The maximum width and area of rectangle are 475 feet and 225625 sq. feet respectively.
How we can make the area of rectangle maximum?Any given rectangle has ONE region - there is no base or most extreme, simply a region. To find the region of a rectangle shape, increase the length times the width. For instance, a rectangle shape 4′ long by 5′ wide will have an area of 20 square feet.
According to question:We have
l×w = area of rectangle-------------------------(1)
2w + l = 950
l = 950 - 2w
Put the value if l in equation (1)
(950 - 2w) × w = area
This is a quadratic equation for maximum value of w we have of it one zeros is zero
so,
950 - 2w = 0
w = 950/2
W =475 feet
Te
Then length = 950 - 475 =475
Area of rectangle = 475 × 475 = 225625 sq. feet
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SOLVE what is J
3j + 4 = 10
J =
Answer: The answer is 2
Step-by-step explanation:
3j + 4 = 10 J = 2
3x2=6
6+4= 10
Super confused! Please help! Explanation would be amazing, thanks! :)
Answer:
A = 29°
Step-by-step explanation:
set
(3x-4) + (9x+17) + (6x-31) = 180
Solve for x
18x - 18= 180
18x = 198
x = 11
So A will be
A = 3x - 4
A = 3(11) - 4
A = 29°
Answer:
116°Step-by-step explanation:
total angle of a triangle: 180°thus, (3x-4)+(9x+17)+(6x-31)= 180°.3x-4+9x+17+6x-31= 180° 18x-18= 180° 18x= 198° x= 198°/18 x= 11°angle of A: (9x+17)°9(11)+17= 99+17 = 116°The vertices of triangle ABC are A(−4, 3), B(4, 3), and C(−4, −6). The triangle is dilated with a scale factor of 3. Estimate the perimeter of the dilated figure to the nearest whole number.
The perimeter of the image of the triangle is approximately equal to 87 units.
How to determine the perimeter of the image of a triangle
In this problem we find the coordinates of the vertices of a triangle: A(x, y) = (- 4, 3), B(x, y) = (4, 3), C(x, y) = (- 4, - 6), of which we must determine the perimeter of its image, which is the result of a scale factor of 3. The perimeter is the sum of the lengths of the triangle. The length of each side of the image of the triangle can be found by Pythagorean theorem and definition of dilation:
l = √[(Δx)² + (Δy)²]
Where:
l - Side lengthΔx - Change in the x-direction.Δy - Change in the y-direction.And the perimeter of the image of the triangle is described below:
p = k · (AB + BC + AC)
Where k is the scale factor.
First, determine the lengths of sides AB, BC and AC:
Side AB
AB = √[[4 - (- 4)]² + (3 - 3)²]
AB = 8
Side BC
BC = √[(- 4 - 4)² + (- 6 - 3)²]
BC = √[(- 8)² + (- 9)²]
BC = √145
Side AC
AC = √[(- 4 - 4)² + (- 6 - 3)²]
AC = 9
Second, determine the perimeter of the image:
p = 3 · (8 + √145 + 9)
p = 3 · (17 + √145)
p = 51 + 3√145
p ≈ 87.125
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What is the solution for system of equations???
Answer:
(1, -2)
Step-by-step explanation:
The line is tangent to the parabola, so it intersects in only 1 point.
Answer: (1, -2)
Skyler is able to complete 18 push ups in 30 seconds. If she keeps up the same rate, approximately how many sit ups can Skylar complete in 1 1/2
Answer: 54
Step-by-step explanation: 3 x 30seconds = 90 seconds (1 1/2)
3 x 18 = 54
Use the definition of the integral (the long way) to evaluate the integral
The answer is 10.67. It can be calculated by integrating and then applying the limits.
What is the integration of [tex]x^n[/tex]?
The integration of power of a variable is given by the following formula:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}[/tex]
If limits are there then limits can be applied after integration.
Consider the given function.
[tex]\int^3_1(x^2-4x+9)dx[/tex]
Now, apply integration on each term as follows:
[tex]\int^3_1x^2dx-4\int^3_1xdx+9\int^3_1dx[/tex]
Now, use the following formula to integrate:
[tex]\int x^ndx=\frac{x^{n+1}}{n+1}[/tex]
Now, the integration will look like as follows:
[tex][x^3/3]^3_1-4[x^2/2]^3_1+9[x/1]^3_1[/tex]
Now, apply limits to find the answer as follows:
[tex][3^3/3-1^3/3]-4[3^2/2-1^2/2]+9[3-1]\\[/tex]
[tex][9-\frac{1}{3}]-4[9/2-1/2]+18\\10.67[/tex]
Hence, the answer is 10.67. It can be calculated by integrating and then applying the limits.
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The variable y varies jointly with x and w when y = - 42, x = 2, and w = -3.
1.) Find the constant of variation.
k=
Answer:
k = 7
Step-by-step explanation:
given y varies jointly with x and w then the equation relating them is
y = kxw ← k is the constant of variation
to find k use the condition when y = - 42, x = 2 and w = - 3 , then
- 42 = k × 2 × - 3
- 42 = - 6k ( divide both sides by - 6 )
7 = k
constant of variation is k = 7
A cone with height h and radius r has volume V = 1/3πr^2h. If a certain cone with a height of 6 in. and a volume of V = 8πx^2 + 24πx + 18π, what is its radius r in terms of x?
A. R = 3x + 2
B. 4x^2 + 12x +9
C. 2x + 3
D. (2x + 3) (2x -3)
Which one is the answer? A explanation would be nice too! (Many points!)
Answer: C. 2x+3
Step-by-step explanation:
[tex]\displaystyle\\V=\frac{\pi r^2h}{3} \\\\V=\frac{\pi r^2(6)}{3}\\\\V=2\pi r^2\\\\\\8\pi x^2+24\pi x+18\pi \\\\V=2\pi (4x^2+12\pi +9)\\\\V=2\pi ((2x)^2+2(2x)(3)+3^2)\\\\V=2\pi (2x+3)^2\\\\THUS,\\[/tex]
[tex]2\pi r^2=2\pi (2x+3)^2[/tex]
Divide both parts of the equation by 2π:
[tex]r^2=(2x+3)^2[/tex]
Extract the square root of both parts of the equation:
[tex]r=2x+3[/tex]
please see the attached the answer is wrong that i have
I dont understand this could you help me?
Answer:
Option 2 —› (56 - 42) / 7 = 2
Step-by-step explanation:
First you use PEMDAS to check.
P- parentheses
E- Exponents
M- Multiplication (can be switched with D)
D- Division (can be switched for M)
A- Addition
S- Subtraction
Now you need to solve each problem.
Option 1: INCORRECT
(56 - 42) / 7 = 5
(14) / 7 = 5
2 = 5
Option 2: CORRECT
(56 - 42) / 7 = 2
(14) / 7 = 2
2 / 2
I'll do the rest, so you can see how to solve.
Option 3: INCORRECT
56 - (42 / 7) = 2
56 - 6 = 2
50 = 2
Option 4: INCORRECT
(56 - 7) / 42 = 5
(49) / 42 = 5
1 1/6 = 5
Two UNO students want to start a business selling slushies at the Gene Leahey Mall during the summer. They will have an initial cost of $500 to buy equipment and an additional $1.25 cost for each slushie they sell. They plan to charge $3.50 for each slushie. Let C(x) represent the cost (in dollars) associated with starting and running the business and R(x) represent the revenue (in dollars) earned from sales. Let × represent the number of slushies sold
a. Write a linear function for cost.
C(x)
Write a linear function for revenue.
R(x)=
c. Find C(50). Show your work.
• Write C(50) as an (x, y) coordinate point. ——
• Write a sentence that explains the meaning of the point in the context of the problem.
D. Find R(50).
Represent R(50) as an (x, y) coordinate point. ——-
Write a sentence that explains the meaning of the point in the context of the problem?
e. If the students sell 50 slushies, do they make a profit? Use mathematical work to help explain your answer. Complete the sentence below.
If the students sell 50 slushies. do they make—— a profit? Because——
F. How many slushies do the students need to sell to break even? Use complete sentences to explain your problem solving strategy and your conclusion.
G. How many slushies do the students have to sell to make a profit of $1250? Use complete sentences to explain your problem solving strategy and your conclusion.
The linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
From the data:
The linear function:
C(x) = 500 + 1.25x
For revenue:
R(x) = 3.50x
R(50) = 3.50(50) = $175
Using the C(x) and revenue function we can find the number of slushies and profit.
Thus, the linear function is C(x) = 500 + 1.25x and the revenue function is R(x) = 3.50x.
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Suppose we flipped a coin and rolled a die, what is the probability of getting a tail on the coin or a 3 on the die?
Answer:
The probability of a head of a die is 1/6 and that of a side of a coin
Two dice are rolled, find the probability that the total showing is less than 10.
The probability that the total showing is less than 10 is 5/6.
What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -
P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes
Given are two dices rolled.
The total number of favorable outcomes can be calculated as -
[a] = (1,1) to (1,6) = 6
[b] = (2,1) to (2,6) = 6
[c] = (3,1) to (3,6) = 6
[d] = (4,1) to (4,5) = 5
[e] = (5,1) to (5,4) = 4
[f] = (6,1) to (6,3) = 3
n(A) = [a] + [b] + [c] + [d] + [e] + [f] = 6+6+6+5+4+3 = 30
n(S) = 36
So, the probability of occurrence of an event 'A' -
P(A) = n(A)/n(S)
P(A) = 30/36
P(A) = 5/6
Therefore, the probability that the total showing is less than 10 is 5/6.
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If a publisher of nontechnical books takes great pains to ensure that its books are free of typographical errors the probability of any given page containing at least one such error is 0.005 and errors are independent of the page-to-page. What is the probability that one of its 400-page novels will contain exactly one page with errors? At most three pages with errors?
Part A: Probability that one of 400-page novels will have exactly one error-free page is 24.06%.
Part B.) No more than three pages contain errors: 40.06%.
Explain the term binomial distribution?The possibility that a value would take one among two independent values given a particular combination of factors or assumptions is summarized by the statistical distribution known as the binomial distribution.The given data in the question-
X has a binomial distribution that includes,400 pages make up the novel's page count.Error probability p = 0.005Probability of error-free page q = 01 - 0.005 = 0.995The following is the probability mass function (PMF) for X:
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
Part A.) One of 400-page novels will have exactly one error-free page.
P(x = 1) = ⁿCₓ . pˣ . qⁿ⁻ˣ
n = 400, x = 1
P(x = 1) = ¹⁰⁰C₁ . (0.005)¹ . (0.995)¹⁰⁰ ⁻ ¹
P(x = 1) = 0.2706
Thus, probability that one of 400-page novels will have exactly one error-free page is 24.06%.
Part B.) No more than three pages contain errors.
P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
P(x = 0) = ¹⁰⁰C₀ . (0.005)⁰ . (0.995)¹⁰⁰ ⁻ ⁰
P(x = 0) = 0.01346
P(x = 1) = ¹⁰⁰C₁ . (0.005)¹ . (0.995)¹⁰⁰ ⁻ ¹
P(x = 1) = 0.0270
P(x = 2) = ¹⁰⁰C₂ . (0.005)² . (0.995)¹⁰⁰ ⁻ ²
P(x = 2) = 0.00068
P(x = 3) = ¹⁰⁰C₃ . (0.005)³ . (0.995)¹⁰⁰ ⁻ ³
P(x = 3) = 0.0000027
Thus, P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
P(x ≤ 3) = 0.01346 + 0.00068 + 0.00068 + 0.0000027
P(x ≤ 3) = 0.4060021
Consequently, the likelihood of at maximum three pages having typographical errors is 40.06%.
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Divide (5x^4-33x^3+13x^2+25x+20) by (x-6) using long polynomial divison.
Point of intersections=
how to solve for reflection under transformation
pre calc
combine radicals/fractional exponents
[tex]\begin{array}{llll} ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \end{array} ~\hfill \begin{array}{llll} \textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{6x^{-1}y^{-1}}{\sqrt[4]{xy^4}}\implies \cfrac{6x^{-1}y^{-1}}{\left( xy^4 \right)^{\frac{1}{4}} }\implies \cfrac{6x^{-1}y^{-1}}{x^{\frac{1}{4}} y^{4\cdot \frac{1}{4}}}\implies \cfrac{6x^{-1}y^{-1}}{x^{\frac{1}{4}} y^1}\implies \cfrac{6x^{-1}y^{-1}x^{-\frac{1}{4}} y^{-1}}{1}[/tex]
[tex]6x^{-1}x^{-\frac{1}{4}}y^{-1} y^{-1}\implies 6x^{-1-\frac{1}{4}} y^{-1-1}\implies {\Large \begin{array}{llll} \underset{\textit{\small a}}{6} \stackrel{\textit{\small ~~ b}}{x^{-\frac{5}{4}}} \stackrel{\textit{\small ~~ c}}{y^{-2}} \end{array}}[/tex]
Find the sum (9 + 6) (mod 10)
Answer:
15d10mo
Step-by-step explanation:
Simplify:
(9+6)(mod10)
=15d10mo
The high school a athletic director is asked if football players are doing as well as academically asthe other students athletes. We know from a previous study that the average GPA for the student athletes is 3.10. after an initiative to help improve the GPA of students athletes, the athletic director randomly samples 20 football players and finds that the average GPA of the sample is 3.18 with a sample standard deviation of 0.54 is there a significant improvement use a 0.05 significance level
The athletic director can therefore draw the conclusion that the average academic standing of football players is comparable to the average standing of other student athletes.
Explain the term t-distribution?Whenever the population's standard deviation is unknown and the data come from such a normally distributed population, the t-distribution characterizes the standardized distances between the sample means and the population mean.The following formula is used to determine the test statistic:
SRS, s = 0.54, n = 40 > 30,
x = 3.18
H0: μ = 3.10
H1: μ > 3.10
α = 0.05
The t-distribution table and our alpha level of.05 are then used to determine our crucial values.
Our critical values are 2.093 for a two specimens with 19 levels of freedom and α = 0.05 level of significance.
t = x - μ / s/√n
t = 3.18 - 3.10/ 54/√20
t = 0.66
This indicates that the measured sample mean of football players, 3.18, is 0.66 standard errors higher than the 3.10 number that was predicted. We are unable to disprove the null hypothesis because the test statistic's value is below the threshold of 2.093.As a result, It is clear that sampling error is the only possible explanation for the discrepancy between both the sample mean as well as the hypothesized value.
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Identify the slope and y-intercept of the line below.
Slope=?
y-intercept=?
Answer:
Slope- y=1/4x-6
Y intercept= (0,-6)
Hope this helps!
The quotient of twenty and a number, decreased by 4, is equal to zero
The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say that number is x,
Quotients of 20 and x will be given as 20/x
20/x - 4 = 0
20/x = 4
x = 20/4 = 5
Hence"The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5".
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Donna buys 4 hardcover books for h dollars each and 5 paperback books
for p dollars each. Sales tax is 8%. Which expression represents the total
cost of Donna's purchase?
A (4h + 5p) (1.08)
B. (4h + 5p)(0.08)
C. (4h + 5p) + 1.08
D. (4h + 5p) + 0.08
A surveyor makes the measures indicated in Fig. 19-71. For the figure, angle A = 34o and the Hypotenuse c = 159 ft. Note the angles are named with Capital Letters A, B, and C and the names or the sides opposite the angles are named with small letter
All parts of the triangle should be solved The parts of the triangle to include in the Problem Solution are: (1) degrees of all 3 angles A, B and C, (2) lengths of the two legs a, b , rounded to the nearest whole number, (3) length of the hypotenuse and (4) the area of the triangle with the proper units. That is 7 answers total.
The side lengths of the triangle are 89 ft, 132 ft and 159 ft
The angles of the triangle are 34 degrees, 56 degrees and 90 degreesThe area of the triangle is 5874 square unitsThe sides of the triangleThe given parameters are
Angle, A = 34 degrees
Hypotenuse = 159 ft
The length BC is calculated as
sin(A) = BC/Hypotenuse
So, we have
BC = Hypotenuse * sin(A)
This gives
BC = 159 * sin(34 degrees)
Evaluate
BC = 89 ft
The length AC is calculated as
cos(A) = AC/Hypotenuse
So, we have
AC = Hypotenuse * cos(A)
This gives
AC = 159 * cos(34 degrees)
Evaluate
AC = 132 ft
The angles for the triangleHere, we have
Angle, A = 34 degrees
Because the triangle is a right triangle, we have
Angle, C = 90 degrees
The sum of angles in a triangle is 180
So, we have
Angle B = 180 - 90 - 34
Angle B = 56
The area of the triangleThis is calculated as
Area = 0.5 * BC * AC
So, we have
Area = 0.5 * 89 * 132
Evaluate
Area = 5874
Hence, the area is 5874 square units
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Help plss!
A- 10 units
B- 24 units
C- 36 units
D- 64 units
Answer:
Step-by-step explanation:
24
Answer: 24!
Step-by-step explanation:
hope this help
Band students are tested on, and required to pass, a certain number of scales during the year. As of today, Becky has passed 4 scales, whereas her friend Charlotte has passed 8 of them. Going forward, Becky has committed to passing 4 scales per week, and Charlotte has committed to passing 2 per week. At some point soon, the two friends will have passed the same number of scales. How long will that take? How many scales will that be?
They each will pass 12 scales.
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
It is given that Becky has passed 4 scales, whereas her friend Charlotte has passed 8 of them.
Going forward, Becky has committed to passing 4 scales per week, and Charlotte has committed to passing 2 per week.
Let number of weeks be x
Becky has passed 4x + 4
Charlotte has passed 2x + 8
According to question:
4x + 4 = 2x + 8
4x - 2x = 8 - 4
2x = 4
x = 4/2 = 2
Becky has passed 4x + 4 = 4(2) + 4 = 8 + 4 = 12
Charlotte has passed 2x + 8 = 2(2) + 8 = 4 + 8 = 12
Therefore, They each will pass 12 scales.
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Ash spent 50% of his time at the gym lifting weights. If he spent 45 minutes lifting weights, how many minutes was he at the gym? Use any strategy to solve.
f(x) =x^3 + 2x^2 -2x
Help fast please!!!!!!!Simplify.
(-√7) (-√7)
O A. √7
B. -7
OC.
C. 7
о
O
D. 49
E. -49
K
Answer:
7
Step-by-step explanation:
seven is the value e you would get
36 berries are in a bowl James eats 21 of the berries then he put 14 more berries in the bowl how many fewer berries are in the bowl now
The berries is the bowl is 6 berries fewer than the original amount
How to find the amount fewer of berried=s that are in the bowlThe amount of berries in the bowel is solved using addition and subtraction property of equality
36 berries are in a bowl James eats 21 of the berries
= 35 berries - 21 berries
= 15 berries
he put 14 more berries in the bowl
= 15 berries + 14 berries
= 29 berries
How many fewer is solved by
= 35 berries - 29 berries
= 6 berries
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