Help me please and thank you !!!!

Help Me Please And Thank You !!!!

Answers

Answer 1

The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]

What is a positive exponent?

A positive exponent indicates that the base should be multiplied by that many.

An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite. Negative exponents like xn can be rewritten as 1 / rs. As an illustration, qr^-4  s^6 q ^-8 s^6 q^-1 rs^6

The Power Rule for Exponents is a further exponent rule that follows from this. You multiply the exponents while keeping the base constant to simplify a power of a power. As an illustration, b for any positive s^6 q ^-8 s^6 q^-1 rs^6 number x and integers q and s.

⇒ qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹

⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹

⇒ qr⁻⁴ × 1q⁻⁸r⁻¹×1q⁻¹rs⁹

⇒ qr⁻⁸ × r⁻⁴ × s⁹

[tex]$ \Rightarrow \frac{1}{q^8} \times \frac{1}{r^4} \times s^9[/tex]

[tex]$ \Rightarrow \frac{s^9}{q^8r^4}[/tex]

Thus , The simplification of qr⁻⁴s⁰q⁻⁸r⁻¹s⁰q⁻¹rs⁹ using positive exponent is expressed as [tex]$ \frac{s^9}{q^8r^4}[/tex]

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Related Questions

and number is doubled and the result is increased by 8 if the final result is 36​

Answers

Answer:

14

Step-by-step explanation:

36 - 8 = 28

28 / 2 = 14

On a graph, the line representing Tony's distance covered with respect to time would be speed is Mark's. meters per minute and the unit rate for Mark is 2 3227 Mark's line. So, Tony's walking​

Answers

Tony's walk speed exists 2 meters per minute slower then Tony's walk speed.

What is meant by equation?

An equation in algebra is an equality claim that includes one or more variables or unknowable things.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Two expressions joined by an equal sign form a mathematical statement known as an equation.

A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation.

Tony : d = 108m

Tony walks 108 meters per minute

Mark : (10,1100),(20,2200)

slope = (2200 - 1100) / (20 - 10) = 1100/10 = 110 meters per minute

Therefore, Tony's walk speed exists 2 meters per minute slower then Tony's walk speed.

The complete question is:

Tony writes an equation to represent the distance he walks in meters, d, in relation to the number of minutes he walks, m. d = 108m Mark has created a table to record the number of minutes it took him to walk different distances in meters. Time (minutes) Distance (meters) 10 1,100 20 2,200 40 4,400 Assuming that Tony and Mark both walk at a constant rate, the unit rate for Tony is meters per minute and the unit rate for Mark is meters per minute. On a graph, the line representing Tony’s distance covered with respect to time would be Mark’s line. So, Tony’s walking speed is Mark’s.

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magine you are painting a series of towers built from cubes. You are going to paint only the exposed faces of the cubes. If the tower you paint has 25 exposed faces, how many cubes are in the tower?

Answers

Answer: 6

Step-by-step explanation:

4x + 1 = 25
4x = 24
x = 6

At Lake clay, marine biologist catch, tag, and release 50 small mouth bass. over the next few days, they catch 175 smallmouth bass, of which 7 have the original tags. what is the estimated population of smallmouth bass in lake clay?

Answers

Answer: The estimated population of smallmouth bass in lake clay can be calculated using the Lincoln-Petersen index.

This method is based on the idea that the proportion of tagged fish among all the fish caught will be proportional to the proportion of the total population that was tagged.

Formula: N = (C1 * N1) / (C2 - 1)

where N is the estimated population, C1 is the total number of fish caught, N1 is the number of tagged fish caught, and C2 is the number of tagged fish caught among all fish caught.

In this case:

C1 = 175 (total number of smallmouth bass caught)

N1 = 50 (number of smallmouth bass initially tagged)

C2 = 7 (number of tagged smallmouth bass caught among all fish caught)

So, the estimated population of smallmouth bass in Lake clay is:

N = (C1 * N1) / (C2 - 1) = (175 * 50) / (7-1) = 8750

Therefore, the estimated population of smallmouth bass in Lake clay is 8750.

Step-by-step explanation:

Explain how you can model 3x2/4

Answers

You can model 3x2/4 as the mathematical expression that represents the division of the product of 3 and 2 by 4. The result of this expression is 3/2.

What is division of a product in mathematics?

In mathematics, division is an arithmetic operation that is the inverse of multiplication. Given two numbers, the quotient is the number of times the second number "fits into" the first number.

The product is the result of multiplying two or more numbers together. Dividing a product is the process of finding out how many times one of the factors in the product can be taken to equal the product.

For example, if the product is 12 and the divisor is 3, then the quotient is 4, because 3 x 4 = 12

So, in the example 3x2/4, the product of 3 and 2 is 6 and we divide it by 4 to get the quotient of 3/2.

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Find a formula for the general term a subscript n of the sequenceopen curly brackets 2 over 1 comma space 3 over 4 comma space 4 over 9 comma 5 over 16 comma space 6 over 25 comma space 7 over 36 comma space 8 over 49 comma space 9 over 64 comma space midline horizontal ellipsis close curly brackets Students can use the editor to answer

Answers

The formula of the sequence based on geometric progression is  2(3/8)ⁿ⁻¹

The term geometric progression is defined as let a, r are real numbers and an infinite sequence of the form{arⁿ⁻¹} is said to be a geometric sequence this one is refers n'th term of the sequence.

Here we have know that the sequence is written as,

=> {2/1, 3/4, 4/9, 5/16, 6/25, 7/36, 8/49, 9/64..}

Here the value of r is calculated as,

=> (3/4) / (2/1) = 3/4 x 1/2 = 3/8

Then the general formula by using the geometric progression is written as,

=> 2 x (3/8)ⁿ⁻¹

Complete Question:

Find the formula for the general term a subscript n of the sequence {2/1, 3/4, 4/9, 5/16, 6/25, 7/36, 8/49, 9/64..}

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HElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick please

Answers

The non linear equation is Option B.

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the non linear equation be represented as A

Now , the value of A is

The equation can be calculated as a linear equation if the slope of the point remains the same

So , when the slope m is constant , it will be a linear equation

a)

Let the first point be P ( 2 , 5 )

Let the second point be Q ( 4 , 17 )

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 17 - 5 ) / ( 4 - 2 )

Slope m = 12 / 2

Slope m = 6

Let the third point be R ( 7 , 35 )

Let the fourth point be S ( 13 , 47 )

Now , the slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m = ( 47 - 35 ) / ( 13 - 7 )

Slope m = 12 / 6

Slope m = 2

Hence , the slope between the points is not the same and the equation of line will not be a linear equation

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Example 1: What is the probability of choosing a marble
2 questions with stripes? What is the complement of
choosing a marble with no design?
P(stripes)
P'(no design?

Answers

Answer:

The probability of choosing a marble with stripes, P(stripes), would be 0.2. The complement of choosing a marble with no design, P'(no design), would also be 0.2.

Step-by-step explanation:

1. The probability of choosing a marble with stripes, P(stripes), would depend on the proportion of marbles with stripes in the overall population of marbles available to choose from.

2. If, for example, there are 20 marbles with stripes and 80 marbles without stripes in a set of 100 total marbles, the probability of choosing a marble with stripes would be 20/100, or 0.2.

3. The complement of choosing a marble with no design, P'(no design), would be the probability of choosing a marble with stripes, or P(stripes).

4. This is because the complement of an event is the probability of the event not occurring.

5. So, if the probability of choosing a marble with stripes is 0.2, the probability of not choosing a marble with stripes (i.e. choosing a marble with no design) would also be 0.2.

xyz university claims that their graduates earn more than abc university graduates on average. the average salary of abc university as advertised on their website is $115,275. in this case, for xyz university the correct research hypothesis to test would be:

Answers

The average salary of xyz university = $138330

The average salary of abc university  is $115275 as provided in the question and also mentioned condition on the average salary of xyz university.

given that the average salary of xyz universtiy is greater than abc univeresity by 20% of the average salary of abc university.

so 20% of average salary of abc university = 0.2 * 115275 = 23055

so the average slary of xyz university is 23055 greater than average slary of abc university

so the avergae salary of xyz university is given by:

= 115275 + 23055

=> 138330

so the average salary of xyz university = $138330

To know more about  The average salary of xyz university = $138330

The average salary of abc university  is $115275

given that the average salary of xyz universtiy is greater than abc univeresity by 20% of the average salary of abc university.

so 20% of average salary of abc university = 0.2 * 115275 = 23055

so the average slary of xyz university is 23055 greater than average slary of abc university

so the avergae salary of xyz university is given by:

= 115275 + 23055

=> 138330

so the average salary of xyz university = $138330

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Complete question :

xyz university claims that their graduates earn more than abc university graduates on average. the average salary of abc university as advertised on their website is $115,275. Find the average salary of xyz university given that the difference betwwen the salary is 20 % of avergae salary of abc university.

Therefore $138330 is the average income at xyz university.

According to the information in the question and the conditions on the average pay at xyz university,

the average salary at ABC University = $115275.

the average income at xyz University = 20% higher than the average at ABC University.

,20% of ABC University's average income = 0.2 x 115275,

= 23055.

The average pay at XYZ University is = 115275 + 23055

= 138330

The xyz university's average income is $138330.

the average pay at ABC University = $115275

20% of ABC University's average income = 0.2x115275

= 23055.

the average pay at XYZ University = 115275 + 23055

= 138330

Therefore $138330 is the average income at xyz university.

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Complete question :

xyz university claims that their graduates earn more than abc university graduates on average. the average salary of abc university as advertised on their website is $115,275. Find the average salary of xyz university given that the difference betwwen the salary is 20 % of avergae salary of abc university.

Solve 3x − 2 = 37. a 2 b 5 c 7 d 9

Answers

Answer: x = 13

Step-by-step explanation:

       To solve, we will isolate the variable.

Given:

3x − 2 = 37

Add 2 to both sides equation:

3x = 39

Divide both sides of the equation by 3"

x = 13

i need to know how to find the gcf

Answers

The greatest positive integer that completely divides both of the numbers is known as the greatest common factor, or GCF. The GCF or HCF is composed of two or more non-zero integers.

In other words, the greatest common factor (GCF) among all the factors of the provided numbers is the case when there are two or more numbers. The Highest Common Factor of the Given Numbers is another name for it.

The approaches that are utilized to discover the GCF are listed below.

citing common elements:

Here, we list the common components of the given numbers and highlight those that are most frequently occurring.

main determinants:

In order to determine the highest common factors from both prime factor lists, we must write the given numbers as the product of prime numbers.

division strategy

Here, we must use the long division method to divide the greatest integer by the lowest number until the result is zero. The GCF of the given integers will make up the rest of the divisor when we reach the point where we have zero.

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Work out the surface area of this cylinder.
Give your answer in terms of .
10 cm
22 cm
Optional working
Answer+ cm²

Answers

The approximate surface area of the given cylinder is 2010cm^2. The solution has been obtained using area of cylinder.

What is area of cylinder?

The entire area a cylinder occupies in three dimensions is known as the cylinder's area. The combined areas of the two circular bases and the curving surface make up the cylinder's surface area. In right cylinders, the axis line creates a right angle to the base, and the two circular bases are perfectly over one another. It is referred to as an oblique cylinder if one of the circular bases is misaligned and the axis does not make a right angle with the base.

We are given radius(r) as 10cm and height(h) as 22cm.

We know that area of cylinder (A) = 2πrh + 2πr^2

So, using this, we get

⇒A = 2*3.14*10*22 + 2*3.14*10*10

⇒A = 1381.6 + 628

⇒A = 2009.6 = 2010cm^2

Hence, the approximate surface area of the given cylinder is 2010cm^2.

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These two images show steps in a proof of the Pythagorean theorem. Which of the following statements about the proof is false?

Brainliest if correct.



A. the area of the interior square in step 2 is equal to the combined area of the two interior squares in step 1.

B. The triangles in step 1 have the same combined area as the triangle in step 2.

C. The area of the interior square in step 2 is equal to c2 + ab.

D. The proof shows that a2 + b2 = c2.

Answers

Step 2's inside square has a larger area than Step 1's two interior squares taken together.

Explain about the Pythagoras theorem?

According to the Pythagorean theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the two shorter sides.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

Assume that the triangle ABC has sides measuring a, b, and c, and that a2 + b2 = c2. A second triangle with sides of lengths a and b and a right angle should be built. The hypotenuse of this triangle has length c = a2 + b2, matching the length of the hypotenuse of the first triangle according to the Pythagorean theorem.

According to the Pythagorean theorem, two squares added together equal the square of the longest side.

The Pythagoras theorem's equation is as follows:

H² = P² + B²

The procedures of proving the Pythagorean theorem are depicted in these two pictures.

Step 2's inside square has a larger area than Step 1's two interior squares taken together.

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On a coordinated plane, polygon GHIJ translates 8 units to the left to form polygon G1 H1I1J1 what of the following is not necessary true

Answers

The initial coordinates of the polygon will change by the rule -

(x, y) → (x - 8, y).

What is the difference between upward, downward, leftwards and rightwards translation?Upward translation : [k] units = When the upward translation take's place then, each point will have its y - coordinate shifted upwards by +k units.Downward translation : [k] units = When the downward translation will take place then, each point will have its y - coordinate shifted downwards by -k units.Leftward Translation : [k] units = When the leftward translation will take place then, each point will have its x - coordinate shifted by -k units to the left.Rightward Translation : [k] units = When the rightward translation will take place then, each point will have its x - coordinate shifted by +k units to the right

Given is on a coordinated plane, polygon GHIJ translates 8 units to the left to form polygon G1 H1 I1 J1.

Since the polygon is shifted to left, this means only the {x} - coordinate will change. So, the coordinates will change as -

(x, y) → (x - 8, y)

Therefore, the initial coordinates of the polygon will change by the rule -

(x, y) → (x - 8, y).

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To estimate the sum of two mixed numbers, Grace rounds one number to 7 and the other number to 4.

Which could be the number she rounds to 7?

A. 7 5/9

B. 7 11/15

C. 6 2/5

D. 6 9/14

Answers

According to the concept of fraction, the estimated sum of two mixed number is 7 5/9

In math the term called fraction is defined as a part of a whole number, and a way to split up a number into equal parts.

Here we know that Grace rounds one number to 7 and the other number to 4.

And here we have to find the number she rounds to 7.

Let us consider that x be the number.

And here we have know that

=> x - 7/4 = 7

=> x = 28/7

=> x = 4

Then the resulting number is calculated as,

=> 4 - 7/4 = 16 -7/4

=> 9/4

Then the rounded number is to 7 is 7 5/9.

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. All of the following are true about robo-advisors, EXCEPT…
*
Robo-advisors generally have lower fees than a traditional financial advisor
Robo-advisors generally have a higher account minimum than a traditional financial advisor
Robo-advisors use an algorithm to automate the investing process
Robo-advisors generally invest your portfolio based on your goals and risk tolerance

Answers

False: Robo-advisors often invest your account in accordance with your objectives and risk tolerance.

what is amount ?

aggregate aiming to figure out the amount total number, or time needed. The amount in front of you or being thought about is quite active. the final outcome, its significance, or its import. three accountings: principal, interest, and the third. Word forms include amounts, amounting, and amounted. supple noun How much something is, much you have, the amount that you require or how many you get is its quantity. He needs that much cash to get by.

given

It is true that robo-advisors typically charge less than a traditional financial advisor.

It is true that robo-advisors typically require larger account minimums than a traditional financial advisor.

It is true that robo-advisors automate the investing process using an algorithm.

False: Robo-advisors often invest your account in accordance with your objectives and risk tolerance.

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a study suggests that 35% of all business executives are willing to switch companies if offered a higher salary. if a recruiter randomly contacts a simple random sample of 100 executives, what is the probability that over 41% will be willing to switch companies if offered a higher salary?

Answers

The probability that 41% of the sample will be willing to switch companies is 0.0024.

To find the exact probability that over 41% of a random sample of 100 executives will be willing to switch companies if offered a higher salary, we can use the cumulative distribution function (CDF) of the binomial distribution.

The CDF is given by the formula:

P(X <= x) = (n x) p^x (1-p)^(n-x)

Where x is the number of successful outcomes, n is the number of trials, and p is the probability of success in each trial.

To find the probability of getting over 41% of the sample willing to switch companies, we need to find the probability of getting 42 or more successful outcomes (people willing to switch companies) out of 100 trials.

So we need to find P(X <= 42) + P(X <= 43) + .... + P(X <= 100) = 1 - P(X>=41)

P(X<41)= 1 - 0.9976 = 0.0024

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How do I solve by multiplying Imaginary Numbers? (10√-6) (√42)

Answers

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Answer:60i and the square root if 7

Solve by substitution.
x - 2y = 3
2x + 4y = 6
([?], [ ]
Enter

Answers

[tex]\begin{cases} x-2y=3\\ 2x+4y=6 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{x-2y=3}\implies x=2y+3 \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{2(\underset{x}{2y+3})+4y=6}\implies 4y+6+4y=6\implies 8y+6=6 \\\\\\ 8y=0\implies y=\cfrac{0}{8}\implies \boxed{y=0}\hspace{5em}\stackrel{2(0)+3}{\boxed{x=3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (3~~,~~0)~\hfill[/tex]

while logistic regression and classification and regression trees (cart) have the same end goal, each model approaches the goal in a different way. discuss the differences in the two models. provide a specific example of a situation where employing a cart model would be preferable to a logistic regression model. explain what makes the cart model superior in your example.

Answers

Logistic regression models the probability of a binary outcome, while CART models segment data into categories. For example, CART is preferable when data has complex interactions, as it can partition data into multiple categories.

Logistic regression and classification and regression trees (CART) are two different machine learning models used for binary classification problems. Logistic regression models the probability of one class or the other based on a linear combination of input variables. This makes it useful for predicting a binary outcome, such as whether a customer will purchase a product or not. On the other hand, CART is a decision tree model that divides data into categories. It uses a tree-like structure to split the data into segments based on the input features. This makes it useful for dealing with data with complex interactions, as it can partition data into multiple categories. For example, a CART model would be preferable to a logistic regression model if there are multiple underlying factors that affect the binary outcome. In this case, a CART model could more accurately identify the categories that are associated with a particular outcome. Overall, CART models are superior for dealing with data with complex interactions, whereas logistic regression is better for simpler data.

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suppose in mathlandia 11 peak dollars is equivalent to 22 sal dollars if a hamburger is 45 peak dollars what is the cost of the hamburger in sal dollars

Answers

The cost of the hamburger in sal dollars will be 90

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Suppose in Mathlandia 11 peak dollars is equivalent to 22 sal dollars. Then the ratio of the sal dollar to the peak dollar will be constant. Then the ratio is given as,

Ratio = 22 / 11

Ratio = 2

If a hamburger is 45 peak dollars. Then the number of sal dollars is given as,

⇒ 2 x 45

⇒ 90

The cost of the hamburger in sal dollars will be 90

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1. Circle C is centered at the origin. Is point (5, 5) on the circle? -8 -6 -4 -2 8 6 4 2 101 -2 -4 -6 -8 2 4 6 ++ 8​

Answers

Answer: d

Step-by-step explanation:

put some clothes on

what do you enjoy yourselves 200 times by you don't even listen to me and I got rid of 100 times​

Answers

Answer: ? what is the question

Step-by-step explanation:



Tom Sullivan's charge account statement shows an unpaid balance of $1,392. 8. The periodic rate is 2. 5% of

the unpaid balance. If he also has new purchases of $152. 87, what is his new balance?

Answers

Tom Sullivan's new account balance after all the transactions that has occurred as per the information provided will be $1,580.49.

Unpaid balance = $1,392. 8

Periodic rate = 2.5%

New purchase = $152.87

New Balance = $1,392. 8 + 2.5% + $152.87

A financial institution's account balance is the sum of money it has on hand during the current accounting period. It is the balance carried forward from the previous month plus the net difference between the credits and debits posted in any given accounting cycle.

An account balance offers current and convenient information about how much money you currently have on hand. An account balance offers a convenient way to manage the money coming in and going out while keeping track of all transactions.

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An athlete runs 100 metres in 10.4 seconds work out his average speed in kilometres per hour give your answer to one decimal place 

Answers

The average speed in kilometers per hour is 34.61 KMPH if an athlete runs 100 meters in 10.4 seconds .

What is speed ?

Speed is a measure of how fast an object is moving or how quickly an action is taking place. It is usually measured in units of distance per unit of time, such as miles per hour (mph) or kilometers per hour (kph).

Given ,

An athlete runs 100 meters in 10.4 seconds.

And we have to find the average speed in kilometers per hour.

So, average speed = total distance / total time taken

= 100 / 10.4

= 1000/104 meters/sec

So, we have to change units from meters/sec to kilometers per hour

So we multiply with 18/5 .

= 1000 / 104  *  18/5

= 200 * 9 / 52

= 1800 / 52

= 34.61 kmph.

Hence, The average speed in kilometers per hour is 34.61 KMPH if an athlete runs 100 meters in 10.4 seconds .

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groups of 20 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age. what is the range of the ticket prices after the discount is used

Answers

In a case whereby groups of 20 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age.  the range of the ticket prices after the discount is used is $8 to $12.

How can the Discounted ticket range  be calculated?

The concept that will be used is discount. Discount is the term used to describe a sum or a percentage subtracted from an item's usual selling price.

Since the ticket prices are been seen from the range from $10 to $15 so then we can say that the new range  can have two figures reduced by 20%.

Then we can calculate the $10 after the discount as :

= [10 * (1 - 20%)]

= $8

Then we can calculate the $15 after the discount as :

=[ 15 * ( 1 - 20%)]

= $12

The we can calaculate the Discounted ticket range  as

= $8 to $12

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complete question:

Groups of 20 or more receive a 20% discount at the LA Zoo. Tickets range from $10 to $15, depending on age. What is the range in ticket price after the 20% discount?

What is an equation of the line that passes through the points \(4,1) and (8,−4)?

Answers

m = (1--4) / (4-8)

m = 5 / -4

m = -1.25

y = mx + c

1 = -1.25(4) + c

1= -5 + c

c = 6

y = -1.25x + 6

A meteorologist drew the accompanying graph to show the changes in relative humidity during a 24-hour period in New York City. What is the range of this set of data?

Answers

The range of the data varies from 30 to 80. The correct answer is 30 < y < 80. The option C is correct

What are a domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.

Given that there is a graph in which the y-axis represents relative humidity and the x-axis represents time.

The range will be the variation of the y value on the graph from minimum to maximum.

The y value varies from 30 to 80 from minimum to maximum respectively. The inequality can be written as 30 < y < 80.

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a new medical complex being built has a rectangular base. it is 400 ft long, 180 ft wide, and 40 ft tall. if the architect's scale model is 30 in. long, what are the width and height of the model?

Answers

The width and height of the model are;

Width of model = 13.5 inches

Height of model = 2.25 inches

How to Interpret the scale Model?

A scale model is defined as a physical model that is geometrically similar to an object. Scale models are usually smaller than large prototypes such as vehicles, buildings, or people. However, these scale models may be larger than small prototypes such as anatomical structures or subatomic particles.

Now, we are given that the dimensions of the new medical complex are;

Length = 400 ft

Width = 180 ft

Height = 40 ft

Thus, for a scale model with length of 30 in(2.5 ft) long, the scale factor is; Scale factor = 2.5/400

Thus;

Width of model = 180 * (2.5/400)

= 1.125 ft = 13.5 inches

Height = 30 * (2.5/400)

= 0.1875 ft = 2.25 inches

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The bottom 30% of students failed the final examination. The mean score for the test was 120 and the standard deviation was 17. What was the passing score?

Answers

The passing score of the student when the standard deviation and mean are given is calculated to be 111.1.

Standard deviation = 17

Mean = 120

Percentage of students failed in the exam = 30%

Let us find Z such that P(Z< (X - 120)/17) = 0.3

By referring the table, the Z value corresponding to 0.3 probability is observed to be -0.525.

This means that (X - 120)/17 = -0.525

(X - 120) = 17 × -0.525

(X - 120) = -8.925

X = 120 - 8.925 = 111.07 ≈ 111.1

Thus, the required passing score is calculated to be 111.1.

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