Answers
The values of the exponential expressions are follows;
3. [tex] {x}^{m \times n} [/tex]
4. [tex] {\frac{1}{4} }^{16} [/tex]
5. [tex] {( - 3)}^{5} [/tex]
6. [tex] 5.3 \cdot {( - 4)}^{11}[/tex]
7. [tex] {(2.9)}^{10} [/tex]
How can the exponential expressions be simplified?The given expression that can be used to show the Power of a Power Exponent law are as follows;
3. The Power of a Power Exponent law states that;
[tex] {( {x})^{m} }^{n} = {x}^{m \times n} [/tex]
4. The given expression is presented as follows;
[tex] { ({( \frac{1}{4} )}^{2} )}^{8} ={\frac{1}{4} }^{2 \times 8} = {\frac{1}{4} }^{16} [/tex]
5. [tex] {( - 3)}^{4} \times - 3 = {( - 3)}^{4 + 1} = {( - 3)}^{5} [/tex]
6. [tex]5.3 \cdot {( - 4)}^{11} = 5.3 \cdot {( - 4)}^{11}[/tex]
7. [tex] {(2.9)}^{2} \cdot {(2.9)}^{5} \cdot {(2.9)}^{3} = {(2.9)}^{2+5+3} [/tex]
[tex] {(2.9)}^{2+5+3}={(2.9)}^{10} [/tex]
Therefore;
[tex] {(2.9)}^{2} \cdot {(2.9)}^{5} \cdot {(2.9)}^{3} = {(2.9)}^{10} [/tex]
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Related Questions
What is -33.44/-1.9 in division?
Answers
The division of the number -33.44/-1.9 is 17.6.
What is referred as division?Division is one of four fundamental mathematical operations, along with addition, subtraction, as well as multiplication.
Division is defined as the separating of a large group in to other smaller groups so that each group has an equal amount of items.Division is a process of repeated subtraction. It is the inverse operation of multiplication.It is characterized by the creation of equal groups. When we divide numbers, we break them down into smaller numbers so that the multiplication of the those smaller numbers equals the larger number taken.For the given expression;
= -33.44/-1.9
as, both numerator and denominator is negative values, both negative signs will be cancelled.
Now, divide numerator 33.44 by denominator by 1.9, we get 17.6.
Thus, the division of the number -33.44/-1.9 gives quotient 17.6.
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Write √-45 in simplest radical form.
Answers
Answer: 3[tex]\sqrt4[/tex]
Step-by-step explanation:
Simplified radical form of the square root of 45
Square root of 45 can be expressed as, √45 = √(9 × 5) = 3√5. 45 is not a perfect square, so, it remains within roots. The simplified radical form of the square root of -45 is 3√5.
Answer:
3√5i
Step-by-step explanation:
[tex]\sqrt{-45}=\sqrt{-1}\sqrt{45}\\\sqrt{-1}\sqrt{45}\\i\sqrt{45}\\**Prime\:Factorization*\\3 \times 3 \times 5 = 45\\=3\sqrt{5}i[/tex]
➲ Hope this helps.
What is the equation of a line that is parallel to y = 6x + 7 and passes through (0, 9)? Enter your equation in the box.
Answers
Answer:
y = 6x + 9
Step-by-step explanation:
parallel lines have equal gradients.
y - y1 = m(x -x1)
since the lines are parallel your m = 6.
y - y1 = 6(x - x1)
(x1 ; y1) is given (0 ; 9)
y - 9 = 6 (x -0)
y = 6x + 9
Find the distance between B (3,−4) and C (5,−5). Round to the nearest tenth, if necessary.
Answers
Using the distance formula, the distance between B and C is calculated as: 2.3 units.
How to Find the Distance Between Two Points?The distance formula to apply is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the following:
B (3,−4) = (x1, y1)
C (5,−5) = (x2, y2)
Plug in the values into the distance formula
BC = √[(5−3)² + (−5−(−4))²]
BC = √[(2)² + (−1)²]
BC = √(4 + 1)
BC = √5
BC = 2.236068 ≈ 2.3 units.
Therefore, using the distance formula, the distance between B and C is calculated as: 2.3 units.
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A speculative statement about the relationship between two or more variables is known as a? a-correlation b- hypothesis c- sample d- research design
Answers
A speculative statement about the relationship between two or more variables is known as a b - hypothesis.
Variables:
A variable is a measurable trait or characteristic that is subject to change under different conditions.
Given,
Here we need to find what is meant by a speculative statement about the relationship between two or more variables.
The definition of Hypothesis is,
It is basically a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
So, a speculative statement about the relationship between two or more variables is known as a b - hypothesis.
So, the option (b) - Hypothesis is correct.
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Makayla is taking a math course and is working with the perimeter of rectangles. She knows the perimeter and length of her rectangle but wants to solve for the width. Rearrange the following equation for W, where P is the perimeter, L is the length, and W is the width of the rectangle.
P = 2L + 2W
Answers
Step by step
- Subtract 2L from both sides of the equation to isolate W
P = 2L -2L + 2W
P -2L = 2W
- Divide both sides of the equation by 2 to solve for W
P-2L/2 = 2/2 W
P - 2L /2 = W
So W = P - 2L/2 is your answer
A sample in a 1-cm cuvette is assessed with a spectrophotometer set to 620 nm. If the sample returns a transmittance of 62%, then what is the approximate absorbance of the sample?.
Answers
The absorbance of the given sample is 0.2076.
Length of the cuvette = 1 cm
Wavelength of the spectrophotometer = 620nm
Transmittance of the sample = 62%
We know, absorbance is related to transmittance by the formula written below;
A = log(1/T) equation 1
Also, percent transmittance %T = 100T
or we can write, T = (%T) / 100
On substituting value of T in equation 1 , we get
A = log(100/(%T))
⇒ A = log(100) - log (%T)
⇒ A = log([tex]10^{2}[/tex]) - log(%T)
⇒ A= 2log(10) - log(%T)
We know, log10 = 1. On substituting the value of log 10 in above equation, we get
A = 2 - log(%T)
⇒ A = 2 - log(62)
⇒ A = 2 - 1.7924
⇒ A = 0.2076
The absorbance of the given sample is 0.2076.
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are the ratios 1:4 and 3:5 equivalent
Answers
Answer:no
Step-by-step explanation:1:4 is not equivalent to 3:5
A town's population is 42,975. About 125 people move out of the town each month. Each month, 150 people on average move into town. A nearby town has a population of 45,225. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
Answers
It would take 10 months to equate the population of both the towns
Let the number of months required to equate the population of both the town( Town A and Town B) be x
This question can be solved using linear equations
So, town A's population would be current population adjusted with migration of people which is 42975-125x+150x
And town B's population would be current population adjusted with migration of people which is 45225 -200x
As at the end of x months the population of the two towns is equal, so equating both the linear equations
42975 -125x +150x = 45225-200x
Now solving the equation for x
150x-125x+200x= 45225-42975
225x=2250
Therefore x= 2250/225= 10
Hence it would take 10 months to equate the population of both the towns
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what is the answer for this it’s pre algebra pls answer quickly it’s due in 10 mins
Answers
The answer is k⁴n⁶/3 after solving the expression.
Given, the expression is kn/3k⁻³n⁻⁵
now we must simplify the expression with the help of the negative exponent rule.
A base that is on the fraction line's denominator side can be indicated by a negative exponent. In other words, according to the negative exponent rule, a number with a negative exponent should be added to the numerator and vice versa.
that is, a⁻ⁿ = 1/aⁿ
therefore, kn/3k⁻³n⁻⁵ = knk³n⁵/3
Multiply the monomials.
Monomials should be multiplied by adding the exponents to the coefficients before moving on to the variables. You can sum the exponents of monomials while multiplying them by the same base. The Product of Powers Property is used to describe this.
k⁴n⁶/3
Hence we get the answer after simplification as k⁴n⁶/3
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How do I write A number is equal to twice the sum of the same answer and ten write as an equation that matches the verbal sentence
Answers
The number that fits in the given situation is -20.
