To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the equations (r, θ) = (√(x² + y²), atan2(y, x)).
Explanation:To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the following equations:
(r, θ) = (√(x² + y²), atan2(y, x))
(a)(i) For the Cartesian coordinates (6, -6),
(r, θ) = (√(6² + (-6)²), atan2(-6, 6))
(r, θ) = (√(36 + 36), atan2(-6, 6))
(r, θ) = (6√2, -45°)
(a)(ii) For the Cartesian coordinates (6, -6),
(r, θ) = (-√(6² + (-6)²), atan2(-6, 6) + π)
(r, θ) = (-6√2, -45° + π)
(b)(i) For the Cartesian coordinates (-1, 3),
(r, θ) = (√((-1)² + 3²), atan2(3, -1))
(r, θ) = (√(1 + 9), atan2(3, -1))
(r, θ) = (√10, 116.57°)
(b)(ii) For the Cartesian coordinates (-1, 3),
(r, θ) = (-√((-1)² + 3²), atan2(3, -1) + π)
(r, θ) = (-√10, 116.57° + π)
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.21. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03
Answer:
We need a sample size of at least 383.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
85% confidence level
So [tex]\alpha = 0.15[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.15}{2} = 0.925[/tex], so [tex]Z = 1.44[/tex].
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03
We need a sample size of at least n.
n is found with [tex]M = 0.03, \pi = 0.21[/tex]
Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.44\sqrt{\frac{0.21*0.79}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.44\sqrt{0.21*0.79}[/tex]
[tex]\sqrt{n} = \frac{1.44\sqrt{0.21*0.79}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.44\sqrt{0.21*0.79}}{0.03})^{2}[/tex]
[tex]n = 382.23[/tex]
Rounding up
We need a sample size of at least 383.
To estimate the proportion of tenth graders reading at or below the eighth grade level with an 85% confidence level and a 0.03 margin of error, a sample size of 550 students is needed.
To estimate the fraction of tenth grade students with reading skills at or below the eighth grade level with an 85% confidence interval and a margin of error of at most 0.03, we use the following formula for sample size:
⇒ n = (Z² × p × (1 - p)) ÷ E²
Where:
Z is the z-value corresponding to the desired confidence level.p is the estimated population proportion (0.21).E is the desired margin of error (0.03).For an 85% confidence level, the z-value is approximately 1.44. Plugging in the values:
Calculate the numerator:⇒ Z² × p × (1 - p) = 1.44² × 0.21 × (1 - 0.21)
≈ 0.494668.
Calculate the denominator:⇒ E² = 0.03²
= 0.0009.
Divide the numerator by the denominator:⇒ 0.494668 ÷ 0.0009 ≈ 549.63.
Round up to the next integer: 550.Therefore, the required sample size is 550 students.
Complete question:
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.21. How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 85% confidence level with an error of at most 0.03? Round your answer up to the next integer.
En una granja hay 500 animales. Si hay el triple de vacas que de ovejas, ¿ cuantas animales hay de cada especie
Answer:
Hay 375 vacas y 125 ovejas
Step-by-step explanation:
Para resolver este problema simplemente tenemos que plantear una igualdad entre vacas y ovejas
b = oveja
v = vaca
v = 3b
b + v = 500
reemplazamos la b por (3v) en la segunda ecuacion
b + v = 500
b + 3b = 500
4b = 500
b = 500/4
b = 125
reemplazamos este valor en la primer ecuacion
v = 3b
v = 3(125)
v = 375
Hay 375 vacas y 125 ovejas
(3 + 5) * 2Y = (5 * 8) - (2 * 4). What does Y equal?
Answer:
pretty sure y should equal 15
The solution of the linear equation (3 + 5) × 2Y = (5 × 8) - (2 × 4) will be 2.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given below.
(3 + 5) × 2Y = (5 × 8) - (2 × 4)
Simplify the equation, then the value of the variable y will be
8 × 2Y = 40 - 8
16Y = 32
Y = 32 / 16
Y = 2
The solution of the linear equation (3 + 5) × 2Y = (5 × 8) - (2 × 4) will be 2.
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Determine Whether the triangle with the given side lengths is a right triangle
6,8,10
Right Triangle
Not A Right Triangle
Answer:
Yes, right triangle
Step-by-step explanation:
Since it is a right triangle, we can use Pythagorean Theorem.
a^2+b^2=c^2
a and b are the legs, or shorter sides, and c is the hypotenuse, or the longest side.
We have 3 side lengths: 6, 8 and 10
6 and 8 are the shorter legs, so they are a and b.
10 is the longest leg, so it is c
Substitute the values into the equation, and see if it is true.
6^2+8^2=10^2
Evaluate the exponents
36+64=100
100=100
Since this is a true statement, these sides can make a right triangle.
The average age of online consumers a few years ago was 24.1 years. As older individuals gain confidence with the Internet, it is believed that the average age has increased. We would like to test this belief. Answer parts a) through e) below. a) Write the appropriate hypotheses. Choose the correct answer below. A. Upper H 0 : mugreater than24.1 years Upper H Subscript Upper A Baseline : muequals24.1 years B. Upper H 0 : muless than24.1 years Upper H Subscript Upper A Baseline : muequals24.1 years C. Upper H 0 : muequals24.1 years Upper H Subscript Upper A Baseline : mugreater than24.1 years D. Upper H 0 : muequals24.1 years Upper H Subscript Upper A Baseline : muless than24.1 years
Answer:
The correct option is (C).
Step-by-step explanation:
A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.
It is a hypothesis of no difference.
It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.
Whereas the alternative hypothesis is a contradicting statement tot he null hypothesis. It is denoted by Hₐ.
In this case we need to test whether the average age of online consumers has increased or not.
From previous data we know that the average age of online consumers a few years ago was 24.1 years.
A one-sample mean test can be used to determine whether the mean age has increased or not.
The hypothesis for the test can be defined as follows:
H₀: The average age of online consumers is 24.1 years, i.e. μ = 24.1.
Hₐ: The average age of online consumers is more than 24.1 years, i.e. μ > 24.1.
Thus, the correct option is (C).
A car travels at an average speed of 52 mph. Jow long does it take to travel 169 miles?
To calculate the time it takes for the car to travel 169 miles at an average speed of 52 mph, divide the distance by the speed. The car would take approximately 3.25 hours.
Explanation:To calculate the time it takes for the car to travel 169 miles, we can divide the distance by the average speed. The formula for speed is:
Speed = Distance / Time
Rearranging the formula to solve for time, we get:
Time = Distance / Speed
Plugging in the values, we have:
Time = 169 miles / 52 mph
Calculating this, the car would take approximately 3.25 hours to travel 169 miles.
A country's balance of payments is divided up into three categories, the
current account, capital account and financial account. The current account
mainly measures
A) the flow of credit.
B) the flow of goods and services.
c) purchases and sales of nonfinancial assets.
D) purchases of sales of stocks and bonds and other financial assets.
Answer:
B) the flow of goods and services
Step-by-step explanation:
Balance of payments (BOP) is a statement of all transactions made between one country and the rest of the world at a particular period of time. It is also called balance of international payment. BoP is divided into current and capital account.
1. The current account: This is account of country's net trade in goods and services, net earnings on cross-border investments, and its net transfer payments. The current account measures the flow of goods and services.
2. The capital account: This is a country's imports and exports of capital and foreign aid. It can also be called financial account.
The sum of all transactions recorded in the balance of payments should be zero.
Balance of payment deficit is when a country's import is higher than its export.
Balance of payment surplus is when a country's export is greater than its import.
Which best describes the complement of spinning any number less than 3?
spinning a 4
spinning a 3 or 4
spinning a 1 or 2
spinning a 1, 2 or 3
Answer:
spinning a 1 or 2
Step-by-step explanation:
less than 3 is 1 or 2
Answer:
B
Step-by-step explanation:
taking the test too
The yearly tuition at lewis college is set at $13,494 for the year maria will graduate, which is a 568% increase from 1995 when her mother graduated from there. How much was tuition when her mother graduated? Round your answer to the nearest dollar
Answer:
$2375.70
Step-by-step explanation:
5.68x=13,494
x=2375.70
The operator of a beachfront hotel in a tropical island wishes to select a new paint for the hotel’s exterior walls. Three different paints are applied to sample pieces of plywood, then exposed to a heat lamp and sprayed continuously with salt water until the paint begins to peel. Five plywood samples are used for testing each paint. The hours needed in order for the paint to begin to peel are listed below: • Paint A: 25, 27, 28, 28, and 30 hours. • Paint B: 23, 28, 30, 31, and 32 hours. • Paint C: 30, 31, 33, 33, and 37 hours. The hotel operator believes that there is no fundamental difference in longevity/endurance between the three types of paint. Do you agree or disagree? Perform ANOVA to justify your answer.
Find the given attachment for complete answer and solution
A graph shows the horizontal axis numbered 2 to 8 and the vertical axis numbered 10 to 50. A line increases from 0 to 4 then decreases from 4 to 9.
Which type of function best models the data shown on the scatterplot?
Answer:
Quadratic
Step-by-step explanation:
Took a test and got it right
Answer:
quadratic
Step-by-step explanation:
A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. What percent of candidates have a GPA above 3.9?
Answer:
Only 0.0668 of the candidates, or 6.68%, have a GPA above 3.9.
Step-by-step explanation:
The GPA, according to the question, is a random variable normally distributed. A normal distribution is determined by its parameters. These parameters are the population mean, [tex] \\ \mu[/tex], and the population standard deviation, [tex] \\ \sigma[/tex]. The normal distribution for GPA has a [tex] \\ \mu = 3.3[/tex], and [tex] \\ \sigma = 0.4[/tex].
To find probabilities related to normally distributed data, we can use the standard normal distribution. To use it, we first need to find the corresponding standardized score or z-score for the value we want to obtain the probability. This value, in this case, is x = 3.9. The related z-score or standardized value is given by the formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
A z-score tells us the distance from the mean in standard deviations units. A negative value indicates that the value is below the mean. A positive value is, conversely, above the mean.
And we already have all the necessary data to use [1].
Thus
[tex] \\ z = \frac{3.9 - 3.3}{0.4}[/tex]
[tex] \\ z = \frac{0.6}{0.4}[/tex]
[tex] \\ z = 1.5[/tex]
This value for z tells us that the "equivalent" raw score, x = 3.9, is above the mean, and it is at 1.5 standard deviations units from the population mean.
We can find the probabilities for standardized values in the cumulative standard normal table, available on the Internet or in Statistic books (we can also use statistical packages or even spreadsheets).
To use the cumulative standard normal table, we have the z-score as an entry. With this value, we find the z column on this table, and, since it is z = 1.5, we only need to select the first column (which has two decimal places, that is, .00). Then, the cumulative probability for P(z<1.50) = 0.9332.
However, we are asked for the percent of candidates that have a GPA above 3.9 (z-score = 1.50). This probability is the complement of P(z<1.50) or 1 - P(z<1.50). Mathematically
[tex] \\ P(z<3.9) + P(z>3.9) = 1[/tex]
[tex] \\ P(z<1.50) + P(z>1.50) = 1[/tex] (standardized)
[tex] \\ P(z>1.50) = 1 - P(z<1.50)[/tex]
[tex] \\ P(z>1.50) = 1 - 0.9332[/tex]
[tex] \\ P(z>1.50) = 0.0668[/tex]
That is, only 0.0668 of the candidates, or 6.68%, have a GPA above 3.9.
We can see this probability in the graph below.
-3+(-4) • 5 + 10???? I need help!!!
Answer:
-13
Step-by-step explanation:
used a calculator ._.
n is an integer and -2
Answer:
-1, 0,1
Step-by-step explanation:
Hope this helps.
plz answer this asap
Answer:
100 inches square
Step-by-step explanation:
The surface is a trapezoid
Area = ½ × (sum of // sides) × height
= ½ × (5+15) × 10
= ½ × 20 × 10
= 100 in²
A toy car can go 5 mph. How long would it take to go 7 miles?
Answer:
by the way what grade are you in? If you are more than 7th grade can you help me? https://brainly.com/question/16233847
35 mph
Step-by-step explanation:
7 times 5
Which sentence is written correctly? Kino said that if play practice does not start on time, the director “will be mad.” Kino said that if play practice does not start on time, the director “Will be mad”. Kino said that if play practice does not start on time, the director “will be mad”. Kino said that if play practice does not start on time, the director “Will be mad.”
The correct sentence is: Kino said that if play practice does not start on time, the director "will be mad."
Explanation:The correct sentence is: Kino said that if play practice does not start on time, the director "will be mad."
In this sentence, the verb "will" is correctly written in lowercase, as it is not a proper noun or the start of a sentence. Additionally, the punctuation marks, such as the quotation marks and the comma, are correctly placed.
It is important to use proper capitalization and punctuation to ensure clear and effective communication in writing.
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What is the value of x in the equation 2(6х+4)- 6+ 2х = 3(4х+3) + 12
оооо
Answer:X= 19/2
Step-by-step explanation:
The snack bar at the soccer field is charging $12 for 9 hamburgers. At that rate, how many hamburgers could you get for $20?
Answer:
6
Step-by-step explanation:
12 = 9 so u do 12 divided by 9
$20 to get 15 hamburgers. By dividing the price to produce one unit of your product by the number of items you have created, you can use the total variable cost.
locate total variables cost?By dividing the price to produce one unit of your product by the number of items you have created, you can determine the total variable cost.
Multiply the cost of producing one unit of your product by the total number of items you have produced to determine variable costs. Total Variable Costs = Cost Per Unit x Total Number of Units is the calculation for this cost.
For instance, if producing one unit of your product costs $12 and you produced 9 pieces, your total variable cost would be $12 x 9, or $108.
$12/9 = 1.34 then $20 to get 15 hamburgers.
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Is the mean age at which American children learn to walk less than 15 months? A study of 40 American children found a mean walking age of = 13.2 months. If the population of all American children has mean age μ until they begin to walk and standard deviation σ, which of the following null and alternative hypotheses should we test to answer this question? H 0 : μ ≥ 13.2 vs. Ha : μ < 13.2 H 0 : μ = 13.2 vs. H a : μ ≠ 13.2 H 0 : μ = 15 vs. H a : μ ≠ 15 H 0 : μ ≥ 15 vs. Ha : μ < 15
Answer:
We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.
Null hypothesis: [tex]\mu \geq 15[/tex]
Alternative hypothesis: [tex]\mu <15[/tex]
And for this case the best answer would be:
H 0 : μ ≥ 15 vs. Ha : μ < 15
Step-by-step explanation:
We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.
Null hypothesis: [tex]\mu \geq 15[/tex]
Alternative hypothesis: [tex]\mu <15[/tex]
And for this case the best answer would be:
H 0 : μ ≥ 15 vs. Ha : μ < 15
And the data given from the sample is:
[tex]\bar X = 13.2[/tex] represent the sample mean
[tex]\sigma[/tex] represent the population deviation
[tex] n = 40[/tex] represent the sample size
And the statistic would be given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Is 9/10 greater than 3/20
Answer:
Yes.
Step-by-step explanation:
9/10 is equal to 18/20, which is evidently greater than 3/20.
HELP!! pls pls pls
The average price of a movie ticket in 1990 was $4.22. Since then, the price has increased by approximately 3.1% each year. Write an exponential function to model this situation, then find the price of a ticket in 2016. Is this growth or decay?
Answer:
$9.33
Exponential growth.
Step-by-step explanation:
The formula for an exponential function is:
abˣ = y OR
a(1 + r)ˣ = y
a is the initial value (4.22)
r is the rate of increase (3.1% or 0.031 in dec. form) where 1 + r is b
x is the time (26 years)
y is the ending value.
If we plug those values in, the equation will turn out to be 4.22(1 + 0.031)²⁶ = y
Plug it into a calculator and you will get 9.333354216
This is exponential growth because x, the initial value, increases to get to y, the ending value.
The mayor of a large city claims that the average net worth of families living in this city is at most $300,000. A random sample of 25 families selected from this city produced a mean net worth $288,000. Assume that the net worth of all families in this city have a normal distribution with the population standard deviation of $80,000. What is the parameter of interest?
Answer:
Check the explanation
Step-by-step explanation:
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 300000
Alternative Hypothesis, Ha: μ < 300000
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (288000 - 300000)/(80000/sqrt(25))
z = -0.75
P-value Approach
P-value = 0.2266
As P-value >= 0.05, fail to reject null hypothesis.
The parameter of interest is the average net worth of families living in the city. Hypothesis testing can be used to evaluate the mayor's claim using a random sample of households. The test statistic can be calculated using the sample mean, sample standard deviation, and sample size.
Explanation:The parameter of interest in this question is the average net worth of families living in the city. The mayor claims that the average net worth is at most $300,000. To determine if this claim is true, a random sample of 25 families is selected. The mean net worth of this sample is $288,000. This mean is an estimate of the population mean net worth.
Based on the information given, the population standard deviation of net worth for all families in the city is $80,000. This information allows us to perform hypothesis testing to evaluate the claim made by the mayor.
Null Hypothesis (H0): The average net worth of families living in the city is $300,000.Alternative Hypothesis (Ha): The average net worth of families living in the city is less than $300,000.Using the sample mean of $288,000, the sample standard deviation ($80,000), and the sample size (25), we can calculate the test statistic.The test statistic is calculated as follows:Test Statistic = (Sample Mean - Population Mean) / (Sample Standard Deviation / sqrt(Sample Size))
Plugging in the values:
Test Statistic = (288,000 - 300,000) / (80,000 / √25)
After calculating the test statistic, we can compare it to the critical value of the test (based on the desired significance level) to determine if we reject or fail to reject the null hypothesis. If the test statistic is less than the critical value, we reject the null hypothesis and conclude that there is evidence to support the claim that the average net worth of families living in the city is less than $300,000.
By providing a random sample from the population, we can use hypothesis testing to evaluate the mayor's claim and determine if there is evidence to support it.
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several years ago wolves were reintroduced in to a national park in north carolina in north carolina. Researchers have monitored the populations over the last severals years and the per capita growth rate of the population is .5. If the current population size is 100, what equation would you use to determine how large the population will be in ten years
Answer: [tex]5766.503\ \text{wolves}[/tex]
Step-by-step explanation:
Given
Current Population of wolves is [tex]P_o=100[/tex]
If the growth rate is [tex]=0.5[/tex]
So the population in next year is
[tex]P_1=100+100\times 0.5[/tex]
[tex]P_1=100(1+0.5)[/tex]
similarly [tex]P_2=100(1+0.5)^2[/tex]
So population after n years is [tex]P_n=P_o(1+r)^n[/tex]
Population after 10 years is
[tex]P_{10}=100(1+0.5)^{10}[/tex]
[tex]P_{10}=5766.503\ \text{wolves}[/tex]
First to answers gets marked brainliest
Drag the tiles to the correct boxes to complete the pairs. Match each event to the probability of its occurrence. the probability of getting a six when a six-sided die is rolled the probability of randomly picking a vanilla-scented candle from a set of 3 vanilla-scented candles, 8 rose-scented candles, and 10 lavender-scented candles the probability of selecting a girl named Maria to be line leader from a class of 32 girls in which 4 students are named Maria the probability of getting an even number when a six-sided die is rolled
1/2 : the probability of getting an even number when a six-sided die is rolled.
1/6 : the probability of getting a six when a six-sided die is rolled.
1/7 : the probability of randomly picking a vanilla-scented candle from a set of 3 vanilla-scented candles, 8 rose-scented candles, and 10 lavender-scented candles.
1/8 : the probability of selecting a girl named Maria to be line leader from a class of 32 girls in which 4 students are named Maria.
Use the Venn diagram to calculate probabilities.
Which probabilities are correct? Select two options.
P(AIC) =
PCB) = 0
PLA) =
PC)
PBIA) = 3
Corrected Question
These are the given probabilities. The Venn diagram is also attached. are (A) P(A|C) = 2/3
(B) P(C|B) = 8/27
(C) P(A) = 31/59
(D) P(C) = 3/7
(E) P(B|A) = 13/27
Answer:
A and C
Step-by-step explanation:
[tex]P(A|C)=\dfrac{P(A\cap C)}{P(C)}= \dfrac{14/59}{21/59}=\dfrac{14}{21}=\dfrac{2}{3}[/tex]
[tex]P(C|B) =\dfrac{P(C\cap B)}{P(B)}= \dfrac{11/59}{27/59}=\dfrac{11}{27}\neq \dfrac{8}{27}\\\\P(A) = \dfrac{31}{59}\\\\P(C) =\dfrac{21}{59}\neq \dfrac{3}{7}\\\\P(B|A)=\dfrac{P(B\cap A)}{P(A)}= \dfrac{13/59}{31/59}=\dfrac{13}{31}\neq\dfrac{13}{27}[/tex]
From the above, only A and C are correct.
Answer: A and C
Step-by-step explanation:
Edg 2021
Which number line models the expression 1/8-(-3/4)
The number line to model the expression 1/8 - (-3/4) would start at 1/8, and move 6/8 steps to the right to reach 7/8 because subtracting a negative is the same as adding a positive.
Explanation:To solve the mathematical expression 1/8 - (-3/4), we need to understand that subtracting a negative number is equivalent to adding a positive number. Hence, we rewrite the expression as 1/8 + 3/4.
Before you can add these two fractions, they must have a common denominator. The least common denominator (LCD) for 8 and 4 is 8, so we rewrite 3/4 as 6/8 to match the denominator of 1/8.
Now, you can add 1/8 + 6/8 to get 7/8.
A number line that models this expression would start at 1/8 and go forward 6/8 (equivalent to 3/4) steps to end at 7/8.
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To model the expression 1/8 - (-3/4) on a number line, you would first convert the expression to 1/8 + 3/4 by changing the minus negative to a plus. Then, find a common denominator and add the fractions to get 7/8. This result is represented on a number line by starting at 1/8 and moving right to reach 7/8.
Explanation:To model the expression 1/8 - (-3/4) on a number line, we need to understand that subtracting a negative is the same as adding its positive counterpart. Therefore, the expression simplifies to 1/8 + 3/4. To add these fractions together, they must have a common denominator. The least common denominator for 8 and 4 is 8. So, we convert 3/4 to 6/8, since 3 multiplied by 2 gives us 6, and 4 multiplied by 2 gives us 8. Adding 1/8 to 6/8 gives us 7/8.
On a number line, we would start at the point representing 1/8 and then move to the right by 6/8 (which represents 3/4) to arrive at 7/8. This portrays the answer to our initial expression, 1/8 - (-3/4) = 7/8.
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A trampoline has a diameter of 10ft. What is it’s area ?
Answer: 78.5 feet squared for short answer
Step-by-step explanation:
If the diameter is 10 feet, then the radius is half of that, or 5 feet. feet squared is the EXACT answer, and we surely didn't need a calulator for this one. However, a real world answer is probably more appropriate if you were trying to measure the area. So the area of our trampoline is about 78.5 feet squared.
Answer:
78.54 square feet
Step-by-step explanation:
The formula to find the area of a circle is πr², and since we know the diameter is 10 ft we know the radius is 5 feet, so π5²=78.54
Katrina bought a package of 500 stickers. These sheet in the package has 20 stickers. 25% of the stickers on each sheet our hearts. The remaining stickers are stars. Select all the statements that are true. A Katrina has 100 heart stickers B Katrina has 375 star stickers C the package contains 20 sheets of stickers D 75% of the stickers on each sheet our stars see the number of heart stickers is the same number I start stickers
Answer:B
Step-by-step explanation:
Given
There are total of 500 stickers
Each sheet has 20 stickers out of which 25 % is Hearts and remaining are stars
So in each sheet 5 are hearts and 15 are stars
therefore in [tex]\frac{500}{20}=25[/tex] sheet
There are [tex]25\times 5=125[/tex] heart stickers
and [tex]25\times 15=375[/tex] star stickers
So statement B is true
Mr. De Leon's Geometry class has 34 students. After lunch everyone returns to the classroom. Within an hour, each person produces 800 BTUs. The room is 25 feet by 32 feet by 12 feet. How many BTUs per cubic foot were produced?
Plz provide the work.
Answer:
2.833 BTUs per cubic foot were produced.
Step-by-step explanation:
BTU's produced by one person = 800
No. of students = 34
Therefore no. of BTU's produced by 34 person = 800 * 34 = 27,200 BTU
Dimension of class 25 feet by 32 feet by 12 feet
Volume of class = length * width * height = 25 * 12 * 32 = 9,600 cubic feet
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BTUs per cubic foot produced = Total BTU's produced by 34 person/ Volume of class
Substituting the value of Total BTU produced and volume of class
BTUs per cubic foot produced = 27,200 BTU/ 9,600 cubic feet
= 2.833 BTUs per cubic foot
2.833 BTUs per cubic foot were produced.