Step-by-step explanation:
it does not say what the card deck consists of, and how many cards of what type there are.
so, I assume a standard playing card set of 52 cards (no jokers) with 4 suits of
Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K
in that ranking of value.
so there are 4 cards of each of the 13 different types.
a card with a number greater than 9 means a 10, a J, a Q, or a K.
so, in total there are 4×4 = 16 such cards in the deck.
a card with a number less than 4 means an Ace, a 2, or a 3.
so, in total there are 4×3 = 12 such cards in the deck.
to get a number greater than 9 and a number less than 4 is a combination of the first card being greater than 9 and the 2 card being less than 4 OR the first card being less than 4 and the second card being greater than 9.
an "and" operation (without overlap) we represent by a multiplication, and an "or" operation (without overlap) by an addition.
remember, a probability is always
"desired cases / total possible cases".
so, the probability to draw a first card greater than 9 is
16/52 = 4/13
the probability to draw a second card greater than 9 (after a first card less than 4) is
16/51
because we still have all the large cards, but one of the smaller ones is now gone.
the probability to draw a first card less than 4 is
12/52 = 3/13
the probability to draw a second card less than 4 (after a first card greater than 9) is
12/51.
so, the complete probability of the scenario is
4/13 × 12/51 + 3/13 × 16/51 = 48/663 + 48/663 = 96/663 =
= 32/221 = 0.14479638...
if my assumptions about the cards are wrong, please adapt the numbers accordingly. but the basic structure of the calculation is the same.
The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8000.
Find the revenue function R when x energy drinks are sold.
could you help me with 15 please?
Answer: 11 pounds
Step-by-step explanation:
Total weight of the first 8 backpacks
8*14
= 112 pounds
Total weight of the second 12 backpacks
12*9
= 108 pounds
Total weight of the whole 20 backpacks
112+108
= 220 pounds
therefore the mean weight of the 20 backpacks is
220 / 20
= 11 pounds
find the center and the radius of the circle (x-7)^2+(y+4)^2=81
A circle is a curve sketched out by a point moving in a plane. For the given equation of a circle, the centre will lie at the coordinate (7,-4), while the radius will be equal to 9 units.
What is the equation of the circle with radius r units, centred at (x,y)?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
If a circle O has a radius of r units length and it has got its centre positioned at (h, k) point of the coordinate plane, then, its equation is given as:
(x-h)² + (y-k)² = r²
Given the equation of the circle is (x-7)²+(y+4)²=81. The equation can be rewritten as,
(x-7)² + [y-(-4)]² = 9²
Hence, For the given equation of a circle, the centre will lie at the coordinate (7,-4), while the radius will be equal to 9 units.
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What is the unfilled volume inside the cylinder? 320π cubic units 597π cubic units 640π cubic units 725π cubic units
The unfilled volume inside the cylinder is 640π cubic units
How to find unfilled volume?Volume of a cylinder = πr²h
= π × 8² × 15
= π × 64 × 15
= 960π cubic unit
h = heightr = radiusl = slant heightVolume of a cone = 1/3πr²√l² × r²
= 1/3 × π × 8² √17² × 8²
= 1/3 × π × 64 √289 × 64
= 1/3 × π × 64 √353
= 320π cubic unit
Unfilled volume = 960π cubic unit - 320π cubic unit
= 640 cubic unit
The complete question:
A solid oblique cone with a slant length of 17 units is inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. What is the unfilled volume inside the cylinder? 320π cubic units 597π cubic units 640π cubic units 725π cubic units
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Answer:
640pi
Step-by-step explanation:
How many full cases and additional items are needed to fulfill the order
There are 13 full cases and 2 additional items needed to fulfill the order
How to determine the full cases and additional items?The given parameters are:
Items ordered = 80Items per case = 6The number of cases is:
Case = 80/6
Evaluate
Case = 13 Remainder 2
This means that:
The full case is 13 and the additional item is 2
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Sue is traveling to Florida for vacation. Her flight takes off and the plane travels at a constant speed of 337 miles per hour. It takes her 5 hours to get to her destination. How many miles did she travel?
PLEASE HELP!!!
Answer:
Sue traveled 1,685 miles.
Step-by-step explanation:
337 x 5
(300 x 5) + (30 x 5) + (7 x 5)
1,500 + 150 + 35
1,650 +35
1,685
On a scale drawing, 9 inches
represents 11 miles. How many
inches represent 55 miles?
Answer: you will get 45
Step-by-step explanation:
If you do 9x5=45 and 11x5=55
So the answer would be 45
what is the midpoint of (4,10) (16,0)
Answer:
Midpoint(10,5)
Step-by-step explanation:
Midpoint of coordinatesTo find the midpoints add the x-coordinates and divide that by 2 & add the y-coordinates and divide by 2
[tex]\boxed{\text{\bf midpoint=$\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$}}[/tex]
[tex]\sf = \left(\dfrac{4+16}{2},\dfrac{10+0}{2}\right)\\\\=\left(\dfrac{20}{2},\dfrac{10}{2}\right)\\\\= \left(10,5\right)[/tex]
Work out the sheet below
Answer:
It might be 235.62
Step-by-step explanation:
Answer:
[tex]235.6\ cm^3[/tex]
Step-by-step explanation:
Volume of a cone: [tex]\frac{1}{3} \pi r^2 h[/tex]
[tex]\frac{1}{3} \pi r^2 h\\r = 5\\h = 9\\\frac{1}{3} \pi (5)^2(9)\\\frac{1}{3} \times \pi \times 25 \times 9\\= 75 \pi\\= 235.619449...\\= 235.6\ \text{(1 d.p.)}\ cm^3[/tex]
In a particular class of 28 students, 12 are men. What fraction of the students in the class are men?
Answer:
12/28
Step-by-step explanation:
the answer is 12/28 because 12 are men and the rest are mos likely girls,
Answer:
12 / 28
Step-by-step explanation:
Given:
- 28 students total
- 12 are men
so 12 out of the 28 are men which is the same as 12 / 28
Juan went to the store to buy a plant for his mother, but forgot to ask which kind to get. Out of 30 plants, nine of them are a kind that his mother would want. If Juan chooses one randomly, what is the probability that he will choose a kind that his mother would want?
A. 40%
B. 30%
C. 0.3%
D. 9%
Answer:
B
Step-by-step explanation:
because 30% out of 30 is 9
Dan bought x pounds of potatoes for $0.85 per pound and y pounds of grapes for $1.29 per pound. The total cost was less than $5. Which inequality represents his purchase?
1.29x + 0.85y < 5
1.29x + 0.85y > 5
0.85x + 1.29y > 5
0.85x + 1.29y < 5
Answer:
0.85x + 1.29y < 5
Step-by-step explanation:
x and y will be the numbers of grapes and potatoes he purchased.
in descending order: 0.03, 1.03, 0.13, 1.13
Answer:
1.13, 1.03, 0.13, 0.03
.....
Answer:
1.13, 1.03, 0.13, 0.03.
Step-by-step explanation:
Highest value is 1.13 and lowest is 0.03.
2
Two figures are similar, and the scale factor is
2
Over
3
If a side of the larger figure is 12, then the corresponding side in the smaller figure is…..
6
8
12
18
Choose an answer
Solve the system by substitution.
y= -6x-7
y= -7x
Answer:
x = 7
y = -49
Step-by-step explanation:
Solving system of equation by substitution method.y = -6x - 7 ---------------(I)
y = -7x -------------------(II)
Substitute y = -7x in equation (I)
-7x = -6x - 7
-7x + 6x = -7
-x = -7
Multiply both sides by (-1)
[tex]\sf \boxed{\bf x = 7}[/tex]
Substitute x =7 in equation (II)
y = -7*7
[tex]\sf \boxed{\bf y = -49}[/tex]
Answer:
X = 7 Y = -49
Step-by-step explanation:
Y= -6 X -7---------(1)
Y= -7 X ------------(2)
using substitution method, substitute equation two into equation one-7 X = -6X -7
-7 X+6X = -7
- X = -7
cancelling the - sign on bothsides
X = 7
put X = 7 into equation (2)
Y = -7(7)
Y = -49
therefore, X = 7 Y= -49
Britney is buying a shirt and a hat at the mall. The shirt costs $32.61, and the hat costs $19.82. If Britney gives the sales clerk $100.00. how much change should she receive? (Ignore sales tax.)
A. $44.47
B. $57.32
C. $52.43
D. $47.57
Answer:
D. $47.57
Step-by-step explanation:
Add up the cost of the two items
$32.61 + $19.82 = $52.43
subtract the cost for the $100
100-52.43 = 47.57
The change is D. $47.57
Answer:
$47.57
Step-by-step explanation:
cost of the t-shirt = $32.61
cost of the hat= $19.32
total cost of items she bought= 32.61+19.82= $52.43
Amount of change she received= 100-52.43= $47.57
Tanner bought 6 chocolates. Maggie bought c times as many chocolates as Tanner. Write an expression that shows how many chocolates Maggie bought.
Answer:
The equation that we most use to find how many chocolates Maggie bought would be:
6 x c = how many chocolates Maggie bought
Maggie bought c times as many chocolates as Tanner. This means to find how many chocolates Maggie bought we would multiply the c (Being how many times more chocolates Maggie bought) by 6 to find the number of chocolates Maggie bought`.
For example:
If the question stated Maggie bought 4 times as many chocolates as Tanner, the equation would be; 6 x 4 = how many chocolates Maggie bought. Which would be 24 chocolates.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
If B is 60% more than A, then A is
A. 37.5% less than B.
B. 37.5% of B
C. 60% less than B
D. 60% of B
Answer:
37.5% less than B
Step-by-step explanation:
It is given that B is 60% more than A.
A (160%) = BA = B / (160%)A = B / (8/5)A = 5B/8A = 0.625BA = (62.5%) BSince A is 62.5% of B, it is 37.5% less than B.
Answer:
A. 37.5% less than B
Step-by-step explanation:
We can write an equation to model this:
B being 60% more than A means that:
B=0.6A+1A
B=1.6A
Let's isolate A.
A=B/1.6
Multiply the top and bottom by 10 to get whole numbers
A=10B/16
Simplify
A=5B/8
5/8 = 62.5%
A=0.625B
Therefore, A is 62.5% of B
This means that A is 37.5% less than B.
How many solutions are there to the equation below?
4(x - 5) = 3x + 7
Ο Α. Ο
O B. Infinitely many
O c. 1
2 x - 5 + 7 y - 3 = 9 x - 1 - y -8 Solve For X AND Y (SHOW WORK PLEASE)
(Just so people can get points :D)
Answer:
[tex]\large\boxed{\sf x = \frac{8y+1}{7} }[/tex]
[tex]\large\boxed{\sf x = \frac{7x-1}{8} }[/tex]
Group the Variable's:
2 x - 5 + 7 y - 3 = 9 x - 1 - y -8
2x -9x + 7y +y = -1 -8 +5 + 3
-7x + 8y = -1
From this find x and y
For X
-7x + 8y = -1
-7x = -1 -8y
7x = 8y + 1
x = (8y +1)/7
For Y
-7x + 8y = -1
8y = -1 +7x
y = (7x -1)/8
Jesse measured a farm and made a scale drawing. The scale of the drawing was 1 centimeter = 4 meters. If the actual width of the goat pen is 8 meters, how many centimeters wide is the goat pen in the drawing?
The LCM of 8ab and 12a^2 is
A. 48a³b.
B.) 48a²b.
C. 24a²b.
D. 24ab.
E. 48a².
of 8ab
Answer:
C. 24a²bStep-by-step explanation:
8ab = 4a × (2b)
12a² = 4a × (3a)
Then
LCM(8ab , 12a²) = 4a × (2b) × (3a)
= (4×2×3) × (a×a×b)
= (24) × (a²×b)
= 24a²b
Mrs Rohit gave a total of $64.90 to her three sons. The eldest son receive $4.30 more than the youngest son. The second son received $7.80 less than the youngest son. How much did the eldest son received?
NO ALGEBRA PLEASE! I HAVENT LEARN IT YET!
Answer: $25.90
Step-by-step explanation:
We will have x as the youngest son's share, (the youngests son's share is the basis)
(x + 4.30) as the eldest son's share, (the eldest received 4.30 more than the youngest)
(x - 7.80) as the second son's share, (the second received 7.80 less than the youngest)
and 64.90 as their share altogether.
To find the youngest son's share:
(x) + (x + 4.30) + (x - 7.80) = 64.90
x + x + 4.30 + x - 7.80 = 64.90
x + x + x = 64.90 - 4.30 + 7.80 (group all of the like terms together. variables with variables, numbers with numbers. 4.30 became negative since it was moved to the other side, the same happened with 7.80 since it was a negative, it became a positive when it moved to another side)
Solve...
x + x + x = 64.90 - 4.30 + 7.80
3x = 68.40 (divide both sides by 3)
[tex]\frac{3x}{3} = \frac{68.40}{3}[/tex]
x = 22.80
(The youngest son's share is $22.80)
To get the eldest son's share:
x + 4.30 (substitute x since it has already been solved)
22.80 + 4.30 = 27.10
The eldest son's share is $27.10
Math
What can you say about the mean rainfall when comparing the two time periods?
The mean in period 2 is higher than the mean in period 1.
The mean in period 1 is higher than the mean in period 2.
The mean in period 1 is the same as the mean in period 2.
Answer:
[tex]\bullet \ \large\text{The mean in period 2 is higher than the mean in period 1.}[/tex]
Step-by-step explanation:
the mean in period 1 :
(2.3+2.1+2.2+2.2+2.2+2.1+2.4+2.5+2.2+2.0+1.9+1.9+2.1+2.2+2.3)÷15=21.733...
the mean in period 2 :
(2.3+2.1+3.3+1.5+3.6+1.6+3.0+1.1+4.7+2.1+2.4+1.9+2.8+0.5+2.3)÷15=23.466...
Since 23.466 > 21.733 then “The mean in period 2 is higher than the mean in period 1”.
HURRY PLS
Explain how an enlargement or a reduction in the dimensions of a building would cause a change in the scale factor.
The enlargement or a reduction in the dimensions of a building would cause a change in the scale factor is defined below:
What is Scale Factor?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.
A dilation is a transformation that enlarges or reduces a figure in size. This means that the pre image and image are similar and are either reduced or enlarged using a scale factor.
As seen in the graphics below. A reduction (think shrinking) is a dilation that creates a smaller image, and an enlargement (think stretch) is a dilation that creates a larger image.
If the scale factor is between 0 and 1 the image is a reduction.
Using dilation scale factors, we can shrink or expand a figure to the size we desire, knowing that each angle is congruent, each segment is proportional, the slope of each segment is maintained, and the perimeter of the pre image and image have the same scale factor.
Hence, this is how an enlargement or a reduction in the dimensions of a building would cause a change in the scale factor.
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Csc2x=2. Please help me !!!
Answer:
[tex]x=\frac{\pi }{4}[/tex]
Step-by-step explanation:
csc(2x) = 2
is also the same as
sin(2x) = 1/2
so we have to solve for sin(x)=1/2
[tex]x=\frac{\pi }{2}[/tex]
but we want to sin(2x) = 1/2 so we make it.
[tex]\\2x=\frac{\pi }{2} \\x=\frac{\pi }{4}[/tex]
What is the mean absolute deviation.
Answer:
1.56 rounded 1.6
Step-by-step explanation:
MAD (Mean Absolute Value):
step 1: Find the mean of the data
formula: sum of the data set / total number of terms
sum of the data set: 4 + 9 + 4 + 5 + 3 = 24
total number of terms: there is 5 numbers in the data set
mean = 24 / 5
mean = 4.8
step 2: Find the distance between each data and mean.
3, 4, 4, 5, 9
Distance between 3 and 4.8 is 1.8 (4.8 - 3 = 1.8)
Distance between 4 and 4.8 is 0.8 (4.8 - 4 = 0.8)
Distance between 4 and 4.8 is 0.8 (4.8 - 4 = 0.8)
Distance between 5 and 4.8 is -0.2 (4.8 - 5 = -0.2)
Distance between 9 and 4.8 is -4.2 (4.8 - 9 = -4.2)
step 3: take the absolute value of any negative numbers
|-0.2| and |-4.2| is 0.2 and 4.2
step 4: add all the distances
1.8 + 0.8 + 0.8 + 0.2 + 4.2 = 7.8
step 5: divided it by the number of data
7.8 / 5 = 1.56
Let me know if you have any questions !
Someone help me with this question please
Answer:
0.6.
Step-by-step explanation:
Sin A = opposite side / hypotenuse
= 3/5 = 0.6.
Answer: 0.6.
Step-by-step explanation:
Sin A = opposite side / hypotenuse
= 3/5 = 0.6.
The volume of a cone of height hand base radius r is given by:
The volume of a cone is calculated using the formula [tex](\frac{1}{3} )r^2h[/tex], where "h" is the cone's height and "r" is the radius of the base.
Answer:
The formula for the volume of a cone is (1/3)πr2h, where, "h" is the height of the cone, and "r" is the radius of the base.
Step-by-step explanation:
hope it helps you :)
one last question! so i am doing this equation 6x-5=8x+2 but as I am doing it I got 7/-2 but in my answer key both are negative? what am I doing wrong?
this is what I have so far
6x-5=8x+2
6x-8x=5+2
-2x=7
Answer:
6x - 5 = 8x + 2
or -5-2 = 8x-6x
or -7 = 2x
or -7 / 2 = x
this is correct answer because in fraction form if one number is negative whole fraction is negative
Hey there!
IF YOUR EQUATION IS:
6x - 5 = 8x + 2
THEN:
SUBTRACT 8x to BOTH SIDES
6x - 5 - 8x = 8x + 2 - 8x
SIMPLIFY IT!
-2x - 5 = 2
ADD 5 to BOTH SIDES
-2x - 5 + 5 = 2 + 5
SIMPLIFY IT!
-2x = 2 + 5
-2x = 7
DIVIDE -2 to BOTH SIDES
-2x/-2 = 7/-2
SIMPLIFY IT!
x = -7/2
The step you had a partial mistake was step 2 because that’s not what had to simplify to get the 7/-2. You should’ve converted your equation to: -2x - 5 = 2 (as I put for STEP 1.1) but your overall result is correct x DOES equal to 7/-2.
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)