Probability of (a) George winning is 0.1
(b) Julia winning is 0.05
Given in question,
Total ticket sold = 100
George bought tickets = 10
Julia bought tickets = 5
Winning ticket = 1
Selecting 1 ticket from 100 = [tex]\left[\begin{array}{ccc}100\\1\\\end{array}\right][/tex]
= 100
Selecting 1 ticket from 10 = [tex]\left[\begin{array}{ccc}10\\1\\\end{array}\right][/tex]
= 10
Selecting 1 ticket from 5 = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
= 5
Probability = favorable outcome/total outcome
Probability of George winning = [tex]\frac{10}{100}[/tex]
= 0.1
Probability of Julia winning = [tex]\frac{5}{100}[/tex]
= 0.05
Hence, probabilities are 0.1 and 0.05 respectively.
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Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle below.
The figure shows a right triangle with legs marked 30 and 16.
Answer:
A:
Answer:65Step-by-step explanation:C^2= A^2 + B^2C^2 = (60)^2 + (25)^2 C^2 = 4225Take the square root of CC = 65
Find the coordinate of the midpoint of the segment with the given endpoints.
- 5 and 4
The midpoint of the segment with the given endpoints.-5 and 4 is -0.5.
What are coordinates?
A pair of numbers is used to express a point's position on a coordinate plane using the horizontal and vertical distinctions from the two reference axes.
What is a midpoint?
A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line.
Here,
A midpoint can also be written as an average or mean of two points.
Mean of -5 and 4 = (- 5 + 4)/2 = -0.5
Hence "The midpoint of the segment with the given endpoints.-5 and 4 is -0.5".
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What is -1/6 divided by 2/9
Answer:
Step-by-step explanation:
1. List out the numbers and divide
-1/6/2/9=
2. In division for fractions, the number or numbers on the right of the division side flip and change to multiply!
-1/6/2/9= -1/6*9/2= -9/12
3. Simplify!
-9/12= -3/4
Answer:
-3/4
Step-by-step explanation:
so you leave -1/6 but then you change the sign to multiply and the other fraction change it so if you had 2/9 it will be 9/2
so we get -1/6×9/2.
if you don't know how to multiply fractions i can explain just ask.
Zahra and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags
of popcorn and 5 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Total cost, 8 bags of popcorn and 5 drinks:
Total cost, p bags of popcorn and d drinks:
Differentiate the function with respect to x.
Differentiation of the function [tex]f(x) = (-x^{2} - 4)x^{5}[/tex] with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].
What is the differentiation of the function?
A function differentiation is a method of displaying the rate of change of a function at a given moment. It is the slope of the tangent line at a point on a graph for real-valued functions.
We have,
[tex]f(x) = (-x^{2} - 4)x^{5}[/tex]
By simplifying the given function, we get
[tex]f(x) = -x^{7} - 4x^{5}[/tex]
Now, we will differentiate the given function with respect to [tex]x[/tex].
[tex]\frac{d}{dx} f(x) = \frac{d}{dx} (-x^{7} - 4x^{5})[/tex]
[tex]f'(x) = \frac{d}{dx} (-x^{7}) - \frac{d}{dx} (4x^{5}))[/tex]
[tex]f'(x) = -7x^{6} - 20x^{4}[/tex]
Hence, differentiation of the given function with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].
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Find the side length of x. Round your answer to nearest hundredth
Answer:
9
Step-by-step explanation:
I hope this helps!
A cone has a volume of 2411.52 cubic millimeters and a radius of 12 millimeters. What is its height? Use ≈ 3.14 and round your answer to the nearest hundredth.
The height of the cone given the volume of 2411.52 cubic millimeters and a radius of 12 millimeters is 16 millimeters.
How to find height of a cone?Volume of a cone = 2411.52 cubic millimetersRadius of the cone = 12 millimetersVolume of a cone = 1/3πr²h
2411.52 = 1/3 × 3.14 × 12 x 12 × h
2411.52 = 1/3 × 3.14 × 144h
2411.52 = 452.16h / 3
cross product7,234.56 = 452.16h
divide both sides by 452.16h = 7,234.56 / 452.16
h = 16 millimeters
In conclusion, the height of the cone is given by 16 milliliters.
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The store bought a pair of shoes for $50 and sold them for $80. What percentage was the markup?
Answer: They resold them for $30 more than the original price.
Answer: 37.5%
Step-by-step explanation:
$80 - $50 = $30,
$30/$80 = 0.375 > 37.5%
ABCD is a quadrilateral.
Work out angle x.
Optional working
Answ
4
+
B.
8 cm
A
X
6 cm
D
29%
13 cm
C
The require angle of x is 52.4°
Given is a quadrilateral
The given diagonal divides the quadrilateral in two parts
the first part is a right angled triangle
Thus to find the side BD
we will use the Pythagoras theorem ;
So according to this theorem
AB² + AD² = BD² [ because BD is the hypotenuse ]
Given AB = 8 cm and AD = 6 cm
8² + 6² = BD²
this implies 64 + 36 = BD²
100 = BD which implies BD = 10 cm
To find x
we know that in triangle BCD
BD = 10 cm and CD = 13 cm
tan theta = [tex]\frac{13}{10}[/tex]
this means theta = [tex]tan^{-1}[/tex] [tex]\frac{13}{10}[/tex]
theta = 52.4°
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Answer:
39.07
use pythagros to find bd then use the sine rule substitute in the values
bd=10
beacuse a²+b²=c²
substitute in 8²+6²=c²
This is not college level I just don't know how to change it but can I get some help?
Applying angle relationships, the measures of the numbered angles are:
m∠1 = 90°
m∠2 = 68°
m∠3 = 112°
m∠4 = 112°
m∠5 = 68°
m∠6 = 56°
m∠7 = 124°
m∠8 = 124°
How to Apply Angle Relationship?To calculate angle measurements that are formed by a transversal and parallel lines, we can apply the knowledge of the angle relationships that exist between the angle pairs in concerned. Some angle relationships are:
Corresponding angles are equal.Linear pair angles are equal to 180 degrees.Alternate interior angles are equal.Base angles of isosceles are equal.m∠1 = right angle [corresponding angles is the angle relationship]
m∠1 = 90°
m∠2 = 180 - m∠1 - 22 [triangle sum theorem]
Substitute
m∠2 = 180 - 90 - 22
m∠2 = 68°
m∠3 = 180 - m∠2
Substitute
m∠3 = 180 - 68
m∠3 = 112°
m∠4 = m∠3
m∠4 = 112°
m∠5 = 180 - m∠4
m∠5 = 180 - 112
m∠5 = 68°
m∠6 = 1/2(180 - m∠5)
m∠6 = 1/2(180 - 68)
m∠6 = 56°
m∠7 = 180 - 56
m∠7 = 124°
m∠8 = m∠7 [alternate interior angles is the angle relationship]
m∠8 = 124°
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Which of the following choices would move this curve to the RIGHT 17 units and up 4 units: y=(x+6)^2 - 2
If we start with the parent quadratic function, then the transformation is:
g(x) = (x - 17)^2 + 4
Which transformations move the graph in the desired way?The definitions of translations are:
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.If N is negative, the shift is to the right.
Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.If N is negative, the shift is downwards.
Then if the parent function is:
f(x) = x^2
The translation of 17 units to the right and 4 units up is:
g(x) = f(x - 17) + 4 = (x - 17)^2 + 4
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Which defines a circle?
two rays with a common endpoint
a piece of a line with two endpoints
a piece of a line with one endpoint
all coplanar points equidistant from a given point
The term that defines a circle is "all coplanar points equidistant from a given point". Then the correct option is D.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The definition of the circle is written as "A circle is a shape comprising of all places in a plane that are at a given separation from a given point, the middle."
The circle is a two-dimensional shape.
The term that defines a circle is "all coplanar points equidistant from a given point". Then the correct option is D.
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Answer: D) all coplanar points equidistant from a given point
Step-by-step explanation:
Tina has 5345 beads . She has 3687 fewer beads than her sister . How many beads does her sister have ?
Answer:
Her sister has 9032 beads
Step-by-step explanation:
All you have to do is Tina's beads plus the extra number of beads that her sister has
5345 + 3687 = 9032
A car drives 160 miles in the same amount of time that a plane flies 840 miles. The plane is going 170 mph faster than the car. How fast is the car going?
The speed of the car is 40mph
What is rate?A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.
Distance covered by car = 160 miles
distance covered by plane = 840 miles
let the time taken to cover 160 miles by car be x
speed of car = 160/x
speed of plane which is 170mph faster than speed of car = 170 + 160/x
time taken to cover 840 miles by plane,
time = distance/speed = [tex]\frac{840}{170 + \frac{160}{x} }[/tex]
By simplifying,
time taken by plane = [tex]\frac{840x}{170x + 160}[/tex]
since it takes same time for both to get to their destination,
Then,
x = [tex]\frac{840x}{170x + 160}[/tex]
By cross multiplying
x( 170x + 160) = 840x
divide both sides by x, it reduces to
170x + 160 = 840
170x = 840 - 160
170x = 680
x = 680/170
x = 4
Speed of car = 160/x
speed of car = 160/4
speed = 40mph
In conclusion, the care moves at the speed of 40mph
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A metal strip is being installed around a rectangular workbench that is 11 feet long and 4 feet wide. If the stripping costs
$5 per foot, find the total cost of the stripping.
total cost =$?
Step-by-step explanation:
that is the same as calculating the perimeter of the rectangle (the way 1 time around the rectangle).
the perimeter of a rectangle is
2×length + 2×width
in our case that is
2×11 + 2×4 = 22 + 8 = 30 ft
the stripping costs $5 per foot, and we have 30 ft.
so, the total costs are
5 × 30 = $150
A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is 24-ft by 26-ft rectangle, and the pavers measure 6 inches across the flats, how many pavers are needed?To surface a driveway about _ pavers are needed
The number of pavers required is 961.
The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.
Given data
A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is a 24-by-26-foot rectangle with pavers 6 inches wide across the flats.
We have to determine how many pavers are needed
We know that area of a regular hexagon
A = (3√3)/2 a^2
= (3√3)/2 〖(6)〗^2
= (3 x 1.732)/2 x 36
= 93.528 sq.inches
Now area of rectangle
= l x w
= 24 x 26 x (12)2 (1feet = 12 inches)
= 89856 sq.inches
Now pavers required
= 89856/93.528
= 960.73
= 961
Therefore the number of pavers required is 961.
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What is the range of the given function?
{(-2, 0), (-4, -3), (2, −9), (0, 5), (−5, 7)}
O {x|x = -5, -4, -2, 0, 2)
Oyly = -9, -3, 0, 5, 7)
{x|x = -9, -5, -4, -3, -2, 0, 2, 5, 7}
Oyly = -9, -5, -4, -3, -2, 0, 2, 5, 7}
The range of the given function is:
Range: {-9,-3,0,5,7}
We are given ordered pair of set (x,y)
where, first value of ordered pair shows domain of function and second value of ordered pair shows range.
Range: It is output value of function.
Ordered pair: {(–2, 0), (–4, –3), (2, –9), (0, 5), (–5, 7)}
We can write as:
f(-2)=0, f(-4)=-3, f(2)=-9, f(0)=5, f(-5)=7
The values of f(x) are the range of function.
We will make a set of second value of all ordered pair of given set.
Range: {-9,-3,0,5,7}
Hence we get the required range of the function.
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Katyhas$100,000inasavingsaccount.Theinterestrateis8%peryearandisnotcompounded.Howmuchwillshehaveintotalin2years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $
The amount that Katy would have saved in her savings account in 2 years is $16, 000
How to find the amount saved?Given that the interest on the savings account is not compounded, the amount that Katy would have saved in 2 years can be found by the formula:
= Principal x Interest Rate x Time
Principal = $100, 000
Interest rate = 8%
Time = 2 years
The amount that Katy would have saved is:
= Principal x Interest Rate x Time
= 100, 000 x 8% x 2
= $16, 000
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Marvin is helping his teachers plan a field trip. There are 136 people going on the field trip and each school bus holds 51 people. What is the minimum number of school buses they will need to reserve for the trip?
Answer: 3 busses
Step-by-step explanation:
what is the total change in the cats weight for all 3 months?
The total change in the cats weight for all 3 months is -0.5 pounds.
How to find the total change?Since we have 3 months which is from April to June, Now let add up the change in weight in pounds so as to find the total change
Let x represent the total change
x = -0.7 + 0.5 + (- 0.3 )
x = -0.5 pounds
Therefore the -0.5 pound is the change in weight.
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Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
x < –3
x > –3
x < 3
x > 3
Answer: x < 3
Explanation: Once you reach step 3, you divide -2 on both sides. -2x cancels out, and -6 divided by -2 is 3
how to find the area with a circumfernece of 18
The area of the circle with the circumference 18 units is 25.80 square units
How to calculate the area of the circle?The given parameters are
Circumference = 18 units
As a general rule, circumference are represented by the variable C
So, we have the following representation equation
C = 18
The circumference of the circle can be calculated as
C = 2πr
Next, we substitute the value of the variable C in the above equation
i.e. C = 18
So, we have the following equation
2π * r = 18
Divide both sides by 2π
r = 9/π
The area of the circle can then be calculated using the following area formula
A = πr²
Next, we substitute the value of the variable r in the above equation
i.e. r = 9/π
A = π * (9/π)²
Evaluate the exponents
This gives
A = π * 81/π²
Evaluate the products
So, we have
A = 81/π
As a general notation, π = 3.14
So, we have the following equation
A = 81/3.14
Evaluate the quotient
A = 25.80
Hence, the area is 25.80 square units
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WILL GIVE BRAINLIEST
You walk 10km North then turn and walk 5km East. What is your displacement from where you started? Show your work
Answer:
A hiker walks 10 km East, then 5 km in a direction 60 degrees North of West, then 8.7 km in a direction 30 degrees South of West. Find her resultant displacement.
Since you walk 10km North then turn and walk 5km East, your displacement from where you started is approximately 11.18 km.
How to determine the displacementFrom the information given, we have that you walked 10 km north (which represents the vertical side of the triangle) and 5 km east Using the Pythagorean theorem, the displacement (d) can be determined as;
[tex]d^2 = (10 km)^2 + (5 km)^2[/tex]
Find the square values, we get
d² = 100 km² + 25 km²
add the squares, we get
d² = 125 km²
Find the square root of both sides of the equation, we have;
d = 125km²
d = 11.18 km
Therefore, your displacement from where you started is approximately 11.18 km.
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The time difference, t, in minutes, taken for an object to travel from point A to B and the return journey is given by the equation (t+6) (t-8)=72. By solving the equation (t+6) (t-8)=72, find the time difference t in minutes.
Answer:
t = 12
Step by step explanation:
(t + 6)(t - 8) = 72
t² - 8t + 6t - 48 = 0
t² - 2t - 120 = 0
(t + 10)(t - 12) = 0
t + 10 = 0 OR t - 12 = 0
t = -10 OR t = 12
(reject)
15. Graph 6 and 6 on the number line.
A++
-6 5 4 3 2 1 0 +1 +2 +3 +4 +5 +6
Page 6
Wilson says both 6 and 6 have an absolute value of 6. Is
Wilson correct? Use the number line and words to explain why
or why not.
Yes, Wilson is right since "negative numbers" don't exist when you find the absolute value.
How Do You Define Absolute Value?Without taking into account direction, absolute value describes how far a number is from zero on the number line.A number's absolute value can never be negative.A number or phrase is most frequently represented by the absolute value sign, which consists of two vertical straight lines, around it|-6| = 6 denotes that "6 is -6 in absolute terms.""The absolute value of the phrase -2 minus x" is what |-2 - x| denotes.The meaning of -|x| is "the opposite of the absolute value of x."The number line can be used to graph equalities and inequalities that contain expressions with absolute value in addition to displaying the distance from zero.Therefore, Wilson is correct as there is no negative term in absolute value.
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Wanda walked 43.4 km in 14 days. At this rate, how far would she walk in 40 days?
She would walk__km in 40 days.
Answer:
124 km
Step-by-step explanation:
Wanda walked 43.4 km in 14 days. At this rate, how far would she walk in 40 days? She would walk__km in 40 days.
First, figure km per day:
43.4/14 = 3.1 km per day
3.1 * 40 = 124 km
She would walk 124 km in 40 days.
ching and his 4 brothers set up computers at their family company. how many computers did they set up if they each set up the same number of computers?
There are '5n' computers set up if they each set up the same number of computers.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Ching and his 4 brothers set up computers at their family company.
Now,
Let the number of computers for each person = n
The total number of persons = 5
So, We can formulate;
⇒ The number of computers set up if they each set up the same number of computers = 5n
Thus, There are '5n' computers set up if they each set up the same number of computers.
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33.21 divided by 9
What is the answer? And can you explain pls
Answer:
[tex]33.21 = \frac{3321}{100} \\ \\ \frac{33.21}{9} = \frac{3321}{100 \times 9} = \frac{3321}{900} = \frac{369}{100} = 3.69[/tex]Step-by-step explanation:
Thanks
Evaluate the exponential functions
I hope this helps. Have a great rest of your day!
3. One batch of pancakes needs 1 1/4 cups of pancake mix. One box has 9 cups of pancake mix How many batches of pancakes can be made with one box of pancake mix?