A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman. sophomore. junior, and senior classes to complete the survey. This plan is an example of which type of sampling ? a. Cluster
b. Convenience c. Simple random d. Stratified random e. Systematic

Answer:

  a.  y = 2.5x

  b.  markup: $30; retail price: $42

  c.  75%

  d.  y = 0.75x

Step-by-step explanation:

You want equations relating markup, retail price, and sale price on a phone that costs $12, is marked up 250%, then put on sale for $31.50.

The problem statement tells you the markup is 250% of the cost. You could write the equation as ...

  y = (250%)x

Or you can simplify it to a decimal number:

  y = 2.5x

The markup amount is ...

  y = 2.5(12) = 30

The markup amount is $30.

That is added to the cost to get the retail price:

  retail = $12 +30 = $42

The retail price of the phone is $42.

The sale price as a percent of the retail price is ...

  percent = (sale price)/(retail price) × 100%

  percent = 31.50/42 × 100% = 75%

The sale price is 75% of the retail price.

As in part (a), we could write this as ...

  y = (75%)x

or, in decimal, as ...

  y = 0.75x

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David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

Here we have been given that David invested $220.

The interest rate was 1.7%

Since the amount was compounded continuously, there is no fixed date of when it was compounded, the whole process is taken as an exponential distribution.

There were no withdrawals or additional deposits to this, so our Principal is constant. Hence we can write the formula

Amount = Principal X eᵃˣ

where a = rate of interest/100

x = time

Therefore, we can say that

Ampunt after 10 years = 220 X e¹⁰ ˣ ⁰°⁰¹⁷

= $260.76707

rounding off to the nearest 10 dollars we get

= $260

Hence David's deposit of $220 compounded continuously at a rate of 1.7% will become $260 after 10 years.

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X is 55 after rearranging the equation given

It will take 25 hours for Jenny to fill up the tank.

To solve this problem, we divide the capacity of the tank by the rate at which it is being filled:

500 gallons / 20 gallons/hour = <<500/20=25>>25 hours

Answer:

#1 multiply

#2 divide

#3 subtract

#4 subtract

#5 divide

Answer:

m = 2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

We see the y increase by 4 and the x increase by 2, so the slope is

m = 4/2 = 2

So, m = 2

He needs to make 1 and a half trips to the well to fill the barrel which has a height of 15 inches and  radius 10 inches.

A cuboid is a three-dimensional geometric shape that has six rectangular faces, three of which meet at each corner. A cuboid has three dimensions: length, width, and height. It is also commonly referred to as a rectangular prism. The formula for the volume of cuboid is [tex]V = l *w * h[/tex], where l is the length, w is the width, and h is the height. The formula for the surface area of a cuboid is [tex]2lw + 2lh + 2wh[/tex]. Cuboids are used in everyday life such as building blocks and package boxes.

The cylindrical barrel has a volume of [tex]\pi * r^2 * h = \pi * 10^2 * 15 = 1500\pi[/tex] cubic inches.

The hemisphere has a volume of [tex](2/3) * \pi * r^3 = (2/3) * \pi * 10^3 = (2000/3)\pi[/tex] cubic inches.

So, to fill the barrel, Brad must make [tex]1500\pi / (2000/3)\pi = 3/2 = 1.5[/tex] trips to the well.

In other words, he needs to make 1 and a half trips to the well to fill the barrel.

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Answer:

74,779,038,221

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

[tex]5^3*7^5+9^8+0+0+0+0+0+0+9^7*5^6[/tex]

We can eliminate all the zeroes.

[tex]5^3*7^5+9^8+9^7*5^6[/tex]

Evaluate each term.

Raise 5 to the power of 3.

[tex]125*7^5+9^8+9^7*5^6[/tex]

Raise 7 to the power of 5.

[tex]125*16807+9^8+9^7*5^6[/tex]

Raise 9 to the power of 8.

[tex]125*16807+43046721+9^7*5^6[/tex]

Raise 9 to the power of 7.

[tex]125*16807+43046721+4782969*5^6[/tex]

Raise 5 to the power of 6.

[tex]125*16807+43046721+4782969*15625[/tex]

Multiply 125 by 16807.

[tex]2100875+43046721+4782969*15625[/tex]

Multiply 4782969 by 15625.

[tex]2100875+43046721+74733890625[/tex]

Add 2100875 and 43046721.

[tex]45147596+74733890625[/tex]

Add 45147596 and 74733890625.

[tex]74779038221[/tex]

A calculator would help but here you go.

Answer:

90

Step-by-step explanation:

If we know that for every cup, we can take 3 of 1/3-ounce cups, we can use an equation that looks like this:

number of cups × 3 = total 1/3-ounce cups

If there are 30 cups, then we can simply insert 30 into the equation.

30 × 3 = 90

Therefore, you can make 90 1/3-ounce cups from the cereal box.

Answer:

y = -x - 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise / run or (y2 - y1) / (x2 - x1)

Let's pick 2 points ( -6, 0) (-5, -1)

We see the y decrease by 1 and the x increase by 1, so the slope is

m = -1

The y-intercept is located at (0,-6)

So, our equation is

y = -x - 6

x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]  , y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]   is the general solution of the sytem of differention eqution dx/dt = 4x+ 5y , dy/dt = 10x + 9y .

given  dx/dt = 4x+ 5y  and dy/dt = 10x + 9y

X'(t) = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]  X

where X = [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]

so A = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]

now we need to find eigen value of the matrix and the corresponding eigen vector.

| A- λI | = 0

so after equation the value to zero

λ = 14 and λ = -1

now for the  λ = 14 corresponding eigen vector = [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]

for λ = -1 corresponding eigen vector =  [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]

So general equation is given by:

X(t) = [tex]c_1e^1^4^t[/tex]  [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]  +  [tex]c_2e^-^t[/tex]   [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]

after solving this

x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]

y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]

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The data of the rainfall amount in inches to the locations are used to plot the attached line plot created with MS Excel.

A line plot is a graph is the graphical display of data as check marks or points above a number line.

A line plot shows the frequency of the values in the data on the number line, using dots or check marks. The frequency of the data is shown above the specified locations on the graph of a line plot.

The line plot is therefore, indicative of how frequent particular values in the dataset are.

The possible data in the question are presented as follows;

Rainfall Amount; 1/8,[tex]{}[/tex] 3/8,  3/4,  3/4,     1/4,    1 1/4, 1/8,     1/4,    1,     1/8

Location;     [tex]{}[/tex]          1,    2,     3,      4,        5,       6,     7,       8,      9,    10

The frequency of the data in a tabular form are;

Rainfall        [tex]{}[/tex]  Frequency

1/8        [tex]{}[/tex]          3 locations

3/8        [tex]{}[/tex]         1 location

3/4        [tex]{}[/tex]         2 locations

1/4       [tex]{}[/tex]           2 locations

1 1/4       [tex]{}[/tex]         1 location

1        [tex]{}[/tex]              1 location

The above frequency values can be used to create the attached line plot created with MS Excel

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Most likely one of these unrelated factors that could possibly have an impact on how long it takes to finish the race is the environment

Therefore the correct option is a) Number of people the stadium can hold

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Answer:

1/ 0.8 kilograms

2/ 800 grams

Step-by-step explanation:

We know

1/

Baseball bat = 28 ounces

1 kilogram = 35 ounces

To find weight in kg we take

28 / 35 = 0.8 kg

2/

We know

1 kg = 1000 g

0.8 kg = 800 grams

So, the baseball bat weights 0.8kg or 800 grams

On solving the provided question, we can say that - on doing the fraction we have  [tex]\frac{1}{10} ; \frac{1}{100} ; \frac{1}{10000}[/tex]

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here we have,

0.1 = 1/10

0.01 = 1/100

0.0001 = 1/10000

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Answer:  sqrt(2)

Step-by-step explanation:

Remember that sec x = 1/cos x.

That means that sec 7pi/4 = 1/cos(7pi/4)

cos(7pi/4) = -cos(7pi/4 - pi)

                 = -cos(3pi/4)

cos(3pi/4) is a special angle which evaluates to -sqrt(2)/2.

Hence, -cos(3pi/4) evaluates to simply sqrt(2)/2

Since cos(7pi/4) is equal to -cos(3pi/4),

cos(7pi/4) is equal to sqrt(2)/2.

Lastly, sec 7pi/4 = 1/cos(7pi/4) , which is the reciprocal of sqrt(2)/2, that is 2/sqrt(2).

Rationalizing the answer 2/sqrt(2) gives sqrt(2)

Therefore, the multiple of the given equations is 10x^2yz + 6xyz^2, 5x^3y^2 + 14x^3y^3, and -10x^5 + 15x^4 - 30x^3 + 40x^2.

The process of multiplying two or more polynomials together is known as polynomial multiplication. Applying the distributive property to the multiplication of polynomials allows us to conduct polynomial multiplication.

Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number. For instance, if we multiply 2 by 3, then implies that 3 gets multiplied by itself twice, meaning 3 + 3 = 6. Children can multiply numbers easily with the help of this method.

1. (5xy+3yz) * 2xz = 10x^2yz + 6xyz^2

2. (6/7x2y) * (35/6xy + 14/3 xy2) = 5x^3y^2 + 14x^3y^3

3. (2x3-3x2+6x-8) * (-5x2) = -10x^5 + 15x^4 - 30x^3 + 40x^2

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Answer:

The area of the dog pen is 522 [tex]ft^2[/tex].    (feet squared)

The perimeter of the dog pen is 94 feet

Step-by-step explanation:

Area

Here is the formula for the area of a rectangle.

[tex]A=lw[/tex]

We are given

[tex]l=29\\w=18[/tex]

Lets evaluate [tex]A[/tex].

[tex]A=29*18\\A=522[/tex]

Perimeter

Here is the formula for the perimeter of a rectangle.

[tex]P=2w+2l[/tex]

We are given

[tex]l=29\\w=18[/tex]

Lets evaluate [tex]P[/tex].

[tex]P=2l+2w\\P=(2*29)+(2*18)\\P=58+(2*18)\\P=58+36\\P=94[/tex]

The polygon presented will have nine sides. This suggests that a nonagon is the necessary polygon.

Divide the number of triangles in the polygon by 180° to determine the sum of its inner angles. Where is the number of sides, the formula for computing the sum of internal angles is (n 2) 180. In a regular polygon, all internal angles are equal.

The following are crucial polygon formulas: A polygon with "n" sides has a total interior angle sum of 180 degrees (n-2) A "n-sided" polygon has [n(n-3)]/2 diagonals. A regular n-sided polygon's internal angles are measured as [(n-2)180°]/n.

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A grocer makes a display of cans in which there are 10 rows.

The top row has one can and each lower row has two more cans than the row above it.

We can write it as sequence:

1, 3, 5, 7, . . .

We can observe that it's an arithmetic sequence: 1, 3, 5, 7, . . . , 2n-1

We know that the formula for the sum of n-terms of arithmetic sequence:

S(n) = (n/2)(1 + 2n-1)

Here, Sn = 100

So, (n/2)[1 + 2n-1] = 100

n(1 + 2n + 1)

n(2n) = 200

2n^2 = 200

n^2 = 100

n = 10

Hence, the number of rows = 10

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Rotation is the process of turning a figure a specific amount around a point. When we dilate a figure, we increase or decrease its size.

The circular movement of an item about a primary axis is referred to as rotation or spin. A revolving object in two dimensions only has one conceivable central axis and can revolve either clockwise or counterclockwise. There are many conceivable central axes and rotating orientations for a three-dimensional object.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

On a coordinate plane, forms can be rotated and dilated in addition to translated and reflected. When a shape is rotated, the new shape is consistent with the old. When you dilate a shape, the resulting shape is similar to the original.

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For this question u have to assume value of either x or y

For example

to find the value of x

side calculation (7000/35 = 200)

let x = 200

then 35(200) +60y = 7000

7000 + 60y = 7000

60y = 7000-7000

so y = 0

so value of x should be greater than or equal to 200

x >(or equal to) 200

to find the value of y

side calculation ( 7000/60 = 116.67)

let y = 116.67

then 35x + 60(116.67) = 7000

35x + 7000 = 7000

35x = 7000-7000

35x=0

so x = 0

so the value of y should be greater than or equal to 116.67

y >( or equal to 116.67)

The trigonometric functions are sin D = 28/53, sin E = 45/53, cos D =45/53, and cos E = 28/53 as fractions.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric functions are given in the question

Apply the sine ratio on the given right triangle

⇒ sin(θ) = Perpendicular/hypotenuse

sin D = EF/DE

sin D = 28/53

sin E = DF/DE ,

sin E = 45/53

Apply the cosine ratio on the given right triangle

⇒ cos(θ) = Base/hypotenuse

cos D = DF/DE

cos D =45/53

cos E = EF/DE

cos E = 28/53

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Nate's car was filled with 16 gallons of gas.

The concept is used in this is equations. An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. An equation is the set of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division balanced by an equal sign. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

As gas is $2. 09 per gallon at the gas station.

$2. 09 → per gallon

and Nate filled up his car and spent $33. 44.

$33. 44 for fully filled → how many gallons ?

So,

33.44 / 2.09 = 16 gallons.

Therefore, Nate filled 16 gallons gas in his car.

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Answer:

It should be 6 because 6x6 is 36

Answer:

Step-by-step explanation:

fractions are division so just divide 36 by 6 and you will get 6 which is your answer

36/6 =

36 : 6 =

6

The increase was 250% over the original price.

percentage, a relative value indicating hundredth parts of any quantity.

let 'x' represent the original price, then 'x+0.25x' represents the first increase of 25%

six times greater, converted to a percentage:

(x+0.25x)×2×100 a second increase of six-fold

1.25x×2×100

250

The increase was 250% over the original price.

Hence, the increase was 250% over the original price.

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^answer:^

~10 cubic feet~

^step by step explanation:^

first, calculate the volume of the front “panel” of the shape. (5 cubic centimeters because 5 times 3 is 15 and 15 times 1/3 is 5. 5 times 2 is 10.

Answer:

yes, it uses the Associative Property

Step-by-step explanation:

The two expressions (8 + 27) + 52 and 8 + (27 + 52) are equivalent because they both equal 87. This is an example of the Associative Property of Addition which states that the order of the terms within an expression can be changed without changing the result.

Answer:

  It isn't.

  The correct relation is 4r·Area = abc.

Step-by-step explanation:

You want to show the relation between the product of triangle side lengths and the product of the triangle area and the radius of the circumcircle.

The area of the triangle in the attached diagram can be found by ...

  Area = 1/2(bc)sin(α)

The inscribed angle theorem tells you the measure of the arc subtended by an inscribed angle is twice the measure of the inscribed angle. That means the opposite chord will be twice the length of the product of the radius and the inscribed angle value:

  a = 2r·sin(α)

The product of the circumradius and the area of the triangle is ...

  r·Area = r·(1/2)(bc)sin(α) = 1/4(bc)(2r·sin(α)) = 1/4abc

Without the fractions, the relation is ...

  4r·Area = abc

__

Additional comment

As a simple example, consider a 3-4-5 right triangle. The area of the triangle is ...

  A = 1/2(3)(4) = 6

The circumradius is half the length of the hypotenuse, r = 5/2.

The relation of interest is ...

  4r·Area = abc

  4(5/2)(6) = 3·4·5

  60 = 60 . . . . . . . . . . as expected

This could be a very simple way to find the circumradius of a triangle.