Which of the pairs of events below is mutually exclusive?
Select the correct answer below:
drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards
drawing a 2 and drawing a 4 with replacement from a standard deck of cards
drawing a heart and then drawing a spade without replacement from a standard deck of cards
drawing a jack and then drawing a 7 without replacement from a standard deck of cards
Answer:
Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.
Step-by-step explanation:
Given four pair of events:
1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards
2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards
3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards
4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards
To find:
Which of the pairs is mutually exclusive?
Solution:
First of all, let us have a look at the definition of mutually exclusive events.
Mutually exclusive events do not have any case in common.
In other words, two events are known as mutually exclusive when both the events can not occur at the same time.
Now, let us have a look at the given options one by one:
1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.
We know that there is only one ace of spades in a standard deck.
Therefore, the two events can not occur one after the other, so these are mutually exclusive events.
2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards.
The two events can occur one after the other, so these are not mutually exclusive.
3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards.
Separate cards are drawn one after the other, so not mutually exclusive.
4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards.
Separate cards are drawn one after the other, so not mutually exclusive.
If 12 roses cost 30.4 how much will 18 roses cost?
Answer:
45.6
Step-by-step explanation:
We can write a proportion to solve
12 roses 18 roses
------------ = -----------
30.4 x
Using cross products
12x = 30.4 * 18
12x=547.2
Divide each side by 12
12x/12 = 547.2/12
x = 45.6
Which series of transformations would result in a figure that is congruent to the triangle ABC?
rotation of 180' clockwise about the origin and then dilation with a scale factor of -1, centered at the origin
rotation of 180' clockwise about the origin and then dilation with a scale factor of 2, centered at the origin
reflection across the line y ox and then dilation with a scale factor of -3, centered at the origin
translation 3 units to right and then dilation with a scale factor of 3, centered at the origin
Answer: rotation of 180' clockwise about the origin and then dilation with a scale factor of -1, centered at the origin
Step-by-step explanation:
Two triangles are congruent if all the corresponding angles are equal, and if the corresponding side lengths are equal.
Now, this means that if we have a given triangle, and we apply a dilation/contraction, then the resultant triangle will have different side lengths than the initial triangle, then those two triangles can not be congruent.
So we can already discard all the options with dilations.
Now, remember how the dilation works.
If we have a point that is at a distance L of the origin, and we do a dilation of scale factor K centered at the origin, then the new distance of the point and the origin will be K*L.
Notice that if the scale factor is equal to 1, then there is no change.
In the options, we have one where the scale factor is -1.
The minus sign means that will cause the enlargement to appear on the other side of the center of enlargement. But the scale factor still is of absolute value 1, so it will not change anything.
Then the only option that not dilates the triangle is:
Rotation of 180' clockwise about the origin and then dilation with a scale factor of -1, centered at the origin
So this is the only transformation that results in a figure congruent to the triangle ABC
If a Ferris wheel takes 45 seconds to make a complete rotation, how many rotations will it complete in 3 hours?
Answer:240 rotations
Step-by-step explanation: 1 rotation/45 seconds * 60 seconds / minute * 60 minutes / hour * 3 hours = 3600*3/45 = 240 rotations
What is the equation in slope-intercept form of the line that passes through the points (−12, −4) and (4, 8)?
A. y = −43 − 20
A. , y = −43 − 20
B. y = 43 − 12
B. , y = 43 − 12
C. y = −0.75 − 13
C. , y = −0.75 − 13
D. y = 0.75x +5
D. , y = 0.75x +5
Answer:
Choice D. [tex]y = 0.75\, x + 5[/tex].
Step-by-step explanation:
The general equation for the slope-intercept form of a line in a cartesian plane is [tex]y = m\, x + b[/tex], where:
[tex]m[/tex] is the slope of the line, and[tex]b[/tex] is the [tex]y[/tex]-intercept of the line. (The [tex]y\![/tex]-intercept of a line in a cartesian plane is the [tex]y\!\![/tex]-coordinate of the point where the line intersects the [tex]\! y \![/tex]-axis.)Start by finding the value of [tex]m[/tex]. The slope of a line is equal to its rise-over-run. For the two points in this question:
The "rise" is the [tex]y[/tex]-coordinate of the first point minus that of the second: [tex]\text{rise} = (-4) - 8 = -12[/tex].The "run" is the [tex]x[/tex]-coordinate of the first point minus that of the second. The order of these two points should stay the same: [tex]\text{run} = (-12) - 4 = -16[/tex].Calculate the slope of this line:
[tex]\displaystyle m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{-12}{-16} = 0.75[/tex].
The equation of the line becomes:
[tex]y = \underbrace{0.75}_{m}\, x + b[/tex].
Substitute the coordinates of either of the two points to find [tex]b[/tex]. For example, for the first point [tex](12, -4)[/tex], substitute in the following:
[tex]x = -12[/tex], and[tex]y = -4[/tex].The equation becomes:
[tex]-4 = 0.75 \times (-12) + b[/tex].
Solve for the value of [tex]b[/tex]:
[tex]b = 5[/tex].
Hence, the slope-intercept form of this line shall be:
[tex]y = 0.75\, x + 5[/tex].
If the quarter note equals one beat, how many beats would this note be worth?
Answer:
4 beats
Step-by-step explanation:
that is a whole note and 4 quarters are equal to one whole
What line is perpendicular to y=2/7x+11/7 travel through (-3,8)
Answer:
y=−7/2x−5/2
Step-by-step explanation:
Find the negative reciprocal of the slope of the original line and use the point-slope formula
y−y1=m(x−x1) to find the line perpendicular to y=2/7x+11/7.
Subtract the equation
-7 - 12 =
Answer:
-19
Step-by-step explanation:
Answer:
-19
Step-by-step explanation:
Solve the following equation algebraically. Show your work.
6=x+23
Answer: 23+x=6
-23 -23
1x/1 -17/1
x=-17
Step-by-step explanation:
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-6*x-(23)=0
Step by step explanation :
Pulling out like terms
Pull out like factors :
-6x - 23 = -1 • (6x + 23)
Solving a Single Variable Equation:
2.1 Solve : -6x-23 = 0
Add 23 to both sides of the equation :
-6x = 23
Multiply both sides of the equation by (-1) : 6x = -23
Divide both sides of the equation by 6:
x = -23/6 = -3.833
Therfor the answer is : x = -23/6 = -3.833
Yousef typed a 36-word paragraph in 23 minute. What is his typing speed, in words per minute?
Answer:
1.5652173913 words per minute.
Step-by-step explanation:
When you divide 36 words/ 23 minutes, you get 1.5652173913.
What are the slopes of the perpendicular lines?
1: y=-5/2x-8
2: y=5x
3: y=3x-8
Answer:
1. 2/5
2. -1/5
3. -1/3
Step-by-step explanation:
the parpendicular slope is found by taking the original slope and finding the opposite reciprocal. so just flip the slope and make it the opposite sign
-5/2 ---> 2/5
+5/1 ---> -1/5
+3/1 ---> -1/3
If we double the sum of the numbers x and -21, we get the number -100. What is x?
Step-by-step explanation:
2{x + (-21) }= –100
= 2x – 42 = –100
= 2x= –100 + 42
= 2x= –58
= x = –58/2
x= –29
Multiply -2.6 (-3.4)=
Answer:
8.84
Step-by-step explanation:
Answer:
8.84
Step-by-step explanation:
Marc eats an egg sandwich for breakfast and a big burger for lunch every day. The egg sandwich has 250 calories. If Marc has 5,250 calories for breakfast and lunch for a week in total, how many calories are in one big burger.
Answer:
21 calouris
Step-by-step explanation:
5250/250
Answer:
500
Step-by-step explanation:
250 X 7 = 1750
5250 - 1750 = 3500
3500 divided by 7 =500
Which measurement statement is correct?
Answer:
What do you need help with?
Compare: -7 -4
PLEASE HELP ME!
3x-(-54x)=45= whats the sum
Answer:
x= 15/19 = 0.789
Step-by-step explanation:
Answer: 0.789 is the correct answer plz brainliest big brother
What other story element is most affected by the narrator's point of view?
Answer:
I belive it is the theme that is the most affected.
Step-by-step explanation:
Answer:
answer is the setting!!!!!!!!!!!!!!!!!!!!!
The ratio of Vicki's savings to Donna's savings is 4 : 7. Vicki saved $225 less than Donna. How much money did Vicki save?
Answer:
300
Step-by-step explanation:
4:7
7-4=3
225/3=75
75x4=300
Which 2 subjects are 2 unit apart
Answer:
I believe that your answer is C and Moon.
Mai says that -8 > -4 . Do you agree with her? Explain or show your reasoning.
Answer:
No
Step-by-step explanation:
-8 is less than -4. Negative numbers reverse the logic of positive ones: since positive 8 is more than positive 4, negative 8 is less than negative 4.
Rosita is making pizzas for a party. Each pizza requires 1 cups of sauce and 1 cups
of cheese. How many whole pizzas can Rosita make if she only has 8 cups of sauce
and 132 cups of cheese?
Answer:
8 pizzas
Step-by-step explanation:
I cAn Do mAtH!!
Answer:
She can only make 8 pizzas.
Step-by-step explanation:
She only needs 1 cup of sauce and 1 cup of cheese. She has 8 cups of sauce, so she can only make 8 pizzas. What can she do with all the cheese in her refrigerator? Hmmmmm...
most ants can lift 50 times their own weight. If an ant weighs 5 milligrams, how many ants would it take to lift a 500 gram bag of sugar?
Answer:
2000
Step-by-step explanation:
5*50=250 mg
250*4=1000 mg
1000*500=500 m
4*500=2000
It would take 2,000 ants to hoist a 500-gram bag of sugar.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, most ants can lift 50 times their own weight.
also given every ant has 5 mg weight.
So, 1 ant can lift = 5mg * 50 = 250mg
Since 1 gram has 1000 mg
Ant can lift = 1/4 grams
thus,
1/4 gram of sugar can be lifted by = 1 ant
1 gram of sugar can be lifted by = 4 ant
500 grams of sugar can be lifted by = 4 * 500 ant = 2000 ants
Therefore, 2000 ants would it take to lift a 500-gram bag of sugar.
Learn more about proportionalities here:
https://brainly.com/question/3254974
#SPJ2
Find the length of the side x in simplest radical form with a rational denominator.
Answer:
2.449489743
Step-by-step explanation:
The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
Answer:
I think it might be zero
Step-by-step explanation:
you might want to look into this all the way beforyou trust put it into*
[tex]lx+3l \leq 5[/tex]
9514 1404 393
Answer:
-8 ≤ x ≤ 2
Step-by-step explanation:
We assume you intend the absolute value equation ...
[tex]|x+3|\le5\\\\{-}5\le x+3\le5\qquad\text{rewrite as a compound inequality}\\\\\boxed{{-}8\le x\le2}\qquad\text{subtract 3}[/tex]
Solve the following step by step
Answer:
12
by-step explanation:
Can anyone please solve this question
An airplane is flying overhead at a constant elevation of 4090 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 700 ft/s, at what rate is the distance between the person and the plane increasing when the plane passes over the radio tower
Answer:
415 ft/s
Step-by-step explanation:
I've attached a diagram showing the triangle formed between the plane, the person and the radio tower.
From the attached diagram, x represents the position between the person and the position on the ground directly below the airplane while s represents the distance between the person and the plane.
The constant elevation remains 4090 ft while the value of x and s varies with time.
Thus, x varies with respect to time as dx/dt while s varies with respect to time as ds/dt.
Now, we are told that the plane is flying at the rate of 700 ft/s. This means that; dx/dt = 700 ft/s
Now we want to find the rate at which the distance between the person and the plane is increasing when the plane passes over the radio tower.
This means that we want to find ds/dt when x = 3010 ft
From pythagoras theorem if x = 3010 ft and the Elevation remains 4090 ft, we can find s as;
s = √(4090² + 3010²)
s = √25788200
s ≈ 5078.21 ft
Since we want to find ds/dt at x = 3010 ft, from the diagram, we can say from pythagoras theorem that;
x² + 4090² = s²
Differentiating x and s with respect to t, we have;
2x(dx/dt) = 2s(ds/dt)
2 will cancel out to give;
x(dx/dt) = s(ds/dt)
ds/dt = (x/s)(dx/dt)
Plugging in 700 for dx/dt, 3010 for x and 5078.21 for s, we have;
ds/dt = (3010/5078.21) × 700
ds/dt ≈ 415 ft/s
Area =
44 ft?
(x - 12) ft
(x - 5) ft
length:
width:
ft
Answer:
x= 16 ft
length = 4 ft
width = 11 ft
Step-by-step explanation:
The area is length* width
so the length is ( x - 12 )
and the width is ( x - 5 )
the area is 44ft
so now set up an equation and solve for x
( x - 12 ) ( x - 5 ) = 44
distribute
x^(2) - 17x + 60 = 44
inverse operations
x^(2) - 17x + 60 = 44
- 60 - 60
x^(2) - 17x = -16
factor
x^(2) - 17x = -16
x ( x - 17 ) = -16
now it is pretty clear that the answer is:
x = 16
just substitute it into the equation and check
( x - 12 ) ( x - 5 ) = 44
( 16 - 12 ) ( 16 - 5 ) = 44
( 4 ) ( 11 ) = 44
44 = 44
this also shows that
the length is 4
because:
( x - 12 )
= ( 16 - 12 )
= 4
and the width is 11
because:
( x - 5 )
= ( 16 - 5 )
= 11