what is the equation of the line in standard form through each point? (3,1) & perpendicular to -4c + y - 1= 0
Answers
Related Questions
I can’t figure this out!! My answer is way different then the book!
Answers
Given:
\(\frac{1}{3}p^3\text{ + }\frac{3}{4}p^2\text{ - p -\lbrack}\frac{1}{2}p^3\text{ + }\frac{1}{3}p^2\text{ + }\frac{1}{2}p]\)Simplifying:
\(\begin{gathered} =\text{ }\frac{1}{3}p^3\text{ + }\frac{3}{4}p^2\text{ - p -}\frac{1}{2}p^3\text{ - }\frac{1}{3}p^2\text{ - }\frac{1}{2}p \\ Collect\text{ like terms} \\ =\text{ }\frac{1}{3}p^3\text{ - }\frac{1}{2}p^3\text{ + }\frac{3}{4}p^2\text{ - }\frac{1}{3}p^2\text{ - p - }\frac{1}{2}p \end{gathered}\)Simplifying further:
\(\begin{gathered} =\text{ }\frac{2-3}{6}p^3\text{ +}\frac{9-4}{12}\text{ p}^2\text{ +}\frac{-2-1}{2}p \\ =-\frac{1}{6}p^3\text{ + }\frac{5}{12}p^2\text{ - }\frac{3}{2}p \end{gathered}\)Answer:
\(=-\frac{1}{6}p^3\text{ + }\frac{5}{12}p^2\text{ - }\frac{3}{2}p\)g) (-6t + 2z) - (7z - 7t)
Answers
Answer:
-13t - 5z
Step-by-step explanation:
-6t + 2z - 7z - 7t
= -13t - 5z
Given a
6 and a common
difference of – 12, find the
18th term in the sequence.
Answers
Answer:-210
Step-by-step explanation:6, -6, -18, so, you multiply -12 by 18, and you can find that number. -12 times 18=-216, and -216+the first number 6, equals 210
a solid is composed of a cube with a side length of $6$ meters and a hemisphere with a diameter of $6$ meters. find the volume of the composite solid. round your answer to the nearest hundredth.
Answers
The volume of the composite solid made up of a cube with a side length of 6 meters and a hemisphere with a diameter of 6 meters can be found by adding the volume of the cube and the volume of the hemisphere, which yields 216 + 56.55approx 2762.55 cubic meters rounded to the nearest hundredth.
First, let's find the volume of the cube. The formula for the volume of a cube is V = s^3, where V is the volume and s is the side length. In this case, the side length is 6 meters. So, the volume of the cube is:
V_cube = 6^3 = 216 cubic meters
Next, we'll find the volume of the hemisphere. The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius. Since we're dealing with a hemisphere, we'll need to take half of the sphere's volume. The diameter of the hemisphere is 6 meters, which means the radius is 3 meters. The volume of the hemisphere is:
V_hemisphere = 0.5 * (4/3)π(3)^3 = 0.5 * (4/3)π(27) ≈ 56.55 cubic meters
Now, we'll add the volume of the cube and the volume of the hemisphere to find the total volume of the composite solid:
V_total = V_cube + V_hemisphere ≈ 216 + 56.55 ≈ 272.55 cubic meters
Rounded to the nearest hundredth, the volume of the composite solid is approximately 272.55 cubic meters.
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Russel has a biased coin for the which the probability of getting tails is an unknown p. He decide to flip the coin n and writes the total number of times X he gets tails. How large should n be in order to know with at least 0.95 certainty that the true p is within 0.1 of the estimate X/n ? What if he wants 0.99 certainty?
Answers
n should be a whole number, we round up to the nearest integer, giving n = 540. Therefore, if Russel wants 0.99 certainty, n should be at least 540.
To determine how large n should be in order to have a certain level of certainty about the true probability p, we can use the concept of confidence intervals.
For a binomial distribution, the estimate of the probability p is X/n, where X is the number of successes (in this case, the number of times tails is obtained) and n is the number of trials (the number of times the coin is flipped).
To find the confidence interval, we need to consider the standard error of the estimate. For a binomial distribution, the standard error is given by:
SE = sqrt(p(1-p)/n)
Since p is unknown, we can use a conservative estimate by assuming p = 0.5, which gives us the maximum standard error. So, SE = sqrt(0.5(1-0.5)/n) = sqrt(0.25/n) = 0.5/sqrt(n).
To ensure that the true p is within 0.1 of the estimate X/n with at least 0.95 certainty, we can set up the following inequality:
|p - X/n| ≤ 0.1
This inequality represents the desired margin of error. Rearranging the inequality, we have:
-0.1 ≤ p - X/n ≤ 0.1
Since p is unknown, we can replace it with X/n to get:
-0.1 ≤ X/n - X/n ≤ 0.1
Simplifying, we have:
-0.1 ≤ 0 ≤ 0.1
Since 0 is within the range [-0.1, 0.1], we can say that the estimate X/n with a margin of error of 0.1 includes the true probability p with at least 0.95 certainty.
To find the value of n, we can set the margin of error equal to the standard error and solve for n:
0.1 = 0.5/sqrt(n)
Squaring both sides and rearranging, we get:
n = (0.5/0.1)^2 = 25
Therefore, n should be at least 25 to know with at least 0.95 certainty that the true p is within 0.1 of the estimate X/n.
If Russel wants 0.99 certainty, we need to find the value of n such that the margin of error is within 0.1:
0.1 = 2.33/sqrt(n)
Squaring both sides and rearranging, we get:
n = (2.33/0.1)^2 = 539.99
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What is the equation for the line perpendicular to the line represented by the equation Y =1/3 X -2 that passes though the point (4,-7)
Answers
Answer:
Step-by-step explanation:
perp. -3
y + 7 = -3(x - 4)
y + 7 = -3x + 12
y = -3x + 5
It costs Widgeco $2,000 to purchase a machine that produces widgets and $2.75 to produce each widget. If widgets are sold for $4.99 each, which of these represents the profit, P(w), received when Widgeco sells w widgets?
A
P(w) = 2.24w + 2,000
B.
P(w) = 7.74w + 2,000
C.
P(w) = 2.24w – 2,000
D.
P(w) = 7.74w – 2,000
Answers
Answer:
B
Step-by-step explanation:
You would add the 2.75 and 4.99 to get 7.74 and you would add the variable for how much widgets are made and since its the profit you would have to add the 2,000 so the equation would be P(w) = 7.74w + 2,000
Hope this helps
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Which of the following expressions are equivalent?
Only expressions 1 and 2 are equivalent.
B.
Only expressions 1 and 3 are equivalent.
C.
Only expressions 2 and 3 are equivalent.
D.
Expressions 1, 2, and 3 are equivalent.
Answers
i’ll pick 2
and solve the equations
1. 6(2+12)
12+72
84
2. 6(2)+12
12+12
24
3.3(2(2)+4)
3(4+4)
3(8)
24
your answer is D
expressions 2 and 3 are equivalent
Expressions 1, 2, and 3 are equivalent is the correct statement of the given expressions.
What is Expression?An expression is combination of variables, numbers and operators.
The given three expressions are 6(a+2), 6a+12 and 3(2a+4)
Now we have to check which of the given expressions are equivalent.
Equivalent expressions are expressions that work the same even though they look different.
Let us find the value of 3 expressions by taking a value as 1.
6(a+2)
6(1+2)=18
Now second expression
6(1)+12=18
Third expression
3(2a+4)
3(2+4)
18
The value of three expressions is same.
Hence, Expressions 1, 2, and 3 are equivalent is the correct statement of the given expressions.
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X+y=0,5x+y=4 using substitution method
Answers
Answer:
(1, - 1 )
Step-by-step explanation:
x + y = 0 → (1)
5x + y = 4 ( subtract 5x from both sides )
y = 4 - 5x → (2)
substitute y = 4 - 5x into (1)
x + 4 - 5x = 0
4 - 4x = 0 ( subtract 4 from both sides )
- 4x = - 4 ( divide both sides by - 4 )
x = 1
substitute x = 1 into (1) and solve for y
1 + y = 0 ( subtract 1 from both sides )
y = - 1
solution is (1, - 1 )
The lengths of the two legs of a right triangle are 2 root 3 and 5 what is the hypotenuse? Leave the answer in simplified radical form.
Answers
Answer:
√37Step-by-step explanation:
As per Pythagorean theorem:
c = √a² + b²Substituting values
c = √ (2√3)²+5² = √12 + 25 = √37how many solutions to x^2 =-16
Answers
Answer:
no real solutions
Step-by-step explanation:
Convert the following Product of Sums expression for f′ to a Sum of Products expression for f using DeMorgan's Laws, and select the terms which result.Convert the following Product of Sums expression for f
′
to a Sum of Products expression for f using DeMorgan's Laws, and select the terms which result. f
′
=(a+b
′
)(w+x+y) becomes f=+ Answer 1: ab
′
Answers
By applying DeMorgan's Laws and selecting the appropriate terms, the Sum of Products expression for f becomes f=ab'.
DeMorgan's Laws state that the complement of a product of variables is equal to the sum of their complements, and the complement of a sum of variables is equal to the product of their complements.
In the given expression f'=(a+b')(w+x+y), we can apply DeMorgan's Laws to convert it into a Sum of Products expression for f. First, we apply the complement operator to each term within the parentheses:
a' and (b')'.
Using the first law, the product (a+b') becomes the sum (a'+(b')').
Next, we distribute the sum (a'+(b')') over the remaining term (w+x+y) to obtain:
f=(a'w+a'x+a'y+(b')'w+(b')'x+(b')'y).
Simplifying further, we can see that the terms ab' are present in the expression. Hence, the selected resulting term is ab'. Therefore, by applying DeMorgan's Laws and selecting the appropriate terms, the Sum of Products expression for f becomes f=ab'.
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Can someone please help me with this please
Answers
Answer:
The first is not a function. The second is.
Step-by-step explanation:
See attachment.
I need help on the question in the picture attached. i tried posting it but no one is answering it and this was due last week. please help fast
Answers
Answer:
Yes
Explanation:
To find our whether Marrissa's budget will be enough for the party, we need to find the linear equation relating the cost and the number of guests. The linear equation is the form
\(y=mx+b\)where y is the cost in dollars. m is the cost per guest, and b can be interpreted as additional charges for the party facility.
The cost per guest is given by the slope of cost vs. guest graph.
Let us pick two values (100, 1325) and (50, 725) and compute the slope:
\(\frac{\$1325-\$750}{100-50}=\frac{\$12}{\text{guest}}\)With the value of slope m in hand, we now find b by using the values x = 100, y = 1325 (the choice of these values is arbitrary)
\(\begin{gathered} 1325=12(100)+b \\ 1325=1200+b \\ \therefore b=125 \end{gathered}\)Hence, the equation relating the cost and the number of guests is
\(y=12x+125\)Now, for 75 guests the cost will be
\(\begin{gathered} y=12(75)+125 \\ y=\$1025.\text{ } \end{gathered}\)Therefore, Marrissa's budget, which is $1200, is greater than the cost of the party, meaning it will be enough.
#ofstudents is 30, not 463. please answer all parts. It is a reviewfor a test, so please try to explain your steps as well. Thankyou7. A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the randomly selected 30+63 students was x
Answers
The mean response of the randomly selected 30 students is x, which is also the mean response of the entire class.
To find the mean response for the randomly selected students, we need to use the formula:
mean = (sum of all responses) / (number of students)
Since we are given that the # of students is 30, not 463, we need to adjust our calculation accordingly.
Let's say the sum of all the responses for the 30 students is S. Then the formula becomes:
mean = S / 30
We don't know the exact value of S, but we can use the information given to make an estimate. The mean response of the 30+463 students is x, so we can write:
(x) = (S + 463y) / (30+463)
where y is the mean response of the remaining 463 students. We want to solve for x, so we need to isolate it on one side of the equation:
(x) = (S + 463y) / (30+463)
x(30+463) = S + 463y
30x + 463x = S + 463y
493x = S + 463y
x = (S + 463y) / 493
Now we need to use the fact that y is not given, but we can make an assumption based on the information given. The mean response of the entire class is likely to be somewhere between the mean response of the randomly selected 30 students and the mean response of the remaining 463 students. So we can assume that:
y is close to x
This allows us to simplify the equation:
x = (S + 463x) / 493
Multiplying both sides by 493 gives:
493x = S + 463x
30x = S
So we can see that the sum of the responses for the 30 students is 30 times the mean response, which is x. Therefore:
S = 30x
Plugging this back into the formula for the mean, we get:
mean = S / 30
mean = (30x) / 30
mean = x
So the mean response of the randomly selected 30 students is x, which is also the mean response of the entire class.
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The base of a solid S is the region enclosed by the graph of y=√ln(x), x=e, y=0. If the cross section of S perpendicular to the x-axis are squares, determine the volume V, of S.1) 1 cu. units.2) 13(e3−1) cu. units.3) 12 cu.units.4) 23 cu.units.5) 2(e3−1) cu.units.
Answers
The volume V of solid S is e - 1 cubic unit.
What is Volume?
Volume refers to the measure of three-dimensional space occupied by an object or a region. It quantifies the amount of space enclosed by the boundaries of an object or contained within a given region. In mathematical terms, volume is often calculated by integrating the cross-sectional areas of the object or region along a particular axis. Volume is typically expressed in cubic units, such as cubic meters (m^3) or cubic centimeters (cm^3). It is an essential concept in geometry, physics, engineering, and other scientific fields where the measurement of three-dimensional space is involved.
To find the volume of solid S, we need to integrate the areas of the cross sections perpendicular to the x-axis along the interval \([e, \infty).\)
The area of each square cross-section is equal to the square of the side length, which in this case is \(y = \sqrt{\ln(x)}.\)
Therefore, the volume V of solid S can be calculated as:
\(V = \int_{e}^{\infty} (\sqrt{\ln(x)})^2 dx\)
To evaluate this integral, we can simplify the expression:
\(V = \int_{e}^{\infty} \ln(x) dx\)
Using integration by parts, we let \(u = \ln(x)\)and dv = dx:
\(du = \frac{1}{x} dx\\v = x\)
Applying the integration by parts formula:
\(V = [uv] - \int v du= [x \ln(x)] - \int x \left(\frac{1}{x}\right) dx= x \ln(x) - \int dx= x \ln(x) - x + C\)
Evaluating the definite integral:
\(V = [x \ln(x) - x]_{e}^{\infty}= (\infty \cdot \ln(\infty) - \infty) - (e \cdot \ln(e) - e)= \infty - 0 - (1 - e)= e - 1\)
Therefore, the volume V of solid S is e - 1 cubic unit.
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YALL, I NEED HELP PLEASE HELP ME!
Answers
Answer:
16/r
Step-by-step explanation:
16 is how many people there is in total, r is how they are being divided :)
he cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.
What is the administration fee?
$50
$54
$55
$60
Answers
The one-time administration fee is (d) $60
How to determine the administration fee?From the question, we have the following parameters that can be used in our computation:
12 months costs $660.
15 months costs $810.
This means that
(x, y) = (12, 660) and (15, 810)
For the one-time administration fee, we have
(x, y) = (0, y)
So, we calculate the slope using
slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
(y - 660)/(0 - 12) = (810 - 660)/(15 - 12)
This gives
(660 - y)/12 = 50
So, we have
660 - y=600
This gives
y = 60
Hence, the administration fee is $60
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5/14 + -14/5
Can someone please help me I need it quick
Answers
Answer:
-171/70Step-by-step explanation:
5/14 + (-14/5) =
5/14 - 14/5 =
(25 - 196)/70 =
-171/70
F(x)=4x-3
g(x)=X^3+2x
Find (gof)(-3)
Answers
Answer:
Step-by-step explanation:
- 6a+7(-2a - 4)=???
Answers
Answer:
−20a−28
Step-by-step explanation:
thats what i got, sorry
The answer to this problem is -20a-28
which equation represents a line that is parallel to y = 4x + 3 and passes through the point (-3, 2)
50 points
Answers
Answer:
it should be y= -4x + 10
Step-by-step explanation:
hope this helps.
abby is comparing monthly phone charges from two companies. phenix charges $30 plus $.5 per minute. Nuphone charges $40 plus $.10 per minute. in how many minutes will the total be the same
Answers
Answer:
In 25 minutes, the monthly phone charges of both companies will be the same.
Step-by-step explanation:
If we allow m to represent the number of minutes, we can create two equations for C, the total cost of phone charges from both companies:
Phoenix equation: C = 0.5m + 30
Nuphone equation: C - 0.10m + 40
Now, we can set the two equations equal to each other. Solving for m will show us how many minutes must Abby use for the total cost at both companies to be the same:
0.5m + 30 = 0.10m + 40
Step 1: Subtract 30 from both sides:
(0.5m + 30 = 0.10m + 40) - 30
0.5m = 0.10m + 10
Step 2: Subtract 0.10m from both sides:
(0.5m = 0.10m + 10) - 0.10m
0.4m = 10
Step 3: Divide both sides by 0.4 to solve for m (the number of minutes it takes for the total cost of both companies to be the same)
(0.4m = 10) / 0.4
m = 25
Thus, Abby would need to use 25 minutes for the total cost at both companies to be the same.
Optional Step 4: Check the validity of the answer by plugging in 25 for m in both equations and seeing if we get the same answer:
Checking m = 25 with Phoenix equation:
C = 0.5(25) + 30
C = 12.5 + 30
C = 42.5
Checking m = 25 with Nuphone equation:
C = 0.10(25) + 40
C = 2.5 + 40
C = 42.5
Thus, m = 25 is the correct answer.
The um of two number i 61. The larger number i 4 more than two time the maller number. What i the maller number?
A
21
B
48
C
19
D
There i not enough information to tell. (NOT THE ANSWER)
Answers
The smaller number of the given sum is 15.
What is summation (sum)?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.The result that is produced when we add numbers, objects, or other things is referred to in mathematics as the sum. For instance, the sum of the addends 14 and 6 is 20.Completed question :
The sum of two numbers is 80. If the larger number exceeds four times the smaller by 5, what is the smaller number?
Given data :
Given, sum of two numbers is 61.
Let the smaller number be x
Thus the larger will be 61 - x
Also given, larger number exceeds four times the smaller number by 4.
Therefore, 61 - x = 4x + 5
5x = 56
x = 15
Thus the smaller number is 15.
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bounded by the paraboloid z = 4 + 2x2 + 2y2 and the plane z = 10 in the first octant
Answers
As a result, the solid's volume in the first octant, which is restricted by the paraboloid z = 4 + 2 x + 2 y, is 9.
We must determine the limits of integration for x, y, and z in order to determine the volume of the solid in the first octant bounded by the paraboloid z = 4 + 2x + 2y + 2 and the plane z = 10.
At z = 10, where the paraboloid and plane overlap, we put the two equations equal and find z:
4 + 2x^2 + 2y^2 = 10
2x^2 + 2y^2 = 6
x^2 + y^2 = 3
This is the equation for a circle in the xy plane with a radius of 3, centred at the origin. We just need to take into account the area of the circle where x and y are both positive as we are only interested in the first octant.
Integrating over the circle in the xy-plane, we may determine the limits of integration for x and y:
∫∫[x^2 + y^2 ≤ 3] dx dy
Switching to polar coordinates, we have:
∫[0,π/2]∫[0,√3] r dr dθ
Integrating with respect to r first gives:
∫[0,π/2] [(1/2)(√3)^2] dθ
= (3/2)π
So the volume of the solid is:
V = ∫∫[4 + 2x^2 + 2y^2 ≤ 10] dV
= (3/2)π(10-4)
= 9π
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The population of a town is 25\times 10^(6) and the population of a village is 5\times 10^(3). How many times is the population of the town larger than the population of the village? Give your answer in scientific notation.
Answers
The population of the town is 5,000 times larger than the population of the village.
To determine how many times larger the population of the town is compared to the village, we can calculate the ratio of the town's population to the village's population.
Population of the town = 25 × 10^6
Population of the village = 5 × 10^3
To find the ratio, we divide the population of the town by the population of the village:
Ratio = (25 × 10^6) / (5 × 10^3)
When dividing numbers in scientific notation, we subtract the exponents and divide the coefficients:
Ratio = 25 / 5 × 10^(6-3) = 5 × 10^3
Therefore, the population of the town is 5,000 times larger than the population of the village. This means that the town's population is 5,000 times greater than the village's population.
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*WILL MARK BRAINLIEST!!!!!!*
Answers
Answer:
y=1
Step-by-step explanation:
The value of y where the function is undefined
[Question 1] You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium. During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population. F
Answers
:According to the question:You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium.
During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population.
According to the Hardy-Weinberg equilibrium equation p² + 2pq + q² = 1, the frequency of D (p) and d (q) alleles are:p + q = 1Thus, the frequency of q is 0.4. Here are the calculations for the Hardy-Weinberg equilibrium:p² + 2pq + q² = 1(0.6)² + 2(0.6)(0.4) + (0.4)² = 1After simplifying, it becomes:0.36 + 0.48 + 0.16 = 1This means that the population is in Hardy-Weinberg equilibrium. This is confirmed as the frequencies of DD, Dd, and dd genotypes
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Order -3,5, 16, and -10 from least to greatest.
Then order the same numbers from closest to
zero to farthest from zero. Describe how your
lists are similar.
Answers
Closet to farthest from 0: -3, 5, -10, 16
Pleaseee help if you can. :’) many points
Answers
explanation:
combine the 2 sides since their congruent
x+18=3x
subtract x from both sides
18=2x
divide 2 from both sides
x=9