The result of simplifying each number x²/₇ . x³/₁₄ using the exponent rules is [tex]\sqrt{}[/tex]x
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(x²/₇) * (x³/₁₄)
Base= x
Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:
(x) ⁽²/₇ ⁺ ³/₁₄⁾
(x) ⁽⁴⁺³⁾/₁₄
(x) ⁽⁷/¹⁴⁾
(x) ⁽¹/²⁾
As we have a fractional exponent, you must convert the exponent to root:
[tex]\sqrt{}[/tex]x
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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PLEASE I REALLY NEED HELP !!!
79°
73°
Find the value of the missing angle x.
||
२००
Answer:
152 =x
Step-by-step explanation:
180 - 152= 28
180-28= 152
show that theorem 2.6, the additive law of probability, holds for conditional probabilities. that is, if a, b, and c are events such that p(c) > 0, prove that p(a ∪ b|c)
P(AUB|C)=P(A|C) + P(B|C) - P(AnB|C) is the correct answer.
From distributive law we have,
P((AUB)nC)=P(AnC) + P(BnC)-P(AnBnC)
Dividing both sides by P(C)
P((AUB)nC)/P(C)=P(AnC)/P(C) + P(BnC)/P(C) - P(AnBnC)/P(C)
P(AUB|C)=P(A|C) + P(B|C) - P(AnB|C)
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someone please help me i’ve been stuck on this for the longest
Answer:
-3/2
Step-by-step explanation:
Slope:
Rise: The difference between the y -coordinates of the two points is called the rise.
Run: The difference between the x-coordinates of the same two points is called the run.
First plot two points on the line.
(0, 6 ) and (4 , 0)
Rise = 6 - 0 = 6
Run = 0 - 4 = -4
[tex]\sf \boxed{Slope = \dfrac{Rise}{Run}}[/tex]
[tex]\sf =\dfrac{6}{-4}\\\\=\dfrac{-3}{2}[/tex]
Based on the stemplot, which of the following is a correct comparison of the eastern and western states’ expenditures?
Going by the stemplot, a correct comparison to make between eastern and western states’ expenditures is The eastern states have, on average, a higher per-pupil expenditure than the western states.
How to read a stemplot?Reading a stemplot requires looking at the stem first which is the number in the middle. Then combine this with the leaf to find the actual number. For instance, a stem of 7 and a leaf of 6 in the attached photo is $76,000.
From the attached photo, we see that the Eastern states have more numbers of per-pupil expenditure which means that on average, they have a higher per-pupil expenditure than the western states.
Options for this question are:
The western states exhibit more variability in their expenditures than the eastern states. The eastern states have, on average, a higher per-pupil expenditure than the western states. The distribution of per-pupil expenditures in the eastern states is more symmetric than the distribution of the western states. The distribution of the western states' per-pupil expenditure is skewed left, while the distribution of the eastern states' per-pupil expenditure is skewed right. Valid conclusions comparing the distributions cannot be made, since there is a different number of states in each group.Find out more on stemplots at https://brainly.com/question/22400218
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The coordinated of point T are (0,4). The midpoint of ST is (4,-5). Find the coordinates of point S
Answer:
(8,-14)
Step-by-step explanation:
mid piont is (4,-5) So let us consider that S(x,y)
Now,
from mid point formula,
[tex]4 = \frac{x + 0}{2} \\ x = 8[/tex]
[tex] - 5 = \frac{y + 4}{2} \\ - 10 = y + 4 \\ y = - 10 - 4 \\ y = - 14[/tex]
There were four hundred fifty-seven employees working in an office building. fifty-two of them left to go have lunch. 204 cars are still in the parking lot. how many emplyees are left in the building
Please Help, Consider the following sets in the universal set U, which is the set of all elements of the three given sets below. List the elements of the sets being described.
B = {d, o, I, e} I = {p, i, n, a, y} J = {p, i, n, o, y}
The solutions are;
1. U = {a, d, e, i, l, n, o, p, y}
2. E ∪ I = {a, d, e, i, l, n, o, p, y}
3. E ∩ I = { }
4. J' = {a, d, e, l}
5. I ∪ J = {p, i, n, a, o, y}
6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}
7. E' = {a, i, n, p, y}
8. I' ∪ J = {d, e, l, o, p, i, n, y}
9. (E ∩ I) ∩ (I ∪ J) = { }
10. (J ∪ I)' = {d, e, l}
What is Union of the set?
Union of two or more set is the set containing all the elements of the given set.
Here, U is the universal set, which is the set of all elements of the three given sets.
And, Three sets are;
⇒ E = {d, o, I, e}, I = {p, i, n, a, y}, J = {p, i, n, o, y}
Now, We find the universal set as;
1. U = {{a, d, e, i, l, n, o, p, y}
2. And, E ∪ I = {d, o, I, e} ∪ {p, i, n, a, y}
= {a, d, e, i, l, n, o, p, y}
Hence, E ∪ I = {a, d, e, i, l, n, o, p, y}
3. E ∩ I = {d, o, I, e} ∩ {p, i, n, a, y}
Since, It cannot contain any common elements.
So, Intersection of E and I is null set.
Hence, E ∩ I = { }
4. Since, J' = U - J
J' = {a, d, e, i, l, n, o, p, y} - {p, i, n, o, y}
J' = {a, d, e, l}
Hence, J' = {a, d, e, l}
5. I ∪ J = {p, i, n, a, y} ∪ {p, i, n, o, y}
= {p, i, n, a, o, y}
Hence, I ∪ J = {p, i, n, a, o, y}
6. ( J ∩ I ) ∪ E = ({p, i, n, o, y} ∩ {p, i, n, a, y}) ∪ {d, o, I, e}
= {p, i, n, y} ∪ {d, o, I, e}
= {d, o, l, e, p, i, n, y}
Hence, ( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}
7. E' = U - E
= {a, d, e, i, l, n, o, p, y} - {d, o, I, e}
= {a, i, n, p, y}
Hence, E' = {a, i, n, p, y}
8. I' ∪ J = (U - I) ∪ J
= ( {a, d, e, i, l, n, o, p, y} - {p, i, n, a, y}) ∪ {p, i, n, o, y}
= {d, e, l, o} ∪ {p, i, n, o, y}
= {d, e, l, o, p, i, n, y}
Hence, I' ∪ J = {d, e, l, o, p, i, n, y}
9. (E ∩ I) ∩ (I ∪ J) = ( {d, o, I, e} ∩ {p, i, n, a, y}) ∩ ({p, i, n, a, y} ∪ {p, i, n, o, y})
= { } ∩ {p, i, n, a, o, y}
= { }
Hence, (E ∩ I) ∩ (I ∪ J) = { }
10. (J ∪ I)' = U - (J ∪ I)
= {a, d, e, i, l, n, o, p, y} - ({p, i, n, a, y} ∪ {p, i, n, o, y})
= {a, d, e, i, l, n, o, p, y} - {p, i, n, a, o, y}
= {d, e, l}
Hence, (J ∪ I)' = {d, e, l}
So, The solutions are;
1. U = {a, d, e, i, l, n, o, p, y}
2. E ∪ I = {a, d, e, i, l, n, o, p, y}
3. E ∩ I = { }
4. J' = {a, d, e, l}
5. I ∪ J = {p, i, n, a, o, y}
6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}
7. E' = {a, i, n, p, y}
8. I' ∪ J = {d, e, l, o, p, i, n, y}
9. (E ∩ I) ∩ (I ∪ J) = { }
10. (J ∪ I)' = {d, e, l}
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im stuck help , i would really appreciate it
Answer:
7. 123
8. 38
10. 65
11. 113
[tex]5xx^{2} -9x-10[/tex]
Answer:
Step-by-step explanation:
5
2
−9x−10
Calculate 5 to the power of 2 and get 25.
25−9x−10
1
Calculate 10 to the power of 1 and get 10.
25−9x−10
Subtract 10 from 25 to get 15.
15−9x
Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
f(x)-2 g(x)
The values for f(x)-2 g(x) = -2x² + 8x - 1
What are the domain of the function f(x)-2 g(x)?Given : f(x)=2 x+5
g(x)=x²-3 x+2
Solution:
2g(x)=2x²-6x+4
f(x)-2 g(x) = 2 x+5 - (2x²-6x+4)
f(x)-2 g(x) = 2 x+5 - 2x² + 6x - 4
f(x)-2 g(x) = -2x² + 8x - 1
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You score 84 points in 5 games. How many points do you score per game?
Answer:
16.8
Step-by-step explanation:
84 / 5 = 16.8
Answer:
17 points(Rough estimate)
Step-by-step explanation:
Using long division,
[tex]5|84\\5 \times 1 = 5\\8 - 5 = 3\\\mathrm{Drop~4~onto~3~to~get~34}\\5 \times 6 = 30\\34 - 30 = 4[/tex]
Round 16 to nearest ones place
[tex]\mathrm 16 = 17[/tex]
Therefore,
You scored ≈ 17 points per game out of 5 games.
if you need the exact value, it's 16.8
Any concerns, let me know. Have a good day!
simplify completely 5√28+√63
The expression is completely simplified to give 13√7
What are surds?Surds are defined as square root values that cannot be further decreases to integers or whole numbers.
Another name for surds are irrational numbers.
Given the surd forms;
5√28 + √63
Now, let's find the factors of the value 28 with perfect squares.
√28 = √4 × 7
The factors of 63 with perfect squares
√63 = √9 × 7
Now, let's substitute the values
5√4 × 7 + √9 × 7
Find the perfect squares
5 × 2√7 + 3√7
Multiply through
10√7 + 3√7
Since the values have common roots, add the coefficient and keep the root the same.
We have;
13√7
Thus, the expression is completely simplified to give 13√7
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The numbers in this sequence increase by 8 each time.
38 ...
The sequence is continued with the same rule.
Which number in the sequence will be closest to 100?
Optional working
14
22 30
The number 102 in the sequence will be closest to 100.
A sequence in which each next term gets increased or decreased from the preceding by a constant value is called an arithmetic progression.
The difference of any two consecutive terms in an arithmetic progression is called the common difference of the AP (arithmetic progression).
Here each terms increases by 8. So, the common difference d is 8.
The first term is given to be 38.
So our sequence will be,
38, 46, 54, 62,...
nth term in an AP can be calculated by using the formula,
aₙ = a₁ + (n-1)d
To find the term nearest to 100,
100 = 32 + (n-1)8
68/8 = (n-1)
9.5 = n
But the value of n can not be a non-integer,
So the term nearest to 100 will be 9th or 10th term.
a₉ = a₁ + (9-1)d
a₉ = 8 + (8 x 8)
a₉ = 94
and,
a₁₀ = a₁ + (10-1)d
a₁₀ = 8 + (9 x 8)
a₁₀ = 102.
We can see,
a₁₀ = 102 is closest to 100.
Hence, 10th term is closest to 100.
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44. The Loveland town council wants to build a bandstand. Architects were asked to submit plans. In the plan shown, the floor has the shape of a regular octagon. a) What is the area of the floor of the bandstand in this plan? 20 ft b) What would the dimensions be of a square bandstand with the same area as the octagon above? c) Which one has the largest perimeter?
Area of the floor of the bandstand in regular octagon is 1931.2 ft²
dimensions of a square bandstand with the same area as the octagon is 43.94 ft
square bandstand has largest perimeter.
floor has the shape of a regular octagon
Area of a regular octagon = 2a²(1+[tex]\sqrt{2}[/tex])
a = length of the side of the octagon
here a = 20 ft
Area = 2a²(1+[tex]\sqrt{2}[/tex]) = 2(20)(20)(1+[tex]\sqrt{2}[/tex])
= 800(1+1.414)
= 800(2.414)
= 1931.2 ft²
square bandstand with the same area as the octagon
Area of square = b²
b = length of the side of the square
1931.2 = b²
b = 43.94 ft
Perimeter of regular octagon = 8a
= 8(20)
= 160ft
Perimeter of Square = 4b
= 4(43.94)
= 175.78ft
area of the floor of the bandstand in regular octagon is 1931.2 ft²
dimensions of a square bandstand with the same area as the octagon is 43.94 ft
square bandstand has largest perimeter.
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HELP!! 30 POINTS!
The sum of three consecutive integers is -51. Find the value of the greatest of the three.
Answer:
Answer: 16, 17, and 18.
Step-by-step explanation: What I'll do I'll just let explain how to solve it and that will instantly solve your question!
The first case of business to make things easier would be to try and put this on a linear equation so...
Let the first integer be x.
Then the next consecutive two integers will be x + 1 and x + 2
x + (x + 1) + (x + 2) = 51 [Sum of the 3 consecutive integers is 51]
-> 3x + 3 = 51
-> 3x = 51 - 3
-> 3x = 48
-> x = 48/3
-> x = 16,
Thus, x + 1 = 17, x + 2 = 18
Therefore, the three consecutive integers are 16, 17, and 18.
Hope it helps ^^
ZA and ZB are supplementary angles. If m/A= (2x - 20)° and m
LB = (3x+15)°, then find the measure of ZB.
The required measure for the supplementary angles EB is calculated as 126°.
Given that,
Two supplementary angles are given ZA and ZB.
ZA = 2x - 20 ; ZB = 3x + 15
To determine the measure of ZB.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The sum of the supplementary angle is 180°.
ZA + ZB = 180°
2x - 20 + 3x + 15 = 180
5x - 5 = 180
5x = 180 + 5
5x = 185
x = 37
Now,
the measure of angle,
ZB = 3x + 15
ZB = 3 * 37 + 15
ZB = 126°
Thus, the required measure of the angle EB is 126°.
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The probability mass function of a binomial distribution is given as
Select one:
a. 1x! ℮-λ λx
b. n!x!n-x! px (1-p)n-x
c. px (1-p)n-x
d. ℮-λ λx
The probability mass function of the binomial distribution is given by:
B. [tex]\frac{n!}{x!(n-x)!} \times p^{x} \times (1-p)^{n-x}[/tex]
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.Hence, considering the combination formula, the probability mass function of the binomial distribution is given by:
B. [tex]\frac{n!}{x!(n-x)!} \times p^{x} \times (1-p)^{n-x}[/tex]
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F(2x) graph and domain and range
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
( -∞ , ∞ )
Set-Builder Notation:
{ x | x ∈ R }
The range is the set of all valid y values. Use the graph to find the range.
Interval Notation:
( -∞ , ∞ )
Set-Builder Notation:
{ y | y ∈ R }
Determine the domain and range.
Domain: ( −∞ , ∞ ), { x | x ∈ R }
Range: ( −∞ , ∞ ), { y | y ∈ R }
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Anursery owner buys 8 panes of glass to fix some damage to his greenhouse. The 8 panes cost $18 80. Unfortunately, he breaks 3 more panes while repaining the damage. What is the cost of another
3 panes of glass?
Another 3 panes of glass cost:
Answer:
Step-by-step explanation:
If 8 panes cost 1880
then 1 pane cost 1880 divided by 8
1 pane = $ 235
3 pane = $235 x 3
= $ 705
$1715 + $705 = $ 2420
Kym is renovating the first floor of her house. She bought 750 square feet of laminate flooring and 525 square
feet of carpet and paid $2717.25. She went back to the store and bought an additional 100 square feet of
laminate flooring and 75 square feet of carpet and paid $374.75. Find the cost per square foot of each type of
flooring. equation
Using simultaneous equations in two variables we get that the cost of laminate is $ 0.65 per sq. feet and the cost of carpet is $ 4.12 per sq. feet.
Equations in algebra that involve two or more variables simultaneously, such as x and y, are referred to as simultaneous equations. The equations are referred to as simultaneous equations since they are solved simultaneously. There are countless possible solutions to just these equations.
A set of finite equations for which common solutions are sought makes up a system of equations, often known as an equation system.
Let the cost per sq feet of laminate be x and the cost per sq feet of carpet be y.
Now it is given that the cost of 750 sq feet of laminate and 525 square foot of carpet is $2717.25
∴ 750x+525y=2717.25
Again the cost of 100 sq feet of laminate and 75 square foot of carpet is $374.75
∴ 100x + 75 y = 374.15
Now we solve the pair of simultaneous equations to find the value of x and y:
Multiplying the second equation by 7 and subtracting from the first we get:
750x + 525y = 2717.25
600x + 575 y = 2619.05
150x = 98.20
or, x = 0.654...
Substituting this value in the first equation we get:
y= 4.115...
Therefore the solution of the simultaneous equation is:
x = $ 0.65 and y = $ 4.12
Therefore the cost of laminate is $ 0.65 per sq. feet and the cost of carpet is $ 4.12 per sq. feet.
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The number below is not correctly written in scientific notation.
0.0038 × 105
What is the new exponent for the power of 10 after rewriting the number correctly in scientific notation?
3.8 × 10?
Write the new exponent value in the blank below.
Answer: use a picture math thing
Step-by-step explanation:0.0038 x 105=0.399 so move the decimal point over 1 then it should look like 0.038 x 10.5=0.399 then repeat.
Riverstones Whitewater Rafting charges $77.25 per person for a half-day rafting trip. Karen, her mom, and her dad take a half-day rafting trip and then buy 1 souvenir water bottle for $7.99 after the trip. How much money did Karen's family spend in all?
Answer: $239.74 :)
Step-by-step explanation:231.75 for Karen, mom, and dad's rafting, plus 7.99 for the water bottle=239.74 USD
find the midpoint of points A(8,10)and B(0,5) graphically
Answer:
Step-by-step explanation:
Midpoint coordinates(x, y) of 2 points (x1, y1) and (x2, y2) are given by
x = (x1 + x2)/2
y = (y1 + y2)/2
So in this situation
x = (8 + 0)/2 = 8/2 = 4
y = (10 + 5)/2 = 15/2 = 7.5
Midpoint is at (4, 7.5)
Check the graph attached
Please Help! Determine the range of the following graph:
Answer:
- 4 ≤ y ≤ 2 or [ -4; 2 ]Step-by-step explanation:
The range of the function is the set of all y- values.
The range on the graph can be determined by minimum and maximum points if the graph is continuous.
Looking at the given graph we observe:
The minimum is y = - 4,The maximum is y = 2,The graph is continuous between these two points.The range is:
- 4 ≤ y ≤ 2 or[ -4; 2 ]Solve this linear quadratic system
y = 3x + 4
y + x² = 0
Answer:
x = -1, y = 1
Step-by-step explanation:
Solve the following system:
{y = 3 x + 4 | (equation 1)
y = x + 2 | (equation 2)
Express the system in standard form:
{-(3 x) + y = 4 | (equation 1)
-x + y = 2 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{-(3 x) + y = 4 | (equation 1)
0 x + (2 y)/3 = 2/3 | (equation 2)
Multiply equation 2 by 3/2:
{-(3 x) + y = 4 | (equation 1)
0 x + y = 1 | (equation 2)
Subtract equation 2 from equation 1:
{-(3 x) + 0 y = 3 | (equation 1)
0 x + y = 1 | (equation 2)
Divide equation 1 by -3:
{x + 0 y = -1 | (equation 1)
0 x + y = 1 | (equation 2)
Collect results:
Answer: {x = -1, y = 1
What’s 181 x 42 step by step
answer: 7,602
explanation: 2×3×7×181
Answer:7602
Step-by-step explanation:First line up the numbers vertically and match the places from the right like this.
181
942
* ____
Now multiply the first number with the 1 st digit in 2 nd
number to get intermediate results. That is Multiply 181 with 2. Write the result 362 at the end leaving 0 spaces to the right like this.
181
42
*_____
362
Now multiply the first number with the 2nd digit in 2nd
number to get intermediate results. That is Multiply 181 with 4. Write the result 724 at the end leaving 1 spaces to the right like this.
181
42
*______
362
724
______-
Now add the intermediate results to get final answer.
181
42
*_____
362
724
______
7602
Draw a scatter plot and find the line of best fit for each set of data. (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14)
The scatter plot is shown in attached images and the line of best fit for the data set is y=1.9821x+2.1937.
The given data set is (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14).
Plot the points on a coordinate plane.
Calculate the means of the x -values and the y -values.
[tex]\begin{aligned}\bar{X}&=\frac{0+1+2+3+4+5+6}{7}\\ &=\frac{21}{7} \text{ or } 3\\ \bar{Y}&=\frac{2+4+6.5+8.5+10+12+14}{7}\\ &=\frac{57}{7}\text{ or }8.14\end[/tex]
Now, we will calculate the [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})[/tex] and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}[/tex], we get
[tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}=28[/tex]
and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})=55.5[/tex]
Calculate the slope.
[tex]\begin{aligned}m&=\frac{\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})}{\sum_{i=1}^{n}(x_{i}-\bar{X})}\\ &=\frac{55.5}{28}\\ &=1.9821\end[/tex]
Calculate the y -intercept.
Use the formula to compute the y -intercept.
[tex]\begin{aligned}b&=\bar{Y}-m\bar{X}\\ &=8.14-(1.9821\times3)\\ &=8.14-5.9463\\ &=2.1937\end[/tex]
Use the slope and y -intercept to form the equation of the line of best fit.
The slope of the line is 1.9821 and the y -intercept is 2.1937 .
Therefore, the equation is y=1.9821x+2.1937 .
Draw the line on the scatter plot.
Hence, the scatter plot is shown in attached image and the line of best fit for given data set (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14) is y=1.9821x+2.1937.
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3(w-2)=9 please
answer
Answer:
w=5
Step-by-step explanation:
3(w-2)=9
3w-6=9
w=5
Answer:
w = 5
Step-by-step explanation:
The equation is 3(w - 2) = 9
1st : Distribute 3 to w and -2
Should equal 3w and -6
2nd : Add 6 on both sides
Should equal 3w = 15
3rd : Divide 3 on both sides
Should equal w = 5
Hope this helps!
--Blu
Mark and Gary had a basketball game Saturday. Mark had three times as many rebounds as Gary. If together they had 28 rebounds, how many rebounds did Mark have?
Answer: 19
Step-by-step explanation:
For each annual rate of change, find the corresponding growth or decay factor. +0.1%
The growth factor for the annual rate of change +0.1 % is 1.001.
A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.
With the function displayed to the right, you may represent exponential growth or decay.
A(x) = a( 1 + r)ˣ
Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.
Now, we have the annual rate of change as:
r = + 0.1% = + 0.1 / 100 = + 0.001
From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.
So, let B = 1 + r
B = 1 + r
B = 1 + (+0.001)
B = 1.001
Now, the value of B is greater than 1 therefore, the corresponding growth factor is 1.001.
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