*PLEASE HELP SOON* Simplify each part of the expression using the laws of exponents.
What laws or properties did you use to simplify each part? What is the value of the expression?
Answers
Using the laws of exponents to simplify the expression, we have; 5 1/3
What is an exponential expression?When the power of one or more terms of an expression is greater than 1, then the expression is in an exponential form. Thus some laws can be require to simplify an exponential expression.
In the given question,
2^7/ 2^5 + (4^5)^0 + 3^-1
Thus applying the division law of indices to the first term, we have;
2^7/ 2^5 = 2^(7 - 5)
= 2^2
In the second term, anything to the power of zero is 1. So that;
(4^5)^0 = (1024)^0
= 1
In the third term, applying the inverse law of indices. We have;
3^-1 = 1/ 3
Therefore,
2^7/ 2^5 + (4^5)^0 + 3^-1 = 2^2 + 1 + 1/3
= 4 + 1 + 1/3
= 5 + 1/3
= 16/ 3
= 5 1/3
The value of the expression is 5 1/3.
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Related Questions
Simplify fully.
[tex]3\cdot \log_{\frac{4}{9}}(\sqrt[4]{\dfrac{27}{8}})[/tex]
I know how to get the fourth root fraction inside the log to [tex](\dfrac{3}{2})^{3/4}[/tex] but don't understand how to advance from there
Answers
Answer:
-9/8
Step-by-step explanation:
You want a full simplification of ...
[tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}[/tex]
Rules of logarithmsThe relevant rules of logarithms are ...
log(ab) = log(a) +log(b)
log(a/b) = log(a) -log(b)
log(a^b) = b·log(a)
logₐ(b) = log(b)/log(a)
Application[tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}=\dfrac{3}{4}\log_{\frac{4}{9}}\left(\dfrac{27}{8}\right)=\dfrac{3}{4}\cdot\dfrac{\log\dfrac{27}{8}}{\log\dfrac{4}{9}}\\\\\\=\dfrac{3(\log(3^3)-\log(2^3))}{4(\log(2^2)-\log(3^2))}=\dfrac{3(3\cdot\log(3)-3\cdot\log(2))}{4(2\cdot\log(2)-2\cdot\log(3))}\\\\\\=\dfrac{9(\log(3)-\log(2))}{8(\log(2)-\log(3))}=\boxed{-\dfrac{9}{8}}[/tex]
__
Additional comment
We have reduced everything to the difference of the logs of 2 and 3. You could stop the reduction to smallest parts at any point where you recognize things that will cancel. You could write numerator and denominator in terms of powers of (3/2), for example.
Four points B, A, E, and L are on a straight line, as shown. The point G is off the line so that angle BAG = 120 degrees and angle GEL = 80 degrees. If the reflex angle at G is x degrees, then what does x equal?
Answers
Given that the reflex angle at G is x degrees, then x is equal to
What is a reflex angle?A reflex angle is a type whose value falls within 180^o and 360^o. This implies that the value of the angle is greater than 180^o, but less than 360^o.
Considering the reflex angle given in the question, it can be deduced that;
m<AGE + m<GAE + m<GEA = 180^o
But,
i. m<GAB + m<GAE = 180^o (sum of angles on a straight line)
120 + m<GAE = 180
m<GAE = 180 - 120
= 60
m<GAE = 60^o
ii. m<GEA + m<GEL = 180^o
m<GEA + 80 = 180
m<GEA = 180 - 80
= 100
m<GEA = 100^o
Thus,
m<AGE + m<GAE + m<GEA = 180^o
m<AGE + 100 + 60 = 180
m<AGE = 180 - 160
= 20
m<AGE = 20^o
Therefore,
x + m<AGE = 360 (sum of angles at a point)
x + 20 = 360
x = 360 - 20
= 340
x = 340^o
x is equal to 340^o.
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There are 50 bacteria present initially in a culture. In 3min., the count is 204800.
What is the doubling period?
Answers
Answer: The doubling period is the time it takes for the population of bacteria to double. To find the doubling period in this case, we need to determine how often the population doubles during the 3-minute period.
We know that the initial population is 50 and the final population is 204800, which means that the population has grown by a factor of 204800/50 = 4096. Since this is a multiplication by a factor of 4096, this means that the population has doubled 4096 times in 3 minutes.
To find the doubling period, we need to divide the total time (3 minutes) by the number of doublings (4096).
So, the doubling period is:
3 minutes / 4096 = 3/4096 minutes ≈ 0.0007 minutes ≈ 0.042 seconds
So, the population of bacteria doubles every 0.042 seconds
Step-by-step explanation:
stressed out, part ii. in a study evaluating the relationship between stress and muscle cramps, half the subjects are randomly assigned to be exposed to increased stress by being placed into an elevator that falls rapidly and stops abruptly and the other half are left at no or baseline stress. can this study be used to conclude a causal relationship between increased stress and muscle cramps?
Answers
The following type of study can be concluded as an observational study.
An observational study is a type of study that is used to gather data on the characteristics and behaviors of a particular group of people or subjects without actively manipulating or interfering with the subjects.
This study can be used to suggest a causal relationship between increased stress and muscle cramps, but it cannot conclusively prove causality.
There are several reasons why this study design cannot be used to conclude a causal relationship. First, the study is a non-randomized, uncontrolled experiment, which means that there may be other factors that could be influencing the results.
For example, the subjects in the stress group may have other characteristics or preexisting conditions that are related to muscle cramps. Additionally, the study does not have a control group for comparison, so it is not possible to determine if the muscle cramps are caused by stress or by some other factor.
Second, the study design is a single-blind study, which means that only the subjects are not aware of their group assignment, but the experimenter knows which group the subjects are in. This can lead to bias in data collection, analysis, or interpretation.
Therefore, The following type of study can be concluded as an observational study.
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Half of this two digit number is 3 times half of 28 this number is ?
Answers
Answer:
84
Step-by-step explanation:
x/2=3*28/2=3*14 = 42
x=84
Monomial of 9p^3 and 4p
Answers
Answer: A monomial is a polynomial with only one term. So 9p^3 and 4p are monomials.
9p^3 is a monomial with coefficient 9 and exponent 3 in the variable p.
4p is a monomial with coefficient 4 and exponent 1 in the variable p.
Step-by-step explanation:
Jacob is a construction worker who earns a yearly Income given by the expression 2000x + 3000, where X is the number of
hours he works each week. Carlos works with Jacob and earns a yearly Income given by the expression 3800x - 39000.A
manager predicts that if Carlos and Jacob each work 42 hours, they will earn the same amount of money.
Answers
Answer:20
Step-by-step explanation:
you do it
two side lengths of a triangle are 11 and 17. what is the longest possible integer length of the third side of the triangle?
Answers
Therefore, the potential length of a triangle's third side is 17-11<x<17+11 is equals to 6 < x< 28.
A triangle's third side must always have a length that falls between (but not exactly equal to) the sum and difference of the other two sides. Consider the examples 2, 6, and 7 as an example. The third side length must therefore be larger than 4 and less than 8.
According to the Triangle Inequality Theorem, any two triangle sides must add up to more than the third side's length. To find the potential length of a triangle, multiply the sum of the two sides by the difference of the two sides.
Therefore, the potential length of a triangle's third side is 17-11<x<17+11.
= 6 < x< 28
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As a result, the third side of a triangle may be equal to 17-11<x<17+11 is equals to 6 < x< 28.
The third side of a triangle must always have a length that is between the sum and difference of the other two sides, but is not exactly equal to either. As an illustration, think about cases 2, 6, and 7. Therefore, the third side length must be more than 4 and lower than 8.
The Triangle Inequality Theorem states that any two triangle sides must add up to greater than the length of the third side. Multiply the sum of the two sides by the difference of the two sides to determine the potential length of a triangle.
Consequently, 17-11<x<17+11.= 6 < x< 28 is the possible length of the third side of a triangle.
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Sammy wants to know what percent of students at her high school have a driver’s license. She surveys all students in her statistics class and finds that 68% of the students in her sample have a driver’s license.
What type of sample did Sammy obtain?
Explain why this sampling method is biased. Is 68% likely to be greater than or less than the percent of all students at her high school who have a driver’s license?
Explain how Sammy could avoid the bias described in part (b)
Answers
Sammy obtained a convenient sample.
The sampling method is biased because the students in the statistics class are not representative of the entire high school population. The sample only includes the students in one particular class and does not account for the experiences or characteristics of other students in the school.
68% is likely to be greater than the percent of all students at the high school who have a driver's license.
To avoid the bias, Sammy could use a more representative sample, such as a simple random sample or a stratified sample, to ensure that the sample includes a diverse group of students from various backgrounds, classes, and demographics. This would give a more accurate representation of the experiences and characteristics of the entire high school population.
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The_____area includes all surfaces.The______area does not include bases
1st blank (lateral surface or total surface)
2nd blank (lateral surface or total surface)
Answers
For the translation below, give the vertices of ABC
Answers
Answer:
see explanation
Step-by-step explanation:
a translation [tex]T_{(-5,-4)}[/tex]
means subtract 5 from the original x- coordinate and subtract 4 from the original y- coordinate.
A (2, - 1 ) → A' (2 - 5, - 1 - 4 ) → A' (- 3, - 5 )
B (- 4, - 2 ) → B' (- 4 - 5, - 2 - 4 ) → B' (- 9, - 6 )
C (3, 2 ) → C' (3 - 5, 2 - 4 ) → C' (- 2, - 2 )
Determine the intercepts of the line.
Do not round your answers.
y=-3x+12
y-intercept:
x-intercept:
Answers
Answer:
y- intercept = 12, x- intercept = 4
Step-by-step explanation:
to find the y- intercept, the point where the line crosses the y- axis.
let x = 0 in the equation and solve for y
y = - 3(0) + 12 = 0 + 12 = 12
then y- intercept = 12
to find the x- intercept, where the line crosses the x- axis.
let y = 0 in the equation and solve for x
0 = - 3x + 12 ( subtract 12 from both sides )
- 12 = - 3x ( divide both sides by - 3 )
4 = x
then x- intercept = 4
solve. 10) what are the dimensions of a right triangle with a 5 inch hypotenuse and an area of 6 square inches?
Answers
Answer:
The dimensions are 3, 4 and 5 inches.
Step-by-step explanation:
Area = 1/2 * height * base
6 = 1/2 * h * b
h * b = 12.
As the hypotenuse is 5 inches long
H^2 + B^2 = 5^2
From the third line: h = 12/b, so we have
(12/b)^2 + b^2 = 25
144/b^2 + b^2 = 25
144 + b^4 = 25b^2
b^4 - 25b^2 + 144 = 0
Let B = b^2, so
B^2 - 25B + 144 = 0
(B - 16)(B - 9) = 0
B = 16, 9
So, b = 4, 3
h = 12/b
= 3 , 4.
Can I get help on this question ?
Answers
The solution of the expression is 3m-5.
How to simplify the equation?Basic Guidelines and Procedures for Condensing Any Algebraic Expression
By multiplying factors, remove the parentheses and brackets.If the terms have exponents, you should eliminate grouping using the exponent rule.Add or subtract coefficients to combine similar terms.Incorporate the constants.step1:
(6m² -13m+5)/(2m-1): 3m-5
6m² -13m+5/2m-1
factor 6m² -13m+5 : (2m-1) (3m-5)
=(2m-1) (3m-5)/2m-1
step2:
cancel the common factor 2m-1
=3m-5
The solution of the expression is 3m-5
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how many different paths from a to b are possible if each path must avoid the point with the circle around it?
Answers
This depends on the number of paths that exist between point a and point b. If there are more than one path, then the number of paths that avoid the point with the surrounding circle will be one less than the total number of paths.
The number of paths from point a to point b that avoid the point with the surrounding circle will depend on the total number of paths between the two points. If there are multiple paths between the two points, then the number of paths that avoid the point with the circle will be one less than the total number of paths.
For example, if there are three paths between a and b, then two of those paths will avoid the point with the circle.
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Alg Fndins 1 A
Order of Operations
Evaluate each expression.
(Help me please)
Answers
•What turtle won the race?
•How long did the race take to complete?
•What speed was the Blue turtle traveling from 6-13 hours?
•Which turtle maintained a consistent speed through the entire race?
Answers
The time that it took to complete the race is the time it took for them to stop at the same position, hence it is of 16 hours.
For the Blue turtle, we have that:
At hour six, she was at a position of 10 km.At hour 13, she was at a position of 10 km.The velocity is given by the change in position divided by the change in time, hence:
v = (10 - 10)/(13 - 6)
v = 0.
The red turtle maintained a consistent speed through the entire race, as the slope of her line is constant.
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I need help understanding how to do this
Answers
Answer:
113.04
Step-by-step explanation:
see attached
Find the area of shaded region?
Please help me!!!!
Answers
The are of shade part of semi-circle is 75.36 cm^2.
What is a circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
The equation of circle in the plane is given as:
(x-h)^2 + (y-k)^2 = r^2
where (x, y) are the coordinate points
(h, k) is the coordinate of the center of a circle
and r is the radius of a circle.
and Area of circle = πr²
Now,
Area of the shaded region=area of large semicircle-2*area of small semicircles
radius for large semicircle=7cm
radius for small semicircle=3.5cm
Therefore,
Area of the shaded region=πR^2-2*πr^2
=3.14(7^2-2*3.5^2)
=3.14*(49-25)
=3.14*24
Area of the shaded region =75.36 cm^2
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I. Jill is training for a marathon
and runs 2 ⅓ miles three times
a week. How far will she run in
six weeks?
Answers
Answer:42 miles
Step-by-step explanation: She runs 3 times a week so 2 1/3 times 3 is equal to 7.
7x6=42
Your savings account increased by 3% in the last year. Write an expression as a product to represent the amount of money in your savings account(s) now.
Answers
Solve the equation with the quadratic
formula. Enter the smallest solution
first and round to the nearest tenth.
2x² - 4x - 48 = 0
x = [?], [?]
Answers
For the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.
What is quadratic equation?
The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients. Here, the variable "X" is unknowable.
ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
We have a quadratic equation;
2x² - 4x - 48 = 0
To find the value of x we have to follow these steps ;
(2x^2 - 4x) - 48 = 0
Pull out like factors :
2x^2 - 4x - 48 = 2 • (x^2 - 2x - 24)
x2 multiplied by 2x and 24
x^2 is the initial term, and it has a coefficient of 1.
The coefficient of the middle term, which is -2x, is 2.
"The constant," the final term, is -24.
⇒ x^2 - 6x + 4x - 24
⇒ (x+4) • (x-6)
⇒ 2 • (x + 4) • (x - 6) = 0
therefore x+4 = 0
x = -4
and x-6 = 0
Add 6 to both sides of the equation :
x = 6
Hence, for the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.
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Jose has scored 320 points on his math tests so far this semester. To get an A for the semester, he must
score at least 389 points.
Part 1 out of 2
Enter an inequality to find the minimum number of points he must score on the remaining tests in order to
get an A. Let n represent the number of points Jose needs to score on the remaining tests.
The inequality is
+ n (select)
HELP ME WAAKAIAKAKAKAK
Answers
The inequality that represents the minimum number of points he must score on the remaining tests in order to get an A is 320 + n ≥ 389, n ≥ 69, where n is the number of points.
When we use ≥ symbol, as at least means greater than or equal to.
320 + n ≥ 389
Subtracting 320 on both the sides,
n ≥ 69,
n represents the score he must receive on the remaining tests. Then n + 320 represents his total score for the semester.
Thus, the required inequality is n ≥ 69, which means that n is the minimum scored points to get A.
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the area of trapezoid $abcd$ is $80$. one base is $12$ units longer than the other, and the height of the trapezoid is $5$. find the length of the median of the trapezoid.
Answers
The trapezoid abcd median is 16 lengths long.
Regarding the query,
Considering that,
The trapezoid's area is equal to 80,
The trapezoid abcd is 5 inches tall.
Let a be the base of the trapezoid abcd.
So, b = a + 12 ,
In the formula Area of the trapezoid = A =(a+b)h/2, the value is substituted.
(a + a + 12)5/2 = 80
(2a + 12)5 = 160
2a + 12 = 160/5
2a + 12 = 32
2a =32 - 12
2a = 20
a = 20/2
a = 10 units
additional base is 10 + 12 = 22 units.
Therefore, the median's length will be equal to (10 + 22)/2.
= 32/2 = 16 units
As a result, the median's length is 16.
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Find the difference (-3x+8)-(x+10)
Answers
Answer: After doing the problem I got, -4x-2
Amadou i going to invet $11,000 and leave it in an account for 9 year. Auming the interet i compounded continuouly, what interet rate, to the nearet tenth of a percent, would be required in order for Amadou to end up with $14,000?
Answers
The required interest rate would be 6.9% to the nearest tenth of a percent.
We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.
In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.
Plugging these values into the percent formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.
We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.
In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.
Plugging these values into the formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.
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Write this polynomial in descending order:
Photo Below
Answers
The polynomial in descending order is
[tex]x^7[/tex] - 4[tex]x^5[/tex] + 4x³ + 2[tex]x^4[/tex] - 10
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
-4[tex]x^5[/tex] + 4x³ + [tex]x^7[/tex] - 10 + 2[tex]x^4[/tex]
Arranging in descending order means arranging the terms in their descending order of power.
Now,
[tex]x^7[/tex] > [tex]x^5[/tex] > [tex]x^4[/tex] > x³
So,
[tex]x^7[/tex] - 4[tex]x^5[/tex] + 4x³ + 2[tex]x^4[/tex] - 10
Thus,
The polynomial is:
[tex]x^7[/tex] - 4[tex]x^5[/tex] + 4x³ + 2[tex]x^4[/tex] - 10
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A composite figure is shown.
A five-sided figure with two parallel bases. The top one is 4 inches. The vertical height between these bases is 2.3 inches. That vertical height intersects the bottom base, leaving 2.5 inches between it and the vertex to the left. The side on the right is the longest at 5.2 inches. There is a horizontal line connecting the vertex of the bottom base to the 5.2-inch side and that line is 3 inches.
Which of the following represents the total area of the figure?
Answers
The total area of the figure is 14.35 square inches
How to determine the total area of the figure?The six-sided figure is not given, however we can deduce the following parameters from the question:
The shape is made of a triangle and a trapezoid
The side lengths derived from the question are:
The triangle on top:
base: 4 inches and height: 2.3 inches
The trapezoid at the bottom:
Parallel sides: 2.5 inches and 4 inches with a height of 3 inches
So, we have the total area of the figure to be
Area of figure = 1/2 * 4 * 2.3 + 1/2 * (2.5 + 4) * 3
Area of figure = 14.35
Hence, the total area is 14.35 square inches
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Answer:
Step-by-step explanation:
dddcdcdcdc its d
I'LL DO ANYTHING!! PLEASE
Answers
The original length is 250 meters and the scale drawing width is 0.67 cm
The original length of the landFrom the question (see attachment), we have the following parameters that can be used in our computation:
Scale length = 0.5 meters
So, we have
Original length = 0.5/(1/500)
Evaluate
Original length = 250
This means that the original length is 250 meters
The scale drawing widthHere, we have
Scale drawing width = 335 * 1/500
Scale drawing width = 0.67 cm
Hence, the scale drawing width is 0.67 cm
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Quadrilateral U is a scaled copy of quadrilateral T.
What scale factor takes quadrilateral T to quadrilateral U?
Answers
The scale factor that takes quadrilateral T to quadrilateral U would be = 1.6
What is a scale factor?A scale factor is defined as the factor that is used to creat a similar shape of an object with a different dimension.
The formula that is used for the new object = original object × scale factor
The original object = quadrilateral T
The new object = quadrilateral U.
The scale factor the was used to form U using the length of the quadrilateral as 16;
16 = 10 * Scale factor
This gives
Scale factor = 16/10
Scale factor = 1.6
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