Answer:
Step-by-step explanation:
We can use the fact that the ratio of the volumes of two similar solids is equal to the cube of their corresponding linear dimensions, also known as the volume-scale factor:
(volume of image) / (volume of original) = (linear dimension of image / linear dimension of original)^3
(40 cubic units) / (10 cubic units) = (linear dimension of image / linear dimension of original)^3
4 = (linear dimension of image / linear dimension of original)^3
Taking the cube root of both sides, we get:
(cube root of 4) = (linear dimension of image / linear dimension of original)
Simplifying, we have:
2 = (linear dimension of image / linear dimension of original)
Therefore, the linear dimensions of the image are two times greater than those of the original. Thus, the scale factor is 2.
Can anybodyhelp me with these please? I need help please!
1: The measure of arc JML is: arc JML = 176°
3: m∠WXY = 59°
5: The measure of the arc is: arc FE = 54°
7: The measure of the angles are: m∠A = 79° and m∠B = 112°
9: The value of x is: x = 9
How to find the angle or arc measure in a circle?
No. 1
The measure of inscribed angle is half the measure of its intercepted arc. That is:
∠ JKL = 1/2 * arc JML
88 = 1/2 * arc JML
arc JML = 2 * 88
arc JML = 176°
No. 3
arc WY = 360 - 86 - 156 = 118° (sum of angles in a circle)
m∠WXY = 1/2 * arc WY
m∠WXY = 1/2 * 118
m∠WXY = 59°
No. 5
An angle inscribed in a semicircle is a right angle. Thus, m∠DFE = 90°
m∠EDF = 180 - 90 - 63 = 27° (sum of angles in a triangle)
m∠EDF = 1/2 * arc FE
27° = 1/2 * arc FE
arc FE = 2 * 27
arc FE = 54°
No. 7
The opposite angle in a cyclic quadrilateral add up to 180°. That is:
m∠A + m∠C = 180°
m∠A + 101 = 180
m∠A = 180 - 101
m∠A = 79°
m∠B + m∠D = 180°
m∠B + 68 = 180
m∠B = 180 - 68
m∠B = 112°
No. 9
67 = 1/2 * (16x - 10)
67 * 2 = (16x - 10)
16x - 10 = 134
16x = 134 + 10
16x = 144
x = 144/16
x = 9
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Describe a series of transformations that moves the blue figure to the red figure. If there is a : Translation - show number and direction Reflection - give axis of reflection
Rotation - give direction (clockwise or counterclockwise) and degree amount
Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.
Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.
Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.
This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.
To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.
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does the confidence interval suggest that the difference, if any, observed in this sample will also generalize to the larger population?
In the following question, Yes, the confidence interval suggests that the difference observed in this sample will also generalize to the larger population.
What is a confidence interval? A confidence interval is a probability statement that provides an interval of plausible values that are likely to contain the value of a population parameter. It is a way to infer the population parameter value from sample data.
A confidence interval is calculated as a range of values that are predicted to include the unknown population parameter, based on the sample statistic. The confidence interval suggests that the difference, if any, observed in this sample will also generalize to the larger population.
A confidence interval with a high level of confidence (e.g. 95%) would have a wider range of values and a higher probability of including the population parameter. The interpretation of the confidence interval is that we are 95% confident that the actual population parameter falls within the calculated interval. Therefore, it implies that the sample data is likely to be representative of the population data.
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claire invests £200000 in a saving account foe 4 years .the account pays compound interest at a rate of 1.6% per annum
calculate the total amount of interest claire will get at the end of four years
Answer:
We can use the compound interest formula to find the total amount of interest Claire will get at the end of four years:
A = P(1 + r/n)^(nt)
Where:
A = the total amount of money in the account at the end of the four years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = £200000
r = 0.016 (1.6% expressed as a decimal)
n = 1 (compounded annually)
t = 4
So, the formula becomes:
A = £200000(1 + 0.016/1)^(1*4)
= £200000(1.016)^4
= £219,463.18
To find the total amount of interest Claire will get, we need to subtract the principal amount from the total amount of money in the account at the end of four years:
Total interest = £219,463.18 - £200,000
= £19,463.18
Therefore, Claire will get £19,463.18 in total interest at the end of four years.
PLEASE HELP NEED IT DONE RN !!
Answer: rectangleular pyramid
Step-by-step explanation:
how far will 560J raise a block weighing 8 N
a force of 560J can raise a block weighing 8 N to a height of 70 meters. It's important to note that this calculation assumes no energy is lost due to friction or other factors, so in reality, the block may not reach exactly 70 meters.
How to calculate work?
To calculate the height to which a block weighing 8 N can be raised by a force of 560J, we need to use the formula for work done:
Work (W) = force (F) x distance (d) x cos(theta)
where theta is the angle between the force and the displacement. In this case, the force is the weight of the block (8 N), the distance is the height the block is raised (h), and theta is 0 degrees because the force is acting vertically upward and the displacement is in the same direction.
So, we can rearrange the formula to solve for the height (h):
h = W / (F x cos(theta))
Substituting the values we have, we get:
h = 560 J / (8 N x cos(0 degrees))
Since the cosine of 0 degrees is 1, we can simplify to:
h = 560 J / 8 N
h = 70 meters
Therefore, a force of 560J can raise a block weighing 8 N to a height of 70 meters. It's important to note that this calculation assumes no energy is lost due to friction or other factors, so in reality, the block may not reach exactly 70 meters.
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In the past month, Henry rented 1 video game and 4 DVDs. The rental price for the video game was $3.40. The rental price for each DVD was $4.10. What is
the total amount that Henry spent on video game and DVD rentals in the past month?
Answer:
Let x = the cost of a movieLet y = the cost of a gameUsing these variables,
we can set up equations.3x + 5y = 42 eq19x + 7y = 72 eq2
We have here a system of equations, where we have two or more equations with two or more different variables.
We use the elimination method to solve for the variables.
Multiply eq1 by 3. Keep eq2.
9x + 15y = 126 eq1
9x + 7y = 72 eq2
Subtract eq2 from eq1 to eliminate the x terms.
8y = 54y
= 6.75
This rental cost of one video game is $6.75
Substitute the value of y into eq1 to solve for x.
This will give you the rental cost of one movie.
Step-by-step explanation:
Solve this quadratic equation.
x⁴ - x³ - 4x² - x + 1 = 0 is the solution of quadratic equation.
What in mathematics is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0. Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution.
The answer could be simple or complicated. The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once.
x² + 1/x² - x - 1/x - 4 = 0
x⁴ + 1 -x³ - x - 4x²/x² = 0
x⁴ - x³ - 4x² - x + 1 = 0
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Ramon earns $1,710 each month and pays $53.60 on electricity. To the nearest tenth of a percent, what percent of Ramon's earnings are spent on electricity each month? SHOW WORK!
Answer:
3.1% of Ramon's earning are spent on electricity.
Step-by-step explanation:
Ramon's monthly salary
= $1,710
Electricity rent
=$53.60
*work show below*
[tex]\frac{53.60}{1,710} *100[/tex]
0.0313450292397661*100=3.134502923976608
3.134502923976608 rounded to the nearest tenth is 3.1%...
Thus my-our answer checks out! have a great day bestie!
Shirts are on sale for 30% off the oringal price of one shirt is 15 what is the total cost of 2 of these shirts at the sales price including a 7% sales tax
The sales price of the two shirt with 30%off on original price and 7% sales tax is equal to $22.47.
Original price of one shirt = $15
Number of shirts bought = 2
Sale discount = 30% off on original price
Sale price of one shirt = Original price - 30% of the original price
Substitute the value we get,
⇒Sale price of one shirt = 15 - (0.30)(15)
⇒Sale price of one shirt = $10.50
The cost of two shirts is equal to,
2 x $10.50 = $21.00
Sales tax = 7% of the total cost.
Substitute the value we have,
⇒Sales tax = 0.07 x $21.00
= $1.47
Total cost of two shirts = Cost of two shirts + Sales tax
⇒ Total cost of two shirts = $21.00 + $1.47
⇒ Total cost of two shirts = $22.47
Therefore, the total cost of two shirts at the sale price including the 7% sales tax is $22.47.
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write the equation of an exponential decau function with a range of (-inifinage,10) verticlal shrink of 3/4 and vertical shift up 10 units
The equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.
An exponential decay function can be written as f(x) = ab^x where b is the base of the exponential function and a is the initial value. If b is between 0 and 1, the function will exhibit exponential decay. Since we need a vertical shrink of 3/4, we can set b = 3/4.
We also need a vertical shift of 10 units, so we add 10 to the function. The resulting function is: f(x) = 10 - (3/4)^x. Therefore, the equation of an exponential decay function with a range of (-∞,10), vertical shrink of 3/4, and vertical shift up 10 units is f(x) = 10 - (3/4)^x.
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write a polynomial function in standard form with real coefficients whose zeros include 2,8i,-8i
If the zeros are 2, 8i, and -8i, the the polynomial has factors of (x-2), (x-8i), and (x+8i).
If we multiply those factors, we'll get our polynomial:
(x-2)·(x-8i)·(x+8i) = (x-2)·(x^2+64)
= x^3 - 2x^2 + 64x - 128
The Computer has labeled the lines you graphed a and b. What are the equations of the lines? Enter them into the table below
The equation of the line is 9x+8y + 19 = 0 and 5x - 4y+ 19 = 0 According to the given graphs, these are the equations of the graph.
Consider two points on the blue line.
The points are (5, -8) and ( -3,1 ).
Equation of the blue line is:
y - 1 = [tex]\frac{-8-1}{5+3} (x+3)[/tex]
8 (y - 1) = -9 ( x + 3)
8y - 8 = -9x -27
9x + 8y + 19 = 0
Therefore, the Equation of the blue line is 9x + 8y + 19 = 0.
Consider two points on the red line.
The points are (-3, 1) and ( 1,6 ).
Equation of the red line is:
y - 1 = [tex]\frac{6-1}{1+3} (x+3)[/tex]
4 (y - 1) = 5 (x + 3)
4y - 4 = 5x + 15
5x - 4y+ 19 = 0
Therefore, the Equation of the red line is 5x - 4y+ 19 = 0.
Hence, the equations for the given blue and red lines are completed.
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On pose, pour tout n E N, Un = Un - 5.
(a) Montrer que (Un) est une suite géométrique; préciser sa raison et son premier terme.
(b) Donner l'expression de Un en fonction de n: en déduire l'expression de un en fonction de n.
(c) En déduire la valeur de U12
Answer:
(a) Pour montrer que la suite (Un) est géométrique, il suffit de vérifier que le quotient de deux termes consécutifs est constant. Soit n un entier naturel non nul. Alors :
Un+1 / Un = (Un-4) / (Un) = 1 - 5/Un
Donc, pour tout n E N*, on a :
Un+1 / Un = 1 - 5/Un = (Un / Un) - (5/Un) = (Un - 5) / Un
On a bien trouvé une raison q = -5/1, et un premier terme U1 = U1 - 5.
(b) La raison de la suite (Un) est q = -5/1. En utilisant la formule générale de la suite géométrique, on obtient :
Un = U1 * q^(n-1) = (U1 - 5) * (-5)^(n-1)
En particulier, on a :
U_n = U_1 * q^{n-1} = (U_1 - 5) * (-5)^{n-1} = U_12 = (U_1 - 5) * (-5)^{12-1}
(c) On n'a pas suffisamment d'informations pour déterminer la valeur de U1, donc on ne peut pas calculer directement la valeur de U12.
Diana uses 30 grams of coffee beans to make a 48 fluid ounces coffee. When guests come,she makes 96 fluid ounces of coffee. How many grams of coffee beans does Diana use when she has visitors?
Diana needs 60 grams of coffee beans to make 96 fluid ounces of coffee for her guests.
What does a percentage formula mean?Determine whether two ratios or fractions are equivalent using the proportion formula. Dividing the provided values will reveal the value that is missing. As an example of the percentage formula: A and d are the extreme terms, while b and c are the mean terms. Hence, b::c: d = a/b = c/d.
We can resolve the issue by using proportions.
The ratio of coffee beans to liquid ounces in Diana's ordinary coffee must first be determined.
48 fluid ounces / 30 grammes
By reducing the numerator and denominator by 6, we may simplify the ratio:
Eight fluid ounces/5 grammes
We can now apply this proportion to determine how many grammes of coffee beans Diana needs to prepare 96 ounces of coffee:
5 grams/8 fluid ounces = 96 fluid ounces x grammes
After cross-multiplying and finding x, we obtain:
x = (96 ounces * 5 grammes) / 8 ounces
x=60 grammes.
In order to prepare 96 fluid ounces of coffee for her visitors, Diana needs 60 grammes of coffee beans.
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a die is continuously rolled 104 104 times. what is the probability that the total sum of all rolls does not exceed 375 375 ?
The probability that the total sum of all rolls does not exceed 375 is approximately 0.7165
Assuming the die is a fair six-sided die, the possible outcomes for each roll are numbers 1 through 6, each with a probability of 1/6.
Let X be the total sum of all rolls. Then X follows a discrete uniform distribution with parameters n = 104 (number of rolls) and a = 1 (minimum value of each roll). The expected value of X is:
E(X) = n × (a + b) / 2 = 104 × (1 + 6) / 2 = 365
The variance of X is
Var(X) = n × (b - a + 1)^2 / 12 = 104 × 6^2 / 12 = 312
The standard deviation of X is
SD(X) = sqrt(Var(X)) = sqrt(312) = 17.67
To calculate the probability that the total sum of all rolls does not exceed 375, we need to calculate the cumulative distribution function (CDF) of X and evaluate it at 375
P(X <= 375) = F(375)
where F(x) = P(X <= x) is the CDF of X.
Using the normal approximation to the binomial distribution, we can approximate X as a normal distribution with mean E(X) = 365 and standard deviation SD(X) = 17.67
Z = (X - E(X)) / SD(X)
Z follows a standard normal distribution with mean 0 and standard deviation 1.
P(X <= 375) = P(Z <= (375 - E(X)) / SD(X))
= P(Z <= (375 - 365) / 17.67)
= P(Z <= 0.566)
Using a standard normal distribution table or a calculator, we can find that P(Z <= 0.566) is approximately 0.7165.
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The given question is incomplete, the complete question is :
A die is continuously rolled 104 times. what is the probability that the total sum of all rolls does not exceed 375 ?
the smith family has $4$ cats and $3$ dogs. in how many ways can these $7$ pets be placed in a row of $7$ chairs such that at least $2$ cats are next to each other?
There are 4896 ways of arranging 7 pets in a row of 7 chairs such that at least 2 cats are next to each other.
Arrangement of entities can be done using permutation and combination in mathematics.
Consider the distributions where 2 cats are not next to each other as
C D C D C D C.
There are 4! ways to seat the cats, and 3! ways to seat the dogs that gets us N=4! 3! = 144
There are a total of 7!=5040 possible ways to seat both cats and dogs.
At least 2 cats seat together= All possible arrangements- None of the cat seat together.
Thus the number of seatings where at least 2 cats are adjacent is
5040-144 = 4896
So, there are 4896 arrangements can be made so that at least 2 of the cats seat together.
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A video goes viral on social media, the number of views per day can be modeled with the equation y = -0.75x² +9.75x where is the number of days after the video is posted and y is the number of views per day in thousands. According to the model, after how many days do people stop watching the video?
Answer:
Step-by-step explanation:
To find when people stop watching the video, we need to find the maximum point of the quadratic function y = -0.75x² + 9.75x.
The x-coordinate of the maximum point of a quadratic function can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic function.
Using the formula with a = -0.75 and b = 9.75, we get:
x = -9.75 / 2(-0.75)
x = -9.75 / -1.5
x = 6.5
Therefore, the maximum number of views per day will occur on the 6.5th day after the video was posted.
To determine when people stop watching the video, we need to check the values of y after this point.
When x > 6.5, the quadratic function becomes negative, which means that the number of views per day will start to decrease. Therefore, people stop watching the video after 6.5 days (or sometime around the 7th day).
Vincent bought a lot with an area of 105. 7 square meters at 12,500. 00 pesos per square meter. He paid -0. 45 of the amount in cash and the rest 24 equal monthly installments. How many much is his monthly installment?
The amount to be paid as monthly installment for 24 equal monthly installments is given by 30,278.65 pesos.
Area bought by Vincent = 105. 7 square meters
Cost per square meters = 12,500. 00 pesos per square meter.
The total cost of the lot is the product of the area and the price per square meter,
Cost
= 105.7 sq m ×12,500.00 pesos/sq m
= 1,321,250.00 pesos
Amount paid by Vincent in cash is equals to
= 0.45 × 1,321,250.00 pesos
= 594,562.50 pesos
The remaining balance to be paid in installments is equals to,
= 1,321,250.00 pesos - 594,562.50 pesos
= 726,687.50 pesos
This balance will be paid in 24 equal monthly installments, so the monthly installment amount is equals to,
= 726,687.50 pesos / 24 months
= 30,278.65 pesos per month (rounded to the nearest cent)
Therefore, amount paid by Vincent as monthly installment is equal to 30,278.65 pesos.
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calculate the probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460. (use salt. round your answer to four decimal places.)
The probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460 is very low, almost zero.
To calculate the probability of obtaining a sample result of a mean of $470 or more, we need to use the sampling distribution of the mean.
Assuming that the sample size is large enough and that the sample means are normally distributed, we can use the central limit theorem to approximate the sampling distribution of the mean to a normal distribution. We can standardize the sample mean using the formula
z = (x - μ) / σ,
where x is the sample mean, μ is the population mean, and σ is the standard error of the mean.
In our case, we want to find the probability of obtaining a sample mean of $470 or more. We can convert this to a z-score by standardizing it using the formula
z = (470 - 460) / (σ / √n),
where n is the sample size.
If the sample size is 100 and the population standard deviation is 10, then the standard error of the mean is 1. We can then calculate the z-score as
=> z = (470 - 460) / (1 / √100) = 10.
We can look up the probability of obtaining a z-score of 10 or greater in a standard normal distribution table, which is almost zero.
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The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 3 comma negative 2, a point at negative 5 comma 2, and a point at negative 1 comma 2.
What is the equation of g(x) in vertex form?
g(x) = (x − 3)2 − 2
g(x) = (x − 3)2 + 2
g(x) = (x + 3)2 − 2
g(x) = (x + 3)2 + 2
Answer:
g(x) = (x + 3)2 - 2
Step-by-step explanation:
I think that's the one I just did this class so
Do anybody know this?
The coordinate of the point U that divides the line ST in the ratio 2:5 is: (12:6)
What are the coordinates of the division of the line segment?The formula for the division of line segments in the ratio m:n is
P = {[(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]}
We are given the coordinates of line Segment ST as: S(10, 2) and T(17, 16)
Thus, if the ratio is 2:5, we have:
U(x, y) = {[(2*17 + 5*10)/(2 + 5)], [(2*16 + 5*2)/(2 + 5)]}
U(x, y) = (84/7), (42/7)
U(x, y) = (12, 6)
Thus, that is the coordinate of the point U that divides the line ST in the ratio 2:5.
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Describe how it is possible to calculate the enthalpy of formation for a compound that cannot be synthesized directly from the constituent elements.
The enthalpy change of each step in the cycle must be added together to obtain the enthalpy of formation of the desired compound.
The enthalpy of formation of a compound that cannot be synthesized directly from the constituent elements can be calculated using the Hess's Law. Hess's Law states that the enthalpy change of a reaction is independent of the route taken from reactants to products. This law allows for the enthalpy of formation of a compound to be determined by summing the enthalpy changes of a series of known reactions, referred to as a ‘thermochemical cycle’, which lead to the compound of interest. To use this law, the enthalpy of formation of the intermediate species formed during the reaction must be known.
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Given triangle XYZ with ZX = 30°, ZY= 20° and ZZ = 2aº, what is the value of a?
A. 130
B. 65
C. 40
D. 20
According to the question, we are given a triangle XYZ
where,
∠X = 30° ∠Y = 20° ∠Z = 2a°Angle sum property states that sum of all the angles of triangle is 180°. So by adding all the three angles we will get the required value of a.
∠X + ∠Y + ∠Z = 180°
30° + 20° + 2a° = 180°
50° + 2a° = 180°
2a° = 180° - 50°
2a° = 130°
a° = 130/2
a° = 65°
Therefore, required value of a is 65°
Answer:
B
Step-by-step explanation:
remember : the sum of all angles in a triangle is always 180°.
are you sure the third angle is called ZZ ?
I am rather sure it would be called XY !
so,
180 = ZX + ZY + XY = 30 + 20 + 2a
130 = 2a
a = 130/2 = 65°
find the surface area of this figure
The Surface area of the given cuboid is found to be 872 sq, in.
Explain about the cuboid?Three-dimensional shapes with length, breadth, and height are called cuboids. Six of the cuboid's sides are referred to as faces.
Every corner of a cuboid's faces, which usually refer to as vertices, are at a 90-degree angle. Hence, a cuboid is any object that has the shape of a box.The only thing that cuboids have are straight angles. It is not a cuboid if it has additional kinds of angles. The same is true for cubes. A cube and even a cuboid have the same number of edges, faces, and vertices: 12 edges, 8 vertices, and 6 faces.Surface area of a cuboid is = 2(lw + 2lh + hw0
l= lengthw= width.h = heightS.A = 2[(17)*(8) + (8)*(12) +(12)*(17)]
S.A = 2*436
S.A = 872
Thus, the Surface area of the given cuboid is found to be 872 sq, in.
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To fill a pool, Barb uses two hoses. The first hose is rated to fill the pool in
10 hours. The second hose is rated to fill it in 5 hours. If Barb adds a third
hose that uses the slower rate, how long will it take to fill the pool.
It will take [1] hours to fill the pool.
Using division operation, the length it will take the three hoses to fill the pool is 8.33 hours.
What is the division operation?The division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
The division operation involves the dividend, the divisor, and the result called the product.
In this situation, it will take Hose A 10 hours to fill the pool and Hose B 5 hours. If the two hoses are in use, it will 7.5hours (10 + 5)/2.
When the third hose is added, it will take 8.33 hours (10 + 5 + 10)/3.
The first hose's filling rate for the pool = 10 hours
The second hose's filling rate for the pool = 5 hours
The third hose's filling rate for the pool = 10 hours (the slower rate)
The total number of hours used by the three hoses = 25 hours (10 + 5 + 10)
The number of hoses used = 3
The length of time it will take the 3 hoses to fill the pool = 8.33 hours (25/3)
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A trazpodizi has an aera of 35 mm2 what is the height
The height of the trapezium is 5mm, given that the two parallel sides have lengths of 6mm and 8mm, and the area of the trapezium is 35mm².
To find the height of a trapezium given its area and the lengths of its parallel sides, we use the formula:
Area = (a + b) * h / 2
where a and b are the lengths of the parallel sides, h is the height, and Area is the area of the trapezium.
In this case, we are given that the area of the trapezium is 35mm², and we know that the two parallel sides have lengths 6mm and 8mm. So, we can substitute these values into the formula and solve for h:
35 = (6+8) x h/2
Simplifying the right-hand side of the equation, we can combine the two lengths of the parallel sides and multiply by h, and then divide by 2 to get:
35 = 14h / 2
Multiplying both sides by 2, we get:
70 = 14h
Dividing both sides by 14, we get:
h = 5
Therefore, the height of the trapezium is 5mm.
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A student was asked to factor
Answer:
Step-by-step explanation:
1) [tex]6x^4 \times 6x^4 = 36x^8[/tex] (needs to be [tex]36x^{16}[/tex] )
2) [tex](4y^2) \times (4y^2) =16y^4[/tex] (needs to be [tex]25y^4[/tex] )
1) Change both [tex]6x^4 \text{ terms to } 6x^8.[/tex]
2) Change both [tex]4x^2 \text{ terms to } 5y^2.[/tex]
Bonus:
Need to change a minus to a plus,
[tex]36x^{16}-25y^4=(6x^8+5y^2)(6x^8-5y^2)[/tex]
1-0.004326suppose it is believed that the probability a patient will recover from a disease following medication is 0.8. in a group of ten such patients, the number who recover would have mean and variance respectively given by (to one decimal place):
The mean number of patients who recover is 8, and the variance is 1.6.
This scenario follows a binomial distribution, where the number of patients who recover from the disease out of a sample of ten patients follows a binomial distribution with parameters n = 10 (sample size) and p = 0.8 (probability of success).
The mean (μ) and variance (σ^2) of a binomial distribution are given by
μ = np
Substitute the values in the equation
= 10 x 0.8
Multiply the numbers
= 8
σ^2 = np(1-p)
Substitute the values in the equation
= 10 x 0.8 x (1-0.8)
= 1.6
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a restaurant offers a special pizza with any 6 toppings. if the restaurant has 16 topping from which to choose, how many different special pizzas are possible?
To calculate the number of different special pizzas possible with any 6 toppings out of 16, we can use the combination formula:C(16,6) = 16! / (6! * (16-6)!) = (161514131211) / (654321) = 8008
there are 8,008 different special pizzas possible with any 6 toppings out of 16.
To calculate the number of different special pizzas possible with any 6 toppings out of 16, we need to use the combination formula, which is given by:
C(n, k) = n! / (k! * (n - k)!)
where n is the total number of items to choose from, and k is the number of items we want to choose.
In this case, n = 16 (the total number of toppings available), and k = 6 (the number of toppings we want to choose).
Plugging these values into the formula, we get:
C(16, 6) = 16! / (6! * (16 - 6)!)
= (16 * 15 * 14 * 13 * 12 * 11) / (6 * 5 * 4 * 3 * 2 * 1)
= 8008
Therefore, there are 8,008 different special pizzas possible with any 6 toppings out of 16.
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