A certain sum of money at simple interest amount to $1300 in 4 years and to $1525 in 7 years. Find the sum and the rate percent​

The coefficient of variation for the off-cuts lengths is 30.0%, which indicates a relatively high degree of variability in the data.

The coefficient of variation (CV) is a measure of relative variability, which is calculated by dividing the standard deviation by the mean, and expressing the result as a percentage. It is used to compare the variability of different datasets, particularly when they have different units or scales.

To calculate the CV for the off-cuts lengths in this problem, we first need to calculate the mean and the standard deviation. The mean is calculated by adding all the values together and dividing by the number of values:

Mean = (5.2 + 6.6 + 3.5 + 8.9 + 7.5 + 7.3) / 6 = 6.5 cm

Next, we need to calculate the standard deviation, which measures the dispersion of the data points from the mean. We can use the formula:

Standard Deviation = √(Σ(xi - x)² / (n - 1))

where xi is the value of each data point, x is the mean, and n is the number of data points.

Standard Deviation = √[(5.2 - 6.5)² + (6.6 - 6.5)² + (3.5 - 6.5)² + (8.9 - 6.5)² + (7.5 - 6.5)² + (7.3 - 6.5)²] / 5

Standard Deviation = 1.951 cm

Finally, we can calculate the coefficient of variation by dividing the standard deviation by the mean, and multiplying by 100 to express the result as a percentage:

CV = (1.951 / 6.5) x 100 = 30.0%

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Answer:

Answer = 30° , 90° , 150°

Step-by-step explanation:

Hope it helps you

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

[tex]\implies 3J + 5A = 27[/tex]

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

[tex]\implies 9J + 7A = 51[/tex]

Therefore, the system of equations is:

[tex]\begin{cases}3J+5A=27\\9J+7A=51\end{cases}[/tex]

To solve the system of equations, multiply the first equation by 3 to create a third equation:

[tex]3J \cdot 3+5A \cdot 3=27 \cdot 3[/tex]

[tex]9J+15A=81[/tex]

Subtract the second equation from the third equation to eliminate the J term.

[tex]\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}[/tex]

Solve the equation for A by dividing both sides by 8:

[tex]\dfrac{8A}{8}=\dfrac{30}{8}[/tex]

[tex]A=3.75[/tex]

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

[tex]3J+5(3.75)=27[/tex]

[tex]3J+18.75=27[/tex]

[tex]3J+18.75-18/75=27-18.75[/tex]

[tex]3J=8.25[/tex]

[tex]\dfrac{3J}{3}=\dfrac{8.25}{3}[/tex]

[tex]J=2.75[/tex]

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

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Is it probability ???

The 8th term of the geometric sequence is -4374.

Given that we need to find the 8th term of the geometric sequence with the first term 2 and common ratio -3.

So,

aₙ = a₁ rⁿ⁻¹

So,

the 8th term of the geometric sequence =

a₈ = 2 (-3)⁸⁻¹

a₈ = 2 × (-3)⁷

a₈ = 2 × (-2187)

a₈ = -4374

Hence, the 8th term of the geometric sequence is -4374.

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Answer:

1a+12

Step-by-step explanation:

The volume of a cylinder is thrice the volume of a cone with the same base and height.

The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height of the cylinder.

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.

If we take a cone with the same base and height as a cylinder, the radius of the cone's base would be equal to the radius of the cylinder's base. Therefore, we can compare the volumes of a cylinder and a cone with the same base and height as follows:

Vcylinder = πr²h

Vcone = (1/3)πr²h

Dividing the volume of the cylinder by the volume of the cone, we get:

Vcylinder / Vcone = (πr²h) / [(1/3)πr²h]

Vcylinder / Vcone = 3

So the volume of a cylinder is three times the volume of a cone with the same base and height.

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Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

The simplification of the cube root of the given expression  ∛ ( 576000 × 4 × 48 ) is equal to 480.

The expression is equal to ,

  ∛ ( 576000 × 4 × 48 )

Write all the factors of the given numbers,

576000 = 576 × 1000

⇒ 576000 = 24 × 24 × 10³

Now,

48 = 24 × 2

And 4 = 2 × 2

Simplify this expression,

Use the fact that the cube root of a product is equal to the product of the cube roots of the factors.

∛ (a × b × c) = ∛a × ∛b × ∛c

Using this property, simplify ∛(576000 × 4 × 48) as follows,

∛(576000 × 4 × 48) = ∛(576000) × ∛(4) × ∛(48)

Rewrite the given expression in the factor form,

∛ ( 576000 × 4 × 48 )

= ∛ 24 × 24 × 10³ × 2 × 2 × 2 × 24

= ∛ 24³ × 10³ × 2³

= ∛(24)³ × ∛(10)³ × ∛(2)³

= 24 × 10 × 2

= 480

Therefore, the simplification of the given expression is equal to 480.

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The above question is incomplete, the complete question is:

Simplify   ∛ ( 576000 × 4 × 48 )

The prove of the trig identity gives sin²θ + cos²θ = 1.

The proof of the trig identity is determined as follows;

Let's consider a right triangle with one acute angle θ.

Let the hypotenuse have length 1

Let the length of the adjacent side = cosθ

then, the opposite side length = sinθ

Apply Pythagorean theorem, to determine the hypotenuse side;

(sinθ)² + (cosθ)² = 1²

sin²θ + cos²θ = 1

Thus, we have proved the identity.

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Answer:( 175/6)

Step-by-step explanation: 5*35/6=175/6 sour our numerator is 175/6. So sour answer is (175/6)/35

1. <C= 90 degree

AC =  13.25 unit

<B= 60 degree

2.  <C= 90 degree

AC =  13.

<B= 60 degree

1. Using Sine law

sin C/4 = sin 30/2 = sin B/ AC

so, sin C/4 = 1/4

sin C = 1

C= 90 degree

and, <B= 180 - 30- 90= 60 degree

So, sin 30/2 = sin 60/ AC

1/4 AC = √3/2

AC = 2√3

2. Using Sine law

sin 30/ 7.65 = sin B / 15.3

1/15.3 = sin B/15.3

sin B= 1

B = 90 degree

and, <C= 180 - 90 - 30 = 60

So, 1/15.3 = sin 60/ C

C = 13.25

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Answer:  -14

Step-by-step explanation:

I hope this helps

The total cost of repainting the 4 walls and floor of the pool would be $2800

Given that;

A swimming pool is in the shape of a right rectangular prism. the pool is 40 feet long,20 feet wide and 4 feet deep the cost of repainting the pool is $2.50 per square foot.

Here, The first step is to calculate the total surface area of the pool, which includes the four walls and the floor.

The area of the floor is simply the length times the width:

Area of floor = 40 ft x 20 ft = 800 square feet

The area of each of the four walls is the height times the width:

Area of each wall = 4 ft x 20 ft = 80 square feet

Since there are four walls, the total area of the walls is:

Total area of walls = 4 x 80 sq ft = 320 square feet

To find the total surface area of the pool, we add the area of the floor to the area of the walls:

Total surface area = Area of floor + Total area of walls

Total surface area = 800 sq ft + 320 sq ft = 1120 square feet

Finally, we can calculate the total cost of repainting the pool by multiplying the total surface area by the cost per square foot:

Total cost = Total surface area x Cost per square foot

Total cost = 1120 sq ft x $2.50/sq ft

Total cost = $2800

Therefore, the total cost of repainting the 4 walls and floor of the pool would be $2800

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Applying the inscribed angle theorem, the measure of the angle is calculated: 35°.

Recall the following based on the inscribed angle theorem:

Measure of an arc = 2(measure of inscribed angle)

Also not that half of a circle is equal to 180 degrees. Therefore, we have:

Measure of arc QR = 180 - 110 = 70 degrees.

Measure of angle QRS = 1/2(measure of arc QR)

Plug in the values:

Measure of angle QRS = 1/2(70)

Measure of angle QRS = 35°

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Answer:

Putting the values of x and y in the given polynomial

[tex] = 8({1})^{2} + 6(3)(1)[/tex]

[tex] = 8(1) + 18[/tex]

[tex] = 8 + 18[/tex]

[tex] = 26[/tex]

Hence the value of polynomial is 26

The length of carbon rod is needed to obtain a resistance of 10 ohms is 0.00897 or 8.97 × 10⁻³ meters.

In Mathematics and Science, the resistance of any conductor (wire) in terms of length can be calculated by using this formula:

Length = RA/ρ

Where:

By substituting the parameters, we have:

Length = Rπr²/ρ

Length = [10 × 3.142 × (0.0001)²]/3.5 × 10⁻⁵

Length = 3.142 × 10⁻⁷/3.5 × 10⁻⁵

Length = 0.00897 or 8.97 × 10⁻³ meters.

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Complete Question:

A carbon bar of radius 0.1 mm is used to build a resistor. The resistivity of this material is 3.5 x 10-5 Ω. m. What length of carbon rod is needed to obtain a resistance of 10 ohms?

Answer: the answer is D

Step-by-step explanation:

Remember that the coordinates (3,7π6) tell us the radius r=3 and the angle θ=7π6. So the point should be on the circle labeled 3 and form an angle of 7π6 with the positive x-axis. Point D is the correct point.

To find the circumscribed side of a triangle, the steps to follow are:

1. Construct the perpendicular bisector of one of the sides of the triangle.

2. Construct the perpendicular bisector of the second side of the triangle.

3. Identify the point of intersection for the two perpendicular bisectors. This is the circumcenter of the triangle and the center of the circumscribed triangle.

4. Construct a circle that has a radius that is the length from the circumcenter to one of the vertices of the triangle.

A circumscribed triangle is one in which a circle is drawn in the center of the triangle and the circle goes round while touching only three vertices of the triangle.

To draw the circumscribed side of a triangle, you can start by constructing the perpendicular bisector of one of the sides and then the second side. Next, identify the point of intersection, and finally construct the circle.

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To center the picture both horizontally and vertically on the wall, Jon should hang it 3.75 feet from the left edge of the wall and 3 feet from the top edge of the wall.

First, we need to convert the dimensions of the picture from inches to feet Width: 54 inches = 4.5 feet and Height: 24 inches = 2 feet

To center the picture horizontally, we need to find the distance between the left edge of the wall and the left edge of the picture, and then subtract this distance from the distance between the right edge of the wall and the right edge of the picture.

The difference should be zero if the picture is centered.

Distance between left edge of wall and left edge of picture = (12 ft - 4.5 ft) / 2 = 3.75 ft

Distance between right edge of wall and right edge of picture = (12 ft - 4.5 ft) / 2 = 3.75 ft

So, the picture is centered horizontally.

To center the picture vertically, we need to find the distance between the top edge of the wall and the top edge of the picture, and then subtract this distance from the distance between the bottom edge of the wall and the bottom edge of the picture.

The difference should be zero if the picture is centered.

Distance between top edge of wall and top edge of picture = (8 ft - 2 ft) / 2 = 3 ft

Distance between bottom edge of wall and bottom edge of picture = (8 ft - 2 ft) / 2 = 3 ft

So, the picture is centered vertically.

Therefore, Jon should hang the picture 3.75 feet from the left edge of the wall and 3 feet from the top edge of the wall to center it both horizontally and vertically.

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The probability of having regular illness is (0.16) when compared to those with good sleep (0.12).

Let's calculate the probability of having regular illness given poor sleep:

P(regular illness | poor sleep) = 16% = 0.16

Now, let's calculate the probability of having regular illness given good sleep:

P(regular illness | good sleep) = 24 / (24 + 176) = 0.12

Hence, the probability of having regular illness is (0.16) when compared to those with good sleep (0.12).

This supports the doctor's claim that poor sleep increases the probability of having regular illness.

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Answer:

  £44,384

Step-by-step explanation:

Given the recurrence relation for profit is ...

you want the profit in 2021.

Using the given relations we have ...

  P[2019] = a·P[2018] +800

  29600 = a·24000 +800

  28800 = a·24000

  a = 288/240 = 1.2

Then the profit for the next two years is ...

  P[2020] = 1.2·P[2019] +800 = 1.2·29600 +800 = 36320

  P[2021] = 1.2·36320 +800 = 44384

The profit is predicted to be £44,384 in 2021.

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Answer:

A. -2.7, -9, -30, -100, ...

B. -1, 2.5, -6.25, 15.625, ...

C. 9.1, 9.2, 9.3, 9.4, ...✔️

D. 8, 0.8, 0.08, 0.008, ...✔️

E. 4, -4, -12, -20, ... ✔️

Hope you understand

Let me know if you need further explaination

Answer:

The easiest method to remember when dividing fractions is Keep Change Flip (KCF)

Step-by-step explanation:

I wrote out some examples of KCF. Once you use KCF, you just multiply the fractions normally and then don't forget to write the improper fractions (ex: 12/7) as a mixed number (1 5/7)

If you have any questions about the steps just let me know. I hope this helps ^-^

Only [tex]0.03125 ml[/tex] of the technetium-99m will be left after 24 hours.

After 6 hours, half of the original amount will decay.

After another, leaves 1/4 of the original amount.

After another, leaves 1/8 of the original amount.

After another, leaves 1/16 of the original amount.

We will below formula calculate the amount of technetium-99m left after 24 hours: N = N0 * (1/2)^(t/T)

N = 0.5 * (1/2)^(24/6)

N = 0.5 * (1/2)^4

N = 0.5 * 1/16

N = 0.03125 ml

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Answer:

[tex]\textsf{1)}\quad y = \dfrac{4}{3}x-\dfrac{13}{3}[/tex]

[tex]\textsf{2)} \quad y = \dfrac{3}{2}x-6[/tex]

Step-by-step explanation:

To find the equation of a line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1), we first need to find the slope of the line joining (1, 2) and (-2, -2).

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-2}{-2-1}=\dfrac{-4}{-3}=\dfrac{4}{3}[/tex]

Parallel lines have the same slope, so the slope of the parallel line is m = 4/3.

Substitute the found slope and point (4, 1) into the point-slope formula:

[tex]\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - 1 &= \dfrac{4}{3}(x - 4)\\\\y - 1 &= \dfrac{4}{3}x-\dfrac{16}{3}\\\\y &= \dfrac{4}{3}x-\dfrac{13}{3}\end{aligned}[/tex]

Therefore, the equation of the line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1) is:

[tex]\boxed{y = \dfrac{4}{3}x-\dfrac{13}{3}}[/tex]

[tex]\hrulefill[/tex]

To find the equation of a line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3), we first need to find the slope of the line joining (2, -3) and (-1, -1).

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-(-3)}{-1-2}=\dfrac{2}{-3}=-\dfrac{2}{3}[/tex]

The slopes of perpendicular lines are negative reciprocals, so the slope of the parallel line is m = 3/2.

Substitute the found slope and point (2, -3) into the point-slope formula:

[tex]\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - (-3) &= \dfrac{3}{2}(x - 2)\\\\y+3&= \dfrac{3}{2}x-3\\\\y &= \dfrac{3}{2}x-6\end{aligned}[/tex]

Therefore, the equation of the line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3):

[tex]\boxed{y = \dfrac{3}{2}x-6}[/tex]

Answer:

Theoretical Probability

Step-by-step explanation:

Total number of possible outcomes