Answer:
27.71
Step-by-step explanation:
Using Google, we can find that if we plug in the area, a, the formula for the area of the triangle is [tex]\frac{\sqrt{3} }{4} a^{2}[/tex]. Plugging it in, we get [tex]\frac{\sqrt{3} }{4} * 64[/tex] = 27.71 (approximately)
Area of an equilateral triangle that has sides that are [tex]8[/tex] inches long is equal to [tex]\boldsymbol{16\sqrt{3}}[/tex] square inches
A triangle is a polygon that consists of three sides and three angles.
An equilateral triangle is a triangle in which all sides are equal and all angles are equal.
Length of a side of an equilateral triangle [tex](l)=8[/tex] inches
Area of an equilateral triangle [tex](A)=\boldsymbol{\frac{\sqrt{3}}{4}l^2}[/tex]
[tex]=[/tex][tex]\boldsymbol{\frac{\sqrt{3}}{4}(8)^2}[/tex]
[tex]=\boldsymbol{16\sqrt{3}}[/tex] square inches
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Jose spent 2 3/10 hours playing basketball outside, and he played outside for a total of 5 hours. How many hours did he NOT spend playing basketball?
Answer:2 7/10 hours
Step-by-step explanation:
Subtract 2 3/10 out of 5
Answer: 2 7/10
Step-by-step explanation:
Hours spent in basketball= 2 3/10
Total hours spent outside= 5 hours
To get The number of hours he didn't basketball will be (5hours - 2 3/10)
5 - 23/10 = 2 7/10 .
A group of science students spotted 53 birds there were six times as many sparrows as Blue Jays and there were four Falcons how many of each bird were there
Final answer:
We found there were 7 Blue Jays, 42 sparrows, and 4 Falcons.
Explanation:
The question involves solving a simple algebraic problem to determine the number of sparrows and Blue Jays when given the total number of birds and the number of Falcons.
To solve this, let's define the number of Blue Jays as x.
The number of sparrows is six times the number of Blue Jays, so we can express that as 6x.
We are told there are four Falcons.
The total number of birds spotted is 53.
We can set up the equation as:
x + 6x + 4 = 53
Solving this equation:
Combine like terms: 7x + 4 = 53Subtract 4 from both sides: 7x = 49Divide both sides by 7: x = 7Since x represents the number of Blue Jays, there are 7 Blue Jays.
To find the number of sparrows, multiply 7 by 6, which gives us 42 sparrows.
We were also told there are four Falcons.
So the group saw 42 sparrows, 7 Blue Jays, and 4 Falcons.
A textbook store sold a combined total of 257 math and psychology textbooks in a week. The number of math textbooks sold was 87 more than the number of psychology textbooks sold. How many textbooks of each type were sold?
Answer:
85 psychology172 mathStep-by-step explanation:
Let p represent the number of psychology textbooks sold. Then the total number sold was ...
p + (p+87) = 257
2p = 170 . . . . . .subtract 87; next divide by 2
p = 85 . . . . . . . psychology books sold
p+87 = 172 . . . math books sold
85 psychology textbooks and 172 math textbooks were sold.
Explanation:Let's denote the number of psychology textbooks sold as x. According to the problem, the number of math textbooks sold, which is 87 more than the psych books, can be represented as x + 87. The total number of textbooks sold is expressed in the problem as 257, which is the sum of the psych books (x) and the math books (x + 87). So:
x (psych books) + x + 87 (math books) = 257
We can simplify this to 2x + 87 = 257. If we subtract 87 from both sides, we'll get 2x = 170. Dividing both sides by 2 results in x = 85. This tells us that 85 psychology books were sold.
Then to find the number of math books, we can use the original relationship given: math books = psychology books + 87, therefore, 85 + 87 = 172 math books.
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Two non-common sides of adjacent supplementary angles form a _____ angle.
A. reflex
B. acute
C. straight
D. obtuse
Answer:
C. straight
Step-by-step explanation:
A Linear Pair is two adjacent angles whose non-common sides form opposite rays.
If two angles form a linear pair, the angles are supplementary.
A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.
In the figure given in attachment, AB and BC are two non common sides of ∠ABD and ∠DBC.
∠1 and ∠2 form a linear pair.
The line through points A, B and C is a straight line.
∠1 and ∠2 are supplementary.
Thus two non-common sides of adjacent supplementary angles form a straight angle.
The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm , find the dimensions of the poster with the smallest area.
Answer:
24 cm wide by 36 cm high
Step-by-step explanation:
The poster with the smallest area will have an aspect ratio that makes the margin dimensions the same percentage of overall dimension in each direction.
Since the ratio of margin widths is 6:4 = 3:2, the poster and printed area will have an aspect ratio of 3:2. That is, the width is ...
width of printed area = √(2/3·384 cm²) = 16 cm
Then the width of the poster is ...
width = left margin + printed width + right margin = 4cm + 16 cm + 4 cm
width = 24 cm
The height is 3/2 times that, or 36 cm.
The smallest poster with the required dimensions is 24 cm wide by 36 cm tall.
_____
If you need to see the calculus problem, consider the printed area width to be x. Then the printed height is 384/x and the overall dimensions are ...
(x + 8) by (384/x + 12)
We want to minimize the area, which is the product of these dimensions:
a = (x +8)(384/x +12) = 384 +12x +3072/x +96
a = 12x + 3072/x +480
This is a minimum where its derivative is zero.
a' = 12 -3072/x^2 = 0
a' = 1 -256/x^2 = 0 . . . . . . divide by 12; true when x^2 = 256
This has solutions x=±16, of which the only useful solution is x=16.
The music department of a department store sold 12 jazz CDs last month. Jazz sales during that month made up 2% of the music departments total sales. Determine the number of CDs that the store sold during that month
12 CDs ............... 2 %
x CDs .............100 %
x = 12×100/2 = 1200/2 = 600 Cds/month
The required number of CD that was sold last month is 600 CD's.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the number of total CDs sold be x,
The music department of a department store sold 12 jazz CDs last month.
Jazz sales during that month made up 2% of the music department's total sales.
2% of x = 12
x = 12 / 2%
x = 12 / 0.02
x = 600
Thus, the required number of CD that was sold last month is 60 CD's.
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What is DC ?
Enter the answer in the box.
Answer:
DC = 30
Step-by-step explanation:
Point D is the circumcenter of triangle ABC, so it is equidistant from A, B, and C.
We are given the measures of DE and AE, so we can figure AD using the Pythagorean theorem:
AD² = AE² + DE² . . . . . . . . . . . . . . . E bisects AB, so AE=AB/2=18
AD = √(18² +24²) = √900 = 30
DC = AD
DC = 30
If A is the initial amount put into an account, P is the annual percentage rate of interest, which remains fixed, and the account compounds quarterly, which of the following is an expression, in terms of A and P, for the amount in the Account after 5 years?
A 4A(p100)5
B A(p100)20
C 4A(1+p100)5
D A(1+p25)20
E A(1+p400)20
Answer: The amount in the account is A = A(1 + P/400)^20
Step-by-step explanation:
Initial amount deposited into the account is A. This means that the principal is A, so
P = A
It was compounded quarterly. This means that it was compounded once in four months. So
n = 4
The rate at which the principal was compounded is P%. So
r = P/100
It was compounded for a total of 5 years. So
n = 5
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of n years.
Let A = B
B = A(1 + (P/100)/4)^4×5
A = A(1 + P/400)^20
Final answer:
The correct expression for the amount in an account after 5 years, where interest is compounded quarterly, is D. [tex]A(1 + \frac{P}{25})^{20}[/tex].
Explanation:
When calculating the future value of an investment with compound interest, it's important to consider the initial amount A, the annual interest rate P, the number of times the interest is compounded per year, and the total number of years the money is invested. In this question, where the account compounds quarterly for 5 years, the formula for compound interest applies, which is:
P(t) = [tex]A(1 + \frac{r}{n})^{nt}[/tex]
Here, r represents the annual nominal interest rate in decimal form [tex](\frac{P}{100})[/tex], n is the number of times interest is compounded per year, and t is the number of years the money is invested. Given that the account compounds quarterly, n equals 4. So after 5 years, the formula would be:
P(5) = [tex]A(1 + \frac{P}{400})^{(4 \times 5)}[/tex]
Based on the options provided in the question, the correct expression for the amount in the account after 5 years, in terms of A and P, when compounded quarterly is:
D. [tex]A(1 + \frac{P}{25})^{20}[/tex]
In order to obtain a sample of voters in Pennsylvania, a simple random sample of 10 counties is selected. From each of the selected counties, 10 precincts are chosen at random. Finally, from each of these 100 precincts , a simple random sample of 20 voters students is selected. Thus, the final sample consists of 2,000 voters.
This is an example of which type of sampling strategy?a) Simple random samplingb) Stratified samplingc) Multistage samplingd) Convenience sampling
Answer:
c) Multistage sampling.In statistics, there are several strategies to select a sample. Remember that a sample is a sub group selected from a population. This sample selection must be random to have more reliability in the research, each answer option represents a type of sampling.
In this case, the researcher is using a multistage sampling, because it consists in taking smaller sample units at each stage, which is being done in this example. First, is selected a number of counties, then the precincts, and at the end the voters. By this way, the sample is being reduced to less subjects at each stage.
The sampling strategy described is an example of c) multistage sampling. This technique helps in reducing complexity and cost.
The sampling strategy described in the question is an example of multistage sampling.
In this process:
A simple random sample of 10 counties in Pennsylvania is selected.From each of these counties, 10 precincts are chosen randomly.Finally, from each of these 100 precincts, a simple random sample of 20 voters is selected.This results in a final sample of 2,000 voters.Multistage sampling is used to reduce the complexity and cost of data collection by breaking the population into smaller groups at each stage.
When 3010 adults were surveyed in a poll, 27% said that they use the Internet. Is it okay for a newspaper reporter to write that "1 divided by 4 of all adults use the Internet"? Why or why not? Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
The test statistic is z = ?. (Round to two decimal places as needed.)The P-value is ?. (Round to four decimal places as needed.)Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim. (Assume a 0.05 significance level.)
Answer:
Null hypothesis:[tex]p=0.25[/tex]
Alternative hypothesis:[tex]p \neq 0.25[/tex]
z=2.53
pv=0.0114
So based on the p value obtained and using the significance given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they use the Internet differs from 0.25 or 25% .
Step-by-step explanation:
1) Data given and notation
n=3010 represent the random sample taken
X represent the people who says that said that they use the Internet.
[tex]\hat p=\frac{X}{106}=0.27[/tex] estimated proportion of people who says that said that they use the Internet.
[tex]p_o=0.25[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that 50% of people who says that they would watch one of the television shows.:
Null hypothesis:[tex]p=0.25[/tex]
Alternative hypothesis:[tex]p \neq 0.25[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.27 -0.25}{\sqrt{\frac{0.25(1-0.25)}{3010}}}=2.53[/tex]
4) Statistical decision
P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
We have the significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z>2.53)=2*(0.0057)=0.0114[/tex]
So based on the p value obtained and using the significance given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they use the Internet differs from 0.25 or 25% .
Craig has £13.40 he sees this offer in a restaurant :main courses £8.90 each.Buy one main course and get the second half price. Can he afford to buy two main courses?Show your working
Answer:
Yes
Step-by-step explanation:
Full price for first course: £8.90
Half price: £4.45
One and one half times
full price is then: £13.35
Since this is less than Craig's £13.40, he can just barely afford to buy two main courses at these prices.
Suppose that a baseball is thrown upward with an initial velocity of 132 feet per second (90 miles per hour) and it is released 4 feet above the ground. Its height h after t seconds is given by hequalsminus16tsquaredplus132tplus4. After how many seconds does the baseball reach a maximum height?
Answer: it will take 8.25 seconds to reach maximum height
Step-by-step explanation:
Initial velocity, u of baseball = 132 feet per second. The height of the baseball, h in feet after t seconds is given by the function h = −16t^2 + 132t + 4
The given function is a quadratic equation. If values of height attained is plotted against time, the graph will take the shape of a parabola whose vertex corresponds to the maximum height attained by the baseball
Vertex of the parabola = -b/2a
a = - 16
b = 132
Vertex = - 132/-16× 2 = -132/32
Vertex = 4.125
The maximum height is 4.125 feets
To determine the time it will take to reach the maximum height of 4.125 feets, we will substitute h = 4.125 in the equation
4.125 = −16t^2 + 132t + 4
−16t^2 + 132t - 0.125 = 0
Applying the general formula for quadratic equations,
t = [- b ± √b^2 - (4ac)]/2a
a = -16
b = 132
c = -0.125
t = [- 132 ± √132^2 - 4(-16 × - 0.125)]/2× -16
t = [- 132 ± √17424 - 8)]/-32
t = [- 132 ± √17416]/-32
t = (-132 ± 132)/-32
t = (-132 + 132)/-32 or (-132 -132)/-32
t = 0 or -264/-32
t = 8.25 seconds
Final answer:
The baseball reaches its maximum height after 8.25 seconds.
Explanation:
To find the time when the baseball reaches its maximum height, we need to determine the time at which the vertical velocity becomes zero. The equation for the height of the ball as a function of time is given as h = -16t² + 132t + 4. To find the time at which the velocity becomes zero, we need to solve the equation v = -16t + 132 = 0. Solving for t, we get t = 8.25 seconds. Therefore, the baseball reaches its maximum height after 8.25 seconds.
In a 1995 Corporation for Public Broadcasting poll of TV viewership, one question was, "A recent study by a psychology professor at a leading university concluded that the amount of violence children see on television has an effect on their likelihood of being aggressive and committing crimes. From what you have seen or heard about this subject, do you agree strongly with that conclusion, agree somewhat, or disagree strongly?" Is this question appropriate, or is it flawed in some way? Comment briefly.
The question is flawed due to its opinion-based and leading nature. It presupposes information, leads the participant, and doesn't provide a full range of response options.
Explanation:This question, as posed by the 1995 Corporation for Public Broadcasting poll, is opinion-based and leading. There are several factors that make this question flawed. Firstly, it presupposes information by referencing a psychological study that potentially not all participants may be aware of, providing an initial bias. Secondly, it leads the participant in the direction of agreeing with the study, providing no neutral or mixed opinion option. Lastly, the question does not allow for participants to disagree somewhat, only strongly, which may influence the responses to be more in line with the premise of the study. In reliable polling, questions should offer sufficient options for the participant to choose from that captures the range of potential opinions and should avoid leading language or assumptions to obtain an accurate representation of the participants' views.
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What is the volume of the cone? Use π ≈ 3.14. 12.56 cubic units 18.84 cubic units 20.93 cubic units 25.12 cubic units
Answer:
volume of cone = 12.56 cubic units
Step-by-step explanation:
Volume of cone = 1/3 π r² h
r = 2
h = 3
then
V= 1/3 3.14 * (2) ² 3
= 12.56 cubic units
Answer:
12.56 cubic units
Step-by-step explanation:
Right on Edge 2022
A bag of sawdust costs $5.00 and can cover 9 feet of ground. By buying part of the bag, how much would it cost to buy enough to cover 1 foot of ground?
Standing on the edge of a cliff 30 m tall, Bob notices a kayak on the lake. If the angle of depression to the kayak is 400, what is the distance, to the nearest meter, from the kayak to the base of the mountain?
Answer:
36 mExplanation:
The vertical height of the cliff, 30 m tall, and the horizontal distance from the kayak to the base of the mountain form a right triangle.
The angle of depression is 40º.
By the alternate interior angles theorem, that depression angle is congruent to the elevation angle from the kayak to the spot where Bob is standing on.
The tangent trigonometric ratio relates the height (30 m) with the distance from the kayak to the base of the mountain:
tan(40º) = height of the cliff / distance from the kayak to the base of the mountaintan(40º) = 30 m / xx = 30m / tan(40º) ≈ 35.75 m ≈ 36 mConsider the following Polynomial.
S(x)= -3x^2 +x-9
Describe the behavior of the graph of S(x) as x ---> +/- ∞
S(x)--> ? as x--> -∞
S(x)-->? as x-->∞
Answer:
S(x) → -∞ as x → -∞S(x) → -∞ as x → ∞Step-by-step explanation:
The leading term tells you what you want to know. It is of even degree, so the value of S(x) is the same regardless of the sign of x as the magnitude of x gets large.
The sign of S(x) matches the sign of the leading coefficient (-3), so is negative as x gets large.
Hence ...
S(x) → -∞ as x → -∞S(x) → -∞ as x → ∞
On a certain multiple-choice test, 9 points are awarded for each correct answer, and 7 points are deducted for each incorrect or unanswered question. Sally received a total score of 0 points on the test. If the test has fewer than 30 questions, how many questions are on the test?
Answer:
21
Step-by-step explanation:
99 POINTS BRAINLIEST!! no fake answers please!
In a game, you have a 1/36 probability of winning $94 and a 35/36 probability of losing $8. What is your expected value?
ALSO ANSWER QUESTIONS IN PICTURE, THANK YOU
I think the answer would be -$5.17 because you would have to find the unexpected value.
I think the answer to this picture is 0.122
Game:
1/36(94) + 35/36(-8) = 94/36 -280/36 = -186/36 = -5.17
4. Add the probabilities together for 5 and under:
0.122 + 0.061 + 0.022 + 0.006 + 0.001 = 0.212
Airline :
Given: P = 70, P = 97% = 0.97, q = 1-0.97 = 0.03
Probability of being greater than 68:
(70 * 0.97^69 * 0.03^1) + (1*0.97^70*1)
= 0.2567 + 0.1185
= 0.375
In 2000, the population of a country was approximately 6.13 million and by 2015 it is projected to grow to 7 million. Use the exponential growth model Upper A equals Upper A 0 e Superscript kt, in which t is the number of years after 2000 and Upper A 0 is in millions, to find an exponential growth function that models the data.
Answer:
A = 6.13e^(0.00884769t)
Step-by-step explanation:
The exponential growth model can be written two ways. Comparing them, we can find the value of k.
A = 6.13×(7.00/6.13)^(t/(2015-2000)) = 6.13×e^(kt)
Dividing by 6.13 and taking natural logs, we get ...
t/15×ln(7.00/6.13) = kt
k = ln(7.00/6.13)/15 . . . . . divide by t
k ≈ 0.00884769
Then the exponential growth function can be written as ...
A = 6.13e^(0.00884769t)
A conical tank is 8 meters high. The radius of the top is 2 meters. At what rate is the water running out if the depth is 3 meters and is decreasing at the rate of 0.4 meters per minute
Answer:
DV/dt = 0,2355 m³/min
Step-by-step explanation:
Conical tank volume V = 1/3 *π*r²*h
r radius at the top 2 meters
when depth of water is 3 meters the radius of the level of water is:
let α angle of vertex of cone then
tan∠α = 2/8 tan∠α = 1/4 tan∠α = 0,25
At the same time when water is at 3 meters depth radius is
tan∠α = r/3 0,25*3= r r = 0,75 m
Now
DV/dt = (1/3)*π*r²*Dh/dt
Dh/dt = 0,4 meters/min
By substitution
DV/dt = 0,2355 m³/min
Suppose your local school district decides to randomly test high school students for attention deficit disorder (ADD). There are there high schools in the district, each with grades 9-12. The school board pools all of the students together and randomly samples 250 students. Is this a simple random sample?
a. Yes, because the students were chosen at random
b. Yes, because each student is equally likely to be chosen
c. Yes, because they could have chosen any 250 students from throughout the district
d. No, because we can't guarantee that there are students from each school in the sample
e. No, because we can't guarantee that there are students from each grade in the sample
f. Yes, because they could have chosen any 250 students from throughout the district
Answer:
Option C is correct. Option f is the same as option C
Step-by-step explanation:
From the question, There are three high schools in the district, each with grades between nine to twelve. The school board decided to pool all of the students together and randomly samples 250 students in the whole district that has schools between the grade of nine to twelve.
In order to test for high school students in the district for Attention Deficit disorder(ADD), they could have chosen any 250 students from any school with grades betweem nine to twelve throughout the district.
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ?
Answer: The weight of X is [tex]33\dfrac{1}{3}\%[/tex] of weight of mixture.
Step-by-step explanation:
Since we have given that
Percentage of seed mixture X for ryegrass = 40%
Percentage of seed mixture Y for ryegrass = 25%
If a mixture of X and Y contains 30 percent ryegrass,
Let total seed mixture be 100
So, for seed X = x
For seed Y = 100-x
So, According to question,
[tex]0.4x+0.25(100-x)=30\\\\0.4x+25-0.25x=30\\\\0.15x=30-25\\\\0.15x=5\\\\x=\dfrac{5}{0.15}\\\\x=\dfrac{100}{3}[/tex]
So, weight of mixture X is given by
[tex]\dfrac{\text{Weight of X}}{\text{Weight of mixture}}\times 100\\\\=\dfrac{\dfrac{100}{3}}{100}\times 100\\\\=\dfrac{100}{3}\%\\\\=33\dfrac{1}{3}\%[/tex]
Hence, the weight of X is [tex]33\dfrac{1}{3}\%[/tex] of weight of mixture.
There are 4 positive integers a,b,c,d, such that 4cos(x)cos(2x)cos(4x) = cos(ax)+cos(bx)+cos(cx)+cos(dx) for all values of x. Find a+b+c+d.?
Final answer:
To find the values of a, b, c, and d in the equation 4cos(x)cos(2x)cos(4x) = cos(ax)+cos(bx)+cos(cx)+cos(dx), we can compare the coefficients of the cosine terms on both sides of the equation. By expanding and comparing coefficients, we can determine that a = 12, b = 10, c = 6, and d = 8. Therefore, a + b + c + d = 36.
Explanation:
To find the values of a, b, c, and d, we need to equate the coefficients of cos(ax), cos(bx), cos(cx), and cos(dx) on both sides of the equation.
4cos(x)cos(2x)cos(4x) = cos(ax)+cos(bx)+cos(cx)+cos(dx)
By expanding the left side and comparing coefficients, we get:
cos(ax) = 4cos³(x) = 4(4cos³(x) - 3cos(x))cos(bx) = 2cos(2x)cos(4x) = 2(2cos²(2x) - 1)(2cos²(x) - 1)cos(cx) = 2cos(x)cos(4x) = 2(2cos²(x) - 1)(2cos²(4x) - 1)cos(dx) = 2cos(x)cos(2x) = 2(2cos²(x) - 1)(2cos²(2x) - 1)From these equations, we can determine that a = 12, b = 10, c = 6, and d = 8.
Therefore, a + b + c + d = 12+10+6+8 = 36.
The number of houses that can be served by a water pipe varies directly as the square of the diameter of the pipe. A water pipe that has a 10-centimeter diameter can supply 40 houses. a. How many houses can be served by a water pipe that has a 30-centimeter diameter? b. What size of water pipe is needed for a new subdivision of 1440 houses?
Answer:
Step-by-step explanation:
Given
no of houses that can be served by water is directly Proportional to the square of diameter
[tex]N\propto d^2[/tex]
[tex]N=kd^2[/tex]
where k =constant
10 cm diameter can supply 40 houses
[tex]40=k(10)^2[/tex]-----------1
For d=30 cm Pipe
[tex]N_1=k(30)^2[/tex]-------------2
divide 1 & 2
[tex]\frac{N_1}{40}=(\frac{30}{10})^2[/tex]
[tex]N_1=40\times 9=360 [/tex]
(b)for N=1440 houses
[tex]1440=k(d_2)^2[/tex] ----------------3
[tex]\frac{1440}{40}=(\frac{d_2}{10})^2[/tex]
[tex]d_2=6\times 10[/tex]
[tex]d_2=60 cm[/tex]
A water pipe with a diameter of 30 cm can serve 360 houses. And to serve 1440 houses, a water pipe with a diameter of 60 cm is required.
Explanation:The relationship between the number of houses that could be supplied by the water pipe and the diameter of the pipe can be described as a direct square relationship. This means if you square the diameter of the pipe, you'll get the number of houses that can be served. We know from the given info that a 10 cm diameter pipe can serve 40 houses. Therefore, the constant of variation (k) can be calculated as k=No. of houses/diameter². Hence, k=40/10²=0.4.
a.) A pipe with a 30 cm diameter can serve 0.4*(30)² = 360 houses.
b.) For a new subdivision of 1440 houses, we rearrange the formula to find the required diameter: Diameter= sqrt(No. of houses/k) = sqrt(1440/0.4) = 60 centimeters.
Learn more about Direct Variation here:https://brainly.com/question/9775007
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A man is flying in a hot-air balloon in a straight line at a constant rate of 6 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 37°. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 38°. At that time, what is the distance between him and his friend?
Answer: 336.4447 feet
Step-by-step explanation: from the picture I attached to this answer, you will see how I represented the question in a diagram
Point A being the point of his friends car, point B being the point of the hot air balloon when he noticed the angle of depression to his friends car to be 37 degrees, point C being the point of the hot air balloon after passing his friends car and noticing the angle of depression to be 38 degrees
From my diagram, I labeled y as the distance between B and C and we are told he traveled when a speed of 6 feet per second with a constant altitude, and after 1 and a half minutes he reached point C, which is 90 seconds
To get value of y we multiply the speed and the time, 90 multiplied by 6 which will give 540 feet
From my diagram, I calculated the angle inside the triangle to be 105, we all know the sum of angles in a straight line to be 180, and also knowing alternate angles, we have 37 and 38 degree as the angle outside the triangle at that point, so adding both angle 37+38=75 and subtracting that from 180 we get 105
So the get the distance between him and his friends when the angle of depression is 38 degree, which is the distance between point A and C which I labeled x, we use the sin rule
Sin rule states that the ratio between the length of a side of a triangle and the sin of the angle opposite it is constant for all sides of the triangle,
The steps are also solved in the picture I sent
So we have the ratio of x and sin37 is also equal to the ratio of 540 and sin105
So x divided by sin37 equals 540 divided by sin105
Sin37 equals 0.6018, sin105 equals 0.9659
So making x the subject of formula
We get x will be equal to (540*0.6018)/0.9659 which will give you 336.4447 feet
Using trigonometry and applying the concept of tangent to the angles of depression, we can construct two right triangles to calculate the horizontal distances and then use the Pythagorean theorem to calculate the distance from the balloon to the friend's car.
Explanation:The question involves a man in a hot-air balloon tracking his distance from a car in a parking lot using the angles of depression before and after flying over the car. To solve this question, we will apply trigonometry specifically, the concept of tangent which relates the angle of depression to the sides of a right triangle formed by the observer's altitude and the horizontal distance.
Firstly, let's find the horizontal distance the man travels in a minute and a half at 6 feet per second:
Distance = speed × time = 6 feet/second × 90 seconds = 540 feet
Now, we form two right triangles: one before he flies over the car and one after. Both have the same altitude (since he maintains a constant altitude).
For the first triangle, using the 37° angle of depression, we can denote:
For the second triangle, using the 38° angle of depression, we can denote:
Solving these two equations we find the horizontal distance (x) and then can find the direct line distance using Pythagoras' theorem.
To find the distance, we will use the tangent of 38° (the angle of depression after passing the car) since that relates the perpendicular distance from the balloon to the car (which we are interested in) to the horizontal distance. Let's denote the perpendicular distance as 'h' (altitude of the balloon).
Tan(38°) = h / (x - 540 feet)
After some algebraic manipulation and applying trigonometry, we can solve for 'h' and find the direct line distance from the balloon to the car.
A company had 3,000 people come try their product. 21 out of the 3,000 people had an allergic reaction. What is the percent of the people that had an allergic reaction.
Answer: number of people that had allergic reactions is 0.7%
Step-by-step explanation:
The total number of people that came to try the company's product is 3000
21 out of the 3,000 people had an allergic reaction. We want to determine how many percent of the total number of 3000 people that tried the product is 21 people that had reaction
Percentage of people that had allergic reactions = number of people that had allergic reactions / total number of people that tried the products × 100
Percentage of people that had an allergic reaction
= 21/3000× 100
= 0.007 × 100 = 0.7%
Elena is feeding her neighbor's dogs each dog gets two thirds cup of dog food and she uses three and one third cups of food how many dogs does her neighbor have
Answer:
Total number of dogs is 5.
Step-by-step explanation:
Cups of food each dog gets=[tex]\frac{2}{3}[/tex]
Here,each dog eats two-third cups of dog food.
Amount of dog food used=[tex]\frac{10}{3}[/tex]
A total of three and one-third cups of food is used up.
Let the number of dogs be x.
To find the number of dogs,divide total dog food used by the amount of dog food eaten by each dog.
Hence, x =[tex]\frac{\frac{10}{3} }{\frac{2}{3} }[/tex]
x =[tex]\frac{10}{2}[/tex]
x =5
Quiz: The Discriminant and Modeling Data 7:Solving Quadratic Equations
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Find the number of real number solutions for the equation. x2 - 10x + 25 = 0
oo
O
1
2
cannot be determined
100%
For this case we must find the solution of the following quadratic equation:
[tex]x ^ 2-10x + 25 = 0[/tex]
Where:
[tex]a = 1\\b = -10\\c = 25[/tex]
Then, the solution is given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
Substituting the values:
[tex]x = \frac {- (- 10) \pm \sqrt {(- 10) ^ 2-4 (1) (25)}} {2 (1)}\\x = \frac {10 \pm \sqrt {100-100}} {2}\\x = \frac {10 \pm \sqrt {0}} {2}\\x = \frac {10} {2} = 5[/tex]
Thus, we have two equal real roots.
[tex]x_ {1} = 5\\x_ {2} = 5[/tex]
Answer:
We have two equal real roots.
Answer:
cannot be determined
Step-by-step explanation:
i tried 1,0,2 dont work
A political analyst found 43% of 300 randomly selected republican voters feel that the federal government has too much power. Find the 95% confidence interval of the population proportion of republican voters who feel this way.
Answer:
Step-by-step explanation:
We want to determine 95% confidence interval of the population proportion of republican voters who feel that the federal government has too much power.
43% of 300 randomly selected republican voters feel that the federal government has too much power. This means that
p = 43/100 = 0.43
q = 1 - p = 1 - 0.43 = 0.57
n = 300
mean, u = np = 300 × 0.43 = 129
Standard deviation, s = √npq = √129×0.57 = 8.575
For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean +/- z ×standard deviation/√n
It becomes
129 +/- 1.96 × 8.575/√300
= 129 +/- 0.9704
= 129 +/- 0.9704
The lower end of the confidence interval is 129 - 0.9704 =128.0296
The upper end of the confidence interval is 129 + 0.9704 =129.9704
Therefore, with 95% confidence interval, the mean of the population proportion of republican voters who feel that the federal government has too much power is between 128.0296 and 129.9704
To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, use the formula CI = p ± Z * √((p*(1-p))/n), where p is the sample proportion, Z is the Z-score for the desired confidence level, and n is the sample size. Given the sample proportion of 0.43, sample size of 300, and desired confidence level of 95%, the confidence interval is approximately 0.381 to 0.479.
Explanation:To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, we can use the formula:
CI = p ± Z * √((p*(1-p))/n)
Where:
p is the sample proportionZ is the Z-score for the desired confidence level (in this case, 95%)n is the sample sizeGiven that the sample proportion is 0.43, the sample size is 300, and the desired confidence level is 95%, we can calculate the 95% confidence interval:
CI = 0.43 ± 1.96 * √((0.43*(1-0.43))/300)
Simplifying the equation, we get:
CI = 0.43 ± 0.049
Therefore, the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power is approximately 0.381 to 0.479.