Faith invests £800 for 3 years in a bank account.
The account pays simple interest at a rate of 0.4% per year
Work out the total amount of interest Faith has got at the end of the 3 years.

Answer:

x = 9.75

Step-by-step explanation:

1 / 4 * ( 8x + 2) = 20

( 8x + 2) = 20 / (1/4)

8x + 2 = 20 * 4

8x + 2 = 80

8x = 78

x = 9.75

Answer:

x=39/4  (39 over 4 as a fraction)

Answer:

Step-by-step explanation:

we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base  (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.

6 * 8 + 4 * 5 =                     remember PEMDAS

48 + 20 =

68 m²

Answer:

a. To find the weight corresponding to the highest 20 percent of coffees, we need to find the z-score that corresponds to the 0.8 cumulative probability.

Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.8 is 0.8416.

Next, we use the z-score formula to find the weight:

Weight = Mean + (z-score * Standard Deviation)

Weight = 400 + (0.8416 * 20) = 448.32 g

So, the weight corresponding to the highest 20 percent of coffees is approximately 448.32 g.

b. To find the weight corresponding to the middle 60 percent of coffees, we need to find the z-scores that correspond to the cumulative probabilities of 0.2 and 0.8.

Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.2 is -0.8416, and the z-score corresponding to a cumulative probability of 0.8 is 0.8416.

Next, we use the z-score formula to find the weights:

Weight Lower Bound = Mean + (z-score * Standard Deviation)

Weight Lower Bound = 400 + (-0.8416 * 20) = 351.68 g

Weight Upper Bound = Mean + (z-score * Standard Deviation)

Weight Upper Bound = 400 + (0.8416 * 20) = 448.32 g

So, the weight corresponding to the middle 60 percent of coffees ranges from approximately 351.68 g to approximately 448.32 g.

c. To find the weight corresponding to the highest 80 percent of coffees, we use the same process as in (a) to find the z-score that corresponds to the cumulative probability of 0.8, which is 0.8416.

Next, we use the z-score formula to find the weight:

Weight = Mean + (z-score * Standard Deviation)

Weight = 400 + (0.8416 * 20) = 448.32 g

So, the weight corresponding to the highest 80 percent of coffees is approximately 448.32 g.

d. To find the weight corresponding to the lowest 15 percent of coffees, we need to find the z-score that corresponds to the cumulative probability of 0.15.

Using a standard normal table or a calculator that can compute z-scores, we can find that the z-score corresponding to a cumulative probability of 0.15 is -0.9332.

Next, we use the z-score formula to find the weight:

Weight = Mean + (z-score * Standard Deviation)

Weight = 400 + (-0.9332 * 20) = 346.64 g

So, the weight corresponding to the lowest 15 percent of coffees is approximately 346.64 g.

Step-by-step explanation:

The population at 0 hours is 1,000, at 4 hours is 1,000,024, and at 8 hours is  1,000,016.

To calculate how the number of bacteria changes over time, let's use the function provided and replace the variable t = time.

0 hours:

Population = 10^6 + (10^4)0 -(10^3)0^2

Population = 10^6 - 10^3

Population = 10^3 or 1,000

4 hours:

Population = 10^6 + (10^4)4 -(10^3)4^2

Population= 10^6 + 40,000 - 16,000

Population= 1,000,024

8 hours:

Population = 10^6 + (10^4)8 -(10^3)8^2

Population= 10^6 + 80,000 - 64,000

Population= 1,000,016

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The short-run total cost is TC is wL + rK and short-run average cost curve is TC/Q. The SMC is 4.01 and the SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost.

A. To calculate the firm’s short-run total cost curve, we need to calculate the total cost at each level of output. The short-run total cost can be represented as follows:

TC = wL + rK,

where w is the wage rate, L is the labor used, r is the interest rate, and K is the capital used. In this case, w = $4 and r = $1.

To calculate the short-run average cost curve, we need to divide the total cost by the level of output:

SAC = TC / Q

Where Q is the level of output.

B. The short-run marginal cost function can be calculated as the change in total cost for a small change in the level of output:

SMC = dTC / dQ

At a level of output of 25, the labor used is L = 25 / 2 = 12.5. The total cost can be calculated as follows:

TC = 4 * 12.5 + 1 * 100 = 50 + 100 = 150

So, the short-run average cost is SAC = 150 / 25 = $6 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:

Q = 2 * sqrt(KL)

Taking the derivative with respect to L, we get:

dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))

Substituting the values, we get:

SMC = 4 + (1 / (sqrt(100 * 12.5)))

At a level of output of 200, the labor used is L = 200 / 2 = 100. The total cost can be calculated as follows:

TC = 4 * 100 + 1 * 100 = 400

So, the short-run average cost is SAC = 400 / 200 = $2 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:

Q = 2 * sqrt(KL)

Taking the derivative with respect to L, we get:

dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))

Substituting the values, we get:

SMC = 4 + (1 / (sqrt(100 * 100)))

SMC = 4.01

C. To draw the graph for the SAC and SMC, we need to calculate the SAC and SMC for different levels of output. We can then plot the SAC and SMC against the level of output to obtain the graphs.

D. The SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost. When the level of output is low, the marginal cost is high and the fixed cost is a large portion of the total cost. As the level of output increases, the marginal cost decreases and the fixed cost becomes a smaller portion of the total cost. As a result, the average cost decreases and reaches a minimum at the point where the marginal cost intersects the average cost.

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Weighed averages show that the student has a grade point average of 2.33.

The grade point average (GPA) is calculated by multiplying the unit value for each course in which a student receives one of the aforementioned grades by the grade point total for that grade. Divide the total of these products by the total number of units. By dividing the total grade points by the total number of units, the cumulative GPA is determined.

A. The student's weighted mean grade point score is (3 classes) × (3 credits per class) × (3 points for a B) ÷ (9 total credits) = 3.00.

B. The student's weighted mean grade point score is (1 class) × (3 credits) × (1 point for a D) ÷ (3 total credits) = 1.00.

C. The student's weighted mean grade point score is (1 class) × (4 credits) × (2 points for a C) ÷ (4 total credits) = 2.00.

D. The student's weighted mean grade point score is (1 class) × (2 credits) × (2 points for a C) ÷ (2 total credits) = 2.00.

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Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.

What is continuously compounded interest?

Continuous compounded interest indicates that an account balance is constantly earning interest and reinvesting that money so that it, too, earns interest.

The formula for continuous compounding is given by:

[tex]A = Pe^{rt}[/tex]

where A is the amount in the account after t years, P is the principal amount (the amount invested), r is the annual interest rate, and e is the base of the natural logarithm.

We want to find P when A = $15,000, r = 0.04, and t = 5 years.

Substituting these values into the formula, we get:

[tex]15000 =Pe^{0.04*5}[/tex]

Simplifying the right-hand side, we get:

[tex]15000 =Pe^{0.2}[/tex]

Dividing both sides by e^(0.2), we get:

[tex]P= \frac{15000}{e^{0.2}}[/tex]

Using a calculator, we get:

P ≈ $10,994

Therefore, Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.

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Option D is correct, SA = 2π(1.3)2 + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that cylinder with diameter labeled 2.6 feet and height labeled 4.4 feet

The surface area of cylinder is given by the formula =2πrh+2πr²

The radius is Diameter/2

2.6/2=1.3

The radius is 1.3

Surface area =2π(1.3)(4.4)+2π(1.3)²

So =2.6π(4.4)+2π(1.3)²

Hence, Option D is correct, SA = 2π(1.3)² + 2.6π(4.4) square feet is used calculate the surface area of the cylinder.

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Answer:

Step-by-step explanation:

STEP 1: a1 = 6.

STEP 2:  r = 0.75

STEP 3: The common ratio is less than one.

STEP 4: The sum of the  Sum of the Infinite Geometric series is Sn = 24

Since we have the expression for the sum of the infinite geometric series

[tex]\[ \sum_{n=0}^{\infty} 6(0.75)^{n} \][/tex]

STEP 1:

The first term of the infinite geometric series is 6. Thus, a1 = 6.

STEP 2:

The common ratio of the infinite geometric series is 0.75. Thus, r = 0.75

STEP 3:

The common ratio is less than one.

Because Sn = a/(1 - r)  is the formula we use when the common ratio is less than 1.

STEP 4:

Sn = a/(1 - r)

Sn = 6/(1 - 0.75) = 24

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Answer:

EF, GH

Step-by-step explanation:

both go on forever from one point

Answer:

A and B

Step-by-step explanation:

Because they go infinitly in one direction and end in another.

The value of x in the given equation using laws of exponents is; x = 512

The different laws of exponents include;

1) Product of powers rule.

2) Quotient of powers rule.

3) Power of a power rule.

4) Power of a product rule.

5) Power of a quotient rule.

6) Zero power rule.

7) Negative exponent rule.

We have the equation as;

x^(2/3) = 64

We can write 64 as (∛512)²

This can be further expressed as;

512^(2/3)

Thus, we have;

x^(2/3) = 512^(2/3)

Thus, by identity rule;

x = 512

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The pair of opposite angles formed by two intersecting straight lines are known as Vertical Angles.

In the given figure, there are two pairs of vertical angles~

That are :

[tex]\qquad \sf  \dashrightarrow \: \angle1 \: \: and \: \: \angle3[/tex]

and

[tex]\qquad \sf  \dashrightarrow \: \angle2 \: \: and \: \: \angle4[/tex]

Also, vertical opposite angles are equal in measure.

The resulting image of the dilated figure has vertices at (-8, -4), (8, -8), and (4, 8).

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.

To dilate the given figure by a factor of 4 centered at the origin, we need to multiply the coordinates of each vertex by 4.

The new coordinates of B will be:

x-coordinate: 4 x (-2) = -8

y-coordinate: 4 x (-1) = -4

So the new vertex B' is (-8, -4).

The new coordinates of C will be:

x-coordinate: 4 x (2) = 8

y-coordinate: 4 x (-2) = -8

So the new vertex C' is (8, -8).

The new coordinates of D will be:

x-coordinate: 4(1) = 4

y-coordinate: 4(2) = 8

So the new vertex D' is (4, 8).

Therefore, the image of the resultant figure is given in the image below.

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The numbers on a number line is

    |-------|-------|-------|-------|

    0      1       2       3       4

                  *       *

               1 1/2   2 2/5

From the question, we have the following parameters that can be used in our computation:

Plot 1 1/2 and 2 2/5

To plot 1 1/2 and 2 2/5 on a number line, we can follow these steps:

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a).The function1 changes at greater rate of 45.

b). At x = 1; the function1 = 45 and function2 = 50.

c).The functions are equal to 90 at x = 2.

A function in the equation form "y = mx + c" represents a straight line in a two-dimensional coordinate system. "y" and "x" are variables representing the coordinates of points on the line, "m" is the slope of the line, and "c" is the y-intercept, which is the point at which the line crosses the y-axis.

The slope "m" represents the rate at which the line rises or falls as x increases. The y-intercept "c" determines the location of the line along the y-axis. This equation is known as the slope-intercept form of a linear equation.

For the function1, when y = 0 and x = 0, we can solve for c and m as follows:

0 = 0m + c

c = 0

when y = 90 and x = 2;

90 = 2m + 0

m = 45

Hence, the function1 with y = 45x changes at a greater rate of 45.

At x = 1:

for function1;

y = 45(1) + 0 = 45

for function2;

y = 40(1) + 10 = 50.

At the point when x = 2:

for function1;

y = 45(2) + 0 = 90

for function2;

y = 40(2) + 10 = 90.

Therefore, the function1 changes at greater rate of 45. At x = 1; the function1 = 45 and function2 = 50. The functions are equal to 90at x = 2.

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The answer choice which is true about the given equation; y = -2x as required to be determined is; It is a linear function because its graph is a straight line.

It follows from the task content that the given function y = -2x as required be identified as being a linear equation or not and why?

On this note, since the graph of the equation is such that g

it yields a straight line, it follows that the given function; is a linear function because its graph is a straight line.

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Answer:

Step-by-step explanation:

Let's call the smallest of the three consecutive even integers "x". Since they are consecutive and even, we know that the next two integers must be "x + 2" and "x + 4".

Now we can set up the equation for the problem:

4 * (x + (x + 2) + (x + 4)) = 240 + 6x

Expanding the parentheses on the left side:

4 * (3x + 6) = 240 + 6x

Simplifying the left side:

12x + 24 = 240 + 6x

Subtracting 6x from both sides:

6x + 24 = 240

Subtracting 24 from both sides:

6x = 216

Dividing both sides by 6:

x = 36

So the smallest of the three consecutive even integers is 36, and the others are 38 and 40.

The area of the composite figure is 41 ft square.

The figure is a composite figure. A composite figure is a figure that has two or more shapes.

Therefore, the area of the composite figure is the sum of the individual area of the shapes.

Therefore,

area of the figure = area of rectangle 1 + area of rectangle 2

area of rectangle 1 = lw

where

Therefore,

area of rectangle 1 = 2 × 4 = 8 ft²

area of rectangle 2 = 11 × 3 = 33 ft²

Hence,

area of the figure =  = 8 + 33

area of the figure = 41 ft²

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Answer: A tangent to the x-axis means that the y-coordinate of the point of tangency is 0. So, we can find the possible values of d by setting y = 0 and solving for x:

0 = x^3/3 + 7x^2/2 + 10x + d

This is a cubic equation, so it can be solved using various methods such as factoring, completing the square, or using a numerical method such as the Newton-Raphson method. If the equation can be factored or the method used is numerical, there might be multiple possible values of d. If the method used is completing the square, there would be only one possible value of d.

However, without a specific method, it's not possible to find the exact value(s) of d. The possible values of d will depend on the specific solution method used to solve the equation.

Step-by-step explanation:

The numbers could be:

6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

The place value of a number is given as:

Example:

1234.567

1 = thousand place value

2 = hundred place value

3 = tens place value

4 = ones place value

5 = tenths place value

6 = hundredths place value

7 = thousandths place value

We have,

Shawn rounded a number to the nearest tenth and got 6.5.

When he rounded it to the nearest whole number, he got 6.

Now,

The number = 6.45

Rounded to the nearest tenth = 6.5

Rounded to the nearest whole number = 6

The numbers can be 6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

Thus,

The possible numbers are:

6.45, 6.46, 6.47, 6.48, 6.49, 6.50, 6.51, 6.52, 6.53, and 6.54.

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Answer:

degree 2 and 10

Step-by-step explanation:

the degree of a polynomial is the value of the largest exponent of the variable.

r(x) = 10x² + 4x - 7

has largest exponent 2

this is a polynomial of degree 2

the leading coefficient is the coefficient of 10x²

that is leading coefficient is 10

An equation of a line that has a slope of -5/7 and passes through the point (-35, 10) is y = -5x/7 - 15.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-35, 10), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 10 = -5/7(x - (-35))

y - 10 = -5/7(x + 35)

y - 10 = -5x/7 - 25

y = -5x/7 - 15

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Answer:

$660

Step-by-step explanation:

If she gets $12/ an hour and works for 40 hours, 12*40=480. For every hour over 40, she gets $18/an hour, so if she works for 50 hours, you do 18*10 since she only worked 10 hours over 40. 18*10=180. To get the total amount, you do 480+180, which is 660.

Hope this helps! Please give brainliest!

Answer:

Therefore, Kayla will make $660 for working 50 hours.

Step-by-step explanation:

Let H be the number of hours worked in a week. The total pay can be represented as a piecewise function as follows:

f(H) =

12 * min(H, 40) +

18 * max(0, H - 40) if H >= 0

So, for H = 50 hours worked, we have:

f(50) = 12 * min(50, 40) + 18 * max(0, 50 - 40)

= 12 * 40 + 18 * (50 - 40)

= 480 + 180

= $660

Therefore, Kayla will make $660 for working 50 hours.

The probability that at least 1 of the 4 cards drawn is a face card is 0.6.

A typical deck contains 52 cards in total. There are 51 cards left in the deck after the first spectator draws a card. The replacement card leaves 52 cards in total, which is the same as before. The number of cards remains 52 for all four draws since each succeeding audience member will draw a card and replace it.

Finding the likelihood that none of the four cards are face cards and subtracting it from one will give us the chance that at least one of the four cards is a face card.

A deck of cards has 12 face cards (4 jacks, 4 queens, and 4 kings). Consequently, the likelihood that a single draw will not provide a face card is:

P(not a face card)=(52 - 12)/(52)=(40/(52)=(10/13).

The likelihood that none of the four draws will produce a face card is:

P(no face cards are present) = (10/13)4 = 0.432

As a result, the likelihood that at least 1 of the four cards revealed is a face card is as follows:

P(none are face cards) = 1 - P(at least one is a face card) = 1 - 0.432 = 0.568

The chance, rounded to one decimal place, is roughly 0.6.

Consequently, there is a 0.6 percent chance that at least one of the four cards will be a face card.

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The value of the quadratic like equation is given as y = 1 and y = 81.

The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be favoured over the cross-multiplication method and the elimination method for straightforward equations without a lot of complicated calculations.

The equation is:

[tex]y^{\frac{1}{2} } - 4y^{\frac{1}{4} } + 3 = 0[/tex]

Using the exponent property we can write the equation as follows:

[tex](y^{\frac{1}{2} })^{\frac{4}{4} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{\frac{4}{2} } - 4y^{\frac{1}{4} } + 3 = 0\\\\(y^{\frac{1}{4} })^{2} - 4y^{\frac{1}{4} } + 3 = 0[/tex]

Now suppose the value of [tex]y^{\frac{1}{4} } = x[/tex].

x² - 4x + 3 = 0

x² - 3x - x + 3 = 0

x(x - 3) -1 (x - 3) = 0

(x - 1)(x - 3) = 0

x = 1

x = 3

Now, back substituting the value of [tex]y^{\frac{1}{4} } = x[/tex].

[tex]y^{\frac{1}{4} } = 1\\\\y^{\frac{1}{4} } = 3\\[/tex]

Raise to four on both sides of the equation we have:

y = 1

y = (3)⁴

y = 81

Hence, the value of the quadratic like equation is given as y = 1 and y = 81.

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A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.

Simple Random Sample (SRS) is a statistical technique for selecting a sample from a population, where each individual or item in the population has an equal chance of being selected for the sample. In other words, a simple random sample is a representative subset of a population where every individual or item in the population has an equal chance of being selected for the sample.

To take a simple random sample, each individual in the population is assigned a unique number, and then random numbers are generated to select the required number of individuals for the sample. This method ensures that the sample is not biased towards any particular subset of the population, and that the sample is representative of the whole population.

A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.

B) np^≥10n p^​ ≥10n, p, with, hat, on top, is greater than or equal to, 10 and n(1−p^)≥10n(1− p^​ )≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10 - Since the problem does not provide the value of p, we cannot determine if the condition np^≥10n and n(1−p^)≥10n are satisfied.

C) Individual observations can be considered independent. - The problem does not provide information about whether the individual observations can be considered independent. However, we can assume that since it is a random sample, the observations are independent.

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Step-by-step explanation:

A set is a collection of distinct elements, and a subset is a collection of elements taken from a larger set. In this case, the set is {10, 15, 14, 20, 11}.

To calculate the number of subsets, we can use the formula for the number of subsets of a set with n elements, which is 2^n. So, the number of subsets of the set {10, 15, 14, 20, 11} is 2^5 = 32.

To calculate the number of proper subsets, we need to exclude the empty set (Ø) and the set itself from the total number of subsets. So, the number of proper subsets is 32 - 2 = 30.

Therefore, there are 32 subsets and 30 proper subsets of the set {10, 15, 14, 20, 11}.