To interpret the residual plot, we need to understand that the residuals are the differences between the actual values and the predicted values from the regression model.
What is the regression model?I. The residual plot can give us an indication of the linearity of the relationship between the two variables. If the plot shows a clear pattern or curvature, it suggests that the relationship is non-linear. From the given information, we cannot see the residual plot and thus cannot determine if the relationship between the number of employees at Microsoft and the year is non-linear.
II. If the regression equation overestimates the number of employees at Microsoft in 1982, it means that the actual number of employees in 1982 was lower than what the regression equation predicted. Looking at the residual plot, if the residuals for the year 1982 are mostly positive (i.e., above the horizontal line), it suggests that the regression equation overestimated the number of employees in 1982. We cannot see the residual plot from the given information to determine if this statement is true.
III. If the number of employees at Microsoft decreased from 1976 through 1982, it means that the actual number of employees in 1982 was lower than the number of employees in 1976. Looking at the residual plot, if the residuals for the years from 1976 to 1982 are mostly negative (i.e., below the horizontal line), it suggests that the regression equation overestimated the number of employees during those years, which would be consistent with a decrease in the number of employees. Therefore, this statement could be true based on the residual plot.
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Can y’all tell me 4 positive slope equations (y=mx+b)
Answer:
1. y = 4x + 2
2. y = 3x – 7
3. y = 7x + 6
4. y= 2x + 8
Step-by-step explanation:
1. y = 4x + 2
2. y = 3x – 7
3. y = 7x + 6
4. y= 2x + 8
These 4 equations have a positive slope because remember in the equation (y=mx+b) m = slope and since these equations have positive numbers in the m spot the slope of these equations are positive.
pretty please helpppp
Answer: 2(n6)
And true states are
The two operations are mulitplication and substraction
The constants are 2 and 6
The expression is written as 2(n-6)
Step-by-step explanation:
Answer:
A,C,D,E should be correct.
A. Replace “a number” with the variable, n.
C. The two operations are multiplication and subtraction.
D. The constants are 2 and 6.
E. The expression is written as 2(n – 6).
hope this helped!
Determine the equation of the hyperbola with and co-vertices (1, 5) and (-7, 5) and
asymptotes y = x+8 and y = -x +2.
The equation of the hyperbola is [tex](x + 3)^2/16 - (y - 5)^2/36[/tex] = 1.
What is hyperbola?The collection of all points in a plane such that the distance between any point on the curve and two fixed points (referred to as the foci) is constant is known as a hyperbola. Hyperbolas are a sort of conic section. A hyperbola contains two distinct branches and has the appearance of two curving branches that are mirror reflections of one another. A hyperbola's center, vertices, co-vertices, foci, and asymptotes are some of its most important characteristics. The center, which is the point around which the hyperbola is symmetric, is the midway of the line segment connecting the vertices.
Given that, the co-vertices are (1, 5) and (-7, 5).
Now, using the midpoint formula we have:
center = ((1+(-7))/2, (5+5)/2) = (-3, 5)
Now, the distance between center and vertex is a = 4.
Also, the distance between the center and each co-vertex is b = 6.
Now, the equation of the hyperbola is:
[tex](x - (-3))^2/4^2 - (y - 5)^2/6^2 = 1\\(x + 3)^2/16 - (y - 5)^2/36 = 1[/tex]
Hence, the equation of the hyperbola is [tex](x + 3)^2/16 - (y - 5)^2/36[/tex] = 1.
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true or false: we conduct a test of hypothesis by assuming that ha is correct, since that is the hypothesis we are trying to show is true. group of answer choices true false
Given statement "We conduct a test of hypothesis by assuming that ha is correct, since that is the hypothesis we are trying to show is true." is true. Because we start by assuming that the null hypothesis is correct, not the alternative hypothesis, when conducting a test of the hypothesis.
When conducting a test of hypothesis, we do not assume that Ha (the alternative hypothesis) is correct.
Instead, we begin by assuming that the null hypothesis (H0) is true.
The null hypothesis typically represents a statement of "no effect" or "no difference" between two groups or variables.
The alternative hypothesis (Ha) represents the statement we are trying to prove or gather evidence for but we must start with the assumption that the null hypothesis is correct.
State the null hypothesis (H0) and the alternative hypothesis (Ha).
The null hypothesis typically represents the status quo or a baseline assumption, while the alternative hypothesis represents the claim you want to prove or gather evidence for.
Determine the level of significance (α), which is the probability of rejecting the null hypothesis when it is actually true. Common significance levels are 0.05, 0.01, and 0.001.
Select an appropriate test statistic, which depends on the type of data and the hypothesis being tested. Examples include the t-test, chi-square test, and ANOVA.
Collect data and calculate the value of the test statistic based on the data.
Compare the calculated test statistic value to the critical value for the chosen level of significance.
If the test statistic is more extreme than the critical value, we reject the null hypothesis in favor of the alternative hypothesis.
Otherwise, we fail to reject the null hypothesis.
Hence, the statement is false.
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A primary credit cardholder's card has an APR of 22. 99%. The current monthly balance, before interest, is $4,528. 34. Determine how much more the cardholder will pay, making monthly payments of $200, until the balance is paid off, instead of paying off the current balance in full
The cardholder will pay an additional $1,471.66 in interest by making monthly payments of $200 until the balance is paid off instead of paying off the current balance in full.
First, we need to calculate the total interest that will accrue on the current balance of $4,528.34. We can do this using the formula
Interest = Balance x (APR/12)
where APR is the annual percentage rate and is divided by 12 to get the monthly interest rate. Plugging in the values, we get:
credit card Interest = $4,528.34 x (22.99%/12) = $87.80
So the total interest that will accrue on the current balance is $87.80.
Next, we need to calculate how long it will take to pay off the balance by making monthly payments of $200. We can use a credit card repayment calculator to do this, but we'll use a simplified formula here
Months = -log(1 - (Balance x (APR/12))/Payment) / log(1 + (APR/12))
where Payment is the monthly payment amount. Plugging in the values, we get
Months = -log(1 - ($4,528.34 x (22.99%/12))/$200) / log(1 + (22.99%/12)) = 29.6 months
So it will take about 30 months (or 2.5 years) to pay off the balance by making monthly payments of $200.
Finally, we can calculate how much more the cardholder will pay in total by subtracting the current balance from the total amount paid over 30 months
Total amount paid = $200 x 30 = $6,000
Total interest paid = $6,000 - $4,528.34 = $1,471.66
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Hugo made a bunch of batches of pancakes for his summer camp. For each batch, Hugo used 1/3 cup of milk. Hugo used a total of 3 cups of milk. Let b represent the number of batches Hugo mad
The number of batches of pancakes made by Hugo using 3 cups of milk is equal to 9 batches.
Number of cups of milk used by Hugo for each batch = 1/3 cup of milk ,
The total amount of milk used for b batches would be,
Total milk = (1/3) × b
The total milk used was 3 cups,
Substitute the value in the equation we have,
⇒ (1/3) × b = 3
Solve for b we get,
Multiply both sides of the equation by the reciprocal of 1/3,
Reciprocal of ( 1/3 ) = 3/1 or simply 3
⇒ (1/3) × b × 3 = 3 × 3
⇒ b = 9
Therefore, Hugo made 9 batches of pancakes.
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The above question is incomplete, the complete question is:
Hugo made a bunch of batches of pancakes for his summer camp. For each batch, Hugo used 1/3 cup of milk. Hugo used a total of 3 cups of milk. Let b represent the number of batches Hugo made . Find the value of b?
Please help me with this homework
Answer:sasa
Step-by-step explanation:
what is the probability that the largest among these random samples is greater than the population median?
The probability that the largest of n random samples is greater than the population median M is bounded above by[tex]1 - F(M)^(n-1) \times F(X(n))[/tex].
Assumptions about the population and the sampling method.
Let's assume that the population has a continuous probability distribution with a well-defined median, and that we are taking independent random samples from this population.
Let [tex]X1, X2, ..., Xn[/tex] be the random samples that we take from the population, where n is the sample size.
Let M be the population median.
The probability that the largest of these random samples, denoted by X(n), is greater than M.
Cumulative distribution function (CDF) of the population distribution to calculate this probability.
The CDF gives the probability that a random variable takes on a value less than or equal to a given number.
Let F(x) be the CDF of the population distribution.
Then, the probability that X(n) is greater than M is:
[tex]P(X(n) > M) = 1 - P(X(n) < = M)[/tex]
Since we are assuming that the samples are independent, the joint probability of the samples is the product of their individual probabilities:
[tex]P(X1 < = x1, X2 < = x2, ..., Xn < = xn) = P(X1 < = x1) \times P(X2 < = x2) \times ... \times P(Xn < = xn)[/tex]
For any x <= M, we have:
[tex]P(Xi < = x) < = P(Xi < = M) for i = 1, 2, ..., n[/tex]
Therefore,
[tex]P(X1 < = x, X2 < = x, ..., Xn < = x) < = P(X1 < = M, X2 < = M, ..., Xn < = M) = F(M)^n[/tex]
Using the complement rule and the fact that the samples are identically distributed, we get:
[tex]P(X(n) > M) = 1 - P(X(n) < = M)[/tex]
= [tex]1 - P(X1 < = M, X2 < = M, ..., X(n) < = M)[/tex]
=[tex]1 - [P(X1 < = M) \times P(X2 < = M) \times ... \times P(X(n-1) < = M) \times P(X(n) < = M)][/tex]
[tex]< = 1 - F(M)^(n-1) \times F(X(n))[/tex]
Probability depends on the sample size n and the distribution of the population.
If the population is symmetric around its median, the probability is 0.5 for any sample size.
As the sample size increases, the probability generally increases, but the rate of increase depends on the population distribution.
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Determine the scale ratio for this map given that the distance from Wellspring to Red Creek is 4 inches on the map and 10 miles in reality.
The scale ratio for this map is 0.0000063.
What is scale ratio?
Scale ratio is the ratio between the measurements of an object or distance on a map or drawing and the actual measurements of the object or distance it represents in real life. It allows us to compare and relate the sizes or distances of objects in a drawing or map to their actual sizes or distances in the real world.
The scale ratio can be found by dividing the distance on the map by the corresponding distance in reality:
scale ratio = distance on map / distance in reality
In this case, the distance from Wellspring to Red Creek is 4 inches on the map and 10 miles in reality. So the scale ratio is:
scale ratio = 4 inches / 10 miles
To simplify this ratio, we need to convert the units so that they are the same. Let's convert inches to miles:
1 mile = 63,360 inches
So, we can convert the inches on the map to miles as follows:
4 inches * (1 mile / 63,360 inches) = 0.000063 miles
Now we can rewrite the scale ratio as:
scale ratio = 0.000063 miles / 10 miles
Simplifying this ratio by canceling out the units of miles, we get:
scale ratio = 0.0000063
Therefore, the scale ratio for this map is 0.0000063.
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Four friends want to play a game. In how many ways can the friends from teams, if both team dont have name
The friends can form teams in 6 different ways.
If the four friends want to form two teams, we can count the number of ways they can do this using combinations.
The number of ways to choose two people out of four is given by the combination formula,
C(4,2) = 4! / (2! * (4-2)!) = 6
We can list them as follows, where each team is represented by the letters A and B,
AB | CD
AC | BD
AD | BC
BC | AD
BD | AC
CD | AB
This means that there are 6 different ways the four friends can be split into two teams.
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1. Suppose we have the following annual risk-free bonds Maturity Price Coupon Rate YTM 1 98 0% 2.01% 2 101 2.48% 3 103 2.91% 4 101 2% 1.73% 5 103 5% 4.32% 39 a) Find the zero rates for all 5 maturities Note: for an extra challenge, try using lincar algebra to find == A + where 98 00 -- 3 103 0 2 2 5 5 0 104 2 0 0 0 0 0 0 1020 5 105 5 1 b) Suppose we have a risk-free security which pays cash flows of $10 in one year, $25 in two years, and $100 in four years. Find its price
a) The zero rates for the five maturities are: 1 year is 2.01%, 2 years is 2.48%, 3 years is 2.77%, 4 years is 1.73%, and 5 years is 4.32%.
b) The price of the security is $128.31.
a) To find the zero rates for all 5 maturities, we can use the formula for the present value of a bond:
PV = C / [tex](1+r)^n[/tex]
where PV is the present value,
C is the coupon payment,
r is the zero rate, and
n is the number of years to maturity.
We can solve for r by rearranging the formula:
r = [tex](C/PV)^{(1/n) }[/tex]- 1
Using the bond data given in the question, we can calculate the zero rates for each maturity as follows:
For the 1-year bond, PV = 98 and C = 0, so r = 2.01%.
For the 2-year bond, PV = 101, C = 2.48, and n = 2, so r = 2.48%.
For the 3-year bond, PV = 103, C = 2.91, and n = 3, so r = 2.77%.
For the 4-year bond, PV = 101, C = 2, and n = 4, so r = 1.73%.
For the 5-year bond, PV = 103, C = 5, and n = 5, so r = 4.32%.
Alternatively, we can use linear algebra to find the zero rates. We can write the present value equation in matrix form:
PV = A × x
where A is a matrix of coefficients, x is a vector of unknowns (the zero rates), and PV is a vector of present values.
To solve for x, we can use the equation:
x = ([tex]A^{-1}[/tex]) x PV
where ([tex]A^{-1}[/tex]) is the inverse of matrix A.
Using this method, we can solve for the zero rates as follows:
[2.01% ]
[2.48% ]
[2.77% ] = x
[1.73% ]
[4.32% ]
PV = [tex]A^{-1}[/tex] x [98]
[101]
[103]
[101]
[103]
PV = [-0.0201]
[ 0.0248]
[ 0.0277]
[-0.0173]
[ 0.0432]
b) To find the price of the security which pays cash flows of $10 in one year, $25 in two years, and $100 in four years, we can use the formula for the present value of a series of cash flows:
PV = [tex]C1/(1+r)^1 + C2/(1+r)^2 + C3/(1+r)^4[/tex]
where PV is the present value, C1, C2, and C3 are the cash flows, r is the zero rate, and the exponents correspond to the number of years until each cash flow is received.
Using the zero rates calculated in part (a), we can calculate the present value of each cash flow:
PV1 = $10 /(1+2.01 % [tex])^1[/tex] = $9.80
PV2 = $25/(1+2.48%[tex])^2[/tex] = $22.15
PV3 = $100/(1+1.73%[tex])^4[/tex] = $81.36
Then, the price of the security is the sum of the present values:
PV = $9.80 + $22.15 + $81.36 = $128.31
Therefore, the price of the security is $128.31.
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What is the smallest positive integer divisible by 6 and 2 you can write using at least one 2 and one 6?
The smallest positive integer divisible by 6 and 2 that can be written using at least one 2 and one 6 is 6.
The smallest positive integer that is divisible by both 2 and 6 is their least common multiple (LCM), which is equal to the product of the highest power of each prime factor that appears in the factorization of 2 and 6.
The prime factorization of 2 is simply 2, while the prime factorization of 6 is 2 × 3. The highest power of 2 that appears in the factorization of 6 is just 2 itself, so the LCM of 2 and 6 is 2 × 3 = 6.
We are asked to write this integer using at least one 2 and one 6. We can do this by simply writing 6, which is the LCM of 2 and 6 and is divisible by both of them. Since 6 contains one 2 and one 6, this meets the requirement of the problem. Therefore, the smallest positive integer divisible by 6 and 2 that can be written using at least one 2 and one 6 is 6.
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The diameter of a circle is 12.5 cm. What is the circumference of the circle? Question 1 options: 19.63 cm 35. 25 cm 39.25 cm 78.5 cm please tell me quick!!!!
Answer:
The circumference of a circle is given by the formula:
C = πd
where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.
In this case, the diameter of the circle is given as 12.5 cm.
Substituting this value into the formula, we get:
C = π(12.5)
C = 39.25 cm
Therefore, the circumference of the circle is 39.25 cm.
Hence, the answer is 39.25 cm.
The area of (V is 624.36 square meters. The area of sector
SVT is 64.17 square meters. Find the indicated measure.
1. The radius of V is approximately 14.04 meters.2.The circumference of V is approximately 88.24 meters. 3.mST arc is 26.85 degrees. 4.the length of ST arc is approximately 6.61 meters. 5.34.69 meters. 6.88.24m.
Describe Sector?In geometry, a sector is a part of a circle enclosed by two radii and an arc. Essentially, a sector is a slice of a circle. The two radii that form the sector are equal in length and share a common endpoint, which is the center of the circle. The arc of the sector is a portion of the circumference of the circle and its length is proportional to the measure of the central angle that it subtends.
We can use the given information to solve for the following:
1. Radius of V:
The area of a circle is given by the formula A = πr². We are given the area of V as 624.36 square meters, so we can solve for the radius r as:
A = πr²
624.36 = πr²
r² = 624.36/π
r ≈ 14.04 meters
Therefore, the radius of V is approximately 14.04 meters.
2. Circumference of V:
The circumference of a circle is given by the formula C = 2πr. Using the radius we just found, we can solve for the circumference of V as:
C = 2πr
C = 2π(14.04)
C ≈ 88.24 meters
Therefore, the circumference of V is approximately 88.24 meters.
3. mST arc:
The area of the sector SVT is given as 64.17 square meters. The area of a sector is given by the formula A = (θ/360)πr², where θ is the central angle of the sector in degrees. We are not given the value of θ, but we can solve for it as:
A = (θ/360)πr²
64.17 = (θ/360)π(14.04)²
θ ≈ 26.85 degrees
Therefore, the central angle of the sector SVT is approximately 26.85 degrees, and mST arc is also 26.85 degrees.
4. Length of ST arc:
The length of an arc of a circle is given by the formula L = (θ/360)C, where θ is the central angle of the arc in degrees, and C is the circumference of the circle. We can use the values we have already calculated to solve for the length of ST arc as:
L = (θ/360)C
L = (26.85/360)(88.24)
L ≈ 6.61 meters
Therefore, the length of ST arc is approximately 6.61 meters.
5. Perimeter of shaded region (sector):
The perimeter of a sector is the sum of the length of the arc and the lengths of the two radii that form the sector. Using the values we have already calculated, we can solve for the perimeter of the shaded sector as:
Perimeter = L + 2r
Perimeter = 6.61 + 2(14.04)
Perimeter ≈ 34.69 meters
Therefore, the perimeter of the shaded region (sector) is approximately 34.69 meters.
6. Perimeter of unshaded region (remaining circle part):
The perimeter of a circle is given by the formula C = 2πr. Using the radius we previously calculated, we can solve for the perimeter of the unshaded region as:
Perimeter = 2πr
Perimeter = 2π(14.04)
Perimeter ≈ 88.24 meters
Therefore, the perimeter of the unshaded region (remaining circle part) is approximately 88.24 meters.
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sue works 5 out of the 7 days of the week. how many possible schedules are there to work on tuesday or friday or both?
Sue works 5 out of 7 days a week, which implies that she has two days off. We need to discover how numerous conceivable plans there are for her to work on Tuesday or Friday or both.
There are two cases to consider:
1. Sue works on Tuesday as it were, Friday as it were, or both Tuesday and Friday.
2. Sue does not work on Tuesday or Friday.
For the primary case, there are three conceivable outcomes:
1. Sue works on Tuesday as it were and has Friday off.
2. Sue works on Friday as it were and has Tuesday off.
3. Sue works on both Tuesdays and Fridays.
For the moment case, there are two conceivable outcomes:
1. Sue works on one of the other 5 days of the week and has both Tuesday and Friday off.
2. Sue has Tuesday and Friday off.
In this manner, there are added up to 3 + 2 = 5 conceivable plans for Sue to work on Tuesday or Friday or both.
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. which one of the following statements is true? a. if you are given a sample percentage of 43%, you would need to know the sample size in order to convert this percentage to a proportion. b. the test statistic is affected by the size of the sample. c. the larger the p-value, the more evidence you have against the null hypothesis. d. we always begin a hypothesis test by assuming that the null hypothesis is false. e. none of the above statements are true.
If you are given a sample percentage of 43%, you would need to know the sample size in order to convert this percentage to a proportion.
The conversion formula is proportion = percentage/100. However, the proportion alone does not give information about the sample size, which is necessary for inference and hypothesis testing. The other statements are not true.
The test statistic is not affected by the sample size, but its value can be used to determine the significance of a hypothesis test. A larger p-value indicates weaker evidence against the null hypothesis, not stronger evidence. Finally, we assume the null hypothesis is true until we have sufficient evidence to reject it.
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An article on the relation of cholesterol levels in human blood to aging reports that average cholesterol level for women aged 70-74 was found to be 230m/dl. If the standard deviation was 20mg/dl and the distribution normal, what is the probability that a given woman in this age group would have a cholesterol level
a) Less than 200mg/dl
b) More than 200mg/dl
c) Between 190mg/dl and 210mg/dl
d) Write a brief report on the guidance you would give a woman having high cholesterol level in this age group
a) The probability of a given woman in this age group having a cholesterol level less than 200mg/dl is 6.68%.
b) The probability of a given woman in this age group having a cholesterol level more than 200mg/dl is 93.32%.
c) The probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl is 15.87%.
d) If a woman in this age group has a cholesterol level higher than 230mg/dl, it is considered high and puts her at risk of heart disease
To calculate the probability of a given woman in this age group having a cholesterol level less than 200mg/dl, we need to find the z-score first. The z-score is the number of standard deviations that a given value is from the mean. The formula to calculate the z-score is:
z = (x - μ) / σ
where x is the given value, μ is the mean, and σ is the standard deviation.
For a cholesterol level of 200mg/dl, the z-score is:
z = (200 - 230) / 20 = -1.5
We can then use a z-table or calculator to find the probability of a z-score being less than -1.5, which is 0.0668 or approximately 6.68%.
Next, to find the probability of a given woman in this age group having a cholesterol level more than 200mg/dl, we can use the same process but subtract the probability of a z-score being less than -1.5 from 1 because the total probability is always 1.
So, the probability of a given woman in this age group having a cholesterol level more than 200mg/dl is:
1 - 0.0668 = 0.9332 or approximately 93.32%.
Finally, to find the probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl, we need to find the z-scores for both values.
For a cholesterol level of 190mg/dl, the z-score is:
z = (190 - 230) / 20 = -2
For a cholesterol level of 210mg/dl, the z-score is:
z = (210 - 230) / 20 = -1
We can then use the z-table or calculator to find the probability of a z-score being between -2 and -1, which is 0.1587 or approximately 15.87%.
Finally, a brief report on the guidance that you would give a woman having high cholesterol levels in this age group is:
It is essential to make lifestyle changes such as eating a healthy diet, exercising regularly, quitting smoking, and managing stress to lower cholesterol levels.
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The answer to this question
The volume of the basketball is approximately 4.2x³.
How to solve for the volumea. The formula for the volume of a sphere is:
V = (4/3)πr³
where r is the radius of the sphere. In this case, the radius is given as x, so we have:
V = (4/3)πx³ ≈ 4.2x³
Therefore, the volume of the basketball is approximately 4.2x³.
b. The volume of a cube is given by:
V = s³
where s is the length of one of its sides. Since the basketball touches all of the sides of the case, the length of one of its sides is equal to the diameter of the basketball plus the length of a side of the basketball. This is equal to 2x + 2x = 4x. Therefore, we have:
V = (4x)³ = 64x³
Therefore, the volume of the box is 64x³.
c. The volume of air in the box is equal to the volume of the box minus the volume of the basketball. We can substitute the formulas we obtained in parts (a) and (b) to get:
V_air = V_box - V_basketball = 64x³ - 4.2x³ = 59.8x³
Therefore, the volume of air in the box is approximately 59.8x³.
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What is the solution to the system of equations graphed below? A. (0,6) B. (6,0) C. (0,3) D. (1,5)
The correct option is - D. (1,5). The solution to the system of equations for the given graph is at (1,5).
Explain about the solution of system of equations:A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.
The points where the lines representing the intersections where two linear equations intersect are referred to as the conclusion of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of both the system of linear equations.For the given graph, the solution of the system of equation is obtained as the point where the lines intersect.
The two lines in the graph intersect at the (1,5). Thus, the solution to the system of equations for the given graph is at (1,5).
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On Sunday a local hamburger shop sold 356 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday
The number of hamburgers sold on Sunday was 89
How many hamburgers were sold on SundayLet's assume that the number of hamburgers sold on Sunday was x.
According to the problem, the number of cheeseburgers sold was three times the number of hamburgers sold.
Therefore, the number of cheeseburgers sold can be expressed as 3x.
The total number of hamburgers and cheeseburgers sold was 356.
Therefore, we can write an equation to represent this information:
x + 3x = 356
Simplifying the left-hand side of the equation, we get:
4x = 356
Dividing both sides by 4, we get:
x = 89
Therefore, the number of hamburgers sold on Sunday was 89, and the number of cheeseburgers sold was 3 times that, or 267.
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Find the volume
of the figure below:
Step-by-step explanation:
Use Pythagorean theorem to find the base of the right triangle
221^2 = 195^2 + b^2
b = 104 km
triangle area = 1/2 base * height = 1/2 * 104 * 195 = 10140 km^2
Now multiply by the height to find volume
10140 km^2 * 15 km = 152100 km^3
What is the most upper (+3) or (-7)? Help please
Answer: Of the two numbers you provided, +3 is greater than -7. So, +3 is the most upper of the two numbers.
Answer: +3
Step-by-step explanation: Positive 3 is greater than negative 7. Therefore, +3 is the greater value.
n.2 multi-step word problems with positive rational numbers jvu you have prizes to reveal! go to your game board. on friday night, suzie babysat her cousin for 3 1 2 hours and earned $8.50 per hour. on saturday, she babysat for her neighbors for 4 1 2 hours. if she made a total of $72.50 from both babysitting jobs, how much did suzie earn per hour on saturday?
Answer:
$9.50
Step-by-step explanation:
You want Suzie's hourly rate on Saturday if she babysat for 3.5 hours on Friday, earning 8.50 per hour, and for 4.5 hours on Saturday, earning a total of 72.50 from both jobs.
EarningsFor (hours, rates) of (h1, r1) and (h2, r2), Suzie's total earnings for the two jobs are ...
earnings = h1·r1 +h2·r2
Filling in the known values, we can find r2:
72.50 = 3.5·8.50 +4.5·r2
72.50 = 29.75 +4.5·r2 . . . . . . . simplify
42.75 = 4.5·r2 . . . . . . . . . . . subtract 29.75
9.50 = r2 . . . . . . . . . . . . divide by 4.5
Suzie earned $9.50 per hour on Saturday.
__
Additional comment
The steps of the "multistep" problem are ...
find Friday's earningssubtract that from the total to find Saturday's earningsdivide by Saturday's hours to find the hourly rateEffectively, these are the steps to solving the equation we wrote.
An expression is shown.
3(-12.5)
What is the value of the expression?
Answer: -37.5
Step-by-step explanation: You can simply do this in the calculator by doing 3 times -12.5. the parenthesis is a sign to multiply
Answer:
the answer is -75/2= - 37.5
The function f is given by f(x) = 10x + 3 and the function g is given by g(x) = 2×. For each question, show your reasoning
1. Which function reaches 50 first
2. Which function reaches 100 first?
1. x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.
2. x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.
1. Which function reaches 50 first?
To answer this, we need to solve for x in each function when the output is 50:
For f(x): 50 = 10x + 3
47 = 10x
x = 4.7
For g(x): 50 = 2x
x = 25
Since x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.
2. Which function reaches 100 first?
Similarly, we'll solve for x in each function when the output is 100:
For f(x): 100 = 10x + 3
97 = 10x
x = 9.7
For g(x): 100 = 2x
x = 50
Since x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.
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an airline passenger is planning a trip that involves three connecting flights that leave from airports a, b, and c, respectively. the first flight leaves airport a every hour, beginning at 8:00 a.m., and arrives at airport b 2 1/2 hours later. the second flight leaves airport b every 20 minutes, beginning at 8: 00 a.m., and arrives at airport c 1 1/6hours later. the third flight leaves airport c every hour, beginning at 8:45 a.m. what is the least total amount of time the passenger must spend between flights if all flights keep to their schedules?
An airline passenger is planning a trip with three connecting flights from airports A, B, and C.
The least total amount of time the passenger must spend between flights, assuming all flights keep to their schedules, is 55 minutes.
This occurs when the passenger takes the first flight from airport A at 8:00 a.m., arriving at airport B at 10:30 a.m., catches the second flight from airport B at 10:40 a.m., arriving at airport C at 11:50 a.m., and then takes the third flight from airport C at 12:45 p.m.
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How do you simplify this.
Answer:
[tex] \sqrt{7y} ( \sqrt{27y} + 5 \sqrt{12y} )[/tex]
[tex] \sqrt{7y} ( \sqrt{9} \sqrt{3y} + 5 \sqrt{4} \sqrt{3y} )[/tex]
[tex] \sqrt{7y} (3 \sqrt{3y} + 10 \sqrt{3y} )[/tex]
[tex]13 \sqrt{7y} \sqrt{3y} [/tex]
[tex]13y \sqrt{21} [/tex]
i need help with problem.
Answer:
[tex]y=5-2x[/tex]
Step-by-step explanation:
You have to give the equation in the form [tex]y=mx+c[/tex], where m is the gradient and c is the y-intercept (where the line crosses the y-axis).
From the graph, we can see the line crossed the y-axis at (0,5), so the y-intercept is (0,5), which means c is 5.
We can work out the gradient with the two points (2,1) and (1,3) by doing:
[tex]\frac{change in y}{change in x} =\frac{1-3}{2-1}=-2[/tex]
So the gradient of the line, m, is -2.
Thus the equation of the line is [tex]y=5-2x[/tex].
∠A=6x−2
∘
start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 2, degrees, end color #11accd \qquad \green{\angle B} = \green{4x +48^\circ}∠B=4x+48
∘
, angle, B, equals, start color #28ae7b, 4, x, plus, 48, degrees, end color #28ae7b
Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:
The given information describes the measures of two angles, A and B. Angle A is represented as ∠A and has a measure of 6x-2 degrees. Angle B is represented as ∠B and has a measure of 4x+48 degrees. These measures are respectively shown in the colors #11accd and #28ae7b.
The question gives us two equations, one for angle A and one for angle B, in terms of x. We will have to solve for x and then find the measure of angle A.
To solve for x, we can set the expressions for ∠A and ∠B equal to each other and solve for x
∠A = ∠B
6x - 2 = 4x + 48
Subtracting 4x from both sides we get
2x - 2 = 48
Adding 2 to both sides we get
2x = 50
Dividing by 2 we get
x = 25
Now that we have found the value of x, we can substitute it into the expression for ∠A
∠A = 6x - 2
∠A = 6(25) - 2
By multiplying 6 with 25 we get
∠A = 150 - 2
By Subtracting we get
∠A = 148
Hence, the measure of angle A is 148 degrees.
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Evaluate the following.
Write an exponential function of the form y = ab^x that has the given points
(−1,6 3/4), (2, 1-4)
Answer:
Step-by-step explanation:
y = abx
a is the y-intercept
y = 16bx
Now substitute 2 for x and 1296 for y
1296 = 16(b)2
81 = b2
b = 9
y = 16(9)x