The equation of the required line would be x - 4y = 8.
What is the slope-point form of the line?
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
A line goes through the point (-1, 1) and (0,-3)
so the slope of the given line would be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-3-1}{0-(-1)}\\\\m=-4[/tex]
And we have to find the line which passes through the point (-4, -3) and the required line is perpendicular to the given line.
As we know the product of slopes of perpendicular lines is -1.
So the slope of the required line would be = 1/4
By using a slope-point form of the line, we get
[tex]y - y_1=m(x-x_1)\\\\y-(-3)=\frac{1}{4}(x-(-4))\\\\4(y+3)=x+4\\\\4y+12=x+4\\\\x-4y=8[/tex]
Hence, the equation of the required line would be x - 4y = 8.
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Answer:
C
Step-by-step explanation:
Let f(x) = -3x² - 1 and g(x) = -5x. Find f(g(x)).
-15x²-1
0-75x²-1
15x²+5
15x² + 5x
Answer:
[tex] \huge{ \boxed{f(g(x)) = - 75 {x}^{2} - 1}}[/tex]
Step-by-step explanation:
To find f(g(x)), substitute g(x) into f(x). That is for every x found in f(x), replace it by g(x) and solve.
[tex]f(x) = - 3 {x}^{2} - 1 \\ g(x) = - 5x[/tex]
[tex]f(g(x) )= - 3 ({ - 5x})^{2} - 1 \\ = - 3(25 {x}^{2} ) -1 \\ = - 75 {x}^{2} - 1 \: \: \: \: \: \: [/tex]
We have the final answer as
[tex] \bold{f(g(x)) = - 75 {x}^{2} - 1}[/tex]
Researchers at the Washington University School of Medicine randomly placed 480 rats into one of three
chambers containing radio antennas. one group was exposed to digital cell phone radio waves the second
to analog cell phone waves and the third group to no waves. two years later the rats were examined for
signs of brain tumors. in June 2002 the scientist said that differences among the three groups were not
statistically significant.
a) is this a study or an experiment? explain
b) explain in this context what "not statistically significant" means.
c) comment on the fact that this research was funded by Motorola, a manufacturer of cell phones.
The answer to following questions are as follows:-A)experiment
B)meaning “statistically non significant” C)explained below
What is a wave?A wave is a dynamic disturbance that propagates over one or more quantities in the domains of physics, mathematics, and allied sciences. When waves are periodic, those parameters repeatedly oscillate around an equilibrium value at a certain frequency.
The answers are: a) It is an experiment since some claims are not supported by evidence.
b) When the analysis reveals that there are substantial variations between the observed, "not statistically significant" refers to "statistically non significant." And we are unable to analyse any of the statistics' results.
c) The fact that Motorola, a cell phone company, funded this research reveals to us that this claim is untrue because Motorola conducts this research to boost their sales.
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Assume Waterland and Aquataste make a nonbinding, informal agreement that each will produce 250 gallons of water, charge $1.50 per gallon, and evenly split the profit of $750.
If Aquataste sticks to the agreement, Waterland has an incentive to renege on the agreement by producing 350 gallons because Waterland's profits would then increase from $375 to ______
If Aquataste reneges on the agreement and produces 350 gallons, Waterland has an incentive to renege on the agreement by producing 350 gallons because Waterland's profits would increase to _____, which is better than the $312.50 Waterland would earn by sticking with the agreement.
$437.50
If one cheats they will get sell 350 gallons at the new market price of $1.25 (now a total qty of 250+350=600). $1.25*350=$437.50
$350
If Waterland also reneges and produces 350, market qty supplied is now 700 and price is $1. Each firm earns profit of $350 ($1*350). This is better for waterland than before since they were selling the 250 gallons at $1.25 (Profit = 250*1.25=312.50)
If Aquataste sticks to the agreement, Waterland has an incentive to renege on the agreement by producing 350 gallons because Waterland’s profits would then increase from $375 to $525.
If Waterland and Aquataste both produce 250 gallons each and charge $1.50 per gallon.
There would be 500 gallons in total, and the total revenue would be
$1.50 × 500 = $750
which when shared equally between Waterland and Aquataste would result in each of them getting $375 each.
But if Aquataste sticks to the agreement, Waterland has an incentive to renege on the agreement by producing 350 gallons, still charging $1.50 and Waterland’s profits would then be
$1.50 × 350 = $525
If one cheats they will get sell 350 gallons at the new market price of $1.25 '.
