Answers
The function rule for the functions f(x) and g(x) given by the table are;
f(x) = Log₁₀x
g(x) = 2ˣ
What is the function rule of the table?
1) In the first table of the function f(x), we see the coordinates as;
(10, 1), (100, 2), (1000, 3), (10000, 4), (100000, 5)
Thus, we see that;
Log 10 = 1
Log 100 = Log 10² = 2 Log 10 = 2
Log 1000 = Log 10³ = 3Log 10 = 3
Thus, the function rule is Log₁₀x
2) In the second table of the function g(x), we see the coordinates as;
(1, 2), (2, 4), (3, 8), (4, 16), (5, 32)
Thus, we see that;
2¹ = 2
2² = 4
2³ = 8
Thus, the function rule here is 2ˣ
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Related Questions
Henry read for 20 minute each day alicia rate for 30 minute each day they both read 7 Day of a week how many more doe Alicia read then Henry in 2 week
Answers
Alicia read 140 minutes more then Henry in 2 week .
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main body:
Henry read for 20 minute each day.
Alicia rate for 30 minute each day.
as they read 7 day of a week , so
total minutes read by Henry = 2 *7 *20
= 280 minutes
total minutes read by Alicia = 2 *7 *30
=420 minutes
difference between henry , alicia reading = 420 - 280 = 140 minutes.
Hence , Alicia read 140 minutes more then Henry in 2 week .
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part 2 of important test, all solutions need to be the same
helppp
Answers
The solution of the quadratic equation using the quadratic formula is
x = 4 + 2√6 or 4 - 2√6
How to solve a quadratic equation using quadratic formula?The quadratic formula is a formula used to solve quadratic equations, which are equations of the form ax² + bx + c = 0 where a, b, and c are constants. The quadratic formula is:
x = (-b±√(b²-4ac))/(2a)
Given: x² - 8x - 84 = 0
Here, a = 1, b = -8 and c = -84
x = (-b±√(b²-4ac))/(2a)
x = [-(-8)±√((-8)²-[4×1×(-8)])]/(2a)
x = [8±√(96)]/2
x = (8± 4√6)/2
x = 4 ± 2√6
x = 4 + 2√6 or 4 - 2√6
Thus, the solution is x = 4 + 2√6 or 4 - 2√6
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Mr. Croland aked tudent to factor the expreion 28x−8
28
x
−
8. The tudent offered the anwer hown in the box. Which tudent() offered anwer() equivalent to the original expreion?
Answers
The students who offered the answer equivalent to original expression are Carlos and Irene.
The original expression can be traced back by solving the solution of each student. Thus, taking each solution.
Carlos
Performing multiplication of the solution
Expression = 2(14x - 4)
Expression = 28x - 8
Danny
Performing multiplication of the solution
Expression = 7(4x - 1)
Expression = 28x - 7
Irene
Performing multiplication of the solution
Expression = 4(7x - 2)
Expression = 28x - 8
Thus, Carlos and Irene gave the correct factors of the original expression.
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The complete question is -
Mrs. Crosland asked students to factor the expression 28 x − 8 . The students offered the answers shown in the box
Carlos: 2(14x - 4)
Danny: 7(4x - 1)
Irene: 4(7x - 2)
The equation, A equal to 1,500 plu quantity 1 plu 0. 06 over 2 end quantity all raied to the power of 2 time t, repreent the amount of money earned on a compound interet aving account. What doe the value 1,500 repreent?
Answers
The equation states that the total amount in the savings account will be equal to the initial deposit .The value 1,500 represents the initial amount deposited into the savings account.
The equation A = 1,500 + (1 + 0.06/2)^2t represents the amount of money earned on a compound interest savings account. The value 1,500 represents the initial amount that was deposited into the savings account. The equation states that the total amount in the savings account will be equal to the initial deposit (1,500) plus the amount that is earned by compounding the interest rate on the initial deposit. This is calculated by first adding the initial deposit (1) to the interest rate (0.06/2). This sum is then raised to the power of 2 times the number of years (t) the money has been in the account. This total amount is then added to the initial deposit (1,500) to give the total amount earned on the savings account.
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Answer:
The value 1,500 represents the initial value, which means the account started with a balance of $1,500.
Step-by-step explanation:
I got it right.
the interest charged on a $50,000, 60-day note payable, at the rate of 6%, would be
Answers
If the interest charged on a $50,000, 60-day note payable, at the rate of 6%, would be $500.
In the given question, we have to find the interest charged on a $50,000, 60-day note payable, at the rate of 6%.
The note payable = $50,000
Rate = 6% = 0.06
Period outstanding = 60
The total interest formula is a way to calculate the total simple interest on a sum of money over time at a specific interest rate.
Total Interest charged = Note Payable * rate * period outstanding
Total Interest charged = $50,000 * 0.06 * 60/360
Total Interest charged = $500
Hence, if the interest charged on a $50,000, 60-day note payable, at the rate of 6%, would be $500.
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Marvin works Monday through Thursday 6am-12pm with a 30 minute
unpaid lunch. On Saturday he works from 12pm - 8:30pm with a 30 minute
unpaid lunch. If Marvin earns $14.75 per hour, answer the following.
How many hours and minutes does Marvin work for the week?
What is Marvins gross pay?
Answers
Answer:
The answer is $492.88. This is Marvin's gross pay for the week, calculated by multiplying his hourly wage of $14.75 by the number of hours he worked, which is 33.5 hours.
Step-by-step explanation:
Marvin works 6 hours a day on Monday through Thursday, for a total of 6 * 4 = <<64=24>>24 hours.
On Saturday he works 8.5 hours, for a total of 24 + 8.5 = <<24+8.5=32.5>>32.5 hours.
Marvin works for 30 minutes unpaid during the week, and 30 minutes unpaid on Saturday for a total of 30 * 2 = <<302=60>>60 minutes.
In hours, 60 minutes is 60 / 60 = <<60/60=1>>1 hour.
Therefore, Marvin works for a total of 32.5 + 1 = <<32.5+1=33.5>>33.5 hours in a week.
Marvin earns $14.75 per hour, so his gross pay is 14.75 * 33.5 = $<<14.75*33.5=492.88>>492.88
Select the correct answer. What is the end behavior of the radical function represented by this graph? The graph shows the square root function. The function starts at the point (minus 3, 0) and extends upwards and to the right. Some major points on the graph are (0, 3), (2, 4), and (5, 5). A. As x decreases in value, increases in value. As x increases in value, decreases in value. B. As x decreases in value, increases in value. As x increases in value, increases in value. C. As x decreases in value, decreases in value. As x increases in value, decreases in value. D. As x decreases in value, decreases in value. As x increases in value, increases in value.
Answers
The end behavior of the function is that;
D. As x decreases in value, f(x) decreases in value.
As x increases in value, f(x) increases in value.
What is the end behavior of the radical function?
The end behavior of a function f(x) describes the behavior of the graph of the function at the "ends" of the x-axis.
Now, in the graph attached, at the end point of the curve on the left of the x-axis, we see that the coordinate is (-3, 0) and to the right which is when x has increased to 9 and now has a coordinate point of (9, 6).
Thus, we conclude that we see that as the value of x increased from left to right, f(x) also increased and as the value of x decreased from right to left, f(x) also decreased.
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Write 0.302 repeating as a fraction. show your work.
Answers
Answer:
x = 302/999
HERE THE ANSWER
Step-by-step explanation:
9,16,23,...
Find the 46th term?
Answers
The 46th term is 324.
Which of these words is a synonym for vulnerable?
separated
unemployed
unprotected
freed
Answers
What is the center of dilation? How do you know?
Answers
Answer:
A
Step-by-step explanation:
You want the center of dilation when ∆ABC is dilated by a factor of 1/2 to get ∆AED.
Center of dilationIn any dilation, the center of dilation is invariant. It doesn't move.
Since point A is common to both triangles, it didn't move. Point A is the center of dilation.
Write the equation of the line with
slope -3 that goes through the point (-1,3).
Switch the equation to slope y intercept form.
Answers
Answer:
y = -3x
Step-by-step explanation:
You want the slope-intercept equation of the line with slope -3 through the point (-1,3).
Point-slope formThe equation of the line with slope m through point (h, k) can be written ...
y -k = m(x -h)
For slope -3 and point (-1, 3), the equation is ...
y -3 = -3(x +1)
Slope-intercept formEliminating parentheses gives ...
y -3 = -3x -3
Adding 3 gives the equation ...
y = -3x
__
Additional comment
As you can see, the y-intercept is 0.
02.03 Focus Questions- please help 50+ points
What are linear equations and functions?
What are the different ways of representing a linear function?
How are key features of a linear function identified and interpreted from a graph?
How are key features of a linear function identified and interpreted from a table?
How are key features of a linear function identified and interpreted from an equation?
How are key features of a linear function identified and interpreted from a description?
Answers
Step-by-step explanation:
first of all, a function is an equation.
it associates a function result variable (typically called y) with a calculation based on an input variable (usually caked x), or in more complex mathematics based on a group of input variables.
but not every equation is a function. to be a function every valid x value must have exactly one associated y value.
e.g. x = 5 is an equation. but it does not restrict y in any way. so, any value of y (infinitely many) is valid for x = 5.
therefore, this is not a function.
a linear equation/function is a straight line (hence the name).
it is characterized by an inclination (typically called slope or rate of change) and its absolute position typically incentives by the interception points particularly with the y-axis on a coordinate grid.
there are various ways to describe a line in a formal way.
the slope-intercept form :
y = ax + b
a being the slope, b being the y-intercept (y-value when x = 0).
the point-slope form
y - y1 = a(x - x1)
again, a is the slope, (x1, y1) is an identified point (coordinates) on the line.
the general (often called standard) form
gx + hy = c
g, h, c are not describing anything directly, but after transforming this standard form they build the "a" and "b" terms of the other forms.
the slope is the ratio of (y coordinate change / x coordinate change) when going from one point on the line to another. for a line this is constant for any pair of points you can pick on the line.
in other words it tells us how many units y changes, when x changes by a certain amount of units
basically, a line is the collection of all the points for which the given equation is true (when using the x coordinate in the equation we get the corresponding y as calculation result, or when using x and y of any point on the line in the equation, then the equation is true).
graph :
the slope is found by checking 2 points and calculating the y diff / x diff ratio. e.g. starting with (0, 0) if that point is in the line, we increase x by 1 and check the y value there : (1, y).
so, the slope is for that example (y - 0)/(1 - 0) = y.
the y-intercept is found by checking the y-value for x = 0.
the y-interception point is therefore (0, b).
the x-intercept is the x-value when y = 0.
the x-interception point is therefore (x-intercept, 0).
table :
for the slope we pick again 2 data points of the table and calculate y diff / x diff.
as explained this has to be constant for any picked pair of data points of the table. then you know it is a linear equation.
if we are lucky, the table contains data points with x = 0 and/or y = 0. then we have the corresponding intercept values.
but if not, we need to use the coordinates of 1 point in the e.g. slope-intercept form to create an equation with 1 variable : b. and then we solve it to get b.
equation :
we need to bring the equation into a form that we get
y = ...
then the factor of x is the slope. and the constant term (even if it is not there, as it means it is 0) defines the y-intercept
everything else is as described above
description :
the description needs to give us either data points or an indication about the slope and the y-intercept.
when we have 2 points, we can define a line through them. in other words, any pair of points defines a line.
A questionnaire was given to students. The first question asked was "How stressed have
you been in the last week on a scale of 0 to 10 with O being not stressed at all and 10
being as stressed as possible?" The responses are shown to the right.
Answers
a. Stress rating describes the greatest number of students is: 8 out of 10
b. There are 156 students that responded with this rating.
How to calculate the stress rating?A questionnaire is a research tool made up of a list of questions used to collect data from respondents during a survey or statistical analysis. Typically, a research questionnaire will contain both closed-ended and open-ended questions.
From the table, the total students will be the addition and this will be:
= 6 + 2 + 5 - 16 + 20 + 20 + 11 + 21 + 24 + 19 + 12
= 156
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Warner received 7 letters. Each letter weighed between 3.92 ounces and 4.1 ounces. Warner estimates a reasonable weight of all the letters to be 30 ounces.
Is this a reasonable estimate?
Answers
The estimate made by Warner is 95% reasonable.
What is inequality? What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Warner received 7 letters and each letter weighed between 3.92 ounces and 4.1 ounces.
If the we take the maximum possible weight of each letter, which is 4 ounces, then the total weight of 7 letters will be equal to (4 x 7) = 28. But since the weights are weighted between 3.92 ounces and 4.1 ounces, let us assume that the weight of each letter is equivalent to -
w(a) = (3.92 + 4.10)/2 = 8.02/2 = 4.01
So, the weight of 7 letters would be -
W{7} = w(a) x 7 = 7 x 4.01 = 28.7
28.7 = 29 (round off) ≈ 30
So, yes the estimate of the Warner is reasonable.
Therefore, the estimate made by Warner is 95% reasonable.
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Geometry: 6.7_law_of_cosines: 15 Points
Answers
Answer:
52.61 degrees to the nearest hundredth.
Step-by-step explanation:
8^2 = 7^2 + 10^2 - 2.10.7cos A
cos A = (8^2 - 7^2 - 10^2) / (-140)
= -85/-140
= 0.60714
< A = 52.61 degrees.
choose the equation of the graphed function.
Answers
Answer:
g
Step-by-step explanation:
shifts the graph down by 6 units
-55 − (-37) = A) -32 B) -18 C) 18 D) 92
GIVING BRAINLIST! + 90 POINTS!
Answers
Answer:
-18
Step-by-step explanation:
-55 - - 37 = -55 + 37 = 37 - 55 = -18
Answer:
B) - 18----------------------------------------
Solve in steps:
- 55 - ( - 37) = (- 1)*55 - ( -1)*37 = Rewrite as factors of - 1(- 1)*(55 - 37) = Factor out - 1( - 1)*18 = Simplify - 18 Answerthe confidence interval for the mean of y is always narrower than the prediction interval for an individual response y given the same data set, x value, and confidence level. group of answer choices true false
Answers
The statement 'the confidence interval for the mean of y is always narrower than the prediction interval for an individual response y given the same data set, x value, and confidence level.' is True.
In this question, we have been given a statement 'The confidence interval for the mean of y is always narrower than the prediction interval for an individual response y given the same data set, x value, and confidence level. '
We need to state whether the given statement is true or false.
We know that the confidence interval = sample mean ± margin of error
The confidence interval for the mean of y is narrower when the x value is close to the mean of all of the x values.
Therefore, the confidence interval for the mean of y is always narrower than the prediction interval for an individual response y given the same data set, x value, and confidence level is True.
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The owner expects to sell 800 snow cones next week. He earns a profit of $2.29 on each snow cone sold. Based on last week's results, how much profit can the owner expect to earn from cherry snow cone sales next week? Cherry was sold 120 times last time.
Answers
Based on last week's results, the profit that the owner expect to earn from cherry snow cone sales next week is $1832.
How much profit can the owner expect to earn from cherry snow cone sales next week?From the information, the owner expects to sell 800 snow cones next week and he earns a profit of $2.29 on each snow cone sold. Based on last week's results.
The profit can the owner expect to earn from cherry snow cone sales next week will be:
= Number of cheery × Profit on each
= 800 × $2.29
= $1832
The profit is $1832.
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Tomorrow, Mrs. Wendel's class will be using toothpicks for a science project. Each student must use at least 6 toothpicks for the project.
Mrs. Wendel knows that there is already a bag of 50 toothpicks in the class storage room. She plans to buy x additional toothpicks this afternoon to make sure her class will have enough.
If her class has 28 students, which number sentence represents this situation?
Answers
in an experiment designed to measure the distance a golf ball is hit by clubs made of different material, the independent variable would be:
Answers
In studies intended to measure the distance a golf ball is struck with weapons made of various materials, the material of the golf ball and the direction of the wind at the moment the experiment was done become standardized variables.
In tests intended to assess the distance a golf ball is struck with clubs made of various materials, the kind of material the club is composed of is an independent variable.
Independent variables are those that a researcher tries to manipulate or control to observe how they impact the dependent variable. In this experiment, the effect of different club construction materials on golf ball distance is investigated.
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Evaluate the Expression P(7, 5)?
Responses:
35
2,520
21
3,500
Answers
Based on the values you've listed, it appears that the expression P(7, 5) represents a combination calculation. In combinatorics, the notation P(n, k) represents the number of ways to choose a subset of k items from a set of n items, without regard to the order in which the items are chosen. This is also known as the number of k-permutations of n items.
In this case, the expression P(7, 5) would represent the number of ways to choose a subset of 5 items from a set of 7 items. Using the formula for combinations, this would be calculated as follows:
P(7, 5) = 7! / (5! * (7 - 5)!)
= 7! / (5! * 2!)
= 7 * 6 * 5 * 4 * 3 / (5 * 4 * 3 * 2 * 1 * 2 * 1)
= 7 * 6 / 2
= 21
Therefore, the correct answer for the expression P(7, 5) is 21.
Write an inequality for the statement:
negative two thirds is a minimum of the product of a number and negative seven eighths
negative seven eighths ≤ negative two thirdsw
negative seven eighths ≥ negative two thirdsw
negative two thirds ≥negative seven eighthsw
negative two thirds ≤ negative seven eighthsw
Answers
The required linear inequality is [tex]-\frac{2}{3} \geq -\frac{7}{8}x[/tex]
What is linear inequation?
A linear inequation is an equation that contains one or more variables, such as x, and involves linear functions. Unlike a linear equation, its solution set is not a single point, but a range of values. Linear inequations are used to represent situations where the exact value of a variable is not known, but a range of values can be determined based on certain conditions. For example, if x represents the amount of money a person makes in a year and we know that it must be greater than $50,000, then we can write the linear inequation x > 50,000.
Let the number be x
[tex]-\frac{2}{3}[/tex] is a minimum of the product of a number and [tex]-\frac{7}{8}[/tex]
[tex]-\frac{2}{3} \geq -\frac{7}{8}x[/tex]
This is the required linear inequality
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Find u•v where theta is the angle between u and v
Answers
Answer:
124.45
Step-by-step explanation:
u•v=8*22*cos(π/4)=124.45
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Write the expression in simplest form.
the quantity negative two thirds x minus 7 end quantity minus the quantity negative 12 plus one sixth x end quantity
(A) three sixths x plus 5
(B) negative three sixths x minus 5
(C) five sixths x minus 5
(D) negative five sixths x plus 5
Answers
Answer:
[tex]\textsf{D)} \quad -\dfrac{5}{6} x+5[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(- \dfrac{2}{3} x - 7\right) - \left(- 12 +\dfrac{1}{6}x \right)[/tex]
Remove the parentheses applying the rules -(-a) = a and -(a) = -a
[tex]- \dfrac{2}{3} x - 7+12-\dfrac{1}{6}x[/tex]
Collect like terms:
[tex]- \dfrac{2}{3} x-\dfrac{1}{6}x - 7+12[/tex]
Add the numbers -7 and 12:
[tex]- \dfrac{2}{3} x-\dfrac{1}{6}x+5[/tex]
Rewrite the first fraction so that its denominator is 6:
[tex]- \dfrac{2 \cdot 2}{3\cdot 2} x-\dfrac{1}{6}x+5[/tex]
[tex]- \dfrac{4}{6} x-\dfrac{1}{6}x+5[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]
[tex]\dfrac{-4-1}{6} x+5[/tex]
Simplify:
[tex]-\dfrac{5}{6} x+5[/tex]
consider a standard normal random variable z. what is the value of z if the area to the right of z is 0.4404?
Answers
The value of z if the area to the right of z is 0.4404 is; 0.15
How to find the probability of the z-score?To find the value of z if the area to the right of z is 0.4404 is expressed as; P(Z > z) = 0.4404
Now, this means we have to go and trace the value of this area on the standard normal distribution table to know that z-score that it represents.
Now, by looking at the table of standard normal distribution, we can trace that the z-score area to the right of z is 0.4404 is;
z = 0.15
Thus, we conclude that the z-score above is the required one for the given area.
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The three perpendicular bisectors of a triangle intersect in one point called the: _______
Answers
it is estimated that 70% of ucf students participate in anti-racist practices. in a sample of 50 ucf students, how many would you expect to participate in anti-racist practices?
Answers
35 expect to participate in anti-racist practices.
anti-racist practices=Anti-racism encompasses a range of ideas and political actions which are meant to counter racial prejudice, systemic racism, and the oppression of specific racial groups. Anti-racism is usually structured around conscious efforts and deliberate actions which are intended to provide equal opportunities for all people on both an individual and a systemic level. As a philosophy, it can be engaged in by the acknowledgment of personal privileges, confronting acts as well as systems of racial discrimination, and/or working to change personal racial biases. Major contemporary anti-racism efforts include Black Lives Matter organizing and workplace antiracism.
Expect value= n*p=0.70*50
=35
Answer=35
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Triangle a b c is cut by line segment f g. line segment f g goes from side a b to side a c. the length of b f is x 6, the length of f a is x 1, the length of c g is x 3, and the length of g a is x minus 1. which value of x would make line segment f g is parallel to line segment b c? 1 3 6 9
Answers
Triangle a b c is cut by line segment f g. line segment f g goes from side a b to side a c. then x= 9
The problem description can be shown in the figure below. Since FG is parallel to BC, both sides AB and AC are split in proportional segments. It can be expressed in several ways. We'll use this one:
x+1/x+6= x-1/x+3
Operating in both sides:
4x+3=5x-6
Simplifying
x=9
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Answer: D). 9
Step-by-step explanation: