Based on the calculations, the amount of money she invested is equal to $3,520.
How to determine the amount invested?First of all, we would assign variables to the amount of money that he invested at different interest rates as follows:
Let x be the amount of money she invested at 11%.Let y be the amount of money she invested at 14%.Since Lydia invested the same amount of money in both stocks, we have:
x = y ....equation 1.
At the two interest rates, the total amount Lydia gets is given by:
0.11x + 0.14y = 440 ....equation 2.
Solving the equations simultaneously, we have:
0.11y + 0.14y = 440
0.25y = 440
y = 440/0.25
y = $1,760.
Thus, the total investment is given by:
Total investment = 1760 + 1760
Total investment = $3,520.
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Problem
A prime trio is a collection of three prime numbers [tex]\{p,q,r\}[/tex] in arithemtic progression, with common difference [tex]q-p=r-q[/tex]. For example, the prime trio [tex]\{3,5,7\}[/tex]has common difference 2.
(a) Find a prime trio with common difference 50.
(b) Find two prime trios with common difference 60.
(c) Prove that there is no prime trio with common difference 70.
Answer:
(a) 50:
3 53 103
(b) 60:
7 67 127
11 71 131
Step-by-step explanation:
OK, I think you can prove this with the theorem that any prime greater than 3 is 6n-1 or 6n+1, for integer n. In other words, any prime is near a multiple of 6; it is either one less or one more. The proof for this is very easy, look it up.
Given this fact, if two primes (p,q) are 70 a part, this means the first one has to be a case of 6n+1 and the second one has to be a case of 6n-1. Why? Because the nearest multiple of 6 is 72 and with +1 on one end and -1 on the other end, you can reach a "gap" of 70.
Now for the next two primes (q,r) the same must hold. Only, it can't because this requires q to be both 6n-1 and 6n+1.
Given that a bag of m&ms has 21 brown candies, 15 orange candies, 10 yellow candies, 14 red candies, and 5 green candies, find the probabilities
The probability of drawing brown candies , orange candies, yellow candies, red candies, green candies is 0.323 , 0.231 , 0.154 , 0.215 ,0.077
What is Probability ?Probability is the study of likeliness of an event to happen.
It is given that a bag of candies that have
21 brown candies
15 orange candies,
10 yellow candies,
14 red candies,
5 green candies,
probabilities of drawing each candy =?
Total Candies = 21 +15+10+14+5 = 65
Probability = No. of chances / Total outcomes
Probability of drawing Brown candies = P(B) = 21 /65 = 0.323
Probability of drawing Yellow candies = P(Y)= 10/65= 0.154
Probability of drawing Orange candies = P(O) = 15/65= 0.231
Probability of drawing Red candies =P( R) = 14/65= 0.215
Probability of drawing Green candies = P(G) = 5/65= 0.077
Therefore the probability of drawing brown candies , orange candies, yellow candies, red candies, green candies is 0.323 , 0.231 , 0.154 , 0.215 ,0.077.
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Find the missing value of the ordered triple that will make the solution to the equation x + 2y – 3z = 8 true.
7. (4, , 0)
8. ( , -2, -2)
9. (2, 3, )
10. (-3, -2, )
The missing value of the ordered triple for questions 7,8,9 and 10 will be y=2,x=6,z=0, and z=-5 respectively.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
The given equation in the problem is;
7) (4, ,0)
Substitute the values in the equation;
⇒x+2y-3z = 8,
⇒4+2y-3(0) = 8
⇒2y=8-4
⇒2y=4,
⇒y=4/2
⇒y=2
8) (, -2, -2)
Substitute the values in the equation;
x+2(-2) -3(-2)= 8
x-4+6 =8
x= 8-6+4
x=8-6+4
x=6
9)(2, 3, )
Substitute the values in the equation;
⇒2+2(3)-3z = 8
⇒8-3z = 8
⇒-3z = 0
⇒z = 0/-3
⇒z= 0
10) (-3, -2, )
Substitute the values in the equation;
⇒-3+2(-2) -3z = 8
⇒-7 -3z = 8
⇒-3z = 15
⇒z = 15/-3
⇒z = -5
Hence, the missing value of the ordered triple for questions 7,8,9, and 10 will be y=2,x=6,z=0, and z=-5 respectively.
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Which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x2? Check
all that apply.
p(x) = 14(x + 7)² + 1
g(x) = -5(x + 10)² - 1
s(x) = –(x − 1)? +0.5
g(x) = 2x² + 10x-35
t(x) = -2x² - 4x - 3
Using translation concepts, the functions that have a maximum and are transformed to the left and down of the parent function are given by:
g(x) = -5(x + 10)² - 1t(x) = -2x² - 4x - 3What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
For the translations, we have that:
Shift left, hence x -> x + a, a > 0.Shift down, hence y -> y - a, a > 0.Having a maximum means that the leading coefficient is negative.The functions that respect these conditions are:
g(x) = -5(x + 10)² - 1t(x) = -2x² - 4x - 3 = -2(x² + 2x) - 3 = -2(x + 1)² - 1More can be learned about translation concepts at https://brainly.com/question/4521517
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how long would it take to drive 18 miles while going 18 mph
Answer:
1 hour
Step-by-step explanation:
18 miles because if u go 18 miles per hour it takes a hour
Two friends, Olivia and Melanie, took summer jobs. The equation y=22.2xy=22.2x represents Melanie's earnings in dollars and cents, yy, for working xx hours. Olivia earned $1156 in 40 hours. How much less per hour does Melanie earn than Olivia?
Answer:
$6.70 per hour
Step-by-step explanation:
We want to compare the pay for 1 hour's work.
Melanie's payThe equation tells us that her pay for working 1 hour can be found from the equation using x=1.
y = 22.2x
y = 22.2×1 = 22.2 . . . . pay for 1 hour
Melanie earns $22.20 per hour.
Olivia's payWe assume that Olivia's pay is proportional to hours worked, so pay for 40 hours will be 40 times 1 hour's pay.
pay per hour = $1156/(40 h) = $28.90/h
Olivia earns $28.90 per hour.
Pay differenceThe difference in their rates of pay is ...
$28.90 -22.20 = $6.70
Melanie earns $6.70 less per hour than Olivia.
Dr. Dominic Estores has written a prescription for a patient to take a preoperative medication at 2200 on the evening before his scheduled surgery. Using the standard time system, what time should you tell the patient to take his medication?
Using the conversion from the 24-hour system to the AM/PM system, the patient should take the medicine at 10 PM.
How to convert from 24 hours to AM/PM?If the hour is between 0 and 11:59, the hour is kept with AM.If the hour is 12, it is PM.If the hour is between 13 and 23:59, the hour the remainder of the division of the hour and 12, PM.22 divided by 12 has remainder 10, hence 22 is equivalent to 10 PM.
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Find the angle between the vectors A = <2,-3> asnd B = <-2, -5> to the nearest tenth of a degree.
Answer:
55.5
Step-by-step explanation:
answer is 55.491477012331599 which rounded to the nearest tenth is 55.5
when you said to the nearest tenth of degree i assume that meant like rounding to the nearest tenth
Work out the surface area of the triangular prism below. Give your answer in cm cm². 17 cm 14 cm 15 cm 8 cm
Answer:
Step-by-step explanation:
A= 2AB+(a+b+c)h
AB= s (s﹣a) ( s﹣b) (s﹣c)
s = a+b+c
2
Solving for A
A= ah +bh+ch+1
2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=17·8+14·8+15·8+1
2·﹣174+2·(17·14)2+2·(17·15)2﹣144+2·(14·15)2﹣154≈ 567.35897
The coordinates of the points P, Q and R are given by (-2, 1), (1, 4) and (4, k) respectively. Find the value(s) of k if
(b) PQ=QR(clue:distance).
There are two values of k based on the assumption that PQ = QR and the definition of distance and the Pythagorean theorem, k₁ = 7 and k₂ = 1.
How to find the missing value of a coordinate
Herein we can find the value of the missing coordinate of point by the Pythagorean theorem, which is described below:
PQ = QR (1)
[tex](Q_{x}-P_{x})^{2} + (Q_{y}-P_{y})^{2} = (R_{x}-Q_{x})^{2} + (R_{y}-Q_{y})^{2}[/tex]
If we know that P(x, y) = (- 2, 1), Q(x, y) = (1, 4) and R(x, y) = (4, k), then the missing value of the point R is:
[1 - (- 2)]² + (4 - 1)² = (4 - 1)² + (k - 4)²
(k - 4)² = 9
k - 4 = ± 3
k = 4 ± 3
There are two values of k based on the assumption that PQ = QR and the definition of distance and the Pythagorean theorem, k₁ = 7 and k₂ = 1.
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ANSWERS QUCIK PLS AND THINK U
Answer:
50.3cm²
Step-by-step explanation:
Formula: The area of a circle is found by A = πr²
Given:
radius is 4cmπ = 3.142Plug in:
A = πr² → A = (3.142)(4)²
→ A = (3.142)(16)
→ A = 50.272
"1 decimal places", round up to 50.3
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Evaluate the following expression.
(5x)^0
Hello,
Answer:
1
Step-by-step explanation:
(5x)⁰ = 1
Rule : a⁰ = 1
Answer:
1
Step-by-step explanation:
(5x)^0
Any base raised to the zero power is 1
a^0 = 1
5^0 =1
(5x)^0 =1
At a restaurant levys total bill is 46 bucks, if he wants to tip 15 percent how much should he leave as a tip?
Giving brainliest to first accurate answer
Answer:
x<3
Step-by-step explanation:
There isn't a question that I can see for the first image, and I cannot see the yellow part, so I am not 100% sure if this is an accurate answer to the question you were asking.
does 6(2x-6)=-7(-2x+4) have no solution or infinite solution
Answer:
It does not.
Step-by-step explanation:
[tex]6(2x - 6) = -7(-2x + 4); \\ 6 * 2x - 6 * 6 = -7 * (-2x) + (-7) * 4; \\ 12x - 36 = 14x - 28; \\ 14x - 12x = -36 + 28; \\ 2x = -8; \\ x = -4.[/tex]
[tex]\{-4\}[/tex] is our set of solutions. Answering your question, it does not.
what mixed number is equivalent to the fraction 28/5
The mixed number equivalent to the fraction 28 / 5 is 5 3 / 5
What is mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction.
Therefore, it is a combination of a whole number and a proper fraction.
Hence,
The fraction is in improper fraction, let's convert it to mixed fraction.
Therefore,
28 / 5 = 5 3 / 5
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Please help me....trying to get my HS diploma, i did not graduate :(
Kevin wants to buy an area rug for his living room. He would like the area rug to be no smaller that 48 square feet and no bigger than 80 square feet. If the length is 2 feet more than the width, what are the range of possible values for the length?
Answer:
It would be B.
Step-by-step explanation:
[tex]area = l \times w \\ but \: w = l - 2[/tex]
[tex]area = l(l - 2) = l {}^{2} - 2l[/tex]
[tex]l {}^{2} - 2l \geqslant 48 \\ l {}^{2} - 2l - 48 \geqslant 0 \\ (l + 6)(l - 8) \geqslant 0[/tex]
[tex]l {}^{2} - 2l \leqslant 80 \\ l {}^{2} - 2l - 80 \leqslant 0 \\ (l + 8)(l - 10) \leqslant 0[/tex]
Sol 1: L in ]-∞,-6]U[8,∞[Sol 2: L in [-8,10]Intersection:L belongs [-8,-6[U[8,10]But Length cannot be negativeL belongs [8,10] or 8≤L≤10The graph of f(x) was vertically translated down by a value of k to get the function g(x) = 5x + k. What is the value of k?
The value of k in g(x) = 5^x + k is -7
How to determine the value of k?The complete question is added as attachment
The functions are given as:
f(x) = 5^x
g(x) = 5^x + k
From the attached graph, we can see that:
f(x) is shifted down by 7 units to form g(x)
This means that:
g(x)= f(x) - 7
This gives
g(x) = 5^x - 7
Substitute g(x) = 5^x - 7 in g(x) = 5^x + k
5^x + k = 5^x - 7
This gives
k = -7
Hence, the value of k in -7
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The ages of 30 students in a class are given below. Construct a frequency table for grouped data using 6 classes. For convenience, the data has been ordered from smallest to largest. 15, 17, 18, 19, 25, 25, 27, 28, 29, 30, 30, 32, 33, 36, 38, 45, 45, 48, 49, 50, 52, 53, 55, 56, 57, 58, 59, 59, 63, 68 All responses should be whole numbers. Provide your answer below:
Here is the frequency table:
Class Frequency
15 - 24 4
25 - 34 9
35 - 44 2
45 - 54 7
55 - 64 7
65 - 74 1
What is the frequency table?A frequency table is used to track the frequency of a data set. The data ranges from 15 to 68, if the classes are to be 6, then the class interval would have to be 9.
Class Frequency
15 - 24 4
25 - 34 9
35 - 44 2
45 - 54 7
55 - 64 7
65 - 74 1
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sari ran for class president. each student in her class voted one time. sari won 25% of the student votes. if sari recived 60 votes, how many students voted altogether
The number of students who voted is 240.
How many students voted?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
The number of students who voted = number of votes Sari received / percentage number
60 / 0.25 = 240
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The auto parts department of an automotive dealership sends out a mean of 4.2 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 3? Round your answer to four decimal places.
The probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.
What are some of the properties of Poisson distribution?The Poisson distribution is a discrete probability distribution that describes the likelihood of a specific number of events occurring in a specified span of time or space, if these events occur at a constant mean rate and regardless of the time since the last occurrence.
Let X ~ Pois(λ)
Then we have:
E(X) = λ = Var(X)
Since standard deviation is the square root (positive) of variance,
Thus,
The standard deviation of X = [tex]\sqrt{\lambda}[/tex]
Its probability function is given by
[tex]f(k; λ) = Pr(X = k) = \dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]
Given the mean is 4.2.
We have to find the probability that on any day, the number of special orders sent out will be exactly 3. Therefore, the value of x will be 5.
Using the Poisson distribution,
[tex]P(x) = \dfrac{e^{-\lambda}\lambda ^x}{x!}\\\\P(5) =\dfrac{e^{-4.2}(4.2)^5}{5!}\\\\P(5) = 0.1633[/tex]
Hence, the probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.
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Which statements are true? Select three options.
You can use for reference ;)
Describe the transformation of the function, y=1/7 x from y = x.
The transformation of the function, y=1/7 x from y = x is y = 7x
How to determine the transformation?The function is given as:
y = 1/7x
The transformation rule is given as:
y = x
This means that we swap x and y.
So, we have:
x = 1/7 y
Multiply through by 7
y = 7x
Hence, the transformation of the function, y=1/7 x from y = x is y = 7x
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A coach in a train can seat exactly 72 people for a trip. The train has 12 such coaches. If the train made 156 trips in full capacity this year, how many people has it carried in that time. I will give brain to the first person who answers this question correctly.
Answer:
134,784 people
Step-by-step explanation:
Hello!
Let's first find the number of people it can carry on 1 trip. We can do this by multiplying the number of people per coach, by the number of coaches.
72 x 12864The train carries 864 people per trip. We can find the number of people in 156 trips by multiplying 864 by 156.
864 x 156134,784The train, in full capacity, will carry 134,784 people in 156 trips.
how would i explain my students proportional reasoning
Answer:
proportional reasoning involved thinking about relationship and making comparisons of countries are values in the words of John went Diwali portion reasoning is difficulty find it is not something that you can or not to but is diploma over 3 reasoning
X. y.
-1. 1/10
0. 1/2
1. 5/2
2. 25/2
3. 125/2
What is the rate of change of the function described in the table?
a. 12/5
b. 5
c. 25/2
d. 25
Answer: B
Step-by-step explanation:
Each time x increases by 1, y is multiplied by 5.
20 people show up to the party and robert decides to give them
Answer:
This question looks and sounds like a "personal opinion question" to me.so from my opinion Robert give them a Smack in their ases .
Hope this helps .
Good luck ✅.
What is the slope of a line parallel to the line with equation 2x−5y=9?
25
−25
−95
−52
Answer:
For this one the parallel slope is going to be 2/5
Step-by-step explanation:
3) Which letter has a perpendicular line segment?
A. Y
B. L
C. R
D. U
Answer: L
Step-by-step explanation:
The two segments that form L meet at a 90 degree angle.
Silva the formula I=Prt, in general, to find the principal, p.
Dividing both sides by rt,
[tex]\boxed{P=\frac{I}{rt}}[/tex]