Answer:
i) $500 at 5% simple interest for two years. Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years.
Interest = 530.88 - 500 = $30.88
Step-by-step explanation:
i) $500 at 5% simple interest for two years.
Initial amount, P = $ 500
Rate of interest, r = 0.05
Time in years, t = 2
Therefore Final amount A = P(1 + rt) = 500(1 + (0.05 [tex]\times[/tex] 2) ) = $550
Therefore Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years
Initial or Principal Amount, P = $500
Rate of interest, r =0.03
number of conversions, m = 12
Time in years, t = 3
Therefore final amount, [tex]A = P(1 + \frac{r}{m}) ^{mt} = 500( 1 + \frac{0.03}{12} )^{(12\times2)} = 500( 1 + \frac{0.03}{12} )^{24}[/tex] = $530.88
Therefore Interest = 530.88 - 500 = $30.88
PLEASE ANSWER
What is the slope of the graph?
Answer:
[tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Slope = [tex]\frac{4-(-1)}{3-0} =\frac{5}{3}[/tex]
Mr. Black bought 2 magazines for $9.95 each and 1 book for $14.95. If the sales tax is 6%, what is the total cost of Mr. Black's purchases?
Answer:
$36.94
Step-by-step explanation:
Okay, so. This is what we do. There is two magazines and they cost 9.95 each multiply 9.95 times 2
9.95 x 2 = 19.90
Okay, then he buys a book for 14.95 we add 19.9. and 14.95
19.90 + 14.95 = 34.85
Then we have a sales tax of 6% we would multiply 34.85 time 6%
34.85 x 6% = 2.09
Then we would add. 34.85 + 2.09
34.85 + 2.09 = 36.94
Therefore your answer is $36.94
Hope this helps!!!
The answer is $36.94. You add up the total purchases, multiply them by .06, then add that number to you total purchases.
What is the place value of the underlined number 4,382
Answer:4 is thousands place
3 is hundredths place
8 is tens place
2 is ones place
Step-by-step explanation:
The place value of the underlined number 4,382 is,
4 is thousands place
3 is hundredths place
8 is tens place
2 is ones place.
What is place value?Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.
The number 42,316 is different from 61,432 because the digits are in different positions.
here, we have,
the underlined number 4,382
so, we get the place value,
4 is thousands place
3 is hundredths place
8 is tens place
2 is ones place.
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the length of one of the diagonals of a quadrilateral is 10 cm and the particular drawn from the opposite vertices to this diagonal are the are of length 2.8 cm and 4.2 cm find the area of the quadrilateral
Answer:
Therefore the area of the quadrilateral =35 cm²
Step-by-step explanation:
Given, the length of one of diagonal of quadrilateral is 10 cm and perpendicular drawn from the opposite vertices to this diagonal are the length of 2.8 cm and 4.2 cm.
A diagonal divided a quadrilateral into two triangle.
Therefore the area of the quadrilateral
= sum of the area of the triangles
[tex]=(\frac{1}{2}\times 10\times 2.8+ \frac{1}{2}\times 10\times 4.2)[/tex]cm² [ area of a triangle[tex]= \frac{1}{2}\times base\times height[/tex]]
=35 cm²
5,-15,45,-135,? what is the next number
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by
3
gives the next term. In other words,
a
n
=
a
1
⋅
r
n
−
1
.
Geometric Sequence:
r
=
3
This is the form of a geometric sequence.
a
n
=
a
1
r
n
−
1
Substitute in the values of
a
1
=
5
and
r
=
3
.
a
n
=
(
5
)
⋅
(
3
)
n
−
1
Remove parentheses.
a
n
=
5
⋅
3
n
−
1
what is the volume of the pyramid if the height is 215 and the base is 339
Final answer:
The volume of a pyramid with a height of 215 units and a square base of 339 units on each side is calculated using the formula V = (1/3)Bh, resulting in a volume of 1,304,688.67 cubic units.
Explanation:
To find the volume of a pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. If the base is a square with each side being 339 units, then the area of the base (B) can be calculated as 339×339 square units. Given the height (h) of the pyramid is 215 units, the volume can then be calculated.
First, calculate the area of the base:
B = 339×339 = 114921 square units.
Then, use the volume formula by plugging in B and h:
V = (1/3)×114921×215 = 1,304,688.67 cubic units.
Therefore, the volume of the pyramid is 1,304,688.67 cubic units.
In 20 days Ken drove 334.9 miles. How many miles did Ken drive each day?
I
Jerry is building an indoor beach volleyball court.
He has ordered 14,000 cubic feet of sand.
The dimensions of the court will be 30 feet by 60 feet.
Jerry needs to have a 10-foot boundary around the
court for safety. Be a math detective and determine
how deep the sand will be if Jerry uses all the sand.
Answer:
The deep of the sand will be 3.5 feet
Step-by-step explanation:
step 1
Find out the area of the court plus a 10-foot boundary around the court for safety
[tex]A=(30+10+10)(60+10+10)\\A=(50)(80)\\A=4,000\ ft^2[/tex]
step 2
Find the deep of the sand
we know that
The volume of the sand is equal to
[tex]V=Ah[/tex]
where
A is the area of the base
h is the height or deep of the sand
substitute the given values
[tex]14,000=(4,000)h[/tex]
Solve for h
[tex]h=14,000/4,000=3.5\ ft[/tex]
Jerry's indoor beach volleyball court, including a 10-foot boundary, would have an area of 4,000 square feet, and with 14,000 cubic feet of sand, it would result in the sand being 3.5 feet deep.
Explanation:Since Jerry wants to build an indoor beach volleyball court with a 10-foot boundary around it and has ordered 14,000 cubic feet of sand, we need to calculate the volume of the sand to determine how deep it will be when spread evenly over the entire area, including the boundary. The dimensions of the volleyball court are 30 feet by 60 feet, and adding a 10-foot boundary around it increases each dimension by 20 feet (10 feet on each side), resulting in a total area dimension of 50 feet by 80 feet.
To calculate the depth of the sand, we first calculate the area of the court including the boundary: Area = length × width = 50 feet × 80 feet = 4,000 square feet. Next, we divide the total amount of sand by the area to find the depth: Depth = volume / area = 14,000 cubic feet / 4,000 square feet = 3.5 feet deep. Therefore, if Jerry uses all the sand, it will be 3.5 feet deep.
-5x + sy=-10
- 3x +2y=3
Solve for systems of equations substitution
The dimensions of a triangle are multiplied by 1/4.The area
of the smaller triangle can be found by multiplying the area
of the original triangle by what number?
Please help
Thank you!
Answer:
1/16
Step-by-step explanation:
Area is the product of linear dimensions.
Suppose the area of the triangle is the product of two dimensions p and q*:
A = pq
Then the smaller triangle will have an area that is ...
A = (1/4p)(1/4q) = (1/4)²pq = (1/16)pq . . . . . . 1/16 of the original area
__
If each of the linear dimensions of the triangle is multiplied by 1/4, the area will be multiplied by (1/4)² = 1/16.
_____
* No doubt, you have learned the area formula for a triangle is ...
A = (1/2)bh
In the above, we might have p=1/2b and q=h. Or, there could be some other relationship between triangle dimensions and p and q.
Evaluate the following expression.
-7+(63/9)
63 divided by 9 is 7, so -7+7 is 0
Hope this helped
Answer:
0
Step-by-step explanation:
using PEMDAS
63/9 = 7
-7 + 7 = 0
find an obtuse angle whose sine is
a) 0.25
b) 0.75
c) 0.875
d) 0.3465
Answer:
a) 165.52 degrees.
b) 131.41 degrees.
c) 118.96 degrees.
d) 159.73 degrees.
Step-by-step explanation:
The sine of an obtuse angle is positive as it is in the second quadrant.
a) Using a calculate the angle whose sine ( arcsin) is 0.25 = 14.478 degrees
so the obtuse angle = 180 - 14.478 = 165.52 degrees to nearest hundredth
b) c) and d) are calculated in the same way.
Please help me with this question im stuck on it for an hour im so confused i dont know how to do a but i can do b :)
96 m
2 m/sec²
Step-by-step explanation:
Step 1:
In a velocity and time graph , the area which is under the plotted line represents the distance traveled
In the given graph , the plotted line from t=0 to t=4 ( for the first 4 secs) is a triangle with base = 4 and height = 8
Area of this triangle is (1/2) * b * h = (1/2)* 4*8 = 16 m
Step 2 :
The plotted line from t = 4 to t = 14 is a rectangle with length equal to 10 and breadth equal to 8
Hence its area = length * breadth = 10 * 8 = 80 m
Step 3 :
Total distance traveled is 80 + 16 = 96 m
Step 4 :
In the velocity time graph , slope denotes the acceleration at any given time. Since we want the acceleration for the first 4 secs, we need to find slope of line in from t = 0 to t= 4
when t = 0, v =0 and t= 4, v = 8
Slope = 8-0/4-0 =2 m/sec²
Which products result in a difference of squares or a perfect square trinomial? Check all that apply.
(5x + 3)(5x - 3)
(7x + 4)(7x + 4)
(2x + 1)(x + 2)
(4x – 6)(x + 8)
(x – 9)(x – 9)
(-3x - 6)(-3x + 6)
Answer:
A (5x + 3)(5x – 3)
B (7x + 4)(7x + 4)
E (x – 9)(x – 9)
F (–3x – 6)(–3x + 6)
in other words, A,B,E, and F on edge-nuity. just completed with 100%
Step-by-step explanation:
Find the value of x and y. Round to the nearest hundredth (2 decimal places)
To find the values of x and y requires solving equations, refining the solution through iterative methods like the extended Newton-Raphson technique, and validating results with approximation checks.
Explanation:In answering this mathematical question, we are attempting to find specific values for the variables x and y. To solve for these variables, we employ various mathematical methods such as the Newton-Raphson technique for refinement.
Keeping the referenced data in consideration, the equations provided reveal that we manipulate these equations to gradually reach a more accurate result. For instance, taking the quadratic equation y²-0.30068y +0.022500 = 0 and using the quadratic formula y = 0.30068 ± √(0.30068)² – (4)(1)(0.022500) allows us to find the value for y, and an iterative process enhances the precision of x and y.
Remember to always retain a few extra significant figures to minimize rounding errors in the computational process. Additionally, entering our data into a calculator or a computer program will help in writing the linear equation, which needs to be rounded to an appropriate number of decimal places for accuracy. Examples mentioned illustrate evaluating the coordinates of a point, substituting values into equations, and analyzing the relation between variables through a graphical approach.
To validate our results, we compare the approximation to the actual value to ensure that our error margin is acceptable, especially when dealing with extrapolations from implicit differentiation in calculus contexts.
12 5/6x - 14x + 1/6x ?
The result of the given expression 12 5/6x - 14x + 1/6x is -x
Given the expression
12 5/6x - 14x + 1/6x
Convert the mixed fractions into improper fractions as shown:
[tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]
Collect the like terms;
[tex]= \frac{77}{6} x+\frac{1}{6}x - 14x\\= \frac{77x+x}{6} - 14x\\= \frac{78x}{6} - 14x\\= 13x - 14x\\= -x[/tex]
Hence the result of the given expression is -x
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The simplified form of the expression is -x .
Given, expression [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex] .
Expression: [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex]
Firstly solve the mixed fraction.
[tex]12\frac{5}{6} x\\= \frac{77}{6}x[/tex]
Rewriting the expression :
= [tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]
Solve the terms with common denominator.
= [tex]\frac{77+1}{6} x[/tex]
= [tex]13x[/tex]
Solve the like terms,
[tex]= 13x - 14x\\\\=- x[/tex]
Hence the simplified form of expression is -x .
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Angle x and angle y are complementary. angle x is supplementary to a 128 angle.What are the measures of angle x and angle y?
Answer:
y = 38°
Step-by-step explanation:
If Angle x and angle y are complementary, then x + y = 90°
Also, if angle x is supplementary to a 128 angle, then x + 128° = 180°.
Solving the latter equation for x, we get x = 52°.
Therefore, by the first equation, x + y = 90° becomes 52° + y = 90°, yielding
y = 38°
Answer:
[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]
[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to solve for the measures of angles x and y.}[/tex]
[tex]\textsf{First, x is supplementary to an angle that equals 128}^{\circ}.[/tex]
[tex]\Large\underline{\textsf{What are Supplementary Angles?}}[/tex]
[tex]\textsf{Supplementary angles are 2 or more angles that add up to \underline{180}}^{\circ}.[/tex]
[tex]\large\underline{\textsf{This means that;}}[/tex]
[tex]\mathtt{x+128^{\circ}=180^{\circ}.}[/tex]
[tex]\large\underline{\textsf{Subtract 128 from both sides for x:}}[/tex]
[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]
[tex]\Large\underline{\textsf{What are Complementary Angles?}}[/tex]
[tex]\textsf{Complementary angles are 2 or more angles that add up to \underline{90}}^{\circ}.[/tex]
[tex]\large\underline{\textsf{This means that;}}[/tex]
[tex]\mathtt{x+y=90^{\circ}.}[/tex]
[tex]\textsf{Because we know x, we can solve for y.}[/tex]
[tex]\large\underline{\textsf{Substitute:}}[/tex]
[tex]\mathtt{52^{\circ}+y=90^{\circ}.}[/tex]
[tex]\large\underline{\textsf{Subtract 52 from both sides for y:}}[/tex]
[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]
What's greater 3/10,1/2,2/5?
[tex]\text{Hey there!}[/tex]
[tex]\bf{What\ is\ greater: \dfrac{3}{10}, \dfrac{1}{2},\&\dfrac{2}{5}?}[/tex]
[tex]\bf{Well, let's\ turn\ our\ fractions\ into\ decimals\downarrow}[/tex]
[tex]\bullet\ \bf{\dfrac{3}{10}=0.30(also\ known\ as\ 0.3)}\\\\\bullet \ \bf{\dfrac{1}{2}=0.50(also\ known\ as\ 0.5)}\\\\\bullet \ \bf{\dfrac{2}{5}=0.40(also\ known\ as\ 0.4)}[/tex]
[tex]\bf{The\ fractions\ in\ percentages\downarrow}[/tex]
[tex]\bullet \ \mathsf{\dfrac{3}{10}=30\%}\\\\\bullet \ \mathsf{\dfrac{1}{2}=50\%}\\\\\bullet \ \mathsf{\dfrac{2}{5}=40\%}[/tex]
[tex]\text{Now that we have that out the way. Let's solve for your answer!}[/tex]
[tex]\bf{\dfrac{1}{2}}\rightarrow\dfrac{2}{5}\rightarrow\dfrac{3}{10}}}} \leftarrow( that's\ for\ GREATEST\ to\ LEAST)[/tex]
[tex]\boxed{{\bf{Answer: \dfrac{1}{2}\ would\ be\ your\ GREATEST\ or \ BIGGEST\ one}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
april bought some sports drinks and slices of pizza for her friends. She bought 3 more sports drinks than slices of pizza. If her total order was 21.25, how many sports drinks did she purchase? one slice of pizza cost 2.25 and one sport drink cost 1.25
Answer: She purchased 8 sports drinks,
Step-by-step explanation:
Let be "d" the number of sports drinks that April purchased and "p" the number of slices of pizza that April purchased.
Set up a System of equations:
[tex]\left \{ {{d=p+3} \atop {2.25p+1.25d=21.25}} \right.[/tex]
In order to solve the System of equations you can use the Substitution Method:
1. Solve for "p" from the first equation:
[tex]d=p+3\\\\p=d-3[/tex]
2. Substitute it into the second equation:
[tex]2.25(d-3)+1.25d=21.25[/tex]
3. Finally, you must solve for "d" in order to find its value. You get that this is:
[tex]2.25(d-3)+1.25d=21.25\\\\2.25d-6.75+1.25d=21.25\\\\3.5d=21.25+6.75\\\\d=\frac{28}{3.5} \\\\d=8[/tex]
Answer:
Step-by-step explanation:
8 sport drinks
You are selling lemonade for $1.50,a bag of kettle corn for $3, and a hot dog for $2.50 at a fair.write and simplify an expression for the amount of money you receive when p people but one of each item.
Answer:
$7
Step-by-step explanation:$1.50 + $2.50 will equal to $4. $4 added with$3 would be $7. There's your answer
rationalize √3+√2/√3-√2
Answer:
5 + 2[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Multiply top and bottom by sqrt(3) + sqrt(2)
Top = (sqrt (3) + sqrt(2)) * (sqrt(3) + sqrt(2))
Top = 3 + sqrt(6) + sqrt(6) + 2
Top = 5 + 2sqrt(6)
Bottom = (sqrt (3) - sqrt(2)) * (sqrt(3) + sqrt(2))
Bottom = (3 - sqrt(6) + sqrt(6) - 2)
Bottom = 1
So, the answer is 5 + 2[tex]\sqrt{6\\}[/tex]
Answer: 5+2√6
Step-by-step explanation: attachment
The equation of a straight line graph is y = 12 - 0.5x find the coordinates of the intercept on the y axis
Yo sup??
Equation of the given line is
y=12 - 0.5x
on the y axis the x coordinate will be , therefore at x=0 we get
y=12 - 0.5*0
y=12
Therefore the coordinates of the y intercept are (0,12).
Hope this helps.
Final answer:
The y-intercept for the equation y = 12 - 0.5x is found by setting x to 0, resulting in y = 12, giving us the coordinates of the y-intercept as (0, 12).
Explanation:
The equation of a straight line is given by y = mx + b, where m represents the slope of the line, and b is the y-intercept. In your case, the equation is y = 12 - 0.5x. To find the coordinates of the intercept on the y-axis, we set x to 0 and solve for y. This gives us the y-intercept directly from the equation without needing to graph it.
For the equation y = 12 - 0.5x, when x = 0:
y = 12 - 0.5(0)
y = 12 - 0
y = 12
Therefore, the coordinates of the intercept on the y-axis are (0, 12).
1.1. Which statement explains why the two systems of equations below have the
same solution?
16x + 8y = -10
12x - 5y = 12
s 8x + 3y = 2
1 12x +16y = - 20
help!!
Answer:
This is Equivalence system of equations. The first equation in B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2
The organic garden at a restaurant is rectangular in shape and has a perimeter of 84 feet. If the length l
l
of the garden is 24 feet longer than the width w
w
of the garden, what is the area of the garden, in square feet?
Answer:
Area of the garden is [tex]306feet^2[/tex]
Step-by-step explanation:
Given:
Perimeter of the garden=84 feet
Let the width of the garden be 'W'
Length of the garden is 24 feet longer than the width of it
so, length of the garden= W+24 feet
To find the width 'W'
Perimeter of a rectangle= 2(Length+Width)
[tex]84 =2(W+24+W)\\ 84 =4W+48\\ 84-48=4W\\ 4W=36\\ W=9[/tex] feet
Width=9 feet
Length=W+24= 9+24= 34 feet
Area of the garden= Length*width
[tex]=34*9\\ =306 feet^2[/tex]
Area of the garden is 306 square feet
10. A cube has surface area 6534 square feet.
What is its volume?
Answer:
Step-by-step explanation:
[tex]6a^{2}=6534\\\\a^{2}=\frac{6534}{6}\\=1089\\\\a=\sqrt{1089}\\\\ a=33ft\\\\volume=a^{3}\\\\=33*33*33\\\\=35937[/tex]
To find the volume of a cube with a given surface area, we can use the formula for surface area and rearrange it to find the side length. Once we have the side length, we can calculate the volume of the cube.
Explanation:To find the volume of a cube, we need to determine the length of one side. Since a cube has 6 equal sides, we can calculate the length of each side using the formula for surface area: surface area = 6 * side length * side length. Let's rearrange the formula to find the side length: side length = sqrt(surface area / 6). Once we have the side length, we can calculate the volume using the formula: volume = side length * side length * side length. Plugging in the given surface area of 6534 square feet, we find that the volume of the cube is approximately 2314 cubic feet.
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What is the value of the expression when n = 3?
StartFraction 6 (n squared plus 2) Over n EndFraction
The value of expression when n = 3 is 22
Solution:
Given expression is:
[tex]\frac{6(n^2 + 2)}{n}[/tex]
We have to find the value of expression when n = 3
Substitute n = 3 in given expression
[tex]\rightarrow \frac{6(3^2 + 2)}{3}\\\\Simplify\ the\ above\ expression\\\\\rightarrow \frac{6(9+2)}{3}\\\\Solve\ the\ terms\ inside\ the\ bracket\\\\\rightarrow \frac{6(11)}{3}\\\\Divide\ 6\ by\ 3 \\\\\rightarrow 2 \times 11 = 22[/tex]
Thus the value of expression when n = 3 is 22
Answer:
22
Step-by-step explanation:
Write the polynomial in factored form.
p(x) = (x + 5)(x - 1 )(x +
Answer: 4)
Step-by-step explanation:
Answer:
1st one is 3, 2nd is 4
Step-by-step explanation:
are the two expressions equivalent when x=2 7^2+4x 4x+(7×7)
Answer:
[tex]Give\ Two\ expressions\ are\ equivalent.[/tex]
Step-by-step explanation:
[tex]First\ expression=7^2+4x\\\\At\ x=2,\ value\ of\ first\ expression=7^2+4\times 2=49+8=57\\\\Second\ expression=4x+(7\times 7)\\\\Second\ expression=4x+7^2\ \ \ \ \ \ \ \ \ \ \ as\ m\times m=m^2\\\\Second\ expression=7^2+4x\ \ \ \ \ \ \ \ using\ commutative\ property\ of\ addition\\\\At\ x=2,\ value\ of\ second\ expression=7^2+4\times 2=49+8=57\\\\Hence\ these\ two\ expressions\ are\ equivalent.[/tex]
Hey guys i need help please its slope and im struggling
Answer:
Slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].
Step-by-step explanation:
The slope of the line can be determined by simplifying the given equation to its standard form.
In the standard form, y = mx + c, m represents the slope of the line.
We are given: [tex]$ y - 2 = - \frac{2}{3}(x + 1) $[/tex]
[tex]$ \implies y = -\frac{2}{3}x - \frac{2}{3} + 2 $[/tex]
[tex]$ \implies y = - \frac{2}{3}x + \frac{(-2 + 6)}{3} $[/tex]
[tex]$ \implies y = -\frac{2}{3}x + \frac{4}{3} $[/tex]
Comparing it with the standard equation, we can see that the slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].
Hence, the answer.
1. X-2y7-8
xty2 1
X-2y>-8
X+y>1
Answer:
x+y>1
Step-by-step explanation: