For Allison's lemonade recipe, 16 lemons are required to make 12 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade?​

Sagot:

100 cm

Hakbang-hakbang na paliwanag:

Kung ganoon :

Distansya na sakop ng Ruben = 900 centimetri

Distansya na sakop ng Jamie = 10 metro

Pagko-convert sa centimeter:

100 cm = 1 m

x cm = 10 m

Paggamit ng multiplikasyon ng krus:

x = 100 * 10

x = 1000 cm.

Dahil dito Distansya ni Jamie = 1000 cm

Distansya sa pagitan ng Jamie at Ruben;

1000 cm - 900 cm = 100 cm

Period 1 is with highest grade.

Given,

Histograms for three periods.

Now,

Period 1:

Total grade = 1 + 5 + 14 + 12

Total grade = 32

Period 2 :

Total grade = 0 + 4 + 19 + 8

Total grade = 31

Period 3 :

Total grade = 0 + 4 + 10 + 10

Total grade = 24

Hence the data from histogram shows that the highest grade is from period 1 that is 32.

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A spherical astroid has a radius of approximately 8.5 x 10^2 m. Using  the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

a spherical astroid has a radius of approximately 8.5 x 10^2 m.

we know,

the volume =  4/3 π r^3

so, by calculating, we get.

volume = 2.57 x 10^9 m^3

Hence, a spherical astroid has a radius of approximately 8.5 x 10^2 m. Using  the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.

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Answer: I am here to nswer

Step-by-step explanation: so first to this then do another thing

Answer:

Step-by-step explanation:

6 - 2x = 5x - 9x + 10  {add the like terms}

6 - 2x = - 4x + 10        {add (-6) to both side}

6 - 2x - 6 = - 4x + 10 - 6

-2x = - 4x + 4         {add 4x to both sides}

-2x + 4x = -4x + 4 + 4x

2x = 4           {divide both sides by 2}

2x/2x = 4/2

x = 2

Answer:

Has one solution

Step-by-step explanation:

3 x+1-1=10-1

3x=9

9÷3

x=3

Answer:

K is the midpoint of JL.

I hope this helps:)

Sarah is the beneficiary of a trust fund that was established for her 30 years ago at her birth with an initial amount of £50,000. The money in the trust fund earns interest at a rate of 5% per year.

a. If the interest is compounded annually, we can use the formula for compound interest to calculate the final amount in the trust fund. The formula is:

Final amount = Initial amount * \((1 + interest rate)^number of years\)

Plugging in the values, we have:

Final amount = £50,000 *\((1 + 0.05)^30\)

Evaluating this expression will give us the total amount that Sarah will receive from the trust fund.

b. If the interest is compounded quarterly, we need to adjust the formula for compound interest. The formula is modified to account for the compounding period. The new formula is:

Final amount = Initial amount * (1 + interest rate/number of compounding periods)^(number of years * number of compounding periods)

In this case, the interest rate is still 5% per year, but we need to consider quarterly compounding. There are 4 quarters in a year, so the number of compounding periods is 4. Plugging in the values, we have:

Final amount = £50,000 *\((1 + 0.05/4)^(30 * 4)\)

Evaluating this expression will give us the total amount that Sarah will receive from the trust fund with quarterly compounding.

By calculating the final amounts using the appropriate formulas, we can determine how much Sarah will receive from the trust fund based on the given interest rate and compounding frequency.

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The probability of Bob and Joan's fourth child having sickle cell disease, given that their first three children are healthy, is 6.25%.

When Bob and Joan have children, each child has a 25% chance of inheriting two copies of the sickle cell gene and thus developing the disease, a 50% chance of inheriting one copy of the sickle cell gene and being a carrier like their parents, and a 25% chance of inheriting two copies of the normal gene and not carrying the disease.

To understand this probability calculation mathematically, we can use the laws of probability. We can define the probability of the fourth child inheriting the sickle cell gene as P(s), and the probability of the fourth child inheriting the normal gene as P(n).

Since Bob and Joan are each heterozygous carriers for the sickle cell gene, we know that P(s) = 0.25 (25%), and P(n) = 0.75 (75%). We can use the multiplication rule of probability to calculate the probability of their fourth child inheriting two copies of the sickle cell gene, which is:

P(sickle cell disease) = P(s) x P(s) = 0.25 x 0.25 = 0.0625 or 6.25%

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Complete Question:

Bob and Joan know from a blood test that they are each heterozygous (carriers) for the autosomal recessive gene that causes sickle cell disease. If their first three children are healthy, what is the probability that their fourth child will have the disease?

Answer:

14x-21y

Step-by-step explanation:

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. This is:

  7(2x – 3y)

= 7(2(6) – 3(-2))

= 7(12 + 6)

= 7(18)

a. 80% of 90 is the same as of 90 - False

b. 45% of 60 is 27 - True

c. 20% of 90 is the same as as of 90- True

d. 25 is 35% of 80 -False

a. 80% of 90 is not the same as 90. To find 80% of 90, we multiply 90 by 0.8, which gives us 72. Therefore, the statement is false.

b. To find 45% of 60, we multiply 60 by 0.45, which gives us 27. Therefore, the statement is true.

c. 20% of 90 is the same as of 90. To find 20% of 90, we multiply 90 by 0.2, which gives us 18. Therefore, the statement is true.

Lastly, for question d. 25 is not 35% of 80. To find 35% of 80, we multiply 80 by 0.35, which gives us 28. Therefore, the statement is false.

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Answer:

By the Distance Formula, BA=5√5,  TA=√5, A F=√5, and AG=5√5. Since, BA/TA = AG/A F = 5/1, and ∠A≅∠A by the Reflexive Property, △BAG∼△TAF by SAS ∼.

Hope this helps!

Step-by-step explanation:

Answer:

if your solving for a its a=10b/9

Step-by-step explanation:

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Part (a):

[0 1 0]

[0 2 -2]

[3 1 -2]

To find the standard matrix of T, we need to determine the images of the standard basis vectors.

T(1,0,0) = (0,0,3)

T(0,1,0) = (1,2,1)

T(0,0,1) = (0,-2,-2)

The standard matrix of T can be formed by arranging the images of the standard basis vectors as columns:

[0 1 0]

[0 2 -2]

[3 1 -2]

Part (b): -6

To show that T is invertible, we need to show that the standard matrix of T is invertible. We can do this by checking if the determinant of the standard matrix is non-zero.

Determinant of the standard matrix = (0)(2)(-2) + (1)(-2)(3) + (0)(1)(0) - (0)(-2)(3) - (1)(0)(-2) - (0)(2)(0)

= 0 + (-6) + 0 - 0 + 0 - 0

= -6

Since the determinant is non-zero (-6 ≠ 0), the standard matrix of T is invertible. Therefore, T is invertible.

To find the vector T^(-1)(x,y,z), we can solve the equation T(x,y,z) = (x',y',z') for (x,y,z) using the inverse of the standard matrix:

[x'] [0 1 0]⁻¹ [x]

[y'] = [0 2 -2] * [y]

[z'] [3 1 -2] [z]

Multiplying the inverse matrix by (x',y',z'), we get:

[x] [ 2 -1 0] [x']

[y] = [ 1 0 2] * [y']

[z] [-3 1 1] [z']

So, T^(-1)(x',y',z') = (2x' - y', x' + 2z', -3x' + y' + z').

Part (c): the pre-image of (3,4,-1) under T is (-1, 3, 1).

To find the pre-image of (3,4,-1) under T, we need to solve the equation T(x,y,z) = (3,4,-1).

This gives us the system of equations:

y = 3

y + 2z = 4

3x + y - 2z = -1

From the first equation, we have y = 3. Substituting this into the second equation, we get 3 + 2z = 4, which gives z = 1. Substituting y = 3 and z = 1 into the third equation, we have 3x + 3 - 2 = -1, which gives x = -1.

Therefore, the pre-image of (3,4,-1) under T is (-1, 3, 1).

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The standard equation of the circle is x² + y² = 6²

A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.

The standard equation of a circle is given by:

(x-h)² + (y-k)² = r²

The equation given is ;

x² + y² - 36 = 0

The equation can be rewritten as;

(x - 0)² + (y - 0)² = 6²

x² + y² = 6²

NB: The radius is 6

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Answer:

c) 30

The determinant of Given Matrix |A| = 30

Step-by-step explanation:

Explanation:-

Given Matrix

              \(A = \left[\begin{array}{ccc}-2&2&b\\0&3&a\\0&0&-5\end{array}\right]\)

The determinant of |A|

\(A = \left|\begin{array}{ccc}-2&2&b\\0&3&a\\0&0&-5\end{array}\right|\)

\(|A| = -2\left|\begin{array}{ccc}3&a\\0&-5\\\end{array}\right|-2\left|\begin{array}{ccc}0&a\\ 0 -5\\\end{array}\right|+b\left|\begin{array}{ccc}0&3\\ 0 0 \\\end{array}\right|\)

we know that determinant of matrix

|A| = |ad -bc|

|A| = -2(-15-0)-2(0-0)+b(0-0)

|A| = 30

The normal approximation for the distribution of (outcome - point spread is (np(1 - p)0.5

What is Normal Distribution?

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

Reason:

The number of trials n in the binomial setting and the constant success probability p for each of these trials decide the proper normal distribution to choose. Our binomial variable has a mean of np and a standard deviation of (np(1 - p)0.5, which approximates a normal distribution.

It can be demonstrated using simple mathematics that there are a few circumstances in which we must apply a normal approximation to the binomial distribution. To ensure that both np and n(1 - p) are higher than or equal to 10, the number of observations n must be sufficient, as must the value of p. This is a generalization that is supported by statistical theory. The standard approximation can always be used, however it may not be a very accurate approximation if these requirements are not met.

The normal approximation for the distribution of (outcome - point spread is (np(1 - p)0.5

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Answer:

use geogebra app you can install it on your pc

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer: C

: Miriam multiplied correctly, but her third fraction should be .S

Step-by-step explanation: Miriam used the unit conversation upside down. The 7000 g should have been multiplied by 1oz/28.35g

The grams cancel and the division of 7000 be 28.35 results in 246.91 oz Round to 252oz.

Alternative: 7kg (2.21 lb/kg)(16oz/lb)=252.5oz

The kg and lbs cancel and the amount of ounces remains.

Answer:

it is c on egen

Step-by-step explanation:

Answer: x=0  y=4

Step-by-step explanation:

6x - 3(2x + 4) = 12

6x - 6x - 12 = 12

0 = 0

therefore, x = 0

substitute x=0 into y = 2x + 4

y = 2(0) + 4 = 4

Answer: Joseph can prepare 4 vegetable plates with the given amount of cucumbers and carrots.

Step-by-step explanation:

To divide the cucumbers and carrots evenly with nothing left over, we need to find the greatest common factor (GCF) of 20 and 48.

One way to find the GCF is to list the factors of each number and find the largest factor they have in common. The factors of 20 are 1, 2, 4, 5, 10, and 20. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The largest factor they have in common is 4.

Therefore, we can divide both the cucumbers and carrots into groups of 4. Each group will have 5 cucumbers and 12 carrots.

To find the total number of vegetable plates Joseph can prepare, we need to divide the total number of cucumbers and carrots by the number of vegetables in each plate.

The number of plates = (total number of cucumbers + total number of carrots) / (number of cucumbers + number of carrots in each plate)

The total number of cucumbers is 20, and the total number of carrots is 48. The number of cucumbers and carrots in each plate is 5 + 12 = 17.

Number of plates = (20 + 48) / 17 = 4

Therefore, Joseph can prepare 4 vegetable plates with the given amount of cucumbers and carrots.

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The age of Safia is 26 years old

Consider,

Rajiv's age = x

Safia's age = x + 5 (since she is 5 years older than Rajiv)

We know that the sum of their ages is 47, so we can write an equation

x + (x + 5) = 47

Simplifying this equation, we get:

2x + 5 = 47

Subtracting 5 from both sides, we get:

2x = 42

Dividing both sides by 2, we get:

x = 21

So Rajiv is 21 years old. We can use this to find Safia's age

Safia's age = Rajiv's age + 5

Safia's age = 21 + 5

Safia's age = 26

Therefore, Safia is 26 years old.

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The one of many solutions of the system is x = 0 and y = 0.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A system of equations,

x + 6y = 0

30y = -5x

Simplifying,

x + 6y = 0

Both are the same equation,

so there are infinitely many solution possibles.

Therefore, solution is x = 0 and y = 0.

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The maximal flow from node 1 to node 7 in the given network needs to be determined, along with identifying the associated minimal cut. Additionally, the associated linear-programming problem needs to be written.

To find the maximal flow from node 1 to node 7, various algorithms like the Ford-Fulkerson algorithm or the Edmonds-Karp algorithm can be used. These algorithms iteratively find augmenting paths and update the flow until no more augmenting paths exist. The maximal flow represents the maximum amount of flow that can be sent from the source (node 1) to the sink (node 7).

The associated minimal cut can be found by identifying the set of edges whose removal would disconnect the source from the sink. The minimal cut represents the minimum capacity required to disconnect the source and sink nodes.

To write the associated linear-programming problem, we need to define decision variables, objective function, and constraints that represent the flow network. The objective function is typically to maximize the flow from the source to the sink, subject to capacity constraints on the edges and flow conservation constraints at each node.

Detailed calculations and graph analysis would be required to find the specific maximal flow, associated minimal cut, and formulate the linear programming problem for the given network.

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Answer: 1. Not a right triangle 2. Right Triangle 3. Right triangle 4. Right triangle 5. Not a right triangle

Step-by-step explanation:

the right triangle has to have a pattern to go by, so only evens or only odd sides.