Kate stands 2 meters from a lamppost. She is 2.1 meters tall and casts a shadow 3 meters long in the light from the lamp. How tall is the lamppost? See diagram below.​

Kim and Sarah Carson applied for a $120,000 mortgage loan at an 8.25% annual interest rate, total amount paid is approximately $329,698.80.

We can apply the formula for the monthly payment on a fixed-rate mortgage to determine the amount of the monthly payment, the total amount paid, and the total interest charged for a $120,000 mortgage loan at an annual interest rate of 8.25% over 30 years.

We know that, for monthly payment:

\(M = P * r * (1 + r)^n / ((1 + r)^{(n - 1)})\\\\\)

P = $120,000

r = 8.25% / 100 / 12 = 0.006875

n = 30 * 12 = 360

M = \(120,000 * 0.006875 * (1 + 0.006875)^{360} / ((1 + 0.006875)^{360 - 1})\)

The monthly payment M is approximately $915.83.

Amount Paid = Monthly Payment * Total Number of Payments

Amount Paid = $915.83 * 360

The total amount paid is approximately $329,698.80.

Total Interest Charged = Amount Paid - Loan Amount

Total Interest Charged = $329,698.80 - $120,000

The total interest charged is approximately $209,698.80.

Thus, the answer is $915.83, $329,698.80, and $209,698.80 respectively.

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Answer:

12 photos fit on page = 1

432 photos fit on page = 432/12

= 36 pages

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

36 pages

Step-by-step explanation:

There are 12 photos per page, and Robert has 432 photos. So, we can divide the number of photos he has by the number of photos that fits on each page. By doing so, you'll calculate the number of pages he needs. This calculation is shown below:

\(\frac{432 \ photos}{1} *\frac{1 \ page}{12 \ photos} = 36 \ pages\)

You can see that the units for photos cancel out, resulting in units for pages.

So, Robert will need 36 pages in order to fit all 432 photos into his photo album.

The monopolist's marginal revenue from selling the 11th sweatshirt is $25.Marginal revenue is the change in total revenue that results from selling an additional unit of a product

In this case, the monopolist initially sells ten sweatshirts at a price of $40, resulting in a total revenue of 10 x $40 = $400.

To sell the 11th sweatshirt, the firm must lower the price to $35. This means that the revenue from selling the 11th sweatshirt is $35. However, it's important to note that reducing the price for the 11th sweatshirt affects the price and quantity demanded for all previous units as well. So, the marginal revenue from selling the 11th sweatshirt is not simply $35.

To determine the marginal revenue, we need to compare the total revenue before and after selling the 11th sweatshirt. Before selling the 11th sweatshirt, the total revenue was $400. After selling the 11th sweatshirt, the total revenue becomes 11 x $35 = $385. The change in total revenue is $385 - $400 = -$15.

Therefore, the marginal revenue from selling the 11th sweatshirt is -$15, indicating that the revenue decreased by $15 when the 11th sweatshirt was sold. However, since marginal revenue is typically defined as a positive value, we take the absolute value, which is $15, to represent the marginal revenue from selling the 11th sweatshirt.

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Answer:

option C

Step-by-step explanation:

2, 4, 6

i don't know whether it is correct or not...

To find the radius of the crystal ball, we can use the formula for the volume of a sphere: V = (4/3) * π * r^3, where V is the volume and r is the radius.

Given that the volume of the crystal ball is 113.14 cm³, we can solve for r:

113.14 = (4/3) * π * r^3

To find the radius, we can rearrange the equation:

r^3 = (3/4) * (113.14 / π)

r = (3/4) * (113.14 / π)^(1/3)

Using a calculator, we can evaluate the expression to find the approximate value of the radius.

To find the volume of foam required to fill the vacant space inside the box, we need the volume of the box. However, the dimensions of the box are not provided in the question, so we cannot calculate the volume of foam accurately.

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Approximately 34.1% of students earn a score between 75% and 89%.
the correct answer is 34.1%.

Approximately what percent of students earn a score between 75% and 89%?

To solve this problem, we need to calculate the area under the normal distribution curve between 75% and 89%.
First, we need to convert the scores into z-scores using the formula:
z = (x - mean) / standard deviation

For 75%, the z-score is (75 - 89) / 14 = -1
For 89%, the z-score is (89 - 89) / 14 = 0

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two z-scores.

The area between -1 and 0 is approximately 0.3413, which is equivalent to 34.1%.

Therefore, approximately 34.1% of students earn a score between 75% and 89%.

So the correct answer is 34.1%.

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Answer:

(-2,4] and [7,α)

Step-by-step explanation:

the domain is open at -2 but closed at 4 and also closed at 7 but open till infinity..

The domain of the given function is (-2,4] U [7, ∞), which is the correct option (B).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

f(x) = x²+1 if (-2,0]

This the sub-function define between the interval (-2,0].

f(x) = -1 if (0, 4]

This the sub-function define between the interval (0, 4].

f(x) = -(x-7)² if [7, ∞)

This the sub-function define between the interval [7, ∞).

Thus, the domain of the given function is (-2,4] U [7, ∞).

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Answer:

The class and exam medians are approximately equal

Step-by-step explanation:

Answer:

The class and exam medians are approximately equal.

Step-by-step explanation:

Since the line for the medians is at the same place on the number line, the medians will be the same.

Answer:

B and C

Step-by-step explanation:

Tahnks for the brainlt

The wildflowers in this population, the white allele is present in about 30% of the individuals, while the red allele is present in about 70% of the individuals.

The frequency of the white allele (CW) in the population can be determined by subtracting the frequency of the red allele (CR) from 1, since the frequencies of all alleles in a population must add up to 1.

So, the frequency of the white allele (CW) can be calculated as follows:

CW = 1 - CR

Given that the frequency of the red allele (CR) is p = 0.7, we can substitute this value into the equation:

CW = 1 - 0.7

  = 0.3

Therefore, the frequency of the white allele (CW) in this population is 0.3.

In genetic terms, alleles are alternative forms of a gene, and the frequencies of different alleles within a population can be used to study genetic variations. In this case, we are considering a population of wildflowers and examining the frequencies of the red allele (CR) and white allele (CW).

The total frequency of alleles in a population is always 1 since each individual carries two alleles (one from each parent). Therefore, the frequency of the white allele can be obtained by subtracting the frequency of the red allele (0.7 or 70%) from 1. This is because the sum of the frequencies of all alleles must equal 1.

By performing the calculation, we find that the frequency of the white allele in this population is 0.3 or 30%.

This means that among the wildflowers in this population, the white allele is present in about 30% of the individuals, while the red allele is present in about 70% of the individuals.

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Complete Question

Consider a population of wildflowers in which the frequency of the red allele CR is p = 0.7.

What is the frequency of the white allele (CW ) in this population?

Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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These gym scales are designed to provide users with accurate weight measurements, but various factors can impact their accuracy.

Gym scales are the most commonly used weight measurement instruments in gyms and fitness centers around the world. However, their accuracy is sometimes questioned by gym-goers. These gym scales are designed to provide users with accurate weight measurements, but various factors can impact their accuracy. Gym scales appear to be a measure that is accurate but not precise. These scales are accurate because they provide results that are near to the actual weight of the person being weighed. This can be verified by noting that the scale showed a weight of 180 pounds on each of the four days. If the scale was inaccurate, it would have shown a different weight each time it was used. On the other hand, gym scales are not considered precise because they are not consistent in their readings. If the weight of an individual is 150 pounds, and the scale reads 180 pounds, then it is clear that there is a difference between the actual weight and the scale reading.

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The number with a subscript of 12 or number base 12 that is equal to 888₉ + 555₆ + 222₂ is 689.

Using the number base conversion system,  the sum of the given numbers in base ten is determined as follows:

888₉ + 555₆ + 222₂ = X₁₂

888₉ = 8 * 9² + 8 * 9¹ + 8 * 9⁰

888₉ = 728

555₆ = 5 * 6² + 5 * 6¹+ 5 * 6⁰

555₆ = 215

222₃ = 2 * 3² + 2 * 3¹ + 2 * 3⁰

222₃ = 26

888₉ + 555₆ + 222₂ = 728 + 215 + 26

888₉ + 555₆ + 222₂ = 969

969 = X₁₂

969 = 689₁₂

Hence, X = 689

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The function values are: 1, 3, 5, 7, 9, and 11. The interpretation of these function values means the number of points awarded to the player for rolling each of the possible values on the die.

The appropriate domain for the function is all possible values that can be rolled on a six-sided die.

The function f(x) = 2x - 1 assigns a certain number of points to a player based on the value rolled on a six-sided die. The possible values of x are 1, 2, 3, 4, 5, and 6. When we plug each of these values into the function, we get the following function values:

f(1) = 2 * 1 - 1 = 1

f(2) = 2 * 2 - 1 = 3

f(3) = 2 * 3 - 1 = 5

f(4) = 2 * 4 - 1 = 7

f(5) = 2 * 5 - 1 = 9

f(6) = 2 * 6 - 1 = 11

Therefore, the function values for this function are 1, 3, 5, 7, 9, and 11. These values represent the number of points awarded to the player for rolling each of the possible values on the die.

The appropriate domain for this function is all values of x between 1 and 6, inclusive. This includes all possible values that can be rolled on a six-sided die.

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Answer:

20d+4

Step-by-step explanation:

A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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Setting x1 to zero in the equation 2x1 + 1x2 = 30 results in the value of x2 being 30.

The given equation is 2x1 + 1x2 = 30, where x1 and x2 represent variables. To find the value of x2 when x1 is set to zero, we substitute x1 with zero in the equation.

By replacing x1 with zero, we have 2(0) + 1x2 = 30. Simplifying further, we get 0 + 1x2 = 30, which simplifies to x2 = 30.

When x1 is set to zero, the equation reduces to a simple linear equation of the form 1x2 = 30. Therefore, the value of x2 in this scenario is 30.

Setting x1 to zero effectively eliminates the contribution of x1 in the equation, allowing us to focus solely on the value of x2. In this case, when x1 is removed from the equation, x2 becomes the sole variable responsible for fulfilling the equation's requirement of equaling 30. Thus, x2 is determined to be 30.

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There is a 44.37% chance that none of the suspects will be falsely accused of lying based on the lie detector test.

The process of lie detector with the help of probability :-

Assuming the lie detector test is accurate, the probability of showing a positive reading (indicating a lie) is 0.15, and the probability of showing a negative reading (indicating truth) is 0.85.

If all six suspects are telling the truth, the probability of observing no positive readings in the sample can be calculated as follows:

P(no positive readings) = P(negative reading for suspect 1) * P(negative reading for suspect 2) * P(negative reading for suspect 3) * P(negative reading for suspect 4) * P(negative reading for suspect 5) * P(negative reading for suspect 6)

= 0.85 * 0.85 * 0.85 * 0.85 * 0.85 * 0.85

= 0.4437053125

Therefore, the probability of observing no positive readings if all suspects are telling the truth is approximately 0.4437 or 44.37%.

This means that there is a 44.37% chance that none of the suspects will be falsely accused of lying based on the lie detector test. However, it is important to note that the accuracy of lie detector tests is often questioned, and they are not considered reliable evidence in many legal systems.

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The spoken statement "six metres less than four times the width is 4w -6" has an algebraic equivalent.

An algebraic expression:

An expression that has been created utilizing integer variables, constants, and algebraic operations is known as an algebraic expression. 3x 2 2xy + c is a nice illustration of an algebraic expression.

As per the data given in the above question are as bellow,

Let's say the value is v.

To get: the product of w multiplied by four.

As a consequence, we must multiply w and 4 the result we get 4w.

To get: the subtract 6 meter less than four times the width.

As a consequence, we must subtract 6 meter less than four times the width the result we get 4w -6.

The following is the mathematical expression.

4w-6

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1. How to find f(4)?

2. Substitution and Evaluate

\( \large{f(4) = - {(4)}^{2} - 6(4) + 12} \)

Follow BODMAS/PEMDAS rules as well! Exponent first.

\( \large{ f(4) = - 16 - 24 + 12} \\ \large{f(4) = - 40 + 12} \\ \large{f(4) = -2 8}\)

3. Final Answer

Null space is defined as the set of vectors 'x' in Rn that are solutions to the matrix equation A*x = 0. False: The set of all vectors of the form 1 x y where x and y range over all real numbers is a subspace of R3. True: The set of all vectors of the form 0 x y where x and y range over all real numbers is not a subspace of R3.

1) False Null space can consist of zero vector only. A null space is defined as the set of vectors 'x' in R^n that are solutions to the matrix equation A*x = 0.

2) True The number of columns can never be less than the number of rows of the matrix in order for a null space to exist, hence a 4x3 matrix may have the null space of only the zero vector.

3) True The set of all vectors of the form 1 x y where x and y range over all real numbers, is a subspace of R^3. This set contains zero vector because for x=0 and y=0, we get the vector as [0,0,0]. Hence it is a subspace of R^3.

4) False The set of all vectors of the form 0 x y where x and y range over all real numbers, is not a subspace of R^3 as it doesn't contain zero vector. To have a subspace of R^3, it should contain a zero vector.

So, the correct options are:1) False2) True3) True4) False

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The distance between the ships changing at 92.29 Knots

                              \(d(t) = \sqrt{(18t)^{2} + (40+17t)^{2} } \\\)

The rate of change of distance is -

                              \(\frac{dd}{dt} = \frac{36t + 2(40 + 17t)17}{2\sqrt{18t^{2} + (40 + 17t) } }\)

after putting t = 5 into this rate of change ,

we get, answer = 92.29

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Answer:

Yes, this set of lengths can form a triangle.

Step-by-step explanation:

55+76 = 131

131 > 112

Since the sum of smaller lengths is greater than 112, these numbers can form a triangle.

Answer:

Distance is 10

Step-by-step explanation:

distance between y1=2x-3 and y2= 2x+7

y2 - y1 = (2x +7) - (2x - 3) = 10

Answer:

10

Step-by-step explanation:

.

.

.......... ......

A sculpture formed from a cylinder resting on top of a cuboid is referred to as a composite solid. In geometry, a solid is said to be composite when it is made up of two or more simpler figures.

A cylinder is a three-dimensional shape that consists of two parallel circular bases that are connected by a curved lateral surface. Where as a cuboid is a three-dimensional shape that has six rectangular faces, eight vertices, and twelve edges. So, the cylinder is resting on top of the cuboid. The solid will have three dimensions, length, width, and height. Therefore, the composite solid will have a circular base.

That is the same size as the cylinder and a rectangular base that is the same size as the cuboid. The height of the composite solid will be equal to the height of the cylinder plus the height of the cuboid. In general, the formula to calculate the volume of a composite solid is V = V1 + V2, where V is the total volume of the composite solid, V1 is the volume of the cylinder, and V2 is the volume of the cuboid. In conclusion, we can say that a sculpture formed from a cylinder resting on top of a cuboid is a composite solid.

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Answer:

150

Step-by-step explanation:

I guess you're asking percentage of 3/2 into percentage so I took 3/2 × 100 to change it into percentage form and I got 150 if it's not the answer please tell me right away.

Answer:

i cant see the words

Step-by-step explanation:

It sounds like you may be experiencing a bug with your Alexa device. This is likely due to a software update or miscommunication between the device and the server.

To resolve this issue, you may need to restart your device by unplugging it from the power source and plugging it back in. You can also try clearing the cache of your device. Additionally, you may need to update the software of your device by visiting the Amazon website and downloading the most recent version of the software. If the issue persists, you may need to contact Amazon customer service for further assistance.

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