Here is a list of ingredients for making 24 Rocky Road Crunchy Bars.




Silvester wants to make 30 Rocky Road Crunchy Bars.


Work out the amount of marshmallows he needs.

Answer:

Ans; (657.3÷10)-(94.5÷5) = 65.73 – 18.9 = 46.83

I hope I helped you^_^

Answer:

Top-left system: (3,5)

Bottom-right

system: (-1,0)

Step-by-step explanation:

One way to solve a system of equations is to graph them. The solution is the point of intersection (where the lines cross). If you need to give the x-value and y-values separately, the first number in the pair is the x and the second number is the y.

Answer:

2 5/4

Step-by-step explanation:

if you add the 5/4 to the 2 you are left with 3 1/4

The linear functions that define their distances are given as follows:

The number of hours after noon in which they will be the same distance away from the stadium is of:

8 hours.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

In the context of this problem, the meaning of each parameter is:

They will be the same distance away at the point of intersection of the graph given at the end of the answer, which is of 8 hours.

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The best predictiοn οf the number οf times the spinner landed οn a space numbered greater than 4 is 172.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Since there are six spaces οf equal area οn the spinner, the prοbability οf landing οn any οne space is 1/6. The prοbability οf landing οn a space numbered greater than 4 is the sum οf the prοbabilities οf landing οn space 5 and space 6, which is:

P(5 οr 6) = P(5) + P(6) = 1/6 + 1/6 = 1/3

Sο, οut οf 500 spins, we can expect that:

E(number οf spins οn 5 οr 6) = P(5 οr 6) x tοtal number οf spins

= (1/3) x 500

= 166.67

Since we can't have a fractiοn οf a spin, we shοuld rοund this expected value tο the nearest whοle number, which is 167. Therefοre, the best predictiοn οf the number οf times the spinner landed οn a space numbered greater than 4 is 167, which is clοsest tο 172.

Hence, the answer is 172.

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The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

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Answer:

at o to a the speed increases from a to b the speed is constant the from b to c the speed is decreasing there is a stop from c to d the speed increases at d to e going constant again at e to f

Step-by-step explanation:

Answer:

Other bicylce should on the profit of 36 % or Rs.47,600

Step-by-step explanation:

1 st profit = 20%

2nd profit = x

 So

   To find x

      20% + x   = ( 28% ) ×2

 x = 56 %  - 20 %

   x = 36 %

Answer:

2 bicycles costs 35,000 each

This means that 1 bicycle costs 35,000

He sells one at a profit of 20%

20/100 ×35000 + 35000

7000+35000

=42,000

How much should he sell the other bicycle to make a profit of 28% on both bicycles

28/100× 35,000

=9,800

Remember that the profit on the first bicycle was 20% which was equal to 7000

and now the trader's goal is to make a profit of 28% on both bicycles

remember that the cost of both bicycles is 35,000+35,000

=70,000

so 28% ×70,000

= 19,600

So, to get the profit he needs to add to the second bicycle

19,600-7000

= 12,600

Now, add 12,600 to 35,000

= 47,600

The trader should sell the other bicycle for 47,600 to make a profit of 28% on whole.

a. The value of c in the probability mass function when x is a discrete random variable is 0.15

b. The value of P(x > 3)  is 0.25

c. The value of P(3 ≤ x ≤ 5) is 0.15

d.  the probability that x is less than 6 given that it is greater than or equal to 1 is approximately 0.353.

In probability mass function, sum of the probabilities for all possible values of x must be equal to 1

Thus,

0.2 + 2c + 0.2 + c + 0.1 = 1

Solve for c

c = 0.15

Hence, the probability mass function for x can be rewritten as;

x:      0     1     2   4     10

p(x): 0.2 0.3 0.2 0.15 0.1

To find P(x > 3), add the probabilities for all values of x that are greater than 3. The values greater than 3 are 4 and 10

sum of their  probabilities

P(x > 3) = P(x = 4) + P(x = 10)

= 0.15 + 0.1

= 0.25

To find P(3 ≤ x ≤ 5),sum the probabilities for all values of x between 3 and 5, inclusive:

P(3 ≤ x ≤ 5) = P(x = 4)

= 0.15

To find P(x < 6 | x ≥ 1), use the formula for conditional probability:

P(x < 6 | x ≥ 1) = P(x < 6 and x ≥ 1) / P(x ≥ 1)

To find the numerator, we sum the probabilities for all values of x between 1 and 5, inclusive

P(x < 6 and x ≥ 1) = P(x = 1) + P(x = 2) + P(x = 4)

= 0.3

To find the denominator, we sum the probabilities for all values of x greater than or equal to 1:

P(x ≥ 1) = P(x = 1) + P(x = 2) + P(x = 4) + P(x = 10)

= 0.85

Therefore, we have

P(x < 6 | x ≥ 1) = (0.3 / 0.85) ≈ 0.353

Thus, the probability that x is less than 6 given that it is greater than or equal to 1 is approximately 0.353.

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It would take 370 days to build the wall with the given conditions.

If 60 men can build a wall in 40 days, then the total man-days required to build the wall is:

60 men x 40 days = 2400 man-days

However, 55 men quit every ten days, which means that after 10 days, there are only 60 - 55 = 5 men left to work on the wall. After 20 days, there are only 5 - 55 = -50 men left, which means that the remaining 5 men cannot work any faster than they were already working. Therefore, we can assume that the remaining 5 men complete the wall on their own.

The number of man-days required for the first 10 days is:

60 men x 10 days = 600 man-days

The number of man-days required for the second 10 days is:

5 men x 10 days = 50 man-days

The total number of man-days required for the first 20 days is:

600 man-days + 50 man-days = 650 man-days

The remaining work can be completed by the 5 men in:

2400 man-days - 650 man-days = 1750 man-days

Therefore, the total time needed to build the wall is:

20 days + 1750 man-days / 5 men = 20 + 350 days = 370 days

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Answer:

There were 4 thieves. They went off to steal from the king, hearing about the great treasure he kept locked in his vault. They managed to break in and sneak out without any of the guards even noticing them. They rode back to their run down hide out and opened the treasure, only to find it was a tarp. They decided they would sell it to the highest bidder, but there was four of them and they all wanted the profits. They couldn't decide who would sell it so the leader sliced it with his sword into four equal pieces, each person getting 1. How much of the tarp did each thief get?

The division story will be that there are 16 boys who want to share 4 oranges. What fraction will each person get?

Fraction that each person will get will be:

= Number of oranges / Number of boys

= 4/16

= 1/4

Each boy gets 1/4.

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Step 1: Find the LCD (Least Common Denominator)

The LCD between 4 and 8 is 8. Therefore, if I change all of the fractions to have a denominator of 8, the problem is as such:

3/8 - 2/8 = ?

Step 2: Subtract

3/8 - 2/8 = 1/8

Hope this helps!

Answer:

\(\frac{1}{8}\) (1/8)

Step-by-step explanation:

8·1=8

4·2=8

LCD=8

If the denominator is multiplied, the numerator also has to be multipled by the same value.

Hope this helped! Please mark brainliest :)

Solution

For this case we have the following distribution:

and we want to find this probability:

We can use the z score formula and we got:

Using the normal distribution table we got:

Then the final answer is 0.5

Answer:

Rita earned $90,510

Step-by-step explanation:

If you multiply each sale price by 0.03 (what 3% is in decimal form), you'd get the amount Rita made for each house. Add all these up, and you get $90,510, the total amount she made in one year.

The interest rate on the mortgage is 5 %

Let's begin by using the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed), r is the interest rate, and t is the time (in years).

For Mr. G's mortgage, we know that the principal is $155,000 and the time is 30 years. We can use this information to solve for the interest rate, r.

First, we need to calculate the total amount that Mr. G will pay over the life of the loan (the principal plus the interest):

A = P + I

where A is the total amount, P is the principal, and I is the interest.

We know that Mr. G will pay $232,500 in interest, so we can solve for A:

Let's begin by using the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed), r is the interest rate, and t is the time (in years).

For Mr. G's mortgage, we know that the principal is $155,000 and the time is 30 years. We can use this information to solve for the interest rate, r.

First, we need to calculate the total amount that Mr. G will pay over the life of the loan (the principal plus the interest):

A = P + I

where A is the total amount, P is the principal, and I is the interest.

We know that Mr. G will pay $232,500 in interest, so we can solve for A:

A = P + I

A = $155,000 + $232,500

A = $387,500

Now we can use the formula for simple interest to solve for the interest rate, r:

I = P * r * t

$232,500 = $155,000 * r * 30

r = $232,500 / ($155,000 * 30)

r = 0.05 or 5%

Therefore, Mr. G's interest rate is 5%.

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Answer:

The price of an adult ticket it $5

Step-by-step explanation:

To solve this, we would find the system of equations. We would set up two equations that will represent the situation.

Let c = price per children ticket

Let a = price per adult ticket

Santo:

5c + 1a = 16.25

Hulda:

4c + 3a = 24

5c + 1a = 16.25 -> a = 16.25 - 5c

4c + 3a = 24

4c + 3(16.25 - 5c) = 24

4c + 48.75 - 15c = 24

-11c + 48.75 = 24

       -48.75   -48.75

-11c = -24.75

/-11       /-11

c = 2.25

5c + a = 16.25

5(2.25) + a = 16.25

11.25 + a = 16.25

-11.25        -11.25

a = 5

a = $5 , c = $2.25

1. Daily earnings of an amusement park before any 2$ increases

2. Number of tickets sold after x increases of 2$

Hopefully this helps!

The answers are daily earnings of the amusement park before any $2 increases and the number of tickets sold after x increases of $2.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

\(\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

An amusement park prices tickets at $55 and sells an average of 500 tickets daily.

From the question, we have a polynomial that represents the daily earnings of the amusement park.

P(x) = -40x² - 100x + 27,500

The constant of the polynomial expression represents the daily earnings of the amusement park before any $2 increases.

And (500 - 20x) represents the number of tickets sold after x increases of $2

Thus, the answers are daily earnings of the amusement park before any $2 increases and the number of tickets sold after x increases of $2.

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Answer:

A=22

X=96 degrees

Step-by-step explanation:

Answer:

x=96 a=22

Step-by-step explanation:

x is equivalent to the 96 since its a mirror image.

a is 22 since to perimeter is 64. 20 is taken by the two 10 sides and the other two sides are equal so 44 divided by 2 gives you a.

In this question, we use the slope equation and its further calculation can be defined as follows:

Slope equation \(=\bold{\frac{y_2-y_1}{x_2-x_1}}\)

\(\to \bold{f(x)= y=\frac{2}{8-x}}\\\\\\\to \bold{P(9,-2)=(x_2,y_2)}\\\\\to \bold{q(x_1, f(x))}\)

Calculating the Slope:

\(=\bold{\frac{-2-(\frac{2}{8-x})}{9-x}}\)

\(=\bold{\frac{-16+2x-2}{(9-x)(8-x)}}\\\\=\bold{\frac{(2x-18)}{(9-x)(8-x)}}\\\\=\bold{\frac{-2(9-x)}{(9-x)(8-x)}}\\\\=\bold{\frac{-2}{(8-x)}}\)

When

\(x=8.9\\\\m= \bold{\frac{-2}{(8-8.9)}} = \bold{\frac{-2}{(0.9)}}=-2.222222222\)

When

\(x=8.99\\\\m= \bold{\frac{-2}{(8-8.99)}} = \bold{\frac{-2}{(0.99)}}=-2.020202020202\)

When  

\(x=8.999 \\\\m= \bold{\frac{-2}{(8-8.999)}} = \bold{\frac{-2}{(0.999)}}=-2.002002\)

When

\(x=9.1\\\\m= \bold{\frac{-2}{(8-9.1)}} = \bold{\frac{-2}{-1.1}}=1.818181\)

When

\(x=9.01\\\\m= \bold{\frac{-2}{(8-9.01)}} = \bold{\frac{-2}{-1.01}}=1.98019802\)

When

\(x=9.001\\\\m= \bold{\frac{-2}{(8-9.001)}} = \bold{\frac{-2}{-1.001}}=1.998002\)

When

\(x=9.0001\\\\m= \bold{\frac{-2}{(8-9.0001)}} = \bold{\frac{-2}{-1.0001}}=1.99980002\)

For point b:

\(P(9, -2)\\\\m = 2\)

For point c:

Line equation:

\(\to \bold{y= m(x- x_1)+y_1}\\\\\to \bold{y= 2(x-9)+(-2)}\\\\\to \bold{y= 2x-18-2}\\\\\to \bold{y= 2x-20}\\\\\)

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The solution is

The monthly attendance from June to August decreased by 672 people

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

Let the equation be represented as = A

Now , the value of A is given by

The attendance of people in the baseball game in June = 120,000 people

Now ,

The percentage increase in attendance in July = 13 %

So , the attendance of people in July = attendance of people in the baseball game in June + percentage increase in attendance x attendance of people in the baseball game in June

Substituting the values in the equation , we get

The attendance of people in July = 120,000 + ( 13/100 ) x 120,000

The attendance of people in July = 120,000 + ( 0.13 x 120,000 )

The attendance of people in July = 120,000 + 15,600

The attendance of people in July = 135,600 people

Now , the percentage decrease in attendance is August = 12 %

So , the attendance in August = attendance of people in the baseball game in July+ percentage decrease in attendance x attendance of people in the baseball game in July

Substituting the values in the equation , we get

The attendance of people in August = 135,600 - ( 12/100 ) x 135,600

The attendance of people in August = 135,600 - ( 0.12 x 135,600 )

The attendance of people in August = 135,600 - 16,272

The attendance of people in August = 119,328 people

So , the attendance change from June to August is = 120,000 people - 119,328 people

Attendance change from June to August is = 672 people

Therefore , the attendance has decreased 672 people from June to August

Hence ,

The monthly attendance from June to August decreased by 672 people

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If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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The number is -4.

A Linear equation is an equation in which the highest power of all the variables is not more than 1.

Here, we are given that a number when divided by 2 is equal to the number increased by 2.

Let the number be x

then x divided by 2 = x/2

and the number increased by 2 = x + 2

Then, we get the following equation-

x/2 = x + 2

simplifying the equation further we get-

x = 2(x + 2)

x = 2x + (2)(2)

x = 2x + 4

x - 2x = 4

-x = 4

x = -4

Thus, the number is -4.

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On solving the provided questions, we can say that Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

he diameter of the ball bearings varies according to a distribution that is approximately Normal

mean 11.5 mm and standard deviation 0.05 mm

the probability that the difference in the diameters of the two ball bearings is less than 0.06 mm

Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

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Answer:

10000

Step-by-step explanation:

100 hugs x 100 hugs

= 10,000 hugs.

The jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.

An equation is a mathematical statement that shows that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems by finding the values of the variables that make the equation true.

Let x be the number of bracelets made, and y be the number of necklaces made.

Then, we can create the following system of equations:

Equation 1: 7x + 24y = 172 (the total amount of gold used is 172 grams)

Equation 2: y = x + 2 (the number of necklaces made is 2 more than the number of bracelets made)

So, the variables are x (the number of bracelets made) and y (the number of necklaces made).

We can solve this system of equations to find the values of x and y. We can use substitution or elimination to solve for one variable and then plug it into the other equation.

Substitution method:

From Equation 2, we have y = x + 2. Substituting this into Equation 1, we get:

7x + 24(x+2) = 172

7x + 24x + 48 = 172

31x = 124

x = 4

So, the jeweler made 4 bracelets.

Plugging this into Equation 2, we get:

y = x + 2 = 4 + 2 = 6

So, the jeweler made 6 necklaces.

Therefore, the jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.

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Hello

2/7 = 2x5/7x5 = 10/35

10/35 > 6/35

=> 2/7 > 6/35

given that v1,v2 ,v3,v4 is linearly independent vector so in order for a set of vectors to be linearly independent it must satisfy the below conditon:

   \(x_1v1+x_2v2+x_3v3+x_4v4\) =0  --(i)

  where \(x_1, x_2,x_3 ,x_4\) is some real numbers.

a) so in order to show that v1,v2+v4,v3 is linearly independent we have to

check if equations formed by these vectors can be transformed into some equation of equation (i) form.

 so we have :

   \(x_1v1+x_2(v2+v4) +x_3v3\)   ---(ii)

    where \(x_1, x_2,x_3\) is some real numbers.

  after evaluating equation (ii) we have:

     \(x_1v1+x_2v2+x_3v3+x_2v4\)  

     so the above equation is now transformed in the form of equation (i) where \(x_2 = x_4\)  

and hence \(x_1v1+x_2v2+x_3v3+x_2v4\) =0  ----(iii)

equation (iii) shows that the set of given vectors are linearly independent.

b)  so in order to show that v1 +v2, v3, v4  is linearly independent we have to check if equations formed by these vectors can be transformed into some equation of equation (i) form.

 so we have this equation:

   \(x_1(v1+v2)+ x_2v3 + x_3v4\)      where \(x_1, x_2,x_3\) is some real numbers.

  after evaluating equation (iv) we have:

     \(x_1v1+x_1v2+x_2v3+x_3v4\)  

     so the above equation is now transformed in the form of equation (i) where the cofficient of v2 is also \(x_1\)  

and hence \(x_1v1+x_1v2+x_2v3+x_3v4\) =0  ----(v)

equation (v) shows that the set of given vectors are linearly independent.

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Complete question :

let v be a real vector space. suppose that v1, v2, v3, v4 are vectors in v which are linearly independent. show that the vectors a) v1, v2+v4, v3 and   b) v1 +v2, v3, v4 are also linearly independent.

The vectors v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent is hence proved.

let v be a real vector space.

The v1, v2, v3, v4 are vectors in v which are linearly independent.

V={v1, v2, v3, v4} then set V is called  linearly independent if \(\forall \alpha_i \in F \\\).

∝1v1+∝2v2+∝3v3+..........+∝nvn=0

then, \(\forall \alpha_i =0 \\\) i=1,2,3......n.

let ∝1,∝2,∝3,∝4 ε F

∝1v1+∝2(v1+v2)+∝3(v1+v2+v3)+∝4(v1+v2+v3+v4)=0

v1(∝1+∝2+∝3+∝4)+v2(∝2+∝3+∝4)+v3(∝3+∝4)+v4.∝4=0

Since  v1, v2, v3, v4 are linearly independent vectors.

So ∝1+∝2+∝3+∝4=0......(1)

∝2+∝3+∝4=0....(2)

∝3+∝4=0....(3)

∝4=0...(4)

Solving eq(1), (2), (3), (4)

we get ∝1=∝2=∝3=∝4=0

So according to definition of linearly independent vectors.

A set of vectors is called linearly independent if no vector in the set can be expressed as a linear combination of the other vectors in the set. If any of the vectors can be expressed as a linear combination of the others, then the set is said to be linearly dependent.

So v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent vectors hence proved.

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Answer:

(9, -5)

Step-by-step explanation:

If you rotate a figure 90 degrees counterclockwise, the coordinates will go from (x, y) to (-y, x).

So, let's start out with -y. The y-value of (-5, -9) is -9, and the negative value of that is -(-9) or 9. That goes first in our point: (9, x.) Now, we just keep our x-value the way it is, -5, and put that in our y-value: (9, -5). And there's our point after a 90 degree counterclockwise rotation.

Answer:

A.

positive and negative 5 and square root of 29