Answer:
y = 12 + 6x
y = 12x
Step-by-step explanation:
From the information provided, the following equations are derived:
y = 12 + 6x ------- Eqn 1
y = 12x ------- Eqn 2
Since Eqns 1 and 2 have the same subject, we equate them to solve for x. We have:
12x = 12 + 6x
Putting like terms together, we have:
12x - 6x = 12 ⇒ (12 - 6)x = 12
6x = 12 ⇒ x = 2
x = 2
Substitute x into Eqn 1 or 2
Eqn 1
y = 12 + 6x
y = 12 + 6(2) = 12 + 12
y = 24
Eqn 2
y = 12x
y = 12(2)
y = 24
It means that it will take Ms. Ironperson and Mr. Thoro 2 days apiece to produce the same number of posters at the current rate (which is 24 posters). Both Ms. Ironperson and Mr. Thoro will individually take 2 days to produce 24 Avenger posters apiece.
Which of the following functions is graphed below
Answer:
B
Step-by-step explanation:
If this rectangle is dilated using a scale factor of One-half through point B, what is the result? Point B is the bottom left corner of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and point B is at the bottom left corner. Point B is the bottom left corner of rectangle X. Rectangle X prime is double the size of rectangle X and is outside of rectangle X. Point B is the bottom left corner of rectangle X. Rectangle X prime is half the size of rectangle X and is outside of rectangle X.
Answer:
the first one
Step-by-step explanation:
I just took it on edge.
Answer:
It is B just took the unit quiz
Step-by-step explanation:
The table represents a function. A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12. Which value is an output of the function? –6 –2 4 7The table represents a function. A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12. Which value is an output of the function? –6 –2 4 7
Answer:
-2 is an output of the function.
Step-by-step explanation:
The given table is as follows:
[tex]\left[\begin{array}{cc}{x}&f(x)\\-6&8\\7&3\\4&-5\\3&-2\\-5&12\end{array}\right][/tex]
Here, the values written on the left side of table i.e. values of [tex]x[/tex] are known as the domain values or input values to a function.
The values written on the right side of table i.e. values of [tex]f(x)[/tex] are known as the range values or output values of the function [tex]f(x)[/tex].
Let us consider the pairs of values:
(-6,8) then left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]
i.e. when [tex]x=-6[/tex], the output value [tex]f(x) =8[/tex].
The same thing applies for all the pairs of values.
similarly for the pair (3,-2):
Left side value is of [tex]x[/tex] and right side value is of [tex]f(x)[/tex]
i.e. when [tex]x=3[/tex], the output value [tex]f(x) =-2[/tex].
So, the answer is:
-2 is an output of the function.
Answer:
-2
Step-by-step explanation:
What translation was used to ABCD to produce A’ B’C’D’
What is the mode of this set of data?
Answer:
The mode is 15
Step-by-step explanation:
The mode is the number which appears most often in a set of numbers. Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).
Answer:
The mode of this set is 15.
Step-by-step explanation:
the mode is 15 bcoz 15 is repeated two times where as other numbers aren't repeated..
A clothing store determines that in order to sell x shirts, the price per shirt should be p(x)=100−x dollars. Getting x shirts from the supplier costs the store C(x)=1,600+20x dollars. If the store’s revenue from selling x shirts is R(x)=x⋅p(x), for what value of x will the store’s cost and revenue be equal?
Answer:
x= -40
Step-by-step explanation:
Cost
C(x)=1,600+20x
P(x)=100-x
Revenue=x*p(x)
=x*(100-x)
=100x-x^2
Cost=Revenue
1600+20x=100x-x^2
1600+20x-100x+x^2=0
1600-80x+x^2=0
Solve using quadratic formula
Formula where
a = 1, b = 80, and c = 1600
x=−b±√b2−4ac/2a
x=−80±√80^2−4(1)(1600) / 2(1)
x=−80±√6400−6400 / 2
x=−80±√0 / 2
The discriminant b^2−4ac=0
so, there is one real root.
x= −80/2
x= -40
A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. If they randomly decide who
what is the probability that there are at least 3 girls in the group that watch the movle?
Answer:
53.57%
Step-by-step explanation:
We have to calculate first the specific number of events that interest us, if at least 3 are girls, they mean that 2 are boys, therefore we must find the combinations of 3 girls of 5 and 2 boys of 3, and multiply that, so :
# of ways to succeed = 5C3 * 3C2 = 5! / (3! * (5-3)!) * 3! / (2! * (3-2)!)
= 10 * 3 = 30
That is, there are 30 favorable cases, now we must calculate the total number of options, which would be the combination of 5 people from the group of 8.
# of random groups of 5 = 8C5 = 8! / (5! * (8-5)!) = 56
That is to say, in total there are 56 ways, the probability would be the quotient of these two numbers like this:
P (3 girls and 2 boys) = 30/56 = 0.5357
Which means that the probability is 53.57%
Answer:
Actually, the correct answer for plato users is option D
Step-by-step explanation:
D. 0.821
If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the
youngest
Answer:
The age difference between the youngest and the oldest is 48
A fuel oil tank is an upright cylinder, buried so that its circular top is 8 feet beneath ground level. The tank has a radius of 6 feet and is 18 feet high, although the current oil level is only 12 feet deep. Calculate the work required to pump all of the oil to the surface. Oil weighs 50\, \hbox{lb/ft}^3.
Answer:
1.504×10⁶ ft·lb
Step-by-step explanation:
We understand the top of the oil in the tank is 12 ft below ground level, and the bottom of the tank is 8+18=26 ft below ground level. Then the average depth of the oil is (12+26)/2 = 19 ft below ground level.
The height of the oil in the tank is 26-12=14 ft, so the volume of it is ...
V = πr²h = π(6 ft)²(14 ft) = 504π ft³ ≈ 1583.36 ft³
__
So, the work required to raise that volume of oil to the surface is ...
(1538.36 ft³)(50 lb/ft³)(19 ft) = 1.504×10⁶ ft·lb
Suppose U.S. consumers 21 years and older consumed 26.4 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:
H0: μ ≤ 26.4
Ha: μ > 26.4
(a) Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?
a) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence lower than throughout the United States.
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
c) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence higher than throughout the United States.
d) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence lower than throughout the United States.
(b) What is the Type I error in this situation? What are the consequences of making this error?
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
b) The type I error is not rejecting H0 when it is true. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually less than or equal to 26.4.
c) The type I error is not rejecting H0 when it is false. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually greater than 26.4.
d) The type I error is rejecting H0 when it is false. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually greater than 26.4.
(c) What is the Type II error in this situation? What are the consequences of making this error?
a) The type II error is accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is less than or equal to 26.4.
b) The type II error is not accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is not.
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
d) The type II error is not accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is greater than 26.4.
Answer:
Step-by-step explanation:
A. If the null hypothesis was rejected, the conclusion would be
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
B. The correct option is
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
C. The correct option is
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
I really need help :( anybody ??
_______________________________
Hey!!
Answer:{2,4,5}
Explanation:
RangeLet R be relation from A to B.The set of second components or the set of elements of B are called range.
Hope it helps..
_______________________________
How do I find the value of x for which line a is parallel to line b?
Answer:
x = 20
Step-by-step explanation:
3x + 6x = 180, if you make them supplementary then they will be parallel
9x = 180
x = 20
Which of the following is a geometric sequence?
Answer:
D. 1, 1/2, 1/4, 1/8, ...
Step-by-step explanation:
Only one of the listed is a geometric sequence:
D. 1, 1/2, 1/4, 1/8, ... with the common ratio 1/2According to the Rational Root Theorem, Negative two-fifths is a potential rational root of which function?
f(x) = 4x4 – 7x2 + x + 25
f(x) = 9x4 – 7x2 + x + 10
f(x) = 10x4 – 7x2 + x + 9
f(x) = 25x4 – 7x2 + x + 4
Answer:
Neither expression satisfies the given rational root.Step-by-step explanation:
To find the right answer, we just need to replace the given root in each expression and see which one gives zero.
First expression.[tex]f(x)=4x^{4} -7x^{2} +x+25\\f(-\frac{2}{5})= 4(-\frac{2}{5})^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+25=\frac{64}{625}-\frac{28}{25} -\frac{2}{5} +25 \approx 23.58[/tex]
Second expression.[tex]f(x)=9x^{4}-7x^{2} +x+10=9(-\frac{2}{5} )^{4} -7(-\frac{2}{5} )^{2} +\frac{2}{5} +10 \approx 9.5[/tex]
Third expression.[tex]f(x)=10x^{4}-7x^{2} +x+9=10(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+9 \approx 7.7[/tex]
Fourth expression.[tex]f(x)=25x^{4}-7x^{2} +x+4=25(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+4 \approx 3.12[/tex]
Therefore, neither expression satisfies the given rational root.
Answer:
D. f(x) = 25x^4 - 7x^2 + x + 4.
Step-by-step explanation:
The correct answer to your question is D.
Which of the following sets would have a graph with an open circle on 5 and a ray pointing right on the number line?
The open circle means we do not include the endpoint, hence the use of a greater than symbol. If we were to include the endpoint, then we'd have greater than or equal to. We can rule out choice B due to this reasoning.
The ray pointing to the right indicates we are talking about x values larger than 5, so we can rule out choice A and conclude the answer is C.
Side note: The notation [tex]x \in \mathbb{R}[/tex] is saying "x is a real number"
What is the solution to this equation?
10x - 3(x- 6) = x + 30
O A. x = 8
O B. x = 2
C. X= 4
[tex]answer \\ 2\\ solution \\ 10x - 3(x - 6) = x + 30 \\ or \: 10x - 3x + 18 = x + 30 \\ or \: 10x - 3x - x = 30 - 18 \\ or \: 7x - x = 12 \\ or \: 6x = 12 \\ or \: x = \frac{12}{6} \\ x = 2 \\ hope \: it \: helps[/tex]
Answer:
x=2
Step-by-step explanation:
10x - 3(x- 6) = x + 30
Distribute
10x -3x+18 = x+30
Combine like terms
7x + 18 = x+30
Subtract x from each side
6x+18 = 30
Subtract 18 from each side
6x = 30-18
6x = 12
Divide by 6
6x/6 = 12/6
x =2
Let A be an n # n matrix, b be a nonzero vector, and x0 be a solution vector of the system Ax D b. Show that x is a solution of the nonhomogeneous system Ax D b if and only if y D x!x0 is a solution of the homogeneous system Ay D 0.
Complete Question
Let A be an n x n matrix, b be a nonzero vector, and x_0 be a solution vector of the system Ax = b. Show that x is a solution of the non-homogeneous system Ax = b if and only if y = x - x_0 is a solution of the homogeneous system Ay = 0.
Answer:
Step-by-step explanation:
From the question we are told that
A is an n × n matrix
b is a zero vector
[tex]x_o[/tex] us the solution vector of [tex]Ax = b[/tex]
Which implies that
[tex]Ax_o = b[/tex]
So first we show that
if [tex]x[/tex] is the solution matrix of [tex]Ax = b[/tex]
and [tex]y= x-x_o[/tex] is the solution of [tex]Ay = 0[/tex]
Then
[tex]A(x-x_o) = 0[/tex]
=> [tex]Ax -Ax_o = 0[/tex]
=> [tex]b-b = 0[/tex]
Secondly to show that
if [tex]y= x-x_o[/tex] is the solution of [tex]Ay =0[/tex]
then x is the solution of the non-homogeneous system
[tex]Ax = b[/tex]
Now we know that [tex]y = x-x_o[/tex] is the solution of [tex]Ay =0[/tex]
So
[tex]Ay = 0[/tex]
=> [tex]A(x- x_o) = 0[/tex]
=> [tex]Ax - Ax_o = 0[/tex]
=> [tex]Ax - b = 0[/tex]
=> [tex]Ax = b[/tex]
Thus this has been proved
Please answer this correctly
Answer:
1607.68 square miles
Step-by-step explanation:
use pi r squared
Answer:
Step-by-step explanation:
diameter = 64 miles
r =64/2 = 32 miles
Area of semicircle = πr²/2
= 3.14*32*32/2
= 1607.68 sq.miles
2/5 of the members of a school band are 6th graders. What percent of
the students in the band are non-sixth graders?
Answer:
60%
Step-by-step explanation:
3/5 is 60%
Answer:
60%
Step-by-step explanation:
5/5 minus 2/5 is 3/5
5 divided by 3 is .6
in order to find out the percent move the decimal over to the right
What is the measure of
55°
The sum or measures of interior angle in a triangle is 180°.
Angle A, 35° + Angle C, 90° =125°
Angle B= 180°-125°=55°[angle B]
600000000*100000000000000000000000000000000000000000000
Answer:
6e+52
Step-by-step explanation:
cAlCuLaToR
Answer:
6e+52
Step-by-step explanation:
multiply
What percentage of the total number of microstates are in one of the three most likely macro states of 100 coins being tossed (49 heads and 51 tails, 50 heads and 50 tails, or 51 heads and 49 tails)
Answer:
Step-by-step explanation:
Idk
Indicate in standard form equation of the line passing through the given 
Answer:
x + y = 6
Step-by-step explanation:
slope is rise/run so -6/6 = -1
y = -x+b
solve for b by plugging in any point
6 = 0 + b -> b = 6
y = -x+6
x + y = 6
(-1/4 - 1/2) ÷ (-4/7)
Answer:
1 5/16
Step-by-step explanation:
(-1/4 - 1/2) ÷ (-4/7)
PEMDAS says parentheses first
Get a common denominator
(-1/4 - 2/4) ÷ (-4/7)
(-3/4) ÷ (-4/7)
Copy dot flip
-3/4 * -7/4
21/16
Change to a mixed number, 16 goes into 21 1 time with 5 left over
1 5/16
A 50 ft kite string is flying on the beach above an umbrella. You are holding the end
of the string and are 12 feet from the umbrella. How high in the air is the kite flying?
Round to the nearest degree.
Answer:
The height of the kite is 48.54 feet
The angle of elevation is 76.11°
Step-by-step explanation:
To find the height of the kite, we can use the Pythagoras' theorem in the triangle created by the length of the string (hypotenuse), the height of the kite and the distance to the umbrella (catheti).
Then, we have:
50^2 = 12^2 + height^2
height^2 = 2500 - 144
height^2 = 2356
height = 48.54 ft
So the kite is 48.54 feet high in the air.
The angle of elevation can be calculated using the cosine relation:
cos(angle) = 12 / 50
cos(angle) = 0.24
angle = 76.11°
Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?
Flip a fair two sided coin 4 times. Find the probability the first or last flip is a tail.
Answer:
1/4
Step-by-step explanation:
Flip a fair two sided coin 4 times, the probability the first or last flip is a tail is
P = (1/2) x 1 x 1 x (1/2) = 1/4
(The probability of getting tail in first flip = 1/2, in the 2nd and 3rd flip, tail and head are both accepted, the probability of getting tail in last flip = 1/2)
Hope this helps!
Ariana is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Arians will earn $40 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Ariana earned a total of $500 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Arianas songs were played. Define the variables that you use to write the system.
Answer:
Commercials x = 7
Movies y = 2
Step-by-step explanation:
Let commercials = x
Let's movies = y
$40 is for commercials
$110 is for movies.
Commercials plus movies for the Year = 9
She earned total of $500
X+ y = 9..... equation 1
40x + 110y = 500.... Equation 2
Multipling equation one by 40
40x + 40y = 360
Subtracting equation one from equation 2
70y = 140
Y = 2
If y = 2
X + y = 9
X + 2 = 9
X = 9-2
X = 7
16. Model with Math What must be the sum of
the two remaining numbers, x and y? Write an
equation to show how to find this sum.
Answer:
The sum of the two remaining numbers, x and y = 60
Question:
The question isn't clear enough as some information have been omitted. Let's consider the following:
Model with Math. The average of six numbers is 18. If the average of four numbers is 12. What must be the sum of the two remaining numbers, x and y?
Write an equation to show how to find this sum.
Step-by-step explanation:
Mathematical models are applied to represent things in the real world in order to solve problems.
The formula we would use to solve this problem is an example of a mathematical model.
Types of mathematical model we can use include equations and graphs.
Using equations:
Average of six numbers = 18
Average of four of the numbers = 12
Total sum of the four numbers = 4×12 = 48
the two unknown numbers are x and y
Average of six numbers = (Sum of all 6 numbers)/6
=(Total sum of four numbers + x + y)/6
(48 + x + y)/6 = 18
The equation that shows how to find the sum:
(1/6)(48 + x + y) = 18
48 + x + y = 18×6
48 + x + y = 108
x + y = 108-48
x+y = 60
The sum of the two remaining numbers, x and y = 60
Suppose that the functions p and q are defined as follows.
Answer:
Step-by-step explanation:
Hello,
qop(2)=q(p(2))
p(2) = 4+3=7
[tex]q(7) = \sqrt{7+2}=\sqrt{9}=3[/tex]
so
qop(2)=3
and poq(2)=p(q(2))
[tex]q(2)=\sqrt{2+2} = \sqrt{4}=2[/tex]
p(2) = 7
so poq(2)=7
thanks
The answer is "[tex]\bold{(q \circ p)(2)= 3}\ and \ \bold{(p \circ q)(2)=7}[/tex]" and the further explanation can be defined as follows;
Given:
[tex]\to \bold{p(x)=x^2+3}\\\\\to \bold{q(x)=\sqrt{x+2}}[/tex]
Find:
[tex]\bold{(q \circ p)(2)=?}\\\\\bold{(p \circ q)(2)=?}[/tex]
Solve the value for [tex]\bold{(q \circ p)(2)}\\\\[/tex]:
[tex]\to \bold{(q \circ p)(2)= q \circ p(2) =q(p(2))}\\\\[/tex]
[tex]\therefore\\\\ \to \bold{p(2)=2^2+3= 4+3=7}\\\\\ \because \\\\ \to \bold{q(p(2))=\sqrt{7+2}=\sqrt{9}=3}[/tex]
Solve the value for [tex]\bold{(p \circ q)(2)}\\\\[/tex]:
[tex]\to \bold{(p \circ q)(2)= p \circ q(2)= p (q(2))}\\\\[/tex]
[tex]\therefore\\\\ \to \bold{q(2)=\sqrt{2+2}=\sqrt{4}=2}\\\\\ \because \\\\ \to \bold{p(q(2))=2^2+3= 4+3=7}[/tex]
Therefore the final answer of "[tex]\bold{(q \circ p)(2)= 3}\ and \ \bold{(p \circ q)(2)=7}[/tex]"
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