A standard deck has 52 cards, there are four suits in the deck, "clubs", "diamonds", "hearts", and "spades". There are 13 ranks in each suit.
You know that the card drawn at random is a club. This means that there are 13 possible outcomes: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K.
→ You have to determine the probability of drawing an "8" given that the card is a club. There is only one 8 of clubs between the 13 cards of the suite, the probability is equal to the number of successes divided by the total number of outcomes:
[tex]P(8|Club)=\frac{1}{13}[/tex]→ You have to determine the probability of drawing a 10 or an ace, given that the card is a club. Once again, since you know that the card's suit is a club, you have to calculate the probability considering the 13 ranks that conform to the suit.
The events "drawing the 10 of clubs" and "drawing the ace of clubs" are mutually exclusive, which means that the probability of the union between both events is equal to the sum of their individual probabilities:
[tex]P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club)[/tex]There is only one 10 within the 13 ranks of the suit, the probability can be expressed as follows:
[tex]P(10|Club)=\frac{1}{13}[/tex]You can calculate the probability of drawing the Ace of Clubs using the same logic:
[tex]P(Ace|Club)=\frac{1}{13}[/tex]Now you can calculate the union between both events:
[tex]\begin{gathered} P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club) \\ P((10|Club)\cup(Ace|Club))=\frac{1}{13}+\frac{1}{13} \\ P((10|Club)\cup(Ace|Club))=\frac{2}{13} \end{gathered}[/tex]The following sets of data show the high temperatures in four different cities for a week in December
the data that have the greatest spread are
(3, 12, 25, 34, 51)
If A= { 1,2,4,5,7,9} and B= {2,3,4} and U = {1,2,3,4,5,6,7,8,9} Find A’
SOLUTION
Given the sets in the question tab, the following are the solution steps to get the answer
Step 1: Write the given sets
[tex]\begin{gathered} A=\mleft\lbrace1,2,4,5,7,9\mright\rbrace \\ B=(2,3,4\} \\ U=\mleft\lbrace1,2,3,4,5,6,7,8,9\mright\rbrace \end{gathered}[/tex]Step 2: Find A'
A' denotes the complement of set A. The complement of set A is defined as a set that contains the elements present in the universal set but not in set A. The Universal set is denoted by capital letter U.
Hence, the elements in set A' will be the elements present in the set U but not set A
[tex]A^{\prime}=\mleft\lbrace3,6,8\mright\rbrace[/tex]18 in3.4.35 km5.6.15.6 amy7 mm7.8.58 yd10.2 m78-* 306.3: 243.47: 144:: 497: 8171 267*: 8417
We need to calculate the area of the circle
[tex]\begin{gathered} \text{Area of circle =}\pi r^2 \\ \text{radius of circle = 29ft,} \\ Area\text{ of circle = }\pi\text{ }\times(29ft)^2 \\ \text{Area of circle = }\pi\text{ }\times841ft^2 \\ \text{Area of circle = 84}1\pi ft^2 \end{gathered}[/tex]Therefore
The area of the circle is 841 square feet
GM no isiecrjreieief G k if f D F hi it
Solution
Proportion is represented by colon:
Part II: Graph the following inequalities on the coordinate grid provided. 5. y > 2x + 1 4. y
Given the inequality;
[tex]y\ge2x+1[/tex]to draw the inequality, first we need to graph the line y = 2x + 14
As the sign is > or equal , so the line will be solid line
So, the following image is the graph of the inequality
the shaded area represents the solution of the inequality
Every time I type this in a calculator it’s shown 9.99999999999999999999
Given
[tex]\frac{2}{11}\times\frac{1}{2}[/tex]Answer
[tex]\begin{gathered} \frac{2}{11}\times\frac{1}{2} \\ =\frac{1}{11} \\ =0.909090\ldots \end{gathered}[/tex]The distance between two distinct points: ordered pair 1 (x , y) and ordered pair 2 (x, y) is given by the formula ____?____.(I need the formula)
Given an ordered pair 1:
[tex]\mleft(x,y\mright)[/tex]And a distinct ordered pair 2:
[tex](x,y)[/tex]You can rewrite them as:
[tex]\begin{gathered} (x_1,y_1) \\ \\ (x_2,y_2) \end{gathered}[/tex]According to the Pythagorean Theorem, for Right Triangles:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Where "c" is the hypotenuse and "a" and "b" are the legs of the Right Triangle.
Then, you can set up that:
Then, to find the hypotenuse of the Right Triangle or the distance "d" between the points, you can apply the Pythagorean Theorem and set up that:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, the answer is:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]After watching some fish 40 feet below the surface of the water, a scuba diver went up 15 feet to explore a coral reef Use a number line to help you create an equation that shows the location of the coral reef in relation to the water's surface. mo Interpret the sum in the context of the problem A. The equation is -40 (-16) 28 The coral reef is 5 feet belo the water's surface
First he was 40 feet below surface, so he was at -40 feet
The he went up 15, so now he is -40 + 15 = -25, that means 25 feet below surface
So the right equation is D and for the line:
Simplify the expression:9m + 6( m + 7 )
ANSWER
15m + 42
EXPLANATION
We want to simplify:
9m + 6(m + 7)
To do this, first expand the bracket:
9m + 6m + 42
Now, collect like terms and simplify:
15m + 42
That is the simplified expression.
Graph the following relation. Use the graph to find the domain and range (in interval form) and indicate whetherthe graph is the graph of a function.y = -4 Domain: Range { }
Given:
[tex]y=-4[/tex]Required:
To draw the graph and find the domain and range.
Explanation:
The graph of the function will be,
We know that,
The domain is the set of all input values for the function and the range is the set of all output values for the function.
Therefore, we get,
[tex]\begin{gathered} Domain:(-\infty,\infty) \\ Range:\lbrace-4\rbrace \end{gathered}[/tex]Yes, it is a function.
Because each input value has exactly one output value.
Final answer:
[tex]\begin{gathered} Domain:(-\infty,\infty) \\ Range:\lbrace-4\rbrace \end{gathered}[/tex]
And it is a function.
y=8x+3 ordered pairs
Answer: (1, 11) and (-1, -5), OPTION C
We are given the equation
y = 8x + 3
This implies that the value of y is a function of x
Firstly, we need to test the options
For (1, 11)
From the point given, let x = 1 and y = 11
Substitute the value of x and y in the above equation
Since, y = 8x + 3
11 = 8(1) + 3
11 = 8 + 3
11 = 11
This implies that (1, 11) satisfied the equation y = 8x + 3
For (-1, -5)
Let x = -1 and y = -5
-5 = 8(-1) + 3
-5 = -8 + 3
-5 = -5
The point (-1, -5) satisfies the equation y = 8x + 3
Hence, the answer is (1, 11) and (-1, -5)
a)Kat's equation b) Carter's equation c) After how many car washes will they both have the same amount of money? d) How much money will they each have
Answer:
a) Kat's equation is 10 + 12x = Amount
b) Carter's equation is 85 + 7x = Amount
c)
Explanation:
Kat has $10 saved up in her account and charges $12 for each car she washes, the equation representing this is:
10 + 12x
Where x is the number of cars she washes.
Carter's equation is:
85 + 7x
I
use the function g=f+4 to find the value of g when f=1use the function u=10c to find the value of u when c=5how about this one use the function u=n-5 to find the value of u when n=7this one use the function h=g+13 to find the value of h when g =1use the function w=14f to find the value of w when f =4
Given function g=f+4
To find the value of g at f=1
substitute f=1 in the given equation
[tex]\begin{gathered} g=f+4 \\ g=1+4 \\ g=5 \end{gathered}[/tex]So, at f=1, the value of g will be 5.
(b).
At u=10c
to find the value of u at c=5
substitute the value c=5 in the given equation
[tex]\begin{gathered} u=10c \\ u=10\times5 \\ u=50 \end{gathered}[/tex]The value of u at c=5 is 50
(c).
Given function u=n-5
to find the value of u at n=7
substitute the value of n=7 in the given equation
[tex]\begin{gathered} u=n-5 \\ u=7-5 \\ u=2 \end{gathered}[/tex]So the value of u at n=7 is 2
(d).
Given function h=g+13
to find the value of h at g=1
substitute the value g=1 in the given equation
[tex]\begin{gathered} h=g+13 \\ h=1+13 \\ h=14 \end{gathered}[/tex]The value of h at g=1 is 14
(e).
Given function w=14f
to find the value of w at f=4
substitute the value f=4 in the given equation
[tex]\begin{gathered} w=14f \\ w=14\times4 \\ w=56 \end{gathered}[/tex]The value of w at f=4 is 56
Maria drove 871 miles in 13 hrs. At the same rate, how many miles would she drive in 8 hours?
Given data: Distance= 871 and time =13 hrs
Required: Find the distance
Method: Find the speed first and then get the distance
Step 1: Find the average speed
[tex]\text{speed}=\frac{\text{distance covered}}{\text{time taken}}[/tex][tex]\text{speed}=\frac{871}{13}=67\text{ miles/hour}[/tex]Step 2: Find the distance to be covered in 8 hours
[tex]\text{Distance}=\text{ spe}ed\text{ x time taken}[/tex][tex]\begin{gathered} \text{Distance}=67\text{ miles/hour x 8 hours } \\ \text{Distance =536 miles} \end{gathered}[/tex]Therefore, Maria will drive 536 miles in 8 hours
suppose that R(x) is a polynomial of degree 12 whose coefficients are real numbers. Also, suppose that R(x) has the following zeros. Answer the following.Edit: if its ok please double-check the answers.
According to the polynomial roots description, we can conclude that 5-i is another zero of R(x), the maximum number of real zeroes that R(x) can have is 8, and the maximum number of non-real zeroes that R(x) can have is 4.
It is given to us that -
R(x) is a polynomial of degree 12 whose coefficients are real numbers.
The zeroes of R(x) are -
-6, -2+3i, -2-3i, 5+i
We have to find out -
(a) Another zero of R(x)
(b) The maximum number of real zeroes that R(x) can have
(c) The maximum number of non-real zeroes that R(x) can have
Since R(x) is a polynomial of degree 12, there are in total 12 roots.
(a) If a non-real, complex, root 5+i exists, then so it's conjugate 5-i exists which is another zero of R(x).
(b) Now, the total number of zeroes of R(x) can be stated as -
-6, -2+3i, -2-3i, 5+i, 5-i
From the above list of zeroes, we can see that there are at least 4 non-real zeroes. So, R(x) has a total of 12 zeroes and we know that there are at least 4 non-real zeroes.
Thus, we can say that the maximum number of real zeroes that R(x) can have is 12-4 = 8 real zeroes.
(c) The non-real complex zeroes always exist in conjugate pairs. And the total number of zeroes that R(x) can have is 12. And we already have determined that R(x) can have a maximum of 8 real zeroes.
Thus, the maximum number of non-real zeroes that R(x) can have is 12-8 = 4 non-real zeroes.
Therefore, according to the polynomial roots description, we can conclude that 5-i is another zero of R(x), the maximum number of real zeroes that R(x) can have is 8, and the maximum number of non-real zeroes that R(x) can have is 4.
To learn more about polynomial roots visit https://brainly.com/question/11906453
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What is the area of parallelogram ABCD?This is a diagram of parallelogram ABCD. Point A is located at (2,1). Point B is located at (8,1). Point C is located at (11,5). Point D is located at (5,5).A. 30 units²B. 55 units²C. 24 units²D. 12 units²
If we draw the given points, we have the following:
The area of a parallelogram can be calculated as the height of it multiplied by its lenght of the base.
In this case, the height will be the distance of the coodinate y = 1 to the coordinate y = 5, which is equal to Δy = 5-1 = 4.
And the base is the distance from the point A to point B, which can be calculated as Δx = 8 - 2 = 6
Now, using the formula, we have:
[tex]\begin{gathered} A_{parallelogram}=b\times h \\ \\ A_{parallelogram}=6\times5 \\ \\ A_{parallelogram}=30\text{ }units² \end{gathered}[/tex]From the solution developed above, we are able to conclude that the correct answer for the present question is:
A. 30 units²draw out the system on the bottom of the graph and chose what postulate proves the triangle is congruent hlsssaassasasa
The given postulates are:
hl: Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
sss: Two triangles have the corresponding three sides congruent (3 corresponding sides have the same measure)
aas: Two angles and a side not between those angles are congruent.
sas:Two sides and an angle between those sides are congruent.
asa: Two angles and a side between those angles are congruent.
---------------------
In the system you have two triangles that share side AC. Then one side is congrent in the triangles.
The line AC bisects angles BAD and BCD, it means taht the angle is equal up and down that line.
Then, the system has two angles and the side between those angles congruent. Triangles are congruent by asaPlease ensure that you provide the important points (the x and y - intercepts, and the vertices),and please clearly label them on the Cartesian coordinate system. [15 points]
Given the piece-wise function
[tex]k(x)=\begin{cases}|x|,x\ge3 \\ \\ 2x^2-4x+3,x<3\end{cases}[/tex]The graph of
[tex]|x|\text{ for x }\ge3[/tex]Is shown below
The graph of
[tex]2x^2-4x+3\text{ for x < 3}[/tex]Is shown below
The graph of the piece-wise function is shown below
The blue curve represents the quadratic function and the red line represent the absolute function
COMPARING METHODS Consider the equation x+ 2 = 3x – 4.a. Solve the equation using algebra.
Answer: 2
We are given the equation
x + 2 = 3x - 4
To solve for x.
Firstly, we need to collect the like terms
x - 3x = -4 - 2
-2x = -6
Divide both sides by -2
-2x/-2 = -6/-2
x = -6/-2
Negative sign will cancel negative sign
x = 6/2
x = 2
The answer is 2
Ab and CD are opposite sides so ab are congruent to CD 2a=34 a=17 find the value of each variable
Two segments of lines or two angles are congruent if the have the same length and the same measure, respectively. In a parallelogram, a geometric figure which opposite sides are parallel, opposite sides are congruent and opposite angles are also congruents.
In this case CD is opposite to AB, so they are congruent and have the same length. Since the segment AB measures 2a and the segment CD mesures 34, then we have the equation
[tex]\begin{gathered} 2a=34 \\ a=\frac{34}{2} \\ a=17. \end{gathered}[/tex]Similarly, the angles A and C are congruent since they are opposite, so their measurement is the same. Since the angle A measures 8b and the angle C measures 112, then we have the next equation
[tex]\begin{gathered} 8b=112 \\ b=\frac{112}{8} \\ b=14 \end{gathered}[/tex]
I need to see if I answer the problem Correctly
For every 2 green rattles, it sells 7 yellow rattles.
The ratio of green to yellow rattles sold is: 2:7
Total rattles sold: 108
Yellow rattles sold:
(total rattles/sum of ratio) x yellow ratio
(108/9)*7 = 12*7 = 84 rattles
84 yellow rattles
Find an equation for the perpendicular bisector of the line segment whose endpoints are (-2,1) and (-6,5)
Here, we want to find the equation of the perpendicular bisector of th line segment with the given endpoints
We start by calculating the slope of the line segment
Mathematically, we can have that as;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ m\text{ = }\frac{5-1}{-6-(-2)}=\text{ }\frac{4}{-4}\text{ = -1} \end{gathered}[/tex]So, we have the slope of the line as -1
Mathematically, the slopes of two lines which are perpendicular to each other have a product of -1
Thus;
[tex]\begin{gathered} m_2\text{ }\times\text{ (-1) = -1} \\ \\ m_2\text{ = 1} \end{gathered}[/tex]Now, we need the midpoint segment coordinates as it is the point through which the perpendicular bisector will pass through
We can get these coordinates using the mid-point formula
That will be;
[tex]\begin{gathered} (x,y)\text{ = (}\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}) \\ \\ (x,y)\text{ = (}\frac{-2-6}{2},\frac{1+5}{2}) \\ \\ (x,y)\text{ = (-4,3)} \end{gathered}[/tex]So we use the point-slope formula to get the equation
That will be;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3\text{ = 1(x+4)} \\ y-3\text{ = x + 4} \\ y\text{ = x + 4 + 3} \\ y\text{ = x + 7} \end{gathered}[/tex]Derive the following functionsa) (2x+1)⁴b) f(x) = [tex] \sqrt{6x + 3} [/tex]
Given:
18.
[tex]f(x)=\sqrt[]{6x-3}[/tex]To find the derivative of the given function, we apply chain rule first:
Therefore, the answer is :
[tex]\frac{3}{\sqrt[]{6x-3}}[/tex]Events A and B are independent. The P(A) = 3/5, and P(not B) = 2/3. What is P(A and B)?
Given:
Events A and B are independent.
P(A)=
[tex]\frac{3}{5}[/tex]P(not B)=
[tex]\frac{2}{3}[/tex]Required:
P(A and B).
Answer:
We have given that P(A)=
[tex]\frac{3}{5}[/tex]P(not B)=
[tex]\frac{2}{3}[/tex]Then P(B)=
[tex]\begin{gathered} P(B)=1-P(not\text{ B}) \\ P(B)=1-\frac{2}{3}=\frac{1}{3} \end{gathered}[/tex]Hence, P(A and B)=
[tex]P(A)\cdot P(B)=\frac{3}{5}\times\frac{1}{3}=\frac{1}{5}[/tex]Final Answer:
P(A and B)=
[tex]\frac{1}{5}[/tex]which price below has the same unit rate as 3 cans for $ 1.98? Select All That Apply●6 cans for $4.00 ●5 cans for $5.90●2 cans for $1.32 ●4 cans for $3.60
Divide the price of 3 cans over 3 to find the unit rate:
[tex]\frac{1.98}{3}=0.66[/tex]Perform the same operation with the other rates to find which of them have the same unit rate:
6 cans for$4.00
[tex]\frac{4}{6}=0.67[/tex]5 cans for %5.90
[tex]\frac{5.90}{5}=1.18[/tex]2 cans for $1.32
[tex]\frac{1.32}{2}=0.66[/tex]4 cans for $3.60
[tex]\frac{3.60}{4}=0.9[/tex]Therefore, the only one which has the same rate as 3 cans for $1.98 is 2 cans for 1.32
Which expressions are equivalent to the one below? Check all that apply.log71 •logg 25O A. 2• log77OB. 1O COO D. 5.7
Problem
[tex]\log ^1_7\text{ . }\log ^{25}_5[/tex][tex]\begin{gathered} =\text{ }\log ^{1\text{ }}_7\text{ x }\log ^{5^2}_5 \\ =\text{ }\log ^1_7\text{ x 2}\log ^5_5 \\ \log ^1_7\text{ = 0 and }\log ^5_5\text{ = 1} \\ =\text{ 0 }\times\text{ 2 }\times\text{ 1} \\ \text{= 0} \end{gathered}[/tex]Final answer
Option C is equivalent to the expression.
The lines represented by the equations y + 3/2x = 7 and 9y - 6x = 27 are O parallel Submit Answer the same line O neither parallel nor perpendicular O perpendicular
y+3/2x=7 (a)
9y-6x=27 (b)
Express both lines in slope-intercept form:
y= mx+b
Where :
m= slope
b= y-intercept
a.
y= -3/2x+7
m= -3/2
b.
9y-6x=27
9y= 6x+27
y= (6x+27)/9
y= 2/3x+3
m= 2/3
Both slopes are negative reciprocals of each other.
If two lines have negative reciprocal slopes, they are perpendicular lines.
PERPENDICULAR.
Exercise #1: We would like to find the distance between points A and B if they have coordinates A(2,3) and B(14, 12). B (a) Sketch the right triangle below that could be used to calculate the length of AB and find its length using the Pythagorean Theorem. (b) How could we calculate the lengths of the legs of the right triangle in (a) from the coordinates of points A and B.
Answer
Check Explanation
Explanation
We've been asked to find the length of the distance between points A (2, 3) and B (14, 12).
a) First of, we've been asked to sketch the right angle triangle that coulb be used to calculate the distance AB
The sketch will be shown below
So, the figure above represents the right angle triangle that can be used to calculate the distance AB
Distance AB = hyp = ?
Distance between the x-coordinates of points A and B = x = 14 - 2 = 12
Distance between the y-coordinates of points A and B = y = 12 - 3 = 9
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are x and y respectively,
x² + y² = (hyp)²
For this question,
x = 12 units
y = 9 units
hyp = AB = ?
x² + y² = (hyp)²
12² + 9² = AB²
144 + 81 = AB²
225 = AB²
We can rewrite this as
AB² = 225
Take the square root of both sides
√(AB²) = √(225)
AB = 15 units
b) The second part of the question asks how we calculated the legs of the right angle triangle that we used to solve this distance between AB.
Since both points lie on given x and y axis levels in the coordinate system, the length of the legs of this right angle triangle is obtained simply by taking the difference between respective x and y coordinates.
For the base of the triangle,
Distance between the x-coordinates of points A and B
= x
= 14 - 2
= 12 units
For the height of the triangle,
Distance between the y-coordinates of points A and B
= y
= 12 - 3
= 9 units
Hope this Helps!!!
The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is y=-0.2x + 1. Graph the equation and use it to answer questions 1 and 2. a. What is the x-intercept? What does it represent? b. What is the y-intercept? What does it represent?c. After how many hours is the battery power at 75%d. what is the percentage of battery power remaining at 3 hours?
The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is given by
[tex]y=-0.2x+1[/tex]Let us graph the above equation
a. What is the x-intercept? What does it represent?
The x-intercept is the point where the line intersects the x-axis.
From the graph, we can see that the x-intercept is (5, 0)
The x-intercept represents that it takes 5 hours for the battery power to go to 0%
You can manually find out the x-intercept by substituting y = 0 into the given equation
[tex]\begin{gathered} y=-0.2x+1 \\ 0=-0.2x+1 \\ 0.2x=1 \\ x=\frac{1}{0.2} \\ x=5 \end{gathered}[/tex]Therefore, the x-intercept is (5, 0)
b. What is the y-intercept? What does it represent?
The y-intercept is the point where the line intersects the y-axis.
From the graph, we can see that the y-intercept is (0, 1)
The y-intercept represents that the battery power is 1 (100%) when x = 0 hours.
You can manually find out the y-intercept by substituting x = 0 into the given equation
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(0)+1 \\ y=1 \end{gathered}[/tex]Therefore, the y-intercept is (0, 1)
c. After how many hours is the battery power at 75%
We need to substitute y = 0.75 (that means 75%) into the equation to find out x (number of hours)
[tex]\begin{gathered} y=-0.2x+1 \\ 0.75=-0.2x+1 \\ 0.75+0.2x=1 \\ 0.2x=1-0.75 \\ 0.2x=0.25 \\ x=\frac{0.25}{0.2} \\ x=1.25\: \text{hours} \end{gathered}[/tex]Therefore, after 1.25 hours, the battery power is at 75%
d. what is the percentage of battery power remaining at 3 hours?
We need to substitute x = 3 hours into the equation to find out y (remaining battery power)
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(3)+1 \\ y=-0.6+1 \\ y=0.4 \end{gathered}[/tex]Therefore, the remaining battery power is 40% after 3 hours.
The slope of a graph is ratio of the change in the y - variable to the change in the x - variable True or false
ANSWER
True
EXPLANATION
We want to understand the meaning of slope.
The slope of a graph is known as the rate of change of the dependent variable with the independent variable.
It is the rate of change of the graph.
This means that it tells us how the y values of the graph vary with the x values.
Therefore, the slope of a graph is ratio of the change in the y - variable to the change in the x - variable.