Answer:
xy + 8x - y - 8
Step-by-step explanation:
We can use the FOIL method to expand these two binomials. FOIL stands for First, Outer, Inner, Last.
F: The First means that we multiply the first terms of each binomial together. In this case, that would be x · y = xy.
O: The Outer means that we multiply the outer terms, or the first term of the first binomial and the second term of the last binomial, together. In this case, that would be x · 8 = 8x.
I: The Inner means that we multiply the inner terms, or the second term of the first binomial and the first term of the second binomial, together. In this case, that would be (-1) · y = -y.
L: The Last means that we multiply the last terms of each binomial together. In this case, that would be (-1) · 8 = -8.
Adding all of these together, we get xy + 8x - y - 8 as our final answer.
Hope this helps!
Answer:
[tex]xy+8x-y-8[/tex]
Step-by-step explanation:
=> (x-1)(y+8)
Using FOIL
=> [tex]xy+8x-y-8[/tex]
A car travelling from Ibadan to Lagos at 90 km/hr
takes 1 hour 20 min. How fast must one travel to
cover the distance in one hour?
Answer:
A velocity of 120km/h is needed to cover the distance in one hour
Step-by-step explanation:
The velocity formula is:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the time.
A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.
This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]
We use this to find d.
[tex]v = \frac{d}{t}[/tex]
[tex]90 = \frac{d}{1.3333}[/tex]
[tex]d = 90*1.3333[/tex]
[tex]d = 120[/tex]
The distance is 120 km.
How fast must one travel to cover the distance in one hour?
Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So
[tex]v = \frac{d}{t}[/tex]
[tex]v = \frac{120}{1}[/tex]
[tex]v = 120[/tex]
A velocity of 120km/h is needed to cover the distance in one hour
If TU = 6 units, what must be true? SU + UT = RT RT + TU = RS RS + SU = RU TU + US = RS
Answer:
Since RT = 12, TU = 6 and RS = 24, T and U are the midpoints of RS and TS respectively. This means that SU + UT = RT.
Answer:
su+ut=rt
Step-by-step explanation:
Which of the following represents the set of possible rational roots for the
polynomial shown below?
2^2+ 5^2 – 8x– 10 = 0
What is the solution to the system of equations?
y=-3x – 2
5x + 2y = 15
0 (-40. 19)
(-19.55)
(19-40)
(55.-19)
Answer:
Step-by-step explanation:
y = -3x - 2
5x + 2y = 15
5x + 2(-3x -2) = 15
5x -6x - 4 = 15
-x - 4 = 15
-x = 19
x = -19
y = -3(-19) - 2
y = 57 - 2
y = 55
(-19, 55)
solution is b
Which of the following is false? Correlation coefficient and the slope always have the same sign (positive or negative). If the correlation coefficient is 1, then the slope must be 1 as well. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Correlation measures the strength of linear association between two numerical variables.
Answer:
If the correlation coefficient is 1, then the slope must be 1 as well.
Step-by-step explanation:
Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.
If the correlation coefficient is 1, then the slope must be 1 as well.
The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated.
Correlation coefficient and the slope both quantify the direction and strength of the relationship between two numeric variables. When the correlation (r) is negative, the regression slope (b) will be negative. When the correlation is positive, the regression slope will be positive.If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them.
So, the false statement is:
If the correlation coefficient is 1, then the slope must be 1 as well.
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Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice. Set A Set B The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 42.8 with standard deviation of about 1.86. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set A’s low temperatures have a greater variability than Set B temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set B is about 41.56 with standard deviation of about 6.07. The mean for Set A is about 43.8 with standard deviation of about 14.8. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set A means that Set A’s low temperatures have a greater variability than Set B temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.4. The mean for Set B is about 41.5 with standard deviation of about 6.7. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set B’s low temperatures have a greater variability than Set A temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 43.8 with standard deviation of about 14.8. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set B’s low temperatures have a greater variability than Set A temperatures.
Answer:
Explained below.
Step-by-step explanation:
The question is:
Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.
Set A: {36, 51, 37, 42, 54, 39, 53, 42, 46, 38, 50, 47}
Set B: {22, 57, 46, 24, 31, 41, 64, 50, 28, 59, 65, 38}
The five-number summary is:
MinimumFirst Quartile Median Third Quartile MaximumThe five-number summary for set A is:
Variable Minimum Q₁ Median Q₃ Maximum
Set A 36.00 38.25 44.00 50.75 54.00
The five-number summary for set B is:
Variable Minimum Q₁ Median Q₃ Maximum
Set B 22.00 28.75 48.00 58.50 65.00
Compute the mean for both the data as follows:
[tex]Mean_{A}=\frac{1}{12}\times [36+51+37+...+47]=44.58\approx 44.6\\\\Mean_{B}=\frac{1}{12}\times [22+57+46+...+38]=44.58\approx 44.6[/tex]
Both the distribution has the same mean.Compare mean and median for the two data:
[tex]Mean_{A}>Median_{A}\\\\Mean_{B}>Median_{B}[/tex]
This implies that set A is positively skewed whereas set B is negatively skewed.Compute the standard deviation for both the set as follows:
[tex]SD_{A}=\sqrt{\frac{1}{12-1}\times [(36-44.6)^{2}+...+(47-44.6)^{2}]}=6.44\approx 6.4\\\\SD_{B}=\sqrt{\frac{1}{12-1}\times [(22-44.6)^{2}+...+(38-44.6)^{2}]}=15.56\approx 15.6[/tex]
The set B has a greater standard deviation that set A. Implying set B has a greater variability that set B.For the data set represented by this box plot, what is the value of the maximum? maximum:
Answer:
140
Step-by-step explanation:
The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84
Answer:
the other person is correct!
Step-by-step explanation:
Which statement best interprets the factor (r+7) in this context?
Answer:
the height of the cylinder is 7 units greater than the radius
Step-by-step explanation:
When you match the forms of the equations ...
[tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]
you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...
the height of the cylinder is 7 units greater than the radius.
Lee watches TV for 2 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
Answer:
$1.08
Step-by-step explanation:
30 days × (2 hrs/day) × (150 W) × (1 kW / 1000 W) × (0.12 $/kWh) = $1.08
The polynomial-7.5x^2 + 103 + 2142 models the yearly number of visitors (in thousands) x years after 2007 to a park. Use this polynomial to estimate the number of visitors to the park in 2021.
Answer:
In that year approximately 2114 thousand people visited the park.
Step-by-step explanation:
Since the expression [tex]y(x) = -7.5*x^2 + 103*x + 2142[/tex] models the number of visitors in the park, where x represents the number of years after 2007 and 2021 is 14 years after that, then we need to find "y" for that as shown below.
[tex]y(14) = -7.5*(14)^2 + 103*14 + 2142\\y(14) = -7.5*196 + 1442 + 2142\\y(14) = -1470 + 3584\\y(14) = 2114[/tex]
In that year approximately 2114 thousand people visited the park.
How do you calculate the y-intercept of a line written in Standard Form?
Answer:
y-int = C/B
Step-by-step explanation:
Ax + By = C
y-int = C/B
Answer:
I hope this helps.
Step-by-step explanation:
Brainliest to whoever gets this correct! Does this graph show a function? Explain how you know.A.No; there are y-values that have more than one x-value.B.No; the graph fails the vertical line test.C.Yes; the graph passes the vertical line test.D.Yes; there are no y-values that have more than one x-value.
Answer:
B. No; the graph fails the vertical line test.
Step-by-step explanation:
If you hold a pencil up to the graph, the parabola would technically touch the pencil at more than one point. That means it failed the test, and therefore it is not a function.
hope this helped :)
1/4 ÷ 3/8 simplest form
Answer:
2/3
Step-by-step explanation:
divide by a fraction = multiply by reciprocal
1/4 * 8/3
2/3
Answer:
⅔
Step-by-step explanation:
= ¼ ÷ ⅜
= ¼ × ⁸/3
= ⅔
Have a great day !
Which shapes have the same volume as the given rectangular prism?
Don’t know this one
Answer:
B
Step-by-step explanation:
The answer is B because in order for the square root of a number to be equal to another number, the answer squared should be the number under the square root.
B. [tex](-4)^2\neq -16[/tex].
Hope this helps.
Each of 100 students in the Allen School can only take 1 CSE class each, between the four classes CSE 311, CSE 312, CSE 331, and CSE 332. Each student (independently of others) takes CSE 311 with probability 0.3, CSE 312 with probability 0.4, CSE 331 with probability 0.1, and CSE 332 with probability 0.2. What is the probability that exactly 31 sign up for CSE 311, 39 sign up for CSE 312, 7 sign up for CSE 331, and 23 sign up for CSE 332
Answer:
[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Step-by-step explanation:
Sample space, n = 100
Let the number of students signed up for CSE 311 = a
Let the number of students signed up for CSE 312 = b
Let the number of students signed up for CSE 331 = c
Let the number of students signed up for CSE 332 = d
Probability of taking CSE 311, [tex]P_a[/tex] = 0.3
Probability of taking CSE 312, [tex]P_b[/tex] = 0.4
Probability of taking CSE 331, [tex]P_c[/tex] = 0.1
Probability of taking CSE 332, [tex]P_d[/tex] = 0.2
[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Graph the line y=-1/3x+2
Answer:
Graphed below.
Step-by-step explanation:
The slope of the line is -1/3.
The y-intercept is at (0, 2).
The x-intercept is at (6, 0).
PLEASE HELP!!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
Answer:
1140 ways.
Step-by-step explanation:
The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).
The 17 identical candies, can be distributed among the 4 children in :
=(17 + 4 - 1)C(4–1) = 20C3 ways.
= 20!/((20–3)!*3!) ways.
= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways
= 20*19*3 ways.
=1140 ways.
What is the measure of angle S?
480
56°
930
101°
Answer:
m∠s = 93°
Step-by-step explanation:
We know that any quadrilateral's sum of angles adds up to 360°. In that case,
360 - (56 + 132 + 79) = m∠s
m∠s = 93°
Answer:
S° = 93 °
Step-by-step explanation:
[tex]The- diagram- is- a- trapezoid (quadrilateral)\\Sum- of- angles-in a- quadrilateral = 360\\ 132\° + 56\° + 79\° + x\° = 360\° \\267\° + x\° = 360\° \\x = 360 \° - 267 \° \\x\° = 93\°[/tex]
What is the answer? ACB ~ EFD
Answer:
y=4solution,
[tex] \frac{ac}{ef} = \frac{cb}{fd} \\ or \: \: \frac{12}{y} = \frac{15}{5} \\ or \: 15 \times y = 12 \times 5( \: cross \: multiplication) \\ or \: 15y = 60 \\ or \: y = \frac{60}{15} \\ y = 4[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
The value of y is 4
Step-by-step explanation:
What is similarity ?
In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
Given,
ΔACB~ΔEFD
The proportional sides are equal.
[tex]\frac{AC}{EF}=\frac{CB}{FD}=\frac{AB}{DE} \\\frac{12}{y}=\frac{15}{5} \\y=12*\frac{5}{15}\\\\ y=4[/tex]
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ga political candidate has asked you to conduct a poll to determine what percentage of people support her. if the candidate only wants a 8% margin of error at a 95% cnofidence level, what size of sample is needed
Answer: 151
Step-by-step explanation:
if prior population proportion is unknown , then the formula is used to find the sample size :
[tex]n=0.25(\frac{z_{\alpha/2}}{E})^2[/tex]
, where [tex]z_{\alpha/2}[/tex] = Two tailed critical value for significance level of [tex]\alpha.[/tex]
E = Margin of error.
Given : margin of error = 8%= .08
For 95% confidence level , two tailed critical value = 1.96
Now, the required sample size :
[tex]n=0.25(\frac{1.96}{0.08})^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151[/tex]
Hence, the size of the sample needed = 151.
Gregoire sold 24 cars to his friend for $71.76. What was the price per car?
a. $47.76
b. $2.99
c. $17.22
d. $3.25
Answer:
2.99
Step-by-step explanation:
Take the total cost and divide by the number of cards
71.76/24 = 2.99
The cost per car is 2.99
Answer:
b. $2.99.
Step-by-step explanation:
To get the price per car, you get the total price divided by the total number of cars.
That would be 71.26 / 24 = 2.969166667, which is most close to b. $2.99. Those are some cheap cars!
Hope this helps!
LM=9, NR=16, SR=8. Find the perimeter of △SMP.
HURRY FIRST ANSWER I WILL MARK YOU AS BRAINLILIST PROMISE
Answer:
perimeter of △SMP = 25Step-by-step explanation:
The perimeter of the triangle △SMP is the sum of al the sides of the triangle.
Perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
Note that the triangle △LRN, △LSM, △MPN and △SRP are all scalene triangles showing that their sides are different.
Given LM=9, NR=16 and SR=8
NR = NP+PR
Since NP = PR
NR = NP+NP
NR =2NP
NP = NR/2 = 16/2
NP = 8
From △LSM, NP = PR = MS = 8
Also since LM = MN, MN = 9
From △SRP, SR = RP = PS = 9
Also SR = MP = 8
From the equation above, perimeter of △SMP = ||MS|| + ||MP|| + ||SP||
perimeter of △SMP = 8+8+9
perimeter of △SMP = 25
Julie has three boxes of pens. The diagram shows expressions for the number of pens in each box. Look at these equations.
Equals B +12
B equals C +4
Write an equation to show the relationship between a + c
Answer:
a=c+16here,
a=b+12
b=a-12----> equation (i)
b= c+4
putting the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
hope this helps...
Good luck on your assignment...
The value of a + c is 16.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
a=b+12
So, b=a-12 ---- equation (i)
and, b= c+4
Substitute the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
Hence, the value of a+ c is 16.
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Which feature of a database displays data in a certain sequence, such as alphabetical order? Chart Filter Search Sort
Answer:
data bar
Step-by-step explanation:
Answer:
chart
Step-by-step explanation:
Select all the correct equations.
Which equations have no real solution but have two complex solutions? PLZ 20 POINTS
Answer:
You did not post the options, but i will try to answer this in a general way.
Because we have two solutions, i know that we are talking about quadratic equations, of the form of:
0 = a*x^2 + b*x + c.
There are two easy ways to see if the solutions of this equation are real or not.
1) look at the graph, if the graph touches the x-axis, then we have real solutions (if the graph does not touch the x-axis, we have complex solutions).
2) look at the determinant.
The determinant of a quadratic equation is:
D = b^2 - 4*a*c.
if D > 0, we have two real solutions.
if D = 0, we have one real solution (or two real solutions that are equal)
if D < 0, we have two complex solutions.
Answer:
This was for 5 points. not 20 my dude. Also the first answer is correct.
Step-by-step explanation:
An experiment consists of dealing 7 cards from a standard deck of 52 playing cards. What is the probability of being dealt exactly 4 clubs and 3 spades?
Answer: 0.00153
Step-by-step explanation:
Given: An experiment consists of dealing 7 cards from a standard deck of 52 playing cards.
Number of ways of dealing 7 cards from 52 cards = [tex]^{52}C_7[/tex]
Since there are 13 clubs and 13 spades.
Number of ways of getting exactly 4 clubs and 3 spades=[tex]^{13}C_4\times\ ^{13}C_3[/tex]
Now, the probability of being dealt exactly 4 clubs and 3 spades
[tex]=\dfrac{^{13}C_4\times\ ^{13}C_3}{^{52}C_7}\\\\\\=\dfrac{{\dfrac{13!}{4!(9!)}\times\dfrac{13!}{3!10!}}}{\dfrac{52!}{7!45!}}\\\\=\dfrac{715\times286}{133784560}\\\\=0.00152850224271\approx0.00153[/tex]
Hence, the probability of being dealt exactly 4 clubs and 3 spades = 0.00153
The population of Adamsville grew from 6000 to 13000 in 7 years. Assuming uninhibited exponential growth, what is the expected population in an additional 3 years?
Answer:
18107.32
Step-by-step explanation:
Set up the exponential function in the form:
[tex]P = P_0(R)^t[/tex]
so P is the new population, [tex]P_0[/tex] is the original population, R is the rate of increase in population, and t is the time in years.
You have to use the information given to find the rate that the population is increasing and then use that rate to find the new population after more time passes.
[tex]13000 = 6000(R)^7\\\\\\frac{13000}{6000} = R^7\\\\\sqrt[7]{\frac{13000}{6000} } = R\\\\\\ R = 1.116786872[/tex]
Now that you found the rate, you can use the function to find the population after another 3 years.
[tex]P = 13000(1.116786872)^3\\P = 18107.32317\\[/tex]
So the population is 18107, rounded to the nearest whole number.
PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answer:
Answer is Y
Step-by-step explanation:
If f(x)=8x and g(x)=2x+1, what is (f×g)(x)
Answer:
(f * g)(x) has a final product of 16x² + 8x.
Step-by-step explanation:
When you see (f * g)(x), this means that we are going to be multiply f(x) and g(x) together.
f(x)=8x
g(x)=2x+1
Now, we multiply these terms together.
(8x)(2x + 1)
Use the foil method to multiply.
16x² + 8x
So, the product of these terms is 16x² + 8x.