Colin invests £1100 into his bank account. He receives 5% per year simple interest. How much will Colin have after 6 years?

Answer:

B

Step-by-step explanation:

Here, we want to calculate the square root of -√- (75)

That will be

-√(25)(-3)

= -5 √(-3)

√(-3) is same as 3i

So we have the root as;

-5i√3

Given :-

To Find :-

Answer :-

Here in ∆ABC and ∆EDC ,

Therefore by AA similarity criterion , we can say that ∆ABC ~ ∆EDC . Also we know that corresponding sides of similar triangles are proportional . So ,

→ AC/EC = BC/DC

→ AC/9 = 8/12

→ AC = 8/12 * 9

→ AC = 6

Hence the measure of side AC is 6 .

I hope this helps.

Answer:

5x + 15

Step-by-step explanation:

Given

9x + 6 - 4x + 9 ← collect like terms

= (9x - 4x) + (6 + 9)

= 5x + 15

The given statement "A group of normal distributions can have equal arithmetic means but different standard deviations" is True  because the mean and standard deviation are two separate parameters that describe different characteristics of a normal distribution.

The mean is the measure of central tendency and represents the location of the peak of the distribution, while the standard deviation is a measure of the spread of the distribution.

Therefore, it is possible for multiple normal distributions to have the same mean, but different standard deviations. For example, consider two normal distributions with means of 50 and standard deviations of 10 and 20, respectively.

Both distributions have the same mean of 50, but different standard deviations, indicating that one distribution has a tighter cluster of data around the mean, while the other is more spread out.

Therefore, it is important to consider both the mean and standard deviation when analyzing and comparing normal distributions.

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The approximate length of the minor arc AB is given as follows:

B. 15.7 cm.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius for this problem is given as follows:

r = 10 cm.

Hence the circumference for the entire circle is given as follows:

C = 2π x 10

C = 62.8 cm.

The minor arc AB has an angle of 90º, which is 90/360 = one fourth of the circle, hence the length is given as follows:

62.8/4 = 15.7 cm.

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Answer:

i think photomath will help you with those

Step-by-step explanation:

go to your appstore and download photomath

Answer:

Step-by-step explanation:

Converse: If two angles are complementary, then the angle measures add up to 90 degrees.

Inverse: If two angle measures don't add up to 90 degrees, then the angles are not complementary.

Contrapositive: If two angles are not complementary, the two angle measures do not add to 90 degrees.

This can be written as a biconditional statement because there is no other case for which two angles will be complementary - this is only possible if their angle measures add to 90 degrees.

The expression that can be used to represent the list price of the smartphone is 5179.99 * (1- 25%) and the value is 3884.9925

The given parameters are:

Discount = 25%

Sales price = 5179.99

The expression that can be used to represent the list price of the smartphone is

Expression = Sales price * (1- discount)

So, we have:

Expression = 5179.99 * (1- 25%)

Evaluate

Expression = 3884.9925

Hence, the expression that can be used to represent the list price of the smartphone is 5179.99 * (1- 25%) and the value is 3884.9925

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Answer:

When 2 lines are parallel, the sum of interior corresponding angles = 180

120 + b = 180

b = 180 - 120 = 60

a + 30 = 180

a = 180 - 30 = 150

Let the distance between towns A and B be "d". Then, we have:

On the first trip:

- The bus travels half the distance, which is d/2, at 40 mph. The time it takes to cover this distance is given by: time = distance / speed = (d/2) / 40 = d/80.

- The bus travels the other half of the distance, which is also d/2, at 50 mph. The time it takes to cover this distance is given by: time = distance / speed = (d/2) / 50 = d/100.

- The total time for the first trip is the sum of the times for each half of the distance: time = d/80 + d/100 = 9d/400.

On the return trip:

- The bus travels for the first 2 hours at 35 mph. The distance it covers during this time is given by: distance = speed x time = 35 x 2 = 70.

- The remaining distance is d - 70, which the bus travels at 40 mph. The time it takes to cover this distance is given by: time = distance / speed = (d - 70) / 40.

- The total time for the return trip is the sum of the times for each part of the trip: time = 2 + (d - 70)/40 = (d + 30)/40.

We know that the trip from B to A is an hour longer than the trip from A to B, so:

(d + 30)/40 - 1 = 9d/400

10d + 300 = 1440d/400

4000d + 120000 = 1440d

2560d = 120000

d = 46.875

Therefore, the distance between towns A and B is approximately 46.875 miles.

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Based on both the p-value method and the critical value method, we fail to reject the null hypothesis and cannot infer that the two groups differ in the mean number of pictures printed.

To determine if the two groups (digital camera owners and standard camera owners) differ in the mean number of pictures printed, we can conduct a hypothesis test using both the p-value method and the critical value method.

Let's define our hypotheses:

Null Hypothesis (\(H_0\)): The mean number of pictures printed is the same for both groups.

Alternative Hypothesis (\(H_1\)): The mean number of pictures printed differs between the two groups.

We'll use a significance level of 0.05 (5%).

First, let's calculate the test statistic for the two-sample t-test using the provided summary statistics:

Digital:

Mean = 18.25

Standard Deviation = 6.5

Sample Size = 8

Standard:

Mean = 16.5

Standard Deviation = 19.2

Sample Size = 8

Using the formula for the two-sample t-test, the test statistic (t) is given by:

\(t = (mean_1 - mean_2) / \sqrt{(s_1^2/n_1) + (s_2^2/n_2)}\)

Substituting the values, we have:

\(t = (18.25 - 16.5) / \sqrt{(6.5^2/8) + (19.2^2/8)}\)

t ≈ 0.75

Now, let's perform the hypothesis test using both methods:

1) P-value Method:

Using the t-distribution with \((n_1 + n_2 - 2)\) degrees of freedom, we can calculate the p-value associated with the test statistic.

The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

Using a t-table or statistical software, we find that the p-value corresponding to t ≈ 0.75 is approximately 0.47.

Since the p-value (0.47) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean number of pictures printed differs between the two groups.

2) Critical Value Method:

Using the t-distribution with \((n_1 + n_2 - 2)\) degrees of freedom and a significance level of 0.05, we can find the critical value.

The critical value is the value beyond which we would reject the null hypothesis.

For a two-tailed test at a 5% significance level and 14 degrees of freedom (8 + 8 - 2), the critical value is approximately ±2.145.

Since the test statistic (0.75) does not exceed the critical value (±2.145), we fail to reject the null hypothesis. There is not enough evidence to conclude that the mean number of pictures printed differs between the two groups.

In conclusion, based on both the p-value method and the critical value method, we do not have sufficient evidence to infer that the two groups differ in the mean number of pictures printed.

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Answer:

(sqrt1)/2 or 1/4

Step-by-step explanation:

It is not simplifiable any more. It is 1/4 if you don't want the square root.

The dimension of the solution space of Ax = 0 is 2.

The size or distance of an object, region, or space in one direction is measured in terms of its dimensions. It is just the measurement of an object's length, width, and height.

The rank of a matrix A is the maximum number of linearly independent rows or columns of the matrix. In this case, the rank of the 7 × 5 matrix A is 3.

We know that the dimension of the null space (also called the solution space) of a matrix A is given by:

dim(null(A)) = n - rank(A)

where n is the number of columns of A.

In this case, n = 5 and rank(A) = 3, so we have:

dim(null(A)) = 5 - 3 = 2

Therefore, the dimension of the solution space of Ax = 0 is 2.

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Answer:

270

Step-by-step explanation:

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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Our confidence interval is (66, 102).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

Now, here:

Mean, μ = 84

Standard deviation, σ = 9

It is a 95% confidence interval. We know that, within 2 standard deviations of the mean lies 95% of the population. Hence, z = 2.

Now, calculating μ - z.σ and μ + z.σ to find the intervals.

μ - z.σ  = 84 - 2x9 = 66

μ + z.σ = 84 + 2x9 = 102

Thus, our confidence interval is (66, 102).

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The ball reaches its maximum height after 2 seconds.

To determine when the ball reaches its maximum height, we need to find when its velocity changes from positive to negative. The velocity of the ball is given by the derivative of its height, which is the function h'(t) = -16t. The ball's velocity is 0 when h'(t) = 0, so we need to solve -16t = 0.

The solution to this equation is t = 0. When t = 2, h'(t) = -32, which is negative, indicating that the ball is moving downward. So, the maximum height is reached when the velocity changes from positive to negative, which is at t = 2 seconds.

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Answer:

Yea ill do it

Step-by-step explanation:

Step-by-step explanation:

-k + 4(k + 1) = 2k

-k + 4k + 4 = 2k

-k + 4k - 2k = -4

(-1 + 4 - 2)k = -4

k = -4

Answer:

idk

Step-by-step explanation:

Answer (#2):

125 (degrees)

Step-by-step explanation:

<ATH= 180 - x

the sum of the degrees in a triangle is 180, so <ATH=180-43-82=55 (degrees)

x=180-55=43+82=125 (degrees)

Answer (#3):

x=11, <C=12 (degrees)

Step-by-step explanation:

(3x+28)+(5x+52)+(2x-10)=10x+70=180

x=110/10=11

Answer:

36

Step-by-step explanation:

ik it bc im smart

The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

\(\frac{x}{a} +\frac{y}{b} =1\)

If they make an equal intercept

\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)

Put the value of the point in the axis, and we get.

\(1+2=a\\a=3\)

Put the value in the equation, and we get.

\(x+y=3\)

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Answer:

A (-439)

Step-by-step explanation:

To find the value of (s•t)(-7), we need to first evaluate s(t(-7)) which means we substitute -7 for x in the function t, and then substitute the resulting value in the function s.

So, we have:

t(-7) = 3(-7) = -21

s(-21) = 2 - (-21)^2 = 2 - 441 = -439

Therefore, the value of (s•t)(-7) is -439, which corresponds to option A.

So, the correct answer is A(-439).

Answer:

A

Step-by-step explanation:

I believe you mean

(s ￮ t)(- 7)

to evaluate, first evaluate t(- 7) then substitute the value obtained into s(x)

t(- 7) = 3(- 7) = - 21 , then

s(- 21) = 2 - (- 21)² = 2 - 441 = - 439

Answer:

Equation for Angle 3- 90-38=52

Angle 3= 52

Angle 5= 38

Angle 6= 52

Step-by-step explanation:

Angle is 90 degrees.

Angle 2 is 38 degrees.

If you are just looking at the bottom half(Angle 6, Angle 1, and Angle 2) They are all supposed to add up to equal 180 degrees because it is a supplementary angle.

So you add 90 and 38 and it gives you 52(Angle 6).
90+38+52=180

Then a complementary angle is two angles that equal 90 degrees.

So if you take Angle 2(38 degrees) and subtract it from 90, you get 52. Which is Angle 3.

You do the same with Angle 6 and Angle 5.

Angle 6(52 degrees) subtract from 90 and you get 38.

Then you add 38 and 52 and you get 90.

Then 180-90=90, so Angle 4 is 90 degrees.

Answer:

You need to find what x is bro

Step-by-step explanation:

The values could represent the linear function f(x) =3x

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

x    f(x)

0     0

1      3

2      6

From the above function, we can see that

As the values of the variable x increases by 1, the values of the variable y increases by 3 at a constant rate

This means that the table of values is a linear function, and the slope is

Slope = 3/1

Evaluate

Slope = 3

A linear equation is represented as

y = mx + b

Where

slope = m

b = y when x = 0

This means that

b = 0 and m = 3

So, we have

y = 3x + 0

Evaluate

y = 3x

Hence, the values are linear functions

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Answer:

390.7ft³ is the answer

Answer:

28

Step-by-step explanation:

Hi there! :)

Answer:

a = 12 units.

Step-by-step explanation:

Using the Pythagorean Theorem (c² = a² + b²), where

c = length of the Hypotenuse

a = length of the shorter leg

b = length of the longer leg

We can calculate the length of "a" by substituting in the values into the equation:

c = 15

a = "x"

b = 9

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

15² = x² + 9²

Simplify the squares:

225 = x² + 81

225 - 81 = x²

144 = x²

Take the square root of both sides:

√144 = x

x = 12 units.

Therefore, the length of a = 12 units.

Answer:

a= 12

Step-by-step explanation:

Pythagorean Theorem: a²+b²=c²

b= 9

c= 15

a= x = what we are looking for

For this problem, we need to set c² equal to x² and b², which would look like:

15²= x²+9²

225= x²+81

Subtract 81 from both sides

144=x²

Square root both sides

x=12

a= 12