The relative change is solved as percentages and the absolute change is also solved
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the initial value be represented as A = 13.60 at time t = 0
Now , when the value is changed to 17.00
The absolute change = 17.00 - 13.60 = 3.40
The relative change = 3.40 / 13.60 = 0.25 = 25 %
Now , the percentage = 25 %
And , when the value is changed to 21.25
The absolute change = 21.25 - 17.00 = 4.25
The relative change = 4.25 / 17.00 = 0.25 = 25 %
And , when the value is changed to 26.56
The absolute change = 26.56 - 21.25 = 5.31
The relative change = 5.31 / 21.25 = 0.25 = 25 %
Now , the percentage = 25 %
And , when the value is changed to 33.20
The absolute change = 33.20 - 26.56 = 6.64
The relative change = 6.64 / 26.56 = 0.25 = 25 %
And , when the value is changed to 41.50
The absolute change = 41.50 - 33.20 = 4.25
The relative change = 8.3 / 33.20 = 0.25 = 25 %
Now , the percentage = 25 %
Hence , the relative change is given by the equation A = 25 %
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pls help it’s due today
The average rate of change between interval 5 to 11 is 4.5.
Define average rate of change.It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function. The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
Given
Average rate of change
= Change in output/ Change in input
= 45 - 18/ 11 -5
= 27/6
4.5
The average rate of change between interval 5 to 11 is 4.5.
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A recent study of the lifetimes of cell phones found the average is 24.3 months. The standard deviation is 2.6 months. If a company provides its 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months
An ordinary bend is a ringer molded bend that gives probabilities of irregular factors taken in a nonstop conveyance. The z score formula is used to standardize the random variables into a z score.
Using the z score formula and the z table, standardize the value of x and use it to denote the cellphone's lifetime in months.
For what reason is likelihood region under typical bend?The area under the probability density function curve in a given range is the probability that a continuous random variable fall within a given range. Because the value of a random variable must be in the sample space, the total area under the curve for any pdf is always 1.
What is the absolute likelihood under the ordinary circulation bend?A continuous probability distribution is the normal distribution. Probability is affected in multiple ways by this. 1 is the total area under the normal curve. A normal random variable X has a 0 chance of matching any given value.
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Full Question = A recent study of the lifetimes of cell phones found the average is 24.3 months. The standard deviation is 2.6 months. If a company provides its employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a normally distributed variable.
Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x+ 6 = 12
X =
Answer:
x=6
Step-by-step explanation:
12-6=6 or 6+6=12
Write the following number in scientific notation: 0.0003005
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10.
If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Which graph represents the solution set of the system of inequalities?
Answer:
Step-by-step explanation:
Rx: 325 mL of 30% NaCl Soln. Your Pharmacy stocks 22% and 40% NaCl Soln. How may mL of 22% NaCl Soln would you need to formulate the prescription? (Round to the nearest mL with no units!)
I need help with this.
Answer:
8/17
Step-by-step explanation:
You want the ratio of 32 mm to 6.8 cm, compared in mm.
RatioThe ratio of interest is ...
(32 mm)/(6.8 cm) = (32 mm)/(68 mm) = (4·8)/(4·17) . . . . . mm cancels
= 8/17
The ratio of ball diameters is 8/17.
If you invest $4064 in an account that pays simple interest of 7% How much interest will you have earned after 6 years?
Answer:
You would have $6055.36 in 7 years.
Step-by-step explanation:
the daily info newspaper charges a fee of $650 plus $80 per week to run an ad. the peoples paper charges $145 per week. for how many weeks will the total cost at the peoples paper be less expensive
The total cost at the peoples paper be less expensive will represent by the inequality 650 + 80w < 145w.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given that the daily info newspaper charges a fee of $650 plus $80 per week to run an ad.
Assume that after w weeks the total cost at the peoples paper be less expensive.
To run ad. for w week, the cost will be 80w.
The total cost of material of newspaper is p(w) = 650 + 80w
The peoples paper charges $145 per week.
The peoples paper charges after w week will be f(w) = 145w.
According to the question:
p(w) < f(w)
650 + 80w < 145w
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Help!!! It doesn’t give the isosceles congruent angles??
Answer: y = 11 , x =3
Step-by-step explanation:
Since its an isosceles triangle , two angles or two side are equal.
So lets take 5y - 3 as one of the equal angles, so
5y-3+ 5y-3 + 76 = 180 (angles in a triangles should add up to 180)
10y - 6 + 76 = 180
10y = 180 - 70
10y =110
y = 110/10
y = 11
Now, since we found y we need to find x.
Lets us take 8x and 13x - 15 as the equal sides.
8x = 13x - 15
8x - 13x = -15
-5x = -15
x = -15 / -5
x = 3
so we found the values of x and y !
Answer:
x = 3y = 11Step-by-step explanation:
You want the values of x and y, given an isosceles triangle with congruent sides JK=8x and KL=13x-15, angle K=76°, and angle J=(5y-3)°.
Congruent sidesJK = KL
8x = 13x -15
15 = 5x . . . . . . add 15-8x
3 = x . . . . . divide by 5
Sum of anglesThe sum of the angles in the triangle is 180°.
2(∠J) +∠K = 180°
2(5y -3) +76 = 180 . . . . substitute known values, divide by °
10y +70 = 180 . . . . . . simplify
y +7 = 18 . . . . . . . . divide by 10
y = 11 . . . . . . . . . subtract 7
The values of x and y are 3 and 11, respectively.
Here is an equation: 2x+4 y-31=123
1. Solve for x.
x=
2. Solve for y.
y=
X=77
y=77by 2
answer is complete
Natalie drives from London to Sheffield.
Natalie leaves London at 9.15am.
Natalie drives for 2 hours before stopping for a break.
The break lasts for 20 minutes.
Natalie then takes another 85 minutes to reach Sheffield.
What time does Natalie arrive in Sheffield?
Answer:
Natalie arrives is Sheffield at 1:00 pm
Step-by-step explanation:
A barrel of U.S. oil is 42 gallons. How many liters is this? Round off to the nearest whole number. Note: 1 gallon = 4 quarts. Strategy: you must convert from gallons quarts liters. Use two conversion factors ( 1 gallon = 4 quarts )
Answer:
158 liters.
Step-by-step explanation:
G=gallons
L=Liters
Q=Quarts
42G * 4Q = 168Q
1Q = 3.785L
3.785L * 42G = 158L or another way is to go by the formula is by dividing the volume value by 1.057:
168Q divide by 1.057 = 158
Compute the product of 0.123(overline) and 9, and write your result as a fraction in simplified form.
The product of 0.123(overline) and 9 is equal to 149/142.
To multiply 0.123(overline) and 9, we can first rewrite 0.123(overline) as a fraction. To do this, we can express 0.123(overline) as a fraction with a denominator of 1000, which represents the number of thousandths that 0.123(overline) represents:
0.123(overline) = 123/1000 = 123/10^3To find the product of 123/1000 and 9, we can use the distributive property:
(123/1000) * 9 = 123 * 9 / 1000 = 1047 / 1000To simplify this fraction, we can divide both the numerator and the denominator by their greatest common factor, which is 7:
1047 / 1000 = 149 / 142Therefore, the product of 0.123(overline) and 9 is equal to 149/142.
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The dosage of a certain medication is determined by a patient's body weight. This medication's dosage is 2.5 mg per kilogram of body weight. What would be the dose for a patient who weighs 72 pounds? (1 lb = 0.453 kg) (Doses are rounded to the nearest 25 mg.)
Show work please
Answer:
75 mg
Step-by-step explanation:
You want the dose for a 72 pound person at the rate of 2.5 mg/kg.
Unit conversionWe multiply by conversion factors that cancel unwanted units, leaving the units we want.
At the end of the unit conversion, we need to determine if the calculated dose is closer to 75 mg or 100 mg. It is less than 87.5 mg, so is closer to 75 mg.
[tex]\dfrac{2.5\text{ mg}}{\text{kg}}\times(72\text{ lb})\times\dfrac{0.453\text{ kg}}{\text{lb}}=2.5\times72\times0.453\text{ mg}\approx81.54\text{ mg}\\\\\approx\boxed{75\text{ mg}}[/tex]
__
Additional comment
We found the nearest 25 mg dose by dividing by 25 mg, and rounding the 3.26 dose result to 3 doses of 25 mg each.
given a program with an instruction count of 105 instructions divided into classes as follows: a: 20%, b: 30%, c: 20%, d: 30%
The program can be broken down into four classes, each with a different percentage of instructions.
What is program?Program in math is a set of instructions or steps that are used to solve a problem. It is a systematic approach to problem-solving, using algorithms and data structures to store and manipulate data. Program in math can be used to solve a variety of problems, from simple arithmetic operations to complex calculations such as solving equations or finding the optimal solution for a game. Program in math helps us to make decisions, find patterns, and solve problems in an efficient and organized way.
Class A consists of 20% of the instructions,
Class B consists of 30%,
Class C consists of 20%
Class D consists of 30%.
This breakdown allows for a better understanding of the program, making it easier to analyze and determine what needs to be done to improve it.
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The program can be broken down into four classes, each with a different percentage of instructions.
What is program?Program in math is a set of instructions or steps that are used to solve a problem. It is a systematic approach to problem-solving, using algorithms and data structures to store and manipulate data. Program in math can be used to solve a variety of problems, from simple arithmetic operations to complex calculations such as solving equations or finding the optimal solution for a game. Program in math helps us to make decisions, find patterns, and solve problems in an efficient and organized way.
Class A consists of 20% of the instructions,
Class B consists of 30%,
Class C consists of 20%
Class D consists of 30%.
This breakdown allows for a better understanding of the program, making it easier to analyze and determine what needs to be done to improve it.
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Part B
Complete the proof of the vertical angles theorem.
Given: Lines AB and CD intersect at point E.
Prove: Angle AED is congruent to angle BEC.
Enter the missing statements and reasons in the table.
BIVX¹ X₂ 14pt
Statement
ZAED and ZDEB are a linear pair.
A
m2DEB+m
mZAED+ m2DEB=mZDEB + m2BEC
Reason
given
Linear pairs are supplementary.
definition of linear pair
Linear pairs are supplementary.
subtraction property of equality
definition of congruency
V
Therefore, we have proven the vertical angles theorem by using congruency properties.
The vertical angles theorem's meaning is what?The intersection of two straight lines produces two sets of linear pairs with congruent angles, according to this theorem. Moreover, it indicates that the neighboring angles created by the junction of these two lines are supplementary, or 180 degrees.
Here,
THEOREM:
According to the Vertical Angles Theorem, two crossing lines' opposing (vertical) angles must be equivalent.
THE ISSUE:
Show that ∠1 ≅∠3 and ∠2 ≅ ∠4
PROOF:
(1) A straight line measures 180 degrees; m∠1 + m∠2 = 180°
(2) m∠3 + m∠2 = 180°; the length of a straight line is 180.
(3) Since the sum of the two left-hand sides of the equation equals 180 degrees, the transitive principle of equality holds that m∠1 + m∠2 = m∠3 + m∠2
(4) m∠1 = m∠3 which demonstrates the equality's subtraction property ( m∠2 is subtracted from both sides).
Definition of congruent angles: (5) ∠1 ≅ ∠3
Likewise, for ∠2 ≅∠4:
(1) m∠3 + m∠2 = 180° a straight line has a 180° length.
(2) m∠3 + m∠4 = 180° a straight line has a 180° length.
(3) Since both of the equation's left-hand sides add up to 180 degrees, the expression m∠3 + m∠2 = m∠3 + m∠4 / transitive property of equivalence.
(4) m∠2 = m∠4 , demonstrating the equivalence of subtraction (m∠3 is subtracted from both sides).
// definition of congruent angle , ∠2 ≅ ∠4
We have therefore established the theorem.
Therefore, we have proven the vertical angles theorem by using congruency properties.
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A researcher performs six independent hypothesis tests each at the 5% significance level. Determine the probability of observing at most two Type Errors. (Round your final answer to the nearest hundredth of a percent, e.g., 12.63% Rounding counts
At the 5% significance level, a researcher conducts six separate hypothesis tests. the likelihood of finding two or fewer Type Errors.
What is the 5 step process in statistics?Declare your null and alternate hypotheses in Step 1. Data collection is step two. Perform a statistical test in step three. In step four, you must choose whether to reject or not to reject your null hypothesis. Deliver your results in Step 5. Five steps make up the statistical process: design the study, assemble the data, Analyze the data, draw conclusions, and take action. In a planned experiment, the variables are under the researchers' control.
Utilizing sample data, hypothesis testing is a method used to determine whether a hypothesis is tenable. The test offers proof that, given the available data, the hypothesis is plausible. By measuring and reviewing a representative sample of the population under study, statistical analysts can evaluate a theory.Procedures for testing hypotheses Identifying the null hypothesis is the first step.
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Q2) A company is evaluating the extension of credit to a new group of customers.
Although these customers will provide $180,000 in additional credit sales, 12% are likely
to be uncollectible. The company will also incur $16,200 in additional collection
expense. Production and marketing costs represent 72% of sales. The firm is in a 34% tax
bracket and has a receivables turnover of four times. No other asset buildup will be
required to service the new customers. The firm has a 10% desired return.
has a
a. Calculate the incremental income after taxes and the return on incremental
investment. Should the company extend credit to these customers?
b. Based on the income level determined in (a), should credit be extended if an
additional investment in inventory is considered? Assume an inventory turnover
of 1.6 times.
Answer:
Step-by-step explanation:
a. To calculate the incremental income after taxes, we need to determine the incremental costs and revenues associated with extending credit to the new customers. The additional credit sales will generate $180,000 in revenue, but we need to subtract the expected uncollectible amount of 12% * $180,000 = $21,600. The net additional credit sales will be $180,000 - $21,600 = $158,400.
The production and marketing costs will be 72% * $180,000 = $129,600. The total incremental costs will be $129,600 + $16,200 (collection expense) = $145,800.
The incremental income before taxes will be $158,400 - $145,800 = $12,600. The income tax will be 34% * $12,600 = $4,284. The incremental income after taxes will be $12,600 - $4,284 = $8,316.
To calculate the return on incremental investment, we need to determine the incremental investment required to extend credit to the new customers. Since no additional investment in assets is required, the incremental investment will be equal to the incremental costs of $145,800. The return on incremental investment will be $8,316 / $145,800 = 5.7%.
Based on the return on incremental investment of 5.7%, the company should not extend credit to the new customers, as it is below the desired return of 10%.
b. If an additional investment in inventory is required to extend credit to the new customers, we will need to recalculate the incremental income after taking into account the additional investment. If the additional investment in inventory is $x, the incremental investment will be $145,800 + $x. The incremental income before taxes will be $158,400 - ($129,600 + $16,200 + $x) = $12,600 - $x. The income tax will be 34% * ($12,600 - $x) = $4,284 - $x * 0.34. The incremental income after taxes will be ($12,600 - $x) - ($4,284 - $x * 0.34) = $8,316 - $x * 0.34.
To determine whether credit should be extended, we need to compare the return on incremental investment to the desired return of 10%. The return on incremental investment will be ($8,316 - $x * 0.34) / ($145,800 + $x). Setting this equal to the desired return of 10% and solving for x, we find that the additional investment in inventory cannot exceed $24,764 for the company to meet its desired return. If the additional investment in inventory is less than or equal to $24,764, the company should extend credit to the new customers. If it is greater than $24,764, the company should not extend credit to the new customers.
What’s greater, 9 or 9.1?
Answer:
9.1
Step-by-step explanation:
9.1 would be greater because it is basically 9 + 0.1.
Please find what the rent per unit needs to be to have a Net Operating Income (NOI) of $100,000.
Assumptions
Please use the following assumptions below:
Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income) 5%
Operating Expenses (% of Effective Gross Income) 30%
Number of Units 18
*Please fill out the blue area Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income)
Operating Expenses (% of Effective Gross Income)
Number of Units
The rent per unit will be $8,354.22 to have a Net Operating Income (NOI) of $100,000.
What is the net operating income?The net operating income (NOI) is the difference between the gross operating income and the operating expenses.
The net operating income excludes some fixed or period expenses.
Total
Rent per unit (per month) = $696.19 ($8,354.22/12) $150,376
Vacancy Rate (5% of Potential Gross Income) 7,519
Effective Gross Income $142,857
Operating Expenses (30% of Effective Gross Income) 42,857
Net Operating Income (NOI) $100,000
Number of Units 18
Working Backwards:Gross operating income = net operating income + operating expenses
Operating expenses = 30% of effective gross income
Net operating income = 70% of effective gross income (100 - 30%)
= $100,000
Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)
Vacancy rate = 5% of potential gross income
Effective Gross Income = 95% (100 - 5)
Potential gross income = $150,376 ($142,857 ÷ 95%)
Number of units = 18
Rent per unit = $8,354.22 ($150,376/18)
Rent per month = $696.19 ($8,354.22 ÷ 12)
Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.
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Determine whether an equation in the form x = a , where a is a constant is sometimes, always, or never a function. Explain your reasoning.
An equation in the form x = a , where a is a constant can never be a function.
What is a function?
A function is defined as a relation between a set of inputs having one output each.
In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Every function has a domain and codomain or range.
A function is generally denoted by f(x) where x is the input.
The general representation of a function is y = f(x).
According to the given question:
An equation is in the form x = a , where a is a constant.
This equation is a vertical line parallel to y axis. For a function a relation of y = f(x) is missing in the given equation since a is a constant.
Hence, x = a can never be a function.
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Describe the graph of proportional relationship represented by the equation Y equals eight minus 5X
The description of the proportional relationship represented by the equation y = 8 - 5x is A. The graph is a line that goes through points (0, 8) and ( 4, -12 ).
How to describe the graph ?The graph is given in the form of a linear equation which is y = mx + b. In this equation, b is the y - intercept, or the point the line crosses the y - axis when x is 0. This point on y = 8 - 5x, is 8.
If the line passes through the x axis at point 4, then the y - intercept would be :
= 8 - 5 ( 4)
= 8 - 20
= - 12
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Options for this question are:
The graph is a line that goes through points (0, 8) and ( 4, -12 ).The graph is a line that goes through points (0, 5) and (15, 2).The graph is a line that goes through points (0, 4) and (12 , 1).The graph is a line that goes through points (0, 5) and (1, 12 ).a quadrilateral has vertices (2,0), (0,-2), (-2,4) and (-4,2) which special quadrilateral is formed by connecting the midpoints of the sides a. kite
b. rectangle
c. trapezoid
b. rhombus
The quadrilateral that has vertices (2,0), (0,-2), (-2,4) and (-4,2) is option
b. rectangle
Why is it a rectangle?To determine the special quadrilateral that is formed by connecting the midpoints of the sides of the quadrilateral with vertices (2,0), (0,-2), (-2,4) and (-4,2), we can find the midpoints of each side and then determine the shape formed by these points.
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line segment. To find the midpoint of a line segment, we can take the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.
We can find the midpoint of the side between (2,0) and (0,-2) by taking the average of the x-coordinates (2 and 0) and the average of the y-coordinates (0 and -2), which gives us the point (1,-1).
We can find the midpoint of the side between (0,-2) and (-2,4) by taking the average of the x-coordinates (0 and -2) and the average of the y-coordinates (-2 and 4), which gives us the point (-1,1).
We can find the midpoint of the side between (-2,4) and (-4,2) by taking the average of the x-coordinates (-2 and -4) and the average of the y-coordinates (4 and 2), which gives us the point (-3,3).
We can find the midpoint of the side between (-4,2) and (2,0) by taking the average of the x-coordinates (-4 and 2) and the average of the y-coordinates (2 and 0), which gives us the point (-1,1).
Therefore, the special quadrilateral formed by connecting the midpoints of the sides of the given quadrilateral is a rectangle.
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Determine how many ounces are in 15 liters. Show every step of your work
pls help
Answer:
15 liter = 507.210848 Fluid Ounces
because 1 liter = 33.8140565 so you do 33.8140565 x 15 = 507.210848
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hope this helps you
Step-by-step explanation:
which of the following best describes why you might want to add both l1 and l2 regularizers to an ordinary least squares linear regression model
L1 (Ridge Regression) regularization is better than L2( Lasso regression). A regularization term two general types of regularization L1 and L2 regularization is added to solve the overfitting problem.
Let's use a linear regression formula for this explanation, y = mx + c
This is the simplest formula, so if there is only one feature, this is the formula. But in the real world, we rarely deal with just one feature. Most of the time we have multiple functions.
y = m₁ x₁ + m₂x₂ + ----+ mₙxₙ
To create simpler (sparse) models when the dataset has a large number of features, here are some of the regularization techniques used to correct overfitting and feature selection. A regression model that uses the L1 regularization method is called a Lasso regression. Lasso regression (least absolute shrinkage and selection operator) is Add "absolute size".
∑(Yᵢ ) - ∑Xᵢβⱼ)² + λ ∑|βⱼ|
Models using L2 are called ridge regression Ridge Regression adds the "squared magnitude" of the coefficients as a penalty term to the loss function. where the highlighted part represents the L2 regularization factor and the cost function
∑(Yᵢ - ∑Xᵢβⱼ )² + λ ∑β²
The L1 regularization is more robust than the L2 regularization for fairly obvious reasons. Since we take the weights squared, the cost of outliers present in the data increases exponentially. L1 regularization takes the absolute value of the weights, so the cost increases only linearly. Both L1 and L2 can add cost penalties depending on the complexity of the model, so when calculating the cost using the loss function, an auxiliary component called the regularization term adds complexity to the model. Added for segmentation.
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find the distance between the points (-9.3 , 6.7) and (-9.3, -5.5)
Answer:
0, -12
Step-by-step explanation:
Select the correct answer from each drop-down menu. Consider the equation below. − 2 ( 5 x + 8 ) = 14 + 6 x The equation was solved using the following steps. Step 1: − 10 x − 16 = 14 + 6 x Step 2: − 16 x − 16 = 14 Step 3: − 16 x = 30 Step 4: x = 30 − 16 Step 5: x = − 15 8 Complete the statements below with the process used to achieve steps 1-4. Step 1: -2 to 5x and 8. Step 2: 6x. Step 3: 16. Step 4: -16.
Answer:
x = -1.875
Step-by-step explanation:
-2 (5x + 8) = 14 + 6x
-10x - 16 = 14 + 6x
-16x = 30
x = 30/-16
x = -1.875
A local little league has a total of 70 players, of whom 40% are right-handed. How many
right-handed players are there? HELP
The number of right-handed players in the local little league given its percentage is 28
How many right-handed players are there?Based on the given task content; the number of right-handed players there can be determined by solving the percentage of right-handed players.
Total number of players in the local little league = 70Percentage of right-handed players = 40%Number of right-handed players = Percentage of right-handed players × Total number of players in the local little league
= 40% × 70
= 40/100 × 70
= 0.4 × 70
= 28
In conclusion, the total number of right-handed players is 28
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Find the standard form of the equation of the line through (8,-3) that is parallel to the line 3y=4x+8
The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41
How to represent equation in standard form?The equation of the line in standard form can be represented as follows:
Ax + By = C
where
A, B and C are constantTherefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;
Parallel lines have the same slope.
Hence,
3y = 4x + 8
y = 4 / 3 x + 8 / 3
The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.
y = 4 / 3 x + b
-3 = 4 / 3 (8) + b
b = -3 - 32 / 3
b = -9 - 32/ 3
b = -41 / 3
Hence,
y = 4 / 3 x - 41 / 3
multiply through by 3
3y = 4x - 41
Therefore, the standard form is 4x - 3y = 41
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