What exactly are equations?An equation, in its most basic form, is a mathematical statement that shows that multiple mathematical expressions are equal.For example, 3x + 5 = 14 is an equation in which 3x + 5 and 14 are two expressions detached by a 'equal' sign.Now,
Let us suppose the number is x.
The sum of the same number and ten will be written as x + 10.As a result, the next condition is twice the sum, which can be written as:
2 × (x + 10)As a result of the condition, we can write the equation as:
x= 2 × ( x + 10 ) or 2x + 20 = xSolve for x: x = 2x + 20
2x + 20 = xTaking 20 off both sides:
2x + 20 - 20 = x - 20 2x = x- 20 2x - x = -20 x = -20Therefore, the number that fits in the given situation is -20.
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-3h ≤ 42
-v/2 ≤ 9.5
-4/5m ≥ -8
i dont know how to solve these
Answers
The solutions to the inequalities are h ≥ -14, v ≥ -19 and m ≤ 10
How to solve the inequality expressions?To do this, we simply solve the expressions one after the other
So, we have:
-3h ≤ 42
Divide both sides by -3
So, we have
h ≥ -14
-v/2 ≤ 9.5
Multiply both sides by -2
v ≥ -19
-4/5m ≥ -8
Multiply both sides by -5/4
m ≤ 10
Hence, the solutions to the inequalities are h ≥ -14, v ≥ -19 and m ≤ 10
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Which venn diagram represents x
Answers
Answer:
Step-by-step explanation:
A
Rashon needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged him $141 for parts. The total was $332.25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
Answers
Answer:
Step-by-step explanation:
The cost of labor per hour is $45.
The total cost of the parts is $141.The total time for which the technician worked is 4.25 hours.The total cost of repair is $332.25.Let the cost of labor per hour be "x".The total cost of labor is the product of the total time for which the technician worked and the cost of labor per hour.The cost of labor is 4.25*x.The total cost of repairing the computer is the sum of the cost of the parts and the cost of labor.The total cost of repairing the computer is $141 + 4.25*x.The equation is as follows:332.25 = 141 + 4.25*x191.25 = 4.25xx = 191.25/4.25x = 45Thus, the cost of labor per hour is $45.To learn more about equation, visit :
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A(n) ____ turns a figure a certain number of degrees around a point.
Answers
In geometry, shapes are changed through three forms of variance: transformations, dilations, and rotations. In transformation, a point is moved around a fixed amount of space. In a dilation, a scale factor is used to either enlarge or shrink a figure. In a rotation, a shape rotates a certain number of degrees around a point.
Answer Recap: A rotation turns a figure a certain number of degrees around a point.
NEED HELP IMMEDIATELY!
Simplify 10√2y + 5√2y + 3√2y.
A. 18√6y
B. 18√2y
C. 12√2y
D. 18√6y^3
(ANSWER IS NOT A)
Answers
18 root
2
Step-by-step explanation:
In this question imagine there is no y
It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2
Which graph models function
Answers
The function g(x) models a downward facing parabola shape which is option A
The function g(x) have the solutions which are given in the form of coordinates
This can be solved on a sheet of graph using coordinate geometry
(-3,0), (-2,-4) , (-1, -6) , (0, -6 ), (1,-4),(2,0) and (3,6)
If we will plot all the given seven points given on the graph and join the points we would get a downward sloping parabola model which looks like reverse 'U' shaped whose highest point is between -1 and 0 that is -0.5
lies in second quadrant of the graph sheet.
Hence the given function g(x) models a parabola shape which is option A
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3 is subtracted from three times a number
“a number” is x
Answers
Answer:
3x - 3
The answer above matches with the statement:
"Three is subtracted from three times a number."
Hope this helps :)
A salesclerk is creating a display of 12 polo shirts and 48 team shirts. Only one type of shirt can be in each row. What is the maximum number of shirts in each row so that all the rows are equal in length? 12 4 3 2
Answers
The maximum number of shirts in each row so that all the rows are equal in length is 12.
How to illustrate the information?From the information, the salesclerk is creating a display of 12 polo shirts and 48 team shirts and only one type of shirt can be in each row.
It should be noted that the value van be found by knowing the highest common factor for the numbers.
The highest common factor for 12 and 48 is 12.
Therefore, the correct option is A.
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A triangle with vertices A(1,1), B(3,4), C(6,3) is rotated counterclockwise about the origin 90°. What are the coordinates of the vertices of the new triangle?]
Answers
The coordinates of the vertices of the new triangle are A'(-1,1) ,B'(-4,3), C'(-3,6)
Rotation means the circular movement over the object around the center.
Rotation can be done in both directions like clockwise as well as counter clockwise It requires rotation implies negative magnitude A counter clockwise turns has a positive magnitudeVertices of triangle = A(1,1) , B(3,4), C(6,3)
Triangle is rotated counterclockwise about the origin 90°.
In counterclockwise rotation (x,y) becomes (-y,x)Then
the new coordinates of triangle are A', B', C'
A(1,1) = A'(-1,1)
B(3,4) = B'(-4,3)
C(6,3) = C'(-3,6)
The coordinates of the vertices of the new triangle are A'(-1,1) ,B'(-4,3), C'(-3,6)
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HELP I WILL GIVE BRAINLIEST!!!! M14. Select all the situations that could be represented by the expression 40. (-18).
A hot air balloon descends 18 inches per a second for 40 seconds.
A hot air balloon ascends 40 inches per a second for 18 seconds.
Trey withdraws $18 from his checking account once a week for 40 weeks.
Suzanne deposits $18 into her savings account once a week for 40 weeks.
Morty withdraws $40 from his checking account once a month for 18 months.
Answers
The statements that could be represents the expression 40×(-18) is
A hot air balloon descends 18 inches per a second for 40 secondsTrey withdraws $18 from his checking account once a week for 40 weeks.Morty withdraws $40 from his checking account once a month for 18 months.The expression= 40×(-18)
A hot air balloon descends 18 inches per a second for 40 seconds=40×(-18)
A hot air balloon ascends 40 inches per a second for 18 seconds=40×18
Trey withdraws $18 from his checking account once a week for 40 weeks=40×(-18)
Suzanne deposits $18 into her savings account once a week for 40 weeks=40×18
Morty withdraws $40 from his checking account once a month for 18 months=40×(-18)
Hence, The statements that could be represents the expression 40×(-18) is
A hot air balloon descends 18 inches per a second for 40 secondsTrey withdraws $18 from his checking account once a week for 40 weeks.Morty withdraws $40 from his checking account once a month for 18 months.Learn more about expression here
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Solve negative four and one third ÷ two and one fifth.
Answers
Answer: -2/15 according to the calculator.
Answer:
-1.9681
the 81 is repeating
Step-by-step explanation:
imagine the biology department needs to decide which lab curriculum yields better student outcomes. five sections are assigned to curriculum a, and five sections are assigned to curriculum b. all sections are administered a pre- and post-test that measures students’ attitudes toward science and knowledge of biology. the department wants to see if students’ gains are greater in one curriculum or the other. what statistical test should be done to determine if there is a significant difference? explain why you chose this test.
Answers
The statistical test that should be done to determine if there is a significant difference is the independent t-test.
What're is an independent t-test?
It should be noted the independent t-test or students t-test for two samples should be used.
The Independent Samples T-Test compares the means of two independent groups to determine whether there is statistical evidence that the associated population means are significantly different.
In this case, the biology department needs to decide which lab curriculum yields better student outcomes, the.t text can be applicable.
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Devante will buy 3 packs of gum and four candy bars.gum is 21 cents a pack and candy bars are 45 cents each.how much will devante spend in dollars and cents?
Answers
Devante spent 2 dollars 43 cents
In this question,
A gum is 21 cents a pack and candy bars are 45 cents each.
Devante buy 3 packs of gum.
So for 3 packs of gum total amount would be,
3 × 21 = 63 cents
Devante buy 4 candy bars.
So for the four candy bars the total amount would be,
4 × 45 = 180 cents
Total purchase would be,
63 cents of packs of gum + 180 cents of candy bas
= 243 cents
We know that 1 dollar = 100 cents
S0, 243 cents = 2.43 dollars
Therefore, Devante spent 2 dollars 43 cents
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I have looked from answer sheet but i still didn’t get it…
Answers
Answer:
Xyz E number
Step-by-step explanation:
I think Xyz is right
Answer:
A. AB = xyzx
Step-by-step explanation:
You want AB when A = BC, B = x, and C = yz.
SubstitutionYou can evaluate the unknown expression by making substitutions until you can't anymore.
AB = (BC)(B) . . . . . . . . substitute BC for A
AB = ((x)(yz))(x) . . . . . . substitute x for B (2 places), yz for C
AB = xyzx . . . . . . . . . . remove the unnecessary parentheses
State the property that justifies the statement.
If m∠ 1=25 and m∠2=25 , then m∠1=m∠2.
Answers
The equality property that justifies the statement "If m∠ 1=25 and m∠2=25 , then m∠1=m∠2" is; Substitution Property
What is the property of equality used?The substitution property of equality states that 'If a variable C is equal to another variable D, then C can be substituted in place of D in any equation/expression and D can be substituted in place of C in any equation/expression.
Now, we are given the expressions;
If m∠ 1 = 25 and m∠2 = 25 , then m∠1 = m∠2.
Thus, we can also say that the property used here is called substitution property because the parameters were interchanged and still equal.
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Taylor makes $13 per hour at the grocery store. she always works between 10-15 hours per week to leave time for her homework and band practice. her gross wages can be modeled as w(h) = 13h, where h is the number of hours worked per week.
1. how much will her gross wages be if she works 12 hours this week?
2. what is the domain of this function?
3. what is the range of this function?
Answers
a) Her gross pay will be $156
b) The domain is D: [10, 15]
c) The range is R: [$130, $195]
What will be her gross wage if she works 12 hours this week?
We know that Taylor earns 13 dollars per hour on her job at the grocery store.
Then, if she works x hours in the week, her gross wage will be given by the linear equation:
g(x) = $13*x
So, if she works 12 hours, her gross pay will be:
g(12) = $13*12 = $156
what is the domain of this function?
we know that she works between 10 and 15 hours peer week, so the domain (set of the possible inputs of the function) is:
10 ≤ x ≤ 15 or [10, 15] in interval notation.
what is the range of this function?The range is the set of the outputs, the minimum of the rane is:
g(10) = $13*10 = $130
The maximum of the range is:
g(15) = $13*15 = $195
The range of the linear function is: [$130, $195]
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What is the quotient of 81/(-9)/(-3)
Answers
Answer:
3
Step-by-step explanation:
81/(-9)/(-3)=3
The number 3 is prime number.
9. What is the slope of the graph of y= 12 x - 19?
Answers
12
Explanation:
Slope Intercept form is: y=mx+b
m would be the slope
So in y=12x-19, 12 would be the slope in this case.
A rectangular field is 15m longer than it is wide.
The area of the field is 800m²
Work out the length of the field.
Give your answer to 1 decimal place.
Answers
The length of rectangular field is 36.76 m.
What is a length?Distance is quantified by length. A quantity with the dimension of distance is called length in the International System of Quantities. Most measurement systems choose a length base unit from which all other units are derived. The fundamental unit for length in the International System of Units is the metre.
The term "length" refers to the measurement or size of something from end to end. In other terms, it is the greater of the upper two or third dimension of a geometric shape or object.
Area of rectangle is L × W = 800
given L = 15 + W
W × ( 15+ W) = 800
15W + [tex]W^{2}[/tex] = 800
[tex]W^{2}[/tex] + 15W - 800 = 0
by solving the above quadratic equation W= 21.76 m.
L = 15 + W
L = 36.76 m
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