Answer:
Step-by-step explanation:
48 cups of trail mix
A linear function has a slope of -7 /9 and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = -7/9 (x minus 18)?
Answer:
both functions have the same graph
Step-by-step explanation:
The first function is described in terms of its slope and y-intercept, so can be written in slope-intercept form as ...
y = mx + b . . . . m = slope (-7/9); b = y-intercept (3)
y = -7/9x +3
__
The second function is written in point-slope form:
y -k = m(x -h) . . . . m = slope (-7/9), point = (h, k) = (18, -11)
y +11 = -7/9(x -18)
If we rearrange the second equation to the form of the first, we get ...
y = -7/9x +14 -11 . . . . eliminate parentheses, subtract 11
y = -7/9x +3 . . . . . . . matches the equation of the first function
__
Both functions describe the same relation.
Can someone please help me with this? What would be the measure of angle R to the nearest tenth?
Answer:
Step-by-step explanation:
There are two ways to do this.
1. You could make an accurate diagram and measure R. This works but the computer won't like it. However you will know if you are correct. An answer ± 2 degrees would tell you that you are likely correct.
2. The second way is to find <C. Similarity guarantees that <C and <R are equal. The adjacent side to angle C is the second longest line. The second longest line in PQR is the adjacent side of <R.
Naturally we will use the second method, but you ought to try the first method. It's cumbersome but it will teach you how to read the values of triangles to make clear the trig functions.
Tan(C) = opposite over adjacent
Tan(C) = 7 / 9
Tan(C) = .77777777...
<C = tan-1(0.7777777...)
<C = 37.87
<C = 37.9
What is the value of X?
What are two decimals equivalent to 9.60
Answer:
9.600
9.6
Step-by-step explanation:
These two decimals above are equivalent to 9.60 because no matter the amount of zeroes there are, as long as the numbers before the zeroes maintain the same location (in this case, ones and tens place) the decimals will be equivalent. For example, 9.60 is also equivalent to 9.600000000000000000000000...
a small book publisher knows that 15 books weigh 29 lbs. How much do 31 books weigh?
Answer:
I believe the answer would be 59.93333
The dot plots below show rainfall totals in the Highlands and Lowlands areas of a certain region.
Which statement comparing the shapes of the dot plots is true?
Options:
A. Both the Highlands and the Lowlands data points are evenly distributed around the center.
B. Both the Highlands and the Lowlands data points are clustered toward the left of the plot.
C. The Highlands data points are evenly distributed around the center, while the Lowlands data points are clustered toward the left of the plot.
D. The Highlands data points are clustered toward the left of the plot, while the Lowlands data points are evenly distributed.
Answer:
B. Both the Highlands and the Lowlands data points are clustered toward the left of the plot.
Step-by-step Explanation:
From the dot plots displaying rainfall totals for highland and lowland areas as shown in the diagram attached below, we can clearly observe that most of the dots on the plot tend to be more concentrated towards the left of the plot, compared to the concentration of dots toward the right of the plot.
Invariably, we can infer that data points for lowlands and Highlands are clustered toward the left of the plot.
Therefore, the statement that is true, comparing the shapes of the dot plot is B. "Both the Highlands and the Lowlands data points are clustered toward the left of the plot."
Answer:B
Step-by-step explanation: I took the edge quiz
The value of homes in Baltimore, Maryland is dropping by 2.5% each month. If a house
costs $215,000 now, how much is it expected to be worth in 6 months
Answer:
The house will be worth $184,699.6847 in 6 months.
Step-by-step explanation:
Since the cost of the houses is dropping by 2.5 % per month, then it is decreasing exponentially and can be modeled by the following formula:
[tex]cost(x) = 215000*(1 - \frac{2.5}{100})^t\\cost(x) = 215000*(1 - 0.025)^t\\cost(x) = 215000*(0.975)^t\\[/tex]
After 6 months:
[tex]cost(6) = 215000*(0.975)^6\\cost(6) = 184699.6847[/tex]
The house will be worth $184,699.6847 in 6 months.
A city doubles its size every 50 years. If the population is currently 500,000, what will the
population be in 200 years?
______ people?
Answer:
8,000,000 or 2,000,000
Step-by-step explanation:
For 8,000,000=
1st 50 years= 500,000+500,000= 1,000,000
2nd 50 years= 1,000,000+1,000,000= 2,000,000
3rd 50 years= 2,000,000+2,000,000= 4,000,000
4th 50 years= 4,000,000+4,000,000= 8,000,000
For 2,000,000=
200 years ÷ 50 years= 4
500,000×4= 2,000,000
I can't decide
A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with five different members. There are 15 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below. There are nothing different ways to appoint the officers. b. How many different ways can the committee be appointed? There are nothing different ways to appoint the committee. c. What is the probability of randomly selecting the committee members and getting the five youngest of the qualified candidates? P(getting the five youngest of the qualified candidates)equals nothing (Type an integer or a simplified fraction.)
Answer:
(a) There are 32,760 different ways to appoint the officers.
(b) 3003 different ways can the committee be appointed.
(c) Probability of getting the five youngest of the qualified candidates is 0.00033.
Step-by-step explanation:
We are given that a corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with five different members.
There are 15 qualified candidates, and officers can also serve on the committee.
(a) The number of officers are 4, i.e; A president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO).
There are 15 qualified candidates.
To find the number of ways to appoint the officers, we will use permutation because here the order of selecting the officer's matters.
So, the number of ways to appoint the officers = [tex]^{15}\text{P}_4[/tex]
= [tex]\frac{15!}{(15-4)!}[/tex] {[tex]\because ^{n}\text{P}_r = \frac{n!}{(n-r)!}[/tex] }
= [tex]\frac{15!}{11!}[/tex] = 32,760 ways
(b) The number of committee numbers to appoint include five members.
There are 15 qualified candidates.
To find the number of ways in which the committee can be appointed, we will use combination because here the order of selecting the members doesn't matter.
So, the number of ways to appoint the committee = [tex]^{15}\text{C}_5[/tex]
= [tex]\frac{15!}{5! \times (15-5)!}[/tex] {[tex]\because ^{n}\text{C}_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{15!}{5! \times 10!}[/tex] = 3003 ways
(c) The probability of randomly selecting the committee members and getting the five youngest of the qualified candidates is given by;
Number of ways of selecting the committee = 3003
Selecting the five youngest of the qualified candidates = 1
So, the required probability = [tex]\frac{1}{3003}[/tex]
= 0.00033
The sum of three consecutive even numbers is 66. What is the smallest of these numbers?
Answer:
20
Step-by-step explanation:
one way is guess and check method, you draw a table and try out 3 different consecutive even numbers to see which 3 add up to 66
What is the value of y?
Answer:
65
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
130 = y+y
130 = 2y
Divide by 2
130/2= 2y/2
65=y
Answer:
D. 65
Step-by-step explanation:
I agree with the above reasoning
ABC transforms to produce A’ B’C’ which transformation did NOT take place. A. Rotation 180° counterclockwise about the origin
B. Reflection across the origin
C. Rotation 180 clockwise about the origin
D. Reflection across the Line y=x
find the average rate of change over the interval 7 less than or equal to X less than or equal to 10, of the function defined by the table
X. Y.
1 1
4 16
7 49
10 100
A. 8
B. 17
C. 5
D. 11
Answer:
B. 17
Step-by-step explanation:
The average rate of change is:
m_avg = (y₂ − y₁) / (x₂ − x₁)
m_avg = (100 − 49) / (10 − 7)
m_avg = 17
. In a sale, there is twenty-five per cent off all prices.
A chair costs £45 in the sale.
How much was it before the sale?
Answer:
€60
Step-by-step explanation:
€45 = 75%
100% (original) = (100/75)
[tex](100 \div 75) \times 45 = 60[/tex]
One assumption underlying linear regression is that the Y values are statistically dependent. This means that in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for any other X value.
A. True
B. False
Answer:
The statement provided is TRUE.
Step-by-step explanation:
The four principle assumptions of the simple linear regression model are,
The linearity of the relationship between the dependent variable and the independent variable. That is, value of y, the dependent variable for each value of x the independent variable is, [tex]y = \beta_{1} + \beta_{2}x + e[/tex]. Normality of the error distribution. That is, [tex]e_{i} ~\sim N (\mu, \sigma^{2})[/tex]. Thus, the variance of random error e is [tex]Var (e) = \sigma^{2}[/tex]. Statistical independence of the errors or specifically no correlation between consecutive errors. That is, if [tex]Corr (e_{i}, e_{j}) = 0[/tex], it implies that[tex]Cov (e_{i}, e_{j}) = 0[/tex]. Homoscedasticity of the errors, i.e. constant variance.The first assumption clearly indicates that the y-values are statistically dependent upon the x-values.
Thus, the statement provided is TRUE.
6.
The city's water department charges $3 per month, plus 46c for every 100 gallons of water used.
Let w be the number of gallons of water, in hundreds, used in one month. Express the total monthly cost for water, in dollars, as an equation in terms of w.
cost
Last month, one homeowner used 1,600 gallons. Write 1,600 gallons in terms of hundred gallons.
hundred gallons
What is the homeowner's total cost in dollars) for water last month?
$
The homeowner received a bill for $13.36. Was the billing correct?
Yes
Or No
Answer:
cost in term of w is
c= 0.46 w+3
1600 in terms of hundred gallons is: 16 hundred
c= 0.46*16 +3 = 10.36 dollars
no
Step-by-step explanation:
The cost in terms of w is c= 0.46 w+3 and the total cost will be $10.36.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that the city's water department charges $3 per month, plus 46c for every 100 gallons of water used.
The equation will be written as:-
Let w be the number of gallons of water, in hundreds, used in one month. Express the total monthly cost for water, in dollars, as an equation in terms of w.
c= 0.46 w+3
1600 in terms of hundred gallons is: 16 hundred
c= 0.46 x 16 +3 = 10.36 dollars
Therefore, the cost in terms of w is c= 0.46 w+3 and the total cost will be $10.36.
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The chances of a tax return being audited are about 21 in 1 comma 000 if an income is less than $100,000 and 29 in 1 comma 000 if an income is $100,000 or more. Complete parts a through e. a. What is the probability that a taxpayer with income less than $100,000 will be audited? With income of $100,000 or more? Upper P (taxpayer with income less than $ 100 comma 000 is audited )equals nothing (Type an integer or a decimal.) What is the probability that a taxpayer with income of $100,000 or more will be audited? Upper P (taxpayer with income of $ 100 comma 000 or higher is audited )equals nothing (Type an integer or a decimal.) b. If five taxpayers with incomes under $100,000 are randomly selected, what is the probability that exactly one will be audited? That more than one will be audited?
Answer:
a) p=0.021
b) p=0.029
c) Exactly one audit: P=0.0965
More than one audit: P=0.0042
Step-by-step explanation:
a) If the income is less than $100,000, there is a probability of 21 in 1,000 of being audited. This is:
[tex]p_1=\dfrac{21}{1,000}=0.021[/tex]
If the income is equal or more than $100,000, there is a probability of 29 in 1,000 of being audited. This is:
[tex]p_2=\dfrac{29}{1,000}=0.029[/tex]
b) If we have 5 taxpayers with incomes under $100,000, and we want to know the probability that exactly one will be audited, we can model this a binomial randome variable, with p=0.021 and n=5:
[tex]P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\[/tex]
There is a probability of 0.0965 that exactly one out of a sample of five taxpayers with incomes under $100,000 will be audited.
To calculate the probability that more than one will be audited, we use the same distribution:
[tex]P(x>1)=1-[P(x=0)+P(x=1)]\\\\\\P(x=0) = \dbinom{5}{0} p^{0}q^{5}=1*1*0.8993=0.8993\\\\\\P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\\\P(x>1)=1-[P(x=0)+P(x=1)]\\\\P(x>1)=1-(0.8993+0.0965)\\\\P(x>1)=1-0.9958\\\\P(x>1)=0.0042[/tex]
There is a probability of 0.0042 that more than one out of a sample of five taxpayers with incomes under $100,000 will be audited.
The expression 1,000(1.0215)4t represents the amount of money in an account after t years.
The interest is compounded [annually/semiannually/quarterly/monthly], and the effective annual interest rate on the account is [2.15%/4.00%/8.60%/8.88%].
What are the two correct answers that complete the sentences? Choose from the brackets above.
Answer:
The interest is compounded quarterly.
The effective annual interest rate on the account is 8.60%.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
We are given:
[tex]A(t) = 1000(1.0215)^{4t}[/tex]
Comparing to the general formula.
[tex]P = 1000[/tex]
[tex]1 + \frac{r}{n} = 1.0215[/tex]
[tex]nt = 4t[/tex]
From the last one:
[tex]n = 4[/tex]
Which means 4 compoundings per year. This means that the interest is compounded quarterly.
Interest rate:
[tex]1 + \frac{r}{n} = 1.0215[/tex]
Since n = 4.
[tex]\frac{r}{4} = 1.0215 - 1[/tex]
[tex]\frac{r}{4} = 0.0215[/tex]
[tex]r = 4*0.0215[/tex]
[tex]r = 0.0860[/tex]
So the interest rate is of 8.60%.
Answer:
the answer is quarterly and 8.88
Step-by-step explanation:
got 100 on the test
which of the following options is an odd function?
Answer: The answer is C
Step-by-step explanation:
How old is that dog if his sister is 12 and he is 3 years older
The dog is 15 year old in dog years.
In our eyes he's one, however in the eyes of a dog he is 15
small edit! thank you brainliest!!
Find the perimeter of the figure when l = 15 m, w = 9 m, x = 3 m, and y = 6 m
Answer:
54
Step-by-step explanation:15+15+9+9+3+3=54
hii pls answer it guys plz help me
Answer:
7) 7/2 (its the only number between 3 and 4)
8) 7/10 ( its the only number between 3/5 and 4/5)
9) 5/8 (its the only number between 1/2 and 3/4)
Sociology graduates, upon entering the workforce are normally distributed and earn a mean salary of $30,000 with a standard deviation of $4000. Jessica is an honors sociology student. Upon graduation, she would like to take a job that starts at $40,000. What is the probability that randomly chosen salary exceeds $40,000
Answer:
0.62% probability that randomly chosen salary exceeds $40,000
Step-by-step explanation:
Problems of normally distributed distributions are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 30000, \sigma = 4000[/tex]
What is the probability that randomly chosen salary exceeds $40,000
This is 1 subtracted by the pvalue of Z when X = 40000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40000 - 30000}{4000}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a pvalue of 0.9938
1 - 0.9938 = 0.0062
0.62% probability that randomly chosen salary exceeds $40,000
The local historical Society wants to preserve two buildings. The total age of the buildings is 292 years. If one building is three times as old as the other, what are the ages of the two buildings?
The newer building is years old, and the older building is years old.
Answer:
building one is 292 years old and building two is 879 years old
Step-by-step explanation:
292x3= 879
The newer building is 73 years old,
And, The older building is 219 years old.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The total age of the buildings is 292 years.
Now,
Let the newer building is = x years old,
Then, The older building is = 3x years old.
Here, The total age of the buildings is 292 years.
So, We get;
⇒ x + 3x = 292
⇒ 4x = 292
⇒ x = 73
Thus, The newer building = x years old,
= 73 years old
And, The older building = 3x years old.
= 3 × 73
= 219 years old
Therefore, The newer building is 73 years old,
And, The older building is 219 years old.
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A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program. (a) List all possible two-course selections. (b) Comment on the likelihood that EPR 646 and EPR 679 will be selected.
Answer:
A) A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program.
The courses were not listed, but let's assume the courses are:
EPR 646,
EPR 602
EPR 679
EPR 622
EPR 684
In this case, we can see there are 5 possible courses.
Selecting them:
[tex]^5C_2 = \frac{5*4*3*2*1}{2*(5-2)!} = 10[/tex]
Therefore, there are 10 selections.
All possible two course selections:
(622,602); (622, 684); (622, 679); (622, 646); (646, 602); (646, 679)
(646,684); (602, 684); (602, 679);
(679, 684)
b) Likelihood that EPR 646 and EPR 679 will be selected
From the data abeve, EPR 646 and EPR 679 can be selected just once.
Therefore, the likelihood =
P(selecting EPR 646 and EPR 679) = [tex]\frac{num. of . times. event. occured}{total. number. of. outcome} =\frac{1}{10}[/tex]
Likelihood that EPR 646 and EPR 679 will be selected is [tex]\frac{1}{10}[/tex] = 0.1
Answer:A student entering a doctoral program in educational psychology is required to select courses from the list of courses provided as part of his or her program.
(a) List all possible -course selections.
(b) Comment on the likelihood that will be selected
Step-by-step explanation:
The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2. Find:
Chapter Reference
b
Surface area of the pyramid
Answer:
228 cm²
Step-by-step explanation:
The base of the pyramid is a regular quadrilateral (a square), so there are 4 congruent lateral faces.
The total surface area is therefore:
A = 36 cm² + 4 (48 cm²)
A = 228 cm²
The zeros of the function p(x) = x2 – 2x– 24 are
1) -8 and 3
3) -4 and 6
2) -6 and 4
4) -3 and 8
Can u show work too
Answer:
3) -4 and 6
Step-by-step explanation:
I find it easiest to solve these by factoring. Here, you're looking for factors of the constant (-24) that have a sum equal to the coefficient of the linear term (-2). You know the divisors of 24 are ...
-24 = 1(-24) = 2(-12) = 3(-8) = 4(-6)
The sums of these factors are, respectively, -23, -10, -5, -2. So, the last pair of factors are the ones we're looking for. These are the constants that go into the binomial factors of the function:
p(x) = x^2 -2x -24
p(x) = (x +4)(x -6)
Then the zeros are the values of x that make these factors zero:
x +4 = 0 ⇒ x = -4
x -6 = 0 ⇒ x = 6
The zeros of the function are -4 and 6.
____
The graph of the function confirms these values.
The number of hours of daylight measured in one year in Ellenville can be modeled by a sinusoidal function. During 2006, (not a leap year), the longest day occurred on June 21 with 15.7 hours of daylight. The shortest day of the year occurred on December 21 with 8.3 hours of daylight. Write a sinusoidal equation to model the hours of daylight in Ellenville.
Answer:
[tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]
Step-by-step explanation:
Solution:-
- We are to model a sinusoidal function for the number of hours of daylight measured in one year in Ellenville.
- We will express a general form of a sinusoidal function [ f ( t ) ] as follows:
[tex]f ( t ) = A*sin ( w*t ) + c[/tex]
Where,
A: The amplitude of the hours of daylight
w: The angular frequency of occurring event
c: The mean hours of daylight
t: The time taken from reference ( days )
- We are given that the longest day [ [tex]f ( t_m_a_x )[/tex] ] occurred on June 21st and the shortest day [ [tex]f ( t_m_i_n )[/tex] ] on December 21st.
- The mean hours of daylight ( c ) is the average of the maximum and minimum hours of daylight as follows:
[tex]c = \frac{f(t_m_a_x ) +f(t_m_i_n ) }{2} \\\\c = \frac{15.7 + 8.3}{2} = \frac{24}{2} \\\\c = 12[/tex]
- The amplitude ( A ) of the sinusoidal function is given by the difference of either maximum or minimum value of the function from the mean value ( c ):
[tex]A = f ( t_m_a_x ) - c\\\\A = 15.7 - 12\\\\A = 3.7[/tex]
- The frequency of occurrence ( w ) is defined by the periodicity of the function. In other words how frequently does two maximum hours of daylight occur or how frequently does two minimum hours of daylight occur.
- The time period ( T ) is the time taken between two successive maximum duration of daylight hours. We were given the longest day occurred on June 21st and the shortest day occurred on December 21st. The number of days between the longest and shortest day will correspond to half of the time period ( 0.5*T ):
[tex]0.5*T = 7 + 31 + 31 + 30 +31 +30 +21\\\\T = 2* [ 181 ] \\\\T = 362 days[/tex]
- The angular frequency ( w ) is then defined as:
[tex]w = \frac{2\pi }{T} = \frac{2\pi }{362} \\\\w = 0.01736[/tex]
- We will now express the model for the duration of daylight each day as function of each day:
[tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]
I need this asap
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(2,-3) B(4, -3) C(4, 5) D(2,5)
What is the perimeter of the rectangle ABCD?
Answer:
20
Step-by-step explanation:
The rectangle is 2 x 8.
2 + 2 + 8 + 8 = 20
Perimeter=8+8+2+2
=20
Four expressions are shown below which expression are equivalent A:10 (10 +5y) B:5(20x + 25y) C:5 (2x + y) D: 0.25(400x + 500y)
Answer:
Step-by-step explanation:
remove parentheses by multiplying factors.
use exponent rules to remove parentheses in terms with exponents.
combine like terms by adding coefficients.
combine the constants.
