Answer: w=9cm l=21cm
Step-by-step explanation
l=3w-6
l+l+w+w=60
3w-6+3w-6+w+w=60
8w-12=60
8w=60+12=72
w=72/8
w=9
l=3w-6
l=27-6
l=21
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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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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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:
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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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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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:
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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Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 16. Complete parts (a) through (c) below.
a)The standard deviation is given by σ = sqrt(np(1-p)) = sqrt(24 × 0.75 × 0.25) = 2.12 . b)Significantly low: μ - 2σ = 18 - 2 × 2.12 ≈ 13.76 ,Significantly high: μ + 2σ = 18 + 2 × 2.12 ≈ 22.24 ,c)z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08.
How to calculate standard deviation?A group of 24 peas with green pods has a binomial distribution with n = 24 and p = 0.75. The mean is calculated as = np = 24 0.75 = 18, and the standard deviation is calculated as = sqrt(np(1-p)) = sqrt(24 0.75 0.25) = 2.12 (rounded to two decimal places).
b) The range rule of thumb states that results that deviate from the mean by more than two standard deviations are considered significantly low or significantly high. In this case, the values separating significantly low and significantly high results are:
Significantly reduced: - 2 = 18 - 2 2.12 13.76
Significantly greater: + 2 = 18 + 2 2.12 22.24
c) To see if a result of three peas with green pods is significantly low, we must calculate its z-score, which is given by:
z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08
Because the z-score is much lower than -2, the cutoff for significantly low results, we can conclude that a result of 3 peas with green pods is significantly low.
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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]
A pack of gray wolves was reintroduced to a forest. The table gives the size of
this population of wolves over time.
Which model,in which t represents that time in year,best fits the data in the table
The exponential regression equation that best fits the data in the table is given as follows:
C. f(t) = 11.9(1.12)^t.
How to obtain the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which:
a is the value of y when x = 0.b is the rate of change.For this problem, we have that the parameters are estimated as follows:
a = 11.9, as when x = 0, y = 12, and the closest option to 12 is a = 11.9.b = 1.12, as the population increases over time, hence b > 1.This means that the correct option is given by option C.
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If 0 = 2x +9 and W = 2(2x-6), what is the measure of p
Answer:
Angle P= Angle W=2(2x-6)
=4x-12
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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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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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
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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Choose the ratio below that is equivalent to the greatest fraction.
A. 5:3
B8:4
C. 2:7
D 9:5
The ratio that is equivalent to the greatest fraction is B. 8:4.
What is a ratio?A ratio is a relative size or value contained in another quantity. It is computed as the quotient of the smaller and larger values.
Ratios are fractional values, which we can depict as fractions, decimals, or percentages.
Ratios are also depicted using the ratio symbol (:), describing the numerical relationship between two or more values or variables.
Ratio 5:3The sum of ratios = 8
5/8 = 0.625
Ratio 8/4The sum of ratios = 12
8/12 = 0.67
Ratio 2:7The sum of ratios = 9
2/9 = 0.22
Ratio 9:5The sum of ratios = 14
9/14 = 0.64
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.3 cubic feet ofwater weigh in pounds? In tons?
To find the weight of 4.3 cubic feet of water, we need to first find the number of gallons of water that 4.3 cubic feet holds and then multiply that by the weight of 1 gallon of water.
1 cubic foot holds 7.48 gallons of water, so 4.3 cubic feet holds 4.3 x 7.48 = 31.964 gallons.
1 gallon of water weighs 8.33 pounds, so 31.964 gallons of water weigh 31.964 x 8.33 = 265.9012 pounds.
Therefore, 4.3 cubic feet of water weigh 265.9012 pounds.
To find the weight in tons, we need to divide the weight in pounds by 2000:
265.9012 pounds ÷ 2000 = 0.13295 tons
So 4.3 cubic feet of water weigh 0.13295 tons.
Answer:
0.13314 tons.
Step-by-step explanation:
We can start the calculation by first converting the cubic feet of water to gallons and then converting the gallons to pounds.
Conversion from cubic feet to gallons:
4.3 cubic feet = 4.3 cubic feet * 7.48 gallons/cubic foot = 32.084 gallons
Conversion from gallons to pounds:
32.084 gallons = 32.084 gallons * 8.33 pounds/gallon = 266.279 pounds
Conversion from pounds to tons:
266.279 pounds = 266.279 pounds / 2000 pounds/ton = 0.13314 tons
So, 4.3 cubic feet of water weigh 266.279 pounds or 0.13314 tons.
Three different accounts are described below. Order the accounts according to their values after 10 years, from greatest to least.
You deposit $950 in an account that earns 5% interest semiannually.
You deposit $800 in an account that earns 7.5% annual interest compounded quarterly.
You deposit $700 in an account that earns 7.75% annual interest compounded monthly.
Answer:
$800 at 7.5%$950 at 5%$700 at 7.75%Step-by-step explanation:
You want to order the accounts greatest to least by their value after 10 years.
$950 at 5%, compounded semiannually$800 at 7.5%, compounded quarterly$700 at 7.75%, compounded monthlyValueThe value of each account can be found using the compound interest formula:
A = P(1 +r/n)^(nt)
Principal P earning rate r compounded n times per year for t years.
For the three accounts, the corresponding values are ...
950(1 +0.05/2)^(2·10) = 1556.69800(1 +0.075/4)^(4·10) = 1681.88 . . . . . . . greatest value700(1 +0.0775/12)^(12·10) = 1515.63 . . . . . least valueComparisonThe order, greatest to least, according to the account values is ...
$800 at 7.5%$950 at 5%$700 at 7.75%__
Additional comment
The $700 account will overtake the $950 account after 11 years. It will take about 46 years for it to overtake the $800 account. Eventually, the higher interest rate with greater frequency of compounding wins out.
<95141404393>
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.
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.
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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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:
Faith invests £800 for 3 years in a bank account.
The account pays simple interest at a rate of 0.4% per year
Work out the total amount of interest Faith has got at the end of the 3 years.
Faith earned £96 in interest at the end of the 3 years.
How to calculate the interest rateUsing the simple interest formula:
I = P x r x t
where
I is the interest earned,
P is the principal or initial amount invested,
r is the interest rate as a decimal, and t is the time period in years.
In this case, Faith invested £800 for 3 years at a simple interest rate of 0.4% per year, or 0.04 as a decimal. Plugging in the values:
I = £800 x 0.04 x 3
= £96
Therefore, Faith earned £96 in interest at the end of the 3 years.
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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
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
3 1/2x - 5 1/3x , x = 2/5
The value of the expression is -11/15
How to determine the value of the expressionIt is important to note that algebraic expressions are expressions having factors, constants, variables, coefficients and terms.
From the information given, we have that;
3 1/2x - 5 1/3x
turn into improper fractions
7x/2 - 16x/3
Now, let's determine the value by substituting the value of x as 2/5 in the expression, we have;
7(2/5)/2 - 16(2/5)/3
Multiply the values
14/5/2 - 32/5 /3
Take inverse of the denominator
14/5 ×1/2 - 32/5 × 1/3
7/5 - 32/15
21 - 32/15
-11/5
Hence, the value is -11/15
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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
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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What is the least number and greatest number of shells he would need
Answer:
Step-by-step explanation:
What is the least number and greatest number of shells he would need
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.
