A recipe requires 3/4 of a cup of milk for every 1 1/2 cups of flour how many cups of milk are needed for each cup of flour

Answer:

This is proved using Proof by induction method. There are two steps in this method

Let P(n) represent the given statement  ∪ \({ {{n} \atop {j=1}} \right.\) \(A_{j}\) ⊆ ∪ \({ {{n} \atop {j=1}} \right.\) \(B_{j}\)

1. Basis Step: This step proves the given statement for n = 1

2. Induction step: The step proves that if the given statement holds for any given case n = k  then it should also be true for n = k + 1.

If the above two steps are true this means that given statement P(n) holds true for all positive n and the mathematical induction P(n): ∪ \({ {{n} \atop {j=1}} \right.\) \(A_{j}\) ⊆ ∪ \({ {{n} \atop {j=1}} \right.\) \(B_{j}\) is true.

Step-by-step explanation:

Basis Step:

For n = 1

∪\({ {{n} \atop {j=1}} \right.\) \(A_{j}\) = ∪\({ {{1} \atop {j=1}} \right.\) \(A_{j}\) = A₁ ⊆ B₁ = ∪\({ {{1} \atop {j=1}} \right.\) \(B_{j}\) = ∪\({ {{n} \atop {j=1}} \right.\) \(B_{j}\)

We show that

∪\({ {{1} \atop {j=1}} \right.\) \(A_{j}\) = A₁ ⊆ B₁ = ∪\({ {{1} \atop {j=1}} \right.\) \(B_{j}\)  for n = 1

Hence P(1) is true

Induction Step:

Let P(k) be true which means that we assume that:

for all k with k≥1, P(k): ∪\({ {{k} \atop {j=1}} \right.\) \(A_{j}\) ⊆ ∪\({ {{k} \atop {j=1}} \right.\) \(B_{j}\) is true

This is our induction hypothesis and we have to prove that P(k + 1) is also true

This means if ∪ \({ {{n} \atop {j=1}} \right.\) \(A_{j}\) ⊆ ∪ \({ {{n} \atop {j=1}} \right.\) \(B_{j}\) holds for n = k  then this should also hold for n = k + 1.

In simple words if P(k): ∪\({ {{k} \atop {j=1}} \right.\) \(A_{j}\) ⊆ ∪\({ {{k} \atop {j=1}} \right.\) \(B_{j}\) is true then ∪\({ {{k+1} \atop {j=1}} \right.\) \(A_{j}\) ⊆ ∪\({ {{k+1} \atop {j=1}} \right.\) \(B_{j}\) is also true

∪\({ {{k+1} \atop {j=1}} \right.\) \(A_{j}\) = ∪\({ {{k} \atop {j=1}} \right.\) \(A_{j}\) ∪ \(A_{k+1}\)

           ⊆ ∪\({ {{k} \atop {j=1}} \right.\) \(B_{j}\) ∪ \(A_{k+1}\)                 As ∪\({ {{k} \atop {j=1}} \right.\) \(A_{j}\) ⊆ ∪\({ {{k} \atop {j=1}} \right.\) \(B_{j}\)

           ⊆ ∪\({ {{k} \atop {j=1}} \right.\) \(B_{j}\) ∪ \(B_{k+1}\)                 As  \(A_{k+1}\) ⊆ \(B_{k+1}\)

           =  ∪\({ {{k+1} \atop {j=1}} \right.\) \(B_{j}\)

The whole step:

∪\({ {{k+1} \atop {j=1}} \right.\) \(A_{j}\) = ∪\({ {{k} \atop {j=1}} \right.\) \(A_{j}\) ∪ \(A_{k+1}\) ⊆ ∪\({ {{k} \atop {j=1}} \right.\) \(B_{j}\) ∪ \(A_{k+1}\) ⊆ ∪\({ {{k} \atop {j=1}} \right.\) \(B_{j}\) ∪ \(B_{k+1}\) =  ∪\({ {{k+1} \atop {j=1}} \right.\) \(B_{j}\)

shows that the P(k+1) also holds for ∪ \({ {{n} \atop {j=1}} \right.\) \(A_{j}\) ⊆ ∪ \({ {{n} \atop {j=1}} \right.\) \(B_{j}\)

hence P(k+1) is true

So proof by induction method proves that P(n) is true. This means

P(n): ∪ \({ {{n} \atop {j=1}} \right.\) \(A_{j}\) ⊆ ∪ \({ {{n} \atop {j=1}} \right.\) \(B_{j}\) is true

Answer:

Step-by-step explanation:

Sales Revenue:  $800.00

Cost of good sold:  $350,000.00

Subtract:                   $450,000.00

Sales Revenue:         $795,000.00

Cost of good sold:     $600,000.00

Subtract Sales             $195,000.00

Revenue from Cost

of goods sold.

Answer:

57

Step-by-step explanation:

this is the boybfiend

Answer:

6x - 30

Step-by-step explanation:

Distribute:

=(−2)(9)+(−2)(−x)+(4)(x)+(4)(−3)

=−18+2x+4x+−12

Combine Like Terms:

=−18+2x+4x+−12

=(2x+4x)+(−18+−12)

=6x+−30

Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Answer:

7

Step-by-step explanation:

apply the Pythagorean theorem

\(10 {}^{2} = ( \sqrt{51} ) {}^{2} + x {}^{2} \\ 100 = 51 + x {}^{2} \\ 100 - 51 = x {}^{2} \\ 49 = x {}^{2} \\ x = 7\)

Answer:

B

Step-by-step explanation:

To find the equation, we can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is a point.

First, we will need to find the slope. Since we have two points, we can use the slope formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Let (2, -1) be (x₁, y₁) and let (0, 5) be (x₂, y₂). Substitute and evaluate:

\(\displaystyle m=\frac{5-(-1)}{0-2}=6/-2=-3\)

Therefore, the slope m is -3.

Now, we can use the point-slope form. We also need a point. Let’s use (2, -1) for consistency. So, we will substitute -3 for m and (2, -1) for (x₁, y₁). This yields:

\(y-(-1)=-3(x-2)\)

We will now convert this to slope-intercept form. Simplify the left and distribute the right:

\(y+1=-3x+6\)

Subtract 1 from both sides. Therefore, our equation is:

\(y=-3x+5\)

Thus, our answer is B.

Answer:

\( \frac{19 + 6 \sqrt{3} }{2} \)

Step-by-step explanation:

\(2a - \frac{1}{ \sqrt{a} } + \frac{1}{a} \: \: \: when \: \: a = 4 + 2 \sqrt{3} \)

\(2 \times (4 + 2 \sqrt{3} ) - \frac{1}{ \sqrt{4 + 2 \sqrt{3} } } + \frac{1}{4 + 2 \sqrt{3} } \)

Expand the brackets (multiply every term inside the bracket by the term on the outside) and make the denominator the same (4 + 2√3):

\( \frac{(8 + 4\sqrt{3} )\times(4 + 2 \sqrt{3} ) }{4 + 2 \sqrt{3} } - \frac{ \sqrt{4 + 2 \sqrt{3} } }{4 + 2 \sqrt{3} } + \frac{1}{4 + 2 \sqrt{3} } \)

\( \frac{32 + 16 \sqrt{3} + 16 \sqrt{3} + 24 - \sqrt{4 + 2 \sqrt{3} } + 1}{4 + 2 \sqrt{3} } \)

Collect like-terms:

\( \frac{57+ 32 \sqrt{3} - \sqrt{4 + 2 \sqrt{3} } }{4 + 2 \sqrt{3} } \)

\( \frac{57 + 32 \sqrt{3} - \sqrt{( {1 + \sqrt{3}) }^{2} } }{4 + 2 \sqrt{3} } \)

\( \frac{57 + 32 \sqrt{3} - (1 + \sqrt{3} )}{4 + 2 \sqrt{3} } \)

Eliminate the parentheses:

\( \frac{57 + 32 \sqrt{3} - 1 - \sqrt{3} }{4 + 2 \sqrt{3} } \)

Collect like terms:

\( \frac{56 + 31 \sqrt{3} }{4 + 2 \sqrt{3} } \)

\( \frac{56 + 31 \sqrt{3} }{4 + 2 \sqrt{3} } \times \frac{4 - 2 \sqrt{3} }{4 - 2 \sqrt{3} } = \frac{224 - 112 \sqrt{3} + 124 \sqrt{3} - 186}{16 - 4 \times 3} = \frac{38 + 12 \sqrt{3} }{4} \)

\( \frac{2(19 + 6 \sqrt{3}) }{4} = \frac{19 + 6 \sqrt{3} }{2} \)

We are given the following system of equations:

To solve the system we will use the method of elimination. We will add equations (1) and (2) so that the variable "y" gets canceled out, like this:

Adding like terms:

Now, we divide both sides by 3:

Therefore, the value of "x" is -2. Now, we determine the value of "y" by substituting the value if "x" in equation (1):

Now, we add 2 to both sides:

Now, we divide both sides by -6:

Therefore, the solution of the system is:

Answer:

The coefficient is 2520

Step-by-step explanation:

Given

\((x + y + z)^{10\)

Required

The coefficient of \(x^3y^2z^5\)

To do this, we make use of:

\(k = \frac{n!}{n_1!n_2!....n_m!}\)

Where

\(k \to\) coefficient

\(n = 10\) the exponent of the given expression

\(n_1=3\) -- exponent of x

\(n_2=2\) --- exponent of y

\(n_3=5\) --- exponent of z

So, we have:

\(k = \frac{n!}{n_1!n_2!....n_m!}\)

\(k = \frac{10!}{3!2!5!}\)

Expand

\(k = \frac{10*9*8*7*6*5!}{3!2!5!}\)

\(k = \frac{10*9*8*7*6}{3!2!}\)

\(k = \frac{30240}{3!2!}\)

Expand the denominator

\(k = \frac{30240}{3*2*1*2*1}\)

\(k = \frac{30240}{12}\)

\(k = 2520\)

Answer:

10yd

Step-by-step explanation:

area= 1/2bh

area=32yd²

b= 6.4, ¹/2b=3.2

therefore, 32= 3.2h

h= 32/3.2

= 10yd

Answer:

I believe the answer is A.

Step-by-step explanation:

I don't really know how to really explain it tho

a. The probability that a piece selected at random is a white rook is 1/16.

b. 256 ways can you choose one white piece and one black piece.

c. 8 ways can you choose 3 pieces from the 4 kings and queens to place on 3 specific spaces on the chessboard.

Given that, a chess set has 32 pieces, 16 black and 16 white. In each colour, there are 8 pawns, 2 rooks, 2 knights, 2 bishops, 1 queen and 1 king.

The formula to find the probability of an event is P(E)=Number of favourable outcomes/Total number of outcomes.

a. The probability that a piece selected at random is a white rook

=2/32=1/16

Therefore, the probability that a piece selected at random is a white rook is 1/16.

b. Number of ways can you choose one white piece and one black

piece=16×16=256

Each white piece can go with a black piece 16 times and the same the other way.

Hence, 256 ways can you choose one white piece and one black piece.

c. nPr=P(4,3)=4!/3=24/3=8 ways.

Hence, 8 ways can you choose 3 pieces from the 4 kings and queens to place on 3 specific spaces on the chessboard.

This is a permutation.

a. The probability that a piece selected at random is a white rook is 1/16.

b. 256 ways can you choose one white piece and one black piece.

c. 8 ways can you choose 3 pieces from the 4 kings and queens to place on 3 specific spaces on the chessboard.

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Answer:

Step-by-step explanation:

\(x=r cos \theta=7 cos150=7cos(180-30)=-7cos ~30=-\frac{7\sqrt{3} }{2} \\y=r~sin~\theta=7~sin ~150=7~sin~(180-30)=7~sin~30=\frac{7}{2} \\so ~coordinates ~are~(-\frac{7\sqrt{3}}{2} ,\frac{7}{2} )\\C\)

Answer:

Hello there! I believe b or d

Answer:

n>11

Step-by-step explanation:

The solution to the inequality 7n - 1 > 76 is n > 11, so the correct option is C.

To determine and graph the inequality 7n - 1 > 76;

First Add 1 to both sides of the inequality to isolate the variable term.

7n - 1 + 1 > 76 + 1

7n > 77

Divide both sides of the inequality by 7 to solve for n.

(7n) / 7 > 77 / 7

n > 11

Since n is greater than 11, the graph will be an open circle on 11, and an arrow extending to the right.

Therefore, the solution to the inequality 7n - 1 > 76 is n > 11, so the correct option is C.

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Answer:

  B.  quadratic

Step-by-step explanation:

You want to know the kind of function that would best fit the points shown on the graph.

The points on the graph demonstrate a slope that starts out positive and decreases through 0 to a slope with a negative value.

A linear function has a constant slope.

An exponential function has a continuously increasing or continuously decreasing slope.

A quadratic function has a slope that changes sign, matching the slope of the curve joining the given points.

The equation that best fits the given data will be quadratic.

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Answer:

6384 is the exact answer.

6000 is the answer rounded to the nearest thousand

Step-by-step explanation:

Answer:

6000

Step-by-step explanation:

532 X 12 = 6384 rounded would be 6000 miles a yr

Answer: x + 5 > 23

x is at least 19

Step-by-step explanation:

Answer:

10 my fault

Step-by-step explanation:

please trust

11. Angle KEF = 40°, Angle KEJ = 50°

12. Angle HEF = 115°, Angle KED = 140°

13. Angle JEF = 90°, Angle KEF = 90°

14.   Angle DEF = 180°

The study of points, lines, and shapes in two and three dimensions, as well as their properties and relationships, is the focus of the mathematical discipline known as geometry.

11.  Acute angles: Those angles are less than 90 degree angles.

     Angle KEF = 40°

     Angle KEJ = 50°

     Angle KEH = 75°

     Angle JEH = 25°

     Angle HED = 65°

12. Obtuse angles: Those angles are more than 90 degree angles.

     Angle HEF = 115°

     Angle KED = 140°

13. Right angle: Those angles are 90 degree angle.

     Angle JEF = 90°

     Angle KEF = 90°

14. Straight angle: Those angles make 180 degree angle.

     Angle DEF = 180°

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The total cost spent by the soccer team is given by 5x + 7y + 4z

An equation shows the relationship between numbers and variables.

Let x represent the cost of small yogurts, y represent the cost of medium yogurt and z represent the cost of large yogurts.

Since the team ordered 5 small, 7 medium, and 4 large frozen yogurts. Hence:

Total cost = 5x + 7y + 4z

Let us assume that small yogurt cost $1, medium cost $1.5 and large cost $2. Hence:

Total cost = 5(1) + 7(1.5) + 4(2) = $23.5

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The equation to show the perimeter of the rectangle is P = 2(2w + 5)

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

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

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Answer:

I'm not exactly sure, but I'm positive that it's 60 degrees.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

90 = 30 + (4x)

60 = 4x

x = 60/4 = 15

30° and (4x)° must add up to 90° because they are complementary angles

To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Answer:

if its rounded to the nearest hundreds the answer iz 12.347

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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To calculate the merit increase based on your annual review score, we can use the given information that merit increases start at 0.5% for a score of 2.6 and increase by 1% every 0.4 points.

First, we need to determine the difference between your score and the starting score of 2.6:

3.4 - 2.6 = 0.8

Next, we divide this difference by 0.4 to determine the number of 0.4-point intervals:

0.8 / 0.4 = 2

Since each 0.4-point interval corresponds to a 1% increase, we multiply the number of intervals by 1% to find the total increase:

2 * 1% = 2%

Therefore, you will be receiving a merit increase of 2%.