There are y children in an orphanage and they shared $x among themselves. If each of them got $7 there were $4 left.If there were $5 more,each would get $8.
(a) Write the pair of simultaneous linear equation connecting x and y.
(b) Hence, find
(i) x
(ii) y

Answer: 3 dimes

Step-by-step explanation:

Let n represent the number of nickels and d represent the number of dimes Reese has in his pocket.

Given system : [tex]n+d=11........(1)\\5n+10d=70............................(2)[/tex]

Divide equation (2) by 3 on both sides, we get

[tex]n+2d=14................................(3)[/tex]

Subtract equation (1) from (3), we get

[tex]d=3[/tex]

Hence, there are 3 dimes in Reese's pocket.

Answer:

3 dimes are in Reese's pocket.

Step-by-step explanation:

Here, n represent the number of nickels and  d represent the number of dimes.

Given the system of equations:

[tex]n+d = 11[/tex]           .....[1]

[tex]5n+10d = 70[/tex]             .....[2]

Multiply both sides by 5 in [1] we have;

[tex]5n+5d=55[/tex]             .....[3]

Subtract equation [3] from [2] we have;

[tex]5d = 15[/tex]

Divide both sides by 5 we have;

d = 3

Therefore, 3 dimes are in Reese's pocket.

Final answer:

The volume of the cone with a height of 7.5 inches and a radius of 5.62 inches is calculated using the formula V = (1/3)πr²h and is approximately 589.05 cubic inches.

Explanation:

To find the volume of a cone with a height of 7.5 inches and a radius of 5.62 inches, you use the formula for the volume of a cone, which is V = (1/3)πr²h. Here, r represents the radius and h represents the height of the cone.

First, calculate the area of the base (A) which is π times the radius squared:

A = π × (5.62 in)²

This gives us the area of the base. Then, multiply by the height (7.5 inches) and divide by 3 to find the volume:

V = (1/3) × A × h = (1/3) × π × (5.62 in)² × 7.5 in

Now, plug in the value for π (approximately 3.14159) and calculate:

V ≈ (1/3) × 3.14159 × (5.62²) × 7.5

V ≈ 589.05 cubic inches (rounded to two decimal places).

Therefore, the volume of the cone is approximately 589.05 cubic inches.

Answer:  The correct option is (C) [tex]\dfrac{1}{2}.[/tex]

Step-by-step explanation:  Given that Jane altered by using [tex]\dfrac{3}{4}[/tex] of the amount of butter called for the recipe and she used 6 tablespoons of butter.

We are to find the number of cups of butter that the recipe call for.

Let x represents the total number of teaspoons of butter that the recipe call for.

Then, according to the given information, we have

[tex]\dfrac{3}{4}x=6\\\\\Rightarrow 3x=24\\\\\Rightarrow x=8.[/tex]

So, the total number of tablespoons of butter that the recipe call for is 8.

Now, 16 tablespoons = 1 cup.

Therefore, we get

[tex]8~\textup{tablespoons}=\dfrac{1}{16}\times 8=\dfrac{1}{2}~\textup{cups}.[/tex]

Thus, the recipe call for [tex]\dfrac{1}{2}[/tex] cup of butter.

Option (C) is CORRECT.

Answer:

c) [tex]5^{6}[/tex]

Step-by-step explanation:

We have been given that there are [tex](5^3)^2\cdot 5^0[/tex] hens in a bird enclosure. We are asked to find the total number of hens in the enclosure.

Using exponent property [tex]a^0=1[/tex], we will get:

[tex](5^3)^2\cdot 1[/tex]

[tex](5^3)^2[/tex]

Using exponent property [tex](a^b)^c=a^{b\cdot c}[/tex], we will get:

[tex]5^{3\cdot 2}[/tex]

[tex]5^{6}[/tex]

Therefore, there are total number of hens in the enclosure would be [tex]5^{6}[/tex].

Answer:

y = 9

Step-by-step explanation:

A horizontal line will stay at the same height across the entire domain.  This means that while its x-coordinates change, its y-coordinate does not.  

Since it passes through the point (-5, 9), this means the y-coordinate is 9.  It will be y=9 throughout the entire graph; this means the equation is y=9.

The equation of the horizontal line that passes through the point (−5, 9) is y=9. The correct option is B.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

For a horizontal line, the value of the slope of the line is 0. Therefore, the value of m is 0. Given the point (-5,9) through which the equation passes, therefore, the value of the constant in the equation of the line can be found by substituting values in the equation.

Therefore, the equation can be written as,

y = mx + c

9 = 0(-5) + c

c = 9

Now, substitute the value of slope and constant in the equation of the line.

y = mx + c

y = 0(x)+ 9

y = 9

Hence, the equation of the horizontal line that passes through the point (−5, 9) is y=9.

Learn more about Equation of Line here:

https://brainly.com/question/21511618

#SPJ5

present dimensions = 5*7

dimensions after scaling with factor 3 = 15*21

dimensions after reducing by scale factor 0.5 = 7.5*10.5

area of rectangle = length * breadth

so area of yearbook = 7.5*10.5 = 78.75

because, 78.75<80

so, the yearbook will fit in area of 80 inches^2

Answer:

The required expression is [tex]25-2g[/tex]

She left with 23 tokens after playing 1 game.

She left with 17 tokens after playing 4 game.

She left with 13 tokens after playing 6 game.

She left with 5 tokens after playing 10 game.

She left with 1 tokens after playing 12 game.

Step-by-step explanation:

Consider the provide information.

Part (A)

At a video arcade, Jenny buys 25 tokens. She uses two tokens for each game She plays.

Let the number of games she plays represented by g.

For each game she need to use 2 tokens.

Thus for g games she will use 2g tokens.

Thus, the required expression is: [tex]25-2g[/tex]

Part (B) Find the number of tokens Jenny has left after playing 1,4,6,10 and 12 games.

The number of tokens Jenny has left after playing 1, is:

[tex]25-2(1)[/tex]

[tex]25-2[/tex]

[tex]23[/tex]

Hence, she left with 23 tokens after playing 1 game.

The number of tokens Jenny has left after playing 4, is:

[tex]25-2(4)[/tex]

[tex]25-8[/tex]

[tex]17[/tex]

Hence, she left with 17 tokens after playing 4 game.

The number of tokens Jenny has left after playing 6, is:

[tex]25-2(6)[/tex]

[tex]25-12[/tex]

[tex]13[/tex]

Hence, she left with 13 tokens after playing 6 game.

The number of tokens Jenny has left after playing 10, is:

[tex]25-2(10)[/tex]

[tex]25-20[/tex]

[tex]5[/tex]

Hence, she left with 5 tokens after playing 10 game.

The number of tokens Jenny has left after playing 12, is:

[tex]25-2(12)[/tex]

[tex]25-24[/tex]

[tex]1[/tex]

Hence, she left with 1 tokens after playing 12 game.

The ratio of the number of children who own a dog to the total number of children in the class is [tex]\frac{ 5 }{ 12}[/tex], after simplifying the fraction [tex]\frac{ 10 }{ 24}[/tex] by dividing both the numerator and denominator by 2.

The question asks to find the ratio of the number of children who own a dog to the total number of children in the class. Ten children own a dog and fourteen do not, making the total number of children in the class twenty-four. To find this ratio, we divide the number of children who own a dog by the total number of children:

Ratio = number of children who own a dog ÷ total number of children in the class

Ratio = [tex]\frac{ 10 }{ (10 + 14)}[/tex]

Ratio = [tex]\frac{ 10 }{ 24}[/tex]

The simplified form of this ratio is found by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

Simplified Ratio = [tex]\frac{ 5 }{ 12}[/tex]

This is a clear example of positive reinforcement. Positive reinforcement involves the addition of a positive stimulus that act as a reinforcement to a desired behavior in order to make the behavior more likely happen again in the future. When Jemma praises and hugs his baby, she is using positive reinforcement, so her baby associates the behavior of saying “thank you” with a reward making him more inclined to say thank you again in the future.

We can conclude that Jemma's reinforcement schedule is positive reinforcement.

Final answer:

The numbers 4.5, 6, and 7.5 can form the sides of a right triangle as their squared lengths satisfy the Pythagorean theorem where 4.5² + 6² equals 7.5².

Explanation:

To determine whether the numbers 4.5, 6, 7.5 can form the sides of a right triangle, we can apply the Pythagorean theorem.

This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

According to the given numbers, if we assume that 7.5 is the length of the hypotenuse, then:

4.5² + 6² should equal 7.5²

Calculating each term gives us:

Adding the squares of the possible legs:

20.25 + 36 = 56.25, which is indeed the square of the hypotenuse. This confirms that 4.5, 6, and 7.5 can indeed form a right triangle.