The length of a rectangle is four more than triple the width. If the perimeter is 160 inches, find the dimensions.
The length and the width of the rectangle are 61 inches and 19 inches, respectively
How to determine the dimensions of the rectangle?The mathematical statement from the question is given as
Length of a rectangle is four more than triple its width.
Mathematically, this can be represented as
Length = 3Width + 4
The perimeter is given as
Perimeter = 160 meters
The perimeter is calculated as
Perimeter = 2 x (Length + Width)
So, we have
2 x (3Width + 4 + Width) = 160
Divide by 2
3Width + 4 + Width = 80
This gives
4Width= 76
Divide by 4
Width = 19
Recall that
Length = 3Width + 4
So, we have
Length = 3 * 19 + 4
Evaluate
Length = 61
Hence, the dimensions are 61 inches by 19 inches
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the population of the world in 2010 was 7 billion and the annual growth rate was estimated at 1.2 percent per year. assuming that the world population follows an exponential growth model, find the projected world population in 2044. round your answer to one decimal place.
With annual growth rate of 1.2% per year, the projected world population in 2044 is 10.5 billion
The formula for the exponential growth model is:
X(t) = Xo (1 + r)^t
Where:
X(t) = value of X at time t
Xo = initial value
t = time interval
r = growth rate
Parameters given:
Xo = 7 billion = 7 x 10⁹
t = 2044 - 2010 = 34
r = 1.2% = 0.012
Hence,
X(t) = 7 x 10⁹ (1 + 0.012)³⁴
X(t) = 10.5 x 10⁹ = 10.5 billion
Therefore,
The projected world population in 2044 = 10.5 billion
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Find the distance between the points ( – 9.3,3) and ( – 9.3, – 7.5).
We have that the data is: (x₁ =–9.3, y₁=3) and (x₂=– 9.3, y₂=–7.5). The formula to calculate two distance between two points is:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(x_1-x_2)^2+(y_1-Y_2)^2 } } \end{gathered}$}}[/tex]
When we calculate the distance between two points, we solve what goes inside the parentheses, then it is calculated to the power of 2, and we continue adding the two numbers of the previous results, and finally the square root is calculated.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(-9.3-(-9.3))^2+(-7.5-3)^2 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(0)^2+(-10.5)^2 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{0+110.25 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{110.25 } } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=10.5 } \end{gathered}$}}}[/tex]
The distance between the points ( – 9.3,3) and ( – 9.3, – 7.5) is 10.5QUESTION 8/10 HELP ASAPP
Answer:
y = - 2x - 4=================
The slope- intercept form:
y = mx + bUse two points on the graph to find the slope:
(-2, 0) and (0, - 4)Find the slope:
m = (- 4 - 0)/(0 - (-2)) = - 4/2 = - 2The y-intercept is b = - 4.
The equation is:
y = -2x - 4PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
11r+2
Step-by-step explanation:
combine the two numbers with the same variable and then leave the 2 by itself, that would be 4r+7r=11r and then bring the 2 down that makes 11r+2
According to a study conducted by an organization, the proportion of americans who were afraid to fly in 2006 was 0. 10. A random sample of americans results in indicating that they are afraid to fly. Explain why this is not necessarily evidence that the proportion of americans who are afraid to fly has.
According to the the concept of hypothesis testing, there is no evidence that the proportion of Americans who are afraid to fly has decreased.
Hypothesis testing:
Basically, in math hypothesis, it test the population on the basis of the sample data taken from the population using a simple random sampling.
Given,
According to a study conducted by an organization, the proportion of Americans who were afraid to fly in 2006 was 0. 10. A random sample of 1300 Americans results in 117 indicating that they are afraid to fly.
Now, we need to explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has.
While we looking into the given question,
Sample size, n = 1300
Number of Americans who were afraid to fly, x = 117
Now, we have to computing the sample proportion of Americans who afraid to fly,
Therefore, p = 117 / 1300 = 0.09
Then the Formulation of Hypotheses is written as,
Here the Null Hypothesis: H0: p≥0.10
And the alternative Hypothesis: Ha: p<0.10
Then the Left-tailed test of Test statistic is written as,
Here Let us assume that the level of significance, α = 0.05.
Then the Critical value, z≈−1.645
And the Decision rule is written as
If the value of |z|<|z0.05|≈1.645: Do not reject the null hypothesis.
Otherwise If value of |z|≥|z0.05|≈1.645: Reject the null hypothesis.
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WHAT DOES Y EQUAL PLS HELP ASAP
The standard form of quadratic function is f(x) = 1(x-2)2 - 6
A quadratic function is a two-degree function. A parabola is the graph of a quadratic function. A quadratic function has the general form f(x)=ax2+bx+c, where a, b, and c are real numbers and a0. A quadratic function has the standard form f(x)=a(xh)2+k. The vertex (h,k) has the coordinates h=-b2a,k=f(h)=f(b2a).
Given points (5,3) and (2,-6)
We know that the General form of a quadratic function is
f(x) = ax2+bx+c
Standard form = a(x-h)2 + k
Here point(x,y) = (5,3) and vertex (h,k) = (2,-6)
y = a(x-h)2 + k
3 = a(5-2)2 – 6
3 = a(3)2 – 6
3 + 6 =9a2
9= 9a2
a2 = 9/9
a2=1
a=1
Now substitute a value in standard form
f(x) = 1(x-2)2 – 6
Therefore the standard form of quadratic function is f(x) = 1(x-2)2 – 6
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Mr. Fitch needs to get a loan to replace the air-conditioning system in his home.
The cost of the replacement, including installation, is $4,348.00.
He can apply for a 5-year loan or a 3-year loan.
Both loans involve simple interest with an annual interest rate of 6.5%.
If Mr. Fitch applies for the 5-year loan, how much more will he pay in interest than with the 3-year loan?
If Mr. Fitch applies for the 5-year loan, the amount he will pay in interest with the 3-year loan is: $565.24.
How to find the interest amount?First step is to find the cost of replacement left
Cost of replacement = $4,348 x 6.5%
Cost of replacement =$282.62
Second step is to calculate the amount of 5-year loan
Loan = $282.62 x 5
Loan = $1413.1
Third step is to calculate the amount of the 3-years loan
Loan = $282.62 x 3
Loan = $847.86
Now let find the amount he will pay in interest with the 3-year loan
Amount = $1,413.1- $847.86
Amount =$565.24
Therefore the interest amount is $565.24.
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Simplify your answer as much as possible please.
Answer:
3/5=w
Step-by-step explanation:
the 2 onthe numerator and the 2 on the denominator cancel each other out leaving w byitself.
Answer:
16/5
Step-by-step explanation:
10x3/5=10x w-2/2
What is the value of 43?
Responses
The Answer is : 64
I took the test and it showed this is the correct answer, hope this helped :)
Sketch and Solve. A rectangular page is 2 inches longer than it is wide. If the diagonal of the pag is 52 inches, what is the perimeter of the page
The Perimeter of the Rectangle is 144cm;
What is the Perimeter of a Rectangle?
The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in meters, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.
A rectangle has four 90° angles.
The lengths of a rectangle's diagonals are equal. Rectangle perimeter is calculated using the formula perimeter of a rectangle = 2(l + w), where l is the rectangle's length and w is its width.
According to the question
Let the length of the rectangle be x cm;
So, The breadth of the rectangle will be: (x+2) cm;
And, we have the diagonal = 52 cm;
So,
we can use the Pythagoras triangle to find the value of x cm;
⇒[tex]x^{2} + (x+2)^{2} = (52)^{2}[/tex]
⇒[tex]2x^{2} +4+4x = 2704;\\[/tex]
⇒[tex]2x^{2} +4x = 2700[/tex]
⇒[tex]2x^{2} +4x - 2700 =0;[/tex]
By solving the above equation, we get:
x = 35 cm;
So, the length of the rectangle = is 35 cm;
Breadth of the rectangle = 37 cm;
and
Perimeter of the Rectangle = 2(35 + 37) cm;
The perimeter of the Rectangle = = 144 cm;
Hence,
The perimeter of the Rectangle = = 144 cm;
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Write ap text-style pseudocode for a linear search that searches through a list to find an item x. It should display found if the x is equal to an item in the list.
list <- value, value, value, value
x<-value
FOR EACH item IN the list
{
IF item=x
display "found"
}
Pseudocode is an informal manner of programming description that does not require any strict programming language syntax or underlying era concerns. it is used for growing an outline or a rough draft of a program. Pseudocode summarizes an application's flow but excludes underlying info.
Pseudocode is a synthetic and casual language that facilitates programmers' to increase algorithms. Pseudocode is a "text-primarily based totally" element (algorithmic) layout device. The policies of Pseudocode are fairly straightforward. All statements showing "dependency" are to be indented. the Python pseudocode is a syntax-loose representation of code. So, the Python pseudocode no longer involves any code in it. The Python pseudocode should be a very near illustration of algorithmic good judgment.
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Find the length of the third side. If necessary, write in simplest radical form.
v/7 + 7.1 = -4.1 solve for v
What is a, the starting term, for the function: f(x) = 300(1.16)^x?
The starting term of the function f(x) = 300 (1.16)^x is 300
What is an exponential function?This is a type of function that are of 3 main parts
the starting or initial valuebase function the exponentsConsidering the given problem, f(x) = 300(1.16)^x
the starting = 300
the base = 1.16
the exponents = x
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.
The base is what determines exponential growth or decay
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What is the range of the given function?
Responses
y≤3y is less than or equal to 3 - no response given
y≤0y is less than or equal to 0 - no response given
−6≤y≤3−6≤y≤3 - no response given
R (all real numbers)
The range of the given function, using it's concept, is given by the following option.
y≤3: y is less than or equal to 3.
How to obtain the range of a function?The range of a function is the set that is composed by all the output values on a function.
Om the graph of a function, we have that:
The input values are given by the x-axis, that is, by the horizontal axis.The output values are given by the y-axis, that is, by the vertical axis.Hence from the graph, the range of the function is given by the values of y of the function.
From the graph of the function given at the end of the answer, the function assumes values of 3 and greater, hence the first option is the correct option giving the range of the function.
Missing InformationThe function is given by the image presented at the end of the answer.
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Challenge In basketball, some baskets are worth two points. Others are worth three points. In one game, the ratio of three-point baskets to three-point tries for one team was 2:5. If the team scored 24 points from three-point baskets, how many three-point tries did the team have?
Answer:
20
Step-by-step explanation:
3-point shots made : 3-point shots attempted = 2 : 5
If the team made 24 points out of 3-point baskets, then since 24/3 = 8, it made 8 3-point baskets.
Proportion:
8 made is to 2 as x attempted is to 5
8/2 = x/5
2x = 40
x = 20
a research team believes that a recently discovered treatment will have an effect on the dependent variable. they randomly selects a sample of 12 people, and with their permission, provides them a treatment. they then evaluate the evidence regarding whether their treatment had an effect. here's the data: the mean for their sample is 99. the mean for the population is 102, with a standard deviation of 11. assume a normal distribution for the individual scores. the research team sets their alpha level to .05. . calculate the z test, and decide whether the research team should: 0 - retain the null hypothesis 1 - reject the null hypothesis.
Using the z test the value of z is -0.9404 and the value of z the research team should 0 - retain the null hypothesis.
In the given question,
They randomly selects a sample of 12 people, and with their permission, provides them a treatment.
So n = 12
The mean for their sample is 99.
x = 99
The mean for the population is 102.
μ=102
A standard deviation of 11.
σ = 11
Test statistic z:
z = (x-μ)/σ /√n
Now putting the value
z = 99-102/11/√12
z=-3/11/3.45
z=-3/3.19
z= -0.9404
Test statistic z = -0.9404
From the value of z the research team should 0 - retain the null hypothesis.
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A farmer bought a number of pigs for $168. However, 7 of them died before he could sell the rest at a profit of 5 per pig. His total profit was $36. How many pigs did he originally buy?
Answer:
15$
Step-by-step explanation:
a number increased by 6 is 30
Answer:
the number is 24 good luck :)
Answer:
24
Step-by-step explanation:
1) Break down the question
We are told that a number increased by 6 is 30 meaning a number added to 6 will get 30.
2) Work you way backwards to get your answer
To find the answer to this question we have to subtract 30 from 6.
This is because we are told that a number is added to get 30 so we should subtract to find our number!
30 - 6 = 243) Check you answer
Every question that you may be unsure of or had been struggling with should always be checked.
To check our answer we have to go backwards and see if the numbers match
24 + 6 = 30As we can see the numbers match together and are correct in our equation
Hope this helps, have a great day!
3. What equation matches the graph below?
Answer:
B, or y - 1 = 1/2(x + 2)
Step-by-step explanation:
when you solve B, you get y = 1/2x + 2, which is the equation being shown on the graph.
Radius: 6 mm
Diameter: 12 mm
Area:
Answer:
The area of the circle would be 113.04
Step-by-step explanation:
If you plug the radius into the formula for finding the area of a circle (π·r²), or (3.14 · r²) then you'll get 113.04
Hope this helps! :D
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What constant would be added to the expression x^2+8/3x in order to make it a perfect square
Answer:
Hence, the value of y = b^2 = (-3/2)^2 = 9/4 is your answer
Step-by-step explanation:
only if your answers are
A) 3/2
B) 9/4
C) 6
D) 9
List the first 5 multiples
4:
3:
9:
12:
Answer:
Step-by-step explanation:
3 * 4 = 12 3 * 5 = 15 List of the First 5 Multiples of 3: 3, 6, 9, 12, 15 Notes: The listed multiples are the First 5 Multiples of 3 that are positive (greater than 0) The sum of the digits in Multiples of 3 are divisible by 3
Solve: 9l5n - 8l - 3 < 15
Answer:
9l^5n-8l-3<15
Step-by-step explanation:
a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. (a) how fast is the radius of the balloon changing at the instant the radius is 50 centimeters?
0.015 the radius of the balloon changing at the instant the radius is 50cm
given that
a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute
radius = 50 centimeters
now we need to find the volume of the balloon
Let V = volume of the balloon at time t
r = radius of the balloon at time t
V = (4/3)πr3
Given: dV/dt = 500
Find: dr/dt when r = 50
dV/dt = (4/3)(3πr^2)(dr/dt)
500 = 4π(50)^2(dr/dt)
dr/dt = 1/(20π)
dr/dt = 0.015 cm/min
0.015 the radius of the balloon changing at the instant the radius is 50cm
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Suppose you are able to download 1 free song to your tablet daily and each additional download costs $0. 59. If your monthly bill is $15. 34, how many songs did you download if you downloaded 28 free songs? write an equation and solve for the unknown variable.
For the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including 28 free songs is equal to 54 songs.
As given in the question,
Total free download songs is equal to 28
Let us consider variable 'x' to represent the number of downloaded songs at the rate of $0.59
Total monthly bill of downloaded songs = $15.34
Equation formed :
0.59x = $15.34
⇒ x = 15.34 / 0.59
⇒ x = 26 songs
Total number of downloaded songs including 28 free songs
= 26 + 28
= 54 songs
Therefore, for the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including 28 free songs is equal to 54 songs.
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In the space provided below, solve the equation 4x² 768 = 0 for x algebraically. Write your answer in simplest radical form. Show all work.
Answer:
Step-by-step explanation:-b± √b²-4ac. X =
Distribute and then Combine Like Terms: 5(3x + 4) + 7x
Answer:
22x + 20
Step-by-step explanation:
Distribute:= (5)(3x) + (5)(4) + 7x
= 15x + 20 + 7x
Combine Like Terms:= 15x + 20 + 7x
= (15x + 7x) + (20)
= 22x + 20
Answer:
22x +20
Step-by-step explanation:
5(3x + 4) + 7x
5 x 3x + 5 x 4 +7x
15x + 5 x 4 + 7x
15x + 20 + 7x
22x + 20
Determine the measure of each missing angle:
Angle f= 69
Angle g= 69
Angle h= ??
I found G and F but I’m stuck on H please help me!!
Answer:
Angle f = 69°Angle g = 69°Angle h = 125°Step-by-step explanation:
Angles f and g are congruent as opposite sides are congruent. Therefore:
g = f = (180° - 42°)/2 = 138°/2 = 69°Angles h, 76°, g and the right angle all together form 360°:
h + 76 + g + 90 = 360h + 166 + 69 = 360h + 235 = 360h = 360 - 235h = 125