Then, a total quantity of 250+350=600.
Total profit $1.25 × 350 = $437.50
If Waterland also reneges and produces 350, market qty supplied is now 700 and price is $1. Each firm earns profit of $350 ($1*350). This is better for waterland than before since they were selling the 250 gallons at $1.25
Therefore, Profit = 250 × 1.25
=312.50
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Alr last 1 HELP ME OUT……..
Answer: 89.7
Step-by-step explanation:
a popular brand of pen is available in 15 colors and 3 writing tips. how many different choices of pens do you have with this brand?
45 different choices of pens you have with this band.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
A popular brand of the pen is available in 15 colors and 3 writing tips.
Choosing from one of 15 colors and one of 3 writing tips.
Each color could have one of two different writing tips.
To find the total different pens available multiply the number of colors by the number of tips: 15*3=45
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The ratio of the measures of two complementary angles 7:8 what is the measure of the smallest angle?
Answer: 84
Step-by-step explanation: so 7:8 increased by some number is 180 degrees. add 7 and 8 to get 15. 180/15 is 12 so x = 12 7*12 is 84.
Find the radius of the cirlce
Answer:
R= 2sqrt(13) = about 7.2
Step-by-step explanation:
D^2= 12^2 + 8^2
= 144+64=208
D=4sqrt(13)
R= D/2= 2sqrt(13)
2. what conditions must be met if we want to perform a hypothesis test and answer the question of the management? select all that apply:
1.The following is the 90% confidence interval for the mean difference between the park's tree heights in 2009 and 2019:
(11.59, 14.21)
2. The conditions for the confidence interval are of:
A. Large samples and no extreme outliers.
D. Independently sampled pairs.
Given,
What is a confidence interval for the t-distribution?
When the population's standard deviation is unknown, the t-distribution is utilized, and the boundaries of the confidence interval are provided using the following formula:
x ± t s/√n
When the equation's variables are laid down as follows:
The sample mean = x
The critical value = t
The sample size = n
The standard deviation for the sample = s
Using a t-distribution calculator, the critical value is t = 1.6766 for a two-tailed 90% confidence interval with 50 - 1 = 49 df.
The remaining parameters are given as follows:
x = 12.9, s = 5.52, n = 50
Then the lower bound of the interval is of:
12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.
The upper bound of the interval is of:
12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.
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Question is incomplete. Completed question is given below;
Forest rangers wanted to better understand the rate of growth for younger trees in the park. They took measurements of a random sample of 50 young trees in 2009 and again measured those same trees in 2019. The data below summarize their measurements, where the heights are in feet.
Year Mean SD n
2009 11.4 3.6 50
2019 24.3 8.8 50
Difference 12.9 5.52 50
Round all calculated values to 4 decimal places as appropriate.
1. Construct a 90 confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019.
2. What conditions must be met if we want to perform a hypothesis test and answer the question of the management? Select all that apply:
A. Large samples and no extreme outliers.
B. There must be at least 3 levels of the categorical variable.
C. np^≥10 and n(1−p^)≥10
D. Independently sampled pairs.
explain how the is related to the standard error of the estimated difference in average birth weight for smoking and nonsmoking mothers.
Babies born to nonsmokers typically weighed between 1,000 and 5,000 grams. Babies of smokers typically ranged in weight from 500 to 4500 grams.
Given,
What is the weight at birth?
Birth weight is the term used to describe a newborn's body weight. Typically, newborns of European heritage weigh between 2.5 and 4.5 kilos, on average 3.5 kilograms, at delivery. Babies from South Asia and China typically weigh 3.26 kg.
Here,
Babies of nonsmokers frequently ranged in weight from 1,000 to 5,000 grams. Babies born to smokers frequently weighed between 500 and 4500 grams.
The usual ranges of birth weights between the two groups do show some notable differences, though. Nearly half of neonates among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grams since there are fewer babies in the lower weight ranges. Fewer babies are in the bigger weight groups, with 40 of 74, or 54%, of the newborns delivered to smokers having birth weights between 2,000 and 3,000 grams.
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The wholesale cost of a dining room table at a fumiture store is $1,215.80. The markup for the table is 30%. What is the selling price of the dining room table?
Answer
$1,580.54
1215.80×(1+0.3)= 1580.54
Please Simplify
√81x2
Answer:
18
Step-by-step explanation:
1)since 9*9 = 81 the square root of 81 is 9
9*2
2)simplify
18
What is the area of the triangle with vertices (1, 4), (3, 1) and (11, 1)?
Answer:
Step-by-step explanation:
go to school
A cylinder has a base radius of 6ft and a height of 18ft. What is its volume in cubic ft, to the nearest tenths place?.
2034.72ft³ is the required cylinder volume.
What do we mean by the volume of the cylinder?The capacity of a cylinder determines how much material it can carry, or we may say that the volume of a cylinder is the total number of unit cubes that can fit inside of it.
The volume of a cylinder is r²h, and its surface area is 2πrh+2πr².
The volume of cylinder Formula: V = A × h
We will assume the cylinder is a right circular cylinder.
Then, we have the formula:
V = πr²h
We already know:
Radius = 6ft
Height = 18ft
Now, calculate the volume as follows:
(V) = π× 6² × 18
(V) = 2034.72ft³
Therefore, 2034.72ft³ is the required cylinder volume.
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There are 6 circles and 10 triangles. What is the simplest ratio of circles to total shapes?.
If there are 6 circles and 10 triangles, then the simples ratio of circles to total shapes is 3 : 8
Total number of circles = 6 circles
Total number of triangles = 10 triangles
Total number of shapes = Total number of circles + Total number of triangles
Substitute the values in the equation
Total number of shapes = 6 + 10
= 16 shapes
The ratio of circles to total shapes = Total number of circles : Total number of shapes
Substitute the values
= 6 : 16
Simplify the ratio
= 3 : 8
Therefore, the simplified ratio of circles to total shapes is 3 : 8
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Please Help!!! Hurry!!!
Answer: I think it's 2/5, it is closest to the answer I came up with
an air plane is flying at a height of 6 miles on a flight path that will take it directly over a radar tracking station. the distance d between them is decreasing at a rate of 400 miles per hour when the distance between them is 10 miles. what is the speed of the plane?
500 mph is the speed of the plane.
This creates a right triangle, with the distance between the plane and the radar station serving as the hypotenuse (s). Let y represent the plane's height and x represent its flight route.
s2 = y2 + x2
Given: the constant value of y = 6
negative since decreasing, ds/dt = -400
Trying to locate dx/dt
Taking the implicit derivative of the above equation's two sides
0 + 2xdx/dt = 2sds/dt
(S/X) ds/dt = dx/dt
When x = 8
s = √(62+82) = √100 = 10
dx/dt = (10/8)(-400) = -500 mph, or 500 mph traveling toward the radar station at a distance of 6 miles.
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at a certain university in the u.s., all phone numbers are 7-digits long and start with either 824 or 825. 1) how many different phone numbers are possible?
There are 20,000 different phone numbers possible that is 7-digits long and start with either 824 or 825.
Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.
Based on the given information, all phone numbers are 7-digits long and starts with either 824 or 825. Hence, the four last digits will be the combination of numbers from 0 to 9.
Thus, by Fundamental Principle of Counting, the number of possible outcomes is 20,000.
= (number of phone numbers starting with 824) + (number of phone numbers starting with 825)
= (10 x 10 x 10 x 10) + (10 x 10 x 10 x 10)
= 20,000
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13. A hardware store sells many different sizes of chains. The price of each chain is determined by
its length. The table below shows the price for different lengths of chain.
Price of Chains
Length
(ft)
1.8
3
$1.35
$2.25
$2.55
6.2
$4.65
Which equation best represents the relationship between x, the length of the chain in feet,
and y, the price of the chain?
Price
3.4
The equation y=0.75x is the relationship between x, the length of the chain in feet, and y, the price of the chain.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given that hardware store sells many different sizes of chains.
The price of each chain is determined by its length.
From the table we need to find the equation best represents the relationship between x, the length of the chain in feet, and y, the price of the chain.
Let us find this by taking 0.75 as x and multiplying with lengths to get the price.
1.8×0.75=1.35
3×0.75=2.25
3.4×0.75=2.55
6.2×0.75=4.65
y=0.75x.
Hence, y=0.75x is equation best represents the relationship between x, the length of the chain in feet, and y, the price of the chain.
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A fence is to enclose a field and divide it into 3 equal areas. If there is 1600m of fencing available. Find the dimensions of the field that will allow for the maximum area.
The dimensions of the field that will allow for the maximum area are 200 meters by 400/3 meters
How to determine the dimensions of the field that will allow for the maximum area.From the question, we have
Fencing available, Perimeter = 1600 meters
Number of sections, n = 3
Represent the dimensions with x and y
So, we have:
Area = Number of sections* x * y = 3xy
Perimeter = (Number of sections * 2x + 2(Number of sections) * y) = 6x + 4y
Recall that
Perimeter = 1600 meters
So, we have
6x + 4y = 1600
A = 3xy
Divide 6x + 4y = 1600 by 2
3x + 2y = 800
Make y the subject
y = (800 - 3x)/2
Substitute y = (800 - 3x)/2 in A = 3xy
A = 3x(800 - 3x)/2
So, we have
A = 1200x - 4.5x²
Differentiate and set to 0
1200 - 9x = 0
So, we have
9x = 1200
Divide by 9
x = 400/3
Recall that y = (800 - 3x)/2
So, we have
y = (800 - 3 x 400/3)/2
Evaluate
y = 200
Hence, the dimensions are 200 by 400/3
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: a marketing manager for a phone company claims that the percentage of children aged 8-12 who have phones differs from 52%. in a survey of 832 children aged 8-12 by the national consumers league, 449 of them had phones. can you conclude that the manager's claim is true? use the
The percentage of children aged between the ages of 8 - 12 who own phones are, in fact, lower than the 52% industry average. Of the 832 children aged 8 to 12 who were questioned by the national consumer league, 449 had cell phones.
You must use survey data to calculate the percentage of youngsters between the ages of 8 as well as 12 who own phones to ascertain whether the commercial manager's assertion is accurate. To achieve this, divide the total number of children polled (832) by the total number of kids who own phones (449), multiply the outcome by 100 to get the percentage, and so on.
This estimate gives a percentage of 53.8%, which is slightly higher than the advertising manager's stated figure.
This implies that the claim made by the management could not be genuine, and more investigation would be required to ascertain if it is real or not.
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In each of the following equations, determine which variable represents the angle and which variable represents the value of the trigonometric function. (a) In the equation q = sin d, represents the angle and represents the value of the trigonometric function. (b) In the equation p = tan^1 c, represents the angle and represents the value of the trigonometric function. (c) In the equation arccos n = upsilon, represents the angle and represents the value of the trigonometric function.
a) q= sin d
Angle is represented by d, and value is represented by q.
b) p = tan1 c
Angle is represented by c, and value is represented by p.
c) arccos n = ν
Angle is represented by n, and value is represented by v.
Given that,
We have to find the variables that indicate the angle and the value of the trigonometric function in each of the following equations.
In the following three equations:
(a) q = sin d;
(b) p = tan1 c; and
(c) arccos n = ν,
We know that,
a) q= sin d
Angle is represented by d, and value is represented by q.
b) p = tan1 c
Angle is represented by c, and value is represented by p.
c) arccos n = ν
Angle is represented by n, and value is represented by v.
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14 on a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. what was the number of men on the sight-seeing tour?
The number of men on the sight-seeing tour was 22.
What is the proportion?
A unique class of ratio called a percentage has the numerator and denominator combined. An illustration is the ratio of deaths to men, which is calculated by dividing deaths to men by deaths to men and women (i.e. the total population).
We have,
w/c = 5/2
w/c = 5/2
w = 5x
and c=2x
for some integer x. Q : m =?
(1) on the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11
c/m = 5/11cm
c=5y and m = 11y,
for some integer y. Not sufficient to calculate m.
(2) the number of women on the sight-seeing tour was less than 30 --> w<30. Not sufficient to calculate m.
(1) + (2)
w = 5x < 30w --> x<6x.
c=2x and as c=5y,
c is a multiple of 5 --> x=5x
c = 10 = 5y --> y = 2
m = 11y = 22.
Hence, the number of men on the sight-seeing tour was 22.
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select the first correct reason why the given series converges. a. convergent geometric series b. convergent p series c. comparison (or limit comparison) with a geometric or p series d. alternating series test e. ratio test
Because it diverges using a comparison test, the correct answer is an option (E).
What is a comparison test?The comparison test, also known as the direct comparison test to distinguish it from other closely related tests, offers a method for determining whether an infinite series or an improper integral will converge or diverge.
The test is effective in both situations by contrasting the given series or integral with one whose convergence characteristics are known.
So, refer to the image attached below.
According to the image which has the reason for convergence and divergence, we know that the correct answer would be option (E).
The reason is the comparison test.
Therefore, because it diverges using a comparison test, the correct answer is an option (E).
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8(8 - k) = -72k
please help
Answer:
k=-1
Step-by-step explanation:
Please look at the attachment, hope this helps, have a great day! :D
duke earned $250 washing cars last summer. he spent all of his earning on a new stereo and a new bike. if he paid $190 for the stereo, what percent of his summer earnings did he soend on his bike
Answer: 24%
Step-by-step explanation: First find the percentage of the stereo.
190/250 = 0.76 of 76%
Then subtract 76% from 100% or subtract 190 from 250.
250 - 190 = 60 then 60/250 = 0.24 or 24%
Duke spent 24% of his earnings on his bike.
Solve for rrr.
Give an exact answer.
\dfrac12r-3=3\left(4-\dfrac32r\right)
2
1
r−3=3(4−
2
3
r)start fraction, 1, divided by, 2, end fraction, r, minus, 3, equals, 3, left parenthesis, 4, minus, start fraction, 3, divided by, 2, end fraction, r, right parenthesis
r =r=r, equals
The solution for r in the equation is r = 3
How to determine the solution for r in the equation?From the question, we have the following parameters that can be used in our computation:
\dfrac12r-3=3\left(4-\dfrac32r\right)
Rewrite the above expression properly, as a fraction
So, we have the following representation
1/2r - 3 = 3(4 - 3/2r)
To start with, we need to open the brackets
So, we have the following representation
1/2r - 3 = 12 - 9/2r
Next, we multiply through by 2 to eliminate the fraction
This gives
r - 6 = 24 - 9r
Solving further, we collect the like terms
So, we have
r + 9r = 24 + 6
Evaluate the like terms
10r = 30
So, we have
r = 3 --- by dividing both sides by 10
Hence, the solution is 3
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a study of 1000 randomly selected flights of a major airline showed that 798 of the flights arrived on time.what is the probability of a flight arriving on time?
By using the concept of probability, it can be calculated that
Probability that the flight arrives on time = [tex]\frac{399}{500}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Total number of flights = 1000
Number of flights arriving on time = 798
Probability that the flight arrives on time = [tex]\frac{798}{1000}[/tex]
= [tex]\frac{399}{500}[/tex]
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Describe the relationship between the lines.
1. The lines intersect to form an angle that is 180°
2. The lines intersect to form an angle that is 90°
3. The lines do not intersect.
4. The lines intersect to form an angle that is not 90°
the arithmetic progressions{2,5,8,11, . . .}and{3,10,17,24, . . .}have some common values. what is the largest value less than 500 that they have in common?
The largest value less than 500 that both sets have common is 479.
We have given two arithmetic progression such that,
{2,5,8,11,...} and {3,10,17,24,...}
and we have to find the largest value less than 500 that they have in common.
We know the formula for the nth term of the arithmetic progression,
i.e, an = a + (n - 1)d
for the arithmetic progression {2,5,8,11,...} the formula become
am = 2 + (m - 1)3 ----------- (1)
and for the arithmetic progression {3,10,17,24,...} the formula become
an = 3 + (n - 1)7 ------------- (2)
by solving for m and n we get,
m = 160 and n = 69
so equation (1) implies that,
a(160) = 2 + (159)3 = 479
this is the 160th term in the 1st arithmetic progression
and equation (2) implies that,
a(69) = 3 + (68)7 = 479
this is the 69th term in the 2nd arithmetic expression.
Therefore, the value which less than 500 that both the progressions have in common is 479.
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Can someone Explain to me how to do this step by step
The diameter of IC 1101 is 50 times greater than the diameter of the Milky way.
What does diameter mean?Diameter is a measurement that goes all the way around from starting point to the end point.
Given, the largest galaxy IC 1101 has a diameter of 5 * 10²² and the Milky way has a diameter of 1 * 10²¹.
Diameter of IC 1101 = 5 * 10²²
Rearranging the above term;
Diameter of IC 1101 = 1 * 5 * 10²¹ * 10
Diameter of IC 1101 = 1 * 10²¹ * 50
Diameter of IC 1101 = 50 * diameter of Milky way
Therefore, the answer is 50 times.
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