Final answer:
The simplified form of the expression [tex](-0.2b^{6})^3(5b)[/tex] is [tex]-0.04b^{19}[/tex], obtained through raising to a power and multiplication.
Explanation:
The student's question involves simplifying an algebraic expression by raising a term to a power and then multiplying it by another term. To simplify [tex](-0.2b^{6})^3(5b)[/tex], we must first raise [tex]-0.2b^{6}[/tex] to the third power and then multiply the result by 5b. This will give the answer [tex]-0.04b^{19}[/tex], which can be obtained following the below mentioned steps.
Let's do this step by step:
Raise [tex]-0.2b^{6}[/tex] to the third power: [tex](-0.2)^3[/tex]= −0.008 and [tex](b^{6})^3[/tex]= [tex]b^{18}[/tex]
Multiply the result by 5b: [tex](-0.008)b^{18}*5b[/tex] = [tex](-0.008*5)b^{18+1}[/tex] = [tex]-0.04b^{19}[/tex]
The final simplified expression is [tex]-0.04b^{19}[/tex].
a rectangle has a side length 2x+9 and side width x. If the perimeter is 36 cm, what is the value of x?
which number line represents the solutions to |-2x|=4?
Simplify.
16.3 – (–4.2) + 15.9
16.3 - (-4.2) +15.9 =
16.3 + 4.2 + 15.9 =
36.4
One evening, 2/3 of the students in Rick's class watched television.
Please answer ASAP: Determine which of the following situations can be modeled by the ratio 7/2. Select all situations that apply
For every twenty-eight cats, there are 4 dogs
Sara runs an average of fourteen miles every four days.
An online clothing store charges $7.50 to ship ten clothing items
A recipe calls for 3 cups of flour for every 1 cup of sugar.
Bottled water is on sale this week for a rate of $1.50 for two bottles
the only one that applies is:
Sara runs 14 miles every 4 days = 7 miles every 2 days = 7/2
Which of these statements is true?
A) 4 x 5 – 7 + 9 = 28
B) 4 x 5 – (7 + 9) = 22
C) 4 x 5 – (7 + 9) = 4
D) 4 x 5 – 7 + 9 = 44
Which of the following numbers are divisible by 2? 74 , 296, 1110, 148, 370, 666, 9324, 111, 37, 555 , or 333?
Which is the graph of the function f(x) = x2 + 2x – 6? Mark this and return
The graph of the function f(x) = x² + 2x − 6 is an upward-opening parabola with the vertex at (-1, -7) and a y-intercept at (0, -6). There are no asymptotes for this quadratic function.
Explanation:To find the graph of the function f(x) = x² + 2x − 6, we need to look at the characteristics of this quadratic equation. This is a parabola that opens upward because the coefficient of x² is positive. We can find the vertex of this parabola by using the formula -b/2a for the x-coordinate of the vertex.
Here, a = 1 and b = 2. Applying the formula, we get the x-coordinate of the vertex as -b/2a = -2/(2×1) = -1. Now, we plug this value back into the function to get the y-coordinate of the vertex: f(-1) = (-1)² + 2(-1) − 6 = 1 - 2 - 6 = -7. Therefore, the vertex of the parabola is at (-1, -7). The parabola will intersect the y-axis when x = 0, which gives us the y-intercept f(0) = -6. No asymptotes are present in this quadratic function.
The graph of f(x) is symmetrical about the line x = -1 and has a y-intercept at (0, -6). The vertex at (-1, -7) is the lowest point on the graph since the parabola opens upwards. Thus, we are looking for a graph with these characteristics to represent the function f(x) = x² + 2x − 6.
Mr. Obama would like his daughter to attend Harvard in 6 years when she finishes high school. Mr. Obama would like to invest enough money in a certificate of deposit (CD) now to pay for his daughter’s college expenses. If he estimates that he will need $250 thousand in 5 years, how much should he invest now in a CD that has a rate of 2.8% compounded monthly?
what is 16 divided by 7? and give me a real answer.
Find the radius of a circle with the given circumference.
15 ft.
r =
A.30 ft.
B.30 ft.
C.7.5 ft.
D.7.5 ft.
Answer: [tex]\dfrac{7.5}{\pi}\ ft[/tex]
Step-by-step explanation:
We know that , the circumference of a circle is given by :-
[tex]C=2\pi r[/tex] , where r is the radius of the circle.
Formula for radius :
[tex]r=\dfrac{C}{2\pi}[/tex] , where C is the circumference of the circle.
Given : Circumference of circle = 15 ft.
Then , the radius of a circle will be :-
[tex]r=\dfrac{15}{2\pi}=\dfrac{7.5}{\pi}\ ft[/tex]
Hence, the radius of a circle= [tex]\dfrac{7.5}{\pi}\ ft[/tex]
What is the simplified form of the following expression
To simplify the given expression, factor out the common factors from the denominator and rewrite the expression using the factored form.
Explanation:To simplify the given expression, we first need to simplify the denominator. This can be done by factoring out a common factor of 4 from each term:
(4a + 2)(2a - 3)
Next, we can rewrite the expression using the factored form:
1 / (4a + 2)(2a - 3)
This is the simplified form of the given expression.
The answer is c. [tex]$\frac{\sqrt[3]{20 x}}{5}$[/tex]
Separate the cube root: We can break down the cube root of a fraction into the cube root of the numerator divided by the cube root of the denominator:
[tex]\sqrt[3]{\frac{4 x}{5}} = \frac{\sqrt[3]{4 x}}{\sqrt[3]{5}}[/tex]
Simplify the cube root of 5: Since 5 is a perfect cube (5 = 1 * 5 * 5), its cube root is simply 5:
[tex]\frac{\sqrt[3]{4 x}}{\sqrt[3]{5}} = \frac{\sqrt[3]{4 x}}{5}[/tex]
Rationalize the denominator: To make the expression look more simplified, we can eliminate the cube root in the denominator. We do this by multiplying both the numerator and denominator by the cube root of 5:
[tex]\frac{\sqrt[3]{4 x}}{5} \times \frac{\sqrt[3]{5}}{\sqrt[3]{5}} = \frac{\sqrt[3]{4 x} \times \sqrt[3]{5}}{5 \times \sqrt[3]{5}}[/tex]
This simplifies to:
[tex]\frac{\sqrt[3]{20 x}}{5}[/tex]
Therefore, the simplified form of the expression is [tex]$\frac{\sqrt[3]{20 x}}{5}$[/tex].
Complete Question:
What is the simplified form of the following expression?
[tex]\sqrt[3]{\frac{4 x}{5}}[/tex]
a. [tex]$\frac{\sqrt[3]{4 x}}{5}$[/tex]
b. [tex]$\frac{\sqrt[3]{20 x}}{5}$[/tex]
c. [tex]$\frac{\sqrt[3]{100 x}}{5}$[/tex]
d. [tex]$\frac{\sqrt[3]{100 x}}{125}$[/tex]
True or false? If you took a true "if-then" statement, inserted a not in each clause l, and reversed the clauses, the statement would also be true
Please help..click on picture...I rrally need help
Which function represents the graph of f(x)=|2x| after it is translated 5 units to the left?
g(x)=|2(x−5)|
g(x)=|2x+5|
g(x)=|2x−5|
g(x)=|2(x+5)|
Answer:
g(x) = |2(x+5)|
Step-by-step explanation:
To translate a function left 5 units, replace x with (x+5). In this function, that means
2x ⇒ 2(x+5) . . . . . matches the last choice
Liliana takes 4 breaths per 10 seconds during yoga. At this rate, about how many breaths would Liliana Take in 2 minutes of yoga?
It takes a boat 2 hours to travel 22 miles downstream and 4 hours to travel 20 miles upstream. What is the speed of the boat in still water?
The formula for the circumference C of a circle, in terms of the radius, is C=2πr, where r stands for the radius. Rearrange the quantities in this formula to give a new formula for the radius of a circle in terms of the circumference.
A. r= 2C/3.14
B. r=3.14/2C
C. r=C/2(3.14)
D. r= 1/2(3.14)C
To get the radius of a circle in terms of circumference, divide the formula for the circumference by 2π, thus r=C/(2π). The correct option is C: r=C/2(3.14), considering 3.14 is the approximate value of π.
Explanation:The formula for the circumference of a circle is given by C=2πr. We are asked to rearrange this formula to make the radius (r) the subject of the formula. To achieve this, we divide both sides of the equation by 2π.
So, dividing both sides of the equation by 2π gives r=C/(2π).
Looking at your options, Option C: r=C/2(3.14), is correct if we consider 3.14 to be the value of π. Therefore, the radius of a circle in terms of the circumference is given by r=C/(2π).
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Which is the most accurate way to estimate 23% of 70?
Frank's Factories has a staff of sales people like Anthony, who receives a monthly salary of $2,750.00 plus an incremental commission based on the table below. If he sells $27,300.00, what is his total gross pay for the month?
The total gross pay for the month is $3,930.80 if Frank's Factories has a staff of salespeople like Anthony, who receives a monthly salary of $2,750.00.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Frank's Factories has a staff of salespeople like Anthony, who receives a monthly salary of $2,750.00 plus an incremental commission based on the table below. If he sells $27,300.00,
Fixed monthly salary = $2,750.00
First commission = 4.1% of 15,000 = $615.00
Second commission = 4.6% of (27300 - 15000) = $565.00
Total gross pay for the month = $2,750.00 + $615.00 + $565.80
= $3,930.80
Thus, the total gross pay for the month is $3,930.80 if Frank's Factories has a staff of salespeople like Anthony, who receives a monthly salary of $2,750.00.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
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To calculate Anthony's total gross pay for the month, consider his base salary and incremental commission based on sales, resulting in a total gross pay of $4,934.00.
To calculate Anthony's total gross pay for the month, we need to consider his base salary and incremental commission based on sales.
Base salary: $2,750.00
Commission on $27,300.00 sales: Using the incremental commission table, the commission percentage for sales between $27,194-$31,479 is 8%. Thus, commission = $27,300.00 * 8% = $2,184.00
Total gross pay = Base salary + Commission = $2,750.00 + $2,184.00 = $4,934.00
Please help! First rewrite 17/18 and 11/12 so that they have a common denominator then use <, =, or > to order 17/18 and 11/12
Anyone knows??? And like to help
Find the absolute value of the jacobian, ∣∣∂(x,y)∂(s,t)∣∣, for the change of variables given by x=s+5t,y=3s+8t
Opening up the monthly cell phone bill can be alarming due to the uncertainty of the bill. suppose the amount of minutes used per month is distributed normally with a mean of 700 minutes and a standard deviation of 120 minutes. what is the probability that more than 940 minutes were used?
Answer:
the required probability = 0.25
Step-by-step explanation:
Mean = 700 minutes , Standard Deviation = 120 minutes
To find : the probability that more than 940 minutes were used.
Solution : First find the z-score for 940 minutes and then find the area under the curve to the right of associated standard deviations from the mean.
[tex]z-score=\frac{\mu_2-\mu_1}{\sigma}\\\\\mu_1=700,\mu_2=940,\sigma=120\\\\\implies z-score=\frac{940-700}{120}\\\\\implies z-score=2[/tex]
Now, calculate the area under the curve to the right of 2 standard deviations from the mean.
Take confidence level to be 95%.
The area to the right of 2 standard deviations is 0.5 that is half the area under the standard normal curve.
[tex]\implies Area < \frac{0.95}{2}\\\\\implies Area<0.475[/tex]
Now, to find the probability that more than 940 minutes were used = 0.5 - 0.475 = 0.25
Hence, the required probability = 0.25
Mr. and mrs. harris have six kids aged 5, 6, 8, 10, 16, and 19. the median age of the harris children is _____.
Answer:
The median age is 9 years old
Step-by-step explanation:
We can find the median by getting the average of the center number of the middle two numbers
8 and 10 are the two middle numbers in this scenario. 8 + 10 = 18
18/2 = 9
Find the tax on a dinette set with a cash price of $200 that has been reduced by 20% if the tax rate is 6.5%.
2.60
10.40
11.70
13.00
Answer:
The correct option is B.
Step-by-step explanation:
The initial cash price is $200.
The cash price reduced by 20%.
20% of $200 is
[tex]200\times \frac{20}{100}=40[/tex]
The cash reduced by $40.
The new cash price is
[tex]\$200-\$40=\$160[/tex]
The tax rate is 6.5%.
6.5% of remaining cash is
[tex]160\times \frac{6.5}{100}=10.40[/tex]
Therefore option B is correct.
How many numbers in the data set are within 1 standard deviation of the mean?
a.13
b.14
c.15
d.16
A pinewood derby car can be at most 2 3/4 inches wide. About how many pinwood derby cars can be displayed side-by-side on a shelf that is 31 1/2 inches long?
About 5 11/22 pinewood derby cars can be displayed side-by-side on a shelf that is 31 1/2 inches long.
Explanation:To find out how many pinewood derby cars can be displayed side-by-side on a shelf, we need to divide the length of the shelf by the width of each car. The shelf is 31 1/2 inches long, and each car can be at most 2 3/4 inches wide. So we divide 31 1/2 by 2 3/4:
Therefore, about 5 11/22 pinewood derby cars can be displayed side-by-side on the shelf.
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Which of these story problem describes the sum 19 + (-12)? Check all that apply. Show your work to justify your answer.
Line s is the perpendicular bisector of JK. If line s intersects JK at point L, which of the following statements must be true? Check all that apply. A. Line s is perpendicular to JK B. JL = KL C. Line s is parallel to JK D. Point L is the midpoint of JK E. Line s intersects JK at a 180 angle
Line s, being the perpendicular bisector of JK, must be perpendicular to JK at point L, making JL equal to KL and meaning that point L is the midpoint of JK.
Explanation:If line s is the perpendicular bisector of segment JK and intersects it at point L, we can determine several truths about the geometric relationship between these elements:
A. Line s is perpendicular to JK: Yes, this is true because by definition, a perpendicular bisector not only cuts a line segment into two equal parts but also does so at a 90° angle.B. JL = KL: This statement must also be true. Since line s is a bisector, it divides JK into two equal parts, hence JL (the length from J to L) is equal to KL (the length from K to L).D. Point L is the midpoint of JK: True again, as the point where the perpendicular bisector intersects the line segment is known as the midpoint, implying that point L is equidistant from both J and K.Statements C and E are incorrect. Line s cannot be parallel to JK as it intersects it, and a 180° angle refers to a straight line, not the angle formed by a perpendicular intersection.