A cycle Wheel does 1645 full turns in 7 minutes
work out the number of full turns per minute

Step-by-step explanation:

so, we have

6x² + 8xy + 8y²

and

5x² + 3xy + 16y²

we can combine only terms of the same kind (defined by the type and exponent of the used variables).

this is like adding fruit.

e.g. when we have a mixture of 3 apples, 4 oranges and 5 plums, and we add a mixture of 6 apples, 2 oranges and 3 plums - what do we get ?

we get a new mixture of

3+6 = 9 apples

4+2 = 6 oranges

5+3 = 8 plums

and exactly the same thing happens with mixing terms when adding them up.

so, we get

6+5 = 11x²

8+3 = 11xy

8+16 = 24y²

so, the result is

11x² + 11xy + 24y²

it is really that simple.

The area of Sasha's backyard is 1064 yard square. So the number of bags required would be 20.

What is area?

The measurement that expresses the size of a region on a plane or curved surface is called area. It's S.I. unit is m².

Main Body:

The area of Sasha's backyard = 38*28

= 1064 yd square

Now 1 bag covers 55 yd square

so, bag required for 1064 yd = 1064/55

= 19.3 approximately

Therefore the amount  of required bags are 20.

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The students and courses have one to many relationship.

A one to many relationship is such kind of relation which exist when a particular function is linked to many other functions. It means that many elements of the set A is related to a single element of the set B.

In this case, the course is only one but the students studying the course are more in number. The same course is studied by many student but in different manner but the course is same. This is why we conclude that the relationship between the students and the course is one to many.

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AB has endpoints A (1, 7) and B (5, 4) and DE has endpoints D (-6, -2) and E (-2,-5). The translation is by the rule (x - 7, y - 9), is used to transform AB to DE

Translation is a type of transformation that involve a linear movement.

The translation rule is gotten by comparing the points as below

preimage point A (1, 7) and B (5, 4)

image points D(-6, -2) and E(-2,-5)

x coordinate

using point A and D = -6 - 1 = -7

using point B and E = -2 - 5 = -7

y coordinate

using point A and D = -2 - 7 = -9

using point B and E = -5 -  = -9

Therefore the translation rule is (x - 7, y - 9) that got the image, point D and E from the preimage , point A and B

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Answer: Positive

Step-by-step explanation: It would be positive because the question is asking how much money they lost. The lost a positive amount of money.

Answer:

a) 2.0 x 10^5

b) 8.0 x 10^4

c) 9 x 10^9

d) 1 x 10^10

Answer:

  0.591

Step-by-step explanation:

You want the probability that a height falls between 50.5 and 53.7 when the distribution of heights is normal with mean 53.4 and standard deviation 1.2. All measurements are in inches.

The area under the normal distribution curve with mean 53.4 and standard deviation 1.2 can be found using a suitable calculator. The one in the attachment shows the area between 50.5 and 53.7 is about 0.591

P(50.5 < X < 53.7) ≈ 0.591

__

Additional comment

Any spreadsheet and most graphing calculators have the necessary probability functions. Many special-purpose apps also can answer this question. A calculator answer is shown in the second attachment.

The number of grams of salt in the tank at time t is given by the differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].

The rate is basically a measurement of something's number, amount, or degree in relation to another item. Its the ratio of some quantity to some other quantity.

An equation with a function and one or more of its derivatives is referred to as a differential equation:

At the start, the tank contains A(0) = 30 g of salt.

Salt flows in at a rate of

(1 g/L) * (4 L/min) = 4 g/min

and flows out at a rate of

(A(t)/200 g/L) * (6 L/min) = 3A(t)/100 g/min

so that the amount of salt in the tank at time t changes according to

A'(t) = 4 - A(t)/50

So,

[tex]A'(t) = 4 - \frac{A(t)}{50}[/tex]

The solution of linear differential equation y' + ay = g(x) is in the form,

[tex]e^{ax}y=\int {e^{ax}g(x)} \, dx +c[/tex]

Now, putting the values,

[tex]a=\frac{1}{50} \\g(x)=4[/tex]

[tex]e^{\frac{1}{50}t}A(t)=\int {e^{\frac{1}{50}t}4} \, dt +c\\=4\int {e^{\frac{1}{50}t}} \, dt +c\\=4\times50e^{\frac{1}{50}t}+c\\=200e^{\frac{1}{50}t}+c\\[/tex]

Now,

[tex]A(t)=200+Ce^{-\frac{1}{50}t}\\[/tex]

Putting the initial value,

[tex]30=200+Ce^{-\frac{1}{50}(0)}\\\\200+C=30\\C=-170[/tex]

So, the function will be [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].

Therefore, the number of grams of salt in tank at time t is given by differential equation [tex]A(t)=200-170e^{-\frac{1}{50}t}[/tex].

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Step-by-step explanation:

the triangle above is an isosceles triangle,

two sides and angles are equal

AC=AD

triangle ACB=triangle ABD(because it is an isosceles triangle )

For given expression  (7^3) * (7^x) equivalent expressions are:

343 * 7^x and 7^(3+x)

The correct options are option (C) and option (D)

In this question, we have been given an expression (7^3) * (7^x)

We need to find expressions that are equivalent to given expression.

Consider given expression (7^3) * (7^x)

We know that 7^3 = 343

So given expression becomes, (7^3) * (7^x) = 343 * (7^x)

For given expression, the bases of the exponents are equal.

so, by the properties of exponents

(7^3) * (7^x) =  7^(3 + x)

Therefore, for given expression  (7^3) * (7^x) equivalent expressions are:

343 * 7^x and 7^(3+x)

The correct options are option (C) and option (D)

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Answer:

-2 ; -1 ; 0 ; 1

Step-by-step explanation:

the inequality is satisfied in this interval [-2.5,1].

We are searching the integers: -2 ; -1 ; 0 ; 1

All the values of x that satisfy the inequality will be;

⇒ x = - 2, - 1, 0, 1

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is given.

Now,

The solution of the inequality are given as;

⇒ x ∈ [- 2.5, 1]

But we can find the integers which satisfy the inequality.

Hence, All the values of x that satisfy the inequality will be;

⇒ x = - 2, - 1, 0, 1

Thus, All the values of x that satisfy the inequality will be;

⇒ x = - 2, - 1, 0, 1

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The amount of money that Amelia would spend on five bags of cat food is $22.5.

Amelia needs to buy some cat food. At the nearest store, three bags of cat food cost $13.50. We need to find out the amount of money that Amelia would spend on five bags of cat food.

Let the amount of money that Amelia would spend on 5 bags of cat food be represented by the variable M. We will use the unitary method. First of all, we will calculate the cost of one bag of cat food.

C = $13.50/3

C = $4.5

Now we need to find out the cost of five bags of cat food.

M = $4.5×5

M = $22.5

Hence, the amount of money that Amelia would spend on five bags of cat food is $22.5.

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Answer: 110°

Step-by-step explanation:

Looks like a bit more than 100°.

7 i do not feel like explaining tbh

Vertex form

f(x)= 3(x+2)^2+4

Step-by-step explanation:

I don't see the options and how they are written, but I can tell you the right answer in numbers :

sin(F) = 3/5 = 0.6

cos(F) = 4/5 = 0.8

sin(G) = 4/5 = 0.8

cos(G) = 3/5 = 0.6

why ?

remember the norm circle (radius 1) with ask the trigonometric functions.

the sine of an angle is the vertical height from that point in the circle arc down to x-axis.

the cosine of an angle is the length on the x-axis from the center of the circle to the point, where the sine touches the x-axis.

in any case, sine and cosine enclose the right angle (90°).

each function is now defined for the norm circle with radius = 1.

for angles in larger circles we need to divide the find lengths by the actual radius (we formality do this in the norm circle too, but a division by 1 does not change anything).

for the angles at F and G the radius is the side with the length 5.

Looking at the triangles, the values of x in the figures are

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

figure in 14)

The solution for x

8 / (x + 5) = (x - 9) / 21

21 * 8 = (x + 5)(x - 9)

168 = x^2 - 4x - 45

x^2 - 4x - 213

x = 16.73 or -12.73

using the positive value

x = 17

figure in 15)

The solution for x

(x + 3) / 15 = 4 / (3x + 1)

cross multiplying

(x + 3)(3x + 1) = 15 * 4

3x^2 + 10x + 3 = 60

3x^2 + 10x - 57 = 0

x = 3 OR -6.333

taking the positive value

x = 3

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The largest sample size required is 2886.4.

Here we have to calculate how large of a sample size is required.

The formula:

(Z ∝I2/ E)² × P( 1- P)

The given data:

Margin error (E) = 1.5%

=0.015

As it is given that 90% confident that your estimate is within 1.5% of the true population proportion, therefore we have:

The level of significance(∝) = 1 - 0.90

= 0.10

The z value for the 90% confidence is 1.645

Therefore the largest of a sample size is required = ( 1.645/ 0.015)²× ( 0.4)(1- 0.4)

= 2886.4

The largest a sample size required is 2886.4

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The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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Answer:

b = 10.06 in

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (10.5)² = b² + (3)²

→ 110.25 = b² + 9

→ b² = 110.25 - 9

→ b = √101.25

→ [ b = 10.06 in ]

Hence, value of b is 10.06 in.

Answer:

The factory makes 12,000 (12k) hats each day

Step-by-step explanation:

4000

× 3

--------

12,000

Answer:

3.46

Step-by-step explanation:

[tex]\sqrt{21-9}[/tex]

[tex]\sqrt{12}[/tex]

3.46

Hopes this helps please mark brainliest

This comes to $141, indicating that Ms. Patel spent that money on four sets of pliers, two wrench sets, and a chisel set.

The given condition states that;

Make a ratio first.

This ratio might be expressed as 4:2:1 (in pliers, wrenches, and chisels).

Then, multiply every one of these sums by their respective prices before adding them all up.

Pliers : 4 times 17.50 equals $70

Wrenches : $2 x $21.5 = $43

Chisels : 1 x 28 equals $28

Thus,

Sum = $70 + $43 + $28

Sum = $141

This amounts to $141, proving that she purchased a chisel set, two wrench sets, and four pairs of pliers.

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Answer:

4:1

Step-by-step explanation:

12÷3=4

3÷3=1

white to blue

12 : 1

Answer:

y = -1.5

Step-by-step explanation:

use the method y2 - y1 / x2 - x1

The Kilometer that Alan was left to walk is given as c six and twenty five thirty thirds kilometers

In order to solve for the solution, we would have to write out the expressions in mathematical forms first

eight and two thirds kilometers = [tex]8\frac{2}{3}[/tex]

This is is the time that Alan is said to travel for him to get to school

The expression one and ten elevenths is written mathematically as [tex]1\frac{10}{11}[/tex]

This is the kilometer that he spent running.

We are to find the time that was used to walk to school.

To get this we have to subtract the kilometer that he ran from the total kilometer that he traveled.

[tex]8\frac{2}{3} - 1\frac{10}{11}[/tex]

we have to express as a mixed fraction then we would subtract

26/3 - 21/11

= 286 - 63 / 33

= 223/33

= 6.75

= 6 25/33

Hence the solution is C.

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Equation of the given data y = 1750x -20,000 and graph of the equation is attached.

As given in the question,

Data of the table :

Year :               1                 2                   3              4                5

Investment : $20,000      $21,750      $23,500    $25,250      $27,000

(x₁, y₁) = ( 1, 20,000)

(x₂, y₂) = ( 2, 21,750)

Equation of the given graph is :

( y - 20,000)/ (x -1) = (21,750 - 20,000)/ (2 -1)

⇒ ( y - 20,000)/ (x -1) = 1750

⇒ y = 1,750x -18,250

Graph of the equation  y = 1,750x -18,250 s represented by the graph.

Graph is attached.

Therefore, equation of the given data y = 1750x -20,000 and graph of the equation is attached.

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