From the time you are 21 until the time you turn 51, if you put $500 away quarterly in an account that produces 12% compound interest, you will have around $1,299,994.09 in it by the end of the 30 years.
When does a quarterly monthly occur?Four quarters, numbered Q1, Q2, Q3, & Q4, make up an entire year. There are 3 months in each quarter. About 91 days make up each quarter. Quarterly is defined as once every quarter, or around every 91 days.
The calculation for future value of the an annuity can be used to resolve this issue:
FV = PMT x ((1 + r/n)nt - 1) / (r/n), where FV is just the future value of a annuity, PMT is indeed the payment amount (in this case, $500), r is indeed the interest rate (the value of which in this case is 12% or 0.12), n refers to the number of occasions a year the interest is greatly exacerbated (which in this case is four for quarterly cumulative), and t is the duration of the annuity .
When we enter the data, we get the following result: FV = 500 x (1.03120 - 1) / 0.03 = $1,299,994.09
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Round the solution up to the nearest whole number, if necessary.
A sample size that would give the standard deviation of [tex]\bar{x}[/tex] equal to 0.8 years is 1,227.
How to determine the sample size?In Mathematics and Statistics, a sample size that would result in a standard deviation of 0.8 years can be calculated by using the mathematical equation (formula):
Sample size, n = (zσ/ME)²
Where:
n represents the sample size.z represents the z-score of the desired confidence level. σ represents the standard deviation of the population.ME represents the margin of error.By assuming a confidence level of 95% with a z-score of 1.96, we would substitute the given parameters into the formula for sample size as follows;
Sample size, n = (zσ/E)²
Sample size, n = (1.96 × 14.3/0.8)²
Sample size, n = (28.028/0.8)²
Sample size, n = (35.035)²
Sample size, n = 1,227.45 ≈ 1,227.
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Complete Question:
Suppose the standard deviation of the ages of all Florida panthers is 14.3 years. Let [tex]\bar{x}[/tex] be the mean age for a sample of a certain number of Florida panthers. What sample size will give the standard deviation of [tex]\bar{x}[/tex] equal to 0.8 years?
Round the solution up to the nearest whole number, if necessary.
8) Use a proportion to solve this problem: Two towns are 460 km apart. If the scale on the map is 3 cm to 45 km, how far apart are the towns on the map?
The distance between the two towns on the map was found to be 30.67 centimeters by setting up and solving a proportion between the distances on the map and the actual distances.
The problem provides us with a scale on the map of 3 cm to 45 km, which means that every 3 centimeters on the map represents 45 kilometers in the actual world. Let x be the distance between the two towns on the map in centimeters. Using the proportion, we can set up the relationship between the distances on the map and the actual distances as follows:
3 cm / 45 km = x cm / 460 km
Here, we set up a ratio between the distance on the map and the actual distance, where the distance on the map is x centimeters and the actual distance between the towns is 460 kilometers. We can then cross-multiply to solve for x:
45 km * x cm = 3 cm * 460 km
This gives us:
45x = 1380
x = 1380 / 45
x = 30.67 cm
Therefore, the distance between the two towns on the map is 30.67 centimeters.
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What is 55 increased by 10%
Answer:
60.5
Step-by-step explanation:
Answer: 60.50
Step-by-step explanation:
.
An uncapped fibre contract originally cost R990 per month. It has now fallen in price to R765 per month. What is the percentage decrease in the monthly price of the contract?
Answer:
To find the percentage decrease, we need to find the difference between the original price and the new price, divide that difference by the original price, and then multiply by 100 to express the result as a percentage.
The difference between the original price and the new price is:
990 - 765 = 225
Dividing the difference by the original price gives:
225 ÷ 990 ≈ 0.227
Multiplying by 100 gives:
0.227 x 100 ≈ 22.7
Therefore, the percentage decrease in the monthly price of the contract is approximately 22.7%.
Step-by-step explanation:
5. A deli bought 45kg of tuna salad R1.48 per kg. In warm weather about 5kg usually spoil before they can be sold. What price per kg will give the desired profit of 40% of selling price?
The deli needs to sell the tuna salad at a price of R2.33 per kg to achieve a profit of 40% of the selling price after 5kg spoilage.
What price per kg will give the desired profit of 40% of selling price?A desired profit also known as target profit means expected amount of profit that the managers of a business expect to achieve by the end of a designated accounting period.
First, let's calculate the cost of the tuna salad the deli purchased:
= 45kg x R1.48/kg
= R66.60
How much tuna salad the deli has left after spoilage:
= 45kg - 5kg
= 40kg
To achieve a profit of 40% of the selling price, the selling price should be 140% of the cost price: which is:
= 140% of cost price
= 1.4 x R66.60
= R93.24
To find the price per kilogram, we divide the selling price by the remaining amount of tuna salad:
= Selling price / Remaining amount of tuna salad
= R93.24 / 40kg
= R2.33/kg
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Answer: 6 dolla per kg
Step-by-step explanation:
Pls help step by step (special right triangles)
Value of base and hypotenuse of triangle are 9√3 and 18 respectively.
Define right triangleA right triangle is a triangle with one interior angle measuring 90 degrees, known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are known as the legs of the right triangle. The length of the hypotenuse can be found using the Pythagorean theorem, that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
Height of triangle=9
Base of triangle=y
Hypotenuse of triangle=x
Using trigonometric ratio
Sin30°=Height/Hypotenuse
½=9/x
x=18
Cos30°=Base/hypotenuse
√3/2=y/18
y=9√3
Hence, value of base and hypotenuse of triangle are 9√3 and 18 respectively.
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If your answer is correct I will give brainliest
I think it is A... if the original is Red. It is reflected across the x-axis.
I hope this helps !
write an inequality for x
Meredith drives 5 miles to the northeast, then 15 miles to the southeast, then 25 miles to the
southwest, then 35 miles to the northwest, and finally 20 miles to the northeast. How many miles is
Meredith from where she started?
Which best describes the relationship between the line that passes through the points (8, 2) and (3, 5) and the line that passes through the points (–3, –7) and (0, –12)?
A. parallel
B. same line
C. perpendicular
D. neither perpendicular nor parallel
The best line that represents the relation between the lines that passes through the points (8, 2) and (3, 5) and the line (-3, -7) and (0, -12) is a perpendicular line.
What are perpendicular lines?
In geometry, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90 ∘). The term ‘perpendicular’ originated from the Latin word ‘perpendicularis,’ meaning a plumb line. If two lines AB and CD are perpendicular, then we can write them as AB ⊥ CD.
To determine the relationship between the two lines, we can first find the slope of each line using the two-point formula:
Slope of the line passing through (8, 2) and (3, 5):
m1 = (5 - 2) / (3 - 8) = -3/5
Slope of the line passing through (–3, –7) and (0, –12):
m2 = (-12 - (-7)) / (0 - (-3)) = -5/-3 = 5/3
If the two lines are parallel, their slopes will be equal. However, -3/5 is not equal to 5/3. If the two lines are perpendicular, their slopes will be negative reciprocals of each other. That is,
m1 x m2 = -1
But, (-3/5) x (5/3) = -1, which means that the two lines are perpendicular.
Therefore, the correct answer is C. perpendicular.
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F.BF.1b Combine standard function types using arithmetic o
Give the equation for f(x) + g(x) given that
f(x) = x² - x + 1 and g(x) = 2x + 3
We can easily say that the following about this question:
Functions are polynomial expressions.Arithmetic operations are performed between coefficients of terms of the same degree. Coefficients of different degrees are written as they are, without being changed.[tex]f(x)=x^2-x+1[/tex] and [tex]g(x)=2x+3[/tex] can be combined as;
[tex]f(x)+g(x)=x^2+(2-1)x+(3+1)[/tex][tex]f(x)+g(x)=x^2+x+4[/tex]1. What is the breakeven point in unit sales and dollars for each type of filter at the current sales mix?
