Answer:
The two positive numbers are 12 and 8.
Explanation:
The first phrase in the sentence tells us the difference between numbers equals 4, which can be represented a - b = 4
The second phrase tells us when multiplied together, it equals 96, which can be represented by the ab = 96, or a(b) = 96
So, first step is to list the factors of 96. I prefer to list them as pairs:
1, 96; 2, 48; 3, 32; 4, 24; 6, 16; and 8, 12
Now we plug each these pairs into the first equation to see if they satisfy the equation.
96 - 1 = 95 24 - 4 = 20
95 > 4 20 > 4
48 - 2 = 46 16 - 6 = 10
46 > 4 10 > 4
32 - 3 = 29 12 - 8 = 4
29 > 4 4 = 4
Because a = 12 and b = 8 satisfies both equations that represent the given sentence, the two positive numbers are 12 and 8.
Find m/AEB
A.
10
B.
70
C.
110
D.
170
Suppose the number of calls per hour to an answering service follows a poisson process with rate 4.
a.what is the probability that fewer than 2 calls came in the first hour?
Given that (-3,7) is on the graph of f(x), find the corresponding point for the function f(x + 5).
Answer: (-8,7)
Step-by-step explanation: It;s right
hey can you please help me posted picture of question
Is writing an equation this way ( 4 x 5 )-9-6 correct? If not why?
You are traveling to Chicago for a job interview. You leave Toledo, Ohio, at 5:45 A.M. and arrive in Elkhart, Indiana, at 8:15 A.M.. The distance from Toledo to Elkhart is 136 miles; the distance from Toledo to Chicago is 244 miles. The speed limit is 65 mph. What is the minimum speed you must maintain in order to arrive in Chicago before 10:30 A.M.
Consider the following sets: R = {x | x is the set of rectangles} P = {x | x is the set of parallelograms} T = {x | x is the set of triangles} I = {x | x is the set of isosceles triangles} E = {x | x is the set of equilateral triangles} S = {x | x is the set of scalene triangles} Which statements are correct? Check all that apply. T is a subset of P. E is a subset of I. S is a subset of T. I ⊂ E T ⊂ E R ⊂ P
Answer:
The answers are 2, 3, 6
Step-by-step explanation:
which equation is shown in the graph?
y = [[x]]
y = [[x + 3]]
y = [[x]] - 3
y = |x - 3|
PLEASE PLEASE HELP ME?!?!!? PLEASSEE I ONLY HAVE 2 QUESTIONS!!!
When the function f(x) = 6(9)x is changed to f(x) = 6(9)x + 1, what is the effect?
Select one:
a. There is no change to the graph because the exponential portion of the function remains the same.
b. All input values are moved 1 space to the right.
c. The x-intercept is 1 space higher.
d. The y-intercept is 1 space higher.
Evaluate fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5 . (5 points)
Select one:
a. 9 to the power of negative 1 over 2
b. 9 to the power of negative 1 over 4
c. 9
d. 92
1. Changing f(x) to f(x) + 1 adds 1 to every output value of the function, moving that value "1 space higher". This is true for the y-intercept, too.
___
2. The rules of exponents apply:
a^b · a^c = a^(b+c)1/a^b = a^-bYou apparently want to simplify ...
... 9^(1/4) × 9^(1/2) / 9^(5/4)
... = 9^(1/4 + 1/2 - 5/4)
... = 9^((1+2-5)/4)
... = 9^(-2/4) = 9^(-1/2)
for a bake sale violet wants to use the recipe at the right. If she wants to double the recipe, how much flour will she need
which of the following statements is false?
A. 2 is greater than or equal to 8
B. 2 is less than or equal to 8
c. 8 is less than or equal to 8
Quan Le needs $203 to pay for the cost of an evening class. He has $37 and plans to borrow the rest from his brother. Round each amount to determine about how much he needs to borrow? Check your answer using the inverse operation.
kaitlin is participating in a 5-day cross country biking challenge. She biked for 55,67,56,and 49 miles on the first four days. How many miles does she need to bike on the last day so that her average (mean) is 55 miles per day?
To find out how many miles Kaitlin needs to bike on the last day to average 55 miles per day over a 5-day biking challenge, we calculate the total intended miles (55*5 = 275 miles) and subtract the total miles already biked (275 - (55+67+56+49) = 48 miles). Therefore, Kaitlin needs to bike 48 miles on the last day.
Explanation:In the content-loaded problem, Kaitlin is participating in a 5-day cross country biking challenge. She's has already completed biking for four days with distances of 55, 67, 56, and 49 miles respectively. To find out how many miles she needs to bike on the last day for her to average 55 miles per day, we first need to find the total miles she should cover in 5 days.
The total miles intended to be covered in 5 days should be 55 miles/day * 5 days = 275 miles
Then we subtract the total miles covered in the first four days from this. So, 275 miles - (55 miles + 67 miles + 56 miles + 49 miles) = 48 miles
So, Kaitlin needs to bike 48 miles on the last day to achieve an average of 55 miles per day.
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witch of the following expression is equivalent to the logarithmic expression below. log(3)5/x^2
A)log(3) 5+2 log(3)x
B)log(3) 5-2 log(3)x
C)2 log(3) 5-log(3)x
D)log(3) 5+log(3)x
Answer: The correct option is
(B) [tex]\log_35-2\log_3x.[/tex]
Step-by-step explanation: We are given to select the expression that is equivalent to the following logarithmic expression :
[tex]E=\log_3\dfrac{5}{x^2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following properties of logarithms :
[tex](i)~\log_a\dfrac{b}{c}=\log_ab-\log_ac,\\\\(ii)~\log_ab^c=c\log_ab.[/tex]
From (i), we get
[tex]E\\\\=\log_3\dfrac{5}{x^2}\\\\\\=\log_35-\log_3x^2~~~~~~~~~~~~~~~~~~~~[\textup{Using property (i)}]\\\\\\=\log_35-2\log_3x.~~~~~~~~~~~~~~~~~~~~[\textup{Using property (ii)}][/tex]
Thus, the required equivalent expression is [tex]\log_35-2\log_3x.[/tex]
Option (B) is CORRECT.
Please help soon:)
Select the graph of the equation below.
y=3/2x^2 + 4x - 2
Find the number of ways that an organization consisting of 15 members can elect a president, a treasurer, and q secretary. (assuming no person is elected to more than one position)
Total Members = 15
For electing present number of members = 15
For electing treasurer the numbers of members =14
For electing secretary the numbers of members =13
Find the numbers of possible ways for election of members= ?
Possible ways for election =15*14*13
=2730
These tables of values represent continuous functions. In which table do the values represent an exponential function?
A.
x y
1 3
2 6
3 9
4 12
5 15
B.
x y
1 2
2 6
3 18
4 54
5 162
C.
x y
1 10
2 22
3 34
4 46
5 58
D.
x y
1 7
2 8
3 9
4 10
5 11
Answer:
The correct option is B.
Step-by-step explanation:
A function is called an exponential function if it has common ratio.
A function is called an linear function if it has common difference.
In option A.
[tex]\frac{f(2)}{f(1)}=\frac{6}{3}=2[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]
[tex]2\neq \frac{3}{2}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option A is incorrect.
In option B.
[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=3[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=3[/tex]
[tex]3=3[/tex]
Since the given table has common ratio, therefore it is an exponential function. Option B is correct.
In option C.
[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]
[tex]\frac{11}{5}\neq \frac{17}{11}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option C is incorrect.
In option D.
[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]
[tex]\frac{8}{7}\neq \frac{9}{8}[/tex]
Since the given table has different ratio, therefore it is not an exponential function. Option D is incorrect.
Answer:
Table B represents an exponential function.
Step-by-step explanation:
An exponential function is a function which has common ratio. Using this fact we will evaluate the functions given in the form of a table.
Table A.
f(1) = 3
f(2) = 6
f(3) = 9
Now [tex]\frac{f(2)}{f(1)}=\frac{6}{3}=\frac{2}{1}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{6}=\frac{3}{2}[/tex]
Ratios are not equal so it's not an exponential function.
Table B.
f(1) = 2
f(2) = 6
f(3) = 18
[tex]\frac{f(2)}{f(1)}=\frac{6}{2}=\frac{3}{1}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{18}{6}=\frac{3}{1}[/tex]
Here ratios are same therefore it's an exponential function.
Table C.
f(1) = 10
f(2) = 22
f(3) = 34
[tex]\frac{f(2)}{f(1)}=\frac{22}{10}=\frac{11}{5}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{34}{22}=\frac{17}{11}[/tex]
Ratios are not equal therefore it's not an exponential function.
Table D.
f(1) = 7
f(2) = 8
f(3) = 9
[tex]\frac{f(2)}{f(1)}=\frac{8}{7}[/tex]
[tex]\frac{f(3)}{f(2)}=\frac{9}{8}[/tex]
Ratios are not equal so it's not an exponential function.
Therefore Table B is the correct option.
find the measure of the requested angle. find the complement of 41*
Find the measure of the requested angle. find the complement of 41°.
Solution:
The Sum of Complementary Angles is 90°.
So, Sum of Requested Angle and Given Angle =90°
So,Requested Angle+Given angle=90°
So,Requested Angle+41°=90°
To find, Requested Angle we subtract 41° from both sides,
Requested Angle+41°-41°=90°-41°
Requested Angle+0°=49°
So, Requested Angle=49°
Answer:49°
Make a box and whisker plot that represents the data
Number of chairs in a classroom
30,27,32,25,12,22,20,29,35,35,28
*. suppose that there are 5 dollar bills in a box: three 1 dollar bills, one 5 dollar bill and one 10 dollar bill. you are allowed to pick up two bills at the same time from the box randomly. let x denote the money you get from this game. (a) what's the p.m.f. of x?
To determine the probability mass function (PMF) for the game, one must calculate the probability of each possible sum of money resulting from drawing two bills, with the outcomes being 2, 6, 11, and 15 dollars.
To find the probability mass function (PMF) of the variable X, which represents the money you get from the game, we first identify all possible pairs of dollar bills you could draw from the box and then calculate the probability of drawing each pair. As there are three 1 dollar bills, one 5 dollar bill, and one 10 dollar bill, the possible sums of money (X) we can get by drawing two bills are 2 dollars, 6 dollars, 11 dollars, and 15 dollars.
To calculate the PMF of X, consider:
Picking two 1 dollar bills: The probability is C(3,2)/C(5,2) = 3/10.
Picking one 1 dollar bill and the 5 dollar bill: The probability is (C(3,1) imes C(1,1))/C(5,2) = 3/10.
Picking one 1 dollar bill and the 10 dollar bill: The probability is (C(3,1) imes C(1,1))/C(5,2) = 3/10.
Picking the 5 dollar bill and the 10 dollar bill: The probability is (C(1,1) imes C(1,1))/C(5,2) = 1/10
Therefore, the PMF of X is:
P(X = 2) = 3/10
P(X = 6) = 3/10
P(X = 11) = 3/10
P(X = 15) = 1/10
hello can you please help me posted picture of question
A pattern on a quilt is made up of pieces of fabric in the shape of parallelograms. One piece of fabric is shown. What is the area of one piece of fabric? Enter your answer in the box.
If f(x)=4x-6 and g(x) =2x find f(x) •g(x)
A researcher published this survey result: "74% of people would be willing to spend 10% more for energy from a non-polluting source". The survey was conducted by posing the question on a national radio show and asking listeners to call in. 1,200 listeners responded. What is wrong with this survey?
correlation and causality
voluntary response
nonresponse
precise numbers
in a class of 32 students 11 are men what fraction of the students are men
11 - men 32 - students
So, 11/32 is the fraction.
The answer couldn't be simplified because 11 is a prime number.
You have a box of chocolates that contains 59 pieces of which 37 are solid chocolate, 15 are filled with cashews, and 7 are filled with cherries. All the candies look exactly alike. You select a piece, eat it, select a second piece, eat it, and finally eat one last piece. Find the probability of selecting a solid chocolate piece followed by two cherry-filled chocolates. Round your answer to three decimal places.
The probability of selecting a solid chocolate piece followed by two cherry-filled chocolates in sequence is approximately 0.00407.
The question asks for the probability of selecting a solid chocolate piece followed by two cherry-filled chocolates. There are 59 pieces total in the box, with 37 solid chocolates, 15 filled with cashews, and 7 filled with cherries. To calculate the probability, we use the concept of dependent events since each chocolate is eaten before selecting the next, which changes the total number of chocolates available. The probability of choosing a solid chocolate first is 37/59. After eating it, there are 58 pieces left and still 7 cherry-filled chocolates, so the probability of then picking a cherry-filled chocolate is 7/58. Then there would be 57 pieces left and 6 cherry-filled chocolates, so the probability of finally picking a cherry-filled chocolate would be 6/57. To find the total probability of all events happening in sequence, we multiply the individual probabilities together:
Probability = (37/59) * (7/58) *(6/57)
Calculating this gives us the probability, to three decimal places:
Probability = 0.00407
What position in the distribution corresponds to a z-score of z = +2.00?
A z-score of +200 corresponds to a position that is 2 standard deviations above the mean, and signifies a value within the top 2.5% of a normally distributed data set.
The z-score of z = +2.00 in a distribution indicates that the corresponding value is exactly 2 standard deviations above the mean of the distribution. According to the empirical rule (also known as the 68-95-99.7 rule), approximately 95% of the data falls within two standard deviations of the mean. Therefore, a z-score of +2.00 means the position is within the top 2.5% of the distribution, since it is above the mean and within 95% coverage of the data towards the higher end. This concept is fundamental when assessing data in relation to the normal distribution, and it's widely used to determine how far a particular data point is from the average value in terms of standard deviations.
Where is the second derivative of y = 4xex equal to 0?
Final answer:
The second derivative of the function y = 4x[tex]e^x[/tex] is equal to zero when x = -2. This is determined by differentiating the function twice, setting the second derivative equal to zero, and then solving for x.
Explanation:
The question is asking for the value of x at which the second derivative of the function y = 4xex is equal to zero. To solve this, we first find the first derivative, which is y'(x) = 4ex + 4x[tex]e^x[/tex] (applying the product rule). Next, we find the second derivative, y''(x) = 4[tex]e^x[/tex] + 4[tex]e^x[/tex] + 4x[tex]e^x[/tex], which simplifies to y''(x) = 8[tex]e^x[/tex] + 4x[tex]e^x[/tex]. Setting this equal to zero to solve for x:
0 = 8[tex]e^x[/tex] + 4x[tex]e^x[/tex]
We factor out ex:
0 = [tex]e^x[/tex](8 + 4x)
The exponential function ex is never zero, so we set the remaining factor equal to zero:
0 = 8 + 4x
By solving for x, we find:
x = -2
Therefore, the second derivative of the function y = 4x[tex]e^x[/tex] is equal to zero when x = -2.
Hey can you please help me posted picture of question
since (3/4)^2=3/4•3/4=9/16 what is the value of 2/5^2