Amy is having her birthday party at a roller skating rink. The rink charges a fee of $100 plus $16 per person. A birthday person is not charged. If Amy wants to spend at most $350 for the party, how many people can she invite to her party

Difference in miles travelled by Bus X and Y is  12.8 miles in distance

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route. In other words, velocity is a vector, whereas speed is a scalar number.

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar number. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The length of the entire journey taken to go from one point to another is the distance traveled. Travel distance is not a vector.

Bus X travels 40 miles in 1 hour

Distance travelled in 2 hrs = 40*2 = 80 miles

Bus Y travels 60 miles per hour

Distance travelled in 1.12 hrs = 60*1.12 = 67.2 miles

Difference in miles travelled by Bus X and Y is = 80 - 67.2 = 12.8 miles

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The reflection of  f(x)=6(x–7)2+2 is g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.

What is the reflection of a function?

A reflection is a transformation of the graph of a function over the x-axis or the y-axis (or both). The function retains its basic shape; however, by including a negative sign in the appropriate place in the equation, the graph of the function will flip over one or the other of the axes.

To find the reflection of a function across the x-axis, we can simply multiply the function's y-coordinate by -1.

For f(x) = 6(x–7)^2 + 2,

the reflection across the x-axis is

g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.

Hence, the reflection of  f(x)=6(x–7)2+2 is g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.

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The quantity of fencing that the gardener would need to purchase would be = 1 5/12.

The total quantity of fencing the gardener needs to fence the the square garden = 4⅔

The length of one side of the garden = 3¼

The quantity of fencing the gardener needs to purchase would be = x

4⅔ = 3¼ + X

14/3 = 13/4 + X

X = 14/3 -13/4

X =56-39 /12

X= 17/12

X = 1 5/12ft.

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If a researcher finds that the probability of a word recognition program correctly interpreting a hand-written word is 9/10 . The number of  words that  the researcher expect the program to interpret correctly out of 40 words is 36 words.

Using this formula to find the number of words

Number of words = Probability of correctly interpreting a hand-written word × Expected words

Let plug in  the formula

Number of words = 9/10 × 40

Number of words = 36 words

Therefore we can conclude that the number of words is 36 words.

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By grouping like terms and taking common factors, we will see that the addition of the polynomials gives:

(6x^2 - 3) + (8x^2 - 5x - 1) = 14x^2 - 5x - 4

Here we want to add two polynomials:

6x^2 - 3

And

8x^2 - 5x - 1

To make that addition, we just need to group like terms and take common factors.

We start with:

(6x^2 - 3) + (8x^2 - 5x - 1)

Grouping like terms we will get:

(6x^2 + 8x^2) + (-5x) + (-3 - 1)

Now we can simplify that, so we will get:

(6 + 8)*x^2 - 5x - 4

14x^2 - 5x - 4

That is the addition of the polynomials.

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Given an arithmetic sequence with the first term -6 and the common difference -7, the first five terms are: -6, -13, -20, -27, -34.

The formula for the n-th term of an arithmetic sequence is given by:

a(n) = a(1) + (n - 1) d

Where:

a(1): the first term

d = common difference

The consecutive terms of an arithmetic sequence can be obtained as:

a(n) = a(n - 1) + d

Information available in the problem:

first term = a(1) = -6

common difference = d = -7

Hence,

a(1) = -6

a(2) = -6 - 7 = -13

a(3) = -13 - 7 = -20

a(4) = -20 - 7 = -27

a(5) = -27 - 7 = -34

Therefore the first five terms are: -6, -13, -20, -27, -34

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WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.

If quadrilateral WXYZ is a parallelogram, the opposite sides will be equal, in length from which the value of x will satisfy the two equations.

Given,

WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

The length of the opposite sides of a parallelogram are equal, which gives;

2x - 5 = x + 2

2x - x = 2 + 5

x = 7

Similarly, we have;

x + 8 = 15

x = 15 - 8 = 7

The lengths of the opposite sides are therefore;

2·x - 5 = 2 × 7 - 5 = 9 and x + 8 = 15

The option that indicates if WXYZ is a parallelogram is therefore;

WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

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WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent best explains that WXYZ is not a parallelogram.

Therefore the answer is d) WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.

A parallelogram is a quadrilateral with two pairs of parallel sides. This means that the sides of the quadrilateral are arranged such that opposite sides are parallel and have the same length. In other words, if you draw a line through one pair of opposite sides, the other pair of opposite sides will also be parallel to that line and have the same length.

So, to determine if a quadrilateral can be a parallelogram, we need to check if it has two pairs of parallel and congruent sides. It does not matter what the lengths of the sides are.

In this case, option (d) is the correct answer because it states that one pair of sides can be congruent, but the other pair of sides is not congruent, which means that the quadrilateral cannot be a parallelogram

--The question is incomplete, complete question is given below--

"Which best explains if quadrilateral WXYZ can be a parallelogram?

a) WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

b) WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm.

c) WXYZ cannot be a parallelogram because there are three different values for x when each expression is set equal to 15.

d) WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent."

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The y-coordinate of the point (-3, p) is p = 0.

A line can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

In this case, the slope of the line is given as -3, and the line passes through the point (-4, 3). We can use this information to write an equation for the line in the form y = mx + b:

y = (-3)x + b

We are told that the line passes through the point (-4, 3), so we can substitute these values into the equation to find the value of b:

3 = (-3)(-4) + b

3 = 12 + b

-9 = b

Therefore, the equation for the line is y = -3x - 9.

To find the value of p, we need to substitute the x-coordinate (-3) into the equation and solve for y:

y = (-3)(-3) - 9

y = 9 - 9

y = 0

Therefore, the y-coordinate of the point (-3, p) is p = 0.

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The y-coordinate of the point (-3, p) is p = 0.

Now, According to the question:

y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line. The slope or gradient of a line describes how steep a line is. It can have either a positive or a negative value. When a standard form of a linear equation is of the form Ax + By  = C, where 'x' and 'y'  and 'C' are variables and 'A', 'B' are constants, the slope-intercept form is the most preferred way of expressing a straight line due to its simplicity, as it is very easy to find the slope and the 'y intercept' from the given equation.

In this case, the slope of the line is given as -3, and the line passes through the point (-4, 3). We can use this information to write an equation for the line in the form y = mx + b:

y = (-3)x + b

We are told that the line passes through the point (-4, 3), so we can substitute these values into the equation to find the value of b:

3 = (-3)(-4) + b

3 = 12 + b

-9 = b

Therefore, the equation for the line is y = -3x - 9.

To find the value of p, we need to substitute the x-coordinate (-3) into the equation and solve for y:

y = (-3)(-3) - 9

y = 9 - 9

y = 0

Therefore, the y-coordinate of the point (-3, p) is p = 0.

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Answer:

x = - 12 , x = 13

Step-by-step explanation:

x² - x = 156 ( subtract 156 from both sides )

x² - x - 156 = 0 ← in standard form

(x - 13)(x + 12) = 0 ← in factored form

equate each factor to zero and solve for x

x + 12 = 0 ⇒ x = - 12

x - 13 = 0 ⇒ x = 13

The first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3. (Option C)

In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like ^n for a nonnegative integer n. For a binomial series, the formula for the expansion of any terms is given by

(1+x)^m=1+mx+  m(m-1)/2! x^2+  m(m-1)(m-2)/3! x^3+⋯.

For the given function (1+ x/4)^(-2)

m = -2

x = x/4

Hence, using the above expansion formula

The first term = 1

The second term = mx = (-2)(x/4) = -x/2

The third term =m(m-1)/2! (x/4)^2=  (-2(-2-1))/(2*1*16) x^2=3/16 x^2

The fourth term = m(m-1)(m-2)/3! (x/4)^3=(-2(-2-1)(-2-2))/(3*2*1*64) x^3=-1/16 x^3

Hence, the first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3.

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Answer:

excluded values

y=0

Simplify the expression

3xy−5/y

​

Step-by-step explanation:

By solving a system of equations we will see that she has 9 quarters and 15 dimes.

Let's define the variables.

We know that Moolah has 24 coins, then:

d + q = 24

And the total value is $3.75, then:

q*0.25 + d*0.10 = 3.75

Then we can write the system of equations:

d + q = 24

q*0.25 + d*0.10 = 3.75

We can isolate d on the first equation to get:

d = 24 - q

Replacing that in the other equation we will get:

q*0.25 + (24 - q)*0.10 = 3.75

q*0.15 + 2.4 = 3.75

q*0.15 = 3.75 - 2.4

q*0.15 = 1.35

q = 1.35/0.15 = 9

So Moolah has 9 quarters and 15 dimes.

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Identify two points for each line and connect to graph lines.

Consider that x = 1 is the critical point, which gives us one included point (1, 0) marked as closed circle and one excluded point (1, 3) marked as open circle.

The second point for the first line is selected at x = - 3, which is (-3, 4) and for the second line is selected at x = 3, which is (3, 7).

See the lines attached.

Answer:

Below

Step-by-step explanation:

To find the number of games g that the team could lose and still be eligible for the playoffs, we can write the inequality:

g / 18 ≤ 40%

g / 18 ≤ 0.4

g ≤ 7.2

We can round down to 7 to get the maximum number of games the team could lose and still be eligible for the playoffs.

If the baseball team loses 8 of its remaining games, they will not advance to the playoffs. This is because 8 is greater than the maximum number of games they could lose and still be eligible for the playoffs, which is 7.

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Answer:

  y ≤ -3/2x -2

Step-by-step explanation:

You want the inequality shown on the graph that has a solid line through points (0, -2) and (2, -5).

The slope of the solid boundary line can be found from the slope equation:

  m = (y2 -y1)/(x2 -x1)

  m = (-5 -(-2))/(2 -0) = -3/2

The y-intercept is the point marked on the y-axis: (0, -2).

The boundary line has the slope-intercept equation ...

  y = mx +b . . . . . . . . where m is the slope and b is the y-intercept

  y = -3/2x -2

The shading is to the left and below the boundary line, so y-values in the shaded area are less than those on the line. The inequality reflects this:

  y ≤ -3/2x -2

__

Additional comment

The solid boundary line is included in the solution set, so we use the ≤ symbol, instead of the < symbol that excludes the line. When the < symbol is used, the boundary line is dashed.

We use the term "y-intercept" to refer to both the ordered pair that describes the point on the y-axis, (0, -2), and the y-value in that ordered pair, -2. We understand the x-value of any point on the y-axis is 0.

The given expression [tex]x^{2} +8x+15[/tex] , can be expressed in completely factored form as [tex](x+5)(x+3)[/tex] .

The expression that is to be written in factored form is [tex]x^{2} +8x+15[/tex] ;

we will use the split the middle term method to express it in factored form , in this method we split the middle term and then write down the common factors .

the middle term [tex]8x[/tex] can be written as [tex]3x+5x[/tex] ;

we get ; [tex]x^{2} +3x+5x+15[/tex] ;

taking "x" common from first 2 terms and "5" common from the next two terms ,

we get ;

⇒ [tex]x(x +3)+5(x+3)[/tex] ;

⇒ [tex](x +3)(x+5)[/tex] ;

So , we get that the expression [tex]x^{2} +8x+15[/tex] is equivalent to [tex](x +3)(x+5)[/tex] .

Therefore , the completely factored form is [tex](x +3)(x+5)[/tex] .

The given question is incomplete , the complete question is

What is the completely factored form of the expression [tex]x^{2} +8x+15[/tex] ?

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The equation y = 3/5 x is graphed on a coordinate plane and attached

The equation is graphed using some points for the input which is x values and solving to get the y values

This is called the table of values used to plot on the coordinate plane

The table of values for y = 3/5 x is formed as follows

For x = -10, y = 3/5 * -10 = -6

For x = -5, y = 3/5 * -5 = -3

For x = 0, y = 3/5 * 0 = 0

For x = 5, y = 3/5 * 5 = 3

For x = 10, y = 3/5 * 10 = 6

table of values

x     y

-10  -6

-5   -3

0     0

5     3

6     6

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The probability that three points chosen uniformly and independently on a circle fall on a semicircle is 1/2 or 50%.

The probability of three points chosen randomly and independently on a circle falling on a semicircle is 1/2, or 50%. This is because the probability of a point landing on either side of the semicircle is equal. The points are chosen on a circle, so each point has an equal probability of being on either side of the semicircle. Therefore, the probability of three points randomly chosen on a circle landing on a semicircle is 1/2 or 50%.

Let A, B, and C be the three points chosen on a circle.

The probability that A, B, and C fall on the semicircle is:

P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

= (1/2) x (1/2) x (1/2)

= (1/2)^3

= 1/8

Therefore, the probability that three points chosen randomly and independently on a circle fall on a semicircle is 1/8 or 12.5%.

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The probability that three points chosen uniformly and independently on a circle fall on a semicircle is written as 1/8.

The term probability in math is defined as the chances of something materializing based upon the ratio of its number of outcomes to the number of outcomes of the whole sample space the event relies upon.

While we looking into the given question, here let us consider that A, B, and C be the three points chosen on a circle.

Then the probability that A, B, and C fall on the semicircle is calculated as,

=> P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

Now, we have to apply the value of each probability, then we get

=> (1/2) x (1/2) x (1/2)

Therefore, the resulting value is

=> (1/2)³ = 1/8

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The equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

The equation of the tangent to the curve y = f(x), passing through the point (a, b) can be written as -

(y - b) = (dy/dx) (x - a)

Given is the curve y = f(x) = x⁴ + 6x² − x.

The given curve is -

y = x⁴ + 6x² − x

f'(x) = dy/dx = d(x⁴ + 6x² − x)/dx

f'(x) = dy/dx = 4x³ + 12x + 1

Now -

f'(x){1, 6} = (dy/dx){1, 6} = 4 x 1 x 1 x 1 + 12 x 1 + 1

f'(x){1, 6} = 17

We can write the equation as -

(y - 6) = 17(x - 1)

Therefore, the equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

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The percentage of students in eighth grade who have music is 60%

Total number of eighth grade students = 75

Number of students who goes to music class = 45

Number of students who have art = Total number of eighth grade students - Number of students who goes to music class

= 75 - 45

= 30

Percentage of students who have art = Number of students who have art / Total number of eighth grade students × 100

= 30/75 × 100

= 0.4 × 100

= 40%

Percentage of students who have music = Number of students who have music / Total number of eighth grade students × 100

= 45/75 × 100

= 0.6 × 100

= 60%

Hence, 60% of the eighth grade students have music.

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Answer:

6 & 21

Step-by-step explanation:

Let x be the smaller number. Let y be the larger number.

We have:
x + y = 5x - 3

However, we also know the larger number is 2x + 9 (nine more than twice the smaller). So, we can plug in 2x + 9 for y:

x + (2x + 9) = 5x - 3

x + 2x + 9 = 5x - 3

3x + 9 = 5x - 3

9 = 2x - 3

12 = 2x

x = 6

Now solver for the larger:

2x + 9 = 6*2 + 9 = 12 + 9 = 21

Therefore, the numbers are 6 and 21.

I hope this helps :D

Answer: 56

Step-by-step explanation:

There are 8 runners competing in the 400-meter race, and the fastest 3 runners win a ribbon. This means that there are 3 places that the runners can finish in: first, second, and third.

Since the order in which the runners finish matters, we need to use permutations to find the number of ways that the runners can finish in first, second, and third place.

The number of permutations of a set of n objects taken r at a time is given by the formula:

n! / (n - r)!

In this case, there are 8 runners, so n = 8, and we are selecting 3 runners at a time, so r = 3. Plugging these values into the formula gives us:

8! / (8 - 3)! = 8! / 5! = 8 * 7 * 6 / 5 * 4 * 3 = 56

Therefore, there are 56 ways that the runners can finish in first, second, and third place.

Answer:

The answer is D

Step-by-step explanation:

Trust me on this, its hard to explain but Im 100% sure.

Answer:

13 square centimeters.

Step-by-step explanation:

There are 13 squares making up the shape

The area of the parallelogram is 500 in squared

A parallelogram is a four sided polygon that has opposite sides parallel to each other.

The formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.

A= bh

From the figure, b = 20 in, h= 25 in

Area = 20*25 = 500 in square

Conclusively, taking into consideration the height of the parallelogram as 25 in and the base as 20 in, the area is given as 500 in square

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The value of the vertex(central) angle EJF formed by the given polygon is; 30°

To find the central angle of a polygon, we will simply divide 360 degrees by the number of sides of the polygon.

Now, we are told that the sum of the central vertex angles sums up to 180 degrees. Now, by careful observation, we can tell that the number of isosceles triangles that will be formed in the semi circle are 6. Thus;

Number of polygon sides of the semi circle = 6 sides

Thus;

Central angle = 180/6

Central angle = 30°

Now, we know that the base of isosceles triangles are equal. Since we know that the sum of angles in all triangles is 180 degrees, then we can say that;

∠E = ∠F = [180 - 30]/2

∠E = ∠F = 75°

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The value of x from the given quadrilateral is 3.

A rhombus is a closed two-dimensional plane figure. It is considered a special parallelogram, and because of its unique properties, it gets an individual identity as a quadrilateral. A rhombus is also called an equilateral quadrilateral since all of its sides are equal in length.

Given that, rhombus (6x + 32)º and (17x - 1)º for what value of x is the figure given the special parallelogram.

A rhombus has two diagonals that bisect each other at right angles and diagonal bisects angles.

Now, (6x + 32)º=(17x - 1)º

17x-6x=32+1

11x=33

x=3

Therefore, the value of x is 3.

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The correct option is option a) The critical value depends on the number of categories, not the sample size.

The critical value for a chi-square test is determined by the level of significance (alpha) and the degrees of freedom (df). The degree of freedom is a function of the number of categories in the test, not the sample size. Therefore, increasing the sample size does not affect the critical value for a chi-square test.

The chi-square test is a statistical test used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. It is used to test the independence of two categorical variables.

Therefore, The correct option is option a) critical value depends on the number of categories, not the sample size.

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