The 90% confident sample of size 191 with 23 successes that the true population proportion falls between 0.077 and 0.163 based on the sample data.
To find the 90% confidence interval for a sample proportion, we can use the following formula:
Confidence Interval = sample proportion ± margin of error
where the margin of error is:
Margin of Error = z* (\sqrt{(p*(1-p)/n))}
where z is the z-score corresponding to the level of confidence,
p is the sample proportion, and n is the sample size.
In this case, we have a sample size of n = 191 and 23 successes,
which gives a sample proportion of p = 23/191 ≈ 0.120.
To find the z-score corresponding to a 90% confidence level,
The z-score for a 90% confidence level is approximately 1.645.
Plugging in the values into the formula, we get:
Margin of Error = 1.645 * (\sqrt{(0.120*(1-0.120)/191)}) ≈ 0.043
Therefore, the 90% confidence interval for the population proportion is:
0.120 ± 0.043
which can be expressed as (0.077, 0.163) rounded to three decimal places.
So we are 90% confident that the true population proportion falls between 0.077 and 0.163.
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PLEASE HELP WILL GIVE BRAINLIEST.
Given f(x)=sin x and g(x)=cos x show that f(g(pi/2))=0. Show all your steps.
Answer:
Step-by-step explanation:
xs nxqxm,nswjnej,cebxhjme2ckjwadbcweckslnvc
First, we need to find the value of g(pi/2):
g(pi/2) = cos(pi/2) = 0
Now we can substitute this value into f(x):
f(g(pi/2)) = f(0) = sin(0) = 0
Therefore, f(g(pi/2)) = 0.
Measure the diameter of the tin mm and write down the real diameter in mm
Answer:
Step-by-step explanation:
20x50x30x50 = ?
Please answer someone!!
Answer: 1500000
Step-by-step explanation:
use a calculator
Answer:
1,500,000
Step-by-step explanation:
Breaking it up into an easier problem:
20x50 = 1,000
30x50=1,500
1,000 x 1,500, aka "adding three zeros" to the end of 1,500, as 1,000 is simply 1 x 10 x 10 x 10, and each 10 has one 0 to it.
Thus, the answer is 1,500,000
machines at a factory produce circular washers with a specified diameter. the quality control manager at the factory periodically tests a random sample of washers to be sure that greater than 90 percent of the washers are produced with the specified diameter. the null hypothesis of the test is that the proportion of all washers produced with the specified diameter is equal to 90 percent. the alternative hypothesis is that the proportion of all washers produced with the specified diameter is greater than 90 percent. which of the following describes a type i error that could result from the test? responses the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test does not provide convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is equal to 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. the test provides convincing evidence that the proportion is greater than 90%, but the actual proportion is greater than 90%. a type i error is not possible for this hypothesis test.
Answer:
the test does not provide convincing evidence that the proportion is greater than 90%
Luke bought 4 kilograms of apples and 0.29 kilograms of oranges. How much fruit did he buy
in all?
He bought 4.29 Kilos of fruit.
4+0.29=4.29
Luke bought 4.29 kilograms of fruit in all
Step-by-step explanation:
Simple addition will be used to find the total fruit Luke bought.
Given
Amount of apples he bought = 4 kilograms
Amount of oranges he bought = 0.29 kilograms
so the total fruit will be:
[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]
[tex]=4+0.29[/tex]
[tex]=4.29[/tex]
So,
Luke bought 4.29 kilograms of fruit in all
Keywords: Measurement, addition
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In the past 5 years company A sold 7.5x10^4 reams of paper. Company B sold 9.5 x10^3 reams. How many total reams did they sell altogether and how many more did company a sell than B?
Giving 20 pts please help!
84500 reams of paper are the total amount the two companies sell in the past five years.
65500 is the amount that Company B performed better than company A.
What is a Company?A company can be defined as the part in which the main aim or goal is to earn a profit. This was to generate the income that they will be having in the firm. There are various employees that are present in the company and work towards a common goal.
The Amount that is made by company A is
[tex]7.5 \times 10000[/tex]
[tex]=75000[/tex]
The amount of paper manufactured by company B is
[tex]= 9.5 \times 1000[/tex]
[tex]= 9500[/tex]
A) The total that is made by both companies in 5 years will be
[tex]= \text{Company A + Company B}[/tex]
[tex]= 75000 + 95000[/tex]
[tex]= 84500[/tex]
B) Company B made better products as compared to Company A
[tex]= \text{Company B - Company A}[/tex]
[tex]=75000 - 9500[/tex]
[tex]=65500[/tex]
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Answer:
total: 84,500 or 8.45×10⁴difference: 65,500 or 6.55×10⁴Step-by-step explanation:
You want the sum and difference of 7.5×10^4 and 9.5×10^3.
Scientific notationNumbers are most conveniently added or subtracted in scientific notation when the multipliers have the same exponent. For this we can rewrite Company B's volume as ...
9.5×10^3 = 0.95×10^4
total sales = 7.5×10^4 + 0.95×10^4 = 8.45×10^4 = 84,500
difference in sales = A -B = 7.5×10^4 -0.95×10^4 = 6.55×10^4 = 65,500
__
Additional comment
You can enter the numbers "as is" in a calculator or spreadsheet and format the output in whatever form you need.
At the 2022 Winter Olympics, one country won a total of 150 medals. A circle graph of the medals is shown.
a circle graph titled 2022 Winter Olympic Medals, with three sections labeled gold 20 percent, silver 30 percent, and bronze 50 percent
How many silver and bronze medals were won?
40
80
100
120
The country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.
What is Medal?A medal is a small, flat, and usually round piece of metal that is awarded to individuals or groups as a symbol of recognition or honor for achievement, bravery, or other notable deeds. Medals can be made of various materials, such as gold, silver, bronze, or other alloys, and they often feature intricate designs or engravings that reflect the significance of the award.
According to question:According to the circle graph, gold medals make up 20% of the total medals, which means the country won 20% of 150 medals as gold, or 0.2 x 150 = 30 gold medals.
Similarly, silver medals make up 30% of the total medals, which means the country won 30% of 150 medals as silver, or 0.3 x 150 = 45 silver medals.
Finally, bronze medals make up 50% of the total medals, which means the country won 50% of 150 medals as bronze, or 0.5 x 150 = 75 bronze medals.
Therefore, the country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.
So the answer is 120.
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calculate the centripetal force (in n) on the end of a 52 m (radius) wind turbine blade that is rotating at 0.3 rev/s. assume the mass is 2 kg
The centripetal force is 7384.80 N.
For the centripetal force in N on the end of a 52 m (radius) wind turbine blade that is rotating at 0.3 rev/s and assuming the mass is 2 kg.
Use the following formula:
Centripetal force = (mass x velocity²) / radius
Where; mass = 2 kg
In this case, the radius of the wind turbine blade is 52 m, and it is rotating at 0.3 rev/s, which means that the angular velocity is:
ω = 2π * f = 2π * 0.3 = 1.884 rad/s
where f is the frequency or revolutions per second.
The linear velocity at the end of the blade can be calculated as:
v = r * ω ⇒ 52 * 1.884 ⇒ 98.088 m/s
radius = 52 m
Centripetal force = (2 x 98.088²) / 52
Centripetal force = 7384.80 N
Therefore, the centripetal force on the end of a 52 m wind turbine blade rotating at 0.3 rev/s with a mass of 2 kg is 7384.80 N.
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After randomly selecting 1,009 adults and surveying each of them, 545 of them indicated that they were not comfortable with a drone delivering packages to them. The pollster concluded from the data that precisely 54 percent of all American adults are therefore not comfortable having drones make deliveries to them.
Determine whether the pollster’s conclusion makes sense. Address whether the pollster is correct in drawing this conclusion based upon the given information. In preparing your answer, include the following terms:
statistics and parameters,
estimation,
margin of error,
and any other concepts from the assigned readings and/or class sessions you deem helpful and appropriate.
Based on the information, the pollster's conclusion makes sense.
How do you know if the pollster is right with his conclusion?To know if the pollster is right with his conclusion we must perform the following operation.
1,009 / 100 = 10.0910.09 * 54 = 544.86In accordance with the above, we can infer that the pollster concludes that 54% of the people surveyed are equivalent to 545 people correctly because 0.86 is a minimum margin of error for this type of statistics. In addition, it can be inferred that the pollster correctly uses the statistics and study parameters of a sample to establish a correct conclusion.
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Coin A is tossed three times and coin B is tossed two times. What is the probability that more heads are tossed using coin A than coin B?
The probability that more heads are tossed using coin A than coin B is 5/16.
The given data is: Coin A is tossed three times and coin B is tossed two times. We have to find the probability that more heads are tossed using coin A than coin B.
P(E) = Number of favorable outcomes/ Total number of possible outcomes
Coin toss:
There are two possible outcomes in a coin toss, Head or Tail. The probability of getting a head in a coin toss is
1/2 = 0.5.
Therefore, the probability of getting a tail in a coin toss is also 1/2 = 0.5.
Let's calculate the possible outcomes when coin A is tossed three times.
There are 2 possible outcomes when one coin is tossed.
Number of possible outcomes when three coins are tossed = 2 * 2 * 2 = 8
Likewise, the possible outcomes when coin B is tossed two times are:
The number of possible outcomes = 2 * 2 = 4
Therefore, the total number of possible outcomes = 8 * 4 = 32
Now, we will find out the cases where the number of heads is more when coin A is tossed three times.
HHH HHT HTH HTT THH THT TTH TTT HHT HTT THT TTT TTH TTT HTT TTT THT TTT TTT TTT
Therefore, the number of times when more heads are obtained when coin A is tossed three times is 10. (We have to exclude the case when there is an equal number of heads.)
Therefore, the required probability is: P = Number of favorable outcomes/ Total number of possible outcomes
P = 10/32P = 5/16
Therefore, the probability that more heads are tossed using coin A than coin B is 5/16.
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I NEED HELPP PLEASEEEEEEEE
The slope between the points (-3, 0) and (0, -1) is -1/3.
What is slope?The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.
Let us consider the first two points (-3, 0) and (0, -1).
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
Substituting the values we have:
m = (-1 - 0) / (0 - (-3)) = -1/3
Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.
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I need help with these 2 please
Question 7. C (rectangular pyramid)
Question 8. 17 cm
Answer:
Question 7:C rectangular pyramid
Question 8: C 120 in
A=2(wl+hl+hw)=2·(10·2+5·2+5·10)=160
Step-by-step explanation:
Algebra question help asap
If the value of the Bulls Eye stock has fallen 8% annually since 2010, it will be worth $32.90 in 2015.
What is the mathematical formula for profit?The formula Profit = Selling Price - Cost Price can be used to determine the profit when the selling price and the cost price of a product are known. The formula for calculating profit percentage is then applied, which is profit percentage = (profit/cost price) x 100.
If the value of the Bulls Eye stock has dropped by 8% annually, it has dropped to 92% (100% - 8%) of its value from the prior year.
Since we're moving from 2010 to 2015, we must multiply this loss five times to determine the stock's value in 2015:
Value in 2011 = 92% of $50 = $46
Value in 2012 = 92% of $46 = $42.32
Value in 2013 = 92% of $42.32 = $38.89
Value in 2014 = 92% of $38.89 = $35.77
Value in 2015 = 92% of $35.77 = $32.90
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Simplify these radicals (ASAP!!!)
Answer:
[tex]3.\quad 2\sqrt{7}\\\\4.\quad \dfrac{2}{\sqrt{5}}[/tex]
[tex]5.\quad \dfrac{1}{\sqrt{2}}[/tex]
[tex]6.\quad\dfrac{5}{7}[/tex]
Step-by-step explanation:
To simplify radicals find the factors and simplify the square roots of the factors
#3 : √28
28 = 4 x 7
√28 = √(4 x 7) = √4 x √7 = 2 x √7 = 2√7
========================================================
[tex]\#4:\quad \sqrt{ \dfrac{4}{5}}\\\\\sqrt{ \dfrac{4}{5}} = \dfrac{\sqrt{4}}{\sqrt{5}} = \dfrac{2}{\sqrt{5}}[/tex]
========================================================
[tex]\#5\quad \dfrac{3}{\sqrt{18}}\\\text{Denominator } \sqrt{18 }= \sqrt{9 \times 2} = 3\sqrt{2}\\\\ \dfrac{3}{\sqrt{18}}= \dfrac{3}{3\sqrt{2}} = \dfrac{1}{\sqrt{2}}[/tex]
========================================================
[tex]\# 6 \quad \sqrt{\dfrac{25}{49}}\\\\\sqrt{25} = 5\\\\\\\sqrt{49} = 7\\\\[/tex]
[tex]\sqrt{\dfrac{25}{49}}= \dfrac{5}{7}[/tex]
Write down the smallest possible answer.
Answer:
3
Step-by-step explanation:
We have to find the smallest possible factor of 15 and multiple of 3.
The smallest factor of any positive integer is 1.
The smallest multiple of any positive integer is the integer itself. So the smallest multiple of 3 would be 3 itself.
[tex]1 * 3 = 3[/tex]
And 3 is the answer.
The value of 5^2000+5^1999/5^1999-5^1997
Answer:
Step-by-step explanation:
We can simplify the expression by factoring out a common factor of 5^1999 from the numerator:
5^2000 + 5^1999
= 5^1999(5 + 1)
= 5^1999(6)
And we can also factor out a common factor of 5^1997 from the denominator:
5^1999 - 5^1997
= 5^1997(5^2 - 1)
= 5^1997(24)
So the entire expression simplifies to:
(5^2000 + 5^1999) / (5^1999 - 5^1997)
= (5^1999 * 6) / (5^1997 * 24)
= (6/24) * 5^2
= 5/2
Therefore, the value of the expression is 5/2.
10) When Perry Person got a paycheck, Perry went shopping. He spent $26 on a shirt and twice as much on jeans. Then he spent half of what he had left on a snack. On his way home, he found $10 and ended up with $ 24. How much was Perry's paycheck ?
Perry's paycheck was $100. To find Perry's paycheck, we can work backward from the final amount he had after finding $10 and ending up with $24.
Let's denote Perry's paycheck as "x". After buying the shirt and jeans, he spent a total of $26 + $52 = $78. So he had "x" - $78 left. He then spent half of what he had left on a snack, leaving him with 1/2 * ("x" - $78) = 1/2*x - $39.
When he found $10, he ended up with $24, so we can set up the equation:
1/2*x - $39 + $10 = $24
Simplifying this equation gives us:
1/2*x = $53
Multiplying both sides by 2, we get:
x = $106
Therefore, Perry's paycheck was $100.
In summary, we used a series of calculations to work backward from the final amount Perry had to determine his original paycheck. We accounted for the amount he spent on a shirt, jeans, and a snack, as well as the amount he found on his way home.
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A restaurant owner is buying new tableware for her restaurant. She wants the new pieces to be proportionate, and needs to know the measurements of the different pieces she is buying. The circle-shaped part of the bottom of the glass above has an area of 12.56 in2. What is the radius? Use = 3.14. A. 4 in B. 5 in C. 1 in D. 2 in Reset Submit
The answer is d please
How to graph it on a coordinate plan to the right 5x-3y=18
Tο shift the graph tο the right, we can simply add a pοsitive cοnstant tο the x values οf each pοint befοre plοtting them. Fοr example, if we want tο shift the graph tο the right by 2 units.
