Final Answer:
The correct simplified ratio of US to British stamps is 25 : 2, which corresponds to answer choice E.
Explanation:
To determine the ratio of US to British stamps, we must use the given ratios of US to Indian and Indian to British stamps.
The given ratio of US to Indian stamps is 5 to 2. This means for every 5 US stamps there are 2 Indian stamps. We can represent this as:
US : Indian = 5 : 2
The given ratio of Indian to British stamps is 5 to 1. This implies that for every 5 Indian stamps, there is 1 British stamp. We can write this as:
Indian : British = 5 : 1
To find the ratio of US to British stamps, we need to combine these two ratios. To do this, we should express each ratio such that the Indian stamp part of each ratio is the same. Since the ratios already have the same number of Indian stamps (5 of them), we can directly multiply the US part by the British part across these ratios.
Thus, we multiply the number of US stamps (5 from the first ratio) by the number of British stamps (1 from the second ratio):
US to British = 5 (US) * 1 (British)
US to British = 5
Since we did not have to multiply the number of British stamps by anything (they were only multiplied by 1), the British part of the ratio remains unchanged.
Next, we multiply the Indian part of the first ratio by the British part of the second ratio:
Indian to British = 2 (Indian from the first ratio) * 5 (British from the second ratio)
Indian to British = 10
Now we can combine these two results to express the US to British ratio:
US to British = 5 (US) : 10 (British)
To simplify this ratio, we divide both sides by the common factor between them. In this case, that common factor is 5. So when we divide both numbers by 5, we have:
US to British = (5/5) : (10/5)
US to British = 1 : 2
However, this is not the option given in the question. Let's revisit the calculation and see if there was an error:
The correct approach to combining the ratios is to multiply the two ratios directly:
US : Indian = 5 : 2
Indian : British = 5 : 1
Multiplying across gives us:
US : British = (5 * 5) : (2 * 1)
US : British = 25 : 2
The correct simplified ratio of US to British stamps is 25 : 2, which corresponds to answer choice E.
One inch of rain on a square foot of land weights 5.2 pounds. About how many ghallons of rain are there? round your answer to the nearest tenth
Answer: 0.60 gallon
Step-by-step explanation:
There are 12pounds in a standard US gallon.
12pounds= 1 gallon
5.2 pounds=?
5.2/12 × 1 gallon
0.624 gallon
Rounding to the nearest tenth =0.60
A two-dimensional array can be viewed as ________ and ________. rows, columns arguments, parameters increments, decrements All of these None of these
Answer:
rows, columns
Step-by-step explanation:
Two dimensional array can be viewed as rows and columns.
It is viewed as matrix or grid as well therefore we can conclude that it can be viewed in terms of rows and columns.
The correct option is the first one, A two-dimensional array can be viewed as rows and columns.
How to complete the statement?A two-dimensional array is a data structure that stores elements in a grid-like format with rows and columns. It can be visualized as a table or matrix.
In this context, "rows" refer to the horizontal dimension of the array. Each row consists of a series of elements that are stored sequentially from left to right. The number of rows in the array represents the height or the total count of rows.
"Columns" refer to the vertical dimension of the array. Each column consists of a series of elements that are stored sequentially from top to bottom. The number of columns in the array represents the width or the total count of columns.
By organizing data in rows and columns, a two-dimensional array allows for efficient storage and retrieval of elements. The elements within the array can be accessed by specifying both the row and column indices.
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Luke has 1/5 of a package of dried apricots. He divides the dried apricots equally into 4 small bags. Luke gives one of the bags to a friend and keeps the other three bags for himself. What fraction of the original package of dried apricots did Luke keep for himself?
Answer:
3/80
Step-by-step explanation:
If one fifth of apricots are split into 4 parts, each bag has 1/5 * 1/4 of the original apricots
1/5 * 1/4 = 1/20
Luke keeps 3/4 of those so that's
3/4 * 1/20 = 3/80
Hillary gets divorced in 2016 and is required to pay her ex-spouse $200 per month until her son reaches 18 years of age in 7 years and $120 per month thereafter. How much of her 2019 payments are deductible as alimony?
To know how much of Hillary's payments are deductible as alimony in 2019, we first need to figure out how old her son was when Hillary got divorced in 2016.
Given that Hillary has to pay until her son turns 18 and this occurs 7 years after the divorce, this means that her son was 18 - 7 = 11 years old in 2016.
Therefore, he will be turning 18 in 2025 (2016 + 9 years).
In 2019, which is 3 years after 2016, her son would be 11 + 3 = 14 years old. As her son has not yet reached 18 years old, Hillary is still making $200 payments per month in 2019.
Given there are 12 months in a year, the total amount of alimony payments that Hillary made in the year 2019 is 12 * $200 = $2400.
So, the amount of her 2019 payments that are deductible as alimony is $2400.
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If a ball is thrown in the air with a velocity 44 ft/s, its height in feet t seconds lateris given by y = 44t -16t2. (a) Find the average velocity for thetime period beginning when t = 2 and lasting 0.5second. ft/s(b) Find the average velocity for the time period beginning whent = 2 and lasting 0.1 second. ft/s(c) Find the average velocity for the time period beginning whent = 2 and lasting 0.05 second. ft/s(d) Find the average velocity for the time period beginning whent = 2 and lasting 0.01 second. ft/s(e) Estimate the instantaneous velocity when t = 2.
Answer: a. 28ft/s. b. 40.08ft/s. c. 42.4ft/s. d. 43.68ft/s. e. - 20ft/s
Step-by-step explanation: Since your displacement was given that is (y) , we just have to differentiate y with respect to time t. That is the first derivative only.
I have worked it out and here is the attachment.
Final answer:
To find the average velocity during different time periods, we can calculate the changes in height and time. By substituting the given values of t into the height equation, we can determine the heights at different times. We can then calculate the average velocities by taking the change in height divided by the change in time. Additionally, to estimate the instantaneous velocity when t = 2, we can differentiate the height equation and substitute t = 2 into the derivative.
Explanation:
To find the average velocity for a given time period, we need to calculate the change in height and the change in time. Using the equation y = 44t - 16t^2, we can substitute the values of t = 2 and t = 2.5 to find the heights at these times. Then, we can find the average velocities.
(a) For the time period of 0.5 seconds starting at t = 2, we calculate the heights at t = 2 and t = 2.5: y(2) = 44(2) - 16(2^2) = 36 ft and y(2.5) = 44(2.5) - 16(2.5^2) = 35 ft. The average velocity is the change in height divided by the change in time: (35 - 36) ft / 0.5 s = -2 ft/s.
(b) For the time period of 0.1 second starting at t = 2, we calculate the heights at t = 2 and t = 2.1: y(2) = 36 ft and y(2.1) = 44(2.1) - 16(2.1^2) = 37.644 ft. The average velocity is the change in height divided by the change in time: (37.644 - 36) ft / 0.1 s = 16.44 ft/s.
(c) For the time period of 0.05 second starting at t = 2, we calculate the heights at t = 2 and t = 2.05: y(2) = 36 ft and y(2.05) = 44(2.05) - 16(2.05^2) = 37.079 ft. The average velocity is the change in height divided by the change in time: (37.079 - 36) ft / 0.05 s = 21.58 ft/s.
(d) For the time period of 0.01 second starting at t = 2, we calculate the heights at t = 2 and t = 2.01: y(2) = 36 ft and y(2.01) = 44(2.01) - 16(2.01^2) = 36.764 ft. The average velocity is the change in height divided by the change in time: (36.764 - 36) ft / 0.01 s = 76.4 ft/s.
(e) To estimate the instantaneous velocity when t = 2, we can calculate the derivative of the height function. The derivative of y(t) = 44t - 16t^2 with respect to t is dy/dt = 44 - 32t. Substituting t = 2 into this equation, we get dy/dt = 44 - 32(2) = -20 ft/s.
Suppose that the scores on a test have a normal distribution with mean 24 and standard deviation 4. What is the proportion of scores less than 28?
Answer: 0.8413
Step-by-step explanation:
Given : The scores on a test have a normal distribution with mean 24 and standard deviation 4.
i.e. [tex]\mu= 24[/tex] and [tex]\sigma= 4[/tex]
Let x denotes the scores on the test.
Then, the probability that a student score less than 28 will be :-
[tex]P(x<28)=P(\dfrac{x-\mu}{\sigma}<\dfrac{28-24}{4})\\\\=P(z<1)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=0.8413 \ \ [\text{By z-table}][/tex]
Hence, the the proportion of scores less than 28 is 0.8413 .
The price of nails,n, is $1.29/lb, the price of washers, w, is $0.79/lb, and the price of bolts,b, is $2.39/lb.Write an expression to represent the total price of the supplies.
The expression to represent the total price of the supplies is 1.29n + 0.79w + 2.39b
Solution:
Let "n" be the number of nails
Let "w" be the number of washers
Let "b" be the number of bolts
Given that ,
Price of nail = $ 1.29 per lb
Price of washers = $ 0.79 per lb
Price of bolts = $ 2.39 per lb
To find: Expression to represent the total price of the supplies.
Total price = number of nails x Price of nail per lb + number of washers x Price of washers per lb + number of bolts x Price of bolts per lb
[tex]Total\ price = n \times 1.29 + w \times 0.79 + b \times 2.39\\\\Total\ price = 1.29n + 0.79w + 2.39b[/tex]
Thus the expression to represent the total price of the supplies is found
At the city Museum child omission is $5.70 and adult admission is $9.80. On Tuesday 124 tickets were sold for a total sales of $936. How many child tickets were sold that day
Answer: 68 child tickets were sold
Step-by-step explanation:
Let x represent the number of child tickets that were sold that day.
Let y represent the number of adult tickets that were sold that day.
A total of 124 tickets were sold on Tuesday. This means that
x + y = 124
At the city Museum child admission is $5.70 and adult admission is $9.80. The total sales from tickets was $936. This means that
5.7x + 9.8y = 936 - - - - - - - - -1
Substituting x = 124 - y into equation 1, it becomes
5.7(124 - y) + 9.8y = 936
706.8 - 5.7y + 9.8y = 936
- 5.7y + 9.8y = 936 - 706.8
4.1y = 229.2
y = 229.2/4.1
y = 55.9
y = 56
x = 124 - y = 124 - 56
x = 68
Miss Silverstein bought three cakes for her birthday party she cut each cake in 2/4 and plans to serve each guest a quarter of a cake how many gas can she serve with all her cakes
Answer:
Miss Silver stein can serve for 12 guests with amount of cake that she has bought.
Step-by-step explanation:
Given:
Number of cakes she bought = 3
Amount of cakes given to each guest = [tex]\frac{1}{4}[/tex]
We need to find the number of guest cakes can be served.
Solution:
Now we can say that;
the number of guest can have the cake to can be calculated by dividing the Number of cakes she bought from Amount of cakes given to each guest
framing in equation form we get;
Number of guest can have cake = [tex]\frac{3}{\frac{1}{4}} = 3\times\frac{4}{1} =12[/tex]
Hence Miss Silver stein can serve for 12 guests with amount of cake that she has bought.
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?I. At least one of the homes was sold for more than $165,000.II. At least one of the homes was sold for more than $130,0000 and less than $150,000.III. At least one of the homes was sold for less than $130,000.A. I onlyB. II onlyC. III onlyD. I and IIE. I and III
Answer:
A. 1 only.
Step-by-step explanation:
What is the domain of the function f (x) = StartFraction x + 1 Over x squared minus 6 x + 8 EndFraction? all real numbers all real numbers except –1 all real numbers except –4 and –2 all real numbers except 2 and 4
Answer:
all real numbers except 2 and 4
Step-by-step explanation:
The exceptions in the domain are the values that make the denominator zero. For a denominator of x² -6x +8 = (x -4)(x -2), the values that make it zero are x=4 and x=2.
The domain is all real numbers except 2 and 4.
Answer:
Option D is correct.
The domain of the function f(x) is all real numbers except 2 and 4.
Step-by-step explanation:
f(x) = (x+1)/(x²-6x+8)
The domain of a function expresses the region of values of x, where the function exists.
And logically, a function exists where ever f(x) has a finite value. That is, the only point where A function does not exist is when f(x) gives infinity.
For a rational function, the point where a function doesn't exist is when the denominator of the rational function is equal to 0. Because (numerator/0) --> ∞
So, the denominator in this question is
x²-6x+8
The function doesn't exist when
x²-6x+8 = 0
So, we solve the quadratic equation that ensues to get the values of x where the function doesn't exist.
x²-6x+8 = 0
x² - 4x - 2x + 8 = 0
x(x-4) - 2(x-4) = 0
(x-2)(x-4) = 0
(x-2) = 0 or (x-4) = 0
x = 2 or x = 4
This means that the function doesnt exist at x = 2 and x = 4
Indicating further that the function exists everywhere except at x = 2 and x = 4.
Hence, from the definition of domain given above, it is clear that the domain of the given function is all real numbers except 2 and 4.
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Carlos plans to build a grain bin with a radius of 15 ft. The recommended slant of the roof is 25 degrees. He wants the roof to overhang the edge of the bin by 1 ft. What should the length x be?
Answer: The length x =17.64ft
Step-by-step explanation:
Looking at the diagram,to find x,we ues adj/hyp = cos 25°
16/x=cos25°
Cross multiply
X=16/cos25°
X=17.64ft
Answer:
17 feet 8 in
Step-by-step explanation:
im doing it in class imao
Constant of 15-8y
a.15
b.8
c. -8
d. -15
The constant of the expression 15-8y is 15
Constants are values that are not attached to any variable. For example:
The constant of x + 5 is 5Now given the expression 15 - 8y
First, we can re-arrange to have:
-8y + 15
From the expression, we can see that 15 is not attached to any variable. Hence the constant of the expression is 15
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A college bookstore marks up the price that it pays the publisher for a book by 40 %. If the selling price of a book is $ 81.00 comma how much did the bookstore pay for this book?
Answer:
32.40
Step-by-step explanation:
81 x 40% =48.60
81. -48.60 = 32.40
Answer:the college bookstore paid
$57.86 for the book.
Step-by-step explanation:
Let x represent the price that the college bookstore paid the publisher to get the book.
The college bookstore marks up the price by 40%. It means that the value of the mark up would be .40/100 × x = 0.4 × x = 0.4x
Therefore, the selling price of the book at the college bookstore would be
x + 0.4x = 1.4x
If the selling price of a book is $ 81.00, it means that
1.4x = 81
x = 81/1.4 = $57.86
find the root y=x^2-8x+15
Answer:
{3, 5}.
Step-by-step explanation:
y = x^2 - 8x + 15
(x - 5)(x - 3) = 0
x - 5 = 0 or x - 3 = 0
So the roots are {3, 5}.
The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg?
Approximately 97.72% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg.
Explanation:To find the percentage of 18-year-old women with a systolic blood pressure between 96 mmHg and 144 mmHg, we need to calculate the z-scores for the given values using the formula z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
For X = 96 mmHg, z = (96 - 120) / 12 = -2.
For X = 144 mmHg, z = (144 - 120) / 12 = 2.
Using a standard normal distribution table, we can find that approximately 0.9772 (97.72%) of the values fall within 2 standard deviations from the mean. Therefore, approximately 97.72% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg.
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Final answer:
Approximately 95% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg, as calculated using Z-scores and the standard normal distribution.
Explanation:
The question asks us to determine the percentage of 18-year-old women who have a systolic blood pressure between 96 mmHg and 144 mmHg, given that the systolic blood pressure is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg.
We will use the concept of Z-scores to find this probability. A Z-score represents the number of standard deviations a data point is from the mean. We can calculate the Z-scores for the systolic blood pressure values of 96 mmHg and 144 mmHg and then use the standard normal distribution table to find the percentages. The calculations are as follows:
Z-score for 96 mmHg = (96 - 120) / 12 = -2
Z-score for 144 mmHg = (144 - 120) / 12 = 2
Looking at the Z-score table, we find that the area between Z = -2 and Z = 2 covers approximately 95% of the data under the normal distribution curve. Therefore, about 95% of 18-year-old women will have a systolic blood pressure between 96 mmHg and 144 mmHg.
A local dinner theater sells adult tickets for $105 each and children’s tickets for $60 each. For a certain show, the theater sells 84 tickets for a total of $7155. How many of each type of ticket were sold?
write a system of equations that models this problem and then show all the steps to solve your system of equations using the linear combination.
Answer:
The answer to your question is he sold 47 adult tickets and 37 children tickets.
Step-by-step explanation:
Data
Adult ticket = a = $105
Children ticket = c = $60
Total number of tickets = 84
Total money earn = $7155
Equations
a + c = 84 ------------ (I)
105a + 60c = 7155 -------------(II)
Multiply equation I by -60
-60a - 60c = -5040
105a + 60c = 7155
Simplify
45a = 2115
a = 2115 / 45
a = 47 tickets
Substitute a in equation I
47 + c = 84
c = 84 - 47
c = 37 tickets
You can form linear equations from the given description then use that system to derive the solution.
The amount of each type of tickets sold are:
Children tickets sold = 37
Adult tickets sold = 47
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Using the above methodology to get the system of equation modelling the given situationLet the amount of adult tickets sold be "a"
Let the amount of children tickets sold be "c"
Since the total amount of tickets sold is given as 84
Thus,
Total tickets = children tickets + adult tickets
84 = c + a
a + c = 84
since 1 adult ticket costs $105,
thus, "a" adult tickets cost [tex]105 \times a = 105a \text{\:\:(Written in short)}[/tex] (in dollars)
Similarly,
since 1 children ticket costs $60
"c" children tickets cost [tex]60c[/tex] (in dollars)
Since the price obtained by selling those tickets is $7155
thus,
total amount earned = amount earned by children tickets + amount earned by adult tickets
$7155 = $60c + $105a
Thus, we got the system of equations as:
[tex]a + c = 84\\105a + 60c = 7155[/tex]
Multiplying first equation with -105 to make a's coefficient equal and opposite to make the addition of them eliminate "a":
[tex]-105a -105c = -105 \times 84\\105a + 60c = 7155\\\\\text{Addding both equations}\\\\-45c = 7155 - 8820 = -1665\\\\c = \dfrac{1665}{45} = 37[/tex]
Putting this value in first equation, we get:
[tex]a + c = 84\\a + 37 = 84\\a = 84 - 37 = 47[/tex]
Thus,
The amount of each type of tickets sold are:
Children tickets sold = 37
Adult tickets sold = 47
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At 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal. About how high is the building?
Answer:
203 feet.
Step-by-step explanation:
Please find the attachment.
Let h represent the height of the building.
We have been given that at 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal.
We know that tangent relates opposite side of a right triangle to its adjacent side.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\text{tan}(35^{\circ})=\frac{h}{290}[/tex]
[tex]290*\text{tan}(35^{\circ})=\frac{h}{290}*290[/tex]
[tex]290*0.70020753821=h[/tex]
[tex]h=290*0.70020753821[/tex]
[tex]h=203.0601860809[/tex]
[tex]h\approx 203[/tex]
Therefore, the building is approximately 203 feet high.
A window-washer is climbing a 37-foot ladder leaning against a building. The ladder touches the building 35 feet above the ground. What is the distance from the bottom of the ladder to the base of the building?
Answer: the distance from the bottom of the ladder to the base of the building is 12 feet.
Step-by-step explanation:
The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.
The length of the ladder represents the hypotenuse of the right angle triangle.
The distance from the ground to the point where the ladder touches the wall of the building represents the opposite side
Therefore, to determine the distance from the bottom of the ladder to the base of the building, x, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
37² = 35² + x²
1369 = x² + 1225
x² = 1369 - 1225 = 144
x = √144 = 12 feet
Final answer:
To find the distance from the bottom of the ladder to the base of the building, use the Pythagorean theorem with the given ladder height and building contact point. Calculate the distance as 12 feet.
Explanation:
A window-washer is climbing a ladder leaning against a building. In this scenario, the ladder is 37 feet long and touches the building 35 feet above the ground. To find the distance from the bottom of the ladder to the base of the building, we can use the Pythagorean theorem.
By applying the Pythagorean theorem: a² + b² = c², where a and b are the distances from the bottom of the ladder to the building and from the base to the building, respectively, and c is the length of the ladder, we can calculate the distance to be 12 feet.
Therefore, the distance from the bottom of the ladder to the base of the building is 12 feet.
Given the following triangle find side AC.
A. 11.89
B. 12.87
C. 13.98
D. 14.08
Answer:
The answer to your question is AC = 14
Step-by-step explanation:
To solve this problem, we must use trigonometric functions.
And we must look for a trigonometric function that relates the opposite side and the hypotenuse.
This trigonometric function is the sine
[tex]sin\alpha = \frac{opposite side}{hypotenuse}[/tex]
solve for Opposite side = AC
AC = hypotenuse x sin α
- Substitution
AC = 25 x sin 34
- Simplification
AC = 25 x 0.56
- Result
AC = 14
Taylor purchased one pack of cookies and gave away 5 cookies to her friends. If she had 1 cookie left, what is p, the number of cookies in each package?
Answer:
The number of cookies in each package = 6
Step-by-step explanation:
Given:
Taylor purchased a pack of cookies.
Number of cookies Taylor gave to her friends = 5
Number of cookies she had left = 1
To find the number of cookies 'p' in each package.
Solution:
[tex]p\rightarrow[/tex] Number of cookies in each package.
If Taylor gave away 5 cookies to her friends, then the number of cookies left in the package can be represented as:
⇒ [tex]p-5[/tex]
Number of cookies she had left = 1
So, the equation to solve for [tex]p[/tex] can be given as:
[tex]p-5=1[/tex]
Solving for [tex]p[/tex]
Adding 5 both sides.
[tex]p-5+5=1+5[/tex]
∴ [tex]p=6[/tex]
Thus, number of cookies in each package = 6.
1.Solve.
{y=2x−64x−2y=14
Use the substitution method.
2.Solve.
{y=x−63x+2y=8
Use the substitution method.
3.What is the y-coordinate of the solution for the system of equations?
{x−y=1227+3y=2x
Enter your answer in the box.
4.What is the y-coordinate of the solution of the system of equations?
{y=2x+14−4x−y=4
Enter your answer in the box.
Answer:
The answer to your question is below
Step-by-step explanation:
1.- y = 2x - 64
x - 2y = 14
Substitution
x - 2(2x - 64) = 14
Simplification
x - 4x + 128 = 14
x - 4x = 14 - 128
-3x = - 114
x = 114/3
x = 38
y = 2(38) - 64
y = 76 - 64
y = 12
Solution (38, 12)
2.- y = x - 6
3x + 2y = 8
Substitution
3x + 2(x - 6) = 8
Simplification
3x + 2x - 12 = 8
5x = 8 + 12
5x = 20
x = 20 / 5
x = 4
y = 4 - 6
y = -2
Solution (4 , -2)
3.- x - y = 12
27 + 3y = 2x
x = 12 + y
27 + 3y = 2(12 + y)
27 + 3y = 24 + 2y
3y - 2y = 24 - 27
y = -3
x = 12 - 3
x = 9
Solution y = -3
4.- y = 2x + 14
-4x - y = 4
-4x - (2x + 14) = 4
-4x - 2x - 14 = 4
-6x = 4 + 14
-6x = 18
x = 18/-6
x = -3
y = 2(-3) + 14
y = -6 + 14
y = 8
Solution y = 8
Answer:
There is no solution.
Step-by-step explanation:
I will give brainilest please help!!! ASAP.
PLEASE MARK BRAINLIEST!
Answer:
Life hack in this answer!
Step-by-step explanation:
The correct table is the second one, or the table on the bottom right. (Picture included).
Life hack --> To find the relative percentage/frequency of something, all you have to do is take the frequency you are trying to find, and divide it with the total.
Example: You are trying to find the frequency of REGULAR MALE jeans. What is its frequency? To find, all you have to do is divide 120 from 28. Like this:
28 = male regular jeans
120 = total
28 ÷ 120 = ?
28 ÷ 120 = 0.23333333...
Final answer: 0.23
In this scenario, we must round. But remember that you might not always need or have to round.
And, as predicted, the answer of 0.23 is in the second table under REGULAR MALE jeans.
If you have any questions, let me know!
I hope this helps!
- sincerelynini
A race car travels with a constant tangential speed of 82.6 m/s around a circular track of radius 667 m. Find the magnitude of the total acceleration.
Answer:
TOTAL ACCELERATION =10.229m/s²
Step-by-step explanation:
total acceleration = [tex]\sqrt{centripetal accleration^{2} +tagential acceleration^{2} }[/tex]
since tangential speed is constant , tangential acceleration =0
Thus total acceleration = centripetal acceleration.
centripetal acceleration = v²/r
v=82.6m/s , r= 667m
centripetal acceleration = 82.6²/667
centripetal acceleration = 10.229m/s²
TOTAL ACCELERATION =10.229m/s²
Final answer:
The magnitude of the total acceleration of a race car traveling with a constant tangential speed of 82.6 m/s around a circular track of radius 667 m is 10.20 m/s², which is the centripetal acceleration.
Explanation:
The question asks to find the magnitude of the total acceleration of a race car traveling with a constant tangential speed of 82.6 m/s around a circular track of radius 667 m. In circular motion, the total acceleration is the centripetal acceleration, since the tangential speed (speed along the arc of the circle) is constant and there is no tangential acceleration. The formula for centripetal acceleration (ac) is ac = v2 / r, where v is the tangential speed and r is the radius of the circular path.
Using the given values:
ac = (82.6 m/s)2 / 667 m = 10.20 m/s2
Therefore, the magnitude of the centripetal acceleration of the race car is 10.20 m/s2.
Start with the logistic equation dx dt = kx(M − x). Suppose that we modify our harvesting. That is we will only harvest an amount proportional to current population. In other words we harvest hx per unit of time for some h > 0 (Similar to earlier example with h replaced with hx).
a) Construct the differential equation.
b) Show that if kM > h, then the equation is still logistic.
c) What happens when kM < h?
Answer:
a) [tex] \frac{dx}{dt}= kx (M-x) -hx[/tex]
[tex] \frac{dx}{dt}= kx (M -x- \frac{h}{k})[/tex]
b) [tex] M -\frac{h}{k}>0 [/tex]
Let's say that [tex] a=M -\frac{h}{k}>0[/tex]
If we multiply the woule equation by k we got:
[tex] kM -h >0[/tex]
So then we satisfy that the equation is also logistic since the parameter [tex] a>0[/tex]
c) If we assume that [tex] kM <h[/tex] then we have that [tex] a<0[/tex]
And then [tec] kx (a -x) <0[/tex] for any value of [tex] x>0[/tex]
And if that hhapens then the population will tend to 0 for any initial condition established/
Step-by-step explanation:
For this case we have the following logistic equation [tex] \frac{dx}{dt}= kx (M-x)[/tex]
Part a
We want to modify our harvesting for this case, so we harvest hx per unit of time for some [tex] h>0[/tex]
So then the model with harvesting who is proportional is given by:
[tex] \frac{dx}{dt}= kx (M-x) -hx[/tex]
And we can write like this:
[tex] \frac{dx}{dt}= kx (M -x- \frac{h}{k})[/tex]
Part b
For this case we assume that [tex] kM>h[/tex]and we need to show that the equation is still logistic. So we need that the sollowing quantity higher than 0
[tex] M -\frac{h}{k}>0 [/tex]
Let's say that [tex] a=M -\frac{h}{k}>0[/tex]
If we multiply the woule equation by k we got:
[tex] kM -h >0[/tex]
So then we satisfy that the equation is also logistic since the parameter [tex] a>0[/tex]
Part c
If we assume that [tex] kM <h[/tex] then we have that [tex] a<0[/tex]
And then [tec] kx (a -x) <0[/tex] for any value of [tex] x>0[/tex]
And if that hhapens then the population will tend to 0 for any initial condition established/
Keith does work for his neighbors. When he earns $12 an hour. When he works indoors he earns $8 an hour. Last month he did 18 hours of work outdoors and 16 hours of work indoors. How much did keith earn last month
Answer: he earned $344 in all.
Step-by-step explanation:
When he does work outdoors he earns $12 an hour. This means that if he works outdoors for x hours, he would earn $12x
When he works indoors he earns $8 an hour. This means that if he works indoors for y hours, he would earn $8y.
Last month he worked 18 hours outdoors. This means that the total amount that he earned working outdoors is
12 × 18 = $216
He worked 16 hours indoors. This means that the total amount that he earned working indoors is
8 × 16 = $128
Total amount that he earned is
216 + 128 = $344
A high positive correlation is found between college students' age and their GPA. However, if one student aged 44 with a high GPA is omitted from the study, the correlation all but disappears. This is an example of:
Answer:
Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.
Step-by-step explanation:
Previous concepts
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
By definition an outlier is a point "that diverges from an overall pattern in a sample". The residual for this outiler is usually high and when we have presence of outliers our model probably would be not significant since the tendency is not satisfied.
By definition and influential point is a point that has "a large effect on the slope of a regression line fitting the data:. And usually represent values that are too high or low respect to the others.
Solution to the problem
For this case we assume that we have a high positive correlation between college student's age and the GPA.
So we assume that [tex] 0.7 \leq r \leq 1[/tex]
And We see that after introduce the value of 44 for the age the correlation disappears, that means decrease significantly.
Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.
Sam has a total of 40 dvds, movies and tv shows. The number of movies is 4 less then 3 times the number of tv shows. Write and solove a system of equations to find the number of movies and tv shows.
Answer:Sam has 29 movies.
Sam has 11 TV shows.
Step-by-step explanation:
Let x represent the number of movies that Sam has.
Let y represent the number of TV shows that Sam has.
Sam has a total of 40 dvds, movies and tv shows. This means that
x + y = 40 - - - - - - - - - - -1
The number of movies is 4 less then 3 times the number of tv shows. This means that
x = 3y - 4 - - - - - - - - - - -2
Substituting equation 2 into equation 1, it becomes
3y - 4 + y = 40
4y - 4 = 40
4y = 40 + 4 = 44
y = 44/4 = 11
x = 3y - 4 = 3 × 11 - 4
x = 33 - 4
x = 29
By creating a system of equations from the given problem, m + t = 40 and m = 3t - 4, and solving it through substitution, it was determined that Sam has 29 movies and 11 TV shows in his DVD collection.
Explanation:To solve the given problem, we need to use a system of linear equations. The two variables we need to find are the number of movies (m) and the number of TV shows (t).
According to the problem, the total number of DVDs, which includes both movies and TV shows, is 40. This can be written as an equation: m + t = 40. Additionally, we are told that the number of movies is 4 less than three times the number of TV shows. This gives us a second equation: m = 3t - 4.
Now we have the following system of equations:
m + t = 40m = 3t - 4We can solve this system by substitution. First, substitute the second equation into the first equation:
(3t - 4) + t = 404t - 4 = 404t = 44t = 11Now that we have found the number of TV shows (t), we can calculate the number of movies (m):
m = 3t - 4m = 3(11) - 4m = 33 - 4m = 29Therefore, Sam has 29 movies and 11 TV shows in his collection of 40 DVDs.
Jon's dog weighs ( v ) pounds. His cat weighs 21 pounds less than his dog. His bunny weighs 3 pounds less than his cat? What is the weight of Jon's pets?
Answer: the weight of Jon's pet is
(3v - 25) pounds
Step-by-step explanation:
The weight of Jon's dog is v pounds.
His cat weighs 21 pounds less than his dog. It means that the weight of his cat would be
(v - 21) pounds
His bunny weighs 3 pounds less than his cat. It means that the weight of his bunny would be
(v - 21) - 3 = (v - 24) pounds
Therefore, the weight of Jon's pets would be the sum of the weight of his dog, his cat and his bunny. It becomes
v + v - 21 + v - 24 = (3v - 25) pounds.
Final answer:
Jon's pets' total weight is calculated by adding the weight of the dog (v pounds), cat (v - 21 pounds), and bunny (v - 24 pounds), which results in 3v - 45 pounds.
Explanation:
To find the weight of Jon's pets, we start with the known weight of the dog and calculate the other animals' weights based on the given relationships. Jon's dog weighs ( v ) pounds. His cat weights 21 pounds less than his dog, so the cat weighs v - 21 pounds. The bunny weighs 3 pounds less than the cat, which means the bunny weighs (v - 21) - 3 pounds or v - 24 pounds.
Therefore, to find the total weight of Jon's pets, we add the weights of the dog, cat, and bunny together:
Dog's weight: v pounds
Cat's weight: v - 21 pounds
Bunny's weight: v - 24 pounds
The total weight is v + (v - 21) + (v - 24), which simplifies to 3v - 45 pounds.
this my last question and don't know it
Answer:
i am 70% sure its a
Step-by-step explanation: