If a fair coin is tossed 8 times, what is the probability, rounded to the nearest
thousandth,of getting at least 6 heads?

P(A or B) =

Formula: P(AUB)=P(A)+P(B)-P(A n B)

We roll six-sided die.

Then sample space ={1,2,3,4,5,6}

And

Event A: Roll an odd number.

Odd numbers are {1,3,5}

Event B: Roll a number less than 5

Number less than 5 are {1,2,3,4}

So, Probability P(A)=

Probability P(B)=

Now, the odd number which is less than 5 are {1,3}

So, P(A n B)=

Since P(AUB)=P(A)+P(B)-P(A n B)

Therefore, P(A or B) = 1/6

The approximation of 341.12 to 1 decimal place is 341.1.

To approximate 341.12 to 1 decimal place, you can follow these steps:

For example, if you want to approximate the number 341.12 to 1 decimal place, follow these steps:

341.12 * 10 = 3411.2

Round 3411.2 to the nearest whole number, which is 3411.

3411 / 10 = 341.1

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Answer:

341.1

Step-by-step explanation:

When you round to the first decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down. If the hundredths digit is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.

341.12

The number in the hundredths place is 2, which means that we would round down the first decimal place by keeping it the same:

341.1

Answer:

Each of them will get 42/3 = $14.00

Cami saves half of her money which is 14/2 = $7.00

Cami has 14 - 7 = $7.00 to spend.

We do not obtain a triangle, but rather a straight line with a single side. Contrary to the triangle, which is a closed figure with two sides, the straight line is not closed.

Two points A and B are here collinear. Points that are parallel to or within a single line are referred to as collinear points. In Euclidean geometry, two or more points are said to be collinear if they are situated on a line that is either close to or far from another.

As opposed to non-collinear points, which do not lie on a single straight line, collinear points are two or more points that are located along a straight line. Collinear points are three or more points on the same line. A, B, and C are on the line m, for instance. The two are parallel. Two lines will coincide if their slopes are the same and they cross at the same location.

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Answer:

1. x = 10.46

2. y = 5.2

Step-by-step explanation:

1.

[tex]cos17^{0} =\frac{10}{x}[/tex]

[tex]x=\frac{10}{cos17^{0} }[/tex]

[tex]x=10.46[/tex]

2.

Angle F = 180 - 42 - 48 = 90° (is a right triangle)

[tex]sin48^{0} =\frac{y}{7}[/tex]

[tex]y=7sin48^{0}[/tex]

[tex]y=5.2[/tex]

Hope this helps

Answer:

a=3c/2+5b/2

Step-by-step explanation:

First open parenthesis

5a-5b=3a+3c

Than subtract A's and add b and c's

2a=3c+5b

Divide by two

a=3c/2+5b/2

Answer:

5, -2

Step-by-step explanation:

Answer: You need to exercise for 7 3/4 more hours

You need to do more exercise for  [tex]7\frac{3}{4}[/tex] hours.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, Your goal is to exercise for 15 hours this month. You exercise for [tex]3\frac{1}{2}[/tex] hours the first week and [tex]3\frac{3}{4}[/tex] hours the next week.

To find how much exercise is left, we will add both the hours and subtract it from 15 hours,

Therefore,

Exercise done = [tex]3\frac{1}{2} + 3\frac{3}{4}[/tex]

= 7/2 + 15/4

= (14 + 15) / 4

= 29/4

Exercise left = 15 - 29/4

= 31/4

= [tex]7\frac{3}{4}[/tex]

Hence, you need to do more exercise for  [tex]7\frac{3}{4}[/tex] hours.

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Answer:

0.36km/

Step-by-step explanation:

speed= distance/time

14.4km/40min

= 0.36km/min

Both relation (year, percent of men) and (year, percent of women) are functions.

What is a function?

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

Now,

In given data

For every input (i.e. year) there is a unique output (i.e. percent of men/ percent of women)

Hence, Given relation (year, percent of men) and (year, percent of women) are functions.

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Answer:

System: A system of two equations that can be written in the form of y = mx + b where m is the slope and b is the y-intercept.

Graph: The graph of these two equations would be two straight lines in a coordinate plane.

Solution: The solution of the system would be the point where the two lines intersect on the coordinate plane, which represents the values of x and y that satisfy both equations.

Slope and y-intercept of 4x = y - 6:

Slope: 4 (m)

y-intercept: -6 (b)

Slope and y-intercept of 4y = 3x -5:

Slope: 3/4 (m)

y-intercept: -5/4 (b)

Note that the slope is the coefficient of x in the equation, and the y-intercept is the constant term in the equation. The solution can be found by equating the two equations and solving for x and y.

The expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that Iris has 120 songs on her playlist. Each week, she downloads 4 new songs.

We can write the expression to show the total number of songs on Iris's playlist after {w} weeks as -

y = 120 + 4w

Therefore, the expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.

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Answer:

the answer is in the picture

the triangle are congruent by AAA

What is congruent by AAA?

It can also be stated as the AAA (angle-angle-angle) similarity theorem, which states that two triangles have identical corresponding angles if and only if their corresponding sides are proportionate.given, ABC and XYZ, are congruent according to the AAA rule by looking at the image provided below. According to the AAA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.

In the given two triangles,

The ratio of the sides are similar

And hence the angles are similar.

Hence the triangle are congruent by AAA

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95% of the scores fall within (mean - 2 * standard deviation) and (mean + 2 * standard deviation)

The empirical rule (68-95-99.7% Rule) states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean

95% of the values are within two standard deviation from the mean = mean ± 2 * standard deviation = (mean - 2 * standard deviation, mean + 2 * standard deviation)

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Answer:

Step-by-step explanation:

1.

[tex]\displaystyle\\\frac{1}{5}x+15=-5 \\\\\frac{1}{5}x+15-15=-5-15\\\\\frac{1}{5}x=-20[/tex]

Multiply both parts of the equation by 5:

[tex]x=-100[/tex]

2.

[tex]4-3x=5\\\\4-3x-4=5-4\\\\-3x=1[/tex]

Divide both parts of the equation by (-3):

[tex]\displaystyle\\x=-\frac{1}{3}[/tex]

3.

[tex](3x)^0+(8x+70)^0=180^0\\\\(3x)^0+(8x)^0+70^0=180^0\\\\(11x)^0+70^0-70^0=180^0-70^0\\\\(11x)^0=110^0[/tex]

Divide both parts of the equation by 11:

[tex]x=10[/tex]

[tex]m\angle TRS=(8(10)+70)^0\\\\m\angle TRS=(80+70)^0\\\\m\angle TRS=150^0[/tex]

4.

[tex]\$ 25(5)+\$250=\\\\\$125+\$250=\\\\\$375[/tex]

5.

[tex]\displaystyle\\\frac{x}{15}=\frac{30}{18}[/tex]

Multiply both parts of the equation by 15:

[tex]\displaystyle\\x=\frac{30(15)}{18} \\\\x=\frac{450}{18}\\\\x=25[/tex]

Answer: 45 degrees

Step-by-step explanation:

1 clockwise rotation = 360 degrees

1/8 a clockwise rotation = 360/8 = 45 degrees

The inverse function would be x = (y + 3) / -3 and the domain of the inverse function would be (-infinity, -1/3].

What is the inverse function?

An inverse function is a function that "undoes" another function. The inverse function, denoted as f^-1, reverses the direction of the original function, so that if the original function maps x to y, the inverse function maps y to x.

To find the inverse function of a given function, you can switch the x and y variables and solve for y. The inverse function will also have a different domain and range than the original function.

For example, for the function y = 1 - 3x, where x belongs to the interval [-2, 2],

First, we need to switch the x and y variables to get x = 1 - 3y.

Now we need to solve for y,

y = (x + 3) / -3

So the inverse function of y = 1 - 3x, where x belongs to the interval [-2, 2], is

x = (y + 3) / -3

The domain of the original function is [-2, 2] and the range is (-infinity, -1/3], whereas the domain of the inverse function is (-infinity, -1/3] and the range is [-2, 2].

Hence, The inverse function would be x = (y + 3) / -3 and the domain of the inverse function would be (-infinity, -1/3].

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The two transformation that would map triangle ABC onto triangle A'B'C' include the following:

In Geometry, dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have TO apply a dilation to the coordinates of the preimage by using a scale factor of 1/2 centered at the origin as follows:

Ordered pair A (-2, 2) → Ordered pair A' (-2 × 1/2, 2 × 1/2) = Ordered pair A' (-1, 1).

Ordered pair B (-4, 2) → Ordered pair B' (-4 × 1/2, 2 × 1/2) = Ordered pair B' (-2, 1).

Ordered pair C (-4, 4) → Ordered pair C' (-4 × 1/2, 4 × 1/2) = Ordered pair C' (-2, 2).

Furthermore, by applying a reflection over the y-axis to the coordinates of triangle A'B'C', the image coordinates include the following:

(x, y)                               →              (-x, y)

Ordered pair A' (-1, 1)    →    Ordered pair A'  (-(-1), 1) = (1, 1).

Ordered pair B' (-2, 1)    →    Ordered pair B' (-(-2), 1) = (2, 1).

Ordered pair C' (-2, 2)    →    Ordered pair C' (-(-2), 2) = (2, 2).

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A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve this, we would first need to see how many times 7 can fit into 24.

7 + 7 + 7 = 21.

We can see that is fits 3 times into 24, but what about the remaining 3? We can take that 3 and make it into a fraction of 7, making it [tex]\frac{3}{7}[/tex].

Now, putting the 3 and the 3/7 together, we get  [tex]3\frac{3}{7}[/tex].

Bryn is wrong as he says that the journey will definitely take less than an hour and a quarter

time = 1.17 hours = 1 hour 42 minutes

What is speed?

The definition of speed is. a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.

Average speed= distance / time

time= distance /Average speed = 80/68  hours

time = 1.17 hours = 1 hour 42 minutes

So, Bryn is wrong as he says that the journey will definitely take less than an hour and a quarter.

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Answer:

30 x^2

Step-by-step explanation:

(5x)(7x)-5x^2=30x^2

Simplify the following:

5×7 x x - 5 x^2

5 x×7 x = 5 x^2×7:

5×7 x^2 - 5 x^2

5×7 = 35:

35 x^2 - 5 x^2

35 x^2 - 5 x^2 = 30 x^2:

Answer: 30 x^2

The length of a form represents its perimeter. The provided parallelogram's perimeter will therefore be 38 units.

Quadrilateral's perimeter.The measurement of a shape's perimeter is its length.It takes adding the lengths of all four sides to determine a rectangle's or square's perimeter.

Knowing that the quadrilateral's perimeter equals the sum of its sides (AB + BC + CD + DA), we can write it as ABCD.

The quadrilateral's perimeter is equal to the sum of its four side lengths.

From the accompanying photo,

The supplied parallelogram's perimeter is equal to

AB + BC + CD + DA.= 9 + 10 + 9 + 10

= 38 units

ABCD's circumference is 38 units.

The provided parallelogram's perimeter will therefore be 38 units.

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Jeremy needs an amount of $7.75 cash to buy 3 comic books.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The function f(x) = 5.25x − 8 represents the amount of cash required to purchase x comic books after using his gift card.

To determine the amount of cash Jeremy needs to buy 3 comic books, we can substitute 3 for x in the function f(x) = 5.25x − 8.

So, f(3) = 5.25(3) − 8 = 15.75 − 8 = 7.75

Therefore, he needs $7.75 cash to buy 3 comic books.

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The question seems to be incomplete the correct question would be:

Jeremy has an $8 gift card to use to buy comic books. Each comic book costs $5.25. The function f(x) = 5.25x − 8 represents the amount of cash required to purchase x comic books after using his gift card. How much cash does Jeremy need to buy 3 comic books?

The values of G(x), At x = 0, 2, 4 are G(0) = 0, G(2) = 12 and G(4) = 12.

A function that is piecewise defined by numerous subfunctions, each of which has a separate domain interval for which it is applicable.

Piecewise definition is more of an expression of the function than it is a property of the function.

Given, A piecewise function G(x) defined by,

- 3x, x < 2 and 12, x ≥ 2.

Therefore, The value of G(x), At x = 0 is,

G(0) = - 3(0).

G(0) = 0.

At x = 2 the function G(x) is,

G(2) = 12.

At x = 4, the function G(x) is,

G(4) = 12.

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Answer:

Step-by-step explanation: Hello! I can help you if you include the graph!

The value of q in the arithmetic sequence is 1/2

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k. Example: a1 = 25. a(n) = a(n-1) + 5.

The common difference of arithmetic sequence is found by subtract subtracting the first from the second term. This means

d = 2q+2 - q = q+2

the sum of term is a(n) = a +( n-1)d

for third term it will be a(3) = q+ (3-1) q+2

a(3) = q +2(q+2)

the third term = 5q+ 3

5q+3 = q+ 2q+4 = 3q+4

5q+3 = 3q+4

collect like terms

5q-3q = 4-3

2q = 1

q = 1/2

therefore the value of q = 1/2

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Step-by-step explanation:

Move the decimal point one place to the right