I need help me with my homework(please do not put a complicated answer and it also properties)

We verified that the associative property of addition holds for the given expression below

Let's verify the associative property of addition for the given expression:

2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5

We can simplify both sides of the equation by finding a common denominator for the fractions:

2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5

Multiplying 2/3 by 20/20, we get:

40/60 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5

Multiplying 3/4 by 15/15, we get:

40/60 + 45/60 + 1/5 = (2/3 + 3/4) + 1/5

Combining the first two terms on the left-hand side, we get:

85/60 + 1/5 = (2/3 + 3/4) + 1/5

Simplifying the fraction 85/60, we get:

17/12 + 1/5 = (2/3 + 3/4) + 1/5

Multiplying 2/3 by 4/4, we get:

17/12 + 1/5 = (8/12 + 9/12) + 1/5

Combining the fractions in the parentheses, we get:

17/12 + 1/5 = 17/12 + 1/5

Since both sides of the equation are equal, we have verified that the associative property of addition holds for the given expression:

2/3 + (3/4 + 1/5) = (2/3 + 3/4) + 1/5.

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The value of cos ( 90 - x ), given the side lengths of the right triangle would be B. 3 / 5.

In a right triangle, the sum of the two acute angles is always 90 degrees. If we have a right triangle with side lengths 3, 4, and 5, then it's a 3-4-5 Pythagorean triple, which means the angles are also in a specific ratio.

Now, we want to find cos(90 - x). Since the sum of the two acute angles in a right triangle is 90 degrees, the other angle in the triangle is (90 - x). We know that sin x = opposite / hypotenuse, so in our triangle, sin(90 - x) = 3/5.

The sine and cosine of complementary angles are related by the co-function identity:

cos(90 - x) = sin x

So, cos(90 - x) = sin(90 - x) = 3/5.

The answer is 3/5.

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The radius of the base of the cone can be found by dividing the circumference by 2π:

radius = (8.5π)/(2π) = 4.25 inches

Using the formula for the volume of a cone, V = (1/3)πr^2h, we can substitute the values we know:

V = (1/3)π(4.25^2)(15) ≈ 270.62 cubic inches

Rounding to the nearest hundredth, the volume of the cone in terms of π is approximately 270.62π cubic inches.

The area of a circle is given by the formula:

A = πr^2

where r is the radius of the circle.

Substituting the value of the radius as r = 10 cm, we get:

A = π(10)^2

A = 100π

Therefore, the area of the circle with radius 10 cm is 100π square centimeters.

~~~Harsha~~~

The exponential equation in an equivalent logarithmic form in order to solve for t is t = 4 * log(base 2) (P/270)

To write the exponential equation P = 270(2)^(t/4) in logarithmic form, we can use the following property of logarithms:

log(base a) (x^y) = y*log(base a) (x)

Applying this property to the given equation, we get:

log(base 2) (P/270) = t/4

This is the logarithmic equivalent of the exponential equation. It relates the time t to the average price P of an ounce of gold since 2003.

To solve for t, we can isolate it on one side of the equation:

t = 4 * log(base 2) (P/270)

This formula gives the time t since 2003 (in years) corresponding to a given average price P of an ounce of gold.

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We can use the trigonometric identity for the sine of a difference:

sin(a - B) = sin a cos B - cos a sin B

We are given that sina = -3 and sinß = 3, so we need to find the cosine of each angle. Since the terminal side of a lies in quadrant III and the terminal side of 6 lies in quadrant I, we can use the following relationships:

cos a = -sqrt(1 - sin^2 a) = -sqrt(1 - 9) = -sqrt(-8) = sqrt(8)i

cos ß = sqrt(1 - sin^2 ß) = sqrt(1 - 9) = sqrt(-8) = sqrt(8)i

Note that we use i to indicate the imaginary unit, since the result involves a negative square root. Therefore, we have:

sin(a - B) = sin a cos ß - cos a sin ß

= (-3)(sqrt(8)i) - (sqrt(8)i)(3)

= -3sqrt(8)i - 3sqrt(8)i

= -6sqrt(8)i

Hence, the exact value of sin(a - B) is -6sqrt(8)i.

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The exact value of sin(a - B) if sina = -3 and sinß = 3, and the terminal side of a lies in quadrant III and the terminal side of 6 lies in quadrant  is sin(a - B) =0

We apply the trigonometric identity for the sine of a difference:

sin(a - B) = sin(a)cos(B) - cos(a)sin(B)

We use Pythagorean identity to find the cosine values:

cos^2(a) = 1 - sin^2(a) = 1 - (-3)^2 = -8

cos(a) = ±√8i

cos(a) = -√8 (Since a lies in quadrant III, the cosine value is negative.)

we also have that:

cos^2(B) = 1 - sin^2(B) = 1 - 3^2 = -8

cos(B) = ±√8i

cos(B) = √8. (Since B lies in quadrant I, the cosine value is positive. )

we then substitute these values into the formula for sin(a - B):

sin(a - B) = sin(a)cos(B) - cos(a)sin(B)

= (-3)(√8) - (-√8)(3)

= -3√8 + 3√8

= 0

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If 54 oranges cost 36 naira, then the cost of 3 oranges​ is 2 naira

Unitary method is a method of solving problems by finding the value of one unit and then using that value to find the value of a given number of units

To find the cost of 3 oranges, we can use unitary method which involves finding the cost of one orange and then multiplying it by 3.

Let's first find the cost of one orange

54 oranges cost 36 naira

So, 1 orange will cost:

1/54 of 36 naira = (36/54) naira = (2/3) naira

Now, we can find the cost of 3 oranges by multiplying the cost of one orange by 3

Cost of 3 oranges = 3 x (2/3) naira = 2 naira

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The answer to this question is  x = 6

Thus, the probability that two custard-filled donuts are selected in a row) 11/46.

sampling without replacement is the process of selecting a subset of observations at random; once an observation is chosen, it cannot be chosen again. sampling with replacement, whereby one observation may be chosen more than once and a subset of observations is chosen at random.

Given data:

two-dozen (24) donuts

probability = favourable outcome / total outcome

probability (1st custard-filled donut) = total custard-filled donut / total donuts

probability (1st custard-filled donut) = 12/24

probability (1st custard-filled donut) = 1/2

Now,1 is already taken, now total donuts left are 23 with 11 custard-filled donut.

probability (2nd custard-filled donut) = total custard-filled donut / total donuts

probability (2nd custard-filled donut) = 11/23

Now,

probability (two custard-filled donuts in a row) = 1/2 * 11/23

probability (two custard-filled donuts in a row) = 11 / 46

Thus, the probability that two custard-filled donuts are selected in a row) 11/46.

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The proportionality constant that relates the distance traveled by Olivia to time is 34/13, or approximately 2.615.

The constant of proportionality is related to the distance Olivia travels and the time it takes to travel that distance. You can find it by dividing the distance by the time.

constant of proportionality = distance / time = 34 miles / 13 hours

This division can be simplified by partitioning both the numerator and denominator by their most prominent common divisor, 1.

 constant of proportionality = 34/13

Therefore, the proportionality constant that relates the distance traveled by Olivia to time is 34/13, or approximately 2.615 (rounded to three decimal places).  

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Answer:

a) model a: 50/hr

model b: 40/hr

b) model a

Step-by-step explanation:

b) since the money raised started at 0, the rate of change can be found by calculating 400/8

Answer:

236 cm^2  and  8 cm

Step-by-step explanation:

width=w

240=6(5)(w)

w=8 cm

area=2[(6)(5)+(6)(8)+(5)(8)]

area=236 cm^2

The more bidders there are, the more likely it is that the highest bid variable bmax will be updated multiple times as each agent outbids the previous highest bidder.

Let us denote the expected number of times the variable bmax gets updated by E.

We can start by computing the probability that the ith agent updates bmax. This is equal to the probability that agent i has the highest bid among the first i bids. Since all bids are distinct and the order of the agents is chosen uniformly at random, the probability of this event is 1/i.

Therefore, the expected number of updates to bmax is:

E = ∑i=1 to n P(agent i updates bmax)

E = ∑i=1 to n 1/i

This is the harmonic series, which diverges as n approaches infinity. Therefore, as the number of bidding agents increases, the expected number of updates to bmax increases without bound.

In practical terms, this means that the more bidders there are, the more likely it is that the highest bid variable bmax will be updated multiple times as each agent outbids the previous highest bidder.

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As per the unitary method, the list shows the number of each type of animal on this farm is

Number of pigs = x

Number of horses = 2x

Number of cows = 8x

Let us start by assigning variables to each type of animal on the farm. Let's say the number of pigs is "x".

From the problem statement, we know that there are twice as many horses as pigs. Therefore, the number of horses would be 2x.

Further, we know that there are four times as many cows as horses. So, the number of cows would be 4 times the number of horses. Mathematically, we can represent it as:

Number of cows = 4 * Number of horses

Or, Number of cows = 4 * (2x) = 8x

Therefore, we have the number of each type of animal on the farm as follows:

Number of pigs = x

Number of horses = 2x

Number of cows = 8x

This is the same ratio as we found using the unitary method.

Therefore, our solution is correct.

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To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.

For the ordered pair (1, -5):

x - y = 6 becomes 1 - (-5) = 6, which is true.

y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.

Therefore, (1, -5) is not a point of intersection.

For the ordered pair (1, 5):

x - y = 6 becomes 1 - 5 = -4, which is false.

y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.

Therefore, (1, 5) is a point of intersection.

For the ordered pair (5, -1):

x - y = 6 becomes 5 - (-1) = 6, which is true.

y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.

Therefore, (5, -1) is not a point of intersection.

So the answer is:

(1,-5) - No

(1,5) - Yes

(5,-1) - No

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Answer:y+6=1/3(x+2)

Step-by-step explanation:

Hello!

You need to use the Point slope formula

y-y1=m(x-x1)

Plug your point into the equation with the slope (m)

y-(-6) =1/3(x-(-2))

Then simplify

y+6=1/3(x+2)

The ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.

The quantity of matter in an object is measured by its mass, which is commonly expressed in kilogrammes or grammes. Since mass is a scalar quantity, the gravitational field has no effect on it. The force of gravity acting on an object is quantified by weight, which is commonly expressed in newtons or pounds. Weight is a vector quantity that is influenced by the strength of the gravitational field. While an object's mass is constant, its weight might vary depending on the gravitational field.

The ratio of weight to mass according to the given table is:

weight / mass = 196 / 20 = 98/10

The ratio is constant thus for x we have:

1078 / x = 98 / 10

Using cross multiplication we have:

x = 1078 (10) / 98 = 110

Hence, the ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.

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The complete question is:

Answer: 3

Step-by-step explanation:

$2,560 needs to be invested at time 3 in order to have $3,200 at time 8.

Since the money grows according to the simple interest accumulation function a(t) = 1.05t, the amount of money A at time t, given an initial amount P, can be calculated using the formula:

A = P + Pr(t)

where r is the interest rate (in this case, 5% or 0.05) and t is the time period (measured in years).

To determine how much money needs to be invested at time 3 to have $3,200 at time 8, we can use the above formula and solve for P:

3200 = P + Pr(8-3)

3200 = P + 5P(0.05)

3200 = P + 0.25P

3200 = 1.25P

P = 3200 / 1.25

P = 2560

Therefore, an initial investment of $2,560 at time 3 would be needed to have $3,200 at time 8, assuming a simple interest accumulation function with an interest rate of 5%.

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Answer:4/3

Step-by-step explanation:start by converting the mixed numbers to improper fractions to make the subtraction easier:

5⅔ cups of cereal = 17/3 cups of cereal

4⅓ cups of marshmallows = 13/3 cups of marshmallows

Now subtract the amount of marshmal ows from the amount of cereal: 4/3 of a cup

Answer:

1  1/3

Step-by-step explanation:

so first you must take the 5 2/3 and subtract if from the 4 1/3 which gives:

1  1/3

The interest rate of the given investment is calculated as: 14%

The formula for the simple interest is:

i = prt

where:

p is the principal (starting amount)

i is the interest earned

r is the interest rate expressed as decimal

t is the time period in years

We are given:

i = $245

p = $7000

t = 3 months = 0.25 years

Thus:

r = i/pt

r = 245/(7000 * 0.25)

r = 0.14 or 14%

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There are 35 possible trip choices available to Amy. The solution has been obtained by using the concept of combination.

What is combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

We are given that there are seven different places and from that she can afford only three. Since, here order does not matter so, we will use combinations as in combination order of the selection is irrelevant.

From this, we get

⇒ [tex]^{7} C_{3}[/tex] = [tex]\frac{7!}{3!(7-3)!}[/tex]

⇒ [tex]^{7} C_{3}[/tex] = 35

Total possible trips = 35

Hence, Amy has total of 35 possible trip choices.

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If you choose not to make a payment during the 24-month period, your balance at the end of the promotion will be $3,637.16.

Explain month

A month is a unit of time equal to one-twelfth of a year, or approximately 30.44 days. It is often used to represent periodic phenomena, such as interest rates or seasonal trends, and to calculate the duration between two dates. The number of months between two dates is calculated by dividing the difference in days by 30.44.

According to the given information

If you do not make any payments during the 24-month period, your balance will increase each month due to the interest that accrues. After 24 months, your balance will be:

$2299.99 * (1 + 0.020825)²⁴ = $3,637.16

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The  closest possible  choice is 198.06 ft².

Option C is correct.

The area of the base is gotten as :

length x width = 8 ft x 7 ft = 56 ft².

The length of the pyramid's slant height (s) must be determined in order to determine the area of each triangle face.

We may determine that s = (h2 + (w/2)2) = (62 + (7/2)2) = (36 + 24.5) = 60.5 7.78 ft using the Pythagorean theorem.

The area of each triangular face is

(1/2) x base x height = (1/2) x 8 ft x 7.78 ft

= 31.12 ft².

Hence, the total surface area of the pyramid :

56 ft² + 4 x 31.12 ft² = 192.48 ft².

In conclusion, the closest possible  choice is 198.06 ft².

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The answer to the equation 3x^2 + 6x - 6 = -2x^2 to the nearest tenth is 0.8

To solve the equation 3x^2 + 6x - 6 = -2x^2, we first need to simplify it by moving all the terms to one side of the equation:

3x^2 + 2x^2 + 6x - 6 = 0

Combining like terms, we get:

5x^2 + 6x - 6 = 0

We can then use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 5, b = 6, and c = -6. Substituting these values into the formula, we get:

x = (-6 ± sqrt(6^2 - 4(5)(-6))) / 2(5)

x = (-6 ± sqrt(156)) / 10

x ≈ -1.2 or x ≈ 0.8

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The value of x in the quadratic equation to the nearest tenth is 0.7

A quadratic equation is a polynomial equation of degree two, which means it contains terms raised to the power of two. It typically takes the form of ax² + bx + c = 0, where a, b, and c are coefficients and x is the variable.

From the information given:

3x^2 + 6x - 6 = -2x^2

Collect like terms

3x^2 + 2x^2 + 6x - 6 = 0

5x^2 + 6x - 6 = 0

Solving by using the quadratic formula:

[tex]\dfrac{-b\pm\sqrt{b^2 - 4(a\times c)}}{2a}[/tex]

where;

[tex]\dfrac{-6\pm\sqrt{6^2 - 4(5\times -6)}}{2\times 5}[/tex]

[tex]\dfrac{-6\pm\sqrt{36+120}}{10}[/tex]

[tex]\dfrac{-6\pm\sqrt{156}}{10}[/tex]

[tex]\dfrac{-6\pm\sqrt{2^2 \times 39}}{10}[/tex]

[tex]\dfrac{-6\pm2 \sqrt{39}}{10}[/tex]

[tex]\dfrac{-3\pm2 \sqrt{39}}{5}[/tex]

[tex]x= \dfrac{-3+2 \sqrt{39}}{5} \ \ OR \ \ \dfrac{-3-2 \sqrt{39}}{5}[/tex]

x =  0.64899959  OR  −1.84899959

Therefore, since x cannot be negative, In decimal form to the nearest tenth, x = 0.7

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Answer: We can use a proportion to estimate the total number of fur seal pups in Rookery A. Let x be the total number of fur seal pups in Rookery A. Then we have:

6269/x = 221/1100

Cross-multiplying, we get:

221x = 6269 * 1100

Dividing both sides by 221, we get:

x = 6269 * 1100 / 221

Simplifying, we get:

x = 31,245.25

Rounding to the nearest whole number, we get:

x ≈ 31,245

Therefore, the estimated total number of fur seal pups in Rookery A is 31,245.

Step-by-step explanation:

There are 302,702,400 possible baseball teams of nine that can be formed with three designated pitchers and 12 multitalented players who can play any of the remaining positions.

Since three players are designated as pitchers, we need to choose three players out of the total 15 players on the team. This can be done in C(15, 3) ways, where C(n, r) represents the number of combinations of r objects selected from a set of n objects.

For the remaining six positions, any of the 12 multitalented players can be assigned to any of the positions, which means that there are 12 choices for the first position, 11 choices for the second position, and so on, down to 7 choices for the sixth position.

Therefore, the total number of baseball teams of nine that can be formed is:

C(15, 3) x 12 x 11 x 10 x 9 x 8 x 7

which simplifies to:

(15 x 14 x 13 / 3 x 2 x 1) x (12 x 11 x 10 x 9 x 8 x 7)

= 455 x 665,280

= 302,702,400

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The p-value is greater than 0.05, the researcher would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the average number of sick days taken per year by workers is greater than 5.

It appears that some values are missing in your question, specifically the sample mean and the population standard deviation.

Without these values, I cannot provide a complete answer to your question.

A general idea of how to approach this type of hypothesis test.

To test whether the average number of sick days a worker takes per year is greater than 5, the researcher would need to set up the following hypotheses:

Null hypothesis (H0):

The average number of sick days taken per year by workers is equal to or less than 5.

Alternative hypothesis (Ha):

The average number of sick days taken per year by workers is greater than 5.

The next step would be to collect a random sample of workers and calculate their sample mean and sample standard deviation.

Based on these values, the researcher would then calculate the t-value using the formula:

t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))

The hypothesized population mean in this case is 5, the sample size is 28, and the sample mean and sample standard deviation would be substituted in.

Once the t-value is calculated, the researcher would then use a t-distribution table to find the corresponding p-value based on the degrees of freedom (sample size minus 1) and the level of significance (0.05).

If the p-value is less than 0.05, the researcher would reject the null hypothesis and conclude that there is enough evidence to support the claim that the average number of sick days taken per year by workers is greater than 5.

The specific critical t-value would be based on the degrees of freedom and level of significance.

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