60 people attend a game night. Everyone chooses to play chess, a two-player game, or cribbage, a four-player game. All 60 people are playing either chess or cribbage.

1.Complete this table showing some possible combinations of the number of each type of game being played:he equation. Enter only 1 term in each blank.
2.Write an equation to represent the situation illustrated in the table
3.There are 3 more games of cribbage being played than games of chess being played. Write an equation to represent this relationship. 4.Solve the system of equations you just wrote. There were
chess games, and
cribbage games.

To draw the area of a square, begin by drawing a square with four equal sides. Label the length of each side. Then, draw a triangle inside the square, connecting each corner. Label the length of each side.

Finally, calculate the area of the square by multiplying the length of the square by the length of the triangle.To find the area of any square, use the formula A= s2, where s is one of the sides' lengths.For example, if the length of each side of the square is 4, the area of the square would be 16 (4 x 4 = 16). To draw the area of the square, draw a 4x4 square and then draw a triangle inside it, connecting each corner. Label the length of each side of the triangle and the square. Then use the area formula to calculate the area of the square (A = s^2).

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Answer:

4 x 10 + 5 x 1

Step-by-step explanation:

The expanded form of a number is written as a sum where each digit of the number is multiplied by its place value. Let's understand this concept with an example. To write the number 45 in the expanded form, we split the digits into tens and ones and write it as 4 x 10 + 5 x 1.

Answer:

Step-by-step explanation:

45 in expanded form;

(4x10)+(1x5)= 45

The speed at which Marry was initially driving was 13 miles per hour and with that speed Marry drove 156 miles.

Given, Marry drove 156 miles at a constant rate.

If she had driven 99 miles/hour faster, she could have reduced her driving time by 45 minutes.

we have to find the speed at which Marry was driving.

Let the speed be, v

On using the distance formula, we get

Distance = Speed × Time

156 = vt

If she drive 99 miles/hour faster then her time reduced by 45 min.

156 = (v + 99)(t - 3/4)

156 = 156 + 99t - 3/4v - 297/4

396t = 3v + 297

396t = 468/t + 297

On solving the quadratic equation, we get

t = 12

and v = 13

So, the speed of marry was 13 miles per hour.

Hence, Initially the speed of marry was 13 miles per hour and with that speed Marry drove 156 miles.

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Answer:

(0,3)

Step-by-step explanation:

Answer:0,3

Step-by-step explanation:

Answer:

y= -1/2x+2

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

b is y intercept

To find slope we use y2-y1/x2-1

I will use points (4,0) and (0,2) to show it

2-0/0-4)

2/-4

-1/2 is the slope

y= -1/2x+b

We also know the y intercept because the Line intersects the y axis when y=2

y= -1/2x+2

Hopes this helps

The three ways of solving equations are graphing substitution and elimination.

To solve an equation by graphing, you essentially chart the given equations and discover the point(s) where they all meet. The arrangement of this point will grant you the values of the factors that you simply are tackling. The following method is substitution. Substitution is best utilized when one of the conditions is in terms of one of the factors such as y=2x+4, but the equations can continuously be manipulated. The primary step in this method is to solve one of the equations for one variable. Once an expression for the variable is found, substitute or plug within the expression into the other equation where the initial variable was to solve for the number esteem of the next variable. The final step is to substitute the number esteem that was found for its comparing variable within the original condition. The third method is the elimination, which involves adding the equations together in arrange to make an equation with as it were one variable. This will was done when the coefficients of one variable in both equations are alternate extremes and will cancel each other out once added together.

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Lines b is parallel at an intersection at an angle of 89. 5 degrees.

In the above question, the two parallel lines will be b and d.

How do parallel lines work?

From the illustration, we can see that

Lines b and an intersect at an angle of 89. 5 degrees.

Lines c and an intersect at an angle of 91.5 degrees.

Lines d and an intersect at an angle of 89.5 degrees.

Lines e and an intersect at an angle of 88.5 degrees.

Lines f and an intersect at an angle of 90.5 degrees.

Since the angles created by lines b and an are equal, the result is 89.5.

Consequently, these two lines will never intersect.

However, other lines have different angles, so they can collide at a single location.

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Answer:

A lab needs to make 500 gallons of a 34% acid solution. The only solutions available are a 25% acid solution and a 50% acid solution. How many gallons of each solution should be mixed to make the 34% solution?

***

let x=amount of 25% solution to mix

500-x=amount of 50% solution to mix

.25x+50%(500-x)=34%*500

.25x+250-.50x=170

.25x=80

x=320

500-x=180

amount of 25% solution to mix=320 gal.

amount of 50% solution to mix=180 gal

Step-by-step explanation:

The process to solve the linear  function problem is explained below .

In the question ,

we have been asked how can we solve a linear function problem .

we know that A linear function is a function that represents a straight line in the coordinate plane.

For Example, let the linear function problem be  f(x) = 3x - 2 ,

Step(1) :

to solve it we first have to equate the function to 0 ,

that is 3x - 2 = 0

Step(2) ;

we need to perform the necessary mathematical operation to find the value of x .

adding 2 on both sides of equation 3x - 2,

we get ,

3x = 2

dividing both sides by 3 ,

we have , x = 2/3 ,

the solution is x = 2/3 .

Therefore , the steps to solve a linear function is mentioned above .

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The number of unique orders that Gabriel can arrange for the new flavors of his favourite snak is 6..

The term permutation refers to the mathematical calculation of the number of ways a given set can be arranged. Simply put, permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of placement is important.

P(n,r) = n!/(n-r)!

where n --> total items in the set;

r --> items taken for the permutation;

"!" --> denotes taking the factorial

We have given that,

total possible flavours of Gabriel's favorite snack = 3

He wants to try each of the new flavors one after the other.

We have to calculate the number of ways Gabriel can arrange the new flavors .

For this Use the permutation formula,

ⁿPᵣ = n!/(n-r)!

here , n = 3 , r = 3 then,

P (3,3) = 3!/(3 − 3)!

= 3!/0!

As we know that 0! = 1 so, P(3,3) = 3!

= 3×2×1 (because n! = n(n-1)(n-2)---3.2.1 )

= 6

There are 6 unique orders in which Gabriel can arrange the new flavors.

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Therefore , the answer is  the confidence interval is positive, the researcher can conclude there is a greater proportion of men than women who watch television regularly.

A confidence interval in frequentist statistics is a range of estimates for an unobserved parameter. The most common confidence level for computing confidence intervals is 95%, however other levels, including 90% or 99%, are sporadically employed.

Here,

Assuming that the confidence interval's lower and upper bounds are both positive and that it does, then one of the proportions must be larger than the other as the confidence interval's range corresponds to the difference in proportions. Men watch television more frequently than women do (56/70 vs. 47/85, according to a quick calculation of the proportions).

The reply is "D" The researcher can infer that more men than women routinely watch television because the confidence interval is positive.

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0 in the bank balance represent there is no money in account and there is no negative balance.

Elevation is the process of moving up to a higher or more important position, state, or level.

Example1: Mrs. Bautista has a bank balance of -42 dollars at the start of the month. After she deposits 42 dollars, what is the new balance?

The new balance in Mrs. Bautista account

-42+42=0

Example2: A submarine hovers at elevation 240 meters below sea level. If it elevate farther 150 meters and then elevated back 390 meters to surface, what is its new position?

Now, the new position of a submarine is

(-240-150)+390

= -390+390

= 0

So, 0 is the surface of sea level.

Therefore, 0 in the bank balance represent there is no money in account and there is no negative balance.

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The upper bound for the area is 4527.7056 cm²  and the lower bound for the perimeter is 278 cm.

Area (upper bound) = 4527.7056 cm²

Perimeter (lower bound) = 278 cm

The length and width of the rectangle have been ROUNDED to the nearest tenth. Let's calculate what their actual measurements could be:

LENGTH: rounded to 87.3, actual is between 87.25 and 87.34

87.25 is the lowest number it could be that would round it UP to 87.3

87.34 is the highest number it could be that would round DOWN to  87.3

WIDTH: rounded to 51.8, actual is between 51.75 and 51.84

51.75 is the lowest number it could be that would round it UP to 51.8

51.84 is the highest number it could be that would round DOWN to 51.8

To find the Area of the upper bound, multiply the highest possible length and the highest possible width:

A = 87.34 × 51.84 = 4527.7056

To find the Perimeter of the lower bound, calculate the perimeter using the lowest possible length and the lowest possible width:

P = 2(87.25 + 51.75) = 278

The region is the quantity that expresses the volume of an area at the aircraft or on a curved floor. The vicinity of a plane region or aircraft place refers to the area of a shape or planar lamina, at the same time as floor region refers to the region of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of material with a given thickness that might be necessary to style a version of the shape, or the quantity of paint important to cover the surface with an unmarried coat. it's far the 2-dimensional analog of the length of a curve (a one-dimensional idea) or the extent of a stable (a three-dimensional idea).

The area of a shape can be measured by means of comparing the shape to squares of a hard and fast size. inside the worldwide system of devices (SI), the usual unit of the region is the square meter (written as m2), which is the region of a square whose sides are one meter long. A form with a place of three rectangular meters might have an equal area as 3 such squares. In arithmetic, the unit rectangular is described to have placed one, and the region of any other shape or floor is a dimensionless actual quantity.

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Complete question: -

The lengths of a rectangle have been measured to the nearest tenth of a centimeter they are 87.3cm and 51.8cm what is the upper bound for the area and the lower bound for the perimeter

Answer: Mrs. Robinson

Step-by-step explanation:

Let's find Mrs. Robinson first

100% - 20% = 80% or 0.8

29.99 times 0.8% = $24

29.99 -24 = $5.99 off

Now Let's find Mr.Chang

100% - 10% = 90% or 0.9

25 times 0.9% = $22.50

25 - 22.50 = $2.50 off

So Mrs. Robinson received a better discount!

Answer: neither

Step-by-step explanation:

y=mx+b

y=2x+3

m= 2/1

y-1=1/2(x+2)

y-1=1/2x +1

+1          +1

y=1/2x + 2

m=1/2

Answer:

To find out how many miles per gallon the truck got, we can divide the number of miles it traveled by the number of gallons of gas it used: 84 miles / 4 gallons = <<84/4=21>>21 miles/gallon.

To find out how many miles per gallon the SUV got, we can divide the number of miles it traveled by the number of gallons of gas it used: 72 miles / 3 gallons = <<72/3=24>>24 miles/gallon.

To find out how many more miles per gallon the SUV got than the truck, we can subtract the number of miles per gallon the truck got from the number of miles per gallon the SUV got: 24 miles/gallon - 21 miles/gallon = <<24-21=3>>3 miles/gallon.

The SUV got 3 more miles per gallon than the truck.

Step-by-step explanation:

Answer:The SUV got 3 more miles per gallon than the truck.

Step-by-step explanation:

The value of the given car after 7 years will be $2880 which has been decreasing by 20% every three years.

A car is currently $6,000 and has been decreasing by 20% every three years.

After 7 years, the car will have decreased in value by 7 / 3 = 2 full cycles of 20%.

Each cycle decreases the value of the car by 20/100 × $6,000 = $1200.

After two cycles, the value of the car will be :

$6,000 - 2 × $1,200 = $3,600.

After 7 years, the car will have decreased in value by an additional :

$3,600 × 20/100 = $720.

So, after 7 years, the car will be worth :

$3,600 - $720 = $2880.

Therefore, the value of the given car after 7 years will be $2880.

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The value of the entry will not match will be;

⇒ 10⁻⁶

⇒ [tex]\frac{1}{10^5^/^3}[/tex]

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The number is,

⇒ [tex]10^{\frac{-3}{5} }[/tex]

Now,

Since, The number is,

⇒ [tex]10^{\frac{-3}{5} }[/tex]

Hence, It can be written as;

⇒ [tex]10^{\frac{-3}{5} }[/tex] = [tex]10^({\frac{-3}{5} })[/tex]

           = [tex]\sqrt[5]{10^-^3}[/tex]

           = [tex](\frac{1}{10^{\frac{1}{5} }} )^3[/tex]

Thus, The value of the entry will not match are given as,

⇒ 10⁻⁶

⇒ [tex]\frac{1}{10^5^/^3}[/tex]

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The probability that a teenage boy has a cholesterol level greater than 200 is 0.11507.

Let the distribution of teenage boys' cholesterol levels be x

According to the question,

X follows a Normal distribution with

mean = 170

Standard deviation = 25

Hence, the variance = 25² = 625.

Hence X ~ N(170,25)

Now we need to find P(X>200)

= 1 - P(X<200)

Now to find this we need to convert the problem to a standard normal distribution

for this, we use the formula

P(X<x) = P(Z<x-mean/sd)

Therefore,

P(X<200)

= P(Z<(200 - 170)/25)

= P(Z<30/25)

= P(Z<1.2)

According to Z table,

P(Z<1.2)

= 0.88493

Hence, P(X>200)

= 1 - 0.88493

= 0.11507

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After you dilate a figure , The figure gets bigger or smaller.

Dilation in mathematics is a process of changing the size of an object or a shape without changing its shape.

When you dilate any figure distance between the points changes.

Either the image gets enlarge or shrinks depends on the scale factor.

Things that don't changes are:

Only the size of an image changes not it's shape.

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Answer:

75/4

Step-by-step explanation:

I put all fractions in the same form and multiplied straight across

3/1 * 1/2 * 25/2 =

75/4

The integer value of x is 6.

What is a side of a triangle?

The three vertices of a triangle connect the straight lines that make up its sides. In other terms, we can state that a triangle's sides are line segments that converge at the triangle's vertices.

Here, we have

Given,

the lengths of the sides of a triangle are x, 5, and 8.

x² + 5² < 8²

x² + 25 < 64

x² < 39, now perfect squares less than 39 are 36, 25, 16, 9, 4, 1.

x² + 5² = 8²

x² + 25 = 64

x²  = 39, No integer values.

x² + 5² > 8²

x² + 25 > 64

x² + > 39

Here the possible integer values are infinite.

Hence, the integer value of x is 6.

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The vertex-form definition of the quadratic function is given as follows:

f(x) = −(x + 1)² + 25.

The roots of the quadratic function are defined as follows:

-6 and 4.

Hence the definition of the function is given as follows:

f(x) = a(x + 6)(x - 4)

f(x) = a(x² + 2x - 24).

When x = 1, y = 21, hence the leading coefficient a is obtained as follows:

21 = a(1 + 2 - 24)

-21a = 21

a = -1.

Thus the standard definition of the function is of:

y = -x² - 2x + 24.

The coefficients of the function are of:

a = -1, b = -2, c = 24.

Then the x-coordinate of the vertex is of:

x = -b/2a = 2/-2 = -1.

The y-coordinate of the vertex is of:

y = -(b² - 4ac)/4a = -((-2)² - 4(-1)(24))/-4 = 25.

Meaning that the vertex-form definition of the quadratic function is of:

f(x) = −(x + 1)² + 25

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Answer: B is the answer i got it right on the test

Step-by-step explanation:

The surface area of the resulting solid is 40 cm².

A cube is a three-dimensional figure that has 6 faces and 12 edges and 8 vertices. All of the edges of a cube are of the same length.

If the volume of each of the two cubes is 8 cm³, then the length of its edge is 2 cm.

V = e³

8 = e³

e = 2 cm

Two cubes are glued together. Either side by side or put on top of each other, the dimension of the resulting solid is 4 cm by 2 cm by 2 cm.

Hence, the surface area of the resulting solid is

SA = 2lw + 2lh + 2wh

SA = 2(4 cm)(2 cm) + 2(2 cm)(2 cm) + 2(4 cm)(2 cm)

SA = 40 cm²

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The percentage of customers getting free games is 25%

To calculate the percentage, divide the value by the total value and multiply the result by 100.

Formula for percentage = (Value/Total value) 100

Example: 2/5 of 100 = 0.4 of 100 = 40%

We must use a different formula to calculate the percentage of a number, such as:

X = P% of Number

where X represents the required percentage.

If we remove the % sign, the above formulas must be expressed as;

X = P/100 * Number

Given:

Total number of customers = 120 customers

customers have free game = 30 customers

so, let the percentage will be x%

[tex]percent = \frac{x}{100}whole\\ 30 = \frac{x}{100}120\\ \frac{3000}{120} = x\\x= 25[/tex]

so the percentage of customers getting free games is 25%

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Equation of the line having passing point (-2,8) and has a slope of 2 is 2x - y + 12 = 0

What is the equation of the line?

A straight line's equation is y = mx + c, c is the height at which the line crosses the plane, and m is the gradient. y -axis, often known as the y -intercept. The gradient m is the slope of the line, which is the percentage increase in the y-coordinate relative to the x-coordinate.

Given:

Passing point of line , (-2,8)

Slope of the line = 2

Equation of the line having passing point (a,b) and slope m become

y - b = m (x - a)

Equation of the line ⇒ y - 8 = 2(x + 2)

⇒ y - 8 = 2x + 4

⇒ 2x - y + 4 + 8 = 0

⇒ 2x - y + 12 = 0

Therefore, equation of the line having passing point (-2,8) and has a slope of 2 is 2x - y + 12 = 0.

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Complete Question
What is the equation of a line that contains point(-2,8) and has a slope of 2?

Answer: x = 15/11

Step-by-step explanation:

55x - 20 = 55

      + 20     +20

55x = 75

/55     /55

x = 75/55

x = 15/11

x = 1 4/11

Answer: x=1.36363636364

Answer:

c = 40

Step-by-step explanation: