The height of the pole is 96 feet
In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:[1]
[tex]a^{2}+b^{2}=c^{2},[/tex]
Create a diagram of the scenario first. You would have a right triangle with a hypotenuse (longest side) of h + 4, a longest leg of h - 68, and one leg of length h to represent the pole.
Set up the equation [tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex] using the Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex]).
[tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex]
On simplifying we get
[tex]h^2+h^2-136h+4624 = h^2+8h+16[/tex]
[tex]2h^2-136h+4624=h^2+8h+16[/tex]
[tex]h^2-144h+4608=0[/tex]
Solving using quadratic formula
[tex]h_{1,\:2}=\frac{-\left(-144\right)\pm \sqrt{\left(-144\right)^2-4\cdot \:1\cdot \:4608}}{2\cdot \:1}[/tex]
[tex]h_1=\frac{-\left(-144\right)+48}{2\cdot \:1},\:h_2=\frac{-\left(-144\right)-48}{2\cdot \:1}[/tex]
h1 = 96 feet , h2 = 48 feet
If height would have been 48 feet then the other side would have a negative value as as 48 - 68 = -20 .
Hence the height of the pole is 96 feet
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What property is (3x+7)+(2x+8)=3x+7+2x+8
Answer:
distributive property
Step-by-step explanation:
(3x + 7) + (2x + 8)
each of the parenthesis has a multiplier of 1 , placed outside the parenthesis.
then multiplying the terms inside the parenthesis by 1 gives
3x + 7 + 2x + 8
2 ⋅ √ 2 + √ 8 - simplify
Answer:
[tex]4\sqrt2[/tex]
Step-by-step explanation:
[tex]2\sqrt{2} +\sqrt{8}=2\sqrt{2}+2\sqrt{2}=4\sqrt{2}[/tex]
Step-by-step explanation:
i sent the solution in the photo pls check it
In the graph locate the point (3,0) and draw a line parrallel to Y-axis passing through (3,0). Then your line will cut the graph of f (x) at some point, that point's y-coordinate will be your value of f (3)
The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The graph passes through the point (3, 0) and parallel to the y axis, the equation of this line is x = 3.
The equation of the line passing through the point (3, 0) and parallel to the y axis is x = 3.
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Consider the equality xy=k. Write the following inverse proportion: y is inversely proportional to x. When y = 3, x = 7.
1/7 = k/3
3/1 = k/7
The correct expression for the inverse proportion is k/7 = 3/1
Inverse proportionsGiven the inequality xy = k
If y is inversely proportional to x, then;
y = k/x
Given that y = 3, and x = 7, then;
3 = k/7
Swap
k/7 = 3
k/7 = 3/1
Hence the correct expression for the inverse proportion is k/7 = 3/1
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Graph the line with the equation
The graph of the linear equation can be seen in the image below.
How to graph the linear equation?Here we have the linear equation:
y = (2/5)*x - 6
To graph it, we just need to find two points on the line, and then connect them with a line.
To find the points we just evaluate in two values of x.
if x = 0.
y = (2/5)*0 - 6 = -6
Then we have the point (0, -6)
If x = 5.
y = (2/5)*5 - 6 = 2 - 6 = -4
Then we have the point (5, - 4)
Now we can graph these two points and connect them with a line. The graph of the line can be seen below.
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Which values of m and b will create a system of equations with no solution? Select two options.
y = mx + b
y = –2x + A system of equations. y equals m x plus b. y equals negative 2 x plus StartFraction 3 over 2 EndFraction.
Using linear function concepts, a system of equations with no solutions is created when:
[tex]m = -2, b \neq \frac{3}{2}[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The intersection of two lines is the solution of a system of equations. If two lines have the same slope and different intercepts, they will never intercept, that is, the system will not have a solution.
The lines are given as follows:
y = mx + b.y = -2x + 3/2.Hence, for a system with no solution, we need that:
[tex]m = -2, b \neq \frac{3}{2}[/tex]
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If the fraction of times an event happened in the past is used as the basis for assigning a probability to the event, this is ______ probability.
If the fraction of times an event happened in the past is used as the basis for assigning a probability to the event, this is Empirical probability.
If the events are mutually exclusive, special additional rules can be applied. -Additional general rules can be used if the events are not mutually exclusive. Events A and B must be mutually exclusive.
If the occurrence of one event is not completely affected by the occurrence of another event, such an event is probabilistically called an independent event, and the event affected by another event is a dependent event. Is called dependent events.
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Every weekend me and my brother and my cousin go outside to play basketball and when i was the one who will shoot the ball to the ring i used the things i learned in math so I use SOH-CAH-TOA in measuring it. I want to measure the distance between me and the basketball ring. Supposed the height of the ring is 8ft from the ground and the distance between me and the basketball ring horizontally is 11.5 ft, and the angle of elevation from the ground is 50 degrees, now what is the distance of me and the ring?
Let x be the distance between me and the ring
need urgent answers with equation
by using SOH from SOHCAHTOA
Answer:
10 . 44 ft
Step-by-step explanation:
sin 50 = opposite leg / hypotenuse = 8 / x
8 / sin 50 = x = 10 .44 ft
Answer:
10.433cm
Step-by-step explanation:
Using SOH from TOACAHSOH,
[tex]sin50deg = \frac{opposite}{hypotenuse} [/tex]
From here we know there the opposite is 8ft (height of the ring) and hypotenuse is what we want to find, distance between you and the ring.
[tex]sin(50) = \frac{8}{x} \\ x \sin(50) = 8 \\ x = \frac{8}{ \sin(50) } \\ x = 10.443cm(rounded \: to \: 5sf)[/tex]
What is part of 1 minute and 5 seconds
The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.
Fraction of 5 seconds in 1 minute
The fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is calculated as follows;
1 minute = 60 secs
Fraction = 5 / 60
Fraction = 1/12
Thus, the fraction of 5 seconds in 1 minute or part of 5 seconds in 1 minute is 1/12.
The complete question is below:
What is part of 1 minute is 5 seconds?
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the image of p(m,5-n) when reflected on line y=0 is p'(2m-3,2n-8) find the values of m and n
The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
The rule for the reflection over the line y = 0 (x axis) is (x, y) ⇒ (x, -y)
If the point p(m,5-n) is reflected on line y=0, this would give (m, -(5 - n)) = p'(2m-3,2n-8). Hence:
2m - 3 = m
m = 3
Also:
-(5 - n) = 2n - 8
-5 + n = 2n - 8
n = 3
The value of m and n that shows that point p(m,5-n) when reflected on line y=0 is m = 3, n = 3.
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The athletic boosters club at Coral High plans a car wash to raise funds for the sports program. An average of 10 cars per hour are expected to arrive according to a Poisson distribution. They will be served at an average rate of 12 cars per hour, with exponential service times. What is the utilization rate
The utilization rate is 83.33
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.
An average of 10 cars per hour are expected to arrive according to a Poisson distribution. They will be served at an average rate of 12 cars per hour, with exponential service times,
Then, the utilization rate is 83.33.
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Researchers conducted a study to find out if there is a difference in the use of ereaders by different age groups. randomly selected participants were divided into two age groupsin the to 29year-old group7% of the 628 surveyed use ereaders, while 11of the 2,309 participants 30 years old and older use ereaders(use subscripts let 1 16- to 29-year-old users , and 230 years old and
No, there is significant difference in the use of e readers by different age groups.
Given sample 1 ( 29 years old) [tex]n_{1}[/tex]=628, [tex]p_{1}[/tex]=7%, sample 2( 30 years old)[tex]n_{2}[/tex]=2309, [tex]p_{2}[/tex]=0.11.
We have to first form hypothesis one null hypothesis and other alternate hypothesis.
[tex]H_{0}:[/tex]π1-π2=0
[tex]H_{1}:[/tex]π1-π2≠0
α=0.05
Difference between proportions [tex]p_{1}-p_{2} =-0.04[/tex]
[tex]p_{d}=0.07-0.11=-0.04[/tex]
The pooled proportion needed to calculate standard error is:
[tex]p=(X_{1} -X_{2} )/(n_{1} +n_{2} )[/tex]
=(44+254)/(628+2309)
=0.10146
The estimated standard error of difference between means is computed using the formula:
[tex]S_{p_{1} -p_{2} }=\sqrt{p(1-p)/m_{1}+p(1-p)/n_{2} }[/tex]
=[tex]\sqrt{0.101*0.899/628+0.101*0.899/2309}[/tex]
=[tex]\sqrt{0.000143+0.00003}[/tex]
=[tex]\sqrt{0.000173}[/tex]
=0.01315
Z= Pd-(π1-π2)/[tex]S_{p_{1} -p_{2} }[/tex]
=-0.04-0/0.013
=-3.0769
This test is a two tailed test so the p value for this test is calculated as (using z table)
p value:2 P(Z<-3.0769)
=2*0.002092
=0.004189
P value< significance level of 5%.
Hence there is enough evidence to show the claim that there is a significant difference in the use of e readers by different age groups.
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Question is incomplete as it also includes:
Significance level of 5%.
A=42°, b=10, c=12. What is the length of a to the nearest tentH
The length of a in the triangle to the nearest tenth is 8.1 units.
How to find side of a triangle?The side a of the triangle can be found using cosine formula.
Therefore,
a²= b² + c² - 2bc cos A
a² = 10² + 12² - 2 × 10 × 12 cos 42°
a² = 100 + 144 - 240cos 42
a² = 244 - 178.354758115
a = √65.6453
a = 8.10217871933
a = 8.1
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Which of the following functions best describes this graph?
Answer:
Option D
Step-by-step explanation:
Looking at the graph each jump is 2 units on the x-axis and y-axis :
We are looking for a quadratic with x values of 3 and 6 when y=0
Solving the last quadratic gives us :
(x-3)(x-6)=0
x = 3 , x = 6
Our answer will be Option D
Hope this helped and have a good day
Answer:
D: [tex]y=x^{2} -9x+18\\[/tex]
Step-by-step explanation:
x intercept of the curve is 3 and 6
meaning that when y=0, x is either 3 or 6
mathematically stated:
0 = (x - 3) (x - 6)
0=x(x-6)-3(x-6)
[tex]0=x^{2} -6x-3x+18\\therefore \ y=x^{2} -9x+18\\[/tex]
Use the Law of Cosines to find the specified missing value. Approximate your answer to the nearest tenth.
If B = 150°, a = 150 ft, c = 30 ft, find b.
Work Shown:
[tex]b^2 = a^2 + c^2 - 2*a*c*\cos(B)\\\\b^2 = 150^2 + 30^2 - 2*150*30*\cos(150)\\\\b^2 \approx 31194.22863406\\\\b \approx \sqrt{31194.22863406}\\\\b \approx 176.618879608211\\\\b \approx 176.6\\\\[/tex]
how to show that two triangles are congruent
Answer:
To show that 2 triangles are congruent, both triangles must have the same the same size and shape. Basically both triangles must have the same 3 angles and 3 sides.
Step-by-step explanation:
This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles.
Hope this helped! :D
Answer:
Step-by-step explanation:
Follow this rules
SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side)A spinning wheel has the following numbers.
(There are 1-8 numbers in the wheel)
Cathy spins the wheel and tosses a coin simultaneously.
Find the following probabilities:
Getting a 7 and tails.
Getting a prime number and heads.
Getting a number greater than 5 and tails.
Answer:
[tex]\frac{1}{16}, \frac{1}{4}, \frac{3}{16}[/tex]
Step-by-step explanation:
Recall a probability: [tex]P=\frac{F}{T}[/tex] , where F is a number of favorable outcomes and T is a number of total outcomes.
The probability to get tail is [tex]\frac{1}{2}[/tex] as well as probability to get head.
The probability to choose number 7 of 8 numbers at total is equal to [tex]\frac{1}{8}[/tex].
Therefore, the probability to get number 7 and a tail is:
[tex]\frac{1}{8}\cdot \frac{1}{2}=\frac{1}{16}[/tex]
Prime numbers from 1 to 8 are: 2, 3, 5 and 7, so there are 4 numbers of 8 numbers in total, so the probability to get a prime number is [tex]\frac{4}{8}=\frac{1}{2}[/tex].
The second probability is equal to [tex]\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}[/tex].
The numbers greater than 5 are: 6,7,8, so there are 3 numbers of 8 in total, so the probability to get a number greater than 5 is [tex]\frac{3}{8}[/tex].
The third probability is equal to: [tex]\frac{3}{8}\cdot \frac{1}{2}=\frac{3}{16}[/tex].
I need help please and thank you!!
Hello and Good Morning/Afternoon
Let's take this problem step-by-step
The Line DF is '5x + 7' cm long
The Line DF is made up of two lines DE and EF
⇒ therefore
[tex]DE + EF = \\ 7 + 4x + 3 = 5x + 7\\10+4x=5x+7\\5x-4x=10-7\\x=3[/tex]
Let's plug x's value into '5x + 7'
[tex]\hookrightarrow DF = 5(3) +7=22[/tex]
Answer: 22cm
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Please help!!!!!!!!!!
Using the together rate, it is found that it will take 18 hours for Erick to build the garden box himself.
What is the together rate?The together rate is given by the sum of each separate rate.
In this problem, the rates are given as follows:
Eric's: 1/x.Drew's: 2/x.Together: 1/6.Hence:
[tex]\frac{1}{x} + \frac{2}{x} = \frac{1}{6}[/tex]
[tex]\frac{3}{x} = \frac{1}{6}[/tex]
x = 18.
Hence, it will take 18 hours for Erick to build the garden box himself.
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Complete the statements below that show y = 8x2 32x 17 being converted to vertex form. factor out the leading coefficient. y = 8(x2 4x) 17 form a perfect-square trinomial. y = 8(x2 4x ) 17
Hence, the required algebraic expression is 8([tex]x^2[/tex]+4x+4) + 17 -32
What is an expression?expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
How to solve?We were given y = 8[tex]x^2[/tex]+32x+17
To convert to vertex form, We factor out the leading coefficient which is 8.
Next, we form a perfect square by adding and subtracting 32 to get,
[tex]y=8(x^2+4x)+8(4)+17-8(4)[/tex]
We factor and combine the first two terms with a common factor of 8
This simplifies to,
8([tex]x^2[/tex]+4x+4) + 17 -32
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Answer:
Answer is y = 8(x2 + 4x +
4
) + 17 +
-32
Step-by-step explanation:
Urgent help please help me!
Answer:
(x + 4)(x - 2) = x · x
(option L)
Step-by-step explanation:
we know that area = length × width
So, can write out the lengths and widths that we know:
(note: I will use the square as the reference point, because we can simply say "x" for both of its side lengths--you'll see why this is easier later)
Rug A:
length = x
width = x
Rug B:
length: x + 4
(4 feet greater than rug A length)
width: x - 2
(2 feet less than rug A width)
we can now set these areas to be equal to each other:
(rug A) = (rug B)
(length · width of A) = (length · width of B)
(x · x) = [ (x + 4)(x - 2) ]
So, the equation:
(x + 4)(x - 2) = x · x
can be used to find x (the length in feet) of rug A
hope this helps!! have a lovely day :)
If you have 6 cars, but there is only room in your driveway for 3 cars, in how many ways can you arrange the cars in your driveway if: a. Order does not matter. b. Order of the cars matters. c. What is the probability that the three newest cars end up parked in the driveway
If the order does not matter, cars can be arranged in 20 ways
If an order is important, cars can be arranged in 120 ways
The probability that the three newest cars end up parked in the driveway is 0.167
1. If the order does not matter, combination is used
[tex]\left ({n} \atop {r}} \right.)=\frac{n!}{r!(n-r)!}[/tex]
Here, n=6 r=3
using formula,we get
[tex]\left ( {{6} \atop {3}} \right)=\frac{6!}{3!3!} =5*4=20[/tex]
2. If an order is important, Permutation will be applicable
[tex]^{n}P_{r} = \frac{n!}{(n-r)!} \\[/tex]
∴[tex]^{6} P_{3} =\frac{6!}{3!(6-3)!}=\frac{6!}{3!} =120[/tex]
3. the probability that the three newest cars end up parked in the driveway
P=[tex]\frac{No. of possible outcomes for 3 cars}{total possibilities}[/tex]
=[tex]\frac{6*4*5}{6!}[/tex]
=[tex]\frac{120}{720}[/tex]
=[tex]\frac{1}{6}[/tex] ≈ 0.167
Hence, If the order does not matter, cars can be arranged in 20 ways
If an order is important, cars can be arranged in 120 ways
The probability that the three newest cars end up parked in the driveway is 0.167
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Which relation is a function of x?
O
X
y
-1 7
223
X y
-8 -9
-8
2
1
1
X
-5
-5
-5
-5
8
-4
X
-9
2
y
1
7
-9
2
y
Answer: Option 4
Step-by-step explanation:
Each value of x maps onto only one value of y.
What is the value of y in the triangle 35 POINTS
Answer: y=40
Step-by-step explanation:
because a triangle adds up to 180 degrees, and you subtract 180-15-26.5-90[the right angle]=40
PLEASE HELP!!! FINDING PROBABILITY MATH!!!
i need the answer to question 2, 3, and 4. question 1's answer is 9/28 & 32.1%.
The probability that a person wins the game is 32.1%
How to illustrate the probability?Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.
Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:
= 24 + 4 = 28
The frequency table will be such that 28 or more has a relative frequency of 9. Therefore, the probability that a person wins the game will be:
= 9/28 = 32.1%
When you win 25% of the time, this illustrates that the number of products picked will be:
= 25% × 28
= 7 products.
The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:
= 1/6⁴
= 1/1296
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Smaller triangle L M N P is inside larger triangle L prime M prime N prime P. The length of L M is 4 and the length of M N is 6. The length of L prime M prime is 12.
Rectangle LMNP was dilated using the rule DP,3. Which statements are true? Check all that apply.
The length of line segment M'N' is 18 units.
The length of segment M'N' is 14 units.
The dilation is a reduction.
The dilation is an enlargement.
The scale factor is One-third.
The scale factor is 3.
The statement that are true about the dilation are:
A. M'N' is 18 units.
D. The dilation is an enlargement.
F. Scale factor is 3.
What is Dilation?Given that rectangle LMNP is dilated using the rule Dp.3, it means that rectangle LMNN is enlarged times 3 to get rectangle L'M'N'P'.
This means that the scale factor is 3.
We would have the following:
M'N' = 6 × 3 = 18 units.
Therefore, the statements that are true are:
A. M'N' is 18 units.
D. The dilation is an enlargement.
F. Scale factor is 3.
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Answer: A. The length of line segment M'N' is 18 units, D. The dilation is an enlargement, & F. The scale factor is 3.
Step-by-step explanation: TRUST ME!!! Answer is correct in Edge. :)
Answers: A, D & F.
Work out the
circumference of a circle with diameter 1.8 cm.
Take pi to be 3.142 and give your answer to 1 decimal place.
Step-by-step explanation:
the circumference of a circle is
2×pi×r
with r being the radius, which is always half of the diameter.
r = 1.8 / 2 = 0.9 cm
circumference :
2×pi×0.9 = 1.8×pi = 1.8 × 3.142 = 5.6556 cm ≈ 5.7 cm
Answer:
5.7cm
Step-by-step explanation:
circumference = π · d
(2πr)
{note: "d" is diameter; "r" is radius; "π" is pi}
we know our diameter (d) to be 1.8
let's plug this into our cicumference formula! :
π · d = circumference
(3.142) · (1.8)
3.142 · 1.8 = 5.6556
let's round our answer to 1 decimal place,
remember, if the next digit is ≥5 we round up; < 5 we keep the same
so, our answer is 5.7 cm
hope this helps!! have a lovely day :)
Select all the correct answers.
A survey found that 50% of teenagers prefer to watch a movie at a theater over other viewing options. You want to know the estimated probability that three out of four randomly chosen teenagers do not prefer watching a movie at a theater. How could you design a simulation for this situation?
Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.
Pick a card from a deck of standard playing cards four times, with red suits representing those who prefer watching a movie at a theater and black suits representing those who do not.
Spin a spinner with four equal sections three times, with one section representing each person.
Roll a six-sided die four times, with even numbers representing those who prefer watching a movie at a theater and odd numbers representing those who do not.
Generate a set of four numbers using a number generator, with numbers 0 to 5 representing those who prefer watching a movie at a theater and 6 to 9 representing those who do not.
An equivalent situation, in which the binomial distribution could be used, is given by:
Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the parameters are:
p = 0.5, n = 4;
The other situation that would represent a binomial distribution with the same parameters is given by:
Flip a fair coin four times, with heads representing teenagers who prefer watching a movie at a theater and tails representing those who do not.
The other situations have different values of p, hence they are not equivalent.
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Which polygon is a unit tile in this tessellation
Answer:
Option no. B is a unit tile in that tesselation
i.e rectangular shape
Step-by-step explanation:
Well, it's because we all know that tesselation
only use one shape and it's sum is always 360°
meanwhile sum of rectangle=360°
as each side of rectangle are 90°
90°*4=360°##
I hope it helped you to understand more clearly...
Select the correct answer from each drop-down menu.
A toy chest is shown.
TUFFETY
Which shapes best model the parts of the toy chest?
The bottom part of the chest is best modeled by
The top part of the chest is best modeled by
because each face is a
because some faces are
Answer: What you picked
Step-by-step explanation:
I can't see the dropdown menus, but those answers make sense.
Answer:
The bottom part of the chest is best modeled by rectangular prism because each face is a rectangle The top part of the chest is best modeled by part of a cylinder because some faces are curved