Lattice has £15000 in a savings account at the start of the year. How much will she have at the end of the year if the annual interest rate is 7.5%?

Answer:

50 cm

Step-by-step explanation:

So the first step is to find the height, and to do that you know that the area of a triangle is height * base / 2 =  area. Plugging in the numbers you have, you get:

\(height*48/2=336\)

Then, this becomes

\(height * 24 = 336\)

Divide both sides by 24

\(height = 14\)

Now you can use the base and the height to find the hypotenuse using the Pythagorean Theorem: \(a^{2} +b^{2} =c^{2}\)

\(48^{2} +14^{2} =c^{2} \\2304 + 196 = c^{2}\\2500 = c^2\\50 = c\\c = 50\)

Therefore the length of the hypotenuse is 50 cm

The probability that exactly 10 students attend class in a class of 12, with a 0.84 attendance probability, is approximately 0.4031. This scenario satisfies all the conditions of a binomial distribution.


To calculate the probability that exactly 10 students attend class, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1 – p)^(n – k)
Where:
- P(X = k) is the probability that exactly k students attend class,
- n is the total number of students (12),
- k is the number of students attending class (10), and
- p is the probability of a student attending class (0.84).
Plugging in the values, we get:
P(X = 10) = (12 choose 10) * (0.84)^10 * (1 – 0.84)^(12 – 10)
Calculating this expression:
P(X = 10) = (12!)/(10! * (12-10)!) * (0.84)^10 * (0.16)^2
P(X = 10) = 66 * 0.2346520344 * 0.0256
P(X = 10) ≈ 0.4031
Therefore, the probability that exactly 10 students attend class is approximately 0.4031.

Now, to determine if this scenario satisfies all the conditions of a binomial distribution, we need to check the following conditions:
1. There are a fixed number of trials: Yes, there are 12 students, and each one can either attend or not attend class.
2. Each trial is independent: Yes, the attendance of one student does not affect the attendance of another.
3. The probability of success (p) is constant: Yes, the probability of any student attending class is 0.84.
4. The trials are mutually exclusive: Yes, a student can either attend or not attend class.
Therefore, this scenario satisfies all the conditions of a binomial distribution.

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The statement "Relationships between two categorical variables are less evident when the data is expressed in counts rather than percentages" is false. Categorical variables are those that divide a population into groups. These groups can be classified into one of two categories: nominal or ordinal. The nominal category does not have an intrinsic order, whereas the ordinal category does.

Categorical data is a data type that is collected from observations that are grouped into categories with numerical figures. These variables are frequently defined in nominal terms. The data is expressed in percentages or proportions in a categorical data table instead of counts. When analyzing categorical data, it is best to use percentages, as these provide a better picture of the underlying relationship.

Therefore, relationships between two categorical variables are more evident when data is expressed in percentages rather than counts. When percentages are utilized, it is more straightforward to understand the relationship between two categorical variables. An example of categorical data is the top 150 movies of all time.

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Answer: 350

Step-by-step explanation:

242.50+20=262.5

262.5/3=87.5

87.5+262.5=350

To ensure the survey results are reliable and representative of the district's high schools, Zander needs to consider the following factors:

Sample Size: Zander should determine an appropriate sample size that is large enough to provide statistically significant results. A larger sample size generally increases the reliability and accuracy of the findings.

Random Sampling: Zander should employ a random sampling method to ensure that every high school in the district has an equal chance of being included in the survey. This helps avoid bias and ensures a representative sample.

Survey Design: Zander should carefully design the survey questionnaire, including specific questions related to various sporting events. The questions should be clear, unbiased, and relevant to gather accurate information about participants' preferences.

Data Collection: Zander can choose to collect data through online surveys, paper-based questionnaires, or interviews. He should ensure that the data collection process is standardized and consistent across all participants.

Data Analysis: Once the survey responses are collected, Zander should analyze the data using appropriate statistical methods. He can calculate the frequency or percentage of participants who prefer each sporting event to identify the most popular one.

To find out the most popular sporting event in the district's high schools, Zander conducts a survey on a sample of the population. Conducting a survey allows him to gather data directly from the participants and obtain insights into their preferences.

By conducting a well-designed survey and analyzing the data appropriately, Zander can obtain valuable insights into the most popular sporting event in the district's high schools. These insights can help guide future decisions and investments in sports programs or events.

