selecting christmas presents if a person can select presents from presents under a christmas tree, how many different combinations are there?

Using compounding we know that after 30 years, the account balance has changed by $345.31.

Theoretically, continually compounded interest indicates that interest is continuously earned on an account balance as well as reinvested into the balance so that additional interest is generated.

So, a business owner put $7,000 into a Treasury bond paying a semiannual compound interest rate of 4.3%.

The bond's value after 30 years is $25,084.20.

Instead of compounding twice a year, the investment made by the business owner was made continuously.

After 30 years, we must determine the difference in the account balance.

Think of the continuously compounding recipe:

A = Pe∧rt

We have, p = 7000.

r = 4.3% = 0.043

t = 30

Then,

A = 7000e∧(0.043*30) = 25429..51

A = $25429.51

Therefore, using compounding we know that after 30 years, the account balance has changed by $345.31.

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Correct question:

A business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. After 30 years, the value of the bond will be $25,084.20. If the business owner's investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years?

Answer:

1. SAS

2. Not congruent

Step-by-step explanation:

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

The solution is,

1. SAS

2. AAS

3. SAS

4. Not congruent.

Two triangles are congruent if all three pairs of corresponding sides are equal. Two pairs of corresponding sides and the corresponding angles between them are equal.

here, we have,

we know that,

To identify which triangles are congruent measure the angles and sides of each of the triangles and compare them.

Meaning of congruent:

In mathematics, the word congruent is used if two figures have the same size and shape, although their orientation can be different.

Two triangles are congruent:

In the case of triangles two factors should be considered:

1) Lengths of each side are equal.

2) Angles are equal.

This means that to determine if the triangles are congruent, we must measure each side and angle and make sure these are the same in each triangle.

now, we have,

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second and, similar for 2 & 3 by AAS & SAS.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

Hence, 1. SAS

2. AAS

3. SAS

4. Not congruent.

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Explanatory variable: Cooling time in seconds

Response variable: Impact strength in kj/m2

To find the equation of the linear model that describes the relationship between the predicted value of the response and the explanatory variable, we can use linear regression analysis. Using a statistical software or a calculator, we can find the slope and intercept of the line that best fits the data.

The equation of the linear model is:

Impact strength = -1.23 * Cooling time + 62.61

R-squared (R2) is a statistical measure that represents the proportion of the variance in the dependent variable (impact strength) that is explained by the independent variable (cooling time). It ranges from 0 to 1, with higher values indicating a better fit of the model.

Based on the value of R2, we can say how much of the variation in impact strength can be explained by cooling time. The closer R2 is to 1, the better the model fits the data, and the more likely it is that the impact strength is affected by cooling time. A value of 1 would indicate that all the variation in impact strength is explained by cooling time, while a value of 0 would indicate that cooling time has no effect on impact strength.

          Without knowing the actual value of R2, we cannot say for sure what the relationship is between the explanatory and response variables. However, if the value of R2 is high (close to 1), we can conclude that cooling time has a significant effect on impact strength. If the value of R2 is low (close to 0), we cannot conclude that cooling time has a significant effect on impact strength.

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Answer:

Solution and calculation given below.

The solution is, the distance of the towns is 11.88 km

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have,

So this can be solve by solving the distance of the plane and the town to the west and also the distance of the plane to the town to the east.  

So the town with an angle of depression of 34 degrees

Let x be the distance of the plane and town  

Cos 34 = x / 8

x = 8 cos 34

x = 6.63 km  

So the town with an angle of depression of 49 degrees

Let y be the distance of the plane and town  

Cos 49 = y / 8

y = 8 cos 49

y = 5.25 km  

so the distance of the towns is 5.25 + 6.63 = 11.88 km

Hence, The solution is, the distance of the towns is 11.88 km.

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complete question:

An airplane is flying between two towns at an altitude of 8km. One town is to the west of the plane and the other is to the east. The angle of depression to one town in de34grees and to the other town is 49degrees. What is the distance between the two towns

There is No relation between the variables ggg and hhh.

To determine if the given table shows a proportional relationship between the variables ggg and hhh, we need to check if the ratio of hhh to ggg is constant for all values of ggg.

Let's calculate the ratios of hhh to ggg for each value of ggg:

For ggg = 333, hhh/ggg = 999/333 = 3.

For ggg = 666, hhh/ggg = 363636/666 = 546.

For ggg = 999, hhh/ggg = 818181/999 = 819.

Since the ratios of hhh to ggg are not constant, the given table does not show a proportional relationship between the variables ggg and hhh.

Therefore, the answer is "No, the table does not show a proportional relationship between the variables ggg and hhh."

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The total volume of the space dome theatre is 41867 m³.

In geometry, a sphere is a three-dimensional solid figure, which is round in shape.

The surface area is 4πr².

The volume is (4/3)πr³.

The diameter is 2×radius of the sphere.

A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, The space dome theatre has a base radius of 20m.

Therefore, The volume of the hemispherical dome is,

= (2/3)π(20)³.

= (2/3)π×8000.

= (16000/3)π m³.

And, As the dome base has a radius of 20 m the cylindrical shape will also have the same.

Therefore, The volume of the cylindrical shape is,

= π(20)²×20.

= 8000π m³.

And, The total volume is the sum of the volumes of two shapes,

= 8000π + (16000/3)π m³.

= [(24000 + 16000)/3]π m³.

= (40000/3)π m³.

= 41867 m³.

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Answer:

the domain is: {−3,0,1,6}

the range is:{2,3,4,−6,4}

the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Explanation:

In the relation:

{(−3,2),(0,3),(1,4),(1,−6),(6,4)}:

The domain:

Is the set of all the first numbers of the ordered pairs.

In other words, the domain is all of the x-values.

So in this case the domain is:

{−3,0,1,6}

The range:

Is the set of the second numbers in each pair, or the y-values.

So in this case the range is:

{2,3,4,−6,4}

A relation is a function if it has only One y-value for each x-value.

So in this case the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know the meaning of D(2.60) = 159 if D(p) tells you the number of toys demanded at price p in hundreds.

Compare D(p) to D(2.60) and you see that p=2.60. The problem statement tells you p is the price. This means ...

The problem statement tells you that D(p) is the number of toys in hundreds. When D(p) is 159, the demand is 159 hundred toys.

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The length of the hypotenuse is 11.31 cm

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

A right, isosceles triangle has its legs to be 8cm

Represen the length of the hypotenuse of the isosceles right triangle  with x

Using the above definition as a guide, we have the following:

x = Leg√2

substitute the known values in the above equation, so, we have the following representation

x = 8 * √2

This gives

x = 11.31

HEnce, the hypotenuse is 11.31 cm

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Answer:

Step-by-step explanation:

You want the lateral area, base area, and total area of a square pyramid with a base 3 ft on a side and a slant height of 4 ft.

The area of one triangle is ...

  A = 1/2bh

  A = 1/2(3 ft)(4 ft) = 6 ft²

Then the area of the four triangular faces is ...

  area of triangles = 4×6 ft² = 24 ft²

The area of the square base is ...

  A = s²

  A = (3 ft)² = 9 ft²

The area of the square base is 9 ft².

The total surface area is the sum of the lateral area and the base area:

  total surface area = area of triangles + area of square = 24 ft² +9 ft²

  total surface area = 33 ft²

<95141404393>

The inequality showing the maximum number of days he can rent a car is 10d ≤ 75.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that Passion has a budget of $75 and wants to rent a car for a trip. A fixed daily fee of 10 is charged.

The product of the number of days and the rent per day should be less than the amount he has.

The inequality mathematically can be written as:-

10t ≤ $75

Therefore, the inequality 10d ≤75 shows how many days he can rent an automobile for the most.

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The correct weight of butter is 1/32 pounds. Olivia will use 1/32 pound of butter in each batch of muffins.

Olivia has 1/8 pound of butter that she needs to divide equally among 4 batches of muffins. To find out how much butter is used each batch of muffins, we can divide the total amount of butter by the number of batches. So, the amount of butter in each batch of muffins is: 1/8 ÷ 4 batches = 1/32 pound. So, Olivia will use 1/32 pound of butter in each batch of muffins. A pound (lb) is a unit of weight or mass commonly used in the United States and other countries that follow the customary system of measurement.

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A collegiate basketball player hits 80% of his free throw attempts. Assuming free throw attempts are independent, he will try 100 free throws this season the answers are as follows:

a) The mean of X is 80.

b) The standard deviation of X is 4.

c) The probability that the basketball player makes at least 90 of these attempts is approximately is 0.0062.

d) If the basketball player instead attempts only 10 free throws, the probability that he makes at most 4 of these is 0.0064.

As per the question given,  

a) The mean of X is given by the formula: mean = n * p, where n is the number of trials and p is the probability of success on each trial. In this case, the player attempts 100 free throws with a probability of success of 0.8, so the mean is:

mean = 100 * 0.8 = 80

Therefore, the correct answer is 80.

b) The standard deviation of X is given by the formula: standard deviation = sqrt(n * p * (1 - p)). Substituting the values, we get:

standard deviation = sqrt(100 * 0.8 * 0.2) = 4

Therefore, the correct answer is 4.

c) To find the probability that the player makes at least 90 free throws, we can use the normal approximation to the binomial distribution. The mean is 80 and the standard deviation is 4, so we can standardize the value of X as follows:

z = (90 - 80) / 4 = 2.5

Using a standard normal distribution table, we can find the probability that Z is greater than 2.5, which is approximately 0.0062.

Therefore, the correct answer is 0.0062.

d) If the player attempts only 10 free throws, the number of successful attempts X follows a binomial distribution with n=10 and p=0.8. The probability that he makes at most 4 of these attempts is:

P(X <= 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

Using the binomial distribution formula, we can calculate each of these probabilities and sum them up. Alternatively, we can use a binomial probability table or a calculator to find the cumulative probability.

Using a binomial probability calculator, we get:

P(X <= 4) = 0.0064 (rounded to four decimal places)

Therefore, the correct answer is 0.0064.

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The triangles are congruent by SSS and the transformation rule is (x, y) ⇒ (x - 4, y)

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

Triangles EFD and GH

The triangles are congruent because they have equal corresponding side lengths

The corresponding sides of the triangles are congruent

So, the congruent statement is SSS

From the figure, we can see that:

EFD is shifted left by 4 units

So, the rule is

(x, y) ⇒ (x - 4, y)

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Answer: C

Step-by-step explanation:

The integer 8 represents the amount lost each time the pass was used.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that, every time Ezequiel rides the bus, money is deducted from the value of the pass.

He rode 9 times and $72 was deducted from the value of the pass.

Let x be the integer that represents the amount deducted each time.

The amount deducted after 9 times is 9x.

9x = 72

We have to divide 72 into 9 parts to know the value of x.

x = 72 / 9 = 8

Hence Ezequiel lost $8 each time the pass was used.

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The second year's interest rate is 1.80%.

Compound interest is defined as Since compound interest accrues and is added to the accrued interest from earlier periods, borrowers are expected to pay interest on interest in addition to principal.

We are aware that the compound interest formula is,

A = P(1 + r/100)ⁿ.

Where A is the amount, P is the principle, r is the rate, and n is the number of years.

Given, Katy places $2000 over a three-year period in a savings account.

For the first year, the account offers compound interest at a 2.5% annual rate.

∴ A = 2000(1 + 2.5/100)¹.

A = 2000(1.025). (1.025).

A = 2050.

It now earns x% for the second year.

∴ 2050(1+x/100)² = 2124.46

(1+x/100)² =2124.46/2050

1+x/100 =√(2124.46/2050)

x/100 = √(2124.46/2050) -1

x = (√(2124.46/2050) -1)*100

x = 1.80%.

the interest is 1.80 percent

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Answer:

Step-by-step explanation:

You want to know the number of points and the number of turns when Tony and his cousin will have the same score. Tony has 12 points and earns 10 points per turn; his cousin has 0 points and earns 14 points per turn.

The attachment shows a table of points and turns. It shows the score will be tied at 42 points after 3 turns.

Tony's points can be described by ...

  p = 12 +10t . . . . . . . . 12 points in addition to 10 per turn

Cousin's points can be described by ...

  p = 0 + 14t . . . . . . . . . 14 points per turn added to the current score of 0

These will be equal when ...

  p = p

  12 +10t = 0 +14t . . . . substitute for p in both cases

  12 = 4t . . . . . . . . . . subtract 10t

  3 = t . . . . . . . . . . divide by 4

  p = 14·3 = 42 . . . . the scores after 3 turns

how will his speed compare?  or namely, will he be within speed limits or should we give him a big fat ticket for speeding?

well, the 25 mi/hr limit is expecting anyone on that road to only do 40,234 meters per hour, so since an hour is 60 minutes and a minute is 60 seconds, that means an hour is really (60)(60) seconds, or 3600 seconds, so the limit is expecting anyone on that road to do no more than 40,234 meters per 3600 seconds, let's see how Usain fares

[tex]\begin{array}{ccll} meters&seconds\\ \cline{1-2} 100 & 9.63\\ 40234& x \end{array} \implies \cfrac{100}{40234}~~=~~\cfrac{9.63}{x} \implies 100x=(40234)(9.63) \\\\\\ x=\cfrac{(40234)(9.63)}{100}\implies x\approx 3874.53[/tex]

so Usain will covering those 40,234 meters in about 3875 seconds, that's longer than 3600 seconds, meaning Usain will need more than 3600 seconds to cover those meters so he's really going slower 40,234 meters per 3600 seconds, so he's golden,  he's within speed limits, because the limit is expecting noone to do them in less than 3600 seconds.

The linear inequality that is graphed with y > –x – 2 to create the given solution set is D. y < x + 1

One of the line is having the y intercept -2 and slope -1 having the equation y=-x-2. The shaded region is having the inequality y>-x-2.

The other line is having the y intercept 1 and slope of 1. Hence equation of line is y=x+1.

The shaded part is above the line .The inequality region is represented by the inequality y <x+1.

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Which linear inequality is graphed with y > –x – 2 to create the given solution set?

A=y > x + 1

B=y < x – 1

C=y > x – 1

D=y < x + 1

The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of the variable 'y' is given by the tangent of the angle 27°. Then we have

tan 27° = y / 350

y = 350 tan 27°

y = 178.3

The value of the variable 'y' in the right-angle triangle round to the nearest tenth will be 178.3 feet.

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The missing diagram is given below.

Answer:

Domain is x-value and range is y-values

Step-by-step explanation:

Answer:139.33 or 139 ft high

Step-by-step explanation: since building A is three times as high as building B, we can use the equation 418/3=B, which results in 139.33, and if rounding it needed you could round it to 139

The parcel is 30 acres in size, calculated as 10 acres for the NW 1/4 of the SE 1/4 and 20 acres for the S 1/2 of the SW 1/4 of the NE 1/4.

To solve the problem, we need to know the size of the quarter sections that are being referred to. In the United States, a quarter section is 160 acres.

Using this information, we can break down the given parcel as follows:

NW 1/4 of the SE 1/4: This represents 1/16 of a section, or 10 acres (160 acres / 16 * 1 = 10).

S 1/2 of the SW 1/4 of the NE 1/4: This represents 1/8 of a section, or 20 acres (160 acres / 8 * 1/2 = 20).

To find the total size of the parcel, we simply add these two areas together:

(10 + 20 )acres = 30 acres

Therefore, the parcel is 30 acres in size.

In the United States, a section of land is a unit of area measurement used in land surveys, and it is equal to 640 acres. A quarter section is, therefore, one-fourth of a section, or 160 acres.

The given parcel is described as two parts. The first part is the northwest quarter of the southeast quarter, which is equivalent to one-sixteenth of a section or 10 acres (1/4 x 1/4 x 160 acres = 10 acres).

The second part is the south half of the southwest quarter of the northeast quarter, which is equivalent to one-eighth of a section or 20 acres (1/4 x 1/4 x 1/2 x 160 acres = 20 acres).

To find the total size of the parcel, we add the area of the two parts: 10 acres + 20 acres = 30 acres. Therefore, the parcel is 30 acres in size.

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The solution is, the situation can be modeled as y = 52 - 8x.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.

So, the total area to be painted is (28 + 3 × 8) = 52 square meters.

Let y represent the area (in square meters) left to paint after x hours of painting then the situation can be modeled as

y = 52 - 8x ................ (1) (Answer)

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The mean of the given data is 22.39.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Let us form a table by give data

Score          Frequency        Midpoint(x)          fx

1-7                    13                       4                      52

8-10                  1                        9                       9

11-15                 19                      13                     247

16-20               20                      18                    360

21-35               19                       28                   532

36-50               20                     43                  860

Mean=∑fx/N

=52+9+247+360+532+860/13+1+19+20+19+20

=2060/92

Mean=22.39

Hence, the mean of the given data is 22.39.

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Answer: A. [tex]92cm^{3}[/tex]

Step-by-step explanation:

[tex]V= \frac{4}{3} \pi r^{3}[/tex]

[tex]V=\frac{4}{3}\pi 2.8^{3}[/tex]

[tex]4/3=1.33333333333[/tex]

calculate in calculator

[tex]1.33333333333\pi 2.8^3=91.9523225755[/tex]

round to nearest ones (9 tells 1 to go to 2)

Therefore, A. 92cm^3

Answer:

Step-by-step explanation:

In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.

A millimeter, abbreviated mm, is the smallest unit for length in the metric, or Standard International, system of measurement. It is used to measure small lengths and for precise measurements. Millimeters can be converted to either units within the metric system or the customary system of measurement.

Divide 8500 kilometers by which 500 km equals 17.5 millimeters.

Therefore, In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.

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