The water level increases by 0.608 meters per minute when the water is 3.5 m deep
How to determine the rate?The given parameters are:
Radius, r = 3Height, h = 7Rate in, V' = 4.3m^3/minThe relationship between the radius and height is:
r/h = 3/7
Make r the subject
r = 3h/7
The volume of a cone is;
[tex]V = \frac 13\pi r^2h[/tex]
This gives
[tex]V = \frac 13\pi (\frac{3h}{7})^2h[/tex]
Expand
[tex]V = \frac{3h^3}{49}\pi[/tex]
Differentiate
[tex]V' = \frac{9h^2}{49}\pi h'[/tex]
Make h' the subject
[tex]h' = \frac{49}{9\pi h^2}V'[/tex]
When the water level is 3.5.
We have:
[tex]h' = \frac{49}{9\pi * 3.5^2}V'[/tex]
Also, we have:
V' = 4.3
So, the equation becomes
[tex]h' = \frac{49}{9\pi * 3.5^2} * 4.3[/tex]
Evaluate the products
[tex]h' = \frac{210.7}{346.36}[/tex]
Evaluate the quotient
h' = 0.608
Hence, the water level increases by 0.608 meters per minute
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List all the factors of 66 from least to greatest.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. Out of these factors, the greatest factor of 66. The next highest factor other than 66 is 33. A number which is three more than 33 is 33 + 3 = 36.
The scatter plot shows a correlation between the cost of a helmet and the consumer rating.
The line of regression models that correlation.
Enter a number to complete each statement.
Answer:
1. 65
2. 52
3. 13
Step-by-step explanation:
For these answers, we can look at the graph:
Question 1:
For the helmet that costs 35 dollars, we look at the x-axis until we find the helmet that aligns with 35.
Then, we look at the y-axis and find the blue dot. The blue dot is the actual consumer rating that was recorded, NOT the red line. The red line is the predicted consumer rating in correlation to the price.
Hence, the consumer rating is 65.
Question 2:
For this, we can look back at the graph and apply the same concept as above. Notice how the 65 plot is 13 points away from the point predicted by the red line.
Therefore, 65 - 13 = 52
Question 3:
Just like the last two questions, we can look at the graph for this. The green line gives us this answer flat out, displaying the distance from the actual rating to the predicted rating.
Hence, the actual consumer rating was 13 above the predicted rating.
Which of the following is the graph of y = log3 x - 1
The options are not mentioned , but the correct graph is plotted and attached with the answer.
What is a function ?A function is a mathematical statement that relates a dependent variable with an independent variable .
It is given to find among the options which is the correct graph for
y = log₃ (x-1)
The options are not mentioned , but the correct graph is plotted and attached with the answer.
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Need help finding the quadratic function...15 pts for your help
The function is [tex]y = (x +2)^2 + 5.[/tex]
we use the vertex form of the quadratic equation
We have given a graph,
What is the vertex form of the quadratic equation?y = a(x - h)^2 + k.
Therefore the vertex of the given graph is
See the vertex at (-2, 5)
Since the general way to write the vertex is (h, k), we compare (h, k) to (-2, 5).
[tex]y = a(x - (-2))^2 + 5.\\y=a(x+2)^2+5......(1)[/tex]
Now we have given that (-4,1) use this value in the above equation so we get,
[tex](1)=a(-4+2)^2+5[/tex]
[tex]1=a(-2)^2+5[/tex]
[tex]1=4a+5[/tex]
[tex]1-5=4a[/tex]
[tex]-4=4a[/tex]
[tex]a=-4/4[/tex]
[tex]a=-1[/tex]
Using the value of an in equation (1) we get,
Therefore the function is [tex]y = (x +2)^2 + 5.[/tex]
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Josefin is 32 years younger than Annete. How many years ago was Annetes age twice Josefins age if Annete is 74 now.
Annette's age will be twice Josefin's age 10 years ago.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division
Given that:-
Josefin is 32 years younger than Annette. How many years ago was Annette's age twice Josefins age if Annette is 74 now.
So we can see that their present age Annette is 74 so the present age of Josefin will be 32 years lesser.
J = 74 - 32 = 42 years
The before 10 years ages of both the Josefin and Annettes will be:-
J = 42 - 10 = 32
A = 74 - 10 = 64
The ratio of the ages is:-
A / J = 64 / 32 = 2
A = 2 J
Therefore Annette's age will be twice Josefin's age 10 years ago.
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Tom exercise a total of 150 minutes in two days he exercise 20 minutes less on the first day then on the second day how many minutes did he exercise each day?
Answer:
60 on the first day and 80 on the second
Step-by-step explanation:
the first day was lesser than the second day by 20 minutes.
so the second day was more than the first day by 20 minutes.
Ax^2+bx+c=2(x-1)(2x+3)+(x^2-4x+2)
The quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.
How do we determine the quadratic equation (ax^2+bx+c) from a given set of factors?The quadratic equation that takes the form ax^2+bx+c can be determined from a given set of factors by applying the rule:
a + (b + c) = a + b + cLet us expand the eqaution: 2(x-1) (2x+3)
Ax^2+bx+c = 2(x-1) (2x+3) + x^2-4x+2So, we have:
2(x - 1)(2x + 3) ⇒ 4x² + 2x - 6.
= 4x² + 2x - 6 + x² - 4x + 2
Now, let us group like terms, we have:
= 4x² + x² + 2x - 4x - 6 + 2
= 5x² - 2x - 4
Therefore, we can conclude that the quadratic form ax² + bx + c for the given set of factors is 5x² - 2x - 4.
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Question 1(Multiple Choice Worth 5 points) (04.02 MC) What are the domain and range of the function f of x is equal to the quantity x squared plus 8x plus 7 end quantity divided by the quantity x plus 1 end quantity? D: {x ∊ ℝ | x ≠ 1}; R: {y ∊ ℝ | y ≠ 0} D: {x ∊ ℝ | x ≠ −1}; R: {y ∊ ℝ | y ≠ −6} D: {x ∊ ℝ | x ≠ −7}; R: {y ∊ ℝ | y ≠ 0} D: {x ∊ ℝ | x ≠ −1}; R: {y ∊ ℝ | y ≠ 6}
The domain and the range of the function is (d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}
The complete questionWhat are the domain and range of the function f(x) = x^2 + 8x + 7/x + 1
The domain of the functionWe have the function to be
[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]
Set the denominator to 0
x + 1 = 0
Solve for x
x = -1
This means that the domain of the function is the set of all real numbers except -1
Hence, the domain of the function is {x ∊ ℝ | x ≠ -1}
The range of the functionWe have the function to be
[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]
Factorize the numerator
[tex]f(x) = \frac{(x + 1)(x + 7)}{x + 1}[/tex]
Simplify
f(x) = x + 7
The function is undefined at x= -1.
So, we have:
f(-1) = -1 + 7
f(-1) = 6
This means that the range of the function is the set of all real numbers except 6
Hence, the range of the function is {y ∊ ℝ | y ≠ 6}
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Answer:
It is d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}
Step-by-step explanation:
I took the test
1 If the population of a town increases by 280 people per year, then the growth is LINEAR (or constant). If the population in 2022 is 120,500, then what will the population be in 2023?
The population in the year 2023 is 120,780.
The growth is linear hence, the equation of the growth is
y=ax+b where b represents the initial population and a is the number of people growing yearly.
So, according to the question statement, we have that
y=280x+b where x is the number of years past and y is the population in the xth year.
According to the given problem population in 2022 will be 120,500.
Suppose that the initial population is taken at 2000.
Hence, 120,500=280×(2022-2000)+b
⇒b=120,500-280×22
⇒b=120,500-6,160
=114,340
So, the Linear equation becomes
y=280x+114,340
⇒y=280×(2023-2000)+114,340
⇒y=120,780
Hence, the population in the year 2023 is 120,780.
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What is the solution to the inequality StartFraction d Over 7 EndFraction + 4 ≤ 0? (–∞, –28) (–∞, –28] (28, ∞) [28, ∞)
The solution to the inequality d / 7 + 4 ≤ 0 will be (–∞, –28]. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality equation is given below.
d / 7 + 4 ≤ 0
By simplifying the equation, we have
d / 7 ≤ – 4
d ≤ – 28
Then the value of d must be less than or equal to the negative 28.
Then the correct option is B.
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Review the graph.
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point A is (1, negative 2), B is (1, negative 6), C is (9, negative 2), D is (9, negative 6), z 1 is (3, negative 4), and z 2 is (negative 4, 1).
Which expression is the result of subtracting (z2 – 3i) from (z1 + 2)?
A
B
C
D
[tex]z_{2}-3i=(-4+i)-3i=-4-2i\\\\z_{1}+2=(3-4i)+2=5-4i\\\\(z_{1}+2)-(z_{2}-3i)=(5-4i)-(-4-2i)=9-4i+4+2i=9-2i[/tex]
which corresponds with point C
The expression which is the result of subtracting (z2-3i) from (z1+2) is 9-2i.
Given On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point A is (1, -2), B is (1, -6), C is (9,- 2), D is (9, - 6), z 1 is (3, - 4), and z 2 is (- 4, 1).
Coordinate plane is a two dimensional plane formed by the intersection of two number lines. One is horizontal line and one is vertical. On horizontal line x values are denoted and on vertical line y values are written. There can be three dimensional plane also.
z2-3i=(-4+i)-3i=-4-2i
z1+2=(3-4i)+2=5-4i
(z1+2)-(z2-3i)=(5-4i)-(-4-2i)
=9-4i+4+2i
=9-2i
Hence for the expression (z1+2)-(z2-3i)=9-2i
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Write an expression to represent:
The sum of 5 and the quotient of a
number x and 2
O 2x + 5
O 2/x - 5
O x/2 + 5
Answer:
Step-by-step explanation:
2/x-5
Algebra 2 help please
Blank 1: 3
Blank 2: 27
Blank 3: 21
you have to distribute the three to everything inside the parenthesis, and because it's directly in front of the parenthesis it's being multiplied.
3(x - 9) = 3x - 27
Now you need to isolate the y, in this e ample you need to add 6 to both sides
the final equation should be:
y = 3x - 21
Arturo worked a 40-hour week at $12 per hour. He then received a raise of $1 per hour and worked a 30-hour week. How much more money did he receive for the first week of work than the second?
Arturo receives $90 more in the first week of work than the second.
What are Working Hours?The time a person spends engaged in compensated work is referred to as working time.
Given,
First Week Working hours = 40 hours, per hour rate = $12
The second-week working hours = 30, per hour rate = $13 (With raise of $1)
Calculation of Wages
First Week wages = Total Weekly Hours × Per Hour rate
= 40 × 12 =$480
Second Week wages = Total Weekly Hours × Per Hour rate
= 30 × 13 =$390
The difference between the First week's wages and the Second week's wages is $90 ($480 - $390).
Thus, Arturo earn $90 more in the first week as compared to the second week.
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Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
The best buy is (d) a 9 oz box of rice $1.25
How to determine the best buy?The best buy is the product that has the least unit rate.
The unit rate is calculated as:
Unit = Price/Weight
So, we have:
Box 1:
Unit rate = $0.90/6 oz = $0.150 per oz
Box 2:
Unit rate = $1.93/12 oz = $0.161 per oz
Box 3:
Unit rate = $2.42/16 oz = $0.151 per oz
Box 4:
Unit rate = $1.25/9 oz = $0.139 per oz
The least unit price is $0.139 per oz for box 4
Hence, the best buy is (d) a 9 oz box of rice $1.25
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A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (-4, 0) and (6, 0). The y-intercept
of the first parabola is (0, -12). The y-intercept of the second parabola is (0, -24). What is the positive difference
between the a values for the two functions that describe the parabolas? Write your answer as a decimal rounded to
the nearest tenth.
Answer:
1/2
Step-by-step explanation:
First parabola f(x1) = a ( x+4)(x-6) use point 0,-12 to find a = 1/2
= 1/2 (x+4)(x-6)
Second parabola a ( x+4) (x-6) using point 0, -24 shows a = 1
f(x2) = (1)(x+4)(x-6)
Difference between the 'a' values = 1 - 1/2 = 1/2
Determine the values of x and y.
Answer: x = 130, y = 130
Step-by-step explanation:
By the corresponding angles theorem, x = 130
Thus, by the vertical angles theorem, y = 130
Katie divided a drink with a volume
of 3½ cups into ½ cup servings.
How many servings did she have?
Answer:
Step-by-step explanation:
she has 7 servings. Add 1/2 + 1/2 until you get 3 1/2 and it equals 7
Find the acute x given that tan x=2sinx
The measure of the acute angle is 60 degrees
Trigonometry identityGiven the following trigonometry equation
tan x=2sinx
This can also be written as;
sinx/cosx=2sinx
Simplify to have:
1/cosx =2
2cosx = 1
cosx = 1/2
x = arccos(1/2)
x = 60 degrees
Hence the measure of the acute angle is 60 degrees
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What are the factors of this quadratic function?
Answer:
(x-1) and (x-5)
Given f(x) = 8x+1 2x-9 O As x-00, f(x) → 9; as x → ∞o, f(x) → 9. -> - O As x-00, f(x) O As x-00, f(x) O As x-00, f(x) - - what is the end behavior of the function? ->> -9; as x -4; as x ∞o, f(x) → -9. - ∞o, f(x) → -4. - 4; as x → ∞o, f(x) → 4. -> - Given f ( x ) = 8x + 1 2x - 9 O As x - 00 , f ( x ) → 9 ; as x → ∞o , f ( x ) → 9 . - > - O As x - 00 , f ( x ) O As x - 00 , f ( x ) O As x - 00 , f ( x ) - - what is the end behavior of the function ? - >> -9 ; as x -4 ; as x ∞o , f ( x ) → -9 . - ∞o , f ( x ) → -4 . - 4 ; as x → ∞o , f ( x ) → 4 . - > -
Answer:
D
After graphing, you can analyze it accordingly.
The following confidence interval is'obtained for a population proportion p: 0.87 < p < 0.93 What is the margin error E. The following confidence interval is'obtained for a population proportion p : 0.87 < p < 0.93 What is the margin error E.
The margin error of the confidence interval 0.87<p<0.93 is 0.03.
Given confidence interval 0.87<p<0.93.
We have been given the confidence interval 0.87<p<0.93 and we have to find out the margin error E. The margin error is a statistic expressing the amount of random sampling error in the results of a survey. The margin error depends on whether the problem is two tailed or half tailed but in this question we have not given whether it is two tailed or one tailed. The margin error is the half of the width of the confidence interval.
Confidence interval is 0.87<p<0.93.
Width of the interval= 0.93-0.87
=0.06
=0.03
Hence the margin of error is equal to 0.03.
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Val's whole-house central air conditioner uses 3,000 watts when running. Val runs the AC 8 hours per summer day. Electricity costs (18 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
Step-by-step explanation:
3x8=24
24x30=720
720÷18=40 cents
The size of a mumps virus is
approximately 0.000 000 19 metres.
What is this value in standard form? Give
your answer in metres (m).
Answer:
[tex]1.9 \times {10}^{7} meters[/tex]
is the right answer
Solve the following system of equations and show all work.
y = 2x2
y =
3x -1 (10 points)
Answer: [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]
Step-by-step explanation:
We have [tex]y=2x^{2}[/tex] and [tex]y=3x-1[/tex].
Since both of the equations are set equal to y, we can conclude that:
[tex]2x^2 = 3x-1\\\\2x^{2}-3x+1=0\\\\(2x-1)(x-1)=0\\\\x=\frac{1}{2}, 1[/tex]
If [tex]x=\frac{1}{2}[/tex], then [tex]y=3\left(\frac{1}{2} \right)-1=1[/tex]
If [tex]x=1[/tex], then [tex]y=3-1=2[/tex]
Therefore, the solutions are [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]
The rectangular prism has a vertex at (5, 6, 2). Which
ordered triples represent other vertices of the prism?
Check all that apply.
(0, 0, 2)
(0, 5,6)
(2,0, 5)
(5, 0, 2)
(5, 6, 0)
(6,2,0)
Answer:
A, D, E
Explanation:
It's right on edge lol
Thalia, a quiz show contestant, answered 20 questions. She was awarded 2 points for every correct answer that she gave, but she was penalized 1 point for every incorrect answer. In the end, Thalia had a total of 28 points. In order to determine the number of correct and incorrect answers that she gave, a viewer at home used the system of linear equations x + y = 20 and 2 x + y = 28, with x being the number of correct answers and y being the number of incorrect answers. The viewer solved the system by using the linear combination method as shown.
x + y = 20. + StartFraction Negative 2 x minus y = negative 28 over Negative x = negative 8 EndFraction. StartFraction negative x Over negative 1 EndFraction = StartFraction negative 8 Over negative 1 EndFraction. X = 8.
8 + y = 20. 8 + y minus 8 = 20 minus 8. y = 12.
The viewer calculated that the contestant answered 8 questions correctly and 12 questions incorrectly. What went wrong?
The viewer mistakenly determined that one of the equations in the system should be x + y = 20.Instead modifications should have been made before applying the equation.
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.
The viewer multiplied the equation 2 x + y = 28 by –1 incorrectly.
The viewer added the equations x + y = 20 and Negative 2 x minus y = negative 28 incorrectly.
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28. Instead modifications should have been made before applying the equation.
What is an Equation ?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
Total Questions = 20
Total Points = 28
Correct Answers = +2 points
Incorrect Answers = -1 point
The viewer represents the correct answers with x and the incorrect ones with y.
x+y = 20
for every correct answers 2 points;
and for every incorrect answers, -1 point
This can be written as
2x-y = 28
The viewer's mistake is that; instead of subtracting total incorrect points from the correct points, the viewer added them together;
now
2x-y = 28
x+y = 20
On adding the equations
]3x = 48
x = 16
y = 4
This means that the contestant answered 16 questions correctly and 4 questions incorrectly
The viewer mistakenly determined that one of the equations in the system should be 2 x + y = 28.
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A $96 gadget is discounted 2/5 off the normal price. Find the discounted price.
Answer:
$57.60
Step-by-step explanation:
2/5 = 0.4
0.4*96 is 38.4
96-38.4 = 57.6
The gadget is discounted $38.40 off the original price of $96 and now costs $57.60
urgent help algebra 2
How much extra snow would a child need to take a snowball with a diameter of 8 cm and increase its size to a snowball with a diameter of 12 cm?
The amount of the extra snow would a child need to take a snowball will be 636.71 cubic cm.
What is the volume of the sphere?Let d be the diameter of the sphere.
Then the volume of the sphere will be
V = 1/6 πd³ cubic units
Then the amount of the extra snow would a child need to take a snowball with a diameter of 8 cm and increase its size to a snowball with a diameter of 12 cm will be
Amount of snow = 1/6 π x 12³ - 1/6 π x 8³
Amount of snow = 288 π - 85.33π
Amount of snow = 636.71 cubic cm
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