Create a data set that has 4 values with a mode of 3, a median of 6, and a meanof 10

Is his answer reasonable: No, Emtiaz's answer is not reasonable because he assumed that the rate of descent was proportional.

The average rate of change is a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

Next, we would determine the rate at which the skydiver falls per seconds:

Rate = time/distance

Rate = 100/0.8

Rate = 125

Also, an equation which models the height (h) of the skydiver at a 0.8 seconds is given by:

h = 125t

At 3.1 seconds, we have:

Rate = time/distance

Rate = 500/3.1

Rate = 161.3

At 1.5 seconds, we have:

Rate = time/distance

Rate = 187.5/1.5

Rate = 125

Therefore, the average rate of change at each time interval is not equal and as such Emtiaz's answer is not reasonable because the rate increases as the time increases.

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Answer:

See below

Step-by-step explanation:

Use points given in hint to find slope, m  =  (2000 -1000) /( 6- 8) = -500

    then y = - 500x + b     sub i oneof the points to calculate b = 5000

so   y = - 500x + 5000    

if x = 7.5

      y = -500(7.5) + 5000 = 1250 dollars

Answer:

$324.35

Explanation:

Given a $249.50 cell phone with a 30% markup, to determine the selling price of the cell phone we need to first calculate 30% of $249.50 as seen below;

We'll now add $74.85 to $249.50 to finally get the selling price of the cell phone;

Therefore, the selling price of the cell phone is $324.35.

He spent $14.44 more on groceries this week than last week

From the question, the given parameters are

Amount spent last week = $58.34

Amount spent this week = $72.78

The additional amount that was spent at the grocery store this week is calculated by subtracting the amount spent this week from the amount spent last week

This is represented as

Additional amount = Amount spent this week - Amount spent last week

Substitute the known values in the above equation

So, we have

Additional amount = 72.78 - 58.34

Evaluate the difference

Additional amount = 14.44

Hence, an additional of $14.44 was this week

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From cosecant identity the expression cos(x)+sin(x)/ sin(x) =1+cot(x) was verified.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) ,  cos  (x) and tan  (x) , where:

sin (x) = [tex]\frac{opposite\ leg}{hypotenuse}[/tex]

cos(x)=[tex]\frac{adjacent\ leg}{hypotenuse}[/tex]

tan (x) = [tex]\frac{\frac{opposite\ leg}{hypotenuse} }{\frac{adjacent\ leg}{hypotenuse} } = \frac{opposite\ leg}{adjacent\ leg}[/tex]

The question gives the following identity:  [tex]\frac{cos (x)+sin(x)}{sin(x)}[/tex]

First, you should rewrite the identity using the cosecant  identity -                          csc(x)= 1/sin(x) . Then,

(cos(x)+sin(x)) * csc(x)

After that, you should expand the previous expression.

cos(x)*csc(x) + sin(x)  * csc(x)

cos(x)*1/sin(x) + sin(x)  * 1/sin(x)

cos(x)/sin(x) + sin(x)/sin(x)

cot(x) + 1

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Solution:

Scott paid;

$13.24 for 3.41-pound bag of shrimp

This means,

$18.99 for 4.96-pound bag of shrimp

This means,

Therefore, the bag that is a better buy based on the unit price is the 4.96-pound because of the unit price which is lesser than the unit price for the 3.41-pound bag.

Thus, the 4.96-pound is a better buy.

The system of inequalities is 1.25x + 2y >= 375 and x + y <= 500, while the smallest number of chocolate covered almonds is 400

We make use of the following representations:

x = chocolate bars

y = chocolate covered almond

Using the above as a guide, and the given parameters;

We have:

1.25x + 2y >= 375 -- the amount raised

x + y <= 500 --- number of bars sold

From the question, we have

x = 100

Substitute x = 100 in x + y <= 500

100 + y <= 500

Evaluate

y <= 400

So, the least amount to sell is 400

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Answer:

4

Step-by-step explanation:

put in equation form

7x - 12 = 16

solve for x

7x = 28

x = 4

we have the expression

therefore

Simplify

The probability that the customer came for lunch and did not order dessert is 7/113

The probability that the customer came for lunch or did not order dessert is 93/113

It is the chance of an event to occur from a number of possible outcomes.

It is given by:

Probability = Number of required events / Total number of outcomes

We have,

Total number of customers = 113

             Desert      Non desert

Lunch     7               1 3

Dinner    30             63

The probability that the customer came for lunch and did not order dessert:

= 7 / 113

The probability that the customer came for lunch or did not order dessert:

= (7+13)/113 + (13 + 63)/113

= 20/113 + 73/113

= 93/113

Thus,

The probability that the customer came for lunch and did not order dessert is 7/113

The probability that the customer came for lunch or did not order dessert is 93/113

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The height of the ball at a horizontal distance of R meters from Kaori is H(R)=4H.

Kaori taking a free throw is a guarantee. H(d) simulates the basketball's height (in meters) at d meters of horizontal separation from Kaori.

It is said that H(R) = 4H.

In this case, H(R) displays the height of a basketball instead of H(d). Therefore, it is evident that a basketball's height is 4H since H(R)=4H at d = R.

The horizontal distance from Kaori is R because d is the horizontal distance from Kaori.

Thus the height of the ball is 4H meters at a horizontal distance of R meters from Kaori, according to the expression H(R)=4H.

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The total cost of a Jacket is $124.75 and the cost of pair of sneaker is $74.75.

Let us say that the cost of the pair of sneakers is X dollars.

According to the given situation,

Cost of One jacket is 50 dollars more than the cost of a pair of sneakers.

Cost of one jacket = $(50 + X).

Total cost of one jacket and one pair of sneakers is $200.

Total cost of jacket and sneakers = $200

We get,

X + (X+50.5) = 200

2X + 50.5 = 200

The above equation that we have got is linear equation in one variable because it has degree 1 and one 1 variable.

Further solving the equation,

2X + 50.5 = 200

2X = 149.5

X = 74.75

So, the cost of one pair of sneakers is $74.75

Cost of One jacket is $(X + 50.5).

Cost of one jacket = $124.75.

So, one jacket costs $124.75 and sneakers cost $74.75.

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Solution:

Given:

The dinner bill = $21.00

The tip = 15% of the bill

Hence,

Therefore, the tip will be $3.15

Given:

Find: Area of the figure.

Sol:

The area of Triangle ABH is:

Area

In triangle is:

Base = (9-3)

Height = 8

So Area of ABH is:

Area of rectangle BDFH so,

Width = 8

Multiply the numbers and combine exponents with the same base.

Answer:

(4,-4)

Step-by-step explanation:

(x,y)→(x+2,y−5)

A(2,1) -> (4,-4)

:]

The distance between the points (−3, −5) and (−3, −7) is 2 units.

The distance formula gives the shortest distance between two points in a two-dimensional plane.

The distance formula is a useful tool for calculating the distance between two points.

Therefore,

d = √(x₂ - x₁)²+(y₂ - y₁)²

Let's find the distance between the points (−3, −5) and (−3, −7).

Hence,

x₁ = -3

x₂ = -3

y₁ = -5

y₂ = -7

d = √(-3 + 3)² + (-7 + 5)²

d = √(-2)²

d = √4

d = 2

Therefore, the distance between the point is 2 units.

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Step 1:

Write the equation

Step 2:

Express the equation in exponential form

Final answer

x = 4

ANSWER:

B. Similar - SAS

EXPLANATION:

Given:

Recall that the SAS Similarity Rule states that if two sides of one triangle are proportional to two corresponding sides of another triangle and the included angle in both triangles are congruent, then the two triangles are said to be similar.

Looking at triangles ABC and DEF, we can see that, we can see that;

Since the two corresponding sides of both triangles are in equal proportion and the included angle in both triangles are congruent, then triangles ABC and DEF are similar by the SAS Similarity Rule

x³+2x²+4x+8=0

Rearrange

x³ + 4x + 2x²+ 8 = 0

x ( x² + 4 ) + 2( x² + 4) = 0

(x + 2) ( x² + 4) = 0

The factors are;

(x + 2) (x² + 4)

(x²+ 4) can further be simplified to give (x- 2i) (x + 2i)

Answer:

175,760,000

Step-by-step explanation:

This is the counting principle.

There are 7 positions. Multiply the number of possible characters in each position.

_ × _ × _ × _ × _ × _ × _

The numbers are from 0 to 9, so there are 10 of them.

There are 26 letters in the English alphabet.

10 × 10 × 26 × 26 × 26 × 10 × 10

Answer: 175,760,000

To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.

What is coordinate geometry?

The science of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry).

Finding the difference between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.

m=(rise/run) = (y2-y1)/(x2-x1)

(x1,y1) =  coordinates of the line's first point

(x2,y2) = coordinates of the line's second point

To demonstrate that the diagonal slopes are opposing reciprocals, use the slope formula from coordinate geometry.

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We must write the ratio 7 to 15 and reduce it to the lowest term if possible.

The ratio is:

Because 15 is not divisible by 7, we conclude that the ratio is already in its lowest form.

Answer:

Step-by-step explanation:

Under her cell phone plan, Mei Mei pays a flat cost of $46 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Mei Mei can use while staying within her budget.

The

inequality

for the required

condition

will be 46+5x<70 as she want to keep the

bill

under $70 according to question. Also she can buy 5 gg that is number of

gigabytes

in a month.

What is inequality?

An

inequality

in mathematics is a relationship that makes a non-equal

comparison

between two numbers or other

mathematical

expressions. It is most commonly used to compare the

sizes

of two numbers on a

number

line.

How to solve the inequality?

To solve an inequality, follow these steps: Remove fractions by

multiplying

all terms by the fractions' least common

denominator

.

Simplify

the

inequality

by combining like terms on each side.

Subtract

or add

amounts

to get the unknown on one side and the numbers on the other.

according to the question,

$46 is the fix cost that she has to pay.

$5 is the cost of gg she buys that is variable.

let us assume that x gigabytes she can buy in a month.

$70 is the maximum bill amount she want.

so the inequality would be,

46+5x<70

5x<70-46

5x<26

x<26/5

x<5.2

so, she can

buy

5 gg at

maximum

in a month with the inequality 46+5x<70 for the given conditions.

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Given:

Here the system of eqution is given as

Required:

Solve using the substitution method

Explanaton:

First put

in

we get

now isolate x

now put the value of x first equation

Final answer:

Solution of given system of equation by using elimination is

1.The value of the expression after simplify will be,

''negative 43 over 24 times j plus negative 1 over 12.''

Option D is true.

2. The equivalent expression will be;

⇒ - 19.5b - 6.9

What is mathematical expression?

Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is;

''The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths.''

Now, We can write the expression in mathematical form as;

⇒ (- 1/8  j + 2/3) - (5/3 j + 9/12)

Solve the expression as;

⇒ - 1/8 j + 2/3 - 5/3 j - 9/12

⇒ - 1/8 j - 5/3 j + 2/3 - 9/12

⇒ j (-1/8 - 5/3) + 2/3 - 3/4

⇒ j (- 3 - 40)/24 + (8 - 9)/12

⇒ j (-43/24) + (- 1/12 )

This can be written as;

''negative 43 over 24 times j plus negative 1 over 12''

Therefore, The value of the expression after simplify will be,

''negative 43 over 24 times j plus negative 1 over 12.''

Option D is true.

2. The expression is given as;

3(−4.5b − 2.1) − (6b + 0.6)

Solve the expression as;

3(−4.5b − 2.1) − (6b + 0.6)

3 x -4.5b - 3 x 2.1 - 6b - 0.6

- 13.5b - 6.3 - 6b - 0.6

- 13.5b - 6b - 6.3 - 0.6

- 19.5b - 6.9

Thus, The expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) will be;

⇒ - 19.5b - 6.9

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x³ is N²/15. The index form of a number is that digit written as an exponential expression or an unmarried number presented to another number.

A number's index form is that number written as an exponential expression or as a single number raised to another number. The exponent, or index, of an exponential expression indicates how many times the base must be multiplied by itself to evaluate the expression.

This fact can be used to write a number in index form. An index number is a number that has been multiplied by a power. The power, also known as the index, indicates how many times the number must be multiplied by itself. For example, 25 means multiplying 2 by itself five times

= 222222 = 32. There are several important index number rules:

ya × yb = y.

Therefore,

[tex]$x^3=\frac{N^2}{15}[/tex]

For [tex]$x^3=f(a)$[/tex] the solutions are

[tex]$x=\sqrt[3]{f(a)}, \sqrt[3]{f(a)} \frac{-1-\sqrt{3} i}{2}, \sqrt[3]{f(a)} \frac{-1+\sqrt{3} i}{2}$$$[/tex]

[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2},[/tex][tex]$x=\sqrt[3]{\frac{N^2}{15}} \frac{-1-\sqrt{3} i}{2}$$[/tex]

Simplify

[tex]$\sqrt[3]{\frac{N^2}{15}} \frac{-1+\sqrt{3} i}{2}: \quad-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]

[tex]$x=\sqrt[3]{\frac{N^2}{15}}, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}+\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i, x=-\frac{\sqrt[3]{\frac{N^2}{15}}}{2}-\frac{\sqrt[3]{\frac{N^2}{15}} \sqrt{3}}{2} i$[/tex]

[tex]$x^3=\frac{N^2}{15}[/tex]

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The contrapositive of the statement is:

Jose isn't going for a bike ride if and only if he doesn't woke up early.

What is contrapositive?

A conditional statement's hypothesis and conclusion are switched, and both are then rejected, in a contrapositive. For instance, "if not B then not A" is the opposite of "if A then B." A conditional statement's contrapositive combines the inverse and converse.

The given statement is,

Jose wakes up early if and only if he is going for a bike ride.

We divide the statement into two parts.

1. Jose wakes up early.

2. He is going for a bike ride.

The negative of the statements are,

Jose doesn't wakes up early and he isn't going for a bike ride.

Therefore, the contrapositive of the statement is,

Jose isn't going for a bike ride if and only if he doesn't woke up early.

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We have to estimate how much he expects to make investing $4200 if he should make $12 for every $100.

We can apply the rule of three as:

Answer: he expects to make $504.