The probability of getting at least 4 heads is P ( A ) = 0.648
Given data ,
We can use the binomial probability formula to calculate the probability of getting at least 4 heads in 7 coin tosses:
P(X ≥ 4) = 1 - P(X < 4)
where X is the number of heads in 7 tosses and P(X < 4) is the probability of getting less than 4 heads.
The probability of getting exactly k heads in n tosses of a fair coin is given by the binomial probability formula:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
where (n choose k) is the number of ways to choose k items from a set of n items (i.e., the binomial coefficient), p is the probability of getting a head on a single toss, and (1-p) is the probability of getting a tail on a single toss.
Now , n = 7 and p = 1/2, so we can compute the probability of getting less than 4 heads as
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= (7 choose 0) * (1/2)⁰ * (1/2)⁷ + (7 choose 1) * (1/2) * (1/2)⁶
+ (7 choose 2) * (1/2)² * (1/2)⁵ + (7 choose 3) * (1/2)³ * (1/2)⁴
= 0.352
Therefore, the probability of getting at least 4 heads is:
P(X ≥ 4) = 1 - P(X < 4)
= 1 - 0.352
≈ 0.648 (rounded to the nearest thousandth)
Hence , the probability of getting at least 4 heads in 7 coin tosses is approximately 0.648
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Which best explains why the rotation represents an
isometric transformation?
the angle at point d remained a right angle.
the rectangle did not change shape or size..
point c remained the center of the rectangle.
point c did not remain the center of the rectangle.
The best explanation for why the rotation is isometric is "The rectangle did not change shape or size". Hence the second option is the right choice.
There are four main categories of transformations:
Translation (figure slides in any direction)Reflection (figure flips over a line)Rotation (figure turns about a fixed point)Dilation (the figure is enlarged or reduced)A stiff transformation known as an isometry maintains perimeter and area while also preserving length and angle measurements. In other words, there is congruence between the preimage and the image. Translations, reflections, and rotations are therefore isometric, but dilations are not since the image and preimage are comparable, rather than congruent figures.
The transformation in the question will be isometric when the preimage of the rectangle before 360° rotation, will be congruent to the image after the rotation.
The congruency is best described by the option "The rectangle did not change shape or size", as that is the basis of congruency.
Thus, the best explanation for why the rotation is isometric is "The rectangle did not change shape or size". Hence the second option is the right choice.
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The provided question is incomplete. For the complete question, refer to the attachment.
Which line plot correctly shows the data?
The line plot shown C in the figure is correct.
Given that the recorded lengths of ribbon pieces which is used in project is [tex]11\frac{1}{4},11\frac{1}{4},10\frac{3}{4},10\frac{1}{2},10\frac{7}{8},10\frac{5}{8},9\frac{7}{8},11\frac{1}{4}[/tex].
Frequency refers to the number of times an event or value occurs. A frequency table is a table that lists items and shows how many times those items occurred.
A line plot displays the data using a no. line.
Firstly, we will fimd the frequency of each value
Values Frequency
9 (7/8) 1
10(4/8)=10(1/2) 1
10(5/8) 1
10(6/8)=10(3/4) 1
10(7/8) 1
11(2/8)=11(1/4) 3
Option A is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)
Option B is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)
Option C is correct because the frequency distribution of the data is represented correctly in the line plot.
Option D is incorrect because 11(2/8) has 2 data values in the line plot (i.e., frequency = 2)
Hence, the line plot which correct shows the data is third line plot.
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Someone help pls, its urgent! ASAP!!! (Geometry)
“Complete the proofs”
Question 11
1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)
2) [tex]\angle A \cong \angle A[/tex] (reflexive property)
3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)
4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)
Question 12
1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)
2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)
3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)
4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)
5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)
6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)
7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)
Note: I changed the names of the segments in Question 11 because of the word filter.
THE FIRST ONE TO ANSWER GETS BRAINLIEST OR FIVE STARS!! The earnings of part-time employees at a local computer repair store can be modeled by the equation y = 22x + 125, where x represents the number of hours worked and y represents the total earnings. Jasmine works at a competing store where she earns the same hourly rate. After working for 15 hours, she earned $555. Write an equation to represent Jasmine’s total earnings.
(picture just if I made a typo)
Answer:
In total she got $555 so we have to divide that to see how much she got per hour.
Step-by-step explanation:
y/x=?
$555/15= $37
Now how much money multiplied by how many hours
$37 X 15 = $555
I hope this helps, if you need any more information just comment!
Have an Amazing Day!!!
Use the pythagorean theorem to prove that this point lies on the unit circle. Find csc(0) where 0=-120.
By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.
How to prove this point lies on the unit circle?In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:
Reference angle = 180 - θ
Reference angle = 180 - 120
Reference angle = 60°.
For the coordinates, we have:
sin(-120) = -sin(60) = -1/2.
cos(-120) = -cos(60) = -√3/2.
By applying Pythagorean theorem, we have:
z² = x² + y²
z = √((-1/2)² + (-√3/2)²)
z = √(1/4 + 3/4)
z = √1
z = 1.
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Select the output of this algorithm
START
SET n = 4
SET d = 1
SET sum = 0
WHILE d < = n
IF n/d is integer THEN
sum = sum + d
ELSE
sum = sum + 0
END IF
d = d+1
END WHILE
OUTPUT sum
END
Answer:
bvjh
Step-by-step explanation:
bn
Let u - 4x? - 1. Find du. (4-1) du - Indicate how the limits of integration should be adjusted in order to perform the integration with respect to u. (Enter your answer using interval notation.) [0, 1] - Evaluate the definite integral. 01 Need Help? Read to a Tutor Consider the following. Let u = x + 1. Find du. du- Indicate how the limits of integration should be adjusted in order to perform the integration with respect to L. (Enter your answer using interval notation, [0, 2] - Evaluate the definite integral.
The value of du becomes 4 by integration.
According to the statement
we have given a two statement which are u - 4x and u = x + 1.
And we have to find the value of du by the use of integration.
An Integral assigns numbers to functions in a way that describes the data.
So,
From u - 4x
here du becomes by derivative
du - 4dx/du
du = 4dx/du. -(1)
And in u = x + 1.
here du becomes
du = dx/du -(2)
by comparing both terms from equation (1) and (2) we get the value of du
du = 4.
the value of du is 4.
So, The value of du becomes 4 by integration.
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Please list how long it takes for each person to pack a shelf alone
Jay and Kay can pack the shelves in one aisle of the supermarket in 30 minutes.
Kay and Elle take 35 minutes to do the same job.
When Jay and Elle work together, the job takes 42 minutes.
How long would each person take working individually?
It takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively
What is Rate and Ratio ?A ratio can sometimes be regarded as fraction. While rate has something to do with time.
Given that Jay and Kay can pack the shelves in one aisle of the supermarket in 30 minutes. Kay and Elle take 35 minutes to do the same job. When Jay and Elle work together, the job takes 42 minutes.
Let
J = Jay K = KayE = ElleThe interpretation of the question go thus;
1/J + 1/K = 1/30 ........ (1)
1/K + 1/E = 1/35 .........(2)
1/J + 1/E = 1/42 .........(3)
Make 1/J and 1/E the subject of formula in equation 1 and 2 respectively and substitute them in equation 3
1/J = 1/30 - 1/K ........ (4)
1/E = 1/35 - 1/K .........(5)
1/30 - 1/K + 1/35 - 1/K = 1/42
Collect the like terms
- 1/K - 1/K = 1/42 - 1/30 - 1/35
-2/K = (35 - 49 - 42)/1470
-2/K = -56/1470
1/K = 28/1470
Reciprocate both sides
K = 1470/28
K = 52.5 minutes.
Substitute K in both equation 4 and 5
1/J = 1/30 - 28/1470
1/J = (49 - 28)/1470
1/J = 21/1470
Reciprocate both sides
J = 1470/21
J = 70 minutes
1/E = 1/35 - 28/1470
1/E = (42 - 28)/1470
1/E = 14/1470
Reciprocate both sides
E = 1470/14
E = 105 minutes
Therefore, it takes Jay, Elle and Kay to work individually for 70 minutes, 105 minutes and 52.5 minutes respectively
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Here is a list of numbers: 2 , 8 , 1 , 7 , 4 , 10 , 1 , 15 , 20 State the median.
Answer:
7
Step-by-step explanation:
1, 1, 2, 4, 7, 8, 10, 15, 20
median = 7
Find each difference and show work please !!
Answer:
X-19
Step-by-step explanation:
First you need to distribute the three into the numbers in the parenthesis,
(3 * x) + (3 * -5) - (2x + 4)
That then turns into,
3x - 15 - (2x + 4)
but we aren't done distributing yet, because the second set of parenthesis has a negative sign in front of it we also have to distribute that. (this is because the negative sign is really just -1)
3x - 15 + (-1 * 2x) + (-1 * 4)
that turns into,
3x - 15 - 2x -4
from here all we have to do is add like terms,
(3x - 2x) + (-15 + -4)
and that leaves us with: 1x -19 or x-19
Hope that helped :))
PLS HELP ME PLEASE
To measure the distance across a lake, a surveyor has taken the measurements shown in the diagram below. Determine the distance across the lake.
Using the law of cosines, it is found that the distance across the lake is of 978.5 feet.
What is the law of cosines?The law of cosines states that we can find the angle C of a triangle as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
in which:
c is the length of the side opposite to angle C.a and b are the lengths of the other sides.In this problem, the parameters are:
a = 800, b = 900, C = 70º.
Hence the distance across the lake is c, found as follows:
[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]
c² = 800² + 900² - 2(800)(900)cos(70º)
c² = 957491
[tex]c = \sqrt{957491}[/tex]
c = 978.5.
The distance across the lake is of 978.5 feet.
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HELP HELP HELP HELP
HELP HELP HELP HELP
Answer:
Vertex - (2, -1)
Axis of Symmetry - x = 2
X intercept - (3,0) (1, 0)
Y intercept (0, 3)
Domain - (negative infinity, positive infinity)
Range - [-1, infinity)
Step-by-step explanation:
I graphed with desmos and found it.
Here are the scores of 14 students on a geography test. 58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87 Notice that the scores are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The five-number summary are as follows:
Minimum = 58Lower quartile(Q₁) = 67Median = 79Upper quartile(Q₃) = 82Maximum = 87Interquartile range = 15How to solve for five-number summary?The five-number summary is a set descriptive statistics which consist of the minimum, maximum, median, upper quartile, and lower quartile of a data distribution.
Therefore,
Given:
58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87
Therefore,
Minimum = 58
Lower quartile(Q₁) = 67
Median = 79 + 79 / 2 = 79
Upper quartile(Q₃) = 82
Maximum = 87
Interquartile range = Q₃ - Q₁ = 82 - 67 = 15
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help!>> Which is the best first step in solving the
absolute value inequality
-3 5x+6+1 >6?
Answer:
see explanation
Step-by-step explanation:
- 3 | 5x + 6 | + 1 ≥ 6
First step : subtract 1 from both sides
- 3 | 5x + 6 | ≥ 5
8. Find (f+g)(x) if f(x) = 4x² - 5x and g(x) = 3x² + 6x - 4.
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: (f + g)(x)[/tex]
[tex]\qquad \sf \dashrightarrow \: f(x) + g(x)[/tex]
[tex]\qquad \sf \dashrightarrow \: (4 {x}^{2} - 5x) + (3 {x}^{2} + 6x - 4)[/tex]
[tex]\qquad \sf \dashrightarrow \: 7 {x}^{2} + x - 4[/tex]
PLEASE HELP
place the figure in a coordinate plane and find the indicated length a square with side length n; Find the length of the diagonal
Thanks
For the square with side length n, the diagonal measures:
[tex]d = \sqrt{2} *n[/tex]
How to get the length of the diagonal?The sidelength of the square is n, and we want to get the length of the diagonal d.
Notice that the diagonal is the hypotenuse of a right triangle whose catheti measure n.
Then we can use the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the cathetus;
[tex]d^2 = n^2 + n^2\\\\d^2 = 2n^2\\\\d = \sqrt{2n^2} \\\\d = \sqrt{2}*n[/tex]
That is the length of the diagonal.
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The area of the trapezoid shown is one 20 cm². Find the sum of the links of the two parallel sides.
The sum of the links of the two parallel sides is 5cm
Area of a trapezoidThe formula for calculating the area of a trapezoid is expressed as:
A = 0.5(a+b)h
where
h is the height of the trapezoid
a+b is the sum of the sides
Substitute
20 = 0.5(a+b)8
40 = 8(a+b)
a+b = 40/8
a+b = 5cm
Hence the sum of the links of the two parallel sides is 5cm
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An example of a qualitative variable is Multiple Choice number of children in a family. weight of a person. color of ink in a pen. miles between oil changes.
Due to its subject-specific classification, ink color in pens is a qualitative variable.
What is a Qualitative variable?The factors that cannot be measured with a numerical value are known as qualitative variables. In order to define anything, these quantities are not quantified or tallied; instead, data is categorized.There is no numerical way to express it.Quantitative variableThe other choices are erroneous because the variables that are numerically specified in the other choices—an individual's weight, the number of children, and the number of miles—are these.Therefore, all of those are quantitative variables.Consequently, option (C) is the appropriate choice.
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which facts are true for the graph of the function below check all that apply F(x)=log6x
Based on the graph of the function (F(x) = log6x), the following facts are true:
It is increasing. The x-intercept is (1, 0). What is a graph?A graph is a type of chart that is used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.
By critically observing the graph of the function (F(x) = log6x) attached in the image below, we can infer and logically deduce that its domain and range include all real numbers that are greater than 0 (x > 0).
This ultimately implies that, the following facts are true:
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Complete Question:
Which facts are true for the graph of the function below? Check all that apply. F(x) = log6 x
A. It is increasing.
B. The range is y > 0.
C. The x-intercept is (1, 0).
D. It is decreasing.
E. The y-intercept is (0, 6).
F. The domain is x > 6.
When the decision maker must consider several possible outcomes for each alternative, each with a given probability of occurrence, this is decision making under a. uncertainty. b. risk. c. duress. d. certainty.
This is considered as decision making under risk.
Decision Making Under Risk
A circumstance in which the implications of the chosen course of action and the likelihood that it will occur are understood is referred to as decision-making under risk . For instance, the lottery selection tasks are frequently employed to examine the nature of decision-making in risky situations.
We make the assumption that there are two or more choices and that each alternative's characteristics are explicitly specified. For each attribute, the CV (coefficient of variation) is configured in case of such decision under risks. And, since in the given question, decision maker is supposed to consider several possible outcomes for each alternative, each with a given probability of occurrence. Thus the decision made will be decision under risk.
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ind the hypotenuse of the following triangle. [2]
This is a RIGHT ANGLE triangle!
c2 =a2 +b2
that's the rule
for example
c2=5^2+5^2
c2=25+25
c2=50 square root is
c=7.07^2
Select all of the following problem situations that involve permutations. How many ways can you arrange 4 of the letters of the word SOLVE if no letter can be used more than once
There are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.
Given a word of 4 letters of the word "SOLVE".
We are required to find the number of ways the four letters of the word SOLVE if no letter can be used more than once.
Permutation is an arrangement of objects in a definite order of things.
Factorial of a number is the product of it and its lesser numbers upto 1.
Number of letters=4
Number of ways=4!
=4*3*2*1
=24 ways
Hence there are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.
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If the coordinates of two points are A (-3,5) and B (-9, -6), then find the value of (abscissa of A) + (ordinate of B)
Answer:
abscissa of A = -3
ordinate of B = -6
A+B = -3+(-6)= -3-6=
-9
What part of this question is an hour
using a calculator, or otherwise,determine the value of(12.3)² - (0.246÷3) and write the answer
(i)exactly
(ii)correct to two significant figures
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming the equation is:}[/tex]
[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]
[tex]\huge\textbf{If so, let's start simplifying it:}[/tex]
[tex]\mathsf{(12.3)^2 - (0.246 \div 3)}[/tex]
[tex]\mathsf{= (12.3\times 12.3) - (0.246 \div 3)}[/tex]
[tex]\mathsf{= (151.29) - (0.246 \div 3)}[/tex]
[tex]\mathsf{= 151.29 - 0.246 \div3}[/tex]
[tex]\mathsf{= 151.29 - 0.082}[/tex]
[tex]\mathsf{= 151.208}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\large\boxed{\mathsf{Exactly \rightarrow} \frak{\ 151.208\ } \& \textsf{ Corrected to two significant figures}\rightarrow \frak{150 \ or \ 151}}\large\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Write an equation of the line in slope-intercept form that is parallel to the line y= -4 + 2 and passes through (2,4)
Answer:
Step-by-step explanation:
If the lines are parallel, it means that the slopes are the same. To write an equation in the slope intercept form, we need the slope and the y-intercept. We are given the slope. We need to find the y-intercept. We can use the slope and the point to help us. The point is written in the form (x,y). In this case the point is (2,4) so we will use 2 for x and 4 for y.
y = mx + b Plug in what we know
4 = -4(2) + b b is what we are looking for. It is the y-intercept
4 = -8 + b Now add 8 to both sides
12 = b
Now we can write the equation:
y = -4x +12
What is the slope of a line passing through (-4,-5)
and (-2,-9)?
Answer:
slope = - 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, - 5 ) and (x₂, y₂ ) = (- 2, - 9 )
m = [tex]\frac{-9-(-5)}{-2-(-4)}[/tex] = [tex]\frac{-9+5}{-2+4}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
8 x -1/4 x -7 cara ngerjain nya bagaimana?
Peter sells ice cream for a living. On Monday, his revenue was 150 dollars. On Tuesday, his revenue was 100 dollars. Finally, on Wednesday, his revenue was 50 dollars. How much is Peter's revenue so far?
Answer:
300 dollars
Step-by-step explanation:
Note that:
{Peter's revenue on Monday: 150 dollars
Peter's revenue on Tuesday: 100 dollars
Peter's revenue on Wednesday: 50 dollars}
---------------------------------------------------------------
In this problem, we need to find how much is Peter's revenue so far (total).
We need to use addition to determine how much Peter's revenue is in total.
So, add 150, 100, and 50.
We get 150 + 100 + 50 = 300
Finally, Peter's revenue in total is 300 dollars.
Answer:
$300
Step-by-step explanation:
add 150+100+50
=300
A political campaign wants to estimate the number of adult residents who voted in the last city election. Answer the following. (a) Which of the following surveys probably would best represent the entire adult population of the city? 25 homeowners are randomly selected; 14 voted in the last election. 25 adult residents are randomly selected from the city; 10 voted in the last election. 25 senior residents are randomly selected; 11 voted in the last election. (b) There are 20,600 adults who live in the city. Using your answer from part (a), estimate the number of adults who voted in the last city election.
Using sampling concepts, it is found that:
a) The best method is: 25 adult residents are randomly selected from the city;
b) The estimate is that 11,536 adults voted in the election.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, the sample will be representative if all adults, no matter if senior or not, homeowners or not are represented, hence the best method is:
25 adult residents are randomly selected from the city;
The estimate of the number of adults that voted is:
14/25 x 20,600 = 11,536.
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