Using exponent properties, the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
What is the equivalent expression?The original expression is:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2}[/tex]
When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2} = [y^{-3 - 6}z^{5 - (-4)}]^{-2} = [y^{-9}z^9]^{-2}[/tex]
The negative exponent at the numerator goes to the denominator, hence:
[tex][y^{-9}z^9]^{-2} = \left[\frac{z^9}{y^9}\right]^{-2}[/tex]
The negative outer exponent means that we have to exchange the numerator and denominator, hence:
[tex]\left[\frac{z^9}{y^9}\right]^{-2} = \left[\frac{y^9}{z^9}\right]^{2}[/tex]
Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
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Answer:
y^18/x^18
Step-by-step explanation:
What is the constant term in the following expression?
4x - 2y + 3
The constant term in the expression is 3.
The expression is 4x ₋ 2y ₊ 3.
Here in this equation we have variables and constants.
variables = x and y whose coefficients are 4 and ₋2 respectively.
A variable is anything whose value can change and is not fixed. Typically, the letters x, y, z, etc. are used to indicate variables.
The above equation is in the form ax ₊ by ₊ c
An object with a fixed value in a circumstance is said to be a constant. We are aware that the constant is fixed, even though we do not know its exact value. In general, constants are represented by the letters a, b, c, p, q, etc. if their values are unknown or not given, and by particular numerical values) if their values are known.
Hence we get the constant term as 3.
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A rectangle is 15 cm wide. Find the area and the perimeter of the rectangle if its width is 3/5 of its length
The area and perimeter of the rectangle are 80 cm and 375 cm² respectively.
How to find area and perimeter of a rectangle?The rectangle is 15 cm wide.
The width is 3 / 5 of its length
Therefore, the area and the perimeter of the rectangle can be found as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
w = 15 cm
15 = 3 / 5 × l
cross multiply
75 = 3l
l =75 / 3
l = 25 cm
Therefore,
area of the rectangle = 25 × 15 = 375 cm²
Perimeter of the rectangle = 2l + 2w
Perimeter of the rectangle = 2(l + w)
Perimeter of the rectangle = 2(25 + 15)
Perimeter of the rectangle = 2(40)
Perimeter of the rectangle = 80 cm
Therefore, the area and perimeter of the rectangle are 80 cm and 375 cm² respectively.
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2.4z + 1.2z - 6.5 = 0.7
Answer: z = 2
Step-by-step explanation:
2.4z+1.2z-6.5=0.7
3.6z-6.5=0.7
3.6z=0.7+6.5
3.6z= 7.2
z=7.2/3.6
z=2
A survey showed the 8 about of 20 home owners in a neighborhood had cable television . If there were 320 homeowners in the neighborhood, how many could be expected to have cable television
The number that could be expected to have cable television will be 138 people.
How to calculate the value?From the information, survey showed the 8 about of 20 home owners in a neighborhood had cable television
Therefore, when there were 320 homeowners in the neighborhood, the number that could be expected to have cable television will be:
= 8/20 ×320
= 8 × 16
= 128
The number of people will be 128.
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d= √(7₂ (x2 − ₁)² + (Y2 − ₁)² Evaluate d if (x1, y₁) = (-3, 4) and (x2, Y2) = (−2, 4).
7. Charlotte needs to order thread to sew buttons onto marching band uniforms.
A 400-yard spool of thread is sold for $5.
• Each uniform needs 50 buttons.
There are 100 uniforms that need buttons.
• Each button requires of a yard of thread.
How much money should Charlotte ask for in the budget to spend on thread?
Using proportions, it is found that Charlotte should ask for $62.5 in the budget to spend on thread.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Each uniform needs 50 buttons, and there are 100 uniforms, hence the number of buttons needed is:
50 x 100 = 5000.
Each button requires of a yard of thread, hence the number of yards needed is:
5000 x 1 = 5000 yards.
A 400-yard spool of thread is sold for $5, hence the budget needed is:
(5000/400) x 5 = $62.5.
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lol i still dont get it i need a smartt brainlist help pleaseee
please help,, will mark branliest if its right!!
Answer:
1. DNE
2. DNE
3. (-2, inf)
4. (-3,-2)
Step-by-step explanation:
On a trip to Canada, you may wish to convert the local temperature from Celsius to Fahrenheit. Given the following formula, determine the temperature in degrees Fahrenheit
Answer:
138.2
Step-by-step explanation:
Celsius to Farenheit
(59/5)*9=106.2
106.2+32=138.2 farenheit
Given m(x) = |2x - 91, find x when m(x) = 15.
The value modulus functions of x are found as 12 and -3.
What is defined as the modulus functions?A modulus function returns the magnitude of a number regardless of its sign.
It's also known as the absolute value function. The modulus function, signified by |x| in mathematics, gives the modulus of a real number x. It returns a non-negative value for x. The modulus or absolute value of the a number is often recognized as the number's distance from the origin or zero.The modulus function's value is always non-negative. Whenever f(x) is a modulus function, we get:
For x is positive, then f(x) = xFor x = 0, then f(x) = 0For x < 0, then f(x) = -xfor the given function;
m(x) = |2x - 9|, where m(x) = 15.
then,
15 = |2x - 9|
Open the modulus function in its corresponding positive and negative values;
15 = 2x -9 and also 15 = -(2x - 9).
Solving both;
15 = 2x -9
2x = 15 + 9
2x = 24
x = 12
and, the second functions;
15 = -(2x - 9)
15 = -2x + 9
-2x = 15 - 9
x = -3
Thus, the solution for x are 12 and -3.
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The correct question is-
Given m(x) = |2x - 9|, find x when m(x) = 15.
greg can eat 1/8 of a hamburger in 1/12 of an hour how many hamburgers can greag eat in one hour
Answer: 1.5 Burgers an hour
1/8 x 12 = 1.5
Multiply 1/8 by 12 to get and hour because 12/12ths = 1 hour
An airplane leaves Los Angeles and travels 5 hours to New York City. The return trip travels along the same route and takes 6 hours and 15 minutes because the plane travels 99 mph slower due to a headwind. Find the distance the plane flies between the two cities.
The distance the plane flies between the two cities is 2,475 miles.
Given that, an aeroplane leaves Los Angeles and travels 5 hours to New York City. The return trip travels along the same route and takes 6 hours and 15 minutes because the plane travels 99 mph slower due to a headwind.
We need to find the distance the plane flies between the two cities.
How to find the distance with speed and time?To get the distance, multiply the speed by time. You may see these equations simplified as s=d/t, where s is speed, d is distance, and t is time.
Let the speed of an aeroplane while travelling from Los Angeles to New York City be x.
Then the speed of an aeroplane during the return trip will be x-99.
Now, Distance=Speed × Time
So, x × 5 = (x-99) × 6 1/4
⇒5x=25/4 (x-99)
⇒20x=25x-2475
⇒5x=2475
⇒x=495
The speed of an aeroplane is 495 mph.
Now, the distance = 5x =5 × 495
=2,475 miles
Therefore, the distance the plane flies between the two cities is 2,475 miles.
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Answer: plane
Step-by-step explanation:
plane fliying in the sky it go fl y
How many significant digits are in the number 1.00460? select one: a. 6 b. 3 c. 5 d. 4
There are 6 significant digits in the number 1.00460.
What are digits?In mathematics, digits are the single symbols used to represent numbers. For example, in the number 89, the digits 8 and 9 are both two digits. As a result, numerals such as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 are forms of digits that are used to represent a combination of numbers and perform arithmetic operations in our daily lives.We use ten digits to create all numerals. A numeral is a written number. These are the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.Therefore, there are 6 significant digits in the number 1.00460.
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During its year ending june 31, 2021, giant purchased, $3,551,723 of inventory for sale in its stores. how much did giant recognize/record as cost of goods sold for the year ended june 31, 2021?
Cash paid to the suppliers is 35,56,530$
Given here, The Amount of raw material purchased by company is 35,71,723$.
Firstly, we calculate decrease in Accounts payable = 115492$ - 110685$
= 4807$.
Now, cash paid to the suppliers is calculated by,
Cash paid to the suppliers= Purchases of raw material + Decrease in Account payable.
= 35,71,723$ + 4807$
= 35,56,530$
Thus, the cash paid to the suppliers is 35,56,530$.
The amount of Accounts Payable on a company's balance sheet is significant. If AP rises over the previous period, it indicates that the business is using credit rather than cash to purchase more goods and services. A company's accounts payable (AP) will decline if it is paying its commitments from the prior period more quickly than it is acquiring new things on credit.
Management of accounts payable is essential for controlling a company's cash flow. The top component of the cash flow statement, the cash flow from operational activities, shows the net change in AP from the prior period when the indirect method is used to create the cash flow statement.
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A recent report stated that less than 35 percent of adult residents in a certain city will be able to pass a physical fitness test. Consequently, the city's Recreation Department is trying to convince the City Council to fund more physical fitness programs. The council is facing budget constraints and is skeptical of the report. The council will fund more physical fitness programs only if the Recreation Department can provide convincing evidence that the report is true. The Recreation Department plans to collect data from a sample of 185 adult residents in the city. A test of significance will be conducted at a significance level of a= 0.05 for the following hypotheses.
H0:p=0.35
Ha:p<0.35
where p is the proportion of adult residents in the city who are able to pass the physical fitness test.
The Recreation Department recruits 185 residents who volunteer to take the physical fitness test. The test is passed by 77 of the 185 volunteers, indicating that more than 35 percent of the city is in shape. Describe the primary flaw in the study described in part and explain why it is a concern.
The primary flaw is that the sample will slightly overestimate the physical fitness of the people of the town.
The given hypothesis are,
[tex]H_0:p=0.35\\H_1:p < 0.35[/tex]
Type II error is accepted in null hypothesis when it is not actually true.
In the given question null hypothesis p= 0.35
The conclusion is that in the given sample proportion is not equal to 0.35, though we know that proportion is not equal to 0.35 we accept the null hypothesis, that is wrong.
Now given n=185,x=77 P=0.53 then Q=1-0.35=0.65
[tex]H_0:P=0.35\\H_1:P < 0.35[/tex]
Now test statistic [tex]Z=\frac{p-P}{\sqrt{\frac{PQ}{n}}}[/tex]
Solving for Z using the given values we get :
Z=1.99
Now 1.99>-1.65
So we accept [tex]H_0[/tex]
The primary flaw in the system is that the sample is not randomly selected rather they are volunteers. So it is reasonable to think that the physical fitness of the town will be slightly over estimated by the experiment.
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You are given the equation v = ir, if you compare this to y = mx b, what is the y intercept, b equal to?
The y-intercept is (0, C/B).
What is the y-intercept?A y-intercept or vertical intercept is a point in analytic geometry where the graph of a function or relation intersects the y-axis of the coordinate system, using the common conference that the horizontal axis represents a variable x and the vertical axis represents a variable y. As a result, these points satisfy the condition x = 0.Given:
v = iry = mxbThen,
Ax + By = C, where B ≠ 0By = - Ax + cy = - A/Bx + C/B ......(1)y = mx + bm = - A/B(0, C/B)Therefore, the y-intercept is (0, C/B).
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-5,5 postać ułamka zwykłego -4,8 postać ułamka zwykłego pomocy
Answer:
[tex]-5.5 = \frac{-11}{2}[/tex]
[tex]-4.8 = \frac{-24}{5}[/tex]
Step-by-step explanation:
Postać ułamka zwykłego oznacza postać [tex]\frac{licznik}{mianownik}[/tex].
Zaczynamy od zauważenia, że [tex]-5.5 = -55/10 = -\frac{55}{10} = -\frac{11}{2} = \frac{-11}{2}[/tex]
-4.8 robimy analogicznie, tylko skracamy przez 2 a nie przez 5.
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7-7+5x-5x+2+2x^2+2x
Combine like terms
Answer:
2x^2+2x+2
Step-by-step explanation:
7-7+5x-5x+2+2x^2+2x
ok first off i see 7-7, which is zero so we can leave that out
i also see 5x-5x which is also zero
now we have 2+2x^2+2x left, and to order it properly we put the number with the exponent and variable first, then the number with the variable, and then the number
so your final answer would be
2x^2+2x+2
i hope that helps! if you have any questions just ask!
the height of a frame is 2/3 times its width
The height of the frame is 1 m and the width is 1.5 meters.
The height and width are the two dimensions that are used to measure the perimeter of a rectangular frame.
The perimeter is defined as the sum of all sides of a polygon. For a rectangle it is equal to twice the sum of height and width.
Perimeter(p)=2×[height(h)+width(w)]
The given dimensions of the frame is that the height is [tex]\frac{2}{3}[/tex] the width.
Let us consider the width be x.
Hence height=[tex]\frac{2}{3} x[/tex]
Now perimeter =
[tex]2\times(x+\frac{2}{3}x) \\=\frac{10}{3} x[/tex]
But the given perimeter is 5 meter.
Therefore:
[tex]\frac{10}{3} x=5\\or,x=5\times 3\div 10\\or,x=1.5[/tex]
Therefore the width is 1.5 meters.
Height=[tex]\frac{2}{3} \times 1.5\\[/tex]=1 meter.
So we can conclude that the width is 1.5 meters and the height is 1 meter.
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PLEASE HELP (at least c)
A machinist is required to manufacture a circular metal disk with area 715cm squared
. Give your answers in exact form. Do not write them as decimal approximations.
a) What radius, x , produces such a disk?
b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius?
c) Using the ε / δ definition of a limit, determine each of the following values in this context:
f(x)=
a=
L=
ε=
δ=
The 715 cm² area of the disc and the ±5 cm² error tolerance, gives;
a) x = √(715/π) cm
b) The range for the radius is; [√(710/π) cm, √(720/π) cm]
c)
f(x) = π•x²
L = 715 cm²
E = 5 cm
d = √(5/π) cm
How can the variables in the [tex] \epsilon / \delta [/tex] definition of limits be found?Area of the circular metal disk = 715 cm²
a) Required; The disk radius
Let A represent the area of the disk and let x represent the radius, we have;
A = π•x²
Therefore;
x = √(A/π)
Which gives;
x = √(715/π) cm
b) Allowed area error tolerance = ± 5 cm²
The allowed range of values for the area is therefore;
710 ≤ A ≤ 720Which gives;
√(710/π) ≤ x ≤ √(720/π)
c) From the [tex] \epsilon / \delta [/tex] definition of limits, we have;
[tex] \lim\limits_{x → √(715/π)} f(x) = 715 [/tex]
Which gives;
f(x) = A = π•x²
L = 715
|f(x) - L| < E = 5 cm
|x - √(715/π)| < d = √(5/π)
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4. The
sum of a number z and 16.2 is at most 30.
z + 16.2 ≤ 30
z ≤ 13.8
How many posts does it take to support a straight fence 300 feet long if a post is placed every 25 feet?
12 posts are required to support a straight fence 300 feet long if a post is placed every 25 feet.
The given question can be solved using division. We are given that 25 feet is covered by 1 post. So, we will simply find the number of posts that will cover the 300 feet long fence. Now, calculating the number of posts as shown in steps below -
Number of post that covers 25 feet = 1
So, 300 feet will be covered by number of posts = (1÷25)×300
Performing multiplication and division to find the number of posts required to cover 300 feet long fence
Number of posts required to cover 300 feet long fence = 12 posts
Hence, 12 posts are required to cover 300 feet long fence.
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A 'variable' is defined as when a characteristic of interest differs in kind or degree among various observations. True or false
True ,A 'variable' is defined as when a characteristic of interest differs in kind or degree among various observations.
How do nominal and ordinal differ?
Nominal: The information is only classifiable. Ordinal: The information is classifiable and rankable. Interval: The data can be equally spaced, categorized, and rated. Ratio: The data is evenly spaced, categorizable, rankable, and has a natural zero.What in statistics is a ratio variable?
Multiplicity of ratio variables (statistics) a variable with interval characteristics as well as meaningful ratios between any two of its values, which makes multiplication and division operations comprehensible.
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|x+4|<9
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how do you calculate these numbers from least to greatest −2.0, 0.25, −1.02, 1.98.?
Answer: -2.0, -1.02, 0.25, 1.98
Step-by-step explanation:
Remember that negative numbers always go last. The bigger the negative number is, the smaller its quantity is. So -2.0 is less than -1.02. Then we have the positive numbers: 0.25, and 1.98. 0.25 is less than 1.98 because 1.98 has a whole number and 0.25 doesn't have a whole. Hope this helps :)
After a 20% increase, the new price of a radio is $78. what was the original price?
Answer:
$65
Step-by-step explanation:
The original price was x.
x was increased by 20%, so the new price is
x + 20% of x = x + 0.2x = 1.2x
The new price is 1.2x
The new price is $78
1.2x = 78
x = 78/1.2
x = 65
Answer: $65
2) How many distinguishable letter arrangements can be made from the letters in:
a) FLUKE?
b) PROPOSE?
Answer:
for "FLUKE" its 5! = 120
and "PROPOSE" its 7! /2!×2! = 1260
Step-by-step explanation:
"FLUKE" has no repeating letters.
"PROPOSE" has two repeating letters.
we divide by the repeating letters like I did on "PROPOSE" .
THANK YOU.
What’s the measure of QS?
A ) 6.2 mm
B) 9.5 mm
C)21.9 mm
D)22.4 mm
Please show work because I need to understand
Assume $x is deposited into a savings account. Blank Bank offers an annual rate of r% for y years. Thank Bank offers a rate of ry% for 1 year. Which earns more interest?
Blank bank as well as Thank bank earn equal interest.
In this question, Blank Bank offers an annual rate of r% for y years.
and Thank Bank offers a rate of ry% for 1 year.
Assuming $x is deposited into a savings account, we need to determine which bank earn more interest.
We know that, Interest = principal × rate × time
Now we convert the rates to decimals and to do that we divide by 100.
So, the annual rate of the Blank bank = 0.0r
And the annual rate of the Thank Bank = 0.0ry
Using above formula of interest,
For Blank bank, the interest would be,
I_B = x × 0.0r × y
I_B = xy(0.0r)
I_B = 0.0rxy ....................(1)
here, we find the interest for 'y' years
And for the Thank Bank, the interest would be,
I_T = x × 0.0ry × 1
I_T = I_B = 0.0rxy ....................(2)
From (1) and (2),
I_B = I_T
Both the banks earn equal interest.
Therefore, Blank bank as well as Thank bank earn equal interest.
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6/4 + 0.68
Jason solved this problem by changing 6/4 to 1.2. He then added 1.2 to 0.68 and got 1.88.
This answer is incorrect. What did he do wrong?
Multiple choices accepted
Group of answer choices
1.2 + 0.68 should have equaled 8.0
1.2 + 0.68 should have equaled 0.80
6/4 should have been changed to 1.5
6/4 should have been changed to 1.24
PLEASE ANSWER FASTTT IM TIMED
Answer
1.2 + 0.68 should have equaled 0.80
Step-by-step explanation:
jason solved this problem by changing 6/4 to 1.2. He then added 1.2 to 0.68 and got 1.88.
This answer is incorrect. What did he do wrong?
If Jason solved this problem by changing 6/4 to 1.2, The wrong thing he did is ; 6/4 should have been changed to 1.5. Option C is correct
How to solve the problemTo find the correct answer, let's first evaluate the expression step by step:
1. 6/4 is equal to 1.5, not 1.2.
2. 1.5 + 0.68 equals 2.18, this is not 1.88.
So, the correct answer is: Jason made a mistake in the first step. He changed 6/4 to 1.2, but it should have been 1.5.
Therefore, the correct calculation is 1.5 + 0.68 = 2.18.
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