Blake needs a wooden dowel that is 2 1/6 feet long. Blake needs to cut off 7.4167 feet from the dowel.
What are arithmatic operations?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.
To find out how much Blake should cut off the dowel, we need to subtract the length of the dowel from the required length.
The length of the dowel is -5 1/4 feet, which can be written as -5.25 feet.
The required length is 2 1/6 feet, which can be written as 2.1667 feet (rounded to four decimal places).
To find out how much needs to be cut off, we can subtract the length of the dowel from the required length:
2.1667 ft - (-5.25 ft) = 7.4167 ft
Therefore, Blake needs to cut off 7.4167 feet from the dowel.
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A rectangular dog pen has an area of 384 sq yd. The width is 24 yd. How much does it cost to fence it if the cost for fencing is $9 per foot?
Answer:
$2160
Step-by-step explanation:
Area of a rectangle = Length * Width
A = L * W
Divide both sides by width
W/(A = L * W)/w
[tex]\frac{A}{W} = L[/tex]
Plug in values
[tex]\frac{384}{24} =16[/tex]
Multiply Length and width to find perimeter
2W + 2L = P
plug in values
2(24) + 2(16) = 80
Multiply perimeter by cost per foot
1yd = 3ft
80yd * 3ft = 240ft
240ft * $9 = $2160
I’ve attempted this question so many times I’m stuck please help
Answer:
Step-by-step explanation:
Range: the difference between the highest and lowest values
Heights:
130
142
142
143
144
145
147
147
149
150
151
153
154
154
158
161
162
Formula to find the range
R= H-L
R = range
H = highest value
L = lowest value
R = 160 - 130.
The range is 30.
tyrone runs 1 1/4 miles in 8 1/2 minutes how many miles can he run in 20 minutes
Answer:
2 [tex]\frac{16}{17}[/tex] miles
Step-by-step explanation:
[tex]\frac{miles}{minutes}[/tex] = [tex]\frac{miles}{minutes}[/tex]
[tex]\frac{1 1/4}{8 1/2}[/tex] = [tex]\frac{x}{20}[/tex]
1 [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{4}{4}[/tex] + [tex]\frac{1}{4}[/tex] (1 = [tex]\frac{4}{4}[/tex] )
8 [tex]\frac{1}{2}[/tex] is the same as [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{17}{2}[/tex] (1 = [tex]\frac{2}{2}[/tex])
[tex]\frac{\frac{5}{4} }{\frac{17}{2} }[/tex] = [tex]\frac{x}{20}[/tex]
[tex]\frac{17}{2}[/tex] x = 20 multiply both sides by [tex]\frac{2}{17}[/tex]
[tex]\frac{2}{17}[/tex] [tex](\frac{17}{2})[/tex]x = [tex]\frac{2}{17}[/tex][tex](\frac{20}{1})[/tex]
x = [tex]\frac{40}{17}[/tex]
[tex]\frac{5}{4}[/tex] [tex](\frac{40}{17})[/tex] = x
[tex]\frac{50}{17}[/tex] or 2 [tex]\frac{16}{17}[/tex]
Find the length of the dashed line in the
circle.
The length of the dashed line in the circle is
ft.
4.893 ft
9
17.708 ft →
4.893 f
The length of the dotted line would be 7.922 ft.
What is the diameter of the circle?A circle's diameter is measured from the center of the circle outward. It is equivalent to twice the radius, or the distance a circle's radius is measured from its center to any other point on the circle.
The mathematical formula for a circle's diameter is d = 2r if d is the circumference and r is the radius.
When we subtract the circle's thickness from its outer diameter to determine the provided circle's inner diameter, we obtain q = 17.708 - 4.893 - 4.893.
We can solve this for q = 7.922
The dotted line would be 7.922 feet long as a result.
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To build a new skate park, a community board must have at least 50% of the voters agree to the build. At a recent voters meeting, 125 voters were asked if they would vote for the new skate park and 72 responded yes. Should the community board go ahead and start planning the park?
No, they should not plan for the skate park because the sample had about 42.4% people vote no.
No, they should not plan for the skate park because the sample had about 57.6% people vote no.
Yes, they should plan for the skate park because the sample had about 42.4% people vote yes.
Yes, they should plan for the skate park because the sample had about 57.6% people vote yes.
The solution is Option D.
The skate park should be build as the percentage of votes was 57.6 %
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the percentage of votes be represented as A
Now , the skate park will be built if the percentage of votes is greater than 50 %
Now , the total number of voters = 125 voters
The number of voters who responded to building the park = 72 voters
Substituting the values in the equation , we get
A = ( number of voters who responded to building the park / total number of voters ) x 100
On simplifying the equation , we get
A = ( 72 / 125 ) x 100
A = 0.576 x 100
A = 57.6 %
And , A > 50 %
Therefore , they should plan for the skate park because the sample had about 57.6% people vote yes
Hence , the percentage of votes is 57.6 %
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Add the two expressions 3z - 4 and 2z + 5
We obtain the sum of the expressions as 5z + 1. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
Four fundamental mathematical operations which can be used to express any real number are known as arithmetic operations. The four operations are addition, subtraction, multiplication and division.
We are given two expressions as 3z - 4 and 2z + 5.
In order to add the expressions, we will add the like terms.
On adding the like terms, we get
⇒(3z - 4) + (2z + 5)
⇒3z + 2z - 4 + 5
⇒5z + 1
Hence, we get the expression as 5z + 1.
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Write a couple of paragraphs describing how you can determine the values of x that a) make
the rational function 0, and b) the values of x where the rational function is undefined:
f(x) = x²-2x+1
4x+5
The required paragraphs regarding with given expression f(x) = x²-2x+1/4x+5 have been explained later in the section.
A rational expression is a fraction in which the numerator and denominator are polynomials.
Here,
a) To determine the values of x that make the rational function f(x) equal to 0, we need to solve the equation:
x² - 2x + 1 = 0
Next, we can factor the quadratic on the left-hand side of the equation:
(x - 1)(x - 1) = 0
The quadratic is a perfect square, and we can see that it is equal to 0 when x = 1. So, the value of x that makes the rational function 0 is x = 1.
b) To determine the values of x where the rational function f(x) is undefined, we need to look for values of x that would make the denominator, 4x+5, equal to 0. If the denominator is equal to 0, then we would be dividing by 0, which is undefined.
So, we set the denominator equal to 0,
4x + 5 = 0
4x = -5
x = -5/4
Therefore, the value of x where the rational function is undefined is x = -5/4.
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What is the solution to this inequality 6 - 5y < -34
Answer: y > 8
Step-by-step explanation:
6 - 5y < -34
-5y < -40
y > 8
[tex]6-5y < -34[/tex]
Simplify:
[tex]-5y+6 < -34[/tex]
Subtract 6 from both sides:
[tex]-5y+6-6 < -34-6[/tex]
[tex]-5y < -40[/tex]
Since we are dividing by a negative number, the sign will reverse.
Divide both sides by -5:
[tex]\dfrac{-5y}{-5} > \dfrac{-40}{-5}[/tex]
[tex]\boxed{y > 8}[/tex]
Let A be an m×n matrix and let u be a vector in R^n that satisfies the equation Ax=0. Show that for any scalar c, the vector cu also satisfies Ax=0.[ That is, show that A(cu)=0.]
Using the distributive property of matrix multiplication A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.
We have given that Ax = 0, where A is an m × n matrix and x is an n-dimensional vector in Rn.
To show that A(cu) = 0 for any scalar c, we can use the distributive property of matrix multiplication, which states that A(B + C) = AB + AC for any matrices A, B, and C of appropriate dimensions.
Let us substitute cu for x in the equation Ax = 0, then we get:
A(cu) = A(c × u)
Using the distributive property, we can write:
A(c × u) = c × A(u)
Since u satisfies the equation Ax = 0, we have:
A(u) = 0
Substituting this into the above equation, we get:
c × A(u) = c × 0 = 0
Therefore, we have shown that A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.
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I need help with the picture problem below
Using the fact that the figures are similar, we will find that MN = 12.4
How to find the length of segment MN?We know that both figures are similar, then there is a scale factor that relates them.
We know the length of two correspondent sides, these are:
HI and LM
HI = 3
LM = 18.6
if k is the scale factor, then we can wite:
3*k = 18.6
k = 18.6/3 = 6.2
Now the length of MN will be 6.2 times the length of the correspondent side on the smaller figure:
MN = 6.2*2 = 12.4
That is the lenght.
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Show that ∶ [– 1, 1] → ℝ, given by () =
(2+)
is one-one. Find the inverse of the function
∶ [– 1, 1] → Range . (Hint: For ∈ Range , = () =
(2+)
, for some in [– 1, 1], i.e., =
(2+)
The inverse of the given function is f(x) = 2x/(1 - x)
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.
Given function is
f(x) = x/(2+x)
Assume that y = f(x) = x/(2+x)
Solve y = x/(2+x) for x:
y = x/(2+x)
Multiply (2+x) on both sides:
y(2+x) = x
2y + xy = x
Subtract xy from both sides:
2y = x - xy
2y = x(1 - y)
x = 2y/ (1 - y)
Now replace x with y and y with x:
y = 2x/(1 - x)
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Use the Pythagorean Theorem to find the length of the missing side of the right triangle. Then find the value of each of the six trigonometric functions of .
θ
A
B
C
a = 16
b = 30
c
Question content area bottom
Part 1
The length of the missing side of the right triangle is
1) The length of the missing side of the right triangle is 34.
2) The values of the six trigonometric functions of θ are:
sin θ = sin A = 8/17
cos θ = cos A = 15/17
tan θ = tan A = 8/15
csc θ = csc A = 17/8
sec θ = sec A = 17/15
cot θ = cot A = 15/8
What is Pythagorean Theorem?
Pythagoras Theorem is a method for calculating the missing length of a right-angled triangle. The triangle has three sides: the hypotenuse (which is usually the longest), the opposite (which does not touch the hypotenuse), and the adjacent (which is always the shortest) (which is between the opposite and the hypotenuse).
Part 1
To find the length of the missing side (c) of the right triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we have:
a² + b² = c²
Substituting the given values, we get:
16² + 30² = c²
Simplifying, we get:
256 + 900 = c²
1156 = c²
Taking the square root of both sides, we get:
c = sqrt(1156) = 34
Therefore, the length of the missing side of the right triangle is 34.
Part 2
To find the values of the six trigonometric functions of θ, we need to know one of the acute angles of the triangle. Let's call the acute angle opposite side a as angle A. Using the given values, we can find the sine, cosine, tangent, cosecant, secant, and cotangent of angle A as follows:
sin A = a/c = 16/34 = 8/17
cos A = b/c = 30/34 = 15/17
tan A = a/b = 16/30 = 8/15
csc A = 1/sin A = 17/8
sec A = 1/cos A = 17/15
cot A = 1/tan A = 15/8
Therefore, the values of the six trigonometric functions of θ are:
sin θ = sin A = 8/17
cos θ = cos A = 15/17
tan θ = tan A = 8/15
csc θ = csc A = 17/8
sec θ = sec A = 17/15
cot θ = cot A = 15/8
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Help pls Thank you mwa
Step-by-step explanation:
Same as the triangles. Find the area of the large rectangle and the small rectangle, then subtract.
A = L x W
For the large rectangle
A = 30 x 25 = 750
For the small rectangle
A = 26 x 21 = 546
Now to subtract these two
750 - 546 = 240
The function represented by the data in the table could
model the perimeter of a square whose area is x.
Explain how the function in the table models this
relationship. Be sure to identify how the function
represents area, perimeter, and the length of a side. Then
generalize the pattern in the table.
Type your response in the box.
Note that the pattern in the table is that the perimeter of a square with area x is four times the square root of x. We can express this relationship as:
f(x) = 4 * √(x)
What is the rationale for the above response?We know that the area of a square is calculated as the square of its side length, which means that the side length of a square with area x is the square root of x. Therefore, the length of the side of the square can be expressed as:
s = √(x)
To calculate the perimeter of the square, we simply add up the lengths of all four sides:
P = 4s = 4 * √(x)
So, the function f(x) in the table represents the perimeter of a square with area x, which can be calculated using the equation:
f(x) = 4 * √(x)
To verify this, let us take these examples:
when x = 1, the area of the square is 1, and the side length is 1. Therefore, the perimeter of the square is 4 * 1 = 4, which matches the value in the first row of the f(x) column.when x = 4, the area of the square is 4, the side length is 2, and the perimeter of the square is 4 * 2 = 8, which matches the value in the second row of the f(x) column, and so on.Learn more about Square Roots:
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If f (x) = 5x - 4 find f(2).
10
48
2
6
Answer:
6
Step-by-step explanation:
f(2) = 10-4 = 6
Answer:
[tex] \sf \: d) \: 6[/tex]
Step-by-step explanation:
Given function,
→ f(x) = 5x - 4
We have to find,
→ The required value of f(2).
Now value of f(2) will be,
→ f(x) = 5x - 4
→ f(2) = 5(2) - 4
→ f(2) = 10 - 4
→ [ f(2) = 6 ]
Therefore, the answer is 6.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
11
24
Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
The value of x is 12. The solution has been obtained by using trigonometry.
What is trigonometry?
The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. The angles of 0, 30, 45, 60, and 90 degrees are the most typical trigonometric angles to be utilised in computations.
We are given a right - angled triangle with one angle equal to 24° and the length of the base is 11.
Using trigonometry,
We know that cos theta = adjacent side/hypotenuse
So,
⇒cos θ = 11/x
Here, θ = 24°
So,
⇒cos 24° = 11/x
⇒x = 11/cos 24°
⇒x ≈ 12.04
⇒x ≈ 12
Hence, the value of x is 12.
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Use the given right triangle to find ratios, in reduced form, for sin A, cos A, and tan A.
The ration will be sinA =[tex]\frac{P}{H}[/tex] =[tex]\frac{33}{65}[/tex] , cosA = [tex]\frac{B}{H}[/tex]=[tex]\frac{56}{65}[/tex] & tanA = [tex]\frac{P}{B}[/tex]= [tex]\frac{33}{56}[/tex].
What are a right triangle's three sides?The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use particular terminology to define the sides of right triangles. A right triangle's hypotenuse is always side opposite the right angle.
Would a right triangle have a 90- or 180-degree angle?When one of a triangle's angles is exactly 90 degrees, the triangle is said to be right-angled. The remaining two angles together equal 90 degrees.. The sides that make up the right angle are perpendicular and the triangle's base. The third side, also referred to as the hypotenuse, is the longest of the three sides.
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Scientists plan to use selective breeding to produce a new type of wheat for farmers who live in northern areas with short summer seasons. Which of these traits would be most useful for these farmers?.
The trait would be MOST useful for these farmers is to be considered as the fast growth rate.
What is a scientist's plan?The main goal of science that should create knowledge and understanding.
Since the plan for using the breeding to produce a new type for the wheat for farmers that lived in the northern areas.
The growth rate of a value (GDP, turnover, wages, etc.) measures its change from one period to another (month, quarter, year). It is very generally expressed as a percentage.
The annual average rate of change of the gross domestic product (GDP) at market prices based on constant local currency, for a given national economy, during a specified period of time.
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please help me, be quick!
The simplified value of the expression is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
1/(b² - ab) - 1/(ab - a²)
Take the LCM of the expression
So, we have the following representation
[ab - a² - b² + ab]/[(b² - ab)(ab - a²)]
Evaluate the like terms
So, we have the following representation
[2ab - a² - b²]/[(b² - ab)(ab - a²)]
Open the bracket
[a² + b² - 2ab]/[2a²b² - ab³ - a³b]
Hence, the solution is [a² + b² - 2ab]/[2a²b² - ab³ - a³b]
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Number story that the answer will give me 1/4
Answer:
he division story will be that there are 16 boys who want to share 4 oranges. What fraction will each person get?
Number of boys = 16
Number of oranges = 4
Fraction that each person will get will be:
= Number of oranges / Number of boys
= 4/16
= 1/4
Each boy gets 1/4.
Step-by-step explanation:
As manager for a construction firm, you are in charge of bidding on two large contracts. You believe the probability you get contract #1 is 0.4. If you get contract #1, the probability you also get contract #2 will be 0.3, and if you do not get #1, the probability you get #2 will be 0.5. Complete parts (a) through (c).
Question content area bottom
Answer: a) Calculate the probability of getting both contracts:
The probability of getting both contracts is given by P(Contract 1 and Contract 2) = P(Contract 1) * P(Contract 2|Contract 1) = 0.4 * 0.3 = 0.12
b) Calculate the probability of getting either contract:
The probability of getting either contract is given by P(Contract 1 or Contract 2) = P(Contract 1) + P(Contract 2) - P(Contract 1 and Contract 2) = 0.4 + 0.5 - 0.12 = 0.78
c) Calculate the probability of not getting either contract:
The probability of not getting either contract is given by P(Neither Contract) = 1 - P(Contract 1 or Contract 2) = 1 - 0.78 = 0.22.
So, there is a 22% chance that the construction firm will not get either contract.
Step-by-step explanation:
Which algebraic expression is equivalent to the expression below? 23x+9-5x
Answer:
18x+9
Step-by-step explanation:
Answer: 18x + 9
Step-by-step explanation:
1) Combine like terms 23x -5x to get a new equation of 18x + 9.
Let U = {6, 7, 8, 9, 10, 11, 12}, A = {6, 7, 8, 9}, B = {6, 7, 10, 11}, and C = {8, 10, 12}. List all the members of the given set. (Enter your answers as a comma-separated list.)
A ∪ (B ∩ C)
On solving the provided question we can say that the sets are as
U = {6, 7, 8, 9, 10, 11, 12}, and z(180) = (180-185)/4 = -1.25
what is set?A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,
the sets are as
U = {6, 7, 8, 9, 10, 11, 12},
A = {6, 7, 8, 9},
B = {6, 7, 10, 11},
C = {8, 10, 12}
1){8,10}
2)z(180) = (180-185)/4 = -1.25
P(x < 180) = P(z < -1.25)
3)28c5
4)-4
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help mee please i need help
Answer:
this hard
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Need true or false answers
Given the set of statements according to the questions are:
1) 28 ∈ A - true.
2) 8 ∈ B - true.
3) 31 ∉ A - false.
4) 1 ∈ B - false
What is a set?
In mathematics, a set is a collection of distinct objects or elements that are grouped together as a single entity. The objects in a set can be anything: numbers, people, animals, colors, or even other sets. The elements of a set are usually enclosed in braces, {}.
By using the given data:
A = {28, 29, 30, 31, 32, 33, 34, 35};
B = The set of even numbers greater than or equal to 6 and less than or equal to 12
B = {6, 8, 10, 12}
Now lets find the answer
1) 28 ∈ A - 28 is present in set A hence, this statement is true.
2) 8 ∈ B - 8 is present in set B, hence this statement is true.
3) 31 ∉ A - 31 is present in set A, hence this statement is false.
4) 1 ∈ B - 1 is not present in set B, hence this statement is false.
Hence,
1) 28 ∈ A - true.
2) 8 ∈ B - true.
3) 31 ∉ A - false.
4) 1 ∈ B - false
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A block is 75cm× 40cmx50cm .how many cubes of side 0.1 m can be carved out it
Answer: 150 Cubes.
Step-by-step explanation:
Volume of cuboid is l*b*h, Volume of cube is S^3.
= 75*50*40 = 1,50,000 CM, = 0.1m= 10cm^3= 1000
No of cubes in one cuboid= volume of cuboid/volume of cube
1,50,000/1000= 150 cubes.
Find value of x. Round to the nearest tenth
Answer:
Step-by-step explanation:
x/sin90=17.3/sin53
sin90=1
x=17.3/sin53
x=13.8
The profit a company makes decreases exponentially at a rate of 0.9% per year. In 2014, the profit was $9500. Calculate the profit in 2019.
Answer: The formula for exponential decay is given by:
P(t) = P0 * e^(-rt)
where P(t) is the profit at time t, P0 is the initial profit, r is the rate of decrease in percentage, and t is the time elapsed in years.
In this case, P0 = $9500, r = 0.9%, and t = 5 (the time elapsed from 2014 to 2019).
First, we need to convert the rate of decrease from a percentage to a decimal:
r = 0.9% / 100 = 0.009
Now, we can plug in the values into the exponential decay formula:
P(5) = $9500 * e^(-0.009 * 5) = $9500 * e^(-0.0455)
We can calculate the value of e^(-0.0455) using a calculator or mathematical software. The result is approximately 0.955.
Therefore, the profit in 2019 is:
P(5) = $9500 * 0.955 = $9027.25
So, the profit in 2019 would be $9027.25.
Step-by-step explanation:
Last question: Find the volume of a cylinder where the circular base has a diameter of 7km, and the height of the cylinder is 13.08km.
Note: Find the indicated volumes. Use 3.14 for pi and round your final results two decimal places as needed
Answer:
503.1222
rounded: 503.12
There are 3 swimmers in a race. There will be a first-place and a second-place prize awarded. In how many different ways can the 2 prizes be awarded?
Answer:
Step-by-step explanation:
6
