Matt wants to purchase a watch for $64.50. If there was a 25% discount and the tax rate was 7%, what was the total price that it paid for the watch
$58.32
$43.74
$49.88
$39.95

Answer:

p = 73°

Step-by-step explanation:

The sum of the interior angles of every triangle is always 180°

p = (180 - 34 - 73)° = (180 - 107)° = 73°

Hope this helps

Answer:

Step-by-step explanation:

It's B

7 + 3 = 10

There is 99% confidence that the true proportion of worried adults is between (0.233, 0.303)

We have been given that in a survey of 1020 ​adults, a polling agency​ asked, "When you​ retire, do you think you will have enough money to live comfortably or not.

Sample size = number of persons surveyed

So, n = 1020

X = persons who stated that they were worried about having enough money to live comfortably in retirement

x = 536

Sample proportion p = x/n

p = 536/2000

p = 0.268

q = 1 - p

q = 1 - 0.268

q =  0.732

standard error = √(pq/n)

standard error = √((0.268 * 0.732)/1020)

standard error = 0.0138

Margin of error for 99% = ±2.58 * std error

                                        = ±2.58 * 0.0138

                                        = ±0.035

Confidence interval = p ± Margin of error

                                 = 0.268 ± 0.035

                                 = (0.268 - 0.035, 0.268 + 0.035)

                                 = (0.233, 0.303)

Therefore, There is 99% confidence that the true proportion of worried adults is between (0.233, 0.303)

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This is an example of a sample survey or a sampling method.

Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study. If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.

In the given scenario, you are conducting a sample survey to determine the proportion of each color of Peanut Butter M&Ms. A sample survey is a method used to collect data from a subset of a larger population in order to make inferences about the entire population.

Instead of counting every single Peanut Butter M&M in existence, which would be impractical and time-consuming, you decide to take a smaller representative sample. You purchase 10 packages of Peanut Butter M&Ms, each weighing 1.69 ounces, and count the number of M&Ms of each color in those packages.

By analyzing the data collected from this sample, you can estimate the proportion of each color of Peanut Butter M&Ms in the larger population. This approach is more feasible and provides a reasonable approximation of the overall distribution of colors without having to examine every individual item.

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Answer:

you need to know the length and width of the square or rectangle. This is also referred to as the area of the shape. The formula for calculating square meters is length x width = m2.

well, we know the cash price, that is, if you have cash burning your pockets, is R6900 bucks, however you'd rather do it in installments, or hire purchase with a downpayment of 15% of 6900, hmmm how much is that?

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 6900}}{\left( \cfrac{15}{100} \right)6900}\implies 1035\)

now, to that downpayment let's add the 12 installments of R558.50

\(\stackrel{downpayment}{1035}~~ + ~~\stackrel{ installments }{(12)(588.50)}\implies 1035+6702\implies \text{\LARGE 7737}\)

ohhh man!!! you ended up paying 7737 - 6900 = 837 more on hire purchase.

The Huffman code for the characters with the given frequencies is as follows:
A: 00
B: 01
C: 10
D: 110
E: 1110
F: 11110
G: 11111


1. Sort the characters based on their frequencies in ascending order: G(2), F(3), E(5), D(10), C(20), B(30), A(40).
2. Create a tree by combining the two characters with the lowest frequencies, and add their frequencies: (G,F)=5.
3. Repeat the process, combining the next lowest frequency characters/nodes, and add their frequencies: (E,(G,F))=10.
4. Continue this process until you have combined all characters/nodes into a single tree: (((G,F),E),D,C,B,A).
5. Traverse the tree and assign 0 to the left branch and 1 to the right branch at each level. Read the code from the root to each character.


Using the Huffman coding algorithm, we have generated an efficient binary code for each character based on their frequencies. The resulting tree and codes for each character are as listed in the main answer.

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The p-value in this example would be 1 - 0.99865 = 0.00135.

A p-value is a measure of how likely it is to observe a result from a statistical test, given that the null hypothesis is true. It is calculated by taking the probability of the observed result under the assumption of the null hypothesis, then subtracting this probability from 1.

Formula:

P-value = 1 - Probability(observed result | null hypothesis)

For example, if the observed result is that the mean of a sample is 5 and the null hypothesis states that the mean is 3, the p-value is calculated by taking the probability of observing a mean of 5 or greater under the assumption that the mean is 3. This probability can be calculated from a standard normal distribution table by looking up the z-score corresponding to the mean of 5 and subtracting it from the total area under the curve (which is equal to 1).

Therefore, the p-value in this example would be 1 - 0.99865 = 0.00135.

By interpreting the p-value, we can determine the likelihood that the observed result would occur given that the null hypothesis is true. In this example, the p-value of 0.00135 indicates that it is very unlikely that the mean of the sample would be 5 or greater if the true mean is 3. Therefore, we can reject the null hypothesis and conclude that the true mean is not 3.

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The cost of each message is $0.015.

Option C graph best approximates Jerry's text message plan.

Given,

On Jerry's text message phone plan, she paid $0.30 for every 20 messages she sent.

We need to find what is the cost per message in dollars.

We divide the total cost by the number of items.

Example: 10 pieces cost $20

1 pieces cost = $20/10 = $2

We have,

$0.30 for every 20 messages.

The cost of each message:

= $0.30/20

= $0.300

= $0.015

We can see that in the graph x-axis represents the number of messages and the y-axis represents the cost of each message.

We have,

$0.30 = 20 messages

3 x $0.30 = 3 x 20 messages

$0.90 = 60 messages.

We need a graph that has a point that intersects $0.90 and 60 messages.

We see that in the graph of Option C.

Option C graph best approximates Jerry's text message plan.

Thus,

The cost of each message is $0.015.

Option C graph best approximates Jerry's text message plan.

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The average speed during the two seconds in which the runner moved from 15 meters from the finish line to 3 meters past the finish line is 9 m/s

The average speed of the runner can be determined by using the following formula;

speed = distance ÷ time

As she moved from 15 meters from the finish line to 3 meters past the finish line in 2 seconds, the total distance covered in these 2 seconds by her can be calculated as follows;

distance = 15 meters + 3 meters

distance = 18 meters

Now substituting the values for distance and time in the formula;

speed = 18 / 2

speed = 9 m/s

Hence the average speed of the runner during the two seconds is calculated to be 9 m/s.

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Answer:

Astronomers directly use geometry in their work rather than accountants , judges, pharmacist and politicians.

They used geometry to measure velocity , direction, distance, relativity, momentum, and probability. They used it to look at objects in the sky with a telescope by setting a required angle to get a proper view .

But Accountants, judges, pharmacist and politicians are not in use of geometry directly or frequently.

Hence, Option 'B' is correct.

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Answer:

y = 11°

Step-by-step explanation:

PR and QS and parallel lines and QR is a transversal.

Now,

5y = 55 (alternate interior angles)

y = 55/5

y = 11

Answer:

p=5

Step-by-step explanation:

5p-30+11=4+(-3+p)

5p-19=1+p

5p-p=1+19

4p=20

p=5

The sample that best represents the population is this:

D. A group of 739 students in different middle school grade levels from various states.

A representative sample is the collection of people for a survey or experiment that represents the larger group. In the text, we can see that the intent of the researcher is to determine the number of hours that middle school students spend doing their homework.

Since this is to be on a national level, the population must be evenly distributed and not zoned to one part f the population. The best sample collection is option D.

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Answer:

angle(2) = 118 degree

angle(3) = 118 degree

angle(4) = 62 degree

Step-by-step explanation:

To find angle 2 :

\(62 + angle{2} = 180 \\ angle{2} = 180 - 62 = 118 \: degree\)

The rule (head to head):

angle(2) = angle(3) = 118 degree

And the last one is angle(4) which is the same thing:

angle(4) = angle(1) = 62 degree

\(-\frac{4}{5}\) is the slope of the line that pass  through the point (12, -13) and (-18, 11).

We must calculate the ratio of the difference in the y- and x-coordinates of the two points that comprise the line. The resulting value is the line's slope. It depicts the increase of the y-axis line over the x-axis run.

m =\(\frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}\)

m = slope

\((x_1, y_1)\)= coordinates of first point in the line

\((x_2, y_2)\) = coordinates of second point in the line

passing through the points (12, -13) and (-18, 11)

\(( x_1, y_1) = (12,-13)\\ ( x_2, y_2) = (-18,11)\)

Slope of the line = \(\frac{y_2 - y_1}{x_2 - x_1}\)

 = \(\frac{11- (-13)}{-18-12}\) = \(-\frac{24}{30}\) =\(-\frac{4}{5}\).

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The exponential functions for the two scenarios given are -

a) \(y = 12500 (0.91)^x\), Price of car after 5 years is $7800.40.

b) \(y = 50 (1.03)^x\), Price of baseball card after 5 years is $57.96.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The exponential function is in the form -

\(y=ab^x\)

Here y is the function, a is the constant base value, b is the rate of growth/depreciation and x is the time in years.

The first statement is -

A $12,500 car depreciates 9% each year.

The value for base is a = $12,500.

The value for rate is 9% = 0.09

Since, the price is depreciating the value for b is b = (1 - 0.09)

The exponential function is -

\(y = 12500 (1 - 0.09)^x\)

\(y = 12500 (0.91)^x\)

The value of car after 5 years can be obtained by substituting x = 5.

\(y = 12500 (0.91)^5\\y = 12500(0.6240)\\y=7800.40\)

Therefore, the equation is \(y = 12500 (0.91)^x\) and the value of car is $7800.40.

The second statement is -

A baseball card brought for $50 increases 3% in value each year.

The value for base is a = $50.

The value for rate is 3% = 0.03

Since, the price is increasing the value for b is b = (1 + 0.03)

The exponential function is -

\(y = 50 (1+0.03)^x\)

\(y = 50 (1.03)^x\)

The value of baseball card after 5 years can be obtained by substituting x = 5.

\(y = 50 (1.03)^5\\y = 50 (1.1592)\\y =57.96\)

Therefore, the equation is \(y = 50 (1.03)^x\)and the value of baseball card is $57.96.

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The length of the fence needed to enclose the garden is 27.792 meters.

Given that one side of the garden has a length of 10 meters. Assuming the points at each finish of this side are 44º and 58°.To find, The length of the wall expected to encase the gardenSolution: The triangle is shown below;Let Stomach muscle = 10 meters. BC x BD meters ADC = 44º;

Using the Sine rule, $frac10sin 78 = $fracxsin 44$ $Rightarrow x = $frac10sin 44$ $Rightarrow x = 7.154 meters in a triangle ADC. ABD = 58o. ACD = (180 - (44+58)) = 78o. Using the Sine rule, $frac10sin 58 = $fracxsin 78$; $Rightarrow x = $frac10sin 78$; $Rightarrow x = 10.638$ meters in the triangle ABD. The required fence length to enclose the garden is 27.792 meters, or 10 times 7.154 times 10.638. As a result, the fence that is required to enclose the garden must be 27.792 meters long.

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Tyler charges $8 for an adult ticket.

It is given that Tyler charges $t for adult tickets and $5 for child tickets.

No. of tickets sold by him on Monday is 12 child tickets and 9 adult tickets.

No. of tickets sold by him on Tuesday is 20 child tickets and 4 adult tickets.

Therefore,

Tyler earned $12 X 5 + $9 X t on Monday

= $9t + $60

Tyler earned $20 X 5 + $4 X t on Tuesday

= $4t + $100

According to the problem, the earnings on both the days are same. Hence we get the linear equation as follows

9t + 60 =  4t + 100

bringing all the variables, i.e t's to LHS and constants to RHS we get

9t - 4t = 100 - 60

or, 5t = 40

Bringing 5 to RHS we get

t = 40/5

or, t = 8

Therefore, t = $8

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Answer: 1287

Step-by-step explanation:

when y = 5 in the equation y = -3x + 5, the value of variable x is 0.

An equation is a statement of equality between two mathematical expressions that contain variables and mathematical operations. The goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true.

the steps to find out what x is in the equation y = -3x + 5 for y = 5:

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The complete question is:

I need a step by step process for to find out what, "x" is in this problem. y = -3x +5 for y=5

Answer:

13

Step-by-step explanation:

it is hard

Answer:

-23

Step-by-step explanation:

-31 + |-8|

|-8| = 8

-31 + 8 = -23

I hope this helps!

Answer:

-23

Step-by-step explanation:

|-8| = 8 so you so -31 + 8+ -23 :)

I’m in 7th grade :)

Answer:

28% .................

Answer:

28%

Step-by-step explanation:

100%/x%=160/44.8

(100/x)*x=(160/44.8)*x       - we multiply both sides of the equation by x

100=3.5714285714286*x       - we divide both sides of the equation by (3.5714285714286) to get x

100/3.5714285714286=x

28=x

x=28

now we have:

44.8 is 28% of 160

The probability that the employee is a member of the hourly staff, given that the employee is female is 0.2 or 1/5.

We need to calculate the conditional probability of an employee being a member of the hourly staff given that the employee is female and all the employees of a local university have been classified according to gender and job type.

The given table is:

Job Male Female

Faculty Member 55 5

Salaried Staff 15 25

Hourly Staff 30 20

The total number of female employees is 5+25+20 = 50.

We are to find the probability of an employee being a member of the hourly staff given that the employee is female.

Mathematically, we can represent the above statement as:

P(Hourly staff | Female) = P(Hourly staff and Female) / P(Female)

Now,P(Hourly staff and Female) = 20/100 * 50 = 10P(Female) = 50/100

Therefore,P(Hourly staff | Female) = P(Hourly staff and Female) / P(Female)= 10 / 50= 1/5 = 0.2

Therefore, the probability that the employee is a member of the hourly staff, given that the employee is female is 0.2 or 1/5.

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The change in elevation will be 0.

It should be noted that from the information, Calvin’s toy airplane flew to an elevation of 168 feet then landed back onto the flat sidewalk from where it was launched.

Therefore, when it flew, the expression will be +168.

When it came down, the expression will be -168.

Therefore, the change in elevation will be:

= +168 - 168.

= 0

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