Based on the randomization distribution, a difference in means of -7, -4, and 6 are very unlikely to ever occur just by random chance. A difference in means of 1 and -0.5 are relatively unlikely to occur but might occur occasionally.
What is difference in means?The difference in means refers to the numerical difference between the average values of two groups or samples. It is a measure of the distance between the means of two datasets, and is often used to compare the central tendencies of the groups or samples.
To create a randomization distribution for the test for a difference in means using StatKey, we can follow these steps:
"Randomization Tests" from the list of options select.
Select "Test for a Difference in Means" from the list of randomization tests.
"Two Independent Groups"as we are comparing two groups is to be delected.
Click on the "Upload" button and select the "arrival_time.csv" file provided in the dataset.
choose"Test Hypothesis" button to run the test.
Under the "Randomization Distribution" section, select "Create a Randomization Distribution" and choose a large number of samples, such as 5,000.
Select the "Create Distribution" button to generate the randomization distribution.
To determine the likelihood of each possible difference in means occurring just by random chance, we can compare the observed difference in means with the randomization distribution.
The table below summarizes the results possible difference in means:
Difference in Means Likelihood
-7 Very unlikely to ever occur just by random
chance
1 Relatively unlikely to occur but might occur
occasionally
-4 Very unlikely to ever occur just by random chance
-0.5 Relatively unlikely to occur but might occur
occasionally
6 Very unlikely to ever occur just by random chance
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Select the correct answer.Adam constructed quadrilateral PQRS inscribed in circle O. How can he prove PQRS is a square?A.He needs to show only that the diagonals are perpendicular.B.He needs to show only that the diagonals are perpendicular and congruent.C.He needs to show only that the diagonals are perpendicular and bisect each other.D.He needs to show that the diagonals are perpendicular, congruent, and bisect each other.
Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.
To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.
One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.
If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.
If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.
If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.
Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.
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steve is taking a10 question multiple choice test where each question has 4 choices. what is the probability that guesing randomally at least 8 correct
The probability of guessing randomly at least 8 correct answers in a 10 question multiple choice test where each question has 4 choices is 0.0385 or approximately 3.85%.
To find the probability of guessing at least 8 correct answers, we need to use the binomial probability formula:
P(X ≥ k) = 1 - P(X < k)
where
P(X ≥ k) is the probability of getting k or more correct answers
P(X < k) is the probability of getting less than k correct answers
n is the total number of questions in the test = 10
p is the probability of guessing the correct answer = 1/4
q is the probability of guessing the incorrect answer = 3/4
Now, we need to find the probability of getting less than 8 correct answers:
P(X < 8) = Σ P(X = k) for k = 0 to 7
P(X = k) = nCk * p^k * q^(n-k)
where nCk is the binomial coefficient for choosing k items from a set of n items.
P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 7)
P(X = k) = nCk * p^k * q^(n-k)
P(X = 0) = 10C0 * (0.25)⁰ * (0.75)¹⁰ ≈ 0.0563
P(X = 1) = 10C1 * (0.25)¹ * (0.75)⁹ ≈ 0.1875
P(X = 2) = 10C2 * (0.25)² * (0.75)⁸ ≈ 0.2813
P(X = 3) = 10C3 * (0.25)³ * (0.75)⁷ ≈ 0.2503
P(X = 4) = 10C4 * (0.25)⁴ * (0.75)⁶ ≈ 0.1450
P(X = 5) = 10C5 * (0.25)⁵ * (0.75)⁵ ≈ 0.0586
P(X = 6) = 10C6 * (0.25)⁶ * (0.75)⁴ ≈ 0.0161
P(X = 7) = 10C7 * (0.25)⁷ * (0.75)³ ≈ 0.0028
Therefore, P(X < 8) = 0.0563 + 0.1875 + 0.2813 + 0.2503 + 0.1450 + 0.0586 + 0.0161 + 0.0028 ≈ 1.0 - 0.0385 = 0.9615 or approximately 96.15%
The probability of guessing at least 8 correct answers:
P(X ≥ 8) = 1 - P(X < 8) ≈ 1 - 0.9615 = 0.0385 or approximately 3.85%
The problem seems incomplete, it must have been...
"Steve is taking a 10-question multiple choice test where each question has 4 choices. What is the probability that guessing randomly will give him at least 8 correct answers?"
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The expression tan(0) cos(0) simplifies to sin(0) . Prove it
As the tangent of an angle is given by the division of the sine of the angle by the cosine of the angle, the expression is simplified to the sine of the angle.
How to obtain the tangent of an angle?To calculate the tangent of an angle, you need to divide the length of the side opposite to the angle by the length of the side adjacent to the angle. The side opposite is the side that is opposite to the angle, while the side adjacent is the side that is adjacent to the angle.
An equivalent way to describe the calculation of the tangent is that it is the division of the sine of the angle by the cosine of the angle.
Hence the expression in the context of this problem is simplified as follows:
tan(θ)cos(θ) = sin(θ)/cos(θ) x cos(θ) = sin(θ).
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For what values of a are the following expressions true(|=absolute value):
Pls help!!!
a. |a-5|=5-a
b.|a|=-a
Answer:
10 is the answer of q u estion
find the number of outcomes in the complement of the given event. out of 344 high school students in their senior year, 175 are left-handed.
There are 169 outcomes in the complement of the given event.
To find the number of outcomes in the complement of the given event, which is that out of 344 high school students in their senior year, 175 are left-handed, you need to follow a few steps. So, let's get started. To find the number of outcomes in the complement of the given event, you will first find the total number of students that are right-handed, which can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169Therefore, there are 169 right-handed students.
Next, to find the number of outcomes in the complement of the given event, you will need to subtract the number of outcomes in the given event from the total number of possible outcomes. Since the number of possible outcomes is equal to the total number of students, the number of outcomes in the complement of the given event can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169 Therefore, there are 169 outcomes in the complement of the given event.
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what is (2x+45)° x° = what?
Answer:
x = 45.
Step-by-step explanation:
Given a straight line with the equation.
First collect like terms:
2x + x = 180 - 45
Then calculate:
3x = 135
Finally after dividing both sides by 3:
x = 45
what is the specificity for the test based on these screening results (rounded to three decimal places)?
The specificity of the test based on the given screening results is 0.967 (rounded to three decimal places).
To calculate the specificity, divide the number of true negatives (TN) by the total number of negative results (TN+FP). In this case, that would be 687/(687+22), which is equal to 0.967 (rounded to three decimal places).
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you have spent $2,500 on liquor for your bar. your bar sales have been $12,890. what is your cost of sales for liquor, expressed as a percentage?
The cost of sales for liquor, expressed as a percentage is 19.39%.
What is the cost of sales for liquor in percentage?To compute for the cost of sales for liquor, expressed as a percentage given that you have spent $2,500 on liquor for your bar and your bar sales have been $12,890, you can use the formula:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
where, Cost of Goods Sold (COGS) = Beginning Inventory + Purchases - Ending Inventory (or the total cost of goods sold during the period)
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
Let's compute for the COGS first:
COGS = Beginning Inventory + Purchases - Ending Inventory
= $0 + $2,500 - $0
= $2,500
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
= $12,890 - $0 - $0
= $12,890
Cost of sales is obtained as follows:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
= ($2,500 / $12,890) × 100
= 19.39%.
Therefore, the cost of sales for liquor, expressed as a percentage is 19.39%.
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42 Développer chaque produit, puis réduire les expres-
sions obtenues.
A= 5x-3(x+12)
C = 2x² + x(4x - 5)
B=3x-6+7(2x+4)
D=4x²-x+x(5x-9)
Maggie crochets squares to make a blanket. She has 6 squares made. She then makes 6 squares each hour for 3 hours. Determine which of the following represent the linear relationship described.
The linear relationship of Maggie crocheting squares is y = 6 + 6x graph (b)
How to determine the linear relationshipLet x be the number of hours Maggie spends crocheting squares, and let y be the total number of squares she has made.
Initially, Maggie has 6 squares made,
so y = 6 when x = 0.
For each hour that she spends crocheting squares, Maggie makes 6 more squares.
Therefore, the relationship between x and y is:
y = 6 + 6x
This is a linear relationship with a slope of 6, which means that Maggie is crocheting squares at a rate of 6 squares per hour.
This is represented by graph (b)
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Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.
Now, let's create another linear function using points B and C:
slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1
y-intercept (b) = y - mx = 4 - 1 * 3 = 1
Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:
2 = 1 + 1
This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.
In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.
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Find the product of (7-8x)(3x^3-2x^2+x)
Answer:
Step-by-step explanation:
To find the product of (7-8x)(3x^3-2x^2+x), we need to use the distributive property of multiplication over addition/subtraction.
First, let's distribute the 7 across the second factor:
(7)(3x^3) - (7)(2x^2) + (7)(x)
This simplifies to:
21x^3 - 14x^2 + 7x
Next, we need to distribute the -8x across the second factor:
(-8x)(3x^3) + (-8x)(-2x^2) + (-8x)(x)
This simplifies to:
-24x^4 + 16x^3 - 8x^2
Now, we can combine the two simplifications:
(7-8x)(3x^3-2x^2+x) = 21x^3 - 14x^2 + 7x - 24x^4 + 16x^3 - 8x^2
Finally, we can combine like terms to simplify the expression:
-24x^4 + 37x^3 - 22x^2 + 7x
Therefore, the product of (7-8x)(3x^3-2x^2+x) is -24x^4 + 37x^3 - 22x^2 + 7x.
Suppose Alice uses the RSA methods as follows. She starts with a mes- sage consisting of several letters, and assigns a = 1,b=2, -2=26. She then encrypts each letters separately. For example, if her message is cat, she calculates 3 = mod n 19 = 2 mod n and 209 = mod n. Then she sends the encrypted message {G}=1,2,3 to Bob. Explain how Eva can find the message without factoring n. In particular, suppose n=8881 and e=13. Eva intercepts the message q=4461; = 794; e = 2015,C4 = 2015,3 = 3603 Find the message without factoring 8881.
The solution is {y} = (2311, 2557, 2015) and hence the original message is CAT.
Suppose Alice uses the RSA methods as follows. She starts with a message consisting of several letters, and assigns a = 1,b=2, -2=26. She then encrypts each letter separately. For example, if her message is cat, she calculates 3 = mod n 19 = 2 mod n and 209 = mod n. Then she sends the encrypted message {G}=1,2,3 to Bob.The solution to the given question is as follows:Eva knows that n = 8881 = 79 × 112, where p = 79 and q = 112 are primes.Using the extended Euclidean algorithm and the fact that 13*5081 = 1 (mod 8880), one can compute the inverse of e modulo 8880 as d ≡ 5081 ≡ -3805 (mod 8880).To compute the message, Alice encrypts each letter of the message separately using the encryption function y ≡ x13 (mod 8881).Eva receives {G}=1,2,3 from Alice, and hence she wants to decipher it by computing 13 ≡ y ≡ G13 (mod 8881), where y is the message.To compute y, we have 1^{13} ≡ 1 (mod 8881), 2^{13} ≡ 8192 ≡ - 6889 + 2 (mod 8881) since 8192 = 2 × 4096 and 4096 = 8881 - 4785, hence, 2^{13} ≡ - 4785 × 2 + 2 (mod 8881), i.e., 2^{13} ≡ 2311 (mod 8881), and 3^{13} ≡ 3 × 3^{12} ≡ 3 × (3^{4})^{3} ≡ 3 × 6561^{3} ≡ 3 × 4299 ≡ 12897 ≡ 2557 (mod 8881).Therefore, the decrypted message is {y} = (2311, 2557, 2015) and hence the original message is CAT.Hence, the solution is {y} = (2311, 2557, 2015) and hence the original message is CAT.
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A floor is shaped like a regular pentagon. Each side length is represented by (2×+ 4) inches and (4×-2) inches. Find the length of each side
The length of each side of the regular pentagon is 10 units
Let's use the fact that the floor is a regular pentagon to set up an equation involving the side lengths.
A regular pentagon has five sides of equal length, so we can set the two expressions for the side lengths equal to each other:
2× + 4 = 4 × - 2
Solving for x, we get:
2x = 6
x = 3
Now that we have the value of x, we can substitute it back into either expression for the side length to find the length of each side. Let's use the expression (2× + 4) inches:
2× + 4 = 2(3) + 4
= 6 + 4
= 10 units
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Rosa wants to Invest $1400 a savings account that pays 4.4% simple Interest. How long will take for this investment to double In value? Round your answer to the nearest tenth.
Answer: 31.8 years
Step-by-step explanation:
The formula to calculate the simple interest is:
I = Prt
where:
I = Interest
P = Principal amount
r = Rate of interest
t = Time (in years)
We want to know how long it will take for the investment to double in value. That means the interest earned should be equal to the principal amount. So, we can write:
2P = P + I
Simplifying:
P = I
Now, we can substitute the values given in the problem:
1400 = 14000.044t
Simplifying:
t = 1400/(1400*0.044) = 31.82 years
Therefore, it will take approximately 31.8 years for the investment to double in value.
Doug is selling his autographed baseball. He bought it for $26 and wants to mark it up 20%. What will the new price be?
Answer:
The answer is $31.20
Step-by-step explanation:
do 20% of 26 and add it to the $26
a researcher is interested in exploring the relationship between calcium intake and weight loss. two different groups, each with 26 dieters, are chosen for the study. group a is required to follow a specific diet and exercise regimen, and also take a 500-mg supplement of calcium each day. group b is required to follow the same diet and exercise regimen, but with no supplemental calcium. after six months on the program, the members of group a had lost a mean of 15.6 pounds with a standard deviation of 1.2 pounds. the members of group b had lost a mean of 10.3 pounds with a standard deviation of 1.9 pounds during the same time period. assume that the population variances are not the same. construct a 90% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not. let population 1 be the amount of weight lost by group a, who took a 500-mg supplement of calcium each day, and let population 2 be the amount of weight lost by group b, who did not take a calcium supplement. round the endpoints of the interval to one decimal place, if necessary.
The 90% confidence interval for the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is: resulting in a confidence interval of (4.337, 6.263) pounds.
To construct a 90% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not, we can use a two-sample t-test with unequal variances.
The null hypothesis is that the true difference between the mean amounts of weight lost by the two groups is zero, and the alternative hypothesis is that the true difference is not zero.
We can use the following formula to calculate the confidence interval:
CI = (x_1 - x_2) ± tα/2 * √((s_1)²/n_1 + (s_2)²/n_2)
where
x_1 = 15.6 (mean amount of weight lost by group a)
x_2 = 10.3 (mean amount of weight lost by group b)
s_1 = 1.2 (standard deviation of group a)
s_2 = 1.9 (standard deviation of group b)
n_1 = n_2 = 26 (sample size of both groups)
tα/2 = t0.05/2,24 = 1.711 (degrees of freedom = n_1 + n_2 - 2 = 50)
Plugging in the values, we get:
CI = (15.6 - 10.3) ± 1.711 * √(1.2²/26 + 1.9²/26)
CI = 5.3 ± 0.963
CI = (4.337, 6.263)
Therefore, with 90% confidence, we can estimate that the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is between 4.337 and 6.263 pounds.
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Which property is (n · p) · q = n · (p · q)
The associative characteristic of multiplication is what the equation (n · p) · q = n · (p · q) represents.
what is equation ?A mathematical assertion that establishes the equality of two expressions is known as an equation. It usually consists of two sides, divided by an equal sign (=), with one or more terms on each side, which could be variables, constants, or both. The objective of equation solving is to identify the value(s) of the variable(s) necessary to make the equation correct. There are many mathematical methods for solving equations, including factoring, simplification, substitution, and the quadratic formula.
given
The associative characteristic of multiplication is what the equation (n · p) · q = n · (p · q) represents.
According to this characteristic, a multiplication expression's outcome is unaffected by the way its factors are organized.
In other words, you can arrange the variables however you like and still arrive at the same conclusion.
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For what values of the variables must ABCD be a parallelogram?
The for the values of the variables x = 7 and y = 10, the given must be a parallelogram.
What is parallelogram?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base and height of the parallelogram determine its area.
For the given quadrilateral to be parallelogram the opposite sides need to be parallel and equal.
For the given quadrilateral we have:
2y - 16 = y - 6
2y - y = -6 + 16
y = 10
Also,
2x + 2 = y + 6
Substitute the value of y = 10:
2x + 2 = 10 + 6
2x = 16- 2
2x = 14
x = 7
Hence, the for the values of the variables x = 7 and y = 10, the given must be a parallelogram.
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a college student takes the same number of credits each semester. before beginning college, the student had some credits earned while in high school. after 2 semesters, the student had 45 credits, and after 5 semesters, the student had 90 credits. if c(t) is the number of credits after t semesters, write the equation that correctly represents this situation.
The equation that correctly represents this situation is c(t) = 45 + 45(t-2). This equation states that the total number of credits the student will have after t semesters is equal to 45 (the number of credits they had before beginning college) plus 45 times the number of semesters after two (t-2).
To explain this equation in more detail, we need to break it down. First, the student had some credits earned while in high school, so the equation starts off with c(t) = 45, which is the number of credits the student had before beginning college.
Next, 45(t-2) represents the number of credits earned in the additional semesters since college began. The t-2 part of the equation means that the total number of credits earned in the additional semesters starts at zero for t = 2. Then, for each additional semester, 45 credits are added. So, for example, when t = 5, 45 credits are added to the initial 45 credits the student had before beginning college, resulting in 90 credits.Therefore, the equation c(t) = 45 + 45(t-2) correctly represents this situation.
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60 mi / 1 hr = ? mi / 5 hr
Answer: 300 minuets
Step-by-step explanation:
Answer:
350
Step-by-step explanation:
60 miles is 1 hr. all it is, is a ratio. multiply 60 by 5 to get your answer; 350
Determine the number of 15 boxes in kilograms
Answer:
Step-by-step explanation:
150
What shape is this cross-section?
The crοss-sectiοn in the image shοwn appears tο be a trapezοid.
What is trapezοid?A quadrilateral with at least οne pair οf parallel sides. In this crοss-sectiοn, the tοp and bοttοm sides are parallel, while the οther twο sides are nοt parallel is trapezοid. There are times when people define trapezoids as having at least one pair of opposite sides that are similar, and other times they say there is just one pair.
The parallelogram satisfies the "at least one" interpretation of the definition because it has two pairs of opposite sides that are similar, which qualifies it as both a trapezoid and a parallelogram. The parallelism does not support the "one and only one" interpretation of the description. How students respond to this depends on how they describe themselves.
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Solve for C.
16
17
8
C = [?]°
Round your final answer
to the nearest tenth.
Law of Cosines: c² = a² + b² - 2ab-cosC
69.1° is the value of C by Law of Cosines .
What is the cosine law?
The formula for the Law of Cosines is c2=a2+b22ab cosC. With the exception of the third component, which equals 0 if C is a right angle because the cosine of 90° is 0 and we have the Pythagorean Theorem, this is similar to the Pythagorean Theorem.
The Law of Cosines is given as
c² = a² + b² - 2ab-cosC
substitute the values in a, b, c
Plugging in given values, we get
16² = 8² + 17² - 2 . 8 . 17 . cosC
256 = 64 + 289 - 272. CosC
256 = 353 - 272 . cosC
256 - 353 = 272 . CosC
-97 = 272 . CosC
cosC = -97/-272
C = across(97/272)
C = 69.1°
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Answer:
C= 83.04
Step-by-step explanation:
Can you help me with this question please.
Answer:
[tex]x = 4\sqrt{3}[/tex]
Step-by-step explanation:
The triangle is right-angled
In a right-angled triangle, the following equality holds
[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]
[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]
Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]
Find the probability of
drawing a spade, then
drawing a face card out of a
deck
The likelihood of pulling a spade followed by a face card from a deck is 3/52, or roughly 0.0588. (rounded to four decimal places).
What is the probability?The probability of drawing a spade from a deck of 52 cards is 13/52, or 1/4, since there are 13 spades in the deck.
Once a spade has been drawn and not returned to the deck, there are now 51 cards left in the deck, of which 12 are face cards (the Jack, Queen, and King of each suit). Therefore, the probability of drawing a face card given that a spade has already been drawn is 12/51.
To find the probability of both events happening together (drawing a spade and then a face card), we can multiply the probabilities of each event:
P(drawing a spade, then drawing a face card) = P(drawing a spade) x P(drawing a face card given that a spade has been drawn)
= (1/4) x (12/51)
= 3/52
Therefore, the probability of drawing a spade, then drawing a face card out of a deck is [tex]3/52[/tex] , or approximately [tex]0.0588[/tex] (rounded to four decimal places).
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Graph the line with slope 3 passing through the point (1,-5),
Can somebody help me
Answer:
Step-by-step explanation:
To graph the line with slope 3 passing through the point (1,-5), we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line.
Substituting the given values, we get:
y - (-5) = 3(x - 1)
Simplifying the equation, we get:
y + 5 = 3x - 3
Subtracting 5 from both sides, we get:
y = 3x - 8
Now we have the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Comparing this equation to the one we just found, we can see that the slope is 3 and the y-intercept is -8.
To graph the line, we can plot the y-intercept at (0,-8) and then use the slope to find other points on the line. Since the slope is 3, we can go up 3 units and to the right 1 unit to find another point on the line. We can repeat this process to find more points on the line, and then connect them to graph the line.
The ordering and transportation cost €C for components used in manufacturing process is approximated by the function below, where C is measured in thousands of dollars and is the order size in hundreds_ C(x) = s(x x+3 (a) Verify that C(3) C(6) _ c(3) (b) According to Rolle's Theorem, the rate of change of the cost must be for some order size in the interval (3 answer to the nearest whole number:) components Find that order size (Round vour Need Help? Ialkto Tutor
The value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
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Bernard's rectangular bedroom is 12 feet by 16 feet. What is the diagonal distance from one corner to the opposite corner?
Answer: 20 feet
Step-by-step explanation: To find the diagonal distance from one corner to the opposite corner of Bernard's rectangular bedroom, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two other sides are the length and the width of the room, so we have:
diagonal^2 = 12^2 + 16^2
diagonal^2 = 144 + 256
diagonal^2 = 400
Taking the square root of both sides, we get:
diagonal = √400
diagonal = 20 feet
Therefore, the diagonal distance from one corner to the opposite corner of Bernard's rectangular bedroom is 20 feet.
What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
Answer:
Step-by-step explanation:
120
