Answer:
1/24
Step-by-step explanation:
[tex]a^{-1} =\frac{1}{a} \\24^{-1} =\frac{1}{24}[/tex]
A negative exponent is converted to a fraction while the power goes to the base which is at the denominator.
The graph shows the absolute value parent function. 5 5. -5. Which statement is true? 5 A. (0, 1) is the x- and y-intercept of the function. B. (1, 1) is the x- and y-intercept of the function. C. (0,0) is the x- and y-intercept of the function. k
The function of the absolute value is always positive the correct answer would be option (B).
What is a graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
What is absolute value?
Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.
For example, |5| is 5 because it is 5 units away from 0. Also, |-5| is also 5 because -5 is 5 units from 0.
We have to determine the statement best describes the function.
We have been given that the graph represents the absolute value parent function.
Since the parent function's graph with an absolute value that is always positive.
Therefore, the graph of the absolute value parent function would be always positive.
Hence, the correct answer would be option (B)
pls help help pls this is due today i would appraciate help
Which fraction is closest to zero?
Answer:
8/12=0.667
5/8=0.625
6/10=0.6
2/3=0.667
Step-by-step explanation:
6/10 would be your answer being that it is the smallest of them all
Gabriel misses 2% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 36?
The number of free throws that Gabriel attempted if he missed 36, can be found to be 1, 800 free throws.
How to find the number of free throws?If Gabriel misses 2% of the free throws he attempts in a season, the forumula to find the percentage of free throws missed is:
Free throws missed / Total free throws attempted = 2%
We can then make the free throws missed the subject of the formula:
36 / Total free throws attempted = 0.02
Total free throws attempted = 36 / 0.02
Total free throws attempted = 1, 800
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Please check image for questions!
2)Slope intercept form: y = -2x + 5
Point slope form: y - 5 = -2(x - 4)
Standard form: 2x + y = 13
3)Slope-Intercept Form: y = -2x + 10
Point-Slope Form: y - 6 = -2(x - 4)
Standard Form: -2x + y - 10 = 0
Define Slope interceptThe Slope-Intercept Form is a linear equation written in the form:
y = mx + b
where m is the slope and b is the y-intercept.
Define Point-Slope FormPoint-Slope Form is a linear equation written in the form:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Define Standard FormStandard Form is a linear equation written in the form:
Ax + By = C
where A, B and C are constants.
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Adam sovled 12 math problems in 42 minutes. If he continues at this pace how many minutes will it take him to solve 20 math problems
The number of minutes it will take Adam to solve 20 math problems is 70 minutes.
How to solve ratio problems?Number of math problems Adam solve in 42 minutes = 12
Number of minutes it will take Adam to solve 20 math problem = x
Number of math problem : Time taken
12 : 42 = 20 : x
12/42 = 20/x
12 × x = 20 × 42
12x = 840
divide both sides by 12
x = 840/12
x = 70 minutes
Hence, it will take Adam 70 minutes to solve 20 math problems.
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Write an expression with a value of 12. It
should contain four numbers and two different operations.
The expression having value 12 and contain four numbers and two different arithmetic operations is 2*2+4+4=12.
What are arithmetic operations and its types?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.
The four basic arithmetic operations in Maths, for all real numbers, are:
Addition (Finding the Sum; ‘+’)
Subtraction (Finding the difference; ‘-’)
Multiplication (Finding the product; ‘×’ )
Division (Finding the quotient; ‘÷’)
Now
as we solve given expression by applying arithmetic operations
=2*2+4+4
=4+8
=12
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Write the equation of the line, in slope-intercept form, with the
following information:
Slope: -1/5
Point (10,2)
The linear equation of the line is slope =-1/5 and point is 10,2
How to determine the line equation?The slope is given as:
m = -1/5
The point is given as:
10,2
A linear equation in slope intercept form is represented as:
y = m + p
So, we have:
y is intercept
mx is slope
p is point
y = -1/5x - 10
Add 10 to both sides
y + 10 = -1/5x
Express -1/5x as -1/5(x)
y + 10 = -1/5(x)
Subtract 0 from x
y + 10 = -1/5(x - 0)
Hence, the linear equation of the line is y = -1/5x - 10 and y + 10 = -1/5(x - 0)
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Cameron has a credit limit on his gasoline company credit card of $500. He has no initial balance, but has charged gasoline purchases of $25,25 and $32,33. What is Cameron’s remaining available credit?
