Answer:
Your answer is [tex]T= 123.665974[/tex] inches
What is the percent error if a stick of length 60 inches is measured to be 63 inches long?
If a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .
The Percent Error can be calculated by the formula
Percent Error = (measured value - actual value)/(actual value) ×100
In the question ,
it is given that
the original length of the stick is 60 inches .
the measured length of the stick is 63 inches .
So, the measured value = 63 inches ,
actual value = 60 inches .
Substituting the measured values and actual value in the percent error formula , we get
Percent Error = (63-60)/60 × 100
= 3/60 × 100
= 1/20 × 100
= 100/20
= 5 %
Therefore , if a stick of length 60 inches is measured to be 63 inches long the the percent error will be 5% .
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how many ways are there to distribute 12 distinguishable objects into six distinguishable boxes so that two objects are placed in each box?
By the concept of permutation and combinations there are 7,484,400 ways are there to distribute 12 distinguishable objects into six distinguishable boxes so that two objects are placed in each box.
What are permutation and combination?Putting things or numbers in order is known as a permutation. Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.
The number of ways to sort identifiable things into indistinguishable bins is 11 or "double-factorial," which is defined as 11 (as shown). Given that the bins are distinct, that is multiplied by 6! Following are several explanations for the 11!!11!! There are 11 potential companions for the chosen "first" object. Following that decision, there will be 10 items left, which indicates that the next arbitrary object will have 9 companions. then do it again. A more traditional strategy would be this. The objects that fit in the first container have 122 possibilities, the second bin has 102 possibilities, and so on.
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PLEASE HELP!!!!!!
1. Spencer went to the county fair and spent his money only on ride tickets and fair admission. He bought 17 tickets for the rides and spent a total of $30.75 at a county fair. The county fair charges $1.25 per ticket for the rides and the price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets. (a) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission. (b) Explain your answer to Part 1a.
The linear equation that represents how much he spent is given as y = 1.25x + 9.55
Linear EquationA linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear function is given y = mx + c
m = slopec = interceptTo solve this problem, we can simply use the values given to write a linear equation.
Can be written as
[tex]30.75 = 1.25x + c\\x = 17\\30.75 = 1.25(17) + c\\c = 30.75 - 21.25\\c = 9.55\\[/tex]
The equation to represent this problem is y = 1.25x + 9.55
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what is the possibility of having three boys and one girl and a family with four children assuming there is an equal probability of having a boy or a girl gone to two decimal places
Since girls and boys have equal probability, iin a family with four children, they have probability equal to
[tex]P(\text{girl)}=P(\text{boy)}=\frac{1}{4}[/tex]so, the probability of having 3 boys and 1 girls is
[tex]P(3\text{boys }\cap1girl)=P(3boys)\cdot P(1girl)=\frac{3}{4}\cdot\frac{1}{4}=\frac{3}{16}[/tex]that is, the answer is 3/16 which is equal to 0.19.
Alejandra wants to buy 12 ounces of gluten-free edible cookie dough that costs $1.25 per ounce. Select all equations that correctly represent how much Alejandra will pay for her cookie
dough, Y.
A) y = 12 x 1.25
B) y = 12/1.25
C) 12 + 1.25 = Y
D) 12 • 1.25 = Y
Answer:
A and D
Step-by-step explanation:
its A and D, trust
Solve for x.
A) 6
B) 7
C) 4
D) 5
What is the total number of zeros in the number (100,000,000)^2
A 18
B 12
C 16
D 10
What is the biggest number you can make out of 12 1 4 7 without using any powers and you can't use the numbers more then once and you can use symbols including brackets as much as he wants
The biggest number you can make from the numbers 12, 1, 4 and 7 is given by:
336 = 12 x 1 x 4 x 7.
How to find the biggest number from the given numbers?The operation that leads to the bigger number is the power operation, however, as stated in the problem, you cannot use any powers in this problem.
After the power, the operation that leads to the highest numbers is the multiplication operations.
These are no constraints relating the symbols, only that each number cannot be used more than once, hence the biggest number is obtained multiplying all values, as follows:
12 x 1 x 4 x 7 = 336.
If one of the numbers had been a fraction with a greater denominator than numerator, the fraction should be divided, as dividing by a fraction is the same as multiplying by the inverse of the fraction.
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Do the ratios 5 3 and 17 12 form a proportion?
The Ratios 5 : 3 and 17 : 12 does not form a proportion.
What is Proportion?
A Proportion, in mathematics, can be defined as when two ratios are set equal to each other.
Now, the given ratios are: 5 : 3 and 17 : 12
We can also write the ratios as: [tex]\frac{5}{3}[/tex] and [tex]\frac{17}{12}[/tex]
To determine, if they are a proportion, we can cross multiply and get the same answers on both the sides.
When we multiple, the numerator from the first by the denominator of the second, we get
5 * 12 = 60 …(1)
Now, multiply the denominator from the first by the numerator of the second, we get
3 * 17 = 51 …(2)
Since, (1) and (2) are not equal. Therefore the ratios does not form a proportion.
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PLEASE SOMEONE HELP!!!
Answer: 2,3,4
Step-by-step explanation:
y=1/4x +2
x=0 y=2
x=4 y=3
x=8 y=4
buffy opens a savings account with $100 that earns 9% interest per year, not compounded. how much interest will buffy earn in 2 years?
Answer:
She will earn 18 dollars in interest.
Step-by-step explanation:
0.09*(100*2)
0.09*(200)
18
What is the slope of the line represented by the table of value
Answer:
The slope of the line represented by the table value is -8/5
what is the inverse of f(x)=4x^2-16
√ x/4 + 4 is the inverse of the function f(x)=4x^2-16
How to find the inverse of a functionWhat is inverse function?
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f
Given f(x)=4x²-16
Let f(x) = y
So we can say y =4x²-16
We will then make x the subject:
Since y = 4x²-16
4x² = y + 16
x² = y + 16/4
x = √ y/4 + 4
since x = f⁻¹(y) = √ y/4 + 4
Thus f⁻¹(x) = √ x/4 + 4
Therefore, the inverse of f(x)=4x^2-16 is √ x/4 + 4
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Part A = Gil is shopping for books and CDs. He buys 4 books and no CDs for a total of $32. Write an equation that represents the relationship between the cost of a book, y, and the cost of a CD, x, in standard form.
Part B= what is the slope of the equation?
let a be the area of a circle with radius r that is increasing in size with respect to time. if the rate of change of the area is 3 cm/s, find the rate of change of the radius when the radius is 6 cm.
1/4π is area of a circle when the radius is 6 cm.
What is the circumference of a circle?
The radius squared times pi equals the area of a circle (A = r2). Find out how to apply this formula to determine a circle's area given its diameter.As a result, the circumference of a circle is pi times the diameter or 2 pi times the radius, which is how pi is typically defined as the ratio of a circle's circumference to its diameter. This provides a geometric reason that a circle's surface area is indeed equal to "pi r squared."A = πr²
differentiate both sides with respect to 't'
dA/dt = πr² dr/dt
dA/dt = 2πr dr/dt
dA/dt = 3 , r = 6
3 = 2π * 6dr/dt
dr/dt = 1/4π
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In triangle GHJ, Angle G=25°, Angle H=46°, and h=37mm. Determine the length of side g to the nearest millimeter.
The length of side g from the given triangle GHJ to the nearest millimeter is 83 mm.
Given that, in triangle GHJ, ∠G=25°, ∠H=46°, and h = 37 mm.
What is sine rule in triangle?The sine rule of a triangle is sin A/a = sin B/b = sin C/c.
From triangle GHJ
∠G+∠H+∠J = 180°
⇒ 25°+46°+∠J = 180°
⇒ ∠J = 109°
Using sine rule
sin 109°/g = sin 25°/37
⇒ 0.945/g = 0.4226/37
⇒ 34.965 = 0.4226g
⇒ g = 82.73 mm
⇒ g ≈ 83 mm
Therefore, the length of side g from the given triangle GHJ to the nearest millimeter is 83 mm.
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Use point-slope form to write the equation of a line that passes through the point (20,19)(20,19) with slope 55.
The equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.
As given in the question,
Line passes through the point ( x₁ , y₁ ) = ( 20, 19)
Slope of the line that passes through (20 , 19) is 55
Equation of a line in point-slope form that passes through the point (20,19) with slope 55
y - y₁ = m ( x- x₁)
⇒ y - 19 = 55 (x - 20)
⇒ y -19 = 55x - 1100
⇒ y= 55x - 1091
Therefore, the equation of a line in point-slope form that passes through the point (20,19) with slope 55 is y = 55x -1091.
The complete question is:
Use point-slope form to write the equation of a line that passes through the point (20,19) with slope 55.
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(PLEASE HELP) A function has the function rule y = -2x+1. If the output is 9, what is the input?
9 more than the product of 4 and x
Answer:
4x + 9
Step-by-step explanation:
the product of 4 and x is 4x
then 9 more is addition, so 4x + 9
-1/9 divided by 3/4
-4/27
1/12
1/12
4/27
Answer:
-4/27
Step-by-step explanation:
You start at (-5, 0). You move down 1 unit and right 2 units. Where do you end?
Answer:
(- 3, - 1 )
Step-by-step explanation:
1 down means subtract 1 from the y- coordinate
2 units right means add 2 to the x- coordinate
(- 5, 0 ) → (- 5 + 2, 0 - 1 ) → (- 3, - 1 )
Question 3 of 25
Imagine that you are given two linear equations in slope-intercept form. You
notice that the slopes are different, but the y-intercepts are the same. How
many solutions would you expect for this system of?
For this system of equations, there will be infinitely many solutions.
Two equations are said to represent a line when they have the same slope and y-intercept. In this instance, one equation is created by adding a constant to the other equation.
Such equations will lay on each other on a graph if we plot them since they represent the same line. We can claim that these equations have an endless number of solutions because every point on that line will satisfy both of the aforementioned equations.
Here's an illustration:
Eq. 1: 2x + y = 4.
4x + 2y Equals 8 in equation 2
The second equation is created by multiplying the previous equation by two, as can be seen if you look at the two equations. The same outcome will be obtained for both if we write them in slope intercept form, as illustrated below:
Equation 1's slope intercept form is y = -2x + 4
Equation 2's slope intercept form is 2y = -4x + 8 and y = -2x + 4
The y-intercept and slope of both equations are identical. Equation 2 applies to any place that satisfies Equation 1. We can therefore draw the conclusion that there are an endless number of solutions to two linear equations with the same slope and y-intercept.
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Answer:
1
Step-by-step explanation:
What is the slope of the line that passes through the point (4,7) and (7,16)
Answer: The slope is 3.
Step-by-step explanation: Hope this helps :)
Find the 61st term of the arithmetic sequence -12, -28, -44, ...
The sequence's 61st term is -972.
The sequence is -12 , -28 , -44.
Solution:The following arithmetic sequence is: -12, -28, -44, ..
Find the common difference between the succeeding and preceding terms.
c.d = first term - second term
-28 - (-12) = -28 + 12 = -16
-44 - (-28) = -44 + 28 = -16
As a result, the distinction between the terms remains constant.
This is a mathematical sequence.
The formula for the nth term of an arithmetic sequence is:
an = a1 + (n - 1 ) d
Where,
an is the sequence's nth term.
a1 is the sequence's first term.
The common difference between terms is denoted by d.
-12, -28, -44 are the numbers in the given sequence.
By changing the values in the formula,
a1 = -12
d = -16
Substituting values,
an = -12 + (n - 1 )(-16)
an = -12 - 16n + 16
an = 4 - 16n
Substitute n = 61 to find the 61st term.
a61 = 4 - 16 x 61
a61 = 4 - 976
a61 = -972
As a result, the sequence's 61st term is -972.
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3/5-6/10+9/15-12/20=
Answer:
Step-by-step explanation:
0
the probability that a radish seed will germinate is 0.7. a gardener plants seeds in batches of . find the standard deviation for the binomial random variable x, the number of seeds germinating in each batch. round to three decimals.
The standard deviation for the number of seeds germinating in each batch is 1.3.
Given, the probability that a radish seed will germinate is 0.7.
In binomial distribution, standard deviation is given as:
σ = √np(1-p)
Where "n" is the number of observations
"p" is probability of getting success
We are given that:
Total batches of seed = 8
Probability that a radish seed will germinate is 0.7
Here success is getting radish seed germinated
Then, the standard deviation for the number of seeds germinating in each batch.
Plugging in values in formula, we get:
σ = √(8)(0.7)(1-0.7)
= √(8)(0.7)(0.3)
= √1.68
= 1.29614 ≈ 1.3
Therefore the standard deviation for the number of seeds germinating in each batch is 1.3
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Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are
(
3
x
−
4
)
feet,
(
x
2
−
1
)
feet, and
(
2
x
2
−
15
)
feet.
What is the perimeter of the triangle if
x
=
4
?
Responses
16
feet
16 feet
40
feet
40 feet
76
feet
76 feet
80
feet
The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively. The perimeter of the triangle is 42 feet.
Given that,
Kat is using reflective orange paint to outline a triangle stage prop. The triangle's edges measure (3x - 4) feet, (x² - 1) feet, and (2x² - 15) feet, respectively.
We have to find if x = 4, what is the triangle's perimeter.
The perimeter of the triangle is equal to sum of the three sides of the triangle.
=3x - 4 + x² - 1 + 2x² - 15
=3x²+3x-20
Take the x value as 4
We get,
=3(4)²+3(4)-20
=3×16+3×4-20
=48+14-20
=62-20
=42
Therefore, The perimeter of the triangle is 42 feet.
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5x-19y= 14
How do you put this is slope intercept form
The area of the Caribbean Sea is 2.7182 × 10^6 km2. The area of the South Atlantic Ocean is 4.027 × 10^7 km2. Find the total area. Write the final answer in scientific notation with the correct number of significant digits.
The area of the Caribbean Sea is 2.7182 × 10^6 km2, The area of the South Atlantic Ocean is 4.027 × 10^7 km2, then the total area of the Caribbean Sea and the South Atlantic Ocean is 4.29882 × 10⁷ km².
We are to determine the total area of the Caribbean Sea and the South Atlantic Ocean.
From the given information,
The area of the Caribbean Sea is 2.967 × 10⁶ km² and
The area of the South Atlantic Ocean is 4.149 × 10⁷ km²
To determine the total area, we will add the given areas together,
2.7182 × 10⁶ km²
+ 4.027 × 10⁷ km²
So, That is,
2.7182 × 10⁶ km²
+ 40.27 × 10⁶ km²
----------------------------
42.9882 × 10⁶ km²
So,
We can write,
= 4.29882 × 10⁷ km²
Therefore,
The total area of the Caribbean Sea and the South Atlantic Ocean is 4.29882 × 10⁷ km².
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Marcy is 5 ft 5 in. tall. To find the height of a building, she measured her shadow and the building's shadow. What is the height h of the building?
Marcy is a 5-ft-5 in. She took measurements of both her own shadow. h=520 is the building's height.
Given that,
Marcy is a 5-ft-5 in. She took measurements of both her own shadow and that of the structure in order to determine its height.
We have to find what is the building's height, h.
Use the fact that 1 feet is equivalent to 12 inches to convert all measures to a single unit, inches.
We convert
MN=26×12=312 inches.
QR=3×12+3=36+3=39 inches.
PQ=5×12+5=60+5=65inches.
Since the Sun's rays that generate LN and PR are parallel, they are also parallel. the angles they make with the earth as a result are consistent:
∠N≅∠R
The Right Angle Congruence Theorem illustrates ∠M≅∠Q.
As a result, according to the Angle-Angle Similarity △LMN~△PQR
Calculate a ratio using the known lengths of the sides and the unknown length (height of the building).
PQ/QR=LM/MN
65/39=h/312
h=65×312/39
h=20280/39
h=520
Therefore, h=520 is the building's height.
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