The probability of drawing a lettered card from a deck of shuffled 52 cards is 50%.
Calcuating the probability of drawing a lettered cardThere are 52 cards in a deck, and 26 of them are lettered cards (A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2) while the other 26 cards are suited cards (clubs, spades, hearts, diamonds).
If the deck is well shuffled, each card is equally likely to be drawn.
Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is simply the number of lettered cards divided by the total number of cards:
P(Drawing a lettered card) = Number of lettered cards / Total number of cards
= 26 / 52
= 1/2
= 0.5
Therefore, the probability of drawing a lettered card from a deck of shuffled 52 cards is 0.5 or 50%.
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Find f'(x), where f(x)= (2√x+1){(2-x)/(x^2+3x)}
The derivative of f(x) of (2√x+1){(2-x)/(x^2+3x)}, is f'(x) = (-x^3+5x+6)/[x(x+3)^2√x].
To find the derivative of the function f(x) = (2√x+1){(2-x)/(x^2+3x)}, we can use the product rule and the quotient rule.
First, let's find the derivative of (2-x)/(x^2+3x):
f1(x) = (2-x)/(x^2+3x)
f1'(x) = [(-1)(x^2+3x)-(2-x)(2x+3)]/(x^2+3x)^2
= (-x^2-3x-4x+6)/(x^2+3x)^2
= (-x^2-x+6)/(x^2+3x)^2
Next, let's find the derivative of 2√x+1:
f2(x) = 2√x+1
f2'(x) = 2(1/2√x) = 1/√x
Using the product rule, we get:
f'(x) = f1(x)f2'(x) + f2(x)f1'(x)
= [(2-x)/(x^2+3x)](1/√x) + (2√x+1)(-x^2-x+6)/(x^2+3x)^2
= (2-x)/(x^2√x+3x√x) - (x^2+4x-6)/(x^2+3x)^2√x
= (2-x)/(x(x+3)√x) - (x^2+4x-6)/(x^2+3x)^2√x
Simplifying the expression, we get:
f'(x) = [(2-x)(x^2+3x) - (x^2+4x-6)x]/[x(x+3)^2√x]
= (-x^3+5x+6)/[x(x+3)^2√x]
Therefore, the derivative of f(x) is:
f'(x) = (-x^3+5x+6)/[x(x+3)^2√x]
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Two spheres have volumes of 8Ï€ cm3 and 64Ï€ cm3. if the surface area of the smaller sphere is 16Ï€ cm2, what is the surface area of the larger sphere? a. 64Ï€ cm2 b. 96Ï€ cm2 c. 128Ï€ cm2 d. 256Ï€ cm2
The surface area of the larger sphere is 64π cm². therefore option A. 64π cm² is correct.
To find the surface area of the larger sphere, given the volumes of two spheres and the surface area of the smaller sphere, follow these steps:
1. Determine the ratio of the volumes of the spheres:
Volume ratio = Volume of larger sphere / Volume of smaller sphere
= (64π cm³) / (8π cm³)
= 8
2. Find the cube root of the volume ratio to get the ratio of their radii:
Radii ratio = cube root of volume ratio = cube root of 8 = 2
3. Since the surface area of a sphere is proportional to the square of its radius, find the ratio of the surface areas by
squaring the radii ratio:
Surface area ratio = (Radii ratio)² = (2)² = 4
4. Finally, multiply the surface area of the smaller sphere by the surface area ratio to get the surface area of the larger
sphere:
Surface area of larger sphere = Surface area of smaller sphere × Surface area ratio
= 16π cm² × 4
= 64π cm²
So, the surface area of the larger sphere is 64π cm² (Option A).
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A tower under construction in a rural municipality is 24 feet tall. A man of height 6 feet, standing on the same horizontal level of the tower, observes the top of the incomplete tower and finds the angle of elevation to be 30°.
(a) How high must the tower be raised so that the man finds the angle of elevation of the complete tower to be 60° from the same place?
(b) What will be the height of the tower after completing its construction work?
Step-by-step explanation:
Let's first draw a diagram to better visualize the problem:
* T (top of incomplete tower)
/|
/ |
/ |
/ | h (height of incomplete tower)
/ |
/ |
/θ1 |
/___ | M (man's position, height = 6 feet)
d
We can see that we have a right triangle with the tower's height as the opposite side, the distance between the man and the tower as the adjacent side, and the angle of elevation θ1 as 30°. We can use trigonometry to find the height of the incomplete tower:
tan(30°) = h / d
h = d * tan(30°)
We don't know the value of d, but we can use the fact that the man's height plus the height of the incomplete tower equals the distance from the man to the top of the incomplete tower:
d = h / tan(30°) + 6
Now we can use trigonometry again to find the height of the complete tower. Let's call this height H and the new angle of elevation θ2:
* T (top of complete tower)
/|
/ |
/ |
/ | H (height of complete tower)
/ |
/ |
/θ2 |
/___ | M (man's position, height = 6 feet)
d
We have another right triangle, this time with the height of the complete tower as the opposite side, the same distance between the man and the tower as the adjacent side, and the new angle of elevation θ2 as 60°. We can use the tangent function again:
tan(60°) = H / d
H = d * tan(60°)
We can substitute the value of d we found earlier:
H = (h / tan(30°) + 6) * tan(60°)
Simplifying:
H = h * sqrt(3) + 6 * sqrt(3)
(a) To find how high the tower must be raised, we subtract the height of the incomplete tower from the height of the complete tower:
raise = H - h
raise = h * (sqrt(3) - 1) + 6 * sqrt(3)
Substituting the value of h we found earlier:
raise = 24 * (sqrt(3) - 1) + 6 * sqrt(3)
raise ≈ 38.8 feet
(b) The height of the completed tower is simply the height of the incomplete tower plus the raise we found:
height = h + raise
height = 24 + 38.8
height ≈ 62.8 feet
Therefore, the height of the tower after completing its construction work is approximately 62.8 feet.
Step-by-step explanation:
See image and calcs below
how do you do this problem?
8x^2+40x=0
Answer:
x=0 or x=-5
Step-by-step explanation:
the step by step explanation is uo above in the image. it will help you understand it
Answer:
Step-by-step explanation:
8x^2+40x=0. 8x(x+5)=0. 8x=0. Or x+5=0. So. X=0.x=_5
is this a supplement or congruent
Answer:
The angles are supplementary.
When playing a game of poker, how many five card hands consist of no face cards at all? (Note: face cards include jacks, kings and queens.)
Answer:In a standard deck of 52 cards, there are 12 face cards (4 jacks, 4 queens, and 4 kings) and 40 non-face cards. To find the number of five card hands consisting of no face cards, we need to count the number of hands that include only non-face cards.
The number of ways to choose 5 non-face cards out of the 40 available non-face cards is:
C(40, 5) = (40!)/(5!35!) = 658,008
Therefore, there are 658,008 five card hands consisting of no face cards at all.
Step-by-step explanation:
You roll one die. What is the probability that you roll a 6?
Answer:
1/6
16.667%
well in simple terms 16.6
Step-by-step explanation:
5. A solid with volume 8 cubic units is dilated by a scale factor of k. Find the volume of the image for each given value of k. (Lesson 5-6)
a. k = 1/2
b. k = 0.6
c. k = 1
d. k = 1.5
The volume of the image after the dilation for given scale factor are:
a. k = 1/2: V = 4 cubic units
b. k = 0.6: V = 2.4 cubic units
c. k = 1: V = 8 cubic units
d. k = 1.5: V = 12 cubic units
Explain about the scale factor?The ratio between comparable analyses of an object and an identification of that object is known as a scale factor in mathematics. The copy will all be larger if the scaling factor is a complete number. A fractional scaling factor means that the duplicate will be smaller.
An expansion happens when the scaling factor's absolute value exceeds one.Compression happens when the scale factor's absolute value falls below one.When the scale factor's absolute value is 1, neither expansion nor compression take place.Volume of solid: 8 cubic units
a. k = 1/2
volume of the image : 1/2 *8 = 4 cubic units
b. k = 0.6
volume of the image : 0.6*8 = 2.4 cubic units
c. k = 1
volume of the image : 1*8 = 8 cubic units
d. k = 1.5
volume of the image : 1.5*8 = 12 cubic units
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please answer , I really need an answer
55% of professionals in a large city participate in professional networking. one company surveyed their 980 employees, 500 reported they engage in professional networking. at the 0.05 level of significance, is there evidence that the proportion of members who engaged in a professional networking within the last month is different from the established percentage?
The null hypothesis rejected represents there is evidence the proportion of members engaged in professional networking within last month is different from established percentage.
Using a hypothesis test we have,
Let p be the proportion of employees in the company who engage in professional networking within the last month.
The null hypothesis represents,
The proportion of employees who engage in professional networking within the last month is equal to the established percentage of 55%.
H0: p = 0.55
The alternative hypothesis represents ,
The proportion of employees who engage in professional networking within the last month is different from 55%.
Ha: p ≠ 0.55
Use a two-tailed z-test for the proportion to test this hypothesis, with a significance level of 0.05.
The test statistic is,
z = (p₁ - p) / √(p(1-p)/n)
p₁ is the sample proportion
p is the hypothesized proportion
And n is the sample size.
Here,
p = 0.55
n = 980
p₁ = 500/980
= 0.51.
Substituting these values, we get,
z = (0.51 - 0.55) / √(0.55(1-0.55)/980)
= -1.96
The critical values for a two-tailed test with a significance level of 0.05 are ±1.96.
Since the test statistic (-1.96) falls within the critical region.
Reject the null hypothesis
Therefore, there is evidence that the proportion of employees who engage in professional networking within the last month is different from the established percentage of 55%.
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please help with the following two questions :)
Answer:
10) -1.5
11) 1
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Which of the following options have the same value as
30
%
30%30, percent of
81
8181?
Choose 3 answers:
Choose 3 answers:
Answer: 30, 30%, 8181
Step-by-step explanation:
Step 1: I looked at the question and saw that it was asking which of the given options had the same value as 30%30 and 81 8181.
Step 2: I looked at the list of options and saw that 30, 30%, and 8181 all had the same value as the given numbers.
Step 3: I chose those three options as my answer.
1/2 perecnt as decimal
Answer:
0.5
Step-by-step explanation:
trust me
FELICIA CREATED A FLOOR PLAN FOR A PLAY HOUSE AS SHOWN BELOW WHAT WILL BE THE PERIMETER AND AREA OF FELICIA PLAY HOUSE
The perimeter of Felicia's playhouse is 60ft, and its area is 144ft².
In order to determine the perimeter and area of Felicia's playhouse, we must first analyze the provided diagram:
There are two rectangles and a triangle, therefore we must calculate the area of each shape, and then add the areas together to get the total area.
Area of Rectangle A = lw = 8ft x 10ft = 80ft²
Area of Rectangle B = lw = 4ft x 10ft = 40ft²
Area of Triangle C = (1/2)bh = (1/2)(8ft)(6ft) = 24ft²
Total Area = Area of Rectangle A + Area of Rectangle B + Area of Triangle C = 80ft² + 40ft² + 24ft² = 144ft²
To determine the perimeter, we must add up the lengths of all four sides of the rectangle and the three sides of the triangle.
P = 2l + 2w + a + b + c
P = 2(10ft) + 2(8ft) + 6ft + 10ft + 8ft
P = 20ft + 16ft + 6ft + 10ft + 8ft
P = 60ft
Therefore, the perimeter of Felicia's playhouse is 60ft, and its area is 144ft².
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Question
Felicia created a floor plan for a playhouse, as shown below. 2 ft 23 ft 7 ft 8 ft 844 What will be the perimeter and area of Felicia's playhouse?
What is the measure of JML
Answer:
94
Step-by-step explanation:
∠JKL and ∠JML are supplementary( they add to 180°).
Set their values equal to 180 to find the value of x.
15x - 19 + 13x + 3 = 180
Combine like terms
28x - 16 = 180
Add 16 to both sides to isolate the x
28x = 196
Divide both sides by 28
x = 7
Substitute the value of x into the expression for ∠JML
13(7) + 3 = ∠JML
91 + 3 = ∠JML
94° = ∠JML
To check our answer we can substitute the value of x into the expression for ∠JKL and if they add up to 180 we are correct
15(7) - 19 =∠JKL
105 -19 =∠JKL
86 =∠JKL
94° + 86° = 180°
Therefore we are correct
Write a system of inequalities for each graph
a)System of inequalities of the graph is
y-x-2≤0
y-x+3≥0
b)System of inequalities of the graph is
y-x≥0
y+x≥0
c)System of inequalities of the graph is
y-1≤0
y-x-1≤0
define inequalityIn mathematics, an inequality is a statement that two quantities or expressions are not equal. Specifically, an inequality describes a relationship between two values, indicating whether one value is greater than, less than, or equal to another value.
Part a)First line coordinates
X y
-2 0
0 2
slope=2-0/0+2=1
Equation of line is y=x+2
Second line coordinates
X y
3 0
0 -3
slope=-3-0/0-3=1
Equation of line is y=x-3
System of inequalities of the graph is
y-x-2≤0
y-x+3≥0
Part b)First line coordinates
X y
0 0
-1 -1
slope=-1-0/-1-0=1
Equation of line is y=x
Second line coordinates
X y
0 0
1 -1
slope=-1-0/1-0=-1
Equation of line is y=-x
System of inequalities of the graph is
y-x>0
y+x≥0
Part c)First line coordinates
y=1
Second line coordinates
X y
0 1
-1 0
slope=0-1/-1-0=1
Equation of line is y=x+1
System of inequalities of the graph is
y-1≤0
y-x-1≤0
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Find the missing length.
Answer:
The missing length is 45
Step-by-step explanation:
CD || AB
[tex]\mathrm{\cfrac{EC}{AC} =\cfrac{ED}{BD} }[/tex]
[tex]\mathrm{\cfrac{20}{8} =\cfrac{?}{18} }[/tex]
[tex]\mathrm{\cfrac{?}{18}=\cfrac{20}{8}}[/tex]
Cancel the common factor, which is 4:-
[tex]\mathrm{\cfrac{?}{18}=\cfrac{5}{2}}[/tex]
Multiply both sides by 18:-
[tex]\mathrm{?=45^o}[/tex]
Therefore, the missing length is 45.
________________________
Hope this helps!
An artist recreated a famous painting using a 4:1 scale. The dimensions of the scaled painting are 8 inches by 10 inches. What are the dimensions of the actual painting?
40 inches by 50 inches
32 inches by 40 inches
12 inches by 14 inches
2 inches by 2.5 inches
Answer:
32,40 in
Step-by-step explanation:
please
give brainliest
Romain knows the following information about the 323232 classes he took in high school: He studied for but did not pass 333 classes. He passed 272727 classes in total. He studied for 262626 classes in total. Can you help Romain organize the results into a two-way frequency table? Studied for the class Did not study for the class Passed the class Did not pass the class
Classes studied for, Classes he did not study for Total
Classes Passed, 23 4 27
Classes Failed, 3 2 5
Total, 26, 6 32
Please find attached the two way frequency table formatted on Excel spreadsheet
the details provided are;
32 classes were taken by Romain in total during his high school years.
Three of the classes he attempted but failed to pass
27 out of the total classes Romain took and passed
26 classes were studied for by Romain.
Therefore;
26 - 3 = 23 is the number of classes Romain took, passed, and studied for.
32 - 27 = 5 is the total number of classes Romain failed.
Total classes Romain passed without paying attention: 27 - (26 - 3) = 4.
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HELPPPPPP MEEEEE PLEASEEEEEEEEE
Answer:6x-2y=8
Step-by-step explanation:
[tex]\left \{ {{3x-y=4} \atop {Ax-By=8}} \right. \\\frac{3x}{Ax} =\frac{y}{By} =\frac{4}{8}=\frac{1}{2}\\\frac{3}{A} =\frac{1}{2}\\A=6\\\frac{1}{B} =\frac{1}{2}\\B=2\\so, 6x-2y=8[/tex]
Answer:
6x - 2y = 8
Step-by-step explanation:
If:
3x - y = 4
⇒ 4* 2 = 8
then:
3*2 = 6
-1 * 2 = -2
The answer is:
6x - 2y = 8
Find the ordered pair solutions for the system of equations. I just need the x’s and y’s please.
Answer: (-3, 18) and (-1, 18)
Step-by-step explanation:
Solve the system of equations. [tex]x^{2}[/tex] - 2x + 3 = -6x. [tex]x^{2}[/tex] + 4x + 3 = 0. (x+1)(x+3) = 0. x = -1, -3. Then plug it in. f(x) = 18.
There are 18 flower seeds in each packet. Mr. Doyle buys 14 packets of seeds. How many flower seeds are in the 14 packets? 18 A (A) 612 seeds B) 252 seeds C222 seeds D 60 seeds
There are 252 flower seeds in the 14 packets that Mr. Doyle bought, which is option B.
What is Multiplication?
Multiplication is a mathematical operation that involves combining or adding a number to itself a certain number of times, resulting in a product that represents the total value of those added numbers. It is often represented using the "×" symbol or the asterisk symbol "*".
To find out how many flower seeds are in the 14 packets that Mr. Doyle bought, we can multiply the number of seeds in one packet by the number of packets he bought:
Number of seeds = 18 seeds/packet x 14 packets
Number of seeds = 252 seeds
Therefore, there are 252 flower seeds in the 14 packets that Mr. Doyle bought, which is option B.
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guys can anyone help me with my other SAT question"
The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (Note: Ignore the percent symbol when entering your answer. For example, if the answer is 42.1%, enter 42.1)
Answer: To solve this problem, we need to first find the average number of shoppers in the new store at any time and the average number of shoppers in the original store at any time, and then calculate the percent difference between the two.
Let's start by finding the average number of shoppers in the new store at any time. We know that 90 shoppers enter the store per hour, and each shopper stays for an average of 12 minutes, which is 0.2 hours. So the number of shoppers in the store at any time is:
90 shoppers/hour × 0.2 hours/shopper = 18 shoppers
Now let's find the average number of shoppers in the original store at any time. We don't have any information about the original store, so let's call the average number of shoppers in the original store "x". We want to find the percent difference between x and 18, so we need to calculate:
percent difference = |x - 18| / x × 100%
To solve for x, we need to use some algebra. We know that the number of shoppers entering the original store per hour is equal to the number of shoppers leaving the store per hour (assuming the store has a steady flow of shoppers and no one stays for more than an hour). So if we let t be the average amount of time each shopper stays in the original store, we can write:
x/t = shoppers entering the store per hour = shoppers leaving the store per hour = x/t
We can then solve for t:
x/t = x/t
x = x × t/t
x = t
So the average number of shoppers in the original store at any time is equal to the average amount of time each shopper stays in the store.
We don't know the average amount of time each shopper stays in the original store, but we can make an estimate based on the information we have about the new store. We know that the average amount of time each shopper stays in the new store is 12 minutes, or 0.2 hours. If we assume that the shopping behavior is similar in both stores, we can use this estimate for the original store as well.
So we have:
x = t = 0.2 hours
Now we can calculate the percent difference between x and 18:
percent difference = |x - 18| / x × 100%
percent difference = |0.2 - 18| / 0.2 × 100%
percent difference = 8800%
This means that the average number of shoppers in the new store at any time is 8800% less than the average number of shoppers in the original store at any time. However, this answer seems implausible, since a percent difference greater than 100% means that the new store has a negative number of shoppers!
It's possible that there was an error in the problem statement, such as a typo or a missing decimal point. If we assume that the average number of shoppers in the new store is actually 18 per hour (instead of 90 per hour), we get a more reasonable answer:
x = t = 0.2 hours
percent difference = |x - 18| / x × 100%
percent difference = |0.2 - 18| / 0.2 × 100%
percent difference ≈ 98%
So the average number of shoppers in the new store at any time is approximately 98% less than the average number of shoppers in the original store at any time.
Step-by-step explanation:
company xyz know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 16 years and a standard deviation of 1.4 years. find the probability that a randomly selected quartz time piece will have a replacement time less than 11.9 years?
The probability that a randomly selected quartz timepiece will have a replacement time less than 11.9 years is 0.0007 or 0.07%.
The given information is that a company XYZ knows that the replacement times for the quartz timepieces it produces are normally distributed with a mean of 16 years and a standard deviation of 1.4 years. We need to calculate the probability that a randomly selected quartz timepiece will have a replacement time of less than 11.9 years. Let us solve this problem using the standard normal distribution.
The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the given distribution into the standard normal distribution using the formula:
z = (x - μ)/σ
Where x is the replacement time, μ is the mean and σ is the standard deviation.
Putting the given values, we get:
z = (11.9 - 16)/1.4
z = -3.21
We need to find the probability that the replacement time is less than 11.9 years. This can be calculated as the area under the standard normal distribution curve to the left of z = -3.21.
Using the standard normal distribution table, we find that the area to the left of
z = -3.21 is 0.0007.
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a cube and a sphere both have volume 512 cubic units. which solid has a greater surface area? explain your reasoning.
If the cube and sphere both have volume as 512 cubic units, then the solid that has a greater surface area is Cube.
we first find the side length of the cube and the radius of the sphere.
The volume of the cube is 512 cubic units,
We have,
⇒ side³ = 512,
⇒ side = 8
So, the side length of the cube is 8 units.
Volume of sphere is also 512 cubic units,
We have,
⇒ (4/3)πr³ = 512,
On Simplifying,
We get,
⇒ r = 4.96 units.
So, radius of sphere is = 4.96 units.
Next we can find the surface area of each solid.
The surface-area of cube is = 6×(side)²,
⇒ 6(side²) = 6(8²) = 384 square units,
The surface area of the sphere is = 4πr²,
⇒ 4π(r²) = 4π(4.96²) ≈ 309 square units.
Therefore, the Cube has a greater surface area than the sphere.
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Mr Peterson bought a car for $1200. He spent money on repairing the car. He finally sold the car for $2100 at a profit of 16⅔ % on the cost of buying and repairing the car. Calculate the cost of repairing the car
The cost of repairing the car was $360 after selling the car at a profit of
16⅔ % on the cost of buying and repairing the car.
What is a profit?Profit is the financial gain that is earned by a business or an individual after all the expenses have been subtracted from the revenue. In simple terms, profit is what remains after all costs, including the cost of goods sold, operating expenses, taxes, and other charges, have been deducted from the revenue generated from the sale of goods or services.
According to the given informationLet's call the cost of repairing the car "x". We know that Mr. Peterson bought the car for $1200, spent x dollars on repairing it, and sold it for $2100 at a profit of 16⅔ % on the cost of buying and repairing the car.
We can start by calculating the total cost of buying and repairing the car, which is the sum of the initial cost and the cost of repairs:
Total cost = $1200 + x
Next, we can calculate the profit that Mr. Peterson made on this total cost, which is given as 16⅔ %:
Profit = (16⅔ %) × Total cost
Profit = (16⅔ / 100) × ($1200 + x)
We know that Mr. Peterson sold the car for $2100, so we can set up an equation for the profit:
Profit = Selling price - Total cost
(16⅔ / 100) × ($1200 + x) = $2100 - ($1200 + x)
Simplifying and solving for x, we get:
(5/6) x = $2100 - $1200 - (5/6)($1200)
(5/6) x = $450
x = $360
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there is a 20% chance that a risky stock investment will end up in a total loss. if you invest in 25 independent risky stocks, what is the probability that fewer than six of these 25 stocks end up in total losses?
There is a 20% chance that a risky stock investment will end up in a total loss. If you invest in 25 independent risky stocks, the probability that fewer than six of these 25 stocks end up in total losses is approximately 0.91.
Given data:
Probability of getting a total loss in one investment = 20% = 0.20
Probability of not getting a total loss in one investment = 1 - 0.20 = 0.80
Number of investments = 25
We need to find the probability that fewer than six out of these 25 risky investments end up in total losses.
We will use the binomial distribution formula here:P(X < 6) = Σp(x) (from x = 0 to x = 5)
Here, Σ is the summation signp(x) = probability of x successes in 25 trials, which is given by the formula:
p(x) = [ nCx * p^x * (1-p)^(n-x)]
Where, n = number of trial
s = 25
p = probability of success = 0.80
q = probability of failure = 1 - p = 0.20n
Cx = n! / (x! × (n-x)!) = combination of n items taken x at a time
We need to substitute these values in the formula and calculate the probability:
P(X < 6) = Σp(x) (from x = 0 to x = 5)
P(X < 6) = p(0) + p(1) + p(2) + p(3) + p(4) + p(5)
P(X < 6) = [tex][25C0 * (0.80)^0 * (0.20)^25] + [25C1 * (0.80)^1 * (0.20)^24] + [25C2 * (0.80)^2 * (0.20)^23] + [25C3 * (0.80)^3 * (0.20)^22] + [25C4 * (0.80)^4 * (0.20)^21] + [25C5 * (0.80)^5 * (0.20)^20][/tex]
P(X < 6) ≈ 0.91
Therefore, the probability that fewer than six of these 25 stocks end up in total losses is approximately 0.91.
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find the equation of the parabola below:
The equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is: y = 4x² + 24x + 32.
What is an equation?
Since the parabola is symmetric with respect to the vertical line passing through the vertex (which is in the second quadrant), its axis of symmetry is the line x = -3.
Let's first find the vertex of the parabola. The x-coordinate of the vertex is simply the average of the x-coordinates of the two given points on the x-axis:
x = (-4 + (-2))/2 = -3
To find the y-coordinate of the vertex, we can use the fact that the vertex lies on the axis of symmetry. Therefore, it must also be the midpoint of the distance between the touch point (-3, -1) and the y-axis.
The distance between (-3, -1) and the y-axis is 3 units. Therefore, the y-coordinate of the vertex is:
y = -1 - 3 = -4
So the vertex of the parabola is V(-3, -4).
Since the parabola is open in the second quadrant and its vertex is in the second quadrant, its equation has the form:
y = a(x + 3)²- 4
where a is a positive constant that determines the "steepness" of the parabola.
To find the value of a, we can use one of the given points on the x-axis. Let's use (-2, 0):
0 = a(-2 + 3)² - 4
4 = a
Therefore, the equation of the parabola is:
y = 4(x + 3)² - 4
or
y = 4x² + 24x + 32
So the equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is:
y = 4x² + 24x + 32.
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Complete question is: The equation of the given parabola is: y = 4x^2 + 24x + 32.
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Part 1
Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to 6 if she rolls the two number cubes 252 times?
A sample space is a collection or a set of possible outcomes of a random experiment and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment.
The sample space is represented using the symbol, “S”.
The subset of possible outcomes of an experiment is called events.
A sample space may contain a number of outcomes that depends on the experiment.
So, Let X = a number of times the sum of the two numbers on two cubes is 5.
Two numbered cubes are rolled n = 180 times.
The event of getting a sum of 5 in independent of the other results.
The random variable X follows a Binomial distribution with parameters n = 180 and n = 1/9.
Then,
E(X) = np
Calculate how many times Tamara expects the two dice to sum to 5 as follows:
= E(X) = np
= 180 * 1/9
= 20
Therefore, a sample space is a collection or a set of possible outcomes of a random experiment, and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.
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Complete question:
Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times?
SOMEONE PLEASE HELP ME WITH THIS ASAP <3
Answer:
Mohsin could be first, Yousuf could be second and luke could be third it doesn't matter really wich way roun it could be that yousuf is first or luke thirst.
Step-by-step explanation: