Answer:
b=4
Step-by-step explanation:
[tex]a^{2}+b^{2}=c^{2}[/tex]
[tex]3^{2}+b^{2}=5^{2}[/tex]
[tex]9+b^{2}=25[/tex]
[tex]b^{2}=16[/tex]
[tex]\sqrt{b^{2}} = \sqrt{16}[/tex]
b=4
A rectangle has a width w inches and a height h inches where the width is twice the height
The expression for the rate of change of A with respect to t is dA/dt = 4h * dh/dt in²/s. Option D
How to determine the valueThe formula for calculating the area of a rectangle is expressed as:
A = wh
Given that;
h represents the variable for the heightw represents the variable for the widthFrom the information given, we have that;
If the width is twice the height
This is represented as;
w = 2h
Then, substitute the values into the formula for area of a rectangle
A = (2h)h
A = 2h²
Then, the rate of change of area will be expressed as;
dA/dt
Take the differentiation
dA/dt = dA/dh × dh/dt
dA/dt = 4h * dh/dt in²/s
Hence, the rate is dA/dt = 4h * dh/dt in²/s
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The complete question:
A rectangle has width w inches and height h inches, where the width is twice the height. Both w and h are functions of time t, measured in seconds. If A represents the area of the rectangle, which of the following gives the rate of change of A with respect to t ?
A. dA/dt=4h in/sec
B. dA/dt=3h dh/dt in^2/sec
C. dA/dt=4h dh/dt in/sec
D. dA/dt=4h dh/dt in^2/sec
If a train is accelerating at 30m/s after it takes off from the train station and travels for 60 seconds, what was its final velocity?
The final velocity of the train is 30m/s.
What is acceleration?The rate at which an object's velocity with respect to time changes is referred to as acceleration. When an object's velocity changes, it is said to have or be accelerating.
The rate of change in velocity over time is another name for acceleration. The magnitude of an acceleration vector indicates how much the velocity will change, while the vector's direction indicates how the velocity will change—whether the speed is rising or falling, the vector's direction is changing, or some combination of the three.
Given, initial velocity = 0 m/s (as the train starts from rest)
time = 60 seconds
Acceleration = v - u / t = 30 - 0/ 60 =0.5 m/s square
We know,
v = u + at
v = 0 + (0.5 x 60)v = 30 m/s
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Change the given form into the decimal form. 7 1/4 %
We know that,
With the help of example,
5/3
Numerator= number of equal parts of remaining
Denominator=total number of equal parts.
According to question.
Given data in the question,
Multiply the whole number by the denominator.
7×4=28………………. (1)
Adding 1 in numerator
28+1=29
Divide by 4 in denominator
29 divided by 4
7.25
the decimal form of 7 1/4% is 7.25
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After changing 7 1/4 percent into decimal we get, 7.25.
What is decimal?In mathematics, decimals can be used as an alternative to fractions. You can express a fraction in decimal form, such as 0.5, rather than writing it out as 1/2, with zero in the place of the one and five in the place of the ten. Decimus, which means tenth in Latin, is the root of the word decimal. The decimal system is also known as a base-10 system because it uses 10 as its fundamental unit.
Decimal refers to any number in the decimal system. They are employed in the expression of both whole numbers and fractions. A "." (known as a decimal point) is inserted to demarcate the whole number from the fraction. The space between the digit in the ones place and the digit in the tenth place is known as the decimal point, and it serves as the separator between them.
Given that 7 1/4 %
in proper form it will be written as
=(7×4)+1 /4
= 29/4
now dividing 29 by 4 we get
7.25
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2. JOY leather, a manufacturer of leather Products, makes three types of belts A, B and C which are processed on three machines M1, M2 and M3. Belt A requires 2 hours on machine (M1) and 3 hours on machine (M2) and 2 hours on machine (M3). Belt B requires 3 hours on machine (M1), 2 hours on machine (M2) and 2 hour on machine (M3) and Belt C requires 5 hours on machine (M2) and 4 hours on machine (M3). There are 8 hours of time per day available on machine M1, 10 hours of time per day available on machine M2 and 15 hours of time per day available on machine M3. The profit gained from belt A is birr 3.00 per unit, from Belt B is birr 5.00 per unit, from belt C is birr 4.00 per unit. What should be the daily production of each type of belt so that the profit is maximum?
a) Formulate the problem as LPM
b) Solve the LPM using simplex algorithm.
c) Interpret the shadow prices
The shadow price of a constraint, the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.
What are constraints?A constraint is a condition of an optimization problem that should be satisfied the condition.
We can formulate this problem as a linear programming model (LPM):
Suppose X1 be the number of belt A produced per day, X2 be the number of belt B produced per day and X3 be the number of belt C produced per day
The objective function is to maximize the profit;
3X1 + 5X2 + 4X3.
The constraints are as :
The time spent on machine M1 must be less than or equal to 8 hours per day so we get;
2X1 + 3X2 <= 8
The time spent on machine M2 must be less than or equal to 10 hours per day so we get;
3X1 + 2X2 + 5X3 <= 10
The time spent on machine M3 must be less than or equal to 15 hours per day so we get
2X1 + 2X2 + 4X3 <= 15
Thus number of belts produced must be positive:
X1, X2, X3 >= 0
To solve this LPM using the simplex algorithm,
Also the objective function is to minimize the cost, and all constraints are in the form of "less than or equal to" a certain value.
The pivot row is the row that corresponds to the smallest positive ratio between (RHS) value and the corresponding pivot column element the constraint 2X1 + 3X2 ≤ 8.
Now Interpret the shadow prices.
The shadow price of a constraint is the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.
Here the value of the constraints in the LPM and how they contribute to the optimal solution.
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Nick owns 500 shares in a manufacturing company. The company pays a dividend of $1.05 per share. The shares currently trade for $15.00 in the stock market. What is the current dividend yield on Nick's investment?
Mr. Jones’ doctor told him that he should not be active until he had 50 mg or less of the medicine left in his body. How long did it take for Mr. Jones to be able to be active? Give your answer to the nearest tenth (0.1) of an hour.
Without more information, it is not possible to determine how long it took for Mr. Jones to have 50 mg or less of the medicine left in his body. Factors such as the type of medicine, the dosage Mr. Jones was taking, and his metabolism can all affect the amount of time it takes for the medicine to be metabolized and eliminated from his body. It is important for Mr. Jones to follow the instructions given to him by his doctor and to consult with his doctor if he has any questions or concerns.
30 POINTS The width of a rectangle is 4 inches shorter than its length. If the length of the rectangle is 7 inches, write and solve an addaition equation to find the width of the rectangle
(b) What should be added to the sum of 18x + 19y and 13xy + 12x to get 17xy-11y
Answer:
4xy - 30y - 30x
Step-by-step explanation:
Lets say a=answer
Solve for a:
(18x + 19y) + (13xy + 12x) + a = 17xy-11y
18x + 19y + 13xy + 12x + a = 17xy-11y
18x + 12x + 19y + 13xy + a = 17xy-11y
30x + 19y + 13xy + a = 17xy-11y
30x + 19y-19y + 13xy + a = 17xy-11y - 19y ==> subtract 19y on both sides
30x + 13xy + a = 17xy-30y
30x + 13xy-13xy + a = 17xy-13xy-30y ==> subtract 13xy on both sides to
isolate a
30x + a = 4xy-30y
30x - 30x = 4xy - 30y - 30x ==> subtract 30x on both sides to isolate a
a = 4xy - 30y - 30x ==> simplify
the line of best fit is given as y = 9 - 3x. Find the value of y when x = -3.
Answer:
y = 18
Step-by-step explanation:
⭐Substitute the given x-value into the line of best fit
[tex]y = 9-3x[/tex]
[tex]y = 9-3(-3)[/tex]
[tex]y = 9 +9[/tex]
[tex]y = 18[/tex]
Answer:18
Step-by-step explanation:
9-3(-3)=18
which of these graphs does not show a valid probability distribution? choose 1 answer: choose 1 answer:
The graph that does not show a valid probability distribution is option A.
Probability distribution refers to the mathematical function that provides the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events. In order to determine if a probability distribution is valid, there are two criteria that must be checked. First determine whether each probability is greater than or equal to 0 and less than or equal to 1. Secondly, determine whether the sum of all of the probabilities equals 1. If both the conditions are true, then the probability distribution is valid, otherwise, the probability distribution is not valid. Based on the provided graphs, the first condition is met for all but the second condition is untrue for option A as the sum of probability is less than 1. Hence it is not a valid probability distribution.
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A gamer is observing her acore, y, as she plays a video game. She currently has 4,200 points and is gaining 250 points for every minute, x, she plays.
Which of the following equations can be used to describe this linear relationship
A. y = 250x - 4,200
B. y = 250x + 4,200
C. y = 4,200x - 250
D. y = 4,200x + 250
Find the infinite sum of the geometric sequence with a = 4 , r = 4/6 if it exists.
Answer:
Step-by-step explanation:
The infinite sum of a geometric sequence is given by the formula:
S = a / (1 - r)
where a is the first term of the sequence and r is the common ratio. In this case, a = 4 and r = 4/6 = 2/3. Plugging these values into the formula above, we get:
S = 4 / (1 - 2/3) = 4 / (1/3) = 4 * 3 = 12
Therefore, the infinite sum of the geometric sequence with a = 4 and r = 2/3 is 12.
PLEASE HELP
Shalane wants to open a snow cone shop in Panama City, Florida, but does not know if she should keep her shop open all year round, or just for a portion of the year. She decides to collect data on the relationship between the temperature outside and snow cone sales in Panama City in order to decide if her shop should remain open in the winter months. A scatter plot with a line of best fit that was generated with technology is shown.
The equation for the line of best fit in the slope and the intercept form is given as y₁ = 1.91944X₁ - 65.8518
What is the line of best fit?A straight line that minimizes the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.
y₁ = mX₁ + b
we have m = 1.91944
b = -65.8518
The question requires us to fill in the values that we have into the corresponding equation.
We will have
y₁ = 1.91944X₁ + (-65.8518)
y₁ = 1.91944X₁ -65.8518
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1
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
The diagram represents the design of a triangular-shaped photo frame. Match the segments and angles to the descriptions.
B
58°
82°
ZC
ZB
AC
C
ZA
AB
shortest side
longest side
smallest angle
BC
The description and measure of the segments and angles of the triangular-shaped photo frame, found using the triangle inequality theorem are;
Shortest side → ABLongest side → BCSmallest angle → ∠CLargest angle → ∠AWhat is the triangle inequality theorem?According to a triangle inequality theorem, the measure of the lengths of sides opposite angles of different measure, are also different and the the longest side of a triangle is opposite the largest angle of the triangle.
The interior angles of the photo frame are;'
∠B = 58°, ∠A = 82°
The angle sum property of a triangle indicates that we get the angle ∠C as follows;
∠C = 180° - 58° - 82° = 40°The triangle inequality theorem indicates that the measure of the angles opposite sides that have different lengths are also different, such that the larger angle is opposite the larger side.
According to the triangle inequality theorem, we get;
The shortest side is opposite the smallest angle, which is the angle ∠C = 40°
The side opposite ∠C is AB, therefore, the shortest side is AB
The longest side is opposite the largest angle, which is angle ∠A = 82°.
The side opposite the angle ∠A is BC, therefore, the longest side is BC
The smallest angle is the angle ∠C = 40°
The largest angle is the angle ∠A = 82°
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buddy eats 3 cotton balls out of the 48 that are in the jar. what percentage has buddy eaten?
Answer: 6.25%
Step-by-step explanation:
You can set up a proportion:
[tex]\frac{3}{48}=\frac{x}{100}[/tex]
100 x 3 = 300
300/48 = 6.25
Which statement about the figure MUST be true?
Answer:
The figure is an an isosceles triangle
The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are
n=10, n=20, and n=100,
which value of n should the player choose in order to maximize the probability of winning a prize?
a. n=10 only
b. n =20 only
c. n = 100 only
d. n =10 or n =20 only; the probabilities are the same.
e. n=10 or n=20 or n=100 ; the probabilities are the same.
The probability of winning a prize remains the same for,
e. n = 10 or n=20 or n = 100; the probabilities are the same.
What is the binomial theorem on probability?In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment).
From the information we get,
p = 0.5, So, q = 1 - 0.5 = 0.5.
If 70% of 'n' games are won then 30% of n games must be lost.
Let n = 10.
∴ [tex]P(x = 3) = ^{10}C_3p^7q^3[/tex].
[tex]P(x = 3) = ^{10}C_3(0.5)^7(0.5)^3[/tex].
P(x = 3) = 120×0.0078×0.125.
P(x = 3) = 0.117 Or 11.7% chance.
Now, Changing the value as all the 'n's are multiple of 10 and we'll have the same probability.
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did i answer this correctly
a survey of adults found that 7% say thier favorite sprt is auto racing out of 500 adults what is the probability that the number of people who say auto racing is their favorite sport is a most 41
Answer:
Step-by-step explanation:
let days-on-the-market be the dependent variable and price be the independent variable. b-1. determine the regression equation
To determine the regression equation, we need to fit a line to the data that best describes the relationship between the dependent variable and the independent variable. The equation of the line is typically expressed in the form:
y = a + bxwhere y is the dependent variable, x is the independent variable, a is the y-intercept (the point at which the line crosses the y-axis), and b is the slope of the line (the rate of change of y with respect to x).
If we determine that a = 10 and b = 0.5, the regression equation would be:
Days-on-the-market = 10 + 0.5 * priceThis equation describes the relationship between the dependent variable (days-on-the-market) and the independent variable (price). It tells us that for every unit increase in price, the number of days on the market is expected to increase by 0.5.
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Clarence made a block of scented soap which weighed 2/3 of a pound. He divided the soap into 2
equal pieces. How much did each piece of soap weigh?
Three sets of two-thirds can be created since each whole produces a two-thirds and one half of another two-thirds.
How much the each piece of soap weigh ?The number 0.666 is 2/3 in decimal notation.Consequently, there are a total of 5 components to distribute. (2+3=5) Consequently, you divide the value you want to share by five.Consequently, there are a total of 5 components to distribute. 2 + 3 = 5, therefore you divide the value you want to distribute by 5.
The two most frequent splits are 2-for-1 and 3-for-1, meaning that a stockholder receives two or three shares, respectively, for each share they currently own. When a corporation divides the number of shares that stockholders own, the market price rises in proportion.
Sixteen twenty-fourths (16/24) is a fraction that is equal to two thirds (2/3).
He cut the soap into two equal pieces, making it weigh 0.333333333 pounds.
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May I have help on question 3 please I’ll give you brainliest
Answer:
B
Step-by-step explanation:
Dont think you need this
There are three (3) different sections to sit at a stadium.The number if people who can sit in each section is described below.
~ Red section seats 200 people
~ Blue section seats 20 fewer people than the red section
~ Green section seats 2 times as many people as the blue section
What is the total number of people who can sit in the stadium when it is full?
How did you get an answer?
Answer:
Therefore, when the stadium is full, a total of 740 people can sit in the three sections.
Step-by-step explanation:
The red section seats 200 people.
The blue section seats 200 - 20 = <<200-20=180>>180 people.
The green section seats 180 * 2 = <<180*2=360>>360 people.
The total number of people who can sit in the stadium is 200 + 180 + 360 = <<200+180+360=740>>740 people.
Step-by-step explanation:
this is a college level question ?
and you don't know how to do this (because doing this yourself would have been much faster than posting the question and looking for the answer here) ?
oh my ...
red = 200
blue = red - 20 = 200 - 20 = 180
green = 2×blue = 2×180 = 360
total number = 200 + 180 + 360 = 740
What are the values of } a and b ?
a=
b=
The values of a and b in the given triangle are;
a = 59° and b = 6
What is the value of the missing angle?
From the given image, it is clear that in Triangle YVW that we have;
YV = WV
Now, a triangle that has two sides equal is referred to as an Isosceles triangle which means that the two base angles are equal. Thus;
∠Y = ∠W = 31°
Now, the sum of angles in a triangle is 180° and as such;
∠YVW = 180 - 2(31)
∠YVW = 118°
Since VX is perpendicular to YW and so;
a = 180 - (90 + 31)
a = 59°
Thus; ∠WVX = 59°
This means that WX = YX = 6
Thus, b = 6
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A basket contained 4 times as many blue balls as red balls. After 21
blue balls were taken away, there were twice as many red balls as blue
balls. How many balls were there in the basket at first?
The number of balls in the basket at first is 35.
How to find the number of balls in the basket?A basket contained 4 times as many blue balls as red balls.
Therefore,
let
x = red balls
Hence,
number of blue balls = 4x
After 21 blue balls were taken away, there were twice as many red balls as blue balls.
2(4x - 21) = x
8x - 42 = x
subtract 8x from both sides of the equation
8x - 42 = x
8x - 8x - 42 = x - 8x
-42 = - 7x
divide both sides by -7
x = -42 / -7
x = 6
Therefore,
red balls = 7
blue balls = 4(7) = 28
Total balls = 35
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Answer:
35
Step-by-step explanation:
don't ask
A piece of art is in the shape of a rectangular pyramid like the figure shown.
How much glass is needed to cover the entire pyramid?
A: 102.53 ft2
B: 144.53 ft2
C: 198.06 ft2
D: 289.06 ft2
The area of the given pyramid will be 144.53 ft² thus option (B) is correct.
What is a pyramid?With a base that is a polygon and sides that are three or more triangles that converge at the top.
A pyramid is a three-dimensional object in which three triangles intersect in such a way that the base side becomes a triangle.
As per the given pyramid,
Total surface area = 2 x(1/2)6 x 8 + 2 x (1/2)7 x 7.79 + 7 x 6
Total surface area = 24 + 27.265 + 42 = 144.53 ft²
Hence "The supplied pyramid will have a surface area of 144.53 feet²".
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Based on the data shown in the graph, how many hours will it take the shipping company to pack 180 boxes
Step-by-step explanation:
I need the graph but it could be 216
DUE SOON! PLEASE HELP!
Answer:
A or C, but A is my guess.
Step-by-step explanation:
Answer:
A.) The sum will be an even integer.
Step-by-step explanation:
The conjecture that can be made about the sum of two even integers and one odd integer is that the sum will be an even integer. This is because even integers are numbers that are divisible by 2, and odd integers are numbers that are not divisible by 2.
For example, consider the sum of the even integer 6 and the odd integer 7. The sum of these two numbers is [tex]6 + 7 = 13[/tex], which is an odd integer. However, if we add another even integer to the sum, such as 4, the resulting sum is [tex]13 + 4 = 17[/tex], which is an even integer. This shows that the sum of two even integers and one odd integer is always an even integer.
This conjecture can be proven using mathematical induction. We can start by showing that the sum of any two even integers and one odd integer is always an even integer. Then, we can assume that the sum of any n even integers and one odd integer is also an even integer. Finally, we can show that the sum of n+1 even integers and one odd integer is also an even integer, using the assumption that the sum of n even integers and one odd integer is even. This will prove that the conjecture is always true.
Find the y-intercept of the line: 2x−5y+7=0
Answer:
Below
Step-by-step explanation:
Arrange the given equation into y = mx + b form of a line
'b' is the y-axis intercept
2x-5y+7 = 0
5y = 2x+7
y = 2/5 x + 7/5
Answer:
(0, 7/5)
Step-by-step explanation:
What is a dominate number?