A box is put on a table. The face of the box in contact with the table is in the shape of a rectangle, 2 m by 1.25m. The pressure on the table due to the box is 42 newtons/m² Work out the force exerted by the box on the table.​

The three posts can be given in 4080 ways among 17 students.

It is given that the number of people available to choose the posts from is 17.

There are three posts here- president, vice president, and secretary.

Now, if we choose a candidate for President first, there are 17 students available.

Next, if we select a Vice-President, there are 16 ways to select the vice-president, since one student already is the president.

At, last there are 15 students available to choose the secretary from as two students already hold a post.

Hence, the number of ways to select the President, Vice-President, and Secretary are-

17 X 16 X 15 ways

Therefore we get

4080 ways.

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The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.

Given that,

Jake sold 49 tickets while jeans sold 12 for the school.

In simplest form the ratio of the given case will be;

Simplest form:

A fraction is a number that falls between the whole numbers but is not a whole number. It belongs to the entire. A fraction also consists of a denominator and a numerator. We obtain the fraction in its simplest form when both the numerator and denominator can no longer be independently reduced to any smaller integer.

The ratio we get;

→ 12/49

The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.

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Answer:

you have to add x outside of the parentheses

Step-by-step explanation: hope this helps

Answer:

Step-by-step explanation:

5 + 4 × 3 - 2

9 × 3– 2 =

27–2 = 25

Answer:

477,577 lb

Step-by-step explanation:

Volume of sphere:

V = (4/3)πr³

V = (1/2)(4/3)(3.14159)(14 ft)³ = 5,747.015 ft³

d = 83.1 lb/ft³

W = Vd

W = 5,747.105 ft³ × 83.1 lb/ft³

W = 477,577 lb

Answer:

y ≥ -5 and y > 7

Step-by-step explanation:

Collect like terms

-y ≤ 8 - 3

-y ≤ 5

Divide both sides by -1

-1y/-1 ≤ 5/-1

y ≥ -5

And

y > 9 - 2

y > 7

Answer:

6cm square

Step-by-step explanation:

The length AB of rectangle in terms of x is (4 + x) and values of a and b are 10 and 4.

The side AB measures (4 + x). Hence, the length of AB in terms of x is (4 + x).

The area of rectangle is calculated by the formula-

Area = length × breadth

Keep the values in formula -

28 = (4 + x) (6 + x)

Performing multiplication of both brackets with each other

28 = 24 + 4x + 6x + x²

Solving and rewriting the equation

x² + 10x = 4

Equation in question - x² + ax = b

Comparing both the equations, we get a = 10 and b = 4.

Thus, length of AB is (4 + x) and value fo a is 10 and b is 4.

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(4, 1) is the solution for the given inequalities

Given,

The system of inequalities;

3x + y ≤ 14

3x + 5y < 19

We have to find that (4, 1) is a solution to the given system of inequalities;

So,

(x, y) = (4, 1)

Then,

Substitute the values of x and y in the equation;

3x + y ≤ 14

3 x 4 + 1 ≤ 14

12 + 1 ≤ 14

13 ≤ 14

Next,

3x + 5y < 19

3 x 4 + 5 x 1 < 19

12 + 5 < 19

17 < 19

Here,

(4, 1) is the solution for the given inequalities

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Answer:

option c this is no solution for the equations

Answer:

x=5 y=-8 the calc are in the photo

The probability to win two or more tickets in the lottery is 0.118

It is given that there is a 5% chance to win a lottery ticket.

Therefore, the probability to win a lottery ticket is

0.05

The girl here plays the game 12 times. The above distribution is clearly a Binomial Distribution

ⁿCₓ  X  pˣ  X  (1 - p)ⁿ⁻ˣ

We need to calculate the probability to win 2 or more tickets

= 1 - the probability to win at least one ticket

= 1 - P(X = 0) + P(X = 1)

here,

p = 0.05

1 - p = 0.95

n = 12

P(X = 0)

= ¹²C₀  X  0.05⁰  X  0.95¹²

= 0.54036

P(X = 1)

= ¹²C₁  X  0.05¹  X  0.95¹¹

= 0.34128

Hence we get

P(X ≥ 2) = 1 - 0.54036 - 0.34128

= 0.118

Therefore, we get the probability that the person will win 2 or more tickets to be 0.118

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The height of the tree is 13.2 m.

What is proportional ?

 The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.  

We can set up a proportion comparing the height of each object to the length of the shadow.

Then , [tex]\frac{h}{s}[/tex].

=> [tex]\frac{3.8}{1.3} = \frac{h}{4.5}[/tex]

=> h = [tex]\frac{3.8*4.5}{1.3}[/tex]

=> 13.2 m.

Hence the height of the tree is 13.2 m.

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Answer: y intercept is -1

Step-by-step explanation:

Answer:

For x = -2, y would equal -3.

For x = -1, y would equal -2.

For x = 0, y would equal -1.

For x = 1, y would equal 0.

For x = 2, y would equal 1.

Step-by-step explanation:

So what we have to do is plug in the x-values from the table into the equation.

1) y = -2 -1 => y = -3

2) y = -1 - 1 => y = -2

3) y = 0 - 1 => y = -1

4) y = 1 - 1 => y = 0

5) y = 2 - 1 => y = 1

The value of the expression −2(42−7)+(−5) is -75.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, we want to calculate the value of the expression:

−2(42−7)+(−5)

= -2(35) + (-5)

= -70 - 5

= -75

The value is -75.

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The dimensions required to minimize the cost of fencing is 180ft and 360 ft.

According to question

The cost of fence on opposite side of river is $40.

The cost of fence on other sides of river is $10.

Total yield = 64800 sq. feet

Let the length of fence on the opposite side of fence be x and width of fence on the other side be y.

Area of fence = xy = 64800 sq feet

⇒ [tex]y = \frac{64800}{x}[/tex]

Let C be the cost of making fence.

For cost to be minimum, dC/dx should be equal to zero.

C = 40x + 10y * 2

⇒ C = [tex]40x + 10(\frac{64800}{x})*2[/tex]

⇒ [tex]\frac{dC}{dx} = 40 + 20 * 64800 * \frac{-1}{x^{2} } = 0[/tex]

⇒ [tex]40x^{2} = 20 * 64800[/tex]

⇒ [tex]x^{2} = 32400[/tex]

⇒ [tex]x = 180[/tex]

⇒ [tex]y = \frac{64800}{180} = 360[/tex]

So, the dimensions needed will be 180 ft and 360 ft.

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Ester, Sarai, and Kurry each selected a number: 0.009, 0.09, and 0.9, respectively.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes. For instance, 3+3+3+3+3 can be expressed as 3 5.

the ester's number is equal to one-tenth of the Sarai number.

= 1 / 10 × 0.09 = 0.009

to determine Kurry's number, multiply Sarai's number by 10

= 10 × 0.09 = 0.9

Therefore, it can be inferred that Kurry chose 0.9, Ester chose 0.009, and Sarai chose 0.09.

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The equation of a line in the point-slope form that has a slope of 1/3 and passes through the point (6,-2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex].

Calculation

[tex]y-y_{1} =m(x-x_{1} )[/tex]

[tex]y-(-2) =\frac{1}{3} (x-6 )[/tex]

[tex]y+2 =\frac{1}{3} (x-6 )[/tex]

Therefore, the equation of a line in the point-slope form that has a slope of 1/3 and passes through the point(6, -2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex]

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The distance of the intersection of 3 perpendicular bisectors of a triangle to  the 3 vertices are equal.

In other words, HF = HE = HG.

Therefore, we see that 3 isosceles triangles are identified : HFE, HFG, HGF.

We're given HF = 15, therefore HE = 15.

Since HJ is the perpendicular bisector of line EG, JE = JG.

Therefore, JE = 12.

Now, we use the Pythagorean theorem in the right triangle HJE :

[tex]HE^{2} = HJ^{2} + JE^{2} - > HJ = \sqrt{15^{2} - 12^{2} } =\sqrt{81} = 9.[/tex]

Answer:

324 cm²

Step-by-step explanation:

area of a square = L x L = L²

L = 18cm

(18cm)² = 18cm x 18cm = 324 cm²

The no. of ways could those question be ordered is  1307674368000 ways A combination is what?

When selecting components from a collection using the combination method, the sequence of selection is unimportant, in contrast to permutations. In simpler scenarios, the number of combinations can be counted.

The act of combining n objects into k groups, one at a time, without repetition Repetition-allowed combinations are usually referred to as k-selection or k-combinations with repetition.

Given

that, Total no of question in quiz is 15 The no. of ways could those question be ordered is 15! ways =  1307674368000 ways The number of possible ways for those questions is 1307674368000.

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The linear equation to represent the total cost c =  2.25s + 1,347.85.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Using slope

slope= ( 5847. 75 - 4074 . 85)/( 2000- 1200)

slope= 1800 - 800

slope= 2.25

and, slope- intercept form

c - 4047.85 = 2.25 ( s- 1200)

c - 4047.85 = 2.25s - 2700

c = 2.25s - 2700 + 4047.85

c =  2.25s + 1,347.85

Hence,  linear equation to represent the total cost c =  2.25s + 1,347.85.

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Caina anticipate in income next year  $14000.

What is an income?

The amount of money, property, and other value transfers received over a predetermined period of time in return for goods or services is often referred to as income.

We have,

A scholarship of $6000 and a grant of $3200 together are $9200

6000 + 3200 = 9200.

She will make another $400 per month working a part-time job, so for 12 months she will make $400 × 12 = $4800.

All together will be $9200 + $4800 = $14000.

Therefore, She anticipate in income next year  $14000.

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Answer:

62%

Step-by-step explanation:

1040-110-145-139=646

646/1040=62%

Step-by-step explanation:

3.

we need to find the map size based on actual miles.

so, we find how many map ft are 1 actual mile :

5 ft / 20.5 corresponds to 1 actual mile.

5 / 20.5 = 10/41 ft

now, we have 15.5 actual miles, that is 15.5 times the 1 standard actual mile.

and so, this is

10/41 × 15.5 = 155/41 = 3.7804878048780... map ft

4.

30.5 model cm = 70.6 actual m

1 model cm = 70.6/30.5 = 2.314754098... actual m.

8 model cm = 8×2.314754098... =

= 18.51803279... actual m

5.

7 map m = 14 actual miles

1 map m = 14/7 = 2 actual miles.

14 map m = 14×2 = 28 actual miles.

6.

8 map km = 6 actual miles

we need to calculate the map km, so we need the standard actual mile

1 actual mile = 8/6 = 4/3 = 1.3333333... map km.

50.2 actual miles = 50.2×1.333333... =

= 66.93333333... map km.

7.

80.2 model cm = 40.2 actual m

1 model cm = 40.2/80.2 = 0.501246883... actual m

10 model cm = 10×0.501246883... =

= 5.01246883... actual m

8.

6 map m = 15 actual miles

1 map m = 15/6 = 5/2 = 2.5 actual miles

8.8 map m = 8.8×2.5 = 22 actual miles

9.

5 map ft = 16.5 actual miles

1 actual mile = 5/16.5 = 0.303030303... map ft

45.6 actual miles = 45.6×0.303030303... =

= 13.81818181... map ft

10.

65.8 model cm = 95.6 actual m

1 model cm = 95.6/65.8 = 1.452887538... actual m

12 model cm = 12×1.452887538... =

= 17.43465046... actual m

Answer:

Step-by-step explanation:

yes, it is a function

Answer: no

Step-by-step explanation: you have -2,-5 and -2,0 you cant have 2 or more x values that are the same.

Extend the compass from point T to little more than the midpoint of ST in such a way the arc drawn touches the point R. Similar is to be done from point S. Draw a line through the cut made by the 2 arcs at R.

The value of the correlation coefficient is 0.625.

Correlation coefficients quantify the strength of a relationship between two variables. A correlation coefficient is a number ranging from -1 to 1 that indicates the degree and direction of a relationship between variables. It is a statistical notion that aids in the establishment of a relationship between predicted and actual values collected in a statistical experiment.

In this case, the slope of the model was 2.5 centimeters per pH level, and the standard deviation of the sample of plant heights was 4 centimeters.

The correlation coefficient will be:

= Slope / Standard Deviation

= 2.5 / 4

= 0.625

The coefficient is 0.625.

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Answer:

Step-by-step explanation:

18% of 430 comes out to 77.4 total pictures taken. After rounding it to the nearest whole number because you cant take a fraction of a picture it would be 77 total pictures taken.