The probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.
In the question, we are informed that a card is drawn at random from a standard 52-card deck.
We are asked the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit.
We assume the event of drawing an odd card from the random pick to be A, and the event of drawing a card of spade suit to be B.
The number of outcomes favorable to event A = 16 {4 odd cards of each of the 4 suits, that is, 4*4 = 16}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of event A, P(A) = 16/52.
The number of outcomes favorable to event B = 13 {The 13 cards of spade suit}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of event B, P(B) = 13/52.
The number of outcomes favorable to events A and B both = 4 {4 odd cards of the spade suit}.
The total number of possible outcomes = 52 {The number of cards in the deck}.
Therefore, the probability of events A and B both, P(A ∩ B) = 4/52.
The probability that the randomly drawn card is an odd number or of spade suit is represented by P(A ∪ B), which is calculated by the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 16/52 + 13/52 - 4/52 = 25/52.
Hence, the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.
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Annoying me I’ve been at this for hours
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(5,5)
B(7,5)
C(7,-1)
D(5,−1)
Given these coordinates, what is the length of side of BC Rectangle?
Answer:
6 units
Step-by-step explanation:
5--1=6
Part 2 - Find the error(s) and solve the problem correctly.
The error is present in second step when cancelling numerator and denominator and the solution of the expression [tex](1+1/x)/(1-1/x^{2} )[/tex] is [tex]x/x-1[/tex].
Given Expression [tex](1+1/x)/(1-1/x^{2} )[/tex] and incorrect solution. and we need to identify the error and solve the expression correctly.
The expression is [tex](1+1/x)/(1-1/x^{2} )[/tex]
In the solution given the second step of cancelling 1's in numerator and denominator is wrong.
The solution which is correct is as under:
[tex](1+1/x)/(1-1/x^{2} )[/tex]
firstly take LCM in numerator and denominator
=[tex](x+1)/x/(x^{2} -1)/x^{2}[/tex]
Now we can write the expression properly.
=[tex](x+1)*x^{2} /(x^{2} -1)*x[/tex]
Power of [tex]x^{2}[/tex] to be deducted from x
=[tex](x+1)*x/(x^{2} -1)[/tex]
Now [tex]x^{2} -1[/tex] can be written as (x+1)(x-1)
=[tex](x+1)*x/(x+1)(x-1)[/tex]
(x+1) will be deducted now from numerator and denominator.
=x/(x-1)
Hence the solution of the given expression is x/(x-1).
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The answer to this question is x/x₋1
Given the expression is 1₊1/x /1₋1/x²
Take the LCM of the denominators
we get, x₊1/x / x²₋1/x²
Now multiply the expression
=x₊1/x × x²/x²₋1
=(x₊1) x²/ x(x²₋1)
(x²₋1) is in the form of (a²₋b²)=(a₊b)(a₋b)
Therefore, (x₊1)x²/x(x₋1)(x₊1)
After cancelling like terms we get the answer as:
x/(x₋1)
Hence we get the simplification answer as x/(x₋1).
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Write each square number as a product of its prime factors.
a)9
b)36
c)81
d)144
e)225
f)576
g)625
h)2401
Answer:
the answer is provided down below
Step-by-step explanation:
steps
9 - ( 1 3 x 3 x3)
36 - (3 x 2 x2x3)
81 -( 3 x 3 x 3 x 3)
144 - ( 2 x 3 x 3 x 2 x 2 x 2 x 2)
225 - ( 5 x 5 x 3 x 3)
576 -( 2 x 2 x 2 x 2 x 2 x 2 x 3 x3)
625 - ( 5 x 5 x 5 x5 )
2401 - ( 7 x 7 x 7 x 7)
Reffect shape A in the line y=-x
th
6
2
A
--5-32-10 12345
2 6
M
The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
The rule for the reflection of shape A over the line y = -x is (x, y) ⇒ (-y, -x)
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4. Write the linear equation whose graph contains the
points (-2,5) and (4,1).
Thee linear equation which contains the points (-2,5) and (4,1) is [tex]4x+6y-22=0[/tex]
Graph The points which is in the equation (-2,5) and (4,1).
Equation is basically a relationship between two or more variables and it is usually in equal to form. It is equated to find the value of variables. We can also make graphs of different equations. Linear equation is a equation whose graph looks like straight line means values comes from a relationship. It not necessarily means parallel to any axis.
The linear equation can be found by:
[tex](y-y_{1} )=(y_{2} -y_{1} )/(x_{2} -x_{1} )* (x-x_{1} )[/tex] where the coordinates are [tex](x_{1},y_{1}), (x_{2},y_{2})[/tex]
[tex](y-5)=(1-5)/(4+2)*(x+2)[/tex]
[tex](y-5)=-4/6 *(x+2)[/tex]
[tex]6y-30=-4x-8[/tex]
[tex]y=(22-4x)/6[/tex]
Hence the equation which has points (-2,5)(4,1) is [tex]4x+6y-22=0[/tex]
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Section 6.1 Add and Subtract Polynomials
Add and Subtract Monomials
In the following exercises, add or subtract the monomials.
594. 12q − (−6q)
Answer:
The simplified form of [tex]12 q-(-6 q) \text { is } 18 q[/tex].
Step-by-step explanation:
[tex]- Given: $12 q-(-6 q)$\\ - Simplify.\\ - The simplified form of $12 q-(-6 q)=(12+6) q$ i.e., $18 q$.[/tex]
Please help pleasehelp
Answer:
≥ and ≤ will both be solid dots, as it includes the number
x ≥ -7 is everything greater than -7; x ≤ 4 is everything less than 4.
to include both, you'd click -7, drag right, and stop at 4
Drag each expression or value to the correct box. Not all tiles will be used.
Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost pounds less than times the pounds he lost the first week. The third week, he lost 1 pound more than of the pounds he lost the first week.
Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than times the pounds Luke lost the first week. The second week, he lost 4 pounds less than times the pounds Luke lost the first week. The third week, he lost pound more than times the pounds Luke lost the first week.
Assuming they both lost the same number of pounds over the three weeks, complete the following sentences. Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost 3/2 pounds less than 3/2 times the pounds he lost the first week. The third week, he lost 1 pound more than 3/4 of the pounds he lost the first week.
Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than 3/2 times the pounds Luke lost the first week. The second week, he lost 4 pounds less than 5/2 times the pounds Luke lost the first week. The third week, he lost 1/2 pound more than 5/4 times the pounds Luke lost the first week.
Assuming they both lost the same number of pounds over the three weeks, complete the following sentences.
Answer:Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than 3/2 times the pounds Luke lost the first week. The second week, he lost 4 pounds less than 5/2 times the pounds Luke lost the first week. The third week, he lost 1/2 pound more than 5/4 times the pounds Luke lost the first week.Assuming they both lost the same number of pounds over the three weeks, complete the following sentences.Step-by-step explanation:
See photo, it’s got to do with Pythagoras theorem but I don’t understand. Please help
Answer:
x = 12.0 cm
Step-by-step explanation:
If we draw a line parallel to the 12 cm line right below the line x, a right-angled triangle is formed, with x as the hypotenuse and the shortest side equal to (8 - 7 = ) 1 cm.
∴ x² = 12² + 1²
⇒ x = [tex]\sqrt{12^2 + 1^2}[/tex]
⇒ x = [tex]\sqrt{144 + 1}[/tex]
⇒ x = [tex]\sqrt{145}[/tex]
⇒ x = 12.0 cm [3 s.f.]
Answer:
12.0 cm
Step-by-step explanation:
See attached image for steps. Take the figure and convert it into a rectangle and right triangle by drawing a single line. The Pythagorean Theorem can then be used.
The graph of g(x)=|x-h|+k is shown on the coordinate grid.what must be true about the signs of h and k?
The correct option is the last one. h is negative and k is positive.
What can we say about h and k?
For the absolute value function:
g(x) = |x - h| + k
We know that the vertex is on the point (h, k).
On the graph, we can see that the vertex is on the point (-2, 1), then we have:
h = -2
k = 1
So the sign of h is negative and the sign of k is positive. The correct option is the last one.
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HELP HELP HELP
Quick algebra 1 question for 15 points!
Explain the difference between slope-intercept form and point-slope form.
Answer:
slope intercept is used when you are given a point (most likely a y intercept) on the graph and a slope. The point slope is a larger formula that is used when you are given a slope and the coordinates of a point.
Step-by-step explanation:
slope intercept : y=mx+b
point slope : y-y1= m(x-x1)
What is the inverse of f(x)= 1/3x + 2?
Answer:
y^-1 = 3x - 6
Step-by-step explanation:
f(x) = 1/3x + 2
The inverse function is where we swap out y for x and x for y. f(x) represents y, so we will be replacing it with x. Then, we solve and get a new equation for the inverse of y.
x = 1/3y + 2 (subtract 2 from both sides)
x - 2 = 1/3y (multiply by 3 on both sides)
y^-1 = 3x - 6
Brainliest, please :)
Answer:
f(x) = 3x- 2
Step-by-step explanation:
The easiest way to find the inverse of a function is to replace y with x and rearrange the equation.
x = 1/3y + 2
-2 -2
______________
x-2 * 3 = 1/3y * 3
y = 3x-2
At a farmers market, Samuel bought 3 pounds of apples for x dollars per pound and 2 bags of spinach for y dollars each. The next day he returned and bought 5 pounds of apples for x dollars per pound and 3 bags of spinach for y dollars each. Which expression represents the total amount he spent at the market on both days? 8x Plus 5y 8y Plus 5x 6y + 7x 6x + 7y
Answer:
A. 8x+5y
Step-by-step explanation:
First day: 3x+2y
Second day: 5x+3y
Add both expressions together.
(3x+2y)+(5x+3y) =
= 3x+2y+5x+3y=8x+5y
Hope this helps!
If not, I am sorry.
Total area =
Help please thanks
The total area of the given right trapezoidal prism is gotten as; A = 2592 sq.units
How to find the area of a right trapezoidal prism?The formula to find the Surface Area of a Trapezoidal Prism is;
A = h(b + d) +l(a + b + c + d) unit square.
Where;
h = height
b and d are the lengths of the base
a + b + c + d is the perimeter
l is length
Thus;
A = 12(25 + 15) + 32(13 + 25 + 13 + 15)
A = 480 + 2112
A = 2592 units square
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Part B
Question
Use an online graphing tool to find the equation that best models the data in the table.
Enter the correct equation in standard form. Round parameters to the nearest tenth.
Answer:
y=17.2x²-226.3x+2184.5
Let f(x)=1/x+x, where is a nonzero number.what is the product of all the values of a, such that f(a)=f(2a)?
The product of all the values of a, such that f(a)=f(2a) is -1/2
Functions and expressionsGiven the function below;
f(x)=1/x + x
f(a) = 1/a + a
f(2a) = 1/2a + 2a
If f(a) = f(2a), hence;
1/a + a = 1/2a + 2a
Collect the like terms
1/a - 1/2a = 2a - a
2-1/2a = a
1/2a = a
Cross multiply
2a² = 1
a² = 1/2
a = ±√1/2
The values of a are √1/2 and -√1/2
Product = -√1/2 * √1/2
Product = -1/2
Hence the product of all the values of a, such that f(a)=f(2a) is -1/2
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An amount of money 960gh was contributed by 80 students. If 714gh was contributed equally by 68 girls and the remaining amount was also contributed equally by boys. How much did each
i. Girl contribute
ii. Boy contribute
Each girl contributed 10.50gh
Each boy contributed 20.50gh
These are further explained and computed below:
The measure of central tendency being tested here is the mean, in other words, the resulting average when the total amount contributed by girls or boys is divided by the number of girls or boys.
The fact that 68 of the 80 students are girls means that the remaining 12 students are boys because 80 minus 68 gives 12.
each girl's contribution=total girls' contribution/number of girls
each girl's contribution=714/68
each girl's contribution=10.50gh
Total boys' contribution=total contribution-total girls' contribution
Total boys' contribution=960-714
Total boys' contribution=246
each boy's contribution=Total boys' contribution/number of boys
each boy's contribution=246/12
each boy's contribution=20.50gh
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Each girl contributed 10.5gh and each boy contributed 20.5gh
How to determine the amount contributed?The given parameters are:
Total amount = 960gh
Number of students = 80
Amount contributed by girls = 714gh
Number of girls = 68
The amount contributed by each girl is:
Girl = Amount contributed by girls/Number of girls
This gives
Girl = 714gh/68
Evaluate
Girl = 10.5gh
The amount contributed by each boy is:
Boy = (Total - Amount contributed by girls)/(Total students - Number of girls)
This gives
Boy = (960gh - 714gh)/(80 -68)
Boy = 246gh/12
Evaluate
Boy = 20.5gh
Hence, each girl contributed 10.5gh and each boy contributed 20.5gh
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use the quadratic formula to solve the equation : 10x2 +11x=1
Answer:The answers are 0.084 or -1.184
Step-by-step explanation:
The solution is in the attached file
Find x A. 212√2 B. 212–√ C. 213√2 D. 7
The value of x in the triangle is (d) 7
How to solve for x?The complete question is in the attached image.
From the attached image of the triangle, we can see that the triangle is a right triangle, and x can be solved using the following sine function
[tex]\sin(45) = \frac{x}{7\sqrt 2}[/tex]
Evaluate sin(45)
[tex]\frac 1{\sqrt 2} = \frac{x}{7\sqrt 2}[/tex]
Solve for x
[tex]x = \frac{7\sqrt 2}{\sqrt 2}[/tex]
Divide
x = 7
Hence, the value of x in the triangle is (d) 7
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a cheerleading team plans to sell t-shirts as a fundraiser. the teams goal is to make profit of at least $1248. the profit on each t-shirt sold is $6.50. The teams goal is written as a inequality shown below.
6.5t>1 2 4 8 where t=number of t-shirts sold.
The minimum number of shirt they will sell to make the given profit is 192 shirts
Inequality expressionInequalities are equations not separated by an equal sign.
If a cheerleading team plans to sell t-shirts as a fundraiser and the teams goal is to make profit of at least $1248 with each t-shirt sold at $6.50, then the equation required is;
6.50t ≥ 1246
Divide both sides by 6.50
6.50t/6.50 ≥1246/6.5
t ≥ 192
Hence the minimum number of shirt they will sell to make the given profit is 192 shirts
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need rn!
If a point C is inside AVB, then mAVC + mCVB = ______.
Answer:
Hi sorry if the reply is late! The answer is
OPTION (B)m∠AVC+m∠CVB=m∠AVB
Step-by-step explanation:
Given: It is given that a point C is inside ∠AVB and ∠AVC=39° and ∠CVB=23°.
From the figure, we can see that C is inside ∠AVB, therefore ∠AVB is divided into two parts that is ∠AVC and ∠CVB, thus
m∠AVC+m∠CVB=c
⇒39°+23°=62°
16) Find the lateral area of the regular pyramid. 5 cm www 24 cm
Answer:
LA = 624 cm²
Step-by-step explanation:
h² = 5² + 12²
h = 13
LA = 4 × bh/2
LA = 4 × (24 cm)(13 cm)/2
LA = (48 cm)(13 cm)
LA = 624 cm²
Graph the system below and write its solution.
y = -1/2x+2
3x+y=-3
Note that you can also answer "No solution" or "Infinite
The graph of the system can be seen below, there we can see that the solution is (-2, 3).
How to solve a system graphically?To do so, we just need to graph both equations on the same coordinate axis and see where the graphs intercept.
The interceptions will be the solutions of the system of equations.
Here we have the system:
y = (-1/2)*x + 2
3x + y = -3
The graph can be seen below, where the green line is the first equation, and the blue line is the second equation.
On the graph, you can see that the lines intersect at the point (-2, 3), so that is the solution of the system.
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Price of an article is 400 and sold with discount including 13% vat at 339 find discount rate
Solve a) with Substitution and b) with Elimination (check attached picture)
a) Solve the first equation for [tex]x[/tex].
[tex]x + 3y = 7 \impiles x = 7 - 3y[/tex]
Substitute this into the second equation and solve for [tex]y[/tex].
[tex]2x + 4y = 12 \implies 2(7 - 3y) + 4y = 12 \\\\ \implies 14 - 6y + 4y = 12 \\\\ \implies -2y = -2 \\\\ \implies \boxed{y=1}[/tex]
Solve for [tex]x[/tex].
[tex]x = 7 - 3y \implies x = 7-3\times1 \\\\ \implies \boxed{x = 4}[/tex]
b) Eliminate [tex]y[/tex] by combining the two equations in appropriate parts, namely
[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3)[/tex]
and solve for [tex]x[/tex].
[tex]2 (2x - y) + (3x + 2y) = 2\times3 + (-3) \implies 4x - 2y + 3x + 2y = 6 - 3 \\\\ \implies 7x = 3 \\\\ \implies \boxed{x = \dfrac37}[/tex]
Solve for [tex]y[/tex].
[tex]2x - y = 3 \implies 2\times\dfrac37 - y = 3 \\\\ \implies \dfrac67 - y = 3 \\\\ \implies -y = \dfrac{15}7 \\\\ \implies \boxed{y = -\dfrac{15}7}[/tex]
A father is 38 years old. his sons are 13 and 5 years old, and his daughter is 8 years old. In how many years will the father be the same age as his children put together?
Answer:
6 years
Step-by-step explanation:
So each person's age can be represented as a linear equation, since each year our age increases by 1. It can be represented in the slope-intercept form: y=mx+b. The slope in this case is going to be 1, since the time is going to be years, and each year everyone's age goes up by 1 (of course if you're still alive...) and y-intercept in this case represents their current age.
So the father can be represented as: y=x+38
The sons can be represented as: y = x+13 and y=x+5
The daughter can be represented as: y=x+8
So adding up all his children you get:
(x+13)+(x+5)+(x+8)
This gives you the equation:
3x+26
Now set this equal to the father's age to solve for x (in this context it's years)
3x+26=x+38
Subtract from both sides
2x+26=38
Subtract 26 from both sides
2x=12
Divide both sides by 2
x=6
So in 6 years the father will be the same age as his children put together
The Eiffel Tower in Paris, France is 1063 feet tall. If you took an elevator 3/4 the way up the tower, how far from the ground would you be in feet?
Answer: 797 feet 3 inches
Step-by-step explanation:
[tex]\frac{3}{4} *1063=\frac{3189}{4} =797.25[/tex]
what is the area of a rectangle whose length is 3x and breadth is 2x
Answer:
Your answer is 6x
Step-by-step explanation:
Given,
length(l) = 3x
breadth(b) = 2x
area of a rectangle(A) = ?
Now,
A = l*b
A = 3x*2x
A = 6x ans.
Hope its helpful!
Please mark me as brainlist.
Answer:
6 x^2
Step-by-step explanation:
Area = Length * Breadth
= 3x * 2x = 6x^2
If (x+ 1) is a factor of the polynomial x³ + px² + x + 6 = 0. Find p.
Answer:
p=4
Step-by-step explanation:
plug x=-1 into the polynomial with the unknown
(-1)³+p(-1)+(-1)+6=0
-1-p-1+6=0
-p+4=0
p=4