1. The amount of money in the account after 10 years is 42,317.96 dollars.
2. it will take Pamela and Kevin 7.5 hours to complete the task together
How to find compound interest?Question(1)
Using compound interest formula,
[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]
where
p = principalr = raten = number of timest = timeTherefore,
p = 30,000
r = 3.5% = 0.035
t = 10
n = 1
Therefore,
[tex]A = 30000(1+\frac{0.035}{1} )^{1X10}[/tex]
A = $42,317.96
Question 2:
Pamela takes 12 hours to complete a task.
Kelvin takes 20 hours to complete same task.
The time it will take both of them can be computed as follows:
using rate principle,
let
x = time it will take both of them to do the work together.
[tex]\frac{1}{x}=\frac{1}{12} + \frac{1}{20}[/tex]
[tex]\frac{1}{x}=\frac{20+12}{240}[/tex]
[tex]\frac{1}{x}=\frac{32}{240}[/tex]
cross multiply
240 = 32x
x = 240 / 32
x = 7.5 hours
Therefore, it will take Pamela and Kevin 7.5 hours to complete the task together
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(cot A - tan A)cos A = cosecA-2sinA
Simplify the LHS by using the identities above to get the RHS:
(cot A - tan A)cosA = (cosA/sinA - cosA/sinA)cosA = Identities 2 and 3(cosA/sinA)cosA - (cosA/sinA)cosA = Distributecos²A/sinA - sinA = Simplify/cancel(1 - sin²A)/sinA - sinA = Identity 11/sinA - sin²A/sinA - sinA = Distribute1/sinA - sinA - sinA = Simplify/cancel1/sinA - 2sinA = cosecA - 2sinA Identity 4Proved
In the parallelogram above what is the value of x?Please explain for brainlest
E.36
F.18
G.6
H.5
Answer:
[tex]\boxed{E.~36}[/tex]
Step-by-step explanation:
Supporting drawing in the attachment.
The sum of the measures of two consecutive angles is equal to 180°.
3x° + 2x° = 180°
5x° = 180° I ÷ 5
x° = 36°
E. 36Answer:
36
Step-by-step explanation:
I also did this for shsat
Two people are packing equal numbers of small boxes into large boxes.
One person has 3 large boxes that are full of smaller boxes and 24 small
boxes that are not yet packed. The other person has 5 large boxes that are
full of smaller boxes and 10 small boxes that are not yet packed. Each large
box holds the same number of small boxes. How many small boxes can
each large box hold? What is the total number of small boxes each person
will pack? How many large boxes will each person need in order to pack all of his or her small boxes?
Please answer as quickly as possible and as detailed as possible!!! Thanks!!!!!!
Answer:
29 small boxes
Step-by-step explanation:
THE QUESTION IS DOWN BELOW.
major points when given branliest
The ratios are Surface area ⇒ 4 : 25 Height ⇒ 2 : 5 and Volume ⇒ 8 : 125
How to determine the ratios?The scale factor is given as:
m : n = 2 : 5
For the area, we take the square of the ratios.
i.e.
Area = 2^2 : 5^2
Evaluate
Area = 4 : 25
For the volume, we take the cube of the ratios.
i.e.
Volume = 2^3 : 5^3
Evaluate
Volume = 8 : 125
The given scale factor can be used for the height of the model and the original bicycle
Hence, the ratios are
Surface area ⇒ 4 : 25
Height ⇒ 2 : 5
Volume ⇒ 8 : 125
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Martina runs 3/1/2 miles every day for 7 days . How many miles does she run altogether
Answer:
24.5
Step-by-step explanation:
All you have to is Multiply 3 1/2 by 7
3 1/2 x 7= 24.5
Based on the family the graph below belongs to, which equation could represent the graph?
Answer:
the first option I believe
Please help need answers
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
[tex]\frak{Good\;Morning!!}[/tex]
[tex]\pmb{\tt{Question\;1}}[/tex]
[tex]\star\boldsymbol{\rm{Given-:}}[/tex]
Side length = 7 cm,Side length = 5 cm.[tex]\star\boldsymbol{\rm{We're\;looking\;for-:}}[/tex]
Side length = xThis is how it's done.
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
There's a special formula that we can use if we need to find the longest side of a right triangle. Fortunately, all of these triangles are right ones! Good.
The formula is. [tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]. This formula is known as Pythagoras' Theorem. This formula only works for right triangles.
Since we have a and b, we can just put in the values (7 for a and 5 for b), And then simplify!
[tex]\boldsymbol{\rm{7^2+5^2=c^2}}[/tex] | 7^2 simplifies to 49, and 5^2 simplifies to 25
[tex]\boldsymbol{\rm{49+25=c^2}}[/tex]. | add
[tex]\boldsymbol{\rm{74=c^2}}[/tex] | square root both sides
[tex]\boldsymbol{\rm{8.6=c}}}[/tex]. | the answer is given to 1 decimal place, as the problem required
[tex]\orange\hspace{350pt}\above5[/tex]
[tex]\pmb{\tt{Question\;2}}[/tex]
Once more, we're given two sides, and asked to find the third one,
which is still the longest side.
[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex] is still the formula used here
Put in 5 for a and 3 for b.
[tex]\boldsymbol{\rm{5^2+3^2=c^2}}[/tex] | 5^2 simplifies to 25, and 3^2 simplifies to 9
[tex]\boldsymbol{\rm{25+9=c^2}}[/tex] | add
[tex]\boldsymbol{\rm{34=c^2}}[/tex] | square root both sides
[tex]\boldsymbol{\rm 5.8=c}}[/tex] | once again it's given to one decimal place
[tex]\hspace{350pt}\above5[/tex]
[tex]\pmb{\tt{Question\;3}}[/tex]
This problem is solved the exact same way
[tex]\boldsymbol{\rm{a^2+b^2=c^2}}[/tex]
[tex]\boldsymbol{\rm{8.2^2+4.7^2=c^2}}[/tex]
[tex]\boldsymbol{\rm{67.24+22.09=c^2}}[/tex]
[tex]\boldsymbol{\rm{89.33=c^2}}[/tex]
[tex]\boldsymbol{\rm{9.5=c}}[/tex], rounded to one D.P.
[tex]\orange\hspace{300pt}\above2[/tex]
[tex]\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet[/tex]
[tex]\pmb{\tt{Question4}}[/tex]
Here we have the longest side and one side length-:
[tex]\boldsymbol{\rm{4^2+b^2=7^2}}[/tex] | 4^2 simplifies to 16 and 7^2 simplifies to 49
[tex]\boldsymbol{\rm{16+b^2=49}}[/tex] | subtract 16 from both sides
[tex]\boldsymbol{b^2=33}[/tex] | square root both sides
[tex]\boldsymbol{\rm{b=5.7}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\pmb{\tt{Question\;5}}[/tex]
[tex]\boldsymbol{\rm{3.8^2+b^2=7.9^2}}[/tex]
[tex]\boldsymbol{\rm{14.44+b^2=62.41}}[/tex]
[tex]\boldsymbol{\rm{b^2=47.97}}[/tex]
[tex]\boldsymbol{\rm{b=6.9}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
[tex]\pmb{\tt{Question\;6}}[/tex]
[tex]\boldsymbol{\rm{a^2+6.1^2=7.3^2}}[/tex]
[tex]\boldsymbol{\rm{a^2+37.21=53.29}}[/tex]
[tex]\boldsymbol{\rm{a^2=16.08}}[/tex]
[tex]\boldsymbol{\rm{a=4.0}}[/tex]
[tex]\pmb{\tt{done~!!!}}[/tex]
[tex]\orange\hspace{300pt}\above3[/tex]
Given w =startroot 2 endroot (cosine (startfraction pi over 4 endfraction) i sine (startfraction pi over 4 endfraction) ) and z = 2 (cosine (startfraction pi over 2 endfraction) i sine (startfraction pi over 2 endfraction) ) , what is w – z expressed in polar form?
w-z can be expressed in ploar form as √2∠(7π/4)
Sometimes the expression A(cos(α)+i·sin(α)) is written as A·cis(α). I prefer the notation A∠α, because it is more compact.
Given: w = √2∠(π/4)
z = 2∠(π/2)
And you are asked to find the difference w-z in polar form.
In rectangular form, ...
w = √2∠(π/4) = √2(1/√2 +i/√2) = 1 +i
z = 2∠(π/2) = 2(0 +i·1) = 2i
Then the difference is ...
w -z = (1 +i) -(2i) = 1 -i
You may notice this is the conjugate of w, so will have the opposite angle:
w - z = w* = √2∠(-π/4) = √2∠(7π/4)
In the terms used by the problem statement, ...
w -z = √2(cos(7π/4) +i·sin(7π/4))
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find x and y
pls help
Answer:
x = 14
Step-by-step explanation:
110 + 5x = 180
-110 -110
5x = 70
divide by 5 on both sides
x = 14
to find y add 70 + 40 + missing angle = 2y
missing angle is 70 because 70+40+70 = 180
so 2y = 110
y = 55
Answer:
x=14
y=55
Step-by-step explanation:
5x and 110 form a straight line so they add to 180
5x+110 =180
5x = 180-110
5x = 70
Divide by 5
5x/5 = 110/5
x = 14
We know the exterior angle of a triangle is equal to the sum of the two opposite interior angles
40 + 5x = 2y
Substitute in 14 for x
40 +5(14) = 2y
40 + 70 = 2y
110 = 2y
Divide by 2
110/2 =2y/2
55 = y
Solve the inequalities by graphing. Select the correct graph. 2x - y > 4 2x - y < -2
The solution will be the point of intersection of the lines and since the lines are parallel to each other, there is no solution
System of inequality
Inequality are expressions not separated by an equal sign. Given the following inequalities
2x - y > 4
2x - y < -2
The lines for both inequality must be dashed since they do not include equal sign. The first line will be shaded in the upper part while the second in the lower portion
The solution will be the point of intersection of the lines
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came across this question on my home work can some one please show how to sketch it correctly?
Answer:
Step-by-step explanation:
Solve the following systems of equations
y= 3x^2 + 6x + 4
Y= -3x^2 + 4
show all work and solutions
Answer:
[tex](-1;1)[/tex] and [tex](0;4)[/tex]
Step-by-step explanation:
First of all, even if the system is of 4th degree, by looking at the shape of the equations I am expecting up to 2 solutions.
The easiest way to solve it, since both equation are in the form y= something, is to equate both RHSs.
[tex]3x^2+6x+4=-3x^2+4\\6x^2+6x=0 \rightarrow 6x(x+1)=0[/tex]
which tells us that either [tex]x=0[/tex] or [tex]x=-1[/tex]
Now we can replace these value of x in one of the two to finish our work: [tex]x=0\rightarrow y= 4[/tex]
[tex]x=-1 \rightarrow y= -3+4=1[/tex]
if a 20 ft tree casts a 15ft shadow, how long a shadow is cast
Answer:
25 ft
Step-by-step explanation:
c = √a^2 + b^2 = √20^2 + 15^2 = 25ft
Hooke me up with a 5 star and a thanks :)
8. In AABC, LA is a right angle and mzB = 45°. Find BC.
11√2 ft
√22 ft
2√11 ft
11 ft
Answer:
BC = 11[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin 45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{11}{BC}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
BC = 11[tex]\sqrt{2}[/tex]
How does an earthquake with a magnitude of 7 on the Richter scale compare to one with a magnitude of 5?
50 times stronger
100 times stronger
20 times stronger
2 times stronger
Answer:
100 times stronger
Step-by-step explanation:
The Richter scale is a measurement system for the strength of Earthquakes. The most powerful Earthquakes are at 5-10, while the least powerful ones stay from 1-4.
This is how the Richter scale works:
An earthquake with a magnitude of 2 is 10 times more powerful than an earthquake with a magnitude of 1. Each number is 10 times more powerful than the last.
So, simple math tells us that Magnitude six is 10 times more powerful than magnitude five, and magnitude seven is 100 times more powerful than magnitude 5..
What are the first five terms, a1, a2, a3, a4, a5, of the sequence defined by a Subscript n = StartFraction n squared minus 9 Over n cubed + 3 EndFraction, and how can the sequence be described?
PLEASEEE HELP !!
Answer:
Step-by-step explanation:
So if you look at the numerator the degree is 2, and if you look at the numerator of the denominator, it's 3. This means that the value of the denominator will grow faster than the numerator, so it will diverge.
To find the first 5 terms simply plug in 1, 2, 3, 4, and 5 as n
[tex]a_1=\frac{1^2-9}{1^3+3} = \frac{-8}{4} = -2}\\a_2 = \frac{2^2-9}{2^3+3} = \frac{-5}{11} = -\frac{5}{11}\\a_3 = \frac{3^2-9}{3^3+3} = \frac{0}{30} = 0\\a_4 = \frac{4^2-9}{4^64+3} = \frac{7}{67} = \frac{7}{67}\\a_5 = \frac{5^2-9}{5^3+3} = \frac{16}{128} = \frac{1}{8}[/tex]
It should converge to a limit of 0, since the denominator is growing faster than the numerator
Answer:
C
Step-by-step explanation:
Listed below are measured amounts of caffeine obtained in one can from each of 14 brands. Find the variance, for the given sample data and leave the answer to the nearest hundredths.
57, 34, 30, 44, 33, 41, 60, 47, 56, 41, 31, 22, 12, 40.
Answer:
And here's your answer: 39.14
Step-by-step explanation:
First, add all the numbers up
then divide them all by 14
John owns a clothing store that sells graphic T-shirts and shorts. He sells the
T-shirts for $6 each and the shorts for $14 each. He is limited to the
constraints show by the set of inequalities below. Which of the points (s, t)
will maximize John's profit?
A. (12,0)
B. (0, 13.33)
C. (25,5)
100
s≤ 40-30
s2 12-t
s≤ 30-t
s20
t≥ 0
The points (s, t) that will maximize John's profit is; (12, 0)
How to use Inequality Constraints?We are given the inequality constraints;
s ≤ 12 - 0.5t
s ≥ 10 - t
s ≤ 20 - t
s ≥ 0
t ≥ 0
We are told that John sells the T-shirts for $6 each and the shorts for $14 each. Since the coordinate point is (s, t), when we look at the options and compare with each of the constraints, it is clear that the points (s, t) that will maximize John's profit is; (12, 0)
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the cost of 15kg of apples is 262.50. find the cost of 25kg of apples
Answer:
437.50 is the cost of 25kg of apple's.
Without actual calculating the cubes, evaluate using identities:
[tex]-11^3+8^3+3^3[/tex]
Answer:
-792
Step-by-step explanation:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{-11^3 + 8^3 + 3^3}[/tex]
[tex]\mathsf{= -11\times -11\times -11 + 8\times8\times8 + 3\times3\times3}[/tex]
[tex]\mathsf{= 121\times -11+ 64\times8+9\times3}[/tex]
[tex]\mathsf{= -1,331 + 512 + 27}[/tex]
[tex]\mathsf{= -819 + 27}[/tex]
[tex]\mathsf{= -792}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{-792}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
which line has the same slope as the line passing through (-4, -1) and (-1, 5)
A line which has the same slope as the line passing through the given points is: C. y = 2x + 8.
Given the following data:
Points on x-axis = (-4, -1).Points on y-axis = (-1, 5).How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
[tex]Slope = \frac{5\;-\;(-1)}{-1\;-\;(-4)}\\\\Slope = \frac{6}{3}[/tex]
Slope = 2.
Therefore, y = 2x + 8 is a line which has the same slope as the line passing through the given points.
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Complete Question:
Which line has the same slope as the line passing through (-4, -1) and (-1, 5)?
A. y = 3
B. 9x - 3y = 5
C. y = 2x + 8
D. the line passing through (1, 4) and (1, 7)
In a promotional sale, Roxanne bought one item for its regular price and a second item for $ 1. She paid $ 20 for both items. What fraction of the price of the first item is the price of the second item?
The fraction of the price of the first item is 1/19 if Roxanne bought one item for its regular price and a second item for $ 1.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
In a promotional sale, Roxanne bought one item for its regular price and a second item for $ 1.
Total money Roxanne paid = $20
First item price = 20 - 1 = $19
The fraction of the price of the first item = 1/19
Thus, the fraction of the price of the first item is 1/19 if Roxanne bought one item for its regular price and a second item for $ 1.
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One hundred riders from several countries participated in a bicycle race. Only eighty riders, including Juan and Charlie, finished the race. Juan finished 5th and Charlie was the winner. All the riders' countries of origin and finishing times were recorded on the race register. No two riders who finished had the same time and those who did not finish were recorded as DNF.
Based on this information, determine if each set is well-defined. Yes or No
The set of riders who finished minutes or more after the winner (Yes or No)
The set of the three least tired riders at the end (Yes or No)
The set of riders with the best-looking bicycles (Yes or No)
The set of riders who finished the race (Yes or No)
The set of countries of origin of the riders that didn't finish (Yes or No)
Answer:
Finished minutes or more: Yes
Three least tired: No
Best looking bikes: No
Finished the race: Yes
Countries of origin of riders who didn't finish: Yes
Step-by-step explanation:
Things displayed on the board: name of rider, country of origin, finishing time
Finished minutes or more: anyone who finished who wasn't in first
Three least tired: subjective information, not on the board
Best looking bikes: subjective information, not on the board
Finished the race: everyone who doesn't have DNF next to their name
Countries of origin of riders who didn't finish: countries of anyone with DNF next to their name
what is the formula for finding the area of a sphere
Answer: [tex]4\pi r^{2}[/tex]
Step-by-step explanation:
Area of a circle is pi r squared
what statement is true
Answer:
D. Both graphs are exponential functions.
Step-by-step explanation:
Hope it helps :)
Twice the sum of two consecutive integers is 22. What are the two integers?
The consecutive two integers are 5 and 6
Linear equations
Let the two consecutive integers be (x+1) and (x). If twice the sum of two consecutive integers is 22 then;
2(x+1+x) = 22
x+x+1 = 22/2
2x + 1 = 11
Subtract 1 from both sides
2x = 11 - 1
2x = 10
x = 5
Hence the consecutive two integers are 5 and 6
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I need help with number 13 and 14
Answer:
13)x=59 answer is d 14)x=24
Step-by-step explanation:
180-116(angles on a striaght line sum to 180)180-116=64
angle in a triangle sum to 180
64+x=180
64+57=121
180-121=59
x=59
question 14 answer is 24
90+66=156
sum of a triangle is 180
180-156=24
The radius of a car’s tire is 47.1 cm. Find the circumference of the tire. (This is the distance that the car must drive to rotate the tire exactly once.)
The circumference of the tire as described in the task content is; 295.8cm.
What is the circumference of the tire?It follows from the task content that the tire in discuss is circular and has radius; 47.1cm.
Hence, by the circumference formula; we have;
Circumference = 2πr = 2 × 3.14 × 47.1
Circumference = 295.8cm.
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Fill in the blank with letter of the word that completes the sentence.
The sides of an angle are
In the coin flipping lab, suppose that you simulated the flipping of a weighted coin 30 times and got 5 heads and 25 tails. What is your estimated probability for P(H)?
The estimated probability for P(H) is 0.17.
What is Probability ?Probability is the stream in mathematics that studies about the likeliness of an event to happen.
It is given that
Total number of times coin is flipped = 30
Total number of times the coin gave heads = 5
Total number of times the coin gave tails=25
The P(H) = Total no. of Heads / Total outcomes
P(H) = 5 / 30
= 1/6
= 0.1666
≈ 0.17
Therefore the estimated probability for P(H) is 0.17.
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