Answer:
1 : 3/5
Step-by-step explanation:
1/3 : 1/5
3/3 : 3/5 (multiply both sides of the colon by 3)
1 : 3/5 (simplify)
Hits to a high-volume Web site are assumed to follow
a Poisson distribution with a mean of 10,000 per day.
Approximate each of the following:
(a) The probability of more than 20,000 hits in a day
(b) The probability of less than 9900 hits in a day
(c) The value such that the probability that the number of hits
in a day exceeds the value is 0.01
(d) Approximate the expected number of days in a year (365
days) that exceed 10,200 hits.
(e) Approximate the probability that over a year (365 days)
more than 15 days each have more than 10,200 hits
Given the following, (a) 100 (a) 0 (b) 0.1587 (c) 10233 (d) 8.322 (e) 0.0096
How can I tell if the distribution of my data is Poisson?The ratio of variance to mean in a sample in n counts from a distribution with a Poisson coefficient ought to correspond to a Chi-square population with n-1 angles of freedom. This test depends on the fact that the mean and variance of the Poisson distribution are identical.
a)
Here for Poisson distribution
Here mean of distribution=μ=λ= 10000
Variance =σ2=λ= 10000
Standard deviation σ=√λ= 100.000
Considering that λ is big, we can approximate:
a)
Probability of more than 20000 hits in a day:
Probability =P(X>20000)=P(Z>(20000-10000)/100)=P(Z>100)=1-P(Z<100)=1-1=0
if using ti-84 press -2nd -vars - command :normal cdf(20000,1 2nd EE 99,10000,100)
b)
P(less than 9900 hits):
Probability =P(X<9900)=(Z<(9900-10000)/100)=P(Z<(-1)=0.1587
If using ti-84 press 2nd -vars - command :normalcdf(-1 2nd EE 99,9900,10000,100)
c)
For top 0.01 or 99th percentile critical value of z=2.33
Therefore corresponding value=mean+z*std deviation=10233
If using ti-84: press 2nd-vars-invNorm(0.99,10000,100)
d)
Probability of exceeding 10200:
Probability =P(X>10200)=P(Z>(10200-10000)/100)=P(Z>2)=1-P(Z<2)=1-0.9772=0.0228
Therefore expected number of days that exceed 10200 hits =np=365*0.0228=8.322
e)
Mean of distribution=μ=np= 8.3220
and standard deviation σ=sqrt(np(1-p))= 2.8517
For normal distribution z score =(X-μ)/σx
P(more than 15 days has more than 10200 hits):
Probability =P(X>15)=P(Z>(15-8.322)/2.852)=P(Z>2.34)=1-P(Z<2.342)=1-0.9904=0.0096
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Find the domain of f and write your answer in interval notation. f(x) = 9/10 + 4x + 6
The domain of a function is the set of all posible values that its input can take.
To find it, we should analyze the rule of correspondence of the function to see if it includes restrictions over the variable that works as input. In this case, we can see that x appears inside a square root. The expression inside the square root must be greater or equal to 0. Then:
[tex]\begin{gathered} 10+4x\ge0 \\ \Rightarrow4x\ge-10 \\ \Rightarrow x\ge-\frac{10}{4} \\ \Rightarrow x\ge-\frac{5}{2} \end{gathered}[/tex]The domain of f is the set of all real numbers x such that:
[tex]-\frac{5}{2}\le x[/tex]In interval notation:
[tex]x\in\lbrack-\frac{5}{2},\infty)[/tex]Therefore, the domain of the function is:
[tex]\lbrack-\frac{5}{2},\infty)[/tex]complete the two way relative frequencies using decimels, and round to three places.
To complete the second table, you need to divide all cells in the first table by 41. obtaining:
- One leg of a right triangle is 4 inches longer than the other leg. The hypotenuse is 20 inches long. What is thelength of the shortest side?
Let's name the a, b, c
let side a = x
let side b = 4+x
Let side c = hypotenuse = 20
Using the law of pythagoras
opposite² + adjacent² = hypotenus²
x² + (x+4)² = 20²
open the parenthesis
x² + x² + 4x +16 = 400
2x² + 4x + 16 = 400
2x² + 4x + 16 - 400 = 0
2x² + 4x - 384 = 0 --------------------------------(1)
The is now a quadratic equation
so we will solve and find x
Using the formula method
Quadratic formula is
[tex]x\text{ = }\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Comparing equation (1) with ax² + bx + c = 0
a = 2 b = 4 and c= -384
Inserting the values into the formula
[tex]x\text{ = }\frac{-4\text{ }\pm\sqrt{4^2\text{ - 4(2)(-384)}}}{2(2)}[/tex]simplifying the above
[tex]x\text{ = }\frac{-4\pm\sqrt{16\text{ + 3072}}}{4}[/tex][tex]undefined[/tex]Understanding Ratios
Eliza is a chef at a restaurant. She is making spaghetti sauce and put 21 tomatoes and 6 onions in the pot. Wh
tomatoes to onions in the pot?
Answer: The Answer is 7:2
Step-by-step explanation:
is 7:2
The equation y = 461.19x + 3,492 represents the value of awork of art from 1964 to 2005. What does the number461.19 represent?o yearly increase in valueo yearly decrease in valueO value of the work of art in 2005o value of the work of art in 1964
we have, in
[tex]y=461.19x+3492[/tex]then 461.19 represents the yearly increase in value
answer: the first one, yearly increase in value
My son is in 6th grade and he doesn’t understand why the base is 1/2
Given:
[tex]16\text{ inches}\times\frac{1}{8}\text{ inches}[/tex][tex]16\text{ inches}\times\frac{1}{8}\text{ inches}=2\text{ square inches}[/tex]Write an equation for this phrase "2 cubed is equal to the square root of x"
2 cubed means that you have to make the axponent of 2 by 3, symbolically:
[tex]2^3[/tex]The square root of x can be symbolized:
[tex]\sqrt[]{x}[/tex]If both terms are equal then you can put them together as:
[tex]2^3=\sqrt[]{x}[/tex]This is the expression that sumbolizes the phrase.
Use the following situation to complete Exercise 7. 7. The school photography club charges $10 for each photo in its annual pet photolontest. The club wants to save $75 of its earnings for a pizza party. The club members also want to have at least $50 left over after the pizza party to pay for other club expenses. Write an expression for: a. how much money the club earns by taking p pet photos
Answer:
10p
Explanation:
We are told that the photography club charges $10 for each photo; therefore, if we have p number of photos then the total amount charged will be 10 * p = 10p
1. is the √15 rational or irrational?
2) Is the point you graphed an estimated or exact answer? Explain why.
(1) √15 is an irrational number.
(2) The point graphed on the number line is estimated.
Any number that cannot be stated as a fraction of any integer is considered to be irrational. The decimal expansions of irrational numbers are neither periodic nor do they come to an end. Every number that is transcendental is illogical.
When multiplied by itself, the square root of 15 produces the original integer 15. The square root of 15 is an irrational number since it cannot be expressed in the form of p/q.
Therefore, √15 is an irrational number.
The value of √15 in decimal is 3.87298334621 and hence, the point graphed on the number line is estimated but not an exact answer.
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2x2 and the times tables
Explanation:
The question asked for
[tex]2\times2,and\text{ }the\text{ }times\text{ }table[/tex]Concept:
2 times 2 means the addition of 2 in 2 places
[tex]\begin{gathered} 2\times2=2+2 \\ 2\times2=4 \end{gathered}[/tex]The time table is given below as
Hence,
The final answer is
[tex]\Rightarrow2\times2=4[/tex]The lengths of two sides of a triangle are 8 and 17. What is one possible length of the third side?
One possible length of the third side of the given triangle is 15
Determining a possible length of a side of a triangleFrom the question, we are to determine a possible length of the third side of the triangle
From one of the properties of a triangle, we know that
The sum of any two sides of a triangle is greater than the third side and the positive difference of any two sides of a triangle is lesser than the third side.
Thus,
8 + 17 is greater than the third side
25 is greater than the third side
and
17 - 8 is lesser than the third side
9 is lesser than the third side
If the third side of the triangle is x,
Then,
9 < x < 25
Hence, a possible value of x is 15
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A rectangle has an area ofx2+ 10x + 21Find the expressions that represent the dimensions of the rectangle.O (x - 3) and (x + 7)O (x + 1) and ( x + 21)O 3 and 7O (x + 3) and ( x + 7)
Answer:
The expressions that represent the dimensions of the rectangle are:
(x+3) and (x+7)
Explanation:
The area of the said rectangle is
[tex]x^2+10x+21[/tex]To find an expression that represents the dimensions of the rectangle, we need to factorize the expression for the area.
[tex]\begin{gathered} x^2+10x+21 \\ =x^2+3x+7x+21 \\ =(x^2+3)+(7x+21) \\ =x(x+3)+7(x+3) \\ =(x+3)(x+7) \end{gathered}[/tex]Therefore, the expressions we are looking for are
(x+3) and (x+7)
Solve on the interval [0,27): 2 cscx -3 = -5 ОА. Зл 2 O 2T 4T B. 3.3 7 T 1 IT c O T O D. IS
Answer:
[tex]x\text{ = }\frac{3\pi}{2}[/tex]Explanation:
We want to get the value of x on the interval for which the identity holds true
We have this as follows:
[tex]\begin{gathered} \csc \text{ x = }\frac{1}{\sin \text{ x}} \\ \\ \frac{2}{\sin \text{ x}}\text{ = -5+3} \\ \\ \frac{2}{\sin \text{ x}}\text{ = -2} \\ \\ \sin \text{ x = -1} \\ \\ x\text{ = }\sin ^{-1}\text{ (-1)} \\ \\ x\text{ = }\frac{3\pi}{2} \end{gathered}[/tex]Find the distance between the two points:(7,12), (1,4)
In order to find the distance between the given points, use the following formula:
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]where (x1,y1) and (x2,y2) are the given points,
In this case, you have:
(x1,y1) = (1 , 4)
(x2,y2) = (7 , 12)
By replacing the previous values into the formula for d, you obtain:
[tex]\begin{gathered} d=\sqrt[]{(12-4)^2+(7-1)^2} \\ d=\sqrt[]{8^2+6^2^{}} \\ d=\sqrt[]{64+36} \\ d=\sqrt[]{100} \\ d=10 \end{gathered}[/tex]Hence, the distance between the given points is 10
Factor problem and I'm having difficulty of setting up the problem.
The factor of the given polynomial is (m - 2n)(m - 5n).
What is termed as the factors of polynomial?Factors of polynomials are zeros of polynomials depicted in the form of some other linear polynomial. If we divide a given polynomial by any of its factors after factorisation, the remainder would be zero. We also factor the polynomial in this process by locating its greatest common factor.For the given question, the polynomial is -
= m² - 7mn + 10n²
We know that 10 = 5×2, thus break the equation like.
= m² - 2mn - 5mn + 10n²
Take m common from first two terms and -5n common from last two terms.
= m(m - 2n) - 5n(m - 2n)
Take common, (m - 2n).
= (m - 2n)(m - 5n)
Thus, the required factors of the given polynomial is (m - 2n)(m - 5n).
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Camelle manages her soccer team. She needs to order 4 practice jerseys for each player. There are y players.
Camelle should buy a total of 4y practice jerseys for the team
How to determine the total number of practice jerseys?From the question, the given parameters are:
Number of players in the team = y players
Number of practice jersey for each player = 4 practice jerseys for each player
The total number of practice jerseys is the product of the number of players in the team and the number of practice jersey for each player
This is represented as
Total number of practice jerseys = Number of players in the team x Number of practice jersey for each player
Substitute the known values in the above equation
So, we have the following equation
Total number of practice jerseys = y players x 4 practice jerseys for each player
Evaluate the products
Total number of practice jerseys = y x 4 practice jerseys
This gives
Total number of practice jerseys = 4y practice jerseys
Hence, the number of jerseys is 4y
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Step-by-step explanation:
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The perimeter of a square is equal to four times the length of its side. Write the direct variation equation that represents this situation.
Let y be the dependent variable and let x be the independent variable.
The linear equation representing this situation will be y = 4x, where y is the dependent variable and x is the independent variable.
As per the question statement, it is given that the perimeter of a square is equal to four times the length of its side and we are supposed to write the direct variation equation that represents this situation.
Also given that we have to use "y" and "x" which are dependent and independent variables respectively.
Perimeter = 4*side
So we conclude that perimeter is dependent on the independent value of side of the square.
Therefore, y = 4x would be the appropriate linear equation depicting the situation given.
Linear equation: An equation is said to be linear if the maximum power of all the variables are consistently 1.Dependent Variable: A quantity whose value relies on how the independent variable is altered is referred to as a dependent variable.Independent variable: A variable that indicates a quantity being altered in an experiment is known as an independent variable.To learn more about the concept of linear equations and dependent / independent variables, click on the link given below:
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7 1/4 dividend by 1 2/3
Answer:
6.2
Step-by-step explanation:
i got this answer by guessing, srry.
is 10% greater than or less than 1/8
is 10% greater than or less than 1/8 ?
Convert both of the given to decimals
So, 10% = 10/100 = 0.1
And 1/8 = 0.125
so, 10% is less than 1/8
A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table.
Labor-Hours per Ski
Maximum Labor-Hours
Available per Day
Department
Fabricating
Finishing
Trick Ski
6
1
Slalom Ski
4
1
132
30
If the profit on a trick ski is $50 and the profit on a slalom ski is $30, how many of each type of ski should be manufactured each day to realize a maxi
What is the maximum profit?
The maximum profit will be $2,700.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The profit on a trick ski is $50 and the profit on a slalom ski is $30.
Let the number of Trick ski manufactured = x
And, Number of slalom ski manufactured = y
So, Maximize;
P = 50x + 30y
Subject to we get;
6x + 4y ≤ 108
And, x + y ≤ 24
And, xy ≤ 0
Now, We have to find set of feasible solutions graphically for the number of each type of ski that can be produced.
So, Linear equation in slope form;
6x + 4y = 108
y = -1.5x + 27
And, x + y = 24
y = - x + 24
So, By the graph we get;
The points,
(x , y) = (0, 24) , (6 , 18) (18, 0)
Hence, The maximum profit when 6 trick ski and 18 slalom ski manufactured.
maximum profit = 6 x 50 + 18 x 30 = 840
And, The maximum profit when 18 trick ski and 0 slalom ski manufactured.
maximum profit = 18 x 50 = 900
The maximum profit when 0 trick ski and 24 slalom ski manufactured.
maximum profit = 24 x 40 = 960
Thus, The maximum profit = 840 + 900 + 960
= $2,700
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Which equation is equivalent to 0.05n+ 0.1d = 4.55?
O 5n+d=455
O 0.5n+d=455
O5n+10d=455
0.05d + 0.1n = 455
Answer:
[tex]5n+10d=455[/tex]
Step-by-step explanation:
Multiply both sides of the equation by 100.
Please answer with a detailed explanation.
From a tee box that is 6 yards above the ground, a golfer hit a ball. The Domain of the function is [0,230].
Given that,
In the picture there is a question with a graph.
From a tee box that is 6 yards above the ground, a golfer hit a ball. The graph displays the height of the golf ball above the ground in yards as a quadratic function of x, the golf ball's horizontal distance from the box in yards.
We have to find the domain of the function in the situation.
The domain is nothing but All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.
The domain of a graph is every value in the graph, from left to right. The graph's entire range, from lower to higher numbers, represents the range.
Therefore, the Domain of the function is [0,230].
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f(x) = |x+1|-1; vertical stretch by a factor of 3
The image of the function after vertically stretched by a factor of 3 is f'(x) = 3|x + 1| - 3
How to determine the equation of f(x) after the transformation?From the question, the given parameters are:
f(x) = |x + 1| - 1
The transformation is given as
Vertical stretch by a factor of 3
This implies that we stretch the function f(x) by a factor of 3 across the origin
Mathematically, this transformation can be represented as
(x, y) = (x, 3y)
When represented as a function, we have
f'(x) = 3 * f(x)
Substitute the equation f(x) = |x + 1| - 1 in the equation f'(x) = 3 * f(x)
So, we have the following equation
f'(x) = 3 * (|x + 1| - 1)
Remove the bracket
So, we have
f'(x) = 3 * |x + 1| - 3 * 1
Evaluate the products
So, we have
f'(x) = 3|x + 1| - 3
Hence, the equation of f'(x) is f'(x) = 3|x + 1| - 3
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(7, 17)
(-4,0)
(-3,-13)
(2,2)
(5,10)
match each playing with the option that correctly fills in that blank.
SOLUTION
One way to find the blank 1: least common multiple of two numbers is to list their multiples and find the first number that appears in both list.
Another way is to blank 2: multiply the numbers together, and then divide by their blank 3: greatest common factor.
how many ice cream servings can the 5 sisters buy if they only want to spend 10.00$ on ice creams. Write an inequality. Ice creams is 2.80$
Let the number of ice-cream serving the sisters can buy be "s".
Each serving is $2.80, so the cost of "s" ice-creams will be:
[tex]2.80s[/tex]This cost cannot exceed 10 dollars.
10 dollars is the maximum.
So, we can say that "2.80s" is equal to or less than 10.
We write it in inequality notation:
[tex]2.80s\leq10[/tex]Solving for "s":
[tex]\begin{gathered} 2.80s\leq10 \\ s\leq\frac{10}{2.80} \\ s\leq3.57 \end{gathered}[/tex]So, the logical solution is that the 5 sisters can buy 3 ice-cream servings with their budget.
Table:x y1 172 212 233 264 34Part A:When Hana goes to the mall, she always buys the same lunch and also buys some books. The table shows the number of books she buys x and the total amount of money she spends y. Choose the type of correlation that this data shows.Correlation: negative, positve, or none
PART A.
The data in the table shows a POSITIVE CORRELATION , an increase in variable x is associated with an increase in the variable y.
PART B
A new energy drink advertises 120 calories for 5 oz. How many calories are in 15 oz of drink
A new energy drink advertises 120 calories for 5 oz.
How many calories are in 15 oz?
We can set up a proportion to solve this problem
[tex]\frac{120}{5}=\frac{x}{15}[/tex]Where x is the number of calories in 15 oz
Let us solve the above equation for x
[tex]\begin{gathered} \frac{120}{5}=\frac{x}{15} \\ \frac{x}{15}=\frac{120}{5} \\ x=\frac{120}{5}\cdot15 \\ x=120\cdot3 \\ x=360 \end{gathered}[/tex]Therefore, there are 360 calories in 15 oz of drink.
Graph the function f(x)=3/2x−4.Use the line tool and select two points to graph.
We are meant to graph the function
f(x)=3/2x − 4.
