This recipe makes 20 cupcakes. Deepak only wants to make 16 cupcakes. How much of each ingredient does he need? Recipe: Makes 20 cupcakes 12 ounces butter 10 ounces sugar 15 ounces flour 5 eggs
Answer:
- 9.6 oz butter
- 8 oz sugar
- 12 oz flour
- 4 eggs
Step-by-step explanation:
We know that for 20 cupcakes, we need the following amount for each ingredient:
- 12 oz butter
- 10 oz sugar
- 15 oz flour
- 5 eggs
We now only want 16 cupcakes. To find how much of each ingredient we need, let's write a proportion for each. Say b is the amount of butter we need, s is the amount of sugar, f is flour, and e is eggs:
16 cupcakes / 20 cupcakes = b oz butter / 12 oz butter
16 cupcakes / 20 cupcakes = s oz sugar / 10 oz sugar
16 cupcakes / 20 cupcakes = f oz flour / 15 oz flour
16 cupcakes / 20 cupcakes = e eggs / 5 eggs
These turn out to become:
20b = 16 * 12 ⇒ b = 9.6 oz butter
20s = 16 * 10 ⇒ s = 8 oz sugar
20f = 16 * 15 ⇒ f = 12 oz flour
20e = 16 * 5 ⇒ e = 4 eggs
Thus, our answers are:
- 9.6 oz butter
- 8 oz sugar
- 12 oz flour
- 4 eggs
~ an aesthetics lover
Answer: 9.6 ounces of butter, 8 ounces of sugar, 12 ounces of flour, 4 eggs
Step-by-step explanation: 20 / 16 = 4/5. 16 is four-fifths of 20. So multiply 4/5 with everything.
12 * 4/5 = 9.6 ounces
10 * 4/5 = 8 ounces
15 * 4/5 = 12 ounces
5 * 4/5 = 4 eggs
What is the volume of the cone?
explain a proof of the pythagorean theorem and its converse
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. The theorem can be proven using various methods, one of which is the geometric proof.
Geometric Proof of the Pythagorean Theorem:
Consider a right-angled triangle with sides of lengths a, b, and c, where c is the hypotenuse. By drawing squares on each side, we create four congruent right-angled triangles within the larger square formed by the hypotenuse. The area of the larger square is equal to the sum of the areas of the four smaller squares.
The area of the larger square is c^2, and the area of each smaller square is a^2, b^2, a^2, and b^2, respectively. Therefore, we have c^2 = a^2 + b^2, which is the Pythagorean theorem.
Converse of the Pythagorean Theorem:
The converse of the Pythagorean theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right-angled triangle.
To prove the converse, we assume that a triangle with sides of lengths a, b, and c satisfies the condition c^2 = a^2 + b^2. By comparing this equation to the Pythagorean theorem, we can conclude that the triangle must have a right angle opposite the side of length c.
This is one way to prove the Pythagorean theorem and its converse, demonstrating the relationship between the lengths of the sides in a right-angled triangle.
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Find the missing angle in this triangle
Answer: The 2nd one
Step-by-step explanation:
Suppose we are given the following information.
Line 1 passes through (0, 6) and (6, 4).
Line 2 passes through (-1, -7) and (1, -1).
Are these lines parallel, perpendicular, or neither?
Group of answer choices
Since the product of the slope is -1, hence the lines are perpendicular
Parallel and Perpendicular linesTwo lines are known to be parallel if they have the same slope while if two lines are perpendicular if the product of the slope is -1
Given the coordinates of line 1 passing through (0, 6) and (6, 4), the slope is given as;
Slope = 4-6/6-0
Slope = -2/6
Slope = -1/3
Similarly for the coordinate points (-1, -7) and (1, -1).
Slope = -1+7/1+1
Slope of line 2 = 6/2
Slope = 3
Take the product of the slopes
Slope = -1/3 * 3
slope = -1
Since the product of the slope is -1, hence the lines are perpendicular
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What is the area of a triangle that has a height of 60 and a base length of 7 feet
Answer:
210
Step-by-step explanation:
so the formula for the area of a triangle is base × height ÷ 2
so you do 60 × 7 = 420 then divide by 2 = 210
Simplify: [(23)4]2 a 17666216 b 12222617 c 17222167 d 16777216
None of the provided options is correct. The simplified value of the expression [(23)4]2 is 65536.
To simplify the expression [(23)4]2, we start by evaluating the exponent inside the inner parentheses:
(23)4 = 23 * 23 * 23 * 23
This results in 256. Now, we substitute this value back into the expression:
[(23)4]2 = 2562
Squaring 256 gives us 65536. Therefore, the simplified value of the expression [(23)4]2 is 65536.
So, the correct answer is not listed among the options provided. None of the given options (a) 17666216, b) 12222617, c) 17222167, d) 16777216) match the simplified value of 65536.
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lan scores 44 out of 60 marks in a Maths test.
What is his score as a percentage to 1 decimal place?
Answer:
73.3 %
Step-by-step explanation:
To find the percentage
44/60
.73333333
Change to a percentage by multiplying by 100
73.3 %
━━━━━━━☆☆━━━━━━━
▹ Answer
73.3%
▹ Step-by-Step Explanation
44 ÷ 60 = 0.73333333333* 100→ 73.3%
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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when your coefficients are the same you solve the system using?
When you have a system of linear equations, and you identify terms with the same variable and same coefficients, you can use the subtraction method to obtain an equation in which you can obtain the value of one of the variables.
a room contains several urns. 13 urns contain two gold balls. 6 urns contain one gold ball and one silver ball. 20 urns contain two silver balls. you choose an urn at random and then draw two balls from the urn. if the first ball you draw is gold, what is the probability that the second ball you draw is gold?
The probability that the second ball you draw is gold is 0.619.
What is the probability?
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Here, we have
Given: a room contains several urns 13 urns contain two gold balls, 6 urns contain one gold ball and one silver ball, 20 urns contain two silver balls.
Conditional probability is a measure of the probability of an event occurring given that another event has occurred.
Here given event is that first ball is gold. Hence sample space will have 13+8 = 21 urns.
For second ball to be gold, urn should have 2 gold balls hence it has 13 urns under above condition.
Probability = 13/21 = 0.619
Hence, the probability that the second ball you draw is gold is 0.619.
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This exercise contains only parts a, b, c, d, and e. a) Based on the activity time estimates, the expected times and variance for each of the activities are (round your response to two decimal places): Expected Activity Time 9.83 10.33 9.83 7.83 Variance .69 2.78 .69 1.36 b) The expected completion time of the critical path = 19.66 weeks (round your response to two decimal places). The expected completion time of the path other than the critical path = 18.16 weeks (round your response to two decimal places). c) The variance of the critical path 1.38 weeks (round your response to two decimal places) The variance of the path other than the critical path 4.14 weeks (round your response to two decimal places) d) If the time to complete the activities on the critical path is normally distributed, then the probability that the critical path will be finished in 22 weeks or less -98 (enter as a probability and round your response to two decimal places)
Expected completion time of the path other than the critical path is 18.16 weeks.
a) The expected times and variances for each of the activities are as follows:
Activity 1:
Expected Time = 9.83 weeks
Variance = 0.69 weeks
Activity 2:
Expected Time = 10.33 weeks
Variance = 2.78 weeks
Activity 3:
Expected Time = 9.83 weeks
Variance = 0.69 weeks
Activity 4:
Expected Time = 7.83 weeks
Variance = 1.36 weeks
b) The expected completion time of the critical path is 19.66 weeks.
The expected completion time of the path other than the critical path is 18.16 weeks.
c) The variance of the critical path is 1.38 weeks.
The variance of the path other than the critical path is 4.14 weeks.
d) If the time to complete the activities on the critical path is normally distributed, the probability that the critical path will be finished in 22 weeks or less is -98.
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Find the general solution to y
′′
−y
′
−6y=6x
3
+26sin2x
The general solution to the given second-order linear homogeneous differential equation is y(x) = c1e^(3x) + c2e^(-2x), where c1 and c2 are arbitrary constants.
To find the general solution, we first consider the corresponding homogeneous equation, which is obtained by setting the right-hand side of the given equation to zero:
y′′ − y′ − 6y = 0
The characteristic equation associated with this homogeneous equation is:
r^2 - r - 6 = 0
Solving this quadratic equation, we find two distinct roots: r1 = 3 and r2 = -2. Therefore, the general solution to the homogeneous equation is:
y_h(x) = c1e^(3x) + c2e^(-2x)
Next, we need to find a particular solution to the given non-homogeneous equation. The particular solution takes the form of a polynomial multiplied by the known term on the right-hand side, in this case, 6x^3. Since the degree of the polynomial is 3, we try a particular solution of the form y_p(x) = ax^3 + bx^2 + cx + d.
Substituting this into the non-homogeneous equation, we obtain:
y_p′′ − y_p′ − 6y_p = 6x^3
Simplifying and collecting terms, we can equate coefficients of like powers of x on both sides. After solving the resulting system of equations, we find a particular solution:
y_p(x) = x^3/3
The general solution to the non-homogeneous equation is the sum of the homogeneous and particular solutions:
y(x) = y_h(x) + y_p(x)
= c1e^(3x) + c2e^(-2x) + x^3/3
This is the general solution to the given differential equation. The arbitrary constants c1 and c2 can be determined by applying initial or boundary conditions if provided.
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3) In the Pacific Ocean, a seal was swimming 110 feet below sea level. As he was searching for food, he dove
down another 48 feet. What was the seal's final elevation relative to sea level?
eo
ther
110 €
Answer:
158 feet below sea level
Step-by-step explanation:
110 + 48 = 158
So 158 was the seal's final depth below sea level
if half the tetrahedral holes are occupied, what is the empirical formula of the compound , where m represents the cations and a the anions?
The empirical formula of the compound, with half the tetrahedral holes occupied, can be determined based on the cations (m) and anions (a).
In crystal structures, tetrahedral holes refer to the spaces between close-packed ions. If half of these tetrahedral holes are occupied, it suggests that the compound has a specific arrangement of cations (m) and anions (a).
In a crystal lattice, each tetrahedral hole can accommodate one cation-anion pair. If half of the tetrahedral holes are filled, it means that the compound has a 1:1 ratio of cations to anions. This ratio is the simplest or empirical formula of the compound.
For example, if the cation is denoted as M and the anion as X, the empirical formula would be MX. This implies that for every cation M, there is one anion X present.
Therefore, based on the given information, the empirical formula of the compound would be MX.
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The line representing the equation part of the constraint 7x1 + 4x2 s 28 goes through the following two points (4,0) and (7,0) (0, 4) and (7,0) (4,0) and (0,7) (0, 4) and (0,7) none of the above
( 0, 7 ) and ( 0,4 ) are two points of the equation .
What Is an Equation, exactly?
An equation is a mathematical expression with two equal sides and an equal sign in between.
An equation is, for instance, 4 + 6 = 10. 4 + 6 is visible on the equal sign's left side, and 4 + 6 is visible on the equal sign's right side.
( 4,0) & ( 0,7 )
Given constraint is
7x₁ + 4x₂ ≤ 28
IF x₁ = 0
4x₂ = 28
x₂ = 7
( 0, 7 )
If x₂ = 0
7x₁ = = 28
x₁ = 4
( 4 ,0 )
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You are getting ready for a family vacation. You decide to download as many movies as possible before leaving for the road trip. If each movie takes
1 2/5 hours to download, and you downloaded for 5 1/4 hours, how many movies did you download?
Answer:
3.75 hours
Step-by-step explanation:
Divide them.
Answer:
3
Step-by-step explanation:
i hope this helped
A shape has only three angles, and only one of those angles measures 90 degrees. What is the name of the shape?
Answer:
A right Triangle
Step-by-step explanation:
A right triangle has 3 angles and one of those angles measures 90 degrees.
NOWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
Answer: 60 is the answer.
Step-by-step explanation: We can use the total sum, 180.
To get the missing angle, add the 2 angles, 60 and 60.
60 + 60 = 120.
Then subtract from 180.
180 - 120 = 60.
Hence, 60 is the answer.
Let me know if you have any questions.
~ Lily, from Brainly.
Note to asker: Write this down!
To find 1 missing angle:
A1 + A2 = TA - 180 = X (A1 = Angle1)
i need help!!!!!!!!!
Answer:
Opt B
Step-by-step explanation:
3/4 plus 1/8
4 goes into 8 two times
1/8 stays the same
for 3/4 multiply the numerator and denominator by 2
6/8
Sort the graphs according to whether or not "y" is a function of "x"
The first graph, (the one by the left is not a function)
The second graph (the one by the right is a function)
4/5−3/4 pls help pls
Answer:
1/20
Step-by-step explanation:
4/5 = 16/20
3/4 = 15/20
16-15 = 1
1/20
Answer:
1/20
Step-by-step explanation:
Find the amount to which $500 will grow under each of these conditions: a. 16% compounded annually for 10 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ b. 16% compounded semiannually for 10 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ c. 16% compounded quarterly for 10 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ d. 16% compounded monthly for 10 years. Do not round intermediate calculations. Round your answer to the nearest cent. $ e. 16% compounded daily for 10 years. Assume 365 -days in a year. Do not round intermediate calculations. Round your answer to the nearest cent. $ f
a. The amount to which $500 will grow when compounded annually at a rate of 16% for 10 years is approximately $1,734.41.
b. The amount to which $500 will grow when compounded semiannually at a rate of 16% for 10 years is approximately $1,786.76.
c. The amount to which $500 will grow when compounded quarterly at a rate of 16% for 10 years is approximately $1,815.51.
d. The amount to which $500 will grow when compounded monthly at a rate of 16% for 10 years is approximately $1,833.89.
e. The amount to which $500 will grow when compounded daily at a rate of 16% for 10 years (365 days in a year) is approximately $1,843.96.
a. The amount to which $500 will grow when compounded annually at a rate of 16% for 10 years is approximately $1,734.41.
To calculate this, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (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, P = $500, r = 0.16, n = 1, and t = 10.
Plugging these values into the formula, we get:
A = 500(1 + 0.16/1)^(1*10)
= 500(1 + 0.16)^10
≈ 1,734.41
Therefore, $500 will grow to approximately $1,734.41 when compounded annually at a rate of 16% for 10 years.
b. The amount to which $500 will grow when compounded semiannually at a rate of 16% for 10 years is approximately $1,786.76.
To calculate this, we can use the same compound interest formula, but with a different value for n. In this case, n = 2 because the interest is compounded twice a year.
A = 500(1 + 0.16/2)^(2*10)
≈ 1,786.76
Therefore, $500 will grow to approximately $1,786.76 when compounded semiannually at a rate of 16% for 10 years.
c. The amount to which $500 will grow when compounded quarterly at a rate of 16% for 10 years is approximately $1,815.51.
Using the compound interest formula with n = 4 (compounded quarterly):
A = 500(1 + 0.16/4)^(4*10)
≈ 1,815.51
Therefore, $500 will grow to approximately $1,815.51 when compounded quarterly at a rate of 16% for 10 years.
d. The amount to which $500 will grow when compounded monthly at a rate of 16% for 10 years is approximately $1,833.89.
Using the compound interest formula with n = 12 (compounded monthly):
A = 500(1 + 0.16/12)^(12*10)
≈ 1,833.89
Therefore, $500 will grow to approximately $1,833.89 when compounded monthly at a rate of 16% for 10 years.
e. The amount to which $500 will grow when compounded daily at a rate of 16% for 10 years (365 days in a year) is approximately $1,843.96.
Using the compound interest formula with n = 365 (compounded daily):
A = 500(1 + 0.16/365)^(365*10)
≈ 1,843.96
Therefore, $500 will grow to approximately $1,843.96 when compounded daily at a rate of 16% for 10 years.
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What is 1+10-70
Please help
Answer:
-59
Step-by-step explanation:
use pemdas
1+10-70
11-70
-59
If you reflect FGH across the x-axis, what will be the coordinates of the vertices of the image F’G'H'?
Answer:
F ' = (-2, 1)
G ' = (2, -2)
H ' = (4, 3)
========================================
Explanation:
The rule \((\text{x},\text{y})\to (\text{x},-\text{y})\) reflects any point over the x axis.
We keep the x coordinate the same. The y coordinate flips from positive to negative, or vice versa.
For example, let's use that rule on point F.
\((\text{x},\text{y})\to (\text{x},-\text{y})\\\\(-2,-1)\to (-2,-(-1))\\\\(-2,-1)\to (-2,1)\\\\\)
Therefore, point F ' is located at (-2,1).
Follow that same logic for points G and H.
Let me know if you need to see the steps for the other points.
Two parallel paths 18 m apart run east-west through the woods. Brooke jogs east on one path at 5 km/h, while Jamail walks west on the other path at 6 km/h. If they pass each other at time t = 0, how far apart are they 5 s later, and how fast is the distance between them changing at that moment?(Use decimal notation. Give your answer to three decimal places.)The distance between them at t=5 is L= ______ meters help (decimals)When t = 5, we then have dL/dt = ______ m/s help (decimals)
The rate at which their distance is changing at t = 5 seconds is -11 m/s.
In 1 hour, Brooke covers 5 km, which is equal to 5000 m. Similarly, in 1 hour, Jamail covers 6 km, which is equal to 6000 m. Since they start from 18 m apart and are moving towards each other, their distance is decreasing at a rate equal to the sum of their speeds, which is 5 + 6 = 11 km/h, or 11,000 m/h.
Therefore, in 5 seconds, their distance will decrease by (11,000 m/h) * (5 s / 3600 s) = 15.28 m. Hence, their distance at t = 5 seconds is L = 18 m - 15.28 m = 2.72 m.
To find the rate at which their distance is changing at t = 5 seconds, we differentiate the expression for L with respect to time:
dL/dt = d/dt (18 - 5t - 6t) = -11 m/s.
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A bank manager claims that only 7% of all loan accounts at her institution are in default. An auditor takes a random sample of 200 loan accounts at this institution. Suppose the auditor finds 40 that are in default. a) Calculate the mean of the sampling distribution of the sample proportion
b) Calculate the standard deviation of the sampling distribution of the sample proportion. (round your answer to three decimal places.)
c) Determine whether the following statement is true or false. (Assume this instituion has more than 2.000 loan accounts)
The sampling distribution is normal or approximately normal (T/F)
Therefore, the standard deviation of the sampling distribution of the sample proportion is approximately 0.024, rounded to three decimal places. Therefore, the statement "The sampling distribution is normal or approximately normal" is true.
a) The mean of the sampling distribution of the sample proportion is equal to the population proportion, which is given as 0.07:
μp = p = 0.07
b) The standard deviation of the sampling distribution of the sample proportion is given by the formula:
σp = √[(p*(1-p))/n]
where n is the sample size. Substituting the given values, we get:
σp = √[(0.07*(1-0.07))/200]
≈ 0.024
c) To determine whether the sampling distribution is normal or approximately normal, we need to check two conditions: the sample size and the shape of the population distribution.
The sample size is given as n = 200, which is large enough for the Central Limit Theorem to apply.
The shape of the population distribution is not given, but since the sample size is large, we can assume that the distribution of the sample proportion will be approximately normal by the Central Limit Theorem.
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which of the following statements is correct? a. the binomial distribution is a continuous probability distribution, and the normal distribution is a discrete probability distribution. b. the binomial and normal distributions are both discrete probability distributions. c. the binomial and normal distributions are both continuous probability distributions. d. the binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.
The correct statement is:
d. The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.
What is binomial distribution?
In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either Success or Failure. For example, if we toss a coin, there could be only two possible outcomes: heads or tails, and if any test is taken, then there could be only two results: pass or fail. This distribution is also called a binomial probability distribution.
The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, where each trial can result in only two outcomes (success or failure), and the probability of success is constant. Examples of situations that can be modeled by a binomial distribution include flipping a coin a fixed number of times or counting the number of defective items in a batch of products.
The normal distribution, on the other hand, is a continuous probability distribution that is often used to model naturally occurring phenomena, such as heights, weights, and test scores. The normal distribution is characterized by a bell-shaped curve, and it is used because many phenomena in nature follow a normal distribution pattern.
So, the binomial and normal distributions are both widely used in probability and statistics, but they are fundamentally different types of distributions.
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Which deal is better? H&M, Lulu, or neither? Explain your reasoning.
!Please help me!
Answer:
Lulu
Step-by-step explanation:
If you take the Lulu shirt and take 20% off of it, you have a shirt that is $80
If you take the H&M shirt and take 15% off of it, then take off 5%, you have a shirt that is $80.75
Assuming a population of alpacas has been doubling every 5 years, and the current population is 2,000, what was the population 20 years ago? 8000 0 4000 O 1000 O 750 O 500 O 250 O 200 O 125
The population 20 years ago was 125 alpacas. Answer: 125.
If the current population is 2000 and the population of alpacas doubles every 5 years, then we can write a formula for the population P after t years as:
\(p=p0* 2^{t/5}\)
where P0 is the initial population and t is the time in years. We want to find the population 20 years ago, so we need to solve for P0:
\(2000 = P0* 2^{20/5}\\ 2000 = P0* 2^{4} \\2000 = 16P0\\P0 = 2000/16\\P0 = 125\)
Therefore, the population 20 years ago was 125 alpacas. Answer: 125.
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109-8
y=-x-5
x - 2y = 4
Plot two lines
Answer:
Given the equations, I plotted 2 lines.
Line 1 Line 2
x | y x | y
0 | 101 0 | -5
1 | 101 1 | -6