Consider drawing a card at random from a standard deck of cards,
Part A: Determine the probability that the card is a spade, given that it is black,
Part B: Determine the probability that the card is red, given that it is a heart,
Part C: Determine the probability that the card is an ace, given that it is black.
Part D: Determine the probability that the card is a queen given that it is a face card,
we have 52 cards
A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)
so
Part A: Determine the probability that the card is a spade, given that it is black,
If the card is black, that means the possible outcomes are 26 cards
so
P=13/26
P=0.5Part B: Determine the probability that the card is red, given that it is a heart,
if the card is a heart, that means, the possible outcomes are 13
so
P=13/13
P=1because all the cards that are heart are red
Part C: Determine the probability that the card is an ace, given that it is black.
if the card is black the possible outcomes are 26
therefore
P=2/26
P=1/13Part D: Determine the probability that the card is a queen given that it is a face card
Solve for x in 2(2-x)=4(-2+x)
Given the equation:
[tex]2(2-x)=4(-2+x)[/tex]First, we open the brackets
[tex]4-2x=-8+4x[/tex]Next, we collect like terms. (Bring terms containing x to the left-hand side)
[tex]\begin{gathered} -2x-4x=-8-4 \\ -6x=-12 \end{gathered}[/tex]Finally, we divide both sides by -6 (negative 6) to obtain x.
[tex]\begin{gathered} \frac{-6x}{-6}=\frac{-12}{-6} \\ x=2 \end{gathered}[/tex]The value of x is 2.
Please help me sketch a graph for this sequence (I've already solved it): 2/3, 1, 3/2, 9/4, 27/8
ANSWER and EXPLANATION
We have that the 1 - 5th terms of the sequence are:
2/3, 1, 3/2, 9/4 and 27/8
To plot the graph of this sequence, we have:
=> on the x axis, the term number (i.e. n = 1, 2, 3, 4, 5)
=> on the y axis, the term(i.e. a(n) 2/3, 1, 3/2, 9/4, 27/8)
We will plot the graph of n versus a(n).
That is:
That is the graph.
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Given that f(x)=x2-4/3, f(a)=7, and f(11)=b, a+b can only be a multiple of prime numbers is 5
This calculator for finding the prime factors and the factor tree of an integer is available for use.
How is a prime factor discovered?
The simplest method for determining a number's prime factors is to keep dividing the starting number by prime factors until the result equals 1. When we divide the number 30 by its prime factors, we obtain 30/2 = 15, 15/3 = 5, and 5/5 = 1. We received the balance, thus it cannot be factored any further.
Example: 36 can be written as the product of two prime factors, 22 and 32. The prime factorization of 36 is stated to equal the equation 22 32.
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the difference of twice h and 5 is as much as the sum of h and 4
The value of h by solving the given relationship we get, h = 9
In the above question, a word problem is given with the following relations which are as
First we'll express the given word problem statements into mathematical equation expressions
Therefore, The difference of twice of h and 5 is as much as the sum of h and 4
It can be written as in mathematical equation form as
2h - 5 = h + 4
Now, we need to find the value of h by solving the above mathematical equation formed put of the given relationship
Here,
2h - 5 = h + 4
2h - h = 5 + 4
h = 9
Hence, The value of h by solving the given relationship we get, h = 9
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10x + 45x - 13 = 11(5x + 6)
We have to find the solution for the equation:
[tex]\begin{gathered} 10x+45x-13=11\cdot(5x+6) \\ 55x-13=11\cdot5x+11\cdot6 \\ 55x-13=55x+66 \\ 55x-55x=66+13 \\ 0\cdot x=79 \end{gathered}[/tex]The equation has no solution, becuase there is no value of x that satisfy the equation.
What is the slant height and surface area of the pyramid
we have that
The surface area of the pyramid is equal to the area of its square base plus the area of its four triangular faces
step 1
Find out the area of the square base
A=15^2
A=225 ft2
step 2
Find out the area of one triangular face
the area of a triangle is equal to
A=(1/2)(b)(h)
we have
b=15 ft
h ----> is the slant height
To find out the slant height, apply the Pythagorean Theorem
h^2=10^2+(15/2)^2
h^2=100+56.25
h=12.5 ft
therefore
A=(1/2)(15)(12.5)
A=93.75 ft2
step 3
The surface area is equal to
SA=225+4(93.75)
SA=600 ft2 and the slant height is 12.5 ftThe table shows the temperature (y) at different altitudes (x). This is a linear relationship. Use the equation y = -0.004x + 59 to determine the temperature at an altitude of 5,000 feet. 0 Altitude (ft), x Temperature (°F),y 2,000 51 4,000 43 6,000 35 59 8,000 27 10,000 12,000 19 11 The temperature at an altitude of 5,000 feet Is OF.
EXPLANATION:
We must replace in the equation given the altitude in the variable x ; the exercise is as follows:
[tex]\begin{gathered} y=-0.004x+59 \\ y=-0.004(5,000)+59 \\ y=-0.02+59 \\ y=58.98 \\ \text{ANSWER: The temperature at an altitude of 5,000 is 58.98} \end{gathered}[/tex]There are 12 freshman 6 sophomores 12 juniors and 16 seniors. What percentage of club members are sophomores
Answer:
13% (rounded)Step-by-step explanation:
12 + 6 + 12 + 16 = 46
46 total students
out of those 46 students, 6 are sophomores
so put that into a fraction it becomes
[tex]\frac{6}{46}[/tex]
which equals
0.130434783
which in percentage is
13.0434783%
or 13% rounded
There are four Defenders on a soccer team if this represents 20% of the players on the team which equation can be used to find the total number of players on the team
Given in the question:
a.) There are four Defenders on a soccer team.
b.) This represents 20% of the players on the team.
The baker has 305 cakes to send to the farmers market. If he can pack up to 20cakes in a crate for shipping, what is the minimum number of boxes required toship all of the cakes. Explain your reasoning.
We have 305 cakes. As we know
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The required domain and the range of the given function is (0, ∞) and (-8, -2) respectively.
Given that,
A graph of the function is shown we have to determine the domain and range of the function with the help of the graph.
The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
Here,
As of the graph,
The graph describes as only the positive real number because the graph only consists of the positive x-axis, so the domain of the function is all positive real numbers. While the ordinate of the graph is describe for -8 to -2 on the negative y-axis thus the rang of the given function lies between -8 to -2.
Thus, the required domain and the range of the given function is (0, ∞) and (-8, -2) respectively.
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What is the solution to the equation below? Round your answer to two decimal places.ex = 5.9A.x = 124.50B.x = 1.77C.x = 365.04D.x = 0.77
We have the next given equation:
[tex]e^x=5.9[/tex]Now, we can solve for x using the exponent's properties:
Add both sides ln:
[tex]\ln e^x=\ln5.9[/tex]With the ln we can take down the exponent and simplify ln*e = 1.
Hence,
[tex]\begin{gathered} x=\ln(5.9) \\ x=1.77 \end{gathered}[/tex]Hence, the correct answer is option B.
Use compatible numbers.4,921 ÷ 63
Given:
The objective is to divide the 4921÷ 63 using compatible numbers.
Explanation:
First, the compatible numbers are,
[tex]\begin{gathered} 4921=4920 \\ 63=60 \end{gathered}[/tex]To calculate division:
Now, the division can be performed as,
Hence, the value of the division is 82.
The currency in Kuwait is the Dinar. Theexchange rate is approximately $3 forevery 1 Dinar. At this rate, how manyDinars would you get if you exchanged$54?
It is given that the exchange rate is $3 per Dinar. It is required to find how many Dinars you will get if $54 is exchanged.
Since 1 Dinar is equivalent to $3, it follows that the number of Dinars equivalent to $54 is:
[tex]\frac{54}{3}=18\text{ Dinar}[/tex]The answer is 18 Dinar.
If the cost of a car is $6,345.00, and the tax rate is 6%, how much is the total cost of the car?
Given:
Cost of Car is $6,345
Tax rate is 6%
[tex]\begin{gathered} \text{Tax Amount=6345}\times\frac{6}{100} \\ \text{Tax Amount= \$380.70} \end{gathered}[/tex][tex]\begin{gathered} \text{Total cost of the car =6345+380.70} \\ \text{Total cost of the car = \$6725.70} \end{gathered}[/tex]I NEED CORRECT ANSWER 100 POINTS ONLY ANSWER CORRECTLY
A line passes through the points (7,9) and (10,1). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answer:
[tex]y-9=-\dfrac{8}{3}(x-7)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define the given points:
(x₁, y₁) = (7, 9)(x₂, y₂) = (10, 1)Substitute the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{1-9}{10-7}=-\dfrac{8}{3}[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-9=-\dfrac{8}{3}(x-7)[/tex]
What is the most specific name for each type of special quadrilateral
From the given quadilaterals, let's determine the specific name for each based on the property marked.
• 1a. ,All four sides are marked equal.
Since all four sides are equal, we can say the specific name for the quadilateral is a Square.
A square is a quadilateral with four equal sides.
• 1b. In this quadilateral, we have one pair of parallel sides.
Given that the quadilateral is NOT drawn to scale, the quadilatral here can be said to be a Trapezoid.
A trapezoid is a quadilateral with one pair of parallel side.
• 1c. In this quadilateral, all four angles are marked as right angles.
Given that all four angles are right angles, the specific name for the quadilateral is a Rectangle.
A rectangle is a quadilateral with four interior right angles.
ANSWER:
• 1a. Square
,• 1b. Trapezoid
,• 1c. Rectangle.
Find the volume of each rectangular prism. Round to the tenths.
Answer:
To find the volume of the given cuboid.
Length of the cuboid = 6.8 yd
Breadth of the cuboid = 4.5 yd
Height of the cuboid = 3.4 yd
We get,
Volume of a cuboid is,
[tex]=l\times b\times h[/tex]where l,b and h are the length, breadth and height respectively.
Substitute the values we get,
[tex]=6.8\times4.5\times3.4[/tex][tex]=104.04\text{ yd}^3[/tex]Answer is: Volume of the cuboid is 104.04 cubic yards.
A car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?
A car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?
Applying proportion
28/1=x/8
solve for x
x=(28)*8
x=224 miles
the answer is 224 milesUsing the rotation R, can you create a function R(ABCD) that is equivalent to the reflection of ABCD across both the x-axis and y-axis?
The reflection over the x-axis is given by:
[tex]R(x,y)\to(-x,y)[/tex]And the reflection over the y-axis is given by:
[tex]R(x,y)\to(x,-y)[/tex]Thus, a function that is equivalent to the reflection of ABCD across both axis would be:
[tex]R(x,y)\to(-x,-y)[/tex]Solve the following system of equations by graphing. Graph the system below and enter the solution set as an ordered pair in the form (x,y).if there are no solutions enter none and inter all if there are infinite solutions X + 2y = 3 2x + 4y =12
System of equations:
[tex]x+2y=3[/tex][tex]2x+4y=12[/tex]To solve the system by graphing, we have to remember that the point in which both graphs meet is the solution of the system.
• Graph of both equations:
As we can see, there is no point in which both meet. Then, this system has no solution.
Answer: none
Identify the property of real numbers illustrated in the following equation.(-5) + (y · 7) = (y · 7) + (-5)
By definition, the commutative property of addition says that changing the order of addends does not change the sum, which is precisely what the equation is trying to show by changing the order of the sum, therefore, the property illustrated is the commutative property of addition.
How do you solve this??
Answer:
12-3X=X-3=5
Step-by-step explanation:
Hi, can you help me to solve this problem, please!!
In this problem, we have a vertical parabola open downward
that means
the vertex represents a maximum
looking at the graph
the maximum has coordinates (1,9)
therefore
the vertex is (1,9)Which of the following are rational numbers?A) 42/91B) 10.27C) 8.14 D) 0
It's important to know that a rational number can be expressed as fractions, but also when they are expressed as decimals, the decimal part repeats infinitely, that is, it has a pattern or finite decimal digits.
Having said that, we can deduct that all the answer choices are rational numbers.Determine the largest integer value of x in the solution of the following inequality.
Answer:
From the solution the largest possible integer value of x is;
[tex]-6[/tex]Explanation:
Given the inequality;
[tex]-x-1\ge5[/tex]To solve, let's add 1 to both sides of the inequality;
[tex]\begin{gathered} -x-1+1\ge5+1 \\ -x\ge6 \end{gathered}[/tex]then let us divide both sides of the inequaty by -1.
Note: since we are dividing by a negative number the inequality sign will change.
[tex]\begin{gathered} \frac{-x}{-1}\leq\frac{6}{-1} \\ x\leq-6 \end{gathered}[/tex]Therefore, From the solution the largest possible integer value of x is;
[tex]-6[/tex]
Find the future value in dollars of an 18 month investment of $4900 into simple interest rate account that has an annual simple interest rate of 5.5%
Answer:
$5304.25.
Explanation:
The simple interest formula is given by
[tex]A=P(1+rt)[/tex]where
A = future value
P = princple amount
r = interest rate /100
t = time interval.
Now in our case
A = unknown
P = $4900
r = 5.5 / 100
t = 18 / 12 ( we are converting months to years. 18 months = 18 /12 years )
Putting the above values into the simple interest rate formula gives
[tex]A=4900\lbrack1+\frac{5.5}{100}\times(\frac{18}{12})\rbrack[/tex]which simplifies to give
[tex]\boxed{A=\$5304.25.}[/tex]Hence, the future value is $5304.25.
Rectangle R measures 18 in by 6 in. Rectangle S is a scaled copy of Rectangle R. Select all of themeasurement pairs that could be the dimensions of Rectangle S.24 in by 8 in9 in by 3 in2 in by 1 in6 in by 2 in3 in by 2 in
In order to find possible dimensions for the scaled rectangle, the proportion between the dimensions of the rectangles must be the same.
So first let's find this proportion for rectangle R:
[tex]\frac{18}{6}=3[/tex]Now, let's find the proportion of the possible options of rectangle S:
[tex]\begin{gathered} \frac{24}{8}=3 \\ \\ \frac{9}{3}=3 \\ \\ \frac{2}{1}=2 \\ \\ \frac{6}{2}=3 \\ \\ \frac{3}{2}=1.5 \end{gathered}[/tex]So the correct options are the first, second and fourth options.
(30 points) Solve for the missing side of the triangle. Round to the hundredths place if needed.
Answer:
[tex]6 \sqrt{6} [/tex]
Step-by-step explanation:
The square value of hypotenuse is equal to the square value of sum of the two legs:
[tex] {15}^{2} + {x}^{2} = {21}^{2} [/tex]
225 + x^2 = 441 subtract 225 from both sides
x^2 = 216 find the root of both sides
x = 6√(6)
Plot the point (3,3)
Step-by-step explanation:
Plot the point (3,3):
this means where x = 3 and y = 3
Answer: