Answer: [tex]27a^6[/tex]
Step-by-step explanation:
The question is not clear. So, assuming that the expression you need to simplify is this one:
[tex](3a^2)^3[/tex]
You need to remember a property called "Power of a power property". This property states the following:
[tex](b^m)^n=b^{(m*n)}=b^{(mn)}[/tex]
Therefore, you need to apply the Power of a power property explained before, in order to simplify the expression provided in the exercise, multiplying the exponents inside the parentheses by the exponent outside of the parentheses. Then:
[tex](3a^2)^3=3^{(1*3)}a^{(2*3)}=3^3a^6[/tex]
Now, you must remember that:
[tex]3^3=3*3*3=27[/tex]
Finally, you get:
[tex]=27 a^6[/tex]
If f(x) = 4(3x - 5), find f-1(x)
Answer:
[tex]f^{-1}(x) = \frac{1}{12}(x+20)[/tex]
Step-by-step explanation:
Given: f(x) = 4(3x - 5)
Is required to find f⁻¹(x)
f(x) = y = 4(3x - 5)
∴ y = 4 * 3x - 4 * 5
∴ y = 12x - 20 ⇒ add 20 to both sides
∴ y + 20 = 12x ⇒ divide both sides by 12
∴ [tex]\frac{1}{12} (y+20) = x[/tex]
Replace the places of x and y.
∴ [tex]y=\frac{1}{12} (x+20)[/tex]
∴ [tex]f^{-1}(x) = \frac{1}{12}(x+20)[/tex]
A store advertises a 35% discount on a $951 computer system.
For this case we propose a rule of three:
$ 951 -------------> 100%
x -------------------> 35%
Where "x" is the variable that determines the amount of the discount equivalent to 35%.
[tex]x = \frac {35 * 951} {100}\\x = \frac {33285} {100}\\x = 332.85[/tex]
Thus, the discount is $332.85.
The new price of the computer system is:
$951- $332.85 = $617.5
Answer:
The new price of the computer system is: $617.5
HURRY 12 POINTS
This table is for a two-variable data set. Which is a correct description of the variables?
Name Ray Mary Ed Tia Rhonda Pam
Gender Male Female Male Female Female Female
Preferred Method of Learning Seeing Hearing Seeing Doing Doing Doing
A.
The variables are seeing, hearing, and doing. They are categorical variables.
B.
The variables are seeing, hearing, and doing. They are quantitative variables.
C.
The variables are gender and preferred method of learning. They are categorical variables.
D.
The variables are gender and preferred method of learning. They are quantitative variables.
Answer:
The correct description of the variables is given by as the following -
The variables are gender and preferred method of learning. They are categorical variables.
Step-by-step explanation:
The correct description of the variables is given by as the following -
The variables are gender and preferred method of learning. They are categorical variables.
Answer:
The variables are gender and preferred method of learning. They are categorical variables.
Step-by-step explanation:
Hope this helps
Avarie is cutting a 12 foot long piece of wood into 1/4 -foot sections. How many sections will result
1 foot would be four 1/4 foot pieces.
Multiply total feet by 4:
12 ft x 4 = 48 total pieces.
What percent is 93 out of 930?
Answer:
it is 100 pls give me braiy if I'm right s
What’s the common denominator for 4 and 3
Does the graph represent a function? Yes or NO
A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply.
The sphere has a diameter of 8 in.
The volume of the sphere is StartFraction 2,048 Over 3 EndFraction pi inches cubed.
The sphere has a diameter of 32 in.
The radius’s length is one-half the length of the diameter.
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.
The diameter’s length is one-half the length of the radius.
Answer:
The sphere has a diameter of 32 in. CORRECT: the diameter of a sphere doubles its radio, so if the radio equals 16,the diameter measures the double, in this case, 32.The radius' lenght is one half the length of the diameter. CORRECT: , by definition, the diameter is the maximum distance between two opposite points on the surface of the sphere, and its lenght equals twice the radius because the radius is the distance between the center of the sphere and any point of the frontier of the sphere (then, one colud imagine that the distance between two opposite points in a sphere can be united by two radius, or a diameter).The volume (V) of a sphere can be calculated as [tex]\frac{4\pi r^3}{3}[/tex], where r is the radio. In this case, the volume of the sphere will be [tex]\frac{4\pi\times16^3}{3}=\frac{4\pi\times4096}{3}[/tex], which is also equal to [tex]\frac{16384\times\pi}{3}[/tex].Answer:
The True statements are:
The sphere has a diameter of 32 in.
The radius’s length is one-half the length of the diameter.
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed.
Step-by-step explanation:
The sphere has a diameter of 8 in. FalseThis is false because a radius is half of a diameter. Half of the given diameter of 8 in is 4 in whereas the radius in the question is 16 in.
The volume of the sphere is StartFraction 2,048 Over 3 EndFraction pi inches cubed. FalseThis is false because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.
The sphere has a diameter of 32 in. TrueThis is True because a radius is half of a diameter. Half of the given diameter of 32 in is 16 in and the radius in the question is also 16 in.
The radius’s length is one-half the length of the diameter. TrueThis is True because a radius is half of a diameter
The volume of the sphere is StartFraction 16,384 Over 3 EndFraction pi inches cubed. TrueThis is True because the volume of the sphere is 4πr³/3 = (16,384/3) π cubic inches.
The diameter’s length is one-half the length of the radius. FalseIt is the radius’s length that is one-half the length of the diameter
A recipe calls for 120 mL of milk for each 200 g of flour.Juan is going to use 1 pound of flour. Estimate the number cups of milk Juan should us
Final answer:
To find how much milk Juan should use for 1 pound of flour, convert the flour to grams (454 g), set up a proportion based on the recipe's ratio, solve for the milk in milliliters, and then convert to cups. Juan will need approximately 1.135 cups of milk, or roughly 1 and 1/8 cups.
Explanation:
The question involves calculating how much milk Juan should use in his recipe based on the amount of flour he has. Since the recipe calls for 120 mL of milk for each 200 g of flour, we need to find out the equivalent amount for 1 pound of flour.
First, let's convert 1 pound of flour to grams, knowing that 1 pound is equivalent to approximately 454 grams. The recipe ratio is 120 mL to 200 g of flour, so we set up a proportion:
200 g flour : 120 mL milk = 454 g flour : x mL milk
To solve for x, we use cross multiplication:
(200 g) * (x mL) = (120 mL) * (454 g)
x = (120 mL * 454 g) / (200 g)
x ≈ 272.4 mL
Since there are about 240 mL in 1 cup of milk, we can convert the milliliters to cups:
x ≈ 272.4 mL / 240 mL/cup
x ≈ 1.135 cups of milk
Therefore, Juan should use approximately 1.135 cups of milk for 1 pound of flour. For ease of measuring, Juan can round this to about 1 and 1/8 cups of milk.
Which basic construction if shown here?
A) bisect an angle
B) bisect a like segment
C) construct a parallel line
D) copy a line segment
Answer:
A
Step-by-step explanation:
Consider triangle OAM and OBM. In these triangles,
OA is congruent to OB as radii of one circle;AM is congruent to BM as radii of two congruent circles;OM is congruent to OM by reflexive property (this side is common).Thus, triangles OAM and OBM are congruent by SSS postulate.
Congruent triangles have congruent corresponding parts, so
[tex]\angle AOM\cong \angle BOM[/tex]
Hence, OM is angle AOB bisector.
Answer:
a
Step-by-step explanation:
usatestprep
You want to deliver a package to Japan. The FedEx delivery service charges a $15 flat fee plus $2 per additional kilogram. You can also use the USPS Priority Mail service which charges you $5 per kilogram. After how many kilograms will the total costs of the two options be the same?
Answer:
5kg
Step-by-step explanation:
Step 1.
Write in y=mx+c format
m= $/kg
c=flat fee
x=additional kilograms
FedEx:
y=2x+15
USPS:
y=5x
Step 2.
Keep Changing the x value (the no. of kilograms) in both equations until y is the same number
y=5×5
=25
y=2×5+15
=25
∴It would cost the same for both options at 5kg
Answer:
5kg
Step-by-step explanation:
Step 1.
Write in y=mx+c format
m= $/kg
c=flat fee
x=additional kilograms
FedEx:
y=2x+15
USPS:
y=5x
Step 2.
Keep Changing the x value (the no. of kilograms) in both equations until y is the same number
y=5×5
=25
y=2×5+15
=25
∴It would cost the same for both options at 5kg
Can someone help me with this question please ?
Answer:
57.97 cm²
Step-by-step explanation:
The area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h( a + b)
where h is the perpendicular height between the parallel bases and a, b are the bases.
Here h = 6.2, a = 7.9 and b = 10.8, thus
A = 0.5 × 6.2 (7.9 + 10.8)
= 3.1 × 18.7 = 57.97 cm²
Answer:
Step-by-step explanation:
Area of trapezium = 1/2(a + b)h
a = 7.9cm, b = 10.8cm and h = 6.2cm
Area = 1/2(7.9 + 10.8)×6.2
Area = 1/2 × 18.7 × 6.2
Area = 57.97cm²
e^2x + 3e^x - 18 = 0
Solving e²ˣ + 3eˣ- 18 = 0 involves substituting y = ex to transform it into a quadratic equation. Solving this quadratic equation yields a valid solution, y = 3, leading to x = ln(3). Therefore, the solution is x = ln(3).
To solve the equation e²ˣ + 3eˣ- 18, we perform a substitution to convert it into a quadratic form.
Let y =eˣ. Then the equation becomes:
y² + 3y - 18 = 0.This quadratic equation can be solved using the quadratic formula:This gives us two solutions for y:
y = 3 and y = -6.Since y = eˣ, and eˣ must be positive:
y = -6 is not valid. Thus, y = 3.Finally, solve for x:
eˣ = 3 ⟹ x = ln(3).Therefore, the solution to the equation e²ˣ + 3eˣ- 18 = 0 is x = ln(3).
At a local fitness center, members pay a $12 membership fee and $3 for each aerobics class. Nonmembers pay $4 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same?
For 12 number of aerobics classes, cost for members and nonmembers is same
Solution:
Let "x" be the number of aerobic classes
At a local fitness center, members pay a $12 membership fee and $3 for each aerobics class
Therefore,
Members pay = 12 + 3(number of classes)
Members pay = 12 + 3x ------- eqn 1
Nonmembers pay $4 for each aerobics class
Nonmembers pay = 4x ------- eqn 2
For cost for members and nonmembers be the same, eqn 1 must be equal to eqn 2,
12 + 3x = 4x
4x - 3x = 12
x = 12
Thus for 12 number of aerobics classes, the cost for members and nonmembers will be same
A special deck of cards consists of 5 red cards, 20 blue cards, and 25 green cards. Samuel selects 1 card from the special deck 500 times. How many times can he expect to draw a red card?
Answer:
5
Step-by-step explanation:
Samuel can expect to draw a red card approximately 50 times.
To find out how many times Samuel can expect to draw a red card, we need to calculate the probability of drawing a red card and then multiply it by the number of times he selects a card.
Given:
- Number of red cards = 5
- Number of blue cards = 20
- Number of green cards = 25
- Total number of cards = 5 (red) + 20 (blue) + 25 (green) = 50
The probability of drawing a red card is the ratio of the number of red cards to the total number of cards:
[tex]\[ P(\text{Red}) = \frac{\text{Number of red cards}}{\text{Total number of cards}} = \frac{5}{50} = \frac{1}{10} \][/tex]
Now, to find the expected number of times Samuel will draw a red card, we multiply the probability of drawing a red card by the total number of times he selects a card:
[tex]\[ \text{Expected number of red cards} = P(\text{Red}) \times \text{Total number of selections} \][/tex]
Substituting the values:
[tex]\[ \text{Expected number of red cards} = \frac{1}{10} \times 500 = 50 \][/tex]
So, Samuel can expect to draw a red card approximately 50 times.
h divided by 6 equals 47
multipy 47 by 6 and then plug in your answer into h
Chase purchased a sweatshirt from the clearance rack. The price of the sweatshirt after the discount is represented by the expression 0.75x, where x represents the original price of the sweatshirt.
Which expression also represents the discounted price of the sweatshirt?
A
(0.75 − 0.25)x
B
(0.75 + 0.25)x
C
x – 0.25x
D
x + 0.25x
Answer:B(0.75+0.25)x
Step-by-step explanation:
Is a discount of 0.75 was given the d real value of the sweatshirt would be a whole number
Which is 1-0.75=0.25
Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]y=\sqrt[3]{x+3}+3[/tex]
Step-by-step explanation:
The S-shaped curve is that of the cube root function (choices C or D). The parent function has its critical point at the origin. Here, that has been moved 3 units left and 3 units up.
Replacing x with x-a will move a function's graph to the right by "a" units. Here, we have a=-3, so we expect to see ∛(x-(-3)) = ∛(x+3). The graph of that is moved up 3 units by adding 3 to the function value. This gives ...
y = ∛(x+3) +3 . . . . . matches choice D
which of the following is an example of chemical property
a. boiling point
b. melting point
c. electric conductivity
d. decomposition caused by heat
Heat-induced decomposition is an illustration of chemical property.
Trying to break down is the phenomenon of decomposing. Whenever a substance is heated, it undergoes thermal breakdown, which is a chemical process.
At high temperatures, thermal breakdown processes occur. Before collapsing into the products, the reactions absorb a lot of energy.
So, Option "D" is the correct answer to the following question.
Learn more:
https://brainly.com/question/15143490?referrer=searchResults
Decomposition caused by heat is an example of a chemical property because it involves a substance changing into different substances through a chemical reaction.
Explanation:The question asks which of the following options is an example of a chemical property. Chemical properties are characteristics of a substance that indicate its ability to undergo a chemical change, resulting in the formation of new substances. Options like boiling point, melting point, and electric conductivity are considered physical properties because they describe aspects of a substance that can be observed or measured without changing the substance's chemical identity. In contrast, an option like decomposition caused by heat is a chemical property because it involves a chemical change where the original substance is transformed into different substances as a result of the chemical reaction induced by heat.
Therefore, the correct answer to the original question, "which of the following is an example of a chemical property?" is:
d. decomposition caused by heatSimilarly, from the reference exercises provided, flammability is also a chemical property. It specifies a substance's ability to burn or ignite, causing it to change chemically and form new substances as it reacts with oxygen in the air.
Will Mark as Brainliest whoever answers first
A company that teaches self-improvement seminars is holding one of its seminars in Greenwood. The company pays a flat fee of $264 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $15 to purchase books and supplies. Each attendee will pay $16 for the seminar. Once a certain number of attendee register, the company will be breaking even. What will be the company's total expenses and revenues? How many attendees will that take?
Answer:
Step-by-step explanation:
expenses :
flat fee of 264 + 15 for every attendee (a)
264 + 15a
revenue :
16 per attendee
16a
break even point is when expenses = revenue
264 + 15a = 16a
264 = 16a - 15a
264 = a
total expenses: 264 + 15a......264 + 15(264) = $ 4224
total revenue : 16a......16(264) = $ 4224
attendees taken : 264
The common denominator in this problem
4 6/7 +7 3/14=
Step-by-step explanation:
We have,
[tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex]
To find, the common denominator of [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex] = ?
∴ [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex]
= [tex]\dfrac{4\times 7 +6}{7} +\dfrac{7\times 14 +3}{7}[/tex]
[tex]=\dfrac{34}{7} +\dfrac{101}{7}[/tex]
Taking the common as [tex]\dfrac{1}{7}[/tex], we get
=[tex]\dfrac{1}{7}[/tex][tex](34+101)[/tex]
The denominator = 7
∴ The common denominator of [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex] = 7
Hence, the common denominator of [tex]4\dfrac{6}{7}+7\dfrac{3}{14}[/tex] = 7
Jennifer is completing the square to solve the quadratic equation
X^2 - x - 3 = 0.
What should be her first step?
A- adding -x to both sides of the equation
B- Isolating the constant, -3
C- Isolating the first term, X^2
Isolate the variable by dividing each side by factors that don't contain the variable.
Hope it helps! :)
QuezoMartiinez <3
Answer:
The answer is B- Isolating the constant, -3
**WORTH 75 PONITS*
Lily had 16 tomatoes she give Brandy 1/8 of tomatoes,
sadie 1/2 of the tomatoes,
and Kiley 1/4 of the tomatoes.
how many tomatoes did lily give away?
how many tomatoes did sasha have left?
what fraction of the tomatoes did lily have left?
Answer:
she gave away 14 I think.
If you mean Lilly she had 2 left
1/8 tomatoes left
Step-by-step explanation:
1/8=2 1/2=8 1/4=4. 2+8+4=14
Describe the graph of the system of inequalities:
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x>2\\y\leq4\end{array}\right[/tex]
x = 2
This is a vertical line passing through (2, 0) .
y = 4
This is a horizontal line passing through (0, 4).
<, > - dashed line
≤, ≥ - solid line
<, ≤ - shaded to the left (down) from the line
>, ≥ - shaded to the right (up) from the line
Answer:
Below.
Step-by-step explanation:
The shaded area will be to the right of the vertical dotted line x = 2, and below the horizontal continuous line y = 4.
factorise
24p2 + pq - 23q²
24p² + pq - 23q² =
= 24p² + 24pq - 23pq - 23q²
= 24p(p + q) - 23q(p + q)
= (p + q)(24p - 23q)
The required factorization of the given expression is given as (24p - 23q)(p + q).
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
Given expression in the quesiton is 24p2 + pq - 23q², we have to factorize the given expression,
So,
24p² + pq - 23q²,
Substituting pq = 24 pq - 23pq
= 24p² + 24pq - 23pq - 23q²
= 24p(p + q)-23q(p + q)
= (24p - 23q)(p + q)
Thus, the required factorization of the given expression is given as (24p - 23q)(p + q).
Learn more about Factors here:
https://brainly.com/question/24182713
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Can someone please help me with this question? :)
Answer:
Step-by-step explanation:
[tex]\frac{h*(a+b)}{2}=\frac{6.7*(7+10.4)}{2}\\\\=\frac{6.7*17.4}{2}=\frac{116.58}{2}=58.29[/tex] cm²
A hammer thrower is competing in a track and field meet. He rotates exactly 5 times in 2π seconds, and the motion of his hammer is represented by a sine function.
Which function rule could model this situation?
f(x)=5 sin x
f(x)= sin(5x)
f(x)=5π sin x
f(x)= sin(1/5x)
Answer:
Therefore the correct option is sin(5x).
Step-by-step explanation:
i) The hammer thrower rotates exactly 5 times in 2[tex]\pi[/tex] seconds.
Therefore one rotation is completed in [tex]\frac{2\pi }{5}[/tex] seconds.
ii) Since the motion of the hammer is represented by a sine function therefore
one rotation is considered to be one full cycle and the time period of that cycle
is given in equation i) and it is T = [tex]\frac{2\pi }{5}[/tex] seconds.
iii) the equation of a sine function is given by sin(2[tex]\pi[/tex][tex]\frac{1}{T}[/tex]) which in this case would
be sin(2[tex]\pi[/tex] × [tex]\frac{1}{\frac{2\pi }{5}}[/tex] × x) = sin(5x)
iv) Therefore the answer is sin(5x)
Find PR
PR = 2x
RQ = 25
PQ = 6+3x (adding 2 lengths as seen on diagram)
Answer:
Therefore,
[tex]PR=10\ unit[/tex]
Step-by-step explanation:
Given:
PR = 2x
RQ = 25
Say M divide PQ such that
PM = 6
MQ = 3x
∠PRM ≅ ∠QRM
RM is the angle Bisector of angle PRQ
To Find:
PR = ?
Solution:
Angle Bisector Theorem:
The angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle.
It equates their relative lengths to the relative lengths of the other two sides of the triangle.
Here RM is the angle Bisector of angle PRQ
Therefore,
[tex]\dfrac{PR}{RQ}=\dfrac{PM}{MQ}[/tex] ...Angle Bisector Theorem.
Substituting the values we get
[tex]\dfrac{2x}{25}=\dfrac{6}{3x}\\\\x^{2}=25\\Square\ Rooting\\x=\pm\sqrt{25}\\x=5[/tex]
As x cannot be negative x =5
Substituting x value in PR we get
[tex]PR=2\times 5=10\ unit[/tex]
Therefore,
[tex]PR=10\ unit[/tex]
(Full question above)
The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic millimeters.
A.60
B.300
C.540
D.780
Answer:
B. 300
Step-by-step explanation:
Final figure volume = big cuboid volume - small cuboid volume
Volume of a cuboid = height x width x length
Final figure = (6 x 6 x 15) - (4 x 4 x 15)
Final figure = 540 - 240
Final figure = 300mm^2
To calculate the volume of a solid rectangular prism with a hole, subtract the volume of the hole from the volume of the prism. Without specific dimensions, we cannot determine the exact volume from the given options.
Explanation:To find the volume of a three-dimensional figure that is a solid rectangular prism with a hole through the center, we need to subtract the volume of the hole from the volume of the solid rectangular prism. If the dimensions are not given in the question, we can look at examples provided in similar problems.
For instance, in problem 13, the volume of a rectangular solid with a square face of 5 cm and a length of 10 cm is found by multiplying its dimensions: Volume = length × width × height = 5 cm × 5 cm × 10 cm = 250 cm³. Similarly, we would calculate the volume of the outer prism and the inner prism in the given problem and subtract the inner volume from the outer to find the final volume.
The options provided (A. 60, B. 300, C. 540, D. 780) suggest specific volumes. Given the lack of specific dimensions in the question, it is not possible to determine the correct answer from the options provided without additional information.