Answer:
The interest earned was $50.95
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=1\ year\\ P=\$1,000\\ r=5\%=5/100=0.05\\n=4[/tex]
substitute in the formula above
[tex]A=1,000(1+\frac{0.05}{4})^{4*1}[/tex]
[tex]A=1,000(1.0125)^{4}[/tex]
[tex]A=\$1,050.95[/tex]
Find the interest earned I
we know that
[tex]I=A-P[/tex]
substitute the values
[tex]I=\$1,050.95-\$1,000=\$50.95[/tex]
What is 20 minus 5 as distributive property
Answer:
5(4-1)
Step-by-step explanation:
5(4-1)
20-5
5x4= 20
5x1= 5
A high school drama club is putting on their annual theater production there is a maximum of 800 tickets for the show the cost of the tickets are six dollars before the day of the show and nine dollars on the day of the show to meet the expenses of the shelf book club must sell at least $5000 worth of tickets
Answer:
Step-by-step explanation:
a.) Let x be the number of tickets sold before the event and y the number of tickets sold on the day of the event. Then x + y =< 800 and 6x + 9y >= 5000. (b.) Suppose the club sold 440 tickets before the event, i.e. x = 440, maximum number of tickets remaining to be sold = 800 - 440 = 360. Maximum amount realized from the sales supposing all tickets were sold = 6(440) + 9(360) = 2640 + 3240 = $5880 which is greater than $5000. Therefore, it is possible for the club to sell enough additional tickets on the day of the show to meet the expenses of the show.
HOPE THIS HELPED ;3
Find an ordered pair ( x, y ) that is a solution to the equation. 3x+y=7
Answer:
2,1
Step-by-step explanation:
y=-3x+7
y=-3(2)+7
y=-6+7
y=1
so (2,1)
This table gives a few (z,y) pairs of a line in the coordinate plane.
-56 66
-42 58
-28 50
What is the y-intercept of the line?
Answer:
The y-intercept of the line is 34.
Step-by-step explanation:
There are few points on the z-y plane through which a straight line passes.
The points are (-56,66), (-42,58) and (-28,50).
Now, take the first two points to get the equation of the straight line.
The equation is [tex]\frac{y - 58}{58 - 66} = \frac{z - (-42)}{-42 - (- 56)}[/tex]
⇒ [tex]\frac{y - 58}{- 8} = \frac{z + 42}{14}[/tex]
⇒ 14(y - 58) = - 8(z + 42)
⇒ [tex]y - 58 = - \frac{8}{14}z - 24[/tex]
⇒ [tex]y = - \frac{8}{14}z + 34[/tex]
This equation is in slope-intercept form.
Hence, the y-intercept of the line is 34. (Answer)
please help
Simplify.
(4a5b6)4
16a9b10
256a9b10
16a20b24
256a20b24
Answer:
256a^20b^24
Step-by-step explanation:
write the equation of a line that passes through the point -5,-4 and has a slope of 1/5.
Factor the expression 3x2 + 2x - 8
Answer:
(3x − 4) (x + 2)
Step-by-step explanation:
3x² + 2x − 8
Factor using AC method.
3 × -8 = -24
Factors of -24 that add up to 2 are -4 and 6
Divide by 3 and reduce: -4/3 and 6/3 = 2/1
(3x − 4) (x + 2)
Adrian just got hired for a new job and will make $66,000 in his first year. Adrian was told that he can expect to get raises of $5,000 every year going forward. how much money in salary with Adriene make in his 26th year working at this job? round to the nearest 10th (if necessary).
Answer:
Adrian would make $196000 in his 26th year working.
Step-by-step explanation:
Adrian salary in first year = $66,000
As Adrian is expected to get raises of $5,000 every year going forward.
Here is the sequence of Adrian's raises:
5,000, 10000, 15000, 20000, 25000 .....
As the common difference between consecutive terms is constant.
d = 10000 - 5,000 = 5,000 ⇒ d = 15000 - 10000 = 5,000
So, Adrian's raises is in Arithmetic sequence.
a₁ = 5,000
n = 26
[tex]{\displaystyle \ a_{n}=a_{1}+(n-1)d}[/tex]
Put n = 26 to get the total amount of salary raises in Adrian's 26th year.
[tex]{\displaystyle \ a_{26}=5000+(26-1)5000}[/tex]
[tex]{\displaystyle \ a_{26}=5000+(25)5000}[/tex]
[tex]{\displaystyle \ a_{26}=5000+125000}[/tex]
[tex]{\displaystyle \ a_{26}=130000}[/tex]
Total raises amount after 26th year = $130000
Adding total raises after 26th year to the initial salary would let us figure out the total salary Adrian would make in his 26th year.
So,
Total Salary after 26th year = initial salary + total raises of 26 years
= 66000 + 130000
= $196000
So, Adrian would make $196000 in his 26th year working.
Keywords: arithmetic sequence, salary, raises, common difference
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Ava and Addison are saving for a new cell phone. Ava is starting at 100$ and adding 5$ each week.Addison is starting with 200$ and is adding 4$ each week. Write and solve a problem that can be used to find out after how many weeks Ava and Addison will have the same amount of money saved?
Answer:
The numbers of weeks for which both Ava and Addison have same amount of money saved is 100 weeks .
Step-by-step explanation:
Given as :
The amount of money having with Ava at starting = $100
The money that Ava is saving each week = $5
The amount of money having with Addison at starting = $200
The money that Addison is saving each week = $4
Now, Let The numbers of weeks for which both Ava and Addison have same amount of money saved = n weeks
Now, According to question
The amount of money having with Ava at starting + (The money that Ava is saving each week × numbers of weeks) = The amount of money having with Addison at starting + (The money that Addison is saving each week × numbers of weeks)
Or, $100 + $5 × n = $200 + $4 × n
Or, $5 × n - $4 × n = $200 - $100
Or, n = 100
So, The numbers of weeks for which both Ava and Addison have same amount of money saved = n = 100 weeks
Hence,The numbers of weeks for which both Ava and Addison have same amount of money saved is 100 weeks . Answer
Which are equivalent ratios to 7:13?
Answer:
14:26, 21:39, 28:52, 35:65, 42:78, 41:91
Step-by-step explanation:
All of the above are equivalent ratios. These are only a few. More can be found by just simply multiplying 7 by any amount, and 13 by any amount.
Ratios that are equivalent to 7:13 from the given options are 21:39, 28:52, and 14:26. Option A, C, D is correct.
To find equivalent ratios, we need to multiply or divide both terms of the ratio by the same non-zero number. Let's go through the options provided:
21:39 - If we divide both terms by 3, we get 7:13, which means this is an equivalent ratio.72:128 - If we divide both terms by 8, we get 9:16, which is not equivalent to 7:13.28:52 - If we divide both terms by 4, we get 7:13, which means this is an equivalent ratio.14:26 - If we divide both terms by 2, we get 7:13, which means this is an equivalent ratio.36:48 - If we divide both terms by 6, we get 6:8, which simplifies to 3:4. This is not equivalent to 7:13.Therefore, the equivalent ratios are 21:39, 28:52, and 14:26.
Hence, A. C. D is the correct option.
The complete question is:
Which are equivalent ratios to 7:13?
A) 21:39
B) 72:128
C) 28:52
D) 14:26
E) 36:48
Please please need help on these two
Answer:
( f + g ) (x) = [tex] 2 x^{2} + x - 4[/tex]
g(x) - f(x) = [tex] x^{2} - 2 x - 4[/tex]
Step-by-step explanation:
f(x) = 4 x - 4 and g(x) = [tex] 2 x^{2} - 3 x[/tex]( f + g ) (x) = f(x) + g(x)
= [tex] 4 x - 4 + 2 x^{2} - 2 x[/tex]
= [tex] 2 x^{2} + x -4[/tex]
2. g(x) = [tex] x^{2} + 1[/tex] and f(x) = 2 x + 5
g(x) - f(x) = [tex] x^{2} + 1 - (2 x + 5)[/tex]
= [tex] x^{2} + 1 - 2 x - 5[/tex]
= [tex] x^{2} - 2 x - 4[/tex]
The rectangle below has an area of 70y^8+30y^6.The width of the rectangle is equal to the greatest common monomial factor of 70y^8 and 30y^6. What is the length and width of the rectangle?
Answer:
Width [tex]10y^6[/tex] units
Length [tex]7y^2+3[/tex] units
Step-by-step explanation:
The rectangle has an area of [tex]70y^8+30y^6.[/tex]
The width of the rectangle is equal to the greatest common monomial factor of [tex]70y^8[/tex] and [tex]30y^6.[/tex] Find this monomial factor:
[tex]70y^8=2\cdot 5\cdot 7\cdot y^8\\ \\30y^6=2\cdot 3\cdot 5\cdot y^6\\ \\GCF(70y^8,30y^6)=2\cdot 5\cdot y^6=10y^6[/tex]
Hence, the width of the rectangle is [tex]10y^6[/tex] units.
The area of the rectangle can be rewritten as
[tex]10y^6(7y^2+3).[/tex]
The area of the rectangle is the product of its width by its length, then the length of the rectangle is [tex]7y^2+3[/tex] units.
Find the smaller of two consecutive integers,x, if the sum of the smaller and two times larger is 14. Write an equation and solve
Answer:
4
Step-by-step explanation:
Consecutive integers are e.g. 1, 2, 3, 4, ...
So they are 1 units apart.
If we let one of the integers be "x", then the next consecutive one would be "x + 1".
x is the smaller
x + 1 is the larger
of the two...
Now,
The sum of smaller (x) and 2 TIMES larger (x + 1) is 14, so we can write:
[tex]x+2(x+1)=14[/tex]
We use algebra and solve for x:
[tex]x+2(x+1)=14\\x+2x+2=14\\3x=14-2\\3x=12\\x=4[/tex]
So, the two numbers is 4 & 5
smaller of the two numbers is "4"
To find the smaller of two consecutive integers where the sum of the smaller and two times the larger is 14, set up the equation x + 2(x + 1) = 14 and solve for x to find that the smaller integer is 4.
Explanation:To find the smaller of two consecutive integers x, when the sum of the smaller and two times the larger is 14, we can set up a simple algebraic equation. Let x be the smaller integer; then the larger integer is x+1. The equation based on the given information is:
x + 2(x + 1) = 14
Now, let's solve for x:
x + 2x + 2 = 143x + 2 = 143x = 14 - 23x = 12x = 12 / 3x = 4Therefore, the smaller consecutive integer is 4.
plz hurry!!!! thank you!!!!
Answer:
∠A ≈ 19.47°
Step-by-step explanation:
As you know , the angle that tangent makes with the radius at the point of tangency is 90°.
∴∠OKA = 90°
As AO = 15 and OK = 5 ,
[tex]sin(A) = \frac{OK}{AO}[/tex]
[tex]sin(A) = \frac{5}{15} [/tex]
[tex]sin(A) = \frac{1}{3} [/tex]
∠A = [tex]sin^{-1} (\frac{1}{3} )[/tex]
∠A ≈ 19.47°
Answer:
[tex]\mathbf{m\angle A = sin^{-1}(\frac{1}{3}) \approx 19.47^{\circ}}[/tex]
Step-by-step explanation:
This question involves some basic knowledge of trigonometric function. The following formula only works for right angled triangles.
[tex]\mathbf{sin(x) = \frac{perpendicular}{hypotenuse}}[/tex]
In ΔAKO,
m∠AKO = 90°
Therefore ΔAKO is a right angled triangle. If we take ∠A into consideration then base will be AK, perpendicular will be OK and hypotenuse will be AO.
AO = 15
OK = 5
[tex]\therefore \mathrm{sin(\angle A) = \frac{OK}{AO} = \frac{5}{15} = \frac{1}{3}}[/tex]
[tex]\mathrm{sin(\angle A)=\frac{1}{3}}[/tex]
[tex]\mathrm{\angle A=sin^{-1}(\frac{1}{3})}[/tex]
To calculate [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] use scientific calculator
value of [tex]\mathrm{sin^{-1}(\frac{1}{3})}[/tex] is approximately equal to 19.47°
Therefore [tex]\mathbf{m\angle A \approx 19.47}[/tex]
(NOTE : When a line passing through center of a circle, is drawn to a tangent at the point of tangency then the angle made between then is 90°
Therefore m∠AKO = 90°)
Whats the Answer y=10 4x-5y=3
What is the equation of a line that passes through points (0,4) and (-4,-8)? Y=2x+4, y=2x-4, y=3x+4, y=3x-4
Answer:
(-8 - 4)/(-4 - 0) = -12/-4= 3
y - 4 = 3(x - 0)
y - 4 = 3x - 0
y = 3x + 4
the answer is c
WHO EVER CAN FIGURE THIS OUT GETS THE BRAINLIEST
(34+65)X(98-123)
Answer:
-2475
Step-by-step explanation:
Two numbers have a sum of 1,212 and a difference of 518. What are the two numbers?
Answer:
The two numbers are
518
694
Step-by-step explanation:
As per requirements the two equations will be
X+Y=1212
X-Y=518
When we subtract these equations we get
X=1212-518
X=694
Now put the X value and find the Y value in any equation
X+Y= 1212
Y=1212-X
Where X = 694
Y=1212-694
Y=518
X=694 and Y=518
Answer:
answer is 865.
Step-by-step explanation:
865+347 is 1212 an the diff is 518.
and the largest number out of 865 and 347 is 865
What is the quotient of ã and
?
What is the quotient of 3/4 and 5/6?
Answer:
9/10 ( or 0.9)
Step-by-step explanation:
quotient of 3/4 and 5/6
= 3/4 ÷ 5/6
= 3/4 x 6/5
= 18/20
= 9/10 ( or 0.9)
Answer:
9/10
Step-by-step explanation:
a line intersects the points (13,-4) and (1,12).Find the slope and simplify completely
Answer:
4/-3
Step-by-step explanation:
To find the slope
y2 - y1 / x2 - x1 =
12 - -4 16
---------- = ----
1 - 13 -12
Simplify by dividing both parts by 4
4/-3 is your slope :)
Answer:
Step-by-step explanation:
I've answered this question already.
Zolt Inc. (zolt) stock is selling for $8.22 per share with an EPS of .45 cents per share. What is Zolt's PE ratio? (Round to nearest tenth.)
rev: 09_19_2013_QC_35406
18.3
19.5
8.3
20.0
None of these
Answer:
18.3 ( when EPS is 45 cents), otherwise there is none of these
Step-by-step explanation:
PE = Current Price / EPS
current Price = $ 8.22 = 822 cents
EPS = .45 cents (?) ... is it 45 cents ?
if it is 45 cents : PE = 822 / 45 = 18.26 ≈ 18.3
The required PE ratio of the Zolt's is given as 18.3. Option A is correct.
Given that,
Zolt Inc. (zolt) stock is selling for $8.22 per share with an EPS of .45 cents per share.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
PE = Current Price: EPS
PE = Current Price / EPS
Current Price = $ 8.22 = 822 cents
EPS = 0.45 cents = 45 cents
it is 45 cents per PE
So Ratio = 822 / 45 = 18.3
Thus, the required PE ratio of the Zolt's is given as 18.3. Option A is correct.
Learn more about ratios here:
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In a grocery store’s circular, it states that plant-based meatless ground beef is on sale for $5.99/lb. If you buy a package that weighs 2.37 lbs, how much did it cost (round to the nearest cent)?
$5.99 divided by 100 = 0.0599
0.0599 x 237 = $14.19
7x(x+1.8)=0 I have tried -1.8 and 0, they did not work.
Answer:
x= -12.6/7. you may try this
Good evening ,
Answer:
The solutions of the equation 7x(x+1.8)=0 are -1.8 and 0.
Step-by-step explanation:
7×(0)×[(0)+1.8] = 0×[1.8] = 0×1.8 = 0
7×(-1.8)×[(-1.8)+1.8] = 7×(-1.8)×[0] = 7×(-1.8)×0 = 0.
:)
The Golden Years Senior Citizen Center uses a phone tree to announce when the center will be closed for poor weather. When each person receives a phone call, that person has a list of three more people to call. The function c approximates the total number of calls made after m minutes since the start of the phone tree. c(m) = 3/2 * (3 ^ (m/10) - 1) Approximately how many minutes will it take for the number of calls to reach 363?
Answer:
50 Minutes.
Step-by-step explanation:
The function c approximates the total number of calls made after m minutes since the start of the phone tree.
[tex]c(m)=\frac{2}{3}\times (3^{\frac{m}{10}}-1)[/tex]
We need to find the number of minutes after which the total number of calls will 363.
Substitute c(m)=363 in the given function.
[tex]363=\frac{2}{3}\times (3^{\frac{m}{10}}-1)[/tex]
Multiply 3/2 both sides.
[tex]363\times \frac{3}{2}=(3^{\frac{m}{10}}-1)[/tex]
[tex]242=3^{\frac{m}{10}}-1[/tex]
Add 1 on both sides.
[tex]243=3^{\frac{m}{10}}[/tex]
[tex]3^5=3^{\frac{m}{10}}[/tex]
On comparing both sides we get
[tex]5=\frac{m}{10}[/tex]
Multiply both sides by 10.
[tex]50=m[/tex]
Therefore, the total number of calls will 363 after 50 minutes since the start of the phone tree.
Answer:
50 minutes
Step-by-step explanation:
(SAT Prep) In the given figure, find x for which a ∥ b?
A. 50° B. 65° C. 75° D. 95°
Please explain your answer, and thanks in advance :)
Answer:
x= 65 degrees
Step-by-step explanation:
If the triangles vertices are marked CDE (d as the right angle and c as the leftmost vertex) then:
Alternate interior angles
⇒m∠ACE=85 degrees
m∠ACD=25 and m∠ACD+m∠DCE=m∠ACE=85 degrees
⇒ 25 + m∠DCE= 85 ⇒ m∠DCE=60 degrees
Since the sum of the angles in a triangle is 180 degrees
⇒ 60 + 90 + m∠DEC = 180 ⇒ m∠DEC= 30 degrees
Finally, since ∠BEC is supplementary to the given 85 degree angle
⇒ 30 + 85 + x = 180 ⇒ x=65
Answer:
[tex]\huge\boxed{x = 65 \ \text{degrees}}[/tex]
Step-by-step explanation:
We can use angle relationships to find the measure of [tex]x[/tex] here.
Let's assume that the triangle has the points ABC, where m∠a is the leftmost angle, m∠b is the right angle, and m∠c is the rightmost angle (I've labeled it in the attached picture).
We have to realize here that a and b are parallel lines. This means that the angles on one side will be equivalent to the other as long as the triangle in the center is symmetrical along both.
It's not. However, we can make it symmetrical by realizing that the 85° angle is the exact same as Line A AC. These are alternate interior angles, meaning their angle measurements will be the same. So Line A A C is also 85°.
Line A A C covers the area even in the triangle. Since we know the total measure and the measure outside the triangle, we can find the measure of m∠a.
[tex]25 + a = 85\\\\a = 85-25\\\\a = 60[/tex]
Now we know that m∠a is 60°. We also know that m∠b is a 90° angle. All triangle angles add up to 180°. Since we know two out of the three, let's find the measure of m∠c by adding up what we know and subtracting from 180.
[tex]60+90+c=180\\\\150+c=180\\\\c=180-150\\\\c=30[/tex]
Now that we know m∠c, we can note that the 85° angle, m∠a, and x are supplementary. This means their angle lengths add up to 180°. Since we know two out of the three, we can do a process similar to finding the missing triangle angle.
[tex]85+30+x=180\\\\115+x=180\\\\x=180-115\\\\x = 65[/tex]
Therefore, x is 65°.
Hope this helped!
Erica says that 1/5 of the national flag of Thailand shown on the right is blue. what’s wrong?
Answer:
The blue portion of the flag is actually 2/6 or 1/3 of the flag
Step-by-step explanation:
If you look at the size of the blue portion of the line it takes up twice the space as the white part. Imagine a small line drawn through the middle of the blue rectangle, now you can see that the flag is split up into 6 parts, rather then 5! Since we now have 2/6 of the flag being taken up by blue, that can be reduced down to 1/3 of the flag covered in blue.
What is the answer to 2*3(15-5+3)4*4-6
Answer:
1242
Step-by-step explanation:
[tex]1. \: 6(15 - 5 + 3)4 \times 4 - 6 \\ 2. \: 6(10 + 3)4 \times 4 - 6 \\ 3. \: 6(13)4 \times 4 - 6 \\ 4. \: 78 \times 4 \times 4 - 6 \\ 5. \: 312 \times 4 - 6 \\ 6. \: 1248 - 6 \\ 7. \: = 1242[/tex]
Slope is 4 and (4,6) is on the line
Answer:
y-6=4(x-4)
Step-by-step explanation:
y-y1=m(x-x1)
y-6=4(x-4)
Question 1 of 5
2 Points
What is the simplified fractional equivalent of the terminating decimal 0.25?
O
O A.
CINNICT
O
O c. 1
O D. 25
SUBMIT
Answer:
The simplified fractional equivalent is [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
we know that
A terminating decimal is a decimal that ends. So, it's a decimal with a finite number of digits.
we have
[tex]0.25[/tex]
Let
[tex]x=0.25[/tex]
Multiply by 100 both sides
[tex]100x=25[/tex]
Divide by 100 both sides
[tex]x=\frac{25}{100}[/tex]
Simplify
Divide by 25 both numerator and denominator
[tex]x=\frac{1}{4}[/tex]
line m passes through the points -2,7 and 4,-5 as shown below.
Answer:
y=-2x
Step-by-step explanation:
Answer:
y+2x=8
Step-by-step explanation:
when you put this in slope intercept form it will equal y=-2x+8 . Parallel lines need to have the same slope