n the manufacturing of a plastic material, it is be- lieved that the cooling time has an influence on the impact strength. therefore a study is carried out in which plastic material impact strength is determined for 4 different cooling times cooling time in second : 15 25 35 40 impact strength in kj/m2 : 42.1 36.0 31.8 28.7 a) find explanatory and response variable? b) find equation of linear model that describes re- lationship between predicted value of response and explanatory variable? c) based on r2, what you can say about response and explanatory variable?

Answer:its a graph

Step-by-step explanation:

Answer:

Step-by-step explanation:

a. Fishman, Goron, Smith, other.

b. 98 people

Use the percent formula:

P% of number = x in this case it's 35/100 * 280 = x

x = 98

c. No because it is estimated. I typed it into my calculator and when I did the percentage formula with other and used 280 as my other number, I get 28, when it says 40 people had voted for other.

To determine how many dollars a restaurant makes per day, the restaurateur would need to measure the "revenue" metric.

Revenue is the total amount of money a business earns from its sales or services provided over a specific period of time, in this case, daily. It includes all income generated by the restaurant from selling food and drinks to customers.

Measuring revenue is essential for any business as it helps the owner understand the financial health of their enterprise. By tracking revenue over time, the restaurateur can identify patterns and trends and make informed decisions to increase profits and improve the business's overall performance.

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How to construct the right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm.

Given:

To find:

Construct a right-angle triangle DEF

The constructed right-angle triangle DEF is given below:

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Step-by-step explanation:

So working from the bottom

The last line for x > 20 shows 13 because of the top graph, the last line is 13 and there is nothing below it.

Now for x > 16, we go up a line and see 14

That's where you would add 14 + any number below it

14 + 13 = 27. So for x > 16, you'd write 27

Going up, we have X > 12. Same thing, we go up a line and see 19. So now we just add 29 and any number below that

19 + 14 + 13 = 46. So for x > 12, you'd write 46.

You'll do that for the rest of the table. hope that helps

The coordinates  ( 6,-8 ) are plotted by moving 6 units right and 8 units down.

The intersection of the x- and y-axes creates the two-dimensional coordinate plane known as the cartesian plane. The origin is the point at which the x- and y-axes cross perpendicularly.

here, we have,

Given coordinates (6,-8)

for  the cartesian plane, we know that the origin has points (0, 0)

and divided into four Quadrants,

the left side of the origin is a negative x-axis and the right side is a positive x-axis.

and the upside of the origin is a positive y-axis and the downside is a negative y-axis.

here coordinates of x =6 and y = -8

6 is 6 units right from the origin

and -8 is 8 units down from the origin.

Hence for the coordinates , 6 units to the right and 8 units down , is correct.

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The perimeter of the rectangle is 2ab² ( 5ab² + 3)

The area of the rectangle is 15a³b^6

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let l=5a²b^4  ,   w= 3ab²

Perimeter = 2(l+w)

                 = 2(5a²b^4 + 3ab² )

                 =2 [ ab² ( 5ab² + 3)]

                 = 2ab² ( 5ab² + 3)

Area = l*w

        =  5a²b^4 *3ab²

        = 15a³b^6

The perimeter of the rectangle is 2ab² ( 5ab² + 3)

The area of the rectangle is 15a³b^6

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Mary  age  is ( x -1 ) years old now.  4 years ago=  ( x -1 )-4 =0,  x=4+1=5,

now he is x -1 =5-1=4,  4 years ago=5-4=1 year,  iii) (3*8/3+8)=16 year old

Will he be 8 years from now  .now she is 4  year old now.

if he is x year old . he will be 8 years from now=(3x+8)=0

x=- 8/3. now his age is (3x+8) =(3*8/3+8)=16

A time of human existence, defined in years starting at birth, that is typically characterized by a certain stage or degree of mental or physical development and involves the potential for legal responsibility. the discretionary age. the legal drinking age. The legal drinking age was increased by the state from 18 to 21. Age is a notion that describes a person's age at a specific period. It is described as the measurement of the amount of time that has passed between the date of the live birth to a particular point in time, typically the date the data was collected. Age range, according to the Longman Dictionary of Contemporary English, is the term for a group of people who fall between two certain ages.

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The probability of a gym member attending yoga is 0.625 or 62.5%.

Probability is the likelihood or chance of an event happening. In this scenario, we have information about the number of gym members attending yoga and dance, which can be used to calculate the probability of a gym member attending yoga.

Out of the 400 gym members, 300 regularly attend yoga, and 50 attend both yoga and dance. This means that the number of gym members attending only yoga is 300-50=250. The probability of a gym member attending yoga can be calculated by dividing the number of gym members attending yoga by the total number of gym members.

Probability of a gym member attending yoga= Number of gym members attending yoga/Total number of gym members

Probability of a gym member attending yoga= 250/400

Probability of a gym member attending yoga= 0.625 or 62.5%

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Complete Question:

400 gym members, 300 regularly attend yoga, 80 regularly attend dance, and 50 regularly attend yoga and dance. Using this information, answer each of the following questions.

What is the probability that a gym member attends yoga?

The sequence 3, 18, 108, 648, ..... is a geometric sequence.

The sequence 3.9, 19.5, 97.5, -487.5, ..... is a geometric sequence.

The sequence 1.1, -2.2, 4.4, -8.8, ..... is a geometric sequence.

The sequence 4, 20, 4, 20, ..... is not a geometric sequence.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁ = a₃/a₂

Common ratio, r = 18/3 = 108/18

Common ratio, r = 6 = 6 (geometric sequence).

Common ratio, r = -19.5/3.9 = 97.5/-19.5

Common ratio, r = -5 = -5 (geometric sequence).

Common ratio, r = -2.2/1.1 = 4.4/-2.2

Common ratio, r = -2 = -2 (geometric sequence).

Common ratio, r = 20/4 = 4/20

Common ratio, r = 5 = 0.2 (not a geometric sequence).

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The expression that represents all the possible widths of the rectangle is given as follows:

0 < x < 5.

The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:

A = lw.

For this problem, the length is 5 meters more than five times the width, hence:

l = 5 + 5w.

Hence the area is given as follows:

A = w(5 + 5w)

A = 5w² + 5w.

The area is less than 100m², hence the inequality is given as follows:

5w² + 5w < 100

5w² + 5w - 100 < 0.

w² + w - 20 < 0.

(w + 5)(w - 4) < 0.

Hence the solutions are:

The width cannot be negative, hence the interval is:

0 < x < 5.

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Answer:

Part A:

The graph of g(x) = |x - 7| is a V-shaped graph that opens upward, with a vertex at x = 7 and y = 0. The graph of the function is symmetrical about the vertical line x = 7. The domain of the function is all real numbers, and the range is all non-negative real numbers, including zero.

Part B:

The transformation from f(x) to h(x) is a vertical shift upward by 2 units. The vertex of the parent function f(x) = |x| is at (0, 0), and the vertex of the transformed function h(x) = |x| + 2 is at (0, 2). The range of the parent function f(x) is all non-negative real numbers, including zero. The range of the transformed function h(x) is all non-negative real numbers greater than or equal to 2. The transformation shifts the entire graph of the parent function upward, increasing the y-values of all points on the graph by 2 units.

Answer:

Below

Step-by-step explanation:

Since the center (h,k) is (4,1)   and the circle passes through (4,-4) the radius is 5    ( from y = 1 to -4 ...a distance of 5 )

the equation for a circle is of the form  (x-h)^2 + (y-k)^2 = r^2

  becomes   (x-4)^2 + ( y-1)^2 = 5^2   < ==== graph this equation

radius = 5   then the diameter = 10  then     circumference = pi * d = 10 pi

Answer:

Step-by-step explanation:

your picture is blur. can you repost it?

The segments' lengths and the angles' measurements are FE = 11,  CF = 10,  d = 54, and e = 126

As this is a parallelogram c = e

so 9y = 7y + 28

9y - 7y = 28

2y = 28

y = 14

So e would be 7(14) + 28

= 98 + 28

= 126.

And as d + e = 180, d = 180 - 126

d = 54

And as CF = DE

2x = x + 5

2x - x = 5

x = 5

CF = 2x

= 2(5)

= 10

And lastly CD = FE

CD = 3x - 4

CD = 3(5) - 4

= 15 - 4

= 11

FE = 11

So the answers are:

FE = 11,  CF = 10,  d = 54, and e = 126

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Answer:

ok Let’s calculate the money Sam makes per week, not including sales (or Assuming $0 in sales):

Money per week =$6.45/hour×37.5 hours/week= $241.88/week  

The money he Gains from sales must make up the difference, So

money from sales = $400−$241.88 = $158.12  

This Money is only 6% or 0.06 of the total sales though, so

Total sales = $158.120.06 = $2635.33  

of course, this is Assuming that the money per week is rounded up from $241.875 to $241.88 instead of down to $241.87, in which case Sam would Have to make $2635.50 in sales (about 17 cents more).

Step-by-step explanation:

have a nice day.

The boat will coast approximately 16752.9 feet (or about 3.17 miles) in the first 2 minutes after its motor quits.

From the problem statement, we know that the velocity of the boat, v, changes from 83 ft/s to 23 ft/s over a period of 1 second. Therefore, we can write:

[tex]dv/dt = -k v^2[/tex]

Separating variables and integrating from v = 83 at t = 0 to v = 23 at t = 1, we get:

[tex]∫83^23 dv / v^2 = ∫0^1 -k dt[/tex]

=> [1/83 - 1/23] = k

So the equation for the velocity of the boat as it coasts is:

[tex]dv/dt = -[(1/83 - 1/23)] v^2[/tex]

The differential equation is separable:

[tex]dv/v^2 = -[(1/83 - 1/23)] dt[/tex]

Integrating both sides, we get:

-1/v = [(1/83 - 1/23)] t + C

where C is an integration constant. Using the initial condition v(0) = 83, we get:

C = -1/83

Substituting this back, we have:

-1/v = [(1/83 - 1/23)] t - 1/83

Solving for v, we have:

v(t) = 83 / [1 + (83/23 - 1) t]

To find the distance traveled, we integrate v(t) from t = 0 to t = 120:

s =[tex]∫0^120 v(t) dt[/tex]

Substituting v(t) and simplifying, we have:

s = 23 ln(1 + 3.6087t) + 60.391t + C

where C is another integration constant. Using the initial condition s(0) = 0, we get:

C = 0

Therefore, the distance traveled by the boat in the first 2 minutes after its motor quits is:

s = 23 ln(1 + 3.6087t) + 60.391t

Evaluating this expression at t = 120 seconds, we get:

s = 23 ln(433.044) + 7246.92 ≈ 16752.9 ft

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In a density curve, the proportion of data is represented by the option B) area under the curve and correct classification of shapes of density curves is option E)

A density curve is a curve on a graph that represents the distribution of values in a dataset.

A density curve, also called a density function, is a graphical representation of the relative frequency distribution of a continuous random variable. The type of distribution most commonly represented by a density curve is the normal distribution, but any distribution of a continuous variable may be represented by a density curve.

Normal distribution curve is a bell shaped curve obtained for the distribution having maximum frequency near the central value of distribution and the frequency gradually tapering off symmetrically on both side.so, All → Symmetric → Bell → Normal

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Answer:

To rewrite the expression 27 - 4x + x² in the form (x + a)² + b, we can complete the square.

Starting with x² + (-4x) + 27:

x² - 4x + 4x² = 4x² - 4x

Adding (4/2)² = 4 to both sides:

4x² - 4x + 4 = 4x² - 4x + 4

The expression is now in the form (x - 2)² + 0, so a = -2 and b = 0.

Therefore, 27 - 4x + x² = (x - 2)² + 0.

The value of the variable T is 60

These are described as expressions that are composed of coefficients, factors, constants, variables and terms.

These algebraic expressions are also identified by mathematical or arithmetic operations, such as;

We have;

T= 3db

Substitute the values

T = 3(4)(5)

expand

T = 60

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Answer:

684sq in

Step-by-step explanation:

The surface area of a rectangular prism can be calculated by adding up the areas of all six faces. If the dimensions of the prism are 6 inches, 15 inches, and 12 inches, then the surface area can be calculated as follows:

2(lw + lh + wh)

where l is the length, w is the width, and h is the height.

Substituting the given values, we get:

2(6 * 15 + 6 * 12 + 15 * 12)

= 2(90 + 72 + 180)

= 2(342)

= 684 square inches

So, the surface area of the rectangular prism is 684 square inches.

The equation for this circle is as stated in the above statement: (x-h)² + 2(y-k)² = r²

Today, circles are still significant symbolically; they frequently stand for peace and unity. Check out at the Olympic logo, for instance. It contains five overlapping rings of various colors that collectively symbolize the world's five major continents, which are joined in a great spirit of healthy rivalry.

A circle is a round shape that may be created by following a moving point on a plane while maintaining a constant distance from another point. This Greek word kirkos, which means hoop or ring, is whence the word circle gets its from.

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All the numbers less than -10 and upto negative infinity will make the mentioned statement true.

Let us assume the number to be x. So, twice the number will be 2x. Then, nine more will be represented as: 2x + 9. Now, the total is less than -11, so representing the information in expression along with sign.

2x + 9 < - 11

Rewriting the expression according to 2x

2x < - 11 - 9

Performing subtraction on Right Hand Side of the equation

2x < - 20

x < - 20/2

Performing division on Right Hand Side of the equation

x < - 10

So, the numbers below -10 will make the statement true.

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The value of m for which the parallelogram WXYZ will be a square is (a) 2 .

For the parallelogram WXYZ to be a square ,

We know that , if parallelogram WXYZ is a square all, then all the sides are equal ;

So , we write WX = XY = YZ = ZW ;

To find the value of "m" , we use WX = ZW ;

substituting the values of sides of square from the figure ,

we get ;

⇒ 2m + 4 = m + 6 ;

⇒ 2m - m = 6 - 4 ;

⇒ m = 2 ;

Therefore , the value of "m" for the square WXYZ is 2 .

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The given question is incomplete , the complete question is

What value of m would make parallelogram WXYZ a square ?

(a) 2

(b) 3

(c) 4

(d) 5

The two plans cost the same for 60 minutes of calls. And  the two plans cost the same for 60 minutes of calls.

We can set the cost of the two plans equal to each other and solve for the number of minutes:

Plan A: $15 + $0.12x (where x is the number of minutes)

Plan B: $8 + $0.17x

$15 + $0.12x = $8 + $0.17x

Subtracting $8 from both sides:

$7 + $0.12x = $0.17x

Subtracting $0.12x from both sides:

$7 = -0.05x + $0.17x

Adding 0.05x to both sides:

$7 + 0.05x = $0.17x

Dividing both sides by 0.12:

x = (7 / 0.12) / (1 - 0.17/0.12) = 60 minutes

So the two plans cost the same for 60 minutes of calls. To find the cost, we can plug x = 60 into either equation:

Plan A: $15 + $0.12 x 60 = $15 + $7.20 = $22.20

Plan B: $8 + $0.17 x 60 = $8 + $10.20 = $18.20

So the two plans cost the same when there are 60 minutes of calls, and they both cost $18.20

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Complete Question

A telephone company offers two monthly plans. The a plan costs $15 plus $0. 12 additional for each minute of calls. Plan b costs $8 plus an additional 0.17 for each minute of calls For how many minutes of calls do the two plans cost the same? What is the cost at which two plans cost the same?

The number of combinations that are possible for 4 cell phone models of 6 colors with 5 calling plans is  120 .

We have to find the total number of combinations of cell phone models, colors, and calling plans,

So , we multiply the number of choices for each category.

By Using the multiplication principle of counting:

⇒ Total number of combinations = (number of phone models) × (number of colors) × (number of calling plans) ;

⇒ 4 × 6 × 5

⇒ 120

Therefore, there are 120 possible combinations of cell phone models, colors, and calling plans from this particular cell phone company.

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The given question is incomplete , the complete question is

A particular cell phone company offers 4 models of phones, each in 6 different colors and each available with an one of 5 calling plans. How many combinations are possible ?

The number of cups of flour should be used if 12 cups of sugar are used is 6.

Determine the purpose of the relationship. Start by identifying what you want the ratio to show. Each ratio uses different data, so you need to make sure you're using the correct information to get the details you need.

set the formula. A ratio compares two numbers, usually by division. When comparing one data point (A) to another data point (B), the formula is A/B. That is, divide information A by information B. For example, if A is 5 and B is 10, the ratio is 5/10.

Solve the equation. Divide data A by data B to get the ratio. In the example above, 5/10 = 0.5.

16 cups of flour are mixed with 8 cups of sugar and for 12 cup ratio should be same

so 16/8 = 12 /x

x = 6

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Answer:yes,no,yes,no i think

Step-by-step explanation:

Answer:B

Step-by-step explanation:

R^2=Q^2-P^2

R^2=2025

R=45

Answer:

b) 45cm

Step-by-step explanation:

by pythagoras theorem:

R² = P² - Q²

R² = 53² - 28² = 2809 - 784

R² = 2025

R = √2025

R = 45cm

Hope this helps!

The equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m. The first option from the given options is

Algebraic expressions that produce the same final expression are said to be equivalent expressions. If the values of two algebraic expressions can be obtained by replacing the variables, then the expressions are equivalent. Using the equal symbol (=), equivalent phrases are represented or illustrated to one another.

From the information given;

= 7m - (2 + 4m)

= 7m - 2 - 4m

Therefore, we can conclude that the equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m.

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There are 71,536,320 ways to arrange a standard deck of 52 cards so that all cards in a given suit appear contiguously.

There are 4 suits in a standard deck of 52 cards, and we need to arrange all the cards in a given suit contiguously. Once we choose a suit to be arranged in this way, we can treat it as a block of 13 cards that need to be arranged. Therefore, we have reduced the problem to arranging 4 blocks of 13 cards each, where each block represents a suit.

Within each suit, there are 13! ways to arrange the cards. However, once we arrange the cards in one suit, we fix the relative positions of the cards in the other suits. Therefore, we only need to consider the number of ways to arrange the suits themselves.

There are 4! = 24 ways to arrange the 4 suits. For each of these arrangements, there is only one way to arrange the cards within each suit contiguously. Therefore, the total number of ways to arrange the deck of cards so that all cards in a given suit appear contiguously is:

13! x 24 = 71,536,320

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