From the question, we can deduce the answer using indices which deals with power of numbers, e.g
[tex]\frac{5^2.5^3}{5^4}=\frac{5^{2+3}}{5^4}=\frac{5^5}{5^4}=5^{5-4}=5^1=5[/tex]Also, for the next one,
[tex]\frac{9^4.9^6}{9^8}=\frac{9^{4+6}}{9^8}=\frac{9^{10}}{9^8}=9^{10-8}=9^2[/tex]This applies to every other ones provided in the question,
Considering Option D,
[tex]\begin{gathered} \frac{b^{2k}.b^{3k}}{b^{4k}} \\ \text{where k is 2,} \\ \frac{b^{2(2)}.b^{3(2)}}{b^{4(2)}}=\text{ }\frac{b^4.b^6}{b^8}=\frac{b^{4+6}}{b^8}=\frac{b^{10}}{b^8}=b^{10-8}=b^2 \\ \text{Where k=2, Option D is favoured} \end{gathered}[/tex]Since the equation D favours the solution,
Hence, the best option is D.
Describe how to transform into an expression with a rational exponent. Use full sentence
For any numbers x, a and b, we aply the following rules:
[tex]\sqrt[a]{x^b}=x\text{\textasciicircum(b/a)}[/tex]and
[tex](x^a)^b=x^{ab}[/tex]Therefore, we got:
[tex](\sqrt[6]{x^5})^7=x^{(5\cdot7)/6\text{ = 35/6}}[/tex]The following side lengths, in meters, were given to a carpenter to build a front porch with a triangular design. The carpenter needs to determine which set of lengths will make a triangle to be able to use it in his design. Which of the options would create a triangle for his design?
*
5 points
Side lengths: 4, 4, 8
Side lengths: 6, 8, 10
Side lengths: 6, 6, 13
The pair of side lengths that can create a triangle is 6, 8 , 10.
What is a triangle?A triangle is a polygon with 3 sides. The area of a triangle with base b and height h is given by A = (1/2)bh.
The given pairs of side lengths of the triangle are 4,4,8; 6,8,10; and 6,6,13.
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
(1) The side lengths are 4,4,8.
Since 4 + 4 =8 is not greater than the length of the third side, 8, it won't create a triangle.
(2) The side lengths are 6,8,10.
Note that the sum of any two side lengths is greater than the length of the third side, therefore, this pair of side lengths can create a triangle.
(3) The side lengths are 6,6,13
Since 6 + 6 =12 is not greater than 13, the third side length, won't create a triangle.
Hence, the pair of side lengths that can create a triangle is 6, 8 , 10.
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Find the slope of the line passing through the points (0, 3) and (5, 2).51-1515-51
Given: The points below
[tex]\begin{gathered} Point1:(0,3) \\ Point2:(5,2) \end{gathered}[/tex]To Determine: The slope of the given points
Solution
The slope of two points can be determine using the formula below
[tex]\begin{gathered} Point1:(x_1,y_1) \\ Point2:(x_2,y_2) \\ Slope=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Substitute the given points into the formula
[tex]slope=\frac{2-3}{5-0}=-\frac{1}{5}[/tex]Hence, the slope of given line is -1/5
what are the mixed decimal fraction and the simplified mixed fraction for 9.875
The given decimal fraction is:
[tex]9.875[/tex]This can be expressed into a fraction as:
[tex]\frac{9875}{1000}[/tex]Hence, the mixed decimal fraction is:
[tex]9\frac{875}{1000}[/tex]Hence, the simplified mixed fraction is:
[tex]9\frac{7}{8}[/tex]Put in your own words.What is a quadratic equation?
Answer:
A quadratic equation is an equation that has the following general form:
[tex]ax^2+bx+c=0.[/tex]Any equation that can be rewritten in the above form can be considered a quadratic equation, the important part is that there is a term that includes an
[tex]x^2,[/tex]and that 2 is the greatest exponent of any variable of the equation.
write the decimal using number name,and unit form . 317.098
three hundred and seventeen and ninety-eight thousandths
Explanation:3 = hundreds
1 = ten
7 = ones
Number after the decimal point start in ythe tenth place
0 = tenth
9 = hundredths
8 = thousandths
Naming the number:
three hundred and seventeen and ninety-eight thousandths
1. Let a and b be integers. Prove that if a|b, then a”|6" for all positive integers n.
Solution
- a and b are integers. a | b means that integer a can divide integer b with no remainders.
- Let the Quotient of the division be k, so we can say:
[tex]\begin{gathered} a|b=k \\ \\ \text{ Put in an easier way, we have:} \\ \frac{b}{a}=k \\ \\ where, \\ k\text{ is an integer since }a\text{ directly divides b} \end{gathered}[/tex]- Now, we are asked to find
[tex]a^n|b^n[/tex]- Again, we can rewrite this as:
[tex]\frac{b^n}{a^n}[/tex]- We can rewrite this expression using the law of exponents that says:
[tex]\frac{x^m}{y^m}=(\frac{x}{y})^m[/tex]- Applying this law, we have:
[tex]\frac{b^n}{a^n}=(\frac{b}{a})^n[/tex]- But we already know that
[tex]\frac{b}{a}=k[/tex]- Thus, we have that:
[tex]\begin{gathered} \frac{b^n}{a^n}=k^n \\ \\ That\text{ is,} \\ a^n|b^n=k^n \\ for\text{ all positive integers n} \\ \\ k^n\text{ is an integer as well because }k\text{ is an integer.} \end{gathered}[/tex]- Therefore, we have successfully proved the assertion
a recipe calls for 1/4 cup of flour. Carter only has a measuring cup that holds 1/8 cup.How can Carter measuring cup that holds 1/8 cup.How can Carter measure the flour he needs for his recipe?
We are given that we need to measure 1/4 cup of flour with a measuring device that can only hold 1/8 cup.
To determine the 1/4 cup we need to have into account that:
[tex]\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4}[/tex]Therefore, two times 1/8 is 1/4 therefore, Carter can fill the 1/8 cup two times to get 1/4 cup.
Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.)
Before we can determine the absolute extrema of the function, let's graph the given function first. f(x) = x² - 6x.
For the interval [-1, 6], we can see that the maximum value would be at x = -1.
Let's replace x with -1 in the function above.
[tex]\begin{gathered} f(x)=x^2-6x \\ f(-1)=(-1)^2-6(-1) \\ f(-1)=1+6 \\ f(-1)=7 \end{gathered}[/tex]Therefore, the maximum between the interval [-1, 6] is at (-1, 7).
On the other hand, looking at the interval (3, 7] in the graph, the maximum is found at x = 7. To determine the maximum point, replace "x" with 7 in the function above.
[tex]\begin{gathered} f(7)=7^2-6(7) \\ f(7)=49-42 \\ f(7)=7 \end{gathered}[/tex]Therefore, the maximum at the interval (3, 7] is at point (7, 7).
the regular price of a high quality pair of binoculars is $600.00. This week, binoculars are on sale for 12% off. The tax rate is 3.5%. If you hand the cashier twenty-eight $20.00 bills, how much change should you receive ? show your work.
Answer:
$13.52
Explanation:
Regular Price of the binoculars = $600
Discount = 12%
Therefore, the Sale Price of the binocular will be:
[tex]\begin{gathered} (1-12\%)\text{ of 600} \\ =(1-0.12)\times600 \\ =0.88\times600 \\ =\$528 \end{gathered}[/tex]The tax rate is 3.5%.
[tex]\begin{gathered} \text{Tax}=3.5\%\text{ of \$528} \\ =0.035\times528 \\ =18.48 \end{gathered}[/tex]Therefore, the total amount to be paid will be:
[tex]\begin{gathered} =\text{Sales Price+Tax} \\ =528+18.48 \\ =546.48 \end{gathered}[/tex]If you give the cashier twenty-eight $20.00 bills, the change that you would receive will therefore be:
[tex]\begin{gathered} \text{Change}=(28\times20)-546.48 \\ =560-546.48 \\ =\$13.52 \end{gathered}[/tex]Solve each problem by writing an equation that matches the situationthen solve your equation to find the solution.
Question 2:
- Shakira paid $3 to rent shoes for bowling. At this point, she has spent a total of $3.
- Next, she plays bowling games each worth $4.75. This means that:
For her 1st game, she will pay $4.75
For her 2nd game, she will pay 2($4.75)
For her 3rd game, she will pay 3($4.75)
For her 4th game, she will pay 4($4.75)
And so on.
- We can see that her total cost paying for the games follows a pattern and we can therefore generalize. If Shakira plays n games, it means that:
For her nth game, she will pay n($4.75).
- Thus, the total amount that Shakira pays is the amount paid for the shoes plus the amount paid for the games.
- Thus, we can write the equation showing her total cost as follows:
[tex]\begin{gathered} \text{Total cost}=Amt\text{ paid for the shoes }+Amt\text{ paid for the games} \\ \text{Amt paid for the shoes}=3 \\ \text{Amt paid for the shoes}=4.75n \\ \\ \therefore\text{Total Cost}=4.75n+3 \\ \text{where, n is the number of games} \end{gathered}[/tex]- Since Shakira spent a total of $42, we can find the number of games (n) that she played as follows:
[tex]\begin{gathered} 42=4.75n+3 \\ \text{Subtract 3 from both sides} \\ 42-3=4.75n \\ 4.75n=39 \\ \text{Divide both sides by 4.75} \\ \frac{4.75n}{4.75}=\frac{39}{4.75} \\ \\ \therefore n=8.21 \\ \text{ Since she cannot pay a decimal number of games, we should round the number down} \\ \\ \therefore n=8 \end{gathered}[/tex]Question 3:
- In solving this question, we shall convert the information given to a mathematical equation
- Let the number of Field trips taken last year be f.
- Three times as many field trips as last year implies
[tex]3f[/tex]- Two more than three times as many field trips as last year implies
[tex]2+3f[/tex]- Cornell's class takes Two more than three times as many field trips as last year and this number of trips this year is 8.
Thus, we can say:
[tex]2+3f=8[/tex]- This means we can find the number of field trips last year f by solving the above expression.
[tex]\begin{gathered} 2+3f=8 \\ \text{Subtract 2 from both sides} \\ 3f=8-2 \\ 3f=6 \\ \text{Divide both sides by 3} \\ \frac{3f}{3}=\frac{6}{3} \\ \\ \therefore f=2 \end{gathered}[/tex]Final Answer
Question 2:
- The number of games is 8
- The equation is:
[tex]42=4.75n+3[/tex]
Question 3:
- The number of field trips from last year is 2
- The equation is:
[tex]2+3f=8[/tex]
Geometry formulas Situation: Find the perimeter of a rectangular area with a length of 13 inches and a width of 7 inches. Calculation With Distribution (Show all steps.) Calculation Without Distribution (Show all steps.) I think is easier: to distribute. to not distribute. Why I think it is Easier
a rectangular area with a length of 13 inches and a width of 7 inches.
Length of rectangle = 13 inches
Width of rectangle = 7 inches
With Distribution:
The perimeter of any polygon is the sum of all the sides of the polygon
In the given rectangle we have 2 lengths and 2 widthSo,
Perimeter = length + width + Length+ width
Substitute the value and solve
Perimeter = 13 + 7 +13 +7
Perimeter = 20 + 20
Perimeter =40inches
Without Distribution
The perimeter of rectangle is express as :
Perimeter = 2(length + Width)
Substitute the value and solve
Perimeter=2(13+7)
Perimeter=2(20)
Perimeter-40 inches
It was easier without distribution because it becomes calculation easy.
Answer: Perimeter = 40 inches
It is easier to not distribute
Because it makes calculation easy and short.
Fill in the blanks below.(a) Ivanna lost 40 dollars from her pocket.Write a signed number to represent this change.(b) A car corporation produced 540 more cars this month than last.Write a signed number to represent this month's change in production.
Recall that the signs
[tex]+,\text{ and -}[/tex]helps us indicate if there is an increase or a decrease.
If the number represents a decrease from the previous one, we put a minus sign. If the number represents an increase then we put a plus sign.
Notice that Ivanna lost $40, therefore, the total money she had decreased by 40.
If the company produced 540 more cars this month than last month, then there was an increase of 540 in cars production.
Answer:
(a)
[tex]-40.[/tex](b)
[tex]+540.[/tex]a large Square can be divided into 16 small squares a large Square can be divided into 16 small squares that have equal sides length of 1 cm what is the area of the large Square
ok
According to the information given, if the large square can be divided into 16 small squares, that means that there are only 4 squares on each side of thelarge square, see the picture
here, we can observe 16 squares, ans 4 squares in each row.
So, if each small square measures 1 cm
Area of the large square = 4 x 4 = 16 cm^2
Result
The area of the large square is 16 cm^2
Determine whether the given statement is true or false b ∈ {a,b,c}
ANSWER:
True
STEP-BY-STEP EXPLANATION:
The statement tells us if b belongs to the set by a, b and c.
Therefore, the statement is true, since it can be seen that b belongs to that set.
A stone pyramid in Egypt has a square base that measures 158 m on each side. The height is 96 m. What is the volume of the pyramid?
Given:
The base of the pyramid is 158 m.
Height is 96 m
The volume of the Pyramid is given as,
[tex]\begin{gathered} V=\frac{1}{3}\times Area\text{ of the cross- section}\times height \\ V=\frac{1}{3}\times Area\text{ of the square}\times Height \\ V=\frac{1}{3}\times(s^2)\times h \\ V=\frac{1}{3}\times158^2\times96 \\ V=\frac{2396544}{3} \\ V=798848m^3 \end{gathered}[/tex]Answer: The volume of the Pyramid is 798848 cubic meters.
what is the probability thay Noah will score 60 points if the 50 point circle has a radius 0.25 feet?bean bag throw6 feet ling2 feet wide
SOLUTION
Step 1: We need to find the area of the 50 -point circle of radius, 0.25 feet.
Recall that the Area of the Circle =
[tex]\begin{gathered} \pi r^2\text{ where }\pi\text{ =}\frac{22}{7}\text{ , r= 0.25 f}eet \\ =\text{ }\frac{22}{7}\text{ x 0.25 x 0.25 = 0. 1964 f}eet^2 \end{gathered}[/tex]Step 2: We need to find the Area of the Rectangle,
where length =6 feet and Width = 2 feet
[tex]\begin{gathered} \text{Area of the Rectangle = Length X Width} \\ 6\text{ f}eet\text{ x 2 fe}et\text{ = 12 f}eet^2 \end{gathered}[/tex]Step 3 : We need to find the probability that Noah will sc
PLEASE HELP ASAP 20 POINTS
The simplified form of the algebraic expressions 1, 2, 3, 4 and 5 are -2m-10, 3x + 11, 3²xy + 2z - 16, -7x - 11 and -m + 8 respectively
How to simplify algebraic expressions?An algebraic expression is defined as an expression that is made up of variables and numbers, along with algebraic operations such as addition, subtraction, etc.
Given:
1. -3+ 4m + (-7) -6m = -3 + 4m - 7 - 6m = -2m-10
2. 6x + (-1) - 3x + 12 = 6x - 1 - 3x + 12 = 3x + 11
3. 3xy + 2z - 16 + 6xy = 9xy + 2z - 16 = 3²xy + 2z - 16
4. 4x - 8+ 2x + (-3) - 5x = -4x - 8+ 2x -3 - 5x = -7x - 11
5. 3m² - m + 7 - 3m² + 1 = -m + 8
Therefore, the expressions 1,2,3,4 and 5 simplifies to -2m-10, 3x + 11, 3²xy + 2z - 16, -7x - 11 and -m + 8 respectively
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5. Write a general formula to describe the variation: x varies inversely with y.A: X=K • YB: X=K/YC: X=-K•YD: X=K/Y^2
If x varies inversely as y, then that means
[tex]x=\frac{k}{y}[/tex]where k is a constant of proportionallity. Then, the answer is option B.
Which equation represents a line which is parallel to the line 6y-7x=246y−7x=24?
The answer is very simple
First you need to solve the algebraic operations of the line and take it to its minimum expression
You roll a 6 sided die what is p 2 or less than 6
The sample space for one 6-sided die is given by
[tex]{}\lbrace1,2,3,4,5,6\rbrace[/tex]Then, the probability to get the number 2 or a number less than 6 is given by
[tex]P(2\text{ or less than 6\rparen=P\lparen2\rparen+P\lparen less than 6\rparen-P\lparen2 and less than 6\rparen}[/tex]which gives
[tex]P(2\text{ or less than 6\rparen=}\frac{1}{6}+\frac{5}{6}-\frac{1}{6}=\frac{5}{6}[/tex]that is because the probability to get a number 2 is 1/6, the probability to get a number less than 6 is 5/6 because there are 5 numbers less than 6 and the probability to get a number 2 and a number less than 6 is 1/6 because there is only one number 2.
Therefore, the answer is:
[tex]\frac{5}{6}[/tex]I need help with this question. I have to show work
PART A:
Let the number of days be represented by t. Let the total cost be represented by C.
FOR COMPANY A:
The equation to represent the total charges will be given as
[tex]C=22t+5[/tex]FOR COMPANY B:
The equation to represent the total charges will be given as
[tex]C=20t+16[/tex]PART B:
Company B will charge less over a 9-day rental period.
To confirm this answer, we will calculate the cost using the equations derived above:
FOR COMPANY A:
[tex]\begin{gathered} C=22(9)+5 \\ C=198+5 \\ C=203 \end{gathered}[/tex]FOR COMPANY B:
[tex]\begin{gathered} C=20(9)+16 \\ C=180+16 \\ C=196 \end{gathered}[/tex]Therefore, COMPANY B will charge less over 9 days.
PART C:
To know how much is saved over a 15-day period, we will first calculate the cost of both companies over the period using the equations derived from Part A.
FOR COMPANY A:
[tex]\begin{gathered} C=22(15)+5 \\ C=330+5 \\ C=335 \end{gathered}[/tex]FOR COMPANY B:
[tex]\begin{gathered} C=20(15)+16 \\ C=300+16 \\ C=316 \end{gathered}[/tex]We can, thus, calculate the difference as
[tex]\begin{gathered} 335-316 \\ =19 \end{gathered}[/tex]Therefore, the amount saved will be $19 over 15 days.
Hi I need help with these questions, if you can only answer 1 that’s okay. Thank you!
Each square in the block represents each block of size = 0.1*0.4 = 0.04.
1.
The factor 1.5 is divided into two number because in the figure it is shown that the 1 is up to orange line and 0.5 is up to black line and we want to find only area of divided parts.
That is
1*0.4 + 0.5 * 0.4
= 0.4+0.20
= 0.6
2.
Each square in the block represents each block of size = 0.1*0.4
= 1*4/10*10
= 4/100
= 0.04
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A national trivia tournament starts with 262,144 teams. With each round, there are half as many teams as before. The number of teams after any number of rounds, x, can be modeled with the following function.f(x)=262144(1/2)^xWhich statement compares the mathematical range and reasonable range of the function?1. Both the mathematical and reasonable ranges are limited to real numbers greater than 0 and less than or equal to 262,144.2. Both the mathematical and reasonable ranges are limited to whole numbers greater than 0 and less than or equal to 262,144.3. The mathematical range is all real numbers greater than 0. The reasonable range is all real numbers greater than 0 and less than or equal to 262,144.4. The mathematical range is all real numbers greater than 0. The reasonable range is all whole numbers greater than 0 and less than or equal to 262,144
The given function is
[tex]f(x)=262,144(\frac{1}{2})^x[/tex]This is a decreasing exponential function, due to the base is less than 1. When the base is less than one, the function is decreasing and 1/2 is less than 1.
The range of this exponential function is "all numbers greater than zero" because a power can't result in a null result (nor negative), that is, we can't get zero (or negative number) from a power, no matter what base it has, this applies for every exponential function.
However, the reasonable range refers to those values that make sense to the problem, because not all of the values from the function are valid as a reasonable solution.
Therefore, the reasonable range
[tex](0,262144\rbrack[/tex]Notice that the limit is 262,144, since that's the maximum number of teams possible.
The right choice is the "The mathematical range is all real numbers greater than 0. The reasonable range is all whole numbers greater than 0 and less than or equal to 262,144"
Which set of numbers includes only integers? o -5, -3 1/4, 1 1/8o -3, -2, 2, 3o-6, -4, -2, -1/2o1/2, 2/3, 6/7, 0
It is important to know that integers refer to the numbers that can be written as a fractional component.
For example: -3, -2, 2, 3 are integers.
Hence, the answer is the second option.Why the other answer choices are wrong?
Mainly because the other answer choices include numbers that are decimals, for example, -3 1/4 is equal to -3.25 which is not an integer.
The trip to and from work each day is 5 2/9 kilometers. If gina does this 5 days a week ,how many kilometers does she travel
Answer: Answer is 26.11 Kilometers
Step-by-step explanation:
First, we will convert the mixed fraction into improper fraction for easy calculation. So, the steps to convert mixed fraction to improper fraction are :-
Step 1- Multiply the denominator by the whole number
9 × 5 = 45
Step 2- Add the answer from Step 1 to the numerator
45 + 2 = 47
Step 3 - Write answer from Step 2 over the denominator
47/9
So, Mixed fraction is 47/9.
In other words, she travels 5.22 Kilometers daily.
Now, Gina travels 47/9 km daily to and from for work.
So, Kilometers travelled by her in 5 days are
47/9 * 5 = 26.11 Kilometer
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A carnival equipment manufacturer states that the circular platform of a particular merry-go-round has a circumference of 6.28 yards. What is the platform's area?
Given:
The circumference of the platform is 6.28 yards.
To find: The platform's area
Explanation:
The formula of the circumference of the circle is,
[tex]\begin{gathered} C=2\pi r \\ 6.28=2\times\frac{22}{7}\times r \\ r=6.28\times\frac{1}{2}\times\frac{7}{22} \\ =0.999 \\ \approx1yard \end{gathered}[/tex]The formula of the area of the circle is,
[tex]\begin{gathered} A=\pi r^2 \\ =\frac{22}{7}\times1\times1 \\ =3.137 \\ \approx3.14yards^2 \end{gathered}[/tex]Final answer: The platform's area is 3.14 square yards.
Use the distributive property to write the following expression as an equivalent product:8x -40a) 8(x - 32)(c) 10(-2x -4)(b) 8(x - 5)(d) 2(6x - 38)would it be answer c?:(
The answer is 8(x - 5)
Explanation
8x - 40
this can be re written as
since 8 is a factor of 40 and 40/8 = 5
factorize out 8
the new equation is
8(x - 5)
A license plate has two letters followed by three digits.What is the probability that the license plate are all odd numbers?
The number plate has two letters and three digits
The probability that the license plate are all odd numbers will be ...........
The probability of that the three numbers are odd is 1 / 2 x 1 / 2 x 1 / 2 = 1/8
Which answer best describes the shape of this distribution?uniformbell-shapedskewed leftskewed right
To answer this question, we need to understand the difference between uniform, bell-shaped, skewed left and skewed right.
A uniform distribution is a distribution where the data is equally distributed.
A bell-shaped distribution is a symmetric distribution where most of the data are on the center.
If most of the data are on the left side of the distribution but a few larger values are on the right, the data are said to be skewed to the right.
If most of the data are on the right, with a few smaller values showing up on the left side of the histogram, the data are skewed to the left.
Now that we have those definitions, let's analyze our distribution. Since most of the data is located at the right side, we have a skewed left distribution.