Write an equation in point-slope form of the line that passes through the given point and with the given slope (-7,2); m =7
Answer:
Y = 7x + 51
Step-by-step explanation:
Point-slope form is in this form: y = mx + b where b is the y-intercept and m is the slope. We have the slope, and we already have a point that must be on the line. The only thing we need is the y-intercept, so we can plug in the given point and the slope to solve for b.
Plug in (-7, 2) for x and y and the slope(7) for m. This gives: [tex]2 = 7*-7 + b[/tex], or [tex]2 = -49 + b[/tex]. Now add 49 to both sides to isolate x, and we get that [tex]b = 51[/tex]. We have everything we need for the equation now, so plug in the slope and y-intercept for m and b, giving us y = 7x + 51.\
Hope this helps!
what types of problems can be solved using the greatest common factor?what type of problems can be solved using the least common multiple
The GCF can be applied to problems requiring the division of something into equal groups or an equal number of groups, as well as problems requiring the simplification of a fraction.
The LCM can be used to solve problems involving the overlap of two activities or something similar, as well as problems involving the addition of two or more fractions with different denominators.
What is the GCF?The greatest common factor of two or more integers that are not all zero in mathematics is the largest positive integer that divides each of the integers.
A set's greatest common factor (GCF) is the largest factor that all of the numbers share.
For example, the numbers 12, 20, and 24 all have two common factors: 2 and 4. The greatest is 4, so the GCF of 12, 20, and 24 is 4. The LCM, or smallest common multiple, is the smallest common number or multiple of any two numbers. The least common multiple of 3 and 5 is 15, for example.
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An organic food company needs to paint its new silo. The silo is a cylinder with a height of 24 yards and a base 3 yards in diameter. The paint the company has selected will cover 150 square feet per gallon. How many gallons of paint will be needed to paint the top and lateral surface of the silo?
Applying the formula of the lateral surface area of a cylinder, the number of gallons needed to paint the top and the lateral surface is: 314,901 gallons.
What is the Lateral Surface Area of a Cylinder?The lateral surface area of a cylinder = 2πrh, where h is the height, r is the radius of the cylinder.
Given the following:
Height of the cylinder (h) = 24 yardsDiameter = 3 yardsRadius (r) = 1/2(diameter) = 1/2(3) = 1.5 yardsLateral surface area of the cylinder = 2 × π × 1.5 × 24 = 226.19 yards²
Area of the top = area of circle = πr² = π(1.5²) = 7.07 yards²
Area to be painted = 226.19 + 7.07 = 233.26 yards²
Convert square yards to square feet:
1 square yard = 1 square feet
233.26 square yards = 2099.34 square feet
Gallons of paint needed = 2099.34 × 150 = 314,901 gallons.
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a mother is 21 years older than her son. in 6 years, she will be 5 times as old as her son. where is the father?\
The father is with the son's mother.
Given that,
a mother is 21 years older than her son.
Let us consider M be the age of the mother and S be the age of the son
which implies that,
M = S + 21 ---------------(1)
and in 6 years, mother will be 5 times as old as her son
i.e. M + 6 = 5(S + 6)
M = 5S + 24 ------------- (2)
so equation (1) and (2) implies that,
S + 21 = 5S + 24
21 = 4S + 24
S = - 3/4
That means son is - 3/4 years old or - 9 months.
The time at which we know the father will be with son's mother.
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Help, I don't understand how to do this and it's due tomorrow. (Correct answer shown.)
The minimum value of the function occurs between 4 and 5.
What is a function?A function is a relation where every input is connected to only one possible output from a set of available inputs.
Given the table of values.
Note that the value of the function is a minimum of between 4 and 5.
Hence, the minimum value of the function occurs between 4 and 5.
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It is an association between two sets of objects which is paired according to a certain rule. A. Domain B. Range C. Relation D.Function
Relation is an association between two sets of objects which are paired according to certain rule.
As given in the question,
Given statement is:
Association between the two given sets of objects that are paired according to the certain rule.
Explanation of each option for the given statement:
A. Domain : Domain represents all the input values of any relation.
It is not correct option.
B. Range : It represents all the output values of any relation.
It is not correct option.
C. Relation : It represents the association between two sets which are collection of ordered pairs ( x, y ) where each input value is associated with output value.
It is the correct option.
D. Function : It represents each input is uniquely related to output value.
Not a correct option.
Therefore, relation is an association between two sets of paired objects with certain rule.
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due to construction, the speed limit along an 8-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit?
Due to construction, approximately 5 minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit.
Given that,
length of highway is 8 miles
Reduced length is 55 miles
Hours taken is 35 miles per hour.
Let t₁ is time taken is 55 mph
t₁ = 8/55
Let t₂ is time taken is 35 mph
t₂ = 8/35
Difference in time = 8/35 - 8/55
= 8 × 20 / (35 * 55) hour
= 160 × 60 / (35 × 55) mins
= 4.7
= 5 minutes (approximately)
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A circle has a circumference of 6. It has an arc of length 1. What is the central angle of the arc, in degrees?
Answer:
60 degrees
Step-by-step explanation:
The arc length is 1/6th of the total ....the angle will be 1/6th of the total 360° of the circle
1/6th X 360 = 60 °
Answer:
60 degrees
Step-by-step explanation:
1.) Figure out which portion of the circle that the arc is. Since the total circumference is 6, and the arc is 1, that means that the arc is 1/6 of the circle.
2.) Now, figure out the measure of the angle. Since the total angle measure in a circle is 360 degrees, we multiply 1/6*360 to figure out the measure. This is equal to 60 degrees.
Determine the distance covered by a car traveling 80 km/h each unit and given time round answers to the nearest unit.
A. Kilometers in on hour?
B. Meters in one hour?
C. Meters in one minute?
D. Meters in one second?
Determine the distance covered by a car traveling 80 km/h for each unit and time given. The answer should be in meter in one hour.
What is a kilometer?
1,000 meters is one metric unit of measurement (approximately 0.62 miles).
The car is travelling at the speed of 80 kilometers per hour.
One hour is 60 minutes.
So car will travel in ideal conditions 80 kilometers in one hour which is 60 minutes.
So just convert the kilometers into meters.
1 kilometer = 1000 meters,
Thus,
80 kilometers = 80,000 meters.
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the area of trapezoid $abcd$ is $60$. one base is $4$ units longer than the other, and the height of the trapezoid is $5$. find the length of the median of the trapezoid.
The length of the median of the trapezoid ABCD is 12 .
In the question ,
it is given that ,
the area of the trapezoid ABCD is = 60 ,
the height of the trapezoid ABCD is = 5 ,
let one base of the trapezoid ABCD be = a ,
So, b = a + 4 ,
Substituting the value in the formula for Area of the trapezoid = A =(a+b)h/2
(a + a + 4)5/2 = 60
(2a + 4)5 = 120
2a + 4 = 120/5
2a + 4 = 24
2a = 24 - 4
2a = 20
a = 20/2
a = 10 units
and other base = 10 + 4 = 14 units
So , the length of the median will be = (10 + 14)/2
= 24/2 = 12 units
Therefore , the length of median is = 12 .
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five cards are darwn from a standard deck of cards. how many different hands consist of four queens and one king
2,598,960 many different hands consisting of four queens and one king.
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
To choose 4 kings, there is only one way, and to choose a queen, there are four.
Thus, there are 4 different methods to draw the 5 cards as instructed.
The probability of drawing cards is taken into account while calculating the number of ways to draw 5 cards from a typical 52-card deck.
= 52!/(47!)(5!) = 2,598,960.
Hence, 2,598,960 many different hands consisting of four queens and one king.
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what is the largest integer that is a divisor of $(n 1)(n 3)(n 5)(n 7)(n 9)$ for all positive even integers $n$? (a) 3 (b) 5 (c) 11 (d) 15 (e) 165
The largest integer that is a divisor of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) for all positive even integers is 15
The correct answer is an option (d)
In this question, we need to find the largest integer that is a divisor of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) for all positive even integers n.
We can observe that (n + 1), (n + 3), (n + 5), (n + 7) and (n + 9) are 5 consecutive odd integers
In every 5 consecutive odd positive integers, one of them is always divisible by 3 and one of them is always divisible by 5.
This means, (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will be divisible by both 3 and 5
i.e., (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) will also divisible by 15 (3 * 5 = 15)
Therefore, the largest integer that is a divisior of (n + 1)(n + 3)(n + 5)(n + 7)(n + 9) = 15
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The values for random variables in a Monte Carlo simulation area. selected manually.b. generated randomly from probability distributions.c. taken from forecasting analysis.d. derived secondarily using formulas.
The values for random variables in a Monte Carlo simulation area that were chosen at random from probability distributions are the right answer.
What is Monte Carlo Simulation ?
The Monte Carlo Method, also referred to as the Monte Carlo Simulation or a multiple probability simulation, is a mathematical method for predicting potential outcomes of an uncertain event. To help people make better decisions when faced with uncertainty, John von Neumann and Stanislaw Ulam developed the Monte Carlo Method during World War II.
Therefore, the values for random variables in a Monte Carlo simulation area that were generated at random from probability distributions are the right answer.
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The correct response is the set of values for random variables in a Monte Carlo simulation region that were randomly selected from probability distributions.
In order to represent uncertainty in a model that represents a real system and computes the values of model outputs, a Monte Carlo technique is used. During World War II, John von Neumann and Stanislaw Ulam created the Monte Carlo Method to aid people in making better judgments when faced with uncertainty.
As a result, the correct response is the random values for random variables that were produced using probability distributions in a Monte Carlo simulation area.
blackhawk tech gives four presidential scholarships. if there are 58 nominees, in how many ways can the scholarships be awarded?
If there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.
What are the Permutation and Combination?
Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.
If there are 58 nominees, and Blackhawk can give only four scholarships then the number of ways is =
[tex]=^nC_r\\\\=^{58}C_4\\\\=\frac{58!}{4!*54!}\\\\=\frac{58 * 57 * 56 * 55}{4 * 3 * 2 *1}\\\\=4,24,270[/tex]
Hence, if there are 58 nominees, then the number of ways in which scholarships can be awarded is 4,24,270.
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help me with this i cant figure out the second part
The value of c that will make the expression x² + 24x + c a perfect trinomial is 144.
The perfect squared trinomial as a perfect binomial is (x + 12)²
How to find the value of c in the expression?An expression obtained from the square of the binomial equation is a perfect square trinomial.
In other words, perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial.
If a trinomial is in the form ax² + bx + c is said to be a perfect square, if and only if it satisfies the condition b² = 4ac.
Therefore,
x² + 24x + c
where
a = 1b = 24c = ?Therefore,
b² = 4ac
24² = 4 × 1 × c
4c = 576
divide both sides by 4
c = 576 / 4
c = 144
Therefore,
c = 144
The perfect squared trinomial as a perfect binomial is as follows:
x² + 24x + 144
x² + 12x + 12x + 144
x(x + 12) + 12(x + 12)
(x + 12)(x + 12)
(x + 12)
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1.5 times 4/5 in fraction form
Answer: 1 1/5
Step-by-step explanation: you can write it as 1.5/1 times 4/5.
multiply by numerator and denominator so 1.5*4 which is 6
and 1*5 which is 5.
Now you have 6/5
6 can go into 5 once and you have 1 extra so 1 1/5
if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?
At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, the value of a margin of error of x is 1.534%.
In the given question, at a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, then we have to explain how should we interpret that.
The given confidence interval = 95%.
We can write it as CI = 0.95.
An approval rating is 55%.
We can write it as(p) = 0.55
A margin of error is x.
Let the value of sample size n = 1000.
So the margin of error;
ME = z× {p(1-p)}/√n
The value of z for confidence interval of 95% is 1.96.
Now putting the value
x = 1.96× {0.55(1-0.55)}/√1000
x = 1.96× {0.55×0.45}/31.623
x = 1.96× 0.2475/31.623
x = 1.96×0.00783
x = 0.01534
x = 1.534%
So the margin of error should be 1.534%.
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The right question is:
At a confidence interval of 95%, if a polling result states that a president has an approval rating of 55%, with a margin of error of x, how should you interpret that?
PLEASE HELP ASAPPP. WILL GIVE BRAINLIEST AND 5.0 STAR RATING.
Answer:
$21.6
Step-by-step explanation:
[tex]720*\frac{3}{100} =720*0.03=21.6[/tex]
y varies directly as x. y = 18 when x = 5. Find x when y = 36.
Answer:
Step-by-step explanation:
y varies directly as x.
y = 18 , x = 5
y =36 then x also double,
x = 10
Solve for x. Round to the nearest tenth of a degree, if necessary.
Check the picture below.
[tex]tan(x)=\cfrac{\stackrel{opposite}{50}}{\underset{adjacent}{42}}\implies tan(x)=\cfrac{25}{21}\implies x=tan^{-1}\left( \cfrac{25}{21} \right)\implies x\approx 50^o[/tex]
Make sure your calculator is in Degree mode.
The illustration below shows the graph of yyy as a function of xxx.
Complete the following sentences based on the graph of the function.
Initially, as xxx increases, yyy
.
The slope of the graph is equal to
for all xxx between x=0x=0x, equals, 0 and x=3x=3x, equals, 3.
Starting at x=3x=3x, equals, 3, the function value yyy
as xxx increases.
The slope of the graph is equal to
for xxx between x=3x=3x, equals, 3 and x=5x=5x, equals, 5.
For xxx between x=0x=0x, equals, 0 and x=4x=4x, equals, 4, the function value yyy
000.
For xxx between x=4x=4x, equals, 4 and x=8x=8x, equals, 8, the function value yyy
000.
HELP!! WILL GIVE BRAINIEST
For the function, [tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex], the value of h(4) is h(4) ≈ 8.7
Evaluating a functionFrom the question, we are to determine the value of h(4) in the given function.
The given function is
[tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex]
To determine the value of h(4), substitute 4 for x in the given function
[tex]h(x) = \frac{50}{5.5 + 8e^{-0.9x} }[/tex]
[tex]h(4) = \frac{50}{5.5 + 8e^{-0.9(4)} }[/tex]
[tex]h(4) = \frac{50}{5.5 + 8e^{-3.6} }[/tex]
[tex]h(4) = \frac{50}{5.5 + 8(0.0273237) }[/tex]
[tex]h(4) = \frac{50}{5.5 + 0.21859 }[/tex]
[tex]h(4) = \frac{50}{5.71859 }[/tex]
h(4) = 8.7434
h(4) ≈ 8.7
Hence, the value of h(4) is 8.7
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What is the surface area of this triangular prism?
5 cm
8 cm
3.5 cm
7.2 cm
Answer:130.09
Step-by-step explanation:
Using the formulas
A=2AB+(a+b+c)h
AB=s(s﹣a)(s﹣b)(s﹣c)
s=a+b+c
2
Solving forA
A=ah+bh+ch+1
2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=5·7.2+8·7.2+3.5·7.2+1
2·﹣54+2·(5·8)2+2·(5·3.5)2﹣84+2·(8·3.5)2﹣3.54≈130.08536
Enlarge the triangle by scale factor -3 with centre (3,3)
Dilating a triangle by - 3 with vertices (3, 4), (3, 5), and (5, 5) will be
(- 9, - 12), (- 9, - 15) and (- 15, - 15).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A triangle with vertices (3, 4), (3, 5) and (5, 5).
Now dilating by a scale factor of - 3 will have every point multiplied by - 3 and the new vertices will be (- 9, - 12), (- 9, - 15) and (- 15, - 15).
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A rose cost $3.40 . How much will it cost to buy a dozen roses?
Answer:
$40.8
Step-by-step explanation:
You would do 3.40 * 12 because a dozen is 12 roses.
So 3.40 × 12 = 40.8
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pharmacy technicians are concerned about the rising number of fraudulent prescriptions they are seeing. a small pharmacy sees 1,500 new prescriptions a month, 28 of which are fraudulent. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
The mean and standard deviation of sampling distribution are 0.0187 and 0.010 respectively
The mean is a measure of location which tells us the average of observation.
Standard deviation tells us how dispersed a data is or how much variation our data contains.
According to question,
The population size : N = 1500
Number of fraudulent in a month : 28
Population proportion : P = 28/1500
=> P = 0.0187
Sample size: n = 180
Sample proportion : p = 28 / 180
=> p = 0.156
Therefore The mean of sampling distribution for the sample size 28,
μ = P
=> μ = 0.0187
The standard deviation will be
=> σ = [tex]\sqrt{\frac{p(1-p)}{n}}[/tex]
Substituting the value,
=> σ = [tex]\sqrt{\frac{0.0187(1-0.0187)}{180}}[/tex]
=> σ = 0.010
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Find a number so that 100% of it is 26.
Answer:
would it not be 26? I honestly don't know
If 6a = 5b, what are the following ratios?
2a:7b
Answer:
If 6a = 5b then the ratio of 2a : 7b is 5 : 21
Explanation:
Given that 6a = 5b
We have to find the ratio of 2a : 7b
Let us first solve the given expression and find values of a and b
6a = 5b
So we have found that a = 5 and b = 6
Finding ratio of 2a : 7b
2a : 7b = 2(5) : 7(6)
2a : 7b = 10 : 42
On simplifying to lowest terms,
2a : 7b = 5 : 21
Thus the ratio of 2a : 7b is 5 : 21
A strand of hair grows at a constant rate of 1/2 inch per month. A different strand of hair grows at a constant rate of 4 inches per year.
Find out if this is or isn't a proportional relationship ?
I WILL GIVE BRAINLIEST
Answer:This is not a proportional relationship.
Step-by-step explanation:
Ian's home is represented by the point (4, 4) on the coordinate grid. Joe's home is represented by the point (10, 6) on the coordinate grid. They want to meet at a diner is halfway between their houses (i. E. , divides the line from ian's house to joe's house in a 1:1 ratio). What are the coordinates of the diner?.
(7, 5) are the required coordinates of the diner.
What are coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
You do the reverse to determine a point's coordinates in a coordinate system.
Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there.
To find the y-coordinate, repeat the previous step while adhering to a horizontal line.
So, we must discover the halfway point between Lan's house and Joe's house in order to get the diner's coordinates.
The following equation will determine the midway between any two points:
M(x1 + x2/2, y1 + y2/2)
There are (4, 4), the point, and the point replaces the specified values:
M(4+10/2, 4+6/2)
M(7, 5)
Therefore, (7, 5) are the required coordinates of the diner.
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