Answer:
y = 3
Step-by-step explanation:
9 - y = 2y
+ y + y Add y to both sides
9 = 3y Divide both sides by 3
3 = y When y = 3, the value of 9 - y is twice the value of y.
Which equation is equivalent
Answer:
(4x^2 +9) (4x^2 -9) =0
Step-by-step explanation:
16x^4 - 81 =0
Rewriting
(4x^2) ^2 - 9^2 =0
This is the difference of squares a^2 -b^2 = (a+b)(a-b)
(4x^2 +9) (4x^2 -9)=0
The transformation from function f(x) =3x to the function f(x)=3x-2
Answer:
Translation down 2 units
Step-by-step explanation:
If a number is added or subtracted like that at the end of a function, it will either lift or put down a function however many units the number says. In this case, the number says 2, so the transformation would be a "Translation down 2 units".
How many real solutions does this system of equations have? x2+y2=363x−y+1=0 A. 0 B. 3 C. 2 D. 1
Answer:
Correct option: C -> 2
Step-by-step explanation:
The first equation is:
[tex]x^2+y^2=363[/tex]
And the second equation is:
[tex]x-y+1=0[/tex]
From the second equation, we have:
[tex]y = x + 1[/tex]
Using this value of y in the first equation, we have:
[tex]x^2 + (x+1)^2 = 363[/tex]
[tex]x^2 + x^2 + 2x + 1 = 363[/tex]
[tex]2x^2 + 2x= 362[/tex]
[tex]x^2 + x - 181 = 0[/tex]
Calculating the discriminant Delta, we have:
[tex]\Delta = b^2 - 4ac = 1 + 4*181 = 725[/tex]
We have [tex]\Delta > 0[/tex], so we have two real values for x, therefore we have two solutions for this system.
Correct option: C.
(If the system of equation is actually:
[tex]x^2+y^2=36[/tex]
[tex]3x-y+1=0[/tex]
We would have:
[tex]y = 3x + 1[/tex]
[tex]x^2+(3x+1)^2=36[/tex]
[tex]x^2+9x^2+6x+1=36[/tex]
[tex]10x^2+6x-35=0[/tex]
[tex]\Delta = 36 + 1400 = 1436[/tex]
We also have [tex]\Delta > 0[/tex], so we have two solutions for this system.
Correct option: C.)
Answer:
A. 0
second part: C. The boats' paths do not cross each other
Given that
R
=
2
x
+
9
y
Find
x
when
y
=
3
and
R
=
13
.
Answer:
-7
Step-by-step explanation:
To find x, substitute the values and solve.
R = 2x + 9y
It becomes:
2x + 27 = 13
Rearrange and solve
2x = -14
x = -7
Hope this helps
Answer:
x=-7
Step-by-step explanation:
We are given the expression:
R=2x +9y
We want to find x when R=13 and y=3. Therefore, we must substitute the numbers in for the variables.
13=2x+9(3)
Multiply 9 and 3.
13=2x+27
Now we must solve for x by isolating x on one side of the equation.
27 is being added to 2x. The inverse of addition is subtraction, so subtract 27 from both sides.
13-27=2x+27-27
13-27=2x
-14=2x
x is being multiplied by 2. The inverse of multiplication is division, so divide both sides by 2.
-14/2=2x/2
-14/2=x
-7=x
x=-7
what is the most efficient first step to isolate the variable term on one side of this equation?
-9x=-4x+5
Answer:
Add 4x to both sides
Step-by-step explanation:
on Edge
Highschool students were surveyed about which math and science
Answer:
Starting with Algebra going down is 73%, 70%, 72%
Geometry going down is 27%, 30%, 28%
Totals going down 100%, 100%, 100%
(LOL)
Hope that was helpful.Thank you!!!
Step-by-step explanation:
Add: x5 - 4x + + 7x3 + 8, 9x 3 + 7x2 - 10, and -2x 5 + 7x4 - 3x + 8.
ED
Step-by-step explanation:
x5 - 4x + 7x3 + 8 + 9x3 + 7x2 - 10 - 2x5 + 7x4 - 3x + 8
Arranging
x5 - 2x5 + 7x4 + 7x3 + 9x3 + 7x2 - 4x - 3x + 8 - 10 +8
-1 + 7x4 + 16x3 + 7x2 - 7x + 6
7x4 + 16x3 + 7x2 - 7x + 5
In a class of 25 students, 15 of them have a cat,
16 of them have a dog and 3 of them have neither.
Find the probability that a student chosen at random
has a cat and a dog.
So 3 have no pets, so 25 - 3 = 22 students have a pet.
There are 15 cats and 16 dogs so 15 + 16 = 31.
And then 31 - 22 = 9. The 9 means that 9 students have both pets.
So the probability is 9/25.
Answer:
number of students who have cat and dog
= y
= 9
P( student chosen has a dog and cat )
= 9/25
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 5929 with a mean life of 941 minutes. If the claim is true, in a sample of 109 batteries, what is the probability that the mean battery life would be greater than 948.8 minutes? Round your answer to four decimal places.
Answer:
"The probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.
Step-by-step explanation:
In this case, the quality control expert takes a sample of batteries. From these batteries, we want to find "the probability that the mean battery life would be greater than 948.8 minutes".
Different concepts needed to take into account to solve this question
Sampling Distribution of the Means
For doing this, we need to use the sampling distribution of the means, which results from taking the mean for each possible sample coming from a random variable [tex] \\ x[/tex]. Roughly speaking, each sample will have a different mean, [tex] \\ \overline{x}[/tex], and the probability distribution for any of these means is called the sampling distribution of the means.
The sampling distribution of the means has a mean that equals the population's mean for the random variable [tex] \\ x[/tex], i.e., [tex] \\ \mu[/tex], and its standard deviation is [tex] \\ \frac{\sigma}{\sqrt{n}}[/tex]. We can express this mathematically as:
[tex] \\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex] [1]
Standardized Values for [tex] \\ \overline{x}[/tex]
We can standardized the values for [tex] \\ \overline{x}[/tex] using z-scores:
[tex] \\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]
This random variable [tex] \\ Z[/tex] follows a standard normal distribution, that is, [tex] \\ Z \sim N(0,1)[/tex], and it is easier to find probabilities since the values for them are tabulated in the standard normal table (available in any Statistics book or on the Internet.)
What type of distribution follows the sampling distribution of the means?
A general rule of thumb is that this distribution (the sampling distribution of the means) follows a normal distribution if the sample size, [tex] \\ n[/tex], is bigger than or equal to 30 observations, or [tex] \\ n \geq 30[/tex]. In this case, [tex] \\ n = 109[/tex] batteries. This is a result from the Central Limit Theorem, fundamental in Statistical Inference.
Standard Deviation
We have to remember that the standard deviation is the square root of the variance [tex] \\ \sigma^2[/tex], or [tex] \\ \sqrt{\sigma^2}[/tex].
[tex] \\ \sigma^{2} =5929[/tex][tex] \\ \sigma = \sqrt{5929} = 77[/tex]Therefore, the standard deviation in this case is [tex] \\ \sigma = 77[/tex] minutes.
In sum, we have the following information to answer this question:
[tex] \\ \sigma = 77[/tex] minutes.[tex] \\ \mu = 941[/tex] minutes.[tex] \\ n = 109[/tex] batteries (the sample size is large enough to assume that the sampling distribution of the means follows a normal distribution).[tex] \\ \overline{x} = 948.8[/tex] minutes.What is the probability that the mean battery life would be greater than 948.8 minutes?
Well, having all the previous information, we can use [2] to solve this question (without using units):
[tex] \\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex] \\ z = \frac{948.8 - 941}{\frac{77}{\sqrt{109}}}[/tex]
[tex] \\ z = \frac{7.8}{\frac{77}{\sqrt{109}}}[/tex]
[tex] \\ z = \frac{7.8}{7.37526}[/tex]
[tex] \\ z = 1.05758 \approx 1.06[/tex]
This result is the standardized value or z-score for [tex] \\ \overline{x}[/tex], considering [tex] \\ \mu = 941[/tex] and [tex] \\ \sigma = 77[/tex].
We round z to two decimals digits since standard normal table only uses it as an entry to find probabilities.
With [tex] \\ z = 1.06[/tex], we can consult the cumulative standard normal table. First, we need to find with [tex] \\ z = 1.0[/tex] in the first column in the table. Then, in its first raw, we need to find +0.06. The intersection for these two values determines the cumulative probability for [tex] \\ P(z<1.06)[/tex].
It is important to recall that [tex] \\ P(z<1.06) = P(\overline{x}<948.8)[/tex] because [tex] \\ z = 1.06[/tex] is the standardized value for [tex] \\ \overline{x} = 948.8[/tex] minutes.
Then, [tex] \\ P(z<1.06) = 0.8554[/tex]
However, the question is about [tex] \\ P(\overline{x} > 948.8) = P(z>1.06)[/tex]
And
[tex] \\ P(\overline{x} > 948.8) + P(\overline{x} < 948.8) = 1 [/tex]
Or
[tex] \\ P(z>1.06) + P(z<1.06) = 1[/tex]
Then
[tex] \\ P(z>1.06) = 1 - P(z<1.06)[/tex]
[tex] \\ P(z>1.06) = 1 - 0.8554[/tex]
[tex] \\ P(z>1.06) = 0.1446[/tex]
Therefore, "the probability that the mean battery life would be greater than 948.8 minutes" is 0.1446.
Which rate can you set StartFraction 30 miles Over 1 hour EndFraction equal to in order to find the time it takes to travel 900 miles at 30 miles per hour?
Answer:
[tex]\dfrac{30\,\text{mi}}{1\,\text{h}}=\dfrac{900\,\text{mi}}{t}[/tex]
Step-by-step explanation:
Since you have miles in the numerator of your rate, you need miles in the numerator of the equivalent fraction:
[tex]\dfrac{30\,\text{mi}}{1\,\text{h}}=\dfrac{900\,\text{mi}}{t}[/tex]
This can be rearranged to ...
[tex]\dfrac{t}{1\,\text{h}}=\dfrac{900\,\text{mi}}{30\,\text{mi}}=30[/tex]
Then, multiplying by 1 h gives the solution ...
t = 30 h
It takes 30 hours to travel 900 miles at 30 miles per hour.
the answer is:
d. 900/? hours
Which statement forms part of cell theory?
A.
Cell organelles are capable of reproducing themselves.
B.
Cells differ in shape, but they have identical components.
C.
All cells begin life as prokaryotic cells.
D.
All living things are made up
of cells.
Answer:
D. All living things are made up of cells.
Step-by-step explanation:
D. All living things are made up of cells.
O The cell theory is a widely accepted principle of biology. Scientists that contributed to the cell theory include; Theodor Schwann, Matthias Schleiden, and Rudolph Virchow.
The cell theory states that;
O All living organisms are made up of cells and they may be unicellular or multicellular.
O The cell is the basic structural and functional unit of life.
Cells arise from pre-existing cells.
BRAINLIEST!!!!!!BRAINLIEST!!!! BRAINLIEST!!!!!!BRAINLIEST!!!! BRAINLIEST!!!!!!BRAINLIEST!!!! BRAINLIEST!!!!!!BRAINLIEST!!!!
Answer:
B
Step-by-step explanation:
Answer:2x+4(C)
Step-by-step explanation:
Since all of the variables have integer exponents that are positive this is a polynomial.
Match each function formula with the corresponding transformation of the parent function y = (x - 1)2 1. y = - (x - 1)2 Translated up by 1 unit 2. y = (x - 1)2 + 1 Translated left by 4 units 3. y = (x + 1)2 Translated right by 1 unit 4. y = (x - 2)2 Translated down by 3 units 5. y = (x - 1)2 - 3 Reflected over the x-axis 6. y = (x + 3)2 Reflected over the y-axis
Answer:
1. [tex]y = - (x - 1)^{2}[/tex], Reflected over the x-axis.
2. [tex]y = (x - 1)^{2} +1[/tex] , Translated up by 1 unit.
3. [tex]y = (x + 1)^{2}[/tex] , Reflected over y-axis
4. [tex]y = (x - 2)^{2}[/tex] ,Translated right by 1 unit.
5. [tex]y = (x - 1)^2 - 3[/tex], Translated down by 3 units
6. [tex]y = (x + 3)^2[/tex], Translated left by 4 units.
Step-by-step explanation:
Given that:
Parent function: [tex]y = (x - 1)^{2}[/tex] Please refer to attached Graph4.
1. [tex]y = - (x - 1)^{2}[/tex] Sign of y is changed from + to -, so it gets reflected over x axis. Please refer to attached Graph3.
2. [tex]y = (x - 1)^{2} +1[/tex]: 1 is added to y to translated up (positive y by 1 unit). Please refer to attached Graph3.
3. [tex]y = (x + 1)^{2}[/tex] , Reflected over y-axis, please refer to attached Graph4.
4. [tex]y = (x - 2)^{2}[/tex] : 1 is subtracted from x , it gets Translated right by 1 unit. Please refer to attached Graph5.
5. [tex]y = (x - 1)^2 - 3[/tex], 3 subtracted from y so it getss translated down by 3 units. Please refer to attached Graph6.
6. [tex]y = (x + 3)^2[/tex], 4 added to x, so it gets translated left by 4 units. Please refer to attached Graph5.
Answer:
the other guys answer
Step-by-step explanation:
sorry we have been about your car extended warranty this is are last call
help me asap pleaseeee
Answer:
Last option is the correct choice.
Step-by-step explanation:
[tex]\frac{36}{24}=\frac{12}{x}\\\\\Rightarrow x=8[/tex]
Best Regards!
Is this no solution or is there a solution?
This is solving systems of linear equations by graphing.
Step one is to graph each equation.
Step two is to find the point of intersection which is the solution.
Answer:
No Solution
Step-by-step explanation:
I used a graphing tool to graph the equations. When graphed, the lines are parallel and they do not intercept at a point.
There is no solution; your answer should be correct.
Answer:
yes it is no solution
Step-by-step explanation:
this is because since they both have the same slope, that means the two lines are parallel
and so therefore they will never intersect
so the answer is no solution
If the perimeter of triangle ABC is 4 more than the perimeter of triangle ACD, what is the perimeter of quadrilateral ABCD? AD is 5, DC is 6, AC is unknown, AB is unknown, CB is 7.
Answer:
26 units.
Step-by-step explanation:
AB + BC + AC = AC + AD + DC + 4
AC is common so
AB + BC = AD + DC + 4
AB + BC - AD - DC = 4
Substituting the given values
AB + 7 - 5 - 6 = 4
AB = 4 - 7 + 5 + 6 = 8
So the perimeter of ABCD
= AB + BC + AD + CD
= 8 + 7 + 5 + 6
= 26.
The diagram shows A(-3, 5) and B(8,1).
What is the distance between the points?
Enter your answer as a number, without units.
Round your answer to one decimal place, if necessary, like this: 42.5
Answer:
11.7
Step-by-step explanation:
You can form a right triangle with these points with a base of 11 and height of 4 with the third point as (-3, 1).
Using the Pythagorean Theorem, we get:
[tex]11^2+4^2=c^2\\121+16=c^2\\137=c^2\\c^2=137\\c=\sqrt{137}\\c=11.7[/tex]
The distance from A to B is roughly 11.7 units long.
The answers is AB= 12.5.
What is graph?The graph is nothing but an organized representation of data. It helps us to understand the data. Data are the numerical information collected through observation.
The word data came from the Latin word Datum which means “something given”
After a research question is developed, data is being collected continuously through observation. Then it is organized, summarized, classified, and then represented graphically.
As, per the graph
the base = 11 units and the height = 6 units
So, Using Pythagoras theorem,
11² + 6² = AB²
121+36 = AB²
157= AB²
AB = √157
hence, AB= 12.529
Learn more about graph here:
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Oil flows back and forth between a small and large tank. When oil is moving into the large tank, the flow rate is
positive. When oil is moving into the small tank, the flow rate is negative.
The large tank begins with 600 gallons of oil. The flow rate is recorded as-4 gallons per minute. After a period of 32
minutes, how much oil has been moved and to which tank?
1289 into the large v tank.
After the 32 minutes, how much oil is in the large tank? gallons
Answer:
✔ 128
into the
✔ small
tank.
After the 32 minutes, how much oil is in the large tank?
✔ 472
gallons
Step-by-step explanation: Just did it on Edge
Using the given flow rate and time we found that after a period of 32 minutes 128 gallons of oil is moved from large tank to small one. The oil in large tank after 32 minutes is 472 gallons.
What is rate of work done?Rate of work done is the amount of work done per unit time
rate of work done = amount of work / time taken
Given that flow rate is positive when oil is moving in large tank and rate of flow is negative when oil is moving in small tank
Given that flow rate is recorded -4 gallons per minute, which is negative .
It means that the oil is flowing in the small tank.
Rate of flow, r is 4 gallons per minutes , here work is oil flowing into a tank
Rate of flow, r = oil flown in a tank / time taken
Given that time, t = 32 minutes
∴ rate of flow × time taken = Oil flown in small tank
⇒ r× t = oil flown in small tank = 4 × 32 = 128 gallons
Initially oil in large tank = 600 gallons
Thus, 128 gallons are moved from large tank to small tank in 32 minutes
After 32 minutes remaining oil in large tank = 600 - 128 = 472 gallons
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Four friends’ typing speeds are shown. Who is the fastest? Monica: 10 words in 1 4minute Rachel: 55 words in 5 6minute Charlie: 42 words in 3 4minute Daniel: 25 words in 1 2minute
Answer:
Daniel
Step-by-step explanation:
By far
[25 points!] Please help! Answer this for meee ! xo :)
Answer:
C (rad 2 x rad 5 x rad 2 x rad 5)
Step-by-step explanation:
rad 2 times rad 5 = rad 10
rad 10 times 2 = rad 20
rad 20 times rad 5 = rad 100
rad 100 = 10
10 is rational
What is the measure of env (5x+57)degrees
Answer:
D) 132°
Step-by-step explanation:
8x+12=5x+57 subtract 5x from both sides
3x+12=57 subtract 12 from both sides
3x= 45 divide by 3 from both sides
X=15
5(15)+57=132°
The difference of 2 numbers is 2 and their product is 80
Please respond quick
Answer:
8 and 10
Step-by-step explanation:
10-8=2
10*8=80
Answer:
list factors of 80
1,80
2,40
4,20
5,16
8,10
Which factors have a difference of 2?
80-1=79
40-2=38
20-4=16
16-5=11
10-8=2
10 and 8 have a difference of 2 so 10 and 8 is the answer. Hope this helps
Step-by-step explanation:
What is the divisble test for 861?
Answer:
7 is the correct answer
Solve for X X=6 X=15 X=30 X=90
Answer:
x=30
Step-by-step explanation:
4x+2x=180
6x=180
x=30
The value of x will be 30 for the given supplementary angles.
What are supplementary angles?Supplementary angles are those angles that sum up to 180 degrees. For example, angle 110° and angle 70° are supplementary angles because the sum of 110° and 70° is equal to 180°.
Given ∠EAF and ∠BAF are supplementary angles
Since sum of two supplementary angles = 180
Thus,
∠EAF + ∠BAF = 180
2x + 4x = 180
6x = 180
x = 30
therefore, the value of x will be 30 for the given supplementary angles.
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Type the expression that results from the following series of steps: Start with t, add 6, multiply by 2, then subtract 5.
Answer:
2(t + 6) - 5
Step-by-step explanation:
If we are strictly following the directions, we first add t and 6 together:
t + 6
Then we multiply by 2 AFTER we add the 2 together:
(t + 6)2
At last, we subtract 5 from everything after:
2(t + 6) - 5
And we have our answer!
Answer:
2(t+6)-5
Step-by-step explanation:
The unknown number is t
=> Adding 6 will make it t+6
=> Multiplying by 2 will make it 2(t+6)
=> Subtracting 5 will make it 2(t+6)-5
A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:
Education 3 4 6 2 5 4 8 0
Salary $40 36 56 35 72 47 107 52
a) Find the sample regression equation for the model: Salary = ?0 + ?1Education + ?. (Round intermediate calculations to 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.)
b) Interpret the coefficient for education.
c) What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.)
Answer:
A.) ŷ = 7X + 27.625
B.) check Explanation
C.) $77,000
Step-by-step explanation:
Given the following :
Education(x) : 3 4 6 2 5 4 8 0
Salary (y) : $40 36 56 35 72 47 107 52
A.) Using the linear regression calculator :
ŷ = 7X + 27.625
Salary = 7(education) + 27.625
B.) The Coefficient for education refers to the gradient or slope of the linear graph, the Coefficient is the ratio of the change in salary earned to education. The slope, which is the Coefficient of education is 7.
C.)What is the predicted salary for an individual who completed 7 years of higher education?
ŷ = 7X + 27.625
Salary = 7(education) + 27.625
Salary = 7(7) + 27.625
Salary = 49 + 27.625
Salary = $76.625
Salary = $77,000 ( nearest whole number)
4 x - 6 = 10 x - 3 pls answer
Answer:
[tex]x=-1/2[/tex]
Step-by-step explanation:
[tex]4 x - 6 = 10 x - 3[/tex]
[tex]4 x -10x= - 3+6[/tex]
[tex]-6x=3[/tex]
[tex]-6x/6=-3/6[/tex]
[tex]x=-1/2[/tex]
Answer:
[tex]x = - \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]4x - 6 = 10x - 3 \\ - 6 + 3 = 10x - 4x \\ - 3 = 6x \\ \frac{ - 3}{6} = \frac{6x}{6} \\ x = - \frac{1}{2} [/tex]
What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 2x + y - 1 = 0? 2x - y - 4 = 0 2x + y - 4 = 0 2x + y + 4 = 0
Answer:
2x + y - 4 = 0
Step-by-step explanation:
slope = -2
y = mx + b
2 = -2(1) + b
4 = b
y = -2x + 4
2x + y - 4 = 0
Answer:
the answer is 2x + y - 4 = 0
Step-by-step explanation:
me and my friend did the math and got 2x + y - 4 = 0
Here is a map of a town. It has a scale of 1 : 200,000. A centimetre ruler is shown on the map. What is the real-life distance between the park and the theatre? Give your answer in km.
Answer:
6km
Step-by-step explanation:
==>Given:
Map scale = 1 : 200,000
Distance on map between the park and the theatre = 3cm
==>Required:
Real life distance between the town and the theatre in km
==>Solution:
Note: the map scale given means 1cm on the map represents 200,000 cm in real life.
For a map distance of 3 cm between the town and the theatre, the real life distance would be:
3 × 200,000 = 600,000 cm
=>Convert to km
Thus, 100,000cm = 1km
Therefore, 600,000cm = 6km
Real life distance between the town and the theatre = 6km
determine domain and range for f(x)=72-12x
Answer:
Domain: All real numbers
Range: All real numbers
Step-by-step explanation:
Domain is all the x-value inputs that can be used in the equation.
Range is all the y-value outputs that can be used in the equation.
Since the equation is linear, any value of x and y would work for both domain and range, so both are (negative infinity, positive infinity).