Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.
Define exponents.A number written as a superscript over another number is known as an exponent. In other words, it means that the base has been elevated to a particular level of power. Other names for the exponent are index and power. mn indicates that m has been multiplied by itself n times if m is a positive number and n is its exponent.
Given,
Adding and subtracting to multiplying and dividing bases with different exponents.
Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.
The exponents and variables must match in order to add exponents. The exponents are left constant while the variable coefficients are added. The addition only includes terms with the same variables and powers. Exponents can be multiplied and divided according to this rule.
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Suppose Mack's wage was $7.00 an hour in 2001 and was $12.00 per hour in 2012. The CPI was 94 in 2001 and 201 in 2012. The 2001 wage in terms of 2012 dollars is
A) $14.97.
B) $14.07.
C) $3.48.
D) $13.16.
E) $7.00.
The wage of 2001 in terms of wage in 2012 is option A $14.97
Given,
Mack's wages in 2001 = $7 per hour
Mack's wages in 2012 = $12 per hour
The CPI in 2001 = 94
The CPI in 2012 = 201
We have to fins the wage of 2001 in terms of wage in 2012;
CPI;- Consumer Price Index
The CPI is calculated by the Bureau of Labor Statistics each month using a sample of 94,000 prices. To determine the overall change in prices, the index for each good or service is weighted according to its share of recent consumer spending.
Here,
The wage of 2001 in terms of wage in 2012 = (CPI in present year / CPI in past year) x Wage of earlier year
= (201 / 94) x 7
= 14.97
That is,
The wage of 2001 in terms of wage in 2012 is option A $14.97
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the following information will be used for parts 1 and 2 of this assignment. in 1978 congress established a gas guzzler tax to discourage the production and purchase of fuel-inefficient vehicles. every vehicle currently produced is labeled as a guzzler if its fuel efficiency in mpg is below a certain amount. trucks, suvs and minivans were uncommon in 1978 so are exempt from the tax. if interested, read more: https://www.epa.gov/fueleconomy/gas-guzzler-tax each vehicle in the data set epafe2021data.csv has a projected annual fuel cost that estimates how much the vehicle will cost over a year in fuel. for example, the volkswagen passat has an estimated annual fuel cost of $1450. use the epafe2021data.csv dataset and the comparingtwomeans da6.r script to compare the average annual fuel cost in dollars between guzzlers and non-guzzlers from 2021 vehicles. part 1. (6 points) exploring the data. a. (2 points) visualize the data with a side by side boxplot. i. (1 point) paste the side-by-side box plot of the data. ii. (1 point) add a title and axis labels. iii. optional to change the color of the plot. b. (2 points) describe the distribution in context. is there visual evidence the average annual fuel cost is different between the guzzler and non-guzzler vehicles? explain. c. (2 points) provide an organized table of the summary statistics. include the sample means, standard deviations and sample sizes for each group. round to nearest whole number. mean standard deviation sample size guzzler non-guzzler
This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.
A) 1: proportion of gas-guzzlers manufactured by American firms.
p2: proportion of gas-guzzlers manufactured by international firms.
In this way, the boundary of interest is p1 - p2.
B) H_0: p_1-p_2=0
H_1: p_1-p_2\neq0
C) The following requirements must be satisfied: n (1 p) 10 and np 10.
American Guzzlers do not meet this requirement because np = 7.
D) If H0 is true, the test statistics are as follows: frac(hat p_1-hat p_2)-(p_1-p_2)surfactant p_1(1-hat p_1)n_1+frachat p_2(1-hat p_2)n_2sim N(0,1)
E) The p-value is calculated by multiplying p-value by P(z-3.75) = 0.
F) The 95% confidence interval is calculated as follows: p_1-p_2=hat p_1-hat p_2pm z_0.975sqrtfrachat p_1(1-hat p_1) n_1+frachat p_2(1-hat p_2) n_2 -0.0859 p_1-p_2 -0.0269
g. H0 should be rejected because the p-value is less than the 0.05 significance level.
There is enough evidence for us to reject H0. There is sufficient evidence to draw the conclusion that the proportion of Guzzlers in 2017 automobile models produced by American and international automakers differs.
Additionally, the 95% CI does not contain zero, does it?This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.
