The probability that the card chosen is not a heart is 0.75
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
Sample space ={13 H + 13 D + 13 S + 13 C}
= 52 cards
The total number of cards in a deck is 52
Number of cards with hearts = 13
Therefore, P(getting one heart) = 13/52 = 1/4
P( getting NO heart) = 1-1/4 = 3/4 = 0.75
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What is 1/4 of 268 ?
To find 1/4 of 268, you divide 268 by 4. The result of this operation is 67.
Explanation:Calculating 1/4 of a number involves a simple mathematical operation known as division. In this case, we want to find out what is 1/4 of 268. To do this, you simply divide 268 by 4.
The calculation is as follows:
Divide the number 268 by 4.268 ÷ 4 equals 67.This means that 1/4 of 268 is 67.
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53 ℃ below zero degrees
write 103,727,495 in word form and expanded
Devaughn is 13 years older than Sydney. The sum of their ages is 77 . What is Sydney's age?
A set of equations is given below:
Equation A: y = x + 1
Equation B: y = 4x + 5
Which of the following steps can be used to find the solution to the set of equations?
x + 1 = 4x + 5
x = 4x + 5
x + 1 = 4x
x + 5 = 4x + 1
Answer:
x + 1 = 4x + 5
Step-by-step explanation:
To solve this set of equation you can just equalize them ot one another, as you can see they are already in Y form, which means that they have already been solved for Y, so that makes things easier for us, we just insert the second equation in the place of Y in the first one, and we can solve for "x".
What's the correct answer for this?
There are two aircraft carriers, A and B, and the carrier A is longer in length the carrier B. The total length of these two carriers is 4178 feet, while the difference of their lengths is only 14 feet.
Answer:
Length of carrier A = 2096 feet Length of carrier B=2082 feet.Step-by-step explanation:
Given , two air craft carriers are A and B . The carrier A is longer than the carrier B in length.
Total length of two carriers =4178 feet
Difference of two carriers = 14 feet
Let
Length of carrier A =x feet
And
Legth of carrier B =y feet
According to question
The I equation is
x+y=4178
The II equation is
x-y= 14
Substitution method: In this method step I : we find value of x or y from the equation I
Step II: put the value of x or y in II equation then we get the value of another varaiable x or y
Step : Again put the obatined value of variable x or y from step II in equation I then we get value of other variable x or y .
By using substitution method ,
we find value of x from equation I
x= 4178-y
Now, put the value of x in equation II then we get
4178-y-y=14
4178-2y=14
4178-14=2y
4164=2y
[tex]y=\frac{4164}{2}[/tex]
y= 2082
Again , put the value of y in equation I
2082 +x=4178
x= 4178-2082
x=2096
Hence, the length of carrier A = 2096 feet
The length of carrier B= 2082 feet
Final answer:
To solve the problem, we set up two equations based on the given total length and the length difference of the two aircraft carriers. By solving these equations, we find that carrier A is 2096 feet long and carrier B is 2082 feet long.
Explanation:
The student's question involves solving a system of linear equations to find the lengths of two aircraft carriers, A and B. Given that the total length is 4178 feet and the length difference is 14 feet, we can set up the following equations:
Equation 1: A + B = 4178
Equation 2: A - B = 14
To solve for A and B, we can add the two equations together to eliminate B.
This gives us 2A = 4192, hence A = 2096 feet.
Substituting A back into one of the equations, we find B = 2082 feet.
Therefore, carrier A is 2096 feet long and carrier B is 2082 feet long.
Mark deposited $9,000 into two saving accounts bearing simple interest. One of the accounts has an interest rate of 8% while the other rate is 7%. If the total interest earned after one year is $700, find the amount deposited into each of the accounts
What is the step by step process of solving for the GCF from a list of terms.
Ex. (see picture)
Round 65.85 to the nearest whole number
Two linear equations are shown.
What is the solution to the system of equations?
Answer:
B.
Step-by-step explanation:
Use the half-angle identities to find the exact value of cos 15 degrees.
This is what I have so far:
cos15 degrees = cos1/2(30 degree) = sqrt (1+cos30)/2 = sqrt (1+ sqrt3/2)/ 2
But.. I don't understand how the cos30 turns into sqrt 3/2??
The cosine value of cos(15) is [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
The trigonometry identity of half angles is given as:
cos([tex]\theta[/tex]/2) = [tex]\sqrt{[/tex](1 + cos([tex]\theta[/tex]))/2
Substitute 30 for [tex]\theta[/tex]
So, the equation becomes
cos(30/2) = [tex]\sqrt[/tex](1 + cos(30))/2
In trigonometry, we have:
cos(30) = [tex]\sqrt[/tex]3/2
So, we have:
cos(30/2) = [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
Divide 30 by 2
cos(15) = [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
Hence, the cosine value of cos(15) is [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
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Explain the place value relationship when the same two digits are next to each other in a multi-digit number.
What is the value of b2 - 4ac for the following equation? x(x + 8) = 9 28 64 100
Answer:
C) 100
Step-by-step explanation:
The given equation is x(x + 8) = 9
Distributing x insides, we get
x^2 + 8x = 9
Now set the equation equal to zero.
x^2 + 8x - 9 =0
Here a = 1, b = 8, and c = -9
b^2 - 4ac = (8)^2 - 4*1*-9
= 64 + 36
= 100
Therefore, b^2 - 4ac = 100.
Answer: C) 100
Hope this will helpful.
Thank you.
Answer:
C. 100
Step-by-step explanation:
Find the value of each determinant
The question is about finding the value of a determinant for matrices, a fundamental concept in Mathematics, especially linear algebra. For 2 × 2 matrices, the determinant calculation is straightforward and essential for various applications.
Explanation:The subject of this question is clearly Mathematics, specifically it pertains to linear algebra and the concept of determinants. The task involves finding the value of a determinant for a given matrix. For a 2 × 2 matrix, the determinant is found using a simple formula: if the matrix is given by
\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}\]
then the determinant is calculated as \(ad - bc\). Additionally, the determinant provides important information about the matrix, such as whether the matrix is invertible and the product of its eigenvalues.
To understand determinants for larger matrices, a recursive approach is often used, breaking down the determinant into smaller matrices until 2 × 2 matrices are reached, where the simple formula can be applied. Also of note is that the determinant of the product of two matrices is equal to the product of their determinants (det(AB) = det(A)det(B)).
This fundamental concept is crucial for many applications in mathematics, including solving systems of linear equations, finding eigenvalues, and understanding linear transformations.
a class voted for either kayaking, fishing, or hiking as their favorite summer activity. if hiking got 17% percent of the vote and fishing got 33%, what percentage of the class voted kayaking?
The percentage of the class that voted for kayaking is 50%.
Given data:
To find the percentage of the class that voted for kayaking, use the fact that the total percentage of votes adds up to 100%.
Hiking got 17% of the vote.
Fishing got 33% of the vote.
Let x be the percentage of the class that voted for kayaking.
Since the total percentage of votes is 100%:
17% + 33% + x = 100%
On solving for x:
x = 100% - (17% + 33%)
x = 100% - 50%
x = 50%
Hence, 50% of the class voted for kayaking.
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A and B are mutually exclusive events. P(A) = 1/3 and P(B) = 1/2. What is the P(A or B)?
A dozen eggs cost $1.10 in Dover. In Ensley, the eggs cost 10% more than in Dover. Find the price of a dozen eggs in Ensley.
Final answer:
The price of a dozen eggs in Ensley is $1.21.
Explanation:
To find the price of a dozen eggs in Ensley, we need to consider that the eggs in Ensley cost 10% more than in Dover. If a dozen eggs in Dover cost $1.10, we can calculate the 10% increase by multiplying $1.10 by 1.10:
$1.10 x 1.10 = $1.21
Therefore, a dozen eggs in Ensley cost $1.21.
Round 241,639 to the nearest thousand
From 1980 to 1990, the consumer price index (CPI) increased from 82.4 to 130.7. If a bottle of dish soap cost $0.74 in 1980 and the price of dish soap increased at the same rate as the CPI from 1980 to 1990, by approximately how much did the price of a bottle of dish soap increase from 1980 to 1990?
Using proportions, it is found that the price of a bottle of dish soap increased $0.43 from 1980 to 1990.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The percent increase, as a proportion, of the CPI is given by:
P = 130.7/82.4 = 1.5862.
Hence, for the price of the bottle:
Pb = $0.74 x 1.5862 = $1.17.
The difference is:
1.17 - 0.74 = $0.43.
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Answer: $0.43
Step-by-step explanation:
The cool dude above me already explained it
The building of Jim's Hardware is assessed at $109,000. The tax rate is $86.95 per $1,000 of assessed valuation. The tax due is A. $8,695.45. B. $947.75. C. $9,477.55. D. $8,659.54. E. 94,698.23.
7^-2 without exponent
A rectangular yard measuring 26ft by 40ft is bordered (and surrounded) by a fence. Inside, a walk that is 2ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
Malia is observing the velocity of a cyclist at different times. After two hours, the velocity of the cyclist is 15 km/h. After five hours, the velocity of the cyclist is 12 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 12 hours? (5 points)
Determine whether each of the functions log(n + 1) and log(n2 + 1) is o(log n)
Both functions log(n + 1) and log(n^2 + 1) are not o(log n). For large values of n, log(n + 1) is approximately equal to log n, and log(n^2 + 1) behaves like 2*log n, none of which grows strictly slower than log n.
To determine whether the functions log(n + 1) and log(n2 + 1) are o(log n), we'll use the definition of little-o notation. A function f(n) is said to be o(g(n)) if for any positive constant c > 0, there exists a threshold n0 such that for all n > n0, f(n) < c * g(n). In other words, f(n) grows slower than any constant multiple of g(n) as n approaches infinity.
Analysis for log(n + 1)
When n is very large, the +1 becomes negligible, and log(n + 1) behaves similarly to log n. Therefore,
log(n + 1) ≈ log n when n is large.
This implies that log(n + 1) is not o(log n) because it does not grow strictly slower than any multiple of log n.
Analysis for log(n2 + 1)
Using logarithm properties:
log(n2 + 1) < log(n2 + n2) = log(2n2) = log 2 + 2*log n.
As n grows, the constant term (log 2) becomes insignificant, and the function approaches the behavior of 2*log n. However, since there is a multiple of log n (which is 2*log n), this still means that log(n2 + 1) is not o(log n) because it grows faster, not slower, than log n.
how to solve this linear equation step by step please
Manuel is choosing a 3 -letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?
The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x , where x is his monthly income. f^-1x . The variable x represents in the inverse function. If John's spending limit is $60,000, his monthly income is .
other form to write 600,000+80,000+10
If the rate of inflation is 3.7% per year, the future price pt (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. =pt400( 1.037)t Find the current price of the item and the price 8 years from today. Round your answers to the nearest dollar as necessary.