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\(f(-2) = -4\) for the given piecewise function by using the equation \(f(x) = x - 2\)  if   \(x < 3.\)

A piecewise function is a mathematical function that is defined differently on different parts of its domain.

Instead of having a single formula that applies to the entire domain, a piecewise function has multiple formulas, each applying to a specific interval or subset of the domain.

To find f(-2) for the given piecewise function, we need to determine which piece applies to the input value o  \(f -2\), which is less than 3. Therefore, we use the first piece of the function, which is\(f(x) = x - 2 if x < 3.\)

Substituting x = -2 into this piece, we get:

\(f(-2) = (-2) - 2 = -4\)

Therefore, f(-2) = -4 for the given piecewise function.

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Answer:

6

Step-by-step explanation:

In a right triangle the legs are base and height

area = (1/2) base × height = (1/2) 3 (4) = 6

Answer: 6  square units

The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

Answer:

The price of the desk in the furniture store is $202.8

From the geometric series given, the first term is 21/65 and the common ratio is 4/3

Let's denote the first term of the geometric series as 'a' and the common ratio as 'r'. The sum of a geometric series can be calculated using the formula:

S = a / (1 - r)

Given that the sum of the entire series is 7, we can write the equation as:

7 = a / (1 - r)...eq(i)

Now, let's consider the terms involving odd powers of 'r'. These terms can be written as:

a + ar² + ar⁴ + ...

This is a new geometric series with the first term 'a' and the common ratio r₂. The sum of this series can be calculated using the formula:

S(odd) = a / (1 - r²)

Given that the sum of the terms involving odd powers of 'r' is 3, we can write the equation as:

3 = a / (1 - r³)   eq(ii)

To find the values of 'a' and 'r', we can solve equations (1) and (2) simultaneously.

Dividing equation (1) by equation (2), we get:

7 / 3 = (a / (1 - r)) / (a / (1 - r²))

7 / 3 = (1 - r²) / (1 - r)

Cross-multiplying and simplifying, we have:

7(1 - r) = 3(1 - r²)

7 - 7r = 3 - 3r²

Rearranging the equation, we get a quadratic equation:

3r² - 7r + 4 = 0

This equation can be factored as:

(3r - 4)(r - 1) = 0

Setting each factor equal to zero, we have:

3r - 4 = 0   or   r - 1 = 0

Solving these equations, we find two possible values for 'r':

r = 4/3   or   r = 1

Now, substituting these values back into equation (1) or (2), we can find the corresponding value of 'a'.

For r = 4/3:

From equation (1):

7 = a / (1 - 4/3)

7 = a / (1/3)

a = 7/3

From equation (2):

3 = (7/3) / (1 - (4/3)^2)

3 = (7/3) / (1 - 16/9)

3 = (7/3) / (9 - 16/9)

3 = (7/3) / (65/9)

3 = (7/3) * (9/65)

a = 21/65

For r = 1:

From equation (1):

7 = a / (1 - 1)

Since 1 - 1 = 0, the equation is undefined.

Therefore, the values of 'a' and 'r' that satisfy the given conditions are:

a = 21/65

r = 4/3

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Answer:

Step-by-step explanation:

NOSEEEEEE

Answer:

x = 7.5

Step-by-step explanation:

We see that in order to find x, we need to use tangent, which is opposite over adjacent.

Step 1: Set up equation

tan37° = x/10

Step 2: Multiply 10 on both sides

10tan37° = x

Step 3: Evaluate

x = 7.53554

Step 4: Round

x = 7.5

Answer:

137

Step-by-step explanation:

the way to get it is that part that looks like a square inside the triangle is 90 so when you finish getting all the sides the answer will give you 137

The probability that a 65-year-old man will survive to reach the age of 70 is 88.4%, and also the probability man to survive till his 75th birthday is approx.59.952%.

The probability of a 65-year-old man reaching the age of 70 is the probability of surviving from age 65 to age 70, which is given as

p(70)/p(65) ⇒ 0.657/0.742 ≈ 0.88544 or 88.544%.

The probability of a man who just turned 70 dying within the next 5 years is 0.176.

Therefore, the probability of surviving for the next 5 years after turning 70 is

⇒ 1 - 0.176 ⇒ 0.824.

Thus, the probability of a man surviving till his 75th birthday is the probability of surviving from age 70 to age 75, which is given as

p(75)/p(70) ⇒ 0.657/0.903 × 0.824

≈ 0.59952 or 59.952%.

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The approximate values of the non-integral roots of the polynomial equation are -5.57, -1.95, 0.21, 1.27, and 4.73. These values represent the values at which the polynomial equation evaluates to zero, indicating the roots of the equation.

To find the roots of a polynomial equation, we set the equation equal to zero and solve for the unknown variable. In this case, we have a polynomial equation with non-integral roots.

To obtain the approximate values of these roots, numerical methods such as iterative methods or numerical approximation techniques can be used. These methods involve making educated guesses and refining the guesses until the equation evaluates to zero.

The resulting approximate values for the non-integral roots of the polynomial equation are -5.57, -1.95, 0.21, 1.27, and 4.73. These values are not exact, but they are close approximations to the actual roots of the equation.

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Answer:

56

Step-by-step explanation:

...

The solution is Option A.

The inequality equation is A ≤ 6 where A is the number of DVDs Martin can buy

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the total number of DVDs Martin can buy be = A

Now , the equation will be

The price of 1 DVD is = $ 8.50

The price for shipping and handling = $ 5.00

Now , the total amount Martin decides to spend = not more than $ 56

So , the inequality equation will be

8.50A + 5 ≤ 56

On simplifying the equation and solving for A , we get

Subtracting 5 on both sides of the equation , we get

8.50 A ≤ 51

Divide by 8.50 on both sides of the equation , we get

A ≤ 51 / 8.5

A ≤ 6 DVDs

So , the value of A should be less than or equal to 6

Hence , the inequality equation is A ≤ 6 where A is the number of DVDs Martin can buy

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Given:

The mean number of emails adele received during a week was 51.

The numbers received for the six days were 39, 57, 70, 45, 71, 32.

To find:

The number of emails received on the seventh day.

Solution:

Let x be the number of emails received on the seventh day.

We know that,

\(\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}\)

\(51=\dfrac{314+x}{7}\)

Multiply both sides by 7.

\(357=314+x\)

Subtract 314 from both sides.

\(357-314=x\)

\(43=x\)

Therefore, she received 43 emails on the seventh day.

Answer:

An apportionment is the allocation of a loss between all of the insurance companies that insure a piece of property. This allocation is used to determine a percentage of liability for each insurer.

I'm new here! Sorry if this didn't help

The differential equation that models this situation is dx/dt = kx(M - x) (option c).

To determine the differential equation that models the situation, let's analyze the problem statement.

The rate at which a person can memorize a list of M words is proportional to the product of the number of words memorized and the number of words that have not been memorized.

Let's denote the number of words memorized as "a" and the number of words not yet memorized as "M - a" (where M is the total number of words in the list).

The problem states that the rate of memorization is proportional to the product of "a" and "M - a". We can express this mathematically as:

Rate of memorization ∝ a * (M - a)

To convert this proportionality into an equation, we introduce a positive constant k:

Rate of memorization = k * a * (M - a)

The left side of the equation represents the rate of change of the number of words memorized (da/dt), and the right side represents the product of "a" and "M - a" multiplied by the constant k.

Therefore, the differential equation that models this situation is:

da/dt = k * a * (M - a)

Comparing this with the given options, we can see that the correct choice is option C:

dx/dt = k * x * (M - x)

The complete question is:

At any time t > 0 the rate at which a person can memorize a list of M words is proportional to the product of the number of words memorized and the number of words that have not been memorized. If a denotes the number of words memorized at time t, which differential equation models this situation? Assume k is a positive constant.

A. dx/dt = kx

B. dx/dt = kx(x - M)

C. dx/dt = kx(M - x)

D. dx/dt = kt(M - t)

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Answer: 1/4

Step-by-step explanation:

He needs 4 3/4 whole tiles, you could round it to 5 whole tiles. He needed 4 3/4 whole tiles. To completely fill in all the spaces on the wall evenly, it needs to be 5 even, while, tiles. To fill in the empty space, you must subtract 5 and 4 3/4, which explains why Part A says “How many whole tiles does he need” and the answer “4 3/4” So, Subtraction: 5- 4 3/4 = 1/4!

Your welcome :)

Ken must install 3/4 fraction of tile at the end of the row to totally fill the space.

Given that,
Ken wants to install a row of ceramic tiles on a wall that is 21 3/8 inches wide. Each tile is 4 1/2 inches wide. What fraction of a tile must he install at the end of the row to totally fill the space is to be determined.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Total length of the wall = 21 3 / 8 = 21 . 375
Width of tile = 4 1/2 = 4.5
Now, the ratio of wall to tile = 21. 375 / 4.5
quotient = 18 Remainder = 3.375
Now the ratio of the remainder to the tile = 3.375 / 4.5 = 0.75 or  3 / 4.

Thus, Ken must install 3/4 fraction of tile at the end of the row to totally fill the space.

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The probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles is approximately 0.123

This problem involves the sample mean of a set of data, and we can use the central limit theorem to approximate the distribution of sample means, even if the original distribution is not normal.

Let X be the number of miles driven by a single driver in a year. We know that the population mean µ = 12,000 miles and the population standard deviation σ = 2,580 miles. We also know that the sample size n = 36.

The sample mean X is an estimator of the population mean µ. The distribution of sample means is approximately normal with a mean of µ and a standard deviation of σ/√n, according to the central limit theorem

So, the distribution of sample means can be expressed as

X ~ N(µ, σ/√n)

Substituting the given values, we get

X ~ N(12,000, 2,580/√36) = N(12,000, 430)

Now we need to find the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles. This is equivalent to finding the probability that the sample mean is greater than 12,500

P(X > 12,500) = P(Z > (12,500 - 12,000) / 430)

where Z is a standard normal random variable.

P(Z > 1.16) = 1 - P(Z < 1.16) = 1 - 0.877 = 0.123

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The given question is incomplete, the complete question is:

People drive an average of 12,000 miles per year with a standard deviation of 2,580 miles per year. what is the probability that a randomly selected sample of 36 drivers will drive, on average, more than 12,500 miles?

The statements for the function f( x) = 3x ²- 5 are

f( 5)< 1( false)

f( 0) = 1( false)

Statements for the function f(x) = 3x ²- 5

To find the true or false statement we have to substitute the value for x

First, x= 3

f(x) = 3x ²- 5

f(3)= 3( 5)²- 5

f(3) = 75- 5

f(3)= 70.

Thus, the statement" f( 5)< 1" is false.

Now, at x =0

f(x) = 3x ²- 5

f(0) = 3( 0)²- 5

f(0)= 0- 5

f(0)= -5.

Thus, the statement" f( 0) = 1" is false.

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Answer:

300 m

Step-by-step explanation:

Multiply 0.3 by 1,000. It gives you your answer of 300 m.

Answer:

16 sides

157.5⁰

Step-by-step explanation:

.......

Answer:

B,because it says he wants to have

To sketch the region enclosed by the curves y = sin(x) and y = 5x, we plot the curves and find the bounds of the region. We integrate with respect to x to find the area of the region.

To sketch the region enclosed by the given curves, we first plot the curves y = sin(x) and y = 5x on a coordinate plane.

The curves intersect at two points: (0,0) and (π/6,π/3). The x-coordinates of the bounds of the region are x = 0 and x = π/6. The y-coordinate of the lower bound of the region is y = 0, and the upper bound of the region is y = 5x.

Since the region is bounded by the curves y = sin(x) and y = 5x, we can integrate with respect to x or y. However, since the region is easier to describe in terms of x, we will integrate with respect to x.

A typical approximating rectangle for the region is shown below:

To set up the integral for finding the area of the region, we need to determine the limits of integration. We integrate from x = 0 to x = π/6, and the integrand is given by the difference between the upper and lower bounds of the region:

Area = ∫₀^π/6 (5x - sin(x)) dx

We can evaluate this integral using integration techniques such as integration by parts or numerical methods such as Simpson's rule.

Overall, the region enclosed by the given curves is a triangular region, and we can integrate with respect to x to find its area.

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Answer:

4.8 years

Step-by-step explanation:

10 800 = 8000 e^(i t)        i = decimal interest per year     t = years

10800/8000 = e^(.0625 t)      ln both sides

.300 = .0625 t

t = 4.8 years