A triangle has an area of 14.5 square feet. The base of the triangle is 8 feet. What is the height?

Answer:

standard to vertex form : s*v

In a regular algebra class, completing the square is a very useful tool or method to convert the quadratic equation of the form [tex]y = a {x^2} + bx + c y = ax2 + bx + c[/tex] also known as the “standard form”, into the form [tex]y = a [ (x - h)^2] + k y = a(x - h)2 + k[/tex] which is known as the vertex form.

We first check if all the given values are non-negative. We can see that all the values given are greater than or equal to zero, so this condition is satisfied.

In part a, we are given a set of values and asked to determine if they form a valid probability distribution.

A probability distribution is a function that assigns probabilities to each possible value of a random variable. In order for a set of values to form a valid probability distribution, the following conditions must be met:

All values must be non-negative: This means that the probability of any event cannot be negative. In other words, the probability of any event occurring must be greater than or equal to zero.

The sum of all values must be equal to 1: Since the probability of an event occurring is always between 0 and 1, the sum of all probabilities must add up to 1. This ensures that all possible outcomes of an experiment are accounted for.

In part a, we first check if all the given values are non-negative. We can see that all the values given are greater than or equal to zero, so this condition is satisfied.

Next, we check if the sum of all values is equal to 1. We add up all the given values and get 1.3. Since this value is greater than 1, the sum of probabilities is not equal to 1 and hence, this is not a valid probability distribution.

In parts b, c, d and e, since the given distribution is not valid, we cannot calculate probabilities using it.

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A total of 800 people were in Funland Amusement Park to watch the noontime parade.

To calculate the total number of spectators present for the noontime parade, we need to add the number of visitors from the morning to the number of newcomers.

The park started with 500 guests, and as anticipation for the parade built up, 300 more individuals joined the crowd.

By combining these two amounts (500 + 300), we can determine that a total of 800 people were in Funland Amusement Park to watch the noontime parade.

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At Funland Amusement Park, there were initially 500 visitors present in the morning. As excitement for the noontime parade grew, an additional 300 people arrived just before the event. How many attendees were in the park to witness the parade?

Answer:

Step-by-step explanation:

a) No, there aren't shared rays.

b) Yes.

C) Vertical angles.

d) 2x = 50 + 8

e) x = 29.

Yes, clearly the two angles only share the common vertex which is B, all the rays startat that point, and in this case the rays for ABC are BA and BC.

Whie the rays for DBC are BD and BC.

So no, there aren't shared rays.

b) Yes, when the angles only share the vertex, these are called opposite or vertical angles, and it means that the two angles have the same measure.

c) As we said above, vertical angles.

d) The measures must be equal, then.

2x - 8 = 50

e) Solving that for x we will get:

2x = 50 + 8

2x = 58

x = 58/2 = 29

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√49 is less than 7.1212. In other words, 49−−√ is less than 7.1212.

what is a decimal number?

A decimal number is a real number that is expressed in the decimal system, which is a system of numeration using the base 10. In this system, each digit can take on one of ten possible values, 0 through 9, and the value of each digit is determined by its position relative to the decimal point.

To compare the numbers √49 and 7.1212, we need to find their numerical values.

√49 = 7, since 7 multiplied by itself gives 49.

7.1212 is already a decimal number, so no calculation is required.

To approximate 7.1212, we can look at the digits after the decimal point:7.1212

0.1212

--------

7.0000 + 0.1212

--------

7.1212

Now we can see that 7 is less than 7.1212. Therefore, √49 is less than 7.1212. In other words, 49−−√ is less than 7.1212.

So, the comparison between the two numbers is:

√49 < 7.1212 or 49−−√ < 7.1212.

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The maximum price that consumers are willing to pay for the product is represented by the y-intercept of the parabola, which is 1200. This means that when there is no demand for the product (x=0), the price of the product is 1200 dollars.

The given demand function for a product in dollars is p=1200-0.2x-0.0001x², where 'p' represents the price of the product and 'x' represents the quantity demanded by the consumers.

This demand function is a quadratic function that takes the form of a downward-sloping parabola. It has a negative coefficient for the squared term, which means that the parabola opens downwards. This implies that as the quantity demanded increases, the price of the product will decrease, but only up to a certain point.

The maximum price that consumers are willing to pay for the product is represented by the y-intercept of the parabola, which is 1200. This means that when there is no demand for the product (x=0), the price of the product is 1200 dollars.

As the quantity demanded increases, the price of the product decreases at a decreasing rate. This is because the coefficient of the x-term (-0.2) is smaller than the coefficient of the x²-term (-0.0001x²), which means that the effect of quantity on price decreases as the quantity demanded increases.

However, beyond a certain point, the price starts to increase again, indicating a decrease in demand. This is because the quadratic function is concave downwards, and there is a maximum point (vertex) on the parabola. The quantity demanded at this point is given by the formula

x = -b/2a, where a and b are the coefficients of the x² and x terms, respectively.

Overall, the demand function represents the relationship between the price of the product and the quantity demanded by the consumers. By understanding this relationship, producers can make informed decisions about pricing and production levels to maximize their profits.

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answer 48h. The maximum volume of a rectangular box without a lid can be found using the equation: V = l x w x h, where V is the volume, l is the length, w is the width, and h is the height.

To solve this problem, you need to first determine the length, width, and height of the box. Since you have 48 m2 of cardboard, you can rearrange the equation to solve for one of the variables.

48 m2 = l x w
w = 48/l

Once you have determined the width, you can then use the equation to solve for the length and the height.

V = l x 48/l x h
V = 48h

Therefore, the maximum volume of such a box is 48h, where h is the height of the box.

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The area of the triangle with two of its sides are 8cm, 11cm and 13 cm and the perimeter is 32cm is 8√30 cm².

Since the perimeter of the triangle with sides a, b and c is a+b+c, therefore, perimeter of triangle with sides 8 cm, 11 cm and c cm with perimeter 32 cm is:

32=8+11+c

c=32−19

c=13

So the sides of triangle are  8 cm, 11 cm and 13 cm

We use heron's formula to find the area of the triangle.

Let us find the semi perimeter:

S = (8+11+13)/2

S = 32/2

S = 16

Now area of the triangle is:

A= √s(s−a)(s−b)(s−c)

A = √16(16−8)(16−11)(16−13)

A = √(16×8×5×3)

A = √1920

A =8√30 cm²

Hence, the area of the triangle is 8√30 cm².

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—-------- Correct question format is given below —--------

(Q). Find the area of a triangle, two of its sides are 8cm and 11cm and the perimeter is 32cm.

After answering the prοvided questiοn, we can cοnclude that Therefοre, equatiοn the cοst οf οne apple pie is $8, and the cοst οf οne lemοn meringue pie is $20.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let x be the cοst οf οne apple pie, and y be the cοst οf οne lemοn meringue pie.

[tex]6x+8y=208[/tex]

[tex]6x+ 2y= 88[/tex]

[tex]-24x - 8y = - 352[/tex]

[tex]6x + 8y = 208[/tex]

[tex]-18x =-144[/tex]

[tex]X = 8[/tex]

[tex]6(8) +8y =208[/tex]

[tex]48+8y=208[/tex]

[tex]8y =160[/tex]

[tex]Y= 20[/tex]

Therefοre, the cοst οf οne apple pie is $8, and the cοst οf οne lemοn meringue pie is $20.

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Answer: 18x(8x+1)

Step-by-step explanation:

72x^2 + 72x^2+ 18x

144x^2+18x

72x^2 + 72x^2+ 18x

18(8x^2+x)

18(8x^2+x)

18x(8x+1)

hopes this helps!

The time taken for the tub to empty is approximately 9.18 minutes.

Suppose the drain is opened on a tub containing 34 gallons of water.

Water drains out of the bathtub at a rate of 4 gallons per minute.

However, the tap wasn't closed properly, so water is still flowing into the tub at a rate of 0.3 gallons per minute. How many minutes will it take for the tub to empty.

Solution:

We are given:

Initial quantity of water = 34 gallons.

Water flowing out of the tub = 4 gallons/minute.

Water flowing in to the tub = 0.3 gallons/minute

We need to find: Time taken for the tub to empty.

Let us assume that the time taken for the tub to empty is t minutes.

Now, the water that is still present in the tub is (34 - 4t + 0.3t) gallons.

Let us set this expression equal to zero to find the time taken for the tub to empty.

34 - 4t + 0.3t = 0

Simplifying, 34 - 3.7t = 0 or 3.7t = 34 or t = 34/3.7t ≈ 9.18.

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Out of the given options, the correct statement concerning the median is option B: In a right-skewed distribution, we expect that the median will exceed the mean.

What is the median?

Median is defined as the middle value in a given set of data. It can also be referred to as the central point of the distribution when the data is arranged in ascending or descending order. In other words, the median divides the data into two equal parts

.Median can be determined as follows:

Arrange the data in ascending or descending order .The median is the middle value of the data set.If there are two middle values, find the average of these two values .The mean is the average of the set of data. It is calculated by adding up all the values and dividing by the total number of values in the set of data. Hence, it gives an idea about the central tendency of the data set. According to the statement concerning the median, we expect that the median will exceed the mean in a right-skewed distribution. This means that the right tail is longer or more spread out than the left tail. The skewness of a distribution is a measure of its symmetry. A distribution can be classified as left-skewed, right-skewed or symmetrical depending on the shape of its histogram. Thus, option B is the correct statement concerning the median.

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A large retail company has different stores in the United States and in Europe.

a) i) Sampling method 2, results in a stratified sample of employees and strata is US And Europe.

ii) Sampling method 1, results in a Cluster sample of employees and Clusters: 8 (Employees of each 8 Stores).

b) Advantage and disadvantage of sampling method l is provided below.

c) Accurate Sampling, is statistical advantage of using sampling method 2 over a simple random sample.

We have the following information about problem :

1) In United States company and Europe company have 500 and 300 stores and a total of 100000, 60000 employees respectively (200 per store).

2) benefits offered by company are 1) One additinal day of paid vacation per year 2) Small increase in salary. Company wants to Know which offer is preferred and does employees in US And in Europe has difference of preference.

Now A)

i) Stratified sample of employees

Because in stratified sampling technique researcher identifies the contrubution of each strata in overall population. As in this case company chose 1000 employees out of100000 employees from US And 600 employees out of 60000 from Europe. Dividing them in 2 strata depending on there contribution in the over all population.

ii) Cluster sample of employees

Because in cluster sampling researcher divides sample in different groups (clusters) then researcher choose groups randomly for data analysis. groups get equal chance to be represented. In this example 8 stores (clusters) choosen randomly for study.

B) Sampling method 1 : Statistical advantage:

Accurate sampling is not guaranteed as proper representation of different groups in the population depending upon there representation is not practiced.

C) Statical advantage of sampling method 2 over simple random sample. In Sampling method 2 (Stratified sampling) Researcher identifies the contribution of each starata in population then picks the appropiriate sample size. Thus the most important advantage of method 2 over simple random sample is Accurate Sampling (attribution of each strata is properly represented in the sample chosen from the population).

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Answer:

20 days

Step-by-step explanation:

To find the total time, we will just add up the days.

4 + 3 + 6 + 7 = 20 days.

Answer:

  (d)  not possible to tell from information given

Step-by-step explanation:

You want to know the total completion time for a project with four activities that take 4, 3, 6, and 7 days.

The project completion time will be determined by the dependencies between activities.

If each activity must be completed before the next, then the total time will be 4+3+6+7 = 20 days.

If there are no dependencies and all activities can be done in parallel, then the total completion time is 7 days, the time required for the longest activity.

In short, it is not possible to determine the total time from the information given.

Answer: Therefore, the area that is only planted in corn can be expressed as the polynomial y^2 + 14y.

Step-by-step explanation:

The area of the square piece of land is given by the product of its length and width:

Area of square piece of land = (y + 7) * (y + 7)

The area of the small square that was planted with radish is 7 ft. by 7 ft. Therefore, its area is:

Area of small square = 7 * 7 = 49

The area that is only planted in corn is the difference between the area of the square piece of land and the area of the small square that was planted with radish:

Area planted in corn = (y + 7) * (y + 7) - 49

Expanding the expression on the right side, we get:

Area planted in corn = y^2 + 14y + 49 - 49

Simplifying further, we get:

Area planted in corn = y^2 + 14y

The odd one out from the three given ratios 3:6, 3:9 and 6:12 is 3:9 as 3x2 = 6 and 6x2 = 12 but 3x3 = 9.

A ratio is a means to compare two numbers that are similar or to demonstrate a relationship.

In the previous illustration, B and G are terminology. G is referred to as the consequent term, and B as the antecedent word.

Ratios are used to compare items with the exact same type. To analyze the proportion of boys to girls in your class, for instance, we might use a ratio. Another illustration would be to assess the ratio of peanuts to all other nuts in a container of mixed nuts.

The given ratios are;

3:6,3:9 and 6:12

Here the pattern follows:

3x 2 = 6

3x 3 = 9

6x 2 = 12

Thus, odd one out will be the ratio 3:9.

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Answer:

x=2

Step-by-step explanation:

(12x-23)(8x-15)

-8x        -8x

(4x-23)(-15)

   +23  +23

(4x)(8)

4/4 8/4

x=2

Answer:

The top and the bottom statement are correct. This is an independent compound event because the first choice does not affect the second choice.

The volume of a rectangular prism is 140 inches.

What is the rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Given: A box, in the shape of a rectangular prism, has a length of 3 1/2 inches, a width of 4 inches, and a height of 10 inches.

Length = 3 1/2

Width = 4

Height = 10

The volume of the box is the product of its dimensions

V = Length × width × Height

V = 3 1/2 × 4 × 10

V = 140

Hence, the volume of a rectangular prism is 140 inches.

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Answer:

1. A - [tex]y\leq \frac{3}{2} x+3[/tex]

2. D - (1,5)

Step-by-step explanation:

The equation [tex]y\leq \frac{3}{2} x+3[/tex] fits this graph.

y has to be less than x due to the shaded part of the graph being on the underside of the line

To confirm this we can plug in a value to see if the inequality is true

I will use the origin as an example:

[tex]0\leq \frac{3}{2} (0)+3[/tex]

[tex]0\leq 3[/tex]

This inequality is true meaning this point is in the shaded region of the graph

Also the equation has to have an equal to because it has a solid line and not a dotted line

The point that isn't a solution is (1,5) due to the fact it isn't in the shaded region and when plugged into the equation gives a false inequality

[tex]5\leq \frac{3}{2} (1)+3[/tex]

[tex]5\leq \frac{3}{2}+3[/tex]

[tex]\frac{10}{2} \leq \frac{9}{2}[/tex]

This inequality is false which means the point (1,5) isn't a solution to this equation.

Answer:

1.) A

2.) D

Step-by-step explanation:

1.) find equation of line:

    b=3,   m=1.5

y=1.5x+3

shaded is below therefore

y[tex]\leq[/tex]1.5x+3

*line under inequality because line is solid

2.) (1,5) is not a solution because it is above shaded figure

Answer:

Step-by-step explanation:

If one serving size is 1/3 of a cup, we know that there are 3 servings in 1 cup.

Our ratio is

3 servings : 1 cup

If we now have a 6 cup bag, we simply solve for it using our ratio

3 : 1

x : 6

1*6 = 6

3*6 = 18

so, x = 18.

There are 18 servings in a 6 cup bag of jelly beans

Hope this helps!

The critical value that corresponds to a 90% confidence level is 1.645.

When we are given a confidence level, we can use a confidence interval to calculate the margin of error, and with that we can find the critical value. The critical value is the value that represents the number of standard deviations we need to go from the mean to capture a certain proportion of the distribution.

For example, for a 95% confidence level, we want to capture 95% of the distribution, so we need to go 1.96 standard deviations from the mean.To find the critical value that corresponds to a given confidence level, we need to use a table of critical values for the standard normal distribution. This table tells us how many standard deviations we need to go from the mean to capture a certain proportion of the distribution.

For example, the critical value for a 95% confidence level is 1.96, while the critical value for a 99% confidence level is 2.58. So, if we are given a confidence level of 90%, we need to find the critical value that corresponds to capturing 90% of the distribution.Using the table of critical values, we find that the critical value for a 90% confidence level is 1.645.

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Step-by-step explanation:

Semir = n

Sarah = 2n - 5

Sarah's expression =. 2n-5

Sarah's equation = 18(2n-5)

Semir's equation = 18(2n-5) = 450

n = 15

Sarah walked 2(15) - 5 which is 25 miles.

SungSo:

18x + 72 = 450

x = 21

Answer:

sp

Step-by-step explanation:

1) The difference between the MP and VAT is

mp- VAT AMT. And as we know the formula to find

sp in presence of MP and VAT amt is sp

sp=Mp- Vat AMT

2). For MP after discount is also sp.

sp =MP - discount amt

The length of time it would take you to pay off the balance at $ 50 per month is 29.5 months.

The monthly payment on the credit card if one was to pay off the debt in 2 years is $132.34.

To find out how long it will take to pay off the credit card balance, we can use the TVM (Time Value of Money) solver.

First, we need to convert the APR to a monthly interest rate:

i = (1 + 0.19)^(1/12) - 1 ≈ 0.0149 or 1.49% (monthly interest rate)

Now, we can use the TVM formula to find the number of periods (n):

PV = PMT x (1 - (1 + i)^(-n)) / i

1,245 = 50 x (1 - (1 + 0.0149)^(-n)) / 0.0149

Solving for n:

n = 29.5 months

To find the monthly payment on the credit card, we are given:

PV (Present Value) = $2,456.80

n (number of periods) = 2 years x 12 months/year = 24 months

APR (Annual Percentage Rate) = 23.99%

We can use the TVM formula to find the monthly payment (PMT):

PV = PMT x (1 - (1 + i)^(-n)) / i

2,456.80 = PMT x (1 - (1 + 0.0182)^(-24)) / 0.0182

Solving for PMT:

PMT = $132.34

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