Answer: 2.1 feet
Step-by-step explanation:
The ladder forms a right angle triangle with the wall and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the wall represents the opposite side of the right angle triangle.
The distance, d from the bottom of the ladder to the base of the wall represents the adjacent side of the right angle triangle.
To determine the distance, d from the bottom of the ladder to the base of the wall, we would apply we would apply the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos 65 = d/5
d = 5Cos 65 = 5 × 0.4226
d = 2.1 feet
The edges of a shoebox are measured to be 11.4 cm, 17.8 cm, and 29 cm. Determine the volume of the box retaining the proper number of significant figures in your answer
Answer:
The Volume of the Shoebox is therefore 5884.7[tex]cm^3[/tex]
Step-by-step explanation:
The edges of a shoebox are measured to be 11.4 cm, 17.8 cm, and 29 cm.
We want to determine the volume of the box.
The Shoebox is in the shape of a Cuboid and;
Volume of a Cuboid=Length X breadth X height
Volume of the Shoebox= 11.4.X 17.8 X 29 =5884.68[tex]cm^3[/tex]
=5884.7[tex]cm^3[/tex] (correct to 1 decimal place)
The volume of the box is 5884.68 cubic cm.
Important information:
Dimensions of the box are 11.4 cm, 17.8 cm, and 29 cm.We need to find the volume of the box.
Volume of cuboid:The volume of a cuboid is:
[tex]V=l\times b\times h[/tex]
Where [tex]l[/tex] is length, [tex]b[/tex] is breadth and [tex]h[/tex] is height.
The volume of the box is:
[tex]V=11.4\times 17.8\times 29[/tex]
[tex]V=5884.68[/tex]
Therefore, the volume of the box is 5884.68 cubic cm.
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Cole has 4 regular dice and 1 unique dice that has the value 1 on each of the 6 faces. He picks one at random and rolls 3 ones in a row. What is the probability he picked the unique dice
Answer:
0.008
Step-by-step explanation:
The probability of having chosen the unique dice three times in a row would be the multiplication of the probability of each event.
The event is always repeated. Take the single dice of 5 dice in total. Therefore the probability is 1/5.
Then the final probability would be:
(1/5) * (1/5) * (1/5), and that is equal to 0.008.
The probability that Cole picked the unique die given that he rolled three ones in a row is approximately 49.1%. This is calculated using Bayes' Theorem with the probabilities of rolling three ones with both the unique and regular dice.
Cole has 4 regular dice and 1 unique die that always rolls a 1. Let's calculate the probability that he picked the unique die given that he rolled three ones in a row.
First, find the probability of rolling three ones in a row using a regular die:
Probability of rolling a 1 on a regular die = 1/6Probability of rolling three ones in a row = (1/6) × (1/6) × (1/6) = 1/216Second, since the unique die always rolls a 1, the probability of rolling three ones in a row with it is 1.
Using Bayes' Theorem, we calculate the probability that Cole picked the unique die:
Let A be the event that Cole picked the unique die.
Let B be the event that Cole rolled three ones in a row.
P(A) = 1/5 (since there's 1 unique die out of 5 dice)P(B|A) = 1 (probability of B given A)P(B|A') = 1/216 (probability of B given not A)P(A') = 4/5 (probability of not picking the unique die)P(B) = P(B|A)P(A) + P(B|A')P(A') = 1 × (1/5) + (1/216) × (4/5)P(B) = 1/5 + 4/1080 = 0.2 + 0.0037 = 0.2037Finally, P(A|B) = (P(B|A)P(A)) / P(B) = (1 × 1/5) / 0.2037 ≈ 0.491Thus, the probability that Cole picked the unique die is approximately 0.491 or 49.1%.
HELP PLEASE 98 points
Given: BD¯¯¯¯¯ is an altitude of △ABC .
Prove: sinAa=sinCc
Triangle A B C with an altitude B D where D is on side A C. side A C is also labeled as small b. Side A B is also labeled as small c. Side B C is also labeled as small a. Altitude B D is labeled as small h.
Select from the drop-down menus to correctly complete the proof.
Statement Reason
BD¯¯¯¯¯ is an altitude of △ABC . Given
△ABD and △CBD are right triangles. Definition of right triangle
sinA=hc and sinC=ha
csinA=h and asinC=h
csinA=asinC
csinAac=asinCac Division Property of Equality
sinAa=sinCc Simplify.
Answer:
Given: BD is an altitude of △ABC .
Prove: sinA/a=sinC/c
Triangle ABC with an altitude BD where D is on side AC. Side AC is also labeled as small b. Side AB is also labeled as small c. Side BC is also labeled as small a. Altitude BD is labeled as small h.
Statement Reason
BD is an altitude of △ABC .
Given △ABD and △CBD are right triangles. (Definition of right triangle)
sinA=h/c and sinC=h/a
Cross multiplying, we have
csinA=h and asinC=h
(If a=b and a=c, then b=c)
csinA=asinC
csinA/ac=asinC/ac (Division Property of Equality)
sinA/a=sinC/c
This rule is known as the Sine Rule.
Answer:
For the people on Edge the answers are:
a/f
cf
c/b
cf + ec
c
Wu rolls two fair, six-sided dice. You are not told what the rolls were, but you are told that the sum of the two rolls is a prime. What is the probability that the sum of the two rolls is $5$?
The probability of rolling a sum of 5 when rolling two fair, six-sided dice is 1/18.
Explanation:The probability that the sum of the two rolls is 5 can be found by considering the possible outcomes. There are a total of 36 equally likely outcomes when rolling two fair, six-sided dice.
Out of these, the prime sums are 5, 7, 11, and 17. The sum of 5 can only be obtained by rolling a 1 and a 4 or a 2 and
a 3. Since each die has 6 sides, the probability of rolling a 1 and a 4 is 1/6 × 1/6 = 1/36.
Similarly, the probability of rolling a 2 and a 3 is also 1/36. Therefore, the overall probability of rolling a sum of 5 is
1/36 + 1/36 = 2/36 = 1/18.
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Find the angle of the rotations for the graphs below. The center of rotation is the origin, and the darker image is the preimage. Your answer will be 90°, 270 degrees, or 180 degrees.
Answer:
a. 90°
b. 180°
c. 180°
Step-by-step explanation:
For these problems there is a bit of a shortcut you can take. Each figure is entirely within one quadrant, and the rotation is said to be by 90° (one quadrant), 180° (two quadrants), or 270° (three quadrants) clockwise.
a. The image is in the adjacent clockwise quadrant, so rotation is 90°.
b, c. The image is in the diagonally opposite quadrant, so rotation is 180°.
Alexandra wants to sign up for cell phone service she trying to decide which company she should choose. Telecorp has a flat rate of 7 cents per minute, America's charges 25cents per call and phone busters charges 35 cents per call and 2 cents per min
Answer:
Step-by-step explanation:
Let us assume that she makes 10 minutes of call.
Telecorp has a flat rate of 7 cents per minute. If she uses this cell phone service, the amount that she would pay for 10 minutes of call is
0.07 × 10 = $0.7
America's charges 25cents per call. If she uses this cell phone service, the amount that she would pay for 10 minutes of call is $0.25
Phone busters charges 35 cents per call and 2 cents per min. If she uses this cell phone service, the amount that she would pay for 10 minutes of call is
0.35 + 10 × 0.02
= 0.35 + 0.2
= $0.55
The cheapest service is that of America's. Therefore, she should choose it.
To the right are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event. a. Among three children, there are exactly 2 boys. b. Among three children, there are exactly 3 boys. c. Among three children, there is exactly 1 boy.
Answer:
The probabilities are 3/8, 1/8 and 3/8 respectively
Step-by-step explanation:
The sample space for the provided case can be written as:
S= {(bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg)}
Here, boy child is denoted by "b" and girl child by "g".
Total number of outcomes are 8.
Number of outcomes that show exactly boys = 3.
Number of outcomes that show exactly 3 boys = 1
Number of outcomes that show exactly 1 boy = 3.
Thus, the required probabilities can be calculated as:
(a)
[tex]\\P( Exactly 2 boys) =\frac{3}{8}[/tex]
(b)
[tex]P( Exactly 3 boys) =\frac{1}{8}[/tex]
(c)
[tex]P(Exactly 1 boy)= \frac{3}{8}[/tex]
Thus, the required probabilities are 3/8, 1/8 and 3/8 respectively.
This is a problem in Mathematics, specifically probability, at the High School level. The student is asked to calculate the probability of certain gender distributions among three children. The outcomes are determined and the respective probabilities calculated: the probability for exactly 2 boys and 1 boy is found to be 3/8 each, while for exactly 3 boys it's 1/8.
Explanation:This question pertains to the understanding of probability in a specific scenario: calculating the likelihood of certain outcomes when a couple has three children. Given that each child can be a boy or a girl (2 possibilities), and there are three children, there are 2^3 or 8 total possible outcomes.
a. To find the probability of having exactly 2 boys, we count the outcomes where that is the case: BBG, BGB, GBB. This is three outcomes, so the probability is 3/8.
b. There is only one outcome where all three children are boys (BBB), therefore the probability of exactly 3 boys is 1/8.
c. The outcomes with exactly 1 boy are BGG, GBG, GGB. This gives us three outcomes, hence the probability is also 3/8.
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We learned in that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 year olds. 1. How many people would you expect to have consumed alcoholic beverages? (round to one decimal place) 2. What is the standard deviation? (round to two decimal places) 3. Would you be surprised, if there were 45 or more people who have consumed alcoholic beverages? _
Answer:
(1) The expected number of people who would have consumed alcoholic beverages is 34.9.
(2) The standard deviation of people who would have consumed alcoholic beverages is 10.56.
(3) It is surprising that there were 45 or more people who have consumed alcoholic beverages.
Step-by-step explanation:
Let X = number of adults between 18 to 20 years consumed alcoholic beverages in 2008.
The probability of the random variable X is, p = 0.697.
A random sample of n = 50 adults in the age group 18 - 20 years is selected.
An adult, in the age group 18 - 20 years, consuming alcohol is independent of the others.
The random variable X follows a Binomial distribution with parameters n = 50 and p = 0.697.
The probability mass function of a Binomial random variable X is:
[tex]P(X=x)={50\choose x}0.697^{x}(1-0.697)^{50-x};\ x=0,1,2,3...[/tex]
(1)
Compute the expected value of X as follows:
[tex]E(X)=np\\=50\times 0.697\\=34.85\\\approx34.9[/tex]
Thus, the expected number of people who would have consumed alcoholic beverages is 34.9.
(2)
Compute the standard deviation of X as follows:
[tex]SD(X)=\sqrt{np(1-p)}=\sqrt{50\times 0.697\times (1-0.697)}=10.55955\approx10.56[/tex]
Thus, the standard deviation of people who would have consumed alcoholic beverages is 10.56.
(3)
Compute the probability of X ≥ 45 as follows:
P (X ≥ 45) = P (X = 45) + P (X = 46) + ... + P (X = 50)
[tex]=\sum\limits^{50}_{x=45} {50\choose x}0.697^{x}(1-0.697)^{50-x}\\=0.0005+0.0001+0.00002+0.000003+0+0\\=0.000623\\\approx0.0006[/tex]
The probability that 45 or more have consumed alcoholic beverages is 0.0006.
An unusual or surprising event is an event that has a very low probability of success, i.e. p < 0.05.
The probability of 45 or more have consumed alcoholic beverages is 0.0006. This probability value is very small.
Thus, it is surprising that there were 45 or more people who have consumed alcoholic beverages.
two integers whose product is 90 and whose sum is 21
Answer:
6 and 15
Step-by-step explanation:
Answer:
6 and 15
Step-by-step explanation:
the factors of 90 are:
1 90
2 45
3 30
5 18
6 15
9 10
find the factors that =21
6+15=21 and 6 x 15=21
There is a sale on computers at your local Comp2u. The gaming system that you are interested in has the latest Intel Quad core processor and duel NVIDIA GeForce 9800S graphics card. The sale price on the computer is $1,500.00 plus 5.1% sales tax. Your monthly gross salary is $2,500. How much will you have saved over a two month period and will you be able to afford the computer, given your monthly expenses total $1,250, Social Security is 6.2% of your biweekly income, Medicare is 1.45% of your biweekly income, and you pay State and Federal taxes in the amount of $45.00 and $89.51 biweekly respectively?
Answer:
$1,579.44; yes
Step-by-step explanation:
The student will have saved $2500 over the two month period and will be able to afford the computer.
Explanation:In order to calculate the amount saved over a two month period, we need to calculate the monthly savings. To do this, we subtract the monthly expenses from the monthly gross salary:
$2,500 - $1,250 = $1,250
So the monthly savings is $1,250. To find the savings over a two month period, we multiply the monthly savings by 2:
$1,250 x 2 = $2,500
The cost of the computer is $1,500 plus 5.1% sales tax. To find the total cost, we multiply $1,500 by 1.051:
$1,500 x 1.051 = $1,576.50
Since the savings over a two month period is $2,500, and the total cost of the computer is $1,576.50, the student will be able to afford the computer and have savings left over.
What is the approximate value of log625?
Answer:
2.79588001734
Step-by-step explanation:
If you use the log button on your calculator
log625 or log(625)
you get 2.79588001734
Answer:
2.79588001734
Step-by-step explanation: but you can solve for the nearest ten thousand just use a scientific calculator and input the numbers with or before log. Depends what type of scientific calculator you use.
5. Richard is flying a kite. The kite string makes an angle of 57 with the ground. If
Richard is standing 100 feet from the point on the ground directly below the kite, find
the length of the kite string
So
Answer: the length of the kite string is 183.6 feet
Step-by-step explanation:
The string of the kite forms an angle of 57° with the ground thus, a right angle triangle is formed. Richard's distance from the point on the ground directly below the kite represents the adjacent side of the right angle triangle. The length of the kite, h represents the hypotenuse of the right angle triangle. To determine h, we would apply the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos 57 = 100/h
h = 100/Cos57
h = 100 /0.5446
h = 183.6 feet
Factor the expression. 48g2 – 22gh – 15h2
A. (6g – 5h)(8g + 3h)
B. (6g – 5)(8g + 3)
C. (6g + 5)(8g + 3h2)
D. (6g + 5h)(8g – 3h)
Answer:
A
Step-by-step explanation:
FOIL:First,Inner,Outer,Last
After the polynomial operations are done we can see that A is the answer.
6g*8g=48g^2
6g*3h=18gh
8g*-5h=-40gh
-5h*3h=-15h
After combining like terms we get :
48g^2-22gh-15h^2
Determine if the numerical value describes a population parameter or a sample statistic. 74% of all instructors at your school teach 2 or more classes.
Answer:
Population parameter
Step-by-step explanation:
We are given the following in the question:
74% of all instructors at your school teach 2 or more classes.
Parameter and statistic:
Parameter is the value that describes a population.Population is the collection of all the possible observations of an event.Statistic is the quantitative value that describes a sample.A sample is a part of a population and is always smaller than a population.Population:
all instructors at your school
Parameter:
74% of all the instructors at your school teach 2 or more classes
Thus, 74% describes the population that takes two or more classes.
Hence, it is a population parameter.
A body of water is being drained it begins with 700 gallons of water and is draining 6.5 gallons each hour .If there are now 388 gallons then for how many hours has it been draining
Answer:
Therefore it has been draining 48 hours.
Step-by-step explanation:
Given that a water body is being drained it begins with 700 gallons of water.
Let after x hours the amount of water in the water body will 388 gallons.
The water body is draining 6.5 gallons each hour
It means
The amount of water that drain in 1 hour is 6.5 gallons.
The amount of water that drain in 2 hour is (6.5+6.5) gallons.
=(2×6.5)gallons.
The amount of water that drain in 3 hour is( 6.5+6.5+6.5) gallons.
=(3×6.5) gallons.
Therefore
The amount of water that drain = time ×6.5
The amount of water that drain in x hour is (x×6.5) gallons=6.5x gallons.
Therefore the remaining water
= initial amount of water- drainage water
=(700-6.5x)gallons
According to the problem,
700-6.5x= 388
⇒ -6.5x = 388-700
⇒ - 6.5x = - 312
[tex]\Rightarrow x=\frac{-312}{-6.5}[/tex]
⇒ x= 48
Therefore it has been draining 48 hours.
PLEASE i need help ASAP i beg of you!! due today!!! 50 points! and brainliest!!!!!!!
1. Anthony has a sink that is shaped like a half-sphere. The sink has a volume of
660 pi in^3. One day, his sink clogged. He has to use one of two
cylindrical cups to scoop the water out of the sink. The sink is completely full
when Anthony begins scooping.
(a) One cup has a diameter of 5 in, and a height of 8 in. How many cups of
water must Anthony scoop out of the sink with this cup to empty it?
Round the number of scoops to the nearest whole number.
(b)One cup has a diameter of 10 in, and a height of 8 in. How many cups of
water must he scoop out of the sink with this cup to empty it? Round the
number of scoops to the nearest whole number.
THE ANSWER FOR CUP A IS 660 divided by 157
the answer to cup b is 660 divided by 628.319
brainliest plz
about 30% of the population is left-handed. If two people are random selected what is the probability that both are left handed? What is the probability that at least one is right handed?
Answer:
0.91
Step-by-step explanation:
1 - P(both left handed)
1 - 0.3² = 0.91
Write declaration statements to declare and initialize two variables: one is an integer variable named age, initialized to 18, and the other variable, named weight, is initialized to 114.5.
Answer:
int age;
age=18;
float weight;
weight=114.5F;
Step-by-step explanation:
int age; \\ it is declared as integer because 18 is an integer value
age=18; \\ initialized as 18 is stored in the variable 'age'
float weight; \\ weight is declared as float because it's value is floating or decimal value which cannot be declared as integer value
weight=114.5F; \\ F shows that it's single floating type value of 32 bits, if F is not written then it means it double floating type value which is 64 bits long
In order to declare and initialize two variables, one as an integer named 'age' initialized to '18' and the other named 'weight' initialized to '114.5', you'd write 'int age = 18;' and 'double weight = 114.5;' respectively.
Explanation:To declare and initialize two variables in a programming language such as Java or C++, you would use the following syntax:
int age = 18;
double weight = 114.5;
The keyword 'int' declares an integer variable, and 'double' declares a variable for floating-point numbers. After the variable name, an equals sign ('=') is used to assign or initialize the variable to a specific value.
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Robert and Robert go to the movie theater and purchase refreshments for their friends. Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer: the price of a bag of popcorn is $5.3
Step-by-step explanation:
Let x represent the price of one drink.
Let y represent the price of one bag of popcorn.
Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. This is expressed as
4x + 9y = 65.25- - - - - - - - - - - - - - -1
Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn.
This is expressed as
8x + 3y = 51.75- - - - - - - - - - - - - - -2
Multiplying equation 1 by 8 and equation 2 by 4, it becomes
32x + 72y = 522
32x + 12y = 207
Subtracting, it becomes
60y = 315
y = 315/60
y = 5.25
A rectangular prism with the surface area of 336 and width of 4 is similar to a rectangular prism with the width of 6, what is the surface area of the larger prism
Answer:
The larger surface area would be 756 [tex]Unit^2[/tex]
Step-by-step explanation:
Given the surface area of rectangular prism is 336 [tex]Unit^2[/tex] when its width is 4 [tex]Unit[/tex].
We need to compute the surface area when its width is 6 [tex]Unit[/tex].
Also, it was given that prisms are similar to each other.
Let us assume the [tex]l[/tex] is length [tex]b[/tex] is width and [tex]h[/tex] is the height of the prism.
So, the surface area would be
[tex]S=2(lb)+2(bh)+2(hl)[/tex]
[tex]336=2(4l)+2(4h)+2(hl)[/tex] Equation (1)
Now, the new width is 6 [tex]Unit[/tex]. That is 1.5 times the previous width. And those prisms are similar, which means other dimensions will also be 1.5 times the previous one.
We can write
[tex]b'=1.5\times b=1.5\times 4=6\\l'=1.5\times l\\h'=1.5\times h[/tex]
So, the new surface area would be
[tex]S'=2(l'b')+2(b'h')+2(h'l')\\S'=2(1.5\times l\times 1.5\times 4)+2(1.5\times4 \times 1.5\times h)+2(1.5\times h\times 1.5\times l)\\S'=2.25\times 2(l4)+2.25\times 2(h)+2.5\times 2(hl)[/tex]
[tex]S'=2.25[2(4l)+2(4h)+2(hl)][/tex]
From Equation (1) we can plug [tex]336=2(4l)+2(4h)+2(hl)[/tex]
[tex]S'=2.25\times 336=756\ Unit^2[/tex]
So, the larger surface area would be 756 [tex]Unit^2[/tex]
Can someone answer the blank ones please!!!
The equation is [tex]155p+225f=5050[/tex].
If p = 17, f = 13. This value is a reasonable value in this context.
If f = 28, p = -10. This value is not reasonable in this context.
Step-by-step explanation:
Step 1:
[tex]155p+225f=5050[/tex],
where p is the part-time memberships and f is the number of full-time memberships.
Kiri needs to make $5,050 a month from this rented space.
Each part-time membership costs $155 and each full-time membership costs $225.
Step 2:
We need to calculate the value of f when p = 17,
Substituting the value, p = 17 in the equation, we get;
[tex]125(17)+225f=5050[/tex], [tex]225f=5050-125(17),[/tex]
[tex]225f=2925, f = \frac{2925}{225}, f =13.[/tex]
The value of f = 13 and p = 17. This is a reasonable value in this context.
Step 3:
We need to calculate the value of p when f = 28,
Substituting the value, f = 28 in the equation, we get;
[tex]125p+225(28)=5050[/tex], [tex]125p=5050-225(28)[/tex]
[tex]125p=-1250, p = \frac{-1250}{125}, p=-10.[/tex]
The value of f = 28 and p = -10. This is not a reasonable value in this context. as the values of f and p cannot be negative for this given equation.
Ann works 51/2 hours, Mary works 61/3 hours, and John works 41/4 hours. How many combined hours have they worked? A. 155/12 B. 165/12 C. 161/12 D. 151/12
Answer:
C. 16 + 1/12
Step-by-step explanation:
5 + 1/2 = 11/2 = 66/12
6 + 1/3 = 19/3 = 76/12
4 + 1/4 = 17/4 = 51/12
66/12 + 76/12 + 51/12 = 193/12
193/12 = 16 + 1/12
For a sample of n = 30 scores, X = 45 corresponds to z = 1.50 and X = 40 corresponds to z = +1.00. What are the values for the sample mean and standard deviation?
Final answer:
The sample mean (μ) and standard deviation (σ) are calculated using the provided z-scores and corresponding sample values, resulting in a mean of 30 and a standard deviation of 10.
Explanation:
To solve for the sample mean and standard deviation using the given z-scores and sample values, we can employ the formula for calculating a z-score:
z = (X - μ) / σ
where X is the sample value, μ is the mean, and σ is the standard deviation. For X = 45 with a z-score of 1.50, the equation is:
1.50 = (45 - μ) / σ
For X = 40 with a z-score of 1.00, the equation becomes:
1.00 = (40 - μ) / σ
By solving these two equations simultaneously, we can find the values of μ and σ.
From the first equation, we have:
1.50σ = 45 - μ
From the second equation, we have:
1.00σ = 40 - μ
If we multiply the second equation by 1.5, it becomes:
1.50σ = 60 - 1.5μ
We can set the expressions for 1.50σ equal to each other:
45 - μ = 60 - 1.5μ
Solving for μ gives us the sample mean:
μ = 60 - 45 = 15 / (1.5 - 1) = 15 / 0.5 = 30
To find the standard deviation σ, we substitute μ = 30 into one of the original equations:
1.50σ = 45 - 30 = 15
Therefore, σ = 15 / 1.50 = 10
So, the sample mean (μ) is 30 and the sample standard deviation (σ) is 10.
Final answer:
The sample mean (μ) is 30 and the standard deviation (σ) is 10.
Explanation:
The question is asking to find the sample mean and standard deviation based on given z-scores for specific values in a normal distribution.
To find these parameters, we'll use the formula for calculating a z-score:
z = (X - μ) / σ, where z is the z-score, X is the value, μ is the mean, and σ is the standard deviation.
For X = 45 and z = 1.5, the equation becomes 1.5 = (45 - μ) / σ. For X = 40 and z = 1.0, the equation is 1.0 = (40 - μ) / σ.These two equations can be solved simultaneously to find the values of μ and σ.
Steps for solving them are:
Rewrite the equations:Therefore, the sample mean (μ) is 30 and the standard deviation (σ) is 10.
Simplify this expression.
3^5/3^3
Answer:
3^2
Step-by-step explanation:
3^5/3^3=3^(5-3)=3^2
Answer:
[tex] \frac{ {3}^{5} }{ {3}^{3} } = {3}^{5 - 3} = {3}^{2} = 9[/tex]
Step by step explanation :
When dividing two fraction we subtract the powers if the bases are same.
A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 73,000 + 70 x and [tex]p(x) = 250 - (\frac{x}{20}), 0 \leq x \leq 5000[/tex].(A) Find the maximum revenue.
(B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set.
(C) If the government decides to tax the company $55 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?
(A) The maximum revenue is $_________.
(B) The maximum profit is when sets are manufactured and sold for each.
(C) When each set is taxed at $55, the maximum profit is when sets are manufactured and sold for each.
Answer:
a) The maximum revenue is $312500
b) The maximum profit is $89000, the production level that will realize the maximum profit is 1800, and the price the company should charge for each television set is $160.
C) If the government decides to tax the company $55 for each set it produces, the sets should the company manufacture each month to maximize its profit is 1250. the maximum profit is $70825 What should the company charge for each set is $187.5
Step-by-step explanation:
a) Revenue R(x)
R(x) = p(x) * x = x * [tex](250-\frac{x}{20})[/tex] = [tex](250x-\frac{x^{2} }{20})[/tex]
For maximum revenue, the first derivative of R(x) = R'(x) = 0
R'(x) = [tex](250-\frac{2x}{20}) = 0[/tex]
[tex](250-\frac{2x}{20}) = 0\\[/tex]
[tex]250=\frac{2x}{20}[/tex]
x = 2500
the second derivative of R(x)=R''(x)
R''(x) = -1/10 which is less than 0.
Maximum revenue is at x = 2500
R(2500) = [tex](250*2500-\frac{2500^{2} }{20})=312500[/tex]
b) Profit P(x)
P(x) = R(x) - C(x) = [tex](250x-\frac{x^{2} }{20})-(73000+70x) = -73000+180x-\frac{x^{2} }{20}[/tex]
For maximum profit, the first derivative of P(x) = P'(x) = 0
P'(x) = [tex]180-\frac{2x }{20}=0[/tex]
[tex]180=\frac{2x }{20}[/tex]
x = 1800
the second derivative of P(x)=P''(x)
P''(x) = -1/10 which is less than 0.
For maximum profit, x = 1800
Therefore P(1800)[tex]=-73000+180*1800-\frac{1800^{2} }{20}[/tex] = 89000
The price the company should charge for each television set is p(1800) =[tex](250-\frac{1800}{20}) = 160[/tex]
c) f the government decides to tax the company $55 for each set it produces, the new cost C(x) = 73000 + 125x
Profit P(x)
P(x) = R(x) - C(x) = [tex](250x-\frac{x^{2} }{20})-(73000+125x) = -73000+125x-\frac{x^{2} }{20}[/tex]
For maximum profit, the first derivative of P(x) = P'(x) = 0
P'(x) = [tex]125-\frac{2x }{20}=0[/tex]
[tex]125=\frac{2x }{20}[/tex]
x = 1250
the second derivative of P(x)=P''(x)
P''(x) = -1/10 which is less than 0.
For maximum profit, x = 1250 hence 1250 sets should the company manufacture each month to maximize its profit
Therefore P(1800) =[tex]-73000+125*1250-\frac{1250^{2} }{20}[/tex] = 70825
The price the company should charge for each television set is p(1250) =[tex](250-\frac{1250}{20}) = 187.5[/tex]
Select the TRUE statements.
For the function 48(1.25)x, the parameter for the growth factor is 1.25.
For the function f(x) = 75x + 250, the parameter for the beginning value is 75.
For the function 28(0.5)x, the parameter for the decay factor is 50%.
For the function y = 18x + 72, the parameter for the average rate of change is 18.
Answer:
a) For the function [tex]48(1.25)^x[/tex], the parameter for the growth factor is 1.25
c) For the function [tex]28(0.5)^x[/tex], the parameter for the decay factor is 50%.
d) For the function y = 18x + 72, the parameter for the average rate of change is 18.
Step-by-step explanation:
We are given the following in the question:
a) the parameter for the growth factor is 1.25.
[tex]f(x) = 48(1.25)^x[/tex]
Comparing it to
[tex]y(x) = a(1+r)^x[/tex]
The growth factor is
[tex]1+r = 1.25[/tex]
Thus, the given statement is true
b) the parameter for the beginning value is 75.
We are given the equation
[tex]f(x) = 75x + 250[/tex]
The beginning value is given when x = 0. Putting value, we get
[tex]f(0) = 75(0) + 250 = 250[/tex]
Thus, the beginning value is 250.
Hence, the given statement is false.
c) the parameter for the decay factor is 50%.
[tex]f(x) = 28(0.5)^x[/tex]
Comparing it to
[tex]y(x) = a(1-r)^x[/tex]
The growth factor is
[tex]1-r = 0.5 = 50\%[/tex]
Thus, the given statement is true
d) the parameter for the average rate of change is 18.
[tex]y = 18x + 72[/tex]
Comparing to general form of equation:
[tex]y = mx + c[/tex]
where m is the slope and gives the average rate of change.
Thus, the average rate of change is 18.
Hence, the given statement is true.
Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?
Answer:
5f+3g=5.70
2f+10g=3.60
Step-by-step explanation:
Cost of 1 piece of fudge =f
Cost of 1 piece of bubble gum =g
If Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70.
Chase's Cost:
For 5 pieces of Fudge, his cost is 5f
For 3 pieces of bubble gum, his cost is 3g
His Total, 5f+3g=$5.70
Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60.
Sara's Cost:
For 2 pieces of fudge, her cost is 2f
For 10 pieces of bubble gum, her cost is 10g
Her Total, 2f+10g=$3.60
The system of equation that could be used to determine the cost of 1 piece of budge and bubblegum is then:
5f+3g=$5.70
2f+10g=$3.60
Josiah has 3 packs of toy animals.Each pack has the same number of animals.Josiah gives 6 animals to his sister stephanie.Then josiah has 9 animals left.How many animals were in each park?
Answer:
there are 5 animals in each pack.
Step-by-step explanation:
if you add 9+6= 15 then divide 15 by 3 you will get 5 as your answer
Answer: there were 5 animals in each pack.
Step-by-step explanation:
Let x represent the number of toy animals in each pack.
Josiah has 3 packs of toy animals. Each pack has the same number of animals. This means that the number of animals in the 3 packs is
3x
Josiah gives 6 animals to his sister stephanie. This is expressed as 3x - 6. If she has 9 left, it means that
3x - 6 = 9
3x = 9 + 6
3x = 15
x = 15/3
x = 5
Oak pollen sent 21,000 people to U.S. emergency rooms for asthma in 2010. By 2090 the rate could climb another 5 or 10 percent. If true, what would the numbers then be Show your work.
The probable number of prople sent to US emergency rooms by 2090 can be between 22,050 and 23,100
Step-by-step explanation:
Total sent to US emergency room by 2010= 21000
The estimated increase in the rise of cases = 5 to 10% by 2090
Final numbers in 2090
Hence the final numbers in 2090 would be 5 to 10% more than the total cases in 2010
Lower limit= 5% of 21000= 1050
Hence lower limit of cases in 2090= 21000+1050= 22050
Upper limit of cases in 2090= 10% of 21000= 21000+2100= 23,100
The number would lie anywhere between 22050 and 23,100 in 2090
If f(x) = 2x - 4 and g(x) = x^2+3, find each value.
19. (f - g)(x)
20. (f • g)(x)
Step-by-step explanation:
[tex](f - g)(x) = f(x) - g(x) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2x - 4) - ( {x}^{2} + 3) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2x - 4 - {x}^{2} - 3 \\ \red{ \boxed{\therefore (f - g)(x) = - {x}^{2} + 2x - 7}}[/tex]