Answer:
12π feet
Step-by-step explanation:
The formula for the area of a circle is A = πr², where A is the area and r is the radius. We are given that the area is 36π ft², so we can set up an equation:
36π = πr²
To solve for the radius, we can divide both sides by π:
36 = r²
Taking the square root of both sides, we get:
r = 6
Now that we know the radius is 6 feet, we can use the formula for the circumference of a circle, C = 2πr:
C = 2π(6)
Simplifying, we get:
C = 12π
Therefore, the circumference of the circle is 12π feet.
Hi does anyone know how to do problem 2 and 3 on the worksheet?
2. Using percentage, we can find that Melissa needs to save $34500 in order to purchase the house.
3. The project was worth 97 points.
Define percentage?The denominator of a percentage (also known as a ratio or fraction) is always 100.
As a percentage, "%" is read as "percent" or "percentage" in this context.
You may always "divide by 100" this percent symbol to make it into a fraction or decimal equivalent.
Here we can see that Melissa has already $2500 in her savings account.
Total cost of house = $185000
Now for the loan she needs to have 20% of the mortgage as savings.
20% of $185000
20/100 × 185000
= 37000
Now she already has $2500.
So, the amount she need to save is= $37000 - $2500
= $34500
Now, total grade Brooke received = 87.
10 points have been taken off for her mistakes.
Total worth of test = 87+10 =97points.
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(2,90) and (4,810) as an exponential function
Answer:
y = 10(3)^x
Step-by-step explanation:
The general form of an exponential function is
[tex]y=ab^x[/tex], where x and y are any coordinate in the exponential function, a is the initial value, and b is the base.
Currently, we only have xs and ys, which forces us to find a and b:
[tex]90=ab^2\\810=ab^4[/tex]
We can find b first by dividing the larger x and y (4, 810) by the smaller x and y (2, 90). Thus, we must plug the xs and ys in and create a fraction:
[tex]\frac{810}{90}=\frac{ab^4}{ab^2}[/tex]
We know that a represents a value a number divided by itself is 1 and that 810/90 = 9 so we now have:
[tex]9=\frac{b^4}{b^2}[/tex]
According to quotient rule of exponents, when you divide bases with exponents, you subtract the exponent on the numerator from the base on the denominator:
[tex]9=b^4^-^2\\9=b^2\\3=b[/tex]
Now we can simply plug in our first coordinate and 3 for b to find a:
[tex]90=a(3)^2\\90=9a\\10=a[/tex]
Thus, the equation of the exponential function which contains the points (2,90) and (4,810) is
y = 10(3)^x
1. you purchase 6 bunches of celery, each weighing 2 pounds. how many 2 ounce servings can be made to serve with buffalo wings? celery has a 75% yield.
72, 2-ounce servings can be made to serve with buffalo wings.
Given that 6 bunches of celery each weighs 2 pounds. We have to find out how many 2-ounce servings can be made to serve with buffalo wings. Also, celery has a 75% yield.
[tex]Total weight of celery = 6 bunches * 2 pounds[/tex]
each = 12 pounds
Total weight of celery in ounces
[tex]= 12 pounds * 16 ounces[/tex]
[tex]= 192 ounces[/tex]
75% yield of celery means that 75% of the celery is edible.
The edible portion of celery
= 75% of 192 ounces
[tex]= (75/100)*192 = 144 ounces[/tex]
Now, as we have to find the number of 2-ounce servings that can be made, we need to divide the edible portion of celery by 2 ounces each. Thus, the number of 2-ounce servings can be made to serve with buffalo wings
[tex]= 144/2 = 72.[/tex]
Hence, 72 2-ounce servings can be made to serve with buffalo wings.
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a(n) ? is a device that indicates whether two ac sources to be connected in parallel are in the correct phase relationship.
The device that indicates whether two AC sources to be connected in parallel are in the correct phase relationship is called a synchronizing device.
A synchronizing device is a mechanism that ensures that two AC sources are in sync when they are connected in parallel. It's used to match the voltage, frequency, and phase angle of two alternating current (AC) sources.
It guarantees that the power supplied by both generators is synchronized, allowing them to be combined into a single electrical system without disrupting the balance of the current or causing a short circuit.
As a result, it is critical to the safe and efficient operation of power systems. A phase sequence indicator (PSI) or a synchroscope is often used as a synchronizing device. It works by providing an indication of the voltage difference, the phase angle difference, and the frequency difference between two AC sources that are to be synchronized.
Therefore, a synchronizing device is an instrument that determines whether two alternating current (AC) sources to be connected in parallel are in the appropriate phase relationship.
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which postulate or property can be used to prove that kimball is not between scottsbluff and sidney?
The postulate or property that can be used to prove that Kimball is not between Scottsbluff and Sidney is the Segment Addition Postulate.
The Segment Addition Postulate states that for three points A, B, and C, where B is between A and C,
we have AB + BC = AC.
Given that Kimball is not between Scottsbluff and Sidney, this means that Kimball is either to the west of Scottsbluff or to the east of Sidney.
Let's assume that Kimball is to the west of Scottsbluff.
Then, we can draw the line segment as follows:
Scottsbluff ——————— Kimball ——————— Sidney
Let AB represent the distance between Scottsbluff and Kimball, and let BC represent the distance between Kimball and Sidney. According to the Segment Addition Postulate, AB + BC = AC, where AC is the distance between Scottsbluff and Sidney.
However, if we draw the line segment from Scottsbluff to Sidney without Kimball, we can see that the distance between the two points will always be shorter than the sum of the distances from Scottsbluff to Kimball and from Kimball to Sidney.
This implies that if Kimball is not between Scottsbluff and Sidney, then it is not possible for the segment addition postulate to hold true for the three points.
Therefore, we can use the segment addition postulate to prove that Kimball is not between Scottsbluff and Sidney.
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mary has a rectangular garden in her backyard. the garden measures 5 and three fourths534 feet wide by 7 and one half712 feet long. what is the area of the garden?
The area of Mary's rectangular garden in her backyard is 40 1/8 square feet.
To determine the area of the rectangular garden, the length and width measurements must be multiplied, according to the question.A rectangular garden is one that has four corners, each of which forms a right angle. The width and length of a rectangular garden are typically stated in feet or meters.
The formula for finding the area of a rectangular garden is simply A = LW. A represents the area, L represents the length of the garden, and W represents the width of the garden.The solution for this question will be derived using the formula A = LW, where the length is 7 1/2 feet, and the width is 5 3/4 feet.
A = LW = (7 1/2 feet) * (5 3/4 feet) = (15/2) * (23/4) = 345/8 ft^2 = 43 1/8 ft^2. Thus, the area of Mary's rectangular garden in her backyard is 40 1/8 square feet.
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Find the measures of each of the angles 1-7.
Answer:
1=26°
2=154°
3=26°
4=26°
5=154°
6=154°
7=26°
from her purchased bags, rachel counted 130 red candies out of 520 total candies. using a 95% confidence interval for the population proportion, what are the lower and upper limit of the interval? answer choices are rounded to the thousandths place.
Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.
what is proportionality ?A mathematical concept known as proportionality describes the relationship between two quantities that have different sizes but keep the same ratio or proportion. In other words, to preserve the same ratio, if one item changes, the other quantity must also change in proportion. For instance, if an automobile's speed and distance are proportionate, doubling the distance it travels will cause the car to go twice as quickly while retaining the same speed-to-distance ratio. Equations or ratios in mathematics are frequently used to express proportionality.
given
We can use the following formula to determine the lower and upper bounds of the 95% confidence interval for the population proportion:
Lower limit: sqrt((p * q) / n) * p - z
Upper limit: sqrt((p * q) / n) = p + z
With q = 1 - p, z is the z-score corresponding to the level of confidence, and p is the sample proportion.
Here, p = 130/520 = 0.25, q = 1 - p = 0.75, n = 520, and the z-score is 1.96 at a 95% confidence level (from the standard normal distribution).
Lower limit: 0.210 (0.25" * 0.75") - 1.96 * sqrt(0.25" * 0.75")
The maximum is equal to 0.25 + 1.96 * sqrt((0.25 * 0.75) / 520) = 0.290.
Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.
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Write the linear equation in standard form y=19/14x+13
The linear equation in standard form is 19x - 14y = -182.
What is Linear equation?
A linear equation is a mathematical equation that describes a straight line on a graph. In other words, it is an equation that relates a variable or variables to a constant through a linear function, where the highest power of the variable is one. A general form of a linear equation is:
y = mx + b
To write the linear equation in standard form Ax + By = C, where A, B, and C are integers and A is positive, we need to get rid of the fraction in the equation.
To do this, we can multiply both sides of the equation by the denominator of the fraction, which is 14. This gives:
14y = 19x + 182
Next, we can rearrange this equation by subtracting 19x from both sides:
-19x + 14y = 182
Finally, we can multiply both sides of the equation by -1 to make the coefficient of x positive:
19x - 14y = -182
So, the linear equation in standard form is 19x - 14y = -182.
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11. Find m
H= 5x+8
J= 7x-16
Answer:
let angle GJK be x
GJK=GHK (Base angle of isosceles triangle)
Step-by-step explanation:
x=5x+8
5x-x=8
4x=8
x=8/4
x=2 ans.
Hence,
5x+8
5*2+8
10+8
18.ans
The form of federalism favored by Chief Justice Roger Taney in which national and state governments are seen as distinct entities providing separate services. This model limits the power of the national government.
This model of federalism ensures that both the national and state governments are equal and that neither has the power to override the other.
The form of federalism favored by Chief Justice Roger Taney was a dual-sovereignty system, in which the national and state governments are seen as distinct entities, providing separate services and limiting the power of the national government.
Taney argued that each government should remain supreme within its own sphere, and that there should be a strict division of authority between the two levels of government.
He argued that the Constitution was a compact between states, each of which had the right to govern itself without interference from the other, and that the Constitution created the federal government only to manage matters that could not be handled by the states.
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Salma sells beaded necklaces. Each large necklace sells for $5.10 and each small necklace sells for $4.50. How much will she earn from selling 4 large necklaces
and 1 small necklace?
During halftime of a basketball game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 5 feet with an initial upward velocity of 72 feet per second. Use the equation h(t) = -16²+72t +5, where t is time in seconds and h(t) is height. How long will it take the T-shirt to reach its maximum height? What is the maximum height? The T-shirt takes second(s) to reach its maximum height. (Type an integer or a decimal.) The T-shirt's maximum height is (Type an integer or a decimal.) feet above the court.
The T-shirt takes 2.25 seconds to reach its maximum height and the maximum height is approximately 90.125 feet above the court.
What is the equation for the height of the T-shirt ?The equation for the height of the T-shirt at time t is given as h(t) = -16t² + 72t + 5, where h(t) is the height in feet and t is the time in seconds.
To find the time it takes for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic function. The vertex of a parabola in the form y = ax² + bx + c is given by (-b/2a, c - b²/4a). In this case, a = -16, b = 72, and c = 5. So, the time it takes for the T-shirt to reach its maximum height is:
t = -b/2a = -72/(2(-16)) = 2.25 seconds
To find the maximum height, we need to substitute the value of t we just found into the equation for h(t):
h(2.25) = -16(2.25)² + 72(2.25) + 5 ≈ 90.125 feet
Therefore, the T-shirt takes 2.25 seconds to reach its maximum height and the maximum height is approximately 90.125 feet above the court.
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I need help with this geometry problem
Step-by-step explanation:
Volume of a sphere is given by 4/3 pi r^3
if radius = 3 inches
4/3 pi (3^3) = 36 pi in^3
it is a HEMI- sphere so 1/2 of this would be 18 pi in^3
DUE TOMORROW PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!!!
Here is the graph of a function describing the relationship between the height y, in feet, of the tip of a windmill blade and the angle of rotation Θ made by the blade. Describe the windmill.
However, it is important to note that without additional information about the function and the windmill itself, further conclusions about its design and performance cannot be made.
Hi! I'd be happy to help you describe the windmill based on the provided graph.The graph of the function represents the relationship between the height (y) of the tip of a windmill blade and the angle of rotation (Θ) made by the blade. This function is periodic, indicating that the windmill blade follows a repetitive motion as it rotates.
The height of the blade tip varies sinusoidally with respect to the angle of rotation, suggesting that the windmill has a circular or rotational motion. The amplitude of the function gives the length of the windmill blade, while the period of the function represents a full rotation (360 degrees) of the windmill blade.
In summary, the windmill has a rotational motion, with the height of the blade tip following a sinusoidal pattern. The length of the windmill blade and the time it takes to complete a full rotation can be determined by analyzing the amplitude and period of the function.
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this question pertains to a standard 52-card deck (52 total cards, 4 suits each with 13 possible values: ace, two, king, etc). you draw two cards at random with replacement. what is the probability that at least one card is a spade?
The probability of drawing at least one spade when drawing two cards with replacement from a standard deck of cards is approximately 0.26%.
When drawing two cards at random with replacement from a standard 52-card deck, there are 4 possible outcomes for the first card being a spade and 4 possible outcomes for the second card being a spade.
However, there is also 1 possible outcome where both cards are spades, which would be counted twice if we add the outcomes for the first and second cards separately. Therefore, the total number of outcomes where at least one card is a spade is 4 + 4 - 1 = 7.
The total number of possible outcomes when drawing two cards with replacement is 52 x 52 = 2,704.
Therefore, the probability that at least one card is a spade when drawing two cards with replacement is:
P(at least one spade) = 7 / 2,704 ≈ 0.0026
So, the probability that at least one card is a spade is approximately 0.0026 or 0.26%.
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I will mark BRAINLYIST
Answer:
119% of 550
Step-by-step explanation:
add the percentages
James deposited 10000 into an account that earns 5.5% compound interest, compounded semiannually. How much interest will James earn after 10 years?
James will earn approximately $6,639.12 in interest after 10 years.
What is simple interest?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
To solve this problem, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
where:
A is the final amount (including interest)
P is the principal amount (initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time (in years)
Plugging in the given values, we get:
[tex]A = 10000(1 + 0.055/2)^{(2*10)}[/tex]
[tex]A = 10000(1.0275)^{20}[/tex]
A = 10000(1.664)
A ≈ 16639.12
To find the amount of interest earned, we subtract the principal amount from the final amount:
Interest = A - P
Interest = 16639.12 - 10000
Interest ≈ 6639.12
Therefore, James will earn approximately $6,639.12 in interest after 10 years.
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IF YESTARDAY IS THE DAY BEFORE YESTARDAY OF SATURDAY, WHAT DAY IS DAY AFTER TOMORROW
The required day if yesterday is the day before yesterday of Saturday is Thursday and day after tomorrow is Sunday.
If yesterday was the day before yesterday of Saturday,
Yesterday was Saturday
Day before yesterday is Friday,
then yesterday was Thursday.
Now,
If yesterday was Thursday, then today is Friday.
Day representing tomorrow is Saturday.
And day after Saturday is definitely Sunday.
This implies,
The day after tomorrow would be Sunday.
Therefore, day after tomorrow is Sunday as per given situation.
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Números que multiplicados me den 24 y sumados me den -11
The two numbers that multiply to give 24 and add to give -11 are -3 and -8.
How do we get these numbers?To find these numbers, you can use a system of equations. Let x and y be the two numbers. Then we have:
xy = 24 (because the two numbers multiply to give 24)x + y = -11 (because the two numbers add to give -11)We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for x:
x + y = -11
x = -11 - y
We can then substitute this expression for x into the first equation:
xy = 24
(-11 - y)y = 24
Expanding and rearranging, we get:
y^2 + 11y + 24 = 0
This is a quadratic equation that we can solve using factoring or the quadratic formula. Factoring, we get:
(y + 3)(y + 8) = 0
So either y + 3 = 0 or y + 8 = 0. This means that y can be -3 or -8. Substituting each of these values into x = -11 - y, we get:
If y is -3, then x is -11 - (-3) = -8
If y is -8, then x is -11 - (-8) = -3.
Translated question "Numbers that multiply to give me 24 and add to give me -11"
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How many 1cm^3 beads will it take to completely fill the 5x12x3 bed of this toy truck
Answer:
180 beads
Step-by-step explanation:
5 x 12 x 3
180 beads
hope this helps x
if the matrix product a1b is known, how could you calculate b1a without necessarily knowing what a and b are?
We can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
The matrix product of two matrices, A and B, is defined as the matrix C, where C = AB. To calculate the product of two matrices, we must take the dot product of each row of A and each column of B. If we are given a matrix product A1B, then we can calculate B1A without necessarily knowing what A and B are.
To do so, we must first invert the matrix A1B. We can do this by solving a system of equations. We can set up this system of equations by treating the entries of A1B as the coefficients in a system of equations, and solving for the entries of B1A. Once we have found the inverse, we can calculate the matrix B1A.
Finally, once we have the matrix B1A, we can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
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50 POINTS!!
1. Find a polynomial that represents volume of the fish tank. Explain how you used the
properties of exponents to determine your expression.
HINT: The formula for the volume of a rectangular prism is = ℎ.
2. The volume of each hemisphere is represented by the polynomial 3 − 702 + 360 − 1800.
Explain how to rewrite your answer for question 1 to reflect the volume of the fish tank after the
hemispheres are installed. Then carry out your plan. Show your work.
3. Show that the binomial that represents the length of the fish tank is a factor of the polynomial
you wrote in question 1.
4. Is the binomial that represents the length of the fish tank a factor of the polynomial that
represents the volume of the fish tank after the hemispheres are installed? Support your answer
mathematically.
5. The sanctuary currently has 125 exotic fish. The average amount of the tank allotted for each fish is represented by the binomial (22 − 1). Are the dimensions of the new habitat adequate
for these 125 fish? Explain.
To ensure that the dimensions of the fish tank are adequate, we need to ensure that the volume of the fish tank is greater than or equal to 2625. Since we do not have any information about the dimensions of the fish tank,
What ensures dimensions of the fish tank are adequate?1. Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively. V = l^1 × w^1 × h^1 = lwh. Therefore, the polynomial that represents the volume of the fish tank is V = lwh.
2. Then the volume of each hemisphere is (4/3)πr^3. Since there are two hemispheres, the total volume they take up is 2(4/3)πr^3 = (8/3)πr^3.
Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:
[tex]V_new = lwh - (8/3)πr^3[/tex]
3.The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:
[tex]V = lwh = l(wh) = l(q)[/tex], where q = wh.
Therefore, l is a factor of V.
4. To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:
Let the dimensions of the fish tank be length, width, and height, represented by l, w, and h, respectively.
Then the volume of the fish tank is V = lwh. We can use the properties of exponents to simplify this expression by multiplying the powers of the variables: [tex]V = l^1 × w^1 × h^1 = lwh[/tex] . Therefore, the polynomial that represents the volume of the fish tank is V = lwh.
The volume of each hemisphere is [tex](4/3)πr^3[/tex] . Since there are two hemispheres, the total volume they take up is [tex]2(4/3)πr^3 = (8/3)πr^3.[/tex]
Therefore, the new volume of the fish tank after the hemispheres are installed is V - (8/3)πr^3, where V is the original volume of the fish tank. Substituting V = lwh, we get:
V_new = l [tex]wh - (8/3)πr^3[/tex]
The binomial that represents the length of the fish tank is l. To show that it is a factor of the polynomial V = lwh, we need to show that V is divisible by l, which means there exists a polynomial q such that V = lq. We can see that:
V = lwh = l(wh) = l(q), where q = wh.
Therefore, l is a factor of V.
To determine if the binomial l is a factor of the polynomial V_new = lwh - (8/3)πr^3, we need to check if V_new is divisible by l. We can use polynomial long division to divide V_new by l:
Since there is a remainder of [tex]- (8/3)πr^3[/tex] , we can see that l is not a factor of V_new.
5. The average amount of tank allotted for each fish is represented by the binomial [tex](22 − 1)[/tex] . To determine if the dimensions of the new habitat are adequate for 125 fish, we need to check if the volume of the fish tank is greater than or equal to the space required for 125 fish.
Let the required space for each fish be v, then the total space required for [tex]125[/tex] fish is [tex]125v[/tex] . Substituting the given binomial, we have:
[tex]v = (22 - 1) = 21[/tex]
Therefore, the total space required for 125 fish is [tex]125v = 125(21) = 2625[/tex] . We cannot determine if it is adequate for the given number of fish.
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4. Determine the common ratio or common difference for the given sequence.
-6, 10, 26, 42, . . .
The common difference of the arithmetic sequence -6, 10, 26, 42 is given as follows:
16.
How to obtain the common ratio of an arithmetic sequence?The common difference of an arithmetic sequence is the constant value added or subtracted to each term in the sequence to get to the next term.
The sequence for this problem is given as follows:
-6, 10, 26, 42, . . .
The difference between consecutive terms is given as follows:
42 - 26 = 16, which is constant for the other terms of the sequence.
Hence 16 is the common difference of the arithmetic sequence -6, 10, 26, 42, . . . given in this problem.
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Given f(x) = x^2+ x + 1 and g(x) = x^2 - 9. find: (f + g) (x)
Answer: [tex]2x^{2} +x-8[/tex]
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= [tex]x^{2} +x+1+(x^{2} -9)[/tex]
= [tex]x^{2} +x+1+x^{2}-9[/tex]
= [tex]2x^{2} +x-8[/tex]
hillary took a photograph of her house, which has an actual height of 28.5 feet. if the house measures 3.6 inches tall in the photograph, what is the scale factor?
The scale factor of Hillary's photograph of her house is 1:8. This means that for every 1 inch of the house that is shown in the photograph, the house is actually 8 inches tall in real life.
To calculate the scale factor, you need to divide the actual height of the house by the height shown in the photograph. 28.5 feet divided by 3.6 inches gives a result of 8. In other words, for every 1 inch of the house that is shown in the photograph, the house is actually 8 inches tall in real life.
To explain further, the scale factor is a ratio that is used to compare two different measurements of the same object or shape. It tells us how much bigger or smaller one measurement is compared to another. In this case, we have compared the actual height of the house (28.5 feet) to the height of the house as shown in the photograph (3.6 inches). The ratio of the two measurements (1:8) tells us that the house is 8 times bigger in real life than it appears in the photograph.
The scale factor is an important concept in the field of mathematics and is often used in science, engineering, and architecture. It is used to measure the size and shape of objects, as well as to convert measurements from one unit of measure to another.
Therefore, the scale factor of Hillary's photograph of her house is 1:8, meaning that for every 1 inch of the house that is shown in the photograph, the house is actually 8 inches tall in real life.
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kai and David share £84 in the ratio 1:3 calculate the amount of money kai gets
Answer:
£21
Step-by-step explanation:
We know
kai and David share £84 in the ratio 1:3. Meaning for every £4, Kai receive £1 & David received £3.
Calculate the amount of money kai gets?
To get from 4 to 84, we time 21.
We take
1 x 21 = £21
So, Kai gets £21
How much fencing is required to enclose a circular garden whose radius is 26 m? Use 3. 14 for PI
to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.
To determine the amount of fencing required to enclose a circular garden with a radius of 26 meters, we need to calculate the circumference of the circle. The circumference is the distance around the perimeter of the circle, which can be calculated using the formula:
Circumference = 2 x π x radius
where π is the mathematical constant approximately equal to 3.14, and the radius is the distance from the center of the circle to any point on its perimeter.
So, in this case, the circumference of the circular garden can be calculated as follows:
Circumference = 2 x 3.14 x 26 m
= 163.64 m
Therefore, to enclose the circular garden, we need 163.64 meters of fencing. This means that if we were to wrap a measuring tape or any other material around the perimeter of the garden, it would need to be 163.64 meters long to cover the entire circumference of the circle.
It's worth noting that the formula for calculating the circumference of a circle can be used to find the amount of fencing required for any circular enclosure, such as a circular pond or a circular pool.
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If there are 55 children in a five a side field how many children are on each team
There are 55 children in total, and each team will have 27 children.
Now, you mentioned that there are 55 children in total. To find out how many children are on each team, we need to divide the total number of children by the number of teams. In this case, there are two teams, so we divide 55 by 2.
When we divide 55 by 2, we get 27.5. However, we cannot have half a child on a team, so we need to round the number to the nearest whole number. In this case, the median can be used to determine the most appropriate rounding.
The median is the middle value of a set of numbers. In this case, if we arrange the numbers 1, 2, 3, ..., 55 in ascending order, the median will be the 28th number.
Now, we have two options for rounding. We can either round up to 28 or round down to 27. Since we cannot have a partial player, we must decide which option is most appropriate.
In this case, it's best to have an equal number of players on each team. Therefore, we'll round down to 27. This means that each team will have 27 children.
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A certain bookshop has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their sellilng prices are Rs. 80, Rs. 60 and Rs. 40 each respectively. Find the total amount the bookshop will receive by selling all the books, using matrix algebra
The bookshop will receive a total amount of Rs. 23,200 by selling all the books.
WHAT IS SELLING PRICE ?
The selling price is the price at which a product or service is sold to a customer. It is the amount of money that a seller charges to a buyer for a particular product or service. The selling price may include various factors such as the cost of production, overhead costs, profit margin, taxes, and other charges. It is an important concept in business and commerce, as it determines the revenue generated by a company and its profitability.
We can represent the given information using matrices as follows:
Let A be the matrix of the number of books in dozens, where each row represents a subject and each column represents the number of dozens of books:
A =
| 10 8 10 |
|____________|
Let B be the matrix of the selling prices of each book, where each row represents a subject and each column represents the selling price of each book:
B =
| 80 |
| 60 |
| 40 |
To calculate the total amount the bookshop will receive, we need to multiply the matrices A and B using matrix algebra:
C = A * B
C =
| 10 8 10 | | 80 | | 12000 |
| 60 | = | 7200 |
| 40 | | 4000 |
Therefore, the bookshop will receive a total amount of Rs. 23,200 by selling all the books.
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