The dimensions of the rectangle is 83 feet x 46 feet
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
The perimeter P of the rectangle = 258 feet
Let the length of the rectangle be = L
Let the width of the rectangle be = W
And , The width is 37 feet less than the length. ,
So , W = L - 37
Perimeter P = 2 ( Length + Width )
Substituting the values of L and W in the equation , we get
Perimeter P = 2 ( L + L - 37 )
2 ( L + L - 37 ) = 258
( L + L - 37 ) = 129
2L - 37 = 129
Adding 37 on both sides , we get
2L = 166
Divide by 2 on both sides , we get
Length L of the rectangle = 83 feet
Substituting the value of L in equation ,we get
W = L - 37
Width W of the rectangle = 46 feet
Therefore , Length = 83 feet and Width = 46 feet
Hence , the dimensions of the rectangle is 83 feet x 46 feet
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The box plot shows the times for sprinters on a track team.
(A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 44, 48, 50.5, 53, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.)
What is the value of the upper quartile?
The five number from the box plot is presented as follows:
Minimum value: 44.First quartile: 48.Median: 50.5.Third quartile: 53.Maximum value: 56.What does a box-and-whisker plot shows?A box and whisker plot shows five things of a distribution, listed as follows:
The data set's lowest value.The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.
50% of the data set is less than the median and 50% is more than the median, which is the midpoint value of the data set.The third quartile, which is the median of the data set's top 50% of measurements, is the value that 75% of the measures fall below.The data set's maximum value.
These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.
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5. On a cattle farm, the ratio of beef cattle to dairy cattle is 4:3.
3
(a) Interpret the ratio: For every
beef cattle, there are
cattle.
dairy
(b) If there are 24 dairy cattle, how many
beef cattle would there be? Show your
work.
For every 4 beef cattle there is 3 dairy cattle. For 24 dairy cattle there will be 32 beef cattle as per the given ratio of 3:4.
What is ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls). The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two things.
Here,
a. No for every 4 beef cattle there is 3 dairy cattle.
b. 4/3=x/24
x=4*24/3
x=32 beef cattle
There are 3 dairy cattle for every 4 beef cattle. According to the stated ratio of 3:4, there will be 32 beef cattle for every 24 dairy cattle.
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use the given information about the polynomial graph to write the equation
Degree 5. Roots of multiplicity 2 at x = −3 and x = 2 and a root of multiplicity 1 at x = −2. y-intercept at (x, y) = (0,62).
For the given roots and point, the polynomial is:
p(x) = (62/72)*(x + 3)²*(x - 2)²*(x + 2)
How to write the polynomial?We know that a polynomial with leading coefficient a and the roots:
x₁, x₂, ..., xₙ
Can be written as:
p(x) = a*(x - x₁)*...*(x - xₙ)
Here we have the roots:
-3, -3, 2, 2, -2
Then we can write:
p(x) = a*(x + 3)*(x + 3)*(x - 2)*(x - 2)*(x + 2)
p(x) = a*(x + 3)²*(x - 2)²*(x + 2)
Now we also know that our polynomial passes through (0, 62), then:
p(0) = 62 = a*(0 + 3)²*( 0 -2)²*(0 + 2)
62 = a*9*4*2
62/(9*4*2) = a
62/72
then the polynomial is:
p(x) = (62/72)*(x + 3)²*(x - 2)²*(x + 2)
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Evaluate f(x)=3x-9, when x=-2
A. -18
B. -33
C. -3
D. -15
Answer:
d. -15
Step-by-step explanation:
f(x) = 3x - 9, when x = -2
Input -2 into the function for x and solve:
f(-2) = 3(-2) - 9
f(-2) = -15
Hope this helped :)
A picosecond is one trillionth of a second. If one trillionth = 1 × 10 − 12, how many picoseconds are there in 6 minutes?
The picoseconds that are there in 6 minutes is 3.6 × 10^14.
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
In this case, picosecond is one trillionth of a second. If one trillionth = 1 × 10^12
The seconds in 6 minutes will be:
= 60 × 6
= 360 seconds
= 3.6 × 10^2
The picoseconds in 6 minutes will be:
= 1 × 10^12 × 3.6 × 10^2
= 3.6 × 10^14
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A number cube with faces labeled from 1 to 6 will be rolled once.
The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling a number greater than 3.
If there is more than one element in the set, separate them with commas
The Sample space for number greater than 3= {4, 5, 6}
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
A number cube with faces labeled from 1 to 6 will be rolled once.
so, Sample Space = { 1, 2, 3, 4, 5, 6}
sample space for number greater than 3= {4, 5, 6}
Thus, the probability is 3/6 or 1/2.
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11C8 x 4C3
related to permutations. Please explain in depth because I want to understand.
₁₁C₈ * ₄C₃ as related to permutations is ₁₁P₈ / 8! * ₄P₃ / 3!
Further explanation of combination and permutationThe term combination refers to a method of choosing where order does not matter. an instance forming 3 letter word from ABC. the combination is ₃C₃ = 1
In permutation, order matters hence in choosing or making selection specific order should be followed. an instance here is arranging the 3 letters word from ABC. ₃P₃ = 6
ABCACBBACCABBCACBAAll the items above are different permutations however for combination they are same.
The difference mathematically is dividing by the number of arrangements
₃C₃ = 3! / (3!(3-3)!) = 3! / (3!* 0!) = 3! / 3! = 1
₃P₃ = 3! / (3-3)! = 3! / (0!) = 3! / 1 = 3! = 6
Therefore ₃C₃ = ₃P₃ / 3!
similarly
₁₁C₈ * ₄C₃ = ₁₁P₈ / 8! * ₄P₃ / 3!
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(A) find the perimeter of triangle BCF, to the nearest hundredth
(B) find the area of triangle BCF
Perimeter of triangle BCF is 19.24 units. Area of triangle BCF is 15 [tex]units^{2}[/tex].
Distance formula = [tex]\sqrt{(x1-x2)^{2}+(y1-y2)^{2} }[/tex]
Perimeter = a + b + c
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
s = [tex]\frac{a+b+c}{2}[/tex]
Given, B(3,2), C(1,-2), F(-3,5).
BC = a = [tex]\sqrt{(3-1)^{2} +(2+2)^{2} }[/tex]
= [tex]\sqrt{2^{2} +4^{2} }[/tex]
= [tex]\sqrt{4+16}[/tex]
= [tex]\sqrt{20}[/tex]
= 4.47 units
CF = b = [tex]\sqrt{(1+3)^{2} +(-2-5)^{2} }[/tex]
= [tex]\sqrt{4^{2} +7^{2} }[/tex]
= [tex]\sqrt{16+49}[/tex]
= [tex]\sqrt{65}[/tex]
= 8.06 units
BF = c = [tex]\sqrt{(3+3)^{2} +(2-5)^{2} }[/tex]
= [tex]\sqrt{6^{2} +3^{2} }[/tex]
= [tex]\sqrt{36+9}[/tex]
= [tex]\sqrt{45}[/tex]
= 6.71 units
Perimeter = a + b + c
= 4.47 + 8.06 + 6.71
= 19.24 units
s = [tex]\frac{a+b+c}{2}[/tex]
= [tex]\frac{19.24}{2}[/tex]
= 9.62
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
= [tex]\sqrt{9.62(9.62-4.47)(9.62-8.06)(9.62-6.71)}[/tex]
= [tex]\sqrt{9.62*5.15*1.56*2.91}[/tex]
= [tex]\sqrt{224.91}[/tex]
= 14.99
≈ 15 [tex]units^{2}[/tex]
Hence, perimeter is 19.24 units and area is 15 [tex]units^{2}[/tex].
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A frozen yogurt stand charges per ounce of frozen yogurt purchased. There is an extra charge for a waffle bowl. The total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.
Which statement is true?
A. The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.
B. Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.
C. Each ounce of frozen yogurt costs $0.45 and a waffle bowl is $1 extra.
D. The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.45.
The true statement when the frozen yogurt stand charges per ounce of frozen yogurt purchased is B. Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.
How to explain the function?In the scenario, the total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.
In this case, it is important to note that Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.
For example, for 2 ounces, this will be:
= 0.45f + 1
= 0.45(2) + 1
= 0.9 + 1
= $1.9
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If 10 ops are equal to 1.63 sals, how many sals are equal to a book that costs
12.25 ops?
Answer:
if the selling price of the radio is Arya 4321 and loss e79 find the cost price of the radio
What is the image point of (2,0)(2,0) after the transformation D_{\frac{1}{2}}\circ R_{270^{\circ}}D
2
1
∘R
270
∘
The image of point (2,0) after the transformation involving the dilation and the rotation is given as follows:
(0, -1).
What are the transformations applied to the point?The first transformation applied to the point is a dilation, which multiplies the coordinates of the point by the scale factor.
The point has these following coordinates:
(2,0).
The scale factor of the dilation is:
k = 1/2 = 0.5.
Then each coordinate of the point is multiplied by 0.5, hence:
2 x 0.5 = 1.0 x 0.5 = 0.Hence the coordinates are:
(1,0).
The rule for a rotation of 270º clockwise around the origin is:
(x,y) -> (y,-x).
Then:
x = 1, -x = -1.y = 0.Thus the coordinates of the image are given as follows:
(0, -1).
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16/5 x 25/8 multiply each of the following fractions
Consider Z=x^3-8
A) Find the real root of Z.
B) Write Z as a product of linear terms.
Using the formula, the real of z is 2 and the linear form of z is [tex](x-2)(x^2+2x+4)[/tex].
In the given question,
The given expression is z=x^3−8
We can given expression as [tex]x^3-8=(x)^3-(2)^3[/tex]...............(1)
We have to find the real root of the z.
We also have to find the z as a product of linear terms.
To solve the given expression using the formula
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
If we compare equation 1 to the [tex]a^3-b^3[/tex].
After compare we get a=x and b=2
Now the linear form of the given expression is
[tex]z=(x)^3-(2)^2[/tex]
[tex]z=(x-2)(x^2+2x+(2)^2)[/tex]
Simplifying
[tex]z=(x-2)(x^2+2x+4)[/tex]
Now the real root of of z;
x-2=0
x=2
Hence, the real of z is 2 and the linear form of z is [tex](x-2)(x^2+2x+4)[/tex].
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What is the slope of a line that is perpendicular to y = 6/7x + 2 and passes through point (−2, 3)?
The slope of the line that is perpendicular to y is m=6/7.
What do you mean by slope?
A number used to define a line's direction and steepness in mathematics is called the slope or gradient of the line.
The slope is denoted by m,
m = slope
According to the data in the given question:
We have to determine the slope of line that is perpendicular to y,
y=6/7x+2
For the slope, we need follow this equation, where m is slope,
y=mx+b............(1)
In the given question,
m=6/7
Therefore, the slope of the line is m=6/7.
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calculate the arithmetic mean of the numbers 7 and 17, 1/3 and-2/5, -12 and 7, -121 and 49, -16, -9, and 4
47 POINTSSSSSSSSSSSS
The arithmetic mean of the numbers is -6 11/15
What is arithmetic mean?Arithmetic mean is often referred to as the mean or arithmetic average. It is calculated by adding all the numbers in a given data set and then dividing it by the total number of items in that set.
therefore, arithmetic mean= sum of items/ no of items
The average of numbers,7, 17, 1/3 ,-2/5, -12 ,7, - 121, 49,-16,-9and 4 is obtained by adding the numbers to together and dividing the result by the total frequency.
The sum of the numbers is 7 +17 +1/3-2/5 -12+7 - 121+ 49-16-9+ 4= -1111/15
the total number of items in the set is 11
therefore arithmetic mean = -1111/15÷ 11
= -1111/15×1/11
=-101/15
= -6 11/15
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If the nth term of a number sequence n2-3 find the first 3 terms
Answer:
-1,-2,0
Step-by-step explanation:
n(2-3)
1st term=n(2-3)
substitute value
1(2-3)=-1
2nd term=2(2-3)=-2
3rd term=3(3-3)=0
SOMEONE HELP ASAP PLEASE!!!!! Allie deposited $5,000.00 into a new savings account that earns 11% interest compounded
monthly. How long will it take for the balance to grow to $6,407.00?
Round your answer to the nearest month.
The time taken for the balance to grow is 2.3 years.
What is compound interest?
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
"Interest on interest,
Given, compound interest =6.407
principal = 5,000
rate = 11%
to find the time
we know compound interest = principle(1+rate)^t
6407= 5000(1+11/100)^t
6407/5000= (1.11)^t
1.28 = (1.11)^t
taking log
log (1.28)= log(1.11)^t
0.24/0.104 =t
t = 2.3
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Solve the equations for X. Check
If possible.
a)
3x + 5 = 4x+8-X
b) 3x + 2-(X+3)= X+3-(-3x-4)
Answer:
-4
Step-by-step explanation:
When answering questions like these first, combine like terms you get 3x+5 =3x+8, Subtract 5 from both of the sides you get 3x=3x+3 remove 3x from both sides and you got 0=3 this is a contradicting statement meaning no solution ∅
B) Distribute first, 3x + 2 -x = x + 3 + 3x +4
2, Combine the like terms 2x - 1 = 7 + 4x
3, Isolate variable and constants 2x = 8 + 4x
3(1) Cont- Isolation -2x = 8
Thus divide both side by -2 giving us -4
Pls help asap maths
32/3
Step-by-step explanation:
5 = 3(x-9)
5 = 3x - 27
5 + 27 = 3x
32 = 3x
x = 32/3
2. (01.03 LC)
Landyn is comparing cell phone plans. He does not want to spend more than 10% of his net pay each month. If his current monthly net pay is $560.00, which
plan below fits into his budget? (2 points)
Plan A: 55+55(0.05) -
Plan B: 50+ 50(0.05) -
Plan C: 60+60(0.05) =
Plan A
O Plan B
Plan C
O No plans
The plan that fits to Landyn's budget is plan B
What is percentage and how to calculate it?
A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%." Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. Two methods exist for calculating a percentage. By adjusting the fraction's denominator to 100 and applying the unitary approach.
We are given that Landyn's current monthly net pay is $560
And he does not wish to spend more than 10% of his current net pay
That means not more that $56
Now we are given 3 choices
Out of which the third one is more than 60 hence this rules out the third option. Now the first option the value is 55+55(0.005) which again is more than $56
Consider the option B)
50 + 50(0.05)
= 52.5
Which is less than $56
Hence, The plan that fits to Landyn's budget is plan B
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if q is 3x+ 6 and AC is 8x+8 what is the length of AC? Round your answer to the nearest hundredth
Answer:
AC = 24Step-by-step explanation:
AC is the diagonal of the parallelogram ADCB.
q is half of AC, therefore:
AC = 2qSubstitute values and solve for x:
8x + 8 = 2(3x + 6)8x + 8 = 6x + 128x - 6x = 12 - 82x = 4x = 2Find the length of AC:
AC = 8*2 + 8 = 16 + 8 = 24Johnny is 5 years younger than twice Bobby's age. If the sum of thier ages is over 66 years.
What is the Johnny's minimum age?
The minimum age of Johnny is 21 as calculated by linear inequality.
Let Johnny 's age be x.
hence bobby's age = (x+5)/2
Now the sum of their ages is over 66 years.
So we will set an inequality to find the minimum age of Johnny.
x + (x+5)/2 > 66
or, 2x + x + 5 > 66
or, 3x > 61
or, x > 20 1/3
Therefore age cannot be fraction hence the minimum age of Johnny is 21 years.
In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On that number line, size comparisons between two numbers are typically done. Different notations can be used to represent various kinds of inequalities, including:
A is smaller than b, as shown by the symbol a < b.
When the expression a > b is employed, it means that a is greater than b.
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At the skateboard park, the hot new attraction is the U-
Dip, a cement structure embedded into the ground.
The cross-sectional view of the U-Dip is a parabola that
dips 15 feet below the ground. The width at ground
level, its widest part, is 40 feet across. Sketch the
cross-sectional view of the U-Dip, and find an equation
of the parabola that models it.
The equation of the parabola exists y = 3/80(x - 20)² - 15
What is the standard equation of a parabola?In the coordinate plane, a parabola exists algebraically represented using the standard equation. A parabola's general equation exists written as,
y = a(x - h)² + k
where (h, k) signifies the vertex.
y² = 4ax is the typical equation for a normal parabola.
substitute the values in the above equation, we get
y = a(x - 20)² - 15
simplifying the above equation, we get
0 = a(0 - 20)² - 15
0 = 400a - 15
a = 15/400
a = 3 / 80
Therefore, the equation of the parabola exists y = 3/80(x - 20)² - 15.
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Each of 7 students reported the number of movies they saw in the past year. Here is what they reported. 14,10,16,15,7,15,18
Find the number of movies that the students saw. If necessary, round your answer to the nearest tenth
The total number of movies that the students saw is 105.
I got the answer by adding all of the values that the students saw. So I add 14,10,16,15...etc. which gives me the total of 105.
WILL GIVE BRAINLIEST !!
What does the slope of a position vs. time graph tell you? What does the slope of a velocity vs. time graph tell you?
Answer:
a) velocity
b) displacement
Which equation is equivalent to the given equation
x = x² - 20
A) x^2 - x-20=0
B) x^2 +x -20 =0
C) x^2-x+20=0
D) x^2+x+20=0
Identify the domain and range of the relation, and determine whether the relation is a function.
{(0, 3),(-1/3,0),(-5, 2),(1/3,4)}
Find the amount of money you will have after 20 years if you invest $25,000 at a rate of 12% if interest is compounded a. Quarterly b. Continuously
The compound interest is quaterly then answer is $266,022.2639 and when it is in continuously then answer is $275,579.4095
Quarterly compounding is what?
Compounding quarterly is the term used to describe the amount of interest that is earned on a quarterly basis on a savings account or investment where the interest is also reinvested. As most banks offer interest income on the deposits, which compounds quarterly, this information is useful in computing the fixed deposit income. It can also be used to figure out any revenue from money market instruments or other financial products that pay quarterly income.
What Does Constant Compounding Mean?
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. While this is not attainable in practice, the concept of continually compounded interest is crucial in finance. Given that most interest is compounded on a monthly, quarterly, or semiannual basis, this is an extreme example of compounding.
a) A = P(1 + r/n)nt
P = $25000
r = 12% = 0.12
t = 20 years
n = 4
A = 25000(1 + 0.12/4)(4)(20)
A = $266,022.2639 (Answer)
b) A = Pert
P = $25000
r = 12% = 0.12
t = 20 years
A = 25000e(0.12)(20)
A = $275,579.4095 (Answer)
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A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1600 miles, and the sum of their fuel efficiencies was 45 miles per gallon. What were the fuel efficiencies of each of the cars that week?
If the fuel efficiencies of each of the cars that week is 20 gallons of gas and 25 gallons of gas.
How to find the efficiencies?Let x represent the gallons consumed by car 1
Let y represent gallons consumed by car 2
Formulate an equation:
30x+40y = 1600 equation 1
x+y = 45 equation 2
Substituting equation 2 into equation 1,
30x+40(45-x) = 1600
30x+ 1800-40x = 1600
-10x+1800 = 1600
-10x = -200
Divide both side by -10x
x = -200/-10
x = 20
Substitute value of x into equation 2
x+y = 45
20+y = 45
y = 25
Hence,
Car 1 consumes 20 gallons of gas and Car 2 consumes 25 gallons of gas.
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5x-3/x-1 what is the inverse of this
Answer:
[tex]f^{-1}(x)=\dfrac{3-x}{5-x}, \quad \{x|x\neq 5\}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\dfrac{5x-3}{x-1}[/tex]
As the given function is a rational function, the domain and range are restricted.
Domain: (-∞, 1) ∪ (1, ∞).Range: (-∞, 5) ∪ (5, ∞).f⁻¹(x) is the notation for the inverse of the function.
The inverse of a function is a reflection in the line y = x.
To find the inverse of the given function, swap f(x) for y:
[tex]\implies y=\dfrac{5x-3}{x-1}[/tex]
Rearrange the equation to isolate x:
[tex]\implies y(x-1)=5x-3[/tex]
[tex]\implies xy-y=5x-3[/tex]
[tex]\implies 3-y=5x-xy[/tex]
[tex]\implies 3-y=x(5-y)[/tex]
[tex]\implies x=\dfrac{3-y}{5-y}[/tex]
Swap the x for f⁻¹(x) and the y for x:
[tex]\implies f^{-1}(x)=\dfrac{3-x}{5-x}[/tex]
The range of the function is the domain of the inverse function.
Therefore, the domain of the inverse function is restricted:
Domain of f⁻¹(x): (-∞, 5) ∪ (5, ∞).