well, there are 12 months in a year, so, for a year and 1 month that'll be 13 months, or namely 13/12 ths of a year.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds768\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1.00\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &\frac{13}{12} \end{cases}[/tex]
[tex]A=768\left(1+\frac{1.00}{4}\right)^{4\cdot \frac{13}{12}}\implies A=768(1.25)^{\frac{13}{3}}\implies A\approx \stackrel{\pounds}{2019.78} \\\\\\ \stackrel{~\hfill \textit{interest yielded}}{2019.78~~ - ~~768~~ \approx ~~ \stackrel{\pounds}{1251.78}}[/tex]
f(x) = 3x^2 - 9x + 2
What's the axis of symmetry?
What's the coordinate of the vertex?
Answer:
1) Axis of symmetry = [tex]\frac{3}{2}[/tex]
2) Vertex form = [tex]y=3(x-\frac{3}{2} )^{2} -\frac{19}{4}[/tex]
Rewrite in vertex form and use this form to find the vertex (h,k).
[tex](\frac{3}{2} ,-\frac{19}{4} )[/tex] (coordinates of the vertex)
Step-by-step explanation:
Vocabulary:
Axis of symmetry- A line that passes through a figure in such a way that the part of the figure on one side of the line is a mirror reflection of the part on the other side of the line.
Vertex- The point on an angle where the two sides intersect.
Answer
Thats the answer below!
Step-by-step explanation:
A = 12 and b = 24 ,what Is the area of the pencil
Find the missing length
Answer: 5
Step-by-step explanation:
V = lwh = 20 * 12 * ? = 1200
240 * ? = 1200
? = 5
Find the equation of the line.
Through (-8,11); perpendicular to y=9
Perpendicular lines have slope negative reciprocal to each other .
-1/0=ooEquation of line in point slope form
[tex]\\ \rm\Rrightarrow y-y_1=m(x-x_1)[/tex]
[tex]\\ \rm\Rrightarrow y-11=\infty(x+8)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{y-11}{\infty}=x+8[/tex]
[tex]\\ \rm\Rrightarrow x+8=0[/tex]
[tex]\\ \rm\Rrightarrow x=-8[/tex]
Some formats of line
[tex]\boxed{\begin{array}{c|c}\boxed{\bf Form} &\boxed{\bf Equation} \\ \sf Slope\: intercept\:form &\sf y=mx+b \\ \sf Intercept\:form &\sf \dfrac{x}{a}+\dfrac{y}{b}=1\\ \sf Normal\:form &\sf xcos\omega+ysin\omega=p \\ \sf Two\: point\:form &\sf y-y_1=\left(\dfrac{y_2-y_1}{x_2-x_1}\right)(x-x_1)\\ \sf Point\:slope\:form &\sf y-y_1=m(x-x_1) \\ \sf Standard\:form &\sf Ax+By+C=0 \end{array}}[/tex]
A set of mathematics exam scores are normally distributed with a mean of 80.280.280, point, 2 points and a standard deviation of 444 points. What proportion of exam scores are between 828282 and 85.685.685, point, 6 points? You may round your answer to four decimal places.
Answer:
0.2379
lmk if im wrong :)
Approximately 0.2200 or 22.00% of the exam scores are between 82.2 and 85.6.
To find the proportion of exam scores between 82.2 and 85.6, we need to calculate the z-scores for both values and then use the standard normal distribution table (also known as the z-table) to find the proportion.
The z-score for a value x in a normal distribution with mean μ and standard deviation σ is given by the formula:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
Let's calculate the z-scores:
For x = 82.2:
z₁ = (82.2 - 80.2) / 4 = 2 / 4 = 0.5
For x = 85.6:
z₂ = (85.6 - 80.2) / 4 = 5.4 / 4 = 1.35
Now, we can find the proportion of scores between these z-scores using the z-table. The table gives us the cumulative probability up to a certain z-score.
From the z-table, the cumulative probability for z₁ = 0.5 is approximately 0.6915, and the cumulative probability for z₂ = 1.35 is approximately 0.9115.
Now, we can find the proportion of scores between these two z-scores:
Proportion = P(0.5 ≤ z ≤ 1.35)
= P(z ≤ 1.35) - P(z ≤ 0.5)
= 0.9115 - 0.6915
≈ 0.2200
So, approximately 0.2200 or 22.00% of the exam scores are between 82.2 and 85.6.
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4. Find the center and radius of the circle with equation x2 + y2-2x + 4y -
11 = 0
Answer:
(1 , -2) and r = 4
Step-by-step explanation:
x² + y² - 2x + 4y - 11 = 0
x² - 2x + 1 - 1 + y² + 4y + 4 - 4 - 11 = 0
(x - 1)² - 1 + (y + 2)² - 4 - 11 = 0
(x - 1)² + (y + 2)² = 16
We know equation of circle is of the form
(x - h)² + (y - k)² = r²
So, center is (1 , -2) and radius is 4
what is the total cost of a $12.60 item when 7 1/2% (0.075) sales tax is added?
Answer:
12.60 x 0.075 = $0.945
Total cost:- 12.60 plus 0.945 = $13.55
Step-by-step explanation:
the ratio of the ages of carlo and daniel is 3:5. in 6 years' times the ratio of their ages will be 3:4. how old will carlo and daniel be in 6 years' time?
Here is your answer
I hope this answer is ok
Answer:
Carlo is 12 and Daniel is 16.
Step-by-step explanation:
There is probably a formula for this but I just used guess and check. Im assuming that carlo is the 3 and daniel is the 5.
In Figure 1, the area of square A is 9 square units, the area of square B is 16 square units, and the area of square C is 25 square units.
In Figure 2, the area of square D is 36 square units and the area of square E is 64 square units.
What is the area of square F in Figure 2?
A.
110 square units
B.
100 square units
C.
90 square units
D.
80 square units
Answer:
b) 100 square units as 36 add 64 is 100
The lengths of the bases of a trapezoid are 5 feet and 8 feet. The trapezoid has an area of 104 square feet.
What is the height, h, of the trapezoid?
A = 13 ft
B = 16 ft
C = 20.8 ft
D = 21.4 ft
Answer:16feet
Step-by-step explanation:
The explanation is in the attached file
1. 4x + 5y
2. 2x + (20 - y)
3. X divide 3 + y
4. 4y divide 2 + (8x + 10)
5. Patty made $34 baby sitting on each of 3 weekends. If she spent $50 on gifts for her family, how much money does she have left?
6.Carlos solved 20-(2x6) + 8 divide 4 = 28. Is this the correct answer?
1) 4x + 5y
→ 4*6 + 5*1
→ 24 +5 = 29
2) 2x (20-y)
→ 2*6 (20-1)
→ 12 *19 = 228
3) x ÷ 3 + y
→ 6 ÷ 3 + 1
→ 2 +1 = 3
4) 4y ÷ 2 + (8x + 10)
→ 4*1 ÷ 2 +(8*6+10)
→ 2 + (48+10)
→ 2 + 58
→ 60
5 ) 5. Patty made $34 baby sitting on each of 3 weekends. If she spent $50 on gifts for her family, how much money does she have left?
Money made each weekend = $34
Money made in 3 weekend = $34*3 =$102
Money spent = $50
Therefore ,
→Money left = Money made in 3 weekends - Money spent
→ Money left = $102 - $50 = $52
6.Carlos solved 20-(2x6) + 8 divide 4 = 29. Is this the correct answer? ( In attachment it's written 29 and not 28 .)
Given equation is ,
→ 20 - (2 × 6) + 8 ÷ 4 = 29
Solve inside the brackets ,
→ 20 - 12 + 8 ÷ 4
Perform division ,
→ 20 -12 + 2
Perform addition ,
→ 22 - 12
Perform subtraction,
→ 10
No , he is wrong the answer should have been 10 but he got 29 .
I hope this helps .
as a bag of 16 marbles. If 6 marbles are white, what is the probability of picking a w Out of ss the probability as a percentage: % o
r
Answer:
6/16 and if you want the fraction simplified it would be 3/8. As a percentage 37.5%.
Step-by-step explanation:
PLEASE HELP ME WITH THIS!! ILL GIVE BRAINLIEST.
Answer:
1. Correct
2. Correct
3. Correct
4. Correct
5. Incorrect
6. Correct
7. Incorrect
8. Incorrect
9. Correct
10. Correct
11. Incorrect
Step-by-step explanation:
15×2 2/3 show the steps too please
Answer:
40
Step-by-step explanation:
[tex]15 \times 2 \frac { 2 } { 3 }\\= 15\times \left(\frac{6+2}{3}\right) \\= 15\times \left(\frac{8}{3}\right) \\= \frac{15\times 8}{3} \\= \frac{120}{3} \\\Longrightarrow \boxed{40}[/tex]
Hope it helps ⚜
AABC and ADEF are similar. Find the missing side length.
Answer:
15
Step-by-step explanation:
Given the following question:
ABC = 2, 4, and 5
DEF = 6, and 12
We know the two triangles are similar, so we can use the given information to find the hypotenuse for the second triangle.
[tex]2\times3=6[/tex]
[tex]4\times3=12[/tex]
[tex]5\times3=15[/tex]
DEF is three times larger than ABC
? = 15
Hope this helps.
The number of eggs in the refrigerator e decreased by 8 equals 18.
Enter an equation to represent the situation.
Answer:
e=26
Step-by-step explanation:
e= 8 + 18 = 26
An angle measures 84° more than the measure of its supplementary angle. What is the measure of each angle?
Let ∠1 be x
Let ∠2 be x+84
ATQ,[tex]\rm\:x+x+84= 180 \degree[/tex]
[tex] \rm \: 2x + 84 = 180[/tex]
[tex] \rm \: 2x = 180 - 84[/tex]
[tex] \rm \: 2x = 96[/tex]
[tex]\boxed{ \bf \: x=48 \degree}[/tex]
So,[tex]\begin{gathered} \sf \: ∠1 = x \\ \sf \: = 48 \degree\end{gathered}[/tex]
[tex]\begin{gathered} \sf \: ∠2 = x+84 \\ \sf = \: 48+84 \\ \sf∠2 = 132 \degree\end{gathered}[/tex]
Remember that: Supplementary angles sums upto 180°Complementary angles sums upto 90°Answer:
48°
132°
Step-by-step explanation:
Let the measure of one angle be x°
So, Measure of supplementary angle = (x + 84)°
x° +(x +84)° = 180°
(2x + 84)° = 180°
2x + 84 = 180
2x = 96
x = 96/2
x = 48°
(x + 84)° = 48 + 84 = 132°
The questions are 32? 238? 58? 122?
Answer:
58
Step-by-step explanation:
(360 - 122 -122)/2= 58
please brainliest
Answer:
58°
Step-by-step explanation:
well first we know that the total degrees all the way around are 360° so the total number must add up to 360°.
vertical angles are the angles across from each other when two lines intersect and we know that vertical angles are congruent (the same) so 122° equals d. Next we look at the angles e and c. It might seem difficult but we remember that vertical angles are congruent so e and c are equal. the sum the first angle(122°) and d(which we already found equals 122°) equals 122+122=244. we learned at the beginning that all the angles must be 360 so 360-244=116. 116 is the sum of e and c but we know e and c are equal so 116/2=58. e=58 and c=58 so there is our answer
d=122°
e=58°
c=58°
I hope this helps!
If it takes John 10 hours to paint the fence, how long will it take John and his 2 friends to do the job if they work at the same rate?
A) 1 1/3 hours
B) 1 2/3 hours
C) 2 2/3 hours
D) 3 1/3 hours
Answer:
D) 3 1/3 hours
Step-by-step explanation:
10÷3=3.3=3 1/3
Help me with this I will give brainliest
Answer:
see explanation
Step-by-step explanation:
both linear equations will have the form
y = mx + c ( m is the slope and c the y- intercept )
Chef Mate
c(n) = mn + c
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 14) and (x₂, y₂ ) = (3, 18.5) ← 2 ordered pairs from the table
m = [tex]\frac{18.5-14}{3-2}[/tex] = [tex]\frac{4.5}{1}[/tex] = 4.5 , then
c(n) = 4.5n + c ( n represents ounces )
To find c substitute any ordered pair from the table into c(n)
using (4, 23 )
23 = 18 + c ⇒ c = 23 - 18 = 5
c(n) = 4.5n + 5 ← equation for Chef Mate
--------------------------------------------------------------------
Similarly for Grocery Gourmet
g(n) = mn + c
using (2, 23 ) and (3, 27 ) to find m
m = [tex]\frac{27-23}{3-2}[/tex] = [tex]\frac{4}{1}[/tex] = 4 , then
g(n) = 4n + c
using (4, 31 ) to find c
31 = 16 + c ⇒ c = 31 - 16 = 15
g(n) = 4n + 15 ← equation for Grocery Gourmet
------------------------------------------------------------------
Equate the 2 equations to find when cost is the same
4.5n + 5 = 4n + 15 ( subtract 4n from both sides )
0.5n + 5 = 15 ( subtract 5 from both sides )
0.5n = 10 ( divide both sides by 0.5 )
n = 20
Then when n = 20
c(n) = 4.5(20) + 5 = 90 + 5 = 95
g(n) = 4(20) + 15 = 80 + 15 = 95
Both Chef Mate and Grocery Gourmet charge $95 for 20 ounces of extract
Help me please please please
Answer:
25.6
Step-by-step explanation:
Add 6.4 to all the sides and add them all together-
6.4+6.4+6.4+6.4 = 25.6
Where do I find my work I did with a tutor?
3) Write the following numbers from highest to lowest: 6288, -8, 2301, -282, 202
Answer:
6288 2301 202 -8 -282
im genius
A United States flag is sometimes folded into a triangle shape and displayed in a triangular display case. If a display case has dimensions shown in inches, write a polynomial expression that represents the area of wall space covered by the display case.
Step-by-step explanation:
area of ∆ = .5*b*h
b= x+5
h= x-5/2
let's do (x+5) * (x-5/2)
x^2+5x-5/2x-25/2
x^2+5/2x-25/2
area = .5x^2+5/4x-25/4
The polynomial expression that represents the area of wall space covered by the display case is (1/2)x² + (5/4)x - 25/4.
What do we mean by a Polynomial expression?A polynomial is a mathematical expression made up of two or more algebraic terms that have been added, subtracted, or multiplied (no division). Polynomial expressions generally comprise at least one variable, as well as constants and non-negative exponents.
How do we calculate the area of a triangle?The area of a triangle is calculated using the formula: (1/2)*base*height.
How do we solve the given question?We find the area of the triangle-shaped display case. We can see the base of this triangle is x+5 and its height is x - 5/2.
∴ Area of the display case = (1/2)*(x+5)*(x-5/2)
or, area = (1/2)*(x+5)*(2x-5)/2
or, area = (1/4)(2x² + 5x - 25)
or, area = (1/2)x² + (5/4)x - 25/4.
∴ The polynomial expression that represents the area of wall space covered by the display case is (1/2)x² + (5/4)x - 25/4.
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the numbers of motor vehicle fatalities in the united states for the years
find the value of x. round to the nearest tenth.
Answer:
33.9219 (Rounded: 33.9)
Step-by-step explanation:
To find Leg B or x we will use cos(a) = b/c
Therefore we have a = 32degrees and c = 40
So
Cos(32) = b/40
0.848 = b/40
b = 0.848 * 40
b = 33.9219
Based on this sample, how many defective beach balls might the manufacturer expect in the next shipment?
Answer:
2000 - 150 + 20=
1,870
Help me please please please
Answer:
3.33lbs. repeating?
Step-by-step explanation:
I think it would just be 10/3 and be 3.33333333 and so on. (im just taking a guess)
help i'll give brainlist
Answer:
y = -2
Step-by-step explanation:
The midline is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.
From inspection, curve has a maximum at y = 1 and a minimum at y = -5
The midline between these is [tex]y=\frac{1-5}{2}=-2[/tex]
So the equation for the midline of this graph is y = -2 (shown in red on the attached graph)
A 55" flat screen television is regularly priced at $399.00. It is on sale for
20% off, and there is also an in-store coupon for $15.00 off any purchase
over $100.00. If tax is 5.75%, how much will the television cost?
Answer:
$321.6915
Step-by-step explanation:
original price= $399.00
20% off $399 is $319.2
$319.2-$15.00=$304.2
0.75% of 304.2 is 2.2815
5% of 304.2 is 15.21+2.2815=17.4915+304.2=321.6915
hope this helps
A percentage is a way to describe a part of a whole. The final cost of the television is $321.69.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given that a 55" flat screen television is regularly priced at $399.00. Now, It is on sale for 20% off. Therefore, the cost of the flat screen is,
Cost after discount = $399 - 20% of $399
= $399 - 0.20($399)
= $319.2
The cost after the application of the coupon of $15.00 off on any purchase over $100.00. Therefore, the new cost will be,
New Cost = $319.20 - $15.00
= $304.2
Since the tax on the cost is 5.75%, therefore, the cost after the application of the tax is,
Cost after the tax = $304.2 + 5.75% of $304.2
= $304.2 + 0.00575($304.2)
= $321.69
Hence, the final cost of the television is $321.69.
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