When there is 580 feet of fencing available to complete the job, the largest possible total area of the 5 pens is 7008.33 feet.
What is an area?The quantity area expresses the extent of a region on a plane or curved surface.
STEP 1: We know that,
A=x y
The perimeter equals 580feet.
The equation is,
580=6x+2y
Step 2: Solving y terns with x,
y=-3x+290
This information will assist us in obtaining our Area equation in terms of a single variable (just in terms of x).
Step 3: Using the x-y relationship discovered in Step 2, write your Area equation in terms of x only. You should obtain
A=x y
A=x(-3x+290)
A=-3x²+290x
Step 4: Derive the area equation, A' = -6x+290
Step 5: Set A' = 0
-6x+290=0
x=290/6
x=48.33
Step 6: Find y by substituting 48.33 in x in the perimeter equation then,
y=-3(48.33)+290
y=145.01
Step 7: A=x y
A=(48.33)(145.01)
A=7008.33 feet
The largest possible total area of the 5 pens is 7008.33 feet
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please help me asap
Answer:
z = 52°
Step-by-step explanation:
Formula we use,
→ A + B + C = 180°
Then the value of z will be,
→ 81° + 47 ° + z = 180°
→ 128° + z = 180°
→ z = 180° - 128°
→ [ z = 52° ]
Hence, the value of z is 52°.
Write 2^40 as a pwer with the following base (2^8)
By algebra properties, the resulting expression of the power 2⁴⁰ is (2⁸)⁵.
How to rewrite a power expression according algebra properties
In this problem we must rewrite a power expression in terms of the power 2⁸, which is the base of the resulting expression. This can be done by applying algebra properties:
Step 1 - Write the original expression presented in the statement.
2⁴⁰
Step 2 - By definition of multiplication between real numbers.
2⁽⁸⁾⁽⁵⁾
Step 3 - By the definition of the power of a power.
(2⁸)⁵
The resulting expression is (2⁸)⁵.
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To find the equation of a regression line, y = ax + b, you need these formulas:
Sy
a=rsa
b =ỹ - ax
A data set has an r-value of 0.793. If the standard deviation of the x-
coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772,
what is the slope of the line to three decimal places?
The slope of the line is 0.393.
Define slope.Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").
Given,
A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.
We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:
m = 8ₓ/8ₐ
where m is the slope of the best-fit line.
8ₓ = Standard deviation of the x-coordinates is 5.591,
8ₐ = the standard deviation of the y-coordinates is 2.772.
Slope is:
m = 8ₐ/8ₓ
m = (0.793)(2.772)/5.591
m = 0.393
The slope of the line is 0.393.
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Which equation correctly applies the Associative Property of Addition?
8.9+(6.4 +7.2) (8.9 + 6.4) +7.2
1/6 + 4/6 = 5/6
=
1/3(1/2+3/4)= (1/3 x 1/2) + (1/3 X 3/4)
6-18 = 6 + (-18)
Answer:The equation 8.9+(6.4 +7.2) is correctly applying the Associative Property of Addition.
Step-by-step explanation:
The Associative Property of Addition states that when adding three or more numbers, the order in which the numbers are added does not affect the sum.
Evaluate y² ÷ 8 if y = 4
I wasn't here when they learned this old show work
Answer:
2
Step-by-step explanation:
y² = 4²= 16 (in substitution way)
16÷8= 2
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Answer:
2
Step-by-step explanation:
y^2/8
4^2/8
16/8
2
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write an equation of the line perpendicular to -4x+3y=12 and containing the point (6,8)
The equation of the line perpendicular to - 4x + 3y = 12 and containing the point (6,8) is 3x + 4y = 50.
What is a perpendicular line?
Perpendicular lines: A perpendicular line is a straight line that has been put up so that it forms a right angle with another line. The two lines are parallel to one another.
Here,
The slope of ax + by = c is given by m = -a/b
m = -(-4)/3 = 4/3
m = 4/3 for this line.
A perpendicular line will have a slope -1/m = -3/4
The line through (6, 8) with slope -3/4
y = (-3/4)x + b
8 = (-3/4)(6) + b
b = 8 + 9/2 = 25/2
y = (-3/4)x + 25/2
4y = -3x + 50
3x + 4y = 50
Hence, the equation of the line perpendicular to -4x+3y=12 and containing the point (6,8) is 3x+4y = 50.
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What is the image of the point (-7,5)(−7,5) after a rotation of 180^{\circ}180
∘
counterclockwise about the origin?
The coordinates of the image of the point (-7, 5) are (7, -5).
We are given point P. The coordinates of the point P are (-7, 5). We perform a transformation on the given point. We rotate the given point about the origin counter-clockwise. The angle of rotation is 180°. We need to find the coordinates of the image of the point after rotation.
Let the new coordinates of the image of the point after rotation be denoted by (X, Y). If the coordinates of the original point are (x, y), then the relations between the coordinates of the point and the image are given below.
X = x*cosθ - y*sinθ
X = (-7)*cos(180°) - (5)*sin(180°)
X = (-7)*(-1) - (5)*(0)
X = 7
Y = x*sinθ + y*cosθ
Y = (-7)*sin(180°) + (5)*cos(180°)
Y = (-7)*(0) + (5)*(-1)
Y = -5
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Help quick, State if the two triangles are congruent. If they are state how you know.
The two triangles are congruent and they are congruent by ASA.
How to ascertain if triangles are congruent?Triangles are congruent when they have exactly the same three sides and exactly the same three angles. This simply implies the corresponding sides and angles of the triangles are congruent.
Let's check if the triangles are congruent.
One of the congruent angles in the triangles are vertically opposite angle.
Recall vertically opposite angles are congruent.
In these two triangles, we have a congruent angle pair and a congruent side pair.
Therefore, we can say the triangles are congruent by ASA.
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a random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces. in this problem, what is the 0.7?
In this problem 0.7 is the standard deviation of the contents.
Define standard deviation.It is a statistic that gauges a dataset's dispersion from its mean, and it is calculated as the variance's square root. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean. A dataset's dispersion from its mean is measured by standard deviation. It is determined as the variance's square root. In the financial industry, standard deviation is frequently employed as a gauge of an asset's relative riskiness.
Given,
A random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces.
In this problem 0.7 is the standard deviation of the contents.
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Please help me (see attachment)
A graph of the given equation (x - y = 6) is shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Next, we would rewrite the given equation in standard form as follows:
x - y = 6
Adding y to both sides of the equation, we have the following:
x - y + y = 6 + y
x = 6 + y
Rearranging the equation, we have the following:
y = x - 6
By critically observing the graph (see attachment), the y-intercept is equal to -6 and the x-intercept is equal to 6.
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Morgan is 15 years younger than mrs santos. Their shed combined is 44. (Look at picture pls) (D. M+s= 44 and m= s - 10 ; (27, 17); Morgan is 17 and Mrs. Santos is 27.
Answer:
Step-by-step explanation:
To find Mr.Santos's age subtract morgan's age from their combined age
44-15=29
Therefore Mr. Santos age is 29 years
Hope that helps
Solve for x. (10x + 1) (12x-5)°
283x416 in algorithm
Answer:
120,000
Step-by-step explanation:
To estimate the product of 283 × 416, first round each number so that each number contains only 1 non zero digit.
In this case, we will round 283 to the nearest hundred and we will also round 416 to the nearest hundred. To round 283 to the nearest hundred, the number next to two is higher than 5 so we round up. 283 rounds to 300.
416 rounded to the nearest hundred is 400 because the digit to the right of 4 is less than 5 which means we round down. 416 rounds down to 400.
Now we have 300 × 400 which equals 120,000
This means that 283 x 416 is approximately 120,000.
Simplify the rational expression by rationalizing the denominator. √12/√8x
3√2x is the simplified form of the given expression by rationalizing the denominator.
What is the justification?In the form p q, where p and q are integers and q0, rational numbers can be expressed. The distinction between fractions and rational numbers is that the numerator or denominator of a fraction cannot be negative.
What does a math denominator mean?In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are split into a whole. It is a fraction's divisor.
What does common factor mean?A common factor is a whole number that is a factor of at least two other numbers. The greatest common factor is the biggest factor that may be divided into two or more integers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).
Make the denominator simpler.
12/2√2x
Reject the 12/2 common factor.
6/√2x
Multiply the numerator and denominator by √2x
(6√2x⋅√2x/√2x)
Combine and make the denominator simpler.
6√2x/2x
= 3√2x
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graph the following inequality:
Please help thx
The equations y=3+2 and y=2x+1 both will meet at x=3
What is inequality?A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.a b asserts that a and b are not equal.If a b, then a must be less than b.When a > b, an is greater than b. (those two are known as strict inequality)If a and b are divided, a must be smaller than or equal to b.When a and b are together, an is greater than or equal to b.Acc to our question-
Given, 3x−2<2x+1⇒3x−2x<1+2⇒x<3orx∈(−∞,3)The lines y=3x−2 and y=2x+1 both will intersect at x=3 Clearly, the dark line shows the solution of 3x−2<2x+1.Hence,The lines y=3x−2 and y=2x+1 both will intersect at x=3
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Answer:
B
Step-by-step explanation:
Use the slope-intercept form to find the slope and y-intercept.
Slope: 5
y-intercept: (0,-10)
Answer:
Step-by-step explanation:
The slope is 5
how many Robin eggs, laid end to end, would be about equal in length to two raven eggs? justify your answer.
Answer:
Step-by-step explanation:
The average length of two raven eggs is about 0.1 m.
Since the average length of a robin egg is about 0.02 m, 5 eggs laid end to end would measure about 0.1 m.
In a certain chemical, the ratio of zinc to copper is 4 to 13. A jar of chemical contains 325 grams of copper. How many grams of zinc does it contain
Given -
In a certain chemical, the ratio of zinc to copper is 4 to 13.
The chemical contains 546 grams of copper.
Prove -
How many grams of zinc does it chemical contain.
Answer
suppose that scalar multiple of the zinc and copper be y .
As given
In a certain chemical, the ratio of zinc to copper is 4 to 13.
The chemical contains 546 grams of copper.
Than equation is
13y = 546
13y = 546
y = 42
Zinc contain in the certain chemical = 4y
= 4 42
= 168 grams
Therefore 168 grams of zinc contain in a certain chemical .
an experimenter flips a coin 100 times and gets 56 heads. find the 96.5% confidence interval for the probability of flipping a head with this coin. a) [0.355, 0.615] b) [0.375, 0.665] c) [0.455, 0.665] d) [0.505, 0.510] e) [0.455, 0.465] f) none of the above
The probability of the experiment is = 0.375, 0.665.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
probability that first spin is grey = 6/8probability that second spin is blue = 2/8probability of both = 6/8 * 2/8 = 12/64 which reduces to 3/16learn more about probability click here:
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Sasha is studying a type of coral that grows at a constant rate. Every month, she visits two pieces of the coral and measures their heights. She made this table:
Month 1 2 3
Piece A's height (cm) 24 26 28
Piece B's height (cm) 27 29 31
When Piece A's height is 49cm, what will Piece B's height be?
Answer:
Step-by-step explanation: The constant growth for Plant A is two cm a month and the growth of Plant B is also two cm a month.
In relation, Plant B will also be 3cm taller than Plant A on any month so when Plant A is 49cm, Plant B is 52.
When Piece A's height is 49 cm then the Piece B's height will be 52 cm.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We can see that Piece A's height increases by 2 cm each month and Piece B's height increases by 2 cm each month as well.
To find out what Piece B's height will be when Piece A's height is 49 cm, we need to find how many months it will take for Piece A to reach 49 cm.
From Month 1 to Month 2, Piece A's height increased by 2 cm, and from Month 2 to Month 3, Piece A's height increased by another 2 cm. Therefore, Piece A's height increases by 2 cm per month.
To go from 28 cm (Piece A's height in Month 3) to 49 cm, it takes 21 cm ÷ 2 cm/month = 10.5 months.
So 10.5 months after Month 3 is Month 13.5.
In Month 13.5, Piece A's height will be 49 cm and Piece B's height will be:
Piece B's height in Month 3 + 2 cm/month × (13.5 - 3 months)
= 31 cm + 2 cm/month × 10.5 months
= 52 cm
Therefore, when Piece A's height is 49 cm, Piece B's height will be 52 cm.
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Lora's phone records data for screen time each week. Last week, she used 840 minutes. This week, Lora used 504 screen time minutes on the phone. Calculate the percent decrease in screen time this week.
17%
34%
40%
67%
The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.
Given that, last week, Lora used 840 minutes. This week, Lora used 504 screen time minutes on the phone.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now,
Difference=840-504
= 336
Percentage decrease = Difference in value/Original value ×100
= 336/840 ×100
= 0.4 ×100
= 40%
The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.
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What is the Value of a,b,c and d?
Answer:A is 7 B is -1 C is -9 D is -13
Step-by-step explanation: I hoped i have helped u! Have a wonderful day!
3X + 2Y) (6X + 6Y) what is the answer
Answer:
18X^2 + 18XY + 12YX + 12Y^2
Step-by-step explanation:
you have to moltiplicate the first term with the other two and the same thing for the second term of the first moltiplication
Step-by-step explanation:
what is the question you need an answer for ?
I assume you only need the result of the multiplication of both terms.
remember, when multiplying summary terms, we need to multiply every part of one term with every part of the other term.
(3x + 2y)(6x + 6y) = 18x² + 18xy + 12xy + 12y² =
= 18x² + 30xy + 12y²
Hamad lends $5,500 at a rate of 5 ½%. Find how long it will take for his investment to earn $205 in interest? Round to the nearest day
The time taken to earn the interest of $205 on the investment by Hamad is 2563 days.
Define the term simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest does not really compound, therefore a borrower will only charge interest mostly on principal sum, and a borrower will never be required to pay further interest on the interest that has already incurred.The formula for calculating the simple interest is-
SI = PRT/100
In which,
SI = simple interest (= $205)P = principal amount ($5,500)R = rate of interest (5 ½%) = 11/2 %T= time in years.Put in formula.
205 = 5,500×11×T/200
T = 205×200 / 5,500×11
T = 0.67 years
T = 8.13 months = 253 days.
Thus, the time taken to earn the interest of $205 on the investment by Hamad is 2563 days.
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g) In the figure alongside, AB is an electric pole. When an
electric wire falls, its one end touches the ground at P,
5 m away from the base of the pole. If the length of the wire
from the top of the pole to the ground is 13 m, complete
the following problems.
(i) Find the height of the pole.
(ii)If the other end of the wire touches the grand at Q, 9 m away from the
base to the opposite side of the pole, find the length of the falling wire.
Step by step solution
The height of the electric pole is 12 m
When an electric wire falls, its one end touches the ground at P, 5 m away from the base of the pole,
base = 5
length of the wire from the top of the pole to the ground is 13 m
Height of the plant can be calculated by pythagoras theorem
h² = p² + b²
13² = p² + 5²
p² = 169 - 25
p = √144
p = 12m
Therefore, the height of the electric pole is 12 m
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Select all ordered pairs that are a solution to -5x + 3y > 12
options:
(3, 9)
(-5, 5)
(3, -6)
(-2, -5)
(2, 8)
(-6, 0)
The ordered pairs that are a solution to the given linear equation -5x + 3y > 12 are:
(-5, 5)(2, 8)(-6, 0)How to determine the solution?In order to determine which ordered pairs are true solutions based on the given linear equation, we would have to test each of the ordered pairs by substituting their values into the linear equation as follows;
For ordered pair (3, 9), we have:
-5x + 3y > 12
-5(3) + 3(9) > 12
-15 + 27 > 12
12 > 12 (False).
For ordered pair (-5, 5), we have:
-5x + 3y > 12
-5(-5) + 3(5) > 12
25 + 15 > 12
40 > 12 (True).
For ordered pair (3, -6), we have:
-5x + 3y > 12
-5(3) + 3(-6) > 12
-15 - 18 > 12
-33 > 12 (False).
For ordered pair (-2, -5), we have:
-5x + 3y > 12
-5(-2) + 3(-5) > 12
10 - 15 > 12
-5 > 12 (False).
For ordered pair (2, 8), we have:
-5x + 3y > 12
-5(2) + 3(8) > 12
-10 + 24 > 12
14 > 12 (True).
For ordered pair (-6, 0), we have:
-5x + 3y > 12
-5(-6) + 3(0) > 12
30 + 0 > 12
30-5 > 12 (True).
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find the area of the trapezium
Step-by-step explanation:
To find the Area of a Trapezium, we use 1/2(a+b)*h
where a=2.8 and b=4.4, Height=3.5
1/2(2.8+4.4) *3.5
1/2(7.2)*3.5
3.6*3.5
12.6cm2
Answer:
Step-by-step explanation:
Area of a trapezium = 1/2(a + b) x h
1/2 (2.8 + 4.4) x 3.5
1/2 x 7.2 x 3.5
12.6
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The slope of the given line in the graph is 0.
What is slope?
The steepness and direction of a line are measured by its slope. Any two points along the line can be used to calculate it. A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). The Slope, also known as the Gradient, of a straight line displays how steep the line is. The change in y coordinate relative to the change in x coordinate is known as the slope of an object.
Here the given graph points are,
[tex](x_1-y_1)=(1,1)\\(x_2,y_2)=(4,1)[/tex]
Using slope formula ,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = [tex]\frac{1-1}{4-1}[/tex]
=> slope m = 0/3
=> slope m=0.
Therefore slope of the line is 0.
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s 3)
3) Find the measure of 4A:
5x
130⁰
5x
Please help
Question 2 of 10 Which of the following is equal to the fraction below? (5/8)
The fraction that is equivalent to the fraction expression given as 5/8 is 40/64
How to evaluate the expression?From the question, we have the following fraction expression that can be used in our computation:
Fraction = 5/8
The above expression is a fraction and at the same time it is a rational number
The denominator of the fraction is 8
So, we start by rationalizing the expression by the fraction
This is represented as
5/8 = 5/8 * 8/8
Evaluate the products of the numerator
So, we have the following representation
5/8 = 40/8 * 1/8
Evaluate the products of the denominator
So, we have the following representation
5/8 = 40/64
The above expression cannot be further simplified
Hence, the equivalent expression of the fraction is 40/64
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Possible question
Which of the following is equal to the fraction below? (5/8)
40/64
0.556
2/5