the following data shows the marks of 40
Students in a Chemistry examination.
41.52 37 56 63 48 65. 46 54 32 51
66 74 25 35 61 58 44 49 53 45 57 5
38 59 28 50 49 67 56 36 45 79 68 4
56 26 47 55 71
form a grouped frequency table with the
Class interval 20-29, 30-39, etc..
using an assumed mean method, find the mean

Answer:

1,7

Step-by-step explanation:

you go up one and over seven and i'll be on the other point

Answer:

See below

Step-by-step explanation:

2x = 10

Divide by 2.

x = 5

x has to equal 5 to make the first statement true.

Proof:

2x = 10

2(5) = 10

10 = 10

-3x = 21

Divide by -3.

x = -7

x has to equal -7 to make the second statement true.

Proof:

-3x = 21

-3(-7) = 21

21 = 21

1/3(x) = 6

Multiply by 3 to cancel the fraction.

x = 18

x has to equal 18 to make the third statement true.

Proof:

1/3(x) = 6

1/3(18) = 6

6 = 6

-1/2(x) = -7

Multiply by -2 to cancel the fraction.

x = 14

x has to equal 14 to make the fourth statement true.

Proof:

-1/2(x) = -7

-1/2(14) = -7

-7 = -7

Answer:

The equation that models the situation is \(y = 8 - 0.75t\)

Step-by-step explanation:

Equation of a line:

The equation of a line, in slope-intercept formula, has the following format:

\(y = mx + b\)

In which m is the slope(how much y changes when x changes by 1 unit) and b is the intercept, which is the value of t when x = 0.

A candle is 8 inches tall and burns at 3/4 inch each hour.

Using t as number of hours and y as the height.

Initial height of 8 inches, that is, when \(t = 0, y = 8\), so \(b = 8\)

Burns at 3/4 inch each hour.

That is, the height decreases by a rate of 3/4 inch each hour, so \(m = -\frac{3}{4} = -0.75\)

So

\(y = 8 - 0.75t\)

The weight of the coalition P1, P2, P3 is 36

From the question, we have the following parameters that can be used in our computation:

weighted voting system [20: 9,7,5,3,1]

The variable P1, P2 and P3 are the first three values

So, we have

P1 = 20

P2 = 9

P3 = 7

The weight of the coalition P1, P2, P3 is the sum of the points

So, we have

Coalition = 20 + 9 + 7

Coalition = 36

Hence, the weight coalition is 36

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Step-by-step explanation:

5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105

21,42,63,84,105

(the common factor is 105/105

The characteristics of the function graphed are given as follows:

As the function is increasing, the graph represents exponential growth.

The y-intercept is the value of y at which the graph crosses the y-axis, hence:

y = 2, point (0,2).

Which is also the horizontal asymptote, as it is the lowest value assumed by the function.

The domain and range are given as follows:

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Info given and question

For this case we know that for each two packages of walnut we have three batches of cookies

She decided to write out the recipe for one batch of cookies. If each packages says that it contains 2 1/4 cups of walnut how many cups of Walnut are in each recipe?

Solution

From the info given we have the following proportional rule:

We know that each package containes 2 1/4 cups of Wainut

So we can do the following operation to solve the question:

so then we can conclude that we need 3/2 of cups per each batch

Answer:2 quarts

Step-by-step explanation:

Answer: 12/5 which simplifies to 2 2/5.

Step-by-step explanation: Check attachment.

The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960

We are told that  two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity

The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.

Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;

x + y ≤ 9

x ≥ 2

y ≥ 3

Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;

20x + 50y ≤ 360

Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;

Z = 80x + 120y  maximize

The solution from the graph attached is;

x = 3, y = 6

Thus, the maximum profit is;

Z = 80(3) + 120(6)

Z = 960

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The triangle has another smaller triangle inserted into it as shown by the parallel lines.

By applying the side splitter theorem, the sides of the triangle becomes

Therefore x = 9

Answer:

I think the ratio would be 2/7.

Step-by-step explanation:

The probability that calls last between 4.0 and 4.6 minutes will be around 0.4332.

we have to standardize the values and utilize the standard typical dispersion table or calculator.

To discover the z-scores for 4.0 and 6.0  minutes:

z1 = (4.0 - 6.0  ) / 0.70 = 2.8

z2 = (4.5 - 6.0  ) / 0.70= 2.1

Since Employing a standard ordinary conveyance table, we are able to discover the likelihood of the calls enduring between 4.0 and 4.6 minutes:

P(0 ≤ Z ≤ 2.1) = 0.4332

However the likelihood that calls final between 4.0 and 4.6 minutes is 0.4332, or around 0.4332.

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Answer:

y=-x+10

Step-by-step explanation:

The formula is y=mx+b, where m is the slope and b is the y-intercept. To solve plugin the values for the corresponding variables. It has a slope of -1 and a y-intercept of 10.

Oh there is a free grid sheet that you can put there

Step-by-step explanation:

Search it up and the website will appear where it will give you pretty much all of the information about it

The proportionality constant (mm to cm) is 10 and the complete table is -

9 cm                 90 mm

12.5 cm             125 mm

50 cm               500 mm

88.49 cm          884.9 mm

A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.

Given is a proportional relationship between two scales.

{ 1 } -

We can write the proportionality constant (mm to cm) as -

{k} = (20 - 10)/(2 - 1)

{k} = 10

{ 2 } -

We can write the complete table as -

9 cm                  9 x 10 = 90 mm

12.5 cm             12.5 x 10 = 125 mm

50 cm               50 x 10 = 500 mm

88.49 cm          88.49 x 10 = 884.9 mm

Therefore, the proportionality constant (mm to cm) is 10 and the complete table is -

9 cm                 90 mm

12.5 cm             125 mm

50 cm               500 mm

88.49 cm          884.9 mm

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Answer:

B and D

Step-by-step explanation:

the opposite of -6 is positive 6

Answer:

531.4

Step-by-step explanation:

ED/AE=BC/AB

ED=AE*BC/AB

ED=240*620/280

ED=531.4

Answer:

123.15

Step-by-step explanation:

Where the daily growth factor is 1.15 and the starting height in inches is 7.

a. Given by, the function that calculates the height of the beanstalk in relation to the time since Gregory planted it.

\(f(t) = 7(1.15)^t\)

where the daily growth factor is 1.15 and the starting height in inches is 7.

B). The following ratios can be calculated using the formula from section (a):

f(1)/f(0) = (71.15¹)/(71.15⁰) = 1.15

f(2)/f(1) = (71.15²)/(71.15¹ = 1.15

f(1)/f(1) = (71.15¹)/(71.15¹) = 1

\(f(9.56)/f(8.56) = (71.15^{9.56})/(71.15^{8.56})\) ≈ 1.15

\(f(8.56)/f(8.55) = (71.15^{8.56})/(71.15^{8.55})\) ≈ 1.15

c. For the any value of z, we have:

\(f(z+1)/f(z) = (71.15^{(z+1)})/(71.15^z)\) = 1.15

and

\(f(z)/f(z-1) = (71.15^z)/(71.15^{(z-1)})\) = 1.15

For question 6:

a. As a increases throughout the function's domain, f(z) [Select an answer]

Since the base of the exponential function is less than 1 (0.69 < 1), as x increases, f(x) will approach 0.

b. The 1-unit growth factor of f is

The 1-unit growth factor for f is 0.69, since f(x+1)/f(x) = 0.69.

c. The -unit growth factor of f is

The 1/2-unit growth factor for f is (0.69)¹/₂, since f(x+1/2)/f(x) = (0.69)¹/₂.

d. The 6-unit growth factor of f is

The 6-unit growth factor for f is (0.69)⁶, since f(x+6)/f(x) = (0.69)⁶.

e. The 6-unit percent change of  f is

The 6-unit percent change for f is ((0.69)^6 - 1) * 100%, which is approximately -38.77%.

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1. Number of athletes did not own any of the three items = 259 - 228

= 31.

2. Number of athletes own a convertible and a TV but not a store = 44 - 9

= 35.

3. Number of athletes own a convertible or a TV = 110 + 91 - 44

= 157.

4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

5. Number of athletes owned at least one type of item = 259 - 31

= 228

6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71

= 118.

The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.

Total number of athletes surveyed = 259

Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228

Number of athletes who did not own any of the three items = 259 - 228 = 31.

The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.

Number of athletes who own a convertible and a TV = 44

Number of athletes who own all three items = 9

Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35

The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.

Number of athletes who own a convertible or a TV = 110 + 91 - 44

= 157.

The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.

Number of athletes own a convertible only = 110 - 15 - 9 = 86

Number of athletes own a TV only = 91 - 44 - 9 = 38

Number of athletes own a store only = 120 - 15 - 43 - 9 = 53

Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.

The number of athletes who owned at least one type of item can use the result from part (1).

Number of athletes who owned at least one type of item = 259 - 31

= 228

The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.

Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159

Number of athletes own a TV or a store not a convertible = 13 + 34 +71

= 118.

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Answer:

t = 1.2, -1.2

the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905

Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127

The test statistic :

T = r² / √(1 - r²) / (n - 2)

Sample size, n = 10

Hence,

T = 0.127² / √(1 - 0.127²) / (10 - 2)

T = (0.016129 / 0.3506905)

T = 0.3506905

The value of the test statistic to 2 decimal places is 0.35

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The vertex form is y= (x+ 6)²+1.

The vertex form of a quadratic equation is y = a (x- h)² + k as opposed to the regular quadratic form, which is an x² + bx + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.

a=1

b=12

c=37

Consider the vertex form of a parabola.

a(x+ d)²+e

Now, d= b/2a

d=12/ 2

d=6

and, e= c-b²-4a

e= 37 - (12)²/4x1

e= 37 - 36

e= 1

Then, the vertex form is

y = a(x+ d)²+e

y= 1(x+ 6)²+1

y= (x+ 6)²+1

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The Volume of the box is 12 cubic unit.

We have,

Height = 1 unit

Width = 2 unit

Length = 6 unit

So, Volume of box

= l w h

= 1 x 2 x 6

= 12 cubic unit

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The roots or zeroes of the given trinomial 2x² + 19x + 35 are x = -5/2 and x = -7.

Trinomials are polynomial expressions which consists of three terms.

For example, 2x + 7y + 5 is a trinomial.

Roots of a quadratic equation ax² + b x + c = 0 can be found using the quadratic formula,

x = [-b ± \(\sqrt{b^2-4ac}\) ] / 2a

Here \(\sqrt{b^2-4ac}\) is called the discriminant.

Given is a quadratic expression which is also a trinomial.

Let, 2x² + 19x + 35 = 0

Here, a = 2, b = 19 and c = 35

Discriminant = \(\sqrt{(19)^2-(4*2*35)}\)

                     = \(\sqrt{81}\)

                     = 9

Using the quadratic formula,

x = [-19 ± 9] / 4

x = [-19 + 9] / 4 and x = [-19 - 9] / 4

x = -10/4 and x = -28/4

x = -5/2 and x = -7

Hence the roots of the given equation are x = -5/2 and x = -7.

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The corrected complete question is as follows.

What are the roots of the trinomial 2x² + 19x + 35 ?

Answer:

6 m

Step-by-step explanation:

the Pythagorean theorem :

a²+b²=c²

=> b² = c²-a²

= 10²-8²

= 100-64

=36

so, b = √36 = 6

Answer:

190

Step-by-step explanation:

its 170 because 380-170=190