Harry invests £6000 in a savings account.
The account pays 3.4% compound interest per year.
Work out the value of his investment after 3
Give your answer to the nearest penny.
years.

The basket of pennies will be 1/4 full on the 13th day

From the question, the given parameters are:

The above parameters illustrate an exponential function

An exponential function is represented as

A(n) = A * (r)ⁿ⁻¹

Where

A represents the initial value

It is full on the 15th day

So, we have

1 = A *(2)¹⁵⁻¹

Evaluate

1 = A *(2)¹⁴

Divide by (2)¹⁴

A = (2)⁻¹⁴

Substitute A = (2)⁻¹⁴ in A(n) = A * (r)ⁿ⁻¹

A(n) = (2)⁻¹⁴ * (2)ⁿ⁻¹

When it is one-quarter full, we have

1/4 = (2)⁻¹⁴ * (2)ⁿ⁻¹

Multiply by (2)¹⁴

(2)¹² = (2)ⁿ⁻¹

By comparison, we have

n - 1 = 12

Add 1 to both sides

n = 13

Hence, the basket will be one-quarter full on the 13th day

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Hello there!

If a bag has 12 balls labelled 1 through 12, that means that the balls inside the bag includes:

1  2  3  4  5  6  7  8  9  10  11  12

When creating a fraction for a probability, the numerator usually consists of a specific probability you are trying to find; the denominator usually consists of the total amount of samples in the bag.

In this example: What is the probability of picking an even number?

Ask yourself: What are we trying to find?

We are trying to find the probability of even numbers.

Then ask yourself: What is the amount of possibilities that we can get an even number from the bag?

The bag consists of: 1  2  3  4  5  6  7 8  9  10  11  12

Even numbers are divisible by 2 and has a remainder of 0 ; which means in this bag, the bolded numbers are even.

Then we can conclude that in this bag, counting all of the bolded numbers, we have 6 possibilities of choosing an even number.

Finally, think about: What is the total amount of samples in this bag?

We know that there are 12 balls, so 12 would be the total amount.

To conclude, we can find 6 even numbers in a bag of 12 balls;

Therefore, the chances you can pick an even number is [tex]\frac{6}{12} ,[/tex] or [tex]\frac{1}{2}[/tex].

Answer:

%25 of customers ordered ice tea.

Step-by-step explanation:

To find percentage = Part/Whole x 100

35/140 x 100 = 0.25 x 100 = %25

We have that in Tom's survey he obtained that 20% of the students like the yellow color (see graph above).

Then, in Candance's (small) survey, she asked 15 friends. According to Tom's survey, Candance should have obtained that 20% of her friends like the yellow color.

Therefore, we need to find 20% of 15 (friends) to find the expected number of friends that Candance should have had using the results of Tom's survey. Then, we have:

Hence, according to Tom's survey, Candance's friends would have been expected to be 3 to choose (of her 15 friends) yellow (3 is 20% of 15).

Answer: She already got rid of two red pens, so there's one red pen left.

5-1=4-1=3. 1 red 1 blue 1 green. 100/3=33.3333333… so her chance of getting another red pen is 33.3333333333333333333333% and a 66.66666666666666666666% chance of not.

Step-by-step explanation

Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams. 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.

Given that,

The 1982 change in pennies composition from all copper to zinc with copper coating was made by the US Mint. Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams.

We have to find how many coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.

An issue of quantity and amount. In this context, the term "amount" refers to weight. The variables should be identified with letters that will make them easy to distinguish: Z for largely zinc and C for all copper. Create weight and quantity equations:

C + Z = 1287

3.1 C + 2.5 Z = 3601.5

By multiplying all three components of the first equation by -2.5 and placing them under the second equation, drawing a line, and then subtracting, you can eliminate the Z using this method.

3.1 C + 2.5 Z =  3601.5

-2.5 C -  2.5 Z = -3217.5

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

0.6 C              =    384      

Divide both sides by .6.

C = 640        

Subtract 640 from 1287.

Z = 647

Therefore, 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.

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We have:

And want to find f(8), for this we simply replace x with 8 and operate:

SOLUTION:

Step 1:

In this question, we are given the following:

Consider this system of equations:

Step 2:

The details of the solution are as follows:

CONCLUSION:

The values of x that are the solutions to the system of equations are:

Using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.

So,

(A) P(x > 4.14)

(B) P(4.8 < x < 5.04)

(C) P(x > x) = 0.05

(D) P(x < 5.01)

Therefore, using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.

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Correct question:

The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. a. What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces? b. What percentage of the items weighs between 4.8 and 5.04 ounces? c. Determine the minimum weight of the heaviest 5% of all items produced. d. If 27,875 items of the entire production weigh at least 5.01 ounces, how many items have been produced?

Answer:

20 times

Step-by-step explanation:

Digit 2 appears 20 times in first 100 natural numbers

Answer:

Slope = -2

Step-by-step explanation:

(9, 3), (19, -17)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁         -17 - 3        -20

m = ------------ = ------------ = -------- = -2

        x₂ - x₁         19 - 9         10

y - y₁ = m(x - x₁)

y - 3 = -2(x - 9)

y - 3 = -2x + 18

  +3            +3

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

y = -2x + 21

I hope this helps!

Given:

Initially, the cell phone was 80% charged.

Then started to lose 8% charge for each hour thereafter.

To find:

The equation for B in terms t

This is given point in the fourth quadrant.

In this point, the adjacent is

The opposite is y.

Find hypotenuse h using the pythagorean theorem:

is equal to hypotenuse by adjacent.

is equal to adjacent by opposite.

In the fourth quadrant,

is positive , and

is negative.

So,

Answer: The slope-intercept form for a line with the coordinates of (-2,-1) and (-1,-2) is:

y= -1.00x + -3.00

(results are in decimal form, rounded to the nearest 100th)

i hope i helped it is for if it was for like slope intercept form

Step-by-step explanation:

Step-by-step explanation:

The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of 3/4 is y = (3/4)x - 31/4.

What is the slope-intercept form?

The slope-intercept form of a line is y=mx + c.

Where, x and y are coordinates. m = slope and c = y intercept.

Given, slope (m) = 3/4

Substituting the values of (x, y) as (5, -4) and m = 3/4, we get:

-4 = (3/4) × 5 + c

⇒ c = -4 - (3/4) × 5 = -4 - 15/4 = -31/4

Now, putting the value of c in the standard equation:

y = (3/4)x - 31/4

⇒ 4y = 3x - 31

⇒ 3x - 4y = 31

Answer is Option C

Okay, here we have this:

Considering the provided formula and information, we are going to calculate the requested percent of college freshmen in 2010, so we obtain the following:

So since x corresponds to the number of years after 1980, in this case we will replace x with 30, since it is 30 years after 1980, we have:

p=4x/5+25

Replacing:

p=4(30)/5+25

p=120/5+25

p=24+25

p=49

So, as we can see, the model assumes that in 2010 the percentage was 49%, and the real one is 47%. It means that the model overestimates the real value by 2%.

The roots of the equation is 1 and 3.28

The given equation is a quadratic

To find the roots of a quadratic equation, the formula is

[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]

The equation is 101x^2+231x-334=-2  we need to find the A,B,C

101x^2+231x-332 = 0

here a is 101, b is 231, and c is -332

[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 + \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 + \sqrt{53361 + 134128 } }{202}\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + 433 }{202}\\\\=\frac{202}{202}\\\\ 1[/tex]

[tex]\frac{-b - \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 - \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 - \sqrt{53361 + 134128 } }{202}\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 -433 }{202}\\\\=\frac{664}{202}\\\\ 3.28[/tex]

Therefore, the roots of the equation is 1 and 3.28

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The scale of a topographical map is 1:50000. This means that 1 cm on the map is 50 000 cm on reality.

Now, we can take the

Angle ZWY has a measure of 13 degrees.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.

Given,

Angle WXY has a measure of 133 degrees

Angle ZYX has a measure of 34 degrees

Angle ZWY:

= 180 - 133 -34

= 13

Angle ZWY has a measure of 13 degrees.

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Since y varies directly with x then

So,

Then, 1/4 is the constant of proportionality. So that,

Answer:

100 is perfect square

Step-by-step explanation:

in x² =100, we have x×x=100 and x could be ±10 since both 10² and (-10)² is equal to 100

The mean value of expected value for a binomial distribution is given by the next formula:

Where n is the number of trials and p is the probability of success. So, using the given data:

So the expected value or mean is 48

Answer:

Explanation: We have been given a fraction 7/8 and we need to divide it by 6 and write it in simplest terms.

Dividing and simplifying gives us following:

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

Given,

The cost price of the guitar = $780

The selling price of the guitar = $1396.20

We have to find the markup percent based on the cost;

Markup percentage;

The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.

Markup percent = (Selling price - cost price) / cost price x 100

= (1396.20 - 780) / 780 x 100

= 616.20 / 780 x 100

= 0.79 x 100

= 79%

That is,

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

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The probability the friend finds no one in the first spot is 60%.

Probability is the chance or likelihood that an expected event occurs when there are many possible outcomes or events.

For instance, the probability that when the counting friend goes to the hiding spot, they can or cannot find a friend there.

The two friends can only hide in 2 spots, leaving 3 spots with nobody.

The number of hiding spots = 5

The number of friends hiding = 2

The number of counting friends = 1

The number of spots they can hide = 2 out of 5

The probability of finding a person in a hiding spot = 2/5 or 40%

The probability of not finding a person in a hiding spot = 3/5 (1 - 2/5) or 60% (1 - 40%).

The chances that your friend finds anyone in the first spot are 60%.

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Answer:

y = 2x + 3

Step-by-step explanation:

The y-intercept is where x = 0. Therefore, the y-intercept would be 3. To find the slope, you do Δy/Δx (Δ = Change In). To find that, you go up 4 times, then move to the right 2 times to reach the second dot. Now, you do 4 / 2, which equals 2. Your final equation will be y = 2x + 3.

[tex]=-10x^4-4x^3+6x^2[/tex]

After 100 years:

Replace t by 100:

A (t) = 523 (1/2)^t/30

A (100) = 523 (1/2)^100/30 = 523 (1/2) ^10/3 = 51.88 =52 grams

The initial amount of the sample is 523