Answer:
$63
Step-by-step explanation:
12-5=7
9*7= 63
Answer:
$63 Is the answer.
Step-by-step explanation:
$12 - $5 = $7
$7 x $9 = $63
$16,000 is deposited into a savings account with an annual interest rate of 2% compounded continuously. How much will be in the account after 4 years? Round to the nearest cent.
The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.
Understanding Compound InterestRecall the compounding formula:
A = P * [tex]e^{rt}[/tex]
Where:
A = Final amount in the account
P = Initial principal (deposit)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (as a decimal)
t = Time in years
Given:
Initial principal (P) = $16,000
Annual interest rate (r) = 2% = 0.02
time (t) = 4 years.
Substitute these values into the formula, we get:
A = $16,000 * [tex]e^{0.02 * 4}[/tex]
Using a calculator, we can calculate:
A = $16,000 * [tex]e^{0.08}[/tex]
A = $16,000 * 1.0833
A = $17,332.8
Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.
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A straight line is given as 2 x+4 -2 y-5=-3 z-6 (a) Determine the vector equation of the straight line. (b) Find the intersection point between the straight line with the plane yz
Answer:
a) r(t) = (10, 5, -5) + (5, 5, 0)*t
b) (0, -5, -5)
Step-by-step explanation:
a) 2x + 4 -2y -5 = -3z -6
2x - 2y +3z +5 =0
(10, 5, -5)
(15, 10, -5)
(5, 5, 0)
r = (10, 5, -5) + (5, 5, 0)*t
b) The yz plane is given by the equation x = 0.
x = 0 in the vector equation of a straight line if and only if t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.
NO LINKS!! URGENT HELP PLEASE!!!!
Measuring a Pond: A surveyor is measuring the width of a pond. The transit is setup at point C and forms an angle of 37° from point A to point B. The distance from point C to point A is 54 feet and the distance from point C to point B is 72 feet. How wide is the pond from point A to point B?
Answer:
43.47 feet (2 d.p.)
Step-by-step explanation:
Points A, B and C form a triangle.
We have been given sides a and b, and their included angle C.
The distance between points A and B is side c of triangle ABC.
Therefore, we can solve this problem using the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
Given values:
a = side CB = 72 ftb = side CA = 54 ftC = angle ACB = 37°Substitute the given values into the Law of Cosines formula and solve for side c:
[tex]\implies c^2=72^2+54^2-2(72)(54)\cos(37^{\circ})[/tex]
[tex]\implies c^2=8100-7776\cos(37^{\circ})[/tex]
[tex]\implies c=\sqrt{8100-7776\cos(37^{\circ})}[/tex]
[tex]\implies c=43.4719481...[/tex]
[tex]\implies c=43.47\; \sf ft\;(2\; d.p.)[/tex]
Therefore, the width of the pond from point A to point B is 43.47 feet, to two decimal places.
4. Approximate the solution to this system of equations.
y = -2x+6
y = 4x - 1
The solution of the system of linear equations, is (1.167, 3.667).
Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,
y = -2x+6............(i)
y = 4x - 1.......(ii)
Equating the equations since the LHS is same,
-2x+6 = 4x-1
6x = 7
x = 1.167
Put x = 1.16 to find the value of y,
y = 4(1.16)-1
y = 4.66-1
y = 3.667
Therefore, the solution of the system of linear equations, is (1.167, 3.667).
You can also find the solution using the graphical method,
Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]
Hence, the solution of the system of linear equations, is (1.167, 3.667).
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a girl is 12years old now.what was her age x years ago?
Find the area of this semi-circle with diameter 5cm.
Use the л (pi) button on your calculator and give your answer rounded to 2 decimal places.
No spam, please.
Answer:
Step-by-step explanation:
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The measure,
⇒∠s = 124 degree
In the given figure of kite,
PQRS,
Measure of angle p = 22 degree
And angle R is a right angle
Therefore,
∠R = 90 degree
Now we know that for a kite PQRS
Angle Q and Angle S are equal
Now consider,
Angle s is equal to x degree
Therefore,
∠S = ∠ Q = x degree
We know that,
For a kite the sum of interior angle is equal to 360 degree.
Therefore,
⇒ ∠P + ∠Q + ∠R + ∠S = 360
⇒ 22 + x + 90 + x = 360
⇒ 22 + x + 90 + x = 360
⇒ 2x = 248
⇒ x = 124 degree.
Thus,
Measure of angle s = 124 degree.
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2. Convert the following into a single log statement from the many log statements to 1.
2 Log w+ log 7-3 log x-8 log y
NOTE: You must show this in at least two steps.
1st line should be to convert the 2 the 3 and the 8 only.
2nd line can be the final answer.
A single log statement from the many log statements to 1 is: [tex]log(7wy^{(-8)}/x^3)[/tex]
The exponent that indicates the power to which a base number is raised to produce a given number are called logarithm.
Use the logarithmic identity:
log[tex](a^n)[/tex] = n*log(a)
to convert the coefficients 2, 3, and 8:
log w + log 7 - 3log x - 8log y
= log w + log 7 - log [tex]x^3[/tex] - log [tex]y^8[/tex]
Combine the terms on the right-hand side using the logarithmic identity:
log(a) + log(b) = log(ab)
log w + log 7 - log[tex]x^3[/tex] - log [tex]y^8[/tex]
= log([tex]7wy^{-8}/x^3[/tex])
Therefore, the single log statement is from the many log statements to 1 is: log[tex](7wy^{-8}/x^3)[/tex]
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Which equation is represented by the graph below?
16
&
T
&
4
Oy=e*+5
Oy=e* +4
Oy=Inx+4
2
1
-2 -1₁
7 ?
TY
1
2
3 4
The exponential function graphed in this problem is given as follows:
[tex]y = e^x[/tex]
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The graphed function has an intercept of 1, hence the parameter a is given as follows:
a = 1.
The function has the base e, hence it is given as follows:
[tex]y = e^x[/tex]
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There are 3 feet in a yard. How many centimeters are in a yard?
PLEASE HELPPP!!!!!!!!!
If tanA= 40/9 and sin B = 45/53
and angles A and B are in
Quadrant I, find the value of tan (A-B).
The value of tan (A-B) is equal to 715/2052.
To find the value of tan(A - B), we can use the trigonometric identity:
tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))
Given that tan(A) = 40/9 and sin(B) = 45/53, we can determine the values of cos(B) and tan(B) using the Pythagorean identity:
sin^2(B) + cos^2(B) = 1
cos(B) = sqrt(1 - sin^2(B))
cos(B) = sqrt(1 - (45/53)^2)
cos(B) = sqrt(1 - 2025/2809)
cos(B) = sqrt(784/2809)
cos(B) = 28/53
tan(B) = sin(B)/cos(B)
tan(B) = (45/53)/(28/53)
tan(B) = 45/28
Now we can substitute the values into the formula for tan(A - B):
tan(A - B) = (tan(A) - tan(B))/(1 + tan(A)tan(B))
tan(A - B) = (40/9 - 45/28)/(1 + (40/9)(45/28))
tan(A - B) = [(1120/252 - 405/252)] / (1 + (1800/252))
tan(A - B) = (715/252) / (2052/252)
tan(A - B) = 715/2052
Therefore, tan(A - B) is equal to 715/2052.
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The proof shows that ABCD is a square. Which of the following is the missing
reason?
E
B
AC BD
mZDEC = 90°
The missing reason in the proof is "mZDEC = 90°" or "Angle DEC is a right angle."
The missing reason in the proof is the statement "mZDEC = 90°". This statement implies that the angle DEC is a right angle, which is a crucial piece of information in proving that ABCD is a square.
In a square, all angles are right angles, so if we can establish that an angle in the figure is 90°, we can conclude that the figure is a square. In this case, the angle DEC being 90° is the key piece of evidence that supports the claim that ABCD is a square.
The statement "mZDEC = 90°" indicates that the measure of angle DEC is 90 degrees. This is significant because it confirms that one of the angles in the figure is a right angle, meeting the definition of a square.
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need help fast pls!!!
The volume of solid figure is,
⇒ V = 113 cm³
We have to given that;
A solid figure is shown with a cylinder and a cone.
Now, We know that;
Volume of cylinder = πr²h
And,
Volume of cone = πr²h / 3
Where, 'r' is radius and 'h' is height.
Here, Height of cylinder = 7 cm
And, Radius of cylinder = 4/2 = 2 cm
Hence, WE get;
Volume of cylinder = πr²h
Volume of cylinder = 3.14 x 2² x 7
Volume of cylinder = 87.9 cm³
And, Height of Cone = 6 cm
Radius of Cone = 4/2 = 2 cm
Hence, WE get;
Volume of Cone = πr²h/3
Volume of Cone = 3.14 x 2² x 6 / 3
Volume of Cone = 25.1 cm³
Thus, The volume of solid figure is,
⇒ V = 87.9 cm³ + 25.1 cm³
⇒ V = 113 cm³
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The sector of a circle has an area of 7π/5 square inches and central angle with
measure 56°.
What is the radius of the circle, in inches?
Answer:
3
Step-by-step explanation:
Area = 7pi/5
56/360 × pi r² = 7pi/5
Pi is canceled on both sides.
r² = 7/5 ÷ 56/360 = 9
r = root 9 = 3
Nadeen bought a 91-day T-bill that has an interest rate of
4.30% p.a. and a face value of $5,000.
a) How much did she pay for the T-Bill?
b) After 40 days, Barbara sold the T-bill to her friend when the interest rate for this T-bill in the market increased to 5.30% p.a. What was her selling price?
The 91-day T-bill that Nadeen bought at an interest rate of 4.30% p.a. and face value of $5,000 indicates;
a) Nadeen paid about $4,946.24 for the T-bill
b) Barbara's selling price for the T-bill is about $4,962.74
What is a T-bill?A Treasury bill (T-bill), is a short-term obligation that is issued by the U.S. Department of Treasury and which is backed by the United States government, and has a maturity of less than a year. T-bills are low risk investment as they are backed by the credit and full faith of the U.S. government.
The formula for the price of the T-bill can be calculated with the formula;
Price = Face Value/(1 + (Interest Rate × Days to Maturity/360))
Plugging in the value from the question, we get;
Price = 5000/(1 + (0.043 × 91/360)) ≈ 4946.24
Therefore, Nadeen paid $4,946.24 for the T-billb) The formula for the selling price can be presented as follows;
Selling Price = Face Value/(1 + (Interest Rate × Remaining Days to Maturity/360))
Plugging in the known values, we get;
Selling Price = 5,000/(1 + (0.053 × (91 - 40)/360)) ≈ $4,962.74
Therefore, Barbara sold the T-bill to her friend for $4,962.74
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Find the area of the shape
The area of the given figure with rectangle and triangle is 27.5 square centimeters.
The given figure has a rectangle and two triangles.
The area of the rectangle is length times width
Length = 5 cm
Width = 4 cm
Area of rectangle = 5×4
=20 square centimeters
Area of triangle =1/2 base ×height
=1/2×2.5×3
=3.75 square centimeters
As there are two triangles, 2(3.75)=7.5 square centimeters
Total area = 20+7.5
=27.5 square centimeters
Hence, the area of the given figure with rectangle and triangle is 27.5 square centimeters.
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The figure shows three tennis balls in a can with each tennis ball having a diameter of 2.5 inches. What is the total volume of the air space around the three tennis balls?
The total volume of the air space of spherical ball is A = 12.265625 inches³
Given data ,
Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.
The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.
The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.
The formula for the volume of a cylinder is:
V = πr²h
V = ( 3.14 ) ( 1.25 )² ( 7.5 )
V = 36.796875 inches³
where V is the volume, r is the radius, and h is the height.
So, the volume of the one ball is:
V₁ = ( 4/3 )π(1.25)³
V₁ = 8.177083 inches³
The total volume of three balls is = volume of 3 spherical balls
V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches
Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³
A = 12.265625 inches³
Hence , the volume of air space is A = 12.265625 inches³
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12. Sasha surveys students from her homeroom about the number of
siblings each student has. The results are 1, 0, 2, 2, 3, 0, 1, 1, 4,
and 5. What is the mode(s) of the data? (CC.6.SP.5c)
C 1
(D) 1 and 2
in
(A) 1.5
B 0 and 2
The calculated value of the mode(s) of the data is (a) 1
How to determine the mode(s) of the data?From the question, we have the following parameters that can be used in our computation:
1, 0, 2, 2, 3, 0, 1, 1, 4, and 5
By definition, the mode of a data is the data that has the highest frequency
Using the above as a guide, we have the following:
The data element 1 has the highest frequency of 3
Other data elements have lesser frequencies
Hence, the mode(s) of the data is (a) 1
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Find the area of this trapezoid. Be sure to include the correct unit in your answer.
13 in
10 in
5 in
12 in
Answer:
12
Step-by-step explanation:
206
5x10 12x13=206 it may be incorrect but i not sure if it is incorrect
What is the equation, in slope-intercept form, of the line parallel to y = 5x + 2 that passes through the point with coordinates (-2, 1)? Show your work on the scratchpad. y = C G City 2 E X
Answer:
y = 5x + 11
Step-by-step explanation:
Step 1: When two lines are parallel, they have the same slope, as indicated by the following equation as m2 = m1, where
m2 is the slope of the line you're trying to find, and m1 is the slope of the line you're given.Thus, since the slope of line 1 is 5, the slope of line 2 is also 5.
Step 2: Now we can plug in (-2, 1) for x and y and 5 for m to solve for b, the y-intercept of the other line:
1 = 5(-2) + b
1 = -10 + b
11 = b
Thus, the equation of the line parallel to y = 5x + 2 and passing through (-2, 1) is y = 5x + 11
Write the equation of the ellipse graphed below.
Answer:
(x +4)²/25 +(y -3)²/16 = 1
Step-by-step explanation:
You want the equation of the ellipse with center (-4, 3) and semi-axes 5 and 4 in the x- and y-directions, respectively.
Ellipse equationThe standard form equation for an ellipse with center (h, k) and sem-axes 'a' and 'b' in the x- and y-directions, respectively, is ...
(x -h)²/a² +(y -k)²/b² = 1
Using the given values, we find the equation to be ...
(x +4)²/25 +(y -3)²/16 = 1
__
Additional comment
The longer of the two axes is the "major" axis, and its end points are the "vertices". For the purpose of an ellipse with center, vertices, and co-vertices specified, the equation is not affected by which axis is longer.
Effectively, this is the equation of a circle with different scale factors in the x- and y-directions.
<95141404393>
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The coordinates of vertex D in the parallelogram are (-7, -10).
We have,
To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.
One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.
Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:
Find the vector representing one of the sides of the parallelogram.
We can use the vector AB.
Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)
= (6 - 8, -4 - 2)
= (-2, -6)
Add this vector to point C to find the coordinates of D.
Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)
= (-5 - 2, -4 - 6)
= (-7, -10)
Therefore,
The coordinates of vertex D are (-7, -10).
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find the equation of the line that passes through the points (-3,-7) (-3,10
The equation of the line that passes through point (-3,-7) and point (-3,10) is x = -3.
What is the equation of the line passing through the given coordinates?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the points through which the line passes: (-3,-7) and (-3,10).
The two given points (-3, -7) and (-3, 10) have the same x-coordinate -3
Hence, the two lines lie on a vertical line.
since the slope of the vertical line is undefined.
The equation of the line passing through these two points is simply the equation of the vertical line:
x = -3
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at ghs the ratio of students to teachers is about 14.5 to 1 approximately how many teachers would there be if the school had an enrollment of 205 students
Answer:
14
Step-by-step explanation:
14.5 to 1
205/14.5 = 14
Can someone answer this question
Answer:
The function is given by p(x) = x^2 - 5x^2 + x + 15. The potential rational zeros of the function are given by the factors of the constant term (15) divided by the factors of the leading coefficient (1).
So the potential rational zeros are ±1, ±3, ±5, ±15.
The list of potential rational zeros of the function includes all of the options listed except option (b) -2. Therefore, the answer is (b) -2.
Step-by-step explanation:
A designer is making a sample design that will use 3 different kinds of tiles. The designer has 9 different kinds of tiles from which to choose. How many possible combinations of tiles can the designer choose? The designer will create a sample design by placing 3 tiles side by side. How many different sample designs can the designer make from the 3 chosen tiles?
The designer can choose from 84 possible combinations of tiles, and they can create 6 different sample designs using the 3 chosen tiles when placing them side by side.
To determine the number of possible combinations of tiles that the designer can choose, we can use the concept of combinations.
Since the designer has 9 different kinds of tiles and wants to choose 3 of them, we can calculate the number of combinations using the formula for combinations, which is [tex]nCr = n! / (r! \times (n - r)!).[/tex]
Number of combinations of tiles = 9C3 [tex]= 9! / (3! \times (9 - 3)!)[/tex]
Simplifying further:
[tex]9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]
[tex]3! = 3 \times 2 \times 1[/tex]
[tex](9 - 3)! = 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1[/tex]
Plugging these values into the formula:
Number of combinations of tiles[tex]= 9 \times 8 \times 7 / (3 \times 2 \times 1 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)[/tex]
Simplifying the expression:
Number of combinations of tiles = 84
The designer can choose from 84 possible combinations of tiles, and they can create 6 different sample designs using the 3 chosen tiles when placing them side by side.
Therefore, the designer can choose from 84 possible combinations of tiles.
Now, let's calculate the number of different sample designs the designer can make using the 3 chosen tiles.
Since the tiles are placed side by side, the order of the tiles matters.
To calculate the number of different arrangements, we can use the concept of permutations.
Number of sample designs = 3!
Calculating:
[tex]3! = 3 \times 2 \times 1 = 6[/tex]
Therefore, the designer can create 6 different sample designs using the 3 chosen tiles when placing them side by side.
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Gavin is working two summer jobs making $14 per hour tutoring and $13 per hour landscaping. Last week Gavin worked a total of 10 hours and earned a total of $137. Determine the number of hours Gavin worked tutoring last week and the number of hours he worked landscaping last week.
Solving a system of equations we can see that Gavin worked 7 hours tutoring.
How to find the number of gours that Gaving worked tutoring?Let's define the variables:
x = number of hours tutoring.
y = number of hours land scaping.
We know that he worked for 10 hours and earned $137, then we can write a system of equations:
x + y = 10
14x + 13y = 137
Isolating y on the first equation we get:
y = 10 - x
Replace that in the second one to get:
14x + 13*(10 - x) = 137
14x + 130 - 13x = 137
x = 137 - 130 = 7
He worked 7 hours tutoring.
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Lyndon is making a nylon case for his new snare drum which measures 14 inches in diameter
and is 6 inches deep. If the case fits snugly around the drum, how much nylon will Lyndon
need?
572 square inches nylon will Lyndon need.
To determine how much nylon Lyndon will need to make a case for his snare drum, we need to calculate the surface area of the drum.
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2π[tex]r^2[/tex] + 2πrh
where r is the radius of the base of the cylinder and h is the height of the cylinder.
Since the diameter of the drum is 14 inches, the radius is 7 inches.
The height of the drum is 6 inches.
So, the surface area of the drum is:
Surface Area = 2π[tex](7)^2[/tex] + 2π(7)(6)
Surface Area = 2π(49) + 2π(42)
Surface Area = 98π + 84π
Surface Area = 182π
Surface Area = 182 pi
Surface Area = 182 x 22/7
Surface Area = 572 squae inches
Therefore, Lyndon will need 182π square inches of nylon to make a case for his snare drum.
This is approximately 572 square inches when rounded to the nearest hundredth.
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can u give me an answer
Answer: 0 , 5
Step-by-step explanation:
Imagine a plane taking off, first it drives to gain speed then flies, thats what you can use for coordinates.
X is the driving and Y is the flight.
The X is at 0, and the Y is at 5.
How do you write 37 million as using the power of ten exponent
37 million can be written as 3.7 × 10⁶ in the power of ten exponent notation.
In scientific notation, a number is written as the product of a coefficient and a power of ten.
To convert 37 million to scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10.
Starting with 37 million, we can move the decimal point six places to the left to obtain the number 3.7:
= 37,000,000 -> 3.7
Now, we express this number as a product of the coefficient (3.7) and 10 raised to the power of the number of places we moved the decimal point.
In this case, since we moved the decimal point six places to the left, the exponent of ten is 6:
37 million = 3.7 × 10⁶
Therefore, 37 million can be written as 3.7 × 10⁶ in the power of ten exponent notation.
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