Answer:
$442.42
Step-by-step explanation:
You want the remaining available credit on a credit line of $500 when charges of $25.25 and $32.33 have been made.
Remaining creditThe remaining credit is the original credit amount less the amount of credit used:
$500 -25.25 -32.33 = $442.42
Cameron has credit of $442.42 available.
Please help me solve this problem
Answer: 20 people
Step-by-step explanation:
If each car has 2 benches and 2 people fit on each bench, you have to multiply 2 x 2 which equals 4. Then you have to multiply the number of how many people fit on each car by the number of cars. ( 4 x 5 = 20 ) Hence the answer is 20 people.
Answer:
20 people
Step-by-step explanation:
2 benches × 5 cars = 10 benches
10 benches with 2 people on each of them (10×2)
=20
Which statement is sometimes false?
J
K
The sum of a negative and a positive
number is a negative number.
The product of a negative and
a positive number is a negative
number.
L The quotient of a negative and
a positive number is a negative
number.
M
N
The sum of any two negative
numbers is a negative number.
The quotient of any two negative
numbers is a positive number.
The statement " The sum of a negative and a positive number is a negative number " is false sometimes.
What is an integer?
A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8
The statement " The sum of a negative and a positive number is a negative number " is false sometimes.
When positive number is bigger than the smaller one, sum can be positive
Example:
-4+3 = -1 ( statement is true, 3 is smaller )
but,
-4 + 6 = 2 ( statement is false, 6 is bigger)
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What time should the fifth hand watch show? 1:22 A. 4:13 B. 4:25 C. 4:30 D. 4:45 2:09 2:56 3:43
The time on the first watch reads 2:31, followed by 3:13, 3:55, and 4:37 on the following watches.
What time should the watch's fifth hand display?The time on the first watch reads 2:31, followed by 3:13, 3:55, and 4:37 on the following watches.
Adding 42 minutes to the prior watch, which is currently showing the time 4:37, results in the final time reading of 5:19.
When x minutes have passed, let the clock hands align.
Clock hands align at 21.81 minutes after four.
Option B, 21.81 minutes, is the proper response, therefore.
They need to be 30 minutes apart for them to be moving in the opposing directions.
Minute hand will need to add 50 minute gaps as a result.
It takes 60 minutes to fill 55 minute gaps.
In light of this, 54 6/11 minutes after four is the right response.
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A fifth grader takes a standardized achievement test (mean = 120, standard deviation = 8) and scores a 128. What is the child's percentile rank?
The child's percentile rank is 84.13%.
How do you determine the percentile?To determine the percentile rank of a score, you need to know the mean and standard deviation of the test, as well as the score in question. In this case, the mean is 120 and the standard deviation is 8.
To convert the child's score of 128 to a percentile rank, you would first convert it to a z-score using the formula (score - mean) / standard deviation = z-score.
In this case:
(128 - 120) / 8 = 1
This z-score of 1 represents the number of standard deviations above the mean the child's score is. To convert this z-score to a percentile rank, you can use a table of the standard normal distribution, which shows the proportion of values that are less than or equal to a given z-score.
A z-score of 1 corresponds to a percentile rank of 84.13%
So, the fifth grader who scored 128 on a standardized achievement test has a percentile rank of 84.13%. This means that 84.13% of students scored lower than the child on this test.
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To indirectly measure the distance across a river, Carson stands on one side of the river and uses sight- lines to landmark on the opposite bank. Carson draws the diagram below to show the lengths and angles that he measured. Find PR, the distance across the river. Round your answer to the nearest foot.
The value of the distance across the sea is 302 feet
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Two triangles are said to be similar if the ratio of their corresponding sides are in the same proportion.
Triangle PRE and triangle POC are similar triangles based on the angle - angle similarity. Hence:
PR / PO = RE/OC
substituting:
x/ (x + 135) = 185 / 335
335x = 185x + 45225
150x = 45225
x = 302 feet
The value of PR is 302 feet
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A teenager charges $112 to babysit for 8 hours at this rate how much dose the teenager charge to babysit for 5 hours In dollars
The teenager charge $70 to babysit for 5 hours.
What is Unit rate?The denominator of a unit rate is always 1. Therefore, divide the denominator by the numerator so that the denominator equals one in order to determine the unit rate.
For instance, the unit rate will be 50km/5.5 hours = 9.09 km/hour if 50km is travelled in 5.5 hours.
Given:
A teenager charges $112 to babysit for 8 hours.
So, in one hour the charges would be
= 112/8
= $14
Now, the charges for 5 hours
= 14 x 5
= $70
Hence, the charges for 5 hour is $70.
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The sample space for tossing a coin 3 times is (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT) Determine P(No heads)
A. 12.5%
B. 25%
C. 50%
D. 75%
The answer for an outcome of P(No heads) is 12.5% . Option A is the answer.
How it was obtainedThere is only one outcome of the 3 coin tosses that results in no heads, and that is TTT.
The probability of getting TTT is 1/8, so P(No heads) = 1/8 = 12.5%.
Probability is a mathematical concept that quantifies the likelihood of an event occurring, expressed as a number between 0 and 1. A probability of 0 indicates that an event will never occur, while a probability of 1 indicates that an event is certain to occur. A probability between 0 and 1 represents the degree of uncertainty about the occurrence of an event, with larger values indicating a higher likelihood of the event taking place.
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21.5.3 Test
Question 11 of 25
Which is a correct expansion of (4x+1)(2x² - 2)?
A. 4x 2x² + 4x
(1) + 1 • 2x²+1 • (-2)
B. 4x 2x² + 4x
(-2) +1.4x+1• (-2)
C. 4x2x² + 4x (-2) +1.2x²+1 (-2)
SUBMIT
The answer to the phrase 3+52 expanded is 28.When an expression is expanded, it is reduced to its most basic form.
Which is a correct expansion ?We must multiply out the brackets in order to extend and simplify an expression. The resulting phrase is then made simpler by grouping like terms together.
It is possible to get rid of brackets by expanding them, often known as multiplying out.
Factorization is being done in reverse.Increasing each term inside a bracket by the expression outside the bracket is referred to as expanding it.
3+5^2
= 3 + 5²
= 3 + (5 × 5)
= 3 + 25
= 28
In response to the expression's expansion, 3+52 is 28.
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Option C) The Polynomial is (4x +1)(2x² - 2)
The expansion will be 4x*2x² - 4x*2 + 2x² - 2
What is Expansion of a polynomials ?If no variable is included in parentheses and all terms that are similar have been merged, a polynomial is expanded. Multiply the components of a polynomial (typically by applying the distributive property), or carry out the corresponding operations, to extend it.
A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables. x² + 4x + 7 is an illustration of a polynomial with a single indeterminate x.
When a polynomial with coefficients in a specific field or in integers is factored, its coefficients are expressed as the product of irreducible factors with coefficients in the same field.
The Polynomial is (4x +1)(2x² - 2)
The expansion will be 4x*2x² - 4x*2 + 2x² - 2
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After rolling the two dice 10 times amit Oe simultaneously, Jerome recorded that 20% of the time, he rolled pairs that included at least one six. Based on his results, if Jerome were to roll the die 65 more times, how many pairs could he predict will contain at least one six?
12 pairs could he predict will contain at least one six using empirical probability formula.
What kind of probability exists between the number of times an event's outcome occurred and the total number of trials that were conducted?The empirical probability formula generates a ratio between the total number of times the desired occurrence was attempted to and the number of times it actually occurred. As an illustration, consider the case where I rolled the dice three times and each time I got 12, giving the result a statistical probability of 12/12 or 100%.
Probability is a form of ratio where we measure the likelihood of a given occurrence in comparison to all other possible outcomes.
Explanation:
12/10 * 10 = 6/5 * 10
= 12.
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Please help me with this
Answer:
what do u have to do like what the question
Dash Canada offers two long-distance telephone plans. Plan X costs 6.5 cents per minute for calls between 8 A.M. and 6 P.M. weekdays (business hours) and 4.5 cents per minute at other times. Plan Y costs 5.3 cents per minute any time.
Above what percentage of business-hour usage will Plan Y be cheaper?
The percentage of business-hour usage that the Plan will be cheaper will be 22.6%.
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
In this case, Plan X costs 6.5 cents per minute for calls between 8 A.M. and 6 P.M. weekdays and 4.5 cents per minute at other times. Plan Y costs 5.3 cents per minute any time.
The percentage of business-hour usage that the Plan will be cheaper will be:
= (6.5 - 5.3) / 5.3 × 100
= 1.2 / 5.3 × 100
= 22.6%
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A baker makes 6 loaves of bread using 7 pounds of dough.
If each loaf is the same weight, how many pounds is one loaf
of bread?
A. 6/7 pound
B. 1 pound
C. 7/6 pound
D. 13 pounds
The Gross Domestic Product, GDP, of Oregon¹ is 243 billion dollars with a growth rate2 of 3.10%. Write an
equation that can be used to estimate the size of Oregon's economy in a future year, assuming the same
relative yearly growth rate. Let g be the state's GDP in billions of dollars in t years from now.
a. The equation is:
b. The equation is in the exponential
e family
c. Use the equation to determine Oregon's GDP in 8 years from now? Round to the nearest billion dollars.
billions
a. The equation for the State's GDP growth is g = 243(3.10)^t.
b. The equation is in the exponential family.
c. Oregon's GDP in 8 years from now will be $2072525 billion.
What is exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The Gross Domestic Product, GDP, of Oregon is 243 billion dollars with a growth rate of 3.10%
Let t = time in years
Let g = State's GDP amount
Start with $243 billion and each year add 3.10% growth is seen in the GDP.
1st year: Growth = 243 × (3.10) = $753.3 dollars
This is added to the previous amount -
= 243 + 243 × (3.10)
= 243 (1+3.10)
= 243 (4.10)
= $996.3 billion
2nd year: Previous amount + Growth in the previous amount
= 996.3 (1+4.10)
= 996.3 (5.10)
= $5081.13 billion
So, the exponential formula becomes -
g = 243(3.10)^t
Now, to find the value of GDP growth after 8 years, substitute t = 8.
g = 243(3.10)^t
g = 243(3.10)^8
g = 243(8528.91)
g = $2072525.13 ≈ 2072525 billion
Therefore, the GDP growth after 8 years is $2072525 billion.
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When looking for the range of a graph, which values are you looking for?
A. x-values
B. y-values
When looking for the range of a graph, y-values are looked for.
What is the range?
A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.
Here,
We have to determine when looking for the range of a graph, which values are looking for.
The domain is all x-values or inputs of a function and the range is all y-values or outputs of a function. When looking at a graph, the domain is all the values of the graph from left to right. The range is all the values of the graph from down to up.
Hence, when looking for the range of a graph, y-values are looked for.
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How would I write terms 2,3,4 of an arithmetic sequence where a1=-7 and the common difference is 12?
Therefore , the solution of the given problem of arithmetic mean comes out to be a2=5 ,a3 = 17 and a4 = 29.
The definition of arithmetic mean.The sum of all values in a list multiplied by the total no. all items in the list yields the arithmetic average, often known as the group's means. The growth in arithmetic follows a similar pattern. The following equation + 7 + 9 equals 21, but 21 multiplied by 3 (there's several currently three numbers) equals 7, proving that the mean of the numbers 5, 7, while 9 is 4, and the median of the real numbers 5, 8, and 9 is 3.
Here,
Given : a1 = -7
and common difference d = 12
Thus,
For a2 = a + d = -7 + 12 = 5
a3 = a+2d = -7 + 24 = 17
and a4 = a + 3d = -7 + 36 = 29.
Therefore , the solution of the given problem of arithmetic mean comes out to be a2=5 ,a3 = 17 and a4 = 29.
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Find the value of x
Please help this is due today
Answer: X= 72°
Here if we see the figure is not labelled so I am assuming it to A,B,C AS MAIN TRIANGLE and BD bisector of angle ABC.
We have to find out that angle DBC.
ANGLE CAB = ANGLE DBA
Hence Angle CDB = ANGLE CAB + ANGLE DBA
27° + 27° = CDB = 54° = ACB ( if sides are equal then opposite angles are also equal.)
so required angle x = 180° - 54° - 54° ( sum of angle of triangle equals 180)
so x= 72°
One-half the square of a number is equal
to 16 more than twice the number. What
is the number?
The number is x = 0 or 18.The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.
What is algebra?The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z. Algebraic sign language. Many students find algebra intimidating since it's the first math course they take where they have to deal with variables, abstract ideas, and problem-solving skills. Additionally, there is sometimes insufficient effort made in the classroom to relate algebra to students' daily lives and explain why learning it is important.
Let x be the number. Translation of the given information into algebra gives
√(2x) = x/3
Solve for x. Note x ≥ 0.
2x = x2/9
If x ≠ 0,
2 = x/9 ⇒ x = 18
Solutions are x = 0 or 18.
The complete question is,
The square root of twice a number is equal to one-third of that number. Find the number.
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Which equation does not belong with the other three?
Responses
y=3^x
y is equal to 3 to the x th power
f\left(x\right)=2\left(4\right)^x
f of x is equal to 2 times 4 to the x the power
f\left(x\right)=\left(-3\right)^x
f of x is equal to negative 3 to the x the power
y=5\left(3\right)^x
y is equal to 5 times 3 to the x the power
Question 2
Why did you select this equation?
Because it is the only equation that ___ an exponential function.
The exponential function f(x) = 2(4)ˣ doesn't belong to the other three.
What is an exponential function?
A mathematical function is an exponential function. The word, unless expressly stated differently, refers typically to the positive-valued function of a real variable. However, it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
Here, we have
Given:
y = 3ˣ,
f(x) = 2(4)ˣ
f(x) = (-3)ˣ
y = 5(3)ˣ
We have to determine which equation does not belong with the other three.
We concluded that
All equations are multiples of 3 but f(x) = 2(4)ˣ is not a multiple of 3.
Hence, the exponential function f(x) = 2(4)ˣ doesn't belong to the other three.
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The teacher wrote two numbers on the board. Eric added the numbers and got
58. Olivia subtracted the second number from the first number and got 28. What
is the first number the teacher wrote on the board?
Answer:
Let x be the first number that the teacher wrote on the board and y be the second number. From the problem, we know that:
x + y = 58 (from Eric's calculation)
x - y = 28 (from Olivia's calculation)
To find the value of x, we can add the equations together:
x + y = 58
x - y = 28
2x = 86
x = 43
So the first number that the teacher wrote on the board is 43.
Pavel and Sarah are knitting hats to sell. Pavel spends
£20 on wool and Sarah spends £80. They sell all the hats for a total of
£1000. Is it fair that they get £500 each? Explain your answer.
Consider the equation. What is a constant term or variable term that makes the equation have infinite solutions?
5x + 20 = 5x +_____
A. 5x
B. 15
C. 20
D. -20
A constant term that makes the equation have infinite solutions include the following: C. 20
What are infinitely many solutions?In Mathematics, an equation is said to have an infinitely many solutions when the left hand side and right hand side of the equation or inequality are the same and equal.
This ultimately implies that, an equation or an inequality would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and y-intercept for the two lines are the same.
By applying the rule for an infinitely many solutions, we have:
5x + 20 = 5x + 20
5x - 5x = 20 - 20
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