using the rule of 72, how long will it take $100,000 to equal $200,000 if you can earn 14% annually? question 40 options: 5.1429 years 4.1529 years 2.78 years 1.38 years

Answer: two right-angled triangle, equilateral triangle

Step-by-step explanation:

It is a combination of two right-angled triangle or it is an equilateral triangle.

Explanation:

You want to prove a point P on the perpendicular bisector of segment YZ is equidistant from Y and Z.

1. PX is the perpendicular bisector of YZ . . . . given

2. angles at X are right angles . . . . definition of perpendicular

3. YX = XZ . . . . definition of bisector

4. PX = PX . . . . reflexive property of congruence

5. ∆PXY ≅ ∆PXZ . . . . LL congruence theorem

6. YP ≅ ZP . . . . CPCTC

Answer:

Step-by-step explanation:

We can use the fact that the ratio of the volumes of two similar solids is equal to the cube of their corresponding linear dimensions, also known as the volume-scale factor:

(volume of image) / (volume of original) = (linear dimension of image / linear dimension of original)^3

(40 cubic units) / (10 cubic units) = (linear dimension of image / linear dimension of original)^3

4 = (linear dimension of image / linear dimension of original)^3

Taking the cube root of both sides, we get:

(cube root of 4) = (linear dimension of image / linear dimension of original)

Simplifying, we have:

2 = (linear dimension of image / linear dimension of original)

Therefore, the linear dimensions of the image are two times greater than those of the original. Thus, the scale factor is 2.

The z-score for an IQ score of 122 is 2.

This is calculated by subtracting the mean (100) from the score (122) and dividing by the standard deviation (15). So, 122-100=22, 22/15=2.

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Answer:0.6

Step-by-step explanation: because i got it correct

Jabu's Monthly salary is of R27500.00, with an increase of R1 746.25 per month. Jabu's monthly increase is R1 746.25. The correct answer is option 3.

To find Jabu's previous monthly salary, we can use the formula:

Previous monthly salary = (Annual salary / 12)

Since Jabu's new annual salary is R330 000, his previous annual salary would be:

Previous annual salary = (New annual salary / 1.0635) = (R330 000 / 1.0635) = R310 020.10

Therefore, Jabu's previous monthly salary would be:

Previous monthly salary = (Previous annual salary / 12) = (R310 020.10 / 12) = R25 835.01

To find the monthly increase, we can subtract Jabu's previous monthly salary from his new monthly salary:

Monthly increase = (New monthly salary - Previous monthly salary) = (R27 618.38 - R25 835.01) = R1 783.37

Therefore, Jabu's monthly increase is R1 746.25 (rounded to the nearest cent).

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The area of the circle with circumference 19cm is 6.42cm²( nearest hundredth).

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2. Where r is the radius.

The circumference of a circle is given as ;

C = 2πr

C = 9cm

therefore, 9 = 2× 3.14 × r

9 = 6.28r

r = 9/6.28

r = 1.43 cm

Area of circle = πr²

= 3.14 × 1.43²

= 6.42cm²( nearest hundredth)

therefore the area of the circle is 6.42cm²

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Explanation:

Most people with a mental illness in the United States receive care at some point in their lives, but most receive insufficient or inappropriate care. In any given year, fewer than one-third of people with a diagnosable mental illness obtain treatment.

However, according to a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame.

According to the National Survey on Drug Use and Health (NSDUH), about one in five adults (18.5%) had a mental illness in 2019. It is said that roughly 22.3 million people aged 18 and above received care for a mental health condition in the preceding year.

Treatment may involve medication, therapy, support groups, or a combination of these methods. The majority of people with mental illness may significantly benefit from these treatments.

As per a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame. This statement is true.

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Required value of the given expression is (1+√2)

Given expression is [tex]tan \frac{11\pi}{8} [/tex]

We want to solve it.

Now,

[tex] \tan( \frac{11\pi}{8} ) = \tan( \frac{3\pi}{8} + \frac{8\pi}{8} ) \\ = \tan( \frac{3\pi}{8} + \pi ) \\ = \tan( \frac{3\pi}{8} ) [/tex]

Finding [tex] \tan( \frac{3\pi}{4} ) [/tex]

Let,

[tex] \tan(2t) = \tan( \frac{3\pi}{4} ) = - 1[/tex]

Use half angle identity,

[tex] \tan(2t) = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ - 1 = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ {tan}^{2} t - 2tant - 1 = 0[/tex]

Let,[tex]x = tant[/tex]

So,[tex] {x}^{2} - 2x - 1 = 0[/tex]

Now, [tex]x = 1 \pm \sqrt{2} [/tex]

So,

[tex]tant = tan \frac{3\pi}{8} = 1 \pm \sqrt{2} [/tex]

[tex]tan \frac{3\pi}{8} [/tex] is positive,then required value is 1+√2.

So, option D is the correct answer.

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The formula for percent from the board can be expressed this way:

The total number of students that like pineapple pizza   * 100.

      The total number of students

A (i). The part is the number of students that like pineapple pizza which is 5.

(ii). The whole is the total number of students namely; 7 + 12+ 5 + 3 + 6 = 33.

(iii). Plugging the part and whole into the equation, we will have: 5/33 * 100

(iv). Final answer is = 15.15%

A percentage is a mathematical expression that is aimed at calculating the proportion of a given quantity out of 100. In the question, we are requested to find what proportion of students like pineapple pizza.

To get the answer, we first have to determine the number of students that like pineapple pizza which is 5 according to the table. Next, we get the sum of students which is 33. The percentage will then get the fraction and multiply the result by 100. The final answer is 15.15%.

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The probability of drawing at least one spade when drawing two cards with replacement from a standard deck of cards is approximately 0.26%.

When drawing two cards at random with replacement from a standard 52-card deck, there are 4 possible outcomes for the first card being a spade and 4 possible outcomes for the second card being a spade.

However, there is also 1 possible outcome where both cards are spades, which would be counted twice if we add the outcomes for the first and second cards separately. Therefore, the total number of outcomes where at least one card is a spade is 4 + 4 - 1 = 7.

The total number of possible outcomes when drawing two cards with replacement is 52 x 52 = 2,704.

Therefore, the probability that at least one card is a spade when drawing two cards with replacement is:

P(at least one spade) = 7 / 2,704 ≈ 0.0026

So, the probability that at least one card is a spade is approximately 0.0026 or 0.26%.

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A large bag contains marbles of different colors. there are 10 red marbles, 5 blue marbles and 7 yellow marbles. when selecting 3 marbles without replacement, the probability of selecting 3 red marbles is 1/54.

The probability of selecting 3 red marbles is 1/54.What is a probability?

Probability refers to the likelihood or chance of an occurrence. The probability of an event occurring is the ratio of the number of favourable outcomes to the total number of possible outcomes.

A fraction or a decimal is used to express it.The total number of marbles in the bag is 10 + 5 + 7 = 22 marbles.

There are ten red marbles in the large bag, so the number of ways to select 3 red marbles from ten red marbles is:

[tex]10C_3 = (10 \times 9 \times 8) / (3 \times 2 \times 1) = 120[/tex]

There are 22 marbles in the bag, therefore, the total number of ways to pick 3 marbles from 22 is:

[tex]22C_3 = (22 \times 21 \times 20) / (3 \times 2 \times 1) = 1540[/tex]

Hence, the probability of choosing 3 red marbles out of the 22 marbles in the bag without replacement is:120/1540 = 1/54

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Player A's weight was 0.208 standard deviations below the mean weight of the football team.

To calculate the standard deviation, we first need to calculate the mean weight of the football team

Mean weight = (sum of all weights) / (number of team members)

(174+176+178+184+185+185+185+185+188+190+200+202+205+206+210+211+211+212+212+215+215+220+223+228+230+232+241+241+242+245+247+250+250+259+260+260+265+265+270+272+273+275+276+278+280+280+285+285+286+290+290+295+302) / 52

= 225.5 pounds

Now we can calculate the standard deviation using the following formula:

Standard deviation = sqrt((sum of (x - mean)^2) / N)

Where x is the weight of a team member, N is the total number of team members.

We can simplify this formula by calculating the variance first:

Variance = (sum of (x - mean)^2) / N

So we have

Variance = ((174-225.5)^2 + (176-225.5)^2 + ... + (302-225.5)^2) / 52

= 10764.35

Now we can calculate the standard deviation

Standard deviation = sqrt(Variance)

= sqrt(10764.35)

= 103.76

To find out how many standard deviations above or below the mean Player A's weight was, we can use the following formula

Z-score = (x - mean) / standard deviation

Where x is Player A's weight, mean is the mean weight of the team, and standard deviation is the standard deviation we just calculated.

So we have

Z-score = (204 - 225.5) / 103.76

= -0.208

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The given question is incomplete, the complete question is:

Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.

174, 176, 178, 184, 185, 185, 185, 185, 188, 190, 200, 202, 205, 206, 210, 211, 211, 212, 212, 215, 215, 220, 223, 228, 230, 232, 241, 241, 242, 245, 247, 250, 250, 259, 260, 260, 265, 265, 270, 272, 273, 275, 276, 278, 280, 280, 285, 285, 286, 290, 290, 295, 302

median = 241

the first quartile = 205.5

the third quartile = 272.5

Assume the population was Football Team A. When Player A played football, he weighed 204pounds. How many standard deviations above or below the mean was he?

A = 40,000(1 + 0.07)^3

A = 40,000(1.07)^3

A = 47,676.08

Therefore, the population of the town in 3 years will be approximately 47,676.

Diego can make 56 bags with each bag containing 8 brownies and 12 cookies.

To package both items, he can divide the items into groups of 8 brownies and 12 cookies. He will then make 56 of these groups, ensuring each bag contains 8 brownies and 12 cookies.

Diego has 48 brownies and 64 cookies to package. To make the same combination of items in each bag, he needs to group the items into groups of 8 brownies and 12 cookies.

This can be done by dividing the 48 brownies into 6 groups of 8, and the 64 cookies into 5 groups of 12. He then needs to combine these two groups together, making 56 total bags.

Each of these bags will contain 8 brownies and 12 cookies. This is one way of packaging both items so that each bag has the same combination.

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The fourth equation which is tan x = [tex]\frac{7000}{5000}[/tex] is the correct way to calculate x. This has been obtained by using trigonometry.

What is trigonometry?

Trigonometry is the study of right-angled triangles, which includes the sides, angles, and connections of each triangle.

We are given that the airplane is 5,000 ft above ground and has to land on a runway that is 7,000 ft away with an angle x.

Since, we are not given the hypotenuse so, we will use tan θ.

We know that in trigonometry, tan θ is calculated as the ratio of the opposite side to the adjacent side.

So,

tan x = [tex]\frac{7000}{5000}[/tex]

Hence, the fourth equation is the correct answer.

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The complete question has been attached below

Since the sequence is always decreasing and cannot go below the lower bound, it becomes increasingly closer to the lower bound, and thus converges to a limit.

A sequence is said to be decreasing if each term is smaller than the previous one, and bounded below if there exists a lower bound such that no term in the sequence is smaller than this bound. In this case, the sequence is decreasing and bounded below by 0.

When a sequence is both decreasing and bounded below, it must have a limit because the terms cannot continue to decrease indefinitely, as they cannot go below the lower bound (in this case, 0). This means that as we progress through the terms of the sequence, the difference between consecutive terms will decrease and eventually approach a constant value.

The limit of a sequence is a value that the terms of the sequence approach as they get closer and closer to the end. In this situation, the limit is the smallest possible value that the sequence can approach, without going below the lower bound.

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Answer:

Part A is 8/13 of the whole

Part B is 5/13 of the whole

Step-by-step explanation:

Assuming there are no other parts,

the Whole = A + B is the denominator:

Whole = 40 + 25 = 65

Part A = 40 and Part B = 25 are numerators for each fraction.

The fractions are then:

40/65 and 25/65

Meaning:

Part A is 40/65 of the whole

Part B is 25/65 of the whole

Reducing the fractions, it is also true that:

Part A = 8/13 of the whole

Part B = 5/13 of the whole

Answer:

53°

Step-by-step explanation:

it’s vertical, verticals are always identical, I think  

a)the ratio of the heights of the pyramids is 5:3. b)the volume of the larger pyramid is 23.04 cm³.

what is volume  ?

Volume is a measure of the amount of space that a three-dimensional object occupies. It is usually measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be calculated using different formulas depending on its shape.

In the given question,

a. Let the height of the smaller pyramid be h₁ and the height of the larger pyramid be h₂. Since the two pyramids are similar, their corresponding linear dimensions are in the same ratio as the areas of their bases. Therefore, we have:

(base area of smaller pyramid)/(base area of larger pyramid) = (linear dimension of smaller pyramid)² / (linear dimension of larger pyramid)²

Since the linear dimension is the height in this case, we can substitute the given ratio of the base areas to obtain:

25/9 = (h₁/h₂)²

Taking the square root of both sides, we get:

h₁/h₂ = 5/3

Therefore, the ratio of the heights of the pyramids is 5:3.

b. Since the volume of a pyramid is proportional to the cube of its height, we have:

(volume of smaller pyramid) / (volume of larger pyramid) = (h₁/h₂)³ = (5/3)³ = 125/27

Substituting the given volume of the smaller pyramid, we get:

108 / (volume of larger pyramid) = 125/27

Solving for the volume of the larger pyramid, we obtain:

volume of larger pyramid = (27/125) * 108 = 23.04 cm³ (rounded to two decimal places)

Therefore, the volume of the larger pyramid is 23.04 cm³.

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Answer:18

Step-by-step explanation:

Volume prism is equal to product of width, length and height of prism which is in this case:

[tex]V=4*2*2\frac{1}{4}=8*\frac{9}{4}=18[/tex]

Tyee can afford to rent the car for at most 2 days while staying within his budget.

Let x be the number of days Tyee can rent the car within his budget.

The total cost of renting the car will be the sum of the daily rental fee and the cost of miles driven:

Total cost = rental fee + (cost per mile x miles driven)

Using the given information, we can write the inequality:

74.90x + 0.13(175)x ≤ 210

Simplifying the expression, we get:

74.90x + 22.75x ≤ 210

97.65x ≤ 210

x ≤ 2.15

Therefore, Tyee can afford to rent the car for at most 2 days while staying within his budget.

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Mr. Fransico had average overtime in a day is 2.1 hours.

In mathematics, the central value of a set of data is expressed as the average of a list of data. It is defined mathematically as the ratio of the total number of data points to the number of units in the list. In terms of statistics, the term "mean" also refers to the average of a certain set of numerical data. The average of 2, 3, and 4 is, for instance, (2+3+4)/3 = 9/3 = 3. The center value of 2, 3, and 4 in this instance is 3, thus. Finding the mean value of a bunch of numbers is the definition of average.

For 5 days Mr fransico had a total of 10. 5 hours of overtime in the office

Then the average daily overtime is-

10.5÷5 = 2.1 hours

Hence Mr. Fransico had total overtime in a day is 2.1 hours.

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The expected adult height for a toddler who is 34 inches tall at the 30-month checkup is around 5 feet 7 inches.

To determine the expected adult height, one must multiply the current height by 1.08. Since 34 inches x 1.08 is equal to 36.72 inches, the expected adult height is 5 feet 7 inches.

The calculation for adult height is an approximation. Factors such as nutrition, genetics, and gender play a role in final height.

It is important to note that this calculation is just a guide and the actual adult height may differ from the predicted adult height.

To get a more accurate estimation of the expected adult height, it is recommended to have multiple height checks throughout childhood and take into account growth patterns.

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The number of  pounds that he will have left over from 11 3/7 pounds is  4 2/7

To find out how many bags of granola Alex can fill, we need to divide the total amount of granola he made by the amount of granola in each bag.

We can convert 11 3/7 pounds to an improper fraction:

11 3/7 pounds  = 80/7 pounds

Also, we have

2 2/3 pounds  = 8/3 pounds

Now we can divide the total amount of granola by the amount in each bag:

(80/7) ÷ (8/3)

To divide fractions, we invert the second fraction (change it to its reciprocal) and multiply:

(80/7) × (3/8)

Simplifying, we get:

(80 x 3) / (7 x 8) = 30/7

Divide

(80 x 3) / (7 x 8) = 4 2/7

Hence, the bags is 4 2/7

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Rounded to three decimal places, the probability that the sample mean is between $155 and $160 is 0.072.

To find the probability that the sample mean is between $155 and $160, we will use the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample mean (with a large enough sample size) will be approximately normally distributed with the same mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Mean of the sample distribution: μ = $150
Standard deviation of the sample distribution: [tex]σ/√n = $25/√52 ≈ $3.46[/tex]
Now, we'll calculate the z-scores for $155 and $160:
[tex]Z1 = (155 - 150) / 3.46 ≈ 1.445[/tex]
[tex]Z2 = (160 - 150) / 3.46 ≈ 2.890[/tex]
Using a z-table or calculator, we can find the probability for each z-score:
[tex]P(Z1) ≈ 0.9259[/tex]
[tex]P(Z2) ≈ 0.9981[/tex]
Now, we can find the probability between the two z-scores:
[tex]P(1.445 < Z < 2.890) = P(Z2) - P(Z1) = 0.9981 - 0.9259 = 0.0722[/tex]

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Answer:

48 square centimeters

Step-by-step explanation:

[tex] \frac{1}{2} (4)(8)(3) = 48[/tex]

15 is area of Side of Square .

What is a square, exactly?

All four of the sides and all four of the angles make up the regular quadrilateral known as the square. The square's angles are 90 degrees away from each other or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle.

Length of diagonal of Square =15√2 cm-------------(1)

Let side of Square = a cm

So, Length of Diagonal

By Using Pythagorean Theorem

       = √a² + a²

        =  a√2        ........................(2)

  Equating (1) and (2)

    a√2   =  15√2

      a = 15

 cancelling root 2 from both sides.

     a = 15

Side of Square= 15 cm

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The complete question is -

Find the side of a square whose diagonal is of the given measure. Given = 15√2 cm.

Answer:

45.6%

Step-by-step explanation:

166.50 minus 45.6% equals 90 dollars

Answer: yes, yes, no

Explanation: In order for a figure to be a triangle, the two smallest sides must add up to be larger than the biggest side. The reason why the last one isn't a triangle is because 6+8 EQUALS 14 and is not greater than 14.