Express the following rate as a unit rate. If necessary, round your answer to the nearest tenth. Youwould enter an answer like 13.8 feet/second with 13.8 in the first box and the units feet and secondin the following boxes.RATE: 36 km for 32 gallons

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

Answer:

3 groups

Step-by-step explanation:

6 / 2 = 3 groups

plz mark me brainliest

Answer:3

Step-by-step explanation: 6 divided by 2

The difference between 126 1/4 and 78 7/12 is 143/3 or 47 2/3.

To find the difference between the numbers simplify means;

to subtract 78 7/12 from 126 1/4 .

126 1/4 - 78 7/12

First, convert the mixed fractions into improper fractions.

( 126 × 4 + 1 )/4 - ( 78 × 12 + 7) /12

505/4 - 943/12

Multiply first term by 3/3 which is the same as 1.

( 505/4 × 3/3 ) - 943/12

1515/12 - 943/12

( 1515 - 943) / 12

572 / 12

143/3 or 47 2/3.

Therefore, the difference is 143/3 or 47 2/3.

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Answer:

w - 10d = 4

Step-by-step explanation:

w - 2(5d – 8) = 20

w - 10d + 16 = 20

w - 10d (+ 16 - 16) = 20 - 16

w - 10d = 4

Answer:

i believe is 4

Step-by-step explanation:

If you 2y=-4x+12

need to get the Y by it self

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

a. closed under addition and multiplication

b. not closed under addition but closed under multiplication.

c. not closed under addition and multiplication

d. closed under addition and multiplication

e. not closed under addition but closed under multiplication

Step-by-step explanation:

a.

Let A be a set of all integers divisible by 5.

Let \(x,y\)∈A such that \(x=5m\,,\,y=5n\)

Find \(x+y,xy\)

\(x+y=5m+5n=5(m+n)\)

So, \(x+y\) is divisible by 5.

\(xy=(5m)(5n)=25mn=5(5mn)\)

So,

\(xy\) is divisible by 5.

Therefore, A is closed under addition and multiplication.

b.

Let  A = { 2n +1 | n ∈ Z}

Let \(x,y\)∈A such that \(x=2m+1\,,\,y=2n+1\) where m, n ∈ Z.

Find \(x+y,xy\)

\(x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)\)

So,

\(x+y\) ∉ A

\(xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1\)

So,

\(xy\)∈ A

Therefore, A is not closed under addition but A is closed under multiplication.

c.

\(Let A=\{2,5,8,11,14,...\}\)

Let \(x=2,y=5\) but \(x+y=2+5=7\)∉A

Also,

\(xy=2(5)=10\)∉A

Therefore, A is not closed under addition and multiplication.

d.

Let A = { 17n: n∈Z}

Let \(x,y\) ∈ A such that \(x=17n,y=17m\)

Find x + y and xy

\(x+y=17n+17m=17(n+m)\)

\(xy=(17m)(17n)=289mn=17(17mn)\)

So,

\(x+y,xy\) ∈ A

Therefore, A is closed under addition and multiplication.

e.

Let A be the set of nonzero real numbers.

Let \(x,y\) ∈ A such that \(x=-1,y=1\)

Find x + y

\(x+y=-1+1=0\)

So,

\(x+y\) ∈ A

Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.

Therefore, A is not closed under addition but A is closed under multiplication.

The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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The value of life in minutes is exceeded by 90% probability is 327.025.

What is a normal distribution?

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution. The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.

Here, we have

Given: The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 253 minutes and a standard deviation of 45 minutes.

We have to find the value of life in minutes is exceeded by 90% probability.

= Mean + Z (Standard Deviation)

= 253 + 1.645×45

= 327.025

Hence, the value of life in minutes is exceeded by 90% probability is 327.025.

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Using the supplementary angle theorem, the value for x so that points A, B, and C are collinear is 8.

What is a supplementary angle?

The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.

A line segment AC is drawn.

Point B is in between A and C.

A transversal DE is drawn passing through point B.

Points D, B, and E are collinear.

The measure of angle CBE is 148° and the measure of angle EBA is 4x°.

The angles ∠CBE and ∠EBA forms a pair of supplementary angles.

Their sum result in value of 180°.

Mathematically, this can be represented as -

∠CBE + ∠EBA = 180°

Substituting the values into the equation -

148° + 4x° = 180°

Solving for x, we get -

4x° = 180° - 148°

4x° = 32°

x = 32 / 4

x = 8

Therefore, the value for x is obtained as 8.

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Answer: 65.94 cm

Step-by-step explanation:

Since the wire is bent into a semicircular arc, we can use the formula for the circumference of a circle to find the length of the wire.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

In this case, the length of EF is equal to the diameter of the circle, so the radius is half of that, or 10.5 cm.

Plugging this into the formula, we get:

C = 2 x (22/7) x 10.5

C = 2 x 3.14 x 10.5

C = 65.94

Therefore, the length of the wire is approximately 65.94 cm.

Answer:

L = πr = (22/7) * 6.727 = 21.14 centimeters.

Step-by-step explanation:

Let's assume that the radius of the semicircular arc is 'r' centimeters.

The formula for the circumference of a circle is C = 2πr, where π is approximately equal to 22/7.

Since we are dealing with a semicircle, we need to divide the circumference by 2 to get the length of the wire. Therefore, the length of the wire is:

L = C/2 = (2πr)/2 = πr

Now, we need to find the value of 'r'. We know that the length of EF is 21 centimeters, which is half of the circumference of the semicircle.

So, we can write:

EF = (C/2) = (πr)

Substituting the value of π as 22/7, we get:

21 = (22/7) * r

Multiplying both sides by 7/22, we get:

r = 21 * (7/22) = 6.727 centimeters (approx.)

Therefore, the length of the wire is:

L = πr = (22/7) * 6.727 = 21.14 centimeters.



To earn an average score of 90, the score on the fourth test needs to be 98.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.

Given the score of the first three tests as:

91, 84, 87.

The average is given by the following formula:

Average = Sum of scores ÷ total number of tests

Let us suppose the score of fourth test as x.

Given that A = 90:

90 = (91 + 84 + 87 + x) ÷ 4

x = 98

Hence, the score on the fourth test must be equal to 98, to get an average score of 90.

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Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

Answer:

1. Tenth.

2. 6+ 0.4=6.4.

Answer:

8%

Step-by-step explanation:

Answer:

A

Step-by-step explanation: just divide 71 into 2 which gives you 35.5 making a your answer.

Answer:

y = -8

Step-by-step explanation:

2(y-2)- 6y-28 = 0

2y - 4 -6y - 28 = 0

-4y = 32

y = -8

Answer:

.46%

Step-by-step explanation:

.055/12= .00458= .46%

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

Brian is constructing figures inscribed in circle C.

Equilateral triangle MNQ inscribed in circle C:

This option is possible since the points M, N, and Q are labeled and they lie on circle C.

Equilateral triangle ANP inscribed in circle C:

This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.

Regular hexagon AMNBPQ inscribed in circle C:

This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.

Square MNPQ inscribed in circle C:

This option is not possible based on the given information. The label points do not form a square.

Square ANBQ inscribed in circle C:

This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

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Answer:

-4, 1

Step-by-step explanation:

Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.

A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.

The area of the rectangular patio is given by multiplying its length by its width, so the area is:

A = (1 + 2x)(2 - 3x)

Now using distributive property we get,

A = 2 - 3x + 4x - 6x²

Simplifying further, we get:

A = -6x² + x + 2

Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.

To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:

P = 2(1 + 2x) + 2(2 - 3x)

Simplifying this expression, we get:

P = 2 + 4x + 4 - 6x

P = 6 - 2x

Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.

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1. The rotation of a point in 180 degrees is given by reflecting both of its coordinates. In this case the original point is (-4, 3), so the rotated point will be (4, -3).

2. When we reflect a point around the x-axis we need to invert the signal of the y-coordinate. When we make a translation to the right we need to add the number of units to the x-coordinate of the point, therefore.

Translation:

A' = (-4 + 2, 3) = (-2, 3)

Reflection x-axis:

C = (-2, -3)

3. When we reflect a point around the y-axis we invert the signal of x-coordinate. To perform a translation to the right we add the number of units to the x-coordinates, therefore:

Reflection y-axis:

A'' = (4, 3)

Translation:

D = (4 + 2, 3) = (6,3)

Answer:

20 million = 2 crore

Step-by-step explanation:

Here we will show you how to convert 20 million to crores (twenty million in crores). This may be useful if you for example want to convert 20 million rupees to crore rupees or 20 million dollars to crore dollars.

In some parts of the world like the United States, large numbers are separated with commas in three-digit-interval format like this:

...,BBB,MMM,TTT,HHH

BBB = billions

MMM = millions

TTT = thousands

HHH = hundreds

In certain parts of Asia, the format is a little different. From right to left, it starts out with three digits followed by a comma like the US, but after that, it is in intervals of two digits like this:

..,AA,CC,LL,TT,HHH

AA = arabs

CC = crores

LL = lakhs

TT = thousands

HHH = hundreds

Below we have displayed 20 million with the two number systems, based on the information above:

MM,TTT,HHH

20,000,000

=

C,LL,TT,HHH

2,00,00,000

When you match up 20 million with the C,LL,TT,HHH format above, you can see what 20 million is in crores. The answer to 20 million in crores is as follows:

20 million

= 2 crore

An inverse function reverses the roles of inputs and outputs (of x-values and y-values).  

If (2,4) is on the graph of a function, then (4,2) is on the graph of the inverse function.  

If (9,7) is on the graph of the inverse, then (7,9) would be on the graph of the original function.  

If (a,b) is on the graph of the function, then (b,a) is on the graph of the inverse.  

Getting to your question, which of the points listed has the inverse listed up in the table?

The solutions to the trigonometric equation 12cos²(x) - sin(x) - 6 = 0 are given as follows:

x = 42º and x = 228º.

The equation is given as follows:

12cos²(x) - sin(x) - 6 = 0

The following identity is applied:

sin²(x) + cos²(x) = 1.

Hence:

cos²(x) = 1 - sin²(x).

Replacing this identity into the equation, we have that:

12(1 - sin²(x)) - sin(x) - 6 = 0

12 - 12sin²(x) - sin(x) - 6 = 0

12sin²(x) + sin(x) - 6 = 0.

The following transformation is applied:

y = sin(x).

Hence the equation is:

12y² + y - 6 = 0.

Which, using a calculator, has the solutions given by:

y = -3/4, y = 2/3.

Then the solutions for the variable x are given as follows:

This problem is incomplete and could not be found on any search engine, hence we are going to suppose that it asks for the solutions to the equation.

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The value of the variable x is 30° and the value of the variable y is 10°.

The missing diagram is attached below.

The angle is the distance between the intersecting lines or surfaces.

Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.

Vertically opposite angle – When two lines intersect, then their opposite angles are equal.

Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.

If angle ∠1 = 105°, angle ∠12 = (3x + 15)°, and angle ∠7 = (8y-5)°.

∠1 = ∠5 = ∠9 = 105° (corresponding angles)

∠1 = ∠4 = 105° (Vertical opposite angles)

∠1 + ∠2 = 180° (linear angle)

       ∠2 = 75°

∠2 = ∠3 = 75° (Vertical opposite angles)

∠3 = ∠8 = ∠12 = 75° (corresponding angles)

Then the value of x and y will be

   ∠9 = ∠12

   ∠1 = ∠12

105° = (3x + 15)°

  3x = 90°

    x = 30°

∠6 = ∠7

75° = (8y – 5)°

8y = 80°

  y = 10°

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The acceleration of the car is 8 m/s^2.

The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.

Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.

(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m

(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The expression to determine the perimeter of the triangle in terms of the shortest side (s) is 3s + 15.

To determine the perimeter of the triangle, we need to express the lengths of all three sides in terms of the shortest side (s).

The longest side is three more than twice the length of the shortest side. This can be expressed as 2s + 3.

The third side is twelve feet long.

Now, let's denote the lengths of the sides as follows:

Shortest side = s

Second side = 2s + 3

Third side = 12

To find the perimeter, we sum up the lengths of all three sides:

Perimeter = s + (2s + 3) + 12

Simplifying the expression:

Perimeter = s + 2s + 3 + 12

Perimeter = 3s + 15

Therefore, the expression to determine the perimeter of the triangle in terms of the shortest side (s) is 3s + 15.

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