19
Type A batteries and type B batteries were tested.
The cumulative frequency diagram shows information about the battery life of type A.
19 (a)
80
70
60
50
Cumulative
frequency 40
30
20
10
of
0
Type A
800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800
Battery life (hours)
Estimate the interquartile range for type A.
Answer
hours
[2 marks]

Answer:

c

Step-by-step explanation:

Given direct variation between y and t , then the equation relating them is

y = kt ← k is the constant of variation

To find k use the condition y = 27 when t = 4 , then

27 = 4k ( divide both sides by 4 )

6.75 = k

y = 6.75t ← equation of variation

When t = 12 , then

y = 6.75 × 12 = 81

7.

From the diagram, we can conclude:

Therefore:

Add like terms:

Solve for x:

----------------------------------------------------------------------------------------------

8-9

From the diagram we can conclude:

So:

Therefore:

Answer:

The last year value of the house will be $230,000.

Step-by-step explanation:

GIVEN: Decrease in house price = 20%

            Current house price = $184,000

TO FIND: Value of the house last year

SOLUTION:

If the value of the house decreased by 20% during last year, this means the value of the house this year is 80% of last year's value.

Let the value of the house last year be 'x'.

If the value of the house today is  $184,000, then:

                           \(80/100 * x = 184,000\\\\0.8x = 184,000\\\\x = 184,000/0.8\\\\x = 230,000\)

Therefore, the last year value of the house will be $230,000.

By prime factorization and properties for radical functions, we conclude that the square root of 484 is equal to 22.

There are two kinds of natural numbers: prime numbers and compound numbers. Prime numbers are numbers that are only divided by 1 and by itself and compound numbers are numbers that are products of prime numbers.

First, we determine the form of 484 as a product of prime numbers:

484 = 242 × 2

484 = 121 × 2²

484 = 2² × 121

484 = 2² × 11²

Finally, we proceed to obtain the square root of 484 by applying square roots on both sides of the equation and properties for radical functions:

√484 = √(11² × 2²)

√484 = √11² × √2²

√484 = 11 × 2

√484 = 22

By prime factorization and properties for radical functions, we conclude that the square root of 484 is equal to 22.

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The given polynomial equation is x⁵ - x⁴ + 10x³ - 10x² + 9x - 9 = 0. It is a quintic equation of degree 5. The equation does not have any rational roots, and finding its exact solutions may require numerical methods or approximations.

The given equation is a quintic polynomial equation, which means it is a polynomial of degree 5. The general form of a quintic equation is ax⁵ + bx⁴ + cx³ + dx² + ex + f = 0.

To solve this equation exactly, we can use various methods such as factoring, synthetic division, or the rational root theorem. However, in this case, the equation does not have any obvious rational roots. Therefore, finding its exact solutions may be challenging.

Alternatively, we can use numerical methods or approximations to find the approximate solutions of the equation. This involves using numerical techniques such as the Newton-Raphson method or the bisection method to iteratively approach the roots of the equation.

In conclusion, the given polynomial equation x⁵ - x⁴ + 10x³ - 10x² + 9x - 9 = 0 is a quintic equation with no apparent rational roots. Finding its exact solutions may require numerical methods or approximations.

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Answer:

c) 100

Step-by-step explanation:

The statement "The inverse operation of integration is differentiation" is true. Differentiation is indeed the inverse operation of integration.

Integration and differentiation are two fundamental operations in calculus. Integration calculates the area under a curve, while differentiation determines the rate at which a function is changing. These operations are inversely related to each other.

When we perform integration on a function, we find the antiderivative of that function. The antiderivative represents the family of functions whose derivative is equal to the original function. In other words, integration "undoes" differentiation by finding the function that was differentiated to obtain the given function.

On the other hand, differentiation finds the derivative of a function, which represents the rate of change of that function at any given point. The derivative measures how a function is changing with respect to its input variable. Differentiation "undoes" integration by finding the rate of change or the slope of the function at each point.

Therefore, differentiation and integration are inverse operations of each other. If we differentiate a function and then integrate the result, we obtain the original function (up to a constant). Similarly, if we integrate a function and then differentiate the result, we obtain the original function (up to a constant). This property makes differentiation and integration powerful tools in calculus and mathematical analysis.

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7 : -5, -3, -1, 2, 4

8 : -20, -10, 5, 10, 15

Hi! I understand that you want an explanation for the given code snippet involving sets, disjunction, and logical statements. Here's the breakdown of the code and its meaning:

1. Given sets a and b from the universe u.
2. We have a hypothesis (h) stating that for all elements x, it is not true that x is in both set a and set b (¬ (x ∈ a ∧ x ∈ b)).
3. The goal is to prove disjunction (disj a b), meaning that x belongs to either set a or set b, but not both.

The proof proceeds as follows:

1. We assume an element x.
2. We assume h1, which states that x belongs to set a (x ∈ a).
3. We assume h2, which states that x belongs to set b (x ∈ b).
4. We derive a contradiction (h3) using the assumptions h1 and h2, stating that x belongs to both sets a and b (x ∈ a ∧ x ∈ b).
5. Since we have a contradiction (h3) and our hypothesis (h) stated that such a situation is not possible, we can conclude that our assumption is false.
6. Therefore, we have proved that x cannot belong to both sets a and b simultaneously, confirming the disjunction (disj a b).

In summary, the given code snippet proves the disjunction between sets a and b, given a hypothesis that no element belongs to both sets simultaneously.

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Answer:

20

Step-by-step explanation:

The time taken by 18 bakers is given as 20 hours.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The given problem is the case of Indirect proportion as the time taken is more as the number of bakers are less.

The time taken by 15 bakers is 24 hours.

Then, the time taken by 1 baker is given as 24 × 15 = 360 hours.

The time taken by 18 bakers is computed by taking the ratio as below,

Total time for 1 baker ÷ 18

⇒ 360 ÷ 18 = 20.

The time that will take 18 bakers to complete the work is 20 hours.

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Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer:

12

Step-by-step explanation:

Probability = Expected outcome/Total outcome

GIven

Total outcome = 28marbles

probability of randomly drawing a  blue marble = 3/7

Substitute

3/7 = number of blue marbles/28

Cross multiply

7N = 3* 28

N = 3*4

N= 12

Hence there 12 blue marbles in the bag

Answer: The answer is {x,y}={17/5,-68/5}

Can you give me brainliest? I'm so close to the next level. Answers below.

Step-by-step explanation:

Answer 1. We need to find the area to the right of 72 inches on the standard normal distribution. Using a standard normal table or calculator, we find this area to be approximately 0.1587 or 15.87%. Therefore, about 15.87% of men are more than 72 inches tall.

Answer 2. We need to find the area to the left of 74 inches on the standard normal distribution. Using a standard normal table or calculator, we find this area to be approximately 0.9772 or 97.72%. Therefore, about 97.72% of men are less than 74 inches tall.

Answer 3. We need to find the area to the left of 66 inches on the standard normal distribution. Using a standard normal table or calculator, we find this area to be approximately 0.0228 or 2.28%. Therefore, about 2.28% of men are less than 66 inches tall.

Answer 4. We need to find the area between 68 and 74 inches on the standard normal distribution. Using a standard normal table or calculator, we find the area to the left of 68 inches to be approximately 0.1587 and the area to the left of 74 inches to be approximately 0.9772. Subtracting these two areas gives us approximately 0.8185 or 81.85%. Therefore, about 81.85% of men are between 68 and 74 inches tall.

Answer: The perimeter is 76 inches

Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

ANSWER:

B. For every 1-inch increase in height, walking speed increases by 4.9 m/min

STEP-BY-STEP EXPLANATION:

We have the following expression:

4.9 is the slope of the function, that is, it is the increase in y (walking speed) given by a unit in x (height).

This means that for every 1 inch that the walking speed increases, it increases by 4.9 units.

Therefore, the correct answer is B. For every 1-inch increase in height, walking speed increases by 4.9 m/min

The probability that you win first prize and your friend wins second

prize is option D: 13/2730.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Total number of prizes awarded = 3

Number of people entering the drawing competition = 15

Number of ways to award the prize = 2730

Out of the 3 prizes the first and the second is needed.

So, the prize for the first and the second positions are fixed and there is no need to consider the remaining 13 people to win the prize.

Hence the remaining number of people who can win the 3rd prize  = 13

The number of ways one of them wins the 3rd prize = 13

The total number of ways = 2730

Therefore, the probability of the first 2 prizes fixed and the remaining 3rd awarded to the rest of the 13 people is 13/2730.

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Answer:

0.03703704

Step-by-step explanation:

https://www.hackmath.net/en/calculator/fraction?input=3+1%2F4+%2B+2+1%2F3

Thinking:

Wait so like quadrants as in coordinate planes? If so, all the names of the quadrants are 1,2,3,4.

Answer:

15

Step-by-step explanation:

Answer:

The smallest number is  

14

Explanation:

Let: x= the 1st con.even number

x+2=the 2nd con.even number

x+4=the 3rd con.even number

Add the terms and equate it with the total, 48

x + ( x + 2 ) + ( x + 4 ) = 48 , simplify

x + x + 2 + x + 4 = 48 , combine like terms

3 x + 6 = 48 , isolate x

x = 48 − 6 3 , find the value of x

x = 14

\(36-18=18\)

So, 18 more.

As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given a scatter plot  in terms of the time the player spent practicing and the number of points he scored in the game.

A scatter plot uses dots to represent values for two different numeric variables.

The position of each dot on the horizontal and vertical axis indicates values for an individual data point.

As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.

Hence, As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association

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Annual Medical cost = 1269.86

monthly premium cost to Ronald for the Blue Shield plan = $48.48.

For all doctor office visits, prescriptions, and major medical charges, Ronald will be responsible for 35 percent and the insurance company will cover 65 percent of covered charges.

The annual deductible cost = $630.

Ronald decided to review his medical bills from the previous year to see what costs he had incurred and to help him evaluate his choices. He visited his general physician 6 times during the year at a cost = $105 for each visit.

He also spent $71 and $95 on two prescriptions during the year.

= (Monthly premium cost × 12) + Deductible cost + (Coinsurance percent × Coinsurance expenses)

= (48.48 x 12) + 630 + (0.35 x 166)

= 1269.86

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Answer:

She should walk approximately 1,463.34369 feet along the sidewalk going to the east, then walk the remaining straight line distance along the grass.

====================================================

Explanation:

Refer to the diagram below.

Alaina starts at point A. If she stays on the sidewalk the entire time, then she can go from A to C to D in that order.

If she takes the direct line route, then she would go from A to D across the grass entirely.

The two paths have pros and cons. The optimal solution is a mix of the two routes. This means she'll be on the sidewalk for some amount of time, and then cut along the grass once reaching a certain point.

Let's say point B is the point where she decides to cut along the grass. In the diagram below, I made \(\text{BC} = x\) so that I could find \(\text{BD} = \sqrt{x^2+600^2}\) through the pythagorean theorem fairly quickly.

If \(\text{BC} = x\), then the remaining bit of the east/west side walk is \(\text{AB} = 2000-x\) since the two portions must add to 2000 feet.

----------------

If she travels along the side walk at a rate of 6 ft/sec, and travels 2000-x feet (from A to B), then it will take her

time = distance/speed = \(\frac{2000-x}{6}\) seconds

Then if she cuts across the grass to follow path BD, then she'll take another

time = distance/speed = \(\frac{\sqrt{x^2+600^2}}{4}\) seconds since she's traveling 4 ft/sec here.

----------------

If Alaina goes from A to B to D in that order, then she takes a total of

\(\text{(time from A to B)}+\text{(time from B to D)}\\ = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\)

That represents the total time taken when following this path at those specified speeds mentioned.

The goal is to find the minimum of that function. So we'll need to compute the derivative.

\(f(x) = \frac{2000-x}{6}+\frac{\sqrt{x^2+600^2}}{4}\\\\ f \ '(x) = -\frac{1}{6}+2x*\frac{1}{2*4\sqrt{x^2+600^2}}\\\\ f \ '(x) = -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}}\\\\\)

Set the derivative equal to zero and solve for x

\(f \ '(x) = 0\\\\ -\frac{1}{6}+\frac{x}{4\sqrt{x^2+600^2}} = 0\\\\ \frac{x}{4\sqrt{x^2+600^2}} = \frac{1}{6}\\\\ 6x = 4\sqrt{x^2+600^2}\\\\ (6x)^2 = \left(4\sqrt{x^2+600^2}\right)^2\\\\ 36x^2 = 16(x^2+600^2)\\\\ 36x^2 = 16x^2+16*600^2\\\\\)

\(36x^2 = 16x^2+5,760,000\\\\ 36x^2-16x^2 = 5,760,000\\\\ 20x^2 = 5,760,000\\\\ x^2 = 5,760,000/20\\\\ x^2 = 288,000\\\\ x = \sqrt{288,000}\\\\x \approx 536.65631\)

If you were to perform the first derivative test, you should find that the local min occurs at roughly x = 536.65631

This means she must walk a approximately 2000-x = 2000-536.65631 = 1,463.34369 feet when going from A to B such that to minimize the walking time.

Side note: you can use the minimum feature on your calculator to confirm the answer

Answer:

1620

Step-by-step explanation:

If a number decreased by 95% is 81, then

5% is 81.

So, the number = 100/5 x 81= 20 x 81 = 1620

Hope this helps

Answer:

the answer is 1620

Step-by-step explanation: