Find the equation for the exponential function that passes through the points (4, 3) and (7, 8).
Answers
Given:
The exponential function is expressed as,
\(f(x)=ab^x\)Put the point (4,3) in the above function,
\(\begin{gathered} \text{Let,y}=ab^x \\ 3=ab^4\ldots\ldots\ldots.\ldots..(1) \end{gathered}\)Put the point (7,8),
\(8=ab^7\ldots.\ldots(2)\)Solve equation (1) for a,
\(\begin{gathered} 3=ab^4 \\ a=3b^{-4} \\ \text{Put it in equation (2)} \\ 8=ab^7 \\ 3b^{-4}b^7=8 \\ b^3=\frac{8}{3} \\ b=\frac{2}{\sqrt[3]{3}} \end{gathered}\)The equation (1) becomes,
\(\begin{gathered} 3=ab^4 \\ 3=a(\frac{2}{\sqrt[3]{3}})^4 \\ 3=a\times\frac{2^4}{3^{\frac{4}{3}}} \\ a=\frac{3\times3^{\frac{4}{3}}}{2^4} \\ a=0.8113 \end{gathered}\)So, the exponential function is,
\(\begin{gathered} f(x)=ab^x \\ f(x)=0.8113(\frac{2}{\sqrt[3]{3}})^x \\ f(x)=0.8113(1.3867)^x \end{gathered}\)Answer:
\(f(x)=0.8113(1.3867)^x\)Related Questions
-4y-4+(-3) what is my answer?
Answers
Given data:
The given expression is -4y-4+(-3).
the given expression can be written as,
-4y-4+(-3)=-4y-4-3
=-4y-7
Thus, the given expression can be written as -4y-7.
Factor 4x^2+29x+30=0
Answers
Answer:
= − 5 /4
= − 6
Step-by-step explanation:
Use the sum-product pattern
4 ^2 + 2 9 + 3 0 = 0
4x^2+29x+30=0
4x2+29x+30=0
4 ^2 + 2 4 + 5 + 3 0 = 0
Rewrite in factored form
4 ( + 6 ) + 5 ( + 6 ) = 0
4x(x+6)+5(x+6)=0
4x(x+6)+5(x+6)=0
(4 + 5 ) ( + 6 ) = 0
Solution:
= − 5 /4
= − 6
Step-by-step explanation:
4x^2 × 30 = 120x^2
120x^2 = 24x x 5x
(4x^2) + (24x) + (5x) +30 =0
4x(x+6) + 5(x+6) =0
(4x +5) + (x+6) =0
4x + 5 = 0 , x+6=0
XE = ( -5/4, -6)
Maria has 8 more scarves than Lucy Lucy has 8 scarves. How many scarves does Maria have, write an equation?
Answers
The equation M = 8 + 8 represents the given information. Maria has 16 scarves.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's let "M" represent the number of scarves that Maria has.
According to the problem, "Maria has 8 more scarves than Lucy." We know that Lucy has 8 scarves. So, Maria has 8 more than that.
We can represent this information in an equation:
M = 8 + 8
We add 8 to Lucy's 8 scarves to get the total number of scarves that Maria has, which is 16.
So, Maria has 16 scarves.
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The required Maria has 16 scarves, and the expression models the situation is given as M = 8 + L.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let's use the variable "M" to represent the number of scarves that Maria has. Since Maria has 8 more scarves than Lucy, and Lucy has 8 scarves, we can write an equation as,
M = 8 + L
where L is the number of scarves that Lucy has. Substituting L = 8 into this equation, we get:
M = 8 + 8
M = 16
Therefore, Maria has 16 scarves.
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4. Calculate the Social Security and Medicare tax that would be applied to an annual salary of $56,400.
Answers
Answer:759
Step-by-step explanation:
If DF=9x-39, find EF
Answers
Answer:
\(EF = 58\)
Step-by-step explanation:
Given
\(DF = 9x - 39\)
\(DE = 47\)
\(EF = 3x + 10\)
See attachment
Required
Find \(EF\)
Because E is a point between D and F, then:
\(DF = DE + EF\)
Substitute values for DF, DE and EF
\(9x - 39 = 47 +3x + 10\)
Collect Like Terms
\(9x -3x = 47 +39 + 10\)
\(6x = 96\)
Make x the subject
\(x = \frac{96}{6}\)
\(x = 16\)
Recall that:
\(EF = 3x + 10\)
Substitute 16 for x
\(EF = 3 *16 + 10\)
\(EF = 48 + 10\)
\(EF = 58\)
i need help in what to put this and to understand pls
Answers
Answers:
1st box: -2
2nd box: 6
==================================================
Explanation:
To find the x intercepts, we replace f(x) with 0 and solve for x.
f(x) = -(x+1)(x-3)(x+2)
0 = -(x+1)(x-3)(x+2)
-(x+1)(x-3)(x+2) = 0
x+1 = 0 or x-3 = 0 or x+2 = 0
x = -1 or x = 3 or x = -2
-------------
To find the y intercept, we plug in x = 0 and simplify.
f(x) = -(x+1)(x-3)(x+2)
f(0) = -(0+1)(0-3)(0+2)
f(0) = -1*(-3)*(2)
f(0) = 6
We can confirm these answers with a graph. See below. I used GeoGebra, but Desmos is another good option.
Need ANSWER ASAP
Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1
a) Graph the five key points of Parent function on the provided grid.
b) State the following for the transformed function
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=
c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)
Answers
Answer:
See explanation below.
Step-by-step explanation:
Given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Part (a)The parent function of the given function is: y = sin(x)
The five key points for graphing the parent function are:
3 x-intercepts → (0°, 0) (180°, 0) (360°, 0)maximum point → (90°, 1)minimum point → (270°, -1)(See attachment 1)
Part (b)Standard form of a sine function:
\(\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}\)
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shift (axis of symmetry: y = D)Therefore, for the given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Amplitude = -2Period = 2π/2 = πPhase shift = 45° to the rightEquation of axis of symmetry: y = 1Part (c)See attachment 2.
![Need ANSWER ASAPConsider the following transformed functiony = 2 Sin [2( 45)] + 1a) Graph the five key](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/rHmvQCSFzLuN7xkVIxhNC3hToKfYa2ZX.png)
![Need ANSWER ASAPConsider the following transformed functiony = 2 Sin [2( 45)] + 1a) Graph the five key](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/RTeQ1nKnPwOJZpxZH6e5ecn6PqRfr3g0.png)
Isabel is mailing back packages.each small package cost her $3.30 to send each large package cost her $4.10. How much will it cost her to send 7 small packages and 1 large package??l
Answers
Answer:
$27.20 is the answer. just multiply and then add
Answer:
It will cost her $23.1 to send the little packages and, $4.10 to send one big package.
Step-by-step explanation:
Its very easy multiply the cost which is $3.30 times the amount which is 7 and that your answer $23.1. Than do the same for the big package multiple $4.10 times 1 and you get $4.10.
What is the solution to the system of equations graphed below?
Answers
I’m giving points pls answer quickly (don’t send me a link pls just tell me answer)
Answers
Answer:
15,000 feet cubed
Step-by-step explanation:
15 x 15 = 225
10 x 15 = 150
150 / 2 = 75
225 = 75 = 300
300 x 50 = 15,000 feet cubed
Answer:
15000 ft^3
Step-by-step explanation:
You said you just wanted the answer so I won't explain in depth but let me know if you want an in depth explanation.
15*15=225
225*50= 11250
10*15=150
150/2=75
75*50=3750
11250+3750= 15000
Answer: 15000ft^3
A study was conducted on the educational level of patients with AIDS, it was asume that
with ten years of education will be in group A, between 10 and 20 group B and between 20
group C. After the analysis it was realized that group A had 100 persons while group B and C had 30 persons
(a) If you decide to select based on proportion of 10% from each group how many patien
selected from each group. Show your calculation.
(b) What name can be given to the classified groups?
(c) What method of sampling was employed in the selection process?
1. State and explain the three major data collection techniques.
What is a variable?
What is a Parameter?
Answers
A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.
Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.
(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.
(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.
(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.
The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.
The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.
A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.
Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.
A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.
Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.
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write a definite integral that represents the area of the region. (do not evaluate the integral.) y1
Answers
The definite integral represents the area of the region ∫(x²-3x)dx.
The definite integral is the region beneath the curve of y1 = x2 - 3x between its first intersection with y2 = 0 and its subsequent intersection with y2 = 0. The curve looks like this:
In order to find their intersection, we equalize them:
x2 - 3x = 0
x(x - 3) = 0
x = 0 and x = 3.
Thus, the integral is:
∫(x²-3x)dx
The area lies below the x-axis, hence the result will be negative (see graph). I would argue that we should take this integral's absolute value in order to arrive at the correct answer for the region's area as we are asked to calculate it. Just place absolute value indications all around the integral.
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Which statement about converting metric units of measurement is true? Use the metric table to help answer the question,kilo1,000hecto100deka10Metric Tableunit1deci-0.1centi0.010.001To find the number of centigrams in 34 dekagrams, divide 34 by 1,000,To find the number of hectograms in 4.5 kilograms, multiply 4.5 by 10.To find the number of grams in 81 milligrams, multiply 81 by 1,000.To find the number of dekagrams in 15.6 hectograms, divide by 10.
Answers
The answer is the last option
translate & solve: 616% of what number is 4620
Answers
Answer:
250
Step-by-step explanation:
1540*100 divided by 616
pls help :p i’m stuck
Answers
Answer:
x = 7
Step-by-step explanation:
Answer:
x= 1
Step-by-step explanation:
Add four to both sides of the equation:
10x-4+4 = 2x+4+4
Simplify:
10x = 2x+8
Subtract 2x from both sides:
8x = 8
Cancel out terms:
x=
Simplify:
x=1
Find m
∠
J
L
K
∠JLK.
Answers
Answer:
m∠JLK° = 62°
Step-by-step explanation:
∠JLK = ∠KJL
SO
56°+2(∠JLK)° = 180°
2(∠JLK)° = 180-56
2(∠JLK)° = 124
∠JLK° = 62°
so m∠JLK° = 62°
Answer:
m∠JLK = 62°
Step-by-step explanation:
180 - 56 = 124
124 ÷ 2 = 62
PLEAS ANSWER ASAP I WILL GIVE BRIAINLYIST
The coordinates of the vertices of a polygon are (-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1).
What is the perimeter of the polygon to the nearest tenth of a unit?
A.16.0 units
B.17.2 units
C.15.4 units
D.18.8 units
Answers
The perimeter of the polygon, with the specified coordinate points , found using Pythagorean Theorem iis approximately 16 units
What is the Pythagorean Theorem?The Pythagorean Theorem indicates that the square of the distance between points on the coordinate plans is the sum of the square of the horizontal and vertical distances between the point.
The coordinates of the vertices of the polygon are;
(-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1)
The length of the sides are therefore;
3 - 1 = 2,
√((-1 - (-3))² + (5 - 3)²) = 2·√2
√((2 - (-1))² + (4 - 5)²) = √(10)
4 - 1 = 3
2 - (-3) = 5
The perimeter is therefore;
2 + 2·√2 + √(10) + 3 + 5 ≈ 16
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Simplify Please
-2a +a + 7 - 5
Answers
Answer:
-a+2
Step-by-step explanation:
-2a+a+7-5
=-a+2
Answer: -a + 2
Step-by-step explanation:
-2a+a+7-5
(Order of Operations! PEMDAS)
-2a+a= -a
-a+7-5=-a+2
-a+2
What is the measure of angle ABC
Answers
Answer:
D
Step-by-step explanation:
\(m\angle EBD=33^{\circ} \implies m\angle EBC=33^{\circ} \\ \\ \therefore m\angle DBC=m\angle EBD+m\angle EBC=66^{\circ} \\ \\ m\angle DBC=66^{\circ} \implies m\angle ABD=66^{\circ} \\ \\ \therefore m\angle ABC=m\angle ABD+m\angle DBC=132^{\circ}\)
answer this please!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
200
Step-by-step explanation:
\(a^{2}\) + \(b^{2}\) = \(c^{2}\)
\(120^{2}\) + \(160^{2}\) = \(c^{2}\)
14400 + 25600 = \(c^{2}\)
40000 = \(c^{2}\)
\(\sqrt{40000}\) = \(\sqrt{c^{2} }\)
200 = c
Jesus love you.
1/8 expressed as a percentage is
Answers
Answer:
The answer is 12.5%
Step-by-step explanation:
Hope this helped!
Answer:
12.5%
Step-by-step explanation:
Divide 1 by . Therefore, the fraction 18 is equivalent to 12.5% .
Help PLSSSSSSS If you can now
Answers
Answer:
its the 3rd option not the second
Step-by-step explanation:
can i get help please
Answers
Answer:
20
Step-by-step explanation:
side BC = side AB
so their base angles that is ∠A = ∠C = (3x+20)°
now, total measure of the angles of a triangle is 180° & ∠B = x°
Now,
m∠A + m∠B + m∠C = 180
⇒ 3x + 20 + x + 3x + 20 = 180
⇒ 7x + 40 = 180
⇒ 7x = 140
⇒x = 20
A vet is preparing a diet for a group of dogs. Each serving should be no larger than 8
ounces and must contain at least 29 units of Nutrient I and at least 20 units of Nutrient II.
The diet will be prepared from a combination of 2 brands, brand A and brand B. Each ounce
of brand A contains 3 units of Nutrient I and 4 units of Nutrient II. Each ounce of brand B
contains 5 units of Nutrient I and 2 units of Nutrient II. Brand A costs 3 cents/ounce and B
costs 4 cents/ounce. Determine how many ounces of each brand of dog food should be used
per serving in order to meet the given requirements at a minimum cost.
Answers
Swornima is an unmarried nurse in a
hospital. Her monthly basic salary is Rs
48,000. She has to pay 1% social
security tax on her income up to Rs
5,00,000 and 10% income tax on Rs
5,00,001 to Rs 7,00.000. She gets 1
months' salary as the Dashain
allowance. She deposits 10% of her
basic salary in Citizen Investment Trust
(CIT) and gets 10% rebate on her
income tax. Answer the following
questions. (i) What is her annual
income? How much tax is rebated to
her? (iii) How much annual income tax
should she pay?
Answers
To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:
Monthly basic salary: Rs 48,000
Social security tax rate: 1%
Income tax rate on income up to Rs 5,00,000: 0% (no tax)
Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%
Dashain allowance: 1 month's salary
Deposit in Citizen Investment Trust (CIT): 10%
Rebate on income tax: 10%
(i) Annual Income:
Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:
Annual Basic Salary = Monthly Basic Salary x 12
= Rs 48,000 x 12
= Rs 5,76,000
Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:
Annual Income = Annual Basic Salary + Dashain Allowance
= Rs 5,76,000 + Rs 48,000
= Rs 6,24,000
Swornima's annual income is Rs 6,24,000.
(ii) Tax Rebate:
Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.
(iii) Annual Income Tax:
First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.
Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000
= Rs 1,24,000
Income Tax in this range = Taxable Income x Tax Rate
= Rs 1,24,000 x 0.1
= Rs 12,400
Now, let's calculate the total annual income tax:
Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000
= Rs 12,400
Next, we calculate the rebate on income tax:
Tax Rebate = Total Annual Income Tax x Rebate Rate
= Rs 12,400 x 0.1
= Rs 1,240
Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.
To summarize:
(i) Swornima's annual income is Rs 6,24,000.
(ii) Swornima's tax rebate is Rs 1,240.
(iii) Swornima should pay an annual income tax of R
If a right triangle has a hypotenuse of length 20 units and one leg of length 16 units, find the length of the other leg. A. 12 B. 656 C. 384 D. 36
Answers
Answer:
12
Step-by-step explanation:
Use the Pythagorean theorem which is a^2 + b^2 = c^2
c is hypotenuse and a and b are the legs
we need to find a^2 so
a^2 + 16^2 = 20^2
a^22 + 256 = 400
then subtract 256 from 400
a^2 = 144
square root 144
= 12
Answer:
12 units
Step-by-step explanation:
Find the weight in pounds of a 390 gram person.
Answers
Answer:
0.86 pound
Step-by-step explanation:
i just asked google:))
in an experiment to learn whether substance m can help restore memory, the brains of 20 rats were treated to damage their memories. first, the rats were trained to run a maze. after a day, 10 rats (determined at random) were given substance m and 7 of them succeeded in the maze. only 2 of the 10 control rats were successful. the two-sample z test for the difference in the true proportions. Gives z= 2.25, P< 0.02
Answers
The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
What is probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.
This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).
In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.
Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
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Please Help......If you were to flip a coin 60 times, how many times would you expect the coin to land on heads?
Answers
Answer:
30
Step-by-step explanation:
Again there are TWO sides so it would be 50% chance of getting head, or 50% of getting tail. So it would probably be 30
Answer:
"50% of the time"
Step-by-step explanation:
Because the probability is limited to only 2 sides you have a 50% chance it will land on either heads, or tails.
The average person burns approximately 221 calories per half-hour while bicycling. If a person
does 2 hours of bicycling per day then how many calories will they burn in a week if they work
out 5 days a week?