The weight of the smallest rectangular block is 1400 pounds.
What is density?The density refers to the heaviness of an object. It is the ratio of mass to volume.
Then we have
Density = Mass / Volume
A sculptor is planning to order a rectangular block of composite stone to sculpt a lion.
The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet.
The composite stone weighs 40 pounds per cubic foot.
To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.
Then the weight of the smallest rectangular block will be
Mass = density x volume
The volume will be
V = 5 x 2 x 3.5
V = 35 cubic feet
Then the weight will be
Mass = 40 x 35
Mass = 1400 pounds
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Solve by using Vertical Velocity model: h=-16t^2+vt+s
Where v = velocity
s = starting height
h = ending height
t = time
You can ignore the previous work, just solve B and C. Just there for context
USE VERTICAL VELOCITY MODEL FORMULA.
An equation that models the height of the ball as a function of time t is; h(t) = -16t² + 40t + 3. The maximum height that the ball will reach is 28 ft
How to Solve the Vertical velocity model?We are given the equation for the vertical velocity model as;
h = -16t² + vt + s
Where;
v = velocity
s = starting height
h = ending height
t = time
A) From the question, we have;
v = 40 ft/s
s = 3 ft
Thus, the equation is;
h = -16t² + 40t + 3
B) To find the time that the ball reaches its maximum height, we will equate the height equation to zero and find the roots. Thus;
-16t² + 40t + 3 = 0
Using an online quadratic equation calculator gives;
t = 2.573 s
C) The maximum height that the ball will reach is;
h'(t) = -32t + 40
At h'(t) = 0;
-32t + 40 = 0
32t = 40
Thus;
t = 1.25 s
Max height = -16(1.25)² + 40(1.25) + 3
Max height = 28 ft
D) The height of the ball after 2 seconds is;
h(2) = -16(2)² + 40(2) + 3
h(2) = 19 ft
E) Time for the ball to hit the ground is;
T = 2 * 2.573
T = 5.146 s
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assume that y varies inversely with x. If y= 1.6 when x= 0.5, find x when y= 3.2
Answer:
x = 0.25
Step-by-step explanation:
If y varies inversely with x, then:
[tex]y \propto \dfrac{1}{x} \implies y=\dfrac{k}{x} \quad \textsf{(for some constant k)}[/tex]
Given:
y = 1.6 when x = 0.5Substitute the given values into the found equation and solve for k:
[tex]\implies 1.6=\dfrac{k}{0.5}[/tex]
[tex]\implies k=1.6(0.5)[/tex]
[tex]\implies k=0.8[/tex]
Therefore:
[tex]y=\dfrac{0.8}{x}[/tex]
To find the value of x when y = 3.2, substitute y = 3.2 into the found equation and solve for x:
[tex]\implies 3.2=\dfrac{0.8}{x}[/tex]
[tex]\implies x=\dfrac{0.8}{3.2}[/tex]
[tex]\implies x=0.25[/tex]
Match each pair of equivalent values.
1 .
1
square root of 16
2 .
12
square of 8
3 .
4
4 2
4 .
64
1 2
5 .
16
6 .
2
Answer:
1 - [tex]1^{2}[/tex]
12 - ?
4 - square root of 16
64 - [tex]8^{2}[/tex]
16 - [tex]4^{2}[/tex]
2.828 - square root of 8
Step-by-step explanation:
I need more terms to match
Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.
What are mathematical values?A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42. Every integer or even other mathematical object set to a variable or constant is that object's value.
A mathematical expression's value is the outcome of a computation it describes when its variables and constants are given values. The amount that the function assumes for these argument numbers is the result of a function, assuming the value(s) provided to its argument(s).
Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.
Therefore, Square root of 16 is 4, square root of 8 is 2, but for an answer it would be , 4² is 16, 1² is 2, number 5 would be 64 and number 6 would be 12.
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Omar is going to an amusement park. The price of admission into the park is $25, and once he is inside the park, he will have to pay $5 for every ride he rides on. How much money would Omar have to pay in total if he goes on 8 rides? How much would he have to pay if he goes on r rides?
Cost with 8 rides:
Cost with r rides:
Need answer quickly!
The cost of 8 rides will be equal to $65 and the equation for the r rides will be equal to $25 + $5(r).
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Price of admission into the park = $25
Price to pay for every ride in the park = $5
(a)
Then, the price to pay for 8 rides will be,
$25 + $5(8)
= $25 + $(40)
= $65
(b)
Then, the equation for the price to pay for r rides will be equal to,
$25 + $5(r)
Here, r is the number of rides.
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Which expression is equivalent to |8|+|-7|
Answer:
8 + 7.
Step-by-step explanation: It is absolute value.
The total pages a person reads in x days, if the person reads 6 pages a day
the cost of x boxes of mangoes, if 1 box costs $6 and the shipping charge is $6 per order (for any number of boxes)
the total cost of x notebooks, if one notebook costs $6 and students receive a discount of $1 off their total bill
the total cost of x novels and a pocket dictionary if you buy x novels each at $6 and get a pocket dictionary at $1
what are the corresponding functions for each situation?
The given expression will be written as follows:-
y = 6x
y = 6x + 6
y = 6x - 1
y = 6x +1
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.
A) The total pages a person reads in x days, if the person reads 6 pages a day
y = 6x
B) The cost of x boxes of mangoes, if 1 box costs $6 and the shipping charge is $6 per order (for any number of boxes)
y = 6x + 6
C) The total cost of x notebooks if one notebook costs $6 and students receive a discount of $1 off their total bill
y = 6x - 1
D) The total cost of x novels and a pocket dictionary if you buy x novels each at $6 and get a pocket dictionary at $1
y = 6x + 1
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The _____ _____, denoted , is given by the formula _____, where x is the number of individuals with a specified characteristic in a sample of n individuals.
The sample proportion denoted [tex]\hat{p}[/tex] is given by the formula [tex]\hat{p} = \frac{x}{n}[/tex], where, x is the number of individuals with a specified characteristic in a sample of n individuals.
What is a sample proportion?A sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.
Mathematically, sample proportion can be calculated by using this formula:
[tex]\hat{p} = \frac{x}{n}[/tex]
Where:
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The solution to an inequality is graphed on the number line.
A number line going from negative 5 to positive 5. A solid circle appears between positive 4 and positive 5. The number line is shaded from the circle to negative 5.
What is another way to represent this solution set?
{x | x < 4.5}
{x | x ≤ 4.5}
{x | x > 4.5}
{x | x ≥ 4.5}
The correct answer is option B which is {x | x ≤ 4.5}
What is a number line?
A number line is a representation of a graduated straight line used to represent real numbers in introductory mathematics.
Because the arrow is pointing to the left, the answer to the solution set needs to be less than the number the dot is on.
A solid dot on a number means that that number is included in the solution set.
In the picture the solid dot is on 4.5, so the solution set needs to be equal to or less than 4.5.
Therefore the correct answer is option B which is {x | x ≤ 4.5}
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NEED HELP TODAY PLEASE solve 4(2/5x+7)=−8−4/5x show your work
Answer:
x = -15
Step-by-step explanation:
A group pre-orders 9 tickets for a sightseeing tour, even though they don't have the money to pay for them yet. Each ticket costs 32 dollars , so the debt for one ticket is-32 . The tour company adds a 15 dollar fee for the entire order. Including the fee, which number represents the total debt?
The number that represents the total debt is 303 if the group pre-orders 9 tickets for a sightseeing tour, even though they don't have the money to pay for them yet.
What is debt?
It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
We have:
Each ticket costs 32 dollars, so the debt for one ticket is -$32. The tour company adds a 15-dollar fee for the entire order.
A group of 9 pre-orders 9 tickets for a sightseeing tour.
Total cost of 9 tickets = 9×32 = $288
As this group doesn't have money
The debt for the tickets will be = $288
The tour company adds a $15 fee for the entire order.
The total debt for this tour = $15 + $288 = $303
Thus, the number that represents the total debt is 303 if the group pre-orders 9 tickets for a sightseeing tour, even though they don't have the money to pay for them yet.
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Find the number of turns or bumps in the graph of the function f(x) = x² - 25
Answer:
1 turn
Step-by-step explanation:
this is what the graph would look like:
What multiples to 42 but adds to -13
A farmer has only goats and hens in his farm,on a particular day,he sold 12 animals (goats and hens) and the total number of their legs was 32. how many goats and how many hens did he sell that day?
The number of goats sold is 4 and hens sold is 8.
What is an Equation ?An equation is a mathematical statement which equates two algebraic expression with an equal sign.
Let the total number of goats sold be g
Let the total number of hens sold is h
g + h = 12
The total no. of legs of a goats sold will be 4g
and the total number of legs of a hens sold will be 2h
and it is given that
4g +2h = 32
The system of equation formed is
g + h = 12
4g +2h = 32
Multiplying equation (1) by 2 and then (1) - (2)
-2g = -8
g = 4
Therefore the number of goats sold is 4 and hens sold is 8.
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Gerald purchased a rectangular plot of land. the length of the plot is 20 feet more than the width. the cost of the land was $12 per square foot. gerald also had a fence put around the entire perimeter of the plot, at a cost of s8 per linear foot. the total amount he spent on both the land and the fence was $10,560. part a write an equation in two variables for the perimeter, p, and an equation in two variables for the area, a, of the plot of land where x is the width of the plot in feet. provide evidence to support your equations
Answer:
P =2(x+ y) [tex]ft[/tex].
A =xy [tex]ft^{2}[/tex]
Step-by-step explanation:
perimeter of rectangle (P)= 2(L+B
Area of rectangle (A) = L×B
Given,
width = 'x'
length = y = x+20
therefore using above formula
P = 2(x+20 + x) = 2(2x+20)
A = (x+20)(x)
cost of land per square foot = $12
cost of land per linear foot = $8
total cost of land = $10560
now,
P×8 + A×12 = 10560
2(2x+20)×8 + (x+20)(x)×12 = 10560
32x + 320 + 12x²+ 240x = 10560
12x² + 272x = 10240
12x² + 272x - 10240 = 0
solving this quadratic equation using Discriminant method
x = [-b ±√(b² - 4ac)]/2
where b is the coefficient of x
a is the coefficient of x²
and c is the constant term
by replacing values in the above formula
x = 19.5 , x = -42.24
as the area cannot be negative therefore -42.24 is neglected
hence x = 19.5ft
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What statement is true for f(x) = 3.2^x?
Answer:
Step-by-step explanation:
The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete two rotations every minute.
Write a sine model, y = asin(bt) + k, for the hight (in feet) of the end of one blade as a function of time t (in seconds). assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
Options are displayed in the picture
Answer:
D: y= 10sin([tex]\frac{\pi }{15}t[/tex]) + 30
Step-by-step explanation:
30 feet above the ground is the k value.
10 feet long is how long the blades reach up and down which is also known as the amplitude.
The rest is given in all answers.
If 10% off is 20 what is 23% off?
Does this graph represent a proportional relationship? Explain.
On a coordinate plane, a curved line has 2 curves.
Answer:
No, This graph does not show a proportional relationship. The graph of a proportional relationship is a straight line that passes through the origin.
Step-by-step explanation:
If the graph of a relationship is a line or a ray passes through the origin, then it is proportional. If it is a line or ray that does not pass through the origin, then it is not proportional.
So, it's clear that if a graph has to be proportional then the relationship between the variables should be represented by the graph of a straight line through the origin with a slope equal to the unit rate.
Given relationship is not proportional because they do not have a constant ratio nor does it pass through the origin. If the data on the graph shows a curved line, it is not constant and is not proportional.
For reference, you can check the attached image also.
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Two consecutive odd numbers are such that seven times the smaller , subtracted from nine times the bigger,gives 144.find the two numbers.
Answer:
x = -16
y = 20
Step-by-step explanation:
Please help me I am stuck
Oliver wants to buy apples and blueberries to make a fruit tart. Apples cost $3.50 per pound and blueberries cost $3.25 per pound. How many pounds of fruit does he buy if he buys 2 pounds of apples and 3 pounds of blueberries? How many pounds of fruit does he buy if he buys xx pounds of apples and y pounds of blueberries?
Total pounds, 2 pounds of apples and 3 pounds of blueberries:
Total pounds, xx pounds of apples and y pounds of blueberries:
Need answer quickly as possible!
The total pounds of fruits bought if he buys 2 pounds of apples and 3 pounds of blueberries is $16.75.
The total pounds of fruits bought if he buys x pounds of apples and y pounds of blueberries is $3.50x + $3.25y.
What is the total pounds of fruits bought?The total pounds of fruits bought = (pounds of apples x cost per pound) + (pounds of blueberries x cost per pound)
($3.50 x 2) + (3.25 x 3)
$ 7 + 9.75 = $16.75
($3.50 x x) + (3.25 x y)
$3.50x + $3.25y
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which inequality is equivalent to the given equality of -4(x+7)<3(x-2)
Answer:
x > 22/7
_________________________________________
Notice*
Because there are no options, we must find it algebraically.
_____________________________________________
Let's solve your inequality step-by-step.
−4(x+7)<3(x−2)
Step 1: Simplify both sides of the inequality.
−4x−28<3x−6
Step 2: Subtract 3x from both sides.
−4x−28−3x<3x−6−3x
−7x−28<−6
Step 3: Add 28 to both sides.
−7x−28+28<−6+28
−7x<22
Step 4: Divide both sides by -7.
-7x/-7 = 22/-7
x > -22/7
Answer:
x > −22/7
a recursive formula for the sequence 18,9,4.5,... is
Answer:
A1 = 18
A(n) = A (n-1) -2
Step-by-step explanation:
N represents the number in a sequence and the difference in the sequence is -2 since each time the number is listed in the sequence it is divide by 2.
What is the range of y = sin(x)?
A)-1≤ y ≤1
B)-2π≤y≤2
C)-0.5≤ y ≤0.5
Answer:
A) -1≤ y ≤1
Step-by-step explanation:
If you go on a graphing site and graph out y = sin(x), you will see that it is a wave that forever oscillates between 1 and -1.
(I've attached an image below for more information on sin graphs):
If the inspection division of a county weights and measures department wants to estimate the mean amount of
If inspection department wants to estimate the mean amount with 95% confidence level with standard deviation 0.05 then it needed a sample size of 97.
Given 95% confidence level, standard deviation=0.05.
We know that margin of error is the range of values below and above the sample statistic in a confidence interval.
We assume that the values follow normal distribution. Normal distribution is a probability that is symmetric about the mean showing the data near the mean are more frequent in occurence than data far from mean.
We know that margin of error for a confidence interval is given by:
Me=[tex]z/2* ST/\sqrt{N}[/tex]
α=1-0.95=0.05
α/2=0.025
z with α/2=1.96 (using normal distribution table)
Solving for n using formula of margin of error.
[tex]n=(z/2ST/Me)^{2}[/tex]
n=[tex](1.96*0.05)^{2} /(0.01)^{2}[/tex]
=96.4
By rounding off we will get 97.
Hence the sample size required will be 97.
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The given question is incomplete and the full question is as under:
If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liters bottles to within (0.01 liter with 95% confidence and also assumes that standard deviation is 0.05 liter. What is the sample size needed?
A 4-digit combination lock can be opened only if a correct combination of digits from 0-9 is chosen. Find the probability of guessing the correct combination if: none of the digits are repeated, any of the digits can be repeated, any of the digits can be repeated but the 3 and 8 are not in the combination.
The probabilities are as follows:-
if none of the digits is repeated 0.504If any of the digits can be repeated 1If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability will be calculated as follows:-
Total combinations are = 10⁴ = 10000
A) if none of the digits are repeated:-The combinations will be 10 x 9 x 8 x 7 = 5040
Probability = 5040 / 10000
Probaility = 0.504
B) If any of the digits can be repeated:- The combinations will be 10 x 10 x 10 x 10 = 10000
Probabilityy = 10000 / 10000 = 1
C )If any of the digits can be repeated but the 3 and 8 are not in the combination the combinations will be 7 x 7 x 7 x 7 = 2401
Probability = 2401 / 10000 = 0.24
Therefore if none of the digits is repeated 0.50.If any of the digits can be repeated 1.If any of the digits can be repeated but the 3 and 8 are not in the combination 0.24.
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How many factors does 16 have
Answer:
5
Step-by-step explanation:
1,2,4,8,16 total 5 factors
48 girls, 41 boys, and 5 teachers sat in the gym. Write the ratio of girls to boys in three ways.
I took the text last month
What are the roots of the polynomial equation x cubed minus 5 x 5 = 2 x squared minus 5? use a graphing calculator and a system of equations. round noninteger roots to the nearest hundredth.
The solution to the equation of the polynomial function x³-5x+5 = 2x²-5 is (c) –2.24, 2, 2.24.
What is Polynomial Equation?
A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Here, The function is given as:
x³-5x+5 = 2x²-5
Split the function.
So, we have:
y = x³-5x+5
y = 2x²-5
Using a graphing calculator, we have the x coordinate at the point o intersection of both equations to be
x = –2.24, 2, 2.24
Hence, the solution to the equation is (c) –2.24, 2, 2.24
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I WILL GIVE BRAINIEST
Line AB and Line CD bisect each other at point E. If AE = 3x - 10y + 123, BE = -2x - 7y + 122, CE = 9x + 10y - 171, and DE = 3x + 20y - 249, what are the values of x and y?
The values of x and y are 7 and 12 respectively
Solving simultaneous equationsFrom the question, we are to determine the values of x and y
From the given information,
Line AB and Line CD bisect each other at point E
Then, we can conclude that
AE = BE
and
CE = DE
From the given information,
AE = 3x - 10y + 123
BE = -2x - 7y + 122
CE = 9x + 10y - 171
DE = 3x + 20y - 249
Then, we can write that
3x - 10y + 123 = -2x - 7y + 122
Simplifying
3x +2x -10y + 7y = 122 -123
5x -3y = -1 ----------- (1)
Also,
9x + 10y - 171 = 3x + 20y - 249
Simplifying
9x -3x +10y -20y = -249 + 171
6x -10y = -78 --------- (2)
Now, solve equations (1) and (2) simultaneously
5x -3y = -1 ----------- (1)
6x -10y = -78 --------- (2)
Multiply equation (1) by 10 and equation (2) by 3
10 × ( 5x -3y = -1
3 × ( 6x -10y = -78
50x -30y = -10 ----------- (3)
18x -30y = -234--------- (4)
Then, subtracting equation (4) from equation (3), we get
50x -18x -30y-(-30y) = -10-(-234)
32x -30y + 30y = -10 + 234
32x = 224
∴ x = 224/32
x = 7
Put the value of x into equation (1), to find y
5x -3y = -1
5(7) -3y = -1
35 -3y = -1
35 + 1 = 3y
36 = 3y
∴ y = 36/3
y = 12
Hence, the values of x and y are 7 and 12 respectively
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