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.
Given the following function, find h(4).
h(t) = t - t + 3
h(4) =
If [tex]h(t)=3[/tex] then [tex]h(4)=3[/tex]
Calculate the percent: 9% of 124
Answer:
9% of 124 is 11.16
Of all ladies over the age of 50, 72% report that they color their hair to hide their gray. What is the probability
that under 70% color their hair in a group of 85 older women?
Answer:
0.3409 = 34.09% probability that under 70% color their hair in a group of 85 older women.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the Central Limit Theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex].
72% report that they color their hair to hide their gray.
This means that [tex]\mu = p = 0.72[/tex]
What is the probability that under 70% color their hair in a group of 85 older women?
For a sample of 85, we have that [tex]s = \sqrt{\frac{0.72*0.28}{85}} = 0.0487[/tex]
This probability is the pvalue of Z when X = 0.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.7 - 0.72}{0.0487}[/tex]
[tex]Z = -0.41[/tex]
[tex]Z = -0.41[/tex] has a pvalue of 0.3409
0.3409 = 34.09% probability that under 70% color their hair in a group of 85 older women.
Bentley invested $430 in an account paying an interest rate of 2.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $510?
Answer:
its 11
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
how many inches is 2 1/6 ft
Answer:
26 inches
Step-by-step explanation:
You find out that 1 foot equals 12 inches
times 2 by 12 equaling 24
24 added by 2 is 26
1/6 as a decimal is 1.83 infinitive 3 which is rounded to 2 as the whole number
makes your answer 26 inches
Hope that helps
If each person gets a 1/2 gallon of water, then how many people can share 64 gallons of water?
Answer: 128 people
Step-by-step explanation:
every 2 people get a gallon so 2*64=128
Fourteen school festival tickets were sold to adults and children. A total of $38 was collected from these ticket sales. Adult tickets cost $4 each, and child tickets cost $1 each. If x represents the number of adult tickets sold and y represents the number of child tickets sold, which of the following systems of equations represents this situation?
A. x + y = 38
4x + y = 14
B. 4x + y = 38
x + y =14
C. 2x + y = 14
y - x = 38
D. x + 2y = 14
y - 2x = 38
Answer:
A
Step-by-step explanation:
The number of goats in a farm increases by 5 goats each year. If the farm has a population of 20 goats after the first year, and n denotes the number of years, which recursive equation gives the population of goats, , as a function of the year?
Answer:
f ( 1 )= 20; f ( n )= f (n - 1) + 5, for n > 2
(the > has a line under it)
Step-by-step explanation:
Answer:
f (1) = 20; f (n) = 2 · f (n - 1) - 0.3 · f (n - 1) + 5, for n ≥ 2
Step-by-step explanation:
The other person left some numbers out.
What is the solution to this system of equations? 4x+y=6 x-2y=6
Answer:
it's A!!!
Step-by-step explanation:
hoped I helped
Answer:
The anwser is A.
Step-by-step explanation:
4x+y=6 and x-2y=6 so the answer is 2, and -2
A community center offers yoga classes for $8 per month plus an additional $0.25 per center floor mat used.Write an equation to express this relationship, using m to represent the number of mats used per month and C to represent the total cost in dollars.
(8*P) + (0.25*m)=C
P = People
Answer:
Step-by-step explanation:
A community center offers yoga classes for $8 per month plus an additional $0.25 per center floor mat used.Write an equation to express this relationship, using m to represent the number of mats used per month and C to represent the total cost in dollars.
NeverReady batteries has engineered a newer, longer lasting AAA battery. The company claims this battery has an average life span of 17 hours with a standard deviation of 0.7 hours. Your statistics class questions this claim. As a class, you randomly select 30 batteries and find that the sample mean life span is 16.7 hours. If the process is working properly, what is the probability of getting a random sample of 30 batteries in which the sample mean lifetime is 16.7 hours or less
Answer:
0.020
Step-by-step explanation:
Given that,
μ = 17,
σ = 0.7,
x¯ = 16.7 hours
n(number of batteries) = 30
To find,
The probability(e) by using μ\frac{σ}{[tex]\sqrt{n}[/tex]} = normal cdf
∵ (E - 99, 16.7 , 17, 0.8/[tex]\sqrt{30}[/tex])
The probability of getting a random sample of 30 batteries = 0.020
Hence, the claim is reasonable as only 2% of batteries are likely to last till 16.7 hours.
Substitution 8th grade question , need help. First respond gets brainiest and a thanks.
Answer:
X=5
Step-by-step explanation:
this will basically be 4x+-2(x-8)=26
= 4x+-2x+16=26
2x=10
x=5
y=5-8
-3=5-8
4X5+-2X-3=26
20+6=26
Answer:
Point Form: 5,-3
Equation Form: x=5, y= -3
Explanation:
If 4x+-2(x-8)=26
=4x+-2x+16=26
2x=10
x=
y=5-8
-3=5-8
4x5+-2x-3=26
20+6=26
Cam walked 4 units down and 8 units left to reach the origin. What is the ordered pair of his starting point?
A. 30
B.45
C. 90
D. 60
Answer:
C. 90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Evaluate the expression (14 − 4)2 ÷ 10.
The value of the expression is value of
Answer:
2
Step-by-step explanation:
PEMDAS says to do the equations in parentheses first
(14-4) = 10
PEMDAS then says to do multiplication or division, whichever comes first in the equation, which is multiplication in this case
(10)2 = 20
20 ÷ 10 = 2
Math Question,please help
Answer:
8
Step-by-step explanation:
I am actually in 4th grade but anyway I need see
. Lightning Lucy’s burnable CDs are on sale this
month for 10% off regular prices. If a pack of 10
blank CDs normally costs $15, how much do you
save per CD?
Original unit cost of CDs = $_________ per CD
10% of original cost = $_________
Original cost minus the 10% discount = $_______
Discounted unit cost of CDs = $_______ per CD
Subtract the two unit costs to find
how much saved per CD = $_________
Answer:
Original Cost = $1.50 per CD
Discount = $1.50
Discounted Cost = $13.50
Discounted Cost = $1.35 per CD
You Saved = $0.15 per CD
Step-by-step explanation:
$15/10CDs = $1.50
$15x10% = $1.50
$15-$1.50 = $13.50
$13.50/10CDs = $1.35
$1.50-$1.35 = $0.15
17. It takes one minute to fill (3/7) th of a vessel. What is the time taken in
minutes to fill the whole of the vessel?
Answer:
Given that 1minute =3/7of the vessel
let the time taken in minutes to fill the whole of the vessel be' x' minute.
1min =3/7
xmin =whole vessel =1=7/7
=3x/7=1=x=7/3=2.3min=2min.3sec
Determine the simple interest when: principal: $205,435 interest rate: 2.8%, time: 15 year
Step-by-step explanation:
principle (p) = $205,435rate (r) = 2.8%time (t) = 15 yearssimple interest = (p × r × t) ÷ 100 = (205,435 × 2.8 × 15) ÷ 100 = 8,628,270 ÷ 100 = 86282.7MARK ME AS BRAINLISTPLZ FOLLOW MEa car travels 224 miles in 3 hours and 30 minutes. how many miles does it travel per hour
Answer:
64 miles per hour.
Step-by-step explanation:
we are asked to look for the velocity of this car. to find it, we use the equation [tex]velocity = \frac{distance}{time}[/tex]. we substitute the given to the equation:
[tex]velocity = \frac{224 m}{3.5 hr}[/tex]
velocity = 64 miles per hour
jojo makes 100 working eight hours. Trish earned 25 working one hour. How much more money does Trish make than Jojo after 10 hours?
Answer:
Jojo makes 1000 and Trish makes 250
Step-by-step explanation:
I hope this helped
Answer:
Trish makes $125 more than Jojo after 10 hours
Step-by-step explanation:
$125 jojo
$250 Trish
Rhombus ABCD has vertices A(-1, -2), B(2,2), C(6,5), and D(3,1). The perimeter of the rhombus is
Answer:
The perimeter of the rhombus is approximately 19.999.
Step-by-step explanation:
First of all, we plot all points that constructs the rhombus, whose outcome is attached below. Diagonals of the rhombus are segments AC and BD, whose lengths are determined by Pythagorean Theorem:
Segment AC
[tex]AC = \sqrt{[6-(-1)]^{2}+[5-(-2)]^{2}}[/tex]
[tex]AC \approx 9.899[/tex]
Segment BD
[tex]BD = \sqrt{(3-2)^{2}+(1-2)^{2}}[/tex]
[tex]BD \approx 1.414[/tex]
The perimeter of the rhombus ([tex]p[/tex]) is calculated by the following equation:
[tex]p = 4\cdot \sqrt{\left(\frac{AC}{2} \right)^{2}+\left(\frac{BD}{2} \right)^{2}}[/tex]
[tex]p = 2\cdot \sqrt{AC^{2}+BD^{2}}[/tex]
[tex]p = 2\cdot \sqrt{9.899^{2}+1.414^{2}}[/tex]
[tex]p \approx 19.999[/tex]
The perimeter of the rhombus is approximately 19.999.
A financial analyst constructs a statistical model to represent the market shares of several similar companies. She then collects data over the
next month to evaluate her model. At the end of the month, she finds that for one of the companies, the difference between her model and the
data is 5%.
She decides to collect data for an additional two months. If her model is valid, what could she expect from the total data collected after three
months?
ОА. .
The difference between the data and the model will get smaller.
OB.
The difference between the data and the model will stay the same.
OC.
It is impossible to predict how the difference between the data and the model will change.
OD.
The difference between the data and the model will get larger
Answer:
Gets Smaller
If her model is valid, she expect from the total data collected after three months that the difference between the data and the model will get smaller. The correct option is A.
What is market shares?When some amount of money is used to buy the share of a particular company, then the percentage of total sales generated by that company is called the market share.
A financial analyst collects data over the next month to evaluate her model. At the end of the month, she finds that for one of the companies, the difference between her model and the data is 5%. She decides to collect data for an additional two months.
If the model is valid, then she can assume that her assumptions are correct over the model according to the data. It will result in decreasing the bridge gap between the model and the collected data.
Therefore, If her model is valid, she expect from the total data collected after three months that the difference between the data and the model will get smaller. The correct option is A.
Learn more about market shares.
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Which statement about the slope of the line is true?
A. It is fraction negative 1/3 throughout the line.
B. It is −3 throughout the line.
C. The slope from point O to point A is fraction 1/3 times the slope of the line from point A to point B.
D. The slope from point O to point A is 3 times the slope of the line from point A to point B.
a television Mark 1600 was sold for 1200 what percent discount was given on that television
Answer:
25%
Step-by-step explanation:
Discount = 1600 - 1200 = 400
Percentage discount
[tex] = \frac{400}{1600} \times 100 \\ \\ = \frac{400}{16} \\ \\ = 25\%[/tex]
the sum of a number and its inverse equals 3 29/52, write the mathematical expression
Answer:
Step-by-step explanation:
The sum of a number and its inverse is 3 29/52. Find the number?
x+1/x=329/52
x+1/x-329/52=0
solve the fraction
(
using the quadratic formular
Answer:
Step-by-step explanation:
the yellow is the glow in the dark kind
Find the missing angle measure.
Answer:
x=98
Step-by-step explanation:
all interior angles in a hexagon equals 720, just subtract 720 by every known angle and you are left with the unknown angle
The radius of a circle is 6 in. Find the circumference to the nearest tenth.
Answer:
37.7
Step-by-step explanation:
The orginal answer is 37.699
But you want to round the tenth
So 9 to the 6 you want to rasie the score
6 turns into a 7 and the numbers behind it (9 and the other 9) turn into a zero
37.7 or 37.700
An expression for the perimeter of the shape is below
Step-by-step explanation:
rewrite the expression in redical form x⅔