There exists at least one c in the open interval (a, b) such that f'(c) = 0.
There are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.
To prove that the given equation has exactly 3 distinct real solutions, let's follow the steps mentioned in the question.
First, consider the polynomial p(x) = (x-a)(x-b)(x-c)(x-d). Since a, b, c, and d are distinct real numbers, p(x) has 4 distinct real roots, namely a, b, c, and d.
Now, let's find the derivative p'(x) using logarithmic differentiation. Taking the natural logarithm of both sides, we have:
[tex]ln(p(x)) = ln((x-a)(x-b)(x-c)(x-d))[/tex]
Differentiating both sides with respect to x, we get:
[tex]p'(x)/p(x) = 1/(x-a) + 1/(x-b) + 1/(x-c) + 1/(x-d)[/tex]
Multiplying both sides by p(x) and simplifying, we have:
[tex]p'(x) = (x-b)(x-c)(x-d) + (x-a)(x-c)(x-d) + (x-a)(x-b)(x-d) + (x-a)(x-b)(x-c)[/tex]
Now, we apply Rolle's Theorem, which states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the open interval (a, b) such that f'(c) = 0.
Since p(x) has 4 distinct real roots, there must be 3 intervals between these roots where the function p(x) satisfies the conditions of Rolle's Theorem. Therefore, there are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.
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21. The population of a small town is 15,000. If the population is growing
by 5% per year, how long will it take for the population to reach 25,000?
It will take the population 10.5 years to reach 25,000
How long will it take for the population to reach 25,000?From the question, we have the following parameters that can be used in our computation:
Inital population, a = 15000
Rate of increase, r = 5%
Using the above as a guide, we have the following:
The function of the situation is
f(x) = a * (1 + r)ˣ
So, we have
f(x) = 15000 * (1 + 5%)ˣ
When it reaches 25000, we have
15000 * (1 + 5%)ˣ = 25000
Divide both sides by 15000
(1 + 5%)ˣ = 1.67
Take the logarithm of both sides
x = log(1.67)/log(1 + 5%)
Evaluate
x = 10.5
Hence, the number of years is 10.5
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From a Word Problem
Jack has $10 in his lunch account. He plans to
spend $2 a week on snacks. How long until
Jack's lunch account reaches zero?
Answer:
Sure, here's the solution to the word problem:
Jack has $10 in his lunch account and plans to spend $2 a week on snacks. To find out how long it will take his lunch account to reach zero, we can divide the total amount of money in his account by the amount he spends each week.
```
$10 / $2 = 5 weeks
```
Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.
Here's another way to solve the problem:
We can also set up an equation to represent the situation. Let x be the number of weeks it takes Jack's lunch account to reach zero. We know that Jack starts with $10 and spends $2 each week, so we can write the equation:
```
$10 - $2x = 0
```
Solving for x, we get:
```
x = 5
```
Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.
Answer:
in 5 weeks he will have 0$ in his account
Step-by-step explanation:
a bank account earns 0.06% annual interest compounded monthly the bank B of the account after T months started with the $250 is given by the equation B =250(1.06)^t. How long will it take to triple the balance of the account?
It will take about 387.3 months (or about 32.3 years) to triple the balance of the account.
What is Compound Interest ?
Compound interest refers to the process of earning interest on both the initial principal amount as well as any accumulated interest from previous periods. In other words, it is the interest that is earned on the interest that has been accumulated over time.
We can use the formula for compound interest to solve this problem.
Where:
A = the final amount
P = the initial amount
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this problem, we have:
P = $250
r = 0.06% = 0.0006 (as a decimal)
n = 12 (since the interest is compounded monthly)
A = 3P = $750
Substituting these values into the formula, we get:
750 = 250[tex](1 + 0.0006/12) ^{12t}[/tex]
Dividing both sides by 250, we get:
3 =[tex](1 + 0.0006/12) ^{12t}[/tex]
Taking the natural logarithm of both sides, we get:
㏒(3) = 12t ㏒(1 + 0.0006÷12)
Solving for t, we get:
t = ㏒(3)/(12 ㏒(1 + 0.0006÷12))
Plugging this into a calculator, we get:
t ≈ 387.3 months
Therefore, it will take about 387.3 months (or about 32.3 years) to triple the balance of the account.
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5. A ramp is to be built using a 20 foot long board and an 18 foot long board. To make die stable, the builders would like to add a third board to create a right triangle. How longed that board be, to the nearest hundredth of a foot?
The length of the third board the builders will add to create a right triangle, according to the Pythagorean Theorem is about 8.72 ft
What is the Pythagorean Theorem?Pythagorean Theorem is the relationship between the lengths of the three sides of a right triangle. The theorem states that the square of the length of the hypotenuse is equivalent to the sum of the square of the other two sides of the right triangle.
The specified dimensions of the ramp are;
Length of one side of the ramp = 20 ft
Length of the other side of the ramp = 18 ft
The shape of the triangle the builders would like to create = A right triangle
Let x represent the length of the third board, and let the 20 ft board represent the hypotenuse side. Pythagorean Theorem indicates that we get;
20² = 18² + x²
20² - 18² = x²
x² = 20² - 18² = 76
x = √(76) = 2·√(19) ≈ 8.72
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An a frame house has a front facade measuring 30' across and 20' in height what is the area of the facade
The area of the facade measuring 30' across and 20' in height is 300 square feet.
The front facade of an A-frame house is a triangular shape, with a base of 30 feet and a height of 20 feet. To calculate the area of the facade, we need to use the formula for the area of a triangle, which is 1/2 times the base times the height = 1/2 * b * h, where b is the base and h is the height.
In this case, the base is 30 feet and the height is 20 feet, so we can plug those values into the formula:
Area = 1/2 x 30 x 20
Simplifying the multiplication, we get:
Area = 300 square feet
Therefore, the area of the front facade of the A-frame house is 300 square feet.
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What fraction of 2.4 litres is 400 ml?
The fraction is 1/6. Option D
How to determine the fractionFirst, we need to know the conversion factor the parameters.
Then, we have that';
1 liter = 1000 milliliter
10 milliliters (ml) = 1 centiliter (cl)
10 centiliters = 1 deciliter (dl) = 100 milliliters
1 liter = 1000 milliliters
1 milliliter = 1 cubic centimeter
1 liter = 1000 cubic centimeters
Then, we can say that;
If 1 liter = 1000ml
Then 2 4/8 = 400ml
2.4 liters is equal to 2.4 x 1000= 2400 milliliters.
400/2400
Simplify the fraction;
4/24
Divide the values, we get;
1/6
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In 2003 the social security tax rate was 6. 2% and the maximum taxable income was $87,000. 0. If Linda earned $54,122, how much did she contribute to social security?
Linda contributed $3,355.56 to social security in 2003.
The Social Security tax is a payroll tax that is deducted from employees' paychecks to help fund the Social Security program, which provides retirement, disability, and survivor benefits to eligible individuals.
The Social Security tax rate is typically 6.2% for employees and employers, and the maximum amount of taxable earnings is determined each year by the Social Security Administration (SSA).
In 2003, the maximum taxable earnings was $87,000. This means that any earnings above $87,000 were not subject to Social Security taxes.
To calculate Linda's contribution to social security in 2003, we will use the given social security tax rate of 6.2% and her income of $54,122.
Convert the tax rate percentage to a decimal by dividing by 100.
6.2% / 100 = 0.062
Multiply Linda's income by the decimal tax rate.
$54,122 * 0.062 = $3,355.56
Linda contributed $3,355.56 to social security in 2003.
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Build a power series, write the summation notation for the series, find the interval of convergence for,
f(x) = (x^4)/ (1-3x)
This limit exists and is less than 1 when |x| < 1/3. Therefore, the interval of convergence for the power series is (-1/3, 1/3).
To build a power series for f(x), we can use the geometric series formula:
1 / (1 - r) = ∑(n=0 to infinity) r^n
where r is a constant with |r| < 1. In this case, we have:
f(x) = x^4 / (1 - 3x) = x^4 * 1 / (1 - 3x)
So, we can let r = 3x and use the formula:
1 / (1 - 3x) = ∑(n=0 to infinity) (3x)^n
Multiplying both sides by x^4, we get:
f(x) = x^4 * ∑(n=0 to infinity) (3x)^n
Now we can write the summation notation for the power series as:
f(x) = ∑(n=0 to infinity) (3^n * x^(n+4))
To find the interval of convergence, we can use the ratio test:
lim(n->∞) |(3^(n+1) * x^(n+5)) / (3^n * x^(n+4))| = lim(n->∞) |3x|
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The pie chart below shows the favorite hobbies of 120 children.
The number of children who prefer cycling is 12.
Three times as many prefer football than the number who prefer cycling.
How many children prefer swimming?
A. 42
B. 52
C. 58
D. 40
E. 62
Answer:
72 children prefer cycling
Step-by-step explanation:
Cycling = 12 children
Football = (12×3) = 36 children
120 - (12 + 36) = 72
A shipping company uses baggage tags with 3-letter city codes. The first and third letters of each code are always consonants and the middle letter is always a vowel (CVC). The English language uses 21 consonants and 5 vowels. How many different combinations of tag codes are possible? I will give brainliest to the best
(A) 105
(B)441
(C) 1,638
(D)2,205
The correct answer is (D) 2,205.
How to calculate the number of different combinations of baggage tag codes for a shipping company?To calculate the number of different combinations of tag codes, we need to consider the possible options for each position in the code.
For the first and third positions (consonants), we have 21 options for each position since there are 21 consonants in the English language.
For the middle position (vowel), we have 5 options since there are 5 vowels in the English language.
Therefore, the total number of different combinations is calculated by multiplying the number of options for each position:
21 (consonant options) * 5 (vowel options) * 21 (consonant options) = 2,205
Therefore, the correct answer is (D) 2,205.
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Morgan takes a train from London to Bewford and then another train to Agon.
The tree diagram shows the probabilities of Morgan's trains being late or not late.
to Bewford
to Agon
Late
0.24
Late
0.35
0.76
Not late
Late
0.24
0.65
Not late
0.76
Not
late
Morgan will not catch the train to Agon if the train to Bewford is late and the train to Agon is not late.
Work out the probability that Morgan will catch the train to Agon.
Give your answer as a decimal.
The probability that Morgan will catch the train to Agon is 0.578.
To catch the train to Agon, one of the following conditions must be met:
The train to Bewford is not late and the train to Agon is not late.
The train to Bewford is not late and the train to Agon is late.
The probability of the first condition is:
(0.76) x (0.65) = 0.494
The probability of the second condition is:
(0.24) x (0.35) = 0.084
Therefore, the probability that Morgan will catch the train to Agon is:
0.494 + 0.084 = 0.578 (to three decimal places)
So the probability that Morgan will catch the train to Agon is 0.578.
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40% of a smoothie from Blender Splendor is fruit juice. There are 20 ounces in a smoothie. How many ounces of fruit juice does a smoothie have?
A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.
To find out how many ounces of fruit juice are in a 20-ounce smoothie from Blender Splendor, given that 40% of the smoothie is fruit juice, follow these steps:
1. Convert the percentage to a decimal: 40% = 0.40
2. Multiply the total ounces of the smoothie by the decimal: 20 ounces * 0.40 = 8 ounces
Your answer: A 20-ounce smoothie from Blender Splendor contains 8 ounces of fruit juice.
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(5)/(6)a+4(1)/(4)a
pls help i need it to finish
The required answer to the algebraic fraction [ {(5)/(6)}a + 4 {(1)/(4)}a ] is [ {(11)/(6)}a ] .
We can simplify this algebraic fraction problem by simple rule of fraction addition and with application LCM rule as,
{(5)/(6)}a + 4 {(1)/(4)}a
= {(5)/(6)}a + (1)a
= [{ (5)+ (6) }/(6)]a
= {(11)/(6)}a
The LCM (or, Least Common Multiple) rule is used for the two algebraic fraction here as the value that is divisible by the two given numbers in the denominator of the algebraic fractions. Then by rule, the numerators are multiplied by the factor of LCM of the denominator and then the numerators are added.
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Nora signed up for a streaming music service that costs $5 per month. The service allows Nora to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0. 75 per song. How much total money would Nora have to pay in a month in which she downloaded 30 songs? How much would she have to pay if she downloaded ss songs?
cost of 30 songs:
cost of s songs:
Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.
The cost for downloading 30 songs would be:
$0.75 per song × 30 songs = $22.50
Therefore, Nora would have to pay a total of $5 + $22.50 = $27.50 in a month when she downloaded 30 songs.
If she downloaded "s" songs, the cost would be:
$0.75 per song × s songs = $0.75s
Therefore, Nora would have to pay a total of $5 + $0.75s in a month when she downloaded "s" songs.
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Kirk pays an annual premium of $1,075 for automobile insurance, including comprehensive coverage of up to $500,000. He pays this premium for 8 years without needing to file a single claim. Then he gets into an accident during bad weather, for which no one is at fault. Kirk is not injured, but his car valued at $22,500 is totaled. His insurance company pays the claim and Kirk replaces his car. If he did not have automobile insurance, how much more would have Kirk paid for damages than what he had invested in his insurance policy?
$8,600
$13,900
$21,425
$31,100
Kirk would have paid $13,900 more for damages than what he had invested in his insurance policy if he did not have automobile insurance.
The amount that Kirk would have paid for damages than what he had invested in his insurance policy if he did not have automobile insurance can be determine as follows. Hence,
1. Calculate the total amount Kirk paid in insurance premiums over 8 years:
$1,075 * 8 = $8,600
2. Determine the total value of the car that was totaled:
$22,500
3. Subtract the total amount Kirk paid in insurance premiums from the value of the totaled car:
$22,500 - $8,600 = $13,900
Kirk would have paid $13,900 more for damages.
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Help pls
I need help asap i put the picture below
Answer:
d
Step-by-step explanation:
so b = 4
and the slope is rise over run = 5/2
Answer:
D) [tex]y=\frac{5}{2}x+4[/tex]
Step-by-step explanation:
The line equation of a line is:
[tex]y=mx+b[/tex] with m being the slope and b being the y-intercept.
We can see from the graph that the y-intercept is 4, as that's where the line intercepts the y-axis, and when x=0.
To find the slope, we first need to pick 2 points: (0,4) and (2,9).
The formula for slope is:
[tex]\frac{rise}{run}[/tex]
The rise is how many units you go up/down from one point to another. The run is how many units you go left/right from one point to another.
We can see that we go up 5 units and we go right 2 units. This means our slope is 5/2.
The completed line equation is:
[tex]y=\frac{5}{2}x+4[/tex], which means D is the correct option.
Hope this helps! :)
Which of the following statements is correct about the value of: 13 + √50
A. 13 + √50 is an irrational number
B. 13 + √50 is an integer
C. 13 + √50 is a rational number
D. 13 + √50 is neither a rational or irrational number
The statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number
The statement that is correct about the value of: 13 + √50From the question, we have the following parameters that can be used in our computation:
13 + √50
When the above expression is evaluated we have
13 + √50 = 20.0710678119
The above result (20.0710678119) is an irrational number
This is because the number 20.0710678119 cannot be expressed as a ratio of two integers
Hence, the statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number
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In circle m, secants pamd and pbc are drawn from point p such that mbc = 100 and mcd = 62°. which
of the following is the measure of p?
(1) 19
(2) 22
(3) 34
(4) 40
In the circle, the measure of p is 34 (option 3).
First, we know that angle MBC is an exterior angle to triangle PBC. Therefore, the measure of angle PBC is equal to the sum of angles MBC and MCB, which is 100 + (1/2)(angle MCP) = 100 + (1/2)(angle MQP).
Similarly, angle MCD is an exterior angle to triangle PCD. Therefore, the measure of angle PDC is equal to the sum of angles MCD and MDC, which is 62 + (1/2)(angle MPQ) = 62 + (1/2)(angle MQP).
Since angle PBC and angle PDC are both subtended by the same arc BC, they are equal. Therefore, we can set the expressions for these angles equal to each other and solve for angle MQP:
100 + (1/2)(angle MQP) = 62 + (1/2)(angle MQP)
38 = (1/2)(angle MQP)
angle MQP = 76 degrees
Finally, we can use the fact that angles MPQ and MQP form a linear pair, so they add up to 180 degrees. Therefore, angle MPQ is 180 - 76 = 104 degrees.
Since angle MPQ is an exterior angle to triangle PAB, we can use the exterior angle theorem to find the measure of angle P, as follows:
angle P = angle MPQ + angle PAB = 104 + 100 = 204 degrees
However, angles in a circle cannot be greater than 180 degrees, so we need to subtract 180 from angle P to get the actual measure of angle P:
angle P = 214 - 180 = 34 degrees
Therefore, the answer is option (3).
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Pablo mixed
2
1
2
quarts of fruit juice with
1
gallon of seltzer. If each serving is
8
fluid ounces, how many servings did Pablo make?
A. 20
B. 26
C. 32
D. 36
The number of servings did Pablo make is (B) 26.
What is Unit conversion:Unit conversion is the process of converting a value expressed in one unit of measurement to another unit of measurement that represents the same quantity but is expressed in a different unit.
The given quantities are in different units, so we need to convert them to a common unit to determine the number of servings. For this, we need to convert quarts and gallons to fluid ounces.
Here we have
Pablo mixed 2 1/2 quarts of fruit juice with 1 gallon of seltzer.
Each serving is 8 fluid ounces
Let's first convert the quantities to the same units.
=> 1 gallon = 4 quarts
Total amount of liquid = 2 1/2 + 4 = 6 1/2 quarts
Now, let's find how many 8-ounce servings are in 6 1/2 quarts:
=> 1 quart = 32 fluid ounces
=> 6 1/2 quarts = 6.5 x 32 = 208 fluid ounces
Given that, 1 serving = 8 fluid ounces
Number of servings = 208/8 = 26
Therefore,
The number of servings did Pablo make is (B) 26.
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Complete Question:
Pablo mixed 2 1 /2 quarts of fruit juice with 1 gallon of seltzer. If each serving is 8 fluid ounces, how many servings did Pablo make?
A: 20 B: 26 C: 32 D: 36
The S&P stock Index fell by an average of 8% each day. Write an equation or function that models the data
If the S&P stock index fell by an average of 8% each day, we can model the
data using exponential decay. Let P represent the initial value of the S&P
stock index and t represent the number of days. Then, the equation for the
S&P stock index after t days is:
[tex]P(t) = P * (0.92)^t[/tex]
Here, 0.92 represents the daily decay factor, which is derived from
subtracting 8% from 100% (100% - 8% = 92%). As each day passes, the
value of P(t) decreases exponentially by a factor of 0.92.
It's important to note that this equation assumes that the S&P stock index
falls by exactly 8% each day, which may not be a realistic scenario in real
life. Additionally, this equation only models the decay of the S&P stock
index value and does not take into account any external factors that may
affect its value.
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trains arrive at a specified stop at 15-minute intervals starting at 7am. if a passenger arrives at the stop at a time that is uniformly distributed between 7am and 7:30am, find the probability that she waits a) less than 5 minutes for the train b) more than 10 minutes for the train
The probability of a passengers waiting at the stop less than 5 minutes and more than 10 minutes is equal to 1/6 and 2/3 respectively.
Probability that the passenger waits less than 5 minutes for the train,
Area under the probability density function (PDF) of the arrival time distribution from 7:00am to 7:05am.
Distribution is uniform,
PDF is a constant function over the interval [7:00am, 7:30am] .
With height 1 / (30 minutes - 0 minutes) = 1/30.
Area under the PDF from 7:00am to 7:05am is,
Probability of waiting less than 5 minutes
= area under PDF from 7:00am to 7:05am
= (1/30) ×(5 - 0) minutes
= 1/6
Probability that the passenger waits less than 5 minutes for the train is 1/6.
Probability that the passenger waits more than 10 minutes for the train is
= Area under the PDF from 7:00am to 7:30am - area under the PDF from 7:00am to 7:10am.
Area under PDF from 7:00am to 7:30am
= (1/30) × (30 - 0) minutes
= 1
Area under PDF from 7:00am to 7:10am
= (1/30) × (10 - 0) minutes
= 1/3
Area under PDF from 7:10am to 7:30am
= 1 - 1/3
= 2/3
Probability of waiting more than 10 minutes
= area under PDF from 7:10am to 7:30am
= (1/30) × (30 - 10) minutes
= 2/3
Probability that the passenger waits more than 10 minutes for the train is 2/3.
Therefore, the probability of waiting less than 5 minutes and waiting more than 10 minutes is equal to 1/6 and 2/3 respectively.
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Evaluate ∫∫∫ex dV where E is enclosed by the planes z = 0
and z = x + y + 5 and by the cylinders x^2 + y^2 = 4 and
x^2 + y^2 =9.
The E is enclosed by the planes z = 0 and z = x + y + 5
Why will E is enclosed by the planes z = 0?
The evaluate the triple integral ∫∫∫_E eˣ dV, where E is enclosed by the planes z = 0 and z = x + y + 5, and by the cylinders x² + y² = 4 and x² + y² = 9,
Follow these steps:
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In circle P, if mQR = 80 , and m QRT = 39 , find each measure
In circle P, if m(QR) = 80 , and m(QRT) = 39 , m(QPR) = 39 and m(PT) = 78
Based on the information given, we know that:
- m(QR) = 80 (this is the measure of arc QR)
- m(QRT) = 39 (this is the measure of angle QRT)
To find the other measures, we can use the following formulas:
- The measure of a central angle is equal to the measure of its intercepted arc
- The measure of an inscribed angle is half the measure of its intercepted arc
Using these formulas, we can find the measure of angle QPR and the measure of arc PT as follows:
- m(QPR) = m(QRT) = 39 (since angle QRT and angle QPR intercept the same arc QR)
- m(PT) = 2 * m(QRT) = 78 (since angle QRT and angle PQT intercept the same arc PT, and the measure of an inscribed angle is half the measure of its intercepted arc)
So the final answers are:
- m(QR) = 80
- m(QRT) = 39
- m(QPR) = 39
- m(PT) = 78
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The coach of the soccer team is asked to select 5 students to represent the team in the Homecoming Parade. The coach decides to randomly select 5 students out of the 38 members of the team.
a. What is the population for this problem?
b. What is the sample for this problem?
c. Suggest a method for selecting the random sample of 5 students
The population is 38, and the sample is 5 students.
find out the population, sample, and method for selection?. The population for this problem is the entire soccer team, which consists of 38 members.
b. The sample for this problem is the group of 5 students who are selected by the coach to represent the team in the Homecoming Parade.
c. One method for selecting a random sample of 5 students from the team is to use a random number generator to choose 5 numbers between 1 and 38, representing the 38 team members. The coach can then select the students who correspond to the chosen numbers. Another method is to write the names of all 38 team members on identical slips of paper, place the slips in a container, mix them up, and then randomly select 5 slips to determine the students who will participate in the parade. It is important to ensure that the selection method is truly random to avoid any bias or non-representativeness in the sample.
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Mr. Smiths algebra class is inquiring about slopes of lines. The class was asked to graph the total cost, c, of buying h hotdog that cost 75 cent each. The class was asked to describe the slope between any two points on the graph. Which statement below is always a correct answer about the slope between any two points on this graph?
1)the same positive value
2)the same negative value
3) zero
4) a positive value, but the values vary
The slope of the graph is the same positive value that is 0.75.
Hence the correct option is (1).
We know that the equation of a straight line with slope 'm' and y intercept 'c' is given by,
y = mx + c
Here the model equation
c = 0.75h, where c is the total cost to buy hotdogs
h is the number of hotdogs bought
And 0.75 is the price of one hotdog
Now we can clearly say that c = 0.75h will make a straight line coordinate plane.
Now comparing the equation with slope intercept equation of straight line we get,
m = 0.75 and c = 0
So the slope of the line represented by model equation = 0.75 which is a positive number.
y intercept = 0.
We know that the slope of one particular straight line on cartesian plane is unique.
So, the slope of the graph is the same positive value.
Hence the correct option is (1).
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If the price of a car is $5,900 and has a down payment of 15%, with a tax rate of 8.5%, how much will the amount of the loan need to be for?
Tyler rides his bike from his house to his cousin's house. He bikes a total of 1.8 kilometers to get there and back. What is the distance, in meters, between Tyler's house and his cousin's house?
Answer:
Step-by-step explanation:
Total of rides from Tyler's house to Cousin's house and Cousin's house to Tyler's house = 1.8km = 1800m
So, the distance from Tyler's house to his cousin's house is
= 1800m ÷ 2 = 900m
1 ) If the supplement of an angle is 30 degrees more than the measure of the angle, what is the measure of the angle?
2) If the supplement of an angle is 12 degrees less than twice the measure of the angle, what is the measure of the angle?
a) If the supplement of an angle is 30 degrees more than the measure of the angle, the measure of the angle is 75 degrees.
b) If the supplement of an angle is 12 degrees less than twice the measure of the angle, the measure of the angle is 64 degrees.
a) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 30 degrees more than the measure of the angle. This can be written as:
180 - x = x + 30
Solving for x, we get:
2x = 150
x = 75
b) Let x be the measure of the angle. The supplement of the angle is 180-x. According to the problem, the supplement of the angle is 12 degrees less than twice the measure of the angle. This can be written as:
180 - x = 2x - 12
Solving for x, we get:
3x = 192
x = 64
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Marshall and oliver went to an arcade where the machines took tokens. marshall played 10 games of skee ball and 8 games of pinball, using a total of 44 tokens. at the same time, oliver played 3 games of skee ball and 8 games of pinball, using up 30 tokens. how many tokens does each game require?
Each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.
Let the number of tokens required for each game of skee ball be x and for each game of pinball be y.
From the given information, we can form two equations:
10x + 8y = 44 ... (1)
3x + 8y = 30 ... (2)
Multiplying equation (2) by 3, we get:
9x + 24y = 90 ... (3)
Subtracting equation (1) from equation (3), we get:
- x + 16y = 46
Solving for x, we get:
x = 16y - 46
Substituting this value of x in equation (2), we get:
3(16y - 46) + 8y = 30
Simplifying and solving for y, we get:
y = 2
Substituting this value of y in equation (1), we get:
10x + 8(2) = 44
Solving for x, we get:
x = 2
Therefore, each game of skee ball requires 2 tokens and each game of pinball requires 2 tokens.
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Think about your daily experience how is probability utilized in news papers, television, shows, and radio programs that interest you? What are your general impression of the ways in which probability is used in the print media and entertainment industry
Probability is frequently used in news reports to convey the possibility of an event occurring.
Generally, in my opinion, probability is used well in the media space.
How Probability is Utilized?Probability is frequently used in news reporting to demonstrate the likelihood of an event occurring. A news story, for example, might mention that there is a 50% chance of rain tomorrow. Similarly, sports writers may use probability to forecast the outcome of games and goals to be scored.
Overall, I feel probability is utilized fairly responsibly in the media and entertainment industries, with a focus on informing or entertaining audiences rather than misleading them. However, in some cases, such as political polling or advertising, the use of probability may be incorrect or exploited to influence audiences.
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