For fau/cet filter:
The break-even point in unit sales is 28,571 units.The break-even point in dollar is $2,571,390.For pitcher-filter:
The break-even point in unit sales is 22,222 units.The break-even point in dollar is $2,444,420.How do we calculate breakeven point in unit sales and dollars?Let's start with the fau/cet model:
Contribution margin per unit = selling price - variable cost
Contribution margin per unit = $90 - $25
Contribution margin per unit = $65
Contribution margin ratio = contribution margin per unit / selling price
Contribution margin ratio = $65 / $90
Contribution margin ratio = 0.722
The sales mix is 2 faucet models for every 3 pitcher filters sold, so the contribution margin weighted average is:
= (2/5)($65) + (3/5)($90-$20)
= $42
Now we can calculate the break-even point in units for the faucet model:
= Total fixed costs / contribution margin per unit
= $1,200,000 / $42
= 28,571 units
For pitcher filter:
Contribution margin per unit = selling price - variable cost
Contribution margin per unit = $110 - $20
Contribution margin per unit = $90
Contribution margin ratio = contribution margin per unit / selling price
= $90 / $110
Contribution margin ratio = 0.818
Contribution margin weighted average:
= (2/5)($25) + (3/5)($90-$20)
= $54
Break-even point in units for pitc/her filter:
= Total fixed costs / contribution margin per unit
= $1,200,000 / $54
= 22,222 units
Break-even point in dollars for fau/cet model:
= 28,571 units x $90 per unit
= $2,571,390
Break-even point in dollars for pitc/her-filter:
= 22,222 units x $110 per unit
= $2,444,420
Full question "Multiproduct CVP and decision making. Crystal Clear Products produces two types of water filters. One attaches to the faucet and cleans all water that passes through the faucet. The other is a pitcherfilter that only purifies water meant for drinking. The unit that attaches to the faucet is sold for $90 and has variable costs of $25. The pitcherfilter sells for $110 and has variable costs of $20. Crystal Clear sells two faucet models for every three pitchers sold. Fixed costs equal $1,200,000.
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How much do we need to invest each month at a rate of 8% compounded monthly so that we have a total of $600,000 saved in 25 years?
Please help will mark brainliest
Answer:$163.68
Step-by-step explanation:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = final amount ($600,000)
P = initial amount (unknown)
r = interest rate (8%)
n = number of times interest is compounded per year (12 for monthly)
t = time in years (25)
Substituting in the values, we get:
$600,000 = P(1 + 0.08/12)^(12*25)
Simplifying:
$600,000 = P(1.00666666666667)^300
Dividing both sides by (1.00666666666667)^300:
P = $600,000 / (1.00666666666667)^300
Using a calculator, we get:
P = $163.68
Therefore, we would need to invest $163.68 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.
=
For the cost and price functions below, find a) the number, q, of units that produces maximum profit; b) the price, p, per
unit that produces maximum profit; and c) the maximum profit, P.
C(q) = 70+ 15q; p=63-2q
a) The number, q, of units that produces maximum profit is q =
b) The price, p, per unit that produces maximum profit is p = $
c) The maximum profit is P = $
a) The number of units that produces maximum profit is q = 12.
b) The price per unit that produces maximum profit is p = $39.
c) The maximum profit is P = $386.
What is profit?
a) To find the number of units that produces maximum profit, we need to find the point where revenue equals cost. The revenue function is given by:
R(q) = pq = (63-2q)q = 63q - 2q²
The cost function is given by:
C(q) = 70 + 15q
The profit function is given by:
P(q) = R(q) - C(q) = (63q - 2q²) - (70 + 15q) = -2q² + 48q - 70
To find the number of units that produces maximum profit, we take the derivative of the profit function with respect to q, and set it equal to zero:
P'(q) = -4q + 48 = 0
Solving for q, we get:
q = 12
Therefore, the number of units that produces maximum profit is q = 12.
b) To find the price per unit that produces maximum profit, we substitute q = 12 into the price function:
p = 63 - 2q = 63 - 2(12) = 39
Therefore, the price per unit that produces maximum profit is p = $39.
c) To find the maximum profit, we substitute q = 12 and p = 39 into the profit function:
P = -2q² + 48q - 70 = -2(12)² + 48(12) - 70 = $386
Therefore, the maximum profit is P = $386.
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Sarah spent 5 minutes painting. She spent twice as much time reading
as she spent painting. She spent 35 more minutes hiking than she
spent reading. How many minutes did she spend doing these three
activities?
After answering the provided question, we can conclude that So the total equation amount of time Sarah spent on these three activities is determined by how much time she spent reading.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the statement "[tex]2x + 3[/tex]" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "[tex]x^2 + 2x - 3 = 0[/tex]," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.
Let's call Sarah's reading time "r" in minutes.
We can deduce from the problem:
Sarah painted for 5 minutes.
Because she spent twice as much time reading as she did painting,[tex]r = 2*5 = 10.[/tex]
She hiked for 35 minutes longer than she read, so [tex]h = r + 35.[/tex]
To calculate Sarah's total time spent on these three activities, simply add the times:
Time spent painting + time spent reading + time spent hiking = total time
Time total =[tex]5 + 10 + (r + 35)[/tex]
Time total = [tex]50 + r[/tex]
So the total amount of time Sarah spent on these three activities is determined by how much time she spent reading.
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A study of adult Americans conducted by the polling organization Ipsos asked each person in a sample whether he or she self-identified as an entrepreneur. The responses to the question were used to learn about the population of adult Americans who self identify as an entrepreneur.
(a) What is the question type? (i) Estimation (ii) Hypothesis Testing
(b) What is the study type? (i) Experimental data (ii) Sample data 1
(c) Type (Part 1): Is the data categorical or numerical? (i) Categorical (ii) Numerical
(d) Type (Part 2): How many variables? (i) one (ii) two (iii) more than two
(e) How many samples or treatments are there? (i) one (ii) two (iii) more than two
(f) M: What is the appropriate method for analysis of data? (Use Table 7.1 of Section 7.2 and your answer to the previous questions to complete.) (i) One-sample z confidence interval for a proportion (ii) One-sample z test for a proportion (iii) Two-sample z confidence interval for a difference in proportions (iv) Two-sample z test for a difference in proportions (v) One-sample t confidence interval for a mean (vi) One-sample t test for a mean (vii) Two-sample t or Paired t confidence interval for a difference in means (viii) Two-sample t or Paired t test for a difference in means (ix) ANOVA F Test (x) Multiple Comparisons
Hypothesis Testing ,Sample data , Categorical ,one variable ,one sample and sample z test for a proportion are the responses to the question were used to learn about the population of adult Americans who self identify as an entrepreneur.
(a) The question type in this study is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.
(b) The study type is sample data, as a sample of adult Americans was surveyed to learn about the population of adults who self-identify as entrepreneurs.
(c) The data is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.
(d) There is one variable in this study, as the responses to the question about self-identification as an entrepreneur are the only data collected.
(e) There is one sample in this study, as only one group of adult Americans was surveyed.
(f) The appropriate method for analyzing the data in this study is the one-sample z test for a proportion. This method is used when we have one categorical variable and want to test whether the proportion of a certain response differs significantly from a hypothesized proportion. In this case, the hypothesized proportion would be the proportion of adult Americans who self-identify as entrepreneurs. We would use the z-test to determine if the proportion of respondents who self-identify as entrepreneurs is significantly different from the hypothesized proportion. If the difference is significant, we can conclude that there is a difference between the sample and population proportions, and if the difference is not significant, we cannot reject the null hypothesis that the sample proportion is the same as the population proportion.
Overall, this study is using categorical data to learn about the proportion of adult Americans who self-identify as entrepreneurs. The appropriate method for analyzing this type of data is the one-sample z test for a proportion, which allows us to test whether the sample proportion is significantly different from the hypothesized population proportion.
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15. Mathew waxes a car twice as fast as Andrea. If Andrea takes 24 minutes to wax the car, how much
time will they take together to wax the same car?
A) 8 minutes
B) 18 minutes
C) 12 minutes D) 16 minutes
E) 10 minutes
According to the solving time will they take together to wax the same car 16 minutes
Define minutes?The minute is a unit of time usually equal to 160 (the first sexagesimal fraction) of an hour, or 60 seconds.
According to the given information:Let's assume that Andrea takes x minutes to wax the car. Then Mathew takes x/2 minutes to wax the same car since he waxes twice as fast as Andrea.
We know that Andrea takes 24 minutes to wax the car. So we can substitute this value in the equation and solve for x.
x = 24 * 2 = 48
So Andrea takes 48 minutes to wax the car alone.
Now we can use the formula:
1/x + 1/(x/2) = 1/t
where t is the time taken by both of them together to wax the same car.
Substituting x = 48, we get:
1/48 + 1/24 = 1/t
Solving for t, we get:
t = 16minutes
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These are the questions I was talking about
Tim's score range would be between 20.2 - 56.25 and 20.2 + 56.25, or between -36.05 and 76.45. To find the percentage of games
a. To find the percentage of candy wrappers that would have between 3.4 and 3.6 ounces, we need to calculate the z-scores for each of the values:
[tex]z-score for 3.4 ounces = (3.4 - 3.5) / 0.16 = -0.625[/tex]
[tex]z-score for 3.6 ounces = (3.6 - 3.5) / 0.16 = 0.625[/tex]
Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers between these two values is approximately 47.70%.
b. To find the percentage of candy wrappers that would have less than 3.3 ounces, we need to calculate the z-score for this value:
[tex]z-score for 3.3 ounces = (3.3 - 3.5) / 0.16 = -1.25[/tex]
Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with less than 3.3 ounces is approximately 10.92%.
To find the percentage of candy wrappers with more than 3.62 ounces, we need to calculate the z-score for this value:
[tex]z-score for 3.62 ounces = (3.62 - 3.5) / 0.16 = 0.75[/tex]
Using a z-table or a calculator with a normal distribution function, we can find that the percentage of candy wrappers with more than 3.62 ounces is approximately 22.77%.
c. To find how many of the 1358 packets made that day have between 3.35 and 3.65 ounces, we need to convert these values to z-scores:
[tex]z-score for 3.35 ounces = (3.35 - 3.5) / 0.16 = -0.9375[/tex]
[tex]z-score for 3.65 ounces = (3.65 - 3.5) / 0.16 = 0.9375[/tex]
Using a z-table or a calculator with a normal distribution function, we can find the percentage of candy wrappers between these two values, which is approximately 62.97%. To find how many packets this represents, we can multiply this percentage by the total number of packets made:
[tex]0.6297 * 1358 = 856 packets[/tex]
Therefore, approximately 856 packets made that day have between 3.35 and 3.65 ounces.
d. To find how many games Tim would have scored 22 points or more if he plays 32 games, we first need to calculate the z-score for this value:
[tex]z-score for 22 points = (22 - 20.2) / 25 = 0.072[/tex]
Using a z-table or a calculator with a normal distribution function, we can find the percentage of games with a z-score greater than or equal to 0.072, which is approximately 53.10%. To find how many games this represents, we can multiply this percentage by the total number of games:
[tex]0.5310 x 32 = 17 games[/tex]
Therefore, Tim would have scored 22 points or more in approximately 17 games out of 32.
e. To find how many games Tim would have scored within 2.25 standard deviations from his average if he plays 32 games, we first need to calculate 2.25 standard deviations:
[tex]2.25 x 25 = 56.25[/tex]
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Pls help fast! Will get 20+ and brainliest
Answer:
a) 30 × .5 = 15 days
b) .2 + .1 = .3
Look at this table:
y =
X y
4
6
7
3
5
-24
-29
-34
-39
-44
Write a linear (y = mx + b), quadratic (y = ax2), or exponential (y = a(b)*) function that
models the data. Help plis
It should be noted that the function that can model the data is a linear function since there's a constant difference or -5.The linear function is y = -5x - 9.
How to explain the function.In this case, to determine whether the data is best modeled by a linear, quadratic, or exponential function, we can first plot the data points and see what type of curve they form. However, since we are only given five data points, it can be difficult to make a definitive determination.
One way to estimate the type of function is to look at the differences between the y values. For example, if the differences between the y values increase by a constant amount, then the data may be best modeled by a linear function. If the differences increase by a constant squared amount, then the data may be best modeled by a quadratic function.
Here, the constant difference will be:
= -29 - (-24)
= -5
This depicts a linear function.
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When 60% of a number is added to the number 160, the result is .
Any percentage can be written as that number divided by 100. As a decimal, you find that quotient. You can quickly divide any number by 10 by moving the decimal place to the left for every 0 in that multiple of 10. 100 has 2 zeros, so all you need to do to divide by 100 is to move the decimal place 2 places to the left. Therefore, 60% is .6 as a decimal.
Let's say the number we want to find is x. In word problems, "of" indicates multiplication, so 60% of our number would be 6x.
We then add our number to that, giving us .6x + x
We know the result is 160, so
.6x + x = 160
Since any number multiplied by 1 is itself, that x can be written as 1x.
.6x + 1x = 160
Now, we combine our like terms; we add the numbers in front of the x's (aka coefficients).
(.6 + 1)x = 160
1.6x = 160
We want x by itself. 1.6 is multiplied by our number, so to undo multiplication, we do division. This leaves us with
x = 160/1.6
x=100
In 1970, 11% of Americans completed four years of college
Answer:
Thank you for the statement. Is there a question or additional information you would like me to respond to?
Step-by-step explanation:
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
�
=
−
3
�
2
+
239
�
−
2268
y=−3x
2
+239x−2268
The maximum profit is $2492.08.
What is the selling price?
The cost a consumer pays to purchase a good or a commodity is known as the selling price. It is a price that is higher than the cost price and includes a profit margin. The cost of an item when acquired is referred to as its selling price (S.P.).
Here, we have
Given: A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation.
y = -3x² + 239x - 2268
At a maximum profit, dy/dx = 0, hence:
dy/dx = -6x + 239
0 = -6x + 239
x = 239/6
x = 39.8
The maximum profit is gotten when the selling price of each widget is 39.8. Hence:
y = -3(39.8)² + 239(39.8) - 2268
y = 2492.08
Hence, the maximum profit is $2492.08.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Consider figures 1 and 2 shown on the coordinate plane. Figure 1 has been transformed to produce figure 2.
This transformation of figure 1 has been transformed to produce figure 2, can be described by (x' , y') = (x' -y')
What is transformation in geometry?Transformation describes how an item moves, particularly as they are shown on a coordinate plane.
There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or position. The four methods comprise
rotationdilationreflectiontranslationPre-Image refers to the item's shape before transformation, whereas Image refers to the object's ultimate location and shape.
The linked image's preimage and image may be examined to determine that reflection is the involved translation.
The transformation rule for reflection over the y-axis is as follows:
(x, y) → (x, -y)
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Help with math problems
Answer:
The answer is 7d < -6
Step-by-step explanation:
3d-8<4d+2
3d+4d<-8+2
7d<-6
Add. Write your answer in the simplest form. 2 5/8 + 3 2/5
Answer:
6 1/40
Step-by-step explanation:
21/8 + 17/5
105/40 + 136/40 = 241/40
241/40= 6 1/40
solve for x: p(x)=x^3+6x^2+3x-10=0
Answer:
Step-by-step explanation:
P(x)=x³+6x²+3x-10=0
x³+2x²+4x²+8x-5x-10=0
x²(x+2)+x(x+2)-5(x+2)=0
(x+2)(x²+x-5)=0
either x+2=0,x=-2
or
x²+x-5=0
[tex]x=\frac{-1 \pm \sqrt{1^2-4 \times 1 \times(-5)} }{2 \times 1} \\=\frac{-1 \pm \sqrt{21} }{2} \\Hence ~x=\frac{-1+\sqrt{21} }{2} \\or\\x=\frac{-1 -\sqrt{21} }{2}[/tex]
help me
Simplify this expression:
Answer:
[tex]\frac{x^{7} }{y^{10} }[/tex]
pls help!!! right answer only!! Find the equation of a line perpendicular to y= −3x − 10 that passes through the point (9,−2).
Answer:
y = [tex]\frac{1}{3}[/tex] x - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x - 10 ← is in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (9, - 2 ) into the partial equation
- 2 = [tex]\frac{1}{3}[/tex] (9) + c = 3 + c ( subtract 3 from both sides )
- 5 = c
y = [tex]\frac{1}{3}[/tex] x - 5 ← equation of perpendicular line
A committee of ten health professionals has been selected to investigate the ethical conduct of some health workers in a health facility.A sub committees of four health professionals is to be selected out of the ten health professionals . Find how many ways this can happen
Answer:
Step-by-step explanation: