The values of a and b in the sequence are 18 and 10, respectively.
To find the values of a and b in the sequence given, we can use the fact that the median is 18 and the mean is 17.
Since the median is 18, we know that a and b must be two numbers that are greater than or equal to 18. Since the sequence is numerically ordered, we can see that a must be 18 or greater.
We can also use the fact that the mean is 17 to find the sum of all the numbers in the sequence. We know that the sum of all the numbers in the sequence divided by the number of terms in the sequence must be equal to the mean. Since there are 10 terms in the sequence, we can write:
(7 + a + 12 + 15 + 17 + b + 20 + 22 + 24 + 25) / 10 = 17
Simplifying this expression, we get:
(142 + a + b) / 10 = 17
Multiplying both sides by 10, we get:
142 + a + b = 170
Subtracting 142 from both sides, we get:
a + b = 28
Now we know that a and b are two numbers greater than or equal to 18 that add up to 28. The only two numbers that satisfy this condition are 18 and 10.
Since the sequence is numerically ordered, we know that a must be greater than or equal to 18. Therefore, a = 18 and b = 10.
So, the values of a and b in the sequence are 18 and 10, respectively.
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An elephant control a constant speed of 25 mph while I drive can travel a constant speed at 60 miles in 1/2 hour
The elephant can travel at a constant speed of 25 mph, while I can travel at a constant speed of 60 miles in 1/2 hour.
It's important to note that miles per hour (mph) is a unit of speed that measures how many miles an object can travel in one hour. In this scenario, the elephant can travel at a constant speed of 25 mph, meaning it can travel 25 miles in one hour. On the other hand, I can travel at a constant speed of 60 miles in 1/2 hour, which means I can travel 120 miles in one hour (since 1/2 hour is equal to 0.5 hours). Therefore, in terms of speed, I am faster than the elephant. However, it's important to keep in mind that speed isn't always the most important factor when it comes to transportation, as other variables such as distance, terrain, and mode of transportation can also play a role.
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A Farmer has 2400 feet of fencing and wants to fence off a rectangular field that boarders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area
The dimensions of the rectangular field with the largest area are w = 600 feet and L = 1200 feet.
Let's denote the width of the rectangular field by w and its length by L.
Since the field borders a straight river, we only need to fence three sides of the rectangle, which gives us:
2w + L = 2400
Solving this equation for L, we get:
L = 2400 - 2w
Now, we want to find the dimensions of the field that will give us the largest possible area.
The area of a rectangle is given by A = wL. Substituting the expression for L from above, we get:
A = w(2400 - 2w)
= 2400w - 2[tex]w^2[/tex]
To find the maximum value of this function, we can take its derivative with respect to w and set it equal to zero:
dA/dw = 2400 - 4w = 0
Solving for w, we get w = 600.
Substituting this value back into the equation for L, we get:
L = 2400 - 2w = 1200
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can someone pretty pleaseee find the volume?
Answer: Your answer is 64 m³
Hope it helped :D
what is the circumfrence of a circle with a diameter of 36 inches in terms of pie
If Ella rolls a standard six-sided die until she rolls the same number on consecutive rolls, what is the probability that her 10th roll is her last roll
The probability that Ella's 10th roll is her last roll is 31/108, or approximately 0.2870.
To find the probability that Ella's 10th roll is her last roll, we need to consider the following:
The last roll must be a repeat of the previous roll, so the previous roll cannot be the first roll or the 6th roll, because there is no previous roll in those cases.
Ella must not have rolled the same number on consecutive rolls before her 10th roll.
The probability of rolling the same number on consecutive rolls is 1/6, so the probability of not rolling the same number on consecutive rolls is 5/6.
Let's break down the probability of Ella's 10th roll being her last roll by considering the different cases:
Case 1: Ella's 8th roll is the first roll of a pair, and her 9th roll is the second roll of that pair.
In this case, Ella cannot roll the same number on consecutive rolls, so the probability of her 10th roll being her last roll is simply 1/6.
Case 2: Ella's 8th roll is the first roll of a pair, but her 9th roll is not the second roll of that pair.
In this case, Ella must roll a number different from her 9th roll, and then roll the same number as her 9th roll on her 10th roll.
The probability of rolling a different number on her 9th roll is 5/6, and the probability of rolling the same number on her 10th roll is 1/6.
Therefore, the probability of her 10th roll being her last roll in this case is (5/6)*(1/6) = 5/36.
Case 3: Ella's 8th roll is not the first roll of a pair, but her 9th roll is the second roll of a pair.
In this case, Ella must roll a number different from her 8th roll, and then roll the same number as her 8th roll on her 9th roll.
The probability of rolling a different number on her 8th roll is 5/6, and the probability of rolling the same number on her 9th roll is 1/6.
Therefore, the probability of her 10th roll being her last roll in this case is (5/6)*(1/6) = 5/36.
Case 4: Ella's 8th roll is not the first roll of a pair, and her 9th roll is not the second roll of a pair.
In this case, Ella must roll a number different from both her 8th and 9th rolls, and then roll the same number as her 9th roll on her 10th roll.
The probability of rolling a different number on her 8th roll is 5/6, the probability of rolling a different number on her 9th roll, given her 8th roll, is 4/6, and the probability of rolling the same number as her 9th roll on her 10th roll is 1/6.
Therefore, the probability of her 10th roll being her last roll in this case is (5/6)(4/6)(1/6) = 5/54.
To find the total probability, we need to sum the probabilities from each case:
1/6 + 5/36 + 5/36 + 5/54 = 31/108.
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5/2g +5 (-5g + 3/2)
Answer asap
Please help hurry I’ll mark brainly
a) The person that starts out with more money is: Julie.
b) Both people are depositing the same amount each month.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.George's amount starts out at $125, and increases by $50 each month, hence the function is:
G(x) = 125 + 50x.
Julie's amount starts out at $175, and increases by $50 each month, hence the function is:
G(x) = 175 + 50x.
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When it opened for the day, a cafe had seven gallons of lemonade how many quarts of lemonade did the cafe have?
Answer:
The cafe had 28 quarts of lemonade
4 quarts make 1 gallon so multiply number of quarts by number of gallons
Suppose the competing hypotheses for a test are H0: μ ≤ 10 versus Ha: μ >10. If the p-value is 0.0139 and the level of significance is 5%, what is the correct conclusion?
The correct conclusion is to reject the null hypothesis (H0) and accept the alternative hypothesis (Ha) since the p-value (0.0139) is less than the level of significance (5%).
What is the conclusion for a hypothesis test with H0: μ ≤ 10 and Ha?In hypothesis testing, the p-value is a measure of the strength of evidence against the null hypothesis.
In this case, the p-value is 0.0139, which means that the probability of observing a test statistic as extreme as the one obtained or more extreme, assuming the null hypothesis is true, is only 0.0139.
Since this value is less than the significance level of 5%, we reject the null hypothesis and accept the alternative hypothesis.
Therefore, we conclude that there is enough evidence to suggest that the true mean is greater than 10.
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Your purchase cost, $5,200, including tax. You sign an installment loan for $2,200 after the down payment. The remainder including the finance charge will be paid in 22 equal monthly installments of $114.66 at 16% interest. What is the amount of principal?
Answer:
The finance charge can be calculated by adding up all the monthly payments and subtracting the original loan amount (in this case, $2,200):
Finance charge = 22 x $114.66 - $2,200
Finance charge = $2,524.52 - $2,200
Finance charge = $324.52
To calculate the amount of principal, we need to subtract the finance charge from the total amount borrowed:
Total amount borrowed = $2,200 + finance charge
Total amount borrowed = $2,200 + $324.52
Total amount borrowed = $2,524.52
Amount of principal = Total amount borrowed - Finance charge
Amount of principal = $2,524.52 - $324.52
Amount of principal = $2,200
Therefore, the amount of principal in this loan is $2,200.
Answer: Therefore, the amount of principal is $1,070.80.
Step-by-step explanation:
To find the amount of principal, we need to first determine the total amount being financed, which is the difference between the purchase cost and the down payment:
Total amount financed = Purchase cost - Down payment
Total amount financed = $5,200 - $2,200
Total amount financed = $3,000
Next, we can use the formula for the present value of an annuity to calculate the amount of principal:
Present value of an annuity = Payment amount x (1 - (1 + interest rate)^(-number of payments))) / interest rate
Plugging in the given values, we get:
$114.66 = Payment amount
16% / 12 = 0.013333... = Interest rate per month
22 = Number of payments
Present value of an annuity = $114.66 x (1 - (1 + 0.013333...)^(-22)) / 0.013333...
Present value of an annuity = $2,004.20
Finally, we can subtract the finance charge from the present value of the annuity to get the amount of principal:
Amount of principal = Present value of annuity - Finance charge
Amount of principal = $2,004.20 - ($114.66 x 22)
Amount of principal = $2,004.20 - $2,522.52
Amount of principal = -$518.32
We get a negative value because the finance charge is greater than the present value of the annuity. Therefore, we need to adjust our calculation of the present value of the annuity.
If we assume that the finance charge is included in the total amount being financed, we can recalculate the present value of the annuity using a total amount financed of $3,518.32:
Present value of an annuity = $114.66 x (1 - (1 + 0.013333...)^(-22)) / 0.013333...
Present value of an annuity = $2,447.52
Then, we can subtract the finance charge from the total amount being financed to get the amount of principal:
Amount of principal = Total amount financed - Finance charge
Amount of principal = $3,518.32 - $2,447.52
Amount of principal = $1,070.80
Angie has $1062 in her savings account. If the bank pays 4% simple interest on savings, how much interest does she earn in 3 years
Angie earns $127.44 in interest over the 3-year period.
Angie has $1,062 in her savings account, and the bank pays 4% simple interest on savings. To calculate the interest she earns in 3 years, we need to use the simple interest formula, which is:
Simple Interest = Principal × Rate × Time
In this case, the principal (initial amount) is $1,062, the rate is 4% (or 0.04 as a decimal), and the time is 3 years. Plugging these values into the formula, we get:
Simple Interest = $1,062 × 0.04 × 3
Next, we can calculate the interest:
Simple Interest = $1,062 × 0.04 × 3 = $127.44
So, Angie earns $127.44 in interest over the 3-year period.
In summary, when calculating simple interest, you multiply the principal (initial amount) by the interest rate and the length of time (in years) the money is in the account. In Angie's case, with $1,062 in her account and a 4% interest rate, she earns $127.44 in interest over 3 years.
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Can someone please help me ASAP? It’s due today!! I will give brainliest if it’s all correct
Please do part a, b, and c
Part A: Zachary Used Systematic Sampling
Part B: the percentage of the red car from each sample are:
Sample 1 - Red - 15% Black - 30%
Sample 2- Red - 20% Black - 20%
Sample 3 - Red - 10% Black - 20%
Sample 4 - Red - 15% Black - 25%
Sample 5 Red - 10% Black - 25
In general, sampling allows researchers to collect enough data to address the study question(s) without having to poll the whole population, which saves time and money.
Part A: Based on the image, Zachary used systematic sampling method, and he must have recorded the color of every fifth car that was known to traveled north.
Part B: To know the percentage of red cars and black cars from all of sample, we have to calculate the total number of cars in all sample first and it is done below:
Sample 1:
Total cars = 3 + 5 + 3 + 6 + 3 = 20
The Percentage of red cars = (3/20) x 100%
= 15%
The Percentage of black cars = (6/20) x 100%
= 30%
Sample 2:
Total cars = 4 + 7 + 3 + 4 + 2 = 20
The percentage of red cars = (4/20) x 100%
= 20%
The percentage of black cars = (4/20) x 100%
= 20%
Sample 3:
Total cars = 2 + 6 + 3 + 4 + 5
= 20
The percentage of red cars = (2/20) x 100%
= 10%
The percentage of black cars = (4/20) x 100%
= 20%
Sample 4:
Total cars = 3 + 4 + 4 + 5 + 4 = 20
The percentage of red cars = (3/20) x 100%
= 15%
The percentage of black cars = (5/20) x 100%
= 25%
Sample 5:
Total cars = 2 + 4 + 3 + 5 + 6
= 20
The percentage of red cars = (2/20) x 100%
= 10%
The percentage of black cars = (5/20) x 100%
= 25%
Part C:
From the finding in B above, we can easily conclude that the number of black cars observed were more than those of the red.
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Full Question
All changes saved Zachary took five random samples of cars that passed through the intersection near his school. He recorded the color of every fifth car that traveled north, and the results of his samples are organized in the table below.
Sample 1 Sample 2 Sample 3 Sample 4 Sample5
red 3 4 2 3 2
white 5 7 6 4 4
blue 3 3 3 4 3
black 6 4 4 5 5
gray 3 2 5 4 6
Part A: What sampling method did Zachary use to gather his data?
Part B: Determine the percentage of red cars from each sample and the percentage of black cars from each sample.
Part C: Draw two conclusions about your findings from Part B.
How many five-digit natural numbers are there such that the leftmost digit is odd, the second digit is even, and all five digits are different
There are 6,720 five-digit natural numbers that satisfy the given conditions.
First, we need to choose the leftmost digit which can be any odd digit from 1,3,5,7,9. This can be done in 5 ways.
Then we need to choose the second digit, which can be any even digit from 0,2,4,6,8, except the digit we already chose for the first place. This can be done in 4 ways.
For the third digit, we have 8 remaining digits (since we have used 2 digits already), out of which we can choose any one, giving us 8 choices.
Similarly, for the fourth digit, we have 7 remaining digits to choose from, and for the last digit, we have 6 remaining digits.
Therefore, the total number of such five-digit numbers is given by:
5 × 4 × 8 × 7 × 6 = 6,720
So there are 6,720 five-digit natural numbers that satisfy the given conditions.
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Solve the system of equations -7x+7y=8 -14x+14y=14
For the given system of equations there is no solution.
The given system of equations are -7x+7y=8 -----(i) and -14x+14y=14 -----(ii).
Multiply equation (i) by 2, we get
-14x+14y=16 -----(iii)
Subtract equation (ii) from equation (ii), we get
-14x+14y-(-14x+14y)=16-14
-14x+14y+14x-14y=2
0≠2
So, the is no solution
Therefore, for the given system of equations there is no solution.
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you work at dave's donut shop. dave has asked you to determine how much each box of a dozen donuts should cost. there are 12 donuts in one dozen. you determine that it costs $0.32 to make each donut. each dozen is sold in the box shown. each box costs $0.18 per square foot of cardboard. there are 144 square inches in 1 square foot. in this task, you will answer some questions to help you determine the price to charge for each dozen donuts. Each box contains one dozen donuts. The total cost for one dozen donuts includes the cost to make the donuts and the cost of the box. create an expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet.
The expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet, is $3.84 + $0.18t
The cost to make one donut is $0.32.
Therefore, the cost to make one dozen donuts (12 donuts) is:
12 x $0.32 = $3.84
The cost of the cardboard for one box is $0.18 per square foot. Therefore, the cost of the cardboard for a box with surface area t (in square feet) is:
$0.18t
The total cost for one dozen donuts includes the cost to make the donuts and the cost of the box.
So, the expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet, is $3.84 + $0.18t
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------------------------------------------
Show that the numbers are all rational by writing each number as a ratio of integers.
3/5 + 2/3
We have expressed 3/5 + 2/3 as the ratio of two integers, 19 and 15. Since it can be expressed as a ratio of integers, we can conclude that it is rational.
To show that 3/5 + 2/3 is rational, we need to find a way to write it as a ratio of integers. To do this, we first need to find a common denominator for the two fractions. The least common multiple of 5 and 3 is 15, so we can rewrite the fractions as follows:
3/5 = 9/15
2/3 = 10/15
Now we can add the two fractions:
3/5 + 2/3 = 9/15 + 10/15
Combining the numerators, we get:
3/5 + 2/3 = 19/15
Therefore, we have expressed 3/5 + 2/3 as the ratio of two integers, 19 and 15.
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how do you factor completely:
4x^2 + 20x + 200 = 0
it’s a quadratic equation..
the 4x is squared
The quadratic expression 4x^2 + 20x + 200 = 0 cannot be factored completely
How to factor the expression completelyFrom the question, we have the following parameters that can be used in our computation:
4x^2 + 20x + 200 = 0
Divide through the terms by 5
So, we have
x^2 + 5x + 50 = 0
Next, we check if the above expression has real roots using
D = b^2 - 4ac
So, we have
D = 5^2 - 4 * 1 * 50
Evaluate
D = -175
The above disciminant value is less than 0
This means that the equation has no real root and as such the equation cannot be factored
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Suppose A and B are sets. Describe the conditions under which the following statement would be true. A= A-B A B⊂A 0 B A⊂B 0 ⊂ This statement is true for any sets A and B.
The statement is true for any sets A and B.
What are the conditions for the statement "A = A - B" to be true for sets A and B?
The statement "A = A - B" is true if and only if every element of A is not an element of B.
The set A - B represents the elements that are in A but not in B. Therefore, A = A - B means that A contains no elements that are in B. In other words, A and B have no elements in common. This is equivalent to saying that every element of A is not an element of B.
Now, since A and B have no elements in common, it follows that B is a subset of A (i.e., B ⊂ A). This is because if an element is in B, it cannot be in A (as A contains no elements of B), and if an element is not in B, it must be in A. Similarly, since A contains no elements of B, it follows that 0 ≤ B ⊆ A. Moreover, since every element of A is not an element of B, it follows that 0 ≤ A ⊆ Bᶜ (the complement of B). Finally, since every set is a subset of itself, it follows that 0 ≤ ⊆ A.
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The rectangle and square both have the same perimeter.
The value of x is 4cm and the breadth of the rectangle is 11cm and the side of the square is 9cm.
Let's begin by using the formula for the perimeter of a rectangle:
Perimeter of a rectangle = 2 * (length + breadth)
For the rectangle given in the problem, the length is 7 cm and the breadth is x+7 cm. Therefore, the perimeter of the rectangle can be expressed as:
2 * (7 cm + (x+7) cm) = 2 * (x+14) cm = 2x + 28 cm
For the square, the side length is x+5 cm. Therefore, the perimeter of the square can be expressed as:
4 * (x+5) cm = 4x + 20 cm
We are given that the perimeter of both shapes is the same. Therefore:
2x + 28 cm = 4x + 20 cm
Simplifying the equation by subtracting 2x from both sides, we get:
28 cm = 2x + 20 cm
Subtracting 20 cm from both sides, we get:
8 cm = 2x
Dividing both sides by 2, we get:
x = 4 cm
Therefore, the value of x is 4 cm.
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can someone help thank very much.
Answer:
first one: 1300
Second one: 9.11
Third one : Sorry i dont have time rn to figure it out
Step-by-step explanation:
A counterexample for the expression sin(y)*tan(y)= cos(y) is 0 degrees
Actually, 0 degrees is not a counterexample for the expression sin(y)*tan(y) = cos(y).
To see why, let's substitute y = 0 degrees into the expression:
sin(y)*tan(y) = cos(y)
sin(0)*tan(0) = cos(0)
0*tan(0) = 1
0 = 1
As we can see, the equation does not hold for y = 0 degrees. However, this does not make 0 degrees a counterexample, because 0 degrees is not in the domain of the tangent function.
The tangent function is undefined at odd multiples of 90 degrees (e.g. 90, 270, etc.), because at those angles the denominator of the tangent function becomes zero. Therefore, we cannot substitute y = 0 degrees into the expression sin(y)*tan(y) = cos(y), because it would result in division by zero.
In summary, 0 degrees is not a counterexample for the expression sin(y)*tan(y) = cos(y), because it is not in the domain of the tangent function.
Jason has $4000 in the bank. If every three months he has to pay $300 for
rent on a storage locker, how much will he have spent on rent after
three years?
2. Jane is now four times as old as Rita.
In 6 years, Jane will be only twice as
old as Rita at that time. Find their
present ages.
Answer:
Rita's age = 3 years
Jane's age = 12 years
Step-by-step explanation:
Framing algebraic equations and solving:
Let the age of Rita = x years
Age of Jane = 4 times of Rita's age
= 4*x
= 4x
After 6 years,
Jane's age = 4x + 6
Rita's age = x + 6
Jane's age = twice of Rita's age
4x + 6 = 2* (x + 6)
4x + 6 = 2x + 12 {Distributive property}
Subtract 6 from both sides,
4x = 2x + 12 - 6
4x = 2x + 6
Subtract '2x' from both sides,
4x - 2x = 6
2x = 6
Divide both sides by 2,
x = 6 ÷ 2
x = 3
Rita's age = 3 years
Jane's age = 4 * 3
= 12 years
O is the center of the regular pentagon below. Find its perimeter. Round to the nearest tenth if necessary.
Answer:
P= 29.389 ~ 29.4
Step-by-step explanation:
P= ns = 2rn sin(180/n)...... formula to find perimeter
p= 2(5)(5)sin(36)
p= 2(5)(5)sin(36)P= 50 ×0.5877
p= 2(5)(5)sin(36)P= 50 ×0.5877 P= 29.389 approximate to 29.4
What is the length of side AC, to the nearest tenth of a unit?
- 13.5 units
- 6.6 units
- 16.7 units
- 30.8 units
Answer :
13.5 unitsStep-by-step explanation:
In the given figure,
AB (Hypotenuse) = 15 units AC (Perpendicular) = ?We know that,
[tex] : \implies \rm\dfrac{P}{H}= sin \theta \\ [/tex]
where,
P is perpendicular (AC)
H is Hypotenuse (AB)
[tex]\theta[/tex] is 64°
Substituting the values,
[tex] : \implies \sf \dfrac{AC}{15} = sin \: 65\degree[/tex]
sin 65 = 0.9063 (approximately)
[tex]:\implies \sf \dfrac{AC}{15} = 0.9063 \\ [/tex]
[tex]:\implies \sf AC = 0.9063 \times 15 \\ [/tex]
[tex]:\implies \sf AC \approx 13.59 \\ [/tex]
Therefore, the length of side AC is 13.5 units
Carly got a model train set for her birthday, and it came with 200 assorted pieces of train track. She randomly picks some pieces of track out of the box. So far, she has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks.
Based on the data, what is the probability that the next piece of track Carly picks will be straight?
Write your answer as a fraction or whole number.
The likelihood that the next piece of music Carly selects will be straight is one-third or 0.3333.
The probability of picking a straight piece of track can be found by dividing the number of straight pieces by the total number of pieces:
P(straight) = number of straight pieces / total number of pieces
The total number of pieces Carly has is the sum of the straight, curved, cross, and switch pieces:
total number of pieces = 8 + 7 + 4 + 5 = 24
Therefore, the probability that the next piece of track Carly picks will be straight is:
P(straight) = 8 / 24 = 1/3
So the probability of the next piece of track Carly picks being straight is 1/3 or 0.3333
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13. Triangles ABC and PQR are similar. Which proportion could be used
to find QR? Select all that apply. 8.GR.2.4
c
PQ
BC PQ
QR AC
=
BC
QR
3
=
10 QR
3
10
3= QR
10
=
5
QR
A
75 folvo Problems involving Similar Triangles
5 cm
C
B
3 cm
P
10 cm
R
The proportions that can be used to find QR in the similar triangles are:
AB/PQ = BC/QR
5/10 = 3/QR
How to Apply Proportion to Find the Sides of Similar Triangles?Sides of triangles that are similar usually have lengths that are proportional to each other.
Given that triangles ABC and PQR are similar to each other, their side lengths will be proportional, therefore:
AB/PQ = BC/QR = AC/PR.
Plugging in the given values from the image, we have:
5/10 = 3/QR
Therefore, the proportions we can use are:
AB/PQ = BC/QR
5/10 = 3/QR
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Pete is standing 5 feet away from a mirror on the ground. Pete is 4 feet tall and can just see the top of the tree in the mirror from where he is standing. The two triangles formed in the picture above are similar.
If the mirror is 25 feet away from the base of the tree, how tall is the tree?
Pete is standing 4 feet away from a mirror on the ground, if mirror is 20 feet away from the base of the tree the height of tree is 30 feet.
Here,
let,
Pete is standing 4 feet away from a mirror on the ground.
Pete is 6 feet tall and can just see the top of the tree in the mirror from where he is standing.
We can say two triangles are formed are similar,
So if the mirror is 20 feet away from the base of the tree
After talkig the similarity theorem we get,
So x = 6*5
x = 30 feet.
The height of the mirror is 30 feet.
Height is a measurement of vertical distance, or how high something or someone is (how tall they are) (how "high" a point is).
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complete question:
Pete is standing 4 feet away from a mirror on the ground. Pete is 6 feet tall and can just see the top of the tree in the mirror from where he is standing. The two triangles formed are similar.
If the mirror is 20 feet away from the base of the tree
A.
22 feet
B.
19 feet
C.
13 feet
D.
30 feet
for any given event, the sum of probability of that event and the probability of its _________ Must equal one
For any given event, the sum of probability of that event and the probability of its complement must equal one.
The complement of an event is the set of all outcomes in the sample space that are not in the event. The probability of the complement of an event is the probability that the event does not occur.
Therefore, if P(A) is the probability of an event A, then P(A') is the probability of the complement of A, and we have: P(A) + P(A') = 1
This is known as the complement rule of probability and is a fundamental principle in probability theory. It states that the sum of the probabilities of an event and its complement must equal one, which reflects the fact that either the event occurs or its complement occurs, but not both.
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why couldn't Pythagoras use the pythagorean theorem as we know it?
Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.
It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.
He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.
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