Answer:
(a) {5}
(b) {1, 2, 5, 6}
(c) {1, 2, 5, 6}
The initial population of the town was estimated to be 12,500 in 2005. The population has increased by about 5.4% per year since 2005.
Formulate the equation that gives the population, A(x) , of the town x years since 2005. If necessary, round your answer to the nearest thousandth.
A(x)=__(_)^x
Answer:
[tex]A(x) = 12500(1.054)^x[/tex]
Step-by-step explanation:
Exponential equation for population growth:
Considering a constant growth rate, the population, in x years after 2005, is given by:
[tex]A(x) = A(0)(1 + r)^x[/tex]
In which A(0) is the population in 2005 and r is the growth rate, as a decimal.
The initial population of the town was estimated to be 12,500 in 2005.
This means that [tex]A(0) = 12500[/tex]
The population has increased by about 5.4% per year since 2005.
This means that [tex]r = 0.054[/tex]
So
[tex]A(x) = A(0)(1 + r)^x[/tex]
[tex]A(x) = 12500(1 + 0.054)^x[/tex]
[tex]A(x) = 12500(1.054)^x[/tex]
Will give brainliest
A tablet at a local electronics store is in high demand and will only be available to customers for a limited time. The store initially has 4 cases of the tablet on hand. The store manager receives new supplies of the tablet each week. At the beginning of week 1, the store manager receives an additional order from the distributor of 5 cases of tablets. At the beginning of week 6, the manager receives another order of 10 cases. Which of the following equations best models the scenario for how many cases of the tablet the store can expect to receive each week?
a. y=4
b. y=x+4
c. y=-6x
What is the quotient of the synthetic division problem below, written in
polynomial form?
5)2 1 -55
O A. -2x+11
O B. -2x+9
O C. 2x+11
O D. 2x+9
Answer:
C. 2x+11
Step-by-step explanation:
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
2x+11≈21 -55
What is the x intercept of the graph that is shown below? Please help me
Answer:
(-2,0)
Step-by-step explanation:
The x intercept is the value when it crosses the x axis ( the y value is zero)
x = -2 and y =0
(-2,0)
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 10 (newly deceased) adults, the mean failure strain (%) was 24.0, and the standard deviation was 3.2.
Required:
a. Assuming a normal distribution for failure strain, estimate true average strain in a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about precision and reliability. How does the prediction compare to the estimate calculated in part (a)?
Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
II. Round to the nearest hundred.
11. 582
12. 1,234
13. 640
14. 770
15. 1,104 can you please tell what the answer?
Answer:
582-600
1,234-1,200
640-600
770-800
1,104-1,100
Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the π button on your calculator to solve.
Answer:
628 mi^3
Step-by-step explanation:
the volume of a cylinder is given by:
V = base area x height
thus,
V = (3.14)(5)^2(8)
V = (3.14)(25)(8)
V = 628 mi^3
the volume of the cylinder is 628 cubic miles
The volume of the cylinder is 628 cubic miles.
We have a cylinder of radius 5 mi and height 8 mi.
We have to find the volume of the figure and round it to nearest tenth.
What is the volume of cylinder?The volume of cylinder is given by the formula -
Volume [tex]=\pi r^{2} h[/tex]
We can use the above formula to calculate the volume of cylinder. In our case -
r = 5 mi
h = 8 mi
Substituting the values in the formula -
Volume [tex]=\pi\times5^{2}\times 8\\\\[/tex] = 628 cubic miles.
Hence, the volume of the cylinder is 628 cubic miles.
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A meat packaging plant uses a machine that packages chicken livers in six pound portions. A sample of 91 packages of chicken livers has a standard deviation of 0.47. Construct the 98% confidence interval to estimate the standard deviation of the weights of the packages prepared by the machine. Round your answers to two decimal places.
Lower endpoint______ Upper endpoint__
Answer:
it simple as look
Step-by-step explanation:
He y I a m r a v I t ha n k S
Wowowowowowowowowk
How do you make 2.318181818 a mixed number
The sum of a number and its inverse is 3 29 / 52. Find the number?
Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden. She measured the heights (in inches) of 12 randomly selected plants and recorded the data:
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
What is the sample mean of the heights of the plants in Susan's garden?
Answer:
3.5 inches
Step-by-step explanation:
Sample mean basically means that we need to find the average of the samples.
So the formula for finding average is
Number of observations/ Number of Occurrences
So when we add the values together we get
42.
So there are 12 numbers
So, 42/12 =
3.5 inches
The sample mean of the heights of the plants in Susan's garden is
3.5 inches.
Here,
Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden.
She measured the heights (in inches) of 12 randomly selected plants and recorded the data:
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
We have to find the sample mean of the heights of the plants in Susan's garden.
What is Average?
Average value in a set of given numbers is the middle value, calculate as dividing the total of all values by the number of values.
Now,
The recorded data is;
1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0
To find the sample mean of the heights of the plants in Susan's garden we have to find the average of the recorded data.
Formula for average = [tex]\frac{sum of number of observation}{ number of occurrence}[/tex]
Hence, Average = [tex]\frac{1.0+ 1.4+1.8+2.0+ 2.5+3.5+4.2+4.5+ 4.8+ 5.0+ 5.3+ 6.0}{12} = \frac{42}{12} = 3.5[/tex]
Therefore, The sample mean of the heights of the plants in Susan's garden is 3.5 inches.
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The expression y + y + 2y is equivalent to ??
because ??
Answer:
4y
They would have the same value if a number was substituted for y
Step-by-step explanation:
y+y+2y =
Combine like terms
4y
These are all like terms
They would have the same value if a number was substituted for y
Let y = 5
5+5+2(5) = 5+5+10 = 20
4(5) =20
Suppose that we ask n randomly selected people whether they share your birthday. (a) Give an expression in terms of n for the probability that no one shares your birthday (ignore leap years). $$ Correct: Your answer is correct. (b) What is the least number of people we need to select so that the probability is at least 0.8 that at least one person shares your birthday
Using the binomial distribution, it is found that:
a) The expression is [tex]\left(\frac{364}{365}\right)^{n}[/tex]
b) You need to select at least 587 people.
For each person, there are only two possible outcomes, either they share your birthday, or they do not. The probability of a person sharing your birthday is independent of any other person, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.There are 365 days in a non-leap year, hence, the probability of each person sharing your birthday is [tex]p = \frac{1}{365}[/tex]
Item a:
This probability is P(X = 0), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{n,0}.\left(\frac{1}{365}\right)^{0}.\left(\frac{364}{365}\right)^{n} = \left(\frac{364}{365}\right)^{n}[/tex]
Hence, the expression is [tex]\left(\frac{364}{365}\right)^{n}[/tex]
Item b:
The probability that at least one person shares your birthday is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
We want that:
[tex]P(X \geq 1) \geq 0.8[/tex]
Hence:
[tex]1 - P(X = 0) \geq 0.8[/tex]
[tex]P(X = 0) \leq 0.2[/tex]
Hence:
[tex]\left(\frac{364}{365}\right)^{n} \leq 0.2[/tex]
[tex]n\log{\left(\frac{364}{365}\right)} \leq \log{0.2}[/tex]
[tex]n \geq \frac{\log{0.2}}{\log{\left(\frac{364}{365}\right)}}[/tex]
[tex]n \geq 586.6[/tex]
Rounding up: You need to select at least 587 people.
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A person invests 3500 dollars in a bank. The bank pays 4.75% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 5800 dollars?
9514 1404 393
Answer:
10.7 years
Step-by-step explanation:
The formula for the balance in an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where principal P is invested at annual rate r compounded n times per year for t years. We want to solve for t.
5800 = 3500(1 +0.0475/4)^(4t)
58/35 = 1.011875^(4t) . . . divide by 3500 and simplify a bit
log(58/35) = 4t·log(1.011875) . . . . take logs
t = log(58/35)/(4·log(1.011875)) . . . . divide by the coefficient of t
t ≈ 10.6966 ≈ 10.7
The person must leave the money n the bank for about 10.7 years for it to reach $5800.
Use the compound interest formula to find the annual interest rate, r, if in 2 years an investment of 4,000 grows to 4410 The rate is %.
Answer:
5%
Step-by-step explanation:
Bank amount=PA*(1+r/100)^t
4410=4000*(1+x/100)^2
1.05=(1+x/100), x=5%
The function f is defined by f(x) = 4x + 1. What is the value of f(3)?
O 13
O 17
O 65
O 82
Answer:
13
Step-by-step explanation:
f(x) = 4x + 1
Let x= 3
f(3) = 4*3+1
= 12+1
= 13
The rationalisation factor of 2 + √3 is
step by step for BRAINLIST
Answer:
rationalising factor wud be
2 - root3
as on multiying both and applying identity we end up
2^2 - (root3)^2
4 - 3 = 1
we got a rational number so rationalisng factor is
2 - root3
PLEASE HELP!! WHOEVER HELPS FIRST AND GETS IT CORRECT GETS BRAILIEST!! By the way, TWO people need to answer so I can mark brainliest.
Answer:
0.045
Step-by-step explanation:
(0,4x0,5x0,3)-(0,2x0,5x0,15)
I need help for this math question!
Answer:
D
Step-by-step explanation:
Assuming that the expression is referring to sin²(2πft) and not sin²(2)πft, we can solve as follows:
One trigonometric identity states that sin²x+cos²x = 1. We want to express this in terms of cos²x, so we need to solve for sin²x. Subtracting cos²x from both sides, we get 1-cos²x = sin²x. Plugging (2πft) for x, we get
1-cos²(2πft) = sin²(2πft)
We can plug that into our equation to get
P = I₀²R(1-cos²(2πft)), or D
The total cost, C, for running an advertisement in a local newspaper, The Free Press, is made up of an initial cost of $12 plus a charge of $5 per day. A rival newspaper, The Banner, is currently running a special on advertisements at $8 per day with no initial cost.
a) Write an equation representing the cost in The Free Press.
b) Write an equation representing the cost in The Banner.
c) For each newspaper, create a table of values.
d) Use Rapid Tables (will need to select 2 lines from the drop down - see example in relation to the Jason's Trip graph below) to graph each cost on the same set of coordinate axis. Your two lines will represent The Free Press and The Banner. You are also able to create the graph on other technology or a piece of paper.
e) Which newspaper would you use for an ad that ran 1 day?
f) Which newspaper would you use for an ad that ran 12 days?
Answer:
(a) [tex]C(x) = 12 + 5x[/tex]
(b) [tex]C(x) = 8x[/tex]
(c) Tables
(d) See attachment for graph
(e) Banner newspaper
(f) Free press newspaper
Free Press
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}[/tex]
Banner
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}[/tex]
Step-by-step explanation:
Given
Free Press
[tex]Initial = 12[/tex]
[tex]Rate =5[/tex]
Banner
[tex]Initial=0[/tex]
[tex]Rate =8[/tex]
Solving (a): Free Press Equation
This is calculated as:
[tex]C(x) = Initial + Rate * x[/tex]
Where
[tex]x \to[/tex] days
So, we have:
[tex]C(x) = 12 + 5x[/tex]
Solving (b): Banner Equation
This is calculated as:
[tex]C(x) = Initial + Rate * x[/tex]
Where
[tex]x \to[/tex] days
So, we have:
[tex]C(x) = 0 + 8x[/tex]
[tex]C(x) = 8x[/tex]
Solving (c): Table of values
For free press, we have:
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}[/tex]
C(x) is calculated as:
[tex]x = 1;\ C(1) = 12 + 5* 1 =17[/tex]
[tex]x = 2;\ C(2) = 12 + 5* 2 =22[/tex]
..
[tex]x = 5;\ C(5) = 12 + 5* 5 =37[/tex]
For banner, we have:
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}[/tex]
C(x) is calculated as:
[tex]x = 1;\ C(1) = 8* 1 =8[/tex]
[tex]x = 2;\ C(2) = 8* 2 =16[/tex]
..
[tex]x = 5;\ C(5) = 8* 5 =40[/tex]
Solving (d): Graph of both using rapidtable
See attachment
Solving (e) Newspaper to use for 1 day
From the graph, when [tex]x = 1[/tex]
[tex]Free\ press = 17[/tex]
[tex]Banner = 8[/tex]
So, we use Banner newspaper because it is cheaper
Solving (f) Newspaper to use for 12 days
From the graph, when [tex]x = 12[/tex]
[tex]Free\ press = 72[/tex]
[tex]Banner = 96[/tex]
So, we use free press newspaper because it is cheaper
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and three Chevrolets cost $107 per day, whereas four Nissans, three Fords, and two Chevrolets cost $102 per day. Find the rental rate for the Fords.
Answer:
The rental rate for the Fords is of $12 per day.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the cost of a Nissan.
y is the cost of a Ford.
z is the cost of a Chevrolet.
Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day.
This means that:
[tex]3x + 2y + 4z = 106[/tex]
Two Nissans, four Fords, and three Chevrolets cost $107 per day
This means that:
[tex]2x + 4y + 3z = 107[/tex]
Four Nissans, three Fords, and two Chevrolets cost $102 per day.
This means that:
[tex]4x + 3y + 2z = 102[/tex]
From the first equation:
[tex]4z = 106 - 3x - 2y[/tex]
[tex]2z = 53 - 1.5x - y[/tex]
[tex]z = 26.5 - 0.75x - 0.5y[/tex]
Replacing into the third equation:
[tex]4x + 3y + 53 - 1.5x - y = 102[/tex]
[tex]2.5x + 2y = 49[/tex]
From the second equation:
[tex]2x + 4y + 3z = 107[/tex]
[tex]2x = 107 - 4y - 3z[/tex]
[tex]x = 53.5 - 2y - 1.5z[/tex]
[tex]x = 53.5 - 2y - 1.5(26.5 - 0.75x - 0.5y)[/tex]
[tex]x - 1.125x = 53.5 - 2y - 39.75 + 0.75y[/tex]
[tex]-0.125x = 13.75 - 1.25y[/tex]
[tex]0.125x = 1.25y - 13.75[/tex]
[tex]x = \frac{1.25y - 13.75}{0.125}[/tex]
[tex]x = 10y - 110[/tex]
Find the rental rate for the Fords.
We have to find y, so:
[tex]2.5x + 2y = 49[/tex]
[tex]2.5(10y - 110) + 2y = 49[/tex]
[tex]25y - 275 + 2y = 49[/tex]
[tex]27y = 324[/tex]
[tex]y = \frac{324}{27}[/tex]
[tex]y = 12[/tex]
The rental rate for the Fords is of $12 per day.
the value of M such that 3 3 M + 3 = 9 M + 4
Step-by-step explanation:
If you like my answer than please mark me brainliest
[tex]\\ \sf\longmapsto 33M+3=9M+4[/tex]
Interchange sides[tex]\\ \sf\longmapsto 33M-9M=4-3[/tex]
[tex]\\ \sf\longmapsto (33-9)M=1[/tex]
[tex]\\ \sf\longmapsto 24M=1[/tex]
[tex]\\ \sf\longmapsto M=\dfrac{1}{24}[/tex]
у
х
9
3
Find the value of y.
9514 1404 393
Answer:
(d) 6√3
Step-by-step explanation:
There are several ways to work multiple-choice problems. One of the simplest is to choose the only answer that makes any sense. Here, that is 6√3.
y is the hypotenuse of the medium-sized right triangle, so will be longer than that triangle's longest leg. y > 9
The only answer choice that meets this requirement is ...
y = 6√3
__
In this geometry, all of the right triangles are similar. This means corresponding sides have the same ratio. For y, we're interested in the ratio of long leg to hypotenuse.
long leg/hypotenuse = y/(9+3) = 9/y
y² = 9(9+3) = 9·4·3
y = 3·2·√3 . . . . . . take the square root
y = 6√3
__
Additional comments
You may notice that y is the root of the product of the longer hypotenuse segment (9) and the whole hypotenuse (9+3 = 12). We can say that y is the "geometric mean" of these segment lengths. Similarly (pun only partially intended), x will be the root of the product of the short segment (3) and the whole hypotenuse (12)
x = √(3·12) = 6
This is another "geometric mean" relation.
