Answer:
6,072
Step-by-step explanation:
5,600 - 4,420 = 1,180
They gained 1,180 people over 5 years. Now we need to find how many people they gain every year (roughly).
Since it's 5 years, we are going to divide.
1,180 / 5 = 236
They gained 236 people over 1 year. Since 1998 is two years is before 2000, we're going to multiply 236 by 2.
236 x 2 = 472
Now we add this to the 1998 population.
5,600 + 472 - 6,072
The population in the year 2,000 is 6,072
At a local bookstore, books are on sale for $2 off the regular price. Jose buys 5 books on sale and pays a total of 35$. Each book cost the same amount. Write and solve an equation to find the regular price of each book
Answer: The regular price is $9
Step-by-step explanation: We do 35/5 to find the cost of each book. You get 7,then add 2 to get 9
(35/5)+2
Which of the points lies on the line y = 3x – 5? Explain how you are thinking.
A: (0, 3 ) B: (1, ‒2) C: (2, 2) D: (2, 0) E: (‒1, ‒8)
Answer:
B(1,-2)
Step-by-step explanation:
b is the answer from the above explanation
Reena is completing a 30 km run. So far she had run one sixth of the distance . How far has she run
So Reena has ran a distance of 5 kilometers while only covering one-sixth of the distance.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.
Here,
If Reena has completed one sixth of the 30 km run,
30 km / 6 = 5 km.
So, Reena has run a distance of 5 km so far when she had run one sixth of the distance.
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Find the area of the circle with radius 7.1m. Use 3.14 for π. Round to the nearest hundredth if necessary.
Answer:
158.29 m²
Step-by-step explanation:
A = πr²
A = 3.14 × 7.1 m × 7.1 m
A = 158.29 m²
Topic 3 proportional relationships
Raven needs new winter boots. Both ShoeTown and LaceUp shoe stores carry the boots she wants to buy.
The boots are regularly priced $85.95, but both stores are running sales. ShoeTown has the boots marked
down 15%. LaceUp has the boots marked down 10%, plus Raven has a $5 coupon she can use on the
boots after the markdown is applied.
Raven’s friend Becca tells Raven there is an online shoe store called Run, Don’t Walk that has the boots she
wants for only $71.99. If Raven buys the boots in a local store, she will have to pay 7.16% sales tax on her
purchase. If Raven buys the boots online, she won’t have to pay sales tax, but she will have to pay $6.50 for shipping.
Shoe Town provides the finest ultimate price, so Raven should purchase the boots there.
Equal in proportional to what?possessing an identical or consistent ratio or connection between two quantities: If y/x = k, in which k is the proportionality constant, then the numbers y and x are proportionate.
To determine which one is the best store for Raven let's calculate the price in each case.
Shoe Town
Total price:
Initial price - Mark down + Sales tax
85.95 - 15% + 7.16 %
85.95 - 12.89 + 7.16 %
73.06 + 7. 16%
73.06 + 5.23 = 78.29
Lace Up
Total price:
Initial price - Mark down - Coupon + Sales tax
85.95 - 10% - 5 + 7.15%
89.95 - 8.99 - 5 + 7.15%
80.96 - 5 + 7.15%
75.96 + 7.15%
75.96 + 5.43 = 81.39
Run, Don't Walk
Total price:
Initial price + shipping
71.99 + 6.50 = 78.45
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1. I have 30 water jugs which I am using for a party. I would like to put a piece of lemon in each one. I do not mind how small the pieces of lemon are. I can provide for all 30 jugs using the lemons that I have, and 21 cuts of the knife. Each cut will divide a whole lemon into two pieces, or divide a section of lemon into two smaller pieces.
How many lemons do I have?
You have 7 lemons, by the consideration that you have 21 cuts available to divide the lemons.
What is the division?
A division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each, and so on.
To find out how many lemons you have, you need to take into consideration that you have 21 cuts available to divide the lemons.
With each cut, you can divide one whole lemon into two pieces or divide one section of lemon into two smaller pieces.
So, with 21 cuts, you can have a maximum of 2²¹ (2097152) pieces of lemon.
Since you have 30 jugs and each jug needs to have a piece of lemon, you would need at least 30 pieces of lemon.
