10 cards would have 5 even cards.
First pick would be 5/10 = 1/2 probability of getting an even card.
Without replacing there are 9 cards left with 4 even ones. The probability of picking an even card would be 4/9
The probability of both happening would be Found by multiplying the two probability’s together:
1/2 x 4/9 = 4/18 = 2/9
Two cards are selected from a deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] and once a card is selected, it is not replaced, then Probability of two even numbers is [tex]\frac{2}{9}[/tex] .
What is Probability ?Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.
Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]
We have,
Let [tex]E[/tex] be event of drawing cards.
A deck of cards numbered from [tex]1[/tex] to [tex]10[/tex] .
i.e. total number of possible outcomes [tex]=10[/tex]
And,
Even numbers from [tex]1[/tex] to [tex]10[/tex] are [tex]2,4,6,8,10[/tex]
[tex]=10[/tex]
Total even numbers are [tex]5[/tex].
So,
Probability[tex](E)[/tex] [tex]=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}[/tex]
Probability[tex](E)[/tex] [tex]=\frac{5}{10}*\frac{4}{9}[/tex]
[tex]=\frac{2}{9}[/tex]
So, the Probability of two even numbers is [tex]\frac{2}{9}[/tex] , as there are total [tex]10[/tex] cards and it is said that once a card is selected, it is not replaced, so when one card is selected there remains only [tex]9[/tex] cards, so when next time we select a card then Probability will be from those [tex]9[/tex] cards.
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What error did Amy make in writing the equation in slope-intercept form for the line shown in the graph?
Amy’s equation:
Answer:
letter C
Step-by-step explanation:
She substitue the X-Intercept, (3,0), for B
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Hey, I need help with the questions attached. I need it in 20 minutes, it is last minute homework. Thank you very much.
Answer:
1)
90g strawberry jelly
6 sponge fingers
315ml custard
135g tinned fruit
2) 260 cm²
Step-by-step explanation:
1) 120/4 × 3
90g strawberry jelly
8/4 × 3
6 sponge fingers
420/4 × 3
315ml custard
180/4 × 3
135g tinned fruit
2) area = base × height
= 20 × 13
= 260 cm²
Answers and Step-by-step explanations:
1. Let's find the amount of each ingredient we need for 1 person, and then multiply that by 3 later.
strawberry jelly: we have 120 grams for 4 people, so for 1 person, we need 120/4 = 30 grams
sponge fingers: we have 8 of these for 4 people, so for 1 person, we need 8/4 = 2 sponge fingers
custard: we have 420 mL for 4 people, so for 1 person, we need 420/4 = 105 mL
tinned fruit: we have 180 grams for 4 people, so for 1 person, we need 180/4 = 45 grams
Now, multiply each of these by 3 to find the amount needed for 3 people:
strawberry jelly: 30 grams * 3 = 90 grams
sponge fingers: 2 sponge fingers * 3 = 6 sponge fingers
custard: 105 mL * 3 = 315 mL
tinned fruit: 45 grams * 3 = 135 grams
2. The area of a parallelogram is calculated by the formula: A = Bh, where B is the base length (usually a side length) and h is the height perpendicular to the base. Here, we see that have two potential base lengths: 20 and 15. However, looking at the height, it's only perpendicular to the base with length 20, so we know that B = 20 and h = 13.
Plugging these into the formula, we get: A = 20 * 13 = 260 cm squared.
Hope this helps!
At a restaurant, you decide to order the lunch special that includes one entree, one side and one drink. There are 6 entrees to choose from, 4 sides to choose from and 7 drinks to choose from. How many total options are there when ordering this meal
Answer:
168
Step-by-step explanation:
Total entree = 6
Total slides = 4
Total drinks = 7
Lunch special includes 1 entree, 1 slide, and one drink.
Option for entree
= 6_(c_1 )
= 6
Option for slides
= 4_(c_1 )
= 4
Option for drinks
= 7_(c_1 )
= 7
So, total option ordering meal,
= 6*4*7
= 168
Solve the following: -3x(x-8)+7x=12
Step-by-step explanation:
Hello there!
Solve for x:
-3x(x-8)-7x=12
-3x^2+24x-7x=12
-3x^2+17x+12=0
Can you factor it further?Feel free to ask questions in the comments.
:)
The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1998.
Answer:
The projected world population in 1998 is 6,216,871,541.95
Step-by-step explanation:
Here we have the formula for exponential growth given by
A = P(1 + r)^t
Where:
A = Population at the end of the time period
P = Population at the start of the time period
r = Rate percent of population growth
t = Time period of interest
Therefore, given r = 2% = 2/100 = 0.02, P = 5,000,000,000;
t = year 1998 - year 1987 = 11 years
We have
A = 5,000,000,000 ×[tex](1+0.02)^{11}[/tex]= 6,216,871,541.95
≈ 6.2 billion.
To find the projected world population in 1998, we can use the exponential growth model. The initial population in 1987 was 5 billion with a growth rate of 2% per year. By applying the formula, the projected population in 1998 is estimated to be approximately 6.255 billion.
Explanation:To find the projected world population in 1998, we can use the exponential growth model. The formula for exponential growth is P = P0 * (1 + r)t, where P is the final population, P0 is the initial population, r is the growth rate, and t is the number of years.
In this case, the initial population (P0) in 1987 was 5 billion, the growth rate (r) was 2 percent per year, and we want to find the population in 1998, which is 11 years later.
Using the formula, we can calculate the projected population in 1998 as follows:
P = 5 billion * (1 + 0.02)11P = 5 billion * 1.0211P ≈ 5 billion * 1.251 = 6.255 billionTherefore, the projected world population in 1998 would be approximately 6.255 billion.
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The width of a rectangular rug is 6 feet if the perimeter is 24 feet what is the area of the rug?
Answer:
36 feet squared
Step-by-step explanation:
Finding the perimeter of an object is adding all of the sides together. If the width of the rug is 6 feet then we know that there are two sides that length. Add those together.
6 feet + 6 feet = 12 feet
You would subtract the number you get from the perimeter.
24 feet - 12 feet = 12 feet
And then divide the number by the number of sides left, 2, to get each of their lengths.
12 feet / 2 feet = 6 feet
To find the area of a rectangle you multiply length times width, which in this case both are 6 feets.
6 feet x 6 feet = 36 feet squared
An equation has solutions of m = -5 and m = 9. Which could be the equation?
(m + 5)(m - 9) = 0
(m - 5)(m + 9) = 0
m? - 5m + 9 = 0
m2 + 5m-9=0
Answer:
(m+5) (m-9) = 0
Step-by-step explanation:
An equation with solutions of m = –5 and m = 9 is y = m² − 4m − 45.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation.
Given that, the solutions of an equation are m = -5, and m = 9, we need to find the equation,
(m + 5) (m - 9) = 0
One possibility is that of a quadratic equation.
y = (m + 5) (m - 9)
y = m² - 9m + 5m - 45
y = m² - 4m - 45
Hence, an equation with solutions of m = –5 and m = 9 is y = m² − 4m − 45.
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Debbie scored of her team's 24 points. How
many points did Debbie score?
Answer:
24
Step-by-step explanation:
Answer:
24 points
Step-by-step explanation:
Simplify: 27 : 54 : 9
Answer:
3 : 6 : 1
Step-by-step explanation:
The common multiple between these numbers is 9, so divide everything by nine.
Answer:
3:6:1
Step-by-step explanation:
27/9=3
54/9=6
9/9=1
3:6:1
I hope this helps!
Work out the answers to:
a) 6 × (-3)
b) (-5) × 4
c) (-9) × (-2)
Step-by-step explanation:
a. 6 * (-3) = - 18
b. (-5) * 4 = - 20
c. (-9) * (-2) = 18
A large rainwater collection tub is shaped like a cylinder. The diameter is 28 inches and the height is 40 inches. If the tub is 75% filled, what is the volume of water in the tub? Round to the nearest tenth.
Answer:18472.6
use pie cylinder formula
Multiply the volume of the tub by 0.75 to find the volume of the water.
Step-by-step explanation:
To calculate the volume of water in the tub, you first find the radius of the cylinder, calculate the total volume, and then find 75% of that volume, finally converting the units if necessary and rounding to the nearest tenth, we get volume od water to be approximately 18451.2 cubic inches
To find the volume of water in the tub when it's 75% filled, we first need to find the volume of the entire tub and then multiply it by 75%.
The volume \ V of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- r is the radius of the cylinder,
- h is the height of the cylinder.
Given:
- Diameter d = 28 inches, so radius [tex]\( r = \frac{d}{2} = \frac{28}{2} = 14 \)[/tex] inches,
- Height h = 40 inches.
Substituting these values into the formula:
[tex]\[ V = \pi \times (14)^2 \times 40 \]\[ V = \pi \times 196 \times 40 \]\[ V = 7840\pi \, \text{cubic inches} \][/tex]
Now, to find the volume when the tub is 75% filled, we multiply the volume of the entire tub by 75% (or 0.75):
[tex]\[ \text{Volume of water} = 0.75 \times 7840\pi \, \text{cubic inches} \]\[ \text{Volume of water} = 5880\pi \, \text{cubic inches} \][/tex]
Now, let's compute the value:
[tex]\[ \text{Volume of water} \approx 5880 \times 3.14 \, \text{cubic inches} \]\[ \text{Volume of water} \approx 18451.2 \, \text{cubic inches} \][/tex]
160% of 60 is how much?
please show step by step!
Answer:
96
Step-by-step explanation:
160% is the same as taking the number times 1.6
1.6 x 60 = 96
The box plots show the average wind speeds, in miles per hour, for various cities in two different countries
Average Wind Speeds of Cities in Country A
D
's
8
9
10 11
Average Wind Speeds of Cities in Country B
Which statement describes the symmetry of the data in the two box plots?
The data in country A are more symmetric than the data in country B.
The data in country B are more symmetric than the data in country A
The data in both countries have about the same symmetry.
The symmetry of the data cannot be determined by looking at the box plots.
What is the answer
Answer:
the answer is b.
Step-by-step explanation:
Express the length of the kite string in terms of trigonometric ratios.
Answer:
[tex]\frac{70}{sin40^{\circ}}[/tex]
Step-by-step explanation:
We are given that
Height of the kite from the ground=h=70 feet
[tex]\theta=40^{\circ}[/tex]
We have to find the length of kite string in term of trigonometric ratios.
Let length of string=x
We know that
[tex]sin\theta=\frac{Perpendicular\;side}{hypotenuse}[/tex]
Using the formula
[tex]sin40^{\circ}=\frac{h}{x}[/tex]
[tex]sin40^{\circ}=\frac{70}{x}[/tex]
[tex]x=\frac{70}{sin40^{\circ}}[/tex]
Hence, the length of kite string=[tex]\frac{70}{sin40^{\circ}}[/tex]
The circle below has center K, and its radius is 3 yd. Given that m 2 LKM = 70°, find the length of the major arc LNM.
Give an exact answer in terms of 71, and be sure to include the correct unit in your answer.
Length of major arc LNM :
The length of the major arc LNM, in terms of pi, is 29π/6 yards.
The circle has a radius of 3 yards and the central angle m∠LKM is 70°. Since the question asks for the length of the major arc LNM, we first need to calculate the angle of the major arc. The angle of a full circle is 360°, so the angle of the major arc will be 360° - 70° = 290°.
To find the arc length, we use the formula for arc length (l) which is: l = rθ (in radians). We must convert the angle from degrees to radians by multiplying by π/180. So, 290° becomes (290π/180) radians.
Now, compute the length of the major arc LNM: l = 3 yd * (290π/180) = (870π/180) yd, which simplifies to: 29π/6 yd. Thus, the length of the major arc LNM, in terms of π, is 29π/6 yards.
Which statement is true about point F? a.F is the midpoint of AA' because bisects AA'. b.F is the midpoint of EG because AA' bisects EG. c.F is the midpoint of AA' because AA' bisects EG. d.F is the midpoint of EG because bisects AA'.
Answer:
The correct option is;
a. F is the midpoint of [tex]\overline{AA'}[/tex] because line [tex]\overline{EG}[/tex] bisects [tex]\overline{AA'}[/tex]
Step-by-step explanation:
Here, since we have that the triangle is reflected across EG therefore the location of the point F which is along EG bisects the line [tex]\overline{AA'}[/tex] as the dimensions of the line from A to F must be equal to the dimension of the line that extends from A' to F
Therefore the point F is the midpoint of [tex]\overline{AA'}[/tex] because line [tex]\overline{EG}[/tex] bisects [tex]\overline{AA'}[/tex].
Answer:
A
Step-by-step explanation: i got it right on edge
After 5 years, a $2,450 investment is worth $3,123.75.
What is the simple annual interest rate for this investment?
Answer:
5.5%
Step-by-step explanation:
To solve this problem we can use a modified version of the simple interest formula which is shown below:
[tex]r=\frac{I}{Pt}[/tex]
I = interest amount
P = principal amount
t = time (years)
The first step is to find the interest gained from the investment.
[tex]3,123.75-2,450=673.75[/tex]
Next, plug in the values into the equation:
[tex]r=\frac{673.75}{(2,450)(5)}[/tex] Multiply the bottom values
[tex]r=\frac{673.75}{12,550}[/tex] Divide the values
[tex]r=.055[/tex]
The last step is to convert 0.055 into a percent:
[tex]0.055(100)=5.5[/tex]
The interest rate is 5.5%
A flagpole broke in a storm. It was originally 81 feet tall. 28 feet are still sticking straight out of the ground, where it snap, but the remaining piece has hinged over and touch the
Answer:
45ft
Step-by-step explanation:
The remaining piece has to be found. How far away is the end of the pole from the base of the pole along the ground.
We deduct original to broken 81-28 = 53 feet tall.
PT + to find the other side.
53^2 - 28^2 = S^2
√2025 = 45 = S^2
S^2 = 45ft
How would you write twelve more than the quotient of a number and five
Answer:
n/5 +12
Step-by-step explanation:
What is the price of one crate of flowers?
Write the unit rate as a decimal in dollars and cents.
$
Answer:
$ 2.50
This is the right answer for ed2020
Answer:
$2.50
Step-by-step explanation:
Bc yeah <3
In the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be times the volume of the pyramid that it fits inside. Which expression represents the volume of the cone that is times the volume of the pyramid that it fits inside? (2r2h) (4r2h)
Answer:
D
Step-by-step explanation:
The formula to calculate the volume of the cone is π/4(1/3 x 4r²h).
The correct option is D.
What is a pyramid?A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
Given:
In the derivation of the formula for the volume of a cone,
the volume of the cone is calculated to be π/4 times the volume of the pyramid that it fits inside.
The volume of the cone,
= π/4 (the volume of the pyramid)
= π/4 (1/3 x the base area x height)
= π/4(1/3 x 2r x 2r x h)
= π/4(1/3 x 4r²h)
Therefore, the volume is π/4(1/3 x 4r²h) cubic units.
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The complete question is given in the attached image.
Two brothers are standing 3 feet away
from a mirror. How far away from
the brothers will their reflection
appear to be?
Answer:
3 feet
Step-by-step explanation:
Answer:
3 feet...
Step-by-step explanation:
Kaytlyn must build a sand castle in the form of a square pyramid for a project as shown to the left. She bought 3 bags of sand each containing 1200 inches cubed. Will she save enough sand to build the castle?
Answer:
see the explanation
Step-by-step explanation:
The complete question is
The dimensions of the square pyramid are
Base: 40 inches
Height: 12 inches
step 1
Find the volume of the square pyramid
The volume of the square Pyramid is given by the formula
[tex]V=\frac{1}{3}b^2h[/tex]
where
b is the length side of the square base
h is the height of the pyramid
we have
[tex]b=40\ in\\h=12\ in[/tex]
substitute
[tex]V=\frac{1}{3}(40)^2(12)[/tex]
[tex]V=6,400\ in^3[/tex]
step 2
Find the volume of sand
Multiply the number of bags of sand by the volume of each bag
so
[tex]3(1,200)=3,600\ in^3[/tex]
step 3
Compare the volume of the sand with the volume of the square pyramid
3,600 < 6,400
therefore
Kaytlyn has not enough sand to build the castle
Yasmin arrived home from play practice at 4:25 pm. The walk took 15 minutes. Practice began 20 minutes after the final bell and lasted for a half hour. When did school end
Answer:
3:20 pm.
Step-by-step explanation:
Time Yasmin got home: 4:25
Time it took to walk home: 15 minutes
Practice started: 20 minutes after bell.
Practice lasted for 30 minutes.
For us to find this out, you have to calculate all the activities.
An hour is 60 minutes.
A half hour is 30 minutes.
15 + 20 + 30 = 65 minutes.
65 minutes = an hour and five minutes.
4:25 - 1:05 = 3:20.
Feel free to let me know if you need more help! :)
Answer:
3:20 p.m
Step-by-step explanation:
According to the Rule of Three, when we have a sample size n with xequals0 successes, we have 95% confidence that the true population proportion has an upper bound of StartFraction 3 Over n EndFraction . a. If n independent trials result in no successes, why can't we find confidence interval limits by using the methods described in this section? b. If 40 couples use a method of gender selection and each couple has a baby girl, what is the 95% upper bound for p, the proportion of all babies who are boys
Answer:
0 < p < 0.075
Step-by-step explanation:
Solution:-
According to the rule of three, when we have a sample size = n.
and x = 0 successes ( The lowest possible value of true population proportion ). Then we are 95% confident that the upper bound of the true population proportion is given by:
3 / n
If n = 40 couples use a method of gender selection and each couple has a baby girl, the the possibility of successes is zero. This calls on for the use of Rule of three to determine the upper bound for the true population of couple having a baby girl.
- The 95 % upper bound for true population proportion of all the babies born are girl is determined by:
p = 3 / n = 3 / 40
p ≈ 0.075
- The number of successes were = 0, hence the lower bound for the population proportion is 0 and the upper bound was calculated above. Hence,
0 < p < 0.075
- The range of true population proportion.
the proportion of all babies who are boys is 0 < p < 0.075
Calculation of the proportion:Here we know that the 95% confident that the upper bound of the true population proportion is provided by 3 by n
Since n be 40 couples
So, here the proportion should be
[tex]p = 3 \div n = 3 \div 40[/tex]
p ≈ 0.075
And, The number of successes were = 0
So, the proportion should be 0 < p < 0.075
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please assist me with this problem
Answer:
a) [tex]\sqrt{64+x^2}[/tex]
b) 15
Step-by-step explanation:
a) We know that AB = 8 and BC = x. We can use the Pythagorean Theorem, which states that for a right triangle with sides a, b, and c: [tex]a^2 +b^2=c^2[/tex] , where a and b are the shortest sides and c is the longest.
Here, AB = a = 8 and BC = b = x. So, AC = c. Then:
[tex]AB^2+BC^2=AC^2[/tex]
[tex]8^2+x^2=AC^2[/tex]
[tex]AC=\sqrt{64+x^2}[/tex]
b) We know that AC - AB = 9. Since AB = 8, then AC = 9 + 8 = 17. We also have the expression from above, so set them equal:
[tex]AC=\sqrt{64+x^2}=17[/tex]
[tex]64+x^2=289[/tex]
[tex]x^2=225[/tex]
x = 15
Hope this helps!
Answer:
sqrt(x^2 +64) = AC
x = 15
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle
a^2 + b^2 =c^2 a and b are the legs and c is the hypotenuse
We know the legs are x and 8
x^2 + 8^2 = AC^2
x^2 + 64= AC^2
Solving for AC
Take the square root of each side
sqrt(x^2 + 64) = sqrt(AC^2)
sqrt(x^2 +64) = AC
We are given AC - AB = 9
We know AB = 8
AC -8 =9
Add 8 to each side
AC -8+8 = 9+8
AC = 17
AC is the hypotenuse,
x^2 + 64= AC^2
x^2 +64 = 17^2
x^2 +64 = 289
Subtract 64 from each side
x^2 +64-64 = 289-64
x^2 =225
Take the square root
sqrt(x^2) = sqrt(225)
x =15
As I was going to St Ives I met a man with 7 wives. Each wife had 7 kids. Each kid had 7 cats. Each cat had 7 kittens. How many were going to St Ives?
Answer:
2401
Step-by-step explanation:
7 * 7 * 7 * 7 = 2401
What is the least common multiple of 4 and 5?
Answer:
20
Step-by-step explanation:
Hi there,
To find the least common multiple (LCM) of 2 numbers, I would recommend listing off a few multiples of each number. Since they are small, it shouldn't be too hard.
Multiples of 4:
4, 8, 12, 16, 20
Multiples of 5:
5, 10, 15, 20
As you can see, the first multiple that 4 and 5 both share is 20. So the least common multiple of 4 and 5 20.
Round 44.057 to the nearest hundredth.
Answer:
44.057 to nearest hundredth
44.06
7. What is the measure of ZE ?
Answer:
70 degrees
Step-by-step explanation:
The adjacent angles in a parallelogram are supplementary and add to 180 degrees
∠CDE+∠DEF=180
We know that ∠CDE is 110 degrees, so we can substitute that in
∠CDE+∠DEF=180
110+∠DEF=180
Subtract 110 from both sides
∠DEF= 70
So, ∠E is 70 degrees