The graph of an exponential function passes through (1, 10) and (4, 80). Find the function that describes the graph.
Answer:
y = 5*2ˣStep-by-step explanation:
Exponential function:
y = abˣOrdered pairs given:
(1, 10) and (4, 80)Substitute x and y values to get below system:
10 = ab80 = ab⁴Divide the second equation by the first one and solve for b:
80/10 = b³b³ = 8b = ∛8b = 2Use the first equation and find the value of a:
10 = a*2a = 5The function is:
y = 5*2ˣAnswer:
[tex]y=5 \cdot 2^x[/tex]
Step-by-step explanation:
An exponential function is written in the form:
[tex]y=ab^x[/tex]We can use the given points that the exponential function passes through to solve for a and b.
Create a system of equations by substituting (1, 10) and (4, 80) into the exponential form of a function.
[tex]\text{I}:\ 10=ab^1[/tex] [tex]\text{II}: \ 8 0=ab^4[/tex]Divide Equation I by Equation II in order to cancel out variable a.
[tex]\displaystyle \frac{80=ab^4}{10=ab}[/tex][tex]8=b^3[/tex][tex]b=2[/tex]Now we can solve for a by substituting b back into either equation from the system of equations.
[tex]10=ab[/tex] [tex]10=a(2)[/tex] [tex]a=5[/tex]Substitute 5 for a and 2 for b into the form of an exponential function to find the exponential function that passes through (1, 10) and (4, 80).
[tex]y=5 \cdot 2^x[/tex]y = 5 · 2ˣ is the exponential function that describes the graph.
Help me with my math
Answer:
The first one is correct
Step-by-step explanation:
-3<1-1 - 3<0 correct
-3>1 it is not correct
HELPP PLZZZZZZZZZZ tand thanks
Using the pattern rule, find the missing
value in the table.
y = x + 8
input X 1
output y 9
2 3 4
10 | 11 | [?]
Enter the number that belongs in the green box.
Enter
Answer:
y=12
Step-by-step explanation:
y=x+8
9=1+8
10=2+8
and so in...
y=?
4+8=12
A price floor of $25 per unit will result in a ?
Answer:
HI INEED HELP TOO
Step-by-step explanation:
The product of -13 and K
Answer:
- 13 × k = -13k
good luck, hope this helps :)
choose 2 equivalent expressions
A. 11r - 12r
B. -r
C. 23r
D. -23r
Answer:
C. and D.
Step-by-step explanation:
Kanye and his two friends are sharing the cost of lunch. the total cost of the bill is $15.27 . if Kanye has $20, how much will he have left after he pays his share?
Answer:$4.73
Step-by-step explanation:
Answer:
If Kayne is with his two friends, that means there are three people in total.
If there are three people sharing the price of this lunch, each person would have to pay 15.27/3 dollars.
Dividing, we get that each person must pay 5.09 dollars.
Subtracting 5.09 from 20, we have that Kayne will have $14.91 left after paying his share.
Hope this helps!
alright this is probably the last one i need help with... asap please :)
Write the exponent for 4^? = 64 What number is the question mark? *
e Michael is working on the roof of his house. Michael is on the ground, standing 5 feet away from the house. A ladder touches the house at a point 20 feet above the ground, and the ground at Michael's feet. What is the approximate distance between Michael and the point where the ladder touches the house?
Answer:
Step-by-step explanation:
25
PLEASE HELP ITS URGENT
DONT GUESS
WILL MARK BRAINLIEST (make sure to use yd² and yd³)
Answer:
Perimeter: 210[tex]yd[/tex]
Area: 2106[tex]yd^{2}[/tex]
good luck, hope this helped :)
PLEASE HELP ITS URGENT DONT GUESS ILL MARK BRAINLIEST IF YOU GET IT RIGHT
Answer:
circumference = 301.44
area =7,234.56
Step-by-step explanation:
The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle.
96 x 3.14 = 301.44
area = 3.14r^2
radius = d/2
radius = 48
3.14(48^2)
area =7,234.56
PLEASE I ONLY AHEB 5 minutes left
Jean deposits $730 in an account that pays 2.8% simple interest. He neither adds
more money nor withdraws any money from his account. What amount will be in
Jean's account after 5 years? Show your work.
Answer:
hyujd6dssgshfjf kryaydfhfvjmbnno vfifufiigbff
Distributive property
9(2n/1)
To distribute, multiply 9 times 2n plus 9 times 1.
9*2n+9*1
18n+9 is your final answer.
Step-by-step explanation:
A college has a total of 107 teachers 23 more female teachers than male teachers
What proportion of the teachers are female? use n as the unknown
Answer:
Female reachers = 65
Step-by-step explanation:
Given that,
Total teachers in a college = 107
Let there are n male teachers.
Female reachers = n+23
ATQ,
n+n+23 = 107
2n = 107-23
2n = 84
n = 42
Female reachers = 42+23
= 65
Hence, there are 65 female teachers.
Find the value of x that makes triangle CDE ~triangle FGH
Answer: 5
Step-by-step explanation:
4x + 10- 25
I need help fasttttt! Helpppppp
Answer:
r>12 or r<−4
Step-by-step explanation:
Plz answer i will gibe brainiest
If I understand this right:
3/4=24
24/3=8
8*4=32
You divide the number by the numerator, and then multiply that number by the denominator.
If you mean you want 3/4 of 24 then you divide 24 by 4, which equals 6. And then multiply 6 and 3, which equals 18
What is the area of the parallelogram?
Step-by-step explanation:
to find the area of a parallelogram multiply the base by the height. multiply so 8x4= 32. but thats not it, ill come back when i get it or ask a tutor
Answer:
A=bh
Step-by-step explanation:
Can someone please help me and explain I’ll mark brainliest
Part (a)
Answer: x = -8------------------
Work Shown:
2(x-1) = 3(x+2)
2x-2 = 3x+6 .... distribute
2x = 3x+6+2 .... adding 2 to both sides
2x = 3x+8
2x-3x = 8 .... subtracting 3x from both sides
-x = 8
x = -8 ..... multiply both sides by -1
===========================================================
Part (b)
Answer: x = 5/11------------------
Work Shown:
-4(2x-2) = 3(x+1)
-8x+8 = 3x+3 ..... distribute
-8x = 3x+3-8 .... subtract 8 from both sides
-8x = 3x-5
-8x-3x = -5 ... subtract 3x from both sides
-11x = -5
x = -5/(-11) .... divide both sides by -11
x = 5/11
In decimal form, this is approximately equal to 5/11 = 0.4545
The median number of part-time employees at fast-food restaurants in a particular city was known to be 18 last year. City officials think the use of part-time employees may be increasing. A sample of nine fast-food restaurants showed that seven restaurants were employing more than 18 part-time employees, one restaurant was employing exactly 18 part-time employees, and one restaurant was employing fewer than 18 part-time employees. Can it be concluded that the median number of part-time employees has increased
Answer:
It can be concluded that the median number of part-time employees has increased hence we will reject the null hypothesis ( H0 : p = 0.5 )
Step-by-step explanation:
Test using α = 0.5 to determine whether the median number of part-time employees has increased
number of restaurants with more than 18 part-time employees = 7 ( + sign )
number of restaurants with less than 18 part-time employees = 1 ( - sign )
number of restaurants with exactly 18 part-time employees = 1
first step : ( state the null and alternate hypothesis )
Null hypothesis : ( H0) : median ≤ 18
Alternate hypothesis : ( Ha ) : median ≥ 18
The size of the sample ( n ) can be considered to be 8 because
number of restaurants with more than 18 part-time employees = 7 ( + sign )
number of restaurants with less than 18 part-time employees = 1 ( - sign )
Hence the actual hypothesis that should be tested will be :
H0 : p = 0.5
Ha : p ≠ 0.5
Next apply the binomial distribution to determine the number of + signs
= nP = 8 ( 0.5 ) = 4 + signs ( right tailed test i.e. upper tail of the binomial distribution )
determine the P ( ≥ 7 ) + signs in order to obtain the p-value of this right tailed test ( using the binomial probability table )
P ( ≥ 7 )+ signs = p(7) +signs + p(8)+signs
= 0.0313 + 0.0039 = 0.0352
Hence the P-value = 0.0352 is < 0.05 hence we will reject the Null hypothesis ( H0 : p = 0.5 )
hence It can be concluded that the median number of part-time employees has increased
The true statement is that, the median number of part-time employees has increased
The given parameters are:
[tex]\mathbf{n_1 = +7}[/tex] ---- restaurants with more than 18 part-time employees[tex]\mathbf{n_2 = -1}[/tex] ---- restaurants with less than 18 part-time employees [tex]\mathbf{n_3 = 1}[/tex] ---- restaurants with exactly 18 part-time employeesUsing a 0.5 test of significance, the null and the alternate hypotheses are:
Null hypothesis : [tex]\mathbf{H_0 : p= 0.5}[/tex]Alternate hypothesis : [tex]\mathbf{H_a : p \ne 0.5}[/tex]The sample size (n) is calculated using
[tex]\mathbf{n =n_1 -n_3}[/tex]
So, we have:
[tex]\mathbf{n =7 --1}[/tex]
[tex]\mathbf{n =8}[/tex]
The mean of the distribution is:
[tex]\mathbf{\bar x = np}[/tex]
This gives
[tex]\mathbf{\bar x = 8 \times 0.5}[/tex]
[tex]\mathbf{\bar x = 4}[/tex]
Using the right tailed test, we calculate the probability that a restaurant has more than 7 part-time employees.
This is calculated as:
[tex]\mathbf{P(x \ge 7+) = P(x = 7+) + P(x = 8+)}[/tex]
Using the binomial probability table, we have:
[tex]\mathbf{P(x \ge 7+) = 0.0313 + 0.0039 }[/tex]
[tex]\mathbf{P(x \ge 7+) = 0.0352}[/tex]
By comparison,
When the p-value is less than the level of significance, then we will reject the Null hypothesis
Hence, it can be concluded that the median number of part-time employees has increased
Read more about probabilities at:
https://brainly.com/question/6476990
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
- Colin's third number was 2
- April's sixth number was the same as Colin's first number.
- April's second number was 8.
Step-by-step explanation:
Colin:
First number = 0
Second number = 1
Third number = 2
Fourth number = 3
Fifth number = 4
Sixth number = 5
April:
First number = 10
Second number = 8
Third number = 6
Fourth number = 4
Fifth number = 2
Sixth number = 0
I hope this helps :)
sb pls answer this lollllllll!?
Answer:
y = 1.5x
Step-by-step explanation:
We are to find the equation of the line
The equation is expressed as y = MX+c
m is the slope
c is the intercept
Get the slope
Using the coordnate (10, 15) and (20, 30)
m = 30-15/20-10
m = 15/10
m = 1.5
Get the intercept
Substitute m = 1.5 and (10, 15) into y = mx+c
15 = 1.5(10) + c
15 = 15+c
c = 0
Get the equation
y = mx+c
y = 1.5x+0
y = 1.5x
Hence the required equation is y = 1.5x
Answer:
y=1.5x
Step-by-step explanation:
I need help with this whoever can get it right I will mark you brainlest
A glass contains 0.75 liters of solution. John uses 0.9 of the solution for his experiment
Which of the following functions is quadratic?
A.f(x) = 2/x^2
B. f(x) = 3(3-x)
c. f(x) = 7^2
D. f(x) = 2x^2 +3x - 5
Answer:
D
Step-by-step explanation:
the 'x' term is squared but not in the denominator
1. You want to put new carpet in your bedroom and the dimensions of your room
are 8.74 ft and 10.3 ft. If you want to find the area of your room to put new carpet
in, which of these problems would help you estimate how much carpet will you
need to buy?
Answer: See explanation
Step-by-step explanation:
From the question, we are informed that a new carpet is to be put in the bedroom and that the dimensions of the room are 8.74 ft and 10.3 ft.
The area of the room will be the multiplication of the dimensions given. This will be:
= 8.74 × 10.3
= 90.022
= 90ft²
3/4 + 3/5 how do you solve it
Answer:
3/4 + 3/5 = 1 7/20
Step-by-step explanation:
5 x 4 = 20
3/4 = 15/20
3/5 = 12/20
15/20 + 12/20 = 27/20 = 1 7/20
Answer: 1 7/20 (one and seven-twentieths)
Step-by-step explanation:
1) 3/4 = 15/20 and 3/5 = 12/20
2) 15/20 + 12/20 = 27/20
3) 27/20 = 1 7/20
Good Luck!
What is 63x13
Me give brainliest
And thanks in advance
Answer:
819
Step-by-step explanation: