The total amount accrued, principal plus interest, from simple interest on a principal of $9,100.00 at a rate of 2.5% per year for 3 years is $9,782.50.
Here, we have
Principle amount = P = £9100
interest rate = r = 2.5% per year
Time period = t = 3
Simple Interest = 9100 × 2.5% × 3 = £682.5
Total amount = Principal amount + Simple interest
= 9100 + 682.5
= £9782.5
Therefore, the total amount accrued, principal plus interest, from simple interest on a principal of £9,100.00 at a rate of 2.5% per year for 3 years is £9,782.50.
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complete question:
Colin invests £9100 into his bank account.
He receives 2.5% per year simple interest.
How much will Colin have after 3 years?
Give your answer to the nearest penny where appropriate.
4. Reyes meter family's water consumption is 117 m³. If their previous water reading was 0531, what is their present water meter reading?
5. Last month, the water meter reading of a household was 1552 m3. The following month, it was 1596 m3. If the basic charge of water consumption per cubic meter is P2.55, how much will they need to pay?
4. The present water meter reading for the Reyes family is 0648.
5. The household needs to pay P112.20 for their water consumption.
4. To find the present water meter reading for the Reyes family, we need to add their previous water reading to their water consumption.
Previous water reading: 0531
Water consumption: 117 m³
To add the two values, we can simply add the numerical part and keep the leading zeros:
0531 + 117 = 0648
Therefore, the present water meter reading for the Reyes family is 0648.
5. To calculate the amount the household needs to pay for water consumption, we need to find the difference in water meter readings and multiply it by the basic charge per cubic meter.
Previous water meter reading: 1552 m³
Present water meter reading: 1596 m³
Water consumption: 1596 - 1552 = 44 m³
Basic charge per cubic meter: P2.55
To calculate the payment, we multiply the water consumption by the basic charge per cubic meter:
Payment = 44 m³ * P2.55/m³ = P112.20
Therefore, the household needs to pay P112.20 for their water consumption.
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demarco has a piece of fabric6yd long .he uses a piece 3yd long. he cuts the rest into strips that are each3/4 yd long. how many 3/4yd long strips are there show yor work.
DeMarco can cut 4 strips of fabric, each 3/4 yd long, from the remaining fabric
DeMarco has a piece of fabric 6 yd long, and he uses a piece 3 yd long. So, the length of the fabric he has left is:
6 yd - 3 yd = 3 yd
Now, he cuts the remaining fabric into strips that are each 3/4 yd long. We need to find how many such strips he can get from the remaining 3 yd of fabric. We can set up a proportion to solve for the number of strips:
3 yd / (3/4 yd) = n
Simplifying the right-hand side:
3 yd ÷ (3/4 yd) = 3 yd × (4/3 yd) = 4 strips
So, DeMarco can cut 4 strips of fabric, each 3/4 yd long, from the remaining fabric
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parallelogram what is it
Answer:
a four-sided plane rectilinear figure with opposite sides parallel.
Step-by-step explanation:
basically take a square or rectangle and angle the interior angles of the corners acute angles.
Which of the answers choices below has the same solution set as the inequality y-8<-2
The same choice of solution as the inequality y-8≤-2 would be y - 8 + 2 ≤ -2 + 2. Option D
How do we identify the right solution for the inequality presented?we can identify the right solution for the inequality by solving each solution presented. First we solve for the inequality y-8≤-2 ⇒ y ≤ -2+8 ⇒ y≤6
a. y - 8 + 8 ≥ -2 + 8 ⇒ y ≥ 6 which is different from y ≤ 6
b. y-8 + 8 < -2 + 8 ⇒ y < 6 is different from y ≤ 6
c. y - 8 + 2 ≤ -2 + 8 ⇒ y ≤ 12 is not y ≤ 6
d. y - 8 + 2 ≤ -2 + 2 ⇒ y ≤ 6 is the same as y ≤ 6
The above answer is in response to the full question below;
Which of the answers choices below has the same solution set as the inequality y-8≤-2.
a. y - 8 + 8 ≥ -2 + 8
b. y-8 + 8 < -2 + 8
c. y - 8 + 2 ≤ -2 + 8
d. y - 8 + 2 ≤ -2 + 2
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Find the product. Show all your work.
Reduce all your answers into simplest
form.
2/3 • 5/6
Answer:
5/9
Step-by-step explanation:
Multiply the numerators 2 and 5 to get 10|
Multiply the denominators 3 and 6 to get 18
10/18 simplifies to 5/9
QUESTION 4 4.1 Translate each of the following into a mathematical equation: 4.1.1 If we multiply a number by four and then add six, the answer is 42 4.1.2 If we divide a number by three and then add seven, the answer is twenty (2) (2)
When each of the following mathematical equations are translated, the following is gotten;
4 4.1 = 4x+6
4 4.2 = X/3+ 7
How to translate the given statement into mathematical equations?To translate the given statement into mathematical equations, the following steps should be taken.
The first statement;
multiply a number by four and then add six. Let the unknown number be = X
That is ; 4(x)+6
The second statement;
divide a number by three and then add seven.
That is; X/3+ 7.
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Identify the biconditional for the following statement.
If M is the midpoint of AB¯¯¯¯¯¯¯¯ , then AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯ .
A. M is the midpoint of AB¯¯¯¯¯¯¯¯ only if AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯ .
B. AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯ only if M is the midpoint of AB¯¯¯¯¯¯¯¯ .
C. M is the midpoint of AB¯¯¯¯¯¯¯¯ if and only if AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯ .
D. If AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯ , then M is the midpoint of AB¯¯¯¯¯¯¯¯ .
Answer:
Step-by-step explanation:
The biconditional for the given statement is:
C. M is the midpoint of AB¯¯¯¯¯¯¯¯ if and only if AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯ .
In a biconditional statement, both the conditional statement and its converse are true. The statement "M is the midpoint of AB¯¯¯¯¯¯¯¯" is the condition, and "AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯" is the conclusion. The biconditional connects the condition and the conclusion, stating that they are true if and only if each other is true. Therefore, option C correctly represents the biconditional for the given statement.
The biconditional for the given statement is 'M is the midpoint of AB¯¯¯¯¯¯¯¯ if and only if AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯'.
Explanation:The biconditional for the given statement is M is the midpoint of AB¯¯¯¯¯¯¯¯ if and only if AM¯¯¯¯¯¯¯¯¯≅MB¯¯¯¯¯¯¯¯¯. This means that if M is the midpoint of line segment AB, then AM is congruent to MB, and vice versa. Both conditions must be met in order for the statement to be true. Option C correctly represents this biconditional in the answer choices.
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What is the volume of a hemisphere with a diameter of 47.7 in, rounded to the nearest tenth of a cubic inch?
The volume of a hemisphere with a diameter of 47.7 in, rounded to the nearest tenth of a cubic inch is 28413.4 in³
We are given that the diameter is 47.7 in, then the radius is half that, or 23.85in.
The volume of a sphere is V = (4/3)πr³,
the volume of this hemisphere is (2/3)πr³.
Substituting 28.6 in for r, we get ;
(2/3)(3.14)(23.85)³ in³, = 28413.4 in³
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task 7:Answer the given situation write your answer in your paper. Explain your answer.
Get a medium size chocolate box and a medium sized powdered milk carton. Which do you think has a greater volume? How will you test whick box has a greater volume?
The box or carton which would have greater volume is that which has the greater dimension.
Volume of a bodyThe volume possessed by an object would be affected by it's dimension which are the height and width of the object.
Depending on the carton of Milk or box of chocolate chosen, the one which has a greater dimension would have greater volume.
Testing for VolumeThe boxes may be filled with water. Using a measuring tool, the amount of water held by each box will be measured. The box which hold the larger amount of water would have greater volume.
Hence, either of the boxes could have greater volume depending on the dimension.
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75% to a fraction convert reduce to lowest terms
Answer:
3/4
Step-by-step explanation:
A family has two cars. During one particular week, the first car consumed 15 gallons of gas and the second consumed 25 gallons of gas. The two cars drove a combined total of 1525miles, and the sum of their fuel efficiencies was 75 miles per gallon. What were the fuel efficiencies of each of the cars that week?
The fuel efficiency of the first car is approximately 101.67 miles per gallon, and the fuel efficiency of the second car is approximately 61 miles per gallon.
Let's assume the fuel efficiency of the first car is x miles per gallon, and the fuel efficiency of the second car is y miles per gallon.
Given information:
First car consumption: 15 gallons
Second car consumption: 25 gallons
Total distance driven: 1525 miles
Sum of fuel efficiencies: 75 miles per gallon
From the given information, we can set up the following equations:
Equation 1: First car consumption = Distance driven / Fuel efficiency of the first car
15 gallons = 1525 miles / x miles per gallon
Equation 2: Second car consumption = Distance driven / Fuel efficiency of the second car
25 gallons = 1525 miles / y miles per gallon
Equation 3: Sum of fuel efficiencies
x + y = 75 miles per gallon
We can rearrange Equation 1 and Equation 2 to solve for the fuel efficiencies:
x = 1525 miles / 15 gallons
y = 1525 miles / 25 gallons
Simplifying:
x = 101.67 miles per gallon
y = 61 miles per gallon.
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Help me please and thank you..
Answer:
You will move each point of this shape 1 unit into the right. Then will move each point of this shape 2 units down. The draw line between each point.3. The table below shows the results of an experiment involving the growth of bateria. Find an equation for
the curve of best fit, then estimate the bacteria's growth after 20 minutes. Round to the nearest integer.
Time
Number of Bacteria
1
3
3
24
5
80
7
177
9
315
11
502
An equation for the curve of best fit is y = 3 - 0.5x.
The estimated bacteria's growth after 20 minutes is 876.5 bacteria.
How to determine the equation for the curve of best fit?In this scenario, the time (in minutes) would be plotted on the x-axis (x-coordinate) of the scatter plot while the number of bacteria would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the curve of best fit on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the time (in minutes) and the number of bacteria, a linear equation for the curve of best fit is given by:
y = 49.5x - 113.5
When x = 20 minutes, the bacteria's growth can be determined as follows;
y = 49.5(20) - 113.5
y = 876.5.
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can someone help me this!
Answer:
Start at 0, going right close circled.
Step-by-step explanation:
We know that we start at 0 because the inequality starts at 0. It is closed circle because it could also be equal to 0. the arrow is pointing right because it is greater or equal to 0.
Carver is trying to reproduce a scale drawing where every 3 in. will be equal to 2 feet. How long should Carver make the green line, in feet?
A triangle is drawn from 3 different colored lines. The red side length is 9 inches, the green side length is 12 inches, and the blue side length is 9 inches.
The length of the green line in Feet is 8 feet.
To find the length of the green line in feet, we need to convert the inches to feet based on the given scale.
For every 3 inches, there are 2 feet. Thus, for 12 inches (the length of the green line), we have:
12 inches * (2 feet / 3 inches) = 8 feet
Therefore, the length of the green line in feet is 8 feet.
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Solve the equations:
5_r-2)^2[tex]9x^2=36[/tex]
[tex]5(r-2)^2=35\\[/tex]
[tex]-4(k-8)^2=16[/tex]
1. The solution of 5(r-2)² = 35 is r = ±√7 + 2.
2. The solution of -4(k-8)² = 16 is k = (16 ± √(-16)) / 2.
1. 5(r-2)² = 35
First, divide both side by 5 we get
5(r-2)²/5 = 35 /5
(r-2)² = 7
Take square root on both side
r-2 = ±√7
r = ±√7 + 2
2. -4(k-8)² = 16
Divide both side by -4 we get
(k-8)² = -4
k² + 64 - 16k + 4 = 0
k² - 16k + 68 = 0
On solving the quadratic equation we get
k = (16 ± √(-16)) / 2
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how many degrees are in a rhombus
Answer:
Rhombus angles add to 360.
Angle y = 62 degrees.
Angles x and z are both 118 degrees.
Step-by-step explanation:
All the interior angles of a rhombus add up to 360°.
The opposite angles of a rhombus are equal to each other.
So angle y = 62
360-(62*2) = x+z
360-124 = x+z
236 = x+z
Angles x and z are equal to each other!
So 236/2 = 118
Angles x and z = 118
simplify
5ab7c³(4a6b²c4)
Answer:
[tex]20a^7b^9c^7[/tex]
Step-by-step explanation:
I don't have an explanation... because it's right.
PLEASE HELP I HAVE A TEST TOMORROW AND IM SO CONFUSED
The scale factor of the given diagram above would be = 4
How to calculate the scale factor?To calculate the scale factor of a given figure, the formula that should be used is given below. That is;
Scale factor = Bigger dimensions/smaller dimensions
where;
Surface area of bigger dimension = 1000 ft²
Surface area of smaller dimension = 250 ft²
Therefore scale factor = 1000/250 = 4.
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A researcher posts a newspaper advertisement offering $10 in exchange for participation in a short study. The researcher accepts the first 10
people who respond to the advertisement. Which of the following statements is true about the sample?
A. It is not a valid sample because it is only a short study.
B. It is a valid sample because money is offered to participants.
C. It is a valid sample because the first 10 people were selected to participate.
D. It is not a valid sample because it is not a random sample of the population.
The correct answer is D: It is not a valid sample because it is not a random sample of the population.
For a sample to be valid and representative of the population, it should be selected randomly. In this case, the researcher accepted the first 10 people who responded to the advertisement. This is a non-random sampling method known as convenience sampling and is prone to biases.
The other statements are incorrect:
A) The length of the study does not affect whether the sample is valid.
B) Offering compensation does not automatically make the sample valid.
C) Selecting the first 10 people does not make the sample valid - it needs to be selected randomly.
So in summary, the key issue here is that the sample was not selected randomly from the population, making it not a valid representative sample.
The equation y = –x^2 + 14x + 33 represents the vertical position, y, of a ball thrown from a 33-meter height, relative to its horizontal position, x. How high will the ball go up before it starts falling down?
The maximum height of the ball sill be82 meters.
How high will the ball go up before it starts falling down?To find this, we need to evaluate the quadratic equation in the vertex.
The vertex of:
y = ax²+ bx + c
is at x = -b/2a
So in this case:
y = -x² + 14x + 33
The vertex is at:
x = -14/2*-1 = 7
Evaluating there:
y = -7² + 14*7 + 33 = 82
The maximum height is 82 meters.
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Help as soon as possible !!!!!!!!!!!!!!!!!!!!!!!!!!!
question is in the picture
The number of bags needed to fill the cones is given as follows:
a) 32 bags.
How to obtain the volume?The volume of a cone of radius r and height h is given by the equation presented as follows:
V = πr²h/3.
The dimensions for this problem are given as follows:
r = 4 in, h = 10 in.
Hence the volume is given as follows:
V = π x 4² x 10/3
V = 167.55 cubic inches.
125 cones are needed, hence the total volume is given as follows:
125 x 165.77 = 20721.25 cubic inches.
Each bag fills 720 cubic inches of volume, hence the number of bags is given as follows:
20721.25/720 = 32 bags. (approximated).
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100 POINTS!
In the figure below, lines l and m are parallel. Suppose that m1 = 36 degrees and m2 = 45 degrees.
What are the measures of the other angles?
m3 = __
m4 = __
m5 = __
Please help. This is for a math test. Best answer gets Brainliest.
In the figure below, lines l and m are parallel. Suppose that m1 = 36 degrees and m2 = 45 degrees, then
m3 = 99°
m4 = 36°
m5 = 45°
How is this so?Note that 1, 2, and 3 are on a straight line.
since angles on a Straightline = 180°, thus,
∠3 = 180 - (45+36)
∠3 = 99
Note that angle 4 and angle 1 are corresponding angles and are thus, equal.
So
∠4 = 36°
∠5 is and alternate angle to ∠2 hence,
∠5 = 45°
Checking the sum of all three angles, we have 180 degrees, which confirms that the angels are correct since angles 3, 4 and 5 are for a triangle.
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PLEASE HELP!!! MARKING AS BRAINLIST
Answer:
0.23
Step-by-step explanation:
area of triangle = (bh)/2
= (10*24)/2= 240/2 = 120
area of circle = πr^2
= π * 13^2 = 530.92916
So 120/530.92916 = 0.22601, which rounded to the hundredth is 0.23
The graph shows the relationship between the cost of renting a bounce house and the number of hours for the rental. Which function best represents the relationship shown?
A function that best represents the relationship shown include the following: C. y = 40x + 20.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (100 - 20)/(2 - 0)
Slope (m) = 80/2
Slope (m) = 40.
At data point (0, 20) and a slope of 40, a function for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 20 = 40(x - 0)
y = 40x + 20
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square root of 64 one is 8 what is the other
Pls im struggling help me with it
Answer: 48 (degrees), b= 16.7, c = 22.4
Step-by-step explanation:
8. Look at the graph. A vertex of a rectangle ABCD is located at A(5,-3).
10
9
8
7
6
5
4
3
2
1
-10-9-8-7-6-5-4-3 -2 -1 0
-1
-2
-3
-4
-5
-6
-8
-9
-10
1
3
5 678 9 10
The vertex B is located 5 units upward from A. The vertex D is located 3 units to the
right of A. What is the area of the rectangle ABCD?
A. 15 units²
B. 16 units²
C. 6 units²
D. 14 units²
The area of the rectangle ABCD is ,
A. 15 units²
Now, For the area of the rectangle ABCD, we need to first locate the position of the other two vertices, C and D.
Since, We know that vertex B is located 5 units upward from A, so the y-coordinate of B is,
-3 + 5 = 2.
We also know that vertex D is located 3 units to the right of A, so the x-coordinate of D is,
5 + 3 = 8.
Now we can calculate the length and width of the rectangle.
The length is the distance between A and B, which is,
2 - (-3) = 5 units.
The width is the distance between A and D, which is,
8 - 5 = 3 units.
Hence, we can calculate the area of the rectangle by multiplying the length and width:
5 units x 3 units = 15 units².
Therefore, the area of the rectangle ABCD is ,
A. 15 units²
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8. Which, if any, of the points is a hole of f(x)?
Ext10
f(x)=x2+9x+18
A. A hole exists on f(x) where x = -3.
B. A hole exists on f(x) where x = 5.
C. A hole exists on f(x) where x = -6,
D. The function does not have any holes.
hholow was obtained by tran
Help finish!! ASAP THANKS! brainliest give!
Answer:
Step-by-step explanation:
Answer:
B. 70.2 mm³
Step-by-step explanation:
The solid figure shown is a triangular prism of dimensions 3 x 9.7 x 7.2
The volume of a triangular prism as shown is half the volume of a rectangular prism of the same dimensions
Volume of a rectangular prism = h x l x w
Volume of a triangular prism = h x l x w/2
where h = height of the prism
l, w are the dimensions of the base
we are given
l = 7.2 and w = 3 both in mm
We have to calculate the height
The diagonal of the prism (9.7 mm) and the length of the base(7.2 mm) form a right triangle with the height h as the other side of the triangle
We can use the Pythagorean theorem to compute h
9.7² = 7.2² + h²
h² = 9.7² - 7.2²
= 42.25 mm²
h = √42.25 = 6.5 mm
So volume of the triangular prism
= (3 x 6.5 x 7.2 )/2
= 140.4/2
= 70.2 mm³
This would be option B
