Which of the following relations is a function?
A{(3,-1), (2, 3), (3, 4), (1,7)}
B{(1, 2), (2, 3), (3, 4), (4, 5)}.
C{(3, 0), (4, -3), (6, 7), (4,4)}
D{(1, 2), (1, 3), (2, 8), (3, 9)}
Answer:
B
Step-by-step explanation:
A is not a function because the same x value is repeated twice with different y values. The same goes for C and D so the answer is C.
Answer:
B.
Step-by-step explanation:
Well a relation is a set of points and a function is a relation where every x value corresponds to only 1 y value.
So lets see which x values in these relations have only 1 y value.
A. Well a isn’t a function because the number 3 which is a x value had two y values which are -1 and 4.
B. This relation is a function because there are no similar x values.
C. This is not a function because the x value 4 has two y values which are 4 and -3.
D. This is not a function because the number 1 has 2 and 3 as y values.
A survey of 61,647 people included several questions about office relationships. Of the respondents, 26% reported that bosses scream at employees. Use a 0.05 significance level to test the claim that more than ¼ of people say that bosses scream at employees.
Step-by-step explanation:
n = 61,647, p = 0.26, q = 0.74
μ = p = 0.26
σ = √(pq/n) = 0.00177
At 0.05 significance, z = 1.96.
0.26 ± 1.96 × 0.00177
(0.257, 0.263)
0.25 is outside of the confidence interval, so we can conclude with 95% confidence that the proportion is greater than 0.25.
A contractor is setting up new accounts for the local cable company. She earns $75 for each customer account she sets up. Which expression models this situation, and how much will she profit if she sets up 8 customers? (The variable c represents the number of customers.) Question 4 options: A) c – 75; $9.78 B) 75c; $600 C) c + 75; $600 D) 75/c; $9.78
Answer:
B
Step-by-step explanation:
The contractor gets $75 for every single customer she sets up. Okay, so if she sets up 1 customer, she gets $75, if she sets up 2, she gets $150 and so on.
This is a multiplication expression since multiplication is just repeated addition, which is what is happening in this case, where the contractor gets $75 added to her account every time she sets another person up.
At this point you can just eliminate the other answer options except for B, so it is B.
But to double check... if you multiply 75 by 8, you would get $600, which is B.
Answer:
d
Step-by-step explanation:
75/c; $9.78
Please need help Please
Answer: 14/11
Step-by-step explanation:
When 14/11 is multiplied by 1/4, you get a repeating decimal. All repeating decimals are rational.
Hope it helps <3
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below?
Answer:
[tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
Invert the denominator and multiply.
[tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]
Answer:
[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.
Suppose a random variable x is best described by a uniform probability distribution with range 22 to 55. Find the value of a that makes the following probability statements true.
a. P(X <= a) =0.95
b. P(X < a)= 0.49
c. P(X >= a)= 0.85
d. P(X >a )= 0.89
e. P(1.83 <= x <=a)= 0.31
Answer:
(a) The value of a is 53.35.
(b) The value of a is 38.17.
(c) The value of a is 26.95.
(d) The value of a is 25.63.
(e) The value of a is 12.06.
Step-by-step explanation:
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{55-22}=\frac{1}{33}[/tex]
Here, 22 < X < 55.
(a)
Compute the value of a as follows:
[tex]P(X\leq a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.95\times 33=[x]^{a}_{22}\\\\31.35=a-22\\\\a=31.35+22\\\\a=53.35[/tex]
Thus, the value of a is 53.35.
(b)
Compute the value of a as follows:
[tex]P(X< a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.49\times 33=[x]^{a}_{22}\\\\16.17=a-22\\\\a=16.17+22\\\\a=38.17[/tex]
Thus, the value of a is 38.17.
(c)
Compute the value of a as follows:
[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.85=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.85\times 33=[x]^{55}_{a}\\\\28.05=55-a\\\\a=55-28.05\\\\a=26.95[/tex]
Thus, the value of a is 26.95.
(d)
Compute the value of a as follows:
[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.89=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.89\times 33=[x]^{55}_{a}\\\\29.37=55-a\\\\a=55-29.37\\\\a=25.63[/tex]
Thus, the value of a is 25.63.
(e)
Compute the value of a as follows:
[tex]P(1.83\leq X\leq a)=\int\limits^{a}_{1.83} {\frac{1}{33}} \, dx \\\\0.31=\frac{1}{33}\cdot \int\limits^{a}_{1.83} {1} \, dx \\\\0.31\times 33=[x]^{a}_{1.83}\\\\10.23=a-1.83\\\\a=10.23+1.83\\\\a=12.06[/tex]
Thus, the value of a is 12.06.
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Three hundred feet of fencing is used
dimensions of the playground that maximize the total enclosed area. What is the maximum area?
The smaller dimension is
feet
Answer:
50 ft by 75 ft3750 square feetStep-by-step explanation:
Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...
y = (300 -2x)/3
And the enclosed area is ...
A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)
This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.
The maximum area is enclosed when the dimensions are ...
50 ft by 75 ft
That maximum area is 3750 square feet.
_____
Comment on the solution
The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n. Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle) Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected? Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles) Step 2; m∠p − m∠o = 90 degrees (alternate interior angles)
Answer:
(A)Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
Step-by-step explanation:
In the triangle, the exterior angle = pThe adjacent interior angle =oThe two opposite angles are marked m and nThe steps followed by the student are:
Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
We observe that the student made a mistake in Step 1, it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle).
p is outside the triangle, therefore it cannot form one of the angles in the triangle.
At a DBE lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men nor teachers. Find the number of women teachers attending the lecture
Answer:
20 teachers
Step-by-step explanation:
Because if you take 100 and minus it by 29, 23, 4 and 24 you get 20.
What is the standard form for 80000 + 200+ 2
Answer:
80202
Step-by-step explanation:
Simply add according to number value:
200 - 2 goes into hundreds place
2 - 2 goes into ones place
80000 - 8 goes into ten-thousands place
Find the value of s(t(-3)):
s(x) = - 3x-2
t(x) = 5x - 4
Please helppp!
Step-by-step explanation:
(-3x-2/x) multiply by (-15x+12/x)
solve the proportion for y 11/8=y/13
Answer:
We can use the cross products property.
11/8 = y / 13
8y = 11 * 13
y = 11 * 13 / 8 = 17.875
Answer:
y=17.875
Step-by-step explanation:
[tex]\frac{11}{8} = \frac{y}{13}[/tex]
11(13)=8y
143=8y
y=17.875
A half marathon is 13.1 miles long. Leah is running a half marathon and has completed 7.75 miles. How many miles to
the finish line?
Answer:
5.35 more miles
Answer:
5.35 miles to the finish line
Step-by-step explanation:
Step one
13.1-7.75=
5.35
Can Someone help me!!! I need this ASAP! What number? Increased by 130% is 69? FYI: the answer is less than 69
Answer:
Hey there!
There are a few ways you could solve this problem, but the easiest would to be writing an equation.
You could say-
2.3x=69
Divide by 2.3
x=30
Hope this helps :)
Answer:
30
Step-by-step explanation:
the answer is 30 bc increasing something by 130% is multiplying it by 2.3 so technically you have to divide 69 by 2.3 which equals to 30
The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown. f(x) = 4(x2 + 12x) + 10 (twelve-halves) squared = 36 What is the function written in vertex form?
Answer:
[tex]f(x)=4(x+6)^2-134[/tex]
Step-by-step explanation:
We are required to write the function[tex]f(x) = 4x^2 + 48x + 10[/tex] in vertex form.
First, bring the constant to the left-hand side.
[tex]f(x) -10= 4x^2 + 48x[/tex]
Factorize the right hand side.
[tex]f(x) -10= 4(x^2 + 12x)[/tex]
Take note of the factored term(4) and write it in the form below.
[tex]f(x) -10+4\Box= 4(x^2 + 12x+\Box)[/tex]
[tex]\Box = (\frac{\text{Coefficient of x}}{2} )^2\\\\\text{Coefficient of x}=12\\\\\Box = (\frac{12}{2} )^2 =6^2=36[/tex]
Substitute 36 for the boxes.
[tex]f(x) -10+4\boxed{36}= 4(x^2 + 12x+\boxed{36})[/tex]
[tex]f(x) -10+144= 4(x^2 + 12x+6^2)[/tex]
[tex]f(x) +134= 4(x+6)^2\\f(x)=4(x+6)^2-134[/tex]
The function written in vertex form is [tex]f(x)=4(x+6)^2-134[/tex]
Answer:
C
Step-by-step explanation:
I just finished the unit test on Edge. and got a 100% and I selected "c" as my answer.
CAN SOMEONEHELP PLS ASAP
Answer:
a ≈ 2.2
Step-by-step explanation:
Using the Cosine rule in Δ ABC
a² = b² + c² - 2bc cos A
Here b = 3, c = 4 and A = 32° , thus
a² = 3² + 4² - (2 × 3 × 4 × cos32° )
= 9 + 16 - 24cos32°
= 25 - 24cos32° ( take the square root of both sides )
a = [tex]\sqrt{25-24cos32}[/tex] ≈ 2.2
Find the equation of a line passing through the point (-4,1) and perpendicular to the
line 3y = 12x - 9.
Answer:
A. y=-1/4x
Step-by-step explanation:
We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.
Consider the statement, "Confidence intervals are underutilized" and explain what the implications might be of using or not using confidence intervals.
Answer:
Step-by-step explanation:
Confidence intervals have been underutilized prior to this time.
The implications of not using confidence intervals include:
- The under-representation or over-representation of research results that amounts from the use of a single figure to represent a statistic.
- In Market Research analysis, neglecting the use of confidence intervals will increase the risk of your portfolio.
Implications/Importance of using confidence intervals include:
- Calculation of confidence interval gives additional information about the likely values of the statistic you are estimating.
- In the presentation and comprehension of results, confidence intervals give more accuracy from the data or metrics captured.
- Given a sample mean, confidence intervals show the likely range of values of the population mean.
What is the solution to the system of linear equations below?
x+4y=22
2x+y=9
Answer:
[tex]\boxed{\sf \ \ \ x = 2 \ \ and \ \ y = 5 \ \ \ }[/tex]
Step-by-step explanation:
hello, we have two equation
(1) x + 4y = 22
(2) 2x + y = 9
let's multiply (1) by 2 and subtract (2)
2x + 8y - (2x + y) = 2*22 - 9 = 44 - 9 = 35
<=> 2x + 8y -2x -y = 35
<=> 7y = 35
<=> y = 35/7 = 5
we replace this value in (1) and it comes
x + 4*5 = 22
<=> x = 22 - 20 = 2
so the solution is
x = 2 and y = 5
hope this helps
Let S be a sample space and E and F be events associated with S. Suppose that Pr (Upper E )equals 0.6, Pr (Upper F )equals 0.2 and Pr (Upper E intersect Upper F )equals 0.1. Calculate the following probabilities. (a) Pr (E|F )(b) Pr (F|E )(c) Pr (E| Upper F prime )(d) Pr (Upper E prime | Upper F prime )
Answer:
(a)0.5
(b)0.17
(c)0.625
(b)0.375
Step-by-step explanation:
Pr(E)=0.6
Pr(F)=0.2
[tex]Pr(E\cap F)=0.1.[/tex]
(a)Pr (E|F )
[tex]Pr (E|F )=\dfrac{Pr(E \cap F)}{Pr(F)} \\=\dfrac{0.1}{0.2}\\\\=0.5[/tex]
(b)Pr (F|E )
[tex]Pr (F|E )=\dfrac{Pr(E \cap F)}{Pr(E)} \\=\dfrac{0.1}{0.6}\\\\=0.17[/tex]
(c)Pr (E|F')
Pr(F')=1-P(F)
=1-0.2=0.8
[tex]Pr(E \cap F')=P(E)-P(E\cap F)\\=0.6-0.1\\=0.5[/tex]
Therefore:
[tex]Pr (E|F' )=\dfrac{Pr(E \cap F')}{Pr(F')} \\=\dfrac{0.5}{0.8}\\\\=0.625[/tex]
(d)Pr(E'|F')
[tex]P(E'\cap F')=P(E \cup F)'\\=1-P(E \cup F)\\=1-[P(E)+P(F)-P(E\cap F)]\\=1-[0.6+0.2-0.1]\\=1-0.7\\=0.3[/tex]
Therefore:
[tex]Pr (E'|F' )=\dfrac{Pr(E' \cap F')}{Pr(F')} \\=\dfrac{0.3}{0.8}\\\\=0.375[/tex]
Two cities whose longitudes are 10E and 20W on the equator are apart
Step-by-step explanation:
to be honest I'm not sure how to do
A person has a bag containing dimes and nickels. There are a total of 120 coins in the bag, and the total value of the coins is $9.25. Determine how many dimes and nickels are in the bag. There are _____dimes. There are _____ nickels.
Answer:
There are 65 dimes. There are 55 nickels.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of dimes
y is the number of nickels.
There are a total of 120 coins in the bag
This means that x + y = 120.
The total value of the coins is $9.25.
The dime is worth $0.10 and the nickel is worth $0.05. So
0.1x + 0.05y = 9.25
System:
[tex]x + y = 120[/tex]
[tex]0.1x + 0.05y = 9.25[/tex]
From the first equation:
[tex]y = 120 - x[/tex]
Replacing in the second:
[tex]0.1x + 0.05y = 9.25[/tex]
[tex]0.1x + 0.05(120 - x) = 9.25[/tex]
[tex]0.1x + 6 - 0.05x = 9.25[/tex]
[tex]0.05x = 3.25[/tex]
[tex]x = \frac{3.25}{0.05}[/tex]
[tex]x = 65[/tex]
[tex]y = 120 - x = 120 - 65 = 55[/tex]
There are 65 dimes. There are 55 nickels.
Legal descriptions tend to prefer neat straight lines from point to point, regardless of describing a square, rectangle, triangle or even a smooth circle. When might a property boundary end up being a squiggly line?
Answer:
When describing a property line drawn down the center of a creek bed
The initial population of a town in the year 2010 was 20 000. By 2014, the population had grown exponentially to 32 500 people. Write an equation to represent the population of the town (P) over time in years (n).
Answer:
P = 20000×1.625^(n/4)
Step-by-step explanation:
An exponential equation can be written using the given data:
value = (initial value)×(growth factor in period)^(n/(period))
Here, the growth is by a factor of 32500/20000 = 1.625, and the period is 4 years. Then your exponential equation is ...
P = 20000×1.625^(n/4)
Terry has a collection of 50 coins. There are only quarters and dimes in the collection. The total value of the coins is $8.00. How many dimes does he have?
Answer:
30 dimes and 20 quarters
30×.10=$3.00
20×.25=$5.00
30+20=50
$3+$5=$8
A 37 bag sample had a mean of 421 grams. Assume the population standard deviation is known to be 29. A level of significance of 0.05 will be used. State the null and alternative hypothesis.
Answer: [tex]H_0:\mu=421[/tex]
[tex]H_a : \mu\neq421[/tex]
Step-by-step explanation:
A null hypothesis is a type of hypothesis that is used in statistics that assumes there is no difference between particular characteristics of a population wheres the alternative hypothesis shows that there is a difference.Given: A 37 bag sample had a mean of 421 grams.
Let [tex]\mu[/tex] be the population mean.
Then, the null hypothesis would be:
[tex]H_0:\mu=421[/tex]
whereas the alternative hypothesis would be:
[tex]H_a : \mu\neq421[/tex]
answer if u love cats & dogs
Answer:
(7, 5.25) lies on the graph.
Step-by-step explanation:
We are given the following values
x = 4, 6, 8, 12 and corresponding y values are:
y = 3, 4.5, 6, 9
Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.
Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]y=mx+c[/tex]
where m is the slope.
(x,y) are the coordinates from where the line passes.
c is the y intercept.
Here,
[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]
Formula for slope is:
[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]
Now, the equation of line becomes:
[tex]y=\dfrac{3}{4}x+c[/tex]
Putting the point (4,3) in the above equation to find c:
[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]
So, final equation of given function is:
[tex]y=\dfrac{3}{4}x[/tex]
OR
[tex]4y=3x[/tex]
As per the given options, the point (7, 5.25) satisfies the equation.
So correct answer is [tex](7, 5.25)[/tex].
which of the following equations is equal to 2x^2+8 A. (2x-4i)(x-2i) B. (2x+4i)(x+2i) C. (2x-2i)(x+6i) D. (2x-4i)(x+2i)
Answer:
(2x-4i) (x+2i)
Step-by-step explanation:
2x^2+8
Factor out 2
2 ( x^2+4)
Writing as the difference of squares a^2 -b^2 = (a-b) (a+b)
2 ( x^2 -(2i)^2)
2 ( x-2i) (x+2i)
Multiplying the 2 into the first term
(2x-4i) (x+2i)
Suppose you were given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2). What is the value of a?
Answer:
Hope it helps..........The given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2). Hence, the value of x is 7.5.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
The given the function F(x)=x^4-2x^3+3x^2-10x+3 and the factor (x-2).
here x = 2
Substitute in the function;
F(x)=x^4-2x^3+3x^2 - ax+3
F(2) = 2^4-2(2)^3+3(2)^2 - a(2) +3
F(2) = 16 - 16 + 12 - 2a +3
F(2) = 15 - 2a
15 - 2a = 0
15 = 2a
a = 7.5
Hence, the value of x is 7.5
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the quotient of F and the product of r,s, and T
Behold the quotient of F and the product of r,s, and T: F / (r·s·T)
The numerical of the statement the quotient of F and the product of r,s, and T is F/(r×s×T).
What are quotient, remainder, divisor, and dividend?The number which is being divided is the dividend.
The number with which we are dividing is the divisor.
The result when a dividend is divided by the divisor is the quotient.
A remainder is the extra portion of a number when it isn't completely divisible.
Given, Are some variables F, r, s, and t.
Now, The product of r,s, and T is,
= r×s×T and the complete statement the quotient of F and the product of r,s, and T can be written as,
F/(r×s×T).
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