What is cοοrdinate plan?The intersectiοn οf twο number lines creates a twο-dimensiοnal plane knοwn as a cοοrdinate plane. The x-axis, a hοrizοntal number line, and the y-axis, a vertical number line, are twο examples οf these number lines.
Tο graph the equatiοn 5x - 3y = 18 οn a cοοrdinate plane, we can fοllοw these steps:
1. Sοlve fοr y in terms οf x:
5x - 3y = 18
-3y = -5x + 18
y = (5/3)x - 6
2. Chοοse sοme values fοr x and use the equatiοn tο find the cοrrespοnding y values. Fοr example, we can chοοse x = 0, 3, and 6:
When x = 0: y = (5/3)(0) - 6 = -6
When x = 3: y = (5/3)(3) - 6 = -3
When x = 6: y = (5/3)(6) - 6 = 2
3. Plοt the pοints (0, -6), (3, -3), and (6, 2) οn the cοοrdinate plane.
4. Draw a straight line passing thrοugh these three pοints. This line represents the graph οf the equatiοn 5x - 3y = 18.
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You are dealt five cards from a standard deck of 52 playing cards (A full house consists of three of one kind and two of another. For example, A A A 5-5 and K-K-K 10-10 are full houses) (a) in how many ways can you get a full house? ______ Ways (b) in how many ways can you get a five card combination containing two jacks and three aces ___ ways
The 32 ways to get a five-card combination containing two jacks and three aces.
(a) A full house consists of three of one kind and two of another kind. Therefore, there are 13 different choices for the rank of the triplet and 4 cards of the same rank. Once the triplet has been chosen, there are 12 choices for the rank of the pair and 4 cards of the same rank. Therefore, the number of ways to get a full house is as follows:$${13}{\times}{4}{\times}{12}{\times}{4}={7488}$$Therefore, there are 7488 ways to get a full house.(b) In this case, the two jacks and three aces must be chosen out of the 4 jacks and 4 aces in the deck. Therefore, the number of ways to get a five-card combination with two jacks and three aces is as follows:$$\frac{{4\choose2}{4\choose3}{44\choose0}}{5!}={32}$$Therefore, there are 32 ways to get a five-card combination containing two jacks and three aces.
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The graph shows the velocity, v metres per second, of a car at time t seconds. Work out an estimate for the distance the car travelled for the first 8 seconds. Use 4 strips of equal width. -1-500- -1000- -500 0 V t
please help!!!
To estimate the distance traveled we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.
Define velocity-time graph?A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.
The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.
Using the trapezium rule, the estimated area of each strip is:
Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s
Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s
Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s
Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s
The total estimated area is the sum of the areas of the 4 strips:
Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s
Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:
Estimated distance traveled is = |-4000| = 4000 meters
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The cost price of a book is Rs 20 . It is sold at 10% profit. Find its sale price
Answer:
Cost price (CP) = Rs20
% Profit = 10%
Selling price (SP) = y
By formula:
% Profit = (Profit/CP) x 100%
But Profit= SP - CP
Therefore;
% Profit = [(SP-CP)/C.P)] x 100%
Substituting, we have:
10% = [(y-20)/20] x 100%
10/100 = (y-20)/20
1/10 = (y-20)/20
1 = (y-20)/2
Cross multiply
y - 20 = 2
y = 2 + 20
y = 22
Therefore, the Sale price is Rs 22
what is the product of any two invertible matrices is invertible.
The product of any two invertible matrices is invertible that is (BC) = A⁻¹
Now, let's consider the product of two invertible matrices, say A and B. Since A and B are invertible, they both have an inverse, denoted by A⁻¹ and B⁻¹, respectively.
To show that the product AB is also invertible, we need to find a matrix that satisfies the definition of an inverse. Let's call this matrix C.
If C is the inverse of AB, then we should have:
(AB)C = C(AB) = I
where I is the identity matrix.
Now, we can use the associativity of matrix multiplication to expand the left-hand side of the equation:
(AB)C = A(BC)
Notice that B and C are both matrices, so their product BC is also a matrix. Thus, we can write:
A(BC) = I
Since A is invertible, we can multiply both sides by A⁻¹ to get:
A⁻¹A(BC) = A⁻¹I
The left-hand side simplifies to:
(BC) = A⁻¹
Now, we have found a matrix C that satisfies the definition of an inverse for AB, which means that AB is invertible.
To summarize, the product of two invertible matrices is invertible, and the proof relies on the fact that the inverse of a matrix is unique and the associativity of matrix multiplication.
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Apply De Morgan's law repeatedly to each Boolean expression until the complement operations in the expression only operate on a single variable. For example, there should be no xy¯ or x+y¯ in the expression. Then apply the double complement law to any variable where the complement operation is applied twice. That is, replace x¯¯ with x.
a. 1/ x + yz + u b. 1/x(y + 2)u c. 1/(x + y)(uv + x y) d. 1/xy + yz + xz
The simplified expression using De Morgan's law are a)x'y'z'u b)x'y'u c): x'y'u and d)x'y'z'+xy'z'+xyz.
The main idea is to simplify each Boolean expression by repeatedly applying De Morgan's law until each complement operation operates on a single variable.
Then, apply the double complement law to simplify the expression further. In the end, the simplified expression should contain only AND and OR operations without any complement operators acting on multiple variables.
a. 1/ x + yz + u can be simplified using De Morgan's law to: (x'y'z')u'. Then, applying the double complement law, we get the simplified expression as: x'y'z'u.
b. 1/x(y + 2)u can be simplified using De Morgan's law to: x'(y'+2')u'. Then, applying the double complement law, we get the simplified expression as: x'y'u.
c. 1/(x + y)(uv + xy) can be simplified using De Morgan's law to: (x'y')(u' + x'y'). Then, applying the double complement law, we get the simplified expression as: x'y'u.
d. 1/xy + yz + xz can be simplified using De Morgan's law to: (x'+y')(y'+z')(x'+z'). Then, applying the double complement law, we get the simplified expression as: x'y'z'+xy'z'+xyz.
In summary, to simplify Boolean expressions, we can apply De Morgan's law repeatedly and then use the double complement law to remove complement operators acting on a single variable twice.
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Solve the inequalities 1/3x-1/4(x+2)>3x-4/3
Answer: x < -46/17
Step-by-step explanation:
To solve the inequality:
1/3x - 1/4(x + 2) > 3x - 4/3
First, we simplify the left-hand side by finding a common denominator:
4(1/3x) - 3/4(x + 2) > 3x - 4/3
4/3x - 3/4x - 9/2 > 3x - 4/3
Next, we simplify the equation:
7/12x - 9/2 > 3x - 4/3
To isolate the variable x on one side of the inequality, we will move all the x terms to the left-hand side and all the constants to the right-hand side:
7/12x - 3x > 9/2 - 4/3
-17/12x > 23/6
Finally, we can solve for x by dividing both sides by -17/12, remembering to reverse the inequality because we are dividing by a negative number:
x < (23/6) ÷ (-17/12)
x < -46/17
Therefore, the solution to the inequality is:
x < -46/17
What are the zeros of the function? Set the function = 0, factor, and use the zero-product property. Show your steps!
f(x) = x² + 7x – 60
(100 POINTS AND BRAINLIEST)
The zeroes of the function are -12 and 5.
What is meant by Zeros of the function?Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.
According to the question:
To find the zeros of the function
f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.
So we start with the equation:
x² + 7x - 60 = 0
Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:
x² + 7x - 60 = (x + 12)(x - 5) = 0
Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:
x + 12 = 0 or x - 5 = 0
Solving for x, we get:
x = -12 or x = 5
The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.
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Which angles would the Alternate Exterior Angles Theorem state are congruent?
Which angles would the Alternate Exterior Angles Theorem state are congruent?
Answer:
Choice 2
∠1 and ∠7, ∠2 and ∠8
Step-by-step explanation:
This is a good example of a problem that can be solved by POE(process of elimination)
First choice: ∠2 and ∠3 are on the same straight line so they cannot be congruent. They are supplementary in that they add up to 180°
The same applies for ∠3 and ∠4 (third choice)
The same applies for ∠1 and ∠4 (fourth choice)
That leaves choice 2
We can prove ∠1 ≅ ∠7 as follows:
∠1 ≅ ∠3 since they are vertically opposite angles
∠3 ≅ ∠7 since they are exterior angles
So ∠1 ≅ ∠7
By similar reasoning,
∠2 ≅ ∠8
So correct choice is Choice 2
Use spherical coordinates to find the volume of the region outside the cone phi = pi /4 and inside the sphere rho = 4 cos phi. The volume is ____ . (Type an exact answer, using pi as needed.)
The volume is 63.717 cubic units
The limits of integration for rho are 0 and 4 cos phi, since the sphere has radius 4 cos phi. The limits for phi are π/4 and π/2, since we want to consider the region outside the cone but inside the sphere, and phi is the angle between the positive z-axis and the position vector of a point. Finally, the limits for theta are 0 and 2π, since theta is the azimuthal angle and we want to integrate over the entire azimuthal angle.
Thus, the volume of the region is given by:
V = 8 x ∫(0 to 2π) ∫(π/4 to π/2) ∫(0 to 4 cos phi) ρ² sin phi dρ dphi dtheta
Simplifying the integral using basic calculus, we get:
V = 8 x (64/3 - 16/3√2π) = 63.717
Therefore, the volume of the region outside the cone phi = π/4 and inside the sphere rho = 4 cos phi is 8(64/3 - 16/3√2π), which is an exact answer using π as needed.
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Stacy rented a truck for one day there was a base fee of $16.95 and there was an additional charge of 93 cents for each model driven. stacy had to pay $143.43 when he returned the truck. for how many miles did she drive the truck
Answer:
Stacy rented a truck for one day there was a base fee of $16.95 and there was an additional charge of 93 cents for each model driven. stacy had to pay $143.43 when he returned the truck. for how many miles did she drive the truck
Step-by-step explanation:
Let's start by subtracting the base fee from the total cost:
$143.43 - $16.95 = $126.48
Now, we can divide the remaining cost by the cost per mile:
$126.48 ÷ $0.93/mile ≈ 136 miles
Therefore, Stacy drove the truck for approximately 136 miles.
A classroom is rectangular in shape. If listed as ordered pairs, the corners of the classroom are (−12, 15), (−12, −9), (9, 15), and (9, −9). What is the perimeter of the classroom in feet?
By answering the presented question, we may conclude that Therefore, the perimeter of the classroom is 96√2 + 42 feet (approx. 155.27 feet).
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a hexagon that is fundamental rule, or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
The perimeter-
d = √[(x2 - x1)² + (y2 - y1)²]
So, the perimeter of the classroom is:
d1 = √[(-12 - (-12))² + (15 - (-9))²] = √(24² + 24²) = √(2² × 24²) = 48√2
d2 = √[(-12 - 9)² + (15 - 15)²] = √(21²) = 21
d3 = √[(9 - 9)² + (15 - (-9))²] = √(24² + 24²) = √(2² × 24²) = 48√2
d4 = √[(9 - (-12))² + (-9 - 15)²] = √(21²) = 21
perimeter = d1 + d2 + d3 + d4
= 48√2 + 21 + 48√2 + 21
= 96√2 + 42
Therefore, the perimeter of the classroom is 96√2 + 42 feet (approx. 155.27 feet).
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