Answer:
f(x) = 3.56(2.04)^x
Step-by-step explanation:
Put x as 2, to see whether the output will be close to 16.
116.4 - 42.8 ln(2) = 86.733301
2.04(3.56)^2 = 25.854144
3.56(2.04)^2 = 14.815296
-42.8 + 116.4 ln(2) = 37.882332
Put x as 3, to see whether the output will be close to 30.
116.4 - 42.8 ln(3) =69.379394
2.04(3.56)^3 = 92.040753
3.56(2.04)^3 = 30.223204
-42.8 + 116.4 ln(3) = 85.07847
Put x as 6, to see whether the output will be close to 271.
116.4 - 42.8 ln(6) = 39.712695
2.04(3.56)^6 = 4152.69615
3.56(2.04)^6 = 256.584846
-42.8 + 116.4 ln(6) = 165.760802
Put x as 7, to see whether the output will be close to 522.
116.4 - 42.8 ln(7) = 33.115046
2.04(3.56)^7 = 14783.598295
3.56(2.04)^7 = 523.433085
-42.8 + 116.4 ln(7) = 183.703941
The exponential function that models the data is f(x) = 3.56(2.04)^x.
The two triangles in the diagram are similar. There are two possible values of x. Work out each of these values. State ALL of your workings out.
Answer:
X = 2
Step-by-step explanation:
Since two triangles ΔACD and ΔABE are similar triangles, their corresponding sides will be proportional.
Therefore, [tex]\frac{\text{AC}}{\text{AB}}=\frac{\text{AD}}{\text{AE}}[/tex]
By substituting the measures of the sides in the expression,
[tex]\frac{(x+10)}{10}=\frac{(15+3)}{15}[/tex]
15(x + 10) = 180
x + 10 = 12
x = 12 - 10
x = 2
Therefore, for the given similar triangles value of x = 2
Angela bought 10 stamps that cost $1 or $1.20.
Altogether, her total was $11. How many of each $1 stamps and how many of
each $1.20 stamps did she buy?
Answer:
Let the first equation be x + y = 10
x = 10 -y
2nd equation will be 1x + 1.2y = 11
Substituting in 2nd equation
(10 - y) + 1.2y = 11
10 - y + 1.2y = 11
.2y = 1
y = 5
If y = 5, x = 5: coz x + y = 10
She have buy 5 stamps of each $1 stamps and 5 stamps of each $1.20 stamps.
What is a linear equation?
A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
Let the first equation be;
x + y = 10
x = 10 -y
2nd equation will be,
1x + 1.2y = 11
Substituting in 2nd equation;
(10 - y) + 1.2y = 11
10 - y + 1.2y = 11
0.2y = 1
y = 5
If y = 5, x = 5:
x + y = 10
Hence, She have buy 5 stamps of each $1 stamps and 5 stamps of
each $1.20 stamps.
Learn more about linear equations;
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justify,All functions are relations,but not all relations are functions
Answer: yes this statement is true All functions are relations,but not all relations are functions.
Step-by-step explanation:
Its true because if you think of it like this
a function is a output and like the inner circle
and relations is the outer circle.
Hope this helps :)
Sandpiper Sightseeing Tours purchased a new van for the business.
On the first trip, Jesse drove 2 hours at an average speed of 55 mph.
How far did Jesse travel?
ANYONE GOOD WITH CALCULUS?! PLEASE HELP ME!!! Use the antiderivative formula shown, where f(u) represents a function. Which function represents f(u)?
Answer: B
Step-by-step explanation:
For this problem, we can use Integration by Parts to find f(u).
∫(ln u) du x=ln u dx=1/u du
dv=du v=u
u(ln u)-∫u(1/u)du
u(ln u)-∫1 du
u(ln u)-u+C
Looking at the placement of f(u), we know that f(u) is u (underlined above).
how many 3/8’s are in 3
Answer: 8 times
Step-by-step explanation:
Youre essentially doing 3 divided by 3/8.
3 is equivalent to 3/1. And when you divide fractions, you have to multiply by the reciprocal. the reciprocal of 3/8 is 8/3.
[tex]\frac{3}{1} *\frac{8}{3} = \frac{24}{3} = 8[/tex]
There are eight (8) 3/8’s are in 3
The number of 3/8’s in 3 can be obtained by dividing 3 by 3/8. That is;3 ÷ 3/8N.B: Due to the division sign, the 3/8 is arranged inversely while the sign changes to multiplication (×) as follows:= 3 × 8/3= 24/3= 8This means that there are eight (8) 3/8’s are in 3.Learn more at: https://brainly.com/question/25353016?referrer=searchResults
On a normally distributed anxiety test with mean 48 and standard deviation 4, approximately what anxiety test score would put someone in the top 5 percent?
Answer:
54.56
Step-by-step explanation:
Given:
Mean, u = 48
Standard deviation, [tex] \sigma[/tex] = 4
Test score = 5%
Required:
Find the raw score, X.
Having a test score of 5% means the Zscore has to correspond to 95%, ie, 1 - 0.05 = 0.95.
Thus, [tex] Z_0_._9_5 = 1.64[/tex]
To get X, use the formula:
[tex] mu + z * \sigma [/tex]
= 48 + (4 * 1.64)
= 48 + 6.56
= 54.56
The anxiety test score that would put someone in the top 5% is 54.56
A firefighter sees a woman trapped in a building 15 feet up from the bottom floor. The firetruck is parked 35 feet away from the bottom of the building. At what angle of elevation, to the nearest degree, should the firefighter extend the ladder to reach the woman?
Answer:
70 degrees
Step-by-step explanation:
Answer:
70 that my answer and so they can reach
Which expression gives the distance between the points (2,3) and (4,-3)?
Answer:
D
Step-by-step explanation:
D is the only answer with the correct distance formula format and the correct numbers inside the parentheses
the area of polygon MNOPQR = area of a rectangle that is 15 square units + area of a rectangle that is ___ square units. (input whole numbers only, such as 8)
im not understanding too well so...please help :/
Answer:
The answer is 2.
Step-by-step explanation:
3 - 2 = 1
7 - 5 = 2
2 x 1 = 2
If HK is an altitude of triangle HIJ, IKH = (4x + 50)º, HIK = 43, and KI = x - 7, find Kl.
Plz help now plz
[tex]answer \\ option \: a \\ 3 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
help me for brainliest answer
Answer:
Step-by-step explanation:
Pattern 6 will have 35
uses
Katherine has 27 cups of yogurt to make smoothies. Each smoothie
1 cup of yogurt. What is the maximum number of smoothies that
Katherine can make with the yogurt?
Answer:
27 smoothies
Step-by-step explanation:
if you have 27 cups and one requires one cup, it would be 27 smoothies Katherine can make :)
I really need help!! I don't get this could someone help me?
Answer:
Side a is 35/5=7 inches long
Side b is 30/5=6 inches long
Side c is 15/5=3 inches long
pls Answer it step by step.
I WILL MARK BRAIN LIST.
Answer:
Step-by-step explanation:
Find the values of a and b such that
x^2 + 3x + 4 = (x + a)^2 + b
URGENT!
*silly answers will be reported
Answer:
a = 1.5
b = 1.75
Step-by-step explanation:
First, we need to solve [tex](x+a)^2[/tex] and replace the result in the initial equation as:
[tex]x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b[/tex]
Then, this equality apply only if the coefficient of [tex]x[/tex] is equal in both sides and the constant is equal in both sides.
It means that we have two equations:
[tex]3x=2ax\\4=a^2+b[/tex]
So, using the first equation and solving for a, we get:
[tex]3x=2ax\\3=2a\\a=\frac{3}{2}=1.5[/tex]
Finally, replacing the value of a in the second equation and solving for b, we get:
[tex]4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75[/tex]
Yummy Cookies just opened a brand new cookie bakery. The baker wants to increase the number of cookies he makes and sells each month. So far, the carrot cake cookie has been the best seller. In January, the baker made 14 of these cookies. In February, the baker doubled the January order, and took 5 cookies home to his family. The baker left the rest of the carrot cake cookies at the bakery to be sold. Every cookie left at the bakery sold. If this pattern continues, how many cookies will the baker sell in March and April?
Answer:
Number of cookies sold in March= 46
Number of cookies sold in April= 92
Step-by-step explanation:
Number of cookies made in Feb= 2×14= 28
Number of cookies sold in Feb= 28-5= 23
Number of cookies sold in March= 2× number of cookies sold in Feb
Number of cookies sold in March= 2× 23= 46
Number of cookies sold in April= 46×2= 92
Find the solutions to x^2=27 A x= +/- 9 √3 B x= +/- 3 √9 C x= +/- 3 √3 D x= +/- 9 √2 FIRST TO ANSWER CORRECTLY GETS BRAINLIEST :-)
Answer:
The answer is C.
Step-by-step explanation:
You have to square both sides :
[tex] {x}^{2} = 27[/tex]
[tex]x = ± \sqrt{27} [/tex]
Then, you have to simplify it :
[tex]x = ± \sqrt{9 \times 3} [/tex]
[tex]x = ±( \sqrt{9} \times \sqrt{3} )[/tex]
[tex]x = ±( 3 \times \sqrt{3} )[/tex]
[tex]x = ±3 \sqrt{3} [/tex]
Answer:
Option C) x = ±[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
=> [tex]x^2 = 27[/tex]
Taking sqrt on both sides
=> x = ±[tex]\sqrt{27}[/tex]
=> x = ±[tex]\sqrt{3 * 3*3}[/tex]
=> x = ±[tex]3\sqrt{3}[/tex]
What is the equation of the line shown written in slope-intercept form?
y = -2
y = 2
x = 2
Answer:
The equation of the line is y = 2.
Step-by-step explanation:
When a line is horizontal, it's gradient will be 0. So you have to substitute the coordinates into the equation, y = mx + b, to find the b :
[tex]y = mx + b[/tex]
[tex]let \: m = 0 \\ let \: x = 5 \\ let \: y = 2[/tex]
[tex]2 = 0(5) + b[/tex]
[tex]b = 2[/tex]
[tex]y = 2[/tex]
Answer:
it would be Y=2 as it's a horizontal line at y=2
Given the directrix of y = -1 and focus of (0, 3), which is the equation of the parabola?
Answer:
[tex]y=\dfrac{1}{8}x^2+1[/tex]
Step-by-step explanation:
Since the vertex is right between the vertex and the directrix, the y value of the vertex must be (3+(-1))/2=1. The x coordinate will just be the same as that of the focus, or in this case 0. This means that the vertex will be at (0,1). Since the graph opens toward the focus, it will be opening up, and since its vertex is at (0,1), it will have an equation of:
[tex]y=\dfrac{1}{8}x^2+1[/tex]
Hope this helps!
Answer:
y = one eighth x^2 + 1
Step-by-step explanation:
i took the test and got it right
Please I need help, DONT SKIPP
Answer:
P(Take the bus | Sophomore) = 0.83
Step-by-step explanation:
For a conditional probability (As given in the example),
P(A|B) is read as,
"The probability of event A occurring given that event B has occurred"
Here event A = Sophomore take a bus
Event B (occurred) = (Drive to school + Take the bus + Walk)
Therefore, P(Take a bus | Sophomore) = [tex]\frac{25}{(2+25+3)}[/tex]
= [tex]\frac{25}{30}[/tex]
= 0.833
≈ 0.83
P(Take the bus | Sophomore) = 0.83 will be the answer.
Convert 2 3/4 to a decimal number.
Answer:
2.75
Step-by-step explanation:
3/4 is .75 in decimal
Can somebody help me with this ?? :)
Answer:
Step-by-step explanation:
You need the value of one of angles. If height angle is 90°, then you have 2 90° angles. So you have 2 triangles SAS.
I hope I've helped you.
Find X to the nearest tenth
A 14.4
B 4.8
C 1.7
D 9.4
Answer:
Step-by-step explanation:
The 2 smaller triangles are proportionate to one another because they are 2 parts of the same larger triangle. Setting up the proportion, one triangle at a time:
[tex]\frac{x}{8.3} =\frac{11.6}{6.7}[/tex] and cross multiply to get
6.7x = 96.28 so
x = 14.37 or 14.4, choice A.
The transformation from the function f (x)=3x to the function f(x)=3x+4 indicates
Answer:
Moving 4 to the right on the x axis
Step-by-step explanation:
Please help me………………………
The square root of 81/625 = 0.36
The square root of x^2 = x
The square root of y^2 = y
25 x 0.36 = 9
X *x = x^2
Y*y = y^2
Final answer = 9x^2y^2
Answer:
The answer is option d. 9x²y²
Step-by-step explanation:
25xy√81/625x²y²
= 25xy × 9/25xy
= 9x²y²
Hope this helps.
*WILL MARK YOU BRAINLIEST!!!*
Answer:
C.
Step-by-step explanation:
Look at the image
b) give reasons for your answer
Answer:
80° is the correct answer
Step-by-step explanation:
The angle B is 100° because of the property of the vertically opposite angle.
As we know the property consecutive interior angle that the sum of two angle is 180°
So
Angle B + Angle X =180°
100 °+ Angle X =180°
Angle X=180°-100°
Angle X = 80°
An increase in walking has been shown to contribute to a healthier life-style. A sedentary American takes an average of 5000 steps per day (and 65% of Americans are overweight). A group of health-conscious employees of a large health care system volunteered to wear pedometers for a month to record their steps. It was found that a random sample of 40 walkers took an average of 5430 steps per day, and the population standard deviation is 600 steps. At = 0.05 can it be concluded that they walked more than the mean number of 5000 steps per day?
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 5000
For the alternative hypothesis,
H1: µ > 5000
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 5000
x = 5430
σ = 600
n = 40
z = (5430 - 5000)/(600/√40) = 4.53
Looking at the normal distribution table, the probability corresponding to the z score is < 0.0001
Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, at a 5% level of significance, it can be concluded that they walked more than the mean number of 5000 steps per day.
Since the margin of error is 0.11, it can't be concluded that they walked more than the mean number of 5000 steps per day.
Standard deviationGiven that it was found that a random sample of 40 walkers took an average of 5430 steps per day, and the population standard deviation is 600 steps, to determine if at = 0.05 can it be concluded that they walked more than the mean number of 5000 steps per day the following calculation must be made:
5430 = 100600 = X600 x 100 / 5430 = X60000 / 5430 = X11.04 = XTherefore, since the margin of error is 0.11, it can't be concluded that they walked more than the mean number of 5000 steps per day.
Learn more about standard deviation in https://brainly.com/question/12402189
Find the slope of a line passing through the points (5,-5) and (7,3)
Answer:
The slope of the line passing through the points (5, -5) and (7,3) is 4 . Use the slope formula to find the slope.