The answer is: The answers will vary from person to person.
Which statement about statistical questions is TRUE?The statement that is true about statistical questions is that the answers will vary from person to person. Statistical questions are questions that can be answered using data and statistics. These questions involve gathering information from a population or a sample of that population, analyzing the data, and making conclusions based on the results. Since different people may have different data and different ways of analyzing that data, the answers to statistical questions can vary. This is why it is important to consider the sample size, the sample method, and the statistical methods used to analyze the data when interpreting the results of statistical questions. A well-designed study can help minimize variability and improve the accuracy of the results, but some degree of variability is still expected due to natural differences in the data collected by different individuals or groups
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From a horizontal distance of 80.0 m, the angle to the top of a flagpole is 18°. Calculate the height of the flagpole to the nearest tenth of a meter.
1. 24.7 meters
2. 76.1 meters
3. 26.0 meters
4. 25.3 meters
Answer:
The figure is omitted--please sketch it to confirm my answer.
Set your calculator to degree mode.
Let h be the height of the flagpole.
[tex] \tan(18) = \frac{h}{80} [/tex]
[tex]h = 80 \tan(18) = 25.994[/tex]
The height of the flagpole is approximately 26.0 meters. #3 is correct.
Please help!! URGENT!! I don’t understand
Answer: 14%
Step-by-step explanation:
Our formula is i=prt but we're trying to find the rate (r) so we'll rearrange it to become r=i/pt.
i = $245
p = $7000
t = 3/12= 0.25 years
[tex]r=\frac{245}{(7000)(0.25)} \\r = 0.14[/tex]
call a positive integer kinda-prime if it has a prime number of positive integer divisors. if there are $168$ prime numbers less than $1000$, how many kinda-prime positive integers are there less than $1000$?
There are 173 kinda-prime positive integer less than 1000.
To find the number of kinda-prime positive integer less than 1000, we'll follow these steps:
1. Understand the definition of a kinda-prime number: A positive integer is kinda-prime if it has a prime number of positive integer divisors.
2. Determine the number of prime numbers less than 1000: There are 168 prime numbers less than 1000, as given.
3. Determine the possible prime number of divisors: Since 168 is not too large, we only need to consider 2 and 3 as possible prime numbers of divisors for a kinda-prime number.
4. Analyze the cases:
Case 1: Kinda-prime numbers with 2 divisors (prime numbers)
All prime numbers have exactly 2 divisors (1 and itself). Thus, all 168 prime numbers less than 1000 are kinda-prime.
Case 2: Kinda-prime numbers with 3 divisors
Let N be a kinda-prime number with 3 divisors. Then, N = p^2 for some prime number p. To find the suitable prime numbers p, we need[tex]p^2 < 1000[/tex]. The prime numbers that meet this condition are 2, 3, 5, 7, and 11 (since 13^2 = 169 > 1000). Therefore, there are 5 additional kinda-prime numbers ([tex]2^2, 3^2, 5^2, 7^2, and 11^2[/tex]).
5. Add the total number of kinda-prime numbers from both cases: 168 + 5 = 173.
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[tex]$(\pi(1000)-1)+11=\boxed{177}$[/tex] "kind a-prime" positive integers less than $1000$.
Let [tex]$n$[/tex] be a positive integer with[tex]$k$[/tex] positive integer divisors.
If [tex]$k$[/tex] is prime, then.
[tex]$n$[/tex] is a "kind a-prime" integer.
[tex]$k$[/tex] must be of the form.
[tex]$k=p$[/tex] or [tex]$k=p^2$[/tex] for some prime [tex]$p$[/tex].
If [tex]$k=p$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p-1}$[/tex] for some prime [tex]$p$[/tex]. Since [tex]$p < 1000$[/tex], there are.
[tex]$\pi(1000)$[/tex]possible values of [tex]$p$[/tex].
[tex]$p=2$[/tex] gives [tex]$2^1$[/tex], which is not prime, so we have to subtract.
[tex]$1$[/tex] from [tex]$\pi(1000)$[/tex] to get the number of possible.
[tex]$p$[/tex].
[tex]$\pi(1000)-1$[/tex] values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
If [tex]$k=p^2$[/tex], then [tex]$n$[/tex] must be of the form.
[tex]$p^{p^2-1}$[/tex] for some prime[tex]$p$[/tex].
There are.
[tex]$\pi(31)=11$[/tex] primes less than [tex]$31$[/tex], and each of them gives a different "kind a-prime" integer of this form.
Since [tex]$31^5 > 1000$[/tex], no primes larger than [tex]$31$[/tex]can be used to form a "kind a-prime" integer of this form.
[tex]$11$[/tex] possible values of [tex]$p$[/tex] that give a "kind a-prime" integer of this form.
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Which statement is true?
Please help
a grocery store company wanted to know how well some of their local stores were doing. in order to find out, they hired three different reviewers to rate 10 local stores. the test statistic was 2.3, what is the p value?
Assuming a two-tailed test with 9 degrees of freedom (10 stores minus 1), the p-value for a t-value of 2.3 is approximately 0.040.
In order to calculate the p-value, we need to know the specific test being used and the significance level of the test. Let's assume that the test is a two-tailed t-test with a significance level of 0.05.
Since the test statistic is 2.3, we need to find the probability of getting a t-value of 2.3 or greater (in absolute value) under the null hypothesis. We can use a t-distribution table or a statistical software to find the corresponding p-value.
Assuming a two-tailed test with 9 degrees of freedom (10 stores minus 1), the p-value for a t-value of 2.3 is approximately 0.040. Therefore, if the significance level of the test is 0.05, we would reject the null hypothesis and conclude that there is a significant difference between the ratings given by the three reviewers.
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these four geometry questions i’m not quite sure how to do and have been struggling in them for a while and it’s due tomorrow!!!!
The total areas of each composite shape are:
1) 121 in²
2) 150m²
3) 14.03 ft²
4) 538.36 cm²
How to find the area of the composite figure?1) Formula for area of a rectangle is:
Area = Length * width
Thus:
Area of composite shape = (9 * 8) + (7 * 7)
= 121 in²
2) Formula for area of rectangle is:
Area = Length * width
Area = 12 * 5 = 60 m²
Area of triangle = ¹/₂ * base * height
Area = ¹/₂ * 12 * 15
Area = 90 m²
Area of composite shape = 60 + 90 = 150m²
3) Area of triangle = ¹/₂ * 3 * 7 = 10.5 ft²
Area of semi circle = ¹/₂ * πr²
= ¹/₂ * π * 1.5²
= 3.53 ft²
Total composite area = 10.5 ft² + 3.53 ft²
Total composite area = 14.03 ft²
4) Total composite area = (¹/₂ * π * 7.5²) + (30 * 15)
= 538.36 cm²
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brainliest+100 points
2x + 2y = 4xy is wrong
2x + 2y = 2(x+y) is correct
b.3x+4= 7x wrong
c4x²+5x = 9x² wrong
23x²+3x²+4x = 6x² + 4x = 2x(3x + 2)
3sorry I don't understand this one.....
4-4(3x-5) = -12x + 20
5 120 12 10 4 3 5 26Answer:
120
12 10
4 2 5 2
2 2
armer abe has a budget of $300 to build a rectangular pen to protect his rambunctious sheep. he decides that three sides of the pen will be constructed with chain-link fence, which costs only $1 per foot. farmer abe decides that the fourth side of the pen will be made with sturdier fence, which costs $5 per foot. find the dimensions of the largest area the pen can enclose.
Let x be the length of the pen and y be the width of the pen.
The total cost of the pen is given by:
Cost = 3x + 5y = 300
3x + 5y = 300
3x = 300 - 5y
x = (300 - 5y)/3
The area of the pen is given by:
Area = xy = (300 - 5y)/3 * y
The data for the height and weight of different people was collected the line of best fit for this date it was determined to be Y equals 0. 9 1X -65. 5 where X is the height in centimeters and why is the weight in kilograms is in the equation predict the height of a person who weighs 63 kg
According to the equation, a person who weighs 63 kg is predicted to be approximately 141 centimeters tall.
The equation given is Y = 0.91X - 65.5, where X represents the height in centimeters and Y represents the weight in kilograms. To predict the height of a person who weighs 63 kg, we need to solve for X, the height in centimeters.
To do this, we can plug in the given weight of 63 kg for Y in the equation and then solve for X. So, we have:
63 = 0.91X - 65.5
Adding 65.5 to both sides, we get:
63 + 65.5 = 0.91X
Simplifying, we have:
128.5 = 0.91X
Finally, to solve for X, we divide both sides by 0.91, giving:
X = 141.21
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Keyana puts beads at the ends of her braids. On a single braid, she places 7 beads that are
each 1.03 centimeters long. Then she adds a final bead that is 0.9 centimeter long. The
expression below can be used to find the total length of the beads on one of Keyana's braids.
7 x 1.03 +0.9
What is the total length of the beads on one braid?
A 7.3 centimeters
B.8.11 centimeters
C.9.19 centimeters
D: 10.0 centimeters
The total length of the beads on one braid is 8.11 centimeters
What is the length?Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.
To find the total length of the beads on one braid, we need to evaluate the expression:
7 x 1.03 + 0.9
Multiplying 7 by 1.03 gives us:
7 x 1.03 = 7.21
Then, adding 0.9 gives us:
7.21 + 0.9 = 8.11
Therefore, the total length of the beads on one braid is 8.11 centimeters.
So, the correct answer is B.8.11 centimeters.
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Julian goes to a store an buys an item that costs � x dollars. He has a coupon for 20% off, and then a 4% tax is added to the discounted price. Write an expression in terms of � x that represents the total amount that Julian paid at the register.
The expression that represents the total amount that Julian paid at the register in terms of x is 0.84x.
What is Percentage?
Percentage is a way of expressing a proportion or fraction as a quantity out of 100. The word "percent" means "per hundred," so percentages are often denoted by the symbol %, which represents one part in a hundred.
The first step is to find the discounted price after the 20% discount. This can be found by multiplying the original price by (1 - 0.2), which represents a 20% reduction.
Discounted price = x - 0.2x = 0.8x
Next, a 4% tax is added to the discounted price. This can be found by multiplying the discounted price by (1 + 0.04), which represents a 4% increase.
Total amount paid = (0.8x) * (1 + 0.04) = 0.84x
Therefore, the expression that represents the total amount that Julian paid at the register in terms of x is 0.84x.
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You are helping with some repairs at home. You drop a hammer and it hits the floor at a speed of 4 feet per second. If the acceleration due to gravity (g) is 32 feet/second 2, how far above the ground (h) was the hammer when you dropped it? Use the formula:
Step-by-step explanation:
vf = vo + at vo = 0 in this case ( you dropped it from 'at rest')
4 f/s = 32 t
t = 1/8 s
df = do + vot + 1/2 at^2 df = final position = 0 ft (on the ground)
0 = do + 0 + 1/2 (-32)(1/8)^2
solve for do = 1/4 foot
A=P(1+r/n)^nt Find how long it takes for $1400 to double if it is invested at 7% interest compounded monthly. Use the formula A = P to solve the compound interest problem. TE The money will double in value in approximately years. (Do not round until the final answer. Then round to the nearest tenth as needed.)
It will take 10 years to double the amount.
Given that, the amount $1400 to double if it is invested at 7% interest compounded monthly, we need to calculate the time,
[tex]A = P(1+r/n)^{nt}[/tex]
[tex]2800 = 1400(1+0.0058)^{12t}[/tex]
[tex]2= (1.0058)^{12t[/tex]
㏒ 2 = 12t ㏒ (1.0058)
0.03 = 12t (0.0025)
12t = 120
t = 10
Hence, it will take 10 years to double the amount.
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A football team consists of:
• 10 sixth graders
• 14 seventh graders
• 16 eighth graders
A student on the team will be randomly chosen to participate in the coin toss each of the 40
games of the season.
What is a reasonable prediction for the number of times a sixth or seventh grader will be
chosen?
A reasonable prediction for the number of times a sixth or seventh grader will be chosen is 24 out of the 40 games.
What is reasonable prediction?
A reasonable prediction is a prediction made with a reasonable degree of accuracy or likelihood, based on available information and knowledge. It is based on facts, past events, and logical assumptions, and is not based on conjecture or guesswork. Reasonable predictions can be made about future events, trends, and outcomes, and can be used to inform decisions, plans, and strategies.
The total number of sixth and seventh graders on the team is:
10 sixth graders + 14 seventh graders = 24 students
The total number of students on the team is:
10 sixth graders + 14 seventh graders + 16 eighth graders = 40 students
To find the expected number of times a sixth or seventh grader will be chosen in the coin toss, we can use the proportion of sixth and seventh graders to the total number of students:
(expected number of times) = (proportion of sixth and seventh graders) * (total number of coin tosses)
(expected number of times) = (24/40) * 40
(expected number of times) = 24
Therefore, a reasonable prediction for the number of times a sixth or seventh grader will be chosen is 24.
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What is the slope of the line?
-2
-1
1
2
Answer: positive 2
Step-by-step explanation:
fuel efficiency of manual and automatic cars, part i. each year the us environmental protection agency (epa)releases fuel economy data on cars manufactured in that year. below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions. do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage? assume that conditions for inference are satisfied.
Given the above prompt on hypothesis testing, we can state that specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.
What is the explanation for the above response?
To determine if there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage, we can conduct a two-sample t-test assuming unequal variances. The null hypothesis is that there is no difference in the average city mileage between the two types of transmissions, and the alternative hypothesis is that there is a difference.
The t-test statistic is calculated as follows:
t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2))
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Plugging in the values from the given statistics, we get:
t = (16.12 - 19.85) / sqrt((3.85^2/26) + (4.51^2/26))
t = -3.31
Using a significance level of 0.05 and 50 degrees of freedom (approximated by n1+n2-2), the critical t-value is ±2.01.
Since the calculated t-value (-3.31) is less than the critical t-value, we can reject the null hypothesis and conclude that there is strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average city mileage.
Specifically, cars with manual transmissions have a significantly higher average city mileage than those with automatic transmissions.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
please help!
If r=0.5 m, A = ???
(Use the r key.)
The area of a circle of radius of 0.5 meters is 0.785 square meters.
How to find the area of the circle?Remember that for a circle of radius r, the area is:
A = pi*r²
Where pi = 3.14
Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.
A = 3.14*(0.5m)²
A = 3.14*0.25 m²
A = 0.785 m²
That is the area of the circle.
Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?
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If you spin the spinner 36 times, what is the best prediction possible for the number of times
it will land on green or blue?
The best prediction possible for the number of times the spinner will land on green or blue is given as follows:
30 spins.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Out of six regions, three are green and two are blue, hence the probability of one spin resulting in green or blue is given as follows:
p = (3 + 2)/6
p = 5/6.
Thus the expected number out of 36 trials of spins resulting in green or blue is given as follows:
E(X) = 5/6 x 36
E(X) = 30 spins.
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explain why we call the national halothane study an observational study rather than an experiment, even though it compared the results of using different anesthetics in actual surgery.in order to be an experiment, the subjects would have to be randomly selected from the population. however, these are hospital patients who all have some disease or condition and have not been randomly selected from the population, which includes both healthy and sick people.in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. instead, a patient's anesthetic is selected by his or her doctor(s).there is not enough information to say for sure, but it is safer to assume that it is only an observational study, so that we are not overconfident about the results.actually, it is an experiment and not an observational study.
We the best reason behind why we call National halothane study is an observational study rather than an experiment is: " In order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned." So, option( b) is right one.
We have data from the National Halothane Study that correlates with important research into the safety of anesthetics used in surgery. The above shows the death rate and aesthetic. There is a relationship between the anesthetic used and the death of the patient. The data was collected after that the anesthesia was administered is started. In the observational study, interesting observer in the subjects & any treatment that the subjects recive are beyond the council of the investigators. Here the motion of anaesthesia is anesthetics used her determined by the doctors and the investigators are simply observing. So, it is an observational study due to because in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. Instead, a patient's anesthetic is selected by his or her doctor(s).
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Complete question:
The National Halothane Study was a major investigation of the safety of anesthetics used in surgery. Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics:27 Anesthetic A Death rate B CD 1.7% 1.7% 3.4% 1.9% There is a clear association between the anesthetic used and the death rate of patients. Anesthetic C appears dangerous.
a) in order to be an experiment, the subjects would have to be randomly selected from the population. however, these are hospital patients who all have some disease or condition and have not been randomly selected from the population, which includes both healthy and sick people.
b) in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. instead, a patient's anesthetic is selected by his or her doctor(s).
c) there is not enough information to say for sure, but it is safer to assume that it is only an observational study, so that we are not overconfident about the results.
d) actually, it is an experiment and not an observational study.
The function V(t) = 30000(0.85) value V(t) represents the values v(t) of Nancy's car after t years. What is the depreciation rate of Nancy's car?
The depreciation rate of Nancy is 15%.
What is known by depreciation?Depreciation is the reduction in the value of an asset over time due to wear and tear, obsolescence, or other factors. It is a non-cash expense that is recorded on a company's income statement, which reflects the decrease in the asset's value during its useful life. Depreciation is commonly used in accounting to allocate the cost of an asset over its useful life, and it helps businesses to accurately reflect the true value of their assets on their financial statements.
Define function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output.
The given function V(t) = [tex](30000*0.85)^{t}[/tex]represents the value of Nancy's car after t years.
Depreciation rate is the rate at which the value of an asset decreases over time. In this case, the depreciation rate of Nancy's car is 1 - 0.85 = 0.15 or 15%.
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Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 to describe the relationship.
In the given equation r = 2/5 t "r" is the dependent variable.
Dependent variables:In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.
An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.
A dependent variable is a variable whose value depends on the value of one or more other variables in the equation
Here we have
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups.
She writes the equation r = 2/5 t to describe the relationship.
In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.
Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.
The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.
Therefore,
In the given equation r = 2/5 t "r" is the dependent variable.
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Complete Question:
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.
What is the remainder? Equation is below.
Answer:
-23. In my explanation I will include in my picture how this will look in your final answer
Step-by-step explanation:
So to solve this, I first set x + 3 = 0. This means that x = -3, which we will use soon. Now, here's how you would work out this problem. It would be confusing if I explained over text, so I included a picture of my work.
You would first set up your problem like it is in the picture. Then, bring 2 down. Next, multiply 2 by -3 (for future problems, you would multiply the number you brought down by whatever number is on the side). -3 × 2 = -6, so you would put that under 3 (as shown in the picture). Now, add 3 and -6 (which = -3). Repeat this step each time.
I hope this made sense! Please let me know if you have any questions.
Write a sine function that has an amplitude of 3, a midline of y =2 and a period of 1
the sine function that meets the given conditions is:
[tex]y(t) = 3 \times sin ((2\pi / 1200) \times t) + 2[/tex]
Function with the given characteristics.
The terms and their definitions we need to consider:
Amplitude:
The maximum displacement from the midline (in this case, 3)
Midline:
The horizontal line that passes through the center of the wave (y = 2)
Period:
The length of one complete cycle of the wave (1200)
Now, let's write the sine function:
[tex]y(t) = A \times sin (B \times t) + C[/tex]
Where:
y(t) is the sine function with respect to time (t)
A is the amplitude (3)
B is the frequency (to be determined)
C is the midline (2)
First, we need to find the frequency (B).
The period and frequency are related by the following formula:
[tex]Period = 2\pi / B[/tex]
In this case, the period is 1200:
[tex]1200 = 2\pi / B[/tex]
Now, solve for B:
[tex]B = 2\pi / 1200[/tex]
Now, we can plug in the amplitude (A), frequency (B), and midline (C) into our sine function:
[tex]y(t) = 3 \times sin((2\pi / 1200) \times t) + 2[/tex]
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the integers from 1 to 15, inclusive, are partitioned at random into two sets, one with 7elements and the other with 8. what is the probability that 1 and 2 are in the same set?
The chance/
probability
is
16/33
, or roughly 0.485 that 1 and 2 are in the
same set.
Let's say we divide the range of numbers from
1 to 15
into two sets, each containing seven and eight numbers, respectively. Finding the likelihood that the numbers 1 and 2 are included in the same
set
is our goal.
We can determine the
total number
of ways to divide the numbers into the two sets of
7
and
8
in order to begin solving this issue. Calculating this yields the result 6435 using a formula.
The number of ways in which the pairs 1 and 2 can be found in the same set must then be determined. Considering that there are
seven numbers
in the set, we must select six more from the remaining thirteen to complete the set, presuming that one is among the seven .There are
1716
ways to do this. The number of methods remains the same, 1716, even if we suppose that 2 is among the set of 7 numbers.
Hence, there are
3432
different ways to combine the numbers 1 and 2 into one set. The chance is 16/33, or roughly 0.485, when we divide this number by the total number of possible
divisions
of the numbers.
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Urgent, please help!
It has been proved that the lines MN and PR are parallel because they have the same slope.
How to identify the slope of parallel lines?We are given the coordinates of the points P, Q and R as:
P(-3, -6)
Q(1, 4)
R(5, -2)
Since M is the midpoint of PQ, we have:
M = (-3 + 1)/2, (-6 + 4)/2
M = (-1, -1)
N is the midpoint of QR and so:
N = (1 + 5)/2, (4 - 2)/2
N = (3, 1)
Slope of MN = (1 + 1)/(3 + 1) = 1/2
Slope of PR = (-2 + 6)/(5 + 3)
Slope of QR = 4/8 = 1/2
Both slopes are equal and as such they are parallel lines
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HELP ME PLS
1. If the diameter of a circle is segment AB where Point A is located at (-3, 6), and Point B located at (-8,-1), what is the diameter of the circle?
2√2
√146
√74
74
The diameter of the circle is √74. Answer: C.
What is circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point.
To find the diameter of the circle, we need to find the distance between points A and B, which will give us the length of the diameter.
Using the distance formula, we have:
d = √[(x2 - x1)² + (y2 - y1)²]
where (x1, y1) = (-3, 6) and (x2, y2) = (-8, -1).
Plugging in the values, we get:
d = √[(-8 - (-3))² + (-1 - 6)²]
= √[(-5)² + (-7)²]
= √[25 + 49]
= √74
Therefore, the diameter of the circle is √74. Answer: C.
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A small tree that is 8 feet tall casts a 4-foot shadow, while a building that is 24 feet tall casts a shadow in the same direction. Determine the length of the building's shadow.
6 feet
12 feet
18 feet
48 feet
Answer:
Using similar triangles, we can set up a proportion:
(tree height)/(tree shadow) = (building height)/(building shadow)
Plugging in the given values, we get:
8/4 = 24/x
Solving for x, we get:
x = (24 x 4)/8 = 12 feet
Therefore, the length of the building's shadow is B. 12 feet.
A helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post as shown in the diagram how far is the object from the helicopter to the nearest foot
The distance of the object from the helicopter is 698 ft.
What is distance?Distance is the length between two points.
To calculate how far the object is above the helicopter, we use the formula below.
Formula:
Sin∅ = O/H..................... Equation 1Where:
∅ = AngleO = OppositeH = Hypotenus = Distance of the object from the HelicopterFrom the question,
Given:
O = 250 ft∅ = 21°Substitute these values into equation 1 and solve for H
H = 250/Sin21°H = 697.61 ftH ≈ 698 ftHence, the distance is 698 ft.
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Find the volume of a pyramid with a square base, where the area of the base is 19. 6 ft 2 19. 6 ft 2 and the height of the pyramid is 11. 6 ft 11. 6 ft. Round your answer to the nearest tenth of a cubic foot
If the area of the base is 19. 6 ft^2 and the height of the pyramid is 11. 6 ft, the volume of the pyramid is approximately 79.1 cubic feet.
The formula for the volume of a pyramid is given by:
V = (1/3) × base area × height
In this case, we are given that the pyramid has a square base, so the base area is simply the area of a square with side length s:
base area = s^2 = 19.6 ft^2
We are also given the height of the pyramid:
height = 11.6 ft
Substituting these values into the formula for the volume of a pyramid, we get:
V = (1/3) × base area × height
= (1/3) × 19.6 ft^2 × 11.6 ft
≈ 79.1 ft^3 (rounded to the nearest tenth)
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Monique claims the surface area of the cylinder is about 1001.66 square feet explain Monique's error find the correct surface area.
Answer: Monique's error is likely due to rounding the surface area to two decimal places, which led to an inaccurate result.
The formula for the surface area of a cylinder is:
S = 2πr^2 + 2πrh
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately 3.14.
To find the correct surface area, we need to know the values of r and h. Without this information, we cannot calculate the exact surface area.
However, we can use Monique's estimate to estimate the values of r and h.
1001.66 = 2πr^2 + 2πrh
Dividing both sides by 2π, we get:
500.83 = r^2 + rh
We don't know the exact values of r and h, but we know that the surface area should be greater than 1001.66 square feet. Therefore, we can assume that the radius and height must be greater than a certain value.
For example, if we assume that the radius is at least 5 feet, we can solve for the minimum value of h:
500.83 = 5^2 + 5h
495.83 = 5h
h = 99.166
So if the radius is 5 feet and the height is 99.166 feet, the surface area would be:
S = 2π(5^2) + 2π(5)(99.166)
S = 1570.8 square feet
This is greater than Monique's estimate of 1001.66 square feet, indicating that her estimate was too low due to rounding.
Step-by-step explanation: