The target to the right is in your backyard. What is the probability of hitting the bulls eye (center circle) when you shoot an arrow? The radius of the bulls eye is 2ft and the radius of the target is 6ft. (Use 3. 14 for pi)
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The probability of hitting the bulls eye (center circle) when we shoot an arrow with radius of the bulls eye is 2ft and the radius of the target is 6ft is 11.1%.
Assuming that we are shooting randomly at the target and the arrow can land anywhere within the target area, the probability of hitting the bull's eye (center circle) can be calculated as the ratio of the area of the bull's eye to the area of the entire target.
The area of the bull's eye can be calculated as follows:
Area of bull's eye = π x (radius of bull's eye)²
Area of bull's eye = 3.14 x 2²
Area of bull's eye = 12.56 square feet
The area of the entire target can be calculated as follows:
Area of target = π x (radius of target)²
Area of target = 3.14 x 6²
Area of target = 113.04 square feet
Therefore, the probability of hitting the bull's eye can be calculated as:
Probability of hitting bull's eye = Area of bull's eye / Area of target
Probability of hitting bulls eye = 12.56 / 113.04
Probability of hitting bulls eye = 0.111 or approximately 11.1%
So, the probability of hitting the bull's eye (center circle) when we shoot an arrow randomly at the target is approximately 11.1%.
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Related Questions
Does this table represent a function ? Why or why not
Answers
if other factors are held constant, what is the effect of increasing the sample variance? group of answer choices it will increase the estimated standard error and increase the likelihood of rejecting h0. it will increase the estimated standard error and decrease the likelihood of rejecting h0. it will decrease the estimated standard error and increase the likelihood of rejecting h0. it will decrease the estimated standard error and decrease the likelihood of rejecting h0.
Answers
if other factors are held constant, what is the effect of increasing the sample variance: B. it will increase the estimated standard error and decrease the likelihood of rejecting h0.
What is a sample proportion?In Mathematics, a sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.
Mathematically, the standard error of a sample proportion can be calculated by using this formula:
Standard error = √(p × (1 - p)/n)
Where:
p represents the sample proportion.n represents the sample size.Generally speaking, the effect of increasing the sample variance is an increase in estimated standard error and a decrease in the likelihood of rejecting H_{0} provided that other factors are held constant.
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Mrs. Thapa wishes to grow flowers on the hanging bowls at her home. She bring hemispherical bowls from the market having internal diameter 21 cm and thickness 0.5 cm each and fills the bowls with compost completely. (i) If 1 cm³ of compost weighs 2.31 gm, find the total weight of required comp (ii) If she covers outer curved surface of each bowl with polythene sheet, find Width of the c Length of the Now the area of Hence, the cost o Also, the area of total amount of polythene.
Answers
The total volume of compost required for 16 bowls is 67,493.33 cm³
The total weight of compost required for 16 bowls is 155,906.67 gm
The total amount of polythene required for 16 bowls is: 6400π cm²
How to solve for this(i) The volume of compost required per bowl can be calculated as follows:
V = (4/3)πr^3, where r is the radius of the sphere
The radius of each bowl can be calculated as:
r = (d/2) - t, where d is the diameter (21 cm) and t is the thickness (0.5 cm)
So, r = (21/2) - 0.5 = 10 cm
Plugging the value of r into the formula for volume:
V = (4/3)πr^3 = (4/3)π * 10^3 = 4186.67 cm³
The total volume of compost required for 16 bowls is:
16 * 4186.67 = 67,493.33 cm³
The total weight of compost required for 16 bowls is:
67,493.33 cm³ * 2.31 gm/cm³ = 155,906.67 gm
(ii) To find the total amount of polythene required to cover the outer surface of 16 bowls, we first need to calculate the surface area of one bowl.
The surface area of a sphere can be calculated as follows:
A = 4πr^2
Plugging the value of r into the formula for surface area:
A = 4πr^2 = 4π * 10^2 = 400π cm²
The total amount of polythene required for 16 bowls is:
16 * 400π cm² = 6400π cm²
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Determine whether the statement is true or false. If the statement is false, give a reason. (4, 7, 9) (4, 4, 7, 9, 9) False. The sets do not have the same cardinality O False. Some elements of the first set are duplicated in the second set. O True. Both sets contain the same elements. O False. All elements in the first set should be duplicated in order for the sets to be equal.
Answers
The statement is false. The correct answer is A. False. The sets do not have the same cardinality.
In this case, we are comparing two sets: (4, 7, 9) and (4, 4, 7, 9, 9). To determine if the statement is true or false, we need to check if both sets contain the same elements and if they have the same cardinality.
The first set (4, 7, 9) has a cardinality of 3, as it contains three unique elements. The second set (4, 4, 7, 9, 9) has a cardinality of 5, as it contains five elements (though some are duplicated). Since the two sets have different cardinalities, they cannot be equal, and the statement is false.
Answer B is incorrect because although some elements of the first set are duplicated in the second set, this is not the main reason the statement is false. The primary reason is the difference in cardinality.
Answer C is incorrect because the sets do not contain the same elements; the second set has duplicate elements.
Answer D is incorrect because the requirement for the sets to be equal is not based on duplication but rather on having the same elements and cardinality.
In conclusion, the statement is false because the two sets do not have the same cardinality, and thus, they cannot be considered equal. Therefore, the correct option is A.
The question was incomplete, Find the full content below:
Determine whether the statement is true or false. If the statement is false, give a reason. (4, 7, 9) (4, 4, 7, 9, 9)
A. False. The sets do not have the same cardinality
B. False. Some elements of the first set are duplicated in the second set.
C. True. Both sets contain the same elements.
D. False. All elements in the first set should be duplicated in order for the sets to be equal.
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I would like it if I could get a accurate answer.
Answers
Answer:
60°
Step-by-step explanation:
the triangle need to have 180°. The up right corner is 60 because 120 + 60 = 180. Then I extended to rhombus where you have two sets of same angles. 125 + 55 = 180. 125 + 125 = 250. 360 - 250 = 110. 110 ÷ 2 = 60
If the length of each side of a triangle is doubled then it's perimeter
Answers
The perimeter of a triangle is the sum of the lengths of its three sides. If each side of a triangle is doubled, it means that each side's length is multiplied by 2. If the length of each side of a triangle is doubled, then its perimeter will also be doubled.
The perimeter of a triangle is the sum of the lengths of its three sides. If each side of a triangle is doubled, it means that each side's length is multiplied by 2.
Let's consider a triangle with sides a, b, and c. If we double the length of each side, the new lengths would be 2a, 2b, and 2c.
To find the new perimeter, we add up the new lengths:
New perimeter = 2a + 2b + 2c.
We can factor out the common factor of 2:
New perimeter = 2(a + b + c).
Comparing this to the original perimeter, we can see that the new perimeter is exactly twice the original perimeter.
Therefore, if the length of each side of a triangle is doubled, the perimeter of the triangle will also be doubled.
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00:00 Is the relation shown below a function? Use the graph and justify your answer (0, 0), (2.0), (2, 2), (3, 4) and (6,6) y 9 8 7 6 on 4 3 2 1 х 0 0 1 2 3 4 5 6 7 8 9 00:00 Yes, each x-value has a unique y-value 00:00
Answers
No; Two points have different y-values for the same x-value of 2.
Step-by-step explanation:
Explain, using these theorems, why the function is continuous at every number in its domain. g(t) = cos^-1(e^t -1) a. g(t) is an exponential function, so it is continuous at every number in its domain. b. g(t) is a composition of functions that are continuous on the domain of g(t), so it is continuous at every number in its domain. g(t) is a rational function, so it is continuous at every number in its domain. c. g(t) is a polynomial function, so it is continuous at every number in its domain. d. g(t) is not continuous at every number in its domain. State the domain. (Enter your answer using interval notation.)_______
Answers
The function g(t) = cos^-1(e^t -1) is continuous at every number in its domain. The domain of the function is all real numbers, which can be written as (-∞,∞).
This can be proved using the following theorems:
Theorem 1: If a function is an exponential function, it is continuous at every number in its domain.
Since g(t) = cos^-1(e^t -1) is an exponential function, this theorem applies, and it is continuous at every number in its domain.
Theorem 2: If a function is a composition of functions that are continuous on the domain of the function, then the function is continuous at every number in its domain.
Since g(t) = cos^-1(e^t -1) is a composition of functions that are continuous on the domain of the function, this theorem applies, and it is continuous at every number in its domain.
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Please answer this it is easy
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Answer:
480 people
Step-by-step explanation: 180/x=37.5/100 cross multiply. x=480.
x and y must have same first dimension, but have shapes
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The error message "x and y must have same first dimension but have shaped" typically occurs in programming languages such as Python or MATLAB when trying to operate on arrays or matrices with incompatible dimensions. In this case, the first dimension of the arrays or matrices must be the same, but they are not.
For example, if we have two arrays, x with shape (3, 4) and y with shape (2, 4), we cannot perform certain operations such as addition or multiplication between them because the first dimension, which represents the number of rows, is different.
To resolve this error, we can either reshape one of the arrays to have the same number of rows as the other, or we can transpose one of the arrays so that their dimensions match up. Another option is to adjust the code to ensure that the arrays being used have the same first dimension.
In summary, the "x and y must have the same first dimension but have shaped" error occurs when we attempt to operate on arrays or matrices with incompatible dimensions, and it can be resolved by reshaping, transposing, or adjusting the code.
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Yea imma need help asap. construct the triangle abc, with ab = 7cm, bc = 8cm, and ac = 6cm. measure and state the size of angle acb. i don't understand how you measure it.
Answers
The size of angle ACB in triangle ABC is approximately 35.5 degrees.
To calculate the size of angle ACB, we can use the Law of Cosines, which states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle.
The formula for the Law of Cosines is:
c^2 = a^2 + b^2 - 2ab * cos(C)
Where:
c is the side opposite to angle C (in this case, side AB with length 7cm)
a and b are the other two sides (in this case, sides AC and BC with lengths 6cm and 8cm, respectively)
C is the angle we want to find (angle ACB)
Plugging in the given values, we have:
7^2 = 6^2 + 8^2 - 2 * 6 * 8 * cos(C)
Simplifying the equation, we get:
49 = 36 + 64 - 96 * cos(C)
49 = 100 - 96 * cos(C)
96 * cos(C) = 100 - 49
96 * cos(C) = 51
cos(C) = 51 / 96
To find the angle ACB, we need to take the inverse cosine (also known as arccos) of the value we just calculated:
C = arccos(51 / 96)
Using a calculator, we find that C is approximately 35.5 degrees.
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If three numbers x, y, and z are chosen at random from the interval [0, 27], what is the probability that the three numbers are a solution to the equation x y z = 27?
Answers
The probability that three numbers are the solution of the equation is 1/27.
Total outcome of the number set
The total possible outcome or numbers in the is 27.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27.
total = 27
three numbers whose products is 27xyz = 27
(1)(3)(9) = 27
probability of the numbers whose product is 27 is calculated as follows;
p = possible numbers / total outcome
p = 1/27
Thus, the probability that three numbers are the solution of the equation is 1/27.
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in a box are four cards numbered 5, 10, 15, 20. two cards are taken out at random without replacement, and x is the total; of the numbers on the two card
Answers
By using the formula for mean and variance, it can be calculated that
Mean of X = 25
Variance of X = 51.67
What is mean and variance?
Suppose there is a data set. Mean gives the average of the values of the data set
Variance is the square of the sum of deviation from mean.
Let x be the total; of the numbers on the two card
Possible values of X= 15, 20, 25, 30, 35
P(X = 15) = \(\frac{2}{12}\)
P(X = 20) = \(\frac{2}{12}\)
P(X = 25) = \(\frac{4}{12}\)
P(X= 30) = \(\frac{2}{12}\)
P(X = 35) = \(\frac{2}{12}\)
Mean of X =
\(15 \times \frac{2}{12} + 20 \times \frac{2}{12} +25 \times \frac{4}{12} + 30 \times \frac{2}{12} + 35 \times \frac{2}{12}\\\\\frac{300}{12}\\\\25\)
Variance of X =
= \((225 \times \frac{2}{12} + 400 \times \frac{2}{12}+625 \times \frac{4}{12}+900 \times \frac{2}{12}+1225 \times \frac{2}{12}) - (25)^2\\\\\frac{8000}{12} - 625}\\\\666.67 - 625\\\\51.67\)
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Complete Question
In a box are four cards numbered 5, 10, 15, 20. two cards are taken out at random without replacement, and X is the total; of the numbers on the two card. Find the mean and variance of X .
The linear equation was solved using these steps.
Linear equation: (12x+ 15) = 7
Step 1: 4x + 5 = 7
Step 2: 4x = 2
Step 3: x = Ź
The property that was used in step 1 was the
The property that was used in step 2 was the
The property that was used in step 3 was the
HELPPP!!
Answers
Answer:
Distributive property
Subtraction property
Division property
Step-by-step explanation:
took test
Determine which statistical technique you will employ to measure the quality characteristics of your organization. provide examples to support the rationale.
Answers
To measure the quality characteristics of an organization, one statistical technique that can be employed is Statistical Process Control (SPC).
SPC is a method used to monitor and control processes to ensure they are operating within predetermined limits. It involves the use of control charts to analyze process data and identify any variations that may occur.
SPC provides a visual representation of process performance over time, allowing organizations to identify and address any issues that may affect quality. Control charts, such as the X-bar and R charts or the X-bar and S charts, are commonly used in SPC to monitor the mean and variability of a process.
For example, let's say a manufacturing company wants to measure the quality characteristics of its production line. The company can collect data on key quality indicators, such as product dimensions or defects, at regular intervals. Using SPC, the company can create control charts to track these measurements over time. If the data points fall within the control limits, it indicates that the process is stable and in control. However, if there are any data points outside the control limits or any patterns or trends observed, it may indicate a problem that requires investigation and corrective action.
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the length of each side of a square is 3 inches more than the length of each side of a smaller square. the sum of the areas of the squares is 149 inches squared. find the length of the side of the smaller square.
Answers
The length of the side of the smaller square is 7 inches.
Let x be the length of the side of the smaller square.
The length of each side of a square is 3 inches more than the length of each side of a smaller square. Thus the length of the side of the larger square is
(x + 3) inches.
The area of the smaller square is
x^2 square inches.
The area of the larger square is
(x + 3)^2 square inches.
We can set up the equation:
x^2 + (x + 3)^2 = 149
Expanding and simplifying the equation gives:
x^2 + x^2 + 6x + 9 = 149
Combining like terms:
2x^2 + 6x - 140 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-6 ± √(6^2 - 4 * 2 * (-140))) / 2 * 2
x = (-6 ± √(36 + 1120)) / 4
x = (-6 ± √(1156)) / 4
x = (-6 ± √(596)) / 4
x = (-6 ± 34) / 4
x = -10 or x = 7
The side length of the smaller square can't be negative, so x = 7 inches.
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In circle R with m/QRS = 30 and QR = 4 units, find the length of arc QS.
Round to the nearest hundredth.
R
S
Q
Answers
The length of arc QS is approximately 2.09 units.
The length of an arc of a circle:
Length of arc = (central angle / 360) × 2 × π × radius
Central angle is the angle in degrees formed by the two radii that define the arc and radius is the radius of the circle.
In this case, we are given that m∠QRS = 30 means that the central angle formed by radii QS and QR is 30 degrees.
We are also given that QR = 4 unit
The radius of the circle is also 4 units.
Substituting these values into the formula, we get:
Length of arc QS = (30 / 360) × 2 × π × 4
Simplifying and rounding to the nearest hundredth we get:
Length of arc QS ≈ 2.09
The length of arc QS is approximately 2.09 units.
An arc of a circle's length:
Arc length equals (central angle / 360) divided by 2 and radius.
Radius is the diameter of the circle, while central angle is the angle, in degrees, produced by the two radii that constitute the arc.
In this instance, we are told that mQRS = 30 denotes the centre angle of 30 degrees created by radii QS and QR.
Also stated is that QR equals 4 units.
The circle also has a radius of 4 units.
When these values are added to the formula, we obtain:
Arc length QS = (30 / 360) 2 4
Rounding to the closest hundredth and simplifying, we obtain:
Arc length QS = 2.09
Arc QS has a length of around 2.09 units.
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A quadratic function y=f(x)is plotted on a graph and the vertex of the resulting parabola is (-6, 5). What is the vertex of the function defined as g(x)=f(x-3)?
Answers
Answer:
The answer is (-9, 5). Hope this helps.
find the slope of a line that passes through the points -2,3 and 4,-3
Answers
Answer:
-1
Step-by-step explanation:
y1 - y2
_____
x1 - x2
6
__
-6
6÷ -6= -1
Keith buy 3 yard of material to make a blanket. He trim off a total of 1/6 yard before he begin ewing. How much material remain for the blanket?
Answers
The material remained for the blanket after trimming off by Keith is 2.5 yards.
Simple subtraction and multiplication can provide the result. Beginning will be by the multiplication. Firstly finding the exact amount of material trimmed = 3×1/6
Performing multiplication and division on Right Hand Side of the equation
Trimmed material = 1/2 or 0.5
Now, we need to subtract the trimmed material from overall amount of material
Remaining material = 3 - 0.5
Performing subtraction on Right Hand Side of the equation
Remaining material = 2.5 yards
Hence, 2.5 yards of material remained.
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A rectangle is inscribed in a parabola y^2 = 16x with the side of the rectangle along the latus rectum of the parabola. If the area of the rectangle is maximized, compute its perimeter.
a. 24.63
b. 13.69
c. 14.57
d. 20.69
Answers
The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.
To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.
The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).
To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.
Comparing the two equations, we get:
4a = 16
a = 4
Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.
Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.
Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.
Substituting x = 8 into the equation of the parabola, we get:
\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)
Therefore, the width of the rectangle is approximately 11.31 units.
The perimeter of the rectangle is given by the formula:
Perimeter = 2(length + width)
Plugging in the values, we have:
Perimeter = 2(16 + 11.31)
Perimeter ≈ 2(27.31)
Perimeter ≈ 54.62
Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.
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Can someone please help me with ASAP. I need to do this by tonight thx.
Which equation represents a parabola with focus (3,8)
A. y=1/4(x-3)^2-9
B. y= 4(x+3)^2-8
C. y=1/4(x-3)^2-10
D. 4(x+2)^2+7
also please don't be a bot or a person who says " I don't know" its not helpful
Answers
Answer: C
Step-by-step explanation:
If a parabola is given by \(a(x - h)^2 + k\), the focus is at the point \((h, k + 1/4a)\).
We know the focus is \((3, 8)\), so it should look like \(a(x - 3)^2 + k\). We can cross off B and D.
Let's check if A works: \(8 = -9 + 1/(4 \cdot \frac 14) = -8\). Obviously this is false, so we can cross off A.
Thus it's C by process of elimination.
If A=2r {2}+6r+1 and B=2r-6, find an expression that equals 2A-3B in standard form.
Answers
Please help me with this is my last question
Answers
Answer:
a
Step-by-step explanation:
Answer:
A
........................
- a) The volume of a rectangular tank is (2a³ + a² - 2a - 1) cu. ft. where a>4 ft., the length is longer than its breadth and the breadth is longer than its height. (i) Find its length, breadth and height. (ii) Find the area of the its floor.
Answers
The rectangle with:
The volume of (2a³ + a² - 2a - 1) ft³, a > 4 ftThe length > breadth > heightTo find(i) the dimensions(ii) the area of the floorSolution(i)Factorize the volume expression
2a³ + a² - 2a - 1 = 2a³ - 2a + a² - 1 = 2a(a² - 1) + (a² - 1) = (2a + 1)(a² - 1) = (a - 1)(a + 1)(2a + 1)If a > 4, then:
a - 1 > 4 - 1 ⇒ a - 1 > 3a + 1 > 4 + 1 ⇒ a + 1 > 52a + 1 > 2*4 + 1 ⇒ 2a + 1 > 9Since the longest dimension is the length, it is
2a + 1The breadth is the middle dimension, it is
a + 1The height is the smallest dimension, it is
a - 1(ii)The area of the floor is:
Area = length * breadthArea = (2a + 1)(a + 1) = 2a² + 3a + 1Answer:
i) length > 9 ft
breadth > 5 ft
height > 3 ft
ii) Area of floor > 45 ft²
Step-by-step explanation:
Volume of a rectangular prism
\(\textsf{V}=lbh\)
where:
l is the lengthb is the breadthh is the heightGiven:
\(\sf V=(2a^3+a^2-2a-1)\:\:ft^3, \quad where\:a > 4\:ft\)Part (i)
To find expressions for the 3 dimensions of the tank, factor the expression for Volume.
Using the Factor Theorem, if V(x) = 0 then (a - p) is a factor:
\(\implies \sf V(1)=2(1)^3+(1)^2-2(1)-1=0\)
\(\implies \sf V(-1)=2(-1)^3+(-1)^2-2(-1)-1=0\)
Therefore (a - 1) and (a + 1) are factors:
\(\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+p)\)
(where p is a constant to be found)
To find the value of p, expand:
\(\implies \sf 2a^3+a^2-2a-1=2a^3+pa^2-2a-1\)
and compare coefficients:
\(\implies \sf a^2=pa^2 \implies p=1\)
Therefore:
\(\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+1)\)
If l > b and b > h then:
length (l) = (2a + 1)breadth (b) = (a + 1)height (h) = (a - 1)If a > 4 ft then:
length > 9 ftbreadth > 5 ftheight > 3 ftPart (ii)
The area of the floor can be found by multiplying the found expressions for breadth and length:
\(\begin{aligned}\implies \sf Area\:of\:floor & =(a+1)(2a+1)\\& = 2a^2+3a+1\end{aligned}\)
If a > 4 ft then Area of floor > 45 ft²
4r+12=-16
Work shown!!! Please help
Answers
Answer:
\(r=-7\)
Step-by-step explanation:
\(4r+12=-16\)
Subtract 12 from both sides.
\(4r=-28\)
Divide both sides by 4.
\(r=-7\)
Check our work with substitution:
\(4\cdot-7+12=-28+12=\boxed{-16}\)
We see that our work is correct.
Subtract 12 from both sides.
4r = −16 − 12Subtract 12 from −16 to get −28.
4r = −28Divide both sides by 4.
r = -28/4Divide −28 by 4 to get −7.
r = −7 ==> AnswerOn a coordinate plane, a graph shows Street on the x-axis and Avenue on the y-axis. A line is drawn from Tia to Lei. Tia is at (4, 8) and Lei is at (12, 20). Tia lives at the corner of 4th Street and 8th Avenue. Lei lives at the corner of 12th Street and 20th Avenue. The fruit market is Three-fourths the distance from Tia’s home to Lei's home.
Answers
Answer:
(10, 17)
Step-by-step explanation:
It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.
Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)
From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.
y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.
The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.
x: 4+6 = 10
y: 8+9=17
The fruit market is at point (10,17)
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates
\(x= \dfrac{nx_1+nx_2}{m+n}\)
\(y= \dfrac{ny_1+ny_2}{m+n}\)
Tia is at P(4, 8) and Lei is at Q(12, 20).
The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1
So,
\(x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17\)
Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.
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A square solar panel has an area of 16 square feet. Write the area as a power. Then find the side lengths of the panel.
The area of the solar panel written as a power is ___
square feet.
The side lengths of the solar panel are ___
feet.
Answers
Answer:
\(a : 4^2\\\\b: 4ft\)
Step-by-step explanation:
\(\sqrt{16} = 4\\a : 4^2\\\\b: 4ft\)
The area of the solar panel written as a power is 4 square feet.
The side lengths of the solar panel are 4 feet.
What is the area of a square?
Area of square is the square of its side.
It is given that a square solar panel has an area of 16 square feet.
How we find square roots?By simply using this formula;
\(\sqrt{x} = x^\frac{1}{2}\)
Taking root square we get;
\(\sqrt{16} = 4\)
Thus, power = \(4^{2} ft\)
and lengths are = 4 feet
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Find the volume and surface area of a square pyramid. Volume of a pyramid: v = 1/3(area of base) x (height) surface area of a pyramid: a = 1/2(perimeter of base) x (slant height) + (area of base) a pyramid has a height of 4. 7 in. And a slant height of 5. 2 in. Its base is a square with sides of 3. 5 in. Find the pyramid's volume and surface area. Volume (to the nearest tenth) = in3 surface area (to the nearest tenth) = in2.
Answers
The Volume of the Pyramid=19.19in³
Surface Area of the Pyramid=48.65in²
What is meant by volume?Volume is a unit of measurement for the area occupied in three dimensions. It is widely quantified and measured using SI-derived units, alternative imperial units, or US standard units (such as the gallon, quart, cubic inch). Volume and length (cubed) have a similar meaning.
First, volume was calculated using naturally occurring vessels with a similar shape, and then using standardized containers. Calculating the volume of numerous common three-dimensional forms is made simple by arithmetic formulas. The volumes of increasingly complicated shapes can be calculated using integral calculus.
Given that,
Height of the pyramid =4.7
Pyramid's slant height= 5.2
Base of pyramid is a square with side=3.5
Volume of the pyramid=(1/3)(3.5×3.5)×(4.7)
=19.19 in³
The surface area of a pyramid=((1/2)×(4×3.5)×5.2)+(3.5×3.5)
=18.65in²
Therefore, the volume of the pyramid=19.19 in³
And the surface area of the pyramid=18.65in²
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The algebraic expression below is a polynomial.
(x-1^k)
where k is a real number.
Please select the best answer from the choices provided
T
F
Answers
Answer:
T
Step-by-step explanation:
Just did it