Check each value and decide if it is a factor of 50 or not: 15, 2, 5, 3, 20, 50, 25, 10

Answer:(a)

One step forward from the given statement could be to simplify it to just "p V q".

(b)

One step backward from the goal statement "p V q" could be to add the assumption that "(~p V q) => p V q" to get "(~p V q) => (p V q)".

(c)

Proof sequence:

Given: (~p V q) => p V q

To prove: p V q

Assume ~p V q is true (as the antecedent of the implication)

Since ~p V q is true, either ~p is true or q is true.

If ~p is true, then p is false, but the disjunction p V q is true.

If q is true, then the disjunction p V q is true.

In either case, p V q is true.

Therefore, p V q is true under the assumption that ~p V q is true.

Since the assumption was arbitrary, we conclude that p V q is true regardless of the truth value of ~p V q.

(d)

The proof is not reversible because the contrapositive of the statement "p V q => (~p V q)" is not logically equivalent to the original statement "~p V q => p V q".

Step-by-step explanation:

(a)

One step forward from the given statement could be to simplify it to just "p V q".

(b)

One step backward from the goal statement "p V q" could be to add the assumption that "(~p V q) => p V q" to get "(~p V q) => (p V q)".

(c)

Proof sequence:

Given: (~p V q) => p V q

To prove: p V q

Assume ~p V q is true (as the antecedent of the implication)

Since ~p V q is true, either ~p is true or q is true.

If ~p is true, then p is false, but the disjunction p V q is true.

If q is true, then the disjunction p V q is true.

In either case, p V q is true.

Therefore, p V q is true under the assumption that ~p V q is true.

Since the assumption was arbitrary, we conclude that p V q is true regardless of the truth value of ~p V q.

(d)

The proof is not reversible because the contrapositive of the statement "p V q => (~p V q)" is not logically equivalent to the original statement "~p V q => p V q".

Answer:

Step-by-step explanation:

so the graph shows so 4+9 = 13

The percent of 18 that equals 23 rounded to the nearest tenth is 127.8%.

Percentage is simply number or ratio expressed as a fraction of 100.

Given the data in the question;

Let x% represent the percentage of 18 that is equal to 23.

Note that x% is the same as x/100

Hence;

x/100 × 18 = 23

Solve for x

18x/100 = 23

Cross multiply

18x = 23 × 100

18x = 2300

Divide both sides by 18

18x/18 = 2300/18

x = 2300/18

x = 127.8

Therefore, the required percentage is 127.8%.

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The value of cos θ from the unit circle is cos θ = 0.88235

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

The terminal side of angle θ intersects the unit circle in the first quadrant at ( 15/17,-8/17 )

So , the equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r²   be equation (1)

Substituting the values of x and y in the equation , we get

x = 15/17

And , y = -8/17

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

So , the value of cos θ = ( 15/17 ) and sin θ = ( -8/17 )

On simplifying the equation , we get

cos θ = ( 15/17 )

cost θ = 0.88235

Hence , the value of cos θ = 0.88235

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Answer: x=5

Step-by-step explanation:

3x + y = 13 ------- (1)

2x - 4y =18 ------- (2)

2x = 4y + 18 ------- (3)

(3) x 3

6x = 12y + 54 ------- (4)

(1) x 2

6x + 2y = 26 --------- (5)

sub (4) into (5)

12y + 54 + 2y =26

14y + 54 = 26

14y = -28

y = -2 --------- (6)

sub (6) into (1)

3x - 2 = 13

3x = 15

x = 5

Answer: $675

Step-by-step explanation:

To calculate the monthly payment, we need to determine the number of $2,000 increments that the car costs. $30,000 ÷ $2,000 = 15.

So, the car costs 15 $2,000 increments.

Next, we need to multiply the number of increments by the $45 increase in payment per increment to find the monthly payment. 15 increments × $45/increment = $675.

Therefore, the monthly payment for a $30,000 car would be $675.

Answer:

The answer is 768.0 square inches.

Step-by-step explanation:

The surface area of a square pyramid can be calculated by adding the area of its four triangular faces to the area of its base, which is a square.

First, we'll find the area of the base:

24 inches x 24 inches = 576 square inches

Next, we'll find the area of each triangular face:

1/2 * 24 inches * 20 inches = 240 square inches

So, the total surface area of the pyramid is:

576 square inches + 4 * 240 square inches = 1,536 square inches

Finally, we'll find the surface area that is yellow:

1,536 square inches / 2 = 768 square inches

Rounding to the nearest tenth, we have:

768 square inches = 768.0 square inches

So, the surface area of the toy that is yellow is 768.0 square inches.

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The result of the definite integral by substitution is 214440.6.

In this problem we find the case of a definite integral, that is, an integral with definite limits, that must be simplified by algebraic substitution to be solved quicker. First, write the substitution formula and its derivative:

u = 6 · x - 7

du = 6 dx

f(u) = u⁴

Second, define the new limits of the definite integral:

a = 6 · 2 - 7

a = 5

b = 6 · 5 - 7

b = 23

Third, simplify the integral by means of the substitution formula:

[tex]\frac {1}{6}\int\limits^{23}_{5} {u^{4}} \, du[/tex]

Fourth, integrate the expression:

[tex]I = \frac{1}{30} \cdot u^{5}\left|_{5}^{23}[/tex]

I = (1 / 30) ·  (23⁵ - 5⁵)

I = 214440.6

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Answer:

93.75min

Step-by-step explanation:

Solution:

The rate of fill up is, Rate = 3.2 Gallons / minute = 3.2 g/min

The hut tub volume is 300 Gallons

You can set up this problem as follows:

Every 3.2 gallons require 1 minute, How many minutes 300 gallons require?

3.2  g    1min

300 g     ? min    = (300 gallons x 1min/ 3.2 gallons)=(300/32)min

= 93.75 min

or simply the number minutes is the time required (T) the rate is (R) and the volume is (V)

such that T=V/R= (300g/3.2 g/min)= 93.75 min

There is no conversion of units in this problem, but manipulation of units

Answer:

y = -7x + 4

Step-by-step explanation:

[tex]y=mx+b\\-3=-7(1)+b\\-3=-7+b\\4=b\\\\y=-7x+4[/tex]

All the correct statements are,

a) 3 lb plaster / 1 qt water is a unit rate for the mis.

c) Using the same rate, the potter mixes 9 pounds of plaster with 3 quarts of water.

e) Using the same rate, the potter mixes 12 pounds of plaster with 4 quarts of water.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

A potter mixes 6 pounds of pottery plaster with 2quarts of water.

Now, We get;

The unit rate for the mis = 6/2

                                      = 3/1

Thus, 3 lb plaster / 1 qt water is a unit rate for the mis.

And, Using the same rate, the potter mixes 9 pounds of plaster with 3 quarts of water.

Using the same rate, the potter mixes 12 pounds of plaster with 4 quarts of water.

Thus, All the correct statements are,

a) 3 lb plaster / 1 qt water is a unit rate for the mis.

c) Using the same rate, the potter mixes 9 pounds of plaster with 3 quarts of water.

e) Using the same rate, the potter mixes 12 pounds of plaster with 4 quarts of water.

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The complete question is shown in figure.

Answer:

M

Step-by-step explanation:

The surface area of the pyramid is 3136 square inches.

A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.

Given:

Each side of the base of a square pyramid measures 8 inches.

The height of each lateral face of the pyramid is also 8 inches.

The perimeter of the base P is 32 inches.

The base area B = 8 x 8 = 64 square inches.

The surface area of the pyramid,

= B + 12(P x L)

= 64 + 12(32 x 8)

= 3136 square inches.

Therefore, the surface area is, 3136 square inches.

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Answer:

D. 74

Step-by-step explanation:

Answer:

D=74

Step-by-step explanation:

10 + (8/2)^3

10 + 512/8

10 + 64

Answer: 74

The inventory can the firm purchase without violating its debt agreement is $777,777

Liquidity ratios are a class of financial metrics used to determine a debtor's ability to pay off current debt obligations without raising external capital.

Given that, Ronaldinho Trading Co. is required by its bank to maintain a current ratio of at least 1.75, and its current ratio now is 2.1.

Let X represent the additional borrowing against the firm’s line of credit (which also equals the addition to current assets).

We can solve for that level of X that forces the firm’s current ratio to be at 1.75

$3,500,000 / Current liabilities = 2.1

Current liabilities = $1,666,667

1.75 = ($3,500,000 + X) / ($1,666,667 + X) (1.75 * $1,666,667) + 1.75X

= $3,500,000 + X 0.75X = $3,500,000 – $2,916,667 X

= $777,777

Hence, the inventory can the firm purchase without violating its debt agreement is $777,777

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Answer: this is like multiplying. this is way to easy.the answer is 25.

Step-by-step explanation:

the answer is 25 bc its just saying

whats 5 times 5 which the answer is 25 right ?

The probability the firm will lose money from 10 wells is 0.99 and the probability the firm will gain 1.5 million from the ten wells is  1 minus the CDF of 4 successful wells.

1.

The expected profit from each well is $1 million - $60,000 = $940,000. The expected profit from all ten wells is $940,000 * 10 = $9,400,000. The probability of losing money on all ten wells is 1 - (0.1)^10 = 0.99

2.

To calculate the probability of gaining $1.5 million or more, we can use the cumulative distribution function (CDF) of the binomial distribution, which models the number of successful wells out of ten. The CDF gives the probability of getting a certain number of successful wells or fewer. To get the probability of getting more than a certain number of successful wells, we subtract the CDF of that number from 1. To get the probability of getting 2 or more successful wells, we subtract the CDF of 1 from 1, and so on. To get the probability of getting 5 or more successful wells, we subtract the CDF of 4 from 1, and so on. To get the probability of getting $1.5 million or more, we need to find the probability of getting 5 or more successful wells, since 5 wells at $1 million each give $5 million. The CDF of 4 successful wells can be found using statistical software or by using tables or approximations. The final answer is 1 minus the CDF of 4 successful wells.

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The solution for the system of equations is negative one fourth comma three fourths.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Slope intercept form of a line is y = mx + c, where m is the slope and c is the y intercept.

Given two lines on a graph.

Let y = m₁x + c₁ and y = m₂x + c₂ are the equations of two lines.

One line passes through (0, 1) and (1, 2).

m₁ = (2 - 1) / (1 - 0) = 1

Substituting m₁ = 1 and a point (x, y) = (0, 1) in y = m₁x + c₁,

1 = c₁

Equation of one line is y = x + 1.

Other line passes through (0, 0) and (1, -3).

m₂ = (-3 - 0) / (1 - 0) = -3

Substituting m₂ = 1 and a point (x, y) = (0, 0) in y = m₂x + c₂,

0 = c₂

Equation of second line is y = -3x

Solving both the equations y = x + 1 and y = -3x,

-3x = x + 1

-4x = 1

x = -1/4

y = -3x = 3/4

Solution is (-1/4, 3/4).

Hence the solution of the system of equations is the point (-1/4, 3/4).

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A

The graph of the function g(x) = 1/x + 13 is a transformation of the graph of f(x) = 1/x. The transformation that has been applied is a vertical shift of 13 units upward. This means that every point on the graph of f(x) has been moved upward by 13 units along the y-axis, resulting in the new graph of g(x). In other words, the graph of g(x) will be parallel to the graph of f(x) but shifted upward by 13 units.

[tex]\stackrel{mixed}{24\frac{1}{2}}\implies \cfrac{24\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{49}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]300\cdot 24\frac{1}{2}\implies 300\cdot \cfrac{49}{2}\implies 7350\qquad \textit{now let's add the 1\% for the broker} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{1\% of 7350}}{\left( \cfrac{1}{100} \right)7350}\implies 73.5~\hfill \stackrel{7350~~ + ~~73.5}{\text{\LARGE 7423.5}}[/tex]

Answer:

Yes

Step-by-step explanation:

The lines are parallel. Alternate angles and vertically opposite angles are equal. True by angle axiom.

The sum of the angles of the triangle below are angle A = 34.91°, angle B = 86.41°, and angle C = 58.68°.

According to the triangle sum theorem, a triangle's internal angles can be added up to 180 degrees. The triangle sum theorem, often referred to as the angle sum theorem of the triangle, states that the total of the measures of a triangle's internal angles in a Euclidean space adds up to 180 degrees, whether the triangle is acute, obtuse, or right.

Let a = 8, b = 14 and c = 12 for the given triangle.

Then,

cos (A) = (b² + c² − a²) / 2bc

cos (A) = (14² + 12² - 8²)/ (2)(14)(12)

cos (A) = (196 + 144 - 64)/ 336

cos (A) = 0.82

A = cos⁻¹ (0.82)

A = 34.91°

Similarly, for angle B.

Cos (B) = (c² + a² − b²)/2ca

Cos (B) = (12² + 8² - 14²)/ (2)(12)(8)

A = cos⁻¹ (0.0625)

B = 86.41°

The sum of all the angles of a triangle is 180:

A + B + C = 180°

34.91° + 86.41° + C = 180°

C = 58.68°

Hence, the sum of the angles of the triangle below are angle A = 34.91°, angle B = 86.41°, and angle C = 58.68°.

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Answer:

Step-by-step explanation:

since there are 60 seconds in 1 minute, we can do

5.85 = 60second

5.85/60  to show how many cm happened in 1 second.

0.0975 cm per second.  

The measure of the three missing angles in the parallelogram are,

⇒ ∠x = 122

⇒ ∠ y = 122°

⇒ ∠z = 58°

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.

Given that;

The parallelogram shown in figure.

We know that;

By Opposite Angles Theorem,

In parallelogram, The two opposite angles of a parallelogram are equal to each other.

Hence, We get;

⇒ ∠y = 58°

⇒ ∠x = ∠z

And, The sum of all angles in a parallelogram is 360°.

Hence, We get;

⇒ ∠x + ∠y + ∠z + 58° = 360

⇒ ∠x + ∠x +58+58 = 360

⇒ 2∠x + 116 = 360

⇒ 2∠x = 360 - 116

⇒ 2 ∠x = 244

⇒ ∠x = 122

And, ∠ z = 122°

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Step-by-step explanation:

perimeter means to add all sides

SO

perimeter of triangle is

QR+QP+RP

SO

= 63+70+47

=180

Answer:

perimeter= 180

Step-by-step explanation:

Add 63+70+47=180

63

70

47

+

---------

  180

The formula holds true for matrices A and B.

The formula (A + B)^2 = A^2 + 2AB + B^2 holds true for all matrices A and B that are of the same size and can be added and multiplied. To prove this, we calculate the left-hand side and the right-hand side of the equation:

(A + B)^2 = (A + B)(A + B) = A^2 + AB + BA + B^2

Since AB = BA, we can simplify the equation to:

(A + B)^2 = A^2 + 2AB + B^2

So, the formula holds true for matrices A and B.

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Step-by-step explanation:

x = 2 3/4

y = -1 1/4

I think this is the answer

Pat and John will meet in 3 hours.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

How to calculate the value?

It should be noted that speed = Distance / Time

The appropriate equation will be:

80t + 24t = 312

104t = 312

t = 312/104

t = 3. hours

Therefore, it will take them 3 hours to meet.

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