To the nearest whole percent, the percentage Yvette paid over the price of the sandwiches is 27%.
How is the percentage determined?The percentage represents a proportion of a whole value.
The percentage is determined as the quotient of the difference (increase or decrease) and the initial value, multiplied by 100.
The purchase price of restaurant sandwiches = $22
Sales tax = 8.5%
= $1.87 ($22 x 8.5%)
Additional tip for delivery = 18%
= $3.96 ($22 x 18%)
Total bill = $27.83 ($22 + $1.87 + $3.96)
Difference between the total bill and the purchase price = $5.83 ($27.83 - $22)
Percent difference = 26.5% ($5.83/$22 x 100)
= 27%
Thus, Yvette paid 27% above the price of the sandwiches in form of sales tax and tips.
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oscar bought some markers notebooks and packs of sticky notes for his office he bought the same number of markers as notebooks he bought three more packs of sticky notes than markers and notebooks combined he paid $1.05 for each marker $2.25 for each notebook, and the packs for sticky notes were $1.95. how many of each kind of office supply did oscar buy if he paid $49.05 in all?
The number of each kind of office supply oscar bought is = markers= (43.2 - 4.2y)/3 notebooks = (43.2-3x)/4.2, sticky notes = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3.
Calculation of total office supplyThe number of markers he bought = X
The number of notebooks he bought= y
The number of sticky notes he bought= z= 3 + X+y
The amount he paid for markers = $1.05*X
The amount he paid for notebooks = $2.25*y
The amount he paid for sticky notes= $1.95 (3 + X+y)
The total amount he paid is = $49.05
That is;
$49.05 = $1.05x + $2.25y + $1.95 (3 + X+y)
$49.05 = $1.05x + $2.25y + $5.85 + $1.95x + $1.95y
$49.05 - $5.85 = 3x + 4.2y
$43.2 = 3x + 4.2y
Make X the subject of formula,
3x = 43.2 - 4.2y
X = (43.2 - 4.2y)/3
y= (43.2-3x)/4.2
z = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3
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A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.4 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 3840 MB. How many downloads of the standard version were there?
Step-by-step explanation:
s = number of standard downloads
2s = number of high-quality downloads
2.8s + 4.6(2s) = 2760
2.8s + 9.2s = 2760
12s = 2760
s = 230
The standard version was downloaded 230 times and the high-quality version was downloaded 460 times.
Evaluate the given algebraic expressions replacing x with -2 and y with 1
3x^2
Answer:
12
Step-by-step explanation:
3x^2
because the information provided states that x = -2, that is what we are going to replace x with.
3(-2)^2
the next step is to evaluate the power because that is next in PEMDAS.
(-2)^2 = 4
that leaves us with:
3 * 4 = 12 ( the " * " represents the multiplication sign)
hope this helps!
A shoe repair operation uses a two-step sequence that all jobs in a certain category follow. All jobs can be split in half at both stations. For the group of jobs listed: JOB TIMES (minutes) A B C D E Workstation A 27 18 70 26 15 Workstation B 45 33 30 24 10 Click here for the Excel Data File a. Find the sequence that will minimize total completion time. b. Determine the amount of idle time for workstation B.
1. The sequence that will minimize the total completion time is sequence 4. B-A-C-D-E.
2. The determination of the amount of idle time for Workstation B is 37 minutes.
Johnson's Sequencing Rule:According to Johnson's sequencing rule, start listing jobs with minimum completion time first.
If the job occurs at Workstation A, list it on the left side. If the job occurs at Workstation B, list it on the right side, as below:
Data and Calculations:JOB TIMES (minutes) A B C D E
Workstation A 27 18 70 26 15
Workstation B 45 33 30 24 10
The first job with a minimum completion time is Job E at Workstation B.
The second job with a minimum completion time after Job E is Job B at Workstation A.
The third job with a minimum completion time after Job B is Job D at Workstation B.
The fourth job with a minimum completion time after Job D is Job A at Workstation A.
The last job is Job C at Workstation B.
The sequence that minimizes total completion time is as follows:
B A C D E
A B
Calculation of Idle Time at Workstation B:Job Workstation A Workstation B Idle Time
In Out In Out Workstation B
B 0 0+18 = 18 18 18+33 = 51 18
A 18 18+27 = 45 51 51+45 = 96 19
C 45 45+70 = 115 115 115+30 = 145 0
D 115 115+26 = 141 145 145+24 = 169 0
E 141 141+15 = 156 169 169+10 = 179 0
Total Idle Time at Workstation B = 37 (18 + 19)
Thus, the sequence that minimizes the total completion time is sequence 4, while the idle time at Workstation B is 37 minutes.
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Question Completion with Answer Options:1. A-B-C-D-E
2. E-D-B-C-A
3. D-C-B-A-E
4. B-A-C-D-E
5. C-A-B-D-E
please give answer to these fractions give STEPS
no scam 30 points + BRAINLIEST
1/2 × 3/5 ÷ 9/15 - 6/4 ÷ 4/1
Answer:
1/8
Step-by-step explanation:
Look at the screen shots
The terms 1/64, 1/32, 1/16 form a geometric progression (GP) If the sum of the GP is (2^36 – 2^-6), find the number of terms
If [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio of the series, then the sum of the first [tex]n[/tex] terms is
[tex]S_n = a + ar + ar^2 + \cdots + ar^n[/tex]
Multiply by [tex]r[/tex] on both sides, then subtract that from and solve for [tex]S_n[/tex].
[tex]rS_n = ar + ar^2 + ar^3 + \cdots + ar^{n+1}[/tex]
[tex](1-r)S_n = a - ar^{n+1}[/tex]
[tex]S_n = \dfrac{a(1-r^{n+1})}{1-r}[/tex]
Use the given first and second terms of the sequence to find [tex]a[/tex] and [tex]r[/tex].
[tex]a = \dfrac1{64}[/tex]
[tex]ar = \dfrac1{32} \implies \dfrac r{64} = \dfrac1{32} \implies r = \dfrac{64}{32}=2[/tex]
Solve for [tex]n[/tex].
[tex]S_n = \dfrac{1-2^{n+1}}{64(1-2)} = 2^{36} - 2^{-6}[/tex]
[tex]\dfrac{2^{n+1} - 1}{2^6} = 2^{36} - 2^{-6}[/tex]
[tex]2^{n-5} - 2^{-6} = 2^{36} - 2^{-6}[/tex]
[tex]\implies n-5 = 36 \implies \boxed{n = 41}[/tex]
When first hired, Deondre was earning $5.85 per hour. He has worked his way up in the business and is currently making $12.30 an hour. What is the absolute and relative change in Deondre's hourly pay from when he was first hired to now?
Answer:
$6.45/hour
110.26%
Step-by-step explanation:
The absolute change is the difference between salaries now ands then.
12.30 - 5.85 = 6.45
The relative change in the percent increase.
percent increase = (new number - old number)/(old number) × 100%
percent increase = (12.3 - 5.85)/(5.85) × 100%
percent increase = 110.26%
slove each problem include a diagram. a. A 6m long wheelchair ramp makes an angle of 15 with the ground. How high abouve the ground does the top end of the ramp reach. b.two treees are 120m apart. From the point halfway between them, then angle of the elevation to the top of the trees is 36 and 52. how much taller is one tree than the other.
The height of the ramp above the ground is 1.55 meters.
The difference between the height of the tree is 33.20 meters
How to find sides of a right triangle?The situation forms a right angle triangle.
Therefore, the height the ramp above the ground can be calculated as follows:
Using Pythagoras theorem,
sin 15 = opposite / hypotenuse
sin 15 = x / 6
cross multiply
x = 6 sin 15
x = 6 × 0.2588190451
x = 1.55291427062
x = 1.55
Therefore, the height of the ramp above the ground is 1.55 meters
tan 36 = opposite / adjacent
tan 36 = x / 60
x = 60 tan 36
x = 43.5925516803
x = 43.60 meters
tan 52 = y / 60
60 tan 52 = y
y = 76.7964979316
y = 76.79 meters
The difference between the height of the tree = 76.79 - 43.60 = 33.20 meters
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Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
Ty
O (x, y) - (x, -y)
O (x, y) - (y, x)
O (x, y) -- (-x, -y)
O (x, y) - (-y, -x)
The rule that describes the transformation is (x, y) - (-y, -x).
What is transformation?Transformation is the process of using rules to transform some graphics into something else.When a shape is either reflected, rotated, or translated, the coordinates of the vertices that make up the shape change.The four different forms of transformations—Translation, Reflection, Rotation, and Enlargement—are depicted in the following illustrations.The underlying coordinate system remains fixed while an object transformation modifies the coordinates of each point on the object in accordance with some rule. • A coordinate transformation expresses each point of the object in the new coordinate system by defining it in terms of the old one.The fourth option among the available choices depicts a 180° clockwise or counterclockwise rotation, in which is The vertices' x- and y-coordinates change to their opposites, i.e., x becomes -x and y becomes -y.
The rule that describes the transformation is (x, y) - (-y, -x).
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The lengths of the sides of a pentagons are 2'', 6'', 10'' , 14'', and 24''. calculate the lengths of the sides of a similar pentagon if the shortest side is 5'' .
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"How to get the lengths of the sides of a similar pentagon?
All the measures must be multiplied by the same scale factor to get a similar pentagon.
If in the original pentagon the shortest side measures 2", and in the similar pentagon the shortest side measures 5", then we have:
5" = k*2"
5"/2" = k = 2.5
Then the scale factor is 2.5
To get the other sides of the pentagon, we just need to multiply the other sides of the original pentagon by 2.5
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"If you want to learn more about similar figures:
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Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12)
Here, 12 is the mode.
Step-by-step explanation:
Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12) ?
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode.
So let's talk in brief:-
First, we arrange it in ascending order.
3,3,6,6,9,9,12,12,12,12
and now as we see that we get 12 as the most repeated ones.
reference link-
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For a normal distribution, find the probability of being (a) Between −1 and +1 (b) Between 3 standard deviations below the mean and 2 standard deviations above the mean (c) More than 3.5 standard deviations away from the mean Use the Standard Normal Table in your textbook or Excel to obtain more accuracy.
Using the normal distribution, the probabilities are given as follows:
a) 0.6826 = 68.26%.
b) 0.9759 = 97.59%.
c) 0.0004 = 0.04%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Item a:
The probability is the p-value of Z = 1(0.8413) subtracted by the p-value of Z = -1(0.1587), hence:
0.8413 - 0.1587 = 0.6826
Item b:
The probability is the p-value of Z = 2(0.9772) subtracted by the p-value of Z = -3(0.0013), hence:
0.9772 - 0.0013 = 0.9759.
Item c:
This probability is P(|Z| > 3.5), which is 2 multiplied by the p-value of Z = -3.5, which is of 0.0002.
Hence:
2 x 0.0002 = 0.0004 = 0.04%.
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Please help to solve these 3 questions
Based on the number of goals scored in the football matches, the mode is 4 goals. The median is 3 goals and the mean goals scored is 2.6 goals.
What are the statistics from the football matches?The mode is the number of goals that was scored in the most matches. This number is 4 goals as this was scored in 6 matches.
To find the median, order the numbers:
0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6
The median is:
= (3 + 3) / 2
= 3
The mean is:
= (0 + 0 + 0 + 0 + 1 + 1 + 2 +2 +2 + 3 + 3 + 3 + 4 + 4+ 4 + 4 +4 + 4 + 5 + 6) / 20
= 2.6 goals
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Hence, write down the smallest integer value of x that satisfies 7(6+x) -x>0
Answer:
-6
Step-by-step explanation:
[tex]7(6+x)-x > 0[/tex]
[tex]42 + 7x-x > 0[/tex]
[tex]42+6x > 0[/tex]
[tex]6x > -42[/tex]
[tex]x > -7[/tex]
The smallest integer that satisfies the condition, [tex]x > -7[/tex], is -6.
This is multiple choice pls help
Answer: b and e
Step-by-step explanation:
b - the slope is positive
the slope is 8 not negative 8 because, 4+4/2-1 = 8/1 = 8 since subtracting 4 and -4 makes it 4+4
e - it is possible for x to be positive and for y to be negative
If f(x) = 3x4 + 2x3 - x + 15,
what would be the list of
possible rational roots?
Answer: A. ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
Step-by-step explanation:
± [tex]\frac{1, 3, 5, 15}{1, 3}[/tex]
= ± [tex]1, 3, 5, 15, 1/3, 5/3, 5[/tex]
Rearranging, we get:
= ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
math stuff who ever answers right gets brainlest answer
Answer:
Median is 83
Range: 61
Step-by-step explanation:
The median is the number in the middle. The range is the max. number subtracted from the min number.
The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. (-3, 1)
The information given illustrates that the graph of the function decreasing.
How to illustrate the information?We say that a function is increasing on an interval if the function values increase as the input values increase within that interval.
Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval.
So according to the given graph on the interval (-3, 1) the graph is decreasing.
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which expression is equivalent to 7x^2 sqrt 2x^4 times 6 sqrt 2x^12 if x ≠ 0
The equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]
How to determine the equivalent expression?The expression is given as:
7x^2 sqrt 2x^4 times 6 sqrt 2x^12
Rewrite properly as:
[tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex]
Evaluate the product
[tex]7 * 6x^2 \sqrt{2x^4*2x^{12 }[/tex]
This gives
[tex]42x^2 \sqrt{4x^{16}[/tex]
Take the square root of 4
[tex]2*42x^2 \sqrt{x^{16}[/tex]
Take the square root of x^16
[tex]2*42x^2 *x^8[/tex]
So, we have:
[tex]84x^{10[/tex]
Hence, the equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]
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Answer:
Step-by-step explanation:
The equivalent expression of is
How to determine the equivalent expression?
The expression is given as:
7x^2 sqrt 2x^4 times 6 sqrt 2x^12
Rewrite properly as:
Evaluate the product
This gives
Take the square root of 4
Take the square root of x^16
So, we have:
Hence, the equivalent expression of is
What is it? I am not sure
Answer: I think its A
Step-by-step explanation: maybe
A company’s 5-year bonds are yielding 7% per year. Treasury bonds with the same maturity are yielding 5.2% per year, and the real risk-free rate (r* ) is 2.75%. The average inflation premium is 2.05%, and the maturity risk premium is estimated to be 0.1 3 (t 2 1)%, where t 5 number of years to maturity. If the liquidity premium is 0.7%, what is the default risk premium on the corporate bonds
Based on the required rate of return, the real risk free rate, and the inflation premium, the default risk premium on the corporate bonds is 1.2%
How is the default risk premium found?The default risk premium can be found as:
=real risk free rate + Inflation premium + default risk premium + liquidity premium + maturity risk premium
Solving gives:
= 0.07 - 0.0275 - 0.0205 - (0.1 x (t - 1)%)
= 0.07 - 0.0275 - 0.0205 - (0.1 x (5 years - 1)%)
= 1.2%
The default risk premium refers to the return that the bond is offering over what a risk-free bond would offer.
This means that the corporate bond described is offering 1.2% more than what a risk-free government bond would offer.
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What is the domain of y = 4 log5 (x - 3)?
A. all real numbers
B. all real numbers greater than 4
C. all real numbers greater than 5
D. all real numbers greater than 3.
The domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.
How to determine the domain?The function is given as:
[tex]y=4\log_5(x-3)[/tex]
Set the expression in bracket greater than 0
x -3 > 0
Add 3 to both sides
x > 3
Hence, the domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.
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Write the equation in slope-intercept form of the line that has slope
3 and y-intercept (0,1)
Answer:
y = 3x + 1
Step-by-step explanation:
The formula for equation of a line in slope intercept form is;
y = mx + c
Where;
m is slope
c is y-intercept
Now, since we have coordinates, we will get the equation as;
(y - y1)/(x - x1) = m
(y - 1)/(x - 0) = 3
y - 1 = 3x
y = 3x + 1
To save $5,000 for a vacation in 3 years, how much money must be invested each
year if the investment earns 5% interest compounded annually? Round to the
nearest dollar.
$15,762
$1,586
$3,000
$1,667
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]5000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 5000=P(1.05)^3 \\\\\\ \cfrac{5000}{1.05^3}=P\implies 4319\approx P[/tex]
The amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
How are annual payments or cash flows calculated?The annual payments represent the periodic cash outflows invested in accumulating a future value using an interest rate compounded for a period.
This can be achieved using the future value and present value formulas or factors.
We can also use an online finance calculator, as follows:
Data and Calculations:Future value = $5,000
Investment period = 3 years
Annual compound interest = 5%
N (# of periods) = 3 years
I/Y (Interest per year) = 5%
PV (Present Value) = $0
FV (Future Value) = $5,000 ($4,531.56 + $468.44)
Results:
PMT = $1,510.52
Sum of all periodic payments = $4,531.56 ($1,510.52 x 3_)
Total Interest = $468.44
Thus, the amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
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Question 2: 11 pts
A coin is tossed three times. Find the probability that 2 heads and 1 tail turn up in any order.
Answer:
3/8 or 0.375 or 37.5%
Step-by-step explanation:
So since the coin is tossed three times, it's not to hard to write out every scenario since there will only be 2^3 combinations or 8 combinations. But we can also use Binomial Distribution Formula.
Binomial Distribution Formula:
[tex]P(x)=(^n_x)p^xq^{n-x}[/tex]
Where p = probability of success and q=probability of failure, x=how many successes, and n=total number of trials
Combination Formula:
[tex](^n_x) = \frac{n!}{x!(n-x)!}[/tex]
So let's define the variable values, since it's a coin, the probability of heads/tails should be 50/50 so p=0.50 and q=0.50. Since we want 2 heads then x=2, and since the total number of trials is 3, n=3.
So let's plug the values into the equation:
[tex]P(x)=\frac{3!}{2!}*(0.50)^2*(0.50)^1[/tex]
Rewrite 0.50 as a fraction
[tex]P(x)=\frac{3*2*1}{2*1}*(\frac{1}{2})^2*(\frac{1}{2})^1[/tex]
Cancel out values in fraction, and also square the fraction
[tex]P(x)=3*\frac{1}{4}*\frac{1}{2}[/tex]
Multiply fractions
[tex]P(x)=3*\frac{1}{8}[/tex]
Multiply the two values
[tex]P(x)=\frac{3}{8}[/tex]
This means the probability is 3/8 or 0.375 or 37.5%
I also provided a diagram on how to just draw out each scenario/combination
Mariana and her best friend are attending a concert in a large auditorium. They just climbed up 125 steps. The number of steps they climbed can be represented by
zero
positive
negative
The number of steps they climbed can be represented by positive
How to represent the number of steps?From the question, we understand that they climbed up
Upward movements are usually represented by the positive sign
This means that:
Steps = 125 or +125
Hence, the number of steps they climbed can be represented by positive
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Factor:
y(a−b)-(a−b)
Answer: [tex](a-b)(y-1)[/tex]
Step-by-step explanation:
Factoring out (a-b) gives [tex](a-b)(y-1)[/tex].
Solve the following system of equations by elimination. What is the value of x? x = 1.5 x = -1.5 x = 8 x = -8
Using the elimination method, the value of x in the system of equations is calculated as: 8.
How to Solve a System of Equations by Elimination?To solve a system of equations given using the elimination method, do the following:
Multiply 2x - 5y = 1 by 2 and multiply -3x + 2y = -18 by 5 to get the following:
4x - 10y = 2 --> eqn. 1
-15x + 10y = -90 --> eqn. 2
Add
-11x = -88
Divide both sides by -11
x = 8
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The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based on this data, consider the equation of the regression line, yˆ=b0+b1x, for using the completion percentage to predict the interception percentage for an NFL quarterback. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Table
6 steps
The regression equation is y = -0.42647x + 29.11471 and the correlation coefficient is -0.9607
How to determine the regression equation?The table of values is given as:
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Next, we enter the above values in a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 305Sum of Y = 15.5Mean X = 61Mean Y = 3.1Sum of squares (SSX) = 34Sum of products (SP) = -14.5r = -0.9607Regression Equation = ŷ = bX + a
b = SP/SSX = -14.5/34 = -0.42647
a = MY - bMX = 3.1 - (-0.43*61) = 29.11471
So, the regression equation is
y = -0.42647x + 29.11471
And the correlation coefficient is -0.9607
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A text message plan costs $9 per month plus $0.39 per text. Find the monthly cost for x text message The monthly cost of x messages is dollars. (Use integers or decimals for any numbers in the expression.) *
Answer:
The monthly cost = $9 + $0.39x
Step-by-step explanation: