What type of triangle is this triangle?
•
acute scalene
•
acute isosceles
right scalene
right isosceles

The initial speed of the uniform solid ball rolling smoothly along a floor inclined at 32° is 5.3 m/s.

We can use the conservation of mechanical energy to solve for the initial speed of the ball. The initial mechanical energy of the ball is equal to the final mechanical energy of the ball when it reaches the top of the ramp.

Initial mechanical energy = Final mechanical energy

1/2 mv^2 = mgh + 1/2 mv'^2

where

m = mass of the ball

v = initial speed

g = acceleration due to gravity (9.8 m/s^2)

h = height of the ramp (2.70sin(32°) = 1.43  m)

v' = final speed = 0 m/s

Solving for the initial speed, we get:

v = √(2gh) = √(2 * 9.8 * 1.43) = √(28.04) = 5.3 m/s.

So, the initial speed of the ball is 5.3 m/s.

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Answer:

[tex]\sqrt{27}[/tex]

Step-by-step explanation:

because [tex]\sqrt{27} = 5.19[/tex]

so 5.19<5.34

Answer:

5.34

Step-by-step explanation:

Step 1:

First, we need to find the perfect square that is closest to but less than 27. The closest perfect square is 25 (5^2).

Step 2:

Now we need to divide the number we are trying to find the square root of (27) by the closest perfect square (25). In this case: 27/25 = 1.08

Step 3:

We can now find an approximate value for the square root of 27 by multiplying the closest perfect square (5) by the quotient obtained in step 2 (1.08). So, the approximate value of √27 is 5.40

Step 4:

In order to find a more accurate value of the square root, we can use the long division method.

Step 5:

We set up a long division problem with the dividend being 27 and the divisor being 5.

27 5

2 5

So, the quotient is 5 and the remainder is 2.

Step 6:

Now we bring down the next two digits (0) to get a new dividend of 20.

27 5

20

Step 7:

We divide 20 by 5 and get 4 as the quotient.

Step 8:

The final value of the square root of 27 is 5.4 (5 + 4/10)

Note: The process above is providing the approximate value of square root of 27, while the exact value of the square root of 27 is √27 = √(3^3) = 3.

That's why our answer is 5.34

Answer:

540 minutes or 9 hours :)

Step-by-step explanation:

What I did is I multiplied 6 hours by 60 minutes. Or for the hours skip that step.

6x60=360       or     6/300=0.02

360/300=1.2    or     0.02x450=9

1.2 x450= 540  or         9 hours

540 minutes

540 minutes or 9 hours :D

Goodluck <3

Hope this helps!

Answer:

Answer Below ↓

Step-by-step explanation:

Assume n is a odd number then n-1 will be even and if odd number multiply with even it will be even. So that's for n(n-1) is a even number. If you assume n is an even number then (n-1) will be odd number..Then multiplication of odd and even number will be also even number.. So n(n-1) is always even .

The inequality can be written as y < 1/4x + 3.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

The inequality can be written by finding the equation of the line. The two points on the line are ( 0,3) and ( 4,4).

The slope of the line is,

Slope = ( 3 - 4 ) / 9 0 - 4 )

Slope = 1 / 4

The y-intercept of the line will be calculated as:-

y = mx + c

3 = 0 +c

c = 3

The equation of the inequality can be written as:-

y < (1/4)x + 3

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The negative integer -4°F  represents the change in temperature for every thousand feet a person climbs.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

here,
As a person climbs a mountain, the temperature drops 4°F for every thousand feet climbed.

Change in temperature  = -4°F

Thus, the negative integer -4°F  represents the change in temperature for every thousand feet a person climbs.

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Answer: The candle will take 16.5 cm of wax to burn out.

Step-by-step explanation:

The candle will take 22 - 5.5 = 16.5 cm of wax to burn out.

At the same rate, if the candle burned for 11 minutes and the remaining length was 5.5 cm, it will take 11 * (22/5.5) = 44 minutes to burn out.

A conditional statement is a logical statement that has two parts, a hypothesis [tex]p[/tex] and a conclusion [tex]q[/tex].

When a conditional independence statement is written in if-then form, the "if" part contains the hypothesis and the "then" part contains the conclusion.

The conditional probability of A given B is represented by [tex]P(\frac{A}{B} )[/tex] . The variables A and B are said to be independent if [tex]P(A) = P(\frac{A}{B} )[/tex] (or alternatively if [tex]P(A,B) = P(A) P(B)[/tex] because of the formula for conditional probability ).

In a situation in which we can compute all three probabilities [tex]P(A) , P(B)[/tex] and P(A∩B), it is used to check whether or not the events A and B are independent: If P(A∩B) = [tex]P(A)P(B)[/tex], then A and B are independent.

Conditional independence depends on the nature of the third event. If you roll two dice, one may assume that the two dice behave independently of each other. Looking at the results of one dice will not tell you about the result of the second dice. (That is, the two dice are independent.)

Therefore,

A conditional statement is a logical statement that has two parts, a hypothesis [tex]p[/tex] and a conclusion [tex]q[/tex].

When a conditional independence statement is written in if-then form, the "if" part contains the hypothesis and the "then" part contains the conclusion.

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The solution to the expression is -41000

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

calculate -1000 * 41 in long division​

The above expression is a product expression

This means that it cannot be evaluated using long division

When the expression is evaluated. we have

-1000 * 41 = -41000

Hence, the solution is -41000

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Answer:

37.5% is the answer to this question

Answer:

37.5%

Step-by-step explanation:

General Explanation:

(1m = 100cm

2m = 200cm)

= (75cm ÷ 2m) × 100

= (75 ÷ 200 ) × 100

= 75 ÷ 2%

= 37.5%

_________________________________

Easier Explanation (Decimal to Percentage):

(1m = 100cm

2m = 200cm)

= 75cm ÷ 200cm

= 75 ÷ 200

= 0.375 (3/8 as a fraction)

= 37.5%

The mean of Xt is 0. The autocovariance of Xt is 0, and the autocorrelation is 0 for all lags. Mean: 0. Autocovariance: 2cos(2). Autocorrelation: 2cos²(2).

The mean of Xt is the expected value of the series, which is 0, since the uniform distribution has a mean of 0.5, and when it is multiplied by 2π, it becomes 0. The autocovariance of Xt is the expected value of the product of two variables at different lags, which is 0 because the two variables are uncorrelated. The autocorrelation of Xt is the expected value of the product of two variables at different lags, divided by the product of their variances, which is also 0 since the variables are uncorrelated. The autocovariance and autocorrelation functions are both 2cos²(2πt), which is the expected value of Xt at different lags.

The complete question: Suppose = 2 cos[2( 12 + )], ∈ ℤ, where ~Uniform[0,1]. Find the mean, autocovariance and autocorrelation functions of the time series { , ∈ ℤ}.

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The area of the circle is  36π square meters. Option C is the correct option.

What is the area of an object?

Area is the total amount of space occupied by a flat (2-D) surface or an object's shape. On a piece of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

Given that the diameter of a circle is 12 meters.

The radius of a circle is half of its diameter.

The radius of the circle is 12/2 = 6 meters.

The area of a circle is πr², where r is the radius of the circle.

The area of the circle is π6² = 36π

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Answer:

62 square units

Step-by-step explanation:

Area = 2(lb+lh+bh)

= 2(3×2+3×5+2×5)

= 62

The solid represented by the net is a rectangular prism.

And, The surface area of the solid is , 62.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

The solid represented by the net.

Here, We know that;

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases.

Hence, The solid represented by the net is a rectangular prism.

Here, The length of the rectangular prism (l) = 5

The width of the rectangular prism (w) = 2

The height of the rectangular prism (h) = 3

We know that;

The surface area of the rectangular prism = 2 (wl + hl + hw)

Substitute all the values, we get;

The surface area of the rectangular prism = 2 (2×5 + 3×5 + 3×2)

The surface area of the rectangular prism = 2 (10 + 15 + 6)

The surface area of the rectangular prism = 2 × 31

The surface area of the rectangular prism = 62

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The statement "s1 ⊆ s2" means that every element in set s1 is also an element in set s2. In other words, set s1 is a subset of set s2.

To prove this, we can use a logical contrapositive argument. Assume that s2 is not a subset of s1, meaning there exists at least one element in set s2 that is not in set s1. Then, this means that s1 is not a subset of s2, which contradicts our original assumption that s1 ⊆ s2. Thus, we conclude that if s1 ⊆ s2, then s2 ⊆ s1.

Hence, if set s1 is a subset of set s2, then every element in set s1 is also in set s2. As a result, set s2 is also a subset of set s1.

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Answer:

recipe should have 5.76 cups of sugar.

Step-by-step explanation:

To find out how many cups of sugar should be in Molly's apple recipe, you can use the proportion of sugar to apples in the recipe. Since the recipe is 36% sugary, that means for every 100 cups of apples, 36 cups of it is sugar. We can set up the proportion as:

Sugar / Apples = 36 / 100

To find the number of cups of sugar in 16 cups of apples, we can cross-multiply and divide:

Sugar = (36/100) * Apples

Sugar = (36/100) * 16

Sugar = 5.76 cups

So the recipe should have 5.76 cups of sugar.

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The inequalities that represent the constraints in this situation are r+c≥80 and 1.45R +0.75c≤200 respectively

The amount with victor = $200

Let the number of roses purchased by Victor be R,

Also, Rose cost $1.45 each

Therefore cost of rose = 1.45R

A;so, let the number of carby Victor be C at a cost of $0.65 each nation purchased by victor be $0.65 each

Therefore, cost of carnation = $0.65c

1) The inequality to represent the constraint that every person takes home at least one rose is r+c≥80 and

2) the inequality to represent the cost constraint is 1.45R + 0.65≤200

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Answer:

-1.5 and 1.5

Step-by-step explanation:

Let's call the maximum value of the function "c." The equation for the parabola is now y = x^2 + ax + (b - c).

Using the point (1,1), we can solve for "a" and "b":

1 = 1^2 + a(1) + (b - c)

1 - a + b - c = 1

c - a + b = 0

c = -a + b

And using the fact that the maximum value is -3:

-3 = -a + b

a - b = 3

Combining these two equations:

-3 = -a + b = a - b

-3 = 2a

a = -1.5

Plugging in "a" to either equation:

-3 = -(-1.5) + b

-3 = -1.5 + b

b = -1.5 + 3 = 1.5

So the values of "a" and "b" are -1.5 and 1.5, respectively.

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