The rate of change of an edge of the cube is 0.074 m/min.
What is the rate of change of volume of cube?The rate at which the volume of the cube changes is calculated as follows;
dv/dt = 2 m³/min
where;
v is the volume of the cubeThe length of edge of the cube will be denoted with a, and it is related to the volume of cube in the following equation.
v = a³
a = v^¹/₃
where;
a is the length of the edgeThe change in the edge with volume;
da/dv = 1/3 (1/v)^2/3
The change in edge of the cube with time is given as;
da/dt = da/dv . dv/dt
da/dt = 1/3 (1/v)^2/3 x 2 m³/min
da/dt = 1/3 (1/27)^2/3 /m² x 2 m³/min
da/dt = 1/27 x 2 m/min
da/dt = 2/27 m/min
da/dt = 0.074 m/min
Thus, the rate at which the edge of the cube changes with time is smaller compared to the volume.
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The diagram shows a 5 cm x 5 cm x 5 cm cube.
A
B
5 cm
AB=
5 cm
ļ
5 cm
Calculate the length of the diagonal AB.
Give your answer correct to 1 decimal place.
+ cm
Submit Answer
The length of the diagonal AB of the cube is 8.7 cm.
What is the Diagonal of a Cube?A cube's diagonal is a line segment that joins any two of its non-adjacent vertices.Because it has 12 equally spaced edges and is one of the most prevalent forms in our surroundings, the cube is one of the most significant geometric shapes. A cube is a three-dimensional figure, hence it has two different types of diagonals: the face diagonal and the body diagonal.Length of a face diagonal of cube = √2a, where a = Length of each side of a cube.
Length of body diagonal of a cube = √3a, where a = Length of each side of a cube.
Given:
Side length of the cube(a) = 5 cm
We have to find the length of the diagonal AB which is a body diagonal.
Length of Body diagonal(AB) = √3a
Substituting the given value in the formula,
Length of the body diagonal of cube = √3a
⇒ √3a ⇒√3 × 5 = 8.7 cm
Therefore, the length of AB i.e. the body diagonal of the cube is 8.7 cm.
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Alice went shopping for shirts. she purchased 4 blue shirts and 5 yellow shirts. what is the ratio of blue shirts to the total number of shirts that she purchased?
Answer: 4 : 9
Step-by-step explanation:
Total number of blue shirts purchased by Alice = 4
Total number of yellow shirts purchased by Alice = 5
Hence, total number of shirts purchase by her = 4 + 5
= 9
Therefore, Ratio of number of blue shirts to the total number of shirts
[tex]=\frac{Total~number~of~blue~shirts}{Total~number~of~shirts}[/tex]
[tex]=\frac{4}{9}[/tex]
Hence, Ratio = 4 : 9
48. nbc news reported on may 2, 2013, that 1 in 20 children in the united states have a food allergy of some sort. consider selecting a random sample of 25 children and let x be the number in the sample who have a food allergy. then x∼bin(25,.05). a. determine both p(x≤3) and p(x<3). b. determine p(x≥4). c. determine p(1≤x≤3). d. what are e(x) and σx? in a sample of 50 children, what is the probability that none has a food allergy?
The following are the solutions to the given problems by using binomial probability principle:
P(X ≤ 3) = 0.966 and P(X < 3) = 0.873P(X ≥ 4) = 0.034 and P(1 ≤ X ≤ 3) = 0.689σ(X) = 1.090 and P(X = 0) = 0.0769What is defined as the binomial probability?The probability of precisely x successes on n multiple trials in an experiment with two possible outcomes is referred to as binomial probability (called a binomial experiment).If the success probability on an individual trial is p, therefore the binomial probability is: P(x = x) = nCx * p^x * q^(n-x)p = 0.05q = 1 - 0.05 = 0.95n = sample size = 25 children1.) P(X ≤ 3)
P(X ≤ 3) = p(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)
Use a binomial probability calculator :
P(X ≤ 3) = 0.277 + 0.365 + 0.231 + 0.093
P(X ≤ 3) = 0.966
2.) P(X < 3)
P(X < 3) = p(x = 0) + p(x = 1) + p(x = 2)
Use a binomial probability calculator :
P(X < 3) = 0.277 + 0.365 + 0.231
P(X < 3) = 0.873
3.)P(X ≥ 4)
P(X ≥ 4) = p(x = 4) + p(x = 5) +...+ p(x = 50)
Use a binomial probability calculator :
P(X ≥ 4) = 0.034
4.) P(1 ≤ X ≤ 3)
P(1 ≤ X ≤ 3) = p(x =1) + p(x =2) + p(x =3)
Use a binomial probability calculator :
P(1 ≤ X ≤ 3) = 0.365 + 0.231 + 0.093
P(1 ≤ X ≤ 3)= 0.689
D.) σ(X)
E(X) = np = 25 × 0.05
E(X) = 1.25
σ(X) = √(npq)
σ(X) = √(25 × 0.05 × 0.95)
σ(X) = √1.1875
σ(X) = 1.090
E. Probability for none do have food allergy :
P(X = 0) = ⁵⁰C₀ × 0.05^0 × 0.95^50
P(X = 0) = 0.0769
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Pleez help me im stuck
Answer: c
Step-by-step explanation:
A is 190 divided by 125
B is 190 multiplied with 125 (product of the two numbers)
D is the sum of 190 and 125 (addition)
the difference will be found by subtracting the smaller number from the bigger number
HELP PLS HELPP egrhsdjtkfylkfjhtrgthynbvrshtndgvrehtbgd
Answer:
126
Step-by-step explanation:
The area of the top triangle is (6)(6)/2 = 18 square meters.
The area of the bottom rectangle is (9)(12)=108 square meters.
Adding these, we get the total area to be 126 square meters.
NEED ASAP Create a unique table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer.
A table of data for two different linear functions using the same values of x for both functions is shown below:
From the table, it can be seen that when x = -1, the function y = 2x + 7 has a value of 5 and the function y = -x + 4 has a value of 5.
Therefore, the graph of the two functions will intersect at (1, 5)
The temperature drops to -6 in 1 hour. In the next hour it drops to -8. By how much would the temperature have to rise to get to 0?
The babysitter charges $8 per hour plus $4 for gas to come to the house. If the babysitter earned $36, how many hours did the babysitter work?
Answer: The answer should be 3 hours
Step-by-step explanation: 8+4=12, divide the sum by 36: 36÷12=3
She had worked 3 hours.
Charlie can run 4 miles in 28 minutes. If he runs at a constant pace, how long will it take him to run 3
miles? How long will it take him to run 7 miles?
It will take 18 minutes to run 3 miles. For 7 miles, it will take him 42 minutes.
What is unitary method?The unitary method is an approach for issue that involves first calculating the value of a single unit, then multiplying that value to find the required value. a single state. This has an identity element in math, in an algebra. Whose inverse is equivalent to its linear algebra, mathematical study of a matrix or operator,
Given Data
Charlie can run 4 miles in 28 minutes.
To run 1 mile,
4 miles = 28 minutes
1 mile - 6 minutes
For 3 miles,
3 miles = 3(6)
3 miles = 18 minutes
It will take 18 minutes to run 3 miles.
For 7 miles,
7 miles = 7(6)
7 miles = 42
For 7 miles, it will take him 42 minutes.
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I need to find the slope of (-19, -6), (-19, 20)
The entered points belong to a vertical line. There is no slope.
Equation: x = -19.
5a3 x 2b2 x 4a2b5/ 3a2 x 5b3
5a^3 x 2b^2 x 4a^2 x b^5 / 3a^2 x 5b^3 (rewrite)
= 20a^5 x 2b^7 / 3a^2 x 5b^3
= 40a^5 x b^7 / 15a^2 x b^3
= (8/3) x a^3 x b^5
7c+36
5c+40
Find x
X
Answer:
130 degrees
Step-by-step explanation:
When two lines intersect, the opposite angles are equal, therefore, in this example, 7c+36 = 5c+40. We can find c using this equation.
7c+36 = 5c+40
7c-5c = 40-36
2c = 4
c = 4/2 therefore c=2
now that we know c is equal to 2, we can find out both of those angles.
therefore 5c+40 = (5*2)+40 = 10+40= 50
and 7c+36 = (7*2)+36 = 14 +36 = 50
now we know that those two angles add up to 100.
to find the sum of x and the angle opposite to x, subtract 100 from 360
360-100 = 260
since the angle opposite of x is equal to x, x+x = 260
2x=260
x=260/2 = 130
x is 130 degrees
Answer:
x = 130
Step-by-step explanation:
7c + 36 and 5c + 40 are vertically opposite angles and are congruent , so
7c + 36 = 5c + 40 ( subtract 5c from both sides )
2c + 36 = 40 ( subtract 36 from both sides )
2c = 4 ( divide both sides by 2 )
c = 2
Then
7c + 36 = 7(2) + 36 = 14 + 36 = 50
5c + 36 and x are a linear pair and sum to 180° , that is
50 + x = 180 ( subtract 50 from both sides )
x = 130
let x be the hours that Erica babysits. Write an expression to show the total number of hours Erica works each week.
The expression to represent the number of hours Erica babysits each week is 7x .
In mathematics, an expression that was created using integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number) .
However, since they are not produced from integer constants and algebraic operations, transcendental numbers such as such and e are not algebraic. The production of is often done as a geometric expression, but the definition of e requires an infinite number of algebraic operations.A rational expression is one that can be reduced to a rational fraction using the properties of arithmetic operations ( associative properties and commutative properties of addition and multiplication, distributive property and rules for the various operations on the given fractions).Erica works x hours each day and there are 7 days in a week.
Hence Erica works 7x hours in a week
Therefore the expression to represent the number of hours Erica babysits each week is 7x .
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please help i don’t get it and grades are due soon and i need to get this done would be very helpful if you explain it. thank you
The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.
What is the separation between A and B?Except for when the points coincide, distances in geometry are always positive. The distance between points A and B is equal to their respective distances. We take two points A(a,b) and B into consideration in order to calculate the formula for the distance between two points in the plane (c,d).
What is a sample of the distance formula?In coordinate geometry, the distance between two given points is calculated using the distance formula. D=(x2x1)2+(y2y1)2 D = (x 2 x 1) 2 + (y 2 y 1) 2 is the formula for calculating the distance between two points (x1,y1) (x 1, y 1) and (x2,y2) (x 2, y 2).
Say, for instance, that you are asked to determine the distance between two points at ( -6,-2 ) and ( -1,10).
First step:
Give x 1, y 1, x 2, and y 2 their respective assignments.
Consider the cases where (x 1, y 1 ) = ( -6,-2)) and (x 2, y 2 ) = ( -1,-10).
x1 = -6
y1 =- 2
x2 = -1
y2 = 10
Second Step:
Replace in the Distance Formula
Now that we know the numbers for x1, y1, x2, and y2, we can enter them into the Distance Formula.
d = √(-6,-2)² + (-1-10)²
= √(8)² + (11)²
= √16+22
= √38.
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Write the coordinates of the vertices after a translation 7 units left.
B'=
,
C'=
,
D'=
,
E'=,
please help
The coordinates of the images of the vertices of the rectangle are B'(x, y) = (- 4, 2), C'(x, y) = (- 4, 7), D'(x, y) = (0, 7) and E'(x, y) = (0, 2).
What are the coordinates of the images of the vertices of a rectangle
Rectangles are defined by the location of its four vertices set on Cartesian plane, whose images must be found by using a transformation known as translation, whose formula is defined below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Location of the vertex.T(x, y) - Translation vector.P'(x, y) - Location of the image of the vertex.If we know that B(x, y) = (3, 2), C(x, y) = (3, 7), D(x, y) = (7, 7), E(x, y) = (7, 2) and T(x, y) = (- 7, 0), then the images of the vertices are:
B'(x, y) = (3, 2) + (- 7, 0)
B'(x, y) = (- 4, 2)
C'(x, y) = (3, 7) + (- 7, 0)
C'(x, y) = (- 4, 7)
D'(x, y) = (7, 7) + (- 7, 0)
D'(x, y) = (0, 7)
E'(x, y) = (7, 2) + (- 7, 0)
E'(x, y) = (0, 2)
Now we proceed to present the resulting figure.
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Hey guys! please respond asap! thanx
The equation of the line that has a slope of 7 and passes through the point (4, -2) is: y = 7x - 30.
How to Write the Equation of a Line that Passes Across a Point?If we are given a point on a line (x, y), and we know the slope (m) of the line, we can expressed the equation of the line in slope-intercept form as y = mx + b.
Given the following:
Slope of the line, m = 7
A point on the line = (4, -2).
Find the value of b by substituting x = 4, y = -2, and m = 7 into y = mx + b:
-2 = 7(4) + b
-2 = 28 + b
-2 - 28 = 28 + b - 28 [subtraction property of equality]
-30 = b
b = -30
To write the equation of the line, substitute m = 7 and b = -30 into y = mx + b:
y = 7x + (-30)
y = 7x - 30
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Subtract.
−6/7−(−5/7)
Enter your answer in the box as mixed number in simplest form.
Step-by-step explanation:
-1/7 is exact form and Slash or / is division . -0.142857, Decimal form and horizontal line is division too . It is the simplest form .
Solve the following system of equations.
7x +3y= -12
2x -5y= 20
(See picture attached)
Answer:
x = 0, y = - 4
Step-by-step explanation:
7x + 3y = - 12 → (1)
2x - 5y = 20 → (2)
multiplying (1) by 5 and (2) by 3 and adding will eliminate y
35x + 15y = - 60 → (3)
6x - 15y = 60 → (4)
add (3) and (4) term by term to eliminate y
41x + 0 = 0
41x = 0 ⇒ x = 0
substitute x = 0 into either of the 2 equations and solve for y
substituting into (2)
2(0) - 5y = 20
0 - 5y = 20
- 5y = 20 ( divide both sides by - 5 )
y = - 4
please help! will give brainliest!
Answer:
The correct answer is C. On the vertex of Figure A.
Step-by-step explanation:
Before you can find the answer to the question, you must first know what the center of dilation means in math. The center of dilation is a reference point used to appropriately scale the dilation of a figure. The vertex is the the point opposite to and farthest from the base of a geometrical figure, or the common endpoint of the sides of an angle.
Hope that helps! Have an amazing rest of your day!! :)
The population of a town was 980 in 1970. The population has been growing at a rate of 18% each year. What is the population of the town in the year 1995? Round your answer to the nearest whole number.
The population of the town in the year 1995 will be 61415.
How to illustrate the information?From the information, the population of a town was 980 in 1970 and the population has been growing at a rate of 18% each year.
Therefore, it should be noted the difference in the number of years will be:
= 1995 - 1970
= 25 years
Therefore, the population of the town in the year 1995 is:
= 980 × (1 + 18%)^25
= 980 × (1.18)^25
= 980 × 66.6686
= 61415
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Please helppp. 15 pointtts
Answer:
Y = 60x
Step-by-step explanation:
Find the slope by finding Y2 - Y1/X2 - X1, 1 and 2 being two separate points on the graph. 120-0/2 = 6
Enter the Correct 4 Digit Code (no spaces)
The correct 4 Digit Code (no spaces) is 0164 .
In the question ,
the numbers representing the equation are given
to find
the first statement
-C.P-(-K.I)
From the figure we can see that C=2 ,P=7 ,K=5 ,I=4,
hence -C.P-(-K.I) = -2.7-(-5.4) = -14+20 = 6.0 .....(i)
the second statement
E/H + -L/T
From the figure we can see that E=3 ,H=4 ,L=5 ,T=8
hence E/H + -L/T = 3/4 + -5/8 = 3/4 - 5/8 = 1/8 ...(ii)
the third statement
B/W × -N/T
From the figure we can see that B=2 ,W=9 ,N=6 ,T=8
hence B/W × -N/T = 2/9 × -6/8 = -1/6 ...(iii)
the fourth statement
-F/J ÷ -M/V
From the figure we can see that F=3 ,J=5 ,M=6 ,V=8
hence -F/J ÷ -M/V = -3/5 ÷ -6/8 = 4/5 ....(iv)
From equation (i) , (ii) , (iii) and (iv) , we get
-C.P-(-K.I) = 6.0
E/H + -L/T = 1/8
B/W × -N/T = -1/6
-F/J ÷ -M/V = 4/5
the number from the red color lines are 0,1,6,4
hence the code is 0164 .
Therefore , the correct 4 Digit Code (no spaces) is 0164 .
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please help with portion B. thank you
Starting with part a, question (i):
Find the average rate of change in both populations between 2002 and 2012.
Recall that the average rate of change of a function f(x) in the interval [ a, b] is given by the quotient:
rate of change = ( f(b) - f(a) ) / (b - a)
Therefore, for our population P1 case on the years 2002 and 2012 we have:
[ P1(2012) - P1(2002) ] / (2012 - 2002) = [62 - 42] / 10 = 20 / 10 = 2
for population P2 we have:
22 [72 - 82] /10 = -10/10 = -1
You can proceed doing the same process for the other cases (ii) and (iii).
Case (ii)Now part b of the problem:
Rate of change between 2002 and 2019:
99 [ 76 - 42] / ( 17) = 534 / 17 = 2
2(929 9[ 65 - 82] / 17 = -17 / 17 = -1
Case (iii)
Rate of change between 2007 and 2019:
9797 [76 - 52] / 12 = 24/12 = 2
22 [65 - 77] / 12 = -12 / 12 = -1
We see that the rates of change for each population remained constant over the years.
What we noticed in the table regarding both populations, is that while population P1 is increasing over the years, population P2 is going down in numbers year after year.
We can say therefore that P1 is INCREASING, while P2 is DECREASING. And that the rate of change they experienced was constant over the years.
A camera has a listed price of 819.95 before tax. If the sales tax rate is 7.25 , find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
$21.40
Step-by-step explanation:
List price = $19.95
Sales Tax Rate = 7.25%
Total sales tax = 19.95 x 7.25/100 = $ 1.45
Total cost = 19.95 + 1.45 = $21.40
Rationalize the denominator Square root 12+Square root 6/Square root 3+1
Square root 12+Square root 6/Square root 3+1. After Rationalize the denominator we got 4.68.
Given that,
Square root 12+Square root 6/Square root 3+1
We have to Rationalize the denominator.
If the denominator's radical is a square root, multiply by a square root that, when multiplied by the denominator, produces a perfect square beneath the radical.
The square root of a number is the element that, when multiplied by itself, produces the original number. Squares and square roots are examples of special exponents.
[tex]\sqrt{12}+\sqrt{6} /\sqrt{3+1}[/tex]
Square root of [tex]\sqrt{12} is 2\sqrt{3}[/tex]
[tex]2\sqrt{3}+\sqrt{6}/\sqrt{4}[/tex]
Square root of [tex]\sqrt{4} is 2[/tex]
[tex]2\sqrt{3}+\sqrt{6}/2[/tex]
Calculating the terms
3.46+2.44/2
3.46+1.22
4.68
Therefore, After Rationalize the denominator we got 4.68.
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Arranging
A. Arrange the set of integers in increasing order.
1. 3,-4, 1, 10, 9,-3
2. 4,-12, 12, -5, 9, 0, -1
3. -6, 63, -45, -7, -50
4. 6,-10, 4, 1, -67, -1
5. -5, 7, 13,-34, -52, 25, 0
In ascending order the integers are arranged from the left to right of the integer line. The arrangements are shown below.
The arrangement of the set of integers in increasing order is as follows:
-4<-3<1<3<9<10 -12<-5<-1<0<4<9<12 -50<-45<-7<-6<63 -67<-10<-1<1<4<6 -52<-34<-5<0<7<13<25Every positive integer is greater than a negative integer. Zero is less than every positive integer. Zero is greater than every negative integer. The greater the number, the lesser its opposite,i.e., If a and b are two integers such that a>b, then -a<-b.
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Sally’s employer pays for 38% of her annual health insurance premium of $4,350.00. sally pays the remaining balance by having it deducted in equal amounts from her 26 paychecks throughout the calendar year. how much will sally have deducted from each paycheck? a. $63.58 b. $103.73 c. $137.75 d. $207.46 please select the best answer from the choices provided a b c d
By using percentage, the deductible amount is $103.73 for each paycheck. So, option b is correct.
We are provided by some percentage here. A percentage is a part of a whole that is expressed in hundredths.
Sally paid 38% of her annual health insurance premium of $4,350.00 and left with the 62%.
62% of $4,350.00 is equal to $2697
62/100 x 4,350.00 = 2697
So, the net amount that Sally has to pay is $2697 in equal distribution from her 26 paychecks throughout the calendar year.
Therefore, each paycheck will be deducted as = $2697/26
= $103.73
Hence, $103.73 will be deducted from her paycheck.
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How do I make a percent for a number that is not 100
Answer: If you had a fraction, you would have to turn into a decimal, then a percent. You can turn a decimal into a percent by multiplying the decimal by 100 and adding the percent sign. Hopefully this helps!
Answer: Like so:
30 percent of 50...
30/100= 0.30 (percentage)
0.30*50= 15 (discount, deducted amount, etc...)
Subtract answer from original number:
50-15= 35
30% of 50= 15
New amount= 35
Given that x: y = 10:9 and x - y = 122, find the value of x + y.
Answer:
2318
Step-by-step explanation:
[tex] \frac{x}{y} = \frac{10}{9} [/tex][tex]x = \frac{10y}{9} [/tex][tex] \frac{10y}{9} - y = 122[/tex][tex] \frac{10y - 9y}{9} = 122[/tex][tex] \frac{y}{9} = 122[/tex][tex]y = 9 \times 122 = 1098[/tex][tex]x - y = 122 \\ y = 1098 \\ x = 122 + 1098 = 1220[/tex][tex]x + y = 1220 + 1098 = 2318 \\ x + y = 2318[/tex]HELP MEH PLS PLS WIL GIVE BRAINLY OR WTV
Answer:
It would go 3 to the write of x.
Step-by-step explanation:
If B is the 3 spaces to the left of x and T is three spaces to the right of x, x would be in the middle.
In the picture, you have B=2, X= 5
so T goes if X is the midpoint of BT is
X= (B+T)/2
5 x 2= 2+ T
10 = 2+T
therefore, T = 8