The school that Kathryn goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 1 adult ticket and 8 student tickets for a total of $56. The school took in $14 on the second day by selling 1 adult ticket and 1 student ticket. What is the price of each of on adult ticket and one student ticket

a) -32.06 (To the nearest hundredth)

b) -37.7 (To the nearest tenth)

c) 3.1 (To the nearest tenth)

d) 5.86  (To the nearest hundredth)

f) -4.33  (To the nearest hundredth)

g) 11.44  (To the nearest hundredth)

h) 62x + 45 = 38x + 79

i) 46y - 18 = -37y

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=), and shows the relationship between the variables present in the equation. Equations are used to model real-world problems and find solutions to various mathematical problems.

They can be solved for a specific variable by using various mathematical methods and techniques.

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Answer:

is 41 and 7 are seperated like

a=41

b=7

c=35

Then yes it could make an obtuse scalene triangle

Step-by-step explanation:

Answer:

-0.38

Step-by-step explanation:

0.6-(0.7)(1.4)

0.6-0.98

-0.38

Answer:

C, adding -1 1/2 to the coordinate of point J.

Step-by-step explanation:

J= 1 1/5

Equation : 1 1/5+(-1 1/2)

Use distributive property and by multiplying the + sign by the negative #, you get a negative.

- positive x negative = negative

So, : 1 1/5-1 1/5

= 0

The value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

-5x - 10y = 30 and - 3x + 3y = 27

Solve by using the elimination method,

Divide the equation - 3x + 3y = 27 by 3 and equation -5x - 10y = 30 by 5 on both sides,

(- 3x + 3y) / 3 = 27 / 3  and (-5x - 10y) / 5 = 30 / 5

-x + y = 9  and -x - 2y = 6

Subtract equation

-x + y = 9 - (-x - 2y = 6)

-x + y - 9 = x - 2y - 6

y = 3

and - x + 3 = 9, x = -6

Therefore, the value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.

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The image you described features a number line that goes from 0 to 6.5 in increments of 0.5.

On this number line, there is an arrow that starts at 0 and extends to 2.5, and then continues from 2.5 to 5.

This image can be visualized as follows:

0        1        2        3        4        5        6        6.5

|--------|--------|--------|--------|--------|--------|--------|

        |------------------------|------------------------|

             0 to 2.5                 2.5 to 5

The vertical lines represent the increments of 0.5 on the number line, and the arrow indicates the segments from 0 to 2.5 and from 2.5 to 5.

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Answer:

3/4

Step-by-step explanation:

The amount of cash generated is 78.75 Million.

Price-sales ratio, often known as the P/S ratio or PSR, is a stock valuation indicator. It is computed by dividing the market capitalization of the company by its most recent fiscal year's revenue, or, equivalently, by dividing the share price of the stock by its revenue per share.

The sales ratio will be calculated as below:-

Sales= $450  Million

Fixed Assets= $225  Million

% of capacity utilized. . 65%

Sales at full capacity = actual sales/%of capacity used = 692.31 millions dollars .

Target FA = Full capacity FA/sales = FA/Capacity sales = 32.50%

(225*65% = 146.25, 146.25/450 = 32.50%)

Optimal FA = sales * targeted FA/Sales Ratio = 450*32.50% = 146.25

Cash Generated = Actual FA-optimal FA = 225-146.25 = 78.75 millions dollars

Therefore, the amount of cash generated is 78.75 Million.

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Considering the definition of parallel line, the correct answer is the second option: if the slope of line a is -4, then the slope of a line parallel to it is -4.

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope "m" and different y-intercepts "b".

If the slope of line a is -4, then the slope of a line parallel to it is -4 because two lines are parallel have the same slope "m".

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Answer:

A = 378 in²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = \(\frac{1}{2}\) h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here b₁ = 6 + 15 + 6 = 27 , b₂ = 15 ( equal to middle section of b₁ ), h = 18, so

A = \(\frac{1}{2}\) × 18 × (27 + 15) = 9 × 42 = 378 in²

The graph of the equation 3x + 4y = 0 is a straight line with a negative slope passing through the origin.

The given equation, 3x + 4y = 0, represents a linear graph in the Cartesian coordinate system. Let's analyze its characteristics.

First, note that the equation is in the standard form for a linear equation, which is Ax + By = C, where A, B, and C are constants. In this case, A = 3, B = 4, and C = 0.

To graph this equation, we can rewrite it in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By isolating y, we have y = (-3/4)x + 0. Since the y-intercept (b) is 0, the line intersects the y-axis at the origin (0,0).

Next, we can examine the slope. The coefficient of x, -3/4, represents the ratio of the change in y (vertical) to the change in x (horizontal) as we move along the line. In this case, the slope is negative, indicating that the line descends from left to right. The magnitude of the slope, 3/4, implies that for every 4 units moved horizontally to the right, the line goes 3 units down vertically.

Therefore, we can conclude that the graph of the equation 3x + 4y = 0 is a straight line passing through the origin (0,0) with a negative slope. It extends indefinitely in both directions, with the line getting steeper as we move to the right.

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The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.

The population parameter is the true value of the statistic for the entire population. The probability that the statistic is obtained is the probability that it will be obtained in a single sample from the population. The variance of the values is the amount of variation among the values of the statistic in the sample. The formula for calculating the variance is the sum of the squared deviations from the mean, divided by the number of values in the sample. This can be written mathematically as: Variance = Σ (x - X)2/ n, where x is each value in the sample, X is the mean value, and n is the number of values in the sample.

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Answer:

Identity property is being used

Answer:

critical value = 1.645

The 90% confidence interval = ( -22.62, -17.58)

Step-by-step explanation:

Given that:

the sample  size \(n_1\) = 178

the sample size \(n_2\) = 226

the sample mean \(\overline x_1\) = 54.4

the sample mean \(\overline x_2\) = 74.5

population standard deviation \(\sigma_1\) = 18.58

population standard deviation \(\sigma_2\) = 9.52

level of significance ∝ = 1 - 0.90 = 0.10

The critical value for \(Z_{\alpha/2} = Z _{0.10/2} = Z_{0.005}\) is 1.645

For the construction of our confidence interval, we use 90% since that is used to find the critical value.

∴

The margin of error = \(Z \times\sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}}\)

\(1.645 \times\sqrt{\dfrac{18.58^2}{178} + \dfrac{9.52^2}{226}}\)

\(1.645 \times\sqrt{\dfrac{345.2164}{178} + \dfrac{90.6304}{226}}\)

\(1.645 \times\sqrt{2.34042}\)

\(\simeq\) 2.52

The lower limit = \(( \overline x_1 - \overline x_2) - (M.O.E)\)

= ( 54.4-74.5) - (2.52)

= -20.1 - 2.52

= -22.62

The upper limit = \(( \overline x_1 - \overline x_2) + (M.O.E)\)

= ( 54.4-74.5) + (2.52)

= -20.1 + 2.52

= -17.58

The 90% confidence interval = ( -22.62, -17.58)

\(x^2 -4x +1 = 0\)

According to the Zero-Product Property, if you have the Quadratic Equation, \((x +a)(x +b) =0\), it's roots will be \(x = -h\) and \(x = -k\).

If we want our roots to be \(2 -\sqrt 3\) and \(\frac{1}{2 -\sqrt 3}\\\), then \(-h = 2 -\sqrt 3\) and \(-k = \frac{1}{2 -\sqrt 3}\\\).

Solving for \(h\):

\(-h = 2 -\sqrt 3 \\ -h \cdot -1 = (2 -\sqrt 3) \cdot -1 \\ h = \sqrt 3 -2\)

Solving for \(k\):

\(-k = \frac{1}{2 -\sqrt 3} \\ -k \cdot -1 = \frac{1}{2 -\sqrt 3} \cdot -1 \\ k = \frac{1}{\sqrt 3 -2}\)

Writing the equation:

\((x +h)(x +k) = 0 \\ (x +(\sqrt 3 -2))(x +\frac{1}{\sqrt 3 -2}) = 0\)

Unsurprisingly, the answer shouldn't be that because it shouldn't be that easy. By that, we have to apply the distributive property.

\((x +(\sqrt 3 -2))(x +\frac{1}{\sqrt 3 -2}) = 0 \\ x(x +(\sqrt 3 -2)) +\frac{1}{\sqrt 3 -2}(x +(\sqrt 3 -2)) = 0 \\ x^2 +(\sqrt 3 -2)x +\frac{1}{\sqrt 3 -2}x +\frac{1}{\sqrt 3 -2}(\sqrt 3 -2) = 0 \\ x^2 +((\sqrt 3 -2) +\frac{1}{\sqrt 3 -2})x +1 = 0 \\ x^2 + (\frac{(\sqrt 3 -2)^2}{\sqrt 3 -2} +\frac{1}{\sqrt 3 -2})x +1 = 0 \\ x^2 +\frac{3 -4\sqrt 3 +4 +1}{\sqrt 3 -2}x +1 = 0 \\ x^2 +\frac{8 -4\sqrt 3}{\sqrt 3 -2}x +1 = 0 \\ x^2 +\frac{-4(\sqrt 3 -2)}{\sqrt 3 -2}x +1 = 0 \\ x^2 -4x +1 = 0\)

The quadratic equation will be y = (x - 2 - √3)[x - 1/(2-√3)].

Let b, c, d, and e be the zeroes of the polynomial. And 'a' be the leading coefficient.

Then the polynomial is given as,

⇒ a(x - b)(x - c)(x - d)(x - e)

The degree of the polynomial will be greater than or equal to the number of zeroes.

Write a quadratic equation if its roots are: 2-√3, and 1/(2-√3) assuming that the leading coefficient a = 1.

Then the equation of the quadratic equation will be

y = 1(x - 2 - √3)[x - 1/(2-√3)]

y = (x - 2 - √3)[x - 1/(2-√3)]

The quadratic equation will be y = (x - 2 - √3)[x - 1/(2-√3)].

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Answer:

B

Step-by-step explanation:

On edge

The probabilities is the greatest for a standard normal distribution is

P(-0.5 ≤ z ≤ 0.5) = 0.382.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically towards either extreme. The distribution's mean is another name for the centre of the range.

From the diagram attached below, we can write

1. P( -1.55 ≤ z ≤ -0.5)

= 0.092 + 0.15

= 0.242

or, 9.2%+15%=24.2%.

2. P( -0.5 ≤ z ≤ 0.5)

= 0.191 + 0.191

= 0.382

3. P( 0.5 ≤ z ≤ 1.5)

= 0.15 + 0.092

= 0.242

4. P( 1.5 ≤ z ≤ 2.5)

= 0.044 + 0.017

= 0.061

So, the greatest value is P(-0.5 ≤ z ≤ 0.5) = 0.382

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Mean of the data as per the increasing intervals data is 17.80.

The mean in statistics is calculated by multiplying all the values in a set of data by the total number of values for a given set of observations. To put it another way, all that is necessary to determine the mean of a set of data is to sum up all the values and divide the total by the number of values.

Now in the given table,

The midpoints of the intervals are as follows:

0+10/2 = 5

0+20/2 = 10

0+30 /2 = 15

0+40/2 = 20

0+50/2 = 25.

Now total students × interval midpoints are as follows:

5×5=25

10×10=100

15×14=210

20×17=340

25×20=500

Now, total no of students is = 5+10+14+17+20 = 66

So, mean of the data =

(25+100+210+340+500)/66

= 17.80

Therefore, mean of the data is 17.80.

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Let x be the number of hours spent typing by each student.

Since Mitchell can type at a speed of 3 pages per hour, and has already typed 9 pages, the expression that would model Mitchell's situation is:

Similarly, Roxanne can type at a speed of 2 pages per hour, and has already typed 12 pages, the expression that would model Roxanne's situation is:

Now, we know that after some time both will have the exact same page count. Let's call this number y. This way, we'll have two equations that describe a system of equations:

We'll solve it by substitution, so we'll solve the first equation for x, substitute in the second equation and then find the value of y, as following:

This way, we can conlcude that:

Since we've calculated an expression for x in terms of y , we just have to plug in this value in it to find the value of x:

Therefore, the solution to our system is:

This way, we can conclude that:

Answer:

19.048%

Step-by-step explanation:

The formula for the increase in cost will be :

[(New cost - Original Cost)÷Original Cost] × 100

So let's substitute values in from the question :

[(50-42)÷42] × 100

[8÷42] × 100

0.19048 × 100

19.048%

Hope this helped and have a good day

Answer:

Step-by-step explanation:

Area of a trapezoid is given by

where

a and b are the bases

h is the height

From the question

A = 135 m²

a = 20m

b = 7 m

Substitute the values into the above formula and solve for the height

That's

Divide both sides by 27

That's

We have the final answer as

Hope this helps you

Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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Answer:

Part A) y=1,100x + 4,500

Part B) 14,400

Step-by-step explanation:

Part A)

There is a base fee of $4,500, meaning that the line begins at y=4500 (i.e. The y-intercept is [0,4500], so 'b' in y=mx+b is 4,500). There is a $1,100 hourly rate, which is proportional to the value of x, the amount of hours filmed. Therefore, 'm' in y=mx+b is $1,100.

Thus, the final equation looks like:

y= 1,100x + 4,500

Part B)

x=9

y=1,100x+4,500

y=1,100(9)+4,500

y=9,900+4,500

y=14,400

Answer:

$30.60

Step-by-step explanation:

What we know:

The bill for Mr. Wilson's diner meal is $25.50.

He gives a 20% tip to the waiter.

To figure out this tip, multiply 1/5 by 25.5.

1/5 * 51/2

51/10 = $5.10 tip.

Here, it's asking for the total, including the $5.10 tip. So, add $5.10 to $25.50 for $30.60 total, including the tip.

(For a simpler method *multiply 6/5 by $25.5)

The cost of y glasses of sparkling cranberry juice is $2. 24

Algebraic expressions are described as expressions that consist of variables, factors, constants, terms and coefficients.

They are also described as expressions made up of mathematical operations, which includes;

From the information given, we have that;

Cost of y glasses of sparkling cranberry juice = 1/2($1.48) + 1($1.50)

Find the product

y = $0.74 + $1.50

Add the values

y = $2. 24

Hence, the value is $2. 24

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The dilation transformation of the triangle ABC by a scale factor of 3, with the point P as the center of dilation indicates;

Side A'B' will be parallel to side AB

Side A'C' will be parallel to side AC

Side BC will lie on the same line as side BC

A dilation transformation is one in which the dimensions of a geometric figure are changed but the shape of the figure is preserved.

The possible options, from a similar question on the internet are;

Be parallel to

Be perpendicular to
Lie on the same line as

The location of the point P, which is the center of dilation, and the lines PC and PA of dilation and the scale factor of dilation indicates that we get;

PB' = 3 × PB

PA' = 3 × PA

PC' = 3 × PC

Therefore; The side B'C' will be on the same line as the side BC

The Thales theorem, also known as the triangle proportionality theorem indicates that;

The side A'C' will be parallel to the side AC

The side A'B', will be parallel to the side AB

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Answer:

Andy basically has two stickers

Answer:

4 times

Step-by-step explanation:

The area of a circle is given by the formula A = πr², where "r" is the radius of the circle.

Let's calculate the areas of the two circles:

For the circle with a radius of 4 inches:

=> A₁ = π(4)² = 16π in²

For the circle with a radius of 2 inches:

=> A₂ = π(2)² = 4π in²

To find the ratio of the areas, we divide the area of the circle with a radius of 4 inches by the area of the circle with a radius of 2 inches:

=> A₁/A₂ = (16π) / (4π) = 4

Therefore, the area of a circle with a radius of 4 inches is 4 times greater than the area of a circle with a radius of 2 inches.

Answer:

d. We assume that the new golf ball has an average driving distance that is greater than or equal to that of the current ball. However, if the current model has a mean driving distance that is significantly longer, then we should reject our assumption.

Step-by-step explanation:

Given that :

μ1=population mean driving distance for the current golf ball

μ2=population mean driving distance for the new golf ball

H0 : μ1 - μ2 ≤ 0

H1 : μ1 - μ2 > 0

The Null hypothesis assumes that the average driving distance of the current golf ball is less than or equal to the average driving distance of the current golf ball

For the Alternative ; If there is significant evidence that the average driving distance of the current golf ball is greater or longer than the average driving distance of the new golf ball ;then we reject our initial claim (the Null hypothesis).