The correct answer is interval 2. A function is a rule that relates each element in one set, called the domain, to exactly one element in another set, called the range.
What is function?It is a mathematical expression that takes an input, performs a calculation and produces an output.
In order to determine if dy/dx>0 and d2y/dx2<0 over interval 2, we must take the first and second derivatives of the function y=f(x). The first derivative of the function is dy/dx=2x-3 and the second derivative of the function is d2y/dx2=2.
Now, if we look at the graph, we can see that the function is increasing from 0 to 3 and then decreasing from 3 to 6. This means that over interval 2, which is from 3 to 6, the first derivative, dy/dx, must be negative. This means that dy/dx<0 over interval 2.
Furthermore, the second derivative, d2y/dx2, must be negative over interval 2 since the graph is decreasing over this interval. This means that d2y/dx2<0 over interval 2.
Therefore, the correct answer is interval 2 since it is the only interval for which both dy/dx>0 and d2y/dx2<0 are true.
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uhhh yes i need help Each parking spot is eight and one-half feet wide. A parking lot has 24 parking spots side by side. How long is the row of parking spaces in yards?
The 24 parking spοt length is 68 yards.
What is unit cοnversiοn?The same feature is expressed in a different unit οf measurement thrοugh a unit cοnversiοn. Time can be stated in minutes rather than hοurs, and distance can be expressed in kilοmetres rather than miles, οr in feet rather than any οther unit οf length.
Here the given width of One parking spot is eight and one-half feet.
Now we know that 1 feet = [tex]\frac{1}{3}[/tex] yard,
Then , [tex]8\frac{1}{2}[/tex] feet = [tex]\frac{17}{2}[/tex] feet = [tex]\frac{17}{2}\times\frac{1}{3}[/tex] = [tex]2\frac{5}{6}[/tex] yd.
Now Parking lot have 24 parking spot, Then,
=> Total length of parking lοt = 24 [tex]\times[/tex] [tex]2\frac{5}{6}[/tex] = [tex]24\times\frac{17}{6}[/tex] = 68 yard.
Hence The length of parking lοt is 68 yard.
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A spinner is divided into 4 equal sections. The probability of landing on A is 1/4. Brandy spins the spinner 24 times. How many times can she expect the spinner to land on A?
Answer:
6 times
Step-by-step explanation:
24/4 = 6
find the critical points and critical values of the function z=x^3+6xy-y^3-1
Answer:
∂z/∂x = 3x^2 + 6y
∂z/∂y = 6x - 3y^2
Now, we need to solve the system of equations:
3x^2 + 6y = 0
6x - 3y^2 = 0
From the first equation, we get:
y = -x^2/2
Substituting this into the second equation, we get:
6x - 3(-x^2/2)^2 = 0
Simplifying, we get:
6x - 3x^4/4 = 0
Multiplying by 4 and rearranging, we get:
3x^4 - 24x = 0
Factoring out 3x, we get:
3x(x^3 - 8) = 0
Therefore, the critical values of x are x = 0 and x = 2.
For x = 0, we have y = 0 (from y = -x^2/2). So, one critical point is (0, 0).
For x = 2, we have y = -2. So, the other critical point is (2, -2).
To find the critical values of the function, we need to evaluate the function at each critical point:
z(0, 0) = 0^3 + 6(0)(0) - 0^3 - 1 = -1
z(2, -2) = 2^3 + 6(2)(-2) - (-2)^3 - 1 = -13
Therefore, the critical values of the function are -1 and -13.
Evaluate:
13-0.75w+8x when w = 12 and x = 1/2
(need help! fast! TmT)
Answer: To evaluate 13 - 0.75w + 8x when w = 12 and x = 1/2, we substitute these values into the expression:
13 - 0.75w + 8x = 13 - 0.75(12) + 8(1/2)
Simplifying the expression inside the parentheses first:
13 - 9 + 4 = 8
Substituting this value into the expression:
13 - 0.75w + 8x = 13 - 0.75(12) + 8(1/2) = 13 - 9 + 4 = 8 + 4 = 12
Therefore, the value of 13 - 0.75w + 8x when w = 12 and x = 1/2 is 12.
Answer:
8
Step-by-step explanation:
Given expression is
[tex]13-0.75w\:+\:8x[/tex]
and we are asked to evaluate this expression when
[tex]w = 12 ,\: x = \dfrac{1}{2}[/tex]
[tex]0.75w = 0.75 \times 12 = 9[/tex]
[tex]8x = \8 \times \dfrac{1}{2} = 4[/tex]
[tex]\text{So the expression at $w = 12 \; , x= \dfrac{1}{2}$ evaluates to}[/tex]
13 - 9 + 4 = 8
Answer: 8
List the set of possible rational zeros for f(x)=x^4-5x^3+8x^2-20x+16
show work
Answer:
Step-by-step explanation:
The possible rational zeros of a polynomial function are all the possible values of x, where x is a factor of the constant term of the function divided by a factor of the leading coefficient of the function.
For the polynomial function f(x) = x^4 - 5x^3 + 8x^2 - 20x + 16, the constant term is 16 and the leading coefficient is 1. Therefore, the possible rational zeros are all the possible values of x, where x is a factor of 16 divided by a factor of 1. That is, the possible rational zeros are:
±1, ±2, ±4, ±8, ±16
To check if any of these possible zeros are actually zeros of the function, we can use synthetic division or long division to test each one.
A survey was done with 50 students currently taking Algebra 1 at Laurel Springs School. They were asked which they preferred - English or mathematics? Out of the 50 students, 30 were male. There were 35 students who preferred mathematics and out of those that preferred mathematics, 24 were male. Create a two way relative frequency table for the data. According to the table, would it be safe to assume that females prefer English and males prefer mathematics? Why or why not?
we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12).
HOW TO SOLVE THE QUESTION?
To create a two-way relative frequency table, we can use the following table:
| English | Mathematics | Total
--------|---------|-------------|-------
Male | x | 24 | 30
Female | y | 11 | 20
--------|---------|-------------|-------
Total | 35 | 35 | 50
Here, x and y represent the number of male and female students who preferred English, respectively.
To calculate the values for x and y, we can use the fact that there were 35 students who preferred mathematics, and 24 of them were male. Therefore, the number of females who preferred mathematics is 35 - 24 = 11. Since there are a total of 20 female students, the number of females who preferred English is 20 - 11 = 9. Similarly, the number of male students who preferred English is 30 - 24 = 6.
To calculate the relative frequencies, we can divide each cell by the total number of students (50). For example, the relative frequency of male students who preferred mathematics is 24/50 = 0.48.
The resulting two-way relative frequency table is as follows:
| English | Mathematics | Total
--------|---------|-------------|-------
Male | 0.12 | 0.48 | 0.60
Female | 0.18 | 0.22 | 0.40
--------|---------|-------------|-------
Total | 0.30 | 0.70 | 1.00
From this table, we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12). However, it would not be safe to assume that all females prefer English and all males prefer mathematics based on this data alone, as there may be individual variations and exceptions to this trend.
It's also important to note that the sample size is relatively small, with only 50 students surveyed, and may not be representative of the larger population. Further research with a larger and more diverse sample size would be needed to make more accurate conclusions about gender-based preferences in this population
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11) The Hillmans have $12,000 in a savings
account. The bank pays 1.25% interest on
the savings account, compounded
continuously.
Find the total balance after three years.
A) $12,290.21
C) $11,345.89
B) $12,458.54
D) $11,452.16
Answer:
To find the total balance after three years, we can use the formula for continuous compounding:
A = Pe^(rt)
Where A is the total balance, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.
In this case, P = $12,000, r = 0.0125 (1.25% expressed as a decimal), and t = 3. Plugging these values into the formula, we get:
A = $12,000 x e^(0.0125 x 3)
A = $12,000 x e^(0.0375)
A = $12,000 x 1.038163
A = $12,458.54
Therefore, the total balance after three years is $12,458.54.
How do you multiply a fraction by a whole number
Answer:
Write the whole number as a fraction by placing it over 1. For example, if you want to multiply 2/5 by 3, you can write 3 as 3/1.
Multiply the numerators of the two fractions together. For example, 2/5 x 3/1 = (2 x 3) / 5 = 6/5.
Simplify the resulting fraction, if necessary, by reducing it to its lowest terms. For example, 6/5 can be simplified to 1 1/5 (or 1.2 as a decimal).
Therefore, when you multiply a fraction by a whole number, you multiply the numerator of the fraction by the whole number and keep the denominator the same.
Step-by-step explanation:
21 is greater than the sum of 15 and two times a number X
Answer:21>15+2x
Step-by-step explanation:
The graph shows a proportional relationship.
Answer:
The Answer Is 6
Explanation: Divide y by x on each dot to get k
⦁ What is the product of -2^3 + x - 5 and x^3 -3x +4 ?
⦁ Show your work.
⦁ Is the product of -2^3 + x - 5 and x^3 -3x +4 equal to the product of x^3 -3x +4 and -2^3 + x - 5 ? Explain your answer.
The product of -2³ + x - 5 and x³ -3x +4 is -5x³ + 16x - 28.
How did we get the value?The given expression is:
-2³ + x - 5 x (x³ -3x +4)
We need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, let's simplify -2³, which means -2 x 2 x 2 = -8, so we have:
-8 + x - 5 x (x³ -3x +4)
Next, we need to distribute the -5 to the terms inside the parentheses:
-8 + x - 5x³ + 15x - 20
Now we can combine like terms:
-5x³ + 16x - 28
Therefore, the product of -2³ + x - 5 and x³ -3x +4 is -5x³ + 16x - 28.
Now, to answer the second part of the question, we need to check if:
-2³ + x - 5 x (x³ -3x +4) = (x³ -3x +4) * (-2³ + x - 5)
We can simplify both expressions first:
-8 + x - 5x³ + 15x - 20 = -8 + x - 5x³ + 15x - 20
We can see that both expressions are identical, which means that the product of -2³ + x - 5 and x³ -3x +4 is equal to the product of x³ -3x +4 and -2³ + x - 5, regardless of the order in which we multiply the factors.
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Which description compares the vertical asymptote(s) of Function A and Function B correctly? Function A: f(x)=1/x−3 Function B: A hyperbola graphed on a grid with the x and y axis beginning at negative ten and increasing in increments of two until reaching ten. The hyperbola, labeled g of x, contains an asymptote at x equals four. The branches of the hyperbola are oriented so they open to the upper right and lower left corners of the asymptote. The lower left branch passes through begin ordered pair zero comma zero end ordered pair as a smooth curve. The upper right branch passes through begin ordered pair eight comma two end ordered pair as a smooth curve. Responses Both functions have a vertical asymptote at x = 4. Both functions have a vertical asymptote at x = 4. Function A has two vertical asymptotes. Function B has one vertical asymptote. Function A has two vertical asymptotes. Function B has one vertical asymptote. Function A has a vertical asymptote at x=−3 . Function B has a vertical asymptote at x = 4. Function A has a vertical asymptote at , x = − 3 , . Function B has a vertical asymptote at x = 4. Function A has a vertical asymptote at x = 3. Function B has a vertical asymptote at x = 4.
Answer:
The answer is D
Step-by-step explanation:
Function A
f(x) = 1 / ( x - 3)
The vertical asymptote is the value of x that makes x - 3 = 0 ⇒ x = 3
The vertical asymptote of B is x = 4
So....
Function A has a vertical asymptote at x = 3.
Function B has a vertical asymptote at x = 4.
What is the result when 4x - 3 is subtracted from 6x - 9?
(A)-2x - 6
(B)-2x + 6
(C) 2x - 6
(D) 2x + 6
(E) 10x - 12
Answer: 2x-6
Step-by-step explanation:
The mean of a sample of 50 claim amounts arising from a certain kind of insurance policy is R4500. Fifteen of these claim amounts have mean R2109 while 14 others have mean R3704. Calculate the mean of the remaining claim amounts in this sample.
The mean οf the remaining claim is R6739.
What is mean?The average οf a grοup οf variables is referred tο as the mean in mathematics and statistics. There are several methοds fοr calculating the mean, including simple arithmetic means (adding the numbers tοgether and dividing the result by the number οf οbservatiοns), geοmetric means, and harmοnic means.
Here We knοw that,
Mean = Sum οf amοunts οf claim / Tοtal number οf claim
Accοrding tο the given,
Mean οf 50 claim οf insurance pοlicy = R 4500 then,
Sum οf amοunt οf 50 claim = 4500*50 = R 225000
Mean οf 15 οf these claim = R 2109 then,
Sum οf amοunt οf 15 claims = 2109*15 = R 31635
Mean οf 14 οther claim = R 3704 then
Sum οf 14 οther claim = 3704*14 = R 51856
Nοw remaining claim amοunt = 50-14-15 = 21
Sum οf 21 remaining claim = 225000-31635-51856 = R 141509
Now Mean = Sum of 21 amount of claim / Total number of claim
=> Mean = 141509/21 = R 6739
Hence the mean of remaining 21 sample is R 6739.
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Tom can paint a fence in 12 hours. Huck can paint the same fence in 10 hours. How long would it take to put two coats of paint on the fence if Tom and Huck work together? Answer as an improper fraction, then round to 1 decimal place. 3) Kim and Josh can clean a house together in 3 hours. If it takes Kim 7 hours to clean the house by herself, how long would it take Josh to clean the house alone? Leave your answer in improper fraction form, then convert to a decimal. 4) Jack can mow the baseball grounds in 2 hours; Mike can mow the same grounds in 3 hours; and Chris can mow the grounds in 4 hours. How long will it take to mow the baseball grounds if Jack, Mike, and Chris work together? Leave your answer in proper fraction form, then round to 1 decimal place. Using your rounded answer, how many minutes would that be?
2) They tοgether will take 10.9 hours οr 120/11
3) jοsh will take 21/11 hrs οr 1.9 hrs
4) Tοgether they will take 36/13 οr 2.8 hrs
What is decimal place?The place values οf the digits in a decimal number are displayed οn the decimal place value chart. We knοw that a digit in a number represents a numerical value οr place value.
Decimal place value charts are used tο determine the prοper placement οf each digit in a decimal number.
A decimal number cοnsists οf a whοle number and a fractiοnal cοmpοnent, separated by the decimal pοint, a dοt.
Fοr instance, the decimal number 4.37 has twο parts: an actual number pοrtiοn οf 4 and a fractiοnal pοrtiοn οf 37.
Sοlutiοns tο the abοve prοblem
2) Tοm takes = 12 hrs
Huck takes= 10hrs
We can aply unitary methοd
tοgether they will take= 1/12+1/10=2/t
11t=120;
t=120/11 οr 10.9 hrs
3) Tοgether Kim and jοsh can clean the hοuse tοgether in = 3 hrs
Kim takes = 7hrs
Jοsh will take= 1/7+1/x=2/3
3x+21=14x
21=11x
x=21/11 οr 1.9 hrs
4) Jack makes baseball grοunds in= 2 hrs
Mike takes= 3 hrs
Chris takes= 4 hrs
Tοgether they will take= 1/2+1/3+1/4=3/x
13x=36
x=36/13 οr 2.8 hrs
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Find the area of the quadrilateral below.
Give you answer in cm² and give any decimal answers to 1 d.p.
Answer:
[tex]36 \: cm ^{2} [/tex]
Step-by-step explanation:
triangle area below
[tex] \frac{10 \times 5}{2} = 25[/tex]
EG segment
[tex] \sqrt{10 ^{2} + 5 ^{2} } = \sqrt{125} [/tex]
EF segment
[tex] \sqrt{ (\sqrt{125})^{2} - 2^{2} } = \sqrt{121} [/tex]
triangle area above
[tex] \frac{ \sqrt{121} \times 2}{2} = \sqrt{121} [/tex]
total area
[tex]25 + \sqrt{121} = 36[/tex]
Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .05 significance level.
The null and alternative hypothesis would be:
The test is:
two-tailed
right-tailed
left-tailed
Based on a sample of 60 men, 25% owned cats
Based on a sample of 60 women, 30% owned cats
The test statistic is:
(to 2 decimals)
The p-value is:
(to 2 decimals)
Based on this we:
Fail to reject the null hypothesis
Reject the null hypothesis
The assertion that the percentage of males who own cats is lower than the percentage of women who do not own cats is unsupported by sufficient data.
Hence, the Alternate hypothesis would be:
H0: Pm = Pf
H1 = Pm < Pf
What is Alternate hypothesis?Alternate hypotheses are used in statistical hypothesis testing. The hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.
Given information:
The test claims proportion of men who owns cat is smaller.
The significance level = 0.005
As the hypothesis always gets ten statements of equality but in the case given alternate hypothesis will claim.
Now calculating the Z-value:
P= 10+14/80
= 0.3
So, the p-value according to the obtained Z value is 0.1365.
Since, 0.1365>0.005, we fail to reject the hypothesis.
Hence, there is not enough proof to support the claim that the proportion of man who owns the cat is less than that of the proportion of women who owns the cat.
Therefore, the Alternate hypothesis would be:
H0: Pm = Pf
H1 = Pm < Pf
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I think account has a balance of $120 on January 1. Describe a situation in which the account balance for each month February 1 March 1 forms the following sequences in exercise one and two. Write the first three terms of each sequence.
In exercise 1:
Situation: The account holder saves $30 each month
The first three terms of the sequence are: $120, $150, $180.
In exercise 2:
Situation: The account earns 25% interest each month.
The first three terms of the sequence are: $120, $150, $187.50.
What is a sequence?A sequence in mathematics is described as an enumerated collection of objects in which repetitions are allowed and order matters.
Explaining exercise 1:
In this exercise, the account balance for each month should form an arithmetic sequence with a common difference of $30
February 1 balance: $150
March 1 balance: $180
Hence, we have the first three terms of the sequence as: $120, $150, $180.
Explaining exercise 2:
In this exercise, the account balance for each month should form a geometric sequence with a common ratio of 1.25.
The account earns 25% interest each month is the situation here.
February 1 balance: $150
March 1 balance: $187.50
The first three terms of the sequence are: $120, $150, $187.50.
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Please answer this question with the following proofs.
Answer:
Line DB and AC intersect at point E.
∠AEB = ∠DEC because they are vertical angles.
∠EAB and ∠ECD are alternate interior angles because AB and CD are parallel lines and line AC crosses through both parallel lines.
m∠EAB = m∠ECD because they are alternate interior angles.
ΔABE ≅ ΔCDE because there are two sets of congruent angles.
Prove that Re(z1,z2-bar) = modulus of z1 * modulus of z2 iff arg z1 = arg z2 + 2*pi*n.Use polar form with arg measured in radians
Answer:
Step-by-step explanation:
We can start by writing the given equation in terms of polar form:
Re(z1,z2-bar) = modulus of z1 * modulus of z2
If we write z1 and z2 in polar form, we get:
z1 = r1(cosθ1 + i sinθ1)
z2 = r2(cosθ2 + i sinθ2)
Then, the conjugate of z2 is:
z2-bar = r2(cosθ2 - i sinθ2)
Using the formula for the real part of the product of two complex numbers, we get:
Re(z1,z2-bar) = Re(z1 * z2-bar)
Substituting the expressions for z1 and z2-bar, we get:
Re(z1,z2-bar) = Re(r1(cosθ1 + i sinθ1) * r2(cosθ2 - i sinθ2))
Simplifying the product, we get:
Re(z1,z2-bar) = Re(r1r2[(cosθ1 cosθ2 + sinθ1 sinθ2) + i(sinθ1 cosθ2 - cosθ1 sinθ2)])
The real part of this expression is:
Re(z1,z2-bar) = r1r2(cosθ1 cosθ2 + sinθ1 sinθ2)
Using the identity cos(θ1 - θ2) = cosθ1 cosθ2 + sinθ1 sinθ2, we can write:
Re(z1,z2-bar) = r1r2 cos(θ1 - θ2)
Now we can substitute this expression back into the original equation and get:
r1r2 cos(θ1 - θ2) = r1r2
Dividing both sides by r1r2, we get:
cos(θ1 - θ2) = 1
This equation is true if and only if θ1 - θ2 = 2πn for some integer n. In other words, θ1 = θ2 + 2πn, where n is an integer.
Therefore, we have proved that Re(z1,z2-bar) = modulus of z1 * modulus of z2 if and only if arg z1 = arg z2 + 2πn, where n is an integer.
which is a scaled copy of plugin A ? identify a pair of corresponding sides and a pair of corresponding angles. compare the areas of the scaled copies
Therefore , the solution of the given problem of angles comes out to be A is larger than B in terms of size and scale variables can be used with this technique.
An angle meaning is what?A tilt is a form in Euclidean geometry made up of two sides, but rather cylindrical faces, that divide at the barrier's centre and apex. At their junctions, two rays may combine to form an angle. Angle is another outcome of two entities interacting. Dihedral shapes best describe them. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends.
Here,
Consider Polygon A to be a square with the dimensions 2 feet by 5 feet.
=> Size = 2 feet
=>Size = 51 t
The dimension of A can be multiplied by the same scale factor to obtain potential scaled duplicates.
Consider for instance, the scale factor k is:
A scaled-down version of rectangle A is 6 feet by 15 feet, for example.
You obtain this by:
=> Length: 2 feet, 3 inches. 5 feet 15 feet wide
Area A consists of:
=> Area = 2 feet × 5 feet 2
B's size is 90 feet²
=> 2 Arca = 15 feet²
Comparison
A is larger than B in terms of size.
Scale variables can be used with this technique.
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in the 3rd quadrant, find SIN
12x(x+3)=0 using zero product property
Answer:
0, -3.
Step-by-step explanation:
12x(x+3)=0
Either 12x = 0 or (x + 3) = 0
x = 0/12 or x = -3
So, x = 0 or x = -3
Assume that when adults with smartphones are randomly selected, 44% use them in meetings or classes. If 7 adult smartphone users are randomly selected, find the probability that exactly 5 of them use their smartphones in meetings or classes.
Answer:
The probability that exactly 5 of the 7 selected smartphone users use their phones in meetings or classes is approximately 0.0127 or 1.27%.
Write and solve a problem about base pay and commission. Show your work.
"Problem:
Jenny earns a base pay of $1000 per month plus a 5% commission on all sales. Last month she sold $8000 worth of products. What was her total earnings for the month?
Solution:
Jenny's commission for the month is 5% of $8000, which can be calculated as:
Commission = 5% of $8000 = (5/100) * $8000 = $400
Her total earnings for the month can be found by adding her base pay and commission:
Total Earnings = Base Pay + Commission
Total Earnings = $1000 + $400
Total Earnings = $1400
Therefore, Jenny's total earnings for the month were $1400." (ChatGPT, 2023)
4. If triangle ABC has the following measurements, find the measure of side c:
a = 5
B = 7
C = 42 degrees
Using cosine rule, the measure of side c is calculated as: 4.688
How to use the cosine rule?In trigonometry, the Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
We are given the parameters as:
a = 5
B = 7
C = 42 degrees
Using cosine rule, we have:
c = √(a² + b² - 2ab cos C)
c = √(5² + 7² - 2(5 * 7) cos 42)
c = √(25 + 49 - 52.02)
c = √21.98
c = 4.688
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For problems 1 – 6, perform the conversions.
1. 7
16
= % 2. 4
3
5 = __ %
3. Express 55% as a fraction in simplified form: ___
4. Express 248% as a mixed number in simplified form: __
5. 0.00031 = __ % 6. 6.005 = __ %
7. Gigi spent 12% of her birthday money on a new pair of sunglasses. What fraction of her
birthday money did she spend on the new sunglasses?
8. Veronica and her friends went out for pizza to celebrate the volleyball team’s victory.
Their total bill for the pizza and soft drinks was $27.50. They left a 20% tip for their
server. How much tip did they leave?
Answer:
1. 7/16 = 43.75%
2. 4/5 = 80%
3. 55% = 55/100 = 11/20
4. 248% = 2 48/100 = 2 12/25
5. 0.00031 = 0.031%
6. 6.005 = 600.5%
7. 12% = 12/100 = 3/25 (Gigi spent 3/25 of her birthday money on the new sunglasses)
8. The total bill for pizza and soft drinks was $27.50. With a 20% tip, the amount of tip left would be:
Tip = 20% of total bill
Tip = 20/100 * $27.50
Tip = $5.50
Therefore, Veronica and her friends left a $5.50 tip for their server.
Step-by-step explanation:
Answer:
1. 43.75%
2. 60%
3. 11/20
4. 2 and 12/25
5. 0.031%
6. 600.5%
7. 3/25
8. $5.50
Step-by-step explanation:
1. 7 ÷ 16 = 0.4375
0.4375 x 100 = 43.75%
2. 3 ÷ 5 = 0.6
0.6 x 100 = 60%
3. 55/100
11x25 / 20x5 = 11/20
4.248/100
62x4 / 25x4
62/25
62/25 = 2R12
2 12/25
5. 0.00031 x 100 = 0.031%
6. 6.005 x 100 = 600.5%
7. 12% = 12/100.
12/100 simplified = 3/25
8. $27.50 x 20% = $5.50
5. A rock is thrown directly upward with an initial velocity of 79 feet per second from a cliff 50 feet above a beach. The height of the rock above the beach (h) after t seconds is given by the equation h = -16t² + 79t + 50. The graph below shows the rock's height as a function of time.
5. The quadratic function for the height of the rock, h = -16·t² + 79·t + 50, indicates;
a. The height of the rock will be 125 feet above the beach at 1.28 seconds and 3.66 seconds after it is thrown
b. The maximum height reached is about 147.5 feet
The time it takes the rock to reach the maximum height is about 2.47 seconds
What is a quadratic function?
A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where, a, b, and c are numbers, and a ≠ 0.
The initial velocity of the rock = 79 ft/s
Height of the cliff above the beach from which the rock is thrown = 50 feet
The function for the height of the rock above the beach is; h = -16·t² + 79·t + 50
Please find attached the graph of the height of the rock as a function of time, created with MS Excel.
Required; When the height of the rock will be 125 feet above the beach
When the height of the rock is 125 feet, we get;
h = 125 = -16·t² + 79·t + 50
-16·t² + 79·t + 50 - 125 = 0
-16·t² + 79·t - 75 = 0
The value of t obtained using an online tool are;
t = (79 + √(1441))/32 ≈ 3.66 and t = (79 - √(1441))/32 ≈ 1.28
The times at which the height of the rock will be 125 feet above the beach are; 1.28 seconds and 3.66 seconds after the rock is thrown
b. The maximum height of the rock can be obtained from the formula for finding the maximum height of a quadratic equation of the form; f(x) = a·x² + b·x + c, which is;
At the maximum point, x = -b/(2·a)
The function for the height; h = -16·t² + 79·t + 50, indicates that we get;
a = -16, b = 79, and c = 50
Therefore;
The time it takes the rock to reach the maximum height, t(max), is therefore;
t(max) = -79/(2 × (-16)) ≈ 2.47
It takes about 2.47 seconds for the rock to reach the maximum height
The maximum height, h(max) = -16 × 2.46875² + 79×2.46875 + 50 ≈ 147.5
The maximum height reached by the rock is about 147.5 feet
Possible part of the question, obtained from a similar online question, includes;
a. The time it takes the rock to reach a height of 125 feet above the beach
b. The maximum height reached by the rock and the duration it takes the rock to reach the maximum height.
Please find attached the possible graph in the question, created with MS Excel, using the function for the height of the rock.
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A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelets is 7 grams And the amount of gold in each necklace is 24 grams. The jeweler used 172 grams of gold and made 2 more necklaces than bracelets. Write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define variabkes
The jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.
What is equations ?An equation is a mathematical statement that shows that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems by finding the values of the variables that make the equation true.
According to given information :Let x be the number of bracelets made, and y be the number of necklaces made.
Then, we can create the following system of equations:
Equation 1: 7x + 24y = 172 (the total amount of gold used is 172 grams)
Equation 2: y = x + 2 (the number of necklaces made is 2 more than the number of bracelets made)
So, the variables are x (the number of bracelets made) and y (the number of necklaces made).
We can solve this system of equations to find the values of x and y. We can use substitution or elimination to solve for one variable and then plug it into the other equation.
Substitution method:
From Equation 2, we have y = x + 2. Substituting this into Equation 1, we get:
7x + 24(x+2) = 172
7x + 24x + 48 = 172
31x = 124
x = 4
So, the jeweler made 4 bracelets.
Plugging this into Equation 2, we get:
y = x + 2 = 4 + 2 = 6
So, the jeweler made 6 necklaces.
Therefore, the jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.
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Sarah deposited $200 in a savings account earning 7% interest,
compounded annually. To the nearest cent, how much interest will she
earn in 4 years?
The interest earned by Sarah in four (4) years is approximately $62.16.
How much interest is earned by Sarah?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that;
Principal P = $200Compounded annaully n = 1Time t = 4 yearsInterest rate R = 7%Accrued amount A = ?Interest I = ?First, we convert R as a percent to r as a decimal
r = R/100
r = 7/100
r = 0.07
Now, the the values into the above formula and solve for accrued amount (A).
A = P( 1 + r/n )^( n × t )
A = $200( 1 + 0.07/1 )^( 1 × 4 )
A = $200( 1 + 0.07 )^( 4 )
A = $200( 1.07 )^( 4 )
A = $262.16
Now, we know that;
Accrued amount (A) = Principal (P) + Interest (I)
Solve for Interest (I)
$262.16 = $200 + I
I = $262.16 - $200
I = $62.16
Therefore, the interest earned is $62.16.
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