Answers
Answer:
8.001 percent
Step-by-step explanation:
the numbers of people that auto race divided by the total number of people who took the survey multiplied by a hundred
Answer:
8%
Step-by-step explanation:
in order to find the probability that a random adult from the 2237 will like auto racing we need to divide the number of people who prefer auto racing by the total number of adults
179/2237≈0.08
8%
Related Questions
pls help me and explain how to do this TwT
Answers
Answer:
7
Step-by-step explanation:
index of root = 2
exponent = 2
divide both by 2
2:2 = 1 (the root expires)
2:2 = 1 (the exponent expires)
7
A 5 1/2 inch candle burns down in 11 hours. how far has it burned after 6 1/2 hours?
Answers
The candle has burned down [tex]3 \frac{3}{4}[/tex] inches after 6.5 hours.
To calculate this, we first need to determine the rate at which the candle burns by dividing the total burn time (11 hours) by the total length of the candle ( [tex]5 \frac{1}{2}[/tex] inches). This gives us a burn rate of 2 hours per inch.
Next, we can multiply the burn rate by the time the candle has been burning (6.5 hours) to determine how far the candle has burned. This gives us a result of 13 inches, which is equal to [tex]3 \frac{3}{4}[/tex] inches in standard units. Therefore, the candle has burned down [tex]3 \frac{3}{4}[/tex] inches after 6.5 hours.
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For a fundraiser, a group plans to sell granola bars and bottles of water at the same prices as described in Part A. The group wants the income from the fundraiser to be at least $150.Choose the inequality to show the number of granola bars x and the number of bottles of water y that must be sold.A. 1.4x + 0.75 y > 150B. 1.4x + 0.75y ≥ 150C. 1.4x + 0.75 < 150D. 1.4x + 0.75 ≤ 150
Answers
The group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.
The correct inequality is B. 1.4x + 0.75y ≥ 150. This inequality states that the group must sell at least $150 worth of items in order to make a profit. The cost of a granola bar is $1.40, and the cost of a bottle of water is $0.75. Therefore, the total cost of the items must be greater than or equal to $150. The formula for this inequality is 1.4x + 0.75y ≥ 150, where x represents the number of granola bars sold and y represents the number of bottles of water sold.
To solve this inequality, we can first multiply both sides of the inequality by 100. This will give us 140x + 75y ≥ 15000. Next, we can subtract 75y from both sides to get 140x ≥ 14250. Finally, we can divide both sides of the equation by 140 to get x ≥ 102.86. This means that the group needs to sell at least 103 granola bars in order to make a profit of at least $150. This can be further simplified by rounding up the granola bars sold to 104. Therefore, the group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.
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What is the relationship between the base and the height of an area formula?
Answers
A triangle's area is 1/2(b*h), where b is the base and h is the height. A triangle's base can be any of its sides, and its height is the length of the altitude from the opposite vertex to that base.
What is area?The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
The area of a triangle is 1/2(b*h), where b is the base and h is the height. A triangle's base is any one of its sides, and its height is the length of the altitude from the opposite vertex to that base.
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find the exact length of the curve. y = ln 1 − x2 , 0 ≤ x ≤ 1 9
Answers
The exact length of the curve for the function y = ln(1 - x²) is log(5/4) - 1/9
The general formula for the arc length of the curve y on the interval [a, b] is written as,
[tex]s=\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^2 } } \, dx[/tex]
Here we have given that the function is y = ln(1 - x²)
And the limit is 0 ≤ x ≤ 1/9
When we differentiate the function, then we get the value of y' as,
y' = 1/(1 - x²) × (-2x) = -2x/(1 - x²)
Now, we have to apply the values on the arc length formula, then we get,
[tex]s=\int\limits^{1/9}_0 {\sqrt{1+(\frac{-2x}{1-x^2} )^2 } } \, dx[/tex]
When we simplify this one then we get,
[tex]s=\int\limits^{1/9}_0 {\sqrt{\frac{1+x^4-2x^2+4x^2}{(1-x^2)^2} } } \, dx[/tex]
Now, we have to divide numerator by denominator and expressing using
the rule Dividend/Divisor = Quotient + (Remainder/Divisor)
Then we get the resulting equation as,
[tex]s=\int\limits^{1/9}_0 {-1 + \frac{2}{1-x^2} } \, dx[/tex]
When we apply the limit value, then we get
s = −1/9 + log∣10/8∣−log(1)
When we simplify this one then we get,
s = log(5/4) - 1/9
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1. Ryan works at a store. He is paid an hourly rate plus 17% commission for all products that he sells.
One week, he was paid $459 for working 20 hours and selling $1700 worth of products. What is his
hourly rate?
Answers
Answer:
$8.50
Step-by-step explanation:
To find Ryan's hourly rate, we need to first determine the total amount of money he made from commission. Since Ryan was paid 17% commission for all the products he sold, and he sold $1700 worth of products, he made 17/100 * $1700 = $289 in commission.
Next, we need to subtract this amount from his total pay to find the amount he was paid for working. Since Ryan was paid a total of $459, and made $289 in commission, he was paid $459 - $289 = $170 for working.
Finally, we can use this amount to calculate his hourly rate by dividing it by the number of hours he worked. Since Ryan was paid $170 for working 20 hours, his hourly rate is $170 / 20 = $8.50 per hour.
Therefore, Ryan's hourly rate is $8.50.
To find Ryan's hourly rate, we need to first calculate how much money he made from commissions. We can do this by multiplying his total sales by the commission rate: $1700 * 0.17 = $289.
Next, we need to subtract the commission from his total pay to find his base pay: $459 - $289 = $170.
Finally, we can divide his base pay by the number of hours he worked to find his hourly rate: $170 / 20 hours = $<<170/20=8.50>>8.50 per hour.
Select each pair of equivalent numbers.
Answers
Answer:
B, D
Step-by-step explanation:
To change a fraction to a decimal, divide the numerator (number on top) by the denominator (number on the bottom).
To change a decimal number to a percent, multiply the number by 100%.
A. 40/1000 = 0.04 = 4%
No
B. 6/5 = 1.2 = 120%
Yes
C. 50/33 = 1.5151... = 151.51...%
No
D. 1/8 = 0.125 = 12.5%
Yes
E. 1/3 = 0.333... = 33.333...%
No
Answer: B, D
x^2+4x-7 in the form (x+a)^2-b
Answers
The equation x² + 4x - 7 can be written in the form (x + a)² - b as (x + 2)² - 11
How to write equation in another form?x² + 4x - 7 in the form (x + a)² - b
Where,
b = constant
x² + 4x - 7
= (x + 2)² - 11
Hence,
x² + 4x - 7 = (x + 2)² - 11
Check:
(x + 2)² - 7
= (x + 2) (x + 2) - 7
= x² + 2x + 2x + 4 - 11
= x² + 4x - 7
Therefore, (x + 2)² - 11 is another form the equation x² + 4x - 7 can be written.
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which of the following is not an example of a binomial distribution? a.) the probability of a dart player missing the bullseye seven times in eight attempts. b.) the probability of rolling a die eight times and getting an odd number or a prime number four times. c.) the probability of a basketball player making a free throw seven times in ten attempts. d.) the probability of flipping a coin four times and never landing on tails.
Answers
The answer is B). "the probability of rolling a die eight times and getting an odd number or a prime number four times."
A binomial distribution is a statistical distribution that describes the probability of a certain number of successful outcomes in a fixed number of independent trials. In order for a situation to be a binomial distribution, the following conditions must be met:
There must be a fixed number of trials.
Each trial must have only two possible outcomes (e.g., success or failure).
The probability of success must be the same for each trial.
The first three answer choices all involve situations that meet these conditions and are therefore examples of binomial distributions. The fourth answer choice, however, involves rolling a die, which has more than two possible outcomes (1, 2, 3, 4, 5, or 6). This means that it is not a binomial distribution.
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Kathleen likes to make desserts for bake sales. Last month, she made 1 batch of brownies
and 1 batch of cookies, which called for 7 eggs total. The month before, she baked 1 batch of
brownies and 2 batches of cookies, which required a total of 11 eggs. How many eggs did
Kathleen use for a batch of each dessert?
eggs to make a batch of brownies and
Kathleen uses
of cookies.
Submit
eggs to make a batch
You h
Jay
Answers
Sales is a term used to describe the activities that lead to the selling of goods or services.
What is sales explain with an example?A sale is a transaction between two or more parties in which goods or services are exchanged for money or other assets. In the financial markets, a sale is an agreement between a buyer and seller involving the price of a security and its delivery for agreed-upon compensation.Sales play a key role in the building of loyalty and trust between customer and business. Trust and loyalty are the main reasons why a customer would choose to recommend your company to a friend or family member or write a great review of your product or service online.In general business operations, sales refer to any transactions where money or value is exchanged for the ownership of a good or entitlement to a service. In an accounting context, sales refers to a company's revenue earned from the sales of products or services (net sales).There are two main types of sales that sales representatives deal with: inside sales and outside sales. Inside sales. Inside sales are any sales done remotely or from the home office. These sales include phone, email, CRM platforms, and VOIP sales.Let x represent the number of eggs that she uses for one batch of brownies.
Let y represent the number of eggs that she uses for one batch of cookies.
Last month, she made 2 batches of brownies and 3 batches of cookies. This means that
2x + 3y = 16 - - - - - - - - - -1
The month before, she baked 1 batch of brownies and 1 batch of cookies, which required a total of 6 eggs. This means that
x + y = 6 - - - - - - - - - - - - - 2
Multiplying equation 1 by 1 and equation 2 by 2, it becomes
2x + 3y = 16
2x + 2y = 12
Subtracting, it becomes
y = 4
Substituting y = 4 into equation 2, it becomes
x + 4 = 6
x = 6 - 4 = 2
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Which inequality is true?
A. 2 pi/ 2 < 3
B. 4 pi > 12
C. pi + 6 < 9
D. 3 pi - 1 < 8
Answers
The true inequality is 4π > 12.
How to solve inequality?Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. Therefore, let's solve the inequalities that is true.
Hence,
[tex]\frac{2\pi }{2} < 3[/tex]
π < 3 (This is false because 3.14 is greater than 3)
4π > 12
divide both sides by 4
π > 3 (This is true.)
π + 6 < 9
subtract 6 form both sides
π < 3 (This is false)
3π - 1 < 8
3π < 9
π < 3 (This is false)
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Yesterday at a museum there was a total of 30
adult and children tickets bought. Children
tickets cost 5$ and adult tickets cost 8$. In total
40$ was spent yesterday. What is the total
amount of children tickets bought?
Answers
Thus, total amount of children tickets bought =30 tickets
What is equation ?equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics.
Here,
The total adults and children ticket bought = 50
The cost of one children ticket= 10$
The cost of one adult ticket= 20$
The total spent amount = 700$
let adult be y and children be x
Thus,
equation => x+y=50 and 10x+20y=700
=>x=50-y
=>10(50-y)+20y=700
=>500 -10y +20y =700
=>500+10y =700
=>10y=500-700
=>y=200/10
=>y=20
=>x=50-20=30
=>x=30
Thus, total amount of children tickets bought =30 tickets
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How many integers are there between 1 and 100 which have 4?
Answers
There are 19 such integers with 4 as a digit between 1 and 100, including 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, and 94.
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 3.14 and 1*(1/2) are two examples of numbers that are not integers. The collection of whole numbers and their antipodes is known as the integers. The set of integers does not include fractions or decimals. Integers include, for instance, 2,5,0,12,244,15, and 8.
4-digit numbers are ones with only four digits, the first of which must be one or higher and the remaining three of which may be any number between zero and nine. Four-digit numerals include 5693, 1023, and 9825 as examples. The INTEGER data-type stores whole numbers with a precision of 9 or 10 digits, ranging from -2,147,483,647 to 2,147,483,647. Because it is a reserved value, the number 2,147,483,648 cannot be utilized. The INTEGER value is generally used to store counts, amounts, and other data since it is stored as a signed binary integer.
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I have a lot of this but pls help me
Answers
Step-by-step explanation:
4. 5 Million
5. 6:10
Not sure about 3 tho I'm sorry !
I need help with probability.
Answers
Answer:
Step-by-step explanation:
correct answer is 6 marbles, no doubt.
Which out of the following are expressions with numbers only?
(a) y + 3
(b) (7 × 20) – 8z
(c) 5 (21 – 7) + 7 × 2
(d) 5
(e) 3x
(f) 5 – 5n
(g) (7 × 20) – (5 × 10) – 45 + p
Answers
5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.
What equation contains an expression?
The equal to sign (=) is the best indicator of whether a given problem is an equation or an expression because it indicates that the problem is an equation.
It is only an expression if there isn't an equal to (=) sign present. It contains data that is used to demonstrate value, such as numbers, variables, and operators.
5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.
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How many terms are there in the expression 5x 3xy?
Answers
There are four terms in the expression. Two are numbers and the remaining are variables.
What is mathematical expression?It is a mathematical statement express the relationship between two or more mathematical terms. In an expression there will be one or more mathematical symbols or operator such as addition, multiplication, division or subtraction sign. Beside this there are many other signs such as equal or inequal sign, integration sign, square root or cubic root sign etc.
Terms can be numbers, variables or variables with coefficient.
How many terms are in the expression?In the above question, we have four terms, and one symbol.
5 × 3xy
5 is number and it is called constant
3 is number but it acts as the coefficient of the variables x and y.
x and y are two variables.
there is a multiplication sign among these terms.
the above expression can be described as 5 is multiplied by 3xy.
hence, we have four terms.
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this question is not making sense to me, i need a quick answer.
Answers
Answer:
x-intercept: (-21/2,0)
y-intercept : (0,-21)
What is the relationship between the volume of a pyramid to the volume of a prism?
Answers
Relationship between the volume of the pyramid is one third the volume of the prism with the same base and equal height.
As given in the question,
Formula used to find the volume of the pyramid and prism is given by :
Volume of the pyramid = (1/3) × base area × height
Volume of the prism = Base area × height
If the base of the pyramid and prism is same and height of both pyramid and prism are equal then
Volume of the pyramid = ( 1/3) × Volume of the prism
Therefore, the volume of the pyramid is one third the volume of the prism with same base and equal height.
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What is the quotient x3 3x2 5x 3 )/( x 1?
Answers
The quotient (x3 - 3x2 + 5x - 3) ÷ (x - 1) is x2 - 2x + 3 and remainder becomes zero
What means quotient in math?
Definition of Quotient
The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.
x^3 - 3x^2 +5x -3 / x-1 = x^2 -2x +3
x^3 -+ x^2
------------
0 2x^2 +5x
2x^2 +2x
----------------
0 3x +3
3x +3
---------
0 0
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What is the domain answer?
Answers
If a function f offers a means of successfully generating a single value y while using a value for x to that end, then that selected x-value is said to belong to the domain of f.
what is domain ?A function's domain is the collection of permitted values. Included in this collection are the x values for a function, such as f. (x). Such values are gathered together to demonstrate the variety of values that can be utilized as function input. Inputting an x value causes the function to return this set of values.
here
Take into account the relationship (0,7,0,8,(2,6),(1,6),(1,7),(2,9).
The relation is shown in this case as a set of sorted pairs. The range is the set of y -coordinates, which are (6 ,7 ,8 ,9), and the domain is the set of x -coordinates (0, 1, 2) .
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Graph the inequality on a coordinate plane.
2x - 5y< -10
Answers
Answer:
espero te sirva siuuuuuuuuuuu
What are actual roots of FX according to the rational root theorem The following are potential roots of FX 2x 2 2x 24 4 3 2 3 4?
Answers
All the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12 are 3/4 and -4/5.
We have the given polynomial:
f(x) = 20x4 + x3 + 8x2 + x - 12
All potential polynomial roots are represented by rational numbers, according to the Rational Root Theorem:
x = a/b
Where a is a factor of a constant term
b is the factor of coefficient of leading term
From the given polynomial:
-12 is the constant term and 20 is the coefficient of leading term
The possible factors of -12 are ±1, ±2, ±3, ±4, ±6, ±12
The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20
So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)
Solve for x when the given function is equal to zero
20x4 + x3 + 8x2 + x - 12 = 0
(4x - 3)(5x + 4)(x2 + 1) = 0
So we get:
4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0
x = 3/4, x = -4/5, x =1, x = -1
Hence, the rational roots are x = 3/4, x = -4/5.
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We have the given polynomial:
f(x) = 20x4 + x3 + 8x2 + x - 12
x = a/b
b is the factor of coefficient of leading term
-12 is the constant term and 20 is the coefficient of leading term
The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20
So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)
Solve for x when the given function is equal to zero
20x4 + x3 + 8x2 + x - 12 = 0
(4x - 3)(5x + 4)(x2 + 1) = 0
4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0
x = 3/4, x = -4/5, x =1, x = -1
2. + -15 points SCalcET8 11.1.023.MI. Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) n 5n2 lim an Need Help? Í Readit L at hit 1 lt lal toaT tor ll Master It Talk to a Tutor 3. +-15 points SCalcET8 11.1.029 Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) lim an
Answers
Answer:
15-11=4ans
123-23=100ans
A sum of money is to be divided between Alyah, Byron and Cecil. Alyah receives $1 plus one-third of what is left. Byron then receives $6 plus one-third of what remains. Cecil receives the rest, which amounts to $40. How much did Byron receive? (A) $26 (B) $28 (C) $30 (D) $32 (E) $34
Answers
Answer:
(A) $26
Step-by-step explanation:
You want to know the amount Byron received from the distribution to Alyah, Byron, and Cecil, given Cecil received $40.
SetupLet x represent the amount being distributed, and a, b, c represent the amounts received by Alyah, Byron, and Cecil, respectively.
The given relations tell us ...
a = 1 + 1/3(x -1)
b = 6 + 1/3(x -a -6)
c = x -a -b = 40
SolutionSubstituting for b gives us ...
40 = x - a - (6 +1/3(x -a -6)) = x -a -6 -1/3x +1/3a +2 = 2/3x -2/3a -4
44 = 2/3(x -a) . . . . . . . add 4, factor out 2/3
66 = x -a . . . . . . . . . multiply by 3/2
Substituting for a gives us ...
66 = x -(1 +1/3(x -1)) = x -1 -1/3x +1/3 = 2/3x -2/3 = 2/3(x -1)
99 = x -1 . . . . . . . multiply by 3/2
100 = x . . . . . . add 1
DistributionThen ...
a = 1 + 1/3(100 -1) = 1 + 99/3 = 34
b = 6 + 1/3(100 -34 -6) = 6 + 1/3(60) = 26
Byron received $26.
__
Additional comment
Based on results, the "what is left" is the amount after the $1 or $6 distributions are made.
Alyah: $34, Byron: $26, Cecil: $40, for a total of $100.
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What is the mean of the data 6 7 10 12 13 4 8 12?
Answers
The mean of the data 6 ,7 ,10 ,12, 13, 4, 8 ,12 is 9.
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
The basic formula to calculate the mean is calculated based on the given data set. Each term in the data set is considered while evaluating the mean. The general formula for mean is given by the ratio of the sum of all the terms and the total number of terms. Hence, we can say;
Mean = Sum of the Given Data/Total number of Data
Mean= 6 +7+ 10+ 12+ 13+ 4+ 8 +12 / 8 = 72/8 = 9
Hence, The mean of the data 6 ,7 ,10 ,12, 13, 4, 8 ,12 is 9.
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What is a parabola parent function?
Answers
The parent function of a parabola is y = x².
A function is said to be a parent function if it is expressed in the simplest form and satisfies the definition of a particular type of function.
The simplest function that satisfies the definition of a parabola is given by y = x². It is also called quadratic function.
Its graph passes through the origin (0,0) and lies in first and second quadrant.
One or more parabolas can be easily obtained by transforming the parent function of the parabola.
Therefore, the parent function of parabola is given by y = x².
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A police car notices a speeding car travelling at 60 ft/s East, 5 s after it passes the intersection. The police gives chase immediately, and they start off 650 ft South of the intersection. The police car will run with a velocity of 80 ft/s, going North.
Answers
Answer:
To find out how long it will take for the police car to catch up to the speeding car, you can use the following formula:
t = d / v
Where t is the time it takes to catch up, d is the distance between the police car and the speeding car, and v is the relative speed of the police car compared to the speeding car.
In this case, the distance between the police car and the speeding car is given by the Pythagorean theorem:
d = sqrt((650 ft)^2 + (60 ft/s * 5 s)^2) = 674.22 ft
The relative speed of the police car compared to the speeding car is given by:
v = 80 ft/s - 60 ft/s = 20 ft/s
Plugging these values into the formula, we get:
t = d / v = 674.22 ft / 20 ft/s = 33.71 s
So it will take the police car approximately 33.71 seconds to catch up to the speeding car.
Note: This is just an approximation and the actual time required may vary depending on the exact positions and speeds of the two cars
Answer: it will take the police car 25 seconds and 2000 feet to catch up with the speeding car.
Step-by-step explanation: To determine the distance and time that the police car needs to catch up with the speeding car, we can set up the following system of equations:
Let x be the time it takes for the police car to catch up with the speeding car
Let y be the distance the police car needs to travel to catch up with the speeding car
The distance the speeding car travels in x seconds is given by the equation:
60x = distance
The distance the police car travels in x seconds is given by the equation:
80x = y
The distance between the two cars at the start is given by the equation:
(y - 650)^2 + 650^2 = x^2
We can solve this system of equations by substituting the second equation into the third equation, resulting in:
(80x - 650)^2 + 650^2 = x^2
Expanding and rearranging the terms, we get:
6400x^2 - 19600x + 422500 = x^2
Solving for x, we get:
x = 25 seconds
Substituting this value back into the equation for the distance the police car travels, we get:
y = 80 * 25 = 2000 ft
What is the SSS theorem?
Answers
Side-Side-Side (SSS) Theorem; Two triangles are congruent if three sides of one are equal respectively to three sides of the other (SSS=SSS).
Side-Side-Side or SSS is a kind of triangle congruence rule where it states that if all three sides of one triangle are equal to all three corresponding sides of another triangle, the two triangles are considered to be congruent. Two or more triangles are said to be congruent when the measurements of the corresponding sides and the corresponding angles are equal. Let us learn more about the SSS congruence rule, SSS theorem, the formula, and solve a few examples.
The SSS postulate applies to triangles that have the same measurements for corresponding sides. An example would be a triangle that has side lengths 3, 4, and 5 and a triangle that has side lengths 4, 3, and 5
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What us the third step in sketching the graph of a rational function
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The third step in sketching the graph of a rational function is "Finding the function's zeros and vertical asymptotes and plotting them on a number line".
What is vertical asymptotes?
A graph's vertical asymptote is a vertical line with the equation x = a, where the graph tends to positive or negative infinity as the inputs get closer to the value of a. A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph approaches the line as the inputs go closer to ∞ or –∞.
The steps to sketch a graph of rational function:
1. Ensure that the function's denominator and numerator are listed in decreasing order of power.
2. Discover the domain
3. Completely factor the numerator and denominator. Any shared factors between the numerator and denominator should be eliminated. (Once factors have been cancelled, the reduced function is what remains. For all subsequent actions, employ the reduced function.) Skip Step 4 if there are no common factors.
4. Look for any holes
5. Search for any vertical asymptotes.
6. Find the Horizontal Asymptote.
7. Look for any x- and y-intercepts.
8. Locate test points
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