Answer:
y ≈1*(1+0.59)^t. The rate of change is = 59%
Step-by-step explanation:
We have t mulitplied by 8 in the expression of y. We can write that power with a power of powers, using the property
[tex]a^{bc} = (a^b)^c = (a^c)^b[/tex]
Therefore,
[tex]a^{8t} = (a^8)^t[/tex]
If we replace a with 1.06, we obtain
[tex] y = 1.06^{8t} = (1.06^8)^t \approx 1.59^t = 1*(1+0.59)^t[/tex]
Thus, y ≈1*(1+0.59)^t. The rate of change is ln(1.59) * 1.59^t. After 1 unit of time t, the rate of change is 0.59*100 = 59%
The given function represents exponential growth with a rate of change of 6%. The function already fits the form y = a(1 + r)^t with a = 1 and r = 0.06.
Explanation:To rewrite the function y = (1.06)^8t in the form y = a(1 + r)^t, we can identify a as the initial amount and r as the rate of change. In this case, the initial amount a is implied to be 1 (since it is not explicitly multiplied by the base), and the base 1.06 represents the growth factor. Seeing as the base is greater than 1, this function represents exponential growth.
The percent rate of change can be found by subtracting 1 from the base and then converting it to a percentage. Therefore, the rate r is 1.06 - 1, which equals 0.06 or 6% when expressed as a percentage. Thus, the function in the requested form is y = (1 + 0.06)^8t, or simplifying the exponent, y = (1.06)^8t.
To the nearest percent, the rate of change is 6%.
What function can be used to model the coronavirus growth A)linear b)quadratic c) exponential d) none of the above
Find the quotient.
158
152
A) 1516
B) 1510
C) 156
D) 154
Answer:
D
Step-by-step explanation:
Is the function linear or nonlinear?
_ y = 2x3 + 1
Answer:
it's linear because the line doesn't go through the origin
Step-by-step explanation:
i know that bc it says. +1
hope this helps!
Which three-dimensional object is formed when the shape is rotated about the axis as shown?
pyramid
cylinder
cone
triangular prism
The three-dimensional object formed when the shape is rotated about the axis is a cone.
What is a cone?A cone is a solid which tapers from a circular base to a point. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.
here, we have,
we know that,
When a right triangle is rotated about an axis, a cone is formed.
Find the attached figure to visualize the rotation.
Rotation of the base AB of the right triangle results in the circular base of the cone while rotation of hypotenuse AC results in the lateral surface of the cone.
Hence, The three-dimensional object is formed when the shape is rotated about the axis is a cone.
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Sean and Katherine have been married for two years. They want to start a family soon. However, before having a child, they would like to secure their future and the future of their child. Which financial option will help them secure their family’s future?
A.
invest in in several real estate options
B.
invest in high-risk shares that promise big returns
C.
invest in a joint insurance and retirement plans
D.
become entrepreneurs or invest in a profit-making business
Answer:
C.
invest in a joint insurance and retirement plans
Step-by-step explanation:
this would be the obvious answers because there no risks that would compromise their future
Kylie drew a circle with a diameter of 8 cm. Paige drew a circle with a radius of 3 cm. Approximately how much larger is the area of Kylie’s circle than the area of Paige’s circle? Use 3.14 for Pi and round to the nearest whole number.
22 centimeters squared
88 centimeters squared
173 centimeters squared
351 centimeters squared
Answer:
The answer is 22 centimeters.
Step-by-step explanation:
Answer:
22 centimeters squared
Step-by-step explanation:
trust me just did it on EDG
How far is point E(5,3) from the origin ?
Answer:
It is 5.84 units away from the origin.
Step-by-step explanation:
[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2}} [/tex]
Therefore:
[tex]d = \sqrt{ {(5 - 0)}^{2} + {(3 - 0)}^{2} } \\ d = \sqrt{ {5}^{2} + {3}^{2} } = \sqrt{25 + 9} \\ d = \sqrt{34} = 5.83951...[/tex]
Final answer:
The distance from point E(5,3) to the origin is calculated using the Pythagorean theorem, resulting in \/34 units.
Explanation:
The question asks how far point E(5,3) is from the origin. To find the distance between a point and the origin in a Cartesian coordinate system, we use the Pythagorean theorem. Specifically, the distance ( extit{d}) can be calculated using the formula extit{d} = \/((x_2 - x_1)² + (y_2 - y_1)²), where ( extit{x_1}, extit{y_1}) represents the coordinates of the first point (in this case, the origin (0,0)) and ( extit{x_2}, extit{y_2}) represents the coordinates of the second point (in this case, point E(5,3)).
Plugging in the values, we get extit{d} = \/((5 - 0)² + (3 - 0)²) = \/(5² + 3²) = \/(25 + 9) = \/34. The exact distance between point E and the origin is \/34 units, which can also be approximated as a decimal if necessary.
QUESTION 16 The body temperatures of adults have a mean of 98.6° F and a standard deviation of 0.60° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.5° F. Hint: You will need to use the sampling distribution of the sample mean.
Answer:
34%
Step-by-step explanation:
The body temperatures of adults have a mean of 98.6° F and a standard deviation of 0.60° F.
We want to find the probability that the mean body temperature of 36 randomly selected adults is greater than 98.5° F.
The mean of the sampling distribution of the sample means is the same as the population mean,
[tex] \mu = 98.6 \degree[/tex]
The standard error of the mean becomes the standard deviation of the sampling distribution of the means.
[tex]SE= \frac{ \sigma}{ \sqrt{n} } [/tex]
[tex]SE= \frac{0.6}{ \sqrt{36} } = 0.1[/tex]
By the Central Limit Theorem, the distribution of mean of means is approximately normal
The z-score of 98.5° F
[tex] z= \frac{98.5 - 98.6}{0.1} = - 1[/tex]
By the empirical rule 68% of the distribution is within one standard deviation (-1 to 1).
Therefore from (-1 to 0), it will be approximately 34%
Final answer:
To calculate the probability that the mean body temperature of 36 randomly selected adults is greater than 98.5° F, you'd use the z-score formula after finding the standard error. The final probability is found by subtracting the z-score probability corresponding to a score of -1 from 1. The correct distribution for calculation is the z-distribution due to the known standard deviation.
Explanation:
The question pertains to calculating the probability that the mean body temperature of a randomly selected sample of 36 adults is greater than 98.5° F. Given that the mean is 98.6° F and the standard deviation is 0.60° F, one would first calculate the standard error of the mean (SE) using the formula SE = σ/√n, where σ is the standard deviation and n is the sample size. In this case, SE = 0.60/√36 = 0.10° F.
To find the probability, we can use the z-score formula, which is z = (X - μ) / SE, where X is the value we are finding the probability for, μ is the mean, and SE is the standard error. Plugging in the values, we get z = (98.5 - 98.6) / 0.10 = -1. When we look up the z-score of -1 in the z-tables or use a statistical software, we find the probability to the left of z=-1. However, since we want the probability that the mean temperature is greater than 98.5° F, we need to subtract this value from 1.
The final step will give us the probability that the mean of the selected sample is greater than 98.5° F. It's important to note that while the question hints at using the t-distribution due to not knowing the population standard deviation, since we're using the provided standard deviation of 0.60° F, we're actually using the z-distribution. If we were dealing with smaller sample sizes or truly didn't know the population standard deviation, we would use the t-distribution as suggested.
Which description accurately describes the tide represented by the image below?
Image of the sun and moon at a 90 degree angle to Earth. An oval is around Earth that points toward and away from the moon to show the tidal bulges.
High tide
Lunar tide
Neap tide
Spring tide
Answer:
neap tide
Step-by-step explanation:
Answer:neap tide is the correct one
Step-by-step explanation:
Alison bought some shirts for her
clothing store for $15 each. She received
$50 off her entire purchase and spent a total of $440. How many shirts did Alison purchase for her store?
Answer: $29.10
Step-by-step explanation: 10.20 + 18.90 = $29.10
A sports store I'd having a sale on soccer balls. A soccer coach purchases 10 soccer balls and 2 soccers bags for $155. Another scorer coach purchases 12 soccer balls and 3 soccer bags for $189. What is the cost of a soccer ball and the cost of a soccer ball ?
Answer:
- The price of a soccer ball is $14.5
- The price of a soccer bag is $5
Step-by-step explanation:
To solve this problem, we call:
s = the price of a single soccer ball
b = the price of a soccer bag
We have:
1) A soccer coach purchases 10 soccer balls and 2 soccers bags for $155: so we can write
[tex]10s+2b=155[/tex] (1)
2) Another scorer coach purchases 12 soccer balls and 3 soccer bags for $189: so we can write
[tex]12s+3b=189[/tex] (2)
So we have a system of two equations in two unknown variables:
[tex]10s+2b=155\\12s+3b=189[/tex]
We solve it by multiplying eq.(1) by 3 and eq(2) by 2, and we get:
[tex]30s+6b=465\\24s+6b=378[/tex]
Now we substract eq(2) from eq(1) and we get:
[tex]6s=87[/tex]
So
[tex]s=\frac{87}{6}=14.5[/tex]
And by using eq(1) we also find the value of b:
[tex]10s+2b=155\\b=\frac{155-10s}{2}=\frac{155-10(14.5)}{2}=5[/tex]
So:
- The price of a soccer ball is $14.5
- The price of a soccer bag is $5
To solve this problem, we can set up a system of equations and use the elimination method to find the values of x and y. The cost of a soccer ball is $14.5 and the cost of a soccer bag is $5.
Explanation:To solve this problem, we can set up a system of equations. Let's use x to represent the cost of a soccer ball and y to represent the cost of a soccer bag.
From the first equation, we have 10x + 2y = 155. From the second equation, we have 12x + 3y = 189.
We can solve this system of equations using substitution or elimination method. I will use the elimination method.
Now we can substitute the value of x into one of the equations to find the value of y.
Therefore, the cost of a soccer ball is $14.5 and the cost of a soccer bag is $5.
On a graph, points are grouped closely together and increase.
Try to draw a line to approximate the points in the graph. Is the correlation between the variables positive or negative? Explain.
It is positive because the slope is negative.
It is positive because the slope is positive.
It is negative because the slope is negative.
It is negative because the slope is positive.
Answer: B
Step-by-step explanation:
Answer:B
Step-by-step explanation:
The price of a gallon of apple cider is $7.00 the price of eight 4.23 ounces juice boxes is $2.39 suppose the cider was instead packets like the juice in boxes approximately what is the cost per eight 4.23 ounce boxes of cider
Answer:
$1.85
Step-by-step explanation:
$7.00 is the price of 1 gallon of apple cider
Step 1
The first step would be to find how many ounces make a gallon
And 1 gallon of apple cider juice = 128 ounces
Therefore,
$7.00 makes 128 ounces of apple cider juice
Step 2
The second step is to find how many ounces make 1 packet or package boxes
Eight 4.23 ounces juice boxes = 1 packet
Therefore, 8 × 4.23 ounces = 33.84 ounces.
Step 3
To find cost per eight 4.23 ounce boxes of cider which is the cost per 33.84 ounces,
We used the proportion below.
If 128 ounces = $7
33.84 ounces = Y( we call this y because it is unknown)
We cross multiply
128 ounces × Y = $7 × 33.84 ounces
Y =($7 × 33.84 ounces) ÷ 128 ounces
Y = $1.85
Therefore, 33.84 ounces which is would cost us $1.85.
Therefore, the cost is $1.85 per eight 4.23 ounce boxes of cider.
A man bought a refrigerator, an air conditioner, a TV set and a gas cooker for $150.00, $400.00, $180.00 and $300.00 respectively. In addition he pays 15% VAT for each item. Calculate
Total VAT collected from him
Total amount he had to pay.
Answer:
1184.5
Step-by-step explanation:
150+400+180+300=1030
1030 × 15% = 154.5
(15% is also 0.15)
1030 + 154.5 = 1184.5
I hope this helps you :)
50 POINTS!
a) Write a polynomial for the perimeter of this shape. Simplify the polynomial. (The polynomial is in the photo)
b) Determine the perimeter of the shape when d = 5 m.
Answer:
a) 4d + 18
b) 38 inches
Step-by-step explanation:
a) The perimeter is simply the sum of all the exterior side lengths.
On the top, we've got d and d + 3.
On the left side, we have 2 and an unknown. However, we do know that this "unknown" + 2 will be the same length as the right side, which is 6. So, we have 2 + unknown = 6; hence, the unknown = 4.
The bottom is the same length as the top two lengths, so it's:
d + (d + 3) = 2d + 3
And, the right side is 6.
Adding these together, we have:
d + (d + 3) + 2 + 4 + d + (d + 3) + 6 = 4d + 18
b) We just need to substitute 5 in for d:
4d + 18
4 * 5 + 18 = 20 + 18 = 38 inches
AnswerAnswer:
a) 4d + 18
b) 38 inches
Step-by-step explanation:
a) The perimeter is simply the sum of all the exterior side lengths.
On the top, we've got d and d + 3.
On the left side, we have 2 and an unknown. However, we do know that this "unknown" + 2 will be the same length as the right side, which is 6. So, we have 2 + unknown = 6; hence, the unknown = 4.
The bottom is the same length as the top two lengths, so it's:
d + (d + 3) = 2d + 3
And, the right side is 6.
Adding these together, we have:
d + (d + 3) + 2 + 4 + d + (d + 3) + 6 = 4d + 18
b) We just need to substitute 5 in for d:
4d + 18
4 * 5 + 18 = 20 + 18 = 38 inches
Step-by-step explanation:
Which shows one way to determine the factors of x + 11x2 – 3x – 33 by grouping?
O x2(x + 11) + 3(x – 11)
O x²(x – 11) – 3(x – 11)
O x2(x + 11) + 3(x + 11)
O x2(x + 11) – 3(x + 11)
Answer: x^2 (x + 11) - 3 (x + 11)
Answer:
Answer: x^2 (x + 11) - 3 (x + 11)
Step-by-step explanation:
Edge
Carlos is using the quadratic formula to find the solutions of y=3x^2-5x-2. Which of the following will simplify to the correct solutions? (options on photo)
Answer:
[tex]Fx=\frac{5\pm\sqrt{25+24} }{6}[/tex]
Step-by-step explanation:
A quadratic equation in one variable given by the general expression:
[tex]ax^2+bx+c[/tex]
Where:
[tex]a\neq 0[/tex]
The roots of this equation can be found using the quadratic formula, which is given by:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
So:
[tex]y(x)=3x^2-5x-2=0[/tex]
As you can see, in this case:
[tex]a=3\\b=-5\\c=-2[/tex]
Using the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}=\frac{-(-5)\pm\sqrt{(-5)^2-4(3)(-2)} }{2(3)}=\frac{5\pm\sqrt{25+24} }{6}[/tex]
Therefore, the answer is:
[tex]Fx=\frac{5\pm\sqrt{25+24} }{6}[/tex]
A cartoon last is one 1/2 of an hour. A movie is 6 times longer than the cartoon. How many minutes does it take to watch both the cartoon and the movie? (1hour = 60 minutes)
Final answer:
The cartoon lasts 30 minutes, and the movie is six times longer, adding up to 210 minutes to watch both.
Explanation:
The subject at hand is the duration it takes to watch a cartoon and a movie. The cartoon lasts half an hour (30 minutes), while the movie is six times longer than the cartoon. To find the duration of the movie, we multiply its relative length by the duration of the cartoon. So, 6 times 30 minutes is 180 minutes. To calculate the total time to watch both the cartoon and the movie, we add the two durations together. Therefore, 30 minutes for the cartoon plus 180 minutes for the movie equals 210 minutes in total.
21.
In the standard equation for a line, what does the variable b stand for?
y = mx + b
X-coordinate
y-coordinate
y-intercept
slope
Answer:
b = y intercept
Step-by-step explanation:
y = mx +b
This is the slope intercept form of a line
The m is the slope and the b is the y intercept
Find the x and y intercepts: 7x - 2y = 28
Answer:
x-intercept(s): ( 4, 0)
y-intercept(s): ( 0, -14)
I don't know how to do a math problem because I really am really bad at math so I was wondering if somebody can help me and my mom will help me or my dad so I really need your help please help me thank you
Answer:
uh my good sir whats your question we cant help if we dont know what the questions is.
Step-by-step explanation:
PLEASE HELP FAST Convert the following equation to logarithmic or exponential form:
log subscript 49 left parenthesis 7 right parenthesis equals 1 half
Your answer:
49 to the power of 7 equals 1 half
7 to the power of 49 equals 1 half
open parentheses 1 half close parentheses to the power of 7 equals 49
49 to the power of 1 half end exponent equals 7
Answer:
D
Step-by-step explanation:
I interpret your problem as log49(7)=1/2
This would be the same as 49^1/2=7 because taking a number to the 1/2 power is the same as taking its square root [sqrt(49)=7].
9+___=10
1+____=10
200+500+2000-3000
Answer:
1
Step-by-step explanation:
To solve the equations, subtract the given number from the sum on the left side of the equation to find the missing number. For the arithmetic expression, perform the operations in order.
Explanation:In the first equation, you must find a number that, when added to 9, equals 10. To do this, subtract 9 from 10, which gives you 1. Therefore, the missing number is 1.
In the second equation, you need to find a number that, when added to 1, equals 10. Subtract 1 from 10 to get 9. So, the missing number is 9.
In the last equation, you simply need to perform the arithmetic operations in order: 200 + 500 = 700, 700 + 2000 = 2700, and finally 2700 - 3000 = -300. Therefore, the result of the expression 200 + 500 + 2000 - 3000 is -300.
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factorise this expression as fully as you can 12x^3-9x^2
The factor of the expression 12x³ – 9x² will be 3x² and (4x – 3).
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given below.
⇒ 12x³ – 9x²
Then the factor of the expression will be
⇒ 3x²(4x – 3)
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please i need help it is due in 2 mins
Answer:
mean = 9.3
median = 10
mode =13
Step-by-step explanation:
First put the data in order from smallest to largest
1,1,7,9,9,10,11,13,13,13,15
The mean is the sum of all the numbers divide by how many numbers we have
(1+1+7+9+9+10+11+13+13+13+15)/11102/11=9.272727=9.3
median is the middle number
11/2 = 5.5
The sixth number is the median= 10
mode is most often 13 appears the most
An oblique prism with a square base of edge length x units has a volume of One-halfx3 cubic units. Which expression represents the height of the prism?
Answer:
1/2x units
Step-by-step explanation:
Answer:
1/2x units
Step-by-step explanation:
PLEASE HELP!!!! for the given situation identify the independent and dependent variables and then find a reasonable domain and range of values. Listed below will be four statements that relate to the given situation. She’s the statement that would have to be false given the situation and it’s parameters.
sue has just one evening to study for her math test she believes the more she still needs to hire her test score will be
here are the statements
1) The range will be from 0 to 100 points
2) The dependent variable will be her test score
3) The independent variable be the number of hours to study
4) The domain will be from 0 to 25 hours
Rowan has two pieces of cable, one 15 feet long and the other 12 feet long. For a science project he wants to cut them up to produces pieces of cable that are all the same length, with no cable left over. What is the greatest length, in feet, that he can make them?
Answer:
The greatest length she can cut to have equal length in all the cables, without a left over is 3 feet each
Step-by-step explanation:
in order to solve this, we treat the length of each cable as separate numbers for which we find the highest common factor, since we are told that they must all be of the same length. The highest common factor of two whole numbers, is the highest number which completely divides both number without a remainder. The highest common factor is found as follows:
Factors of 12 are : 1, 2, 3, 4, 6, and 12
factors of 15 are : 1, 3, 5, and 15
from the above, the highest factor that is common to both numbers is 3.
Therefore, if both cables are cut into 3 feet each, , a total of 9 pieces of cables (4 from the 12 feet cable and 5 from the 15 feet cable) of equal length will be obtained without any remainder.
Answer:
3 feet
Step-by-step explanation:
To solve this problem the heed to find the factors of 15 and 12
Factors of both numbers
12 : 1,2,3,4,6,12
15: :1.3,5,15
Then we find the highest common factor between them which is 3, 3 is a factor of both 12 and 15
remainder. The highest common factor is found as follows:
So, if both cables are cut into 3 feet each, you should have a total of 9 piecesa total of 9 pieces of cables.
From the 12 feet long cable you should have 3 feet x 4 meaning 4 pieces
From the 15 fert long cable you should have 3 feet x5 meaning 5 pieces
4+5 makes it 9 pieces without any remainder
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
If interest rates stay at 4% APR and I continue to make my monthly $50 deposits into my retirement plan, I should have at least $30 comma 000 saved when I retire in 25 years.
The statement ___________ because I will have $ ___________ nothing in my retirement account when I retire in 25 years.
(Round to the nearest cent as needed.)
Answer:
False
$25,706.48
Step-by-step explanation:
The annual percentage rate (APR) is 4%, so the monthly rate is 4%/12 = ⅓%.
25 years = 300 months.
The monthly deposit (annuity) is $50.
The future value of the annuities is:
F = A [(1 + i)ⁿ − 1] / i
Given i = 1/300, A = 50, and n = 300:
F = 50 [(1 + 1/300)³⁰⁰ − 1] / (1/300)
F = 25,706.48
The statement is false. The amount after 25 years is less than $30,000.
The statement doesn't make sense because if you make $50 monthly deposits at a 4% APR for 25 years, you will have approximately $41,981.86 in your retirement account, not only $30,000.
Explanation:The statement does not make sense or is clearly false. Let's add up the total deposits over 25 years and calculate the interest gained using the given annual percentage rate (APR) of 4%.
Total deposits = $50/month * 12 months/year * 25 years = $15,000Using formula for compound interest, Final Value = P (1 + r/n)^(nt) where P is principal amount (initial investment), r is annual interest rate (decimal), n is number of times that interest applied per time period, t is time the money is invested for. In this case, P=$50, r=4%/12/100%=0.003333, n=1 (monthly), t=12*25=300. After calculations, the final value comes to approximately $41,981.86Therefore, if you continue to make $50 monthly deposits with a 4% APR for 25 years, you will have just under $41,981.86 in your retirement account, not $30,000 as stated. So, the statement is inaccurate.
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UIME REMAINING
02:44:54
Rate the following bank accounts from most to least liquid: CD, savings account, checking account, money market account
a CD, savings account, checking account, money market account
b. Savings account, checking account, CD, money market account
CD, money market account, savings account, checking account
d. Checking account, savings account, money market account, CD
C
Please select the best answer from the choices provided
Mark this and retum
Save and Exit
Submit
Answer:
b
Step-by-step explanation: