Suppose a sample of 400 participants was randomly selected from the middle schools and high schools in a large city. These participants responded to the question:

Which type of movie do you prefer to watch?

160 participants preferred action movies.
80 participants preferred drama movies.
40 participants preferred science-fiction movies.
240 participants were females.
78 female participants preferred drama movies.
32 male participants preferred science-fiction movies.
60 female participants preferred action movies.

Answer:

Step-by-step explanation:

\(\angle 2,\angle AEG, \angle GEB\)

we express the result in base $b$:  $b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$ (written in base $b$)

To find the result when the base-$b$ number $11011_b$ is multiplied by $b-1$ and then $1001_b$ is added, we can follow these steps:

Step 1: Multiply $11011_b$ by $b-1$.
Step 2: Add $1001_b$ to the result from step 1.
Step 3: Express the final result in base $b$.

To perform the multiplication, we can expand $11011_b$ as $1 \cdot b^4 + 1 \cdot b^3 + 0 \cdot b^2 + 1 \cdot b^1 + 1 \cdot b^0$.

Now, we can distribute $b-1$ to each term:

$(1 \cdot b^4 + 1 \cdot b^3 + 0 \cdot b^2 + 1 \cdot b^1 + 1 \cdot b^0) \cdot (b-1)$

Expanding this expression, we get:

$(b^4 - b^3 + b^2 - b^1 + b^0) \cdot (b-1)$

Simplifying further, we get:

$b^5 - b^4 + b^3 - b^2 + b^1 - b^4 + b^3 - b^2 + b^1 - b^0$

Combining like terms, we have:

$b^5 - 2b^4 + 2b^3 - 2b^2 + 2b^1 - b^0$

Now, we can add $1001_b$ to this result:

$(b^5 - 2b^4 + 2b^3 - 2b^2 + 2b^1 - b^0) + (1 \cdot b^3 + 0 \cdot b^2 + 0 \cdot b^1 + 1 \cdot b^0)$

Simplifying further, we get:

$b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$

Finally, we express the result in base $b$:

$b^5 - 2b^4 + 3b^3 - 2b^2 + 2b^1 + b^0$ (written in base $b$)

Know more about base-$b$ here:

https://brainly.com/question/31939284

#SPJ11

Use the Chinese remainder theorem.

Start with x = 3×5 + 2×7 = 15 + 14 = 29. Now,

• 29 ≡ 15 ≡ 1 (mod7)

• 29 ≡ 14 ≡ 4 (mod5)

Adjust for this by multiplying the first term in x by 3, and the second term by 3 (because 4×3 ≡ 12 ≡ 2 (mod5)).

So now x = 3×5×3 + 2×7×3 = 45 + 42 = 87, and

• 87 ≡ 45 ≡ 3 (mod7)

• 87 ≡ 42 ≡ 2 (mod5)

The CRT then says that x ≡ 87 (mod(7×5)) ≡ 87 (mod35), which is to say any number x = 87 + 35n satisfies both congruences (where n is any integer).

So there are 3 possible 2-digit numbers that work: {17, 52, 87}.

To confirm:

• 17 ≡ 15 + 2 ≡ 2 (mod5) and 17 ≡ 14 + 3 ≡ 3 (mod7)

• 52 ≡ 50 + 2 ≡ 2 (mod5) and 52 ≡ 49 + 3 ≡ 3 (mod7)

• 87 ≡ 85 + 2 ≡ 2 (mod5) and 87 ≡ 84 + 3 ≡ 3 (mod7)

The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

For more such questions on parallelogram visit:

https://brainly.com/question/970600

#SPJ8

Answer:

89999

Step-by-step explanation:

Answer:

  (x, y) = (-1, 5)

Step-by-step explanation:

You want to solve this system of equations by substitution.

The idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.

Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:

  5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y

  x +6 = 5 . . . . . . . . . . simplify

  x = -1 . . . . . . . . . subtract 6

  y = -2(-1) +3 = 5 . . . . . use the second equation to find y

The solution is (x, y) = (-1, 5).

__

Additional comment

Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.

Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.

  4x -y = 3   ⇒   y = 4x -3 . . . . . for example

The attached graph confirms the solution above.

Answer:

b. 402.62 m²

Step-by-step explanation:

The area of two triangles = 2(4×6/2) = 24 m²

The area of the 1st rectangle = 6 × 22 = 132 m²

The area of the 2nd rectangle = 7.21 × 22 = 158.62 m²

The area of the 3rd rectangle = 4 × 22 = 88 m²

Total = 24 + 132 + 158.62 + 88 = 402.62 m²

All of the aforementioned equations have the same solution except: C. y/3 - 5 = -5.

In Mathematics, an equation is said to have zero solution or no solution when the left hand side and right hand side of the equation are not the same or equal when simplified.

This ultimately implies that, an equation would have zero solution or no solution when both sides of the equal sign are not the same and the variables cancel out when simplified.

From the information provided, we have the following equation:

y/-1 - 6 = -5        

Adding 6 to both sides of the equation, we have:

y/-1 - 6 + 6 = -5 + 6

y/-1 = -1

Multiplying both sides of the equation, we have:

-1 × (y/-1) = 1 × -1

y = -1.

-y + 4 = 5

Rearranging the equation by collecting like terms, we have:

y = 4 -5

y = -1

y/3 - 5 = -5

Adding 5 to both sides of the equation, we have:

y/3 - 5 + 5 = -5 + 5

y/3 = 0

y = 0 (different solution).

2y - 5 = -7

Adding 5 to both sides of the equation, we have:

2y - 5 + 5 = -7 + 5

2y = -2

Dividing both sides of the equation by 2, we have:

y = -2/2

y = -1.

Read more on equation here: brainly.com/question/28949611

#SPJ1

A) the 90% Confidence Interval is (2.424, 7.576). B)  the 95% Confidence Interval is (2.24, 7.76).
C)  the 99% Confidence Interval is (1.16, 8.84). D) When sample size is increased, the width of the confidence interval decreases, if all the other factors remain constant.

The given problem is based on normal distribution of data and confidence intervals. A confidence interval provides a range of values for an unknown population parameter; the interval has an associated level of confidence that the true parameter value falls in the interval. The confidence level gives the probability that the interval produced will contain the true parameter of interest. Below are the answers for the given questions.

a. 90% Confidence Interval:
Here, the given data is: 4, 6, 3, 5, 9, and 3.  
To calculate the 90% Confidence Interval, we need to first calculate the sample mean and sample standard deviation of the given data.

Sample mean,

x¯ = (4 + 6 + 3 + 5 + 9 + 3) / 6 = 30 / 6 = 5

Sample standard deviation,

s = √[∑(xi - x¯)² / (n - 1)]
= √[(4 - 5)² + (6 - 5)² + (3 - 5)² + (5 - 5)² + (9 - 5)² + (3 - 5)² / (6 - 1)]
= √[14.0]
= 3.74166

Now, the Confidence Interval can be calculated as,

CI = x¯ ± Z_(α/2) (s / √n)
Where,
α = 1 - confidence level = 1 - 0.90 = 0.10
Z_(α/2) = Z_0.05 = 1.645   (From Z table)

CI = 5 ± 1.645 (3.74166 / √6)
CI = 5 ± 2.576
CI = (2.424, 7.576)

Therefore, the 90% Confidence Interval is (2.424, 7.576).

b. 95% Confidence Interval:
For a 95% Confidence Interval, α = 1 - 0.95 = 0.05 and Z_(α/2) = Z_0.025 = 1.96

CI = x¯ ± Z_(α/2) (s / √n)
CI = 5 ± 1.96 (3.74166 / √6)
CI = 5 ± 2.76
CI = (2.24, 7.76)

Therefore, the 95% Confidence Interval is (2.24, 7.76).

c. 99% Confidence Interval:
For a 99% Confidence Interval, α = 1 - 0.99 = 0.01 and Z_(α/2) = Z_0.005 = 2.58

CI = x¯ ± Z_(α/2) (s / √n)
CI = 5 ± 2.58 (3.74166 / √6)
CI = 5 ± 3.84
CI = (1.16, 8.84)

Therefore, the 99% Confidence Interval is (1.16, 8.84).

d. The effect of increasing the sample size on the width of the confidence intervals:
When sample size is increased, the width of the confidence interval decreases, if all the other factors remain constant. Here, sample mean and sample standard deviation are kept constant. Therefore, with larger sample sizes, the confidence intervals will become narrower.

Know more about Confidence Interval here,

https://brainly.com/question/32546207

#SPJ11

Answer:

Proper: 3 and 1/5  Improper: 16/5

Step-by-step explanation:

4 times 4/5 = 16/5

5*3=15

16-15= 1

3 and 1/5

\( \huge\color{skyblue}\boxed{\colorbox{black}{Answer ☘}}\)

Let's substitute x with 5 to find the value of given expression ~

The value of the expression is 60.

According to the BODMAS rule, when there is a mathematical expression with a bracket, the terms in the bracket should be solved first. So the value of the expression in the bracket would be solved first.

(3(5) + 5)

(15 + 5)

= 20

The second step is to multiply 20 by 3.

20 x 3 = 60

To learn more about multiplication, please check: https://brainly.com/question/3385014

Answer:

81/2

Step-by-step explanation:

you need to divid that o getter

This question is incomplete, the complete question is;

PROBLEM SOLVING WITH PERCENTS: You are planning a wedding reception for 75 guests that will take place in exactly 10 months. There are two different sites that you are contemplating using, with the stipulations on payments as described below. Determine the TOTAL cost of renting each location.

Rental of space = $68 per guest; Down payment = 25% of total cost; Payment due one month before the reception includes a 7.4% interest payment on the balance.

Answer:  Total Cost of Renting = $5312.29

Step-by-step explanation:

Given that;

Rental space = $68 per guest, down payment = 25%,  7.4% interest payment on the balance.

Total Cost of Renting = Down Payment + Remaining payment

Total Cost of Renting = $68 × Guests × 25% + ($68 × Guest - Down payment) ×  (1 + Interest *9/12)

Total Cost of Renting = $68 × 75 × 25% + ($68 × 75 - Down payment) × (1 + 7.40% × 9/12)

Total Cost of Renting = $1275 + ($5100 - 1273) × (1.0555)

Total Cost of Renting = $1275 + 4037.29

Total Cost of Renting = $5312.29

The transform ,D2Y(s) + 4DY(s) + 40Y(s) = (D+2)X(s) Therefore, the zero-input response of the system y0(t) is given asy0(t) = (e -2t) - 2(cos6t + sin6t) + 6/5

Given that, LTIC system described by the complex-root system is given below.(D2+4D+40)y(t)=(D+2)x(t)

The zero-input response of the response for an LTIC system is given by the initial conditions. The initial condition for the given system is given below.y0(0)=2 and y˙0(0)=16.78.

Using the Laplace transform method, find the transfer function of the given system .

1: Finding the Laplace Transform for the given system(D2+4D+40)y(t)=(D+2)x(t). First, we need to take the Laplace transform of both sides of the given equation. We know that the Laplace transform of y(t) and x(t) are Y(s) and X(s) respectively. Therefore, we get,D2Y(s) + 4DY(s) + 40Y(s) = (D+2)X(s)

2: Solving for the Transfer Function. We know that transfer function is H(s)=Y(s)/X(s). Therefore, we getH(s)= (D+2)/(D2+4D+40)Taking the Laplace inverse of H(s) gives the zero-input response of the given system y0(t).

3: Finding the Zero-Input Response of the given system. We need to find the partial fraction of the transfer function. For that, solve the following equation.D2+4D+40 = 0. Using the quadratic formula, we get,D = -2 ± 6iTherefore, we get the partial fraction of the transfer function as, H(s)=1/(D+2) - 2/D + 3/5 + (3/5s)

Therefore, the zero-input response of the system y0(t) is given asy0(t) = (e -2t) - 2(cos6t + sin6t) + 6/5

Learn more about Laplace Transform here:

https://brainly.com/question/14487937

#SPJ11

The  value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

Learn more about Interval

brainly.com/question/4184136

#SPJ11

Answer:

See below

Step-by-step explanation:

\(X - Y = \begin{pmatrix} 1 & 2 & 7 \\ - 1 & 3 & 5 \\ 3 & 1 & 7 \end{pmatrix} \\\\ X + Y = \begin{pmatrix} 1 & 0 & 1 \\ 1 & 1 & 3 \\ - 1 & 3 & 3 \end{pmatrix} \\ adding \: both \: the \: matrices \\ \\ X - Y + X + Y \\ = \begin{pmatrix} 1 & 2 & 7 \\ - 1 & 3 & 5 \\ 3 & 1 & 7 \end{pmatrix} + \begin{pmatrix} 1 & 0 & 1 \\ 1 & 1 & 3 \\ - 1 & 3 & 3 \end{pmatrix} \\\\ 2X= \begin{pmatrix} 1 + 1 & 2 + 0 & 7 + 1 \\ - 1 + 1 & 3 + 1 & 5 + 3\\ 3 - 1 & 1 + 3 & 7 + 3 \end{pmatrix} \\ \\ 2X= \begin{pmatrix} 2 & 2 & 8 \\ 0 & 4 & 8\\ 2 & 4 & 10 \end{pmatrix} \\ \\ X= \frac{1}{2} \begin{pmatrix} 2 & 2 & 8 \\ 0 & 4 & 8\\ 2 & 4 & 10 \end{pmatrix}\\ \\ X= \huge\begin{pmatrix} \frac{2}{2} & \frac{2}{2} & \frac{8}{2} \\ \\ \frac{0}{2} & \frac{4}{2} & \frac{8}{2}\\ \\ \frac{2}{2} & \frac{4}{2} & \frac{10}{2} \end{pmatrix} \\ \\ \huge \red{X= \begin{pmatrix} 1 & 1 & 4\\ \\ 0 & 2 & 4\\ \\ 1 & 2& 5 \end{pmatrix}} \\ \\ subtracting \: the \: value \: of \: x \: from \: matrix \: (2) \\ \\ X + Y - X \\ = \begin{pmatrix} 1 & 0 & 1 \\ 1 & 1 & 3 \\ - 1 & 3 & 3 \end{pmatrix} - \begin{pmatrix} 1 & 1 & 4 \\ 0 & 2 & 4\\ 1 & 2& 5 \end{pmatrix} \\ \\ Y = \begin{pmatrix} 1 - 1 & 0 - 1 & 1 - 4 \\ 1 - 0& 1 - 2 & 3 - 4 \\ - 1 - 1 & 3 - 2 & 3 - 5 \end{pmatrix} \\ \\ \huge \purple{Y = \begin{pmatrix} 0 & - 1 & - 3 \\ 1 & - 1 & - 1 \\ - 2 & 1 & - 2 \end{pmatrix}}\)

We can conclude that the socioeconomic class of the offender is related to the likelihood of arrests.

Based on the information provided, we can conclude that there is a significant relationship between arrests and the socioeconomic class of the offender.
Identify the chi-square critical score: 9.488

Identify the chi-square test statistic: 12.2
Compare the test statistic to the critical score:

If the test statistic (12.2) is greater than the critical score (9.488), then there is a significant relationship between the variables.
In this case, 12.2 > 9.488, so there is a significant relationship between arrests and the socioeconomic class of the offender.
For similar question on socioeconomic.

https://brainly.com/question/31093929  

#SPJ11

Answer:8

Step-by-step explanation:

You are wanting a negative 1

So you start by getting to zero would take 7 “jumps”

Then u need to get into the negative by one

So when you go back one you get 8 jumps total

Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

The correct options regarding the triangle will be:

A)Height: 2.75 CM

Base: 1.76 CM

D)Height: 1.25 cm

Base:0.8 cm

E) height: 2 cm

base: 1.28 cm

We know that if the height and base of triangle B are proportional to the height and base of triangle A, then their ratios of the height to the base must be equal

We need to find out the ratio of the height to the base of triangle A

= 2.75 / 1.75= 1.5

D)Height: 1.25 cm

Base:0.8 cm

= 1.25 / 0.8

= 1.56

E) height: 2 cm

base: 1.28 cm

This also gives 1.56

The correct options are A D and E.

Learn more about triangles on

https://brainly.com/question/13750574

#SPJ1

The coordinates of the points in the table indicates that the coordinates of the image following the reflections, can be presented on the coordinate plane as shown in the attached graph created with MS Excel.

A reflection transformation is one in which the mirror image of the preimage is created across a line of reflection.

The coordinate points of the image after the specified reflections can be presented as follows;

Original   \({}\)Reflection across the x-axis   Reflection across the y-axis   y = -x

(0, 15)      \({}\) (0, -15)                                      (0, 15)                                   (-15, 0)

(1,  15)      \({}\) (1, -15)                                       (-1, 15)                                   (-15, -1)

(1, 13)      \({}\)  (1, -13)                                       (-1, 13)                                    (-13, -1)

(3, 15)      \({}\) (3, -15)                                      (-3, 15)                                   (-15, -3)

(3, 12)      \({}\) (3, -12)                                      (-3, 12)                                   (-12, -3)

(1, 10)      \({}\)  (1, -10)                                      (-1, 10)                                     (-10, -1)

(1, 8)      \({}\)   (1, -8)                                        (-1, 8)                                      (-8, -1)

(3, 10)      \({}\)(3, -10)                                      (-3, 10)                                    (-10, -3)

(3, 7)      \({}\)  (3, -7)                                       (-3, 7)                                      (-7, -3)

(1, 5)      \({}\)  (1, -5)                                        (-1, 5)                                      (-5, -1)

(1, 2)      \({}\)  (1, -2)                                        (-1, 2)                                      (-2, -1)

(4, 4)      \({}\) (4, -4)                                       (-4, 4)                                      (-4, -4)

(5, 7)      \({}\) (-5, 7)                                       (5, -7)                                      (-7, -5)

(7, 8)      \({}\) (7, -8)                                       (-7, 8)                                      (-8, -7)

(6, 5)     \({}\)  (6, -5)                                      (-6, 5)                                      (-5, -6)

(8, 6)     \({}\)  (8, -6)                                      (-8, 6)                                      (-6, -8)

(9, 9)     \({}\)  (9, -9)                                      (-9, 9)                                      (-9, -9)

(11, 10)     \({}\) (11, -10)                                   (-11, 10)                                    (-10, -11)

(10, 7)     \({}\)  (10, -7)                                   (-10, 7)                                     (-7, -10)

(12, 8)     \({}\)  (12, -8)                                   (-12, 8)                                    (-8, -12)

(13, 6)     \({}\)  (13, -6)                                   (-13, 6)                                    (-6, -13)

(11, 5)      \({}\)  (11, -5)                                    (-11, 5)                                     (-5, -11)

(14, 4)      \({}\) (14, -4)            \({}\)                       (-14, 4)                                     (-4, -14)

(12, 3)     \({}\)  (12, -3)                                   (-12, 3)                                     (-3, -12)

(9, 4)      \({}\)  (9, -4)                                    (-9, 4)                                       (-4, -9)

(7, 3)      \({}\)  (7, -3)                                     (-7, 3)                                       (-3, -7)

(10, 2)    \({}\)  (10, -2)                                   (-10, 2)                                     (-2, -10)

(8, 1)      \({}\)  (8, -1)                                      (-8, 1)                                       (-1, -8)

(5, 2)     \({}\)  (5, -2)                                     (-5, 2)                                      (-2, -5)

(2, 0)     \({}\)  (2, 0)                                      (-2, 0)                                      (0, -2)

The above coordinate points can be used to plot the graphs showing the image of the points following the specified reflections across the x-, y-, and y = -x, axis.

Please find attached the required graph of the coordinate points following the reflection transformations, created with MS Excel.

Learn more on reflection transformation here: https://brainly.com/question/29080489

#SPJ1

In the first scenario, a 6.50 percent coupon bond with 18 years left to maturity is priced at $1,035.25. We need to calculate the yield to maturity (interest rate) for this bond, assuming semi-annual compounding.

Scenario 1: To find the yield to maturity for the 6.50 percent coupon bond, we can use the present value formula for bond pricing. The formula is: \(Price = C * [1 - (1 + r)^{(-n)}] / r + F / (1 + r)^n\), where C is the coupon payment, r is the yield to maturity (interest rate), n is the number of periods, and F is the par value. Plugging in the given values, we have \($1,035.25 = (6.50/2) * [1 - (1 + r/2)^{(-182)}] / (r/2) + 1000 / (1 + r/2)^{(182)}\). Solving this equation for r will give us the yield to maturity.

Scenario 2: To find the coupon rate for the bond purchased at $1,135.90, we can again use the present value formula, but this time we need to solve for C. Rearranging the formula, we have \(C = (r * F) / (1 - (1 + r)^{(-n)})\), where C is the coupon payment, r is the required return (interest rate), F is the par value, and n is the number of periods.

Plugging in the given values, we have \(C = (0.08 * 1000) / (1 - (1 + 0.08)^{(-10*2)})\). Solving this equation for C will give us the coupon rate.

By solving the equations in both scenarios using the appropriate compounding periods, we can find the answers for the coupon rate and the yield to maturity.

Learn more about compounding here:

https://brainly.com/question/3433240

#SPJ11

If it is impossible for events A and B to occur simultaneously, the events are said to be mutually exclusive. For such events, P(A or B) is equal to the sum of the individual probabilities of events A and B.

In other words, if A and B are mutually exclusive events, the probability of A or B occurring is equal to the sum of the probabilities of A and B individually.

Mathematically, P(A or B) = P(A) + P(B).

This holds true because when two events are mutually exclusive, the occurrence of one event excludes the possibility of the other event happening at the same time. Therefore, there is no overlap in the outcomes, and we can simply add their probabilities to calculate the probability of either event occurring.

for such more question on probabilities

https://brainly.com/question/13604758

#SPJ11

Answer:

angle SXV

Step-by-step explanation:

Answer:

$36.97  

The cost of the meal was $32.57 and he used a 10% off coupon. You can make 10% equal to 0.1 because . Now do . This is the discount, so you want to subtract this from the original to get the actual price of the meal, .

The tax was 8% so this means he is adding

ANSWER

EXPLANATION

There are six students in the class.

There are 7 days in a week. There are 2 days in the weekend. There are 5 weekdays.

The probability that any student is born on the weekend is given as:

P(weekend) = 2/7

The probability of being born on a weekday is:

P(weekday) = 5/7

Now the probability that 4 out of the six students is born on a weekend will be given as the products of four of them born on a weekend and the remaining two born on a week day:

That is the probability that 4 out of 6 of them are born on a weekend.

The graph that represents the function g(x) = (1/2)^x is given as follows:

The last graph.

The parent function f(x) has the definition presented as follows:

f(x) = 2^x.

The transformation that the function f(x) undergoes is defined as follows:

Reflection over the y-axis.

The rule that defines a function g(x) after a reflection of f(x) over the y-axis is given as follows:

g(x) = f(-x).

Hence the function g(x) is defined as follows:

g(x) = f(-x) = 2^(-x) = (1/2)^x.

As the negative exponent means that the base is inverted.

Then the graph of the exponential function has these following features:

Hence the last graph is the correct option.

More can be learned about reflections at https://brainly.com/question/28980122

#SPJ1

Answer:

9 students have pets

Step-by-step explanation:

From the above question, we are given the following information

Total number of students = 30

Let Pet Dog = D

Pet Cat = C

Pet Fish = F

Number is students that have pet dog

(D) = 10 students

Number of students that have pet cat (C) = 13 students

Number of students that have pet fish (F) = 7 students

Number of students that have Pet dog and cat ( D and C) = 4 students

Number of students that have Pet cat and fish (C and F) = 6 students

Number of student that has pet dog and pet fish (D and F) = 2 students

1 student has all three = ( D and F and C)

Number of student that have a pet Dog only

= n(D) - [n( D and C) + n( D and F) - n(D and C and F)]

= 10 -( 4+ 2 -1)

= 10 - 5

= 5

Number of student that have Pet cat only

= n(C) -[ n( D and C) + n( C and F) - n( D and C and F)]

= 13 -( 4 + 6 - 1)

= 13 - 9

= 4

Number is student that have a pet fish only

= n(F) - [n (C and F) + n( D and F) - n( D and C and F)]

= 7 - [6 + 2 - 1]

= 7 - 7

= 0

The number of students that have pets is calculated as:

(Number of students that have dogs only + Number of student that have cats only + Number of students that have fish only)

= 5 + 4 + 0

= 9

Therefore only 9 students have pets.

Answer:

45

Step-by-step explanation:

divide 25 by 5 to see how they got that, which is 5. then multiply 9 by 5 bc you have to do the same thing, which is 45.

Answer:

5:9 = 25:45

Step-by-step explanation: