Answer:
With monthly compounding, the bank will calculate interest on your account just once per month. It will not update your balance on a daily basis when it calculates how much interest it owes you. Assuming that the APR is the same, accounts with monthly compounding offer a lower APY than accounts with daily compounding.
In ABC, CT is a median. What is the measure of AB?
Fill in the blank by enter in just a number for your answer.
Answer:
AB = 102
Step-by-step explanation:
the median CT bisects the side AB at T , then
BT = AT , that is
7x + 9 = 5x + 21 ( subtract 5x from both sides )
2x + 9 = 21 ( subtract 9 from both sides )
2x = 12 ( divide both sides by 2 )
x = 6
then
AB = 5x + 21 + 7x + 9 = 12x + 30 = 12(6) + 30 = 72 + 30 = 102
The measure of AB is 102.
How to estimate the measure of AB?
The median CT bisects the side AB at T, then
BT = AT
7x + 9 = 5x + 21
subtracting 5x from both sides of the equation, we get
2x + 9 = 21
subtract 9 from both sides, and we get
2x = 12
Divide both sides by 2, we get
x = 6
then, AB = 5x + 21 + 7x + 9
AB = 12x + 30
Substituting the value of x,
12x + 30 = 12(6) + 30
= 72 + 30
AB = 102
Therefore, the measure of AB is 102.
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In 1990, the average monthly bill for cellular telephone service was $80.90. From 1990-1997, the monthly bill decreased by 8.6% per year (in other words, each year the bill is 91.4% of
what is was the previous year (Source: Statistical Abstract of the United States).
Part a: Write a formula for the average monthly cellular telephone bill in terms of the year. Let n = 1 represent 1990.
Part b: What was the average monthly bill in 1993
A)The formula for the average monthly cellular telephone bill in terms of the year will be A = 80.90(0.914)ⁿ⁻¹
B)The average monthly bill in 1993 willl be $ 61.77
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.
The formula for the average monthly cellular telephone bill in terms of the year willl be,
A=P(R/100)ⁿ
A = 80.90(0.914)ⁿ⁻¹
The average monthly bill in 1993 is found as ;
n=4 for 1993
A=P(R/100)ⁿ
A = 80.90(0.914)³⁻¹
A=$ 61.77
Hence the formula for the average monthly cellular telephone bill in terms of the year will be A = 80.90(0.914)ⁿ⁻¹ and the average monthly bill in 1993 willl be $ 61.77.
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A circle inside of a square. The square has side lengths of 5 meters.
Tariq also designs hot tubs. The diameter of the hot tub is 3 meters. What is the area of the deck that surrounds the hot tub? If necessary, round to the nearest tenth.
Answer:
the area is 25/4 π
Step-by-step explanation:
diameter is 5 m
area will be 25/4π
Answer:
17.9 m²
Step-by-step explanation:
The area of the deck is the difference between the area of the square and the area of the circular hot tub.
__
square areaThe area of the square is given by the formula ...
A = s² . . . . where s is the side length
For a side length of 5 m, the area is ...
A = (5 m)² = 25 m²
circle areaThe area of a circle is found from the formula ...
A = (π/4)d² . . . . where d is the diameter
For a diameter of 3 m, the area is ...
A = (π/4)(3 m)² = 9/4π m² ≈ 7.069 m²
deck areaThe area of the deck is the difference between the square area and the circle area:
deck area = 25 m² -7.069 m² ≈ 17.9 m²
The area of the deck surrounding the hot tub is about 17.9 m².
My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between are yellow.) If there are $89$ yellow tiles, how many gray tiles are there
Answer:
1936
Step-by-step explanation:
We can start by removing the center tile, because all four diagonals over lap on that tile. We'll add it back later. 88/4=22. which means there are 22 tiles per half, 44+1(the center tile) total tiles per side, which means there are a total of 1936 tiles.
AOPS ANSWER:
Suppose that we have a square with dimensions [tex]$e \times e$[/tex]. The diagonals each have [tex]$e$\\[/tex] tiles. If [tex]$e$\\[/tex] is even, the number of yellow tiles is [tex]$2e$[/tex], because the [tex]2[/tex] diagonals don't intersect. If [tex]$e$[/tex] is odd, then the number of yellow tiles is [tex]$e+e-1=2e-1$[/tex]. (We have to subtract [tex]1[/tex] because the center tile is counted [tex]2[/tex] times). We know that there are [tex]89[/tex] yellow tiles, which is an odd number, so [tex]$89=2e-1$[/tex]. This implies that [tex]$e = 45$[/tex]. So the dimensions of the floor are [tex]$45 \times 45$[/tex], or [tex]2025\\[/tex] square units. Since all of the other tiles are gray, there are [tex]$2025-89=\boxed{1936}$[/tex] gray tiles.
Need help (pic included)
Answer:
a = 1Step-by-step explanation:
We have the expression:
12x² + ax - 20
3x + 4 is a factor. Therefore:
12x² + ax - 20 = (3x · 4x) + ax + (4 · (-5))
12x² + ax - 20 = (3x + 4)(4x - 5)
(3x + 4)(4x - 5) = (3x)(4x) + (3x)(-5) + (4)(4x) + (4)(-5)
= 12x² - 15x + 16x - 20 = 12x² + x - 20
a = 1Other method:12x² + ax - 20 = (3x + 4)(bx + c)
12x² + ax - 20 = (3x)(bx) + (3x)(c) + (4)(bx) + (4)(c)
12x² + ax - 20 = 3bx² + 3cx + 4bx + 4c
12x² + ax - 20 = 3b² + (3c + 4b)x + 4c
therefore
3b = 12
a = 3c + 4b
4c = -20
3b = 12 ⇒ b = 4
4c = -20 ⇒ c = -5
substitute to a:
a = 3 · (-5) + 4 · 4
a = -15 + 16
a = 1Question 11 of 25
What is an equation of the line that is perpendicular to y + 1 = -3(x-5) and
passes through the point (4, -6)?
Ay-6--(x+4)
OB. y-6=3(x+4)
C. y+6=(x-4)
D. y+6=-3(x-4)
SUBMIT
Answer: y+6 = 1/3(x-4
The equation of line perpendicular to the given line and passes through the point P ( 4 , -6 ) is y + 6 = ( 1/3 ) ( x - 4 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y + 1 = -3 ( x - 5 )
So , the slope of the line is m = -3
Now , the lines are perpendicular , so the slope of the line m₂ is
m₂ = 1/3
Let the first point be P ( 4 , -6 )
And , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - ( -6 ) = ( 1/3 ) ( x - 4 )
y + 6 = ( 1/3 ) ( x - 4 )
Hence , the equation of line is y + 6 = ( 1/3 ) ( x - 4 )
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Which is equivalent to 3√8* ?
O x √8^3
O 8 ^3/x
O 8 ^x/3
O 8^3x
Answer:
O 8 ^x/3
Step-by-step explanation:
Remember that :
[tex]\sqrt[n]{x} = x^\frac{1}{n}[/tex]
………………………………
Then
[tex]\sqrt[n]{8^x} = (8^{x})^{\frac{1}{3}}[/tex]
[tex]= 8^{x\times\frac{1}{3}[/tex]
[tex]=8^{\frac{x}{3}[/tex]
Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.
x + y = 3,500
x – y = 2,342
Write [tex]\frac{1}{22}[/tex] as a decimal, Also please include the working out plus anyone that includes other examples will be given brainlest!
Thank you!
Do long division (see the attachment).
[tex]\dfrac{1}{22}=0.04545\ldots=0.0\overline{45}[/tex]
find the positive square root of 217.05 and 100.2001......with division method
The square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
How to depict the square root?It should be noted that square root is factor of a number that when multiplied by itself will give the original number.
In this case, the square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
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Jacob is calculating the amount of time it takes a rocket to get to the moon. the moon is around 239,000 miles from earth. how many hours would it take a rocket that can travel at 250 miles per minute to travel to the moon? round to the nearest hour.
Answer:
16hr
Step-by-step explanation:
distance= time x speed
250mi/min=250x60mi/hr =15000mi/hr
239000/15000≈15.9333hr
Round up to 16hr
The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2
A function assigns the values. The inverse of the function in terms of the area will be b=(a/7)-5.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is,
The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2. Write a function in terms of area to find the length of the other side.
The given is the function of the area of the trapezoid, a(b)=14 x b+5/2.
The area of a trapezoid is given as,
Area = Height × [(Sum of parallel sides)/2]
The given function can be written in terms of area as,
[tex]a = 14\times \dfrac{(b+5)}{2}\\\\\dfrac{2(a)}{14} = b+5\\\\\dfrac{2(a)}{14} -5= b\\\\\dfrac{(a)}{7} -5= b[/tex]
Hence, the inverse of the function in terms of the area will be b=(a/7)-5.
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What is the function written in vertex form? f(x) = 4(x 6)2 10 f(x) = 4(x 6)2 – 26 f(x) = 4(x 6)2 – 134 f(x) = 4(x 6)2 154
The required vertex form of the given equation is a) [tex]4(x-6)^2 +10[/tex] is correct
the function [tex]y=4x^2+24x+154[/tex] is given,
vertex form of a equation [tex]y=ax^2+bx+c[/tex] is given by [tex]y=a(x-h)^2+k[/tex].
since [tex]y=4x^2+24x+154[/tex]
Now h = - b/2a
h = -N
Now at x = 0
k = 10
vector form can be given by [tex]4(x+6)^2 +10[/tex]
The question is incomplete. The question could be:
what is the correct vertex form of equation [tex]y=4x^2+24x+154[/tex]?
a)[tex]4(x+6)^2 +10[/tex]
b)[tex]4(x-6)^2 -26[/tex]
c)[tex]4(x-6)^2 -134[/tex]
d)[tex]4(x-6)^2 +154[/tex]
Thus, the vector form of the given function is [tex]4(x+6)^2 +10[/tex]
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Find the value of x ??
A. 31
B. 5
C. 11
D. 25
Answer: 11
Step-by-step explanation:
By the trapezoid midsegment theorem, x = (9+13)/2 = 11
Polygon C and polygon D are similar. The perimeter of polygon C is 60 inches,
and the perimeter of polygon Dis 12 inches. If one side of polygon C is 4
inches, what is the length of the corresponding side in polygon D?
A. 0.3 in
OB. 20 in
OC. 4 in
OD. 16 in
k
Answer:
Using the method of ratio and proportion, we find that the length of the side of Polygon D is 0.8in.
Step-by-step explanation:
Given that Polygon C and Polygon D are similar. This means that the ratio of the length of one side of Polygon C to the length of corresponding side of Polygon D will stay same even if we change the lengths.
Perimeter of polygon C = 60in
Perimeter of polygon D = 12in
Length of side of polygon C = 4in
Let us take the number of sides of both the polygons same. Let the length of the side of polygon D x inches. Let the number of sides be n.
First equation, 4n = 60
Second equation, xn = 12
Dividing second by first
(xn) / (4n) = 12 / 60
x / 4 = 1 / 5
x = 4 / 5 = 0.8in
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Suzy invests $2,600 in an account that earns 2.3% annual interest, compounded continuously. What is the value of the account after 10 years? Round to the nearest dollar
Answer:
$3,272
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Given:
P = $2,600r = 2.3% = 0.023t = 10 yearsSubstitute the given values into the formula and solve for A:
[tex]\sf \implies A=2600e^{(0.023 \times 10)}[/tex]
[tex]\sf \implies A=2600e^{0.23}[/tex]
[tex]\implies \sf A=3272.360026...[/tex]
Therefore, the value of the account after 10 years is $3,272 to the nearest dollar.
how to solved theses question (4.2×7)-10.4÷2²+2.9×3-6 explain
Answer:
29.5
Step-by-step explanation:
Use PEDMAS
P - Paraenthesis
E -Exponents
D - Divsion
M - Multiplication
A and S - Addition and subtraction respectively.
First multiply 4.2 and 7 as they are inside the parenthesis
Then find 2² which 4
(4.2 *7) - 10.4 *2² + 2.9*3 - 6 = 29.4 - 10.4 ÷2² + 2.9*3 - 6 {Parenthesis}
= 29.4 - 10.4÷4 + 2.9*3 - 6 {Exponents}
= 29.4 - 2.6 + 2.9*3 - 6 {Division}
= 29.4 - 2.6 + 8.7 - 6 {Multiplication}
= 29.5
Does this graph show a function? Explain how you know.
Answer:
No, the graph fails the vertical line test
Step-by-step explanation:
To determine if the graph is a function, we can use the vertical line test.
Use a vertical line, if the vertical passes through two or more points, the graph is not a function
Looking at the y axis ( which is a vertical line), it passes through two points
This means the graph is not a function
No, the graph fails the vertical line test
30.
10 cm
O
7 cm
10 cm
4 cm
How many triangles are needed to draw the net of this object?
There are two triangles in the figure(triangular prism) option third is correct.
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.
The complete question is:
How many triangles are needed to draw the net of this object?
4321For the figure please refer to the attached picture.
As we can see in the figure we have given a triangular prism:
The triangular prism has two triangles.
A triangle for the base of the prism and a triangle for the top of the prism.
The lateral faces of the prism are rectangular.
Thus, there are two triangles in the figure(triangular prism) option third is correct.
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Need help simple explanation if possible
Answer: 21 sqrt(43)/43
Step-by-step explanation: The tangent identity states that tanx = sinx/cosx. Thus, we get 21/22 / sqrt(43)/22. We can simplify this to 21 sqrt(43)/43
Please mark my answer as brainliest if this helped you.
please answer I've got 10 mins
100 POINTS FOR BRAINLIEST
Determine if the two expressions are equivalent and explain your reasoning.
3(4n) + 2 + 6n and 13n + 2
Answer:
3(4n) + 2 + 6n
12n + 2 + 6n
12n + 6n + 2
18n + 2 is not equal to 13n + 2
hence both the expression are not equivalent
In one class, homework is worth 10% of the final grade, each of 3 projects is worth 20%, and a final exam is worth 30%.
(a) If a student has an 81 homework average and a 95 on the first project, what is the student's grade at this point?
(b) If the same student from part (a) gets a 72 on the second project and a 71 on the third project, what is the lowest grade the student can get on the final exam to get an 80 overall in the course?
(a) The grade at this point is_____
(Simplify your answer. Round to the nearest tenth as needed.)
(b) The lowest possible grade is____
(Simplify your answer. Round to the nearest integer as needed.)
a) At this point, the grade is 27.1
b) The lowest possible grade is 81
How to get the grades of the student?
a) At this point the student has 81 in homework and 95 on the first project.
Remember that the homework is worth 10% of the final grade, and each project is worth 20%, then at this point the final grade is:
F = 0.10*81 + 0.20*95 = 27.1
b) The student gets 72 on the second project and 71 on the third project, at this point the final grade is:
F = 27.1 + 0.20*72 + 0.20*71 = 55.7
Now the student wants to get a final grade of 80, then if we define x as the grade on the final exam (which is worth 30%) we must have that:
55.7 + 0.30*x = 80
Now we can solve this for x:
x = (80 - 55.7)/0.30 = 81
The lowest possible grade that he must get is 81.
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How tall is the tree?
5ft
35°
-20ft-
[? ]ft
Answer:
[tex]\boxed{\bf 19ft}[/tex]Step-by-step explanation:
[tex]\bf tan\:\theta =\cfrac{opp}{adj}[/tex]
[tex]\bf tan(35^o)=\cfrac{x}{20}[/tex]
[tex]\bf 20\;tan (35^o)=x[/tex]
[tex]\bf 14ft=x[/tex]
The height of the tree:-
[tex]\bf x+5ft[/tex][tex]\bf 14ft+5ft[/tex][tex]\bf 19ft[/tex]Answer:
19.00 ft to the nearest hundredth.
Step-by-step explanation:
tan 35 = h / 20
h = 20 tan 35
Now we add the man's height
Total height of the tree
= 20 tan 35 + 5
= 19.00 ft to the nearest hundredth.
Prism M and pyramid N have the same base area and the same height. Cylinder P and prism Q have the same height and the same base perimeter. Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.
The figures
and
have the same volume.
The figures Сone Z and Cylinder Y have the same volume.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
h is the height.r is the radius.Similarly, the volume of a cylinder can be calculated by using this formula:
V = πr²h
In this context, we can infer and logically deduce that Сone Z and Cylinder Y have the same volume because they both have the same base area, while the cone's height is three (3) times the height of Cylinder Y.
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Can someone answer this as soon as possible.
There are 12 ducks and 11 geese in a certain park. Find the ratio of geese to ducks.
Answer:
11:12
Step-by-step explanation:
You first have to put the number of geese to ducks in a ratio form and since 11 and 12 have no common factors one cannot reduce the ratio
solution.
5(4x + 7)-2x = ________+ 21
Answer:
18x + 14
Step-by-step explanation:
First, we need to distribute the 5:
5(4x + 7) - 2x = __ + 21
20x + 35 - 2x = __ + 21
Now, we can combine like terms:
20x + 35 - 2x = ___ + 21
18x + 35 = ___ + 21
> subtract 21 from both sides to isolate "___"
18x + 35 = __ + 21
-21 -21
18x + 14 = ___
now that we have a solution, we should check that it works:
5(4x + 7) - 2x = ____ + 21
5(4x + 7) - 2x = 18x + 14 + 21
{simplify both sides:}
20x + 35 -2x = 18x + 35
18x + 35 = 18x + 35
(TRUE)
So, we know our solution is 18x + 14
hope this helps!!
what is the length of the base? help me please thank u ;)
=============================================================
Explanation:
a = 26 and b = 26 are the congruent legs
angle C = 60 degrees is between sides 'a' and b
c = unknown base which is opposite angle C
We'll use the law of cosines to find this missing side.
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 26^2 + 26^2 - 2*26*26*cos(60)
c^2 = 676
c = sqrt(676)
c = 26
It turns out that all three sides are the same length (26), which means this isosceles triangle is really equilateral. Consequently, it means all three interior angles are 60 degrees each.
---------------
Here's another way to see why we have an equilateral triangle.
The vertex angle is 60 degrees. Let x be the measure of each base angle. Those two base angles add to the 60 degrees to get 180
x+x+60 = 180
2x+60 = 180
2x = 180-60
2x = 120
x = 120/2
x = 60
Each base angle is 60 degrees, so all three angles are 60 degrees. This points us to the triangle being equilateral and we can say all three sides are 26 units long.
If we didn't have an equilateral triangle, then we'd have no choice but to use the law of cosines mentioned earlier.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:base \:\:side = 26 \:\: units [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
As the two sides of the triangle are equal, the corresponding angles opposite to the the sides are equal as well.
[tex] \textsf{let each of those angles measure ' x ' } [/tex]
[tex]\qquad \tt \rightarrow \:x + x + 60 = 180[/tex]
[ sum of all interior angles of a triangle ]
[tex]\qquad \tt \rightarrow \:2x + 60 = 180[/tex]
[tex]\qquad \tt \rightarrow \:2x = 180 - 60[/tex]
[tex]\qquad \tt \rightarrow \:2x = 120[/tex]
[tex]\qquad \tt \rightarrow \:x = \cfrac{120}{2} [/tex]
[tex]\qquad \tt \rightarrow \:x = 60 \degree[/tex]
Therefore, all angles of the triangle are equal. that being the case we can conclude that it's an equilateral triangle.
henceforth, all its sides are equal to one another.
[tex]\qquad \tt \rightarrow \:base \: \: side = \: \: 26 \: \: units[/tex]
The formula for the surface area of a
sphere that has a radius 7 is shown in
the box below.
SA = 4tr-2
A sphere and one of its dimensions are
shown in the diagram below.
5 in.
What is the surface area, in square
inches, of the sphere?
Step-by-step explanation:
hope you can understand
WILL GIVE BRAINLIEST!!!! *20 points*
Answer:
g(-0.0001) = -9
g(0.0001) = -1
g(0) = -1
g(9) undefined
Step-by-step explanation:
g(9) undefined .because the graph have an empty circle
at (9 , 0) which means g is not defined at 9.
