There are 15 different possibilities for the three whole numbers whose product is 120.
To find the different possibilities for the three whole numbers, we need to find all the ways we can multiply three whole numbers together to get 120, which is the product.
We can start by listing out the factors of 120:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
From this list, we can start trying out combinations of three numbers that multiply to 120. For example:
1 x 1 x 120 = 120
1 x 2 x 60 = 120
1 x 3 x 40 = 120
1 x 4 x 30 = 120
1 x 5 x 24 = 120
1 x 6 x 20 = 120
1 x 8 x 15 = 120
2 x 3 x 20 = 120
2 x 4 x 15 = 120
2 x 5 x 12 = 120
2 x 6 x 10 = 120
3 x 4 x 10 = 120
3 x 5 x 8 = 120
4 x 5 x 6 = 120
So there are 15 different possibilities for the three whole numbers that multiply to 120.
To find the different possibilities for the three whole numbers whose product is 120, we need to find the combinations of factors of 120.
Step 1: Find the prime factorization of 120.
[tex]120 = 2*2*2*3*5 (2^3 * 3 * 5)[/tex]
Step 2: Identify the possible factors.
Using the prime factors, we can generate the different whole number factors for 120:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Step 3: Find the possible combinations of three whole numbers.
1. 1 × 1 × 120
2. 1 × 2 × 60
3. 1 × 3 × 40
4. 1 × 4 × 30
5. 1 × 5 × 24
6. 1 × 6 × 20
7. 1 × 8 × 15
8. 1 × 10 × 12
9. 2 × 2 × 30
10. 2 × 3 × 20
11. 2 × 4 × 15
12. 2 × 5 × 12
13. 2 × 6 × 10
14. 3 × 4 × 10
15. 3 × 5 × 8
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Set of factors can be rearranged in six different ways, there are actually 60 possible ways to arrange the factors into three numbers.
The possible combinations of three whole numbers that result in a product of 120.
One way to approach this is to list all the factors of 120 and then group them into sets of three.
Another method is to use prime factorization.
120 as a product of its prime factors: 2 x 2 x 2 x 3 x 5.
The possible combinations of three factors, we can use a combination formula.
The formula for the number of combinations of n items taken r at a time is:
[tex]nCr = n! / (r! \times (n-r)!)[/tex]
In our case, n = 5 (the number of prime factors), and r = 3 (the number of factors we want to choose).
So, the number of possible combinations is:
[tex]5C3 = 5! / (3! \times 2!) = (5 \times 4 \times 3) / (3 \times 2) = 10[/tex]
There are 10 different possibilities for the three whole numbers that multiply to 120.
These are:
[tex][tex]2 \times 2 \times 30, 2 \times 3 \times 20, 2 \times 4 \times 15, 2 \times 5 \times 12, 2 \times 6 \times 10, 3 \times 4 \times 10, 3 \times 5 \times 8, 4 \times 5 \times 6, 3 \times 2 \times 20, and 5 \times 2 \times 12.[/tex][/tex]
The order of the factors does not matter, so[tex]2 \times 3 \times 20[/tex] is the same as[tex]3 \times 2 \times 20[/tex].
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From the top of a 120-foot-high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 19°. How far from the base of the tower is the airplane? Round to the nearest tenth.
1. 126.9 ft
2. 368.6 ft
3. 41.3 ft
4. 348.5 ft
The distance of the base of the tower and the airplane is 348.5 ft, and the right option is 4. 348.5 ft.
What is distance?Distance is the length between two points.
To calculate the distance of the base of the tower and the airplane, we use the formula below.
Formula:
Tan∅ = Opposite(O)/Adjacent(A)Where:
∅ = Angle of depression of the airplaneFrom the diagram,
Given:
Opposite = 120 ft∅ = 19°SUbstitute these values into equation 1 and solve for A
tan19° = 120/AA = 120/tan19°A = 348.5 ftHence, the right option is 4. 348.5 ft.
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can someone please help me with these 3 there due tomorrow!!
Answer:
4. Mean: 89
5. Median: 90
6. Mode: None.
Step-by-step explanation:
To find the mean, add all of the numbers, then divide by the total.
There are 7 numbers in this set.
First, add all of the numbers. Then, divide the sum by 7.
[tex]85+95+88+93+94+78+90= 623\\623/7 =89[/tex]
The mean of this data set is 89!
------------------------------------------------
Now, let's find the median.
The median is the "middle number" of the data set.
First, put all of the numbers in order from least to greatest.
85, 95, 88, 93, 94, 78, 90
↓
78, 85, 88, 90, 93, 94, 95,
The number in the middle of the data set is 90!
Therefore, the median is 90.
------------------------------------------------
Now, let's find the mode.
The mode is the number that appears most frequently.
85, 95, 88, 93, 94, 78, 90
Since each number appears once, then there is no mode.
Let me know if you have any questions.
what is the percent of the total variance that can be explained by the regression equation? (cma adapted)
The size and nature of the dataset, the choice of independent variables, and the assumptions underlying the model, should also be considered when interpreting [tex]R^2[/tex] values.
The percent of the total variance that can be explained by the regression equation is known as the coefficient of determination, denoted as[tex]R^2.[/tex]
It represents the proportion of the total variation in the dependent variable (Y) that is accounted for by the independent variable(s) (X) included in the regression model.
To calculate[tex]R^2[/tex], you can follow these steps:
Obtain the sum of the squared differences between the actual and predicted values of the dependent variable (also known as the residual sum of squares, or RSS).
Obtain the sum of the squared differences between the actual values of the dependent variable and their mean (also known as the total sum of squares, or TSS).
Divide the RSS by the TSS: [tex]R^2 = 1 - (RSS/TSS).[/tex]
[tex]R^2[/tex] ranges between 0 and 1, with higher values indicating a better fit of the regression model.
An[tex]R^2[/tex] of 1 indicates that the regression equation perfectly explains the total variance, while an [tex]R^2[/tex] of 0 indicates that the regression equation does not explain any of the total variance.
Keep in mind that while[tex]R^2[/tex] is a useful measure of model fit, it should not be the only criterion used to evaluate the quality of a regression model.
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The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. Find the given probabilities.
(a) The sum of the numbers is 8.
(b) The sum of the number is 6 or less.
(c) The first number is 2 or the sum is 5
(a) The probability that the sum of the numbers is 8 is 0.1.
(b) The probability that the sum of the number is 6 or less is 0.5.
(c) The probability that the first number is 2 or the sum is 5 is 0.35.
A probability is the number of desired outcomes divided by the number of total outcomes.
The possible outcomes are:
(1,2), (1,3), (1,4), (1,5).
(2,1), (2,3), (2,4), (2,5).
(3,1), (3,2), (3,4), (3,5).
(4,1), (4,2), (4,3), (4,5).
(5,1), (5,2), (5,3), (5,4).
Total outcomes = 20
(a) The sum of the numbers is 8.
There are only two ways to get a sum of 8: (3, 5), (5,3). So the probability of getting a sum of 8 is:
P(sum of 8) = 2/20
= 0.1
Therefore, the required probability is 0.1.
(b) The sum of the number is 6 or less.
To get a sum of 6 or less, we can have the following combinations:(1, 2), (1, 3), (1, 4), (1, 5), (2,1), (2, 3), (2,4), (3,1), (3,2), (4,1), (4,2), (5,1).So the probability of getting a sum of 6 or less is:
Total outcomes = 20
P(sum of 6 or less) = 10/20
=0.5
Therefore, the required probability is 0.5.
(c) The first number is 2 or the sum is 5
There are three ways to satisfy this condition:(2,1), (2, 3), (2,4), (2, 5), (1,4), (3, 2), (4,1). So the probability of getting a number that satisfies this condition is:
Total outcomes = 20
P(first number is 2 or sum is 5) = 7/20
= 0.35.
Therefore, the required probability is 0.35.
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the percentage of the original area of wetlands currently left in the united states is approximately: question 44 options: 10%. 25%. 50%. 65%. 75%.
The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct
option is 50% (option 3).
Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".
According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original
wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,
development, and urbanization. Therefore, the correct answer to the question is 50%.
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The percentage of the original area of wetlands currently left in the United States is approximately 50%.
Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.
There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.
Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.
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1. The area of a rectangle can be represented by a
quadratic function. You are given a rectangle with a length
that is 3 inches more than four times the width, w. Choose
all the answers that give the area as a function of the
width
a) A(w)=w(4+3w)
b) A(w)=w(3+4w)
c) A(w)=4w+3w²
d) A(w)=4w²+3w
-7
The expression that gives the area as a function of the width is 4w²+3w.( option B)
What is area of a rectangle?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The area of a rectangle is expressed as ;
A = l×w, where l is the length and w is the width.
Since the length is 3 inches more than four times the width, then;
l = 3+4w
Representing 3+w for l in the area formula, then we have;
A = (3+4w)(w)
A = 4w²+3w
therefore the expression that represents the area is 4w²+3w
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Xe3-8xe2+18x-12 for this polynomial 2 is a zero
Yes, 2 is a zero of the polynomial [tex]Xe3-8xe2+18x-12[/tex]
To determine if 2 is a zero of the polynomial [tex]Xe3-8xe2+18x-12[/tex], we can plug in 2 for x and see if the result is 0.
So, if we substitute x=2, we get:
[tex](2)^3 - 8(2)^2 + 18(2) - 12 = 0[/tex]
Simplifying this equation, we get:
8 - 32 + 36 - 12 = 0
This equation is true, which means that 2 is indeed a zero of the polynomial [tex]Xe3-8xe2+18x-12.[/tex]
Therefore, we can conclude that the polynomial can be factored as:
[tex](X-2)(X^2-6X+6)[/tex]
This means that the other two zeros of the polynomial are the solutions of the quadratic equation [tex]X^2-6X+6=0[/tex] which can be found using the quadratic formula.
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WILL MARK AS BRAINLEIST!!
Question in picture!!
Note: The graph above represents both functions “f” and “g” but is intentionally left unlabeled
Answer:
f(x) is the blue graph, g(x) is the red graph.
x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2
16 - x^2 = 0 when x = -4, 4
So the area between these two graphs is (using the TI-83 graphing calculator):
fnInt (16 - x^2, x, -4, 4) = 85 1/3
A. A hand of 7-card draw poker is a simple random sample from the standard deck of 52 cards. How many 7 draw poker hands are there? In 7-card stud poker, the cards are dealt sequentially and the order of appearance is important. How many 7 -stud poker hands are there? b. How many hands of 7-draw poker contain the ace of hearts? What is the probability that a 7-card draw hand contains the ace of hearts
A. The number of 7-card stud poker hands is 133,784,560 and the number of 7-card stud poker hands is 674,274,182,400.
B. The number of hands of 7-draw poker that contain the ace of hearts is 18,009,460.
C. The probability that a 7-card draw hand contains the ace of hearts is 0.135.
a) The number of 7-card draw poker hands can be calculated using the combination formula, which is:
[tex]^{n} C_{r}[/tex] = n! / (r! * (n - r)!)
where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).
So, the number of 7-card draw poker hands is:
[tex]^{52} C_{7}[/tex] = 52! / (7! * (52 - 7)!)
= 133,784,560.
The number of 7-card stud poker hands can be calculated using the permutation formula, which is:
[tex]^{n} P_{r}[/tex] = n! / (n - r)!
where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).
So, the number of 7-card stud poker hands is:
[tex]^{52} P_{7}[/tex] = 52! / (52 - 7)!
= 674,274,182,400.
b) To count the number of hands of 7-draw poker that contain the ace of hearts, we can treat the ace of hearts as a special card that must be included in each hand. Then, we need to choose the remaining 6 cards from the 51 cards that are not the ace of hearts.
So, the number of hands of 7-draw poker that contain the ace of hearts is:
[tex]^{51} C_{6}[/tex] = 51! / (6! * (51 - 6)!)
= 18,009,460.
c) To calculate the probability that a 7-card draw hand contains the ace of hearts, we can use the formula:
P(event) = number of favourable outcomes / total number of possible outcomes
The total number of possible 7-card draw hands is 133,784,560, which we calculated in part (a).
The number of favourable outcomes is the number of hands of 7-draw poker that contain the ace of hearts, which we calculated in part (b).
So, the probability that a 7-card draw hand contains the ace of hearts is:
P(ace of hearts) = 18,009,460 / 133,784,560 ≈ 0.135
The required probability is 0.135.
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select the correct answer. the probability of event a is x, and the probability of event b is y. if the two events are independent, which condition must be true?
For events A and B to be independent, the condition that must be true is:
P(A ∩ B) = x * y
The correct condition that must be true if events A and B are independent is:
P(A ∩ B) = P(A) x P(B).
where P(A) is the probability of event A, P(B) is the probability of event B, and P(A ∩ B) is the probability of both events A and B occurring together.
In other words, if events A and B are independent, then the probability of both events occurring together is equal to the product of their individual probabilities.
When two events A and B are independent, the following condition must be true:
P(A ∩ B) = P(A) * P(B)
In your case, the probability of event A is x, and the probability of event B is y.
Therefore, the correct answer is:
P(A ∩ B) = x*y
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true or false? the rule of thumb for estimating the time of completion is 1.5 times what you originally think it will be.
Given statement: The rule of thumb for estimating the time of completion is 1.5 times what you originally think it will be.
Given statement is True.
The reason for this rule of thumb is that tasks often take longer than initially estimated due to unforeseen challenges, dependencies, and other factors that can cause delays.
By estimating the time of completion as 1.5 times the original estimate, you are accounting for these potential delays and allowing for a more realistic timeline.
This rule of thumb is not a hard and fast rule, and there will be cases where tasks take less or more time than 1.5 times the original estimate. However, it can be a helpful guideline for project planning and resource allocation, as it helps to ensure that sufficient time and resources are allocated to complete tasks within a realistic timeframe.
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Homework 18.1.-trigonometric ratios
Find the 3 trigonometric ratios. If needed, reduce fractions.
Step-by-step explanation:
rotate the triangle in your mind (or as actual picture on your phone or computer), so that the right angle is the bottom right or bottom left, and C being the opposite bottom angle.
then we see
28 = cos(C) × 35
21 = sin(C) × 35
and so,
sin(C) = 21/35 = 3/5
cos(C) = 28/35 = 4/5
tan(C) = sin(C)/cos(C) = 3/5 / 4/5 = 3/4
6. The speed of the last 10 pitches thrown by a pitcher: {90, 92, 85, 88, 94, 86, 93, 90, 88, 95}
Best Center:
Why?
The best center of the speed of the last 10 pitches thrown by a pitcher is the mean
Calculating the best centerFrom the question, we have the following parameters that can be used in our computation:
{90, 92, 85, 88, 94, 86, 93, 90, 88, 95}
The possible measure of centers are
MeanMedanModeIn this case, we use the mean
This is because the data values do not have any outlier present in them
Hence, the center is the mean
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What percent of the large square is shaded?
Which ratio is proportional to 80:60?
16:15
16:12
18:15
18:12
Pls answer quickly
Answer:
To determine which ratio is proportional to 80:60, we need to simplify the ratio by dividing both terms by their greatest common factor. In this case, the greatest common factor of 80 and 60 is 20, so:
80/20 = 4
60/20 = 3
Therefore, the simplified ratio is 4:3.
Now we can compare this ratio to the given options to see which one is proportional to 4:3:
16:15 is not proportional
16:12 is proportional (since 16/4 = 4 and 12/3 = 4)
18:15 is not proportional
18:12 is proportional (since 18/3 = 6 and 12/2 = 6)
Therefore, the ratio that is proportional to 80:60 is 16:12.
The price of grapes, g, is $2. 19 per pound. The price of bananas, b, is $0. 59 per pound. The price of pears, p, is $1. 49 per pound. Part A
Write an expression to represent the total price of g pounds of grapes, b pounds of bananas, and p pounds of pears. Drag numbers to complete the expression. 1. 49 added to
2. 19
g +
0. 59
b +
1. 49
p
The expression that represents the total price of buying g pounds of grapes, b pounds of bananas, and p pounds of pears is Total cost = $2.19g + $0.59b + $1.49p
In this case, we need to use the given prices per pound of each fruit to calculate the total cost of purchasing a certain amount of each fruit. We can do this by multiplying the price per pound by the number of pounds of each fruit we want to buy, and then adding up these values.
So, to create the expression, we can start by using the given prices to calculate the cost of each fruit:
Grapes: $2.19/pound
Bananas: $0.59/pound
Pears: $1.49/pound
Next, we can use the variables g, b, and p to represent the number of pounds of each fruit we want to buy. We then multiply each price by its respective variable to get the cost of each type of fruit:
Cost of grapes: $2.19/g x g = $2.19g
Cost of bananas: $0.59/b x b = $0.59b
Cost of pears: $1.49/p x p = $1.49p
Finally, we can add up the costs of all three types of fruit to get the total cost:
Total cost = $2.19g + $0.59b + $1.49p
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if we run a regression with a sample of 30 observations using a dependent variable, 3 independent variables, and a constant how many degrees of freedom does the model have?
The model have 4 degrees of freedom if a regression model has a sample of 30 observations using a dependent variable, 3 independent variables, and a constant.
In a linear regression model, the degrees of freedom for the model are calculated as the number of independent variables plus one (for the constant or intercept term). Therefore, in this case, since the model has 3 independent variables and a constant, the degrees of freedom for the model would be 3 + 1 = 4.
The degrees of freedom for the model represent the number of parameters estimated from the data to build the model. These parameters are the coefficients or weights of the independent variables and the constant term.
The degrees of freedom for the model are used to calculate the F-statistic, which is a measure of the overall significance of the regression model. The F-statistic is calculated as the ratio of the explained variance to the unexplained variance of the model, and it is compared to the F-distribution with degrees of freedom (k, n-k-1), where k is the number of independent variables and n is the sample size.
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- x\3 ≥ 5 help pls?
solve the inequality
Answer:
x> - 15
Step-by-step explanation:
I guess this will help
Please help me with this homework
Lines m and n intersect to form various angles.
Which angle is a vertical angle with ∠6?
∠5
none of these
∠8
∠7
Answer:
Angles 6 and 8 are vertical angles.
please help I have no idea how to do this and I want to sleep
Answer: D
Step-by-step explanation:
Zach won because 3 16/24 is less than 3 15/24. Then, 3.666666 is less than 3.625
compute the residuals. (round your answers to two decimal places.) xi yi residuals 6 6 11 7 15 12 18 20 20 30 (c) develop a plot of the residuals against the independent variable x. do the assumptions about the error terms seem to be satisfied?
The estimated regression equation for the given data is y = -30.7 + 3.409x
To develop an estimated regression equation for the given data, we need to use the method of least squares.
The formula for the slope of the regression line is given by:
b = ∑(xi - x)(yi - y) / ∑(xi - x)²
where xi and yi are the individual values of the two variables, x and y are their respective means.
The formula for the intercept of the regression line is given by:
a = y - b × x
where a is the intercept and b is the slope.
Using the given data, we can calculate the values of x, y, b, and a as follows
x = (6 + 11 + 15 + 18 + 20) / 5 = 14
y = (7 + 9 + 12 + 21 + 30) / 5 = 15.8
∑(xi - x)(yi - y) = (6 - 14)(7 - 15.8) + (11 - 14)(9 - 15.8) + (15 - 14)(12 - 15.8) + (18 - 14)(21 - 15.8) + (20 - 14)(30 - 15.8) = 306.8
∑(xi - x)² = (6 - 14)² + (11 - 14)² + (15 - 14)² + (18 - 14)² + (20 - 14)² = 90
b = ∑(xi - x)(yi - y) / ∑(xi - x)² = 306.8 / 90 = 3.409
a = y - b × x = 15.8 - 3.409 × 14 = -30.7
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The given question is incomplete, the complete question is:
Given are data for two variables, x and y. Develop an estimated regression equation for these data.
the heights of adult men in america are normally distributed, with a mean of 69.8 inches and a standard deviation of 3.5 inches. what is the probability that an american man is 69.8 inches or taller?
the probability that an American man is 69.8 inches or taller is 0.5 (or 50%).
To solve this problem, we can use the properties of the normal distribution and the standard normal distribution.
First, we need to standardize the variable (the height of men) to a standard normal variable (with a mean of 0 and a standard deviation of 1). We can do this using the formula:
[tex]z = (x - mu) / sigma[/tex]
where z is the standard normal variable, x is the original variable, mu is the mean of the original variable, and sigma is the standard deviation of the original variable.
In this case, we want to find the probability that an American man is 69.8 inches or taller. So we need to calculate the z-score for x = 69.8:
[tex]z = (69.8 - 69.8) / 3.5 = 0[/tex]
The z-score is 0 because 69.8 is equal to the mean of the distribution.
Next, we can use a standard normal distribution table (or a calculator with a normal distribution function) to find the probability that a standard normal variable is less than or equal to 0. We can also use the fact that the area under the standard normal curve is 1.
Using a standard normal distribution table, we find that the probability that a standard normal variable is less than or equal to 0 is 0.5.
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what is the slope of the linear regression prediction equation if a person with 12 years of schooling earns $27,000 per year and a person with 13 years of schooling earns $28,600 per year?
The slope of the linear regression prediction equation is 1,600, which means that for each additional year of
schooling, the expected increase in salary is 1,600.
The slope of the linear regression prediction equation can be calculated by using the formula:
slope = (y2 - y1) / (x2 - x1)
where y2 is the second data point (in this case, 28,600),
y1 is the first data point (in this case, 27,000),
x2 is the second value of the independent variable (in this case, 13 years of schooling), and
x1 is the first value of the independent variable (in this case, 12 years of schooling).
Plugging in the values, we get:
slope = (28,600 - 27,000) / (13 - 12)
slope = 1,600 / 1
slope = 1,600
Therefore, the slope of the linear regression prediction equation is 1,600, which means that for each additional year of
schooling, the expected increase in salary is 1,600.
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For a ride on a rental scooter, Hong paid $5 fee to start the scooter plus 9 cents per minute of the ride. The total bill for Hong’s ride was $12.74. For how many minutes did Hong ride the scooter?
Hong rode the scooter for approximately 86 minutes.
Let's start by using algebra to solve for the number of minutes Hong rode the scooter.
Let's say the number of minutes Hong rode the scooter is "m". Then, we can set up the following equation:
Total cost = $5 fee + 9 cents per minute x m minutes
$12.74 = $5 + $0.09m
Next, we'll solve for "m" by isolating it on one side of the equation:
$12.74 - $5 = $0.09m
$7.74 = $0.09m
m = $7.74 ÷ $0.09
m ≈ 86
Therefore, Hong rode the scooter for approximately 86 minutes.
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solve the following equation: log2(16x)= 4
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(16x)=4\implies 2^{\log_2(16x)}=2^4\implies 16x=2^4\implies x=\cfrac{2^4}{16}\implies x=1[/tex]
State the most specific name for each figure
PLS HELP!!
1) The name of the shape is rectangle
2) The name of the shape is trapezoid
3) The name of the shape is rhombus
4) The name of the shape is rectangle
Names of plane shapes
From the question, we are to state the most specific name for each of the given figures
1.
We have a quadrilateral
Opposite sides are parallel and equal
Each interior angle is a right angle
The name of the shape is rectangle
2.
We have a quadrilateral
Only a pair of opposite sides are parallel
The name of the shape is trapezoid
3.
We have a quadrilateral
Opposite sides are parallel and equal
All sides are equal
None of the angle is a right angle
The name of the shape is rhombus
4.
We have a quadrilateral
Opposite sides are parallel and equal
Each interior angle is a right angle
The name of the shape is rectangle
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9. You practice the drums for hour two times each day. How long will you practice the drums in 1 week? O 11 hours O 10 hours 10 1/2 hours 11 1/2 hours
Answer:
11 1/2
Step-by-step explanation:
(2x+3)(3x + 5) what is thisss ??
Answer:
6x² + 19x + 15
Step-by-step explanation:
(2x+3)(3x + 5)
= 6x² + 10x + 9x + 15
= 6x² + 19x + 15
So, the answer is 6x² + 19x + 15
identify the requested point and justify by analyzing an appropriate derivative
The second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve.
To find the leftmost point on the curve defined by the parametric equations x = t² + 2t and y = t² - 2t + 3, we need to find the value of t that corresponds to this point. We can do this by analyzing the derivative of the curve with respect to t.
The leftmost point on the curve corresponds to the point where the slope of the curve is zero or undefined. This occurs when the derivative of y with respect to x is zero or undefined.
We can express y as a function of x by eliminating t from the given parametric equations. Solving for t in terms of x, we get:
t = -1 ± √(x + 1)
Substituting this value of t in the equation for y, we get:
y = (x + 1) ± 4√(x + 1) + 3
y = ±4√(x + 1) + x + 4
To find the leftmost point on the curve, we need to find the value of x that corresponds to this point. We can do this by finding the minimum value of x for which y is defined.
Differentiating y with respect to x, we get:
dy/dx = 1 + 2/√(x + 1)
Setting dy/dx = 0, we get:
1 + 2/√(x + 1) = 0
2/√(x + 1) = -1
Solving for x, we get:
x = 3
Note that this value of x is within the given range of -2 ≤ t ≤ 3. Therefore, the leftmost point on the curve is the point corresponding to t = 1.
To justify that we have found the requested point, we can analyze the second derivative of y with respect to x. The second derivative will tell us whether the point corresponds to a local minimum, local maximum, or inflection point.
Differentiating dy/dx with respect to x, we get:
d²y/dx² = -2/[tex](x + 1)^{(3/2)}[/tex]
Substituting x = 3, we get:
d²y/dx² = -2/64
Since the second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve. Therefore, we have found the leftmost point on the curve as requested.
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The question is -
Identify the requested point and justify that you have found the requested point by analyzing an appropriate derivative. x = t² + 2t, y = t² - 2t + 3, - 2 ≤ t ≤ 3 Leftmost point