Answer:
The correct answer to the question is;
a. number of clusters.
Step-by-step explanation:
Clustering is the process of looking for smaller similar groups of observation within a set of data.
K-means clustering is a vector quantization method used in data mining cluster analysis. The objective of k-means clustering is to a given number of observations into k number of clusters whereby an observation is grouped in a cluster having the closest mean value, hence being representative of tha particular cluster. This is in atempt to make observations in a particular group to be similar.
In k-means clustering, the number of clusters is specified as k.
In k-means clustering, k represents the number of clusters, indicated by answer choice (a). This technique involves partitioning the data into k compact and separate clusters, with the k initial cluster centers often chosen randomly.
Explanation:In k-means clustering, k represents the number of clusters into which the data is to be partitioned. This method involves assigning each data point to the nearest cluster, while keeping the clusters as small as possible. The initial positions of the k clusters are typically chosen at random, and then the mean position of all the points in each cluster is recomputed, and this becomes the new center for the cluster. This process is repeated until the cluster assignments no longer change significantly, meaning the clusters are as compact and as separate as possible. The mean refers to the mean of the data points within each cluster once the clusters have formed. The standard deviation is a measure of the variability of the original distribution of the data. Sample size, denoted as n, is the number of observations in the dataset. Therefore, the answer to the question about what k represents in k-means clustering is (a) the number of clusters.
The mean salary for a new teacher in your town is $48,000. You believe it is higher for new teachers in a neighboring town. State the null and alternative hypotheses.
Answer:
Step-by-step explanation:
Given that the mean salary for a new teacher in your town is $48,000
You believe it is higher for new teachers in a neighboring town.
So to prove or disprove your claim you have to show statistical evidence.
For that hypothesis testing is necessary.
You must conduct a hypothesis test for comparing the mean of salary of new teacher with neighbouring places
The hypotheses wouldbe
[tex]H_0: \mu = 48000\\H_1: \mu >48000[/tex]
where mu is the average for neighbouring states.
What is the leading coefficient of the polynomial?
30x2 + 12x + 18x3 + 10
A) 10
B) 12
C) 18
D) 30
Answer: It is C because if you organize the equation numerically the equation is 18x^3+30x^2+12x+10. So it is 18.
There are about 320 million residents on the United States if 38% of them live in the south,estimate how many live in other areas of the United States?
Answer:
198,400,000
Step-by-step explanation:
Total Approximate Number of Residents in the United States = 320 million
38 per cent of the total number of residents live in the South
That means, as a percentage, 100%-38%=62% live in other areas of the Unjted States.
[tex]62 \% of 320 million[/tex] = [tex]\frac{62}{100}X320000000[/tex]=198,400,000.
Therefore a total of about 198,400,000 live in other areas of the United States.
A road sign between Cincinnati and Dayton shows both mile and kilometer measurements. According to the sign at that point, a driver is 54 kilometers or 34 miles from Dayton. If the sign is accurate, 1 mile=__________Kilometers?
Answer:
The answer to your question is 1.59 km
Step-by-step explanation:
Data
Sign 54 km or 34 mi
1 mi = ? km
Process
1.- Use proportions and cross multiplication to find the answer
54 km ----------------- 34 mi
x km ---------------- 1 mi
x = (1 mi x 54 km) / 34 mi
-Simplification
x = 54 km / 34
-Result
x = 1.59 km
2.- Conclusion
1 mile is equivalent to 1.59 km
You are ordering a hamburger and can get up to 7 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 2 toppings
Answer:
Probability, P(getting 2 toppings)= 0.1984
Step-by-step explanation:
Probability, P(1 toppings)= 1/7
Probability P of getting a particular topping is q = 1 - P = 1 - 1/7 = 6/7
Probability of( getting 2 toppings)= 7!/(2!5!)(1/7)^2 × (6/7)^5
P(getting 2 toopings)= (5040/240) × (0.020)× (0.4627)
P(getting 2 toppings)= 21 × 0.00948 = 0.1984
A particle is moving horizontally along the x-axis. Its position (in ft) is: s(t)=t^3-18t^2+33t+14 where t is in sec.
Find the time at which the particle switches from moving left to moving right.
t= ___ sec.
Answer:
t=11 sec
Step-by-step explanation:
The position of the particle moving along the x-axis is given by:
[tex]s(t) = {t}^{3} - 18 {t}^{2} + 33t + 14[/tex]
The velocity is given by:
[tex]s'(t) = 3 {t}^{2} - 36{t} + 33[/tex]
If s'(t)>0 then the particle is moving right.
[tex]3 {t}^{2} - 36{t} + 33 \: > \: 0 \\ {t}^{2} - 12{t} + 11\: > \: 0[/tex]
[tex] \implies \: t \: < \: 1 \: or \: t \: > \: 11[/tex]
This means that the particle is moving left when
[tex]1 \: < \: t \: < \: 11[/tex]
The particle changes direction at time t=1 or t=11
Leah asked her dance students to each hand out at least 10 flyers advertising their upcoming dance recital. She constructed a histogram to display the number of recital flyers handed out by the students.
Leah asked her dance students to hand out at least 10 flyers for their upcoming dance recital and construct a histogram to display the data.
Explanation:In this question, Leah asked her dance students to each hand out at least 10 flyers for their upcoming dance recital. Then, she constructed a histogram to display the number of recital flyers handed out by the students.
To solve this, Leah can tally the number of students who handed out a specific number of flyers and create intervals on the x-axis of the histogram to represent the number of flyers. The height of each bar in the histogram will represent the number of students who handed out the corresponding number of flyers. By constructing the histogram, Leah can visualize the distribution of the number of flyers handed out by her dance students.
Final answer:
The question is related to Mathematics, specifically the creation and analysis of histograms, frequency tables, and probability distributions, often used in statistics to visualize and interpret various sets of data.
Explanation:
The student's question falls under the subject of Mathematics, specifically related to statistics and data analysis. In this instance, various exercises are mentioned where the creation and interpretation of histograms are central. These exercises are multifaceted, requiring students to compile data, calculate statistical measures such as means and probabilities, and graphically represent data using histograms and other charts.
For example, when Leah asks her dance students to hand out flyers, she is gathering data that can be represented in a histogram to visualize the distribution of flyers handed out. Similarly, the ballet instructor's data on retention rates can form a probability distribution. When Jill delivers flyers for her yard sale, her travel distances and times could be used to create a time series graph.
Histograms, frequency tables, and probability distributions are tools used in these exercises to better understand the data collected, whether it's related to dance flyer distribution, car sales, or family size among classmates.
A dolphin starts at an elevation of -16 3/4 feet. He kicks 5 times and increases his elevation by the same amount for each kick. He is now at an elevation of -5 1/4 feet. Which equation can be used to find x, the number of feet the dolphin traveled with each kick?
Answer:
[tex]x = 2\,\frac{4}{5}\,ft[/tex]
Step-by-step explanation:
The equation of elevation for the dolphin is:
[tex]-\frac{67}{4} + 5\cdot x = -\frac{21}{4}[/tex]
[tex]5\cdot x = \frac{56}{4}[/tex]
[tex]x = 2\,\frac{4}{5}\,ft[/tex]
Answer:
5x -16 3/4 = -5 1/4
Note: This is based off of Study Island's multiple choice answers
Step-by-step explanation:
We're trying to figure out how far the dolphin travels with each kick. The dolphin starts at an elevation of -16 3/4 feet and ends up at an elevation of -5 1/4 feet. In other words, what can we add to -16 3/4 to get -5 1/4?
The elevation is our variable (x). The dolphin kicks 5 times to get from point a to point b. So we should add 5x to -16 3/4 to get -5 1/4. This equation will solve for the length in feet traveled per kick. Our equation is now:
5x + -16 3/4 = -5 1/4
Adding a negative is the same thing as subtracting a positive, so our final equation is:
5x - 16 3/4 = -5 1/4
If we want to solve this:
5x - 16.75 = -5.25
5x = 11.5
x = 2.3 feet per kick
M is a degree 3 polynomial with m ( 0 ) = 53.12 and zeros − 4 and 4 i . Find an equation for m with only real coefficients (i.E. No i in your equation.
Answer:
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
Step-by-step explanation:
Given that M is a polynomial of degree 3.
So, it has three zeros.
Let the polynomial be
M(x) =a(x-p)(x-q)(x-r)
The two zeros of the polynomial are -4 and 4i.
Since 4i is a complex number. Then the conjugate of 4i is also a zero of the polynomial i.e -4i.
Then,
M(x)= a{x-(-4)}(x-4i){x-(-4i)}
=a(x+4)(x-4i)(x+4i)
=a(x+4){x²-(4i)²} [ applying the formula (a+b)(a-b)=a²-b²]
=a(x+4)(x²-16i²)
=a(x+4)(x²+16) [∵i² = -1]
=a(x³+4x²+16x+64)
Again given that M(0)= 53.12 . Putting x=0 in the polynomial
53.12 =a(0+4.0+16.0+64)
[tex]\Rightarrow a = \frac{53.12}{64}[/tex]
=0.83
Therefore the required polynomial is
M(x)=0.83(x³+4x²+16x+64)
You bought 15 1 gallon bottles of orange juice and apple juice for school breakfast. The apple juice was on sale for $1.50 per gallon bottle. The orange juice was two dollars per gallon bottle. You spent $26. How many bottles of each type of juice did you buy
Answer: you bought 7 bottles of orange juice and 8 bottles of apple juice.
Step-by-step explanation:
Let x represent the number of 1-gallon bottles of orange juice that you bought.
Let y represent the number of 1-gallon bottles of apple juice that you bought.
You bought 15 1 gallon bottles of orange juice and apple juice for school breakfast. This means that
x + y = 15
The apple juice was on sale for $1.50 per gallon bottle. The orange juice was two dollars per gallon bottle. You spent $26. This means that
2x + 1.5y = 26 - - - - - - - - - - - - -1
Substituting x = 15 - y into equation 1, it becomes
2(15 - y) + 1.5y = 26
30 - 2y + 1.5y = 26
- 2y + 1.5y = 26 - 30
- 0.5y = - 4
y = - 4/ - 0.5
y = 8
x = 15 - y = 15 - 8
x = 7
Moshe is playing cards and is grouping the cards that have already been played by suit (hearts, clubs, diamonds, and spades). Moshe is using what type of encoding?
Answer:
organizational
Step-by-step explanation:
organizational encoding iis process of categorizing information according to. the relationships among a series of items. Here the categorizing information are hearts, clubs, diamonds, and spades.
Hope it will find you well.
Moshe is using categorical encoding to group the cards that have already been played by suit
Explanation:Moshe is using categorical encoding to group the cards that have already been played by suit. Categorical encoding is a type of semantic encoding, where information is organized and stored based on categories or groups. In this case, Moshe is categorizing the cards into the four suits: hearts, clubs, diamonds, and spades.
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HELP!! I NEED THIS QUICKLY
Jakita examines the ordered pairs ( 3/4, 2/3), (1/4, 2), (1, 1/2) and (1/2, 1), and determines the points form a direct variation with a k value of 1/2.
Which statements about Jakita's conclusion are true? Select two options.
A.) The points actually represent an inverse variation.
B.) The k value of the direct variation is actually 2.
C.) The ordered pairs can be represented by the function y = x/2
D.) The ordered pairs can be represented by the function y = 1/2x
E.) As one quantity increases, the other also increases.
Answer:
A and D
Step-by-step explanation:
We are given that
(3/4,2/3),(1/4,1),(1,1/2) and (1/2,1)
[tex]x_1=\frac{3}{4}[/tex]
[tex]y_1=\frac{2}{3}[/tex]
[tex]x_2=\frac{1}{4},y_2=1[/tex]
[tex]x_3=1,y_3=\frac{1}{2}[/tex]
[tex]x_4=\frac{1}{2},y_4=1[/tex]
k=[tex]\frac{1}{2}[/tex]
Direct proportion:
[tex]\frac{x}{y}=k[/tex]
Inverse proportion:[tex]xy=k[/tex]
[tex]\frac{x_1}{y_1}=\frac{3}{4}\times \frac{3}{2}=\frac{9}{8}\neq \frac{1}{2}[/tex]
Therefore, it is not in direct proportion.
[tex]\frac{1}{4\times 2}=\frac{1}{8}\neq\frac{1}{2}[/tex]
[tex]\frac{1}{\frac{1}{2}}=2\neq \frac{1}{2}[/tex]
[tex]x_1y_1=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}[/tex]
[tex]x_2y_2=\frac{1}{4}\times 2=\frac{1}{2}[/tex]
[tex]x_3y_3=1\times \frac{1}{2}=\frac{1}{2}[/tex]
[tex]x_4y_4=\frac{1}{2}\times 1=\frac{1}{2}[/tex]
Therefore, [tex]xy=k=\frac{1}{2}[/tex]
Hence, the given points form an inverse variation .
[tex]xy=\frac{1}{2}[/tex]
[tex]y=\frac{1}{2x}[/tex]
Option A and D is true.
Answer: A and D
Step-by-step explanation:
Cause edg2020
What is the measure of angle x? 1) 10 2) 18 3) 20 4) 25
Answer:
what is the actual problem?
Step-by-step explanation:
Which equation could you use to solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction? 4 x = 14 4 x = 45 5 x = 13 5 x = 36
Answer:
(b) 4 x = 4 5 is the needed expression to solve for the value of x.
Step-by-step explanation:
Here, the given proportion is simplified as:
[tex]\frac{4}{5} = \frac{9}{x}[/tex]
Now, to simplify any proportion of the form [tex]\frac{a}{b} = \frac{c}{d}[/tex] the simplest way is CROSS MULTIPLICATION.
So, cross multiplying [tex]\frac{a}{b} = \frac{c}{d} \implies ad = bc[/tex]
Similarly cross multiplying [tex]\frac{4}{5} = \frac{9}{x}[/tex], we get:
4 (x) = (9) (5)
or, 4 x = 45
Hence, 4 x = 45 is the needed expression to solve for the value of x.
Answer:
4x=45
Step-by-step explanation:
4/5=9/x, so first you would multiply 5×9 (because cross products are always equal) and you would get 45. Since 4x has to also equal 45, the answer is 4x=45.
Hope this helps (P.S. I got it right on the test)!
Members of a hospital advisory committee will be selected from 5 doctors and 4 nurses. The committee must have 2 doctors and 2 nurses.
How many possible combinations of doctors and nurses could be chosen for the committee?
Answer:
16 possible ways
Step-by-step explanation:
Using the formular Cp,k= p!/I! (P-k)!
Where k= number of selected committee members
P= available number that can sit in the committee
For doctors,there are 5 doctors
C= 5!/2!(3)!= 120/12 = 10ways
For nurses,there are 4
C= 4!/2!(2)! = 24/4 =6ways
Total possible ways=10 + 6 = 16 ways
Answer:
60
Step-by-step explanation:
(2 out of 5 doctors) * (2 out of 4 nurses)
Marcos made a fruit salad. It contains 6 strawberries, 5 mango slices, 18 grapes, and 2 kiwis. What is the ratio of the number of strawberries to grapes? Express the ratio in simplest form.
3:9
3:1
1:3
9:3
Answer:
1 : 3
Step-by-step explanation:
The ratio of strawberries : grapes = 6 : 18 ( divide both values by 6 )
ratio = 1 : 3 ← in simplest form
Answer:
1 : 3
Step-by-step explanation:
The ratio of strawberries : grapes = 6 : 18 ( divide both values by 6 )
ratio = 1 : 3 ← in simplest form
PLEASE HELP...
Write a simplified polynomial expression in standard form to represent the area of the rectangle below:
A picture of a rectangle is shown with one side labeled as 2 x minus 2 and another side labeled as x plus 4.
2x2 + 3x − 20
2x2 + 13x − 1
2x2 + 13x − 20
2x2 + 3x − 1
The area of the given rectangle is of the standard form option 1.[tex]2x^{2} + 3x - 20[/tex].
Step-by-step explanation:
Step 1:
The parameters needed to determine the area of a rectangle are the base length and the width.
The base length of this rectangle is [tex]2x-5[/tex] units while its width is [tex]x+4[/tex] units.
The area of a rectangle is determined by multiplying the base length with the width.
Step 2:
The area of the rectangle [tex]= (length)(width).[/tex]
Here length is [tex]2x-5[/tex] units and the width is [tex]x+4[/tex] units.
The area of the rectangle[tex]= (2x-5)(x+4) = 2x^{2} + 8x -5x-20 = 2x^{2} + 3x - 20.[/tex]
So the area of the given rectangle is of the standard form [tex]2x^{2} + 3x - 20[/tex] which is the first option.
To find the area of the rectangle, we need to multiply the expressions for the lengths of its sides. The sides are given as [tex]\(2x - 2\) and \(x + 4\).[/tex]
First, write the expressions for the sides of the rectangle:
- One side is[tex]\(2x - 2\)[/tex]
- The other side is[tex]\(x + 4\)[/tex]
To find the area, multiply these two expressions:
[tex]\[(2x - 2)(x + 4)\][/tex]
Use the distributive property (also known as the FOIL method for binomials) to expand this product:
[tex]\[(2x - 2)(x + 4) = 2x(x) + 2x(4) - 2(x) - 2(4)\][/tex]
Simplify each term:
[tex]\[= 2x^2 + 8x - 2x - 8\][/tex]
Combine like terms:
[tex]\[= 2x^2 + 6x - 8\][/tex]
So, the polynomial expression in standard form representing the area of the rectangle is:
[tex]\[2x^2 + 6x - 8\][/tex]
Given the options:
- 2x^2 + 3x − 20
- 2x^2 + 13x − 1
- 2x^2 + 13x − 20
- 2x^2 + 3x − 1
None of these options exactly match our result of [tex]\(2x^2 + 6x - 8\),[/tex] indicating a potential error in the problem statement or options provided. The correct simplified polynomial expression for the area, based on the given side lengths, is[tex]\(2x^2 + 6x - 8\).[/tex]
What is the volume of the rectangular prism below?
24 in 3
48 in 3
72 in 3
108 in 3
Answer:
72
Step-by-step explanation:
3 x 4 = 12
12 x 6 = 72
hope i helped
If Naomi were to paint her living room alone, it would take 5 hours. Her sister Jackie could do the job in 8 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.
Answer: it would take them 40/13 hours
Step-by-step explanation:
If Naomi were to paint her living room alone, it would take 5 hours. it means that the rate at which she paint her living room alone is 1/5
Her sister Jackie could do the job in 8 hours. it means that the rate at which Jackie paint the living room is 1/8
If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be
1/5 + 1/8 = (8 + 5)/40 = 13/40
Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,
13/40 = 1/t
t = 40/13 hours
To determine the squirrel population in a city park, researchers tagged 90 squirrels. Later, they counted 630 squirrels, 42 of which had tags. Based on this data, what is the total number of squirrels in the park?
Answer:
1350
Step-by-step explanation:
Initially 90 squirrels were tagged out of a total population of x squirrels.
Similarly, 42 squirrels out of a sample of 630 squirrels had tag
We can use ratio equality to find the total population x.
42:90=620:x
[tex]\frac{42}{90} =\frac{630}{x}[/tex]
Cross multiplying
42 X x = 630 X 90
Dividing both sides by 42
[tex]x=\frac{630 X 90}{42} \\=1350[/tex]
The total number of squirrels in the city park is 1350.
The total number of squirrels in the park is approximately 1350.
To estimate the total squirrel population in the park, we can use the Lincoln-Petersen method, which is a mark-recapture technique. The formula for this method is:
[tex]\[ N = \frac{(M \times n)}{m} \][/tex]
Given the data:
- ( M = 90 ) (the number of tagged squirrels),
- ( n = 630 ) (the total number of squirrels counted in the second sample),
- ( m = 42 ) (the number of tagged squirrels found in the second sample).
Plugging these values into the formula, we get:
[tex]\[ N = \frac{(90 \times 630)}{42} \] \[ N = \frac{56700}{42} \] \[ N = 1350 \][/tex]
Therefore, the total number of squirrels in the park is estimated to be 1350.
Which is the area between the x-axis and y=x from x=3 to x=6
63
45/2
27/2
81
Answer:
27/2
Step-by-step explanation:
The polynomial y=−0.73x4+3.1x3+26.5 describes the billions of flu virus particles in a person's body x days after being infected. Find the number of virus particles, in billions, after 3 days. There are billion virus particles in a person's body 3 days after being infected.
To find the number of virus particles after 3 days, substitute x=3 into the given polynomial. The number of virus particles, in billions, after 3 days is approximately 48.37 billion.
Explanation:To find the number of virus particles after 3 days, substitute x=3 into the polynomial:
y = -0.73(3)^4 + 3.1(3)^3 + 26.5
Calculating this expression:
y = -0.73(81) + 3.1(27) + 26.5 = -59.13 + 81 + 26.5 = 48.37
Therefore, the number of virus particles, in billions, after 3 days is approximately 48.37 billion.
-2 -1 0 1 2 fx 1/8 1/4 1/2 1 2 what is the initial value of the exponential function represented by the table
Answer:
Step-by-step explanation:
The standard form of an exponential function is
[tex]y=a(b)^x[/tex] , where a is the initial value and b is the growth factor.
You will always find your initial value at the y value where x = 0. From your table where x = 0 and y = 1/2:
[tex]\frac{1}{2}=a(b)^0[/tex]
Any number or variable raised to the power of 0 = 1, therefore
[tex]\frac{1}{2}=a(1)[/tex] which gives us an initial value, a, of 1/2.
A population of scores has µ = 50 and σ = 5. If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation?
Answer:
The new mean = 3 × (the old mean) = 150
The new standard deviation is also = 3 × (The old standard deviation) = 15
Step-by-step explanation:
µ = 50 and σ = 5
The mean is the sum of variables divided by the number of variables.
Mean = (Σx)/N = µ = 50
x = each variable
N = number of variables
If each variable changed to 3x
Mean becomes
Mean = (Σ(3x))/N = 3 (Σx)/N = 3 × µ = 3 × 50 = 150.
The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.
The standard deviation measures the rate of spread of the data set around the mean.
Standard deviation = σ = √[Σ(x - µ)²/N]
x = each variable
µ = mean
N = number of variables
If each variable changed to 3x
Recall µ changed to 3µ
Standard deviation = σ = √[Σ(3x - 3µ)²/N]
σ = √[Σ 3² (x - µ)²/N] = √[(3²)Σ(x - µ)²/N] = 3×√[Σ(x - µ)²/N] = 3 × σ = 3 × 5 = 15
If every score is multiplied by 3, it is logical to reason that the average of the new set of numbers also is 3× the old average.
And the new set of numbers spread out similarly around this new mean, only that the new space of spread is now 3× the old one.
When every score in a population is multiplied by a constant, both the mean and the standard deviation are multiplied by that constant. So, in the given example, the new mean would be 150 and the new standard deviation would be 15.
Explanation:In mathematics, when every score in a population is multiplied by a constant, both the mean (µ) and the standard deviation (σ) are also multiplied by that constant.
So, if every score in a population with µ = 50 and σ = 5 is multiplied by 3, the new mean (µ_new) would be 50 * 3 = 150, and the new standard deviation (σ_new) would be 5 * 3 = 15.
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At the moment a hot iron rod is plunged into freezing water, the difference between the rod's and the water's temperatures is 100\degree100°100, degree Celsius. This causes the iron to cool and the temperature difference drops by 60\%60%60, percent every second. Write a function that gives the temperature difference in degrees Celsius, D(t)D(t)D, left parenthesis, t, right parenthesis, ttt seconds after the rod was plunged into the water.
Answer:
[tex]D(t)=100(0.4)^t[/tex]
Step-by-step explanation:
The temp is 100 at time t = 0
After 1 sec, the temp difference would be:
[tex]100-(\frac{100-60}{100})[/tex]
After 2 sec, the temp difference would be:
[tex]100-(\frac{100-60}{100})^2[/tex]
Similarly for 3 seconds, 4 seconds etc.
We notice that the parenthesis part is 40% of it, so we can also write:
100(40%)^t,
where
t is the time
40% can be written as 40/100 = 0.4
SO, the function is:
[tex]d(t)=100(0.4)^t[/tex]
Answer:
[tex]D(t)=100*0.4^t[/tex]
Step-by-step explanation:
Initially, the difference between the rod's and the water's temperatures is 100°
i.e D(t)=100 When t=0
After 1 seconds, the temp drops by 60%.
Therefore, the new value of D will be the old value multiplied by (100-60)%.
D(1)=100 X (100%-60%) = 100*0.4
After 2 seconds, the temp difference would be:
D(2)=100*0.4*0.4= [tex]100*0.4^2[/tex]
We notice that for any t, the percentage at which the difference is reduced is raised to the power of t.
Therefore, temperature difference in degrees Celsius, D(t), t seconds after the rod was plunged into the water is given as:
[tex]D(t)=100*0.4^t[/tex]
2.2.15
Question Help
Number of Children Number of
under 5
Households
To predict future enrollment in a school district, fifty households within
the district were sampled, and asked to disclose the number of
children under the age of five living in the household. The results of
the survey are presented in the table. Complete parts (a) through (c)
below
(a) Construct a relative frequency distribution of the data.
Number of Relative
Children under 5 Frequency
0.34
0.28
0.28
0.06
0.04
(Type integers or decimals. Do not round.)
(b) What percentage of households has two children under the age of 5?
Enter your answer in the answer box and then click Check Answer
Answer:
Step-by-step explanation:
a)
Number of children under 5 Number of household Relative frequency
0 17 17 / 50 = 0.34
1 14 14 / 50 = 0.28
2 14 14 / 50 = 0.28
3 3 3 / 50 = 0.06
4 2 2 / 50 = 0.04
50
Note,
Relative frequency = Class frequency / Total Frequency
b) Percentage of households has two children under the age of 5 ,
= [tex]\frac{14}{50}[/tex] x 100
= 0.28 x 100
= 28%
Final answer:
To calculate the percentage of households with two children under the age of 5, divide the frequency of 2 by the total number of households and multiply by 100.
Explanation:
To calculate the percentage of households with two children under the age of 5, we need to find the relative frequency of 2 in the given data. The relative frequency is calculated by dividing the frequency of 2 by the total number of households, which is 50 in this case. The frequency of 2 is 0.06, so the relative frequency of 2 is 0.06/50 = 0.0012. To convert it to percentage, we multiply by 100, so the percentage of households with two children under the age of 5 is 0.0012 * 100 = 0.12%.
A local car dealership is holding a year-end event because new car models have just been released. Declan has $35,000 to spend on a car. The car Declan decides to buy for his family costs $35,000. However, it is part of the year-end event, which means he receives a 15% discount on the new car. Declan plans to put the money he saves on the car into a new bank account. The bank account has a yearly simple interest rate of 4%, paid at the end of each year. If Declan does not add any other money to this bank account, it will take 6 years for Declan's bank account to reach $6,720.
Answer:
The amount Declan saves from the discount is 15% of $35,000
which is $5250
This Amount $5250 is the amount Declan invests in the bank
This is the Amount the bank pays at the end of the time T of saving
Step-by-step explanation:
The simple Interest is calculated by
I = (P x R x T) / 100
where I is the Interest
R is the rate in percentage
T is the time the money will be saved
Another Important quantity is the Amount A
A = I + P
To discourage students from driving to campus, a university claims students spend an average of 20 minutes looking for a parking spot. One student does not believe it takes so long to find a spot. After taking a random sample of 45 students, a sample mean of 17.4 minutes to find a parking spot was calculated.
To assess the evidence provided by the sample data, what is the appropriate question to ask?
1. The true mean amount of time needed to find a parking spot 17.4 minutes?
2. How likely is it that the true mean amount of time needed to find a parking spot is 20 minutes?
3. How likely is it that, in a sample of 45, the true mean amount of time needed to find a parking spot is 17.4 minutes or less if the true mean is 20?
4. How likely is it that, in a sample of 45, the true mean amount of time needed to find a parking spot is less than 20 minutes?
Answer:
The correct answer to the question is
4. How likely is it that, in a sample of 45, the true mean amount of time needed to find a parking spot is less than 20 minutes?
Step-by-step explanation:
Confidence interval provides a range of likely values for an unknown parameter. The interval is weighted based on probabilities of occurrence, such as 95% or 99% based on the result of a sample of test data.
It gives the probability that a given parameter such as the mean will be of a certain value range based on a given number of times.
As such the confidence level of the given mean amount of time needed to find a parking spot should be known.
In order for a film camera with a lens of fixed focal length F to focus on an object located a distance x from the lens, the film must be placed a distance y behind the lens. F, y, and x are related as follows: 1/F=1/X+ 1/Y. Now suppose a camera has a lens with focal length F = 65.1. Explain what happens to the focusing distance y as the object moves far away from the lens.2. Explain what happens to the focusing distance y as the object moves closer and closer to the lens.3. In general, why is it not possible to cross a vertical asymptote?
Answer:
y will increase if x is increased,
y will decrease if x is decreased.
Step-by-step explanation:
1/F=1/X+ 1/Y
1/F-1/X=1/Y
X-F/FX=1/Y
FX/X-F=Y
Rearranging, Y=FX/X-F
So this is the function in terms of X, and F is just a constant
Therefore, the function becomes Y=65X/X-65
Explanation:
y = focusing distance
x = distance from lens
Focusing distance y will increase if the object x moves far away from the lens i.e. x is increased,
Similarly, focusing distance y will decrease if the object x moves closer and closer to the lens i.e. x is decreased.
An asymptote is a function that mimics a curve f(x) as x approaches infinity.
A vertical asymptote, however, cannot be crossed in a function. Remember that a function cannot have multiple y values for a given x value, hence the vertical line test for a function. If a function crossed a vertical asymptote and then went back to it, then it would have to go back over itself as it becomes arbitrarily close to the asymptote. Therefore, it is not possible to cross a vertical asymptote.
The focal point, F, the object distance from the lens, X, and the image distance from the the lens, Y, vary according to the lens formula
1. The value of the focusing distance, Y, is negative and increases in
magnitude, when X < 65, and positive and decreasing in magnitude when
X > 65, the line X = 65 is a vertical asymptote.
2. When X > 65, the value of Y is positive and increasing as the object
moves closer to the lens. At X = 65, there is no image when 0 ≤ X < 65, the
value of Y is negative and increasing towards 0.
3. A vertical asymptote is a discontinuity, where the function is not defined
Reasons:
Known;
[tex]\dfrac{1}{F} = \dfrac{1}{X} + \dfrac{1}{Y}[/tex]
Where;
F = The focal length
X = Object distance from lens
Y = Location of film = Image distance from lens
(a) Given that F = 65, we have;
[tex]\dfrac{1}{65} = \dfrac{1}{X} + \dfrac{1}{Y}[/tex]
[tex]\dfrac{1}{65} - \dfrac{1}{X} = \dfrac{1}{Y}[/tex]
[tex]Y = \dfrac{65 \cdot X}{X - 65}[/tex]
Given that 65·X > X - 65 When X > [tex]-\dfrac{65}{64}[/tex], we have;
As X is increased, Y is decreases, with the rate of decrease reducing as the
value of X gets larger.
(b) As the object moves closer to the lens, when X > 65, the value of Y
increases, at X = 65, the value of Y is infinity, which is a vertical asymptote,
as the object moves closer, the value of Y becomes negative, with the
value increasing (becoming less negative) and when X = 0, Y = 0
3. It is not possible to cross the asymptote because the function has a
discontinuity at the asymptote, which represent the point where the image
is at infinity, such that giving that the distance of the image increases as X
approaches the asymptote, crossing the asymptote results in the image
located further than infinity (which is impossible).
Learn more here:
https://brainly.com/question/2098689
Amanda wants to attend Baylor University for her 4-year college. She is a National Merit Scholar and scores a 1500 on her SATs. This qualifies her for a yearly scholarship of $44,194. How much additional money does she need to have to attend Baylor for 4 years?
Answer:
$58,544
Step-by-step explanation:
Given that Baylor charges tuition fees at $41,194, Room at $13038 and Required fees at $4598 p.a. We also know that the scholarship pays $44194 p.a.
#The additional money for the four years is the total minus the scholarship multiplied by 4 yrs:
[tex]C_{p.a}=Tution+Room+Required\\\\=41194+13038+4598\\\\=58830\\\\Scholarship=44194\\\\\bigtriangleup p.a=58830-44194\\\\=14636[/tex]
The additional cost to attend the college for the next four years is:
[tex]\bigtriangleup p.a=14636\\\\\sum{\bigtriangleup p.a _i}=4\times 14636\\\\=58544[/tex]
Hence, Amanda needs an additional $58,544 to attend Baylor for the 4 years.