Answer: Every 12th bag has both a T-shirt and socks.
Step-by-step explanation:
Given: T shirt: Every fourth bag
Socks: Every third bag
Least common multiple of 4 and 3 = 12 as 4 and 3 are coprime (i.e. their highest common factor is 1) and 4 x 3 = 12
It implies every 12th bag has both a T-shirt and socks.
Hence, Every twelfth bag has both a T-shirt and socks.
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 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
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 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
PLEASE HELP!!! i’ll give brainliest
Answer:
x = [tex]\sqrt{164[/tex]
Step-by-step explanation:
In order to find the hypothenuse, you need to do [tex]8^{2} + 10^{2}[/tex]. Which equals 164. Therefore, since [tex]a^{2} +b^{2} =c^{2}[/tex], a=8, b=10, and c=[tex]\sqrt{164[/tex].
WILL MARK BRAINLIEST
Match the graph to one of the exponential functions.
ƒ(x) = 2 – 2x
ƒ(x) = 2x – 2
ƒ(x) = 2x + 2
ƒ(x) = 2x – 2
A solid is formed by rotating the region bounded by the curve y = e^-3x/2 and the x axis between x=0 and x=1 around the xaxis. The volume of this solid is pi/3 * (1 - e^-3). Assuming the solid has constant density delta, find x and y.
x=
y =
Answer:
x = .28
y = 0
Step-by-step explanation:
Voume of disk = pi *r^2 = pi * e^-3x deltax
x = integal 0 to 1 of x * delta*pi*e^-3x deltax / mass = (delta*pi) integal 0 to 1 of x * e^-3x deltax/mass = (delta*pi)0.08898/mass
mass = sigma *(volume)=delta(pi/3*(1-e^-3)) =delta(.995)
x = (delta*pi)0.08898/delta(.995) = .28
by symmetry y=0
A solid is formed by rotating the region bounded by the curve y = e^-3x/2 and the x axis between x=0 and x=1 around the x axis. Then value of x is 0.28 and y is 0.
What is Volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
The volume of disk is given by formula πr²
Volume of disk = πr²= π × e⁻³ˣ Δx
[tex]x=\int\limits^0_1 {x} \, \pi e^{-3x} dx[/tex]
= (delta.π) integal 0 to 1 of x × e⁻³ˣ delta x/mass
= (delta. π) 0.08898/mass
mass = sigma ×(volume)=delta( π/3*(1-e⁻³)) =delta(0.995)
x = (delta*π)0.08898/delta(0.995) = 0.28
x=0.28
and by symmetry y=0
Hence the value of x is 0.28 and value of y is 0.
To learn more on volume click:
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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*
What is the slope of a line perpendicular to the line whose equation is
2x – 2y = 20.
Answer:
-1
Step-by-step explanation:
Solve for y into y=mx+b
2x-2y=20
-2y=-2x+20
y=(-2x+20)/-2
y=x-10
the slope is m, so it’s 1
A line perpendicular to that would be -1
0.16
As a repeating fraction
Answer:
0.16161616161616161616161616161616161616161616161616
Step-by-step explanation:
just keep adding whats repeating or put a bar on top of the 16
Solve the following step by step
Answer:
12
by-step explanation:
What's another way to express the expression [4(17) + 3(25)] x 5?
Answer:
715
Step-by-step explanation:
[4(17) + 3(25)] x 5
(68+3*25)*5
(68+75)*5
143*5
175
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...
find x (x+y) 30 24 2x
Answer:
vfvgyfygj
Step-by-step explanation:
gvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvdyu so yeah
Help!!!
Lines b and c are parallel.
What is the measure of 26?
Answer:
m∠6 = 54°
Step-by-step explanation:
∠6 is equal to (5x + 9) because they are vertical angles. But, to be able to find the measure of ∠6, you will need to find the value of (5x + 9). So, since ∠5 is equal to (13x + 9) because they are Corresponding Angles, (5x + 9) and (13x + 9) are supplementary because they are a linear pair.
So:
m∠6 = 5x + 9 and
5x + 9 + 13x + 9 = 180°
18x + 18 = 180
18x = 162
x = 9
To find m∠6, plug in values:
m∠6 = 5x + 9
= 5(9) + 9
= 45 + 9
= 54°
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].
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
Graph the line y=-1/3x+3
Subtract the equation
-7 - 12 =
Answer:
-19
Step-by-step explanation:
Answer:
-19
Step-by-step explanation:
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a
mean of 100 and a standard deviation of 15.
106 124
The area of the shaded region is (Round to four decimal places as needed.)
Answer:
The area of the shaded region is 0.2898.
Step-by-step explanation:
Let X represent the IQ scores of adults.
It is provided that [tex]X\sim N(100,15^{2})[/tex].
Compute the probability of an adult having an IQ between 106 and 124 as follows:
[tex]P(106<X<124)=P(\frac{106-100}{15}<\frac{X-\mu}{\sigma}<\frac{124-100}{15})[/tex]
[tex]=P(0.40<Z<1.60)\\=P(Z<1.60)-P(Z<0.40)\\=0.94520-0.65542\\=0.28978\\\approx 0.2898[/tex]
*Use a z-table.
Thus, the area of the shaded region is 0.2898.
Which measurement statement is correct?
Answer:
What do you need help with?
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.
Which 2 subjects are 2 unit apart
Answer:
I believe that your answer is C and Moon.
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
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
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
-5 is a rational number and an integer yes or no
Answer:
Yes
Step-by-step explanation:
Integers are whole numbers that are positive and negative. Since -5 is an integer then is also a rational number because all integers are rational numbers
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
Find the length of the side x in simplest radical form with a rational denominator.
Answer:
2.449489743
Step-by-step explanation:
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