Answer:
I just did it and got it right so hoped it helped you ;)
1/2
1/2
1/4
Step-by-step explanation:
The probability that both coins will land heads up when Miranda flips them twice, assuming each coin is fair and has an equal chance of landing heads or tails, is 1/4. Each flip has a probability of 1/2 for heads, and these probabilities multiply for sequential independent events.
Explanation:If Miranda flips a coin twice, the probability that both coins will land heads up needs to be calculated by multiplying the probability of the first coin landing heads up by the probability of the second coin doing the same. Since the chance of a coin landing on heads (assuming it is a fair coin) is usually 50%, that is 1/2 for each flip. Therefore, to find the probability of both coins landing heads up, we multiply these probabilities together: 1/2 × 1/2 = 1/4.
In a broader context, the more times you flip a coin, the closer you are likely to get to 50% heads due to the law of large numbers. Notably, in experiments such as one conducted by Karl Pearson, after 24,000 coin flips, the relative frequency of heads was 12,012/24,000 ≈ 0.5005, closely aligning with the theoretical probability of 1/2. An essential assumption in determining these probabilities is that the coin is fair and each flip is independent of the others.
A pair of standard dice is rolled find the probability that the sum of the two dice is greater than 12
Answer:
Probability that the sum of the two dice is greater than 12 is ZERO.
Step-by-step explanation:
Here, when two dices are rolled together, the sample space is given as:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)
(6, 1), (6, 2), (6, 3), (6, 4),(6,5), (6,6) = Total 36 outcomes
Now, E : Event of getting a sum greater than 12.
So here, number of possible outcomes = 0
So, the probability that the sum of the two dice is greater than 12 = 0/36 = 0
So, it is an IMPOSSIBLE EVENT.
It is impossible to roll a sum greater than 12 with two standard six-sided dice, as the maximum sum possible is 12. Therefore, the probability of rolling a sum greater than 12 is zero.
Explanation:The student asked about the probability that the sum of two standard six-sided dice is greater than 12. Since the highest sum one can achieve with two six-sided dice is 12 (when both dice show a 6), it is impossible to roll a sum greater than 12. Therefore, the probability of this event is zero.
When considering every outcome of rolling a die, we must include all possible individual results, which range from 1 to 6 for each die. The sum of two dice ranges from a minimum of 2 (both dice showing 1) to a maximum of 12 (both dice showing 6). Consequently, there are no combinations of dice that can result in a sum that exceeds 12.
The highest sum achievable on two six-sided dice is 6 + 6 which equals 12. This makes sums greater than 12 unattainable, and highlights the importance of considering the specified number of sides on dice when calculating probabilities related to their sums.
Let x represent one number and let y represent the other number. The sum of two numbers is -11 if one number is subtracted from the other their difference is -3 use the given conditions to write of the equation and solve the system find the numbers
Answer:
look at above image for answer. thank you for the question
Using the given conditions, we formed two equations: x + y = -11 and x - y = -3. We then solved these simultaneous equations to find that the two numbers are -7 and -4.
We have been given two conditions to find the values of two numbers, represented by x and y. The first condition can be expressed as the equation x + y = -11. The second condition gives us the second equation x - y = -3.
adding the first and second equation:
(x + y) + (x - y) = -11 + (-3)
2x = -14
x = -7
We can then substitute the value of x back into one of the original equations to solve for y:
-7 + y = -11
y = -11 + 7
y = -4
Thus, the two numbers are -7 and -4.
Find the equation of a line (5,-2) (-3, -2)
Answer:
y=-2
Step-by-step explanation:
y-y1=m(x-x1)
m=slope & (x1, y1) is a point on the line
m=(y2-y1)/(x2-x1)
m=(-2-(-2))/(-3-5)
m=(-2+2)/(-8)
m=0
y-(-2)=0(x-5)
y+2=0
y=0-2
y=-2
The school principal determined that 1/4 of the original student school desks would need to be replaced this year. 50 teachers would also receive new, improved desks. A total of 295 student and teacher desks were purchased.
How many original student desks were there before the
purchase was made?
There were 980 student desks originally before the purchase was made.
Step-by-step explanation:
Total desks purchased = 295
As 50 new desks are for teachers, therefore, we will subtract this amount from total;
Desks purchased for students = 295-50 = 245
Let,
x be the number of original student desks, therefore,
[tex]\frac{1}{4}\ of\ x=245\\\frac{x}{4}=245[/tex]
Multiplying both sides by 4
[tex]4*\frac{x}{4}=245*4\\x=980[/tex]
There were 980 student desks originally before the purchase was made.
Keywords: subtraction, fractions
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Miami and Orlando are 205 miles apart. If a map shows them as 5 inches apart, give the scale.
Answer:
1 inch = 41 miles
Step-by-step explanation:
205 / 5 = 41
1 inch = 41 miles
Answer:
41 miles per inch
could be answered as 41/1 or 41:1
Step-by-step explanation:
Use a ratio to find the scale.
205/5
Divide the numerator and denominator by 5 to simplify.
41/1
A bookcase has 3 shelves with a total of 24 books. The top shelf has 8 mystery books. The middle shelf has 10 math books. The bottom shelf has 6 science books. Two books are now taken off each shelf. What fraction of the books remaining on the three shelves are math books? Express your answer as a common fraction.
Answer:22/24 or 11/12
Step-by-step explanation:
Answer:
Six books are removed from the shelves, so $24-6=18$ books remain. Of these, $10-2=8$ are math books. Therefore, $8/18=\boxed{4/9}$ of the books remaining are math books.
Step-by-step explanation:
4/9
Given the following sequence {a^k} beginning with a0=4
4,11,18,25,32,39
What is the value of a4?
==================================
Explanation:
Simply pair each value given in the sequence with a0,a1,a2,etc like so
a0 = 4
a1 = 11
a2 = 18
a3 = 25
a4 = 32
a5 = 39
What is the equation of the line that passes through the point (-2, 7) and has a slope of zero
Answer:
y = 7 is the equation of the line that passes through the point ( -2, 7 ) and has a slope of zero.
Step-by-step explanation:
Given:
Let,
A ≡ ( x1 , y1 ) ≡ ( -2, 7 )
Slope = m = 0
To Find :
Equation of Line:
Solution:
Formula for , equation of a line passing through a point ( x1 , y1 ) and having a slope m is given by
[tex](y - y_{1})=m(x-x_{1})[/tex]
Now substituting the values of x1 = -2 and y1 = 7 and slope m = 0 we get,
[tex]y-7=0\times(x--2) \\y-7=0\times (x+2)\\y-7=0\\\therefore y=7[/tex]
Which is the required equation of a line passing through the point ( -2, 7 ) and slope zero
The equation of a line that passes through a point is an algebraic equation. It can also be referred to as the Slope-Intercept Equation.
The equation of the line that passes through the point (-2, 7) and has a slope of zero is written as: y = 7
The equation of the line through a point (x1, y1) can be represented by the algebraic equation:
y = mx + c
where:
m = slope
c = y - intercept
From the question,
(x1, y1) = (-2, 7)
m = slope = 0
Substituting these values into the algebraic equation,
7 = (0 x -2) + c
7 = 0
Hence, y = 7
The equation of the line that passes through the point (-2, 7) and has a slope of zero is y = 7
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There are less than 200 apples in a box. It is known that 2, 3, 4, 5, or 6 kids can share these apples evenly. How many apples can be in that box?
Answer:
There can be 180 apples in that box.
Step-by-step explanation:
1. Let's review the information given to answer the question correctly:
Number of apples in a box < 200
2. It is known that 2, 3, 4, 5, or 6 kids can share these apples evenly. How many apples can be in that box?
The answer is that the number of apples that can be in the box is the highest multiple of 2, 3, 4, 5, and 6 that is close to 200.
The common multiples for this set of numbers are 60, 120, 180, 240, 300 and so on with 60 as the constant.
Therefore, the highest number that is multiple for this set of numbers and at the same time lower than 200 is 180.
There can be 180 apples in that box.
Answer:
120 or 180 apples
Step-by-step explanation:
It hasd to be divisible by 5 so it can only end in fives and zeroes next it has to be divisible by 2 so that narrows it tdown to only number that end in zero the it has to be divisible by 3 once yo find that you have two answers
120 or 180 and that is how many apples can be in the box
need some help with this please
Answer:
40 and 50
Step-by-step explanation:
We know that River's mom drove for 45 minutes. Furthermore, at x miles per hour for a time amount y, she drove 10 miles, and at x+10 miles per hour for time amount z, she drove 25 miles. We can set up the equations like this:
x*y = 10
(x+10)*z = 25
y+z = 0.75
I knew to include time as the variable because time was given at the end, and is the only way possible to solve this. Furthermore, we can multiply x and y because we drive for x miles per hour for y hours, so
[tex]\frac{x miles}{hours} * \frac{yhours}{1} = xmiles*y[/tex]
I turned 45 into 0.75 as 45 is 3/4 of an hour, and y and z are in hours.
We're kind of stuck here, so it would be nice if we could limit the variables in an equation. One way to do this would be to solve for y in the first equation, so x=10/y. Then, we can plug that into the second equation to get
(10/y+10)*z=25
Combining that with the third equation, we can solve for z in the second equation to get that 25/(10/y+10)=z, and then plug that into the third to get that
y+25/(10/y+10) = 0.75
Multiplying both sides by 10/y+10 to get rid of the denominator, we get
10+10y+25=7.5/y+7.5
Then we multiply by y to get rid of the denominator
10y+10y²+25y=7.5+7.5y
Subtracting 7.5+7.5y to get everything on one side for a quadratic equation
10y²+27.5y-7.5=0
Plugging this into the quadratic equation, we get than y either equals -3 or 0.25. It's clear that you can't have negative time, so y = 0.25
Then, 0.75-0.25=0.5=z, and 10/0.25=40, so x=40, and x+10=50 for the 2 driving speeds
Enter an equation in point-slope form for the line.
Slope is O and (6, 7) is on the line.
Answer:
[tex]\displaystyle y = 7[/tex]
Step-by-step explanation:
Since the rate of change [slope] is zero, that automatically makes our equation set equal to the y-coordinate of the ordered pair, which in this case is the y-intercept.
I am joyous to assist you anytime.
the slope is 35. The y-intercept is 550. what can you conclude?
If you are given the slope and y-intercept of a line, you can conclude several things about the line and use them to write the equation of the line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
For the values you've given:
- The slope (m) is 35.
- The y-intercept (b) is 550.
From these pieces of information, you can conclude:
1. **Slope (Steepness and Direction):** Since the slope is 35, this tells us that the line is relatively steep and rises quickly. The slope is positive, which means the line slants upwards from left to right. Specifically, for every one unit that x increases, y increases by 35 units.
2. **Y-intercept (Starting Point):** The y-intercept is where the line crosses the y-axis. Since the y-intercept is 550, it indicates that the line will cross the y-axis at the point (0, 550). This is the starting point of the line if you begin plotting from the y-axis.
With these conclusions, you can write the equation of the line in slope-intercept form:
\[ y = 35x + 550 \]
This equation allows you to predict or calculate the value of y for any given value of x along the line. It also enables you to graph the line by plotting the y-intercept and using the slope to determine the direction and steepness of the line. Remember, a line extends infinitely in both directions on the graph, so the portion you draw depends on the context or constraints of the particular situation you are modeling with the line.
868 divided by 4 equals
Answer:
217
Step-by-step explanation:
868/4=217
Answer:
217
Step-by-step explanation:
Solve the equation.
a² = 100
Enter the correct answer in the boxes.
a = 10 or a = ?
help me with this geometry question with proofs
Answer:
m ∠ AMC = 75°
Step-by-step explanation:
Given:
In Δ ABC, m ∠C=90°
m∠ B =30°
CM is angle bisector
We need to find m ∠AMC
In Δ ABC Sum of all angle is 180° so we get,
[tex]m\angle A+m\angle B+m\angle C =180\\m\angle A+90+30 =180\\m\angle A+120 =180\\m\angle A=180-120\\m\angle A=60[/tex]
Now we know that CM is angle bisector of ∠C
∴ [tex]m\angle ACM +m\angle BCM =90\\m\angle ACM +m\angle ACM =90\\2m\angle ACM =90\\m\angle ACM =\frac{90}{2}=45[/tex]
Now in Δ ACM we know that Sum of all angles is 180
[tex]m\angle ACM + m\angle AMC + m\angle A=180\\45 + m\angle AMC + 60 =180\\105 + m\angle AMC =180\\m\angle AMC =180 -105 =75[/tex]
Hence m ∠ AMC = 75°
The sum of two numbers is 48, and their difference is 14. What are the two numbers?
Answer: 17 and 31
Step-by-step explanation:
first number = x
second number = y
x+y=48
-(x-y=14)
---------------
2y=34
y=17
x=31
Answer:
17 and 31
Step-by-step explanation:
17 + 31 = 48, I basically just plugged in random numbers until I got the answer.
Answer each question and explain your reasoning. How long is 50% of 60 minutes? How long is 10% of 60 minutes? How long is 75% of 60 minutes?
Answer:
Step-by-step explanation:
50% of 60? 0.5*60=30
10% of 60? 0.1*60=6
75% of 60? 0.75*60=45
50percent of 60 minutes is 30 minutes, 10percent of 60 minutes is 6 minutes, and 75percent of 60 minutes is 45 minutes.
50percent of 60 minutes: 50percent of 60 minutes is half of 60, which equals 30 minutes.
10percent of 60 minutes: 10percent of 60 minutes is 6 minutes (10percent of 60 is 6).
75percent of 60 minutes: 75percent of 60 minutes is 45 minutes (75percent of 60 is 0.75 * 60 = 45).
M=x1+x2/2 solve for x1
After solving for x1, we get
[tex]x_1 = 2M-x_2[/tex]
Step-by-step explanation:
Given formula is:
[tex]M = \frac{x_1+x_2}{2}[/tex]
In order to solve for x1, we have to isolate x1 on one side of the equation
So,
Multiplying the whole equation by 2:
[tex]2M = \frac{x_1+x_2}{2} * 2\\2M = x_1+x_2[/tex]
Subtracting x2 from both sides
[tex]2M-x_2 = x_1+x_2-x_2\\2M-x_2 = x_1[/tex]
so,
After solving for x1, we get
[tex]x_1 = 2M-x_2[/tex]
Keywords: Formulas, Solving for a variable
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Help?! Can somebody tell me the answer and can they explain how to do it?
Answer:
[tex]15x^7y^5[/tex]
Step-by-step explanation:
Given
[tex]5x^3y^2\times 3x^4y^3[/tex]
Rewrite it as
[tex](5\cdot 3)\times (x^3\cdot x^4)\times (y^2\cdot y^3)[/tex]
Use power property:
[tex]a^m\cdot a^n=a^{m+n},[/tex]
so
[tex]x^3\cdot x^4=x^{3+4}=x^7\\ \\y^2\cdot y^3=y^{2+3}=y^5[/tex]
Then
[tex](5\cdot 3)\times (x^3\cdot x^4)\times (y^2\cdot y^3)=15\times x^7\times y^5=15x^7y^5[/tex]
Sin 60 is what? Exact value please
Answer: 0.8660254038
Find three solution of equation - 4X+2Y-5=0
(x,y) =
(x,y) =
(x,y) =
Answer:
(0,2.5), (-1.25,0) and (3,8.5)
Step-by-step explanation:
we have
[tex]-4x+2y-5=0[/tex]
This is a linear equation (equation of a line)
If a ordered pair is a solution of the linear equation, the the ordered pair must satisfy the linear equation
1) Find the y-intercept
The y-intercept is the value of the y when the value of x is equal to zero
For x=0
substitute the value of x in the linear equation and solve for y
[tex]-4(0)+2y-5=0[/tex]
[tex]2y=5[/tex]
[tex]y=2.5[/tex]
The ordered pair is (0,2.5)
2) Find the x-intercept
The x-intercept is the value of the x when the value of y is equal to zero
For y=0
substitute the value of y in the linear equation and solve for x
[tex]-4x+2(0)-5=0[/tex]
[tex]-4x=5[/tex]
[tex]x=-1.25[/tex]
The ordered pair is (-1.25,0)
3) Assume any value of x or y and solve for the other variable
For x=3
[tex]-4(3)+2y-5=0[/tex]
[tex]-12+2y-5=0[/tex]
[tex]2y=17[/tex]
[tex]y=8.5[/tex]
The ordered pair is (3,8.5)
A Shark Weighs 405 kilograms and 68 grams a second shark weighs 324 kilograms and 75 grams how much more does the first shark weigh in grams than the second shark
Answer:
7 grams
Step-by-step explanation:
If you're asking me grams specifically, and not kilograms, subtract 68 from 75 to get your answer. If it's only kilograms subtract 324 from 405. If it's both of them added together subtract 399 from 473, you're welcome!
Answer:
7 grams
Step-by-step explanation:
A triangle has two sides of length 40 cm and an angle of 110°.
a) Determine the length of the third side. Then find the perimeter of the triangle.
47
b) Determine the area of the triangle
Answer:
a) c = 65.532 cm
P = 145.532 cm
b) A = 751.754 cm²
Step-by-step explanation:
This is an isosceles triangle. The given angle is obtuse, so it must be the vertex angle.
a) One way to find the length of the third side is law of cosine:
c² = a² + b² − 2ab cos C
c² = 40² + 40² − 2(40)(40) cos 110°
c = 65.532
Another way is to cut the triangle in half and use sine.
sin (110°/2) = (c/2) / 40
c = 80 sin 55°
c = 65.532
The perimeter is the sum of the sides:
P = 40 + 40 + 65.532
P = 145.532
b) You can find the area using the SAS equation:
A = ½ ab sin C
A = ½ (40)(40) sin 110°
A = 800 sin 110°
A = 751.754
Another way is to split the triangle in half, find the height using cosine, then use half the base times height.
cos (110°/2) = h / 40
h = 40 cos 55°
h = 22.943
A = ½ ch
A = ½ (65.532) (22.943)
A = 751.754
subtract 3x squared +7x-4 from 8x squared-6+2 your answer should be polynomial in standard form
Answer:
5x² - 13x + 6
Step-by-step explanation:
8x² - 6x + 2 - (3x² +7x -4)
Simplify the expression:
8x² - 6x + 2 - 3x² -7x + 4
Combine like terms:
5x² - 13x + 6
plzzz help !!!!!!!!!!!!!!!!!!!!!!!
Answer:
Y = - 2
Step-by-step explanation:
Put your finger at x= 0 or (0,0) and go down until you hit the black line, thats your y
If 2a = 80 and b = c, what is the measure of b
A.) 40
B.) 50
C.) 80
D.) 100
Answer:
From what I can tell from the image, b is equivalent to B.) 50°
Step-by-step explanation:
So to start off 2a=80° there is 2 a's. so you subtract 80° from 180° to get 100°.
now b=c and their is 100° left over. So 100°/2 is 50° because if b=50° and c=50° both angles equal 100°.
Answer : The correct option is, (B) 50
Step-by-step explanation:
As we are given :
2a = 80
b = c
As we know that:
The sum of interior angles of a triangle is equal to [tex]180^o[/tex].
That means,
[tex]\angle A+\angle B+\angle C=180^o[/tex]
[tex]80^o+\angle B+\angle C=180^o[/tex]
and, [tex]\angle B=\angle C[/tex]
So,
[tex]80^o+2\angle B=180^o[/tex]
[tex]2\angle B=180^o-80^o[/tex]
[tex]2\angle B=100^o[/tex]
[tex]\angle B=\frac{100^o}{2}[/tex]
[tex]\angle B=50^o[/tex]
Thus, the value of 'b' is [tex]50[/tex]
Which ordered pair would form a proportional relationship with the point graphed below?
(10, –20)
(–30, 20)
(–10, 5)
(35, –20)
Answer:
I think it would be either (-10, 5) or (35, -20)
Step-by-step explanation:
Answer:
It Is C
Step-by-step explanation:
Edg 2020
Sandwiches
Veggiburger....... .........03.25
Roast BeetWrap............ $4.50
Ham and Cheese..............$3.75
Side Orders
Steak Fries.....
..$1.50
Salad........
...$2.50
Soup.
$2.25
Beverages
Cola
Ice Tea.
Coffee......
Water...
..$1.50
..$1.75
...$0.90
$1.00
If you and a friend order 2 veggiburgers, one salad, one fries and 2 coffees, what is the total bill
with 4% tax and 15% tip?
$13.70
0
$16.43
$15.67
•
$14.64
Thing
The total bill is $14.64 ⇒ last answer
Step-by-step explanation:
The given is;
Sandwiches
Veggieburger................$3.25Roast Beet Wrap.............$4.50Ham and Cheese....... ....$3.75Side Orders
Steak Fries.......$1.50Salad..................$2.50Soup...................$2.25Beverages
Cola...................$1.50Ice Tea..............$1.75Coffee...............$0.90Water.................$1.00∵ You order 2 veggieburgers, one salad, one fries and 2 coffees
∵ The price of the 1 veggieburgers = $3.25
∵ The price of the 1 salad = $2.5
∵ The price of the 1 fries = $1.5
∵ The price of the 1 of one coffee = $0.9
∴ The cost of the order = 2(3.25) + 1(2.5) + 1(1.5) + 2(0.9)
∴ The cost of the order = 6.5 + 2.5 + 1.5 + 1.8 = $12.3
∵ There is a tax 4%
∴ The tax = 4% × 12.3 = [tex]\frac{4}{100}[/tex] × 12.3 = $0.492
∵ There is a tip 15%
∴ The tip = 15% × 12.3 = [tex]\frac{15}{100}[/tex] × 12.3 = $1.845
To find the total bill add the cost of the order, the tax and the tip
∵ The total bill = cost of the order + tax + bill
∴ The total bill = 12.3 + 0.492 + 1.845
∴ The total bill = $14.637 ≅ $14.64
The total bill is $14.64
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A positive number is multiplied by itself and then 7 is added. The answer is 16. What is the number?
Answer:
3
Step-by-step explanation:
To solve this you have to work backwards with what you are given.
16-7=9
Then we know that a number has to be multiplied by itself to equal nine the only number that follows that criteria is 3
3*3=9+7=16
Answer:
3
Step-by-step explanation:
Work backwards. 16 Subtract 7. Take square root. We take the square root because that is how to undo a number that was multiplied by itself.
16-7=9 √(9)=3
Check this by going through the same steps listed in the question:
A positive number is multiplied by itself. then 7 is added. the answer is 16
3×3=9
9+7=16
A total of 814 tickets were sold for the school play. They were either adult tickets or student tickets. There were 64 more student tickets sold than adult tickets. How many adult tickets
Answer:
STUDENT TICKETS SOLD = 439ADULT TICKETS SOLD = 375814 - 64 = 750
750 ÷ 2 = 375
375 + 64 = 439
The problem can be solved by setting up two equations based on the given information, substituting one equation into the other, and then solving for the variable. In this case, 375 adult tickets were sold.
Explanation:The subject of this problem is mathematics, particularly a class of problems known as linear equations. Let's assign variables to each type of ticket: A for the number of adult tickets and S for the number of student tickets.
According to the problem, S = A + 64 (because there were 64 more student tickets sold) and S + A = 814 (because a total of 814 tickets were sold).
With these two equations, you can substitute the value of S from the first equation into the second equation. Therefore, (A + 64) + A = 814. Simplify this to get 2A + 64 = 814.
To find the number of adult tickets, solve the simplified equation for A. Subtract 64 from both sides to get 2A = 750, and then divide by 2 to find that A = 375.
So, 375 adult tickets were sold.
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