SOLUTION
In a scale model of television, 1cm = 10 inches
\(1cm\colon10\text{inches}\)(a) The length of real TV = 80 inches, then the length of the TV in scale model:
\(\begin{gathered} 1cm\colon10\text{inches} \\ x\colon80\text{inches} \\ x=\frac{80}{10}cm \\ x=8cm \end{gathered}\)Hence the length of the TV in scale model = 8cm
(b) In the scale model, the height of the TV =5cm, the height of the real TV will be:
\(\begin{gathered} 1cm\colon10\text{inches} \\ 5cm\colon x \\ x=5(10)in\text{ches} \\ x=50\text{inches} \end{gathered}\)Hence the height of the real TV = 50inches
Given f(x) = log x, what transformations are needed to produce g(x) = log (x) - 3?
Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3 transformed .
Define function.Mathematics includes the study of numbers, various variable, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship between the number of inputs and the corresponding outputs for each. Simply explained, a function range is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a realm. The letter f is frequently used to denote functions (x).
Here,
Given :
=> f(x) = log x
=> g(x) = log (x) - 3
So , it is transformed as logx = f(x)
it is transformed as :
=> g(x) = f(x) - 3
Therefore , the solution of the given problem of function comes out to be g(x) = f(x) - 3 transformed .
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A recipe calls for 2
1 cup of ingredient A for every 1
3
2 cups of ingredient B.
You use 4 cups of ingredient A. How many cups of ingredient B do you need?
4/(1/2) = 8
8 * 1 1/3 = 8 8/3 = 10 2/3 cups of B
Help pls show work if needed
Let's add up the given scores to get: 97+38+88+75+83 = 381. Then we divide by 5 since there are five scores here. The mean we get is 381/5 = 76.2
So that explains the "76.2" mentioned.
Now we'll replace the "38" with "58" and repeat the same steps as above.
Add: 97+58+88+75+83 = 401
Divide by five: 401/5 = 80.2
The mean is now 80.2; it has increased compared to the previous mean. We can see that if we move any outliers closer to the main cluster, then the mean will be centered more around the main cluster. In the other direction, if we move the outlier further away from the cluster, then the outlier pulls on the mean. Think of a magnetic or gravitational pull.
The smaller outlier 38 made the mean of 76.2 to be smaller than it should be if we focused on the other values only. In short, if your data set has outliers, then the mean may likely not reflect the true center average value of the group. At that point, the median may be the next best thing or you could use a trimmed mean.
Which is an equation of the line with a slope of
1/4
and a y-intercept of -2?
Answer:
The answer 1/4x -2
Answer:
y = 1/4x - 2
Step-by-step explanation:
Slope-intercept form is represented as y = mx + b.
m = the slope, which in this case is 1/4
b = the y-intercept which in this case is -2
Then, you just plug in the values.
Madison hits a tennis ball with an initial velocity of 18 m/s straight up into the air. When she hits the ball, it is 1.2 m above the ground
Which equation can be used to find the time, t, it takes for the ball to reach the ground?
A) -16t^2 + 18t+ +1.2=0
B) 4.9t^2 + 18t + 1.2 = 0
C) 4.9^2 + 1.2t + 18 = 0
D) -16t^2 +1.2t + 18 = 0
PLEASE I HAVE AN HOUR Why might you use the distributive property to simplify 3(30-2)
The following data was collected from a simple random sample from a process (infinite population).
13 15 14 16 12
I've already determined that the point estimate of the population mean is 14 and the point estimate of the population std. deviation is 1.581.
What is the Mean of the Population?
A. 14
B. 15
C. 15.1581
D. Could be any Value.
The mean of the population is 14, which is the point estimate of the population mean that was determined from the simple random sample.
The mean of the population is a measure of the central tendency of the population. It is calculated by taking the sum of all the values in the population and dividing by the total number of values. In this case, the mean of the population would be calculated by adding the values of the sample (13, 15, 14, 16, 12) and dividing by the total number of values (5). The mean of the population is then 14 (13 + 15 + 14 + 16 + 12 / 5 = 14).
To calculate the mean of the population, we first need to calculate the sum of all the values in the population. This is done by adding the values of the sample together (13 + 15 + 14 + 16 + 12 = 70). We then divide the sum of the values by the total number of values in the population (70 / 5 = 14). This gives us the mean of the population, which is 14.
