Answer:
[tex]Outcomes = \{HHHH, HHHT,TTTH, TTTT\}[/tex]
Step-by-step explanation:
Given
[tex]S = \{HHHH, HHHT, HHTH, HHTT,HTHH, HTHT, HTTH, HTTT, THHH, THHT,[/tex]
[tex]THTH, THTT,TTHH, TTHT, TTTH, TTTT\}[/tex]
Required
The outcomes where the first three tosses are the same
To do this, we list out the outcomes that the first three are HHH or TTT.
So, we have:
[tex]Outcomes = \{HHHH, HHHT,TTTH, TTTT\}[/tex]
Find the missing term given below.
14,916,2536,?
Solve for x in the equation x2 - 4x-9 = 29.
Answer:
[tex]x=2+\sqrt{21}\\\\x=2-\sqrt{21}[/tex]
Step-by-step explanation:
One is given the following equation;
[tex]x^2-4x-9=29[/tex]
The problem asks one to find the roots of the equation. The roots of a quadratic equation are the (x-coordinate) of the points where the graph of the equation intersects the x-axis. In essence, the zeros of the equation, these values can be found using the quadratic formula. In order to do this, one has to ensure that one side of the equation is solved for (0) and in standard form. This can be done with inverse operations;
[tex]x^2-4x-9=29[/tex]
[tex]x^2-4x-38=0[/tex]
This equation is now in standard form. The standard form of a quadratic equation complies with the following format;
[tex]ax^2+bx+c[/tex]
The quadratic formula uses the coefficients of the quadratic equation to find the zeros this equation is as follows,
[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the coefficients of the given equation in and solve for the roots;
[tex]\frac{-(-4)(+-)\sqrt{(-4)^2-4(1)(-38)}}{2(1)}[/tex]
Simplify,
[tex]\frac{-(-4)(+-)\sqrt{(-4)^2-4(1)(-38)}}{2(1)}\\\\=\frac{4(+-)\sqrt{16+152}}{2}\\\\=\frac{4(+-)\sqrt{168}}{2}\\\\=\frac{4(+-)2\sqrt{21}}{2}\\\\=2(+-)\sqrt{21}[/tex]
Therefore, the following statement can be made;
[tex]x=2+\sqrt{21}\\\\x=2-\sqrt{21}[/tex]
andrea is planning a birthday party and wants to include a cheese board with the desserts.
she reads online that she should have 110g of cheese per person ,but the cheese is sold in blocks of 500g
How many blocks of cheese should she buy to ensure that each guest can have 110g of cheese?
Step-by-step explanation:
how many people in the party please ?
The U.S. Federal Seed Act establishes germination rates for various fruit and vegetable seeds. Watermelon seeds are to meet a 70% germination standard. A skeptical gardener who has not had very good luck planting watermelons believes that the seed company he purchases seeds from is not adhering to the 70% federal mandate. Once a week for 12 weeks, he purchases a pack of 10 watermelon seeds to act as his sample. He plants the seeds in a greenhouse with good soil to maintain a consistent temperature and watering routine. He finds that the germination rate for the company's watermelon seeds is 55%. Compute a 98% confidence interval to estimate the proportion of watermelon seeds that germinate. Be sure to interpret your interval in the context of the problem.
Answer:
The 98% confidence interval to estimate the proportion of watermelon seeds that germinate is (0.4443, 0.6557). This means that we are 98% sure that the true proportion of all watermalong seeds of the company that germinate is between these two values, which means that there is good evidence that the proportion is below the 70% standard.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Once a week for 12 weeks, he purchases a pack of 10 watermelon seeds to act as his sample. He plants the seeds in a greenhouse with good soil to maintain a consistent temperature and watering routine. He finds that the germination rate for the company's watermelon seeds is 55%.
This means that [tex]n = 12*10 = 120, \pi = 0.55[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 2.327\sqrt{\frac{0.55*0.45}{120}} = 0.4443[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 + 2.327\sqrt{\frac{0.55*0.45}{120}} = 0.6557[/tex]
The 98% confidence interval to estimate the proportion of watermelon seeds that germinate is (0.4443, 0.6557). This means that we are 98% sure that the true proportion of all watermalong seeds of the company that germinate is between these two values, which means that there is good evidence that the proportion is below the 70% standard.
Write the word or phrase that best completes each statement or answers the question. Solve the problem.
Two kinds of cargo, A and B, are to be shipped by truck. Each crate of cargo A is 50 cubic feet in volume and weighs 200 pounds, whereas each crate of cargo B is 10 cubic feet in volume and weighs 360 pounds. The shipping company charges $75 per crate for cargo A and $100 per crate for cargo B. The truck has a maximum load limit of 7200 pounds and 1000 cubic feet. How many crates of each cargo should be shipped on each truck in order to satisfy the load limits and yield the greatest charges? What is the greatest charge?
Answer:
z(max) = 2350
x₁ = 18 x₂ = 10
Step-by-step explanation:
Vol (ft³) W (p) Income ($)
Cargo A (x₁) 50 200 75
Cargo B (x₂) 10 360 100
Max load limit 1000 7200
Objective Function
z = 75*x₁ + 100*x₂
Constraints:
Volume constraint:
50*x₁ + 10*x₂ ≤ 1000
Weight constraint:
200*x₁ + 360*x₂ ≤ 7200
Model:
z = 75*x₁ + 100*x₂ to maximize
Subject to:
50*x₁ + 10*x₂ ≤ 1000
200*x₁ + 360*x₂ ≤ 7200
x₁ ≥ 0 x₂ ≥ 0 x₁ and x₂ integers
After 6 iterations with an on-line solver optimal solution is:
z(max) = 2350
x₁ = 18 x₂ = 10
What number is 18% more than 1257 Round your answer to two decimal places needed,
Force: F = MA; Solve for m.
mass = force / area
this is second law of motion ( Newton's 2nd law)
[tex]\longrightarrow{\blue{ m = \frac{F}{a} }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Explanation}}{\red{:}}}}}[/tex]
F = ma
➺ m = [tex]\frac{F}{a} [/tex]
where,
F = Force
m = mass
a = acceleration
"F = ma" is Newton's second law of motion, which states that force is equal to mass times acceleration.
The SI unit of force is newton, symbol N.
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
1.4 meters is the same as
Answer:
Step-by-step explanation:
1.4 m = 1.4 * 100 = 140.0 = 140 cm
Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard from, given that the point-slope form is y+1=2/3(x-8)
____x+____y=____
Answer: 2/3x-y=19/3
Step-by-step explanation:
Points are useless since we already know the point slope form and we can just simply that
y+1=2/3(x-8)
y+1=2/3x-16/3
y=2/3x-19/3
2/3x-y=19/3
Standard form equation
Answer:
5x+4y=24
Step-by-step explanation:
So Ax+By=C is the standard form equation of a line.
y=mx+b (in which m is the slope and b is the y-intercept) is the equation that most people start off with.
Since the line intersects the y-axis at (0,6), the y-intercept is 6.
So, we can substitute 6 with b, which is y=mx+6.
Now, we can find the slope (m) by either inserting a known point (x,y) or using rise/run. Either way, you get the slope as -5/4 because we go five units DOWN and four units RIGHT from (0,6), one known point, to (4,1), another known point.
The y=mx+b equation becomes: y=(-5/4)x+6.
Now, we subtract (-5/4)x on both sides to get (5/4)x+y=6
Multiply 4 on both sides because standard form requires no fractions or decimals.
The final answer is 5x+4y=24.
That's your answer, fully simplified!
Can someone please answer quickly <3
Study the work shown to find the exact solutions of
this trigonometric equation.
Select all that are solutions of the equation over
the specified domain.
Answer:
first and fourth options
x = pi/6
x= 11pi/6
Step-by-step explanation:
cos(30 degrees) = sqrt(3)/2
as pi stands for a half circle of 180 degrees
30 degrees = pi/6
cos(30) = cos(-30) = cos (330) =
cos(pi/6) = cos(-pi/6) = cos(11×pi/6)
Answer:
A and d
Step-by-step explanation:
Edge:)
2 units
5
2 units
2 units
8 units
2 units
2 units
2 units
6 units
The area of the figure is
square units.
Which graph shows a dilation
Answer:
show the graphs?
Step-by-step explanation:
please help me steps by steps
Answer:
question 19 = no solution because not enough information
question 20 = 18 for volume
Step-by-step explanation:
question 19:
cylinder formula
surface A =2πrh+2πr2
2π times 9 times 7 + 2π times 9 times 2
SA = 508.938009882
volume equals 395.840674352
question 20:
biggest one,
4h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4
V=18 IS the volume
Answer:
The last formulas are called
square based pyramid formula
cone formula
sphere formula
Can help with the first two as im short of time
Hope this helps.
Always remember to check the units^3
Step-by-step explanation:
19) V = π r 2 h = 1781.28303 ft3 = 1781.3ft^3
20) V = 1/2 b h l = 180m^3
Determine whether each of the binary relation R defined on the given sets A is reflexive, symmetric, antisymmetric, or transitive. If a relation has a certain property, prove this is so; otherwise provide a counterexample to show that it does not. (a) A = Z: (a, b) E R if and only if ab > 0. (b) A = R: (a, b) R if and only if a^2=b^2 (c) A = N: (a, be R if and only if a/b is an integer.
Answer:
In explanation
Please let me know if something doesn't make sense.
Step-by-step explanation:
a)
*This relation is not reflexive.
0 is an integer and (0,0) is not in the relation because 0(0)>0 is not true.
*This relation is symmetric because if a(b)>0 then b(a)>0 since multiplication is commutative.
*This relation is transitive.
Assume a(b)>0 and b(c)>0.
Note: This means not a,b, or c can be zero.
Therefore we have abbc>0.
Since b^2 is positive then ac is positive.
Since a(c)>0, then (a,c) is in R provided (a,b) and (b,c) is in R.
*The relation is not antisymmretric.
(3,2) and (2,3) are in R but 3 doesn't equal 2.
b)
*This relation is reflective.
Since a^2=a^2 for any a, then (a,a) is in R.
*The relation is symmetric.
If a^2=b^2, then b^2=a^2.
*The relation is transitive.
If a^2=b^2 and b^2=c^2, then a^2=c^2.
*The relation is not antisymmretric.
(1,-1) and (-1,1) is in the relation but-1 doesn't equal 1.
c)
*The relation is reflexive.
a/a=1 for any a in the naturals.
*The relation is not symmetric.
Wile 4/2 is an integer, 2/4 is not.
*The relation is transitive.
If a/b=z and b/c=y where z and y are integers, then a=bz and b=cy.
This means a=cyz. This implies a/c=yz.
Since the product of integers is an integer, then (a,c) is in the relation provided (a,b) and (b,c) are in the relation.
*The relation is antisymmretric.
Assume (a,b) is an R. (Note: a,b are natural numbers.) This means a/b is an integer. This also means a is either greater than or equal to b. If b is less than a, then (b,a) is not in R. If a=b, then (b,a) is in R. (Note: b/a=1 since b=a)
pls help asap!!
For the following geometric sequence, find the recursive formula.
(-80,20,-5...)
Answer:
asap!!
For the following geometric sequence, find the recursive formula.
(-80,20,-5...)
Step-by-step explanation:
asap!!
For the following geometric sequence, find the recursive formula.
(-80,20,-5...)
Please help me on this!!!!
F(1) is saying the value of x is 1
Look at the graph where x is 1 and find the y value of where the line is.
At x = 1, the line is at y = 1 ( there is actually a dot showing you the location.
The answer is 1
Please help me understand
Answer:
A is is correct since the interquatile or a is 15 since 15 plus 15 equals 30 and 20 plus 20 equals 40
B is incorrect since the interquare are not both 30
C is incorrect since both interquatiles are wrong
D is incorrect since the standrard devations are off
a racer called the whirlwind. Its poster says that in 1/20 hour it covers 7/10 mile. What is the Whirlwind’s speed in miles per hour?
Answer:
Its speed is 14 mph.
Step-by-step explanation:
Given that regarding racer called The Whirlwind, its poster says that in 1/20 hour it covers 7/10 mile, to determine what is the Whirlwind’s speed in miles per hour the following calculation must be performed:
1/20 x 60 = 0.05 x 60 = 3 minutes
7/10 = 0.7
Therefore, every 3 minutes the Whirlwind travels 0.7 miles.
60/3 = 20
0.7 x 20 = 14
Thus, in an hour it travels 14 miles, with which its speed is 14 mph.
what would my grade be if i got 68% on my exam?
Answer:
I am not to sure how the actual grade was calculated, maybe there are some other factors to it, but from the three grades you got, the weighted total is 70.2%, if we add the weighted average of 68 on the exam (with the weight being 20%), we get 83.3%.
Consider the following data representing the price of plasma televisions (in dollars).
1325, 1266, 1123, 1233, 1387, 1249, 1120, 1140, 1347, 1337, 1402, 1259, 1421, 1351, 1452, 1277, 1309, 1232, 1112, 1243, 1429
Copy Data Price of Plasma Televisions (in Dollars) Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency
1067–1126 1127–1186 1187–1246 1247–1306 1307–1366 1367–1426
Determine the class width of the classes listed in the frequency table.
Answer:
[tex]Width = 59[/tex]
Step-by-step explanation:
Given
The above data
Required
The class width
To do this, we simply calculate the difference between the class limits of any one of the classes.
Taking 1187–1246 as a point of reference, the class width is:
[tex]Width = 1246 - 1187[/tex]
[tex]Width = 59[/tex]
Drag each step and justification to the correct location on the table. Each step and justification can be used more than once, but not all steps and justifications will be used.
Order each step and justification that is needed to solve the equation below.
-2x=28-6x
Answer:
Step-by-step explanation:
Steps Justifications
1). -2x = 28 - 6x 1). Given
2). -2x + 6x = 28 - 6x + 6x 2). Addition property of equality
3). 4x = 28 3). Simplification
4). [tex]\frac{4x}{4}=\frac{28}{4}[/tex] 4). Division property of equality
5). x = 7 5). Simplification
How many ounces are equivalent to 9 pounds?(1pound=16 ounces)
Answer: 144
Step-by-step explanation:
If 1 pound is 16 ounces then you have to do 9 X 16
9x16 = 144
Therefore the answer is 144 ounces
Hope this helped!
Activity: Graph Me!
Organize the following data and present it using appropriate graphs or charts. Explain
why you are using such a graph in presenting your data.
a. The following table shows the favorite subjects of 500 students of Mountain Heights High School
Favorite Subjects of 500 students of Mountain Heights High School
b. Mrs. Soni's monthly income is Php 44 400. The monthly expenses of his family on various items are given below.
Monthly Expenses of Mrs. Soni's Family
Answer:
I can graph stuff in different ways. but place share the mentioned tables. the data is missing.
will edit this placeholder answer asap when you show wich data to graph
What's 90cm as a fraction of 2.4m in its simplest form
Answer:
3/8
Step-by-step explanation:
Both measurements should be in same measure.So convert m to cm
2.4m = 2.4 * 100 = 240.0 = 240 cm
[tex]\frac{90}{240}=\frac{9}{24}=\frac{3}{8}[/tex]
Based on a regression analysis, a researcher concluded that 45% of the variance in minutes of activity per day can be explained by age, hours of sleep, and minutes spent on social media. What does the value 45% represent
Answer:
Coefficient of determination, R²
Step-by-step explanation:
The proportion of variation of the dependent variable that can be explained by the regression line is defined by the coefficient of determination, R².
In the scenario described above, the proportion of variation in the number of minutes of activity per day(dependent variable) that can be explained by age, hours of sleep and minutes spent on social media (independent variables) which forms the regression line is 0.45 (45%) is the coefficient of determination while (1 - 0.45) = 0.55 is due to other factors.
What is 1/3 of 30% of 5/6 of 0.6 of 12?
Step-by-step explanation:
[tex] \frac{1}{3 } \times \frac{30}{1} = 10 \\ \\ \frac{10}{1} \times \frac{5}{6} = 8.33 \\ \\ \frac{833}{100} \times \frac{6}{10} = 4.998 \\ \\ \frac{4998}{1000} \times \frac{12}{1} = 59.976[/tex]
Given m||n, find the value of x and y
Hope this might help you (•.•) :)
given that abc=def what is the measure of d
Answer:
C. 47 deg
Step-by-step explanation:
m<A = 180 - 94 - 39 = 47
m<D = m<A = 47