Tom had an average of 74 runs in 3 matches. if he scored 42 and 31 runs in two resent matches, what is his new average?​

Answer:

equation:

2( x - 3 ) = 2

Step-by-step explanation:

you can also solve for x:

2(x-3) = 2

2x - 6 = 2

2x = 2 + 6

2x = 8

x = 8/2

x= 4

Thomas lists all of the different arrangements of the letters in the word CABOOSE. How many of Thomas's arrangements begin with a C and end with an E?

(B) 120

If a b a♣︎b - a - b - 1, then what is the value of 284♣︎1001?

(A) 282435

What is the product of 4% of 112 and 61% of 375?

(D) 105

Josh rolls two standard six-sided dice. What is the probability that the product of the numbers shown on the dice is a multiple of six?

(C) 5/12

What is the remainder when the sum of the terms of the arithmetic series 101 108 + 115 + 290 is divided by 28?

(A) 7

Two right triangles have the same perimeter, and each triangle's side lengths are all whole numbers. One right triangle has legs of length 10 and 24. The other right triangle has a hypotenuse of length 25. What is the area of the second triangle?

(D) 144

A function f is defined for positive integers x as f(x) = 0 if x ≤ 2. Otherwise, f(x) = f(x - 1) if x is not divisible by 3, and f(x) = 2 + f (3) if x is divisible by 3. What is the value of f(2020)?

(B) 14

Answer:

f = 4/7 * 4/5 = 16 / 35      Fraction of spool used

4/7 of spool was originally present and Frank used 4/5 of the yarn left on the spool

Answer:

1 yard and 1 foot

Step-by-step explanation:

7-4=3

3-1 yd and 2 feet

there are three feet in a yard. you can subtract the yard first, leaving you with two yards, then subtract two feet. you will be left with 1 yard and 1 foot.

Answer:

Prisms

Step-by-step explanation:

The only two associated are rectangles and prisms

Answer:

578

Step-by-step explanation:

divide the length value by 1.609

Answer:

see explanation

Step-by-step explanation:

solving the inequality

- 13t ≤ 78

divide both sides by - 13, reversing the symbol as a result of dividing by a negative quantity.

t ≥ - 6

this means that any value of t greater than 6, including 6, is a solution.

listing the solutions from - 10 through to 10 that are solutions when substituted for t

- 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6

The lengths of the diagonals of QRST is 14units.

In a rectangle, the diagonals are equal in length and bisect each other at 90 degrees. This means that the diagonals divide the rectangle into four congruent right triangles.

Since the diagonals of a rectangle are of equal length. then

QS = RT

4x + 2 = 5x - 1

Simplify and solve for the value of x.

4x + 2 = 5x - 1

x = 3

Substitute the value of x in any of the expression for the length of the diagonal.

QS = 4x + 2

length of diagonal = 4(3) + 2 = 14

Hence, the length of the diagonals QS and RT is 14 units.

The problem seems unreadable, it must have been...

"In rectangle QRST, QS = 4x + 2 and RT = 5x - 1. Find the lengths of the diagonals of QRST."

Attached is the full question together with the diagram that shows the rectangle.

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The value of the evaluated iterated integral is = 0.002

As per the given data the iterated integral is,  =  integral. 1 0 s7 cos(s8) dt ds

Here we have to evaluate the given iterated integral.

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as,

= f(b) - f(a)

Where,

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus,  ab f(x) dx is read as the definite integral of f(x) with respect to d x from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

=  integral. 1 0 s7 cos(s8) dt ds

Integrate the given iterated integral.

We get:

=   integral. 1 0 s7 cos(s8) dt ds

= t       when s = 0

= 6         t = 0  

=   ds      when s = 1.....   t = 1

Replace the assumed terms.

Then we get:

=  cos(t)

=   cos(t) dt

=  [sin(t)]

=  [ sin(1) - sin(0) ]

= 0.002

Therefore,

The value of the evaluated iterated integral is = 0.002

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Answer:

(8, -8)

x = 8

y = -8

Step-by-step explanation:

-4x - 5y = 8

7x + 5y = 16

-----------------------

3x = 24

÷3   ÷3

----------------

x = 8

7x + 5y = 16

7(8) + 5y = 16

56 + 5y = 16

-56          -56

----------------------

5y = -40

÷5    ÷5

------------------

y = -8

(8, -8)

I hope this helps!

Answer: B- 7, 24, 25

Hope this helps :)

Step-by-step explanation:

Use the Pythagorean Theorem

a^2 + b^2 = c^2

49 + 576 = 625

625 = 625

Answer:

D

Leah spent y

15 times ryan's

ryan spent x

y = 15x

Step-by-step explanation:

A -  Leah spent x

      15 times more than

      Ryan spent y

x = 15 * y

B - Leah spent y

     15 more

     Ryan spent x

y = x + 15

C- Leah spent x

    15 less

    Ryan spent y

x = y-15

Answer:

slope = 1/2

y-intercept = -1

Step-by-step explanation:

Y=1/2x-1 and it passes through (6, 2) what is the slope and y intercept?

The equation given is: y= 1/2x - 1

y = mx + b

where m = slope and b = y-intercept, so:

slope = 1/2

y-intercept = -1

Answer:

Tracy went to the store to buy half a pound of candy. if 1/4 of the candy she bought was gummy bears,how many pounds of gummy bears did she buy?

1/8 pound

Step-by-step explanation:

A bank statement balance of -R500 means that the account holder has an overdraft of R500. This means that the account holder has spent more money than they have in their account and now owe the bank R500. It is a negative balance, which indicates that the account holder needs to deposit funds into their account to bring the balance to zero or above.

The required probability for the number of phone calls more than two in next 30 minutes is equal to ( 18 / 5)e⁻⁶.

Number of phone calls between 6pm and 8.00 pm 'n' = About 6 calls

Using Poisson's distribution we have,

P ( X = x ) = ( e⁻ⁿ nˣ ) / x!

Probability of receiving more than 2 phone calls in next 30 minutes

= P( X > 2 )

= P ( X = 3 ) + P ( X = 4 ) + P ( X = 5) + P( X = 6)

= ( e⁻⁶ 6³ ) / 3! +  ( e⁻⁶ 6⁴ ) / 4! +  ( e⁻⁶ 6⁵) / 5! +  ( e⁻⁶ 6⁶ ) / 6!

=  ( e⁻⁶ 6³ ) / 3! [ 1 +  (6 / 4) + (6² / 5× 4 ) + ( 6³ / 6 ×5× 4) ]

= ( e⁻⁶ 6³ ) / 3! [ ( 20 + 30 + 72 ) / 20 ]

= ( 18 / 5)e⁻⁶.

Therefore, the probability of more than two phone calls is  ( 18 / 5)e⁻⁶.

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If the variables "r" and "s" are inversely proportional and r=7 when s=6 , then when r = 10 , value of "s" will be 4.2 .

When the two variables are inversely proportional, their product is constant. That means, for two variables "r" and "s" , the it is represented in equation as :

⇒ r × s = k, where k is a constant ;

the value of variable "r" = 7 when s = 6,

First , we have to find the value of k:

⇒ k = r × s = 7 × 6 = 42 ;

So, for any value of r and s, the product "rs" will always be equal to 42.

When r = 10, we can use the equation to find s:

⇒ s = k/r = 42/10 = 4.2

Therefore , when r = 10 , the variable "s" is 4.2.

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Step-by-step explanation:

add it and the answer is 2,453

The results of the survey show that the majority of people prefer a blue car.

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The value (−1,7) is equal to 4. In the limit, when (x,y) is equal to (−1,7), the value of f(x,y) is the same as the limit, which is 4. Therefore, the value of f(−1,7) is 4.

Since the limit of f(x,y) as (x,y) approaches (−1,7) is 4, that means that as (x,y) gets closer and closer to (−1,7) the value of f(x,y) gets closer and closer to 4. Therefore, when (x,y) is equal to (−1,7), the value of f(x,y) is 4.

The limit of the function f(x,y) as (x,y) approaches (−1,7) is 4, which means that as (x,y) gets closer and closer to (−1,7), the value of f(x,y) gets closer and closer to 4. In the limit, when (x,y) is equal to (−1,7), the value of f(x,y) is the same as the limit, which is 4. Therefore, the value of f(−1,7) is 4.

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One alternative method for correcting the external effect between players is the Coasian bargaining solution. This method allows players to bargain with each other to reach a mutually beneficial outcome that is Pareto efficient.

Another alternative method is a Pigouvian tax. Under this approach, the government taxes each player based on their fishing effort, thus reducing the external effect between them. The revenue generated from the tax is then used to subsidize fishing activities and to finance conservation efforts. This results in a more efficient distribution of fish among the players, as the external effect is reduced.  

Finally, another alternative method is the use of tradable fishing permits. Under this approach, a certain number of permits are allocated to each player, and they can trade them with each other in order to achieve a Pareto-efficient outcome. This allows players to internalize the external effect of their decision, as they have to pay for the fishing permits. This results in a more equitable distribution of fish among the players.

Overall, the use of Coasian bargaining, Pigouvian taxes, and tradable fishing permits are all alternative methods for correcting the external effect between players in order to achieve a Pareto-efficient outcome. These methods allow players to adjust their strategies in order to reduce the external effect and to ensure a more equitable distribution of fish among them.

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The number of children is 379 and the number of the adults is 339.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."

Let us suppose the number of children = C, and the number of adults = A.

Given that, 718 people used the public swimming pool:

C + A = 718 people

The cost for one child is 1.25 for children, then the cost for C child is: 1.25C

The cost for one adult is 2.00 for adults, then the cost for A adults is: 2A

The receipts for admission totaled 1151.75:

1.25C + 2A = 1151.75

The two equations are:

C + A = 718

1.25C + 2A = 1151.75

For the first equation we can write:

C + A = 718

C = 718 - A

Substitute the value of C in second equation:

1.25(718 - A) + 2A = 1151.75

897.5 - 1.25A + 2A = 1151.75

0.75A = 254.25

A = 339

Substituting the value of A in the first equation we have:

C + A = 718

C + 339 = 718

C = 379

Hence, the number of children is 379 and the number of the adults is 339.

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The distance between two raisins will increase by a factor of the square root of 2.

As the bread dough rises and doubles in size, each linear dimension of the dough, including the distance between the raisins, will also double. This means that the distance between two raisins will increase by a factor of 2.

However, since the change in distance is related to a change in the linear dimension, and not the area, the increase in distance is proportional to the square root of 2, not 2. This means that the distance between the two raisins will increase by a factor of the square root of 2, or approximately 1.41.

This increase in distance between the raisins is a result of the increase in the volume of the dough, as the yeast ferments the sugars in the dough, producing carbon dioxide and causing the dough to rise. The increase in volume causes the dough to stretch, resulting in the increased distance between the raisins.

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Answer:

12 cubic units

Step-by-step explanation:

Since 1 cube is equal to 1 cubic unit and there are 12 cubes in total, this means the volume is 12 cubic units.

The solution of the expression is Z/57

A ring is a mathematical structure that combines the properties of an additive group with the properties of a multiplicative group.

When we look at solutions to the equation x² = 7 in different rings, we are asking "In what mathematical structures can we find numbers which, when squared, equal 7?"

(a) In the ring Z/19, the solutions are the residue classes modulo 19 that satisfy x² = 7. This means that we only consider the integers 0, 1, 2, ..., 18, and we take their remainders after dividing by 19. In this ring, we use the operations of addition and multiplication modulo 19.

(b) In Z/21, the equation x² = 7 has no solutions. This is because none of the remainders 0, 1, 2, ..., 20 after dividing by 21 can be squared to give 7.

(c) In Z/57, the equation x² = 7 has exactly 2 solutions. This is because there are exactly two residue classes modulo 57 that, when squared, give 7. To find these two solutions, we would need to perform a bit of calculation to determine which residues satisfy x² = 7.

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If everyone shakes hands with everyone else in a group of 20, the number of handshakes take place is 210.

In a group of 20 people, if everyone shakes hands with everyone else, the number of handshakes that take place is equal to the sum of the first 20 positive integers, which can be found using the formula for the sum of an arithmetic series:

= n (n + 1)/ 2

= (20 * 21) / 2 = 210

To understand why this is the case, consider that each person shakes hands with 19 other people, so there are a total of 20 * 19 = 380 handshakes. However, each handshake is counted twice (once for each person involved), so we need to divide the total number of handshakes by 2 to get the actual number of unique handshakes. Hence, the answer is 380 / 2 = 210.

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Answer: See below

Step-by-step explanation:

First, we will use the conversions that you provided to find how many feet are in 3 miles. Since we know that one mile = 5,280 feet, all we have to do is multiply that number by 3 to find the conversion.

5,280 * 3 = 15,840 feet

Now, we can use the value found above to find how many inches are in 3 miles. We know that 12 inches are in one foot, so we have to multiply 12 by 15,840. This equals 190,080 inches.

I hope this helps, and if you need me to show you the step-by-step work for multiplication, let me know!

The balance of your investment account at any given point in time during the week can be calculated using the exponential growth formula:

N(t) = N0 * (1 + r)^t, where N0 is the initial balance (1,459 dollars), r is the growth rate per day (4.73/day), and t is the number of days since the week began (n).

For example, if it is the fourth day of the week (n = 4), then the balance of your investment account would be N(4) = 1,459 * (1 + 4.73/day)^4 = 2,719.37 dollars.

The exponential growth formula is a mathematical equation used to calculate the growth of a population over time. It is expressed as N(t) = N0 * (1 + r)^t, where N0 is the initial population size, r is the growth rate, and t is the time in days.

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Answer:

the two coefficients are 2/3 and -1/6

the sum of the expressions are = 1 /2 q−r+ −3 /4

hope this helps :)