The mean of the population is a measure of the central tendency of the population, and it is calculated by taking the sum of all the values in the population and dividing by the total number of values. In this case, the mean of the population was 14, which is the point estimate of the population mean that was determined from the simple random sample.
The mean of the population is 14, which is the point estimate of the population mean that was determined from the simple random sample.
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Hold on hold on hold on hold on hold on oh my God if seven is an element in the domain of F parentheses X parentheses equals 6X -19 over five what is the corresponding element in the range
The corresponding element in the range of the function F when 7 is in the domain is 4.6.
The expression for the given function F following as:
F(x) = 6(x) - 19 / 5
The corresponding element in the range of the function F is the output of the function when 7 is input into the function.
To find this output, we can substitute 7 for X in the expression for the function F:
F(7) = 6(7) - 19 / 5
F(7) = 42 - 19 / 5
F(7) = 23 / 5
F(7) = 4.6
Thus, when 7 is in the domain, the equivalent element in the range of the function F is 4.6.
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What is the next term in the pattern? 1,1,5,17,71,247
Answer: 1085
Step-by-step explanation:
What happens if you can write a function as a composite in different ways? Do you get the same derivative each time? The Chain Rule says you should. Find
dy/dx if y=x by using the Chain Rule with y as a composite of the following functions. Complete parts (a) and (b) below.
Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.
When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.
To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).
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One angle measures 18°, and another angle measures (6d − 6)°. If the angles are complementary, what is the value of d? d = 2 d = 13 d = 31 d = 36.2
The value of d for the given angles will be equal to d = 13. The correct option is B.
What is the complementary angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Complementary angles are formed when the sum of two angles equals 90 degrees. 30 degrees and 60 degrees, for example, are complementary angles.
Given that one angle measures 18° and another angle measures (6d − 6)°.
The value of d will be calculated as,
18 + 6d - 6 = 90
6d + 12 = 90
6d = 90 - 18
6d = 78
d = 78 / 6
d = 13
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Order |-7|, |-6|, |18|, |0|
Answer:
the correct order is ...
18 , 0 , -6 , -7
20. The graph shows the number of homework problems Amanda has remaining based on the number ofminutes she has been working. Which of the following statements is not true?30272421A. Amanda started with 30 homework questions.B. Amanda finishes 2 homework questions every3 minutes.C. The graph shows the equation y = -3/2x + 30.D. After 10 minutes, Amanda has finished half ofher homework.18PROBLEMS REMAINING15121 2 3 4 5 6 7 8 9 10TIME (MINUTES)
B is not true, because in the graph when x=0 y=30, and when x=3 y is not equal to 28 (that would be true if she finishes 2 homework points every 3 minutes). the final answer will be B
you are standing 200 feet from a tall building . The angle from your feet to the top of the building is 51°.
the sum of angles in a triangle is 180
missing angle + 90 + 51 = 180
missing angle = 180 - 141
missing angle = 39 degrees.
in the triangle,
\(\frac{x}{200}=\tan 51\)x = 200 tan51
x = 200 * 1.234
x = 246.97 ft apporx 247 ft
'so the length x = 247 ft
that is greater than 200
so the answer is
x > 200 ft
A large bag contains 29 balls of different colors. The balls are of the same size, weight, surface, such that besides the color they cannot be differentiated. Among the 29 balls, 8 are green, 4 are yellow, 6 are red, 5 are blue, and 6 are black.
(a) What is the probability of getting exactly 1 green, 1 yellow and 2 red when pulling 8 balls? number (rtol=0.01, atol=0,0001)
(b) What is the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls? number (rtol=0.01. atol=0.0001)
(c) What is the probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls? (Note: If there are remaining balls, they need to be either blue or black) number (rtol=0.01, atol=0.0001)
(d) What is the probability of getting 2 blue and 2 non-blue when pulling 4 balls? number (rtol=0.01, atol=0.0001)
(e) Recalculate part (d) using a binomial distribution. number (rtol=0.01, atol=0.0001)
Answer:
White
6
Red
9
Green
Total number of balls =5+6+9
=20
(i) Probability =
Total cases
favourable cases
P(Green) =
20
9
(ii) P(White or red) =
20
5+6
=
20
11
(iii) P(neither green nor white) = P(Red)
=
20
6
=
10
3
The probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.
The probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.
(a) Probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls:
Total number of balls = 29
Total number of balls to be pulled = 8
Number of ways to choose 1 green out of 8 = C(8, 1) = 8
Number of ways to choose 1 yellow out of the remaining 7 = C(7, 1) = 7
Number of ways to choose 2 red out of the remaining 6 = C(6, 2) = 15
Total favorable outcomes = 8 x 7 x 15 = 840
Total possible outcomes = C(29, 8) = 2,765,905
Probability
= favorable outcomes / possible outcomes
= 840 / 2,765,905
= 0.000303
Therefore, the probability of getting exactly 1 green, 1 yellow, and 2 red when pulling 8 balls is 0.000303.
(b) Total number of balls = 29
Total number of balls to be pulled = 6
Number of ways to choose 1 green out of 8 = C(8, 1) = 8
Number of ways to choose another green out of the remaining 7 = C(7, 1) = 7
Number of ways to choose 2 yellow out of the remaining 5 = C(5, 2) = 10
Number of ways to choose 2 red out of the remaining 3 = C(3, 2) = 3
Total favorable outcomes = 8 x 7 x 10 x 3 = 1,680
Total possible outcomes = C(29, 6) = 593,775
Probability
= favorable outcomes / possible outcomes
= 1,680 / 593,775
= 0.00283
Therefore, the probability of getting first a green, then another green, and then in any order 2 yellow and 2 red when pulling 6 balls is 0.00283.
(c) Probability of getting first and last a green, and then in any order 2 yellow and 2 red when pulling 8 balls:
Total number of balls = 29
Total number of balls to be pulled = 8
Number of ways to choose the first green = C(8, 1) = 8
Number of ways to choose the last green = C(7, 1) = 7
Number of ways to choose 2 yellow out of the remaining 6 = C(6, 2) = 15
Number of ways to choose 2 red out of the remaining 4 = C(4, 2) = 6
Number of ways to choose the remaining 2 balls (either blue or black) = C(5, 2) = 10
Total favorable outcomes = 8 x 7 x 15 x 6x 10 = 50,400
Total possible outcomes = C(29, 8) = 2,765,905
Probability
= 50,400 / 2,765,905 ≈ 0.0182
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What is 1/2÷3 as a fraction?
Answer: 1/6
Step-by-step explanation:
1/2 divided by 3/1 turns into 1/2 x 1/3 and when multiplying numerators and denominators with each other, you get 1/6.
Can you please tell me the sum of the question
Answer:
B) \(4i\sqrt{2}\)
Step-by-step explanation:
\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)
At a soccer game, a vendor sold a combined total of 220 sodas and hot dogs. The number of sodas sold was 46 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
133 sodas
87 hot dogs
I've completed the work in the photo, just trying to reach the letter count lol
given Q= 100K^0.5 L^0.5 w=50 r=40 show how to determine the amount of labor and capital that the firm should use in order to minimize the cost of producing 1,118 units of output. what is the minimum cost?
In this exercise we have to use the knowledge of function to write the minimum production cost, so we have to:
\(K=13.975\)
Thus writing the function that corresponds to this will be:
\(MPK = Q'(K) = 50L^{0.5}/K^{0.5} = 25\\MPL = Q'(L) = 50K^{0.5}/L^{0.5} = 100\)
Now calculating the minimum production cost we have:
\(MPK/r = MPL/w\\MPK/40 = 100/50\\MPK =80\\MPK = 50L^{0.5}/K^{0.5} = 80\\K=(1.118/80)= 13.975\)
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Guided Practice #1
Damaya is baking pies. For every 2 cups of flour, she uses 3
cups of sugar. How many cups of sugar will she need if she
uses 12 cups of flour? Model your answer on the double
number lines below.
0
O.
G
E
Answer:
18 cups of sugar
Step-by-step explanation:
I don't see any answer choices in your post but assuming it she has to use 3 cups of sugar for every 2 cups of flour, then that would mean she has to use 3/2 cups of sugar for every 1 cup of flour.
So if she uses 12 cups of flour she will have to use (3/2) x 12 = 18 cups of sugar
the square root of 50
Answer:
The square root of 50 is approximately 7.07.
Answer:
7.07106781187...
Step-by-step explanation:
its an irrational number
Let be independent random variables with the common distribution function F and suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N (b) Find P(M1} (d) Use (b) and (c) to rederive the probability you found in (a).
suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is nλe^(-nλx)
Given fx (x) = λe^λx
Fx (x) = 1 – e^-λx x…0
To find distribution of Min (X1,….Xn)
By applying the equation
fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)
For minimum j = 1
[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx
= ne^[(n-1) λx] λe^(λx)
= nλe^(-λx[1+n-1])
= nλe^(-nλx)
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Renata is purchasing a condominium for $125,000. She wants to put down a down payment of 20%. Select all the true statements. The proportion that represents the down payment is 20100=125,000 20 100 = 125 , 000 x . The down payment is $25,000. The proportion that represents the down payment is 20100=125,000 20 100 = x 125 , 000 . The down payment is $50,000. The down payment is 15 1 5 of the cost of the house.
The correct options are -
The proportion that represents the down payment is : 20/100 x 125000.The down payment is $25,000What is down payment?When something is bought on credit, an initial payment is made in the form of a down payment.
Given is that Renata is purchasing a condominium for $125,000. She wants to put down a down payment of 20%.
We can calculate the amount she is putting in down payment as -
{x} = 20% of 125000
{x} = 20/100 x 125000
{x} = 20 x 1250
{x} = 25000
Therefore, the correct options are -
The proportion that represents the down payment is : 20/100 x 125000.The down payment is $25,000To solve more questions on functions & equations, visit the link-
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Use the rule x + 3 to find the missing number on the table.
X Y
0 3
3 6
11
7 10
9 12
The missing number on the table using the rule y = x + 3 is 14
How to use equation to find missing number?X Y
0 3
3 6
11 y
7 10
9 12
The rule:
y = x + 3
y = 0 + 3
y = 3
y = 3 + 3
y = 6
y = 11 + 3
y = 14
y = 7 + 3
y = 10
y = 9 + 3
y = 12
Therefore, the missing number on the table is 14
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What is the value of t??
1.4t - 0.4 ( t - 3.1 ) = 5.8
Please explain step by step on how I could get this answer!
1.4t - 0.4(t-3.1)=5.8
Combine terms in paratheses
1.4t - 0.4t + 1.24 = 5.8
Combine t's
(1)t + 1.24 = 5.8
Subtract 1.24 over
t = 4.54If the image is rotated about the x-axis, which of the following images best represents the result?
A. Y
B. Z
C. X
D. W
The images best represents the result is image W.
We have, the image is rotated about the x-axis.
Now, rotating around x axis can give the other half of the image.
Also, rotating about x axis gives the mirror image of the figure.
So, the rotation leads to a circle.
and, In three dimensional we can say that Sphere.
Thus, the required image is W.
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Find the 110 term of the sequence -7,3, 13, 23, ..
Answer:
1083
Step-by-step explanation:
The formula for the nth term of a sequence is a+(n - 1 )d, where a is the first term and d is the difference between each term. Here, a is -7 and d is 10 (terms go up by ten each time).
So, the nth term = -7+(n-1)10 = -7+10n-10 = 10n-17
So, the 110th term = 10(110)-17=1100-17=1083
HELP!!!! Write an exponential function to describe the given sequence of numbers.
Answer:
y = 5^(x+1)
Step-by-step explanation:
y = 5^(x+1)
x = 1 for the initial step
The length of a rectangle is four times its width.
If the area of the rectangle is 144 cm^2 , find its perimeter.
Answer:
Let width of rectangle be x cm.
Width = x cm
Length = 4x cm
Area of rectangle = length x width
4x × x = 144
4x² = 144
x² = 144 ÷ 4 = 36
x = √36 = 6
Width = 6 cm
Length = 6 × 4 = 24cm
Perimeter = 6 + 24 + 6 + 24 = 60 cm
Evaluate the expression when =c24 and =d25. +dc4
The expression given is 3c + 5d and the expression when c = 24 and d =25 will be 197.
How to illustrate the expression?It should be noted that an expression is simply used to illustrate the relationship between the variables.
In this case, the expression given is 3c + 5d.
Therefore, the expression given is 3c + 5d and the expression when c = 24 and d =25 will be:
= 3c + 5d
= 3(24) + 5(25)
= 72 + 125
= 197
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Complete question:
The expression given is 3c + 5d. Evaluate the expression when c = 24 and d =25.