The equation of the line parallel to the line, [tex]y=\frac{3}{2} x-6[/tex] through the point (-6,5) is [tex]3x-2y+28=0[/tex]
What are Parallel Lines?
Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Parallel lines have the same slope.What is Point-Slope Equation of Line?
The Point-Slope Equation of a straight line is given as, [tex]y-y_{1}=m(x- x_{1})[/tex].This method is useful in determining the equation of a straight line when the slope (m) of the line and a point [tex](x_{1}, y_{1})[/tex] are known.Here, it is given that the equation of the line parallel to the given straight line is [tex]y=\frac{3}{2} x-6[/tex] ----(1)
We know that the slope of parallel lines is equal.
So, the slope of (1) will be equal to the given line.
Writing (1) in the form of [tex]y=mx+c[/tex], we get
Slope, [tex]m=\frac{3}{2}[/tex]
Using the Point-Slope Equation of the line, we have
[tex]y-y_{1}=m(x- x_{1})[/tex]
Now, substituting the point (-6,5) in the place of [tex](x_{1}, y_{1})[/tex], we get
[tex]y-5=\frac{3}{2} (x- (-6))\\\implies 2(y-5)=3(x+6)\\\implies 2y-10=3x+18[/tex]
Simplifying, we get
[tex]3x-2y+18+10=0\\\implies 3x-2y+28=0[/tex]
Therefore, the equation of the given line is [tex]3x-2y+28=0[/tex]
Correct Question: Write an equation for the line parallel to the line y=3/2x-6 through the point (-6, 5).
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Differentiate the following functions from first principles
(i) Y=10 x^4+3 x+50(4marks)
The solution of the differentiated equation is dy/dx = 40x³+ 3
How to differentiate the equation?From the question, we have the following equation that can be used in our computation:
Y=10 x^4+3 x+50
Rewrite properly
So, we have
y = 10x⁴ + 3x + 50
The rule of first principle of differentiation is represented as
If y = axⁿ, then dy/dx = naxⁿ⁻¹
Using the above as a guide, we have
dy/dx = 4 * 10x⁴⁻¹ + 1 * 3x¹⁻¹ + 0 * 50
Evaluate
dy/dx = 40x³+ 3
Hence, the equation result is dy/dx = 40x³+ 3
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Solve the following word problems. Show your work in the space below.
19. Demetrius bought 6 boxes of colored pencils. There were 15 pencils in each box.
How many colored pencils were there altogether?
6 Boxes of colored pencils
15 Pencils in each box
Total Number of colored pencils : 15 x 6 = 90 Pencils
At a local college, 198 of the male students are smokers and 792 are non-smokers. Of the female students, 330 are smokers and 770 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers?
The probability that both male and female are non-smokers is 0.56.
Given that, at a local college, 198 of the male students are smokers and 792 are non-smokers.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
Number of male smokers=198
Number of male non-smokers=792
Total number of male smokers=198+792
= 990
Number of female smokers=330
Number of female non-smokers=770
Total number of female smokers=330+770
= 1100
Probability that both are non-smokers is given by
P(both are non-smokers ) = P(Male non-smoker) × P(female non-smoker)
= 792/990 × 770/1100
= 0.8 × 0.7
= 0.56
Therefore, the probability that both male and female are non-smokers is 0.56.
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Alvin is 15 years younger than Elga. The sum of their of their ages is 43. What is Elga's age?
Answer:
Elga is 29Alvin is 14Step-by-step explanation:
You want Elga's age, given that Alvin is 15 years younger and the sum of their ages is 43.
SetupLet e represent Elga's age. Then (e-15) is Alvin's age, and the sum of their ages is ...
e +(e -15) = 43
Solution2e = 58 . . . . . . . add 15
e = 29 . . . . . . . divide by 2
Elga's age is 29.
e -15 = 29 -15 = 14 . . . . Alvin's age
an arctic explorer reached the north pole and decided to erect the national flag . his eyes was 1.6 m from the ground and the angle of elevation to the top of the 3 m flagpole was 28. how far from the base of the flagpole did he stand?
The explorer stood 2.63m away from the flag pole.
What is Angle of Elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
If the pole is 3m high, and his eye is 1.6 meters from the ground.
Then distance from the top of the pole and his eyes would be 3 - 1.6 = 1.4m
The angle of elevation between the line of sight and the horizontal = 28°
so the horizontal, angle of elevation and the distance between sight and top of pole form a right angle triangle.
Let the distance of the explorer from foot of pole be x,
so that,
tan 28 = 1.4/x
by cross multiplying,
x tan28 = 1.4
x = 1.4/tan28
x = 1.4/0.5317
x = 2.63m
In conclusion, the distance of the explorer to the base of the flagpole is 2.63m
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Please help with number 6 and 7
What would $1000 become in a saving account at 3% per year for 3 years when the interest is not compounded (simple interest: p*r*
$1000)?
What would the same amount become after 3 years with the same rate but compounded annually?
S
Do NOT type dollar signs or commas.
Round to the nearest hundredth
Blank 1:
Blank 2
The required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.
Given that,
$1000 become in a saving account at 3% per year for 3 years when the interest is not compounded.
Simple interest is defined as the percentage of earning on the lending for a period of time
Here,
Simple interest earned = P × r × t /100
= 1000 × 3 × 3 /100 = 90
Amount = P + SI = 1000 + 90 = $90
Now, when interest is compounded annually,
Amount = 1000(1.03)³
Amount = $1092.72
Thus, the required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.
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PLS HELP IF U ARE GOOD AT MATH.
Game Station 2: Amazing Race- Each team has to match 9 of the 20 banners with the word “Hello” in different languages with the 9 countries that speak that language
A. Determine the number of ways of selecting and matching nine banners with a country.
B. Determine the number of ways of selecting nine banners without having to match them with a country.
combinations problem btw
The number of ways to select the banners is given as follows:
a. Matching with the country: 362,880, using the arrangements formula.
b. Not matching with the country: 60,949,324,800, using the permutation formula.
What is the arrangements formula?The number of possible arrangements of n elements is obtained by the factorial of n, that is:
[tex]A_n = n![/tex]
For item a, the arrangements formula is used, as the banner has to match the country, hence only the countries are arranged and then the specific banner is matched with this country.
Considering that there are nine countries, the number of ways of selecting and matching nine banners with a country is calculated as follows:
Total = 9! = 362,880.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is obtained by the equation as follows:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
For item b, 9 banners are taken from a set of 20, and the permutation formula is used as the order in which the banners are chosen is important, hence the number of ways of selecting nine banners without having to match them with a country is obtained as follows:
N = 20!/(20 - 9)! = 20!/11! = 60,949,324,800.
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Name the property used to justify the equation. (-2+5) +-7 = -2 + (5 +-7)
What is the ordered pair for Point T?
(1,5)
(0,5)
(5,0)
(5,5)
Answer:
B
Step-by-step explanation:
point T is on the y-axis with x- coordinate 0 and y- coordinate 5, then
the ordered pair for point T is (0, 5 )
Write the explicit formula for the arithmetic sequence below. 14, 9, 4, -1, ...
Step-by-step explanation:
To find the next term or number, we'll need to keep subtracting 5. So the formula is: n-5
PLEASE BE FAST I HAVE 5 MIN LEFT!! <3
Step-by-step explanation:
Original prices of the office equipments
Computer = £650
Calculator = £27.75
Telephone = £69.50
45. The computer has a discount of 15%
[(100 - 15)/100]% × £650
85/100 % × £650
=£552.5
46. The calculator has a discount of 20%
[(100 - 20)/100]% × £27.75
80/100 % × £27.75
=£22.2
47. The telephone has a discount of 10%
[(100 - 10)/100] % × £69.50
90/100 % × £69.50
=£62.55
48. The saving for the computer is
= £(650 - 552.5)
= £97.5
49. The saving for the calculator is
= £(27.75 - 22.2)
= £5.55
50. The saving for the telephone is
= £(69.50 - 62.55)
=£6.95
A candy company sells peanut brittle and almond bark. The information for both types of candy is shown.
graph labeled Peanut Brittle with x axis labeled weight in ounces and y axis labeled cost in dollars with a line from point 0 comma 0 going through 10 comma 10
Almond Bark
Weight (ounces) 2 6 14
Cost (dollars) 3 9 21
Determine how much more one candy costs per ounce than the other candy.
Peanut brittle costs $0.50 more per ounce than almond bark.
Almond bark costs $0.50 more per ounce than peanut brittle.
Peanut brittle costs $0.33 more per ounce than almond bark.
Almond bark costs $0.33 more per ounce than peanut brittle.
Peanut brittle costs $0.33 more per ounce than the almond bark option (C) is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
A candy company sells peanut brittle and almond bark.
Almond: $6/(10 oz) = $0.60/oz
Bark: $9/(10 oz) = $0.90/oz
0.90 - 0.60 = $0.90
Peanut brittle costs $0.33 more per ounce than almond bark.
Thus, peanut brittle costs $0.33 more per ounce than the almond bark option (C) is correct.
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Answer:
Almond bark costs $0.50 more per ounce than peanut brittle.
Step-by-step explanation:
Lisa collected leaves from different trees for a science project. Every day for a week (7 days), she collected 7 leaves. How many leaves did she collect by the end of the week?
Answer:
49 leaves
Step-by-step explanation:
7 days x 7 leaves per day = 49 leaves in total
6. Melissa is making a batch of cookies. The recipe calls for 2/3 cup of
chocolate. Melissa is making only one-fourth of a batch. How much
chocolate will she need in order to make her cookies?
The answer is, 1/6th cup of chocolate will she needs in order to make her cookies using fraction.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
The amount of chocolate required for this recipe is 2/3rd of a cup for a batch.
She has to make for a 1/4th of that batch.
So the amount of chocolate needed is also 1/4 for the batch which will be = 1/4*2/3 of cup.
= 1/6th of the cup.
Hence, 1/6th cup of chocolate will she need in order to make her cookies.
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What percent of 23 is 22? round your answer to the nearest percent.
Answer:
96% rounded to the nearest percent.
Step-by-step explanation:
Divide 100 by 23 which is approximately 4.35
Multiply 4.35 by 22 which is 95.7%.
If you round 95.7 to the nearest percent, it would be 96%.
Answer:
95.6521739%
explanation:
22 is 95.6522% of 23
(b) 12 friends travel to the festival.
5 travel by car, 4 travel by bus and 3 travel by train.
Two people are chosen at random from the 12 friends.
Calculate the probability that they travel by different types of transport.
The probability that they two people are chosen and travel by different transport is 47/144
What is Probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.
Probability is given as sample space / total outcome
Probability to travel by car p(C)= 5/12
Probability to travel by bus P(B)= 4/12=1/3
Probability to travel by train P(T)= 3/12= 1/4
for two people chosen at random
P(C ×B)= 5/12×1/3= 5/36
P(B×T)= 1/3×1/4= 1/12
P(C×T)= 1/4×5/12= 5/48
Therefore the probability that the two chosen travel by different car is
P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48
= 141/432
divide through by 3
= 47/144
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find the slope (4,2) (2,-1)???
pls helppp
Answer:
slope is 3/2
Step-by-step explanation:
m = y2 - y1 / x2 - x1
m = -1 - 2 / 2 - 4
m = -3/-2 ( can be simplified )
simplified ver. = 3/2
Answer:
Slope is 3/2
Step-by-step explanation:
To find slope, subtract the y's, put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction.
(4,2) and (2,-1)
Subtract y's:
2 - -1
=3
Put it on top of a fraction:
3/something
Subtract the x's:
4 - 2
= 2, put that on the bottom of the fraction.
3/2
Slope is 3/2.
What is a common denominator for 3/5 and 2/3
Answer:30
Step-by-step explanation:
For a given right triangle, if
Sin(3x - 7) = Cos(x + 1)
Find x:
A:24
B:3
C:4
D:46.8
Responses
Question 17 of 25 The side lengths of a triangle are 5, 12, and 13. Is this a right triangle? A. Yes, because 5² +12²= 13² OB. No, because 5 + 12 * 13. C. No, because 52+12²*13² D. Yes, because 5² + 12²
Answer:
A
Step-by-step explanation:
Right triangle hypotenuse can be calculated using
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
A retail clothing store offers customers an opportunity to open up a credit card during checkout. One location of the retail clothing store states that the number of credit cards, A, that are opened t months since January can be modeled by the function A(t) = 10 + 2t. The number of credit cards opened at another location, B, is defined by the function B(t) = 25 − t. What is an expression that can be used to determine the total amount of credit cards opened at the two locations?
(A + B)(t) = 35 + t
(A + B)(t) = 35 + 3t
(A − B)(t) = −15 + t
(A − B)(t) = −15 + 3t
The expression that can used to determine the total number of credit cards opened at the two locations can be written as Option A.
( A + B ) ( t ) = 35 + t
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The equation of function for number of credit cards at location A at t months is given by A( t ) = 10 + 2t
The equation of function for number of credit cards at location B at t months is given by B( t ) = 25 - t
Now , A function assigns the value of each element of one set to the other specific element of another set.
So ,
The total number of credit cards that are opened at both the location A and B is given by the equation =
Number of credit cards at location A at t months + Number of credit cards at location B at t months
The total number of credit cards that are opened at both the location A and B is given by the equation = A( t ) + B( t )
= ( A + B ) ( t )
= 10 + 2t + 25 - t
= 35 + t
Hence , the equation for the function of total number of credit cards opened at the two locations is given as ( A + B ) ( t ) = 35 + t
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If a + b = 5 and ab = 6, find the value of a³ + b³
The value of a³ + b³ is 64.184
Here,
a + b = 5 .........(1)
and ab = 6
a = b/6
Substitute above value of 'a' in equation(1)
b/6 + b = 5
7b/6 = 5
7b = 30
b = 30/7
b = 4.28
So, a = 5 - 4.28
a = 0.72
We know that the formula of a³ + b³
a³ + b³
= (a + b)(a² + b² - ab)
= 5 * (0.72² + 4.28² - 6)
= 5 * 12.8368
= 64.184
Therefore, the value of a³ + b³ is 64.184
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x + 20 ≤ -10 please help progress leraning
The value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
It is given that the expression is,
x + 20 ≤ -10
Rearrange the expression as
x≤ -10-20
x≤ -30
Thus, the value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.
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1) Graph the function by plotting the ordered pairs (0, 0) (10, 125) (20, 250) (30, 375) (40, 500) and
drawing a straight line through the points. Label the axes with appropriate
variable
quantities
and units. Label the points with the correct ordered pairs. Include a title for the graph.
The graph of the given ordered pair is plotted and attached below.
Ordered pair:
Ordered pair refers the composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
Given,
Here we have the following ordered pair.
(0, 0) (10, 125) (20, 250) (30, 375) (40, 500)
Now, we have to plot the graph for this ordered pair.
In the given question, we have to perform the following steps.
The first process is to label the axis of the graph as x and y .Now, we have to point the given coordinates on the graphConnect the plotted point to make the straight line on itNow, we have to label the plotted pointsFinally, we have to put the title for the graph as function.After all these steps we get the graph like the following.
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Consider the following observations on a receptor binding measure (adjusted distribution volume) for a sample of 13 healthy individuals: 22, 40, 41, 42, 43, 48, 51, 58, 62, 66, 67, 70, 71.
Calculate an interval for which you can be 95% confident that at least 95% of all healthy individuals in the population have adjusted distribution volumes lying between the limits of the interval. (Round your answers to three decimal places.)
Predict the adjusted distribution volume of a single healthy individual by calculating a 95% prediction interval. (Round your answers to three decimal places.)
The 95% confidence interval for the population mean adjusted distribution volume, using the t-distribution, is given as follows:
(43.479, 61.281).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the rule presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The sample is given as follows:
22, 40, 41, 42, 43, 48, 51, 58, 62, 66, 67, 70, 71.
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 13 - 1 = 12 df, is t = 2.1788.
Using a calculator with the sample, the parameters for the interval are:
[tex]\overline{x} = 52.38, s = 14.73, n = 13[/tex]
Hence the lower bound of the interval is calculated as follows:
52.38 - 2.1788 x 14.73/sqrt(13) = 43.479.
The upper bound of the interval is calculated as follows:
52.38 + 2.1788 x 14.73/sqrt(13) = 61.281.
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Now, suppose this lottery expands to include a second number, ranging from 1-59. What would be your
chances of guessing both these numbers correctly? Round your answer to the nearest thousandth of a percent.
The probability of getting both these numbers correctly is of:
0.028%.
How to calculate a probability?The probability of an event in an experiment is obtained as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.
In this problem, the probabilities are presented as follows:
First trial: one number from a set of 60 numbers.Second trial: one number from a set of 59 numbers, as the first number chosen cannot be chosen again, that is, numbers are not replaced.The probability of getting both these numbers correctly is given by the multiplication of the probabilities of getting the correct number on each trial, hence:
p = 1/60 x 1/59 = 0.00028 = 0.028%.
Missing InformationThe problem states that two numbers are selected from a set of 60, and it asks for the probability that both are guessed correctly.
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A veterinarian has dog patients numbered 1,2,3,4,5, cat patients numbered 1,2,3,4,5,6, and bird patients numbered 1,2. If a single animal is picked at random, what is the probability that the animal patient is NOT a bird?
Provide the final answer as a simiplified fraction.
The probability that the animal patient is NOT a bird as a simplified fraction is 11/13.
What is probability?
The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.
As given in the question,
Number of dog patients is 5,
Number of cat patients is 6, and
Number of bird patients is 2.
So,
Total number of animal patients = 5 + 6 +2 = 13
Total number of ways of picking 1 animal patient = 13C1 = 13
Number of patients that are NOT birds = 11
So,
probability that the animal patient picked is not a BIRD = 11C1 / 13C1 = 11/13
Therefore, the probability that the animal patient is NOT a bird is 11/13.
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Let A be the set of numbers that are multiples of 3 between 1 and 16 and B be the set of even natural numbers up to and including 20. Find A∪B.
Write your answer in proper set notation.
Make sure each element is only listed once.
========================================================
Work Shown:
A = set of multiples of 3 between 1 and 16
A = {3, 6, 9, 12, 15}
B = set of even natural numbers up to and including 20
B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
A u B = {3, 6, 9, 12, 15, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
A u B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20}
---------------
Explanation:
The U stands for "set union". It's where we combine two or more sets together to form a larger set. The duplicates are tossed out. This is what your teacher meant when writing "Make sure each element is only listed once". Writing A u B indicates "the set of values in either set A, set B, or both".
In this case, the duplicates are "6" and "12" since they are found in set A and B simultaneously. They are in the overlapped area of both sets. It might help to draw out a Venn Diagram.
Common convention is to sort the items in the set. Though technically a set like {1,2,3} is the same as {3,1,2}.
Don't forget about the curly braces to indicate to the reader that this is a set of values.
f(x) = 3x + 2, what is f(5)
f(5)=17
Step-by-step explanation:
f(5)=3(5)+3
=15+2=17....