Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41​

Answer:

16.

Step-by-step explanation:

The  null hypothesis and the alterative hypothesis are [tex]H_0[/tex] : [tex]\mu[/tex] > 1220

[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220.

The standardized test statistic is 1.725.

We have,

[tex]\mu[/tex] > 1220,

α = 0.03

[tex]\sigma[/tex] = 202.17

X = 1249.88

n= 300

a) According to the claim and the sample statistics, the null hypothesis and the alterative hypothesis are given by:

[tex]H_0[/tex] : [tex]\mu[/tex] > 1220

[tex]H_\alpha[/tex]: [tex]\mu[/tex] ≤ 1220

b) The standardized test statistic is

=| [tex](\mu[/tex] - X) / ([tex]\sigma[/tex] / √n)|

= |( 1220 - 1249.88) / (202.17/√300)|

= |(-29.88)/ 17.320|

= |-1.725|

= 1.725

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Answer:

  499,237 ft²

Step-by-step explanation:

You want the lateral area of a square pyramid 580 feet on a side and 318 feet tall.

To find the area of each triangular face, we must know its slant height. That can be found from the base and height of the pyramid using the Pythagorean theorem. Once we know the slant height, we can use the formula for the area of a triangle:

  A = 1/2bh

There are 4 congruent triangular faces, so the lateral area of the pyramid will be 4 times the area of one face:

  4A = 4(1/2bh) = 2bh

The slant height of a face of the pyramid is the hypotenuse of a right triangle with one leg equal to the height of the pyramid, and the other leg equal to half the length of a base edge. (This is the distance from the midpoint of the bottom edge of a face to the center of the base, under the peak of the pyramid.)

  h = √((580/2)² + 318²) ≈ 430.3766 . . . . feet

  lateral area = 2(580 ft)(430.3766 ft) ≈ 499237 ft²

The surface area of the glass is about 499237 square feet.

Answer:

The area of one planter is:

4 1/5 in × 1 1/3 in = (21/5) in × (4/3) in = 28/5 in²

In a 3 x 3 array, there are 3 planters in each row and 3 planters in each column, so there are a total of 9 planters.

The area covered by the planters is:

9 × (28/5) in² = 252/5 in² ≈ 50.4 in²

Therefore, the area covered by the planters is approximately 50.4 square inches.

Step-by-step explanation:

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1. The width of the pen must be greater than or equal to the sum of the diameters of the two circular food containers, which is equal to 2x + 2x = 4x:

2. The width of the pen must also be less than or equal to the length of the pen, which is 10 feet:

3. The radii of the gravel bases must be greater than or equal to the radii of the food containers, which is equal to x:

4. The radii of the gravel bases must also be less than or equal to half the width of the pen, which is equal to y/2:

System of inequalities that can be used to determine the width of the pen, y, and the radii of the gravel bases, x, is:

Answer:

Step-by-step explanation:

The sum of the diameters of the gravel bases cannot exceed the width of the pen, so 2⁢x+2⁢x≤y. Rewrite this to get y≥4⁢x as the first inequality in the system.Next, to write the expression for the cost of the fencing, find the perimeter of the rectangle and multiply the perimeter by the cost per foot of fencing. The pen is a rectangle, so the perimeter is 2⁢(10)+2⁢(y), or 20+2⁢y. Multiply the cost ($4.00 per foot) by the perimeter to get 4⁢(20+2⁢y).Now write an expression for the gravel bases for the circular food containers. Because A=π⁢r2 and the cost of the gravel is $2.00 per square foot, multiply the cost of the material by the sum of these areas to get 2⁢(π⁢x2)+2⁢(π⁢x2).The total cost must be less than or equal to $150, so we can say that 4⁢(20+2⁢y)+2⁢(π⁢x2)+2⁢(π⁢x2)≤150. Finally, simplify and solve for y.80+8⁢y+2⁢π⁢x2+2⁢π⁢x2≤15080+8⁢y+4⁢π⁢x2≤1508⁢y≤70−4⁢π⁢x2y≤8.75−0.5⁢π⁢x2So, this is the system.

y≥4⁢x

y≤8.75−0.5⁢π⁢x2

Answer:

there is missing information needed to provide a solution to this problem.

The z-score for 71 is -1.

z-score is a measure of how many standard deviations an observation or data point is away from the mean of a distribution.

It is calculated by subtracting the mean from the observation and then dividing the result by the standard deviation: z = (x - μ) / σ

A positive z-score means that the data point is above the mean, while a negative z-score means that it is below the mean.

Applying the formula to solve our question

Here is a proven formula to use:

z = (x - μ) / σ

where:

x = the data item (x = 71)

μ = the mean of the distribution (μ = 80)

σ = the standard deviation of the distribution (σ = 9)

Substituting the values, we get:

z = (71 - 80) / 9

z = -1

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The likelihood that they will choose to work in an animal shelter for each of the six options they choose is around 0.2214 or 22.14%

The probability is given as,

P = (Favorable event) / (Total event)

The likelihood of choosing an opportunity at an animal shelter is 7/9. If each chance is equally likely to be chosen, the likelihood of choosing six in a row from an animal shelter may be estimated by multiplying the likelihood of choosing one opportunity by itself six times:

P = (7/9) x (7/9) x (7/9) x (7/9)

P = (7/9)⁶

P = 0.2214 or 22.14%

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Answer:

15,136 km

Step-by-step explanation:

Im not 100% sure but everyone meses up sometimes/

To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.

 |---------------------|---------------------|

 0                                            4.472

We have,

To plot the point representing the approximation of √(20), we need to first find the approximate value of √(20):

√(20) ≈ 4.472

This means that the point we want to plot is located approximately 4.472 units to the right of the origin on the number line.

To plot the point, we can draw a horizontal number line, label the origin as 0, and then mark a point 4.472 units to the right of 0.

The resulting point represents the approximation of √(20).

Thus,

A rough sketch of what the plot could look like:

 |---------------------|---------------------|

 0                                            4.472

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The two inequalities of the graph are:

y ≥ 3x - 1

y < -¹/₂x + 4

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

The first inequality with a solid line has a y-intercept of -1 and since it is shaded above the line, we will use ≥.

Two coordinates on the line are: (0, -1) and (1, 2)

The slope = (2 + 1)/(1 - 0) = 3

Thus, inequality is:

y ≥ 3x - 1

The second inequality with a dashed line has a y-intercept of 4 and since it is shaded below the line, we will use <.

Two coordinates on the line are: (4, 0) and (0, 2)

The slope = (2 - 0)/(0 - 4) = -1/2

Thus, inequality is:

y < -¹/₂x + 4

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Answer: Polynomials can be classified by the degree of the polynomial. The degree of a polynomial is the degree of its highest degree term. So the degree of 2x3+3x2+8x+5 2 x 3 + 3 x 2 + 8 x + 5 is 3. A polynomial is said to be written in standard form when the terms are arranged from the highest degree to the lowest degree.

[tex]\sin^2(\theta)+\cos^2(\theta)=1\hspace{9em} \begin{array}{llll} \textit{Symmetry Identities} \\\\ \sin(-\theta )=-\sin(\theta) \\\\ \cos(-\theta )=\cos(\theta ) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\cot(-x)\cos(-x)+\sin(-x)\implies \cfrac{\cos(-x)}{\sin(-x)}\cos(-x)+\sin(-x) \\\\\\ \cfrac{\cos(x)}{-\sin(x)}\cos(x)+[-\sin(x)]\implies \cfrac{-\cos^2(x)}{\sin(x)}-\sin(x) \\\\\\ \cfrac{-\cos^2(x)-\sin^2(x)}{\sin(x)}\implies \cfrac{-( ~~ \cos^2(x)+\sin^2(x) ~~ )}{\sin(x)} \\\\\\ \cfrac{-( ~~ 1 ~~ )}{\sin(x)}\implies -\cfrac{1}{\sin(x)}\implies -\csc(x)[/tex]

The value of the radius is 13.04

Pythagoras theorem states that: The sum of square of the two legs of a right triangle is equal to the square of the other side.

Therefore c² = a² + b²

Since MN is perpendicular to JK , this means MK = JM = JK/2

= 14/2 = 7

HI = JK, therefore LI is also 7

and MN = LN = 11

Therefore,

NI =√ LN)² + LI)²

NI = √ 11² + 7²

NI = √121+49

NI = √ 170

NI = 13.04( nearest hundredth)

therefore the radius of the circle is 13.04

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Answer:

x is 25

Step-by-step explanation:

There is a common ratio between the sides. In this case, 35/28 is 1.25. This is the number you have to multiply to 20. 1.25 * 20 = 25.

The value of the angle 3 as solved is 52 degrees.

The sum of the angles on a straight line is always 180 degrees, and this property is true for any pair of opposite angles formed by two intersecting lines.

We can see that what we have is the angles that are on a straight line

We have from the question that;

< 1= 90

<2 = 38

Thus;

<6 = 180 - (90 + 38) - Sum of angles on a straight line

<6 = 52°

Now;

<4 = 90 degrees (Vertically opposite angles)

<5 = 38 degrees  (Vertically opposite angles)

Then;

<3 = 180 - (90 + 38) - Sum of angles on a straight line

<3 = 52°

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Answer:

5x + 3y = - 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, - 5) ← 2 points on the line

m = [tex]\frac{-5-0}{0-(-3)}[/tex] = [tex]\frac{-5}{0+3}[/tex] = - [tex]\frac{5}{3}[/tex]

the line crosses the y- axis at (0, - 5 ) ⇒ c = - 5

y = - [tex]\frac{5}{3}[/tex] x - 5 ← in slope- intercept form

multiply through by 3 to clear the fraction

3y = - 5x - 15 ( add 5x to both sides )

5x + 3y = - 15 ← in standard form

Answer:

mean=5

Step-by-step explanation:

To find the mean of a set of data, we add up all the values in the set and then divide by the number of values.

Adding up the values in the set, we get:

3 + 5 + 4 + 4 + 5 + 7 + 7 = 35

There are 7 values in the set, so we divide the sum by 7 to get the mean:

mean = sum of values / number of values

mean = 35 / 7

mean = 5

Answer:

Step-by-step explanation:

1. Get mileage per gallon by dividing miles traveled by gallons used

[tex]\frac{125}{5} = 25 mpg\\[/tex]

2. Divide miles you want to travel by the mileage per gallon you got on the first step

[tex]\frac{400}{25} = 16 gallons[/tex]

Both distributions of the total cost of attendance are skewed right

The average cost of attendance is higher for private universities.

The costs of more than 75 % of the public institutions were within the costs of the lowest 25% of private institutions.

Both the range and IQR was higher for private universities

Both distributions have outliers.

A boxplot is a standardized way of displaying the distribution of data based on a five number summary (“minimum”, first quartile [Q1], median, third quartile [Q3] and “maximum”).

It can tell you about your outliers and what their values are

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Answer:

skewed right private 75 private do have outliers

Step-by-step explanation:

The exponential function represented by the given graph is:

y = 2(.5^x)

Here we have an exponential decay, the general form of these functions is:

y = A*(b)^x

Where A is the initial value and b is the base, and it is a decay if 0 < b < 1.

Now let's look at the y-intercept, we can see that it is y = 2, then:

2 = A*(b)^0

2 = A

The function is of the form:

y = 2*(b)^x   with 0 < b < 1.

The option that meets these conditions is the first one: y = 2(.5^x)

So that is the correct option.

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[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(x-7)=2\implies 5^{\log_5(x-7)}=5^2\implies x-7=5^2 \\\\\\ x-7=25\implies x=32[/tex]

The coordinates of vertex B' are (76, -86).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 9 centered at the point D (-5, 5) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate B, we have;

Coordinate B = (4, -4)  →  (9(4 - (-5)) + (-5), 9(-4 - 5) + (-5))

Coordinate B = (4, -4)  →  (9(9) - 5, 9(-9) - 5)

Coordinate B = (4, -4)  →  (81 - 5, -81 - 5)

Coordinate B' = (76, -86).

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Complete Question:

ΔABC with vertices at A (-1, -1). B (4,-4), and C (2, -6) is dilated by a scale factor of 9 to create ΔA'B'C'. The center of dilation is the point (5, -6).

What are the coordinates of vertex B'?

The equation that could be used to determine the amount of money the Hensing apartment complex bills in rent each month when all of their units are rented out is A. y = $(600x^2 - 180).

The Hensing apartment complex rents out each unit for $20 less monthly than the Winberg complex, so the rent for each unit is $200x - $20 = $180x.

The equation that represents this situation is: y = $(600x^2 - 180

So the answer is (A) y = $(600x^2 - 180).

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[tex]\cfrac{10}{x}=\cfrac{x}{7}\implies 70=x^2\implies \sqrt{70}=x[/tex]

The measure of the angle CAB in a right angled triangle ABC using given measurements is equal to  37°.

In the triangle ABC,

From the figure we have,

Measure of angle ABC = 90 degrees

Measure of angle ACB= 53 degrees

Sum of all the interior angles of a triangle is equal to 180 degrees .

⇒Measure of angle ABC + Measure of angle ACB + Measure of angle CAB = 180 degrees

⇒ 90° + 53° + Measure of angle CAB = 180°

⇒143° + Measure of angle CAB = 180°

⇒ Measure of angle CAB = 180° - 143°

⇒ Measure of angle CAB = 37°

Therefore, the measure of the angle CAB is equal to  37°.

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The required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.

We can use trigonometry to solve this problem. Let's call the vertical distance from the top of the slide to the bottom of the pool "h" (in feet). We can use the angle of depression (45°) to find the horizontal distance from the top of the slide to the bottom of the pool. Since the slide has a constant slope, the angle between the slide and the ground is also 45°. It implies that the vertical height is equal to the horizontal projection of the slide.

Apply Pythagorean theorem,
45² = h² + h²
h = 45/√2
h = 31.8

Now, as mentioned that depth of the pool is 12 feet so, the total vertical height is given as,
= h + 12
= 31.8 + 12
= 43.8 feet

Thus, the required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.

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Answer:

32

Step-by-step explanation:

in the word problem “256 chairs in the cafeteria. this is 8 times the chairs in the library.” Which means 8 times the number of chairs in the library equals the number of chairs in the cafeteria.

L = library

8 x L = 256

to find L divided 256 by 8

256/8 = 32

L = 32

Check the answer

8 x 32 = 256

The total weight of all the cantaloupes that weigh more than 2 1 / 2 pounds is 8 2 / 4 lb ​.

As shown on the line plot, the number of cantaloupes with a higher mass than 2 1 / 2 pounds are those which have a weight of 2 3 / 4 pounds.

There are enough of them that when they are added up, we get the sum of 8 2 / 4 lb​ as the total mass of the cantaloupes. This can also be written in decimals as 8. 5 lb.

In conclusion, option D. is correct.

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