Answer:
An exponent is often referred to as a power of 10, for instance, [tex]\sf 6\boxed{^7}[/tex], as the exponent is highlighted. A number can only become a power of 10 under certain circumstances in an expression, on the other hand, you have exponents alone in expressions like "45² + x", the exponent was assigned to a number and that means that we multiply that number by itself that number of times. Logically speaking, it's impossible for a number alone to be a power of 10 or to become one out of the blue, a power of 10 is assigned into an expression and before a whole number before you start working on it, which is the equation.
I hope that answered your question as much as possible, notify me of any concerns.
Answer:
Well:
Step-by-step explanation:
When it has a little 10 on the top of a number. like 7 with a little 10 in the corner. :]
3/4 +1/7 use multiples method to find the lcd and then find the sum or difference
Solve the absolute value inequality |-2z+30| ≤ 30
The answer of the above question is [0,30]
An absolute value inequality is one with an absolute value sign and a variable inside.
An important point to remember: | x |= {x if x ≥ 0 }
| x |= {x if x< 0}
taking the expression |-2z+30| ≤ 30
Write the equivalent compound inequality.
-30≤ -2z+30 ≤ 30
= -30-30 ≤ -2z ≤ 30-30
= -60≤ -2z ≤ 0
= -60/2 ≤ -z ≤ 0
= -30 ≤ -z ≤ 0
Solve the compound inequality.
= 0 ≥ z ≥ 30 (reversing of signs)
Hence, the solution using interval notation [0,30].The check is left to you.
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The average worker in a manufacturing plant produces 27 units every hour the manager of the plant took a sample of 25 workers and gave them special training designed to increase their productivity after the special training was complete the 25 workers produced 28.2 units every hour with stand deviation of 2.9 what is the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher
The probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher is 0.0192.
How to illustrate the information?It should be noted that from the information, after the special training was complete the 25 workers produced 28.2 units every hour with stand deviation of 2.9.
Therefore, the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher will be:
= 1 - P[(Z (28.2 - 27)/29/✓25)]
= 1 - P(Z < 2.07)
It should be noted that this will be looked on the distribution table.
= 1 - 0.9808
= 0.0192
Therefore, the probability of randomly sampling 25 workers from the general population and their mean productivity being 28.2 or higher is 0.0192.
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[tex] \rm If \: \beta = \lim_{x \to0} \frac{ {e}^{ {x}^{3} } - (1 - {x}^{3} {)}^{ \frac{1}3 } + ((1 - {x}^{2} {)}^{ \frac{1}{2} } - 1) \sin x}{x \sin^{2} x} ,\\ [/tex]
then the value of [tex]6 \beta [/tex] is
Expand the limand as
[tex]\dfrac{e^{x^3} - (1 - x^3)^{1/3} + \left((1-x^2)^{1/2} - 1\right) \sin(x)}{x \sin^2(x)} \\\\ ~~~~~~~~ = \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} \cdot \dfrac{x^2}{\sin^2(x)} + \dfrac{(1-x^2)^{1/2} - 1}{x^2} \cdot \dfrac{x}{\sin(x)}[/tex]
Recall that for [tex]a\neq0[/tex],
[tex]\displaystyle \lim_{x\to0} \frac{\sin(ax)}{ax} = 1[/tex]
Then
[tex]\displaystyle \beta = \lim_{x\to0} \left( \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} + \dfrac{(1-x^2)^{1/2} - 1}{x^2}\right)[/tex]
Rationalize the numerators.
[tex]\dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} = \dfrac{e^{3x^3} - (1 - x^3)}{x^3 \left(e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}\right)} \\\\ ~~~~~~~~~~~ = \left(\dfrac{e^{3x^3} - 1}{x^3} + 1\right) \cdot\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}}[/tex]
and observe that
[tex]\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}} \to \dfrac13[/tex]
[tex]\dfrac{(1-x^2)^{1/2}-1}{x^2} = \dfrac{(1-x^2) - 1}{x^2 \left((1-x^2)^{1/2} + 1\right)} \\\\ ~~~~~~~~ = -\dfrac1{(1-x^2)^{1/2} + 1} \to -\dfrac12[/tex]
This leaves us with
[tex]\displaystyle \beta = \lim_{x\to0} \frac{e^{3x^3} - 1}{3x^3} - \frac16[/tex]
The remaining limit is the derivative of [tex]e^{3x^3}[/tex] at [tex]x=0[/tex], so its value is 1, and we find
[tex]\beta = 1 - \dfrac16 = \dfrac56 \implies 6\beta = \boxed{5}[/tex]
What’s is 365x4 area model
Answer:
365 x 4 = 1460
Step-by-step explanation:
The area model shows that 365 multiplied by 4 is equal to 18.
First, we draw a rectangle to represent the number 365. We divide it into three parts vertically to represent the digits 3, 6, and 5.
3 6 5
Next, we draw a rectangle to represent the number 4. We position it to the right of the rectangle for 365.
3 6 5
4
To find the area, we calculate the individual areas of each section and then add them up.
The area of the rectangle representing 3 is 3 times the height, which is 1.
3 6 5
| | |
| | |
| | |
The area of the rectangle representing 3 is 3.
The area of the rectangle representing 6 is 6 times the height, which is 1.
3 6 5
| | | |
| | | |
| | | |
The area of the rectangle representing 6 is 6.
The area of the rectangle representing 5 is 5 times the height, which is 1.
3 6 5
| | | | |
| | | | |
| | | | |
The area of the rectangle representing 5 is 5.
The area of the rectangle representing 4 is 4 times the height, which is 1.
3 6 5
| | | | | |
| | | | | |
| | | | | |
So, the area of the rectangle representing 4 is 4.
Now, the total area, we add up the areas of the individual sections:
= 3 + 6 + 5 + 4
= 18
Therefore, the area model shows that 365 multiplied by 4 is equal to 18.
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PLEASE HELP! DUE IN LESS THAN 2 HOURS! IM STUCK! PLEASE HELP ME! YOU WILL GET 100 POINTS! THANKS QUESTION DOWN BELOW!!! PLEASE SHOW THE WORK!
Answer:
Do you want the equation?
y = [tex]x^{2}[/tex]
Step-by-step explanation:
Answer:
1. One square
2. Four squares
3. Nine squares
4. Sixteen squares
5. Twenty-five squares
6. Thirty six squares
7. 49 squares
8. 64 squares
9. 81 squares
10. 100 squares
Step-by-step explanation:
The pattern is add six squares to the image before the one you’re working.
What is the midpoint of the segment shown below?
-10
(-8,-7)
10
(-7,-8) 10-
10
O A. (-15, -15)
OB. (-¹5-15)
O C. (-15, -15)
O D. (-1/5, -1¹/5)
SUBN
The midpoint of the segment where the segment has the endpoints (-8,-7) and (-7,-8) is (-15/2, -15/2)
How to determine the midpoint of the segment shown below?On the segment, we have the following endpoints
(-8,-7) and (-7,-8)
The midpoint of the segment is calculated using
Midpoint = 1/2 * (x1 + x2, y1 + y2)
Where
(x1, y1) = (-8,-7)
(x2, y2) = (-7,-8)
Substitute the known values in the above equation
So, we have
Midpoint = 1/2 * (-8 + -7, -7 - 8)
Evaluate the difference in the above equation
So, we have
Midpoint = 1/2 * (-15, -15)
Evaluate the product in the above equation
So, we have
Midpoint = (-15/2, -15/2)
Hence, the midpoint of the segment where the segment has the endpoints (-8,-7) and (-7,-8) is (-15/2, -15/2)
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4x + 3 - x = [?]x + [ ]
Answer:
3x + 3
Step-by-step explanation:
4x + 3 - x can be expressed as:
x + x + x + x + 3 - x
If we combine like terms:
x + x + x + x - x + 3
x + x + x + 3
3x + 3
Eliana is playing a card game with her cousins. At the start of this turn, she had −12 points in the game. On this turn, she gets 7 points. What sum could be calculated to find the number of points Eliana now has?
________
Answer:
Step-by-step explanation:-12+7=-5
8.G.A.1- I can verify the properties of rotations, reflections, and translations
Describe the transformation that occurred to get from the figure ABCD to EFGH. Include all necessary components of the transformation (angle of rotation, direction, center of rotation, how many units and in what direction, line of reflection, etc)
The transformation that occurred to get from the figure ABCD to EFGH, including the necessary terminologies is as follows:
Step 1: Reflection
The reflection using the y axis as the line of reflection at point C After the reflection the points changed A = E, D = H, C = G, and B = F
Step 2: Rotation
The rotation occurred with point A now E as the center of rotation. The angle of rotation is 90 degrees anticlockwise direction.
Step 3 Translation
The quadrilateral is now moved 4 units to the left to arrive at the new position.
What is transformation?Transformation is a term used in mathematics to describe some technical movements that objects makes. This objects are usually plotted to ensure that every movement can be calculated.
Some terms in transformation are reflection, rotation, translation and so on. Reflection produces mirror image of the object, Rotation is achieved using a specified angle and the direction is specified with either clockwise or anticlockwise then Translation is more of a straight forward movement.
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Enter your answer in interval notation.
Enter any values to one decimal place.
To enter ∞ , type infinity. To enter ∪ , type U.
Answer:
(-4;2)
Step-by-step explanation:
The graph show us line on the -4 and 2 and I think the answer us (-4;2)
There is a 6m long pool and there are logs that are 1\2 a meter long. How many logs does she need?
HELP! The problem's in the image, if you can't see it tell me.
Answer:
x/(1-x)
Step-by-step explanation:
We start by induction. The first 2 terms are x/(1-x^2) and x^2/(1-x^4), respectively. When we add them together using special factorizations, we get: (x^3+x^2+x)/(1-x^4). We quickly realize that the numerator is a geometric series. Applying the following formula, we can simplify our expression to (x^4-x)/(1-x^4)(x-1). Now, we introduce our 3rd term, and add that to our sum. That gets us: (x^7+x^6+...+x)/(1-x^8). This is another Geometric series, and we apply the exact same formula, for this new fraction: (x^8-x)/(1-x^8)(x-1). We realize this is a pattern, and we can utilize this pattern for the sum of the first n terms.
We look at the exponents. For the first 3 terms, the Degree is 8, for the first 2 terms, the Degree is 4. We take note that this looks like x^2^n.
Using that our general formula IS: (attached to this text) (x^2^n-x)/(1-x^2^n)(x-1). Now, when 0<x<1 and n approaches infinity, what do we get?
all terms x^2^n are so small, it's basically redundant, and can be crossed off. This leaves us with -x/(x-1), which can be simplified to x/(1-x).
Six 3 digit numbers contain the digit 4, 6 and 8. What are they?
Answer:
468
486
648
684
846
864
help me do this plroblem
Answer: $640
Step-by-step explanation:
Answer:
640
Step-by-step explanation:
For Exercises 1 and 2, use the table. It shows the types of
and prices of Jolly Juice Orange Juice.
Bottles of Jolly Juice Orange Juic
Containers
Price
8 oz
$0.96
16 oz
$1.60
32 oz
$2.56
64 oz
$3.84
1. Find the unit rate for an 8-ounce
container of Jolly Juice. Explain your
answer.
2. Find the unit rate for each size. Then order the sizes from least to greatest unit rate
Answer:
I have 5 apples and give u 2 how much I have
The ratio of males to females at a basketball game was 4:5 suppose there were 80 females at the basketball game how many people were at the game all together
Using ratio, we concluded that there are total 144 people at the basketball game.
How do we calculate ratio?Ratios contrast two figures by typically dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.
Let x be the number of people at the basketball game.
4x = number of males
5x = number of females
Total females = 80
⇒ 5x = 80
⇒ x = 16
4x = 4 × 16
⇒ 64
∴ Total males = 64
Total people present = number of males + number of females
⇒ 64 + 80
⇒ 144
∴Total people at basketball game are 144
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the lengths of the four sides as a quadrilateral (in feet) are consecutive integers if the perimeter is 86 ft find the value of the longest of the four side lengths
Let x be the shortest side
Let x+1 be the second side
Let x+2 be the third side
Let x+3 be the fourth and longest side
[tex]perimeter = s_{1} + s_{2} + s_{3} + s_{4} \\ 86 = x + (x + 1) + (x + 2) + (x + 3) \\ 86 = x + x + 1 + x + 2 + x + 3 \\ 86 = 4x + 6 \\ 4x = 80 \\ x = 20[/tex]
Shortest side is 20 cm
Longest side is x+3 so 20+3=23
Answer: 23write an expression as a number in scientific notation
(7 x 10³)(5.4 x 10⁴)/ 9 x 10² ?
4.2x10¹⁰
3.4x10¹⁰
4.2x10⁵
3.4x10⁵
The given expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation is 4.2 × 10^5.
According to the question.
We have an expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10².
Since, we have to write the above expression as a number in scientific notation.
As we know that, scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
Thererefore, the expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation
(7 x 10³)(5.4 x 10⁴)/ 9 x 10²
= (7 × (10^7) × 54)/ 9 × (10^2) × 10
= 7 × 6 × 10^(7 - 3)
= 42 × 10^4
= 4.2 × 10^5
Hence, the given expression (7 x 10³)(5.4 x 10⁴)/ 9 x 10² as a number in scientific notation is 4.2 × 10^5.
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For a class project, Henry needs to know how many students at M College think that
climate change is a serious issue. He surveys the students in his classes, and finds that
205 of the 345 students he surveys agree that climate change is a serious issue. There
are 2960 students at M College. Find the estimated number of students at the M College
who agree climate change is a serious issue. What percent of total students is that? What
assumptions are needed, and what are the limitations of his method?
The estimated number of students at the M College who agree climate change is a serious issue is 1759
The percentage of total students is 59.42%
The method used can be biased.
How many students believe climate change is a serious issue?The students surveyed are the sample while the students in the M College are the population. A population is the party of interest in an experiment. A population consists of all the members of the group. A sample is a smaller group of the population.
The limitation of using a sample to estimate for the population is that the sample might be a biased estimate of the population. If the sample is biased, the result of the experiment would be inaccurate.
Estimated number of students at M College = (sample that agree that climate change is a serious problem / total number of people surveyed) x number of students
(205 / 345) x 2960 = 1759
Percentage = (1759 / 2960) x 100 = 59.42%
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investment will pay $332,640 at the end of next year for an investment of $220,000 at the start of the year. If the market interest rate is 8% over the same period, should this investment be made?
A.
Yes, because the investment will yield $85,536 more than putting the money in a bank.
B.
Yes, because the investment will yield $76,032 more than putting the money in a bank.
C.
Yes, because the investment will yield $95,040 more than putting the money in a bank.
D.
No, because the investment will yield $95,040 less than putting the money in a bank.
Based on the amount the investment would pay at the end of next year, and the market interest rate, C. Yes, because the investment will yield $95,040 more than putting the money in a bank.
How to know if the investment should be made?The investment of $220,000 at the market rate of 8% would earned:
= 220,000 x 8%
= $17,600
The amount that the investment would make instead is:
= 332,640 - 220,000
= $112,640
The difference is:
= 112,640 - 17,600
= $95,040
In conclusion, the investment should be made.
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Can someone help with this question?
Step-by-step explanation:
[tex] {(x + 3)}^{2} + {(y + 7)}^{2} = {16}^{2} \\ {(x + 3)}^{2} + {(y + 7)}^{2} = 256[/tex]
6. BUILDING A horse farm is developing a new indoor arena in a rectangular building. They want the width of the building to be 2y feet and the length to be 4y – 9 feet. Write an expression in simplest form to represent the area A of the building in terms of y.
The area of the rectangular arena can be represented as A = (8y2 - 18y) square feet.
Here, we are given the dimensions of a rectangular arena, which are as follows-
Length = 4y - 9 feet
width = 2y feet
The area of a rectangle is given by the formula-
Area of a rectangle = length x breadth
Thus, in this case, area (A) can be calculated as follows
A = (4y - 9) * 2y
Now, we simplify the equation-
A = (4y)(2y) - 9(2y)
A = 8 - 18y
Thus, the area of the rectangular arena can be represented by the following equation- A = (8 - 18y) square feet.
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Solve the equation m² = 14. Lesson 1-5
Answer:
m=√14,−√14
Decimal Form:
m=3.74165738, -3.74165738
Step-by-step explanation:
Find the value of X then find the measure of each labeled angle.
The value of the angle x is 108 degree.
According to the statement
We have to find that the value of the x in the adjacent angle.
So, For this purpose, we know that the
The adjacent angles is the two angles are said to be adjacent angles when they share the common vertex and side.
From the given information:
When we extend line AB to E
Then ∠EBC is created
Since BC is parallel to AD
So, ∠EBC =∠BAD = x° (corresponding angles are equal )
Linear pair : Two angles are said to be linear if they're adjacent angles formed by two intersecting lines. The measure of a angular unit is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Now With the linear pair property
x+(x-36) = 180
2x - 36 = 180
2x = 180+36
2x = 216
x = 216/2
x = 108.
Then one angle is of 108 degree and second angle is 72 degree.
So, The value of the angle x is 108 degree.
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HELP 50 POINTSThe stingray population in a particular reef is decreasing at a rate of 1.4% per year. The population was 3800 in the year 2008. What is the best prediction of the population in the year 2013?
The best prediction of the population in the year 2013 is 3541 based on the fact that the population decreases by 1.4% every year
What is the number of years between 2008 and 2013?
The number of years between 2008 when the population figure was at 3,800 and 2013 is 5 years, hence when determining the population for the year 2013 we need to bear in mind that the population has decreased by 1.4% over a period of 5 years
FV=PV*(1-r)^N
FV= best prediction of the population in the year 2013
PV=population in 2008=3800
r=decreasing rate of the population=1.4%
N=number of years that have passed between 2008 and 2013
FV=3800*(1-1.4%)^5
FV=3541
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solve 6/58 x -1 2/5 -371/40 -6 1/4 1 1/2 371/40
The simpliified value of the expression 6 5/8 x -1 2/5 is - 371/40
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
6 5/8 x -1 2/5
Convert the mixed fractions to improper fractions
So, we have
6 5/8 x -1 2/5 = 53/8 x - 7/5
Evaluate the product of the numerators in the above expression
So, we have
6 5/8 x -1 2/5 = 53/8 x - 7/5
Evaluate the product of the numerators in the above expression
So, we have
6 5/8 x -1 2/5 = - 371/8 x 1/5
Evaluate the product of the denominators in the above expression
So, we have
6 5/8 x -1 2/5 = - 371/40
Hence, the simpliified value of the expression 6 5/8 x -1 2/5 is - 371/40
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I need help to find the degree
Answer:
Step-by-step explanation:
Find the degree, leading term, and leading coefficient.
Polynomial Degree:
2
Leading Term:
5x²
Leading Coefficient:
5
In the figure below, h
o. Find the values of X and z.
Applying the same-side-interior angles theorem, the values are:
x = 95°
z = 35
What is the Same-Side-Interior Angles Theorem?An examples of angles that are referred to as same-side-interior angles are x° and 85°.
According to the same-side-interior angles theorem, the sum of x and 85 will give 180 degrees if lines h and o are parallel to each other.
Since h║o, therefore:
x + 85 = 180
x + 85 - 85 = 180 - 85
x = 95°
(6z - 115)° and x° are vertical angles, therefore:
6z - 115 = x
Plug in the value of x
6z - 115 = 95
6z - 115 + 115 = 95 + 115
6z = 210
6z/6 = 210/6
z = 35
Thus, applying the same-side-interior angles theorem, the values are:
x = 95°
z = 35
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16. Vocabulary A number written in
expanded form is written as the sum
of each …..
.Write 39,005
in expanded form...