A sum of money deposited at the rate of 4 1/2% p.a. for 48 month yields Rs. 80,000, calculate the deposited amount.​

If a random variable is normally distributed, and has a mean of 228 and

a standard deviation of 16. If a sample of size 12 is taken, then the shape

of the sampling distribution for the sample mean is normally distributed

since the variable is normally distributed. Hence, option B is correct.

A normal distribution is a type of probability distribution in which the

value of the mean, standard deviation, and random variables are well

known. Sampling distribution refers to the probability distribution of the

statistics that have been derived from a sample taken from a population.

As per the Central Limit Theorem, if the sample size is large enough,

then the sampling distribution of the sample means will be normally

distributed, no matter how the population looks. If the random variable is

normally distributed, then the sampling distribution of the sample mean

will also be normally distributed, no matter what the size of the sample is.

Hence, option B is the correct answer as the sampling distribution of the

sample mean is normally distributed since the variable is normally distributed.

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The characteristic of a reliable scientific poll is small sampling error. The small sampling error is a characteristic of a reliable scientific poll.

What is a scientific poll?Scientific polls are surveys that gather and evaluate people's opinions or responses to questions. These surveys are done in a scientific way, implying that pollsters use scientifically proven techniques to gather responses and analyze data.A reliable scientific poll must have a small sampling error. A sampling error is the deviation of the sample mean from the population mean due to random error. The smaller the sample size, the more likely it is that the results will be imprecise. As a result, it's essential to conduct a reliable scientific poll with a sample size that is representative of the population as a whole.The option for the correct answer to this question is; (choice a) small sampling error.

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If the cost price of the goods is R200 and they are sold at a mark-up of 100%, then the selling price is equal to the cost price plus the mark-up, or:

Selling price = Cost price + Mark-up

Mark-up = 100% x Cost price

= 100% x R200

= R200

So the mark-up is R200.

Selling price = Cost price + Mark-up

= R200 + R200

= R400

Therefore, the selling price of the goods is R400.

The sum of the geometric series is 3904/3125.

By using the formula for the sum of a geometric series, we'll have to identify the first term, the common ratio, and the number of terms.

Let's identify the first term, the common ratio, and the number of terms in the given series as shown below;

The first term, a = 4³/5³

Common ratio, r = 4/5

The number of terms, n = 3

We have identified the values of a, r, and n, we can now substitute them into the formula for the sum of a geometric series, shown below;

S_n = a(1 - rⁿ) / (1 - r)

S₃ = {(4³/5³) [1 - (4/5)³]} / [1 - (4/5)]

S₃ = {(64/125) [1 - (64/125)]} / [1/5]

S₃ = (64/125) [(125-64)/125] [5/1]

S₃ = (64/125) (61/125) (5)

Therefore, S₃ = 3904/3125.

Thus, the sum of the geometric series (4³/5³) + (4⁴/5⁴) + (4⁵/5⁵) is equal to 3904/3125.

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The height that the T-short lands on the bleachers is x = 0.65.

The quadratic equation may be solved by adding and subtracting the same number within the parenthesis to get a perfect square trinomial, which is how the quadratic formula is obtained. A version of the equation that can be solved using the square root function is the result of this method.

Given that it can be used to solve any quadratic equation regardless of the values of the variables a, b, and c, the quadratic formula is an effective tool for solving quadratic equations.

The equation of the path of T-shirt is y = -18x² + 4x and that of the height of bleachers is 3y=2x−14 or y = 2/3x - 14/3

To find the height of the T-shirt landing we find the intersection of the two equations as follows:

-18x² + 4x = (2x - 14)/3

-54x² + 12x = 2x - 14

54x² - 10x - 14 = 0

27x² - 5x - 7 = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Substitute the values;

x = (-(-5) ± √((-5)² - 4(27)(-7))) / 2(27)

x = (5 ± √(925)) / 54

x = (5 ± 5√37) / 54

x = (5 + 5√37) / 54 = 0.65 and

x = (5 - 5√37) / 54 = -0.47

Hence, the height that the T-short lands on the bleachers is x = 0.65.

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The list after sorting in ascending order is C) {3 17 44 69}.

Sorting means arranging the numbers in ascending or descending order based on their value. In this case, the numbers are arranged in ascending order, meaning that the smallest number comes first, followed by the next smallest number and so on.

To sort the list, we can use any sorting algorithm such as selection sort, bubble sort, insertion sort, or quicksort. One simple way to sort the list is to use the built-in sort function provided by most programming languages. The sort function takes the list as input and returns a new list with the elements sorted in ascending order.

In summary, the sorted list in ascending order is {3 17 44 69}, and we can use sorting algorithms or built-in functions to sort a list in ascending or descending order based on our requirement.

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We can obtain 6 different numbers by multiplying 2 distinct integer divisors of 10.

The divisors of 10 are 1, 2, 5, and 10.

To determine how many different numbers can be obtained from multiplying 2 distinct integer divisors.

We need to select 2 distinct divisors and find their product.

The possible pairs are:

Therefoore, we can obtain 6 different numbers.

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Answer:

Step-by-step explanation:

To calculate the time it will take a car to travel 140km at an average speed of 35km/h, we can use the formula:

time = distance ÷ speed

Plugging in the given values, we get:

time = 140km ÷ 35km/h

time = 4 hours

Therefore, it will take a car 4 hours to travel 140km at an average speed of 35km/h.

Answer:

ㅤ

Car will take 4 hours

ㅤ

Step-by-step explanation:

ㅤ

[tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{Time = \dfrac{Distance}{Speed}}}}}}}[/tex]

ㅤ

[tex]\large{\leadsto{\sf{Given_{(Distance)} = 140 \: km}}}[/tex]

ㅤ

[tex]\large{\leadsto{\sf{Given_{(Speed)} = 35 \: km/hr}}}[/tex]

ㅤ

[tex]\large{\underline{\underline{\sf{Applying \: Formula:-}}}}[/tex]

ㅤ

[tex]\large{\leadsto{\sf{Required_{(Time)} = \bigg(\dfrac{\cancel{140}}{\cancel{35}}\bigg)} \: hr}}[/tex]

ㅤ

[tex]\large{\purple{\boxed{\leadsto{\sf{Required_{(Time)} = 4 \: hr}}}}}[/tex]

ㅤ

━━━━━━━━━━━━━━━━━━━━━━

[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]

ㅤ

[tex]\large{\dashrightarrow{\sf{Time = \dfrac{Distance}{Speed}}}}[/tex]

ㅤ

[tex]\large{\dashrightarrow{\sf{Speed = \dfrac{Distance}{Time}}}}[/tex]

ㅤ

[tex]\large{\dashrightarrow{\sf{Distance = Speed \times Time}}}[/tex]

Answer:

y = 1/7x + 29/7

Step-by-step explanation:

Slope intercept form is y = mx + b

m = the slope

b = y-intercept

m = 1/7

Y-intercept is located at (0, 29/7)

So, the equation is y = 1/7x + 29/7

Answer: Less than or equal to 45

Step-by-step explanation:

Let's use algebra to write the inequality.

Let h be the number of hamburgers purchased and t be the number of tacos purchased.

Each hamburger costs $5.50 and each taco costs $2, so the total cost of h hamburgers and t tacos is:

5.5h + 2t

Serenity has a total of $45 to spend, so we can write:

5.5h + 2t ≤ 45

This is the inequality that represents the possible values for the number of hamburgers purchased, h, and the number of tacos purchased, t.

Note that the inequality is less than or equal to 45, since Serenity cannot spend more than $45.

To represent the possible values for the number of hamburgers and tacos purchased, an Inequality can be written as 5.5x + 2y ≤ 45.

To write an inequality to represent the possible values for the number of hamburgers purchased (h) and the number of tacos purchased (t), we need to consider the cost of each item and the total amount Serenity has to spend.

Let's assume Serenity buys x hamburgers and y tacos. Each hamburger costs $5.50, so the total cost of hamburgers purchased would be 5.5x. Each taco costs $2, so the total cost of tacos purchased would be 2y.

The total amount Serenity has to spend is $45. Therefore, the inequality that represents the possible values for h and t is: 5.5x + 2y ≤ 45.

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Solve the equation [tex]7/11=18/x+1[/tex] we find the solution is [tex]x = 27.2857[/tex]

Your example is an equation since an equation is any statement with an equals sign. Equations are frequently utilized for mathematical equations since mathematicians like equal signs. A set of instructions for achieving a certain result is called an equation.

A number, a constant, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by such an assignment operator form an equation.

we can cross-multiply,

[tex]7(x+1) = 11(18)[/tex]

Expanding the left side,

[tex]7x + 7 = 198[/tex]

Subtracting [tex]7[/tex] from both sides,

[tex]7x = 191[/tex]

Dividing both sides by [tex]7[/tex],

[tex]x = 191/7[/tex]

Therefore, the solution to the proportion is

[tex]x = 27.2857[/tex]

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The y-intercept for this situation shows that the speed of the ship sailing is 0 miles per second during the time t = 4 seconds, after that the speed keeps on decreasing.

Look into the fact that the vector of acceleration points in the same general direction as the vector of velocity change. This indicates that whether you add to or subtract from the velocity depends on the direction of the acceleration.

The graph is shown for the distance travelled by the ship with time by Clare.

Thus, the y-intercept for this situation shows that the speed of the ship sailing is 0 miles per second during the time t = 4 seconds, after that the speed keeps on decreasing.

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the correct answer is option C: The company rejects H0, making a Type II error. In this hypothesis test, the null hypothesis H0 is that the machine produces no more than 98% high-quality candy, and the alternative hypothesis Ha is that the machine produces more than 98% high-quality candy. The significance level is α = 0.05.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming that the null hypothesis is true. A p-value of 0.15 is greater than the significance level of 0.05, which means that the result is not statistically significant.

However, the company is unaware that the machine is actually producing 99% high-quality candy. This means that the null hypothesis is actually false, and the alternative hypothesis is true. In other words, the machine is producing more than 98% high-quality candy.

Based on these observations, the company failing to reject the null hypothesis (option B) would be a Type II error, as it would mean that the company is not detecting a significant difference in the candy quality when, in fact, the machine is producing candy of higher quality than the null hypothesis assumes.

Therefore, the correct answer is option C: The company rejects H0, making a Type II error.

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Answer:

V = (4y³ + 6y² - 4y - 6) ft³

Step-by-step explanation:

Its a rectangular prism so its Volume is its lenght * its width* its height:

V = l * w * h

V = (4y - 3) ft * (y + 2) ft * (y + 1) ft

V = (4y² + 8y - 6y - 6) ft² * (y + 1) ft

V = (4y² + 2y - 6) ft² * (y + 1) ft

V = (4y³ + 2y² - 6y + 4y² + 2y - 6) ft³

V = (4y³ + 6y² - 4y - 6) ft³

Answer:

  see attached

Step-by-step explanation:

You want the given triangle dilated by a factor of -3 about point A.

To find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.

In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.

This same process can be used to locate the other vertices of the triangle's image.

The possible echelon forms of the given matrix are:

A matrix is in echelon form when it has leading nonzero entries in each row, with each row starting further to the right than the row above it. In the given matrix, the first row does not have any nonzero entries, so it does not meet this criterion. The second row does have a nonzero entry (x) so it can meet the criterion, provided that it is the leading entry.

This is the case for b. 0 x
0 0, c. x *
0 0, and d. x *
0 x.
The other criterion for echelon form is that all starred entries (*) may have any value including zero. This criterion is met in all three cases.

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The expected count for women for the presence of aortic stenosis is 57.7. The correct option is D.

Aortic stenosis is a cardiovascular ailment that causes the aortic valve in the heart to narrow, reducing blood flow from the heart to the rest of the body. Aortic stenosis usually progresses gradually and, in the beginning, may not produce any symptoms.

The severity of aortic stenosis is divided into four categories, ranging from mild to severe. People who are asymptomatic may require monitoring, whereas those who are symptomatic may need to undergo surgery or other procedures.

The expected count for women for the presence of aortic stenosis in this question refers to the number of women who have this condition according to a particular study or statistic.

Therefore, the correct option is D.

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Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

The age at which a person is qualified to receive their full retirement payment under Social Security is determined by their lifetime earnings history. The complete retirement age for anybody born in 1960 or later is 67. The complete retirement age is steadily lowered for people born before 1960, and is 65 for those born in 1937 or before.

Given that, Juanita started collecting benefits at age 65.

Thus, her benefits reduced by 13.3%.

0.133 x $2,128 = $283.10

Deducting the reduction amount from the total:

$2,128 - $283.10 = $1,844.90

Hence, Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

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Answer:

To factorize the quadratic expression f² + 7f + 10, we need to find two numbers that multiply to 10 and add up to 7. These numbers are 2 and 5. So, we can write:

f² + 7f + 10 = (f + 2)(f + 5)

Therefore, the answer is (f + 2)(f + 5).

Answer:

Step-by-step explanation:

[tex]f^2+7f+10=f^2+2f+5f+10=f(f+2)+5(f+2)=(f+5)(f+2)[/tex]

By grouping, we can factor the polynomial. We know that 2+5=7 and 2*5=10, so this is why (f+5) and (f+2) are factors of f²+7f+10.

If a measure that is in 4/4 time has a half note, a quarter note, and an eighth note, a sixteenth note value is missing.

4/4 time signature is also known as a common time signature. In a 4/4 measure, we have four beats or counts, and each quarter note takes one beat or count. A half note gets two beats or counts, a quarter note gets one beat, and an eighth note gets half a beat.

Therefore, if a measure in 4/4 time has a half note, a quarter note, and an eighth note, then a sixteenth note value is missing because a sixteenth note gets one-quarter of a beat or count.

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the sale price of the cell phone after the 35% discount is $315.25.

How to solve and what is sale?

To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:

Sale price = Regular price - Discount amount

Sale price = $485 - (0.35 x $485)

Sale price = $485 - $169.75

Sale price = $315.25

Therefore, the sale price of the cell phone after the 35% discount is $315.25.

A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.

In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.

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The degree measure of the largest angle is 72° in the triangle.

We have, The sum of two angles of a triangle is 6/5 of a right angle.

One of these two angles is 30° larger than the other.

Let A and B be the two angles of the triangle such that A = B + 30°.

We know that the sum of three angles in a triangle is 180°.

⇒ A + B + C = 180°

⇒ B + 30° + B + C = 180°

⇒ 2B + C = 150°

We also know that the sum of two angles of a triangle is 6/5 of a right angle.

⇒ A + B = 6/5 × 90°

⇒ B + 30° + B = 108°

⇒ 2B = 78°

⇒ B = 39°

C = 150° - 2B ⇒ 72°

A = B + 30° ⇒ 39° + 30° ⇒ 69°

Therefore, the degree measure of the largest angle in the triangle is 72°.

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Answer:

fFind the sum of

4

4

​

 and

4

8

4

8

​

 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.

Step-by-step explanation:

The second term in the sequence is equal to the first term, which is -20. Hence, the answer is -20.

The given sequence starts with C(1) = -20. Each subsequent term is obtained by adding 0 to the previous term, which means that the sequence is constant.

The recursive formula for this sequence is given as:

c(1) = -20 and c(n) = c(n-1) + 0

This means that the first term of the sequence is -20, and each subsequent term is obtained by adding 0 to the previous term

Therefore, the second term in the sequence is equal to the first term, which is -20. Hence, the answer is -20.

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The retirement plans that do not come with a guaranteed benefit at retirement are C) I, III, and IV.

A guaranteed benefits refers to the fact that the retiree will be paid a certain amount at retirement.

The 401(k) is an employer-offered retirement plan with defined contributions from the employees.  The employee bears the investment risks and there is no guarantee of benefits.

With fixed annuity, there is a guarantee of an annual payment by the insurance company to the beneficiary or insured.

The Roth IRA does not offer guaranteed benefit just like the traditional IRA.

Thus, only the fixed annuity, an insurance contract, offers a guaranteed benefit at retirement.

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Answer:

64 sq cm

Step-by-step explanation:

triangle area = 1/2*b*h (×4 because 4 triangles)

square area = lw