The table below shows the amount of money needed to buy certain amounts of fabric. If the price is the same for each yard, how much money would 12 yards of fabric cost?
Correct answer will get brainliest
Answers
The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The two points are (3, 5) and (6, 10).
Let 'x' be the number of yards of fabric and 'y' be the cost in dollars. Then the equation is given as,
(y - 5) = [(10 - 5) / (6 - 3)](x - 3)
y - 5= (5/3)x - 5
y = (5/3)x
The cost of the 12 yards of fabric is given as,
y = (5/3) × 12
y = 5 × 4
y = $20
The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.
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[r] bastien, inc. has been manufacturing small automobiles that have averaged 45 miles per gallon of gasoline in highway driving. the company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 45 miles per gallon in highway driving. an independent testing service road-tested 52 of the automobiles. the sample showed an average of 46.1 miles per gallon. the sample standard deviation is 5.3 miles per gallon. conduct an appropriate hypothesis test. find the t-statistic and the appropriate conclusion at the 0.01 level of significance.
Answers
According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
It is given to us that -
Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving
Company now advertises that its new small cars average more than 45 miles per gallon in highway driving
52 automobiles were tested
Sample average is 46.1 miles per gallon
Sample standard deviation is 5.3 miles per gallon
Significance level is 0.01
We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.
Let us assume that -
p = population of average gasoline of new small cars in highway driving
According to the given information,
Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -
[tex]H_{0}[/tex] : [tex]p\leq 45[/tex] miles per gallon
Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -
[tex]H_{A}[/tex] : [tex]p > 45[/tex] miles per gallon
For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.
According to one sample z test, the value of test statistic is given as -
[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }[/tex] ------ (1)
where,
[tex]X_{avg}[/tex] = Sample mean
p = hypothesized population mean
S = Sample standard deviation
n = Sample size
According to the given information, we have
[tex]X_{avg}[/tex] = 46.1 miles per gallon
p = 45 miles per gallon
S = 5.3 miles per gallon
n = 52
Substituting the above values in equation (1), we have
[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }\\= > T = \frac{(46.1 -45)}{\frac{5.3}{\sqrt{52} } }\\= > T = \frac{1.1}{0.735}\\ = > T = 0.634[/tex]
It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.
But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,
0.634 < 2.58
This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.
Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
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According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
It is given to us that -
Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving
Company now advertises that its new small cars average more than 45 miles per gallon in highway driving
52 automobiles were tested
Sample average is 46.1 miles per gallon
Sample standard deviation is 5.3 miles per gallon
Significance level is 0.01
We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.
Let us assume that -
p = population of average gasoline of new small cars in highway driving
According to the given information,
Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -
H0 = p<= 45 : miles per gallon
Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -
HA : p > 45 : miles per gallon
For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.
According to one sample z test, the value of test statistic is given as -
T = (X - p)/(SD/√n)
where,
X = Sample mean
p = hypothesized population mean
S = Sample standard deviation
n = Sample size
According to the given information, we have
X = 46.1 miles per gallon
p = 45 miles per gallon
S = 5.3 miles per gallon
n = 52
Substituting the above values in equation (1), we have
T = 46.1-45/(5.2/√52)
T = 1.1/0.735
T = 0.634
It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.
But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,
0.634 < 2.58
This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.
Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
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Andrea is 165 cm tall, correct to the nearest cm. Joel is 170 cm tall, correct to the nearest 10 cm. Calculate the upper and lower bound for each person.
Andrea lower bound =
Andrea upper bound =
Joel lower bound =
Joel upper bound=
Answers
Answer:
Step-by-step explanation:
andrea lb: 164.5cm
andrea ub: 165.5 cm
joel lb: 165
joel ub: 175
what is the minimum sample size required to estimate a population mean with a confidence of 95%, if the margin of error is 2 units and a standard deviation of 10 units? show formula and your calculations. round to the next whole number.
Answers
The minimum sample size required to estimate a population mean with a confidence of 95%, a margin error of 2 units and a standard deviation of 10 units is 96.
A minimum sample size is the number of participants one needs to maintain their target confidence interval (margin of error) and confidence level while obtaining results that accurately represent the population they are studying.
The formula to calculate the minimum sample size for the population mean is [tex]\bold{n=\left(\frac{z\times \sigma}{E}\right)^2}[/tex]. Here, n is the sample size, z is the confidence level, σ is the standard deviation, and E is the margin error.
Given, the z-value for 95% confidence is 1.96, E is 2 and σ is 10.
Then, the minimum sample size is,
[tex]\begin{aligned}n&=\left(\frac{1.96\times10}{2}\right)^2\\&=(9.8)^2\\&=96.04\\&\approx96\end{aligned}[/tex]
The answer is 96.
