Answer: The probability of getting exactly 4 heads in 4 tosses of a fair coin is 0.0625, or 6.25%.
Step-by-step explanation:
We can use the formula for combinations, which is:
n! / (r! * (n - r)!)
In this case, n is the total number of tosses (4) and r is the number of successes we want to count (4 heads). Plugging these values into the formula, we get:
4! / (4! * (4 - 4)!) = 4! / (4! * 0!) = 4! / (4! * 1) = 1 / 1 = 1
The probability of getting exactly 4 heads in 4 tosses of a fair coin is therefore 1, or 100%. However, this is assuming that the coin is not fair and always lands on heads. If the coin is fair, the probability of getting 4 heads in 4 tosses is actually much lower.
To find the probability of getting 4 heads in 4 tosses of a fair coin, we need to use the formula for binomial probability, which is:
(n! / (r! * (n - r)!) * p^r * (1 - p)^(n - r)
In this case, p is the probability of getting a head in a single toss of the coin (0.5), r is the number of successes we want to count (4 heads), and n is the total number of tosses (4). Plugging these values into the formula, we get:
(4! / (4! * (4 - 4)!) * 0.5^4 * (1 - 0.5)^(4 - 4) = 1 * 0.5^4 * (1 - 0.5)^0 = 0.5^4 * 1 = 0.0625
Thus, the probability of getting exactly 4 heads in 4 tosses of a fair coin is 0.0625, or 6.25%, to the nearest thousandth.
Helppppp meeeee guyssss
NEED HELP ASAP!
Refer to the triangle.
What is the length of side AB?
(Blank) units
After solving the equation the length of AB is [tex]2\sqrt{3}[/tex]
What do you mean by trigonometry?
Trigonometry “triangle” and “measure”) is a branch of mathematics that studies the relationship between the side lengths and angles of triangles.
A trigonometric ratio is the ratio between the edges of a right triangle.
The sine function (sin) defined as the ratio of the opposite side of the angle to the hypotenuse.
In the given triangle ABC , use sin ratio to find AB.
tan θ = P/B
tan 30 = AB/6
[tex]\frac{1}{\sqrt{3} } =AB/6[/tex]
AB = [tex]\frac{6}{\sqrt{3} }[/tex] = [tex]\frac{6}{\sqrt{3} }\times \frac{\sqrt{3}}{\sqrt{3}}= \frac{6\sqrt{3}}{3}=2\sqrt{3}[/tex]
Therefore, length of AB is [tex]2\sqrt{3}[/tex]
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Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem.
1) a n = -11 +7n Find a 34
2) a n = 65-100n Find a 39
3) a n = -7.1-2.1n Find a 27
4) a n = 118 +1 2 n Find a 23
Answer: 59
Step-by-step explanation:
Which expression is equivalent to the perimeter of your the rectangle shown below?
The expression that is equivalent to the perimeter of the rectangle in the image shown is, 6x + 8.
How to Find the Perimeter of a Rectangle?To find the perimeter of a rectangle, add all the four sides of the rectangle. The following formula can be used:
Perimeter (P) = 2(length + width).
In the rectangle shown below, the dimensions are:
Length of rectangle = 2x + 3
Width of rectangle = x + 1
Substitute into the perimeter each expression of the dimensions:
Perimeter = 2[(2x + 3) + (x + 1)]
Open the parentheses by applying the distributive property of equality:
Perimeter = 2(2x + 3 + x + 1)
= 2(3x + 4)
= 2(3x) +2(4)
= 6x + 8
Therefore, the expression is, 6x + 8.
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Given the functions f(x) = x3 + x2 – 3x + 4 and g(x) = 2x – 4, what type of functions are f(x) and g(x)? Justify your answer. What key feature(s) do f(x) and g(x) have in common? (Consider domain, range, x-intercepts, and y-intercepts.)
1. f(x) - cubic function -- polynomial , g(x) - linear function
similar
domain all real numbers (?)range is all real number, end behavior is the sameThe function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.
Domain: -∞ < x < ∞
Range: -∞ < y < ∞
y-intercept = 4
x - intercepts = -2.68
Function g(x)
Domain: x > 0
Range: -4 < y < ∞
y - intercept = -4
x - intercepts = none
By comparing the key features above, we can conclude that the common features in both functions are their range
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Four more than the product of a number and 8 is equal to 7.
Answer: x = 0.375
Step-by-step explanation:
Equation: 8x + 4 = 7
Subtract 4 on both sides
8x = 3
Divide by 8 on both sides
x = 3/8 is 0.375 decimal
x = 0.375 (0.38 round-up)
Answer:
x = 3/8
Step-by-step explanation:
Four more than the product of a number and 8 is equal to 7.
4 + 8x = 7
8x = 7 - 4
8x = 3
x = 3/8
---------------------
check
4 + 8 x 3/8 = 7
4 + 3 = 7
7 = 7
the answer is good
the distribution of scores on a recent test closely followed a normal distribution with a mean of 22 points and a standard deviation of 2 points. for this question, do not apply the standard deviation rule. (a) what proportion of the students scored at least 27 points on this test, rounded to five decimal places?
Therefore ,0.62097 % proportions of students scored at least 27 points on this test
What do you learn from z-scores?The Z-score provides information on how far a given value deviates from the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations above or below the mean a specific data point falls. The level of variability within a particular data collection is effectively reflected in the standard deviation.
Here,
z = (x - μ)/σ
here ,raw score =x ,standard deviation=σ and mean= μ
μ = 22, σ = 2
For x > 27:
z = (27 - 22)/2 = 1
P(z > 1) = 1 - P(z < 1) = 1 - 0.99379 = 0.0062097
Therefore , 0.62097 % of students scored at least 27 points on this test
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Describe fully the single transformation that the maps triangle a onto triangle b
The transformations that took for mapping ΔA onto ΔB are:
a) Translated the triangle A 2 units to the right,
b) Reflected the ΔA' (translated A) over the y-axis,
c) Reflected the ΔA'' (reflected A) over the x-axis, resulting in ΔB.
What are transformation rules applied to triangle A to form triangle B?The transformation rules are:
a) Translation: (x, y) ⇒ (x + 2, y) (In the right side direction)
b) Reflection over the y-axis: (x, y) ⇒ (-x, y)
c) Reflection over the x-axis: (x, y) ⇒ (x, -y)
Calculation:The given vertices of triangle A are: (-2, 3), (-5, 3), and (-5, 5).
a) Applying translation by 2 units to the right to triangle A:
(-2, 3) → (-2 + 2, 3) → (0, 3)
(-5, 3) → (-5 + 2, 3) → (-3, 3)
(-5, 5) → (-5 + 2, 5) → (-3, 5)
So, triangle A is translated to triangle A'.
b) Applying reflection over the y-axis to the triangle A':
(0, 3) → (0, 3)
(-3, 3) → (3, 3)
(-3, 5) → (3, 5)
So, triangle A' is reflected as triangle A''.
c) Applying reflection over the x-axis to triangle A'':
(0, 3) → (0, -3)
(3, 3) → (3, -3)
(3, 5) → (3, -5)
Thus, the formed triangle is B at the vertices (0, -3), (3, -3), and (3, -5).
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help ???????????????
a. 4(x - 5)^2
= 4 * (x - 5)^2
= 4 * ((x - 5) * (x - 5))
= 4x^2 - 40x + 100
b. 3(x + 1) (2x - 9)
= (3(x + 1)) (2x + −9)
= (3(x + 1))(2x) + (3(x + 1))(−9)
= 6x^2 + 6x − 27x − 27
= 6x^2 − 21x − 27
c. -2(4x + 2)^2
= -2 * (4x + 2)^2
= −2 * ((4x + 2) * (4x + 2))
= 32x^2 − 32x − 8
or d. -2(4x + 2)^2 - 5 (with subtracting 5)
= −32x^2 + −32x + −8 + −5
= (−32x^2) + (−32x) + (−8 + −5)
= −32x^2 + −32x + −13
d. -3(5x - 2)^2 + 5 (with negative)
= 75x^2 + −60x + 12 + 5
= 75x^2 + −60x + 12 + 5
= (75x^2) + (−60x) + (12 + 5)
= 75x^2 + −60x + 17
or d. 3(5x - 2^2 + 5 (without negative)
= (3)(5x + −4 + 5)
= (3)(5x) + (3)(−4) + (3)(5)
= 15x − 12 + 15
= 15x + 3
What is the slope of the equation 3x+20=-4?
The slope of the equation 3x+20=-4 is 8.
How may mathematical expressions be made simpler?
Mathematical operations may be made more simpler by using the right order of operations. Exponents, words in parentheses, multiplication, division, addition, and ultimately subtraction are the right order of operations. PEMDAS is a helpful acronym that you may use to remember this.
1. Subtract 20 from both sides
[tex]\begin{aligned}& 3 x+20=-4 \\& 3 x+20-20=-4-20\end{aligned}[/tex]
2. Simplify
Subtract the numbers
3 x=-24
3. Divide both sides by the same factor
[tex]\begin{aligned}& 3 x=-24 \\& \frac{3 x}{3}=\frac{-24}{3}\end{aligned}[/tex]
4 Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
x=-8
Y = mx + b, where m is the slope and b is the y-intercept, is the slope equation utilising the equation of a line.
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The digits in the product of 0.48 and a decimal number between 350 and 400 are 182136. Explain how to correctly place the decimal point without knowing the other factor. Then Place place the decimal point in the product.
The decimal point is to be placed three places to the left.
What are decimal numbers?
When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.
Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.
If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.
Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.
The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.
The decimal point is to be placed three places to the left.
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Solve for x in the circle
An angle is outside a circle if its vertex is outside the circle and its sides are tangents or secants. Here the angle is formed by two tangents,
The value of x is 80°.
What is a Tangent?The tangent is defined as a line touching circles or an ellipse at only one point. Suppose a line touches the curve at P, then the point “P” is called the point of tangency.
Calculation:As we know that the complete angle of the circle is 360°
The answer for x° is 360° - 260° = 100°
⇒ 260°- 100° = 160° now,
⇒ 160°/2 = 80°
∴ x = 80°
Hence, for the given two tangents formed the answer for x° = 80°
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please help, this is my finals & i don’t know it
Answer:
i think that answer is correct
Step-by-step explanation:
find the inverse of f(x)=√x+4-2
one number is 4 less than 3 times a second number. Two times the first number decreased by two times the second is 8. what is the value of the larger number?
A.4
B.12
C.8
D.2
E.14
Answer:
Step-by-step explanation: To solve the problem, we can use the given information to set up a system of equations and solve for the values of $x$ and $y$. Specifically, we are given that one number is 4 less than 3 times a second number, and that two times the first number decreased by two times the second is 8.
Let $x$ represent the larger number, and $y$ represent the second number. We can write the given information as a system of equations as follows:
x &= 3y - 4
2x - 2y &= 8
Solving this system of equations, we find that $x = 12$ and $y = 2$. Therefore, the value of the larger number is 12
a rectangle is 3 feet longer than it is wide. find the dimensions of the rectangle if its area is 208 sq-feet
Dimensions of the Rectangle are : 16 feet by 13 feet .
A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal . A rectangle has two dimensions. we can measure its length and, perpendicular to that, its width.
Rectangle is 3 feet longer than it is wide and its area is 208 sq-feet .
Area of Rectangle = l×b ( Where l = length , b = breadth )
Therefore , Let X be the the width of rectangle . then from given it's length is (X+3).
∴ X × (X+3) = 208
∴ [tex]x^{2}[/tex]+3X-208 = 0
(X+16)(X-13) = 0
X = -16 & X = 13
Distance can't be negative so Width = X = 13 feet.
∴ Length = X+3 = 16 feet.
Thus the Dimensions are 16 feet by 13 feet .
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Question 1
Find the midpoint of the line segment with these
endpoints: (7,-6), (-6, -8)
A) (-18, -10)
B) (6.5, 1)
C) (0,5)
D) (.5, -7)
OB
OC
OA
OD
10 pts
Answer:
D
Step-by-step explanation:
(7+-6)/2
(7-6)/2
1/2
(-6+(-8)/2
(-6-8)/2
-14/2
-7
(.5,-7)
giving barinly to someone who answers in a complete sentence and who is write
Approximate √15 to the nearest integer.
Explain how you got your answer.
The square root of 15 is approximately 4.
To approximate the square root of 15, we can find the perfect squares that are closest to 15. The perfect squares that are closest to 15 are 9 and 16. Since 15 is closer to 16, we can say that the square root of 15 is slightly less than 4.
Another approach could be:
The square root of 15 is approximately 3.87. Rounding to the nearest integer gives us 4. To round a number, we look at the number following the place value we are rounding to. If it is greater than or equal to 5, we round up. If it is less than 5, we round down. In this case, the digit following the ones place is 8, which is greater than 5, so we round up to 4.
Determine if the triangle pairs are similiar.
Yes , the triangles ΔSTU and ΔSRQ are similar triangles
What are similar triangles?
If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔSTU
Let the second triangle be ΔSRQ
Now , for the triangles to be similar , the corresponding sides of the triangles should be in the ratio
So , on simplifying , we get
The measure of side ST = 21
The measure of side SU = 35
The measure of side SQ = 6
The measure of side SR = 10
Now , for similar triangles ,
ST / SQ = SU / SR
Substituting the values in the equation , we get
21 / 6 = 35 / 10
3.5 = 3.5
Therefore , the corresponding sides of the triangles are equal
Hence , the pair of triangles are similar triangles
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A student must save at least $675 plus 3% tax to buy a round-trip ticket to London. The student has $98 saved already.
If the student earns $32 per week and plans to save half of the earnings each week toward the ticket cost, how many weeks will it take the student to save enough money for the ticket?
It will take 38 weeks a student to save enough money for the ticket.
What is division?Mathematical operations come in several types, with division being one. The phrases or numbers are divided into the same number of components during this operation.
Given,
a student must save at least $675 plus 3% tax to buy a round-trip ticket to London.
3% of 675
= 3 x 675 / 100
= 20.25
The student has $98 saved already.
Now student needs ($675 - $98) + 20.25 = $577 + 20.25
= $597.25
If the student earns $32 per week and plans to save half of the earnings each week toward the ticket cost.
That means, $32 / 2 = $16 per week.
To find the amount of enough money:
Divide $597.25 by $16.
597.25 /16
= 37.328125
≈ 38 weeks
Therefore, student will save for 38 weeks.
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help me pls help help
Answer:
6. Scalene, No congruent sides
7. Isosceles, 2 congruent sides
8. Equilateral, All congruent sides
thats all of my points if yo get it right i give u an thanks and i will choose you as the brainlyest answer.
Answer:
3/4
Step-by-step explanation:
B is highlighting 3 for the 4 rows.
If cos2β = 3/4 and ß terminates in quadrant III, find cosβ :
Answer:
cosβ = -1/2
Step-by-step explanation:
Since cos2β = 3/4 and β is in quadrant III, the value of cosβ must be negative. We can find the exact value of cosβ by using the identity cos2β = 2cos^2β - 1. Substituting 3/4 for cos2β and solving for cosβ, we get:
3/4 = 2cos^2β - 1
cos^2β = 1/4
cosβ = 1/2 or -1/2
Since cosβ is negative in quadrant III, the value of cosβ is -1/2. Thus, the answer is cosβ = -1/2.
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Vashti is designing the cover of the school yearbook. She wants to draw a flower on the cover that looks the same for each rotation of 45 degrees. How many petals should the flower have?
The number of petals that the flower should have is of:
8 petals.
When does a figure has rotational symmetry?A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.
In this problem, we want the flower to have a rotation symmetry of 45 degrees.
The total angle measure of the flower is given as follows:
360º.
Then the number of petals needed for the flower to have a rotational symmetry of 45º is calculated as follows:
360/n = 45.
Applying cross multiplication, we have that:
45n = 360
n = 360/45
n = 8 petals.
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Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the
expression 18
3g to
find the number of tickets she has left after playing g games.
Diego correctly wrote another expression, 3(6 -
g), that will also find the number of
tickets Zhi has left after playing g games.
Use the drop-down menus to explain what each part of Zhi's and Diego's expressions
mean.
Answer:
Zhi's Expression:
18: The total number of tickets
3: The number of tickets required for each game
g: The number of games played
Diego's Expression:
3: The number of tickets required for each game
(6 - g): The total number of tickets minus the number of games played
Step-by-step explanation:
(-x-y+2z = −21
(5x-3y - 2z=-23
If the equations above are true, which of the following is a value of X-Y?
A:5
B:16
C:-11
D:0
E:21
Answer: E
Step-by-step explanation:
Winona goes to the store to buy paper towels for her scout troop party. The paper towels Winona likes are sold in packs of 12 rolls for $9.96 per pack. The scout leader needs to know the cost of each roll of paper towels. What is the unit rate in cost per roll?
Answer:
The unit rate in cost per roll is $0.83 per roll.
what is unit rate? how to calculate unit rate of cost?
Unit rate is a type of ratio that compares the quantity of two different types of units. It is calculated by dividing the cost of a given quantity of an item by the number of units in that quantity. For example, if a bag of apples costs $4 and there are 5 apples in the bag, the unit rate of cost for the apples is $0.80 per apple ($4/5= $0.80). Another example would be if a carton of eggs costs $2.50 and there are 10 eggs in the carton, the unit rate of cost for the eggs would be $0.25 per egg ($2.50/10 = $0.25). Unit rate is a useful tool for understanding the cost of items, especially when comparing items of different sizes or quantities. It can also be used to calculate the cost of a certain number of items, as long as the unit rate is known.
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Type the correct answer in the box. Use numbers instead of words.Isha is a pet sitter.She earns $5 for each cat.She earns $12 for each dog.Last week, Isha pet sat for 11 cats and 7 dogs.How much money did Isha earn pet sitting last week?
By evaluating a revenue equation, we will see that she earned $139 last week.
How much money did Isha earn pet sitting last week?We know that Isha is a pet sitter, and she earns $5 for each cat and $12 for each dog.
So, if she pet sats for x cats and y dogs, the revenue will be:
R(x, y) = $5*x + $12*y
In this case we know that she pet sat for 11 cats and 7 dogs, then we have:
x = 11
y = 7
So we need to evaluate the above revenue function, we will get:
R(11, 7) = $5*11 + $12*7
R(11, 7) = $55 + $84
R(11, 7) = $139
Isha earned $139 last week.
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PLEASE HELP ASAP!!!
Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.
Which equation can Sharon use to find c, the average amount the cable company charges per channel?
0.20(c - 300)
0.20c - 300
300(c - 0.20)
300c - 0.20
How much on average does the cable company charge per channel?
The equation Sharon can use to find c, the average amount the cable company charges per channel is 300(c - 0.20) = 180.
The cable company charges an average of $0.80 per channel.
What is an Equation?An equation involves two expressions or statement on two sides connected with an equal sign.
Total number of channels = 300
Let c be the cable company charges per channel.
Then the charge satellite company charges per channel = c - 0.20
Monthly charge of satellite company = 300(c - 0.20)
Monthly satellite bill = $180
So, 300(c - 0.20) = $180
⇒ c - 0.20 = 180/300
⇒ c - 0.20 = 0.60
⇒ c = 0.60 + 0.20
⇒ c = 0.80
Hence the equation used to find the cable company charge per channel is 300(c - 0.20) = 180 and the cable company charge per channel is $0.80.
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in a symmetric distribution, the first quartile will always equal the third quartile. group of answer choices true false
The statement "In a symmetric distribution, the first quartile will always equal the third quartile" is true
The given statement is "In a symmetric distribution, the first quartile will always equal the third quartile"
The symmetric distribution is defined as the distribution that occurs when the values of variables appear at regular frequencies. Usually the mean, mode and the median all are same point in the symmetric distribution.
In the symmetric distribution the left side of the graph will be the mirror image of the right hand side of the graph. So the first quartile will always equal the third quartile.
Therefore, the given statement is true
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