The expression can be written without negative exponents as 1/(bm)³
Simplification of ExponentsExponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6⁴. Here, 4 is the exponent and 6 is the base.
Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a simpler form such that they cannot further be simplified. There are rules in algebra for simplifying exponents with different and same bases that we can use.
Steps to removing exponents are;
Step 1
remove parentheses by multiplying factors.
Step 2
use exponent rules to remove parentheses in terms with exponents.
Step 3
combine like terms by adding coefficients.
Step 4
combine the constants.
In this case, we have an expression;
(bm)⁻³ which can be rewritten using cube.
(bm)⁻³ = 1/ (bm)³
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at 99% confidence, how large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion? assume that past data are not available for developing a planning value for p*. round up to the next whole number.
2276 large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.
Given:
At 99% confidence, how large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.
Error e = 0.027
z score at 99%:
z = 2.576.
sample size n = p(1-p)(z/e)^2
= 0.5(1-0.5)(2.576/0.027)^2
= 0.5*0.5*9102.573
= 0.25*9102.573
= 2275.64
≈ 2276
Therefore 2276 large a sample should be taken to obtain a margin of error of 0.027 for the estimation of a population proportion.
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What is the sale price of the oil change after the discount
The sale price of the oil change after the discount can be found to be $25.50.
How to find the sale price?When given a discount, the selling price of an item is found by the formula:
= Price of item before discount - Discount
The discount on the oil change, given the price of the oil change and the coupon is:
= Price of oil change x Coupon rate
= 30 x 15%
= $4.50
The sale price after the oil change is:
= Price of oil change before discount - discount
= 30 - 4.50
= $25. 50
The first part of the question is:
An oil change at city auto is regularly $30. Mr Allen has a coupon for 15% off.
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Which is the graph of f(x) = x² + 4 and the function g, a reflection of f(x) across the x-axis?
The reflection of function f(x) across the x-axis is [tex]-x^{2} -4[/tex].
It is given to us that the function is -
[tex]f(x)=x^{2} +4[/tex] --- (1)
and a function g
We have to find out the reflection of f(x) across the x-axis.
A function can be defined as an expression that assigns the value of each element of a given set to the another specific element of another given set.
To find out the reflection of f(x) across the x-axis, we have to take -f(x) instead of f(x).
Now,
[tex]-f(x)=-(x^{2} +4)\\= > -f(x)=-x^{2} -4[/tex]
Thus, the reflection of function f(x) across the x-axis is [tex]-x^{2} -4[/tex].
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Write the equation of the function in
slope-intercept form:
A line with a slope of 2 and passes through (-8, 3)
The equation of the function in slope-intercept form with slope of 2 is y = 2x+19.
According to the question,
We have the following information:
Slope = 2 (Note that slope of a line is denoted by m.)
Points through which function is passing = (-8,3)
So, we have x' = -8 and y' = 3.
We know that the following equation is used to find the equation of the function or line:
(y-y') = m(x-x')
y-3 = 2{x-(-8)}
y-3 = 2(x+8)
y-3 = 2x+16
y = 2x+16+3
y = 2x+19
Hence, the equation of the function in slope-intercept form with slope of 2 is y = 2x+19.
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Determine the distance between each set of ordered pairs
(6 7/8,2) and (-3,2)
Answer:
Determine the distance between each set of ordered pairs
(6 7/8,2) and (-3,2)
Step-by-step explanation:
Well if you do delta y over delta x you do -2 - 2 over 3 - 67/8 which will be -4 over -5.375 which will equal 32 over 43 which is you M you b is one point (your choice) then y = mx + b so 2 = 32/43(-3) + b 2 = -96/43 + b then add -96/43 to both sides and you'll get -10/43 = b so y = 32/43x + -10/43
equation - y = 32/43x + -10/43
DEFG has been dilated to D'EF'G'. Use a pair of corresponding sides to determine the scale factor.
a 2/1=2
b 3/2
c1/2
d2/3
The scale factor for a a pair of corresponding sides will be;
⇒ 3 / 2
What is Proportional?
The equality between two ratio is called Proportional.
Given that;
DEFG has been dilated to D'EF'G'.
Now,
Let the coordinates of DEFG are for side DG are;
D = (- 6, 3)
G = (- 3, 3)
And, The coordinates of D'E'F'G' are for side D'G' are;
D' = (- 4, 2)
G' = (- 2, 2)
So, The length of side DG is;
DG = √ (- 3 - (-6))² + (3 - 3)²
= √ 3²
= 3
And, The length of side D'G' is;
D'G' = √ (- 2 - (-4))² + (2 - 2)²
= √ 2²
= 2
Thus, The scale factor for a a pair of corresponding sides will be;
⇒ DG / D'G' = 3 / 2
Therefore, The scale factor for a a pair of corresponding sides will be;
⇒ 3 / 2
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Two sides of a triangle are 30in and 30in, what are the possible lengths of the third side
Answer:
[tex]0 < x < 60[/tex]
Step-by-step explanation:
By the Triangle Inequality Theorem:
30 + 30 > x, so 60 > x ----> x < 60
30 + x > 30, so x > 0
x + 30 > 30, so x > 0
Putting these inequalities together, we have 0 < x < 60. So the length of the third side can be greater than 0 inches but less than 60 inches.
in a city of 246,000 people, there are 34 coffee shops. what is the number of coffee shops per capita? round to 6 decimal places.