Further, the altitude will be the geometric mean of the two segments of the hypotenuse:
h = √(9·3) = 3√3
A way to summarize all of these relations is to say that the legs of the right triangle that are not the hypotenuse are equal to the geometric mean of the segments of the hypotenuse that the leg intercepts.
x = √(3·12)
y = √(9·12)
h = √(3·9)
Find the missing side round to the nearest tenth
======================================================
Work Shown:
sin(angle) = opposite/hypotenuse
sin(29) = x/24
24*sin(29) = x
x = 24*sin(29) ..... exact value
x = 11.635430885912 .... approximate value
x = 11.6
To get the approximate value, you'll need a calculator. Make sure the calculator is in degree mode.
Lesson 1 Skills Practice
Lines For Exercises 1-12, use the figure at the right. In that figure, line m is parallel.
Classify each pair of angles as alternate interior, alternate exterior, or corresponding.
Pictures Below.
9514 1404 393
Answer:
alternate interior: (2, 4), (3, 5)alternate exterior: (1, 7), (43°, 6)corresponding: (1, 5), (2, 6), (3, 7), alternate interior: (2, 4), (3, 5)corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)4)
Step-by-step explanation:
In this geometry, "corresponding" angles are in the same direction from the point of intersection of the transversal with the parallel line.
"Alternate" refers to angles on opposite sides of the transversal. "Interior" and "exterior" refer to angles between and outside of the parallel lines, respectively.
Here, we list all angle pairs in each classification, so you can answer questions 1-12 based on this list.
alternate interior: (2, 4), (3, 5)
alternate exterior: (1, 7), (43°, 6)
corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)
__
Additional classifications are also used:
consecutive (same-side) interior: (2, 5), (3, 4)
consecutive (same-side) exterior: (1, 6), (43°, 7)
vertical: (1, 3), (2, 43°), (4, 6), (5, 7)
linear pairs: (1, 2), (1, 43°), (2, 3), (3, 43°), (4, 5), (4, 7), (5, 6), (6, 7)
look below for the image
Answer:
135.7 yd²
Step-by-step explanation:
Surface area of the cone,
πr²+πrl
= π×3²+π×11.4×3
= 43.2π
= 135.7 yd² (rounded to the nearest tenth)
What are 3 ratios that are equivalent to 8 :5
Answer:
Step-by-step explanation:
8/5 = 16/10 = 24/15
8:5 = 16:10 = 24:15
Please please help!! Quickly
Answer:
pretty sure its D
Answer:
I have to give 2 Ans for my question
A group of hens lays 69 eggs in a single day. On one particular day, there were 7 brown eggs and 62 white eggs. If four eggs are selected at random, without replacement, what is the probability that all four are brown?
Answer:
The probability will 4.32%.
The probability that all four are brown is 35/8,64,501.
Given that, A group of hens lays 69 eggs in a single day. On one particular day, there were 7 brown eggs and 62 white eggs.
What is the probability without replacement?Probability without replacement means once we draw an item, then we do not replace it back to the sample space before drawing a second item. In other words, an item cannot be drawn more than once.
If four eggs are selected at random, without replacement, the probability that all four are brown is 7/69 × 6/68 × 5/67 × 4/66
= 7/69 × 3/34 × 5/67 × 2/33
=7/23 × 1/17 × 5/67 × 1/33
=35/8,64,501
Therefore, the probability that all four are brown is 35/8,64,501.
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8.113 as a fraction PLEASE HELPP
Answer:
8 113/1000(as a mixed number) 8113/1000(as an improper fraction)
Step-by-step explanation:
1. Convert 0.113 to a fraction...113/1000
2. As there is no further simplification needed, add 8 to 113/1000....8 113/1000
3. To convert 8 113/1000 from a mixed number to an improper fraction, multiply 8 (the whole number) and 1,000(the denominator)...8,000. Then add 113 (the numerator) to 8,000...8113. After that, you put 8113 over the denominator of the previous mixed number, getting 8113/1000 as the improper fraction.