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A cruise ship can cover 21 nautical miles in 378 minutes. How many nautical miles will it travel in 108 minutes?
A. 4
B. 8
C. 10
D. 6
Answer: D/ 6.
Step-by-step explanation: First, you have to do division to find out how many minutes = 1 nautical mile.
378 divided by 21= 18.
Then, you would do 108 divided by 18, to find out the answer; 6.
To double check your work, get the answer you got and multiply it by the minutes per mile which is 18.
18 x 6 = 108.
Therefore, it will be 6 nautical miles in 108 minutes.
Without using a calculator, order the following numbers from least to greatest.
Answer:
√78,9,10
Step-by-step explanation:
we know [tex]9^{2}[/tex] is 81
so √78 is less than √81(9) and 10 is obviously more than 9
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The large number of two numbers is nine less than four times the smaller number. If the sum of the two numbers is 76, find both numbers.
Answer: the larger number is 59 and the smaller number is 17.
Step-by-step explanation:
(The lines are parallel)
What is the value of x?
Answer:
x = 14 y = 37
Step-by-step explanation:
180 - (9x + 12) = 3x
180 - 9x - 12 = 3x
168 = 12x
x = 14
4y - 10 + 3(14) = 180
4y - 10 + 42 = 180
4y + 32 = 180
4y = 148
y = 37
Given f(x) = 4x+2 find f(x+3) find terms of x
The function f(x+3) in terms of x is 4x+14.
It is given that -
f(x) = 4x + 2
We have to find out f(x+3) in terms of x.
Now, f(x) = 4x + 2
=> f(x+3) = 4(x+3) + 2 [Substituting (x+3) in place of x]
=> f(x+3) = 4x + 12 + 2
=> f(x+3) = 4x + 14
Thus, the function f(x+3) in terms of x is 4x+14.
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A scientist uses a submarine to study ocean life. • She begins at sea level, which is an elevation of o feet. • She travels straight down for 36 seconds at a speed of 2.9 feet per second. • She then ascends for 24 seconds at a speed of 1.8 feet per second. At this point, what is her elevation, in feet?
Answer:
61.2
Step-by-step explanation:
(36x2.9)-(24x1.8)
how many solutions does 12 + 2x - x = 9x + 6 have?? giving brain and max points
Step-by-step explanation:
Enter a problem...
Pre-Algebra Examples
Popular Problems Pre-Algebra Solve for x 12+2x-x=9x+6
12
+2
x−x=
9x
+6Subtract
x from
2x
12+x
=9x+6
Move all terms containing
x
to the left side of the equation.
Tap for more steps...
12−8x=6
to the right side of the equation.
-8x=−6
Divide each term in
−8x=−6 by −8
and simplify.
The result can be shown in multiple forms.
Exact Form:
x=3/4
Decimal Form:0.75
O LINEAR EQUATIONS
Word problem involving a conversion between U.S. Customary.....
2/5
Jenny is uering 3 bags of cat food from Canada. Each bag has a mass of 5 kg. To determine the shipping costs, Jenny needs to know the total weight in
pounds. What is the weight of the cat food in pounds?
Use 1 kg = 2.2 lb and do not round any computations.
Chloe
Español
Unit conversion is the conversion of one unit to another unit with its standard conversion.
1 kg = 2.2 lb
The weight of the cat food in pounds is 33 lb.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 1000 m
We have,
Number of bags of cat food = 3
Weight of each bag = 5 kg
1 kg = 2.2 lb ______(1)
Weight of 3 bag = 3 x 5 = 15 kg _______(2)
From (1) and (2) we get,
1 kg = 2.2 lb
Multiplying 15 on both sides.
15 x 1 kg = 15 x 2.2 lb
15 kg = 33 lb
Thus,
The weight of the cat food in pounds is 33 lb.
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The weight of meteorite A is 9 times the weight of meteorite B. If the sum of their weights is 230 tons, find the weight of each.
The weight of meteorite A is 207 tons and meteorite B is 23 tons.
How to calculate the value?Let the weight of B = w
Let the weight of A = 9 × w = 9w
Since the weight of meteorite A is 9 times the weight of meteorite B. If the sum of their weights is 230 tons. This will be illustrated as:
9w + w = 230
10w = 230
Divide
w = 230/10
w = 23
meteorite B = 23 tons
meteorite A will be:
= 9w
= 9 × 23
= 207 tons
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22. Which of the following equations is
NOT true?
A
B
225 X 4 = 9,000
225 X 0.04 = 9
22.5 X 4 = 90
D 225 X 0.4 = 90
OMG PLS HELP I SWEAR ITS NOT THAT HARD please yall?
Proving angles are congruent; write a two column proof
Using the Side Angle Side Theorem, ∆KWL ≅ ∆ALW.
In the given question we have to
Prove: ∆KWL ≅ ∆ALW
Given: ∠KWL ≅ ∠WLK, ∠AWL ≅ ∠WLK
As given that
∠KWL ≅ ∠WLK
∠AWL ≅ ∠WLK
WL = WL (Diagonal)
Equal Parallel Sides
WK = AL
WA = KL
From Corresponding Angle Theorem
∠KWL=∠WLK and ∠AWL = ∠WLK
So ∠W=∠L
So from the Side Angle Side(SAS) Theorem
∆KWL ≅ ∆ALW.
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Your cost to produce is $30 and you need to make a markup of 30% on an upcoming bid. A competitor placed a bid for $37. Will you be able to outbid your competitor?.
No, It will not be able to outbid your competitor if your cost to produce is $30 and you need to make a markup of 30% on an upcoming bid. A competitor placed a bid for $37.
Define cost.A cost is the worth of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost. Any system for allocating expenses to a business component is known as costing. Costing is frequently used to establish expenses for customers, distribution channels, personnel, regions, goods, product lines, processes, subsidiaries, and whole businesses.
Given,
Your cost to produce is $30 and you need to make a markup of 30% on an upcoming bid. A competitor placed a bid for $37.
No, It will not be able to outbid your competitor.
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After changing the smaller exponent (-3) to the larger exponent (-1), what does its coefficient change to?
(6.2 x 10-1) + (2.3 x 10-3)
A) .23
B) 230
C) 23
D) .023
After changing the smaller exponent (-3) to the larger exponent (-1), its coefficient change to?l A. 0.23.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
From the information, it should be noted that the value was illustrated as:
= 2.3 × 10^-1
= 2.3 × 0.1
= 0.23
Therefore, the correct option is A.
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An electric guitar costs $830, with a $225 full-replacement warranty. If the manufacturer sells 532,475 warranties and has to honor 12% of them, how much profit did the manufacturer gain from the warranties? a. $105,430,050 b. $66,772,365 c. $53,034,510 d. $508,726,615 please select the best answer from the choices provided a b c d.
A guitar manufacturer sells 532,475 warranties and has to honor 12% of them. The profit the manufacturer gains from the warranties is $66,772,365 (option b)
Profit is calculated as:
Profit = revenues - total cost
While,
Revenues = number of goods sold x price per unit
In the given problem,
Revenues = number of warranty sold x price per warranty
= 532,475 x 225
= 119,806,875
Cost of honored warranty = number of honored warranty x guitar cost
= 12% x 532,475 x 830
= 53,034,510
Hence,
profit from warranty = 119,806,875 - 53,034,510
= 66,772,365
The profit from warranty is $66,772,365 (option b)
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Answer:
its b
Step-by-step explanation:
Which expressions are equivalent to 3^4 * 3^x select all that apply
A. 3^(4+x)
B. 3^(4x)
C. 81 * 3^x
D. 3^(4-x)
E. 9^4x
F. (3*x)^4
Expression which are equivalent to the given expression 3⁴ × 3ˣ are as follow: (3⁴⁺ˣ ) and 81 × 3ˣ.
As given in the question,
Given expression is equal to :
3⁴ × 3ˣ
Using law of indices for multiplication we have ,
mᵃ × mᵇ = mᵃ⁺ᵇ
Here in the given expression m = 3 , a= 4 and b = x
Equivalent expression for the given expression is given by,
3⁴ × 3ˣ
= (3⁴⁺ˣ )
Also,
Now simplify the given expression we get,
3⁴ × 3ˣ
= ( 3 × 3 × 3 × 3) × 3ˣ
= 81 × 3ˣ
Therefore, expression which are equivalent to the given expression 3⁴ × 3ˣ are as follow: (3⁴⁺ˣ ) and 81 × 3ˣ.
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a small dataset contains 5 numbers: 21, 32, x, 99, 40 (where x is unknown). if the average is known to be 50, what is the median?
The median of the given data set is, 40.
What is median?
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.
Let, a data set contains 5 numbers: 21, 32, x, 99, 40.
x is the unknown number.
The average is to be 50.
Since,
Average = Sum of numbers / total numbers
50 = (21 + 32 + x + 99 + 40) / 5
50 x 5 = 192 + x
250 = 192 + x
x = 250 - 192
x = 58
Hence, the unknown number is 58.
Now to find the median,
Since median is the middle number of a data set.
So, write the numbers in ascending order.
21, 32, 40, 58, 99.
In this data set the middle number is, 40.
Therefore, the median is 40.
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can someone help please!
Answer:
Step-by-step explanation:
what is 3/36 times 60
Answer:
5
Step-by-step explanation:
to multiply fractions we multiply numerator with numerator and denominator with denominator
[tex]\frac{3}{36}x\frac{60}{1}[/tex]
[tex]\frac{3x60}{36x1}[/tex]
[tex]\frac{180}{36}[/tex]
5
Hopes this helps please mark brainliest
is y = x/2 + 6 a linear or nonlinear function
is 0 a solution to 2x +0 =4x+10 explain how
Answer:
No, x=-5 is the answer
Step-by-step explanation:
Did this before, trust me
what is the product of 6 x 2/3
Answer: 4
Step-by-step explanation:
6 * 2/3 First simplify the expression.
Then you would get 2 * 2/1 = 2*2
The answer is 4
what’s the correct answer,
the last one says “apply the distributive property” please help. marking brainliest
Answer:
Subtract 6 from both sides
Step-by-step explanation:
how to use the clausius clapeyron equation to answer the following questions. derive the relationship of pressure and temperature for a system consists of vapor and condensed
The relationship between pressure and temperature for a consisting of vapour and condensed phases is [tex]l_{n}(p_{2}/p_{1}) = [ 1/T_{1}-1/T_{2}][(h_{g}-h_{f})/R][/tex].
The Clausius-Clapeyron equation is a differential equation which specifies the temperature dependence of pressure and vapour pressure. The Clausis-Clapeyron equation is named after Rudolf Clausius and Benoit Paul Emile Clapeyron.
The Clausius-Clapeyron equation at saturation temperature and pressure is
[tex]dP/dT[/tex]= [tex]h_{g} - h_{f}/T(v_{g}-v_{f} )[/tex] → 1
Assuming that [tex]v_{g} > > > v_{f}[/tex] , we write
[tex]v _{g}[/tex] = RT/P → 2 ( for both liquid and solid phases)
⇒ dP/dT = P([tex]h_{g} - h_{f}[/tex])/R[tex]T^{2}[/tex]
⇒ dP/P = dT/[tex]T^{2}[/tex]([tex]h_{g} - h_{f}[/tex]/R) → 2
By integrating 2 , we get
[tex]l_{n}(p_{2}/p_{1}) = [ 1/T_{1}-1/T_{2}][(h_{g}-h_{f})/R][/tex] → 3
Therefore, the equation to represent the relationship between pressure and temperature for a system consisting of vapour and condensed phases is equation 3 i.e. [tex]l_{n}(p_{2}/p_{1}) = [ 1/T_{1}-1/T_{2}][(h_{g}-h_{f})/R][/tex]
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Evaluate c−a+bd if a=7/8 , b=−7/16 , c=0.8 , and d=1/4
Answer
-117/640
Step-by-step explanation:
ba + cd
b= -7/16
a= 7/8
c= 08.(4/5)
d= 1/4
Hence it can be calculated as follows
-7/16×7/8 + 4/5×1/4
-49/128 + 1/5
-246+128/640
= -117/640
Find the sum of 102 + (-97) + 3 =
Answer:
8
Step-by-step explanation:
You can solve this a few different ways.
Firstly I did 102 - 97 = 5
Then I took 5 and added 3 to it
5 + 3 ---> which gets us 8 as our final answer.
Hope I helped!
Have a great day!
How does "If the measure of an angle is not 180, then it is not a straight angle" relate to the conditional statement "If an angle is a straight angle, then its measure is 180."
Counterexample
Converse
Inverse
Contrapositive
Given statement " If the measure of an angle is not 180, then it is not a straight angle" when related to conditional statement "If an angle is a straight angle, then its measure is 180." then it represents the example of contrapositive.
As given in the question,
Given statement is equal to:
" If the measure of an angle is not 180, then it is not a straight angle"
And its conditional statement is given by:
"If an angle is a straight angle, then its measure is 180."
Explanation of the given options:
a. Counterexample : Concluding statement is against the given statement .
Here it is false.
b. Converse: If it is not a straight angle then the measure of an angle is not 180.
Here it is false.
c. Inverse : If the measure of an angle is 180, then it is a straight angle.
False.
d. Contrapositive : "If an angle is a straight angle, then its measure is 180."
Here it is true.
Therefore, for the given statement " If the measure of an angle is not 180, then it is not a straight angle" when related to conditional statement "If an angle is a straight angle, then its measure is 180." then it represents the example of contrapositive.
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Balance each of the following equations
Answer:
[tex]2Sb+3I_2=2SbI_3[/tex]
[tex]P_4+3O_2=2P_2O_3[/tex]
[tex]2SO_3=2S+3O_2[/tex]
[tex]2Fe_2O_3+3C=4Fe+3CO_2[/tex]
[tex]CH_4+2O_2=CO_2+2H_2O[/tex]
Step-by-step explanation:
Each side of the equations need to have the same number of each element.
Equation 1
Since there are 2 I on one side of equation 1, and 3 on the other side, I will do the following:
[tex]Sb+3I_2=2SbI_3[/tex]
Now the number of Sb is unbalanced, so I balance it like so:
[tex]2Sb+3I_2=2SbI_3[/tex]
Equation 2
Using the same strategy, I focus on one element at a time. I can balance the P like this:
[tex]P_4+O_2=2P_2O_3[/tex]
Now, I can balance the O. There are 6 on the right, so if I put 3 on the left, there will be 6 there as well!
[tex]P_4+3O_2=2P_2O_3[/tex]
Equation 3
Starting with O this time, I put 2 on the left and 3 on the right to bring them both to 6.
[tex]2SO_3=S+3O_2[/tex]
Now there are 2S on the left and only 1 on the right, so I balance it:
[tex]2SO_3=2S+3O_2[/tex]
Equation 4
Starting with O again, there are 3 on the left and 2 on the right.
[tex]2Fe_2O_3+C=Fe+3CO_2[/tex]
Now, the Fe are unbalanced as well. There are 4 on the left and 1 on the right:
[tex]2Fe_2O_3+C=4Fe+3CO_2[/tex]
Finally, balance the C, there is 1 on the left and 3 on the right.
[tex]2Fe_2O_3+3C=4Fe+3CO_2[/tex]
Equation 5
This one is pretty hard to read, so I will assume that the equation looks like this (please comment if this is incorrect)
[tex]CH_4+O_2=CO_2+H_2O[/tex]
Let's balance the H first:
[tex]CH_4+O_2=CO_2+2H_2O[/tex]
Now the O. There are 2 on the left and 4 on the right.
[tex]CH_4+2O_2=CO_2+2H_2O[/tex]
Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is
2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches. What
expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3:5?
The expression and the length of ribbon that she needs for both pillows is [tex]4(2x^{2} +4x-6)[/tex] , 130 inches .
Given:
The side length of the pillow is 2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches.
The length of ribbon :
= 4([tex]2x^{2} +1[/tex]) + 4(4x - 7)
= 4(2[tex]x^{2} +1[/tex]+4x - 7)
= 4([tex]2x^{2} +4x-6[/tex])
The length at x = 3.5 is,
= 4(2([tex]3.5^{2}[/tex])+4(3.5) - 6)
= 4(24.5+14-6)
= 4(24.5+8)
= 130 inches.
Therefore the expression and the length of ribbon that she needs for both pillows is [tex]4(2x^{2} +4x-6)[/tex] , 130 inches .
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Answer:
Step-by-step explanation:2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches. What
expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3:5?