Coffee shops per capita in city is 7235.294118
What is per capita?
The Latin phrase "per capita" means "by head." In statistics, the term "per capita" is sometimes used in place of "per person" to denote the average per person.
Main Body:
total population of city = 246000
Total coffee shops = 34
Per capita shops for population can be calculated by dividing total population by total shops.
calculatiing,
Per capita shops = total population/ total shops
= 246000/34
= 7235.294118
Hence number of coffee shops per capita is 7235.294118
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one of euler's conjectures was disproved in the 1960s by three american mathematicians when they showed that there is a positive integer such that find the value of .
It quickly becomes apparent that 174 is much too large, so n must be 144.The value of the n is 144.
Taking the given equation modulo 2,3, and 5, respectively, we have
n⁵≡(mod 2)
n⁵≡(mod 3)
n⁵≡( mod 5)
By either Fermat's Little Theorem (FLT) or inspection, we get
n≡(mod 2)
n≡(mod 3)
n≡( mod 5)
By either the Chinese Remainder Theorem (CRT) or inspection, we get n≡ 24 ( mod 30)
It is clear that n>133, so the possible values for n are 144,174,204,...Note that
n⁵ = 133⁵ + 110⁵ + 84⁵ + 27⁵
n⁵ < 133⁵ + 110⁵ +( 84 + 27)⁵
n⁵ =133⁵ + 110⁵ + 111⁵
n⁵ < 3.133⁵
From which (n/133)⁵ < 3
If n>= 174 then,
(n/133)⁵ > 1.3⁵
(n/133)⁵ = 3
which arrives at a contradiction. Therefore, we conclude that n=144
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How do I graph y=3x+2
8. What is the value of point x? X -4 -3
Answer:
x = -9
Step-by-step explanation:
(x1, y1) = (-4, 3) & (x2, y2) = (x, 4)
m = (y2 - y1)/(x2 - x1)
-1/5 = (4 - 3)/(x - (-4) = 1/(x+4)
-(x + 4) = 5
-x - 4 = 5
-x = 5 + 4 = 9
the product of two consecutive nonnegative integers is 240 find the integers and separate them with a comma
The product of two consecutive non-negative integers is 240 and the integers are 15,16.
What are consecutive integers?
The numbers that come after one another are known as consecutive integers. They proceed sequentially or alphabetically. For instance, a group of natural numbers is a sequence of integers. In mathematics, the term "consecutive" refers to an uninterrupted succession or a continuous flow of numbers, so that successive integers follow a sequence in which each succeeding number is one more than the one before it. The mean and median in an array of successive integers (or in numbers) are both identical. In the event that x is an integer, then x + 1 and x + 2 are also integers.Let the numbers be x, x+1
Product is x(x+1)=240
x² + x = 240
x² + x − 240 = 0
x² + 16x − 15x − 240 = 0
x(x+16) − 15(x+16) = 0
(x+16)(x−15)=0
x = 15,−16
So, the product of two consecutive non-negative integers is 240,then numbers are 15, 16.
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. Examine this graph. What are the y-intercept and slope of this line?
*
10 points
Captionless Image
Hey, so because you didn't include the image this is impossible to get the number values. But, essentially you'd solve it something like this.
Remember, the Y axis goes up, and its located when you are at X = 0.
The y intercept is the value of Y, when is 0.
The slope of a line is referred to as "rise/run"
Basically, you take any given spot. For example, from x = 0 to x = 2. The run is 2, because thats how much x value the line covers. So, in that "run" how much do you go up or go down? Lets say in those 2 x's that you travelled, how much did the height change? If you changed by going up 4 units, it would be (rise/run) 4/2 = 2. The slope would be 2. That means that for every time x increases by 1, Y goes up 2.
Find the missing side. Help please
Answer:
Step-by-step explanation:
add 23+14=37-90= 53
answer=53
The tiger at the zoo ate 133 pounds of food in
7 days Find the average change in the zoo's
tiger food supply each day.
Answer:
133/7 = 19
Step-by-step explanation:
"Find the average change in the zoo's tiger food supply each day."
And what does that have to do with anything? It's not like there is a change in diet that we can then easily calculate using derivatives.
The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. When m=8kg and d=5meters, F=100 Newtons. Find F when m=2 kilograms and d=15 meters.
