± \sqrt{ 24} [/tex]
[tex] \small \sf \: x_1, _2 = ± 4.899 [/tex]
The length of a rectangle is 6 inches more than the width. The perimeter is 28 inches. Find the length and the width (in inches).
Answer:
The length of the rectangle is 10 inches, and the width is 4 inches.
Step-by-step explanation:
Given that the length of a rectangle is 6 inches more than the width, and the perimeter is 28 inches, the following calculation must be performed to find the length and the width:
(X + X + 6) x 2 = 28
2X + 2X + 12 = 28
4X = 28 - 12
X = 16/4
X = 4
Therefore, the length of the rectangle is 10 inches, and the width is 4 inches.
You are installing new carpeting in a family room. The room is rectangular with dimensions 2012feet × 1318feet . You intend to install baseboards around the entire perimeter of the room except for a 312 -foot opening into the kitchen. How many linear feet of board must you purchase?
Answer: 1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet
2. 3ft 8in = 3 8/12 or reduced to 3 2/3 12ft 3in = 12 3/12 or reduced to 12 1/4 The fractional part is referring to a fraction of a foot.
3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3 P= 31 5/6 feet
4. The estimate and the actual are very close. They are 1/6 of a foot apart.
5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.
5b. Take the total and divide it by 8ft = 29 7/12 divided by 8= 3.7 You are not buying a fraction of a board so you would need 4 boards.
Which function has a simplified base of 4RootIndex 3 StartRoot 4 EndRoot?
f(x) = 2(RootIndex 3 StartRoot 16 EndRoot) Superscript x
f(x) = 2(RootIndex 3 StartRoot 64 EndRoot) Superscript x
f(x) = 4(RootIndex 3 StartRoot 16 EndRoot) Superscript 2 x
f(x) = 4(RootIndex 3 StartRoot 64 EndRoot) Superscript 2 x
Answer is C f(x) = 4(RootIndex 3 StartRoot 16 EndRoot) Superscript 2 x
Answer:
c is answer
Step-by-step explanation:
yes
Answer:
C
Step-by-step explanation:
took test
2√m^2 if m is greater than or equal to 0
Answer:
[tex] \displaystyle \boxed{|2m| }[/tex]
Step-by-step explanation:
we are given that
[tex] \displaystyle 2 \sqrt{ {m}^{2} } [/tex]
since m is greater than or equal to 0 it's a positive number therefore, the square root of m is defined and recall that √x²=|x| thus
[tex] \displaystyle \boxed{2 |m|}[/tex]
remember that,|a|•|x|=|ax| hence,
[tex] \displaystyle \boxed{ |2m|}[/tex]
and we're done!
Answer:
2m
Step-by-step explanation:
Given :-
2√m² , m is greater than or equal to 0 .By question,
→ 2√m²
→ 2 * m
→ 2m
Can someone please help me, with part B
Step-by-step explanation:
let y = x+5/4
Interchanging x and y , we get ;
x = y+5/4
or, 4x = y+5
or, 4x-5 = y
or, g(x) -1 = 4x-5
Answer:
In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:
4x-5
Answer:
Solution given:
B.g(x)=[tex]\frac{x+5}{4}[/tex]
let
g(x)=y
y=[tex]\frac{x+5}{4}[/tex]
Interchanging role of x and y
we get:
x=[tex]\frac{y+5}{4}[/tex]
doing crisscrossed multiplication
4x=y+5
y=4x-5
So
g-¹(x)=4x-5
Write the rule that describes the first transformation?
RED —> BLUE
Looking at Point A to A', the rectangle moves 5 places to the left which is the x value + 5 and it shifts 1 place down which would be the y value - 1
This gets written as:
(x+5, y-1)
in the number 36,802 if the 8 was replaced with a 2 would the value increase or decrease
Answer:
decrease
Step-by-step explanation:
simplify 3 / 8 (–2 / 7 +(–3 / 8 ×2 / 5)
Answer:
so the answer is 0.16339
2. Commission: A car saleswoman earns a
commission of 7% on each car she sells. How
much did she earn on the sale of a car for
$12,500?
Answer:
Step-by-step explanation:
commission = 0.7% of $12,500
= 0.007×$12,500
= $87.5
A grocery store buys cereal using the cost function
c(n) = {
2n when n < 100
1.9n when 100
Sn = 500
1.8n when n > 500
where n is
the number of boxes of cereal the grocery store
buys and c(n) is the cost of the cereal. The grocery
store then sells the cereal using the sales function
s(c) = 1.3c. What is the cost of the cereal if the
grocery store buys 250 boxes?
The cost of the cereal if the grocery store buys 250 boxes is $475
Cost functionsFunctions are written in terms of variables. If the cost function that represents the cereal is given as C(n), the equivalent expression if the grocery store buys 250 boxes is 1.9n
Substitute n = 250 into the function to have:
C(250) = 1.9(250)
C(250) = $475
Hence the cost of the cereal if the grocery store buys 250 boxes is $475
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Naval intelligence reports that 4 enemy vessels in a fleet of 17 are carrying nuclear weapons. If 9 vessels are randomly targeted and destroyed, what is the probability that more than 1 vessel transporting nuclear weapons was destroyed
Answer:
0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed
Step-by-step explanation:
The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Fleet of 17 means that [tex]N = 17[/tex]
4 are carrying nucleas weapons, which means that [tex]k = 4[/tex]
9 are destroyed, which means that [tex]n = 9[/tex]
What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?
This is:
[tex]P(X > 1) = 1 - P(X \leq 1)[/tex]
In which
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294[/tex]
[tex]P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412[/tex]
[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588[/tex]
0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed
(-3,-7) is it a solution
Answer:
It could be a solution
Step-by-step explanation:
This depends on what equation you are solving. It could be a solution for a quadratic or even a transformation problem.
Tan^2t /sin t = tan t sec t
Answer:
Step-by-step explanation:
[tex]\frac{tan^2t}{sint}=\frac{tan t\times tant}{sin t} =\frac{tan t}{sint} \times \frac{sin t}{cos t} =\frac{tan t}{cos t} =tan t ~sec t[/tex]
a + b·c = a + c·b is an example of the associative property.
Answer:
yes , This is an example of the associative property.
Step-by-step explanation:
NO LINKS AND NO ANSWERING WHAT YOU DON'T KNOW!!! THIS IS NOT A TEST OR ASSESSMENT!!!
Please help and SHOW WORK on these parts.
Unit 1 Assignment- Who's Right?
Answer:
Part 1)
1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.
2) Dylan is perfectly correct.
3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.
Part 2)
Only Skyler's approach was incorrect. When Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.
Step-by-step explanation:
Part 1)
We want to simplify the expression:
[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7}[/tex]
We can divide. Recall that xᵃ / xᵇ = xᵃ ⁻ ᵇ. Hence:
[tex]\displaystyle =0.88\times 10^{-11-7}=0.88\times 10^{-18}[/tex]
In scientific notation, the coefficient is always between 1 or 10.
So, we can multiply 0.88 by 10. To keep the equality, we need to divide 10⁻¹⁸ by 10. Hence:
[tex]\displaystyle =0.88(10)\times \frac{10^{-18}}{10}[/tex]
(You can see that the 10s can cancel out, giving us our original expression.)
Simplify. Thus:
[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7} = 8.8\times 10^{-19}[/tex]
Therefore, as we can see:
1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.
2) Dylan is perfectly correct.
3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.
Part 2)
Reviewing their work, we can see that only Skyler's approach was incorrect.
729 is indeed 3⁶. However, when Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.
Both Robert and Kevin are correct, having set each exponent equal to each other after their bases are equivalent and solving for x.
A photograph has a length that is inches longer than its width, x. So its area is given by the expression square inches. If the area of the photograph is square inches, what is the width of the photograph?
The width of the photograph is blank inches.
Answer:
width is also "inches"
Step-by-step explanation:
A card is drawn from a well shuffled pack of 52 cards . find the probability of '2' of spades
Answer:
[tex] \frac{1}{52} [/tex]Step-by-step explanation:
Given,
Total no. of cards = 52
No. of 2 of spades cards = 1
Therefore,
Probability of getting 2 of spades
[tex] = \frac{no. \: of \: required \: outcomes}{total \: outcomes} [/tex]
[tex] = \frac{1}{52} (ans)[/tex]
BRAINLIEST HELP ME!!!
Which graph shows the solution to this system of linear Inequalities?
ys2x-3
A. Graph
B. Graph B
C. Graph A
D. Graph D
You have some money to invest in one of two accounts. The first account pays
5% simple interest, and the second pays 4% compound interest. How would
you decide which account to use? Discuss your answer.
Answer:
compound interest
Step-by-step explanation:
compound interest yields higher profit than simple interest
Answer:
the simple interest function will be greater in the beginning, but the
compound interest equation will overtake the simple after a while.
it appears that the 4% compound equation will overtake the simple at about 10 years
Step-by-step explanation:
[tex]1 + .05t = 1(1.04)^t[/tex]
x²-7x+5 in the form (x-a)²-b
Answer:
( x - 3.5)² - 29/4
Step-by-step explanation:
Given :-
x² - 7x + 5Writing in ( x - a)² - b form ,
x² - 7x + 5 x² - 7 * 2/2 * x + 5 x² - (7/2) * 2 * x + 5 x² - (7/2)*2*x +(7/2)²-(7/2)²+5( x - 7/2)² + 5 - 49/4( x - 7/2)² + ( 20-49)/4( x - 3.5)² - 29/4The number of measles cases decreased by 7% to 606 cases this year. What was the number of cases prior to the increase? Express your answer rounded correctly to the nearest whole number.
Answer:
652 cases
Step-by-step explanation:
The formula for percentage increase is 100 times the final-initial/final value. If we plug the numbers in and calculate, we get 652 cases. Have a great day!
Solve using the quadratic equation 3x^2+x-5=0
Answer:
comparing with ax²+bx+c=0
a=3, b=1 , c= -5
Solve using the formula now ,,
The denominator of a fraction is three more than twice the numerator. if both numerator and denominator are degreased by seven, the simplified result is 4/13
orgnal fraction. (Don't simplify.)
Answer:
2/7
Step-by-step explanation:
d=2n+3
[tex]\frac{d-7}{2n-4} = \frac{4}{13}[/tex]
13(2n+3) -91 =8n - 16
26n+39 -91 = 8n-16
18n=36
n=2
d=7
Which solution finds the value of x in the triangle below?
A right triangle is shown. The hypotenuse has a length of 8. Another side has a length of x. The angle between the hypotenuse and the other side is 60 degrees.
Answer:
4
Step-by-step explanation:
Since this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees.
We can see that this is a 30-60-90 degree triangle.
The rules of 30-60-90 degree triangles are that the side opposite the 90 degree angle, or the hypotenuse can be measured with the variable [tex]2a[/tex]. The side opposite the 30 degree angle can be measured with [tex]a[/tex], and the side opposite the 60 degree angle will be measured with [tex]a\sqrt{3}[/tex].
We can see that 8 represents [tex]2a[/tex] because it is the hypotenuse. Since the side marked [tex]x[/tex] is separated by the hypotenuse by an angle of 60 degrees, we note that side marked [tex]x[/tex] is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked [tex]a[/tex], and since we already know that 8 is equal to [tex]2a[/tex], we realize that the side marked x is equal to [tex]a[/tex], or 4.
The value of x in the triangle is 4.
What is the Pythagorean theorem ?
The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
It is given this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees. By the sum of all the three interior angles of a triangle is 180 degrees
The side opposite the 90 degree angle, or the hypotenuse can be measured with the variable '2a' . The side opposite the 30 degree angle can be measured with 'a' , and the side opposite the 60 degree angle will be measured with 'a√3'.
8 represents '2a' because it is the hypotenuse. Since the side marked x is separated by the hypotenuse by an angle of 60 degrees, we note that side marked x is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked 'a', and since we already know that 8 is equal to '2a', we realize that the side marked x is equal to
'a' , or 4.
2a=8
a=4
x=a=4
so, the the value of x in the triangle is 4.
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HELP PLEASE!!! So for this problem is got 0.48 however I just wanted to confirm that my answer is correct. Can someone please help me if the answer is wrong and how to solve it. Thank your for your time
Answer:
ur answer is correct
A =xy
A = 1.6×0.3 = 0.48
Let f (x) = x^2 + 3x + 2, and g (x) x - 6. Find and simplify: (f • g) (x)
Answer:
(f • g) (x) = [tex]x^{3}[/tex] - 3[tex]x^{2}[/tex] - 16x - 12
Step-by-step explanation:
(x-6)([tex]x^{2}[/tex] + 3x + 2)
[tex]x^{3}[/tex] + 3[tex]x^{2}[/tex] + 2x - 6[tex]x^{2}[/tex] - 18x -12
[tex]x^{3}[/tex] - 3[tex]x^{2}[/tex] - 16x - 12
. Which equation represents y = −x2 + 4x − 1 in vertex form?
Answer:
Rewrite in vertex form and use this form to find the vertex
(
h
,
k
)
.
(
2
,
3
)
Step-by-step explanation:
