The measure of the sides of the triangle is x = 15√3
Given data ,
We know that in the right triangle supplied, the bottom leg (adjacent side to the 30-degree angle) is "15" and the left leg (adjacent side to the 60-degree angle) is "x"
The ratio of the lengths of the side across from the angle and the side next to it is known as the tangent of an angle in a right triangle
From the trigonometric relations , we get
tan 60 = opposite side / adjacent side
tan(60°) = √3 = x/15
Multiply by 15 on both sides , we get
x = 15√3
Hence , the measure of side is x = 15√3
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I need some help with this.
The mean of the data set A is 6.5
And the mean of the data set B is 3
We know that the mean of the data set is nothing but the ratio of the sum of all data values to the total number of data values in the data set.
From the attached line plot, the data values of data set A would be,
4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9
Using above definition of mean, the mean of data set A would be,
m₁ = (4 + 5 + 5 + 5 + 6 + 6 + 7 + 7 + 8 + 8 + 8 + 9) / 12
m₁ = 78/12
m₁ = 6.5
And the data values of data set B would be,
1,2, 2, 2, 3, 3,3, 4, 4, 4, 5
m₂ = 1 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5
m₂ = 33/11
m₂ = 3
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Question 3 of 10
Polygons AUHS, A'U' H'S', and A"U" H"S" are shown on the coordinate grid.
Y
-8
-6
A'
S" H" U'
-4
-2
S'
H'
U
4
S
6
2
A"
Which sequence of transformations map AUHS to A"U"H"S"?
A translation of (x,y) → (x-4, y-2) then rot:
The sequence of transformations you suggested does indeed map AUHS to A"U" H"S".
Transformation geometry is a branch of mathematics that deals with the study of geometric shapes and their transformations in space.
Apply the transformations to each vertex of polygon AUHS and see if the resulting vertices match the corresponding vertices of polygon A"U"H"S in order to evaluate whether the series of transformations you provided translates AUHS to A"U"H"S.
Let's begin by translating (x,y) (x-4, y-2). Each point is moved 2 units down and 4 units to the left by this transformation. Vertex A(-6,-6) would be changed to A"(-10,-8) in the following manner, for instance:
A'(-6,6) → A"(-10,4)
U'(-2,2) → U"(-6,0)
H'(4,2) → H"(0,0)
S'(-2,-6) → S"(-6,-8)
Let's now think about the rotation of the origin 90 degrees anticlockwise. Each point is rotated 90 degrees anticlockwise relative to the origin using this transformation. Vertex A"(-10,-8) would be rotated to A"(8,-10) in the following manner, for instance:
A"(-10,-8) → A'(8,-10)
U"(-6,0) → U'(0,-6)
H"(0,0) → H'(0,0)
S"(-6,-8) → S'(-8,6)
Therefore, the sequence of transformations you suggested does indeed map AUHS to A"U"H" S".
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A cylinder has a radius of 8cm and a volume of 800cm3. Calculate (a) its height (b) its total surface area. (π = 22/7)
Answer:
r = 22 over 7
Test for symmetry about the vertical line
0 = pie over 2
Therefore, the answer is B
Step-by-step explanation:
I hope this helps :)
COLLEGE Troy’s grandfather gave him $700 to start his college savings account. Troy’s grandfather also gives him $40 each month to add to the account. Troy’s mother gives him $50 each month, but has been doing so for 4 fewer months than Troy’s grandfather. Write a simplified expression for the amount of money Troy has received m months after his mother starting giving him money.
$90m + $500 is the correct expression for the given data.
Troy's grandpa gave him a one-time gift of $700, so let's start there.
Next, let's think about Troy's monthly salary. He receives $40 a month from his grandfather, so in m months he would have gotten 40 million dollars.
He gets $50 a month from his mother, but she just started doing so 4 months after his grandfather, so he would have gotten that amount for (m-4) months. The entire sum he received from his mother would be as follows:
50(m-4)
We can add up the three sums to make the statement for Troy's overall payment after m months simpler:
Total amount = $700 + $40m + $50(m-4)
Condensing the phrase:
Total amount = $700 + $40m + $50m - $200
Total amount = $90m + $500
Therefore, the simplified expression for the amount of money Troy received m months after his mother started giving him money is $90m + $500.
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if you go three times faster than another car, then how many times longer will it take for you to stop the car? how do you know this?
If you go three times faster than another car, it will take nine times longer to stop your car than the other car.
To understand why, we need to consider the physics of stopping a car. The distance required to stop a car depends on the car's speed and braking ability.
Assuming the braking ability is the same for both cars, we can use the equation:
distance = (speed)² / (2 * deceleration)
where deceleration is the rate at which the car slows down.
Since we are assuming that the other car and your car have the same deceleration, we can write:
distance other car = (speed other car)² / (2 * deceleration)distance your car = (speed your car)² / (2 * deceleration)We know that your car is going three times faster than the other car, so:
speed your car = 3 * speed other car
Substituting this into the equation for the distance of your car, we get:
distance your car = (3 * speed other car)²/ (2 * deceleration)
distance your car = 9 * (speed other car)² / (2 * deceleration)
Therefore, the distance required to stop your car is nine times greater than the distance required to stop the other car. Since the time to stop is directly proportional to the distance required to stop, it will also take nine times longer to stop your car than the other car.
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6. Soup Can
a. Create the net for a soup can with the following dimension: r = 6.5
com, h = 14.3 cm. Label the dimensions on your net.
b. Calculate the surface area of the can.
Hint: Area of a circle A = π r2
c. Calculate the volume of the can (in cm3
).
Hint: Volume = (area of the base) × height
d. Convert this volume to mL (you may need to research the
conversion factor).
The surface area and volume of the cylindrical can are resepctively:
849.49 cm² and 1898.07 mL
How to find the surface area and volume of the cylinder?The formula for the surface area of a can or cylinder is:
SA = 2πr (h + r)
we are given:
r = 6.5 cm
h = 14.3 cm
Thus:
SA = 2π(6.5(14.3 + 6.5)
SA = 849.49 cm²
The volume of the can is given by the formula:
V = πr²h
V = π * 6.5² * 14.3
V = 1898.07 cm³
Converting to mL is:
V = 1898.07 mL
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if the volume of a rigjt rectangular prisim is 1.5 in and it’s length and width have a product of 1.5 what is the height of this prisim
If the right rectangular-prism has a volume of 1.5 cubic inches, and product of length and width as 1.5, then the height of prism will be 1 inch.
In order to find the height of the "rectangular-prism", we use the formula for the volume of a rectangular prism, which is:
⇒ Volume = length × width × height;
We know that the volume is 1.5 in³ and
The product of the length and width is given to be 1.5,
So we can write : length × width × height = 1.5, ....equation(1)
length × width = 1.5,
Substituting the product of "length" and "width" in equation(1),
We get,
⇒ 1.5 = 1.5 × height,
⇒ height = 1.5/1.5 = 1 inch.
Therefore, the height of prism will be 1 inch.
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Which shows how you can check
The correct equation is the one in option C:
[tex]\frac{7}{12} = \frac{14}{15}*\frac{5}{8}[/tex]
Which equation is the correct option?Here we have a quotient between fractions:
[tex]\frac{7}{12} /\frac{5}{8} = \frac{14}{15}[/tex]
To check that, we need to multiply both sides by the denominator 5/8, then we will get:
[tex](\frac{7}{12} /\frac{5}{8} )*\frac{5}{8} = \frac{14}{15}*\frac{5}{8}\\\\\frac{7}{12} = \frac{14}{15}*\frac{5}{8}[/tex]
That is the equation that we can see in option C, so that is the correct option.
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Jason made a scale drawing of a campsite .the tent is 5 inches long in the drawing the actual tent is 10 feet long what is the scale factor of the drawing ? Simplify your answer and write it as a fraction
The scale factor of the drawing is 1/24.
We can set up a proportion to find the scale factor
(scale length)/(actual length) = scale factor
We are given that the length of the tent in the drawing is 5 inches, and
the actual length of the tent is 10 feet, which is equivalent to 120 inches. Substituting these values into the proportion, we get:
5/120 = scale factor
Simplifying the fraction on the left-hand side, we get:
1/24 = scale factor
Therefore, the scale factor of the drawing is 1/24.
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The price of P , of a pizza varies directly as the square of its radius R. If a pizza with the diameter of 20cm cost $6.00 . What would a pizza with a radius of 12cm cost ?
Answer: $8.64.
Step-by-step explanation:
P = price of the pizza
R = radius of the pizza
We know that the price of the pizza varies directly as the square of its radius. This means that we can write the following equation:
P = kR^2
where k is a constant of proportionality.
We are given that a pizza with a diameter of 20 cm costs $6.00. This means that the radius of the pizza is 10 cm. We can use this information to find the value of k.
6 = k(10)^2
6 = 100k
k = 0.06
Now that we know the value of k, we can find the price of a pizza with a radius of 12 cm.
P = 0.06(12)^2
P = 0.06(144)
P = 8.64
Therefore, a pizza with a radius of 12 cm would cost $8.64.
The diameter of a circle is 14 kilometers. What is the circle's circumference?
Use 3.14 for .
kilometers
The circle's circumference is approximately 43.96 kilometers.
The circumference of a circle is given by the formula:
C = πd
where C is the circumference, π is the mathematical constant pi (approximately equal to 3.14), and d is the diameter of the circle.
Substituting the given value for the diameter (d = 14 kilometers) into the formula, we get:
C = 3.14 × 14 km
C = 43.96 km
Therefore, the circle's circumference is approximately 43.96 kilometers.
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100 + 100 = 200 true or false
The requried given sum 100 + 100 = 200 is true.
When we add two numbers, we unite them to get a new total value. In this case, we are adding 100 and 100, which gives us a total of 200. Therefore, the statement "100 + 100 = 200" is true based on the rules of addition in mathematics.
If the context of the question is different, for instance, if the "+" symbol represents concatenation (joining of two strings), then the answer might be different. But based on the premise that the "+" symbol represents an addition, the statement "100 + 100 = 200" is true.
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Raashan, sylvia, and ted play the following game. each starts with $1. a bell rings every 15 seconds, at which time each of the players who currently have money simultaneously chooses one of the other two players independently and at random and gives $1 to that player. what is the probability that after the bell has rung 2019 times, each player will have $1? (a) 1 7 (b) 1 4 (c) 1 3 (d) 1 2 (e) 2
The probability that each player will have $1 after 2019 rings of the bell is: (c) 1/3.
To solve this problem, we need to think about the possible outcomes of the game. Each time the bell rings, each player has a 1/2 probability of giving $1 to one of the other two players. This means that after one ring of the bell, there are 2^3 = 8 possible outcomes, as each player can either give or not give money to each of the other players.
After two rings of the bell, there are 2^8 = 256 possible outcomes. After three rings, there are 2^12 = 4,096 possible outcomes. And so on.
To find the probability that after 2019 rings of the bell, each player will have $1, we need to find the total number of possible outcomes and the number of outcomes in which each player has $1.
The total number of possible outcomes after 2019 rings of the bell is 2^(3*2019) = 2^6057.
To count the number of outcomes in which each player has $1, we can use a combinatorial argument. We need to distribute 2019 dollars among the three players in such a way that each player ends up with exactly $1. This is equivalent to choosing two numbers between 0 and 2019, inclusive, and giving the first player the smaller amount, the second player the difference between the larger and smaller amounts, and the third player the remaining amount.
The number of ways to choose two numbers between 0 and 2019 is (2019+2) choose 2 = 2036 choose 2 = 2,066,530.
Therefore, the probability that each player will have $1 after 2019 rings of the bell is:
2,066,530 / 2^6057 = 1/3
So the answer is (c) 1/3.
In the game where Raashan, Sylvia, and Ted each start with $1 and a bell rings every 15 seconds, the probability that after the bell has rung 2019 times, each player will have $1 is (a) 1/7.
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a cab was involved in a hit-and-run accident at night. two cab companies green and blue operate 85% and 15% of the cabs in the city respectively. a witness identified the cab as blue. however, in a test only 80% of witnesses were able to correctly identify the cab color. given this what is the probability that the cab involved in the accident was blue?
From Bayes' Theorem, an event, the probability that the blue cab involved in accident as well as witness also identified it as blue cab is equals to the 0.41 or 41%.
Bayes' Theorem states that the conditional probability of an event, is based on the occurrence of another event, is equal to the like of the second event the first event multiplied by the probability of the first event. According to scenario, it is found that a cab was involved in a hit and run accident at night. Number of cab companies operates in city = 2 (blue and green)
Probability that green cab involved in accident, P(G) = 85% = 0.85
Probability that blue cab involved in accident, P(B) = 15% = 0.15
Now, the cab which is identified by witness was a blue cab. Here, probability that witness is correct to identification a blue cab = P(W/B) = 0.80
Probability that witness is wrong to identify the blue cab = P(W/G) = 0.20
Using the Baye's theorem, Probability that accident was caused by blue cab provided witness identifies is written as [tex]P(B/W) = \frac{ P(B ∩W) }{P(W)} = \frac{ P(B) P( W/B)}{W}[/tex]
Total Probability, [tex]P(W) = \frac{P(B)}{P(W/B)}+ \frac{P(G)}{P(W/G)}[/tex]
= 0.15 x 0.8 + 0.85 x 0.2 = 1.2 + 1.7 =0.29
[tex]P(B/W) = \frac{ P(0.15×0.8}{0.29}[/tex]
= 0.12/0.29 = 0.413 = 41%
Hence, required probability value is 41%.
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PLEASE HELP ME ASAP I BEG YOU
The distance that the tip of the base ball travels is 214 inches.
Given that Kyle is practicing his baseball swing
He made an arc with radius of 48 inches
We have to find the distance the tip of the base ball travels
Radius = 48 in and θ = 255 degrees
Arc length = θ/360 × 2πr
=255/360 ×2×3.14×48
=76867.2/360
=213.52 inches
=214 inches
Hence, the distance that the tip of the base ball travels is 214 inches.
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URGENT - Will also give brainliest to simple answer
Answer:
(π/8)(12^2) = 18π square units
brainliest, multiple choice, and 100 points! i really appreciate the help, and please let me know if you need help on anything, thanks!!
Answer:
C) ΔFHG ≅ ΔPRQ by the AAS triangle congruence theorem----------------------
AAS congruence theorem states that:
If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.We can see two angles and the non-included side are marked as congruent:
∠R ≅ ∠H, ∠Q ≅ ∠G and PQ ≅ FG,Hence the triangles are congruent:
ΔFHG ≅ ΔPRQTherefore the correct choice is C.
whats the answer pls
Answer: 338.5 mm²
Step-by-step explanation:
There are 3 rectangles for the lateral surface area
LA=Ph lateral surface area is the are around which is found Permiter*height
LA=(7.5+10.5+11)9.5=275.5
Total area = LA + 2B B is the area of the base 1/2 bh
A=275.5+2(1/2)(10.5)(6)
=338.5 mm²
90% of what equals 54.9
Answer:
61
Step-by-step explanation:
Quick maths
i need help, its over due, Thank you very much to whoever helps me!
Answer:
x = 7, y = -1
Step-by-step explanation:
3x + 7(x - 8) = 14
3x + 7x - 56 = 14
10x - 56 = 14
10x = 70
x = 7
y = 7 - 8
y = -1
Area of the Triangle Base=
height of the whole prism =
NOW fill in the formula V=B*h, and calculate the final volume:
V =
The volume of the prism is 792 cubic feet.
To find the volume of a rectangular prism, we need to multiply its length, width, and height.
The three-dimensional solid object known as a prism has identical ends and flat sides. The shape of its ends—a rectangular prism or a triangular prism—gives the object its name.
The volume of a prism may be estimated by dividing the area of the base by the height.
Given the dimensions of the prism:
Length = 9 ft
Width = 8 ft
Height = 11 ft
Volume = Length x Width x Height
Volume = 9 ft x 8 ft x 11 ft
Volume = 792 cubic feet
Therefore, the required volume is 792 cubic feet.
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AYUDAAAAAA ES PREGUNTA DE MODLE
Determina el conjunto solución de 1/3>x−1/5>1/9 . a. {x | 14/9 < x < 8/3} b. [14/9, 8/3] c. {x | 14/9 < x ≤ 8/3} d. [14/9, 8/3)
The solution set for the given inequality is:
8/3 > x > 14/9 or in interval form, (14/9, 8/3)
How to find the solution set of the inequality?Here we have the compound inequality:
1/3> (x - 1)/5 >1/9
To solve it, we need to isolate the variable x, so let's do that:
First we can multiply all the inequality by 5, then we will get:
1/3> (x - 1)/5 >1/9
5/3 > x - 1 > 5/9
Now add 1.
5/3 + 1 > x > 5/9 + 1
Now simplify it to get:
8/3 > x > 14/9
Thus, the solution set is (14/9, 8/3)
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Y=35x
If x is hours worked and y is total pay, what is the hourly wage and inning bonus for the person whose pay is given by the equation above?
Using equations, we can find that the person was getting 35 as the hourly wage and the bonus was zero.
Define equations?Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol. It'll be regarded as a term.
The given equation is:
y = 35x
Where, x is hours worked.
And y is total pay.
From the equation, we can get:
The hourly wage for the person is 35 units.
As there are no constants in the equation, we can conclude that the bonus for the person was 0.
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Round 127.576 to the nearest hundredth place
Answer:
Step-by-step explanation:
127.58
this rectangular prism is intersected by a plane that contains points d, e, k, and l. what is the perimeter of the cross section?
The perimeter of the cross-section of the rectangular prism is 42 meters.
The cross-section formed by the plane that contains points D, E, K, and L is a trapezoid with bases DE and KL and height 5.
The length of DE can be found using the Pythagorean theorem: DE = √((EK - DK)² + (EL - DL)²) = √((12 - 4)² + (0 - 0)²) = 8 meters.
Similarly, the length of KL is also 8 meters.
Therefore, the perimeter of the cross-section is the sum of the lengths of the sides of the trapezoid, which is given by
perimeter = DE + KL + 2√((EK - DL)² + 5²)
perimeter = 8 + 8 + 2√((12 - 0)² + 5²)
perimeter = 16 + 2*√(169)
perimeter = 16 + 26
perimeter = 42 meters (rounded to the nearest tenth)
Hence, the perimeter of the cross-section is 42 meters.
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--The given question is incomplete, the complete question is given
" The rectangular prism is intersected by a plane that contains points D, E, K, and L.
What is the perimeter of the cross section?
Enter your answer in the box. Round only your final answer to the nearest tenth.
m
A rectangular prism with height 5 meters, length 12 meters, and width 4 meters. The vertices are labeled as G, D, H, L, E, F, J, and K."--
Help with this question
Answer:
The answer is d: (x+2)(x-6)
Step-by-step explanation:
[tex]x^{2} - 4x - 12[/tex]
[tex]x^{2}[/tex] being a, [tex]- 4x[/tex] being b, and [tex]-12[/tex] being c
Step 1 is to figure out what two numbers can add to b while also multiplying to c
Those two numbers for this equation are [tex]-6[/tex] and [tex]2[/tex]
[tex]x^{2} + 2x - 6x - 12[/tex]
Then we factor it down
[tex]x(x+2)[/tex] and [tex]-6(x+2)[/tex]
The outside properties go in their own parenthesis
[tex](x - 6)[/tex]
and the Inside ones are already one object
[tex](x+2)[/tex]
Therefore the final product is
[tex](x+2)(x-6)[/tex]
Steph lives in Crosby and works in Speke for 5 days a week. Each day she travels to and from work via Bootle. + b) How many miles, in total, does she travel to and from work each week?
The amount of miles in total that Steph travels each week is 160 miles.
What is distance?The distance is a length of path joining two or more points of reference. It is measured in meters and a scalar quantity.
From the given information, Steph travels to and from work via Bootie. Then it can be deduced that;
Distance from Crosby to Bootie = 4 miles
Distance from Bootie to Speke = 12 miles
So the distance traveled in one trip = 4 + 12
= 16 miles
Then distance traveled to and from work each day = 2*16
= 32 miles
Thus,
Total miles travelled to and from work each week can be determined as;
given that she works for 5 days in a week, then;
total distance per week = distance traveled per day x number of days in a week
= 32*5
= 160 miles
Therefore, Steph travels a total of 160 miles to and from work each week.
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n a group of 50 people, what is the expected number of days of the year which are one of their birthdays?
Answer: there's a 50-50 chance of at least two people having the same birthday.
In a group of 50 people, the expected number of days of the year which are one of their birthdays can be determined using the concept of probability which are one of their birthdays is approximately 194 days.
The expected number of days of the year which are one of their birthdays in a group of 50 people can be calculated using the formula E(X) = np, where n is the number of trials and p is the probability of success in each trial. In this case, there are 50 people and 365 days in a year, so each person has a probability of 1/365 of having their birthday on a particular day. Therefore, the expected number of people with a birthday on any given day is 50*(1/365) = 0.137. Since there are 365 possible days, we can multiply this by 365 to get the expected number of days with at least one birthday, which is approximately 50.034 days. So, the expected number of days of the year which are one of their birthdays in a group of 50 people is around 50.034.
In a group of 50 people, the expected number of days of the year which are one of their birthdays can be determined using the concept of probability.
Assuming that each person's birthday is equally likely to fall on any of the 365 days in a year (ignoring leap years), the probability of any particular day being a birthday is 1/365.
Now, the probability of a day not being a birthday for a single person is (364/365). For 50 people, the probability of a day not being any of their birthdays would be (364/365)^50.
To find the expected number of days with at least one birthday, we can calculate the probability of a day having at least one birthday, which is the complement of no birthdays on that day. This probability is:
1 - (364/365)^50
Now, we multiply this probability by the total number of days in a year to find the expected number of days with at least one birthday:
365 * (1 - (364/365)^50) ≈ 194.03
So, in a group of 50 people, the expected number of days of the year which are one of their birthdays is approximately 194 days.
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What is the surface area and volume of a cone with a radius of 3 and a height of 4 (the slant height is 5)
The volume of the cone is 37. 68 cubic units
The surface area is 75. 36 square units.
How to determine the valuesThe formula for calculating the volume of a cone is expressed as;
Volume = πr²h/3
From the information given, we have that;
radius = 3 units
h = 4 units
Substitute the values, we get;
Volume = 3.14 × 3² × 4/3
Divide the values
Volume = 37. 68 cubic units
The formula for surface area is expressed as;
Surface area = πrl + πr²
Substitute the values
Surface area = 3.14 × 3 × 5 + 3.14 × 3²
Surface area = 47. 1 + 28. 26 = 75. 36 square units.
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4. Determine the z-score for each situation using a z-score table or a graphing calculator.
a:
35% of the data is to the left of the
Z-score.
b:
18% of the data is to the right of the
z-score.
The z-scores for each situation are given as follows:
a) 35% of the data is to the left: z = -0.385.
b) 18% of the data is to the right: z = 0.915.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.From the second bullet point, we have that the z-score for which 35% of the data is to the left of the Z-score is z with a p-value of z = 0.35, hence z = -0.385.
The z-score for which 18% of the data is to the right of the data-set, is z with a p-value of 1 - 0.18 = 0.18, hence it is z = 0.915.
More can be learned about the normal distribution at https://brainly.com/question/25800303
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