The force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.
According to the question,
We have the following information:
The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. And when m=8kg and d=5meters then F=100 Newtons.
Now, let's take the constant for this case to be k.
We have the following expression:
F = km/[tex]d^{2}[/tex]
Putting the values in this expression to find the value of k:
100 = 8k/(5*5)
Using the cross multiplication method:
2500 = 8k
k = 2500/8
k = 312.5
Now, we have the following value of F:
F = 312.5*2/15*15
F = 625/225
F = 2.78 Newton
Hence, the force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.
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What is the equation of the graph below?
Oy=-(x-2)²+3
Oy=(x + 2)²+3
Oy=-(x+3)²+2
Oy=(x-3)²+2
The equation of the graph is given by y = ( x + 2 )² + 3
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the equation be represented as A
Now , the value of A is
y = ( x + 2 )² + 3
The given equation is in the standard vertex form of a parabola:
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
By comparing the given equation with the standard vertex form, we can see that:
a = 1, h = -2, and k = 3
Hence , the vertex of the parabola is at the point (-2, 3) and the graph is plotted
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Find 7 5/12−(−3 3/4) . Write your answer as a mixed number in simplest form.
The simplified expression is 11 (1/6).
What is a fraction?A fraction is a part of the whole represented by a/b, where a and b are any integers.
The given expression is 7 (5/12) - (-3 (3/4)).
Simplify the expression as follows:
7 (5/12) - (-3 (3/4))
= 89/12 +15/4
= (89+45)/12
= 134/12
= 11 (1/6)
Hence, the simplified expression is 11 (1/6).
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Mo puts $290000 into savings bonds that pay a simple interest rate of 5.2%. How much money will the bonds be worth at the end of 6 years
Answer:
in six years, Mo will have roughly $393090.4 in savings bonds.
Step-by-step explanation:
(This might not be the most efficient way to do it.)
year one - 290000 x 1.052 = 305080
year two - 305080 x 1.052 = 320944.16
year three - 320944.16 x 1.052 = 337633.256
year four - 337633.256 x 1.052 = 355190.185
year five - 355190.185 x 1.052 = 373660.075
year six - 373660.075 x 1.052 = 393090.399
in six years, Mo will have roughly $393090.4 in savings bonds.
solve for y
18-5x= -9y
Answer:
y= [tex]\frac{5}{9}[/tex]x - 2
Step-by-step explanation:
You want to get y alone so divide both sides by -9 to get: y = [tex]\frac{5}{9}[/tex]x- 2
this is because 2 negatives (-5x and -9) make a positive
Given ∠11≅∠13. Which lines, if any, must be parallel based on the given information? Justify your conclusion.
Based on the information given: A. c║d; converse of alternate exterior angles theorem.
What is the Converse of Alternate Exterior Angles Theorem?Exterior alternate angles are congruent based on the alternate exterior angles theorem. Conversely, it can also be stated that if two angles, which are exterior alternate angles, are congruent to each other, therefore the lines they lie on that is crossed by a transversal are proven to be parallel to each other based on the converse of alternate exterior angles theorem.
Given that angles 11 and 13 are congruent angles, the diagram also shows that they are alternate exterior angles. They lie on each lines, c and d, that are crossed by transversal a.
Therefore, based on the converse of alternate exterior angles theorem, lines c and d are parallel.
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Please help me please
Answer:
m<T = 60°
m<U = 60°
TS = 13
SU = 13
Step-by-step explanation:
Triangle TSU is an equilateral triangle.
All interior angles has equal measures and each = 60° since the sum of interior angles in a triangle is equal to 180 and this divided by 3 = 60
all side lengths are also equal to one another, TU is given as 13 cm so the length of TS and SU is also = 13
URGENT !!! Answer the following questions using the graph.
Describe the y-intercept in this scenario.
Describe the x-intercept in this scenario.
Finish the ordered pairs (2.5, ____ ) and (____,300).
What are the domain and range?
Domain: {h I ___ < h < ____}
Range: {f(h) I ___ < f(h) < ____}
The x-intercept is (8.75,0) and
The y-intercept is (0,700)
The ordered pairs are (2.5,500) and (5,300).
Given that,
In the picture we have a graph with line.
We have to find the x-intercept and y-intercept of the scenario and the ordered pairs (2.5, ___) and (___ , 300)
We know that,
What is x-intercept and y-intercept?The x intercept is the location where the line touches the x axis. The y intercept is the location where the line touches the y axis.
So,
The x-intercept is (8.75,0) and
The y-intercept is (0,700)
The ordered pairs are (2.5,500) and (5,300).
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I will love some help so if you can help that will be wonderful the question is Given the equation k over 34.2 equals 8.7, determine the value of k.
25.5
297.54
3.93
42.9
Answer:
k=297.54
Step-by-step explanation:
i can't really explain it
The value of k that satisfies the equation k/34.2 = 8.7 is approximately 297.54. So, correct option is B.
To determine the value of k in the equation k/34.2 = 8.7, we can solve for k by isolating it on one side of the equation.
We can start by multiplying both sides of the equation by 34.2 to eliminate the denominator:
k/34.2 * 34.2 = 8.7 * 34.2
This simplifies to:
k = 8.7 * 34.2
Evaluating the right side of the equation:
k ≈ 297.54
The correct option from the given choices is 297.54. So, correct option is B.
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how many ordered pairs ( m , n ) of positive integers, such that m > n , have the property that their squares differ by 96 ?
Answer:
4 pairs
Step-by-step explanation:
You want the number of pairs of integers (m, n) such that m > n and m² -n² = 96.
Difference of squaresThe difference of squares is factored as ...
m² -n² = (m -n)(m +n)
In order for the difference to be 96, these factors must be factors of 96.
Factors of 96The prime factorization of 96 is ...
96 = 2^5 · 3
The number of divisors of 96 is the product of the exponents of these factors, each increased by 1:
(5+1)(1+1) = 12
That is, there are 12/2 = 6 factor pairs ab such that a<b. They are ...
96 = 1·96 = 2·48 = 3·32 = 4·24 = 6·16 = 8·12
SolutionThe values of m and n relate to the values of 'a' and 'b' by ...
m = (a+b)/2
n = (b-a)/2
In order for m and n to be integers, the values of 'a' and 'b' must both have the same parity. That is, they must both be even, or both be odd. This eliminates the factor pairs 1·96 and 3·32, leaving 4 (a, b) pairs, hence 4 (m, n) pairs. Possible ordered pairs are ...
(m, n) ∈ {(25, 23), (14, 10), (11, 5), (10, 2)} . . . . . 4 pairs
suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)?
Using the concepts of confidence interval, we got that is he interval estimate for the population proportion if we suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president.
We know that population proportion is given by the fraction of number of positive results to the total number of results
Therefore, Population Control(P)=1608/2400
=>P =0.67
Now, we are given that confidence interval is 0.95 degree or 95%
For 95%,confidence interval is given by =P±√[P×(1-P)]/n
where n is the total number of registered voters, and P is the population control.
confidence interval=0.67±√[0.67×(1-0.67)]/2400
=0.67±√(0.67×0.33)/2400
=0.67±√0.2211/2400
=0.67±(0.47/48.98)
=0.67±0.0095
=0.660 and 0.679
Hence, if we suppose 1,608 of 2,400 registered voters sampled said they planned to vote for the republican candidate for president. using the 0.95 degree of confidence, the interval estimate for the population proportion is (0.660,0.679)
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Simplify and Explain This Equation
-8-3(9-2x)+9x
Two sides of a parallelogram are 190 feet and 740 feet. The measure of the angle
between these sides is 88°. Find the area of the parallelogram to the nearest square
foot.
Answer: About 140,514 ft²
Step-by-step explanation:
The area of a parallelogram is base × height. The base is already determined as 740 ft. You can find the height(h) with trigonometry:
[tex]sin(88)=\frac{h}{190}\\ \\h=190sin(88)=189.88425713[/tex]
Now, multiply the values together:
[tex]740*189.88425713=140514.350[/tex]
A piont is two dimensional ?
Answer:
False.
Step-by-step explanation:
A point is a zero-dimensional object as it has no length, width or height. It has no size.
And it would be great if you can spell "point" correctly.
john recently bought a used car for $\$5000$ for his pizza delivery job. he gets $\$10$ for each pizza he delivers, but he has to spend $\$3$ on gas for each pizza he delivers. what is the minimum whole number of pizzas john must deliver in order to earn back the money he spent on the car he bought?
The minimum number of pizzas that john must deliver to earn back the money he spent on the car he bought is 715 pizzas .
In the question,
it is given that ,
the amount for which John bought the used car for pizza delivery = $5000
the amount John gets for 1 pizza he delivers = $10
the amount John spend on gas for 1 pizza he delivers = $3
So , the amount that John earned for 1 pizza delivered is = 10 - 3 = $7 .
the number of pizza required to sell = (price of car)/(amount earned from 1 pizza)
Substituting the values , we get
number of pizza required to sell = 5000/7 = 714.2857
rounding the answer to whole number ,
we get
= 715 pizzas
Therefore , The minimum number of pizzas that John must deliver to earn back the money he spent on the car he bought is 715 pizzas .
The given question is incomplete , the complete question is
John recently bought a used car for $5000 for his pizza delivery job. he gets $10 for each pizza he delivers, but he has to spend $3 on gas for each pizza he delivers. what is the minimum whole number of pizzas john must deliver in order to earn back the money he spent on the car he bought ?
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