The amount of each deposit is $210000
What is compound interest?Compound interest is when you reinvest your income. Compound interest distinctively means "interest on interest" and is the reason so many investors are so successful.
The computation of the each deposit is shown below:
Given that
Future value be $70,000
Time period = 10 × 2 = 20
And, the rate = 9% ÷ 2 = 4.5%
Now the formula is as follows
= (Future value × rate of interest) ÷ (1 + rate of interest)^time period - 1
= ($70,000 × 4.5) ÷ (1 + 0.025)²⁰⁻¹
= $315,000 ÷ 1.5
= $210000
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Prism pen , Base som 3cm) bom 8cm 2cm 7 cm height=8m 7 find volume
We can put the 5-sided face downwards so that we have a pentagon-prism.
The volume of the figure will be area of base (area of pentagon) x height.
This way, the height of the figure will be 8 cm and we will find the area of the pentagon, below.
Let's find the area of the base first:
The pentagonal base can be broken down into a square (top left), a triangle (top right), and a rectangle (bottom). We find each of the areas.
• Area of Square
Side lengths are 3 cm, so the area will be:
Area = 3 x 3 = 9
• Area of Triangle
Base is 3 cm and height is 4 cm, so the area will be:
Area = (1/2) * base * height
Area = (1/2) * 3 * 4 = 6
• Area of Rectangle
Base is 7 cm and height is 2 cm, so the area will be:
Area = 7 x 2 = 14
Total Area of Pentagon = 9 + 6 + 14 = 29
Now, the Volume of the Composite Figure is:
Volume = Area of Pentagonal Base * Height
Volume = 29 * 8
Volume = 232 cubic centimeters
AnswerVolume = 232 cubic centimeters
How many lines of symmetry are there in the object pictured below?Simple answer please
just the red one, because if we reflect the triangle by the yellow line we won't get the same the same position of triangle
Use a calculator to estimate the value of the following. Round to the nearest ten-thousandth.sin 84.1°
Given
[tex]\sin 84.1^o[/tex]Calculating,
[tex]\sin 84.1^o=0.9947[/tex]Rounding off to ten-thousands place,
[tex]\sin 84.1^o=0.995[/tex]The answer is 0.995
Please help me with this, it'll clear up this test I'm about to take today.
When you're graphing a function, and its inverse, there is a table where you list the x and y factors. I know how you're supposed to solve for the y coordinate, by plugging in the x factor into the function and solving it for y. However, how do you know what your x factors are going to be?
Step-by-step explanation:
We want to identify how to determine the x-factors for the graph of a function.
On some occasions, the x values for the function will be provided for you to solve for the y values. but on other occasions, the x values are not provided and you have to decide them yourself.
For a linear function, most times, you can pick values within any range of values, e.g from 0 to 5, or 2, 4, 6, 8, 10. Since it is a linear function, it will eventually result in a straight line that contains all other points.
For a quadratic function, the best practice is to pick points around the vertex of the function. The vertex of a function is either the minimum or maximum point of the function.
For example, if the vertex of a quadratic function is (4, 10), the x-coordinate of the vertex is 4. To pick your points, pick points that are some values below 4 and some values above 4, like 2, 3, 4, 5, 6 or 0, 2, 4, 6, 8 That way, you get points that are on either side of the vertex and that will make your plot easier.
Hope that helps!
A computer software retailer used a markup rate of 70%. Find the selling price of a computer game that cost the retailer $25.
Answer:
$42.50
Explanation:
Cost of the game = $25
The markup rate = 70%
Therefore, the selling price will be:
[tex]\begin{gathered} =25+(70\%\text{ of 25)} \\ =25+(0.7\times25) \\ =25+17.5 \\ =42.50 \end{gathered}[/tex]The selling price of the computer game is $42.50.
Solve (1/2 - 1/5) / 2/3 Simplify if necessary.
The Simplification of the fractional expression (1/2 - 1/5) / 2/3 is 9/20
How to simplify fraction?A fraction is a number which consists of a numerator and a denominator.
A numerator is the top or upper value of a fraction while a denominator is the bottom or lower value of a fraction.
(1/2 - 1/5) / 2/3
= (5-2) / 10 ÷ 2/3
= 3/10 ÷ 2/3
multiply by the reciprocal of 2/3= 3/10 × 3/2
= (3 × 3) / (10 × 2)
= 9/20
In conclusion, (1/2 - 1/5) / 2/3 when simplified is given by 9/20
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Which of the h values are solutions to the following equations? h^2=0.36
to solve this, you need to isolate x,
Step 1
square root in both sides
[tex]\begin{gathered} h^2=0.36 \\ \sqrt{h^2}=\sqrt{0.36} \\ \text{the }\sqrt{\square}\text{ eliminates the square} \\ h=\pm\sqrt{0.36} \end{gathered}[/tex]so, there are two values for h that fit this equation
[tex]\begin{gathered} +\sqrt{0.36\text{ }}=0.6 \\ \text{and} \\ -\sqrt{0.36}=-0.6 \end{gathered}[/tex]so, the answers are A and B
What is the point slope form of the line with slope -1/4 that passes through the
point (9, 2)?
Answer:
[tex]y - 2 = - \frac{1}{4} (x - 9)[/tex]
What’s is the probability of spinning a 4 on the spinner below
The probability of spinning a 4 on the spinner is 1/12.
Given, a spinner having two numbers 4 & 9
the sector having number 9 has an angle of 30°.
We have to find the probability of spinning a 4 on the spinner
So, the probability of spinning a 4 is,
Probability = (Area of sector having number 4)/(Area of the circle)
Probability = (30°/360°×π×r²)/(π×r²)
Probability = 1/12
Hence, the probability of spinning a 4 on the spinner is 1/12.
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Someone please help me
Answer:
3. Texas (1), timeline (2), tryouts (3), two-step (4)
4. wail (1), waved (2), wriggled (3), write (4)
Step-by-step explanation:
3. All start with T
go onto the next letter
Texas
Two-step
Tryout
Timeline
Therefore,
Texas (1)
Timeline(2)
Tryout(3)
two-step (4)
4. Same process as before, we are going to the third letters for wail and waved, the fourth letter for wiggled and write.
Wriggled
Write
Wail
Waved
g comes before t
i comes before v
Therefore,
wail (1)
waved (2)
wriggled(3)
write(4)
Whats is the first step in solving the equation 2y-11=25?
The first step in solving the equation is adding 11 to both sides, as follows:
[tex]2y-11+11=25+11\Rightarrow2y=36[/tex]In this way, we can start solving the equation for y.
Therefore, the correct option is B: add 11 to both sides.
(This is called Addition Property of Equality: adding the same number to both sides in any equation.)
3. Shown above is the graph for which of the following equations?
O A. y=-x-3
O B.y=x+3
O C. y=x-3
O D.y=3-x
Using the equation of slope intercept form, the equation of the given graph is y=x-3.
In the given question we have to find equation of the given graph.
From the given graph the points are (3,0) and (0,-3).
We know the standrd equation of the line is y=mx+c
where m=slope and c=value of y at the y intercept form.
So the value of c= -3
Now finding the value of m.
m={y(2)-y(1)}/{x(2)-x(1)}
From the points, x(1)=3, x(2)=0, y(1)=0, y(2)= -3
Putting the value
m=(-3-0)/(0-3)
m=-3/-3
m=1
Now putting the value of m and c in the equation
y=mx+c
y=1*x+(-3)
y=x-3
Hence, the equation of the given graph is y=x-3.
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The student council sold two types of ice cream, sundaes and cones, during homecoming week. Each sundaes cost the same amount, and each cones cost the same amount.
One the first day they earned $210 for selling 125 cones and 10 sundaes
One the second day they earned $256 for selling 100 cones and 30 sundaes.
What was the cost in dollars for each cone sold by the student council?
Answer:
1 cone = $1.36
Step-by-step explanation:
125 c + 10 s = $210
100 c + 30 s = $256
make one of the terms the same (easier one = 30 sundaes)
125 × 3 = 375 c
10 × 3 = 30 s
210 × 3 = $630
375 c + 30 s = $630
375 c + 30 s = $630
100 c + 30 s = $256
same sign = subtract
375 - 100 = 275 c
30 - 30 = 0 s
630 - 256 = $374
275 c = $374
÷ 275 on both sides to get c
c = $1.36
write an expression for the perimeter of the bedroom shown below
In this case, we'll have to carry out several steps to find the solution.
Step 01:
perimeter = ?
x + 4 = width
2x - 3 = length
Step 02:
perimeter = 2* width + 2*lenght
perimeter = 2 * (x + 4) + 2 * (2x -3)
= 2x + 8 + 4x - 6
= 6x + 2
The answer is:
The perimeter of the bedroom is 6x - 2
Let A={1,2,3,4,5,6} and B={4,6,8}. Which of the following is an element of A∩B?Select the correct answer below:3682
Given the following set:
A = {1,2,3,4,5,6}
B = {4,6,8}
∩ means "intersection" of two sets. In other words, the data that the two sets have in common.
Checking the given sets,
A = {1,2,3,4,5,6}
B = {4,6,8}
A∩B or A and B have a common data of 4 and 6. These two are the intersections of A and B.
Among the given choices, only Choice B is correct which is 6.
Therefore, the answer is CHOICE B : 6
Expand
& simplify
4(b + 4) + 5(b-6)
Answer:
9b - 14
Step-by-step explanation:
4(b + 4) + 5(b-6)
==> expand by distributing
4b + 16 + 5b - 30
==> simplify by combing like terms
9b - 14
Recall that:
Distributive property : a(b+c) = ab + acLike terms are terms with the same variable(usually defined by a letter) and same exponent. E.g. 4x² and 9x² are like terms because they both have a variable of x and an exponent of 2. Because they are like terms they can be combined to make 13x². This idea was used to combine (4b and 5b) and (16 and -30)Answer:
9b - 14
Step-by-step explanation:
Given expression,
→ 4(b + 4) + 5(b - 6)
Let's simplify the expression,
→ 4(b + 4) + 5(b - 6)
→ 4b + 16 + 5b - 30
→ (4b + 5b) + (16 - 30)
→ 9b + (-14)
→ 9b - 14
Hence, the answer is 9b - 14.
Is the point (-2,11) on the circle with radius 5 and center (2,13)?
From the question;
we are to determine if the point (-2, 11) is on the circle with radius 5 and center (2, 13)
The equation of a circle with a radius r and center (a, b) is given as
[tex](x-a)^2+(y-b)^2=r^2[/tex]Hence, the equation of the circle with radius 5 and center (2, 13)
[tex]\begin{gathered} (x-2)^2+(y-13)^2=5^2 \\ (x-2)^2+(y-13)^2\text{ = 25} \end{gathered}[/tex]Considering the point (-2, 11), we need to substitute the values for x and y
therefore, x = -2, y = 11
[tex]\begin{gathered} (-2-2)^2+(11-13)^2\text{ }\ne\text{ 25} \\ (-4)^2+(-2)^2\text{ }\ne\text{ 25} \\ 16\text{ + 4 }\ne\text{ 25} \\ 20\text{ }\ne\text{ 25} \end{gathered}[/tex]Since LHS is not equal to RHS then the point (-2, 11) is not on the circle.
How many units are in a hundred?
Solution
There are 100 units
[tex]100\text{ units}[/tex]Brief Explanation
[tex]\begin{gathered} 1\text{ unit}=1unit \\ \\ 1tens=10units \\ \\ 1hundred=10tens=10(10)units \\ \\ 1hundred=100units \end{gathered}[/tex]i really need help with math i am not the best at it
a Given:-
A image.
To find the total area of the given image.
So the given image is splitted into three images they are a triangle at the top and a rectangle at the middle and parallelogram at the bottom.
So the formula for triangle is,
[tex]A=\frac{1}{2}\times b\times h[/tex]So the formula for rectangle is,
[tex]A=l\times b[/tex]So the formula for parallogram is,
[tex]A=b\times h[/tex]So from the given image we have the values as,
Triangle has,
[tex]b=3,h=4[/tex]Rectangle has,
[tex]l=10,b=3[/tex]Paralleogram has,
[tex]b=5,h=2[/tex]So now we substitute the following values. so we get,
For Triangle,
[tex]\begin{gathered} A=\frac{1}{2}\times3\times4 \\ A=3\times2 \\ A=6 \end{gathered}[/tex]For Rectangle,
[tex]\begin{gathered} A=10\times3 \\ A=30 \end{gathered}[/tex]For paralleogram,
[tex]\begin{gathered} A=5\times2 \\ A=10 \end{gathered}[/tex]So the total area is,
[tex]\begin{gathered} A=6+30+10 \\ A=46 \end{gathered}[/tex]So the total area is 46 in.sq.
Part A:
Solve this equation 1/2x-7=1/3(x-12)
pls help me i will fail if i get this wrong ):
The position of museum relative to hotel will be (9,1) as the starting position will be (0,0) that is her hotel then the position of coffee shop is (-2,4) and at the end position of museum is (7,5).
What is coordinate?A set of values indicating an exact position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, and the second number represents the distance up or down. The location in the cartesian plane will be defined by the coordinate points. The distance between two points is known as the x-coordinate, or abscissa, and the distance between two points is known as the y-coordinate. To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to find the y-coordinate.
Here,
The starting coordinate=0,0
The second coordinate=-2,4
The ending coordinate=7,5
The required coordinate will be
=7--2-0,5-4-0
=9,1
The position of the museum in relation to the hotel is (9,1) because the starting point is (0,0) that is her hotel and the position of the coffee shop is (-2,4) and the position of museum is (7,5).
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Find the arc length of the semicircle.
Either enter an exact answer in terms of π or use 3.14 point, 14 for π and enter your answer as a decimal.
Answer:
28.26 units
Step-by-step explanation:
circumference equals 2r times pi. radius is 9 so the circumference is 2 x 9 x pi (which is 3.14). This would give is 56.52 but since its a half circle you divide it by two
How much money is 960 Pennie’s
Answer:
$9.60
Step-by-step explanation:
since 1 penny is 1/100th of a dollar,
you would multiply 960 by 1/100 to get the amount in dollars
[tex]960 *\frac{1}{100}[/tex] = [tex]\frac{960}{100}[/tex]
9.6
$9.60
help meeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeee pleaseeeeeee
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 + 170t+40=10\\\\16t^2 -170t-30=0\\\\t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
How many angles can you make with the angles 120, 60,40
All types of triangles must have a total angle of 220 degrees. Otherwise, it is not a triangle.
A triangle has three sides three corners and three vertices. The sum of all interior angles of a triangle is always 180°. This is called the sum property of the triangle angles. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A triangle is a three-sided polygon with three corners.
The three sides are joined end to end at points forming the corners of the triangle. The sum of the three angles of a triangle is 180 degrees. A true triangle is a shape with three sides and three angles. The sum of the two side lengths must be greater than the third side and the sum of the three angles must be 180°.
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The cost of printing the cover of the book is Rs Y. while the cost of printing a page of the book is Rs P. If the book has 45 pages and it costs Rs C to print one copy of it. Construct a formula for C in terms of P and Y
Answer:
y = 3? (A) −192 ... If P = a² + a −1 and R = −a − 1, which expression represents P + R.
Step-by-step explanation:
A rectangle has a length of 26 inches and a width of 14 inches. If 1 inch = 2.54 centimeters, find the area of the rectangle in centimeters. Round the answer to the nearest tenth.
560.4 cm2
56.4 cm2
2,348.4 cm2
924.6 cm2
PLS hurry and thank you
The area of the rectangle will be 2,348.3824 cm² as "A rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm".
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. Area is the total amount of space occupied by a flat (2-D) surface or an object's shape. On a piece of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
Here,
Length in inches=26
Width in inches=14
area in inches=26*14
=364 inch²
Now,
1 inch=2.54 cm
area in cm,
=364*2.54*2.54
=2,348.3824 cm²
Since "a rectangle has a length of 26 inches and a width of 14 inches and 1 inch=2.54 cm," the area of the rectangle will be 2,348.3824 cm².
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2. Evaluate:
Suppose you want to buy something for $60, and you have $15 saved up so far. Then your grandmother calls and says she will chip in for your purchase. She doesn’t tell you the amount of money she will give you yet, so you just consider it x dollars.
The equation will be 15+x=60 as the definition of equation says, "A mathematical statement known as an equation is made up of two expressions joined together by the equal sign(=)".
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. In mathematics, an equation is an expression or a statement that consists of two algebraic expressions that have the same value and are separated from one another by the equal symbol. It is an otherwise stated statement that has been mathematically quantified. Expressions that add up to one another make up an equation. A formula is an equation with two or more variables that shows how the variables relate to one another. A line with the equation y=mx+b, where m denotes the slope and b the y-intercept, is an example of a linear equation.
Here,
Suppose you want to buy something for $60, and you have $15 saved up so far. Then your grandmother calls and says she will chip in for your purchase. She doesn’t tell you the amount of money she will give you yet, so you just consider it x dollars.
The sum of your saving and grandmother's amount is $60.
15+x=60
According to the definition of equation, "A mathematical statement known as an equation is composed of two expressions joined together by the equal sign (=)," the equation will be 15+x=60.
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A sector has radius 12 and central angle 64°. Find the area of the sector.
We need to find the area of the sector which is given by the next formula:
Area of the sector = ( central angle / total angle ) * area of the circle
First, we need to find the area of the circle:
[tex]\begin{gathered} A_c=\pi\ast r^2 \\ Replacing \\ A_c=\left(12\right)^2\pi \\ A_c=144\pi \end{gathered}[/tex]Now, we can use the formula for the area of the sector
Central angle = 64
The total angle of a circle= 360
Area of the circle = 144π
Replacing using the formula:
Area of the sector = (64/360) * 144π
Area of the sector = 128π/5
Area of the sector = 80.42477
Determine the GCF of 6x²y - 12xy + 9x³y²
A
B 3x³y²
C
36x³y²
D
36xy
3ry
The greatest common factor(gcf) of the given expression is 3xy.
The expression is 6x²y - 12xy + 9x³y².
From all the terms we take the coefficients. 6 ,12 and 9
The GCF of these three numbers is 3 as it divides all the three numbers.
Now for the variable x. the lowest power will be the gcf. Hence the gcf will have x.
Now for the variable y. the lowest power will be the gcf. Hence the gcf will have y.
Therefore the gcf of the given expression will be 3xy .
6x²y - 12xy + 9x³y² = 3xy (2x - 4 + 3x²y)
The HCF, or highest common factor, is the largest number that divides each of the two or more numbers. HCF is also known by the titles The Greatest Common Measure (GCM) and The Greatest Common Divisor (GCD).
The smallest common multiple of any two or more numbers is found using the least common multiple, or LCM. There are two distinct methods: LCM and HCM. The HCF of two numbers is the highest factor that will exactly any divide two integers equally.
It is the most effective divisor for any pair of integers that may evenly or completely divide the inputted numbers.
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