So, there are 52 ways to draw two cards such that the first card is a spade and the second card is a queen.
In a standard 52-card deck, there are 13 cards of each suit: spades, hearts, diamonds, and clubs. Each suit has 4 face cards (Jack, Queen, King, and Ace) and 9 numbered cards (2 through 10).
To find the number of ways to draw two cards such that the first card is a spade and the second card is a queen, we first need to determine the number of spades in the deck, and then the number of queens.
There are 13 spades in a standard 52-card deck, so there are 13 ways to draw a spade as the first card.
There are 4 queens in a standard 52-card deck (one from each suit), so there are 4 ways to draw a queen as the second card.
To find the total number of ways to draw two cards such that the first card is a spade and the second card is a queen, we multiply the number of ways to draw each card: 13 * 4 = 52 ways.
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Exit Ticket
DQ,FP, RE are all medians of Ader, and C is the centroid. DQ = 24, FC = 10, RC = 7.
Find DC, CQ, FP, and CE.
P
E
D.
R
Using the property of median, the values of DC = 16, CQ = 8, FP = 15, and CE = 14.
As DQ = 24, FC = 10, RC = 7.
As we know that the centroid divide each median in the ratio of 2:1.
The diagram of the question is given below:
So, we divide the median DQ in the ratio 2:1
2x + x = 24
3x = 24
Divide by 3 on both side, we get
x = 8
So the length of DC = 16 and CQ = 8
Ac FC = 10 which is 2 part of the ratio 2:1.
So the value of 2x = 10
So x = 5. Now the value of CP = 5
Now the value of FP = FC + CP
FP = 10 + 5
FP = 15
As RC = 7 which is 1 part of the ratio 2:1.
So the value of CE = 2x = 2×7 = 14
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How much of a(n) 60% orange juice drink must be mixed with 5 gallons of a 30% orange juice drink to obtain a mixture that is 50% orange juice?
Answer: To obtain a mixture that is 50% orange juice, you must find the amount of 60% orange juice needed to bring the overall concentration of orange juice to 50%.
We can start by using the formula:
(amount of 60% orange juice) / (amount of 60% orange juice + amount of 30% orange juice) = desired concentration
Let's call the amount of 60% orange juice that we need to add x.
So the equation will look like this:
(x) / (x + 5 gallons) = 0.5
We can then solve for x:
x = (0.5 * x + 0.5 * 5 gallons)
x = 2.5 gallons
So, 2.5 gallons of 60% orange juice must be mixed with 5 gallons of 30% orange juice to obtain a mixture that is 50% orange juice.
Step-by-step explanation:
Gina Wilson All Things Algebra Unit 5: Congruent Triangles homework 1 PLEASE HELP
As per the angle sum property, the value of x is 14°
In math the term called angle sum property states that the sum of interior angles of a triangle is 180°.
Here we have the following diagram and we need to find the value of x.
While we looking into the diagram, we have identified the value of the angles are listed as follows:
=> (10x - 11)°
=> (3x - 2)°
=> (3x + 1)°
Now we have to solve this by using the angle sum property then we get,
=> (10x - 11)° + (3x - 2)° + (3x + 1)° = 180°
When we simplify this one then we get,
=> 16x - 12 = 180°
=> 16x = 168°
=> x = 14°
Complete Question
Find the value of x one the following diagram.
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A statistics professor asked her students whether or not they were registered to vote. In a sample of
50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.
1. Find a 95% confidence interval for the true proportion of the professor's students who were
registered to vote. (Make sure to check any necessary conditions and to state a conclusion in
the context of the problem. )
As per the 95% confidence interval, the true proportion of the professor's students who were registered to vote is between 57.3% and 82.7%
The term called confidence interval is defied as the mean of your estimate plus and minus the variation in that estimate.
Here we know that sample of 50 of her students randomly sampled from her 700 students, 35 said they were registered to vote.
Here we have to calculate the true proportion of the professor's students who were registered to vote with 95% confidence interval is,
Here we have a random sample of less than 10% of the professor's students with 35 expected successes and 15 expected failures
Here we have know that both of which are at least ten, so a Normal model applies.
Then the value of n = 50,
=> P =35/50 = 0.70
Then the value of q = 1 - p = 1 - 0.70 = 0.30
Then the value of SE is
=> √(0.70 0.30)/ 50 = 0.065
Then with 95% confidence interval is calculated as,
=> p± SE(p)
Apply the values on it, then we get
=> 0.70±1.96 (0.065)=0.70±0.127
=> 0.573 to 0.827
hence the 95% confident that between 57.3% and 82.7% of the professor's students are registered to vote.
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4 3/4 - 6/4 = ? I need help .
The solution to the mixed fraction 4 3/4 - 6/4 is 3 1/4
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
To solve the question
Convert the mixed fractions into improper fractions
4 3/4 - 6/4
= 19/4 -6/4
we can simplify, since the denominators are the same
19-6/4
=13/4
converting to mixed fractions, we have
3 1/4
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if 3/4 of a certain number is equal to 4 1/2 find the number
Answer:
6
Step-by-step explanation:
4 1/2= 4.5
3/4=0.75
4.5/0.75= 6
just to check, 3/4 x 6 =4.5
Find the solution to the system of equations given below using elimination by addition. 4x + 3y = -20 6x +12y = −10
Answer:8
Step-by-step explanation:
dd
What is the factored form of 4x+16
Answer:
The factored form of 4x+16 is (4x + 8)(2). This can be found by using the distributive property, or by using the prime factorization method.
The input is multiplied by 2, then 5 is subtracted
The function that matches the description is given as follows:
f(x) = 2x - 5.
How to define the function?The parent function for this problem is given as follows:
f(x) = x.
The first transformation is a multiplication by two, hence the function is defined as follows:
f(x) = 2x.
The final transformation is a subtraction by 5, then the function is defined as follows:
f(x) = 2x - 5.
Meaning that the last option is the correct option.
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An open box i to be contructed from a quare piece of heet metal by removing a quare of ide 3 feet from each corner and turning up the edge. If the box i to hold 300 cubic feet, what hould be the dimenion of the heet metal?
The sheet metal should have a total area of 12.9 x 12.9 = 166.41 square feet.
The sheet metal must be large enough to form a cube with a volume of 300 cubic feet, so the side length of the sheet must be the cube root of 300, which is approximately 6.9 feet. To find the dimensions of the sheet metal, we must take into account the four 3 foot squares that will be removed from each corner. Therefore, the sheet metal should have a length of 6.9 feet + 6 feet (4 times the 3 foot squares) = 12.9 feet and a width of 12.9 feet. This will give the box a volume of 300 cubic feet, and the sheet metal should have a total area of 12.9 x 12.9 = 166.41 square feet.
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The cost C (in dollars) of producing x cell phone cases is C=2.2x+10.6. The revenue R (in dollars) for selling x cell phone cases R = 6.91x.
To calculate profit, subtract the cost from the revenue.
(a) Write and simplify an equation for the profit P in terms of x.
P = ?
Answer:
P =4.71x-10.6
Step-by-step explanation:
R = 6.91x
C=2.2x+10.6.
P = R - C = 6.91x-2.2x -10.6 =4.71x-10.6
f(x) = -x + 1; Find f(-10)
Enter the statement, with the values in the same order, but with parentheses so that the statement is true.
7x5-4x5+16+4-26 when
(select) (select) (select) (select)+(select)=(select)-26
The statement "7x5-4x5+16+4-26 when
(select) (select) (select) (select)+(select)=(select)-26", with the values in the same order, but with parentheses such that the statement is true is 7x(5-4x+4)-26 = (7x)(1) - 26
What is factorization?Factorization is the process of finding the factors, or integers that multiply together to give a specific number. It is also known as factoring or prime factorization when the factors are prime numbers. For example, factorization of 12 is 2x2x3, which are the prime factors that multiply to give 12. The process of factorization is used in a variety of mathematical and scientific fields, such as number theory, algebra, and computer science.
It can also refer to a mathematical expression where an algebraic expression can be written as a product of two or more expressions.
In general, factorization is a way of breaking down a number or an expression into smaller parts that can be used to understand or simplify it.
Therefore, when plugged in those values in the same order, the statement become true.
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Write the following as an algebraic expression. Then simplify. the total amount of money (in cents) in x quarters, (x+3) dimes, and 2x nickels.
Answer:(x+3)=2x
Step-by-step explanation:
pls help i will give 20 points
Answer: Your answer would be −2x⁴y²
Step-by-step explanation: I hope this helps!
Answer:
The third question
Step-by-step explanation:
Hope this helps!
Write an explicit formula for
�
�
a
n
, the
�
th
n
th
term of the sequence
28
,
14
,
7
,
.
.
.
28,14,7,....
Answer:
This equation makes no sense post in better quality
Step-by-step explanation:
|x-2|=|4+x| How does this make sense, HOW
The solution of the absolute value equation:
|x-2|=|4+x|
is x = -1
How to solve the equation?Here we want to solve the following equation:
|x - 2| = |4 + x|
A general absolute value function can be rewritten into two equations, in this case these are:
x - 2 = 4 + x
x - 2 = -(4 + x)
The first one has no solution, but the second one does.
x - 2 = -(4 + x)
x - 2 = -4 -x
2x = -4 + 2
2x = -2
x = -2/2 = -1
That is the solution.
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What does it mean when you substitute a value into an equation and the result is a true statement?
What it means when you substitute a value into an equation and the result is a true statement is; The solution of the equation
How to find the solution of an equation?
Solving an equation is very synonymous to trying to find the answer to a puzzle. Now, an algebraic equation states that two algebraic expressions are equal.
In order for us to solve an equation, we will have to determine the values of the variable that makes the equation a true statement. Thus, any number that makes the specific equation to be true will be referred to as a solution of the equation.
A solution to an equation is defined as a value of a specific variable that makes a statement to be true when substituted into the equation. Thus, the process of finding the solution to an equation is simply called solving the equation.
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Leia invests $2658.00 (P) in a retirement
account with a fixed annual interest rate
of 4% (r) compounded monthly (n=12).
What is Leia's ending balance (A) after 5
years (t=5)?
$587.41
$3245.41
$2053.06
$12,145.52
Leia's ending balance after 5 years will be $3245.41. The solution has been obtained by using the concept of compound interest.
What is compound interest?
Both the principal and the interest that has accumulated over the previous period are used to compute interest. Compound interest accounts for the principal when calculating the interest for the subsequent month, in contrast to simple interest, which does not. In mathematics, compound interest is frequently denoted by the letter C.I.
We know that formula for compound interest is
[tex]A= P(1 + \frac{r}{n} )^{nt}[/tex]
So, here P = $2658 , n=12, t=5 and r = 0.04
Thus, we get
[tex]A= 2658(1 + \frac{0.04}{12} )^{60}[/tex]
[tex]A= 2658(1.00333})^{60}[/tex]
A = 2658*1.2207
A = $3245.41
Hence, Leia's ending balance after 5 years will be $3245.41.
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Talia travelled part of the journey by train and the rest by bus.The total fare was sh 400.On return,the fare of the bus was hiked by a half of what he paid and the total fare of the return journey hiked to sh 4800.Find the train fare.
Answer: Let x be the fare of the train, and y be the fare of the bus.
We know that:
x + y = 400 (the total fare of the journey)
And, on the return journey the fare of the bus is hiked by a half of what Talia paid initially, so the fare of the bus on the return journey is:
y * 1.5 = y + (y/2)
And the total fare of the return journey is hiked to 4800, so:
x + y + (y/2) = 4800
We can substitute the first equation into the second equation:
x + (y + (y/2)) = 4800
x + y + (y/2) = 4800
x + (y + (y/2)) = 4800
So, we can solve the system of equations by substituting the first equation into the second equation and solving for x.
x + y = 400
x = 4800 - (y + (y/2))
x = 4800 - y - (y/2)
x = 4800 - y - (1/2)y
x = (4800 - y) - (1/2)y
x = 4800 - (3/2)y
Now we have an equation for x in terms of y. To solve for x, we can use the value of y from the first equation
x = 4800 - (3/2)(400)
x = 4800 - 600
x = 4200
So the train fare is 4200 sh
Step-by-step explanation:
Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not a/d=j
The expression in terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.
What exactly is a phrase?
It is described as blending mathematical operators, constants, and variables.
It follows that:
The sentence is:
hD = m
To account for D Declare D as the subject.
As we know, an arithmetic operation can be defined as an operation in which we add, subtract, multiply, and divide integers. It has four basic operators that are +, -, ×, and ÷.
By dividing both sides by h:
hD/h = m/h
Here h ≠ 0
D = m/h
As a result, if the statement is hD = m, then the expression in terms of m and h is D = m/h, and the solution is D = m/h.
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What number should be added to both sides
2 + 7^3 + 4(9-6)^2/6
Answer:
The answer is 351
Step-by-step explanation:
Hope this helps!
how do i simplify -5x+x and 2p+5p
Answer: For your answer you would add like terms so for -5x+x you would get -4x, and for your other you would get 7p.
express cos V as a fraction in simplest terms
The value of cos v in simplest terms in fraction form is 17/18
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: The triangle ΔXWV with WV=17 , XV=18,
We know cos ∅= base/hypotenuse
here hypotenuse is XV as it is opposite to the right angle. and the base of the triangle is 17
∴ Cos v=17/18
We can also find the measure of the third angle by using the pythogarean theorm as
WX=√18²-17²
=√35
Hence, The value of cos v in simplest terms in fraction form is 17/18
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Consider the equation. X + 5 7 = 31 7 If you use the addition property of equality, what number would you add to both sides of the equal sign to isolate the variable? What is the solution?
Regarding the addition property of equality, the number would add to both sides of the equal sign to isolate the variable x = 26/7.
What amount would you add to both sides of the equal sign if you were to isolate the variable using the addition property of equality?
The official term for the equality-related characteristic that enables one to multiply both sides of an equation by the same amount. One of the most frequently applied properties for solving equations is this one.
To solve the problem, you would take away 5/7 from both sides.
What is the remedy?
x = 3 and 5/7 or 26/7.
x + 5/7 = 31/7
Subtract 5/7 from both sides of the equation:
x + 5/7 - 5/7 = 31/7 - 5/7
x = 26/7
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Answer:
1: -5/7
2: 26/7
Step-by-step explanation:
a measure computed from the entire population is called __________.
A measure computed from the entire population is called parameter.
A limit is a parameter. A parameter is a constant in an equation in mathematics, however today, any system can include parameters that control how it functions. You can provide guidelines for your class discussion.
Greek words para-, which means "beside," and metron, which means "measure," are combined to form the term parameter. Gravity and time are two boundaries that the natural world establishes. The law establishes the boundaries of appropriate conduct in court. While parameters and perimeters are similar, a parameter can contain or define something that is either physically present or abstractly defined, whereas a perimeter is the physical space that surrounds an entity.
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Look at the following speeds.
4mph 8mph 16mph 32mph 64mph 128mph
By what factor did the speeds change for each consecutive speed from the first speed to the sixth speed.
A. 8
B. 32
C. 4
D. 2
The factor by which ths speed increases is 2, then the correct option is D.
By what factor did the speeds change for each consecutive speed?Here we have the sequence of numbers:
4, 8, 16, 32, 64, 128
Where these have units of miles per hour, but can be ignored, as we only care for the numbers. To get the factor by which the speed change for each consecutive speeds, we just need to take the pairs of consecutive numbers and take their quotients.
We will get:
8/4 = 2
16/8 = 2
32/16 = 2
etc.
Then the factor is 2, the correct option is D.
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a mechanical system comprises three subsystems in series with reliabilities of 0.98, 0.96, and 0.94. what is the overall reliability of the system?
The system's total dependability is 0.8813.
The reliability of the individual components determines the overall reliability of multi-component systems.
R = (0.98) (0.96) (0.94)
= 0.8813
The likelihood that a system operates well for a given period of time is known as reliability. When performing this right action:
No maintenance or repairs are necessary. The system correctly complies with the established performance requirements.
The dependability decreases when more time is taken into account for reliability calculations since it obeys the exponential failure rule.
In other words, a system's reliability will initially be high and steadily decline to its lowest level over time.
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The value of the overall reliability of the system is 0.8813.
The possibility that a system will work successfully over a certain time period is referred to as reliability. No repair is necessary or done during this right procedure. The system adheres to the performance standards as specified.
The overall reliability of multi-component systems is determined by the reliability of the individual components.
R = (0.98) (0.96) (0.94)= 0.8813
The possibility that a system will perform well over a particular length of time is referred to as dependability. There is no need for maintenance or repairs while doing this appropriate step. The system satisfies the defined performance criteria.
Because it follows the exponential failure rule, dependability falls as more time is factored into reliability assessments.
In other words, the reliability of a system will begin high and gradually drop to its lowest level over time.
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Write about a real-world situation that can
be represented by the equation y = 7x. Be sure to explain what the variables
represent in the situation.
Answer:
the equation could represent your paycheck at the end of a shift. y is equal to the total amount of money you made, 7 is equal to your hourly wage, and x is equal to the number of hours worked. For example if you worked two hours one day, the equation would be y=7(2), which could be simplified to y=14, so after a two hour shift you would make a total of $14
Step-by-step explanation: