The original price of a skateboard, not including tax, was $96. Charlie bought the skateboard on sale, and he saved 30% off of the original price. What was the sale price of the skateboard?


A. 66. 00


B. 68. 80


C. 67. 20


D. 28. 80

The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.

In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ

where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.

To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.

We have , a = 5 , b = 12 , c= 13

cos α =( 12² + 13² - 5² )/2×12×13= 288/312

=> α = cos⁻¹(0.923 ) = 22.63°

cos β = (5² + 13² - 12² )/2×13×5 = 50/130

=> β = cos⁻¹(5/13) = 67.38°

cos γ = (12² + 5² - 13² )/2×12×5= 0

=> γ = cos⁻¹(0) = 90°

Hence, the required angles are 90°, 22.63°, 67.38°.

To learn more about law of cosines formula, refer:

https://brainly.com/question/4372174

#SPJ4

Answer:

2 or 3

Step-by-step explanation:

The perimeter and area of the given composite figure are:

Area = 50 cm²

Perimeter = 42 cm

To find the total surface area of the composite figure, we will find the area of each individual surfaces and then add them together.

Formula for area of a triangle is:

Area = ¹/₂ * base * height

Formula for area of a rectangle is:

Area = Length * Width

Thus:

T.S.A = 2(¹/₂ * 4 * 5) + (10 * 3)

T.S.A = 20 + 30

T.S.A = 50 cm²

The perimeter will be the sum of the entire boundary length. Thus:

Perimeter = 3 + 10 + 10 + 3 + 3 + 3 + 5 + 5

Perimeter = 42 cm

Read more about composite figure at: https://brainly.com/question/10254615

#SPJ1

Answer:

Step-by-step explanation:

A: quotient  

B: dividend

C: divider

1) The bowler's scores are shown on the horizontal axis, while the frequency is shown on the vertical axis.

2) Groups of 20 points are assigned to the scoring.

3) There are 30 bowlers competing.

4) The distribution is skewed towards the left.

A histogram is a bar graph that shows data that has been divided into equal intervals in terms of frequency. The bars must touch but not overlap, and they must be of equal width.

1) A histogram shows the type of data being measured on the horizontal axis and the number of observations in each bin on the vertical axis.
Here, the horizontal axis displays the bowlers' scores, and the vertical axis displays the frequency at each interval.

2) The categories or bins of the data are listed on the horizontal axis of a histogram. The height of the columns, which represents the frequency or quantity of the occurrences, is listed on the vertical axis.
Here, the scores are arranged into 20-point groups.

3) From the histogram, it is interpreted that:

Bowlers = 2 + 4 + 6 + 8 + 9 + 1 = 30

Therefore, 30 bowlers compete

4) The distribution is skewed left. A distribution is said to be "skewed left" if the tail is to the left. The procedure of determining a "typical value" for the distribution is philosophically more challenging when the distribution is skewed.

To know more about Histogram, refer to this link:

https://brainly.com/question/16819077

#SPJ4

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

To learn more about ratio click here

brainly.com/question/13419413

#SPJ4

Answer:

x = 7.5

Step-by-step explanation:

imagine the 5 and x highlighted green

and the 6 and 9 highlighted blue

green goes on top blue goes on bottom

\(\frac{5}{6}\) = \(\frac{x}{9}\)            now cross multiply

45 = 6x

x = 7.5

you can check your answer by putting 7.5/5 and 9/6 and you get the answer 1.5 for both

hope this helps

Answer:

46 is the answer.

Step-by-step explanation:

12/(2) + 10(2)(4)/2

= 12/(2) + 80/2

= 6 + 40

= 46

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).

It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.

Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.

According to the given data,

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

To know more about Random error,visit;

https://brainly.com/question/14149934

#SPJ1

Answer:

68

Step-by-step explanation:

just put the value of a and b in the expression and you will get the answer

20/a+7.b is

20/4+7×9

5+63

68

Answer:

C. 68

Step-by-step explanation:

Fill in your values.

20/ 4 + 7 x 9

Solve using PEMDAS.

5 + 7 x 9

5 + 63

68

The rate of change of a circle diameter with respect to radius is 0.

The rate of change of a circle diameter with respect to radius (D2(r)) can be calculated by using the formula dD2/dr. This formula states that the rate of change of a function at a given point is equal to the derivative of the function at that point.

To calculate the rate of change of a circle diameter with respect to radius, we must first calculate the derivative of the circle diameter with respect to radius. The formula for diameter of a circle is D = 2r, where r is the radius of the circle. Taking the derivative of the equation with respect to r gives us dD/dr = 2. This means that the rate of change of a circle diameter with respect to radius is 2.

We can also calculate the rate of change of a circle diameter with respect to radius using the formula dD2/dr. This formula states that the rate of change of a function at a given point is equal to the second derivative of the function at that point. Taking the second derivative of the equation for the diameter of a circle with respect to radius gives us d2D/dr2 = 0. This means that the rate of change of a circle diameter with respect to radius is 0.

Therefore, the rate of change of a circle diameter with respect to radius is 0.

Learn more about diameter of a circle here:

https://brainly.com/question/16905087

#SPJ4

It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

To learn more on rate of change click:

https://brainly.com/question/32765463

#SPJ4

When estimating a confidence interval for variance, the statistical table that we use is option (E) The chi square table

When estimating a confidence interval for variance, we are trying to determine a range of values that we are confident the true population variance falls within. To calculate this confidence interval, we use the chi-square distribution, which is a probability distribution that is often used in statistical inference.

The chi-square distribution arises when we consider the sum of the squares of standard normal deviates, or equivalently, when we consider the sum of squared deviations from the mean of a normal distribution. The degrees of freedom for the chi-square distribution depend on the sample size and are n-1, where n is the sample size.

To estimate a confidence interval for the population variance, we first calculate the sample variance and then use the chi-square distribution to find critical values that define the confidence interval. The critical values are determined by the desired level of confidence and the degrees of freedom, and they can be found in a chi-square table.

Therefore, the correct option is (E) The chi square table

Learn more about chi square table here

brainly.com/question/30764634

#SPJ4

Answer:

Hello,

answer : 259269764699508231

Step-by-step explanation:

We must use permutations with repetitions

Answer:

Composite

Step-by-step explanation:

To determine if this is prime or composite, we must solve the expression.

200^2-399

40,000-399=39,601

39,601 is divisible by 199. Therefore, it is a composite number.

Answer:

3. A. ten thousandths

4. C. tenths

5. D. hundredths

6. C. ten thousandths

hope you have a blessed day

Step-by-step explanation:

Answer:Question 3 answer is A.

Question 4 answer is C

Question 5 answer is D

Question 6 answer is C

YOUR WELCOME

Answer:

whats the question sir

Step-by-step explanation:

can you show me it like type it for me

The rectangle's area decreased by 19%.

Length = L

Breadth = B

Original area = L x B

New area = A = L x (1 + 25%) x B x (1 - 25%)

A = L x B x 0.25 x 0.75 = L x B x 1.05

Therefore the area of the rectangle has decreased by 19%.

To find the location of a rectangle, multiply its width by means of its height. If we understand the sides of the rectangle which are different lengths, then we have each the height and the width.

The perimeter P of a rectangle is given through the system, P=2l+2w, wherein l is the period and w is the width of the rectangle. The area A of a rectangle is given by means of the method, A=lw, in which l is the duration and w is the width.

Learn more about rectangle here https://brainly.com/question/25292087

#SPJ4

The correct option is B. The value of the quartile Q3 is 65.3 inches

Quartile is a type of statistical value that represents one-fourth of a dataset. It divides a dataset into four equal parts. Q1, Q2, and Q3 are the first, second, and third quartiles, respectively.

The formula for the third quartile is as follows:

Q3 = μ + (0.67 × σ), where μ is the mean and σ is the standard deviation.

Given:

Mean = μ = 63.6 inches

Standard deviation = σ = 2.5 inches

The value of the quartile Q3 can be found by substituting the given values in the formula.

Q3 = μ + (0.67 × σ)

Q3 = 63.6 + (0.67 × 2.5)

Q3 = 63.6 + 1.675

Q3 = 65.275 ≈ 65.3

Therefore, the value of the quartile Q3 is 65.3 inches. Therefore, option B is the correct answer.

You can learn more about quartiles at: brainly.com/question/15642066

#SPJ11

Answer:

m∠6 = 115°

Step-by-step explanation:

The t-values and degrees of freedom for the given information are:

a. t = 2.3646, df = 7

b. t = 1.8946, df = 7

c. t = 2.5279, df = 20

d. t = 1.7259, df = 20

To find the t-value and degrees of freedom (df) for the given information, we can use the t-distribution table or a statistical software. The t-value corresponds to a specific significance level (a) and degrees of freedom (df).

a. For a significance level (a) of 0.025 and degrees of freedom (df) of 7, we need to find the t-value. We can use a t-distribution table or statistical software to determine the t-value. In this case, the t-value is approximately 2.3646.

b. For a significance level of 0.10 and df of 7, we can again use a t-distribution table or statistical software to find the t-value. The t-value is approximately 1.8946.

c. When the significance level is 0.025 and df is 20, we can find the t-value using a t-distribution table or statistical software. The t-value is approximately 2.5279.

d. Lastly, for a significance level of 0.10 and df of 20, we can use a t-distribution table or statistical software to find the t-value. The t-value is approximately 1.7259.

In summary, the t-values and degrees of freedom for the given information are:

a. t = 2.3646, df = 7

b. t = 1.8946, df = 7

c. t = 2.5279, df = 20

d. t = 1.7259, df = 20

These values can be used in hypothesis testing or further statistical analysis.

Know more about the t-values click here:

https://brainly.com/question/29844684

#SPJ11

Answer:

£10.40

Step-by-step explanation:

Latte = £2.60
2 Hot Chocolates = £6.00
Tea = £1.80
Total = £2.60 + £6.00 + £1.80 = £10.40

Answer:

£10.40

Step-by-step explanation:

Add the cost of the drinks together to find the total cost:

\(\begin{tabular}{r r}Latte & \£2.60\\Hot Choc & \£3.00\\ Hot Choc & \£3.00\\Tea & \£1.80\\\cline{1-2} Total & \£10.40\\\cline{1-2}\end{tabular}\)

The probability of landing heads exactly 11 times when a coin is tossed 20 times is option a) 0.1602

The repeated tossing of a coin follows a binomial distribution

P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ ⁻ ˣ⁾

where,

n = No. of times the experiment was repeated

x = random variable defining the number of "successes"

p = probability of "success"

Here

"succeess" is the event of landing a head.

n = 20

x = no. of times heads should show, i.e 11

p = probability of landing a head in a single toss

= 1/2

Hence, putting all this in the formula above we get

P(X = 11) = ²⁰C₁₁ 0.5¹¹ (1 - 0.5)⁽²⁰ ⁻ ¹¹⁾

= ²⁰C₁₁ 0.5¹¹ 0.5⁹

= ²⁰C₁₁ 0.5²⁰

= 20!/ 11! (20 - 11)! X 0.5²⁰

= a) 0.1602

Complete Question

An unbiased coin is tossed 20 times.

Find the probability that the coin lands heads exactly 11 times

a. 0.1602

b. 0.5731

c. 0.2941

d. 0.1527

e. 0.6374

To learn more about probability visit

https://brainly.com/question/12844710

#SPJ4

There are a total of 1,326 different ways to draw two cards from a standard 52-card deck, with the first card being a diamond and the second card being a king.

The formula for this type of problem is given by the combination formula, which is expressed as C(n,r). In this case, we want to determine the number of combinations of two cards from a standard 52-card deck, with the first card being a diamond and the second card being a king. Therefore, n = 52 and r = 2.

Using the combination formula, we can calculate the number of ways to draw two cards such that the first card is a diamond and the second card is a king as follows: C(52,2) = 1326. This means that there are a total of 1,326 different ways to draw two cards from a standard 52-card deck, with the first card being a diamond and the second card being a king.

Learn more about combinations here:

https://brainly.com/question/20211959

#SPJ4

Answer:

1. 16 miles per gallon

2. 560 miles

Step-by-step explanation:

400miles = 25 gallons

x miles = 1 gallon

x = (400*1)/25

x = 16 miles per gallon

35 gallon = 35*16 = 560 miles

The statistic that the value 24.7 represents in this context is the median of the gas mileages for the cars tested.

Popular magazine that tests cars and trucks for mileage on the road and around the city. They report that 50% of the cars tested had mileages below 24.7 mpg on the road, and the other 50% had mileages above 24.7 mpg. The 24.7 mpg statistic represents the median of the gas mileages for the cars tested. This is because the median is the middle value when the data is arranged in ascending order, and in this case, it separates the lower 50% from the upper 50% of the mileages.

The median is the value that separates the data set into two halves. In this case, the magazine reports that 50% of the cars tested had mileages below 24.7 mpg on the road and the other 50% of the cars tested had mileages above 24.7 mpg. This means that 24.7 mpg is the exact middle value of the distribution of the gas mileages for the cars tested.

Learn more about "median ":

https://brainly.com/question/26177250

#SPJ11

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

To learn about Domain

brainly.com/question/29452843

#SPJ11

Answer:

250

Step-by-step explanation: