Answer:
The possible values are a = -2.5 or a = 4.5.
Step-by-step explanation:
Composite function:
The composite function of f(x) and g(x) is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this case:
[tex]f(x) = 4x^2 - 8x - 20[/tex]
[tex]g(x) = 2x + a[/tex]
So
[tex](f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20[/tex]
Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).
This means that when [tex]x = 0, f(g(x)) = 25[/tex]. So
[tex]4a^2 - 8a - 20 = 25[/tex]
[tex]4a^2 - 8a - 45 = 0[/tex]
Solving a quadratic equation, by Bhaskara:
[tex]\Delta = (-8)^2 - 4(4)(-45) = 784[/tex]
[tex]x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5[/tex]
[tex]x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5[/tex]
The possible values are a = -2.5 or a = 4.5.
Math 120 - 01 Summer 2021
Consuelo Butler
08/07
Homework: Practice
Exam 3
Question 1, 12.1.13
HW Score: 10%, 3 of 30 points
Score: 1 of 1
A professor had students keep track of their social interactions for a week. The
number of social interactions over the week is shown in the following grouped
frequency distribution. How many students had at least 60 social interactions for
the week?
12
Number of Social
Interactions
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
Frequency
9
14
11
15
16
8
7
3
1
1
Step-by-step explanation:
Consuelo Butler
08/07
Homework: Practice
Exam 3
Question 1, 12.1.13
HW Score: 10%, 3 of 30 points
Score: 1 of 1
A professor had students keep track of their social interactions for a week. The
number of social interactions over the week is shown in the following grouped
frequency distribution. How many students had at least 60 social interactions for
the week?
12
Number of Social
Interactions
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
Frequency
9
14
11
15
16
8
7
By calculating the greater than cumulative frequency using the given frequency table, 12 students had at least 60 social interactions for the week.
What is greater than cumulative frequency?The greater than cumulative frequency is also known as the more than type cumulative frequency. Here, the greater than cumulative frequency distribution is obtained by determining the cumulative total frequencies starting from the highest class to the lowest class.
Class interval Frequency Cumulative frequency
30-34 9 85
35-39 14 76
40-44 11 62
45-49 15 51
50-54 16 36
55-59 8 20
60-64 7 12
65-69 3 5
70-74 1 2
75-79 1 1
[We read the cumulative frequencies with respect to the corresponding lower class limits. For example, 85 students had 'more than 30' social interactions, 76 students had 'more than 35 social interactions and so on.]
By reading the greater than cumulative frequency, we find that 12 students had at least 60 social interactions for the week.
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In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠BTA ≅ ∠CTA ∠BAT ≅ ∠CAT
Answer:
Both are true.
Step-by-step explanation:
For the same random sample of adult women, with a sample mean height of x¯=64.3 inches and sample standard deviation of s=2.4 inches, use the Empirical Rule to determine the approximate percent of heights that lie between 59.5 inches and 69.1 inches.
Round your answer to the nearest whole number (percent).
Answer:
95%
Step-by-step explanation:
Mean , xbar = 64.3; standard deviation, s= 2.4
Using the empirical formula where ;
68% of the distribution is within 1 standard deviation from the mean ;
95% of the distribution is within 2 standard deviation from the mean
percent of heights that lie between 59.5 inches and 69.1 inches.
Number of standard deviations from the mean /
Z = (x - μ) / σ
(x - μ) / σ < Z < (x - μ) / σ
(59.5 - 64.3) / 2.4 < Z < (69.1 - 64.3) / 2.4
-2 < Z < 2
Thia is within 2 standard deviations of the means :
2 standard deviation form the mean = 95% according to the empirical rule.
multiply 631.6 by 0.8
Answer: multiply 631.6 by 0.8 = 505.28
double the sum of a number w and 3
Answer:
2(w+3)
Step-by-step explanation:
2(w+3) or 2w+6
A rectangle has a length of 38 meters less than 8 times its width. If the area of the rectangle is 4050 square meters, find the length of the rectangle.
Let
width be x Length=8x-38Area=4050m^2We know
[tex]\boxed{\sf Area =Length\times Width}[/tex]
[tex]\\ \sf\longmapsto x(8x-38)=4050[/tex]
[tex]\\ \sf\longmapsto 8x^2-38x=4050[/tex]
[tex]\\ \sf\longmapsto 8x^2-38x-4050=0[/tex]
By solving[tex]\\ \sf\longmapsto x=\dfrac{81}{4}\:or\:x=25[/tex]
Take x as 25[tex]\\ \sf\longmapsto Length=8x-38=8(25)-38=200-38=162m[/tex]
What is the purpose for post tests?
Answer:
The real reason of post test is to measure it's result in comparison to a pre test and determine d how much student has progressed over a term of instruction.
I'm stuck. Can anyone help please?
log₉(x - 7) + log₉(x - 7) = 1
2 log₉(x - 7) = 1
log₉(x - 7) = 1/2
Take the base-9 antilogarithm of both sides; in other words, make both sides powers of 9:
[tex]9^{\log_9(x-7)} = 9^{1/2}[/tex]
[tex]9^{1/2}[/tex] can also be written as √9 = 3, and [tex]b^{\log_b(a)}=a[/tex], so the equation reduces to
x - 7 = 3
Solve for x :
x = 10
Identify the domain of the graph given below.
Answer:
(-∞,∞) is the domain.
2 is the range
Step-by-step explanation:
HELP! NO SCAMS PLZ, i need to know how to write the proportion.
Answer:
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
4+z/y = 36/18
Step-by-step explanation:
a) Since both triangles are similar triangles, then the ratio of their similar sides is equal to a constant k. Therefore:
16/4 = 18/y
Note that the arrangement depends on which of the triangles sides cones first.
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
b) Same rule in (a) applies to the sum as well. Hence;
4+z/y = 16+20/18
4+z/y = 36/18
Mini wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments
2) Which among the given schemes offers a monthly instalment of less than Rs 5000. ?
a) Scheme A
b) Scheme B
c) Scheme C
d) Both Scheme A and Scheme B
Answer:
Option c, Scheme C
Step-by-step explanation:
scheme A: 45000/6 = 7500 per month
scheme B: 46800/9 = 5200 per month
scheme C: 48000/12 = 4000 per month
-p/3-8=3 what is the variable
Answer:
-33
Step-by-step explanation:
-p/3-8=3
or,(-p-24)/3=3
or,(-p-24)=9
or,-p=33
Therefore, p=-33
The decimal for an irrational number never terminates or repeats. The
rational and irrational numbers together form the set of real numbers.
If false, explair:
Answer:
Step-by-step explanation:
No that is true. I can't make anything more out of it.
Find the dy/dx from
y=3×^2+5×^4 -10
A gardener makes a new circular flower bed. The bed is ten feet in diameter.Calculate the circumference and the area of the circular flower bed
Answer:
It will be 31.4 cm rounded off for circumference
It will be 78.53 cm2 rounded off for area
Step-by-step explanation:
Diameter = 10 cm
Radius = 10/2 cm = 5 cm
Circumference = 2×pi×radius
= 2pi×5
= 31.4 cm
Area = pi × r square
= 25 pi
= 78.53cm2
find the least number that can be divided 9and 12 without leaving remainder
Answer:
By finding LCM of 9 and 12 the answer is 36
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
The sum of two positive integers is 67. When the smaller integer is subtracted from twice the larger, the result is 38. Find the two integers.
Answer:
Step-by-step explanation:
x+y = 67
2x-y = 38
Add the equations together
3x = 108
x = 36
y = 67-x = 31
I’m so confused on this I need help thanks so much!
Answer:
2.5 or 5/2
Step-by-step explanation:
Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines. They are also called vertically opposite angles as they are situated opposite to each other - in other words, separated by the crossing point of the lines and not by the lines themselves.
but that also means they are equal.
8x + 15 = 4x +25
4x = 10
x = 10/4 = 5/2 or 2.5
PLEASE HELP! 50 POINTS
Identify the intervals on which the function is increasing, decreasing or constant. Write your answers in interval notation. Write the end behavior for each function in limit notation.
f(x)=-4x^4+3x^3-2x^2+x-9
(Type a 0 before the decimal to hold the ones place for answers that don't have a value in the ones place. Ex. 0.24)
Use inf for infinity
SOMEONE PLS HELP!!!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 3x + 1
A) This is a polynomial.
B) The base is x + 1.
C) The base is 3.
D) This is not an exponential function because the variable is in the exponent position.
Answer:
Step-by-step explanation:
Is the function f(x) = 3x+1, f(x) = 3ˣ⁺¹, or f(x) = 3ˣ+1 ?
f(x) = 3x+1 is not an exponential function. It is a straight line.
f(x) = 3ˣ⁺¹ Is an exponential function. The base is 3.
f(x) = 3ˣ+1 is an exponential function. The base is 3.
(PLEASE ITS ACTUALLY MY LAST ONE HELP)
Which two figures represent circles of the same size?
A) D and G
B) C and G
C) none of them.
D) C and D
Answer:
B) C and G
Step-by-step explanation:
The radius is equal to 1/2 the diameter
r = 1/2 d
G has a diameter of 45
1/2 (45) = 22.5
C and G are the same
Answer:
c and g!
Step-by-step explanation:
A population of values has a normal distribution with μ= 180.1
and σ=100. You intend to draw a random sample of size n=94
What is the mean of the distribution of sample means?
What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
A sample of size n taken from a normally distributed population with mean µ and standard deviation σ has a sample mean of µ and standard deviation of σ/√n.
So the sample mean would still be 180.1, while the sample standard deviation would be 100/√94 ≈ 10.31.
Let f(x,y) =2x^3 y-xy find the domain
9514 1404 393
Answer:
x, y ∈ all real numbers
Step-by-step explanation:
For your function ...
f(x, y) = 2x^3·y -xy
there appear to be no values of x or y for which the function is undefined. The domain for both x and y is "all real numbers."
Which is the correct label of the line? (1 point)
a
AC
O
CD
D
Ο OllA
Answer:
The correct label of the line is CD
What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101 . . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256 . . .?
Answer:
a.
[tex] \frac{36}{40} [/tex]
The two rectangles have the same perimeters, find the value of x.
Answer:
x = 8ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answer:
x=4
Step-by-step explanation:
2x-2+x+2x-2+x=3+7+3+7
6x-4=20
6x=24
x=4
The rate of change for yyy as a function of xxx is
, therefore the function is
.
For all values of xxx, the function value y\:yy
\:000.
The yyy-intercept of the graph is the function value y=\:y=y, equals
.
When x=1x=1x, equals, 1, the function value y=\:y=y, equals
.
everything seems to be correctly filled.
if you wanted confidence by confirmation: here, take some
It is an exponentially decaying function.
What is an exponential function ?An exponential function is where the independent variable is in the exponent. Generally the the independent variable is in the power of a constant term e.
Exponential functions are of two types one is exponentially growing function and exponentially decaying function.
when the we have a positive exponent the function is exponentially growing and when we have a negative exponent the function is exponentially decaying.
In the given question f(x) = 8e⁻ˣ
when, x = 0 f(x) = 8
f(x) = 8e⁻ˣ
f(0) = 8e⁰
f(0) = 8
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inverse of f(x)=e^(3x-1)
Answer:
f(x) = 3ex - e
Step-by-step explanation:
In this equation we have basically the times e by 3x and -1
so first let's do e times 3x
here...
e X 3x = 3ex
so let's rewrite the equation
3ex - 1
now we times e by 1. (Note - Negative sign stays)
3ex - 1e
we don't have to write 1e cause 1e = e, they are the same.
Therefore the answer is 3ex - 1e
Following are the calculation of inverse:
Given:
[tex]\to f(x)=e^{3x-1}[/tex]
To find:
inverse function=?
Solution:
A function g is the inverse of function F if for [tex]y=f(x), x=g(y)[/tex]
[tex]\to y=e^{3x-1}[/tex]
Replacing the value of x with y
[tex]\to x=e^{3y-1}[/tex]
Solve for [tex]y, x=e^{3y-1}[/tex]
Therefore, the answer is [tex]\frac{\log(x)+1}{3}[/tex].
Learn more about the inverse function:
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(x-1)(x-3)(x+5)(x+7)=297
First simplify the expression into polynomial form,
[tex](x-1)(x-3)(x+5)(x+7)=297[/tex]
[tex]x^4+8x^3-10x^2-104x+105=297[/tex]
[tex]x^4+8x^3-10x^2-104x-192=0[/tex]
Now factor into,
[tex](x-4)(x+8)(x^2+4x+6)=0[/tex]
Which means the solutions are,
[tex]x-4=0\implies\boxed{x_1=4}[/tex]
[tex]x+8=0\implies\boxed{x_2=-8}[/tex]
and then two complex solutions because determinant of the third factor [tex]D\lt0[/tex],
[tex]x^2+4x+6=0[/tex]
[tex]x^2+4x+4=-2[/tex]
[tex](x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}[/tex]
Hope this helps :)
Answer:
x=4
Step-by-step explanation:
(4-1)(4-3)(4+5)(4+7)=297
In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who has a cat also has a dog?
Has a cat Does not have a cat
Has a dog 7 6
Does not have a dog 8 2