To get 30 pieces of lemon with the minimum number of whole lemons, you would need 7 whole lemons (7 * 2 = 14 pieces, 14 * 2 = 28 pieces, 28 * 2 = 56 pieces, 56 - 30 = 26 pieces left over).
Therefore, you have 7 lemons, by the consideration that you have 21 cuts available to divide the lemons.
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Given a right triangle with the longer leg three less than three times the shorter leg and the hypotenuse
is seven less than four times the shorter leg. What are the lengths of the three sides of the triangle? Be
sure to check both solutions to answer the question correctly.
So there are two possible triangles:
(10.5, 35.5, 37) and (35.5, 10.5, 37).
Step by step explanationLet's call the length of the shorter leg x. Then, the longer leg would be 3x - 3, and the hypotenuse would be 4x - 7.
Using the Pythagorean theorem, we have:
x^2 + (3x - 3)^2 = (4x - 7)^2
Expanding and simplifying, we get:
x^2 + 9x^2 - 18x + 9 = 16x^2 - 56x + 49
Combining like terms, we have:
7x^2 - 74x + 40 = 0
Using the quadratic formula, we find the solutions for x:
x = (74 ± √(74^2 - 4 * 7 * 40)) / (2 * 7)
x = (74 ± √(2744 - 560)) / 14
x = (74 ± √2184) / 14
x = (74 ± 46.56)/14
x = (35.5, 10.5)
So there are two possible triangles:
(10.5, 35.5, 37) and (35.5, 10.5, 37).
These are the two solutions for the lengths of the sides of the triangle.
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A new refrigerator has a price of $480.00. The store will discount the price by 15% if the purchaser pays in cash. What is the cash price of the refrigerator?
The cash price of the refrigerator is $408.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, a new refrigerator has a price of $480.00.
The store will discount the price by 15% if the purchaser pays in cash.
Now, the discount is
15% of 480
= 15/100 ×480
= 0.15×480
= 72
Now, 480-72
= $408
Therefore, the cash price of the refrigerator is $408.
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29. A freight elevator
can hold a maximum weight of 2,500 pounds.
A 180-pound person has a load of boxes to
deliver. Some of the boxes weigh 25 pounds
each and some weigh 60 pounds each.
a. Write and graph an inequality that represents
the number of boxes the elevator can hold in
one trip if the person is not in the elevator.
b. Write and graph an inequality that represents
the number of boxes the elevator can hold in
one trip if the person rides in the elevator.
c. Compare the graphs of the two inequalities.
The inequality for the given data can be written as 24x + 60y ≤ 2400 pounds.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that A freight elevator can hold a maximum weight of 2,500 pounds. A 180-pound person has a load of boxes to deliver. Some of the boxes weigh 25 pounds each and some weigh 60 pounds each.
The inequality can be written as:-
24x + 60y ≤ 2400 pounds
The graph of the inequality is attached with the answer below.
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danielle has taken five math tests so far this year. the tests are out of twenty points, and she has gotten the following scores. 17, 19, 20, 14, 16 what is the mode of her scores? which of the central tendancy would danielle wnat her teacher to use in order to describe her test scores
Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that the tests are out of twenty points, and she has gotten the following scores. 17, 19, 20, 14, 16
The mode of a set of data is the value that occurs most frequently. In this case, Danielle's scores are: 17, 19, 20, 14, 16.
There is no mode value.
Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average.
Hence, Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average.
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Use the iterative formula, x = √5x, -8 to calculate a solution to 3 dp
of x³-5x+8=0. Start with x₁ = -3.
Answer:
x ≈ -2.803
Step-by-step explanation:
You want to use the iterative formula x = ∛(5x -8) to find a solution to x³ -5x +8 = 0, starting with x₁ = -3.
IterationYour iterator appears to be found by solving for x:
x³ -5x +8 = 0
x³ = 5x -8 . . . . . . add 5x-8
x = ∛(5x -8) . . . . take the cube root
The attached table shows some iterations using this formula. To 3 dp, the solution is x ≈ -2.803.
__
Additional comment
Using a faster-converging iteration technique, we find the solution to be about ...
x ≈ -2.8025887521
The solution above is accurate to 3 dp.
Substitution of 1/2x + 2y = 8 and 3x - 2/3y = 1
The solution to the system of equations in this problem is given as follows:
x = 1.16, y = 3.71.
How to solve the system of equations?The system of equations for this problem is defined as follows:
x/2 + 2y = 8.3x - 2y/3 = 1.Multiplying the first equation by 2, we have that:
x + 4y = 16
x = 16 - 4y.
Replacing into the second equation, the solution for y is obtained as follows:
3(16 - 4y) - 0.67y = 1
48 - 12y - 0.67y = 1
12.67y = 47
y = 47/12.67
y = 3.71.
Then the solution for x is of:
x = 16 - 4(3.71)
x = 1.16.
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if you draw a random sample of 1,000 observations, what is the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24?
The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.
If the sample size is large enough (typically, n >= 30), we can assume that the sample mean is approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.
Therefore, if we know the population mean and standard deviation, we can calculate the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24. Let's denote the population mean as mu and the population standard deviation as sigma. Then, the standard deviation of the sample mean is sigma / sqrt(n), where n = 1000 is the sample size.
We can standardize the sample mean using the z-score formula:
z = (x - mu) / (sigma / sqrt(n))
where x is the sample mean.
For the sample mean to be greater than 3,011.76, we have:
z = (3,011.76 - mu) / (sigma / sqrt(n)) > 0
And for the sample mean to be less than 2,988.24, we have:
z = (2,988.24 - mu) / (sigma / sqrt(n)) < 0
To find the probability, we need to find the area under the standard normal curve to the right of z for the first case, and to the left of z for the second case. These probabilities can be found using a standard normal table or a statistical software package.
Unfortunately, without knowledge of the population mean and standard deviation, it is not possible to determine the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24.
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What is the expression equivalent to 2x^2-6x+5
Answer:4x−6
That's one
there are four red balls and two white balls in a jar. one ball is randomly removed and replaced with a ball of the opposite color. the jar is then shaken and one ball is randomly selected. what is the probability that this ball is red? express your answer as a common fraction.
The probability that this ball is red after the jar is then shaken and one ball is randomly selected is 11/18.
There are four red balls and two white balls in a jar
P(white removed and then red is chosen)'
P = 2/6 * 5/6
= 10/36
P= 5/18
Probability that the white removed and then red is chosen is 5/18.
P(red removed and then white is chosen)
P = 4/6 * 1/2
= 4/12
= 1/3
P = 6/18
Probability that the red removed and then white is chosen is 6/18.
The probability that this ball is red,
P(red is chosen) = 5/18 +6/18 = 11/18
Therefore, The probability that this ball is red is 11/18.
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I already asked this question but could not see the answer
All the correct expression in each steps are,
⇒ Step 1; (m³ + m²n + mn² - m²n - mn² - n³)
( By multiplication distributor )
⇒ Step 2; m³ - n³
( By combine like terms)
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression to prove is,
⇒ (m - n) (m² + mn + n²)
Now, We can simplify as;
⇒ (m - n) (m² + mn + n²)
Step 1;
⇒ (m³ + m²n + mn² - m²n - mn² - n³)
( By multiplication distributor )
Step 2;
⇒ m³ - n³
( By combine like terms)
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Oplications
Question 16, 6.3.33
Part 1 of 2
HW Score: 38.24%, 13 of 34 points
O Points: 0 of 1
You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $90 and you pay 70% of the manu
recommended list price. Plan B offers an annual membership fee of $20 and you pay 90% of the manufacturer's recommended list price. How
dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?
You have to purchases of merchandise in a year to pay the same amount under both plans.
Answer: $350
Step-by-step explanation:
Pls help Look at the triangles and decide who has chosen the triangle that is similar to ∆EFG? and why? 1. John says triangle A and Jill says B
Answer:
Both Jill and John are correct.
Step-by-step explanation:
Triangle A and B are both similar to the triangle in question. They all have angles of 30, 60, and 90 degrees. We can infer this because all triangles have 180 degrees and the square in the corner means that it is a right angle (90 degrees).
professor grok draws two cards from ms. q's deck at random without replacement. what is the probability that the first card grok draws has an even number, and the second card grok draws has a multiple of $3?$
The likelihood of drawing an average even number first, followed by a number that is a multiple of 3, is frac1850 cdot[tex]$frac1649 = $frac2882450$[/tex].
Since the two events are independent of one another, the likelihood of drawing an even number first and then a multiple of 3 equals the product of the probabilities of the two events. In a deck of 50 cards, there are 18 even numbers and 16 multiples of 3, hence the likelihood of getting an even number is [tex]$frac$[/tex]1850 and the likelihood of drawing a multiple of 3 is frac1650. The likelihood of drawing an even number first, followed by a multiple of 3, is frac1850 cdot frac1650 = frac2882450 because these are separate events
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a regulation-sized gymnasium is 80 feet wide and 100 feet long. if a scale model of the gymnasium is 12 inches long, how wide is the model?
A scale model of a regulation-sized gymnasium that is 12 inches long would be 10 inches wide.
To determine the width of a scale model of a regulation-sized gymnasium, you need to determine the scale factor used to create the model. The scale factor is the ratio of the size of the model to the size of the actual object.
In this case, the length of the model is 12 inches, while the length of the actual gymnasium is 100 feet, or 1200 inches. So, the scale factor is: 12/1200 = 1/100.
To find the width of the model, you would multiply the width of the actual gymnasium, 80 feet, by the scale factor, 1/100. This gives you a width of:
80 × 1/100 = 0.8 feet = 10 inches.
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Someone please help!!!
The components of the vector in rectangular form given magnitude and angle can be found as : x= |56| cos83°, y = |56| sin 83° .
How to determine the magnitude and angle of a vector?Let be a vector in rectangular form, that is, a vector of the form (x, y). The magnitude can be found by applying the square root of the dot product of the vector or the Pythagorean theorem and the direction is determined by applying inverse trigonometric functions:
here, we have,
Magnitude (linear algebra approach)
|r|=√(x,y). (x.y) (1)
Magnitude (algebra approach)
|r|=√(x²+y²) (2)
Direction
θ = tan⁻¹ (y/x) (3)
And the components of the vector can be found by applying the following formulas:
|r|=xcos θ (4)
|r|= y sinθ (5)
The components of the vector in rectangular form given magnitude and angle can be found as: x= |56| cos83°, y = |56| sin 83° ., .
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Which of the following are solutions to the equation below?
Check all that apply.
4x2 - 12x+ 9 = 5
Answer:
x = 3 + √5 / 2
Step-by-step explanation:
4x²-12x+9=5
4(x²-3x+1=0)
x²-3x+1=0
(quadratic formula)
a=1 b=-3 c=1
x= -(-3)+√(-3)²-4x1x1 / 2x1
simplify:
x = 3+√5 / 2
Javin cuts a block of wood along the red line. When he looks at the newly exposed face, What is the shape of the cross- section. A. A rectangle, 4 inches by 2 inches
B. A square, 2 inches by 2 inches. C. A rectangle, 4 inches by 3 inches.D. A rectangle, 2 inches by 3 inches. I NEED ANSWER NOW IF RIGHT I GIVE BRAINLIEST
What will the dimensions of some cross-sections of a cuboid be when cutting depends on the viewpoint.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Suppose we have a cuboid shape of a wooden block.
The height of the wooden block is h, the width of the wooden block is w and the length of the wooden block is l.
Now if we cut the wooden block along the red line a look at it from the top it will look like a rectangle width width 'w' and length 'l'.
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Answer: A. A rectangle 4 inches by 2 inches
Step-by-step explanation:
on a 7 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
The probability of getting at least one question wrong on a 7 question multiple-choice test with two answers for each question is 1 - (1/4)^7, which is approximately 99.2%.
The probability of getting one question wrong on a 7 question multiple-choice test with two answers for each question is 1/4. This is because there are two options for each question, and if you choose the wrong one, you get the question wrong. Therefore, the probability of getting all 7 questions wrong is (1/4)^7, or one in 16,384. The probability of getting at least one question wrong on the test is 1 - (1/4)^7, which is equal to 1 - 1/16,384, or approximately 99.2%. To calculate the probability of getting at least one question wrong, you subtract the probability of getting all 7 questions correct from 1. This is because if you do not get all 7 questions correct, then you must have gotten at least one question wrong.
The complete question: On a 7 question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong? Give your answer as a fraction
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6. A figure has an area of 9 square units. The equation y = √√represents the
scale factor of y by which the solid must be dilated to obtain an image with
area of x square units. Select all points which are on the graph representing
this equation. (Lesson 5-5)
(A.) (0, 0)
(B.) (1, 1)
(1,3)
D.) (3, 1)
E. (9,1)
(F.) (9, 3)
G.) (18,2)
(H.) (36, 2)
The graph represents the function that maps the area of the original figure to the area of the dilated figure. If the original area is 9 square units and the dilated area is x square units, then the equation y = √√x represents the relationship between the two areas. Points (B), (F), (G), and (H) are on the graph because they satisfy the equation y = √√x. Points (A), (C), and (E) are not on the graph because they do not satisfy the equation.
Problem 1
A ladder 15ft in length leans against a vertical wall, with the bottom of the ladder 5ft from the
wall on the horizontal floor. If at that time the bottom end of the ladder is being pulled away at
the rate of 2ft/s at what rate does the top of the ladder slip down the wall.
The top of the ladder slips down the wall at the rate of 5.6 ft/sec.
What is a rate?
The ratio of two related quantities expressed in several units is known as a rate. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
Here, we have
Given: A ladder 15ft in length leans against a vertical wall, with the bottom of the ladder 5ft from the wall on the horizontal floor. If at that time the bottom end of the ladder is being pulled away at the rate of 2ft/s .
Let: x = the distance from the base of the ladder to the base of the wall
y = the distance from the tip of the ladder to the base of the wall, we have:
x² + y² = 15²
y² = 15² - 5² = 225 - 25 = 200 => y = 14.14 ft
2x dx/dt + 2y dy/dt = 0
2 * 5 * dx/dt + 2 * 14.14 * (-2) = 0
10 dx/dt = 56.56
dx/dt = 5.6 ft/sec
Hence, the top of the ladder slips down the wall at the rate of 5.6 ft/sec.
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Two functions are shown.
f(x)=x+2
g(x)=x²-x-3
What is (gof)(x)?
A x²-x-1
Bx²-x+3
C x² + 3x +3
Dx² + 3x - 1
f(x)=2/3x^2 domain and range
The domain and range of function f(x) = 2/3x² are respectively, real numbers and non-negative numbers
What is Domain and Range ?The domain of a function is the set of all input values (independent variable) for which the function is defined and produces a valid output (dependent variable).
The range of a function is the set of all possible output values of the function. It represents the set of all possible values of the dependent variable.
Given that,
The domain of the function f(x) = 2/3x² is all real numbers except x = 0, since division by 0 is undefined.
The function f(x) = 2/3x²
The range of the function f(x) = 2/3x² is all non-negative real numbers.
It is because for any real number x,
the value of 2/3x² will always be non-negative.
To see this, consider the case where x > 0.
In this case, 2/3x² is positive,
and for x < 0, 2/3x² is still positive.
So, the domain of the function f(x) = 2/3x² is all real numbers except x = 0 and the range of the function is all non-negative real numbers.
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Consider the line x+2y=-8
Find the equation of the line that is parallel to this line and passes through the point (6,-3)
Find the equation of the line that is perpendicular to this line and passes through the point (6,-3)
The equation of the line that is parallel to this line and passes through the point (6, -3) is y = x/2.
The equation of the line that is perpendicular to this line and passes through the point (6, -3) is y = -2x + 9.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on the line:
Points = (6, -3).Slope, m = 1/2.In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ 1/2 = 1/2
At data point (6, -3), a linear equation of this line can be calculated by using the point-slope form as follows:
y - (-3) = 1/2(x - 6)
y + 3 = x/2 - 3
y = x/2 - 3 + 3
y = x/2
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
1/2 × m₂ = -1
m₂ = -2
At data point (6, -3), a linear equation of this line can be calculated by using the point-slope form as follows:
y - (-3) = -2(x - 7)
y + 3 = -2(x - 6)
y = -2x + 12 - 3
y = -2x + 9.
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please help me with this worded problem