The flywheel on a steam engine rotates 60 revolutions every 15 seconds.



What is the flywheel’s rate of revolutions per second?





Identify the unit rate.

The latest time Alice can start making the cake batter is 8:33 A.M

Alice is making cake for her mother's birthday

It will take 24 minutes to make the cake batter

The cake also needs to be in the oven for 1 hour 2 minutes

The time needed to make the cake is

1 hour 2 minutes + 24 minutes

= 1 hour 26 minutes

The latest time to start making the cake batter is

9:59 - 1:26

= 8:33

Hence the latest time to start making the cake batter is 8:33 A.M

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Answer:

m1 = 122°

m2= 58°

Step-by-step explanation:

M1 is an alternate interior angle, of 122°, which means that that angle is also 122°.

The line with m1 and m2 added together equal 180°, so we can subtract 122 from 180 to find m2.

180-122= 58

5 = (1/2)2 + 4 is an equation in intercept form for the line passing through the points (2,5) and (6,7)

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope.

We have been asked to write an equation in slope-intercept form for the line passing through (2,5) and (6,7)

First we will find the slope(m)

We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the pairs of points (2,5) and (6,7)

⇒ m = [tex]\frac{7- 5}{6 - 2}[/tex]

⇒ m = [tex]\frac{2}{4 }[/tex]

⇒ m = 1/2

We know that the equation for slope(m) and y - intercept(b) of a line is given by :

y = mx + b

Here lets take equation 5 = (1/2)2 + b .Here x and y is substituted with the first two points.

⇒  5 = (1/2)2 + b

⇒  5 = 1 + b

⇒  b = 5 - 1

⇒  b = 4

The equation in the slope intercept is as follows:-

5 = (1/2)2 + 4

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Answer:

x > 2

Step-by-step explanation:

because , you have to use inverse operation to check your answer .

-6x-4< 2x-20

-6x-4+4<2x-20=4

-6x<2x-16

-6x-2x<2x-16-2x

-8x<-16

(-8x)(-1)>(-16)(-1)

8x>16

8x/8 > 16/8

x>2

Answer: 4.7 gallons

Step-by-step explanation:

The range is the difference in the highest number and the smallest number, so 2.8 - -1.9 = 4.7

Answer:

the square root rounded up is around 8

Step-by-step explanation:

because if the 5 is not beside the number it rounds down and the number was 3 so its 8

Answer:

213.7°

Step-by-step explanation:

The bearing of B from D is angle ADB, which is ∠ADB = arctan(30/45)

≈ 33.7°

The bearing of D from B is that angle plus 180°, so is 180° +33.7° = 213.7°

Answer:

225°

Step-by-step explanation:

In mathematics, a bearing is defined as an angle measured clockwise from north.

See attached graph for a clearer guide to the explanations

Angle ABC is a right isosceles triangle with AB = 25 and AC = 25

m∠BAC =90°

So m∠ABC = m∠ACB = 45°

The angle at BC is 45° from the North (90°-45°)  measured clockwise is 45° so we say the bearing from C to B is 045°  (we use 3 digits for bearing)

The bearing from B to C on the other hand is determined by adding 180° to the bearing in the opposite direction (C to B) so the bearing from C to B is 180° +045° = 225°

(Here I am not sure whether you are supposed to answer the question in mathematical meaning of bearing or just state the direction in which BC lies relative to north. 45° clockwise from the North is in a NE direction so we can say C is NE from B but I am guessing that's not it)

Answer:

22 divided by 2 equals 11, so each shirt at store one, you are getting for $11. Store 2 is having a sale of 10% off 12.99 is 11.69, so each shirt is $11.69. So, Store 1 is a better deal.

Step-by-step explanation:

Answer:

1.38$

Step-by-step explanation:

QUESTION

Two stores are having sales on the same shirt. the sale at store 1 is "2 shirts for $22" and the sale at store 2 is "each $12.99 shirt is 10% off". explain how much will you save by buying at store 1.

EXPLANATION

store one 2 shirts 22$

store 2 1 shirt 12.99/10=1.30 so 12.99-1.30=11.69x2=23.38

23.38-22=1.38

The sum of the solutions are 32/3.

The modulo (or "modulus" or "mod") is the remainder after dividing one number by another.

Example: 100 mod 9 equals 1

Because 100/9 = 11 with a remainder of 1

Another example: 14 mod 12 equals 2

Because 14/12 = 1 with a remainder of 2

12-hour time uses modulo 12 (14 o'clock becomes 2 o'clock)

It is where we end up, not how many times around.

|3y-4|=9

3y-4=9 or 3y-4=-9

3y=13 or 3y=-5

y=13/3 or y-5/3

|y-4|=3

y-4=3 or y-4=-3

y=7 or y=1

The solutions are y=13/3, y=-5/3, y=7, y=1

Hence the sum of the solutions are 32/3.

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Step-by-step explanation:

A and B are similar but not congruent

similar=same shape

congruent=same shape and same size

The total cost of 10 brownies is $4 is the statement that best describes the meaning of f(4) = 10, if f(x) is the total cost, in dollars, of x brownies.

In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are widespread in mathematics and are required for the formulation of physical relationships in the sciences. The present concept of function was initially proposed in 1837 by the German mathematician Peter Dirichlet.

If a variable y is so closely tied to a variable x that whenever a numerical value is assigned to x, there is a rule that determines a unique value of y, then y is said to be a function of the independent variable x.

As we can see it is mentioned that f(x) = total cost = f(4)

So only option d. has 4 as total cost, that why d is the right option and statement as follows The total cost of 10 brownies is $4.

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Answer:

The value of the given series is 49.75

Step-by-step explanation:

This is a problem from geometric progression ,

As we know the formula for geometric progression is aₙ = a₁ r ⁿ⁻¹

Where , a₁ is the first term and r is the ratio , and n is the number of terms.

Ratio is , 40/80 = 1/2

Here , a₄ = 80 . (1/2)⁴ ⁻ ¹ = 80 / 8  = 10

a₅ = 80 . (1/2)⁵ ⁻ ¹ = 80 / 16 = 0.5

a₆ = 80 . (1/2)⁶ ⁻ ¹ = 0.25

a₇ = 80 . (1/2)⁷ - ¹ = 0.125

a₈ = 80 . (1/2) ⁸ ⁻ ¹ = 0.625

Now the series can be written as .

80-40+20- 10 + 0.5 - 0.25 + 0.125 - .625 = 49.75

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 The full quadratic expression is expressed as follows:

x² - 5x + 6.25

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

   To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:

(a - b)² = a² - 2ab + b²

x² - 5x + ?

5x = 2xb

2b =5

b = 5/2

   Let's complete the square

x² - 5x + (5/2)²

x² - 5x + 25/4  

x² - 5x + 6.25

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The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.

What is a triangle similarity criterion?

According to the Angle-Angle (AA) criterion, two triangles are considered comparable if "two angles of one triangle are respectively equivalent to two angles of another triangle."

What distinguishes AA similarity from AAA similarity?

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1,2,5 square root both sides

4x+5x+=6+11

9x=17

x=17/9

☞ user58580~ ♥

Answer:

x= 17/9

Step-by-step explanation:

4x+5x=6+11

Combine like terms

9x=17

x=17/9

Answer:

0.03x+0.05=1.50

Hopely this can help you

Step-by-step explanation:

The standard deviation is 7.35.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79

Determine the difference between each value and the mean and then square the result:

(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)²  + (84- 79)²  + (68 - 79)²  +( 75- 79) ²

64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√432 / 8 = 7.35

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The slope intercept form is y = 1/4x + 13/4

The general expression for slope intercept form is given as follows

                 y = mx + c

        where, m = slope of the line

                       c = intercept

We have been given the equation that is,

         y – 2 = 1/4(x+ 5)

We will solve this step by step to convert it into the general form that is,

       y – 2 = 1/4(x+ 5)

       y – 2 = 1/4x + 5/4

          y = 1/4x + 5/4 + 2

          y = 1/4x +13/4

which is in the general form of   y= mx + c where m = 1/4 and c = 13/4

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Answer: Option (4)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the line we want to find is -5/3.

Of the options, the only one that satisfies this is choice 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

The simplified expression of -35 / (-5) is 7.

Let the given expression be -35 / (-5) then

-35 / (-5) = -35/-5

simplifying the above equation, we get

= 35/5

= 7

Therefore, the value of -35 / (-5) is 7.

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The number is represented by 6 tens 7 ones 67 .

Let the unit's place digit be " x " and ten's place digit be " y ".

Two digit number is given by = 10 y + x      .....(1)

It is given that 6 tens 7 ones.

Putting x = 6 and y = 7 in equation (1) , we get

10(6) + 7 = 60 + 7

              = 67

Hence , the number is 67 .

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the expression representing the total amount earned by Evelyn is $ 25 x + $ 90 y .

We are given that

Evelyn makes x haircuts for $ 25 and y perms for $ 90.

We need to write an expression representing the situation

We will use multiplication for the same.

So, Amount earned from the haircuts = x × $ 25 = $ 25 x

Amount earned from perms = y × $ 90 = $ 90 y

Total amount earned = $ 25 x + $ 90 y

Therefore, we get that, the expression representing the total amount earned by Evelyn is $ 25 x + $ 90 y .

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The value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] at c = -5 is [tex]5(-125 +6\sqrt{10})[/tex]  .

An algebraic expression is an expression having constant and variable joined with algebraic operation(+,-,×,÷).

For Example , 2c+5x+6 is an algebraic expression.

In the given expression

[tex]=5c^{3} -6c\sqrt{-2c}[/tex]

Substituting the value of c = -5 .

We get ;

[tex]=5(-5)^{3} -6(-5)\sqrt{-2(-5)}[/tex]

[tex]=5(-125) +30\sqrt{-2(-5)}\\ \\ =-625 +30\sqrt{10}[/tex]

taking 5 common from both the terms

[tex]=5(-125 +6\sqrt{10})[/tex]

Therefore , the value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] is [tex]5(-125 +6\sqrt{10})[/tex].

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The point P which partitions the line segment AB have coordinates as P(0,3)

Line Segment is a line which joins together two points to form a straight line. It can be extended in either side.

It is given that,

A line segment AB having coordinates such as A(0,0) and B(0,6) respectively

The line segment AB is partitioned by a given point P in two minor line segments AP and PB

We need to find, the coordinates of the partitioning point i.e. P

The given formula will be used,

The coordinates of the point P = ([tex]\frac{x1+x2}{2}[/tex], [tex]\frac{y1 + y2}{2}[/tex])

Now, x1 = 0, x2 = 0, y1 = 0, y2 = 6

Putting values in the formula, we get

([tex]\frac{0+0}{2}[/tex], [tex]\frac{0+6}{2}[/tex])

(0,3)

Hence, the point P which partitions the line segment AB have coordinates as P(0,3)

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I should return after 7.7 minutes later to bathtub.

You want to turn the water off when the level in the bathtub is 8.5

66/8.5

7.7 minutes

A bathtub is a long, typically rectangular container that you sit in to bathe your body after filling it with water.

Let's start with the truth: Showers are cleaner than baths. Showers spray polluted water out of sight while distributing water evenly over your body.

Actually, there is nothing that sets one apart from the other. All of them include jets, bubbles, and frequently different colored lights and other decorations. They are all sizable hot water containers. Overall, the terms "whirlpool bath," "Jacuzzi," and "hot tub" all refer to the same thing.

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The first five terms of the sequence an =5 n-3 are 2, 7, 12, 17  and 22.

According to the question.

We have a formula or a rule for finding the terms of a sequence i.e.

an = 5n -3.

The first term of the sequnence an = 5n - 3 is given by

a(1) = 5(1) -3 = 5 -3 = 2

The second term of the sequence an = 5n - 3 is given by

a(2) = 5(2) - 3 = 10 - 3 = 7

The third term of the sequence an = 5n -3 is given by

a(3) = 5(3) - 3 = 15 - 3 = 12

The fourth term of the sequence an = 5n - 3 is given by

a(4) = 5(4) - 3 = 20 - 3 = 17

The fifth term of the sequence an = 5n - 3 is given by

a(5) =  5(5) - 3 = 25 - 3 = 22

Hence, the first five terms of the sequence an =5 n-3 are 2, 7, 12, 17  and 22.

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