Answer: Explained.
Step-by-step explanation: We are familiar with the theory of probability and the Law of 'Large Numbers'.
According to this law, if same experiment is repeated a large number of times, then the average of the experimental results in each trial shoul be very close to the theoretical probability.
When Jake flipped the magic coin 100 times, the probability of getting hesd was 0.64.
When he flipped 500 times, the probability of getting head was 0.57.
When he flipped 1000 times, the probability of getting head was 0.58
and when he flipped 1500 times, the probability was 0.62.
Also, the theoretical probability of the magic coin coming up head is
[tex]p=\dfrac{1}{2}=0.5.[/tex]
Therefore, we see that as the number of experiments increases, the value becomes closer to the theoretical value which is 0.5.
At the newest animated movie, for every 9 9 children, there are 4 4 adults. There are a total of 3 9 39 children and adults at the movie. How many children are at the movie?
Answer:
27 children.
Step-by-step explanation:
For every 9 children there are 4 adults .
x + y = 39 where x = number of children and y = number of adults.
and x/y = 9/4
so 4x = 9y
then x = 9y/4 , so substituting for x in the first equation:-
y + 9y/4 = 39 Multiplying through by 4:-
4y + 9y = 156
y = 156/13 = 12 so there are 12 adults
and 39 - 12 = 27 children
The problem is solved by using the ratio of children to adults and setting up a proportion. After cross-multiplying and solving the equation, it is determined that there are 27 children at the movie.
Explanation:This is a problem of ratio and proportion. In this case, the ratio of children to adults at the movie is 9 to 4. This means that for every 13 people at the movie (9 children plus 4 adults), 9 are children. We can set up a proportion to determine how many out of the total 39 people at the movie are children.
The proportion is:
9 children / 13 total people = x children / 39 total people
We can solve this problem by cross multiplying: 9 * 39 = 13 * x, which gives us: 351 = 13x. Dividing both sides of the equation by 13, we get: x = 27.
Therefore, 27 children are at the movie.
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Some rectangles are not parallelograms.
A. True
B. False
Someone please answer this for me!!!!
A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
The rectangle is a quadrilateral that has four sides and the opposites are always parallel.
The statement "Some rectangles are not parallelograms" is false.
Option B is the correct answer.
What is a parallelogram?A parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
Some rectangles are not parallelograms.
The rectangle is a quadrilateral that has four sides and the opposites are always parallel.
So,
All rectangles are parallelograms.
Thus,
The rectangle is a quadrilateral that has four sides and the opposites are always parallel.
The statement "Some rectangles are not parallelograms" is false.
Option B is the correct answer.
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Solve the inequality:
-4| 5x+12| -13> -44
Answer:
-79/20 < x< -17/20
Step-by-step explanation:
-4| 5x+12| -13> -44
The first step is to add 13 to each side
-4| 5x+12| -13+13> -44+13
-4| 5x+12| > -31
Divide each side by -4. Remember when dividing by a negative to flip the inequality
-4/-4| 5x+12| < -31/-4
| 5x+12| < 31/4
Now we will have 2 equations, one positive and one negative. Remember to flip the inequality for the negative
5x+12 < 31/4 and 5x+12 >-31/4
Subtract 12 from each side
5x+12-12 < 31/4-12 and 5x+12-12 >-31/4-12
5x < 31/4-12 and 5x >-31/4-12
Get a common denominator of 4
5x < 31/4-48/4 and 5x >-31/4-48/4
5x < -17/4 and 5x > -79/4
Divide each side by 5
x < -17/20 and x >-79/20
-79/20 < x< -17/20
Luke receives an electric bill of $84.21\$84.21$84.21 for the month of April. The electric company charges $0.14\$0.14$0.14 per kilowatt-hour (kWh)(\text{kWh})(kWh) of electricity. Given that April has 303030 days, about how many kilowatt-hours did Luke use per day during the month of April?
Answer:
The answer would be 20.05 hours per day.
Answer: There are 20.05 kwh that Luke use per day during the month of April.
Step-by-step explanation:
Since we have given that
Amount of electric bill = $84.21
Charges of electric company = $ 0.14 per kWh
We need to find the number of kilowatt hours.
Number of days in the month of April = 30 days
According to question,
[tex]84.21=0.14\times 30\times x\\\\84.21=4.2\times x\\\\\dfrac{84.21}{4.2}=x\\\\x=20.05\ kwh[/tex]
Hence, there are 20.05 kwh that Luke use per day during the month of April.
plz answer its easy math.
Answer:
B and E
Step-by-step explanation:
The rules of indicies states:
[tex]x^{a}[/tex] ÷[tex]x^{b}[/tex] = [tex]x^{a-b}[/tex]
So [tex]3^{-8}[/tex] ÷ [tex]3^{-4}[/tex] = [tex]3^{-8 - - 4}[/tex] = [tex]3^{-4}[/tex]
So that means B is one of the correct answers.
To find the other correct value, you can divide the two fractions as stated in the question:
[tex]3^{-8}[/tex] by [tex]3^{-4}[/tex] = [tex]\frac{1}{81}[/tex]
81 is equivalent to 3⁴
So that means E is also correct.
[tex]\text{Use}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\a^{-n}=\dfrac{1}{a^n}\\-----------------------\\\\\dfrac{3^{-8}}{3^{-4}}=3^{-8-(-4)}=3^{-8+4}=\underbrace{\boxed{3^{-4}}}_{\boxed{B.}}=\underbrace{\boxed{\dfrac{1}{3^4}}}_{\boxed{E.}}\\\\Answer:\ \boxed{B.\ and\ E.}[/tex]
What is the measure of each exterior angle for regular hexagon
Answer:
60 degrees.
Step-by-step explanation:
The total measure of the exterior angles of all polygons is 360 degrees,
A regular hexagon has 6 equal exterior angles so the measure of each angle is 360 / 6 = 60 degrees.
Answer:
Measure of each exterior angle for regular hexagon = 60°
Step-by-step explanation:
We have sum of interior angles of a polygon with n sides = (n-2) x 180
Sum of exterior angles = n x 180 - (n-2) x 180 = 2 x 180 = 360 degree.
So whatever be the number of sides the sum of exterior angles of a polygon is 360°.
Here we are asked to find the measure of each exterior angle for regular hexagon.
We know sum of exterior angles = 360°
Number of exterior angles = 6
Measure of each exterior angle for regular hexagon = 360/6 = 60°
Measure of each exterior angle for regular hexagon = 60°
how to answer this problem
Identify an equation in slope-intercept from for the line parallel to y=-3x + 7 that passes through (2, -4)
The slope-intercept form:
y = mx + b
m - slope
b - y-intercept
The parallel lines have the same slope.
We have y = -3x + 7 → m = -3. Therefore y = -3x + b.
Put the coordinates of the point (2, -4) to the equation of a line:
[tex]-4=-3(2)+b[/tex]
[tex]-4=-6+b[/tex] add 6 to both sides
[tex]2=b\to b=2[/tex]
Answer: y = -3x + 2a tv screen is 38.4” wide and 3.2” high. determine the size of the tv
the TV screen would have an area of 122.88 inches
to find this all you would have to do is multiply the 38.4 by 3.2
Answer:
The size of the tv is 122.88", or 122.88 in²
Step-by-step explanation:
a = w * h
w = 38.4
h = 3.2
a = (38.4) * (3.2)
a = 122.88
solve the equation 2x^2+18=0
Final answer:
The quadratic equation 2x² + 18 = 0 is solved by isolating the x² term and taking the square root of both sides, yielding solutions x = 3i and x = -3i.
Explanation:
To solve the quadratic equation 2x² + 18 = 0, you need to first move all terms to one side of the equation to set it equal to zero, which is already done in this case. Next, you would typically factor the quadratic or use the quadratic formula.
However, this equation can be simply factored since it is missing the x term. So, subtract 18 from both sides to isolate the x² term.
2x² = -18
Now, divide both sides by 2 to solve for x².
x² = -9
To solve for x, take the square root of both sides. Remember, when taking the square root of a number, you will have both a positive and negative solution.
x = √{-9} = ±3i
The solutions to the equation are x = 3i and x = -3i, where i is the imaginary unit.
Mrs. Ruiz bought 4 4/5 lbs of strawberries. She used 3/4 of them to bake a pie for dessert. How many lbs of strawberries did she use?
Answer:
3 3/5 lbs
Step-by-step explanation:
We will multiply the pounds of berries by the faction she used to see how much she used for the pie
4 4/5 * 3/4 = amount used in pie
We need to convert the mixed number to an improper fraction
4 4/5 = (5*4+4)/5 = 24/5
24/5 * 3/4 =
I will change the order to make the math easier
24/4 * 3/5
6 * 3/5 =
18/5
Now we need to change it back to a mixed number
5 goes into 18 3 times with 3 left over
3 3/5 lbs
She used 3 3/5 lbs
Last month, a car dealership sold 184 new cars. To determine customer satisfaction, the sales manager asked all of these newcar owners to complete an online survey. Only 32 of them completed the survey, and 24 of them said they were completely satisfied with their purchase. Based on the survey results, how many of all new car owners from last month are not−−− completely satified with their purchase?
Please help !!evaluate the algebraic expression 7x - 5 when x = 4/7
It takes a student 11 seconds to scan their hand at lunch. During one 30 min lunch period, approximately how many students can be scanned??? Is it 18,1008,180,1800. Plzzz I will give you 100 points
It takes 11 seconds to scan one person. So we have this ratio to start with
11 seconds: 1 person
Divide both sides by 11 to get this new ratio
1 second: 1/11 person
1 second: 0.0909 person
So in 1 second, 0.0909 of a person can be scanned. This statement seems silly because we can't have a fraction of a person, but it helps with the next part as shown below. The next step is to multiply both sides by 1800 to get....
1 second: 0.0909 person
1800*1 second: 1800*0.0909 person
1800 seconds: 163.62 persons
In a span of 1800 seconds (equivalent to 30 minutes), about 163 people's lunches can be scanned. Unfortunately, none of the answer choices are 163. The closest thing is 180, but that is an overestimate. So I would ask your teacher if there is a typo somewhere.
Note: if it took exactly 10 seconds for each student (instead of 11), then the answer would be 1800*(1/10) = 1800*0.10 = 180.
Solve by elimination. 7x+3y=25 -2x-y=-8
Answer:
x=1 , y=6
Step-by-step explanation:
7x+3y = 25
-2x-y = -8
Multiply the second equation by 3 so we can eliminate y
3(-2x-y )= -8*3
-6x -3y = -24
Add this equation to the first equation
-6x -3y = -24
7x+3y = 25
----------------------
x = 1
But we still need to find y by substituting x =1
-2x -y = -8
-2(1) -y = -8
-2-y = -8
Add 2 to each side
-2+2 = -8+2
-y = -6
Multiply by -1
y = 6
Solve for y?
y/4-y+1/5=y+2/8
A)y=-4
B)y=-11/3
C)y=18/7
D)y=-6
the correct answer to this question would be: y=8
−(−y+18)+11 =1
y−18+11 =1
y−7 =1
y =8
Jim's weight is 80% of Elijah's weight. Elijah weighs 90 pounds.
Select all the statements that are true about Jim's weight.
Answer Choices
a.Jim weighs 70 pounds.
b.Jim's weight is less than Elijah's weight.
c.The ratio of Jim's weight to Elijah’s weight is represented by the shaded squares to the total squares.
d.The ratio of Jim's weight to Elijah’s weight is represented by the ratio of the number of shaded squares to the number of unshaded squares.
Find the nth term of 3,12,27,48,75
Answer:
3n^2
Step-by-step explanation:
3, 12, 27, 48, 75
List the differences between terms:-
9, 15, 21, 27
Now find the second differences:-
6, 6, 6
The sequence in the question is quadratic and the first coefficient ( that of n^2) = 6/2 = 3. The first term in the nth term formula is 3n^2.
Now we write out the original sequence and the 3n^2 values as follows:-
3 12 27 48 75
3 12 27 48 75
They are the same so the formula for the nth term is 3n^2.
The nth term of the given sequence is 3n².
What is a series?A sequence's series is the total number of terms in the sequence.
A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.
Given the series,
3,12,27,48,75
Since all terms are multiplied of 3
3 × 1 = 3
3 × 4 = 12
3 × 9 = 27
3 × 16 = 48
3 × 25 = 75
It is clear that it is forming a series by 3 and the product of the square root of a natural number.
So, it will be 3n².
Hence "The nth term of the given sequence is 3n²".
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If (-6,-38) and (5,28) are two anchor points on the trend line, then find the equation of the line
Answer:
The equation of the line is y = 6x - 2 .
Step-by-step explanation:
Formula for the equation of line is.
[tex](y - y_{1}) = m (x - x_{1})[/tex]
Where m is the slope.
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
As given
If (-6,-38) and (5,28) are two anchor points on the trend line.
Than
[tex]m = \frac{28 - (-38)}{5 - (-6)}[/tex]
[tex]m = \frac{28 + 38}{5 + 6}[/tex]
[tex]m = \frac{66}{11}[/tex]
m = 6
Put the value in the equation of a line.
[tex](y - (-38)) = 6 (x - (-6))[/tex]
[tex](y + 38) = 6 (x + 6)[/tex]
[tex](y + 38) = 6x + 6\times 6[/tex]
[tex](y + 38) = 6x + 36[/tex]
y = 6x +36 - 38
y = 6x - 2
Therefore the equation of the line is y = 6x - 2 .
On a line segment, C is between B and D. If BC = 3.6 and BD = 8.4, what is CD?
Answer:
4.8
Step-by-step explanation:
b to c is 3.6
b to d is 8.4
if c is in the middle , you would subtract 8.4 and 3.6
Use synthetic division to solve (4x-3x+5x+6)/(x+6). What is the quotient?
The correct solution: 4x^2 -27x +167 - 996/(x+6)
Step-by-step explanation:
Solve the system by elimination state whether the system has one solution infinite solutions or no solution x+3y=-5 4x-y=6
Answer:
one solution, i.e x = 1 and y = -2
Step-by-step explanation:
Given two equations :
x+3y = -5 -------(1)
4x - y =6 ---------(2)
Using elimination method,
Multiply equation (2) by 3 and add it to equation (1)
We get,
x + 3y + {(4x - y)×3} = -5 +(6×3)
x + 12x + 3y - 3y = -5 + 18
13x = 13
x = 13/13 = 1
And corresponding y will be:
x + 3y = -5 , Plug x =1 to get y
1 + 3y = -5
3y = -5 - 1
y = -6/3 = -2
Hence we got only one solution, i.e x =1 and y = -2
Diagram 7 shows a trapezium ABCD. The straight lines AB and CD are parallel.Find
(a) the equation of the straight lines CD
(b)the x-intercept for the straight line CD
Answer:
see explanation
Step-by-step explanation:
(a)
Since lines AB and CD are parallel then their slopes are equal
y = - [tex]\frac{1}{2}[/tex] x + 14 is in slope- intercept form ( y = mx + c )
with slope m = - [tex]\frac{1}{2}[/tex]
Hence slope of CD = - [tex]\frac{1}{2}[/tex]
D is the point (0, 7) ⇒ c = 7
y = - [tex]\frac{1}{2}[/tex] x + 7 ← equation of CD
(b)
to find the x- intercept let y = 0, in the equation and solve for x
- [tex]\frac{1}{2}[/tex] x + 7 = 0 ( multiply through by 2 )
- x + 14 = 0 ⇒ - x = - 14 ⇒ x = 14 ← x- intercept of CD
Please help with this scatter plot question...PLEASE!!!
Answer:
Positive association and nonlinear
Step-by-step explanation:
Answer:
Positive association & Linear Association
Step-by-step explanation:
Positive charts go up from left to right (which this plot does)
Liner plots are any plots that can form a straight line (which this one does)
The formula
[tex]p = 14.7e {}^{ - 0.21x} [/tex]
gives the average atmospheric pressure, P, in pounds per square inch, at an altitude x, in miles above sea level. Find the average atmospheric pressure for an altitude of 2.3 miles. Round your answer to the nearest tenth.
Answer
the answer is P=7.8
Step-by-step explanation:
P=14.7e -0.21x
X=14.7e (-0.63)
take the natrual log of both sides
1n(P)=1n(14.7e(-.63)
1n(P)=1n(14.7)-.63
(because ln(e^a) = a)
1n(P)=2.688 - .63
1n(P)=2.058
P=e 2.058
P=7.8
Final answer:
To find the average atmospheric pressure at an altitude of 2.3 miles, substitute x = 2.3 into the given formula and solve, resulting in approximately 9.1 pounds per square inch.
Explanation:
The average atmospheric pressure for an altitude of 2.3 miles can be found by substituting x = 2.3 into the given formula: [tex]p = 14.7e^{-0.21x[/tex]
Substitute x = 2.3 into the formula:
p = [tex]14.7e^{-0.21(2.3)[/tex]
p ≈ [tex]14.7e^{-0.483[/tex]
p ≈ 14.7 × 0.617 ≈ 9.1 pounds per square inch (rounded to the nearest tenth)
If a sprinkler waters 1 over 12 of a lawn in 1 over 2 hour, how much time will it take to water the entire lawn?
Answer:
12 hours
Step-by-step explanation:
A photographer has 591 photos of animals and 234 photos of plants. He wants to put all of the photos into photo books. Each page of the photo books holds 8 photos. What is the fewest number of pages he could use in the photo books?
Answer:
He could use 104 pages in the photo books .
Step-by-step explanation:
Given :
A photographer has 591 photos of animals and 234 photos of plants.
Each page of the photo books holds 8 photos.
To Find : Fewest number of pages he could use in the photo books.
Solution :
A photographer has 591 photos of animals and 234 photos of plants.
Thus total no. of photos he have = 591+234 = 825 photos
Since he wants to put all the photos into photo book
No. of pages required for 8 photos = 1
No. of pages required for 1 photo = 1/8
No. of pages required for 825 photos:
= [tex]\frac{1}{8} *825[/tex]
⇒103.125 pages ≈ 104 pages
Hence he could use 104 pages in the photo books .
Help me pleeeeaaaase
Answer:
Step-by-step explanation:
4x=2z+5/y
X= 1/4(2z+5/y)
A red die is tossed and then a green die is tossed. What is the probability that the red die shows a number larger than three or the green die shows a number less than three?
The probability that the red die shows a number larger than three or the green die shows a number less than three is 0.83 or 83%.
Explanation:The question relates to the topic of probability in mathematics, which is the measure of the likelihood that an event will occur. In this case, we are looking at the probability of combined events with two standard six-sided dice, one red, and one green.
Firstly, the probability that the red die rolls a number larger than three is 3/6 or 0.5 since, out of 6 possible outcomes (1, 2, 3, 4, 5, 6), 3 (4, 5, 6) are favorable outcomes.
Secondly, the probability that the green die shows a number less than 3 is also 2/6 or approximately 0.33, as there are two favorable outcomes (1 and 2).
To find the probability of the red die showing a number larger than three OR the green die showing a number less than three, we add the two individual probabilities because these are independent events. Hence Probability = 0.5+0.33 = 0.83 or 83%
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The probability of the red die showing a number larger than three or the green die showing a number less than three is 1/9.
Explanation:To calculate the probability of the red die showing a number larger than three or the green die showing a number less than three, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The favorable outcomes are when the red die shows a number larger than three (i.e., 4, 5, or 6) or when the green die shows a number less than three (i.e., 1 or 2).
Since each die has 6 sides, the total number of possible outcomes for each die is 6. Therefore, the total number of possible outcomes for both dice is 6 * 6 = 36.
The number of favorable outcomes is 3 (for the red die) + 2 (for the green die) - 1 (for the outcome where both dice show a number larger than three and a number less than three) = 4.
Therefore, the probability is 4/36 = 1/9.
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decide whether the triangles are similar. If they are , write a similarity statement and state the reason justifying the similarity
I'll do the first one to get you started.
Start at point A as that is the first letter of the sequence ABC. The second letter is B so we'll record the length of segment AB, which is 4 units long.
Note how we have a segment that is also 4 units long in the other triangle; however, we won't use that one just yet. Instead, we'll go for the 2 unit segment. As it turns out, every piece of the triangle on the right side is half that of the left side triangle.
Segment ED is 2 units long. So AB and ED pair up
------------------------------
BC is 8 units long; DF is 4 units long (half of BC). So BC and DF pair up
I started at A, went to B, then to C in that exact order marking the side lengths of 4 and 8 respectively. At the same time for the other triangle, I started at E, moved to D, then to F recording the side lengths 2 and 4
So A pairs up with E, B pairs with D, and C pairs with F
Therefore, triangle ABC is similar to triangle EDF. The order is very important so that the points line up and correspond in the proper manner.
I used the SSS (side side side) similarity theorem to prove the triangles similar. This theorem says that if the sides are in proportion to one another, then the triangles are similar.