Answers
The given algebraic expression would be equivalent to the expression [tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex] which is the correct answer would be an option (B)
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The given algebraic expression is:
[tex](64x^{\frac{2}{3} })^{-\frac{1}{3} }[/tex]
Apply the property of a⁻ˣ = 1/aˣ in the above term,
[tex]\dfrac{1}{ (64x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]
Here 64 = 4×4×4 = 4³
[tex]\dfrac{1}{ (4^3x^{\frac{2}{3} })^{\frac{1}{3} }}[/tex]
Apply the cube root property and Multiply the exponent of the variable x to 1/3
[tex]\dfrac{1}{ 4x^{\frac{2}{3} }^\times^{\frac{1}{3} }}[/tex]
Apply the multiplication operation to the exponent of the variable x to get the solution.
[tex]\dfrac{1}{4(x)^\frac{2}{9} }[/tex]
Hence, the correct answer would be an option (B)
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Related Questions
Which graph represents the solution set of the system of inequalities-2x+y<_4 y>x+2
Answers
The graph of the solution set of the system of inequalities y > x + 2 and
- 2x + y ≤ 4 is shown in figure.
What is mean by Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequalities is,
⇒ y > x + 2
And, - 2x + y ≤ 4
Now,
The inequality is,
⇒ - 2x + y ≤ 4
Add 2x both side, we get;
⇒ - 2x + y + 2x ≤ 4 + 2x
⇒ y ≤ 2x + 4
And, The second inequality is;
⇒ y > x + 2
So, Plot the graph of the inequalities y ≤ 2x + 4 and y > x + 2.
We get the solution set of the system of inequalities.
Which is shown in figure.
Thus, The graph of the solution set of the system of inequalities y > x + 2 and - 2x + y ≤ 4 is shown in figure.
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The data represents the number of cars that the sales staff at Templeton Motors sold this week.
4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3
Which line plot correctly displays the data?
OA.
Formula Sheet
3.
Number of Cars Sold
X X
X X X
X X X X X X
+++
AHH
+
0 1 2 3 4 5 6 7 8 9 10
X
Number of Cars Sold
X X X X X X X
H
0 1 2 3 4 5 6 7 8 9 10
OC.
OD.
←
Number of Cars Sold
X X
X X X
X X X X X X X
++
0 1 2 3 4 5 6 7 8 9 10
X X
Number of Cars Sold
X X
X X X
H11
0 1 2 3 4 5 6 7 8 9 10
Answers
The line plot that correctly displays the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, is: A.
How to Represent a Data on a Line Plot?A line plot is a graphical representation of a data whereby the frequency of each data point is represented by a dot on the line plot.
The dots on each data point on the line plot corresponds to the frequency of a data point in a data distribution.
Given the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, the frequency for each data point is:
2 - 1 dot
3 - 3 dots
4 - 3 dots
5 - 2 dots
6 - 1 dot
7 - 1 dot
8 - 1 dots
Thus, the line plot that correctly represents these data points alongside their frequencies is: A.
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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: 0, ordered pair: (−3,−8)
Answers
The equation (in slope-intercept form) of the line as described whose slope is; 0 and passes through the point given is; y = -8.
What is the equation of the line whose slope is; 0 and passes through the point given;It follows from the task content that the equation of the line whose slope is; 0 and passes through the point; (-3, -8) is to be determined.
Hence, from the slope formula;
slope, m = ∆y/∆x
Therefore; 0 = ∆y/∆x
By cross-multiplication; we have;
∆y = 0
Recall, ∆y = y - y1 = y - (-8)
y - (-8) = 0
y + 8 = 0
y = -8.
Therefore, it follows that the equation of the line described is; y = -8.
Consequently, the line in discuss is a horizontal line.
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HELP ASAP
Solve z3 = 27.
z = 9
z = −9
z = 3
z = ±3
Answers
Z*3=27
Z=27/3
Z=+9
Answer:
the answer is 3
Step-by-step explanation:
40 POINTSSSSS!!!!!!!!!! PLS HELP NO LOOKING IT UP!A polygon is shown on the graph: What effect will a translation 3 units down and 2 units left have on the polygon? Be sure to address how it could impact the angles, side lengths, and congruency between the original pre-image and the image.
Answers
we know that
A translation is a rigid transformation
In a translation the preimage and the image are congruent
that means -----> the angles and side lengths of the image and the preimage are congruent (are equal)
The only difference between the image and the preimage is the location
Remember that
If two figures are congruent, then their corresponding angles and their corresponding sides are equal
Solve the equation for y in terms of x. In other words, algebraicallyrearrange the equation so that the y variable is by itself one side of theequation. Type your answer in the form y = mx + b. If you have a valuethat is not an integer then type it rounded to the nearest hundredth. Donot put spaces between your characters.4.2 + 2y = 8y = ?4x+2y=8
Answers
Given:
[tex]4x+2y=8[/tex]Solve the equation for y,
[tex]\begin{gathered} 4x+2y=8 \\ Subtract\text{ -4 from both sides} \\ 4x+2y-4x=8-4x \\ 2y=8-4x \\ \text{Divide by 2 on both side} \\ \frac{2y}{2}=\frac{8-4x}{2} \\ y=\frac{8}{2}-\frac{4x}{2} \\ y=4-2x \\ \text{ express the equation in the form y=mx+b} \\ y=-2x+4 \end{gathered}[/tex]Answer: y = -2x +4
what is the ratio of 12
Answers
Answer:
12.:1 Is the great answer of this question
ach function is a transformation of the parent sine function. Based on the period, which graph represents each transformed function?
Answers
Given the functions:
• f(x) = sin(-x)
,• f(x) = sin(2x)
,• f(x) = sin(1/2x)
Given that each function is a transformation of the parent sine function, let's select the graph which represents each transformed function.
We have the parent sine function:
f(x) = sin(x).
• For function A.
f(x) = sin(-x)
The graph of this transformed function will be:
• For function B.
f(x) = sin(2x)
The period of this function will be:
[tex]T=\frac{2\pi}{B}=\frac{2\pi}{2}=\pi[/tex]Therefore, the graph which represents this function is:
• Function C.
f(x) = sin(1/2x)
The period of this function will be:
[tex]T=\frac{2\pi}{B}=\frac{2\pi}{\frac{1}{2}}=4\pi[/tex]Therefore, the graph of this function will be:
ANSWER:
Mrs. Smith wants to buy floor covering for her master bedroom. The dimensions of the master bedroom are 11yd by 7yd. The floor covering is sold in square meters. How many square meters of floor covering will she need?
She will need ____ square meters.
Round answer to the nearest hundredth as needed.
Answers
Mrs. Smith will need 64m² of floor covering for her master bedroom.
The length L of the bedroom is 11 yards,
The breadth B of the bedroom is 7 yards.
The floor covering is available only in square meters.
As we know,
One yard = 0.9144 meters.
the length of the bedroom in meter is,
Length L = 0.091144 x 11
Length L = 10.02 meters.
the breadth of the bedroom in meters is,
Breadth B = 0.91144 x 7
Breadth = 6.38 meters.
the Area of Rectangular master bedroom in Meter square is,
Area = Length x Breadth
Area of the bedroom = 10.02 x 6.38
Area of the bedroom = 63.92 m²
Area of floor covering required = Area of the master bedroom.
Area of the floor covering required = 63.92 m².
Rounding off to nearest hundredth = 64m²
Mrs. Smith will need 64m² of floor covering.
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please help! what are the x and y values
Answers
Answer:
1, -2
0, -4
-1,-6
-2,-8
what is 4 divided by 1 over2
Answers
Answer:
4/1÷2 =4×1/2
Step-by-step explanation:
You have to invert and then multiply
so the answer will be 2
1/2(4×5)-2³= what's the awnser
Answers
Explanation:
[tex]\frac{1}{2}(4\times5)-2^3=[/tex]First we have to solve the products, divisions and powers in each term. The terms are separated by + or - signs. In this expression there are two terms.
In the first term there's a product inside a parenthesis. This means that we have to solve that first:
[tex]=\frac{1}{2}\cdot20-2^3[/tex]Now we can solve the multiplication in the first term:
[tex]=10-2^3[/tex]Solve the power in the second term:
[tex]=10-8[/tex]And do the substraction:
[tex]=2[/tex]Answer:
1/2(4x5) - 2³ = 2
Please show and explain this please
Answers
The graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
What is a graph of a function?Defining a function's graph: The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We could also say that the graph of f is the graph of y = f(x). As a result, the graph of an equation is a particular instance of the graph of a function. We merely select a value for x, then determine the value of y that corresponds. Equations that have been solved for y are graphed as functions! In this instance, the graph of f(x) is the graph of y = x² - 3. Making points for the graph is simple.So, the function with which the given graph matches:
The graph of the option (E) f(x) = (x + 10)(x - 3)²(x + 1) is:(Refer to the graph attached below)We can easily see that coordinates of the given graph and the graph of equation (E) match.Therefore, the graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
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find the 12th term of the series; 0.008, 0.04, 0.2
Answers
Answer
12th term = 390,625
Explanation
On close observation, we can see that the given series is in geometric progression.
Geometric progression has a general formula of
aₙ = a (rⁿ⁻¹)
where
aₙ = nth term
a = First term
r = Common ratio
n = number or position of the term
For this question, we need to compute the common ratio
Common Ratio = (Next term) ÷ (Current term)
= (Second term) ÷ (First term)
= (Third term) ÷ (Second term)
For this question,
Common Ratio = 0.04 ÷ 0.008 = 5
OR
0.2 ÷ 0.04 = 5
And we can see that the first term is 0.008
So, the 12th term will have the formula
aₙ = a (rⁿ⁻¹)
a = 0.008
n = 12
r = 5
a₁₂ = 0.008 (5¹²⁻¹)
= 0.008 (5¹¹)
= 0.008 (48,828,125)
= 390,625
Hope this Helps!!!
Write an explicit equation for the arithmetic sequence defined byt(n+1)= t(n)-4t(2) = 10
Answers
We need to find the explicit equation for the sequence:
[tex]\begin{gathered} t\mleft(n+1\mright)=t\mleft(n\mright)-4 \\ \\ t(2)=10 \end{gathered}[/tex]First, we can complete the given table. Notice that when we subtract 4 from the n-th term, we obtain the next term (n+1).
Then, to find a previous term, we can add 4. Thus. we obtain:
n t(n)
0 14+4 = 18
1 10+4 = 14
2 10
3 10-4 = 6
4 6-4 = 2
5 2-4 = -2
Now, observing the above relations, we need to write an expression for t(n) in terms of n:
n t(n)
0 18 = 18 - 0*4
1 14 = 18 - 1*4
2 10 = 18 - 2*4
3 6 = 18 - 3*4
4 2 = 18 - 4*4
5 -2 = 18 - 5*4
...
n 18 - n*4
Therefore, an explicit equation for the sequence is:
[tex]t(n)=18-4n[/tex]K
A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the mean salary.
Salary ($) Employees
5,001-10,000
10,001-15,000
17
15
15,001-20,000
20,001-25,000
25,001-30,000
OA. $7,376.62
B. $17,625
C. $15,862.50
D. $19,387.50
16
13
19
Answers
The mean salary of the employees is $17625.5.
The total number of employees in the company is 80.
The total salary for the first interval is [(5001+10000)/2]*17 = 127508.5.
The total salary for the second interval is [(10001+15000)/2]*15 = 187507.5.
The total salary for the third interval is [(15001+20000)/2]*16 = 280008.
The total salary for the fourth interval is [(20001+25000)/2]*13 = 292506.5.
The total salary for the fifth interval is [(25001+30000)/2]*19 = 522509.5.
In math, a mean is the average of a data collection, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers. The mean salary is the sum of all salaries divided by the total number of employees.
M = (127508.5 + 187507.5 + 280008 + 292506.5 + 522509.5)/80
M = 17625.5
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Write the following sentence using mathematical symbols:
n is greater than or equal to 0.
Answers
The sentence using mathematical symbols would form an inequality as; n ≥ 0.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. The Set of such values is; called the solution set to the considered equation or inequality.
We need to write a sentence using mathematical symbols:
Given that "n is greater than or equal to 0"
The inequality form as;
n ≥ 0
Therefore, the sentence using mathematical symbols would form an inequality as; n ≥ 0.
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The directress of a parabola is represented by the linear equation y=2, and its vertex is located at (3,1).Both of these attributes of the parabola are graphed below. which of the following is the equation that represents this parabola?
Answers
The directrix of the parabola is at y = 2 and its vertex is at (-3,1). Since the directrix is below the vertex, we can say that the parabola will open downwards. The general form to find the equation of the parabola given the directrix and vertex is
[tex]y=-(x-h)^2+k[/tex]The value of h for the problem is -3 while the value of k for the problem is 1. Substitute it on the equation above, we get
[tex]\begin{gathered} y=-(x-(-3))^2+1 \\ y=-(x+3)^2+1 \end{gathered}[/tex]Hence, the answer to this problem is option 2. Note that the equation started in a negative sign because the parabola opens downwards.
a Fill in the blank. If necessary, use the slash mark (/) for a fraction bar. If cosg = then tang =
Answers
We can use a right triangle and the below trigonometric ratios.
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent leg}}{\text{ Hypotenuse}} \\ \tan(\theta)=\frac{\text{ Opposite leg}}{\text{ Adjacent leg}} \end{gathered}[/tex]In this case, we have:
[tex]\cos(\theta)=\frac{3}{5}=\frac{\text{Adjacent leg}}{\text{Hypotenuse}}[/tex]As we can see, we need to know the value of the opposite leg. Since it is a right triangle, we can use the Pythagorean theorem formula.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the legs} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a=3 \\ b=? \\ c=5 \\ a^{2}+b^{2}=c^{2} \\ 3^2+b^2=5^2 \\ 9+b^2=25 \\ \text{ Subtract 9 from both sides} \\ 9+b^2-9=25-9 \\ b^2=16 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ \sqrt{b^2}=\sqrt{16} \\ b=4 \end{gathered}[/tex]Finally, we have:
Then, we can find the value of tan(θ):
[tex]\begin{gathered} \tan(\theta)=\frac{\text{Opposite leg}}{\text{Adjacentleg}} \\ \tan(\theta)=\frac{4}{3} \end{gathered}[/tex]Answer[tex]\tan(\theta)=\frac{4}{3}[/tex]Someone please help me with this!
Answers
The width of the chest is 14.7 inches.
What is a Rectangular Prism?A rectangular prism is a three-dimensional form with six faces, where all of the faces (top, bottom, and lateral faces) are rectangles and all pairings of opposite faces are congruent. The volume of a rectangular prism is the space that it contains. We know that the volume of any prism is calculated by multiplying its base area by its height.Given:
The volume of rectangular prism = 10368 cubic inches or 6 cubic feet
Height of rectangular prism = 24 inches
It is mentioned that the chest will be twice as long as it is wide.
Let the width of the chest be x inches, so its length is 2x inches.
The volume of the chest = length × width × height
Substituting the values,
10368 = 2x × x × 24
10368 = 2x²× 24
x² = 10368/48
x = √216
x ≅ 14.7 inches ( to the nearest tenth of an inch)
Therefore, the width of the chest is 14.7 inches.
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Find the total surface area of the cone. Use the r button on your calculator. altitude = 13 cm, diameter = 11 cm, slant height = 15 cm
Answers
In general, the area of a cone is given by the formula below
[tex]\begin{gathered} A=\pi r^2+\pi rl \\ r\rightarrow\text{ radius} \\ l\rightarrow\text{ slant height} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} r=\frac{11}{2}=5.5 \\ l=15 \\ \Rightarrow A=\pi *5.5^2+\pi *5.5*15 \\ \Rightarrow A=112.75\pi \end{gathered}[/tex]Rounding to two decimal places,
[tex]\Rightarrow A\approx354.22[/tex]The answer is approximately 354.22 cm^, option D.Alan mose lawn in the summer to make money he knows that on an average he can mow 1/2 of a lawn in 1/4 hours calculate his average mowing rate in lawns per hour
Answers
Answer:
2 Lawns Mowed per hour
Step-by-step explanation:
This question requires the concept of: Conversion.
ConversionThe concept of Conversion is about converting to a certain unit value.
Example: 24 Sour Plums per 2 baskets = 12 Sour Plums per basket.
Application:For this question, we are asked to convert the unit from 0.25 hours to 1 hour.
(Note: 1/4 hours = 0.25 hours)
0.25 hours = 0.5 Lawn Mowed
(0.25 ÷ 0.25) hours = (0.5 ÷ 0.25) Lawn Mowed
1 hour = 2 Lawns Mowed per hour.
Note: You can use fractions to solve the problem, it will give you the same result.
a1 = 1; d = 3a1 = 1; d = −3a1 = 17; d = 3a1 = 17; d = −3
Answers
Given:
A graph is given and the points on the graph are as:
(1, 17), (2, 14), (3, 11), (4, 8), (5, 5), (6, 2)
Required:
To determine the value of
[tex]a_1[/tex]and d for the given sequence.
Explanation:
We can observe from the graph that the given sequence is an arithmetic sequence.
Here
[tex]a_1[/tex]represent the first value and d represent the common ratio.
So the values are as:
[tex]\begin{gathered} a_1=1 \\ d=14-17=\text{ -3} \end{gathered}[/tex]Final Answer:
[tex]a_{1=1},\text{ d = -3}[/tex]The second option is the correct answer.
A skating rink charges a group rate of $9 plus a fee to rent each pair of skates. A family rents 7 pairs of skates and pays a total of $30.
Answers
Solve for x.
Subtract 9 from both sides
7x= 21 and divide by 7
X= 3
Answer: One pair of skates costs a total of $3
Step-by-step explanation: 30 (Total) - 9 (Fee) ÷ 7 (Pairs of skates)
Total - Free ÷ Pair of skates
State the null and alternative hypotheses for the claimA report from five years ago said that the average income of accountants was $51,497; but nowadays it's more than that.
Answers
ANSWER and EXPLANATION
We want to state the null and alternative hypotheses for the claim given.
A null hypothesis is a statement about a population parameter such that the likelihood can be tested to either accept or reject the alternative hypothesis.
An alternative hypothesis on the other hand is a statement that directly contradicts the null hypothesis.
Therefore, going by that, we see that the null hypothesis is:
[tex]\mu=\$51,497[/tex]and the alternative hypothesis is:
[tex]\mu>\$51,497[/tex](1/5) -1 as the exponent
Answers
Answer:
1/5
Step-by-step explanation:
6. The National Institute of Health is studying the relationship between number of
smoked per day and the birth weight of babies born to mothers who
smoke cigarettes. A sample of the 6 points is selected are listed below.
cigarettes
No. of Cigarettes per day (X) 22 13 29 11 28 6
Birth weight (Y)
6.1 7.9 5.8 7.4 6.3 8.2
Compute Pearson's sample correlation coefficient.
Compute the equation of the least squares regression line.
ŷ
=
What is the predicted baby weight born for a mother smoke 40 cigarettes per day.
Answers
Using the calculator for the line of best-fit, the measures are given as follows:
Correlation Coefficient: -0.9405.Regression Line: y = -0.1x + 8.77.Baby weight for the mother that smokes 40 cigarettes a day: 4.77 grams.How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) given in the problem in the calculator. These points are given on a table or in a scatter plot in the problem.
From the given table, the points in this problem are as follows:
(22, 6.1), (13, 7.9), (29, 5.8), (11, 7.4), (28, 6.3), (6, 8.2).
Hence:
The correlation coefficient is of -0.9405.The regression line is of: y = -0.1x + 8.77.Hence, for a mother that smokes 40 cigarettes on a day, the predicted weight is of:
y = -0.1(40) + 8.77 = 4.77 grams.
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razy GolfmathsdivThe current value of a baseball card is 60 times its original value v (in dollars). The baseball card is worth$15. Write and solve an equation to find the original value of the baseball card.Equation:= 15Original value: $
Answers
Answer:
Equation: 60v = 15
Original value: $0.25.
Step-by-step explanation:
Current value: $15
Original value: v
The current value is 60 times the original value.
So, the equation is:
Equation: 60v = 15
Now we solve the equation to find the original value.
60v = 15
v = 15/60
v = 0.25
Original value: $0.25.
Find the suma1 = -26/5 , d = -5/3 , n = 10
Answers
The sum of the arithmentic series is -127
Step - by - Step Explanation
What to find? The sum of the arithmetic series.
Parameter Given:
a₁ = -26/5 , d=-5/3 , n=10
To find the sum of the arithmetic series we will use the formula below:
[tex]S=\frac{n}{2}\mleft\lbrace2a+(n-1)d\mright\rbrace[/tex]Substitute the values and evaluate.
[tex]S=\frac{10}{2}\mleft\lbrace2(\frac{-26}{5}_{})+(10-1)(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace2(\frac{-26}{5})+9(-\frac{5}{3})\mright\rbrace[/tex][tex]=5\mleft\lbrace-\frac{52}{5}-15\mright\rbrace[/tex][tex]=-52-75[/tex]=-127
5. Evaluate the following V16