Using an exponential function, it is found that f(7.5) = 45.5.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the rate of change.For this problem, we have that f(3.5) = 12, then:
[tex]y = ab^x[/tex]
[tex]12 = ab^{3.5}[/tex]
[tex]a = \frac{12}{b^{3.5}}[/tex]
We also have that f(9) = 75, then:
[tex]y = ab^x[/tex]
[tex]75 = ab^9[/tex]
Since [tex]a = \frac{12}{b^{3.5}}[/tex]:
[tex]75 = \frac{12}{b^{3.5}} \times b^9[/tex]
[tex]b^{5.5} = \frac{75}{12}[/tex]
[tex]\sqrt[5.5]{b^{5.5}} = \sqrt[5.5]{\frac{75}{12}}[/tex]
[tex]b = \left(\frac{75}{12}\right)^{\frac{1}{5.5}[/tex]
b = 1.39542165
Then:
[tex]75 = ab^9[/tex]
[tex]a = \frac{75}{1.39542165^9}[/tex]
a = 3.7386
Hence:
[tex]y = 3.7386(1.39542165)^x[/tex]
When x = 7.5, we have that:
[tex]y = 3.7386(1.39542165)^{7.5} = 45.5[/tex]
Hence f(7.5) = 45.5.
More can be learned about exponential functions at https://brainly.com/question/25537936
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2/4 - 1/4 please hep i know im not that good
for asking this
The area of one face of a cube is 25 square centimeters. What is the volume, in cubic centimeters, of the cube?
Answer:
125 cubic cm
Step-by-step explanation:
Length^2 = 25 so each side length is 5cm
5^3 = 125 cubic cm
(b)
In how many months will Rs 4800 amount to Rs 5760 at 2 paisa per rupee per
month?
Answer:
This amount will be reached in 1 year and 2 months, that is, in 14 months.
Step-by-step explanation:
Given that 1 paisa is 1 cent of a rupee, at an increase of 2 paisa per rupee per month we are talking about an interest of 2% per month, which annualized is equal to 24% per year (12 x 2).
Thus, given that the initial amount is Rs $ 4800, to determine the period of time in which said interest will take the amount to Rs $ 5760 it is necessary to perform the following calculation:
4800 x 1.02 x X = 5760
4896 x X = 5760
X = 5760/4896
X = 1.17
Thus, this amount will be reached in 1.17 years, with which to calculate the number of months the following calculation must be performed:
1 = 12
0.17 = X
0.17 x 12 = X
2 = X
Thus, this amount will be reached in 1 year and 2 months, that is, in 14 months.
A hexagon can be divided into 4 non-overlapping triangles. Which is the sum of the interior angles of a hexagon?
Answer:
12
Step-by-step explanation:
4 time 3 =12
Why is it reasonable to use the same units to describe circles and measure of angles?
Answer:
The more familiar unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°.
Explanation:
The unit circle, or trig circle as it's also known, is useful to know because it lets us easily calculate the cosine, sine, and tangent of any angle between 0° and 360° (or 0 and 2π radians)
Drag steps into order to correctly solve the equation x−27=62 for x.
Answer:
x - 27 + 27 = 62 + 27
x - 0 = 89
(annex rule)
x = 89
Step-by-step explanation:
please mark brainlist
x^2 and -x^2 for x =-3
Answer:
9 and -9
Step-by-step explanation:
x^2:
all you have to do is (-3)^2 = -3 * -3 = 9
-x^2:
this would be -(-3)^2
the order of operations says to do exponents first, so you would have:
-(9) or -9
What is 288/-32 in its standard form
Answer:
[tex] \frac{288}{ - 32} = \frac{ - 9}{1} \\ = - 9[/tex]
Answer:
the simplest form of 288/-32 is 91.
Step-by-step explanation:
hope this helps sorry if im wrong
Please Help, 20 points and brainiliest, URGENT.
Answer:
Step-by-step explanation:
∠ACB and ∠ECD are vertical angles, so ∠ACB = ∠ECD.
∠D = ∠B
∠A = ∠E
△ABC and △EDC are similar because they have the same angles.
1. The temperature of a body rises from -6°c to 5°c. By how much degrees does it rises?
when doing the increasing function do we use the exact point?
Answer:
Step-by-step explanation:
According to www.cliffsnotes.com it says: The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.
Hope this helps!!
Write an equation of the line in point-slope form that passes through the given points.
(1,5) and (-5,4)
Answer:
y-5=1/6(x-1)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-5)/(-5-1)=-1/-6=1/6
slope is 1/6
y-y1=m(x-x1)
y-5=1/6(x-1)
Help pls asap I really need help this is confusing
solve
1. 1/3n=4
what is n?
Define Love in 10 words. Don't me with this question rn XD
Answer:
uh...love is when you feel a certain way around someone
Step-by-step explanation:
Calcula el área de los rombos.
Answer:
xbxbkzkdkdjd
Step-by-step explanation:
bz va yJnzz
What is the growth?
What is figure 0?
Y=( )X+( )
Can someone help me too those answers I have no clue
Answer:
Figure 0 = 67 Square Units
Step-by-step explanation:
Its correct, I took the test!
12.5(7) + 11.9(8)=?
Answer:the answer is 182.7
Step-by-step explanation:brainliest please Sans Undertale out
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20 PTSS !!!
PLEASE HELPP !!
Because it is extremely hard to find the area of this figure all together, it would be in our best interest to split this figure up into three different pieces: the two horizontal rectangles, and the verticle rectangle. We can find the area of all three and add them up. Be aware that there are two different ways that you can break this figure up, As shown in the attachments. I will be using the first image (the one with the tall horizontal rectangles, NOT the almost-squares).
So, we see that we have enough information to solve for the area of the left-most rectangle. Area = lw. 10 x 4 = 40, so the area is 40. Next, we have to notice, that the horizontal rectangles are also the same, so both of the areas of the two horizontal rectangles are 40.
Now, we can find the middle rectangle. We know that the length of the entire thing is 18, but it is taken up by 8 (4+4) of the horizontal triangles, so 18-8=10, so the length Is 10. We also know that the height of the horizontal rectangles is 10, so 10-3=7. Our dimensions for the rectangle are 10x7 or 70 square units. If we add them all together, 40+40+70=150.
The area is 150 square units
5th grade math. Correct answer will be marked brainliest.
please help with my math homework
Answer:
sorry for that
Step-by-step explanation:
image is so unclear can't even read
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1051 and a standard deviation of 194. Scores on the ACT test are normally distributed with a mean of 19 and a standard deviation of 4.7. It is assumed that the two tests measure the same aptitude, but use different scales.
Required:
a. If a student gets an SAT score that is the 62-percentile, find the actual SAT score.
b. What would be the equivalent ACT score for this student?
c. If a student gets an SAT score of 1563, find the equivalent ACT score.
Answer:
The answer is "1110, 20.4, and 31.408"
Step-by-step explanation:
For point a:
Given:
[tex]\to mean\ ( \bar{x})=1051\\\\\to standard \ deviation \ (\sigma)=194\\\\\to P(Z<=z)=0.62\\\\\to z=0.3055\\[/tex]
Calculating the SAT score:
[tex]=1051+0.3055 \times 194 \\\\ =1110.267 \approx 1110[/tex]
For point b:
Given:
[tex]\to mean \ \bar{x}=19\\\\ \to standard \ deviation \ (\sigma) =4.7\\\\[/tex]
Calculating the equivalent ACT score:
[tex]=19+0.3055 \times 4.7 \\\\ =20.43585 \approx 20.4[/tex]
For point c:
[tex]\to SAT \ Score =1563\\\\\to z=\frac{(1563-1051)}{194}= \frac{512}{194}=2.64\\\\[/tex]
Calculating equivalent ACT score:
[tex]=19+2.64 \times 4.7 \\\\=31.408[/tex]
Which expression is equivalent to 7m + 5 + 6 + 3m?
A. 13m + 8
B. 10m + 11
C. 4m + 11
D. 4m + 8
PLEASE HELP ASAP
Answer:
B.10m + 11
....................
which integer is 3 less than 7
Answer:
b
Step-by-step explanation:
When a system of linear equations has no solution the graph will
a - have parallel lines
b- be the same line
c- have intersecting lines
Answer:
A
Step-by-step explanation:
there is no intersection which means no solution...i dont knwo how to explain sorry
What is the 8th term of the sequence 12, 17, 22, 27, 32,…?
A. 47
B. 42
C. 52
D. None of these choices are correct.
Answer:
A. 47
Step-by-step explanation:
Hope it helps! If you want an explanation, ask in the comments and I'll give you one!
A circular plate has circumference 22 inches. What is the area of this plate? Use 3.14 for it.
The area of this plate is about square inches.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest
thousandth as needed.)
Answer:
38.5 in squared
Step-by-step explanation:
Ally bought 5 different cakes for her birthday. His friends ate 3 1/4 of the amount of cake. Then he gave 1/2 of the cake to his grandmother. How much cake does Ally have left?
Answer:
7/8 of a cake
Step-by-step explanation:
4 4/4 - 3 1/4 = 1 3/4
7/4 x 1/2 = 7/8
Can the triangles be proven similar by AA?
Question options:
A)
No, similar triangles cannot contain a pair of parallel lines.
B)
Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).
C)
Yes, because || .
D)
No, the triangles contain no angles marked congruent.
Answer:
No, similar triangles cannot contain a pair of parallel lines. Yes, because || . Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).
Step-by-step explanation:
Yes, because ∠QUR ≅ ∠TUS (vertical angles) and ∠R ≅ ∠S (alternate interior angles).
What is similarity?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Both triangles are similar as,
∠QUR ≅ ∠TUS (vertical angles)
∠R ≅ ∠S (alternate interior angles).
So, By AA similarity criteria triangles are similar.
Learn more about similarity here:
https://brainly.com/question/17170212
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A study is done by a community group in two neighboring colleges to determine which college graduates students with more math classes. College A samples 11 graduates. Their average is 4 math classes with a standard deviation of 1.5 math classes. College B samples 9 graduates. Their average is 3.5 math classes with a standard deviation of 1 math class. The community group believes that a student who graduates from college A has taken more math classes, on the average. Test at a 1% significance level.
A. Is this a test of two means or two proportions? Are the populations dependent or independent?
B. Are the populations' standard deviations known or not?
C. Which distribution is to be used?
D. What is random variable?
E. Hypothesis
F. Test is two tailed or one tail
G. Test value=_____.
H. Use P-value method) to reach to the conclusion.
Answer:
A) It is a test of two proportions and the populations are independent of each other
B) The population standard deviations are known : For college A the standard deviation is = 1.5 while for College B population the standard deviation is 1
C) The distribution to be used is 1 distribution
D) The Random variable is the size of the community group
E) Hypothesis : H0 : u1 = u2 . Ha : u1 > u2
F) Test is one tailed
G) Test Value > significance level
F) when; P value > significance level ( 0.01 ) we do accept Null hypothesis
when ; P value < significance level ( 0.01 ) we reject Null hypothesis
Step-by-step explanation:
College A :
sample size = 11
x ( mean ) value = 4
std = 1.5
College B :
sample size = 9
x ( mean value ) = 3.5
std = 1
A) It is a test of two proportions and the populations are independent of each other
B) The population standard deviations are known : For college A the standard deviation is = 1.5 while for College B population the standard deviation is 1
C) The distribution to be used is 1 distribution
D) The Random variable is the size of the community group
E) Hypothesis : H0 : u1 = u2 . Ha : u1 > u2
F) Test is one tailed
G) Test Value > significance level
F) when; P value > significance level ( 0.01 ) we do accept Null hypothesis
when ; P value < significance level ( 0.01 ) we reject Null hypothesis