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Which of the following is NOT a criterion for similarity?
A. AA postulate
B. SAS postulate
C. SSS postulate
D. RHS postulate
Answers
Answer:
Answer Option A: AA Postulate
All other options prove two triangles are similar; however, the RHS Postulate proves two right-angle triangles to be congruent, not similar.
how many ways can you distribute 6 faceless players over 4 servers (each of the servers are identical)?
Answers
Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.
1. There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3.
2. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck.
3. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.
4. Therefore, there are 4 x 1128 = 4512 possible 5 card poker hands with at least 3 aces that can be dealt from a standard deck of 52 cards.
There are 4 aces in a standard deck of 52 cards, so the maximum number of aces in a 5-card poker hand is 3. There are C(4,3) = 4 ways to choose 3 aces out of the 4 aces in the deck. For the remaining 2 cards, there are C(48,2) = 1128 ways to choose them from the 48 non-ace cards.
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graph the line that passes through the points (0,-8) and (5,-5) and determine the equation of the line
*I can graph it, I just need the equation*
Answers
The linear equation that passes through the points (0,-8) and (5,-5) is:
y = (3/5)*x - 8
How to find the equation of the line?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
Here we have the two points: (0,-8) and (5,-5)
Then the slope is:
a = (-5 + 8)/(5 - 0) = 3/5
And because of the point (0, -8) we know that the y-intercept is -8, then the linear equation is:
y = (3/5)*x - 8
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find the relative maxima and relative minima, if any, of the function. (if an answer does not exist, enter dne.) g(x)
Answers
The relative maxima and minima of the function g(x) are at the point (-4, 22) at the local maxima and at point (4,-124) at the local minima.
Given:
Function g(x) = x^3 - 48x + 4
Take the derivative and set it equal to zero
3x^2 - 48 = 0
x^2 = 48/3 = 16
x = sqr16 = ±4
At x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124
Point (4,-124) is a local or relative minimum
At x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122
The point (-4, 22) is a local or relative maximum
Refer to this complete question:
Find the relative maxima and minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =?
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Quadrilateral JKLM is similar to quadrilateral NOPQ. Find the measure of side PQ.
Round your answer to the nearest tenth if necessary.
Answers
Answer:
57.8
Step-by-step explanation:
You have quadrilateral JKLM similar to quadrilateral NOPQ with given sides JK = 9, LM = 13.7, NO = 38, and you want the measure of PQ.
ProportionCorresponding sides in similar figures are proportional in length:
PQ/LM = NO/JK
PQ/13.7 = 38/9
PQ = 13.7(38/9) = 2603/45 ≈ 57.8
The measure of PQ is approximately 57.8 units.
the weight of trucks traveling on a particular section of i-475 has a population mean of 15.8 tons and a population standard deviation of 5.2 tons. what is the probability a state highway inspector could select a sample of 52 trucks and find the sample mean to be 14.3 tons or less? a) 0.0188 b) 0.3758 c) 0.1242 d) 0.4812
Answers
Option b is correct.
Therefore, the probability that a state highway inspector would choose a sample of 49 trucks and discover that the sample mean was 14.3 tons or less is equal to 0.3758
Given: The population mean and standard deviation for the weight of trucks moving on a given stretch of I-475 are both tons.
n=49 sample size
Consider x to be the random variable that represents the truck weight.
z-score: z = x - μ ÷ σ/[tex]\sqrt{n}[/tex]
When x=14.3 tons
z = [tex]\frac{14.3 - 15.8}{\frac{4.2}{\sqrt{49} } }[/tex] ≈ -2.5
The likelihood that a state highway inspector will choose 49 trucks as a sample and discover that the sample mean is 14.3 tons or less is as follows:
P(X ≤ 14.3) = P(z < -2.5) = 0.3758
Therefore, the probability that a state highway inspector would choose a sample of 49 trucks and discover that the sample mean was 14.3 tons or less is equal to 0.3758
option b is correct.
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What percent of 200 is 104?
Answers
Answer:
52%
Step-by-step explanation:
What percent of 200 is 104?
104/200 = 0.52
0.52 = 52%
(c) Compute and interpret the mean of the random variable x The mean is activities (Type an integer or a decimal Do not round.) Which of the following interpretations of the mean is correct? O A. As the number of experiments decreases, the mean of the observations will approach the mean of the random variable O B. The observed value of an experiment wil be equal to the mean of the random variable in most experiments O C. As the number of experiments increases, the mean of the observations will approach the mean of the random variable OD. The observed value of an experiment will be less than the mean of the random variable in most experiments (d) Compute the standard deviation of the random variable x The standard deviation is activities (Round to one decimal place as needed )
Answers
The correct answer is : c) As the number of experiments increases, the mean of the observations will approach the mean of the random variable.
Mean of random Variable x :
The expected value of a discrete random variable X, symbolized as E(X), is often called the long-term average or mean (symbolized as μ). This means that if you run the experiment many times over time, you would expect this average. For example, let X = the number of heads you get when you toss 3 fair coins. If we repeat this experiment (tossing 3 fair coins) many times, the expected value of X will be the expected average number of heads per 3 tosses.
Standard Deviation of Random Variable:
A measure of the variance of a random variable distribution that determines how for a value is from its expected value.
The standard deviation of a random variable X is often written as σ or σₓ.
For discrete random variables, the standard deviation is computed by taking the square of the difference between the value of the random variable and the expected value multiplied by the associated probability of the value of the random variable. Calculate the value of a random variable and finally take the square root.
In symbols σ = √ (x - μ)² P(X =x)
The equivalent formula is σ = [tex]\sqrt{E(x^{2}) - [{E(x^2)]}[/tex]
The square of the standard deviation equals the variance Var(X) = σ².
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Mrs. Wu's car is completely out of gas. Gas costs $3.56 per gallon, and the car's gas tank can hold 12.5 gallons. How much money will Mrs. Wu spend to fill the gas tank?
Answers
Answer:It will cost Mrs. Wu $44.5 to fill the gas tank.
Step-by-step explanation: 3.56x12.5= 44.5
How do you write 0.09 as a fraction?
Answers
Answer:
9/100
Step-by-step explanation:
numerator = whole number
denominator = 100
9/100
which of the following represents the average rate of change to the function g(x) = 3/2x + 1 over the interval -2 < x < 8
Answers
The average rate of change to the function is (d) 3/2
How to determine the average rate of change to the function?From the question, we have the following parameters that can be used in our computation:
g(x) = 3/2x + 1
Also, we have the interval to be
-2 < x < 8
This interval can be expressed as
a = -2 and b = 8
So, we start by calculating g(-2) and g(8)
Substitute the known values in the above equation, so, we have the following representation
g(-2) = 3/2 * (-2) + 1
g(-2) = -2
Also, we have
g(8) = 3/2 * (8) + 1
g(8) = 13
The average rate of change to the function is then calculated as
Rate = [g(8) - g(-2)]/[8 + 2]
So, we have
Rate = (13 + 2)/(8 + 2)
Evaluate
Rate = 3/2
Hence, the average rate is 3/2
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erin wants to find the circumference of a circle with radius 7cm . which of following can she use to find the circumference of the circle ?
A. 2x 7 x π
B 2 x 14 x π
C 7/2 x π
D 14 xπ
E. 49 x π
Answers
To find the circumference of a circle with a radius of 7 cm, Erin should use 2×7×π. This is because the circumference of a circle is calculated by the formula 2×π×r.
What is the circumference of a circle?The circumference is the measure of the perimeter of a circle. Since we know that from every point on the circle to its center has an equal length and is said to be its radius, the perimeter of the circle we can write as
Circumference = 2 × π × r units.
Here r is the radius of the circle.
Calculation:It is given that Erin wants to find the circumference of a circle with a radius of 7 cm.
So, first, she has to know the formula for finding the circumference.
Here the radius is given as 7 cm i.e., r = 7 cm
Then, the circumference of the given circle is
= 2 × π × r
On substituting the radius value into the above formula, we get
Circumference = 2 × π × 7 cm
⇒ 14π cm
So, she needs to use option A. 2 × 7 × π for finding the required circumference. This is the first step for finding the circumference of a circle.
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write log7t as a base 2 logarithm. note: if you are using log you need to type it in and use the subscript button on the keyboard. there is no log button.
Answers
By using logarithm principles, log₇t in base 2 logarithm equals log₂t/log₂7.
What is logarithm?The most frequent logarithms are common logarithms with a base of 10, binary logarithms with a base of 2, and natural logarithms with a base of e 2.71828. A logarithm is the number of powers that a number must be raised to in order to acquire another number (see Section 3 of this Math Review for more about exponents). The base ten logarithm of 100, for example, is 2, because ten raised to the power of two equals 100: log 100 = 2.
Here,
logₓy=logₐy/logₐx
log₇t=log₂t/log₂7
log₇t in base 2 logarithm is log₂t/log₂7 by the help of properties of logarithm applied.
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At Smith Mountain Lake Boat Rentals, it cost $25 per hour to rent a pontoon boat, plus a one-time charge for cleaning. The Bengal family rented a boat from 11 am - 6:30 pm and paid $226.50. If the Jones family rented a boat from 8 am- 1pm, how much did the pay?
Answers
Answer: $164
Step-by-step explanation:
25*7=175
175+12.5
226.50-187.50
5*25=125+39
Jones family payed $164
A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 7700 kilograms have already been loaded into the container. Use the drop-down menu below to write an inequality representing cc, the total number of 40-kilogram crates that can be loaded into the shipping container.
Answers
An inequality representing c, the total number of 40-kilogram crates that can be loaded into the shipping container is; 7700 + (40c) ≤ 27500
The maximum number of 40 kg crate is 380.
How to solve Inequality Word Problems?We are given;
Weight of the crate = 40 kg
Greatest weight that the container can load = 27500 kg
Weight of the other shipments on the container = 7700 kg
The greatest number of 40 kg crates is represented by the letter "c".
Thus;
The weight of the other shipment + weight of crate x number of crates ≤ greatest weight of the container
Plugging in the relevant values gives;
7700 + (40c) ≤ 27500
7700 + 40c ≤ 23000
40c ≤ 27500 - 7700
40c ≤ 19800
c ≤ 19800/40
c ≤ 495
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T=4m^2 - 11 Work out the value of T when m = -3
Answers
Answer: T=25
Step-by-step explanation:
T=4m^2 -11
We know that m= -3
-3^2 = 9
So the equation is T=4 (9) -11
T = 36 -11
T= 25
how many numbers less than 2017 are both the sum of two consecutive positive integers, and the sum of five consecutive positive integers?
Answers
201 numbers are less than 2017
If and only if it is odd, a number is the sum of two successive integers.
Only if it is a multiple of 5 is a number considered to be the sum of 5 consecutive integers. If you have any doubts, remember that the product of five consecutive integers equals five times the integer in the middle (this remains true if instead of 5 you put in any odd positive integer).
Consequently, you are seeking odd multiples of 5 below 2017. There are 403 multiples of 5 immediately below 2017, or 2015/5. Of those, 202 are odd. It is necessary to eliminate the number 5 because it is not completely positive when expressed as the sum of its successive integers, which is (-1)+0+1+2+3.
There are 201 numbers left.
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how to solve - |x + 5| < -17
Answers
Answer:
x∈(−∞,−22)∪(12,+∞)
Step-by-step explanation:
Evaluate
−∣x+5∣<−17
Calculate
∣x+5∣>17
Separate the inequality into 2 possible cases
x+5>17x+5<−17
Solve the inequality for x
x>12x+5<−17
Solve the inequality for x
x>12x<−22
Solution
x∈(−∞,−22)∪(12,+∞)
$89.75 scooter ; 7.25% tax
Answers
Answer: $96.25
Step-by-step explanation:
Take 89.75 divided by 100% = 0.8975
Then times 7.25% = $6.5
Total is 89.75 + 6.5 = $96.25
How do you find the maclaurin series expansion of f(x)=(1−x)^−2?
Answers
The Maclaurin series expansion of f(x) = 1/(1-x)² is
1 + 2x + 6x² + 24x³ +......
The general expression for the Maclaurin series is given by the formula:
f(x) = f(0) + xf'(0) + x²f''(0) + ..... + xⁿf⁽ⁿ⁾(0)+...
= ∑ f⁽ⁿ⁾ (0)xⁿ/n!
n= 0 to infinity
Specifying the convergence region completes the Maclaurin series formulation. Detailed five steps for determining the Maclaurin series of
f(x) = 1/(1-x)²
Step 1 : Find Derivatives for f(x)
f(x) = 1/(1-x)²
f'(x) = -2(1-x)⁽⁻²⁻¹⁾ (-1) = 2/(1-x)³
The second derivative of f(x) is the derivative of f''(x) :
f"(x) = 2(-3)(1-x)⁽⁻³⁻¹⁾(-1) = 6/(1-x)⁴
Differentiating again, f"'(x) = 6(-4)(1-x)⁽⁻⁴⁻¹⁾(-1)
= 24/(1-x)⁵
Thus, the nᵗʰ derivative is ,
f⁽ⁿ⁾(x) = (n+1)!/(1-x)⁽ⁿ⁻¹⁾
Step 2: Evaluate These Derivatives and f(x) at x=0 let x = 0 , f(0) = 1
f'(0) = 2 , f"(0) = 6 , ....... , f⁽ⁿ⁾(0) = (n+1)!
Step 3 : Now, the Sum of Products :
f(x) = f(0) + xf'(0) + x²f''(0) + ..... + xⁿf⁽ⁿ⁾(0)+...
xf'(0) = 2x
x²f"(0) = 6x²
x³f"'(0) = 24 x³
----------------------------
xⁿf⁽ⁿ⁾(0)= (n+1)!
Thus, the Maclaurin series for ln(1 + x) is this:
f(x) = (1−x)⁻² = 1 + 2x + 6x² + 24x³ +......
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How do you convert 2−2i to polar form?
Answers
2 - 2i can be written in polar form as [tex]2\sqrt{2} \ cis\frac {-3\pi}{4}[/tex]
To convert a complex number in Cartesian form (such as 2 - 2i) to polar form, you can use the following steps:
Find the magnitude (or absolute value) of the complex number. This is the distance from the origin to the point representing the complex number in the complex plane. The magnitude of 2 - 2i is approximately 2.83.Find the argument of the complex number. This is the angle between the positive real axis and the line connecting the origin to the point representing the complex number in the complex plane. To find the argument, you can use the inverse tangent function (also known as arctangent or atan). The argument of 2 - 2i is approximately -135 degrees, or -2.356 radians.Combine the magnitude and argument to express the complex number in polar form. In polar form, a complex number is written as "magnitude (angle)", where the angle is expressed in either degrees or radians. So, the polar form of 2 - 2i is approximately 2.83 (-135 degrees) or 2.83 (-2.356 radians).To learn more about complex number, visit:
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How do you solve 14p−8=22+20p ?
Answers
The value of p is -5
Simply use cross multiplication :
The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.
Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.
[tex]14p-8=22+20p\\or, 14p-20p=22+8\\or, -6p=30\\or, p=-\frac{30}{6} \\or, p= -5[/tex]
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A rectangle has sides of (4x + 13) and (5x – 2). What is the area of the rectangle?
Answers
Answer:
Below
Step-by-step explanation:
The area is just the two side lengths multiplied together
area = (4x+13)(5x-2) = 20x^2 +57x -26 units^2
what is the slope-intercept form of the function described by this table? x 1 2 3 4 y 1 −2 −5 −8 enter your answer by filling in the boxes. y = x
Answers
The function depicted in the table has the following slope-intercept form:
y = -3x + 4
Explain the equation of straight line?The formula for a straight line is y=mx+c where c is the slope at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.For such equation of every straight line, the slope-intercept form is provided by:
y = mx +c
where:
The slope of the line is m.b is the line's y-intercept.Choose 2 points from the provided table, such as (2,-2) and (3,-5) and to use the evidence that the slope is, to determine the line's slope.
m = (y2 - y1)/(x2 - x1)
m = -5 + 2 / 3 - 2
m = -3
You can use the point (2,-2) or other point listed in the table along with this relation, to determine the y-intercept b.
b = y1 - mx1
b = (-2) -(-3 + 2)
b = 4
Consequently, is the function represented by the table's slope-intercept form: y -3x + 4.
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[tex]6x^{2} = 6[/tex]
Answers
[tex]6x^2=6[/tex]
Divide both sides by 6:
[tex]\dfrac{6x^2}{6} =\dfrac{6}{6}[/tex]
[tex]x^2=1[/tex]
Take square root:
[tex]x=\pm\sqrt{1}[/tex]
[tex]\fbox{x = 1 or x = -1}[/tex]
In AGHI, GI is extended through point I
to point J, m/IGH = (x+16)°,
m/HIJ = (4x – 12)°, and
m/GHI= (x +10)°. Findm/GHI.
Answers
Applying the exterior angles theorem, the measure of angle GHI is: 29°.
What is the Exterior Angle Theorem?The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
In other words, if a triangle, for example triangle GHI, has angles G, H, and I, and angle HIJ is the exterior angle formed by extending side GI through point I to point J, then the measure of angle HIJ is equal to the sum of the measures of angles IGH and GHI.
Given the following:
m<IGH = (x+16)°,
m<HIJ = (4x – 12)°,
m<GHI= (x +10)°
Therefore:
m<HIJ = m<IGH + m<GHI
Substitute:
4x - 12 = x + 16 + x + 10
4x - 12 = 2x + 26
4x - 2x = 12 + 26
2x = 38
2x/2 = 38/2
x = 19
m<GHI= (x +10)° = 19 + 10 = 29°
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Alejandro, a pharmaceutical sales representative, sells statins for a drug maker. He earns a 12% commission of the total sales of the statins that he sells to hospitals. If he earned 60,000 in commissions, what was the total dollar value of the drugs that he sold?
Answers
Answer: x=500,000
Step-by-step explanation:
60,000=.12x
60,000/.12=x/.12
500,000=x
