According to the solving the area of the square is 68.0625.
What's a square's area?As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.
According to the given data:The box formed after cutting the square from each corner will have the dimensions as,
length = 104 - 2x, width = 39 - 2x, height = x.
∴ volume of the box = length × width × height
∴ v = (104 - 2x)(39 - 2x)(x) -----(i)
∴ v = (104 - 2x) (39x - 2[tex]x^{2}[/tex])
∴ v = 104(39x - 2[tex]x^{2}[/tex]) -2x(39x - 2[tex]x^{2}[/tex])
∴ v = 4056x - 208[tex]x^{2}[/tex] - 78[tex]x^{2}[/tex] + 4[tex]x^{3}[/tex]
∴ v = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
let f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x -----(ii)
To, find x for which f(x) is maximum,
⇒we should apply second derivative test ,
According to this test, first we should find critical points at which f'(x) = 0.
then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.
∴ let us consider, f'(x) = 0.
now, f(x) = 4[tex]x^{3}[/tex] - 286[tex]x^{2}[/tex] + 4056x
⇒ f'(x) = 12[tex]x^{2}[/tex] - 572x + 4056. -----(iii)
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014)
⇒ f'(x) = 0.
⇒ f'(x) = 4(3[tex]x^{2}[/tex] - 143x + 1014) = 0
⇒ x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/2a ; where a = 3, b = -143, c = 1014.
∴ x = (-(-143) ± [tex]\sqrt{(-143)^{2} -4(3)(1014)}[/tex])/2×3
∴ x = (143 ± [tex]\sqrt{8281}[/tex])/6.
∴ x = [tex]\frac{143 + 91}{6}[/tex] , x = [tex]\frac{143 - 91}{6}[/tex]
⇒ x = 39, 8.25
the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.
Area of the square is = [tex]x^{2}[/tex] = [tex]8.25^{2}[/tex]
∴ Area = 68.0625
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f(x)=-1²-3x+ 20
Find f(5)
Answer:
6
Step-by-step explanation:
-1^2-3(5)+20
1-15+20
1+5
6
hopes this helps
Solve for an angle in right triangles
I just need the answer :)
Answer:
19.47
Step-by-step explanation:
Answer:
[tex]m\angle A \approx 19.47 \textdegree[/tex]
Step-by-step explanation:
Utilize the trigonometric ratio sine.
[tex]\sin(m\angle A) = \dfrac{2}{6}[/tex]
[tex]\sin(m\angle A) = \dfrac{1}{3}[/tex]
[tex]m\angle A = \sin^{-1}\left( \dfrac{1}{3} \right)[/tex]
[tex]m\angle A \approx 19.47 \textdegree[/tex]
Please help, the blue dot is random
The equation would be 5(x + 3) = 45
To solve:
1) Distribute 5 to x and then 5 to 3
2) That gives you this equation: 5x + 15 = 45
3) Then subtract 15 from both sides
4) You should get this: 5x = 30
5) Then divide 5/5 and 30/5 to isolate the x
6) The answer should be: x = 6
Have a good day/night :)
if you conduct a hypothesis test (for example, a z test), and find a p-value of .30, what is the meaning of the p-value?
The value for p is 30.
Hypothesis.Though there is not so much information, but the fact that $700 is an average. We can work with two hypothesis at first, he first Hypothesis before the downturn the rent are over $700. And the second one, the bedroom rent are under $700.Graphically, the shaded area before the downturn, represents the set of values for Rents greater than $700. So, rent (y) > 700) Graphically, the shaded area after the downturn, represents the set of values for Rents lesser than $700. So, rent 700 <y<0A hypothesis is an educated prediction regarding the solution to a scientific question that is supported by sound reasoning. It is the expected result of the experiment, however it is not proof in an experiment.Depending on the information received, it might be supported or might not be supported at all.learn more about hypothesis click here:
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Convert 386,000 milliliters to kiloliters PLSS THIS IS DUE TOMORROW
Answer:
0.386 kiloliters
Step-by-step explanation:
because I used the calculator all I gotta do is divide the volume :)
14.9 - 15.1 EVALUATE PLEASE.
Answer:
-0.2
Step-by-step explanation:
14.9-15.1= -0.2
To do equations like this in the beginning I used to switch the terms and then add a negative symbol in front of it
I would solve it like this
15.1-14.9
.2
And now since I switched the terms I change the sign to negative
-0.2
Hopes this helps please mark brainliest
X (3x + 5)°
(4x)
Y
(8x - 14)°
B
N
Answer:2
Step-by-step explanation:
1+1 es 2
Evaluate the expression when g = 0.6.
400g2−0.9÷g
I need a quick answer please !!!
——————————————————
The diagram (below) shows a game in which you use the pieces at the top to form solid rows at the bottom. Using only translations and rotations, describe the transformations of the pieces at
the top that will form two solid rows at the bottom.
meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow meow
A police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets. Should he be on a perpendicular bisector, a median, an angle bisector, or an altitude?
ALSO… Draw a picture to show solution to this problem and label all parts of your picture and the name of the segment the police officer should use.
A police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.
Given that, a police officer is parked in a supermarket parking lot located at the junction of two streets. He wants to be equidistant from both streets.
What is a perpendicular bisector?A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90° at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90°.
Perpendicular bisector: A line that bisects a line segment in two equal parts.
Median: The middle number; found by ordering all data points and picking out the one in the middle.
Angle bisector: The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.
An altitude: Height, altitude, elevation mean vertical distance either between the top and bottom of something or between a base and something above it.
Therefore, a police officer wants to be equidistant from both streets. He should be on a perpendicular bisector.
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Factor the polynomial by factoring out the Greatest Common Factor
The factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
We are given an algebraic expression:
18y^4 + 24y^3 + 6y^2
We need to factorize by factoring out the Greatest Common Factor.
In the given algebraic expression, we can see that;
6 is the Greatest Common Factor of 18, 24, and 6.
y^2 is the Greatest Common Factor of y^4, y^3 and y^2.
So, we will take the common 6y^2 from the given expression;
18y^4 + 24y^3 + 6y^2
= 6y^2 (3y^2 + 4y + 1)
So, option A is correct.
Thus, the factored form of the given algebraic expression by factoring out the Greatest Common Factor is 6y^2 (3y^2 + 4y + 1). Option A is correct.
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Compare the governments of Germany and Russia. Make three lists pointing out similarities and differences. In the first list, point out the unique traits of the German government. In the second list, point out the unique traits of the Russian government. In the third list, point out the traits both governments have in common.
DON'T write an entire essay i just need a paragraph
Answer: During the Russian war, The Russians and Germans were at war with each other, Beating them brutally.
Step-by-step explanation:
0. Given a standard 4 color band resistor, what color code is needed on the 4 bands to have a 0.34
Ohm resistor with a tolerance of ± 10% ?
The colour code needed is silver, green, red and blue for the tolerance of ± 10% on the 4 color band resistor.
What is defined as the term resistor?A resistor is a device that controls or restricts how much electrical current can pass across a circuit in an electronic device. A specified voltage can be supplied via resistors to an active device like a transistor.For the given question;
The most popular type of resistor is the 4-band resistor. The first two bands just provide the first two digits of a resistance value, just as a three band resistor. For a 4 band resistor colour coding, we may start by first locating the tolerance band since it is typically gold or silver. The third band stands for the multiplier whereas the fourth band symbolises tolerance. Due to the widening difference between the tolerance band as well as the multiplier band, the tolerance band may also be easily distinguished.Since it is silver in this instance, the resistor colour code table indicates a tolerance of ± 10% .
Thus, the colour code needed is silver, green, red and blue for the 0.34
Ohm resistor with tolerance of ± 10%.
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Please help me solve this
The value of a=2 and b= 4.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
a + 1 / b-1 = 5/1 and a-1/ b+ 1 = 1/1
So, a + 1 / b-1 = 5/1
now, cross multiplying
a+ 1 = 5b - 5
a- 5b = -6............(1)
Also, a-1/ b+ 1 = 1/1
a-1 = b + 1
a - b = 2 ..............(2)
solving Equation (1) and (2) , we get
2+ b - 5b= -6
-4b = -8
b= 2
and, a = 2 + 2 = 4
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Question 11-(3 marks available)
Find the total surface area of this triangular prism.
13 cm
5 cm
12 cm
9 cm
20 cm
Answer: 1080 [tex]cm^{2}[/tex]
Determine the values of b1, b2, and b3, the sides of the triangular base. Also determine the value of h, the height of the triangular base and l, the length of the prism (the length between the bases).
The sides of the triangular base are:
b1 = 13 in.
b2 = 14 in.
b3 = 15 in.
The triangular base is a right triangle, and so the height is one of our sides. We will use
h = 12 in.
The length of the prism is
l = 20 in.
total surface area = bh + (b1+b2+b3)*l
bh = 12*20 = 240 [tex]cm^{2}[/tex]
l * (b1+b2+b3) = 20*(13 + 14+ 15) = 840 [tex]cm^{2}[/tex]
TSA = bh + l * (b1 + b2 + b3) = 240 + 840 = 1080 [tex]cm^{2}[/tex]
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Could someone help quick
The constant of proportionality is 1/7
What is constant of proportionality?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided quantities determine the proportionality constant's value.Direct Variation: The direct proportionality equation is y = kx, which demonstrates that as x rises, y rises at the same pace. Example: y x represents the cost per item(y), which is directly proportional to the number of items(x) purchased.Inverse Variation: The indirect proportionality equation, y = k/x, demonstrates that when y rises, x falls, and vice versa. As shown by the formula y 1/x, the speed of a moving object (y) inversely varies with the amount of time (x) needed to travel a distance.K is constant in both circumstances. The coefficient of proportionality is the name given to this constant's value. The unit rate is another name for the proportionality constant.To learn more about constant of proportionality, refer to https://brainly.com/question/26171814
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Need Help Please! Geometry question! I’m Not Sure with my answer!
∠A= ∠R , and the triangle is congruent.
What are angles?
When two straight lines or rays intersect at a single endpoint, an angle is created.The vertex of an angle is the location where two points come together.The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.acc to our question-
ΔBAT AND ΔCRBwith the help of SAS property we can say thattriangle is congruent and equal.Hence,∠A= ∠R , and the triangle is congruent.
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What is the slope of (-4,1) (0,-1)
The diagram shows the circle with equation x2 + y2 = 53
A
O
A tangent to the circle is drawn at point A with coordinates (-2,7)
Find an equation of the tangent at A.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Explain about the Equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.
A mathematical equation is a statement that two amounts or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account collectively in order to comprehend or describe the overall situation, this is known as an equation.
Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
X2+Y2 =53
= 53 + (50-1)(-4)
= 53-196
= -143
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estion 11 of 42
What is the equation of a line with a slope of 6 and a y-intercept of -2
O A. y = -2x + 6
OB. y = 6x + 2
OC. y = 6x-2
OD. y = 2x+6
What is the correct standard form for 400+3+0.07+0.001 need answer asap
Answer:
403.071
Step-by-step explanation:
add
two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. what is the probability that the first card drawn is a diamond and the second card drawn is not a diamond? a) 0.1875 b) 0.1912 c) 0.0577 d) 0.0588 e) 0.7500 f) none of the above.
The correct answer is Option 'B'.
We are drawing cards without replacement,
So first card is a diamond is 13/52 and
Second not a diamond is 39/51
51 because we have picked 1 card in the first draw.
so final answer is
(13/52) *(39/51) = 0.1912.
Therefore, the probability that the first card drawn is a diamond and the second card drawn is not a diamond is 0.1912.
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain occurrences. The degree to which something is likely to happen is essentially what probability means.
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In a card game, Bryce scores three times as many points as Jordan. Jordan scores four points fewer than Keturah, and Keturah scores two times as many points as Amelia.
If Amelia scores 5 points, how many points did Bryce score?
Group of answer choices
A. 6
B. 10
C. 18
D. 5
Answer:
b
Step-by-step explanation:
b
Answer: Amelia 5, Keturah 10, Jordan 6, Bryce 18
Step-by-step explanation:
If Amelia scored 5 and Keturah scored 2 times of Amelia's score, then 5 x 2 is 10, so Keturah scored 10. If Keturah scored 10 and Jordan scored 4 points fewer than Jordan's score, then 10 - 4 is 6, so Jordan scored 6. If Jordan scored 6 and Bryce scored 3 times of Jordan's score, then 6 x 3 is 18, so Bryce scored 18. So C is the correct answer.
50 POINTS
Your parents have heard about your business and would like to invest in it to help you earn as much money this summer as possible. They decide to give you $100 towards your business. However, there's a catch. They want 10% of the money you make.
1. if you mowed 10 lawns while charging $15 a lawn, how much would you have to pay your parents?
2. if you needed to make $300 to buy a switch, how many lawns would you have to mow?(Hint: don't forget about how much you would have to pay your parents.)
3. With all cost taken into account, your start up money, the money your parents gave you and what you paid your parents, how much profit did you make after 20 lawns?
The profit made from the business that receives an initial $100 investment are as follows;
1. The amount received from the investment is $15
2. The number of lawns that should be mowed to buy the switch is 23 lawns
3. The profit made from the business considering the cost and the initial investment of the parents is $170
What is an investment?An investment is the money directed towards an asset purchase to increase the valuation of the business and products within a time period.
The amount invested = $100
The amount desired as return = 10% of the amount made from the business
1. The amount charged per lawn = $15
The number of lawn mowed = 10
The revenue of the business = 10 × $15 = $150
The amount paid as return on investment = 10% × $150 = $15
2. The amount required to buy the switch = $300
The number of lawns to be mowed, n, is therefore;
300 = 15 × n - 10% × 15 × n = 15·n - 1.5·n = 13.5·n
300 = 13.5·n
n = 300/13.5 ≈ 23 ( rounding up to the nearest whole number)
The number of lawns to be mowed is 23 lawns
3. The revenue from mowing 20 lawns is 20 × $15 = $300
The amount received by the investing parents = 10% × $300 = $30
The amount received from the parents investment = $100
The profit made after 20 lawns = $300 - $30 - $100 = $170
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Need help please look at picture
Answer:
the three dots represent 'therefore'
Step-by-step explanation:
as shown in picture uploaded ^^
3. Tina needs to build a fence. The fence
is 30 feet long and 20 feet wide. She
realizes she needs more so she increases
the length and width by x feet. Create an
expression that represents the perimeter
for the fence.
According to flightstats com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 20 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment (b) Determine the values of n and p. (c) Find and interpret the probability that exactly 12 flights are on time. (d) Find and interpret the probability that fewer than 12 flights are on time. (e) Find and interpret the probability that at least 12 flights are on time. (f) Find and interpret the probability that between 10 and 12 flights, inclusive, are on time.
As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.
The value of p=0.8 and n=20
The probability that exactly 12 flights are on time = 0.1772
The probability that exactly fewer than 12 flights are on time = 0.1049
The probability that at least 12 flights are on time = 0.8951
The probability that between 10 and 12 flights, are on time = 0.1795
(a) Binomial probability is the probability of exactly 'k' successes on 'n' repeated trials in an experiment which has two possible outcomes.
As, in our question we are doing 20 trials to get the number of on-time flights. Hence, this is a binomial experiment.
(b) As, the probability of success on an individual trial is p and here success means the flight is on-time so the value of p be,
p = 80% = 0.8
As, we made 20 trials and n is the total number of trials then,
the value of n be,
n = 20
(c) Now, if the probability of success on an individual trial is p ,
Then the binomial probability is C(n,x)⋅p^x⋅(1−p)^(n−x)
The probability that exactly 12 flights are on time, be
P(X=12) = C(20,12)⋅(0.8)^12⋅(1−0.8)^(20-12)
P(X=12) = C(20,12)⋅(0.8)^12⋅(0.2)^(8)
P(X=12) = 10,07,760×0.0687×0.00000256
P(X=12) = 0.1772
(d) Now, the probability that exactly fewer than 12 flights are on time, be
P(X<12) = 1 - P(X>12)
So, P(X>12) = P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)+P(X=19)+P(X=20)
So, P(X>12) = 0.0545 + 0.0364 + 0.1746 + 0.2182 + 0.2054 + 0.1369 + 0.0576 + 0.0115
P(X>12) = 0.8951
P(X<12) = 1 - 0.8951
P(X<12) = 0.1049
(e) Now, the probability that at least 12 flights are on time, be
P(X>12)=0.8951
(f) The probability that between 10 and 12 flights, are on time, be
P(X=10)+P(X=11)+P(X=12) = 0.0020 + 0.0003 + 0.1772
P(X=10)+P(X=11)+P(X=12) = 0.1795
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Q1 Write a quadratic polynomial
, sum of whose zeroes is 3 and product is -40
The quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.
Define the term quadratic polynomial?When a variable term as in polynomial expression has a highest power of 2, the polynomial is said to be quadratic. A second-order polynomial is another name for a quadratic polynomial. A quadratic equation or quadratic function is created if a quadratic polynomial becomes equal to 0. The roots or zeros of both the quadratic equation are the name given to the solutions of this equation.For the stated values,
Sum of zeroes is 3 and product is -40
Use formula,
x² - x (sum of zeros) + (product of zeros) = 0.
Put the values.
x² - x (3) + (-40) = 0.
x² - 3x + -40 = 0.
Thus, the quadratic polynomial for the given conditions of zeros is found as x² - 3x + -40 = 0.
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Is g = 10 a solution to the inequality below?
g≤ 4
yes
Submit
S
Answer:
yes it is
atleat i think
Please help. Will mark brainliest. Please choose one answer
Which of the following is the most reasonable estimate of the correlation coefficient? Image is provided
0.5
0.7
0.9
1.0
The most reasonable estimate of the correlation coefficient is 0.9
What is the correlation coefficient?The correlation coefficient gives an estimate of how strong is the linear relationship between two variables.
The correlation coefficient, r, is given by the formula;
[tex]r = \dfrac{\sum(x_i-\overline x)\cdot (y_i-\overline y)}{\sqrt{\sum (x_i-\overline x)^2\sum(y_i-\overline y)^2} }[/tex]
Where;
[tex]x_i[/tex] = The ith x-value
[tex]\overline x[/tex] = The mean (average of the x-values)
[tex]y_i[/tex] = The ith y-value
[tex]\overline y[/tex] = The mean (average of the y-values)
The give points on the scatter plot graph are;
(8, 9), (6, 9), (6, 6), (5, 5), (4, 5), (3, 4), (3, 3), (2, 4), (1, 2), (1, 3)
Plotting the above points on MS Excel gives;
The equation of the regression line is; y = 0.9407·x + 1.3313
The square of the correlation coefficient, R² = 0.8322
Therefore, R = √(0.8322) ≈ 0.9122
The option that is the most reasonable estimate of the correlation coefficient is therefore; 0.9
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