Pablo simplified the expression(2^-4)^-2 as shown.
(2^-4)^-2=2^-4*^-2=2^-8
Which statement explains Pablo’s error?
A. He should have added the exponents instead of multiplying them.
B. He should have divided the exponents instead of multiplying them.
C. He should have found 8 as the exponent, not –8.
D. He should have written mc014-3.jpg as mc014-4.jpg.
Answer:
C. He should have found 8 as the exponent, not –8.
Step-by-step explanation:
We have been given an expression [tex](2^{-4})^{-2}[/tex]. We are asked to find the Pablo's error in simplifying the expression.
Let us check steps done by Pablo.
In first step Pablo has simplified [tex](2^{-4})^{-2}[/tex] to [tex](2)^{(-2*-4)}[/tex] using power rule property of exponents which states that to raise a power to a power we have to multiply the exponents. Therefore, his first step is correct.
Now let us check Pablo's second step. We can see that Pablo multiplied -2 by -4 and simplified to [tex]2^{-8}[/tex].
Since we know that multiplying a negative number with another negative number gives a positive result, therefore, Pablo made mistake in second step. He should have found 8 instead of -8 as the exponent.
The correct steps for simplifying the given expression will be [tex](2^{-4})^{-2}=2^{(-2*-4)}=2^{8}[/tex].
Upon looking at our given option we can see that option C is the correct statement about Pablo's error.
Which rule represents R0, 180
Answer:
[tex](x, y) \rightarrow (-x, -y)[/tex]
Step-by-step explanation:
Rotation of any point in the form of (x, y) about the origin O through 180 degree in anticlockwise or counterclockwise direction, it will takes the new position (-x, -y)
i.e,
The rule of rotation about the origin through 180 degree is given by:
[tex](x, y) \rightarrow (-x, -y)[/tex]
For example:
Let the point A(-4, 6) rotate by the rule [tex]R_{0, 180^{\circ}}[/tex]
then;
[tex]A(-4, 6) \rightarrow (4, -6)[/tex]
⇒the coordinate of image of the point A is, (4, -6)
Therefore, the rule represents [tex]R_{0, 180^{\circ}}[/tex] is, [tex](x, y) \rightarrow (-x, -y)[/tex]
Answer:
B
Step-by-step explanation:
Determined whether the graphs of each pair of equations are parallel, perpendicular or neither
Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50a + 3.75b = 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?
adult tickets
Answer: There are 168 adult tickets that were sold.
Step-by-step explanation:
Let the number of adult tickets were sold be 'a'.
Let the number of student tickets were sold be 'b'.
Since we have given that
The ticket sales for opening night totaled as
[tex]10.50a+3.75b=2071.50[/tex]
And the number of students attended = 82
so, b = 82
So, we will put the value of b in the above equation:
[tex]10.50a+3.75\times 82=2071.50\\\\10.50a+307.5=2071.50\\\\0.50a=2071.50-307.5\\\\10.50a=1764\\\\a=\dfrac{1764}{10.50}\\\\a=168[/tex]
Hence, there are 168 adult tickets that were sold.
What is another name for like r.
A restaurant earns $1240 on Friday and $921 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day
Answer:
The restaurant needs to earn $839 on Sunday.
Step-by-step explanation:
Consider the provided information.
Let $x needs to earn on Sunday, to average $1000 per day .
It is given that the average earn should be $1000
[tex]Average=\frac{\text{Sum of observations}}{\text{Total number of observation}}[/tex]
[tex]Average= \frac{1240+921+x}{3}[/tex]
[tex]Average= \frac{2161+x}{3}[/tex]
The average should be $1000, so substitute 1000 for average and solve for x.
[tex]\frac{2161+x}{3} =1000\\\\ 2161+x=3000\\\\x=3000-2161\\\\x=839[/tex]
Thus, the restaurant needs to earn $839 on Sunday.
The required equation is [tex]\frac{1240+921+x}{3}=1000[/tex].
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph, how long will the express train take to overtake the freight train?
Which equation could be used to find the number of miles the trains will travel?
A. 30x = 55(x + 300)
B. x÷30 = (x - 300)÷55
C. x÷30 = (x + 300)÷55
Answer:
The answer is C. x÷30 = (x + 300)÷55
Step-by-step explanation:
The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph.
The equation will be
Total speed = Total distance / time taken
x ÷ 30 = (x + 300) ÷ 55
The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.
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Help me plz? I have no clue how
Select the graph that best represents the solution set for 5x+1≤11
The difference between Alan's and Bea's age is three years. The sum of their ages is twenty-seven years. How old are they if-
A. Alan is older than bea?
B. Bea is older than Alan?
A map is drawn to scale such that 1/8 inch represents 65 feet. if the shortest route from the dorm to the grocery store measures 23 ¼ inches on the map, how many miles is it to the grocery store? round to the nearest tenth.
Geometry- You are designing a poster that will be 3yd wide and 8ft high. How much paper do you need to make the poster? Give your answer in square feet. My answer was 72ft^2, but the textbook says 74ft^2. Can someone please check to see if my answer is correct and the textbook is wrong.
The sum of the page numbers on the facing pages of a book is 629. what are the page numbers
The number of pages of the book is 315.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the sum of the page numbers on the facing pages of a book is 629.
Basically, these numbers have to be consecutive because they're facing pages.
To calculate the number of the pages divide this by 2, and then add one to the second number.
N = 629/2 = 314
Therefore, the number of pages of the book is 315.
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evaluate a/z+bw^2 for a=21 b=3 w=6 z=7
Matching 1. protects against loss from automobile accidents of insured malpractice 2. protects against loss to insured's home and furnishings automobile 3. protects against loss from fire on insured's property liability 4. protects against loss from injury to others on insured's property fire 5. protects against loss from lawsuits against insured life 6. protects against loss from death of insured homeowners
1. protects against loss from automobile accidents of insured - Automobile insurance.
2. protects against loss to insured's home and furnishings - Homeowners insurance
3. protects against loss from fire on insured's property - Fire insurance
4. protects against loss from injury to others on insured's property - Liability insurance
5. protects against loss from lawsuits against insured - Malpractice insurance
6. protects against loss from death of insured - Life insurance
The next train will arrive in 32 minutes and 30 seconds.
In how many seconds will the next train arrive?
____Seconds
You can convert time from minutes to seconds by multiplying the number of minutes by 60. Therefore, if the train is due in 32 minutes and 30 seconds, the train will arrive in 1950 seconds.
Explanation:To answer your question, we need to understand that 1 minute is equal to 60 seconds.
So, if the train arrives in 32 minutes, then it will arrive in 32 minutes * 60 seconds per minute, which equal 1920 seconds. And we have additional 30 seconds. So, the total time the train will arrive in is 1920 + 30 = 1950 seconds.
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Look at the following expression, then factor the sum of terms as a product of the GCF and a sum. 4x + 12 = 4(____ + 3) What term is missing from the solution
The test scores of a geometry class are given below. 90, 75, 72, 88, 85 The teacher wants to find the variance for the class population. What is the value of the numerator of the calculation of the variance?
The value of the numerator of the calculation of the variance= 258
and Variance= 51.6
Step-by-step explanation:We know that in order to calculate the variance we need to follow following steps:
First calculate mean.Then subtract each of the data points from means and square the difference quantity.Lastly calculate the mean of these squared quantity.The data points are:
90, 75, 72, 88, 85
The mean of these data points are:
[tex]Mean=\dfrac{90+75+72+88+85}{5}\\\\\\Mean=\dfrac{410}{5}\\\\\\Mean=82[/tex]
Now on finding the difference terms i.e.
90-82=8
75-82= -7
72-82= -10
88-82=6
and 85-82=3
The square of these difference term is:
8²=64
(-7)²=49
(-10)²=100
6²=36
and 3²=9
Hence, the mean of these squared quantity i.e. Variance is:
[tex]Variance=\dfrac{64+49+100+36+9}{5}\\\\\\Variance=\dfrac{258}{5}\\\\\\Variance=51.6[/tex]
I REALLY NEED THIS ONE IT'S MY LAST ONE.
Verify the identity. Justify each step.
please help and show your work.
Out of 32 students in the class 5 said they rode their bikes to school based on their results how many of the 800 students in the school rode their bikes toschool
What is the algebraic expression for the following word phrase: the quotient of j and 8
A.j-8
B.j+8
C.j
-
8
D.8j
[tex] \frac{j}{8} [/tex]
This is the correct algebraic expression for the quotient of j and 8. Quotient is just a fancy term for the answer to a division problem.
Answer:
[tex]\frac{j}{8}[/tex]
Step-by-step explanation:
the quotient of j and 8
We need to write the given word phrase in algebraic expression
Algebraic expression contains terms with numbers and variables with operators in between.
In the given word phrase , 'j' is the variable
quotient occurs only on division . so we divide 'j' and 8
The expression for word phrase the quotient of j and 8 is
[tex]\frac{j}{8}[/tex]
Martin is logging the number of strikes he bowls per hour. He has determined the function to be f(x) = 2x + 5, where x represents hours and f(x) represents the number of strikes he has bowled. Which of the following options describes the restrictions to the domain and range correctly?
Domain, nonnegative values; range, values greater than −2.5
Domain, nonnegative values; range, values greater than or equal to 5
Domain, nonnegative values; range, values less than −2.5
Domain, nonnegative values; range, values less than or equal to 5
Answer:
B. Domain, nonnegative values; range, values greater than or equal to 5
Step-by-step explanation:
Basically, domain is the set of values that x can take and range is the set of values that the result of f(x) can be.
Since x is the time Martin spends bowling, it cannot be negative. The least he can bowl is zero hours, so x cannot be a negative number.
For the lowest x can be (zero), f(x) is calculated as:
f(x) = 2(0)+5 = 0+5 = 5
For higher values of x, the equation can only yield higher results because the 2 that is multiplying it is positive. Multiplying a two positive numbers (2 and x, which cannot be negative) will always give a positive number. In other words, f(x) is directly proportional to x because its coefficient 2 is positive, which means that when x grows, f(x) grows.
This means that f(x) can never be lower than 5.
The best description is, then, nonnegative values for the domain and values greater or equal to 5 for the range.
What is the period of the function y=5/2 cos x/4?
If the interest rate on a savings account is 0.018%, approximately how much money do you need to keep in this account for 1 year to earn enough interest to cover a single $9.99 Below-Minimum-Balance Fee?
$55,555
$55
$555
$5,555
Leon correctly found the slope and y-intercept of the line that passes through the points (9, –8) and (3, 4) as follows.
m = -8, -4 = -12
9-3 -6 =-2
y = -2x+b
-8=-2(9)+b
-8= -18+b
10=b
a)y=-2x+10
B) y=-2x+10
C) y= 10x-2
D)y=10x +2
Answer:
[tex]\displaystyle y = -2x + 10[/tex]
Step-by-step explanation:
The work is already done. This is EXACTLY how you find the parallel line, however, two answer choices are an EXACT REPLICA of each other. Perhaps there was a typographical error?
I am joyous to assist you anytime.
the correct answer is option
a)y=-2x+10.
How do you locate the slope?pick factors on the line and decide their coordinates. determine the difference in y-coordinates of these two factors (upward thrust). determine the difference in x-coordinates for those two factors (run). Divide the difference in y-coordinates by means of the difference in x-coordinates (upward thrust/run or slope).
How do u find slope-intercept shape?resolve for the slope (m). recollect, the slope is equal to the alternate in y divided with the aid of the change in x (upward push overrun).remedy for the y-fee of the y-intercept (b). replace m and b with their values inside the y=mx+b system.Learn more about slope-intercept shape here: https://brainly.com/question/1884491
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Solve algebraically for x
Please help with both questions thank you.
What is the measure of 1 (1 point) 45 60 120 125?
Answer:
120°
i finished the quiz and that what i got
and for the rest
1.b
2.d
3.a
4.c
and number 5 is the first answer that i wrote
Step-by-step explanation:
I have a 20 question geometry diagnostic due at 1 pm
What is the abbreviation for SI unit of mass