Answers
Answer:
[tex]y = 4(1.4)^x[/tex]
[tex]\text{at x = 5, }y=21.513[/tex]
Step-by-step explanation:
If you think about an exponential function in the form: [tex]f(x) = a(b)^x[/tex]
you'll realize a pattern, which is by definition.
Evaluating the function at x = 1: [tex]f(1) = a(b)^1 \implies a(b)[/tex]
Evaluating the function at x = 2: [tex]f(2) = a(b)^2 \implies a(b * b)[/tex]
Evaluating the function at x = 3: [tex]f(3) = a(b)^3\implies a(b * b * b)[/tex]
Each term just has an additional "b" that it's being multiplied by. This is by definition of an exponential function, repeated multiplication.
You'll also notice something else interesting, we can find this "b" value by dividing any term by it's previous term.
Take for example f(1) and f(2): [tex]\frac{a(b* b)}{a(b)}\to b[/tex]
As mentioned before, as x increases by one, we just have another term to multiply by. So if we divide by the previous term (where x is one less), then we should just have this "b" value, which is the generally expressed in either a growth or decay rate.
So now that we know that, we can divide f(2) by f(1) using the values shown on the graph:
given:
[tex]f(1) = 5.6\\f(2) = 7.84[/tex]
Let's divide the f(2) by f(1) to get: [tex]\frac{7.84}{5.6} \to1.4[/tex]
Lastly to find our "a" value, we just need to find the y-intercept, since when x = 0, the b will be equal to one (since anything raised to the power of zero is one), we can just look at the graph to see the y-intercept.
Looking at the graph, we can see the y-intercept is four, so a = 4.
Another way to do this algebraically rather than visually, would be to use our knowledge of exponentials to realize that as x increases by one (when we're going right), the y-value is just being multiplied by "b" as mentioned before.
So as x decreases by one (when we're going left) the y-value is just being divided by "b".
So f(0) should be equal to f(1) / b, and we know both values! Which are going to substitute into: [tex]\frac{5.6}{1.4}\to 4[/tex]
Anyways, once we plug in "a" and "b" into the standard form of an exponential function, we get: [tex]y = 4(1.4)^x[/tex]
We can now use this equation to find y-values that are not shown in the graph.
To find the x-value at x = 5, simply substitute in "5" as x
[tex]y = 4(1.4)^x\\\\\text{substitute 5 as x}\\\\y=4(1.4)^5\\\\y=4(5.37824)\\\\y\approx 21.513[/tex]
Related Questions
A candy company sells peanut brittle and almond bark. The information for both types of candy is shown.
graph labeled Peanut Brittle with x axis labeled weight in ounces and y axis labeled cost in dollars with a line from point 0 comma 0 going through 10 comma 10
Almond Bark
Weight (ounces) 2 6 14
Cost (dollars) 3 9 21
Determine how much more one candy costs per ounce than the other candy.
Peanut brittle costs $0.50 more per ounce than almond bark.
Almond bark costs $0.50 more per ounce than peanut brittle.
Peanut brittle costs $0.33 more per ounce than almond bark.
Almond bark costs $0.33 more per ounce than peanut brittle.
Answers
The difference between the cost of one candy per ounce and the other candy is that: Almond bark costs $0.50 more per ounce than peanut brittle.
How to determine the cost of candy?Mathematically, a direct proportion can be represented the following mathematical expression:
y = kx
Where:
x represents the weight in ounces of a candy.y represents the cost in dollars of a candy.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for each candy as follows:
For Peanut Brittle, we have the following:
Constant of proportionality (k) = 10/10
Constant of proportionality (k) = 1.0
For Almond Bark, we have the following:
Constant of proportionality (k) = 3/2
Constant of proportionality (k) = 1.5
Next, we would determine the difference in cost:
Difference in cost = 1.5 - 1.0
Difference in cost = $0.50.
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A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set 327$. Find the original selling price of the ski set.
Answers
Answer:$583.93 is the original price
6. Solve the following inequalities for the variable and graph the solution.
3+4x>-5.
Answers
Answer:
3+4x>-5
4x>-5-3
4x>-8
x>-8/4
x> -2
1/3 of the guests choose beef
5/12 choose chicken
69 are vegeterian
How many guests are at the wedding
Answers
The number of guests at the wedding is 276.
How to calculate the number of guests?Since 1/3 of the guests choose beef and 5/12 choose chicken, the fraction for vegetarian will be:
= 1 - (1/3 + 5/12)
= 1 - 3/4
= 1/4
Therefore, let the total number of guests be x.
This will be illustrated as:
1/4 × x = 69
0.25x = 69
Divide
x = 69 / 0.25
x = 276
Therefore, there are 276 guests.
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(-3,6), (0,3), (-1,2), and (2,-1) all lie on a line. Find the Slope of the Line. Make Sure You Do Number 11 On The Paper!
Answers
to get the slope of any straight line, we simply need two points off of it, let's use those two from the picture below
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{-1 +3} \implies \cfrac{ -4 }{ 2 } \implies - 2[/tex]
If a = 2 and b = 3, what is the value of 2a³b2?
Answers
Answer:384
Step-by-step explanation:
first you multiply 2 times 2= 4 then 4 times 4 times 4= 64 then you multiply 3 times 2= 6 lastly you multiply 6 and 64. your welcome:)
Solve the equation: u^6 − 49 u^4 = 0 .
Answers
The given equation solved for u is u = 7 or u = -7
Solving an equationFrom the question, we are to solve the given equation.
The given equation is
u^6 − 49 u^4 = 0
First, we will write the equation properly
The given equation written properly is
u⁶ - 49u⁴ = 0
Now,
To solve the equation, we will determine the value(s) of the variable. The variable in the given equation is u.
Thus,
We will solve for u
u⁶ - 49u⁴ = 0
Add 49u⁴ to both sides of the equation
u⁶ = 49u⁴
Divide both sides by u⁴
u⁶/u⁴ = 49u⁴/u⁴
u² = 49
Then,
u²- 49 = 0
u² - 7² = 0
Factorize by applying the rule for difference of two squares
(u + 7)(u - 7) = 0
Then,
u + 7 = 0 OR u - 7 = 0
u = -7 OR u = 7
Hence, the value of u is -7 OR 7
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2. A local grocery store received 240 turkeys the week prior to Thanksgiving. On Sunday,
they sold 3/8 of them. How many turkeys were sold on Sunday? Solve the problem
using the Draw a Diagram strategy.
Answers
The number of turkeys that they sold on Sunday is 90 turkeys
Total number of turkeys = 240
On Sunday, they sold 3/8 of them
The fraction of turkeys they sold on Sunday = 3/8
To find the number of turkeys that they sold on Sunday we have to find the 3/8 fraction of 240
Then,
The number of turkeys that they sold on Sunday = Total number of turkeys × The fraction of turkeys they sold on Sunday
Substitute the values in the equation
The number of turkeys that they sold on Sunday = 240 × 3/8
= 240 × 0.375
= 90 turkeys
Hence, the number of turkeys that they sold on Sunday is 90 turkeys
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5) A woman drinks 8 bottles of water in 2 days. How many bottles of water would she drink in 4 days?
Answers
Suppose you invest $2000 in equipment to put pictures on T-shirts. You buy each T-shirt for $4. After you have placed a picture on a shirt, you sell it for $20. How many T-shirts must you sell to break even?
Answers
Answer:
25
Step-by-step explanation:
2000/4=500
500/20=25
Answer: 125
Step-by-step explanation: you see if you take your 20$ you ern of of selling a shirt then the price you buy it for 4$ then defied it by 2000$ you get 125.
For the piecewise function, find the values h(-5), h(0), h(5), and h(9).
- 3x-13, for x < -5
h(x) = 5,
h(0) =
h(-5) = (Simplify your answer.)
=(Simplify your answer.)
(Simplify your answer.)
(Simplify your answer.)
=
h(5)=
X+ 7,
h(9) =
for 5≤x<5
for x ≥ 5
2
Answers
Answer:
h(-5) = 5, h(0) = 5, h(5) = 12, h(9) = 16==========================
The given function is the combination of three lines:
h(x) = - 3x - 13, for x < - 5,h(x) = 5, for - 5 ≤ x < 5,h(x) = x + 7, for x ≥ 5.The values of the function at the given points are:
h(-5) = 5, corresponds to second equation,h(0) = 5, same as above,h(5) = 5 + 7 = 12, corresponds to third equation,h(9) = 9 + 7 = 16, same as above.whats 28.2 × 4.42= in decimal form? lol
Answers
Answer:
124.644
Step-by-step explanation:
28.2*4.42=124.644.
Answer:
28.2 × 4.42= 124.644
and in non-decimal it's 124644 removing 3 decimal places
Step-by-step explanation:
Brainiest, please
thank you
X:
6. A two-story building measures 21 feet from
the ground. A scale model shows the building
to be 3 inches tall. How many inches would an
84-foot building be in the model?
height:
Answers
Answer:
12 inches
Step-by-step explanation:
Let be "x" the top inches (in the model) of a eighty four foot building.
According to the information provided in the exercise, we be aware of that the top of a two-story establishing is 21 toes and in the scale model its top is 3 inches.
Knowing this, we can set up the following proportion: 3/21=x/84
The final step is to get to the bottom of for "x" in order to calculate its value.
Explain if Todd’s Conclusion is logical.How did you decide? If it is not logical,what can you do to improve his reasoning?
Answers
Answer:
Todd's conclusion is logical. I know this because all people named Todd are logical beings who always come to logical conclusions. But seriously though, please comment down below more of your question so I can accurately answer it, thanks!
Step-by-step explanation:
The half-life of radium is 1690 years. If 30 grams are present now, how much will be present in 720 years?
Answers
Answer:
22.3 gm
Step-by-step explanation:
720 is this many half lives : 720 / 1690
so there will be this much left 30 gm ( 1/2)^(720/1690) = 22.3 gm
A deck of cards contains RED cards numbered 1,2,3,4,5 and BLUE cards numbered 1,2,3,4,5,6. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Red 3 is an example of which of the following events? Select all correct answers.
Answers
The probability of drawing the Blue 4 is an example of .R′f.E′
Red cards = 1,2,3
Blue cards =1,2,3,4,5,6
Pr(R) = Drawing a red card = 3/9 = 1/3
Pr(B)= Drawing a blue card = 6/9 = 2/3
Pr(E) = Drawing an even card = 4/9
Pr(O) = Drawing an odd number card = 5/9
Probability of drawing the blue 4 ? = Pr(blue, 4) = 1/9
From the options
(A) R or O = Pr(R) + Pr(O) = 1/3 + 1/9 = 8/9 ........(Not equal to 1/9)
(B) B and O = Pr(B) × Pr(O) = 2/3 × 5/9 = 10/21......(Not equal to 1/9)
(C) R or E = Pr(R) + Pr(E) = 1/3 + 4/9 = 7/9.......(Not equal to 1/9)
(D) R and O = Pr(R) + Pr(O) = 1/3 × 5/9 = 5/27.......(Not equal to 1/9)
(E) R'. E' = 1-Pr(R)-1-Pr(E) =
1-1/3 =2/3- 1-4/9 =5/9
2/3-5/9 = 1/9......( equal to 1/9).
Hence, the probability of drawing the Blue 4 is an example of .R′f.E′
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Disclaimer: the question given by you is incomplete, the solution is done as per a similiar question which is
A deck of cards contains RED cards numbered 1,2,3 and BLUE cards numbered 1,2,3,4,5,6. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.Drawing the Blue 4 is an example of which of the following events? Select all correct answers.Select all that apply:a.R OR Ob.B AND Oc.R OR Ed.R AND Oe.R′f.E′
Choose a variable, write a inequality, and solve the inequality.
The sum of a number and -2 is no more than 6
Answers
Answer: 4
Step-by-step explanation: your going to divide -2 by 1 and you get 2 then add 4 and you get 6 pls give me brainliest :)
Consider the following equation:
3|x+3|−12=0
Step 2 of 4: Using the definition of absolute values, convert the standard form of the given equation into two equations without absolute value signs.
Answers
The value of x in the following equation: 3|x+3|−12=0 is -7 and 1
The equation is 3|x+3|−12=0
The modulus function can be positive and negative
Considering it to be negative,
the equation is
3((-1)(x + 3) - 12
3(-x - 3) - 12
-3x - 9 - 12 = 0
3x + 21 = 0
3x = -21
x = -7
3(x + 3) - 12
3x + 9 - 12
3x - 3 = 0
3x = 3
x = 1
Therefore, the value of x in the following equation: 3|x+3|−12=0 is -7 and 1
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Suppose a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual
percentage rate of growth?
A. 20%
B. 3.7%
C. 8.2%
Answers
If a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%
The initial population was 5000
The population in 2015 is 6000
let the rate of growth be r
aₙ = arⁿ-¹
6000 = 5000 r⁵⁻¹
6000/5000 = r⁴
6/5 = r⁴
r = 1.2⁻⁴
r = 0.48
r = 48%
the annual percentage rate of growth 48/5 = 9.6
Therefore, if a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%
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Juan invested $110,000, 10 years ago at 8% compound quarterly. how much has he accumulated?
use the MS Excel FV function
Answers
Answer:
Below
Step-by-step explanation:
The equation ( you need to commit to memory) is:
FV = PV ( 1+i)^n FV = future value PV = present value(110 000)
i = decimal interest per PERIOD = .08 /4 = .02
n = # of periods = 40 (it is a quarterly period by 10 yrs)
FV = 110 000 ( 1 + .02)^40 = 242 884 .36 dollars
solve for x;
2/7 x + 1/5 x=51
Answers
Answer:
x = 105
Step-by-step explanation:
To solve for x, we simply need to isolate it:
[tex]\frac{2}{7}x+\frac{1}{5}x=51\\ \frac{17}{35}x=51\\ x=105[/tex]
Evaluate the following algebraic expression:
64-9p when p = 7
O 14
O 63
O 36
01
Answers
Answer:
63 is the answer.
Step-by-step explanation:
9p=9xp, p=7, so 9x7=63. ;)
1. Write the radical below in the simplest radical form. Decimals are not allowed.
√175
2. Write the radical in simplest radical form. Decimals not allowed
√5/12
number 2 is a fraction btw
Answers
The simplest radical form of the radicals given are:
1. The simplest radical form of √175 is 5 √7.
2. The simplest radical form of √5 / 12 is √5 / 12.
First, let us understand the radical:
A radical can also be called a surd. A surd is an irrational number. We say that it is irrational because it can not be expressed as a terminating decimal.
1.
We are given:
√175
We need to write in the simplest radical form.
175 can be written as:
175 = 5 * 5 * 7
√175 = √ 5 * 5 * 7
√175 = √ 5 * 5 * √7
√175 = 5 √7
So, the simplest form of √175 is 5 √7.
2.
We are given:
√5 / 12
We need to write in the simplest radical form.
√5 / 12 is already in the simplest form.
So, the simplest form of √5 / 12 is √5 / 12.
Thus, the simplest radical form of the radicals given are:
1. The simplest radical form of √175 is 5 √7.
2. The simplest radical form of √5 / 12 is √5 / 12.
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find using substitution method
Answers
Answer:
x = 4 ; y = -1
Step-by-step explanation:
y = -2x + 7
x + 2(-2x+7) = 2
x -4x + 14 = 2
-3x = 2 -14
-3x = -12
-3/-3 x = -12/-3
x = 4
y = -2* 4 + 7
y = -8 + 7
y = -1
Ken, Mike, and Ariel are eating out at their favorite restaurant. They each order a sandwich combo and plan to split the bill evenly. The service they receive at the restaurant is amazing, so they decide to leave a 30% tip. Their bill total is $50.88 before tax. If Florida’s sales tax is 6%, how much will each person pay? Round your answer to the nearest hundredth.
Answers
Each individual paid the sum of $23.4 including state tax at the restaurant
PercentageIn mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%".
In the problem, their total bill is $50.88 and they gave a 30% tip
We should fid 30% of 50.88
0.3 * 50.88 = $15.264
30% of $50.88 is $15.264
If we add this up and then find the state tax to it.
15.264 + 50.88 = 66.144.
Find 6% of 66.144 to determine the state tax.
0.06 * 66.144 = 3.96864
The total amount spent is 66.144 + 3.96864 = 70.11264
We can divide this equally amongst the three people to get the individual payment = 70.11264/3 = 23.37088
Rounding this to the nearest cent, we have 23.4.
We can say each person paid $23.4 at the end of the day
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please help
Our class is studying the effects of mindfulness on mental health. To help with data collection, we will have the support of ten grade 9, eleven grade 10, twelve grade 11 and thirteen grade 12 students. Showing your calculations,how many different groups of 12 volunteers can we make if:
a) the group must have the same number of students from each grade?
b) the group must have at least two grade 9 students? [2A]
c) the group must have James and Lucy (both grade 11 students) in it? [2A]
Answers
The number of groups, using the combination formula, for each case, is given as follows:
a) Same number of students from each grade: 1,245,816,000
b) At least two grade nine students: 31,650,886,995.
c) James and Lucy are in it: 2,481,256,778.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For item a, the groups are taken as follows:
3 students from grade 9, from a set of 10.3 students from grade 10, from a set of 11.3 students from grade 11, from a set of 12.3 students from grade 12, from a set of 13.Hence the number of groups is:
[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]
For item b, the total number of groups, without considering the restriction, is:
[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]
The number of groups with none students from grade 9 is:
[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]
The number of groups with one student from grade 9 is:
[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]
Using complementary events, the number of groups with at least two grade 9 students is:
38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.
For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set of 44, hence:
[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]
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Last week, a candy store sold 6 13 pounds of white chocolate. It sold 4 times as much milk chocolate as white chocolate.
How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?
A)19
B)19 2/3
C)18
D)18 2/3
Answers
Answer: 25 1/3
Step-by-step explanation:
The table shows a set of points on a line.
y
6
5
4
3
What is the slope of the line?
X
-6
-3
0
3
Answers
The slope of the line is -3 and the equation of the line formed by the points is y + 3x = 6.
From the table we can see that the line passes through the points:
(-6,6) ,(5,-3) ,(4,0) and (3,3) .
Let us consider any two points on the line (4,0) and (3,3) .
We know that the slope of the line can be found by using the intercept formula
Hence slope = (3-0) / (3-4) = 3/ -1 = -3
Now the equation of the line is :
y - 3 = -3(x-3)
or, y - 3 = -3x +9
or, y + 3x = 6
The letter m is frequently used to represent the slope of an object that resembles a line in the plane that contains the x and y axes. The slope is defined as the difference in two independent locations along the line expressed in y coordinate less by the equivalent difference in x coordinate.
Therefore slope of the line is -3.
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find the slope of the line passing through the points (-2,2) and (-5,5)
Answers
Answer:
The slope of the line passing through the points [tex](-2, 2)[/tex] and [tex](-5, 5)[/tex] is equal to: [tex]-1[/tex]
Step-by-step explanation:
The slope of a line can be found with the following formula
[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where [tex]x_2 > x_1[/tex]
Then substituting the values with the given ones we have
[tex]m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{2-5}{-2-(-5)}=\frac{-3}{-2+5}=\frac{-3}{3} =-1[/tex]
So the slope of the line passing through the given points is [tex]-1[/tex]
A line passes through the point (2, 7) and has a slope of 5. Write an equation in slope-intercept form for this line.
Answers
Answer: y = 5x - 3
Step-by-step explanation:
It is a line, so its formula is y = mx + b.
Slope(m) = 5Y-intercept(b) =[tex]y=5x+b\\7=5(2)+b\\7=10+b\\b=7-10=-3[/tex]
Therefore, the formula is y = 5x - 3.
Answer:
y=5x-3
Step-by-step explanation: