According to the question, to calculate the probability of the event which states that to draw a card from the standard deck but the condition is getting either ace or heart.
The total number of the playing cards are [tex]52[/tex]
And total number of heart cards are [tex]13[/tex]
And total number of ace cards are [tex]4[/tex]
Therefore, the total number of favorable outcomes in which either heart or ace can be drawn: [tex]4+13[/tex]
As per question, the probability can be written as:
P(h or a) = P(a) + P(h) - P( a and h)
[tex]= \frac{4}{52} +\frac{13}{52} -\frac{1}{52} = \frac{16}{52} = \frac{4}{13} = 30.8%[/tex]
Hence, the probability of getting either an ace or heart card is [tex]\frac{4}{13}[/tex].
The given event is not mutually exclusive because it has [tex]30.8[/tex] percent which is not close to tenth of a percent.
What are mutually exclusive events?
Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.
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A restaurant has 10 booths that will seat up to 4 people each. If 20 people are seated in booths, and NO booths are empty, what is the greatest possible number of booths that could be filled with 4 people?
Answer: 3
Step-by-step explanation:
A function g satisfies g(5) = 3 and g(3) = 0, and a function h satisfies h(3) = -2 and h(0) = 5. what is the value of h(g(3))?.
A function exists described as a relation between a set of inputs containing one output each. The value of h(g(3)) is 5.
What is meant by function?
A relationship between a group of inputs and one output is referred to as a function.
In plain English, a function is an association between inputs in which each input is connected to precisely one output.
A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Where, g(3) = 0
To get h, replace g(3) with 0 in the requested equation (0).
Since h(0) = 5 according to the question, your final response is 5.
Therefore, the value of h(g(3)) is 5.
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What is an equation of the circle with center (5,-2) and radius 8 ? Check your answer.
The equation of the circle with radius 8 and center at (5 , -2) is (x - 5)^2 + (y + 2)^2 = 64.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius 8 and center at (5 , -2), substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (5 , -2)
r = 8
(x - 5)^2 + (y - -2)^2 = 8^2
(x - 5)^2 + (y + 2)^2 = 64
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In the stained glass window design, all of the small arcs around the circle are congruent. Suppose the center of the circle is point O .
What is the measure of each of the small arcs?
The measure of each of the small arcs of the circled glass stained window is 45°.
Congruent in circle:
Circles having the same radii are said to be congruent of one another.
For example,
When two circles are congruent, we can also say that they have the same area and circumference. Thus they can also be said to be equal circles.
Given,
In the stained glass window design, all of the small arcs around the circle are congruent. Suppose the center of the circle is point O.
Here we need to find the measure of each of the small arcs.
We know that.
Congruent circles can be defined as circles which are having the same or equal radii.
So, based on this the circle we need to divided it as equal radius arcs.
We know that, the measurement of the full circle is 360°.
So, here we have to divide it by 8.
Then we have each arc as,
=> 360°/8
=> 45°.
Therefore, each arc has the measurement of 45°.
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Ab and bc form a right angle at their point of intersection, b. if the coordinates of a and b are (14, -1) and (2, 1), respectively, the y-intercept of ab is is y= and the equation of bc
Answer:
Step-by-step explanation:
to find the y intercept of AB, first find the slope of AB: m=(1-(-1))/(2-14)=-1/6
the equation of line AB is y=-(1/6)x+b
use either of the given two points to find out b: 1=(-1/6)*2+b => b=4/3
BC is perpendicular to AB, so the slope of BC is the negative reciprocal of the slope of AB, therefore, the slope of BC is 6
Equation of BC is y=6x+b
find out b by using the coordinates of point B: 1=6*2+b => b=-11
the equation of BC is: y=6x-11
the x coordinate of point C: 13=6*x -11 =>x=4
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Answer: Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4
Step-by-step explanation:
Take sin of 60 to calculate side opposite to angle 60
sin 60=[tex]\frac{\sqrt{3} }{2}[/tex]
cos 60=1/2
7.2 / 1/2=
7.2 * 2=14.4
[tex]\frac{\sqrt{3} }{2}[/tex]*14.4=
[tex]\frac{14.4\sqrt{3} }{2}[/tex]=7.2[tex]\sqrt{3}[/tex]
The hypotenuse:
[tex](\frac{\sqrt{3} }{2})^2[/tex]+(1/2)^2=
3/4 + 1/4 = 1
1 * 14.4 =14.4
Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4
Step-by-step explanation:
The 30-60-90 triangle is one of the most important trigonometry concept you will learn throughout your secondary schooling.
Attached below is a triangle that you should memorize for easy practice. The way this triangle is formed can be proven trigonometrically and/or with the unit circle, but that's not what this question is asking for.
When comparing the numbers on the attachment and your question, we can generate that the side 7.2=x, because the side with the 60 degree angle and right angle contains the variable x.
Since we have x now, all we would have to do is to plug in the x values and solve the question.
The hypotenuse (longest side of the triangle) = 2x = 2(7.2) = 14.4
The side opposite to the 60 degree angle (left most side)= [tex]x\sqrt{3}[/tex] = [tex]7.2\sqrt{3}[/tex] = 12.6
I hope this helped!
The probabilities of four events are shown. List them in order from least to greatest.6/13,3 out of 9,41%,0.2
Answer:
0.2, 3 out of 9, 41%, 6/13
Step-by-step explanation:
6/13 = 0.46
3 out of 9 = 3/9 = 0.33
41% = 0.41 (change percent to decimal by dividing it by 100)
0.2
Now compare:
Least to greatest: 0.2, 3 out of 9, 41%, 6/13
b. Reasoning Could you have used elimination in another way? Explain.
x-2y+3z = 12
2x-y-2z = 5
2x+2y-z = 4
So we are given with three different equations,
[tex]$$\begin{aligned}&x-2 y+3 z=12 \rightarrow(1) \\&2 x-y-2 z=5 \rightarrow(2) \\&2 x+2 y-z=4 \rightarrow(3)\end{aligned}$$[/tex]
We will convert the individual equations into matrices,
[tex]$$\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\2 & -1 & -2 & 5 \\2 & 2 & -1 & 4\end{array}\right]$$[/tex]
[tex]\begin{aligned}&R_2 \leftarrow R_2-2 \times R_1 \\&=\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\0 & 3 & -8 & -19 \\2 & 2 & -1 & 4\end{array}\right]\end{aligned}[/tex]
[tex]\begin{aligned}&R_3 \leftarrow R_3-2 \times R_1 \\&=\left[\begin{array}{rrr|c}1 & -2 & 3 & 12 \\0 & 3 & -8 & -19 \\0 & 6 & -7 & -20\end{array}\right] \\&R_2 \leftarrow R_2 \div 3 \\&=\left[\begin{array}{ccc|c}1 & -2 & 3 & 12 \\0 & 1 & -2.6667 & -6.3333 \\0 & 6 & -7 & -20\end{array}\right]\end{aligned}[/tex]
[tex]\begin{aligned}&R_1 \leftarrow R_1+2 \times R_2 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 6 & -7 & -20\end{array}\right] \\&R_3 \leftarrow R_3-6 \times R_2 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 9 & 18\end{array}\right]\end{aligned}[/tex][tex]\begin{aligned}&R_3 \leftarrow R_3 \div 9 \\&=\left[\begin{array}{ccc|c}1 & 0 & -2.3333 & -0.6667 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 1 & 2\end{array}\right] \\&R_1 \leftarrow R_1+2.3333 \times R_3 \\&=\left[\begin{array}{ccc|c}1 & 0 & 0 & 4 \\0 & 1 & -2.6667 & -6.3333 \\0 & 0 & 1 & 2\end{array}\right]\end{aligned}[/tex]
[tex]\begin{aligned}&R_2 \leftarrow R_2+2.6667 \times R_3 \\&=\left[\begin{array}{ccc|c}1 & 0 & 0 & 4 \\0 & 1 & 0 & -1 \\0 & 0 & 1 & 2\end{array}\right]\end{aligned}[/tex]
[tex]i. e.$$\begin{aligned}&x=4 \\&y=-1 \\&z=2\end{aligned}$$[/tex]
Solution By Gauss elimination method is,
[tex]$x=4, y=-1$ and $z=2$[/tex]
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x + 2y = 15
3x -15 = -6y
can you also right if it has a solution/no solution/many solution!
and show the steps pls tyy
Given equation x + 2y = 15 and 3x -15 = -6y are real numbers so the equation has a solution.
Some equations have no solutions. In these equations, there is no value for the variable that makes the equation true. You can tell that an equation has no solutions if you try to solve the equation and get a false statement.
We have been given that
x + 2y = 15 ..........(1)
3x -15 = -6y ..........(2)
Multiply equation (1) with 3.
3(2y+x)=5
6y+3x=-15
Subtract equation (1) from equation (2)
0=15
Instead of 6y+3x=-15, 3x-15=-6y becomes 6y+3x=15. So, these 2 equations are saying the same thing (this is the first equation times 3), and therefore the solution is all real numbers.
Hence, The equation has a solution since the given values of x + 2y = 15 and 3x -15 = -6y are real numbers.
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a businessman earns a basic salary of r1000 plus r500 commission for every item he sells
5.1write a function for calculaling the salesman's salary (y) if he sells x items
The Salesman's salary is modeled by the linear equation:
y = $1000 + $500*x
How to write a function for the salesman's salary?We know that the businessman earns a basic salary of $1000 (it does not depend on how many items he sells) and $500 for each item he sells as a commission.
Then, if we define x as the number of items he sells, the amount he gets in commissions is: x*$500
Then the equation for his total salary, y, in terms of x which is defined above is:
y = $1000 + $500*x
That is the linear equation we wanted to write.
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Write an example from daily life that uses each type of real number.
rational numbers
Write an example from daily life that uses rational numbers .
Real numbers that may be expressed as p/q, where p, q are integers, and q 0, are rational numbers. The money we have is a rational number. If we spend some sum out of it, it is subtraction of rational number.The running race involves rational numbers if you're an athlete.Rational numbers include the following:the distance runthe time needed to complete the distance,the number of competitors placing first, second, or thirdthe number of heartbeats you take per minute.We use fractions to represent taxes.If you split a pizza or any other food.When you finish a piece of your work, you indicate that you have done half, or 50%.Loan and mortgage interest rates.Savings account interest.To learn more about rational numbers, refer:
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Find the distance from the line to the given point.
y=-3,(5,2)
The distance from the line y = -3 to the point (5,2) is 5 units.
Distance from the line ax+by+c=0 from the point (m,n) is calculated by
[tex]distance=\frac{|am+bn+c|}{\sqrt{a^{2} +b^{2} } }[/tex]
In the given question
the equation of the line is [tex]y=-3[/tex] ⇒ [tex]y+3=0[/tex]
equation of line becomes 0.x+1.y+3=0
given the point (5,2)
Substituting the values in the distance formula we get
[tex]d=\frac{0*5+1*2+3}{\sqrt{0^{2} +1^{2} } }[/tex]
[tex]=\frac{2+3}{1} \\ \\ =\frac{5}{1} \\ \\ =5[/tex]
Therefore , the distance from the line y = -3 to the point (5,2) is 5 units.
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What is the area and perimeter of a circle (-4,2) (-3,4)
Step-by-step explanation:
Let radius of circle is r=18 units
Perimeter of full circle is given by 2πr
Thus, perimeter of three quarters circle is given by,
( ¾ × 2πr) + (2 × r)
The perimeter of this "circle" would be:
( ¾ × 2 × π × 18) + (2 × 18) = 27π + 36 ≈ 120.78 m
PLEEEEAAASEEE HELPPPP.
F: a₁ = 15 and ag = -15
Find a30
yellow
Answer:
a30= -15
Step-by-step explanation:
If x is a real number, for what values of x is the equation (3 x-6)(x-2)⁻¹=3 true?
Answer:
all real x other than 2
Step-by-step explanation:
[tex]\frac{3x-6}{x-2}=3 \\ \\ 3x-6=3x-6[/tex]
Thus, the equation is true for all x in its domain, which is all real x other than 2.
Mr. Drew wants to build a square sandbox with an area of 81 square feet. What is the total length of wood Mr. Drew needs to make the sides of the sandbox?
Answer: 36 feet of wood
Step-by-step explanation:
P=perimeter. P=total length of wood
s= side length. A=area
A=s^2
81=s^2
s^2=9^2
s=9
P=4s
P=4(9)
P=36 feet of wood
Answer:
P = 36 ft
Step-by-step explanation:
The given length is,
→ a = ?
Formula we use,
→ A = a²
Now the length of one side is,
→ A = a²
→ a² = 81
→ a = √81
→ [ a = 9 ]
The total length of wood needed is,
→ P = 4a
→ P = 4 × 9
→ [ P = 36 ]
Hence, the total length is 36 ft.
Quadrilateral PQRS was dilated to form quadrilateral WXYZ.
a. Is the dilation from P Q R S to W X Y Z an enlargement or reduction?
A reduction is a dilation from ▢PQRS to ▢WXYZ.
What do we mean by a Quadrilateral?A quadrilateral is a four-sided polygon with four edges (sides) and four corners in geometry (vertices). The word comes from the Latin words Quadri, a variant of four, and latus, which means "side." In analogy to other polygons, it is also known as a tetragon, which is derived from the Greek words "tetra" which means "four" and "gon" which means "corner" or "angle" (e.g. pentagon). Because "gon" means "angle," it is also known as a quadrangle or 4-angle. ▢ABCD denotes a quadrilateral with the vertices A, B, C, and D.According to the given figure:
▢WXYZ is smaller than ▢PQRS.Therefore, a reduction is a dilation from ▢PQRS to ▢WXYZ.
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The equation of a line is ax + by = c. If the x value of some point on the line is d, what is the full co-ordinate of the point, in terms of a, b, c, d?
The equation of a line is ax + by = c.
full co-ordinate of the point, in terms of a, b, c, d is (d,(c-ad)/b)
equation of a line is ax + by = c
x=d
put x=d in the equation of line
ad + by = c
by = c-ad
y=(c-ad)/b
full co-ordinate of the point, in terms of a, b, c, d is (d,(c-ad)/b)
The phrase equation and its cognates in other languages can also have subtly extraordinary meanings; as an example, in French an équation is described as containing one or more variables, even as in English, any well-shaped components together with two expressions related with an equals sign is an equation.
fixing an equation containing variables includes figuring out which values of the variables make the equality real.
The variables for which the equation must be solved are also referred to as unknowns, and the values of the unknowns that satisfy the equality are referred to as answers of the equation.
There are two kinds of equations: identities and conditional equations. An identity is authentic for all values of the variables. A conditional equation is simplest genuine for particular values of the variables
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y=2x-3
x+y=18
solve for x
solve for y
X= ?
Y=?
Answer:
x=7, y=11
Step-by-step explanation:
Using simultaneous equations we can sub y in equation 1 into equation 2.
Equation 1. y=2x-3
Equation 2. x+y=18
Since y=2x-3 we can replace it so that
2'. x+2x-3=18
Now simplify
= 3x-3=18
Add 3 onto both sides to undo the subtraction of 3 so that,
3x=21
Now divide both sides by three to undo the multiplication of 3 so that,
x=7
Now sub in x (which is 7) into one of the equations to find y
7+y=18
To undo the five, subtract 7 from both sides so that
y=11
Marcel Park is weeding the rectangular vegetable garden. The garden has an area of 599.5 square feet. If the garden is 22 feet wide,how long is the garden? Justify your procedure!
Answer:
27.25 feet long
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
The area is 599.5 square feet and it is 22 feet wide. So in order to find the area we have to multiply the width (22 feet wide) and the legth (unknow number which will stand for "x"). Since we area multiplying the width and legth we need to do the inverse operation which is dividing. We didvide the area 599.5 by the width 22 to get 27.25 feet long.
22x = 599.5
----- -------- <------ Fraction bar/divide
22 22
x = 27.25
Check:
When a number is next to parenthesis it means to multiply the 2 numbers.
22 (27.25) = 599.5
599.5 = 599.5
True statement.
Points!!!!!!!!!!!!!!!!
how to show - 2by3 and 1by2 on the number line
Answer: Hope it help
Step-by-step explanation:
Find the next term in each sequence. 1,5,25,125, . . . . . .
Answer:
Just multiply each by 5
Step-by-step explanation:
5x125= 625
explanation:
multiply the previous term by 5
The midpoint of AB is M(-3,0). If the coordinates of A are (1,-4), what are the coordinates of B?
Applying the midpoint formula, the coordinates of B are: (-7, 4).
How to Apply the Midpoint Formula?The midpoint formula is:
M(x, y) = [(x2 + x1)/2, (y2 + y1)/2]
Given:
M(x, y) = (-3, 0)
A(x1, y1) = (1, -4)
B(x2, y2) = (?, ?)
Plug in the values into the midpoint formula:
M(-3, 0) = [(x2 + 1)/2, (y2 + (-4))/2]
Isolate each coordinate
-3 = (x2 + 1)/2
-6 = x2 + 1
-6 - 1 = x2
x2 = -7
0 = (y2 - 4)/2
0 = y2 - 4
y2 = 4
Therefore, applying the midpoint formula, the coordinates of B are: (-7, 4).
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A farmer has 180 bushels of to sell at roadside stand. sells an average of 16 3/5 each day. Represent the total change in the number of bushels has for sale after 6 days
The total change is 82.5 (or 82 and 2/5) bushels remaining and has sold 82.25 (or 81 and 2/5) bushels
He has sold (16+3/5) bushels/day x 6 days
=(16 x 6 ) + (3 / 5 * 6)
= 96 + 6/5
= 97 + 1/2
= 97.5
The change in the number of bushels is 180 – 97.5 = 82.5 or 82 and 2/5 bushels. A measure of capacity equal to 8 gallons (equivalent to 36.4 litres), used for corn, fruit, liquids, etc. A measure of capacity equal to 64 US pints (equivalent to 35.2 litres), used for dry goods.
Hence , the total change in 82.5 (or 82 and 2/5) bushels remaining and has sold 82.25 (or 81 and 2/5) bushels.
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please help me this is so confusing. I need help.
Answer:
Step-by-step explanation:
OK, so you see how its like 4/10 right? (not four tenths but ya know four on top and ten underneath)
Look how for your Y axis it goes: 2, 4. 6, 8, 10
what comes after ten by counting by twos? 12!
Also the correct equation is; Y = K X ( Y =_ x) ( blank is whatever your constant of proportionality is.
Thank you Pre-Algebra\
Signed~ Earl
Please Help with problem 23 Algebra 1, in the attachment.
Answer:
Step-by-step explanation:
the correct answer would be -5/-1=|6x|
The absolute value equation for each of the graphs are |x + 3| = 2 and |x - 4| = 1 respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An inequality shows the non equal comparison of numbers and variables.
A) For the inequality shown, the midpoint is [(-1) + (-5)]/2 = -3. The distance from each of the endpoint to the midpoint is 2 units (i.e. from -1 to -3 or from -5 to -3). Hence:
Absolute inequality is:
|x - midpoint| = distance from endpoint to midpoint
This gives:
|x - (-3)| = 2
|x + 3| = 2
B) For the inequality shown, the midpoint is [3 + 5]/2 = 4. The distance from each of the endpoint to the midpoint is 1 units (i.e. from 3 to 4 or from 5 to 4). Hence:
Absolute inequality is:
|x - midpoint| = distance from endpoint to midpoint
This gives:
|x - 4| = 1
The absolute value equation for each of the graphs are |x + 3| = 2 and |x - 4| = 1 respectively.
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Spaghettios wraps all their cans in a paper label. One Spaghettios can is 8 inches tall with a diameter of 4 inches. How many square centimeters of paper would Spaghettios need to wrap 12 of their cans.
Answer:
384
Step-by-step explanation:
8x4=32 32x 12 cans=384 sq centimeters
You are organizing your high school’s sports banquet. The banquet hall rental is $250. In addition to this one-time charge, the meal will cost $7 per plate. Let x = the number of people who attend.
Part a: Write an equation that represents the total cost C.
Part b: Write an equation that represents the average cost A per person.
Part c: Use the graph of the model shown below to estimate the number of people who must attend before the average cost drops to $15 per meal.
Part d: Describe what happens to the average cost as the number of people who attend increases.
The required answers are-
Part a: The equation that represents the total cost C is C = 250 + 7x.
Part b: The equation that represents the average cost A per person is A = 250 + 7 = 257.
Part c: The estimate number of people who must attend before the average cost drops to $15 per meal is 25.
Part d: The average cost keeps on decreasing exponentially and then becomes straight.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now it is given that,
Rental of banquet hall = $250
One time charge for meal = $7 per plate
x = the number of people who attend.
Part a: The equation that represents the total cost C
Since there are x people in the banquet
So, number of plates = x
Thus, Total One time charge for meal = 7x
So Total Cost = Rental of banquet hall + Total One time charge for meal
⇒ C = 250 + 7x
this is the equation that represents the total cost C
Part b: The equation that represents the average cost A per person
Putting x = 1 in the above equation of total cost we get,
A = 250 + 7 = 257
this is the equation that represents the average cost A per person
Part c: The estimate number of people who must attend before the average cost drops to $15 per meal
From the graph it is seen that there are 25 people who must attend before the average cost drops to $15 per meal.
Part d: what happens to the average cost as the number of people who attend increases.
The average cost keeps on decreasing exponentially and then becomes straight.
The required answers are-
Part a: The equation that represents the total cost C is C = 250 + 7x.
Part b: The equation that represents the average cost A per person is A = 250 + 7 = 257.
Part c: The estimate number of people who must attend before the average cost drops to $15 per meal is 25.
Part d: The average cost keeps on decreasing exponentially and then becomes straight.
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Why is a simulation better the more times you perform it?
Answer:
Step-by-step explanation:
so you get a better perspective of it
