Therefore, the shortest possible length for the service road is approximately 4.37 miles, rounded to the nearest hundredth.
Let's label the vertices of the right triangle as A, B, and C, with A being the airport, B being the factory, and C being the shopping center. We can also label the intersection of the highways that connect A and B as D.
Since we have a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse AC:
\(AC^2 = AB^2 + BC^2\)
\(AC^2 = 6^2 + 4.8^2\)
\(AC^2 = 36 + 23.04\)
\(AC^2 = 59.04\)
\(AC = \sqrt(59.04)\)
\(AC = 7.68\)
To find DE, we need to first find the length of BD. We can do this by using the Law of Cosines:
\(BD^2 = AB^2 + AD^2 - 2ABADcos(A)\)
\(BD^2 = 6^2 + 3.6^2 - 263.6cos(90)\)
\(BD^2 = 36 + 12.96\)
\(BD^2 = 48.96\)
\(BD =\sqrt(48.96)\)
\(BD = 6.99\)
Now we can use the Law of Sines to find the length of DE:
\(DE/BC = BD/AC\)
\(DE = BCBD/AC\)
\(DE = 4.86.99/7.68\)
\(DE = 4.37\)
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9
Answer:
D) -\(\frac{3}{2}\)
Step-by-step explanation:
if 2 lines are perpendicular, one line has the opposite reciprocal of the other line.
Answer:
D,_3/2
Step-by-step explanation:
when two lines are perpendicular, m¹=_1/m²
find the dimensions of a rectangle of area of 324 square feet that has the smallest possible perimeter.
The dimensions of the rectangle that minimize the perimeter are 18 feet by 18 feet.
To find the dimensions of a rectangle with an area of 324 square feet and the smallest possible perimeter, we need to minimize the perimeter while maintaining the given area. The area of a rectangle is given by the formula:
Area = length × width
Now, let's find the dimensions that result in the smallest perimeter.
The dimensions of the rectangle that minimize the perimeter are 18 feet by 18 feet.
1. We know the area is 324 square feet, so we can write the equation:
324 = length × width
2. To minimize the perimeter, the rectangle should be as close to a square as possible because a square has the smallest possible perimeter for a given area.
3. Find the factors of 324 to determine which pair of numbers is closest to being equal. The factors are:
1×324, 2×162, 3×108, 4×81, 6×54, 9×36, 12×27, and 18×18
4. Among these factor pairs, 18×18 is the closest to being equal, so the dimensions are 18 feet by 18 feet.
5. The smallest possible perimeter is achieved when the rectangle is a square with side lengths of 18 feet. The perimeter can be calculated as:
Perimeter = 2 × (length + width) = 2 × (18 + 18) = 2 × 36 = 72 feet
So, the dimensions of the rectangle with an area of 324 square feet and the smallest possible perimeter are 18 feet by 18 feet, and the perimeter is 72 feet.
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3,200 - 1.931 subtract those
so if u ment to put the dot then its 3198.069
but if u ment to put a comma then its 1269
If al band elf what is the value of y?2.) Show your work.(x + 1)e(x-3)
Considering the lines e, f, and a, angles (x + 1)° and (x - 3)° are same side exterior angles, then they are supplementary, that is,
(x + 1) + (x - 3) = 180
(x + x) + (1 - 3) = 180
2x - 2 = 180
2x = 180 + 2
x = 182/2
x = 91
Considering the lines a, b, and e, angles (x + 1)° and y° are alternate side interior angles. Therefore, they are congruent, that is,
x + 1 = y
Substituting with the value of x:
91 + 1 = y
92° = y
Susan works 40 hours per week and makes $15. 25 per hour. Her tax bracket is 12% answer the following questions
Susan's gross income for the week, given the hours worked and the tax bracket is $610.
Susan pays approximately $64.41 in taxes each week.
How to find the gross income and tax ?Gross income per week = Hourly rate * Hours worked
= $15.25 * 40
= $610
Susan's tax bracket is 12%. Taxable income = Gross income - (Gross income * Tax rate)
= $610 - ($610 * 0.12)
= $610 - $73.20
= $536.80
Tax amount = Taxable income * Tax rate
= $536.80 * 0.12
= $64.41
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The questions are:
What is Susan's gross income for a week of work?
How much does Susan pay in taxes each week based on her tax bracket and income?
will give brainliest
When the line of slope of 3 passes through two points, the value of y is -8.
What is slope?The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.
Here,
m=3
m=(y2-y1)/(x2-x1)
3=(y+5)/(-3+(2))
-3=y+5
y=-8
The value of y is -8 when the line of slope of 3 is passing through 2 points as given.
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Construct separate pie charts for Bible (Feelings about the bible). You will need to select Pie under Graphs-Legacy Dialogs. Make sure you select % of cases under slices represent. In the box for Define slices by insert Bible and in the Panel by columns box insert DEGREE. Compare the pie charts. What difference in feelings about the bible exists between the different educational degree groups?
A. Individuals with higher educational attainment are less likely to believe in the bible.
B. Individuals with higher educational attainment are more likely to believe in the bible.
C. No answer text provided.
D. No answer text provided
The pie charts are not provided in the question. However, by interpreting the given question, it can be said that the following information is required to answer the question: Separate pie charts for the feelings about the Bible Need to select Pie under Graphs-Legacy Dialogs. Must select % of cases under slices represent.
In the box for Define slices by insert Bible, and in the Panel by columns box insert DEGREE. Compare the pie charts. What difference in feelings about the Bible exists between the different educational degree groups From the pie charts, it can be concluded that the option B is correct. The individuals with higher educational attainment are more likely to believe in the bible.
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John is saving to buy a new car that will cost him $24,000. John started his savings at the beginning of the school year and has been able to accumulate $1000 after the first month. John plans to continue his savings at a rate proportional to the amount he still needs to save. Determine John's savings amount as function of time Hint: A variable y is said to be proportional to a variable x if y=cx for some constant c.
John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.
John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.
We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:
S(t) = k * N(t)
where k is a constant of proportionality.
We need to find the value of k to determine John's savings amount at any given time.
Using the initial values, we can substitute t = 0 and t = 1 into the equation above:
S(0) = k * N(0) => $1,000 = k * $24,000 => k = 1/24
Now we have the value of k, and we can write John's savings amount as a function of time:
S(t) = (1/24) * N(t)
Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:
N(t) = $24,000 - S(t)
Substituting the expression for N(t) into the equation for S(t), we get:
S(t) = (1/24) * ($24,000 - S(t))
Simplifying the equation, we have:
24S(t) = $24,000 - S(t)
25S(t) = $24,000
S(t) = $24,000 / 25
Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.
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What is the value of x?
to
x = [? ]°
36°
Enter
I will give you points
Answer:
54 degrees!
Step-by-step explanation:
its a right triangle so we know 2 out of the 3 angles
so 36 + 90 = 126
180 - 126 = 54!
hope this helps :)
Question 2
Which function is equivalent to f(x) = -5(x + 4)2 + 8?
F(x)=-5x2-40x-32
F(x)=-5x2+8x+88
F(x)=-5x2-40-72
F(x)=-5x2+8x+24
( the 2 is squared)
Step-by-step explanation:
-5(x + 4)² + 8 = -5(x² + 8x + 16) + 8 =
= -5x² - 40x - 80 + 8 = -5x² - 40x - 72
so, the third answer option must be correct, but you made a mistake there and forgot the "x" as factor of -40.
Which of the following sets of ordered pairs is a function?
ne:
{(-5. - 4), (-5, -2).(-5, 0))
{(1, 0), (2.0), (3, 0))
((- 3.1).(-2.0), (-3, -2)}
0 (0.3). (0,2), (0, 3))
Answer:
{(1,0), (2,0), (3,0)}
Step-by-step explanation:
x-values can have the same Y-values from another pair, but no Y-value can have the same x-value of another pair
50 apples cost $25. How much would 75 apples cost?
Answer:
[see below]
Step-by-step explanation:
50 apples cost 25 dollars.
25/50 = 0.5
Each apple cost half a dollar.
0.5 * 75 = 37.50
75 apples should cost $37.50.
Hope this helps.
At intel, the thickness of processor chips has a mean of 1 mm with a standard deviation of 0. 2 mm. Multiple random samples, each consisting of 35 processor chips, are taken. The sample mean and standard deviation for each sample are recorded to form a sampling distribution. What is the mean and standard deviation of this sampling distribution?.
The mean of this sampling distribution is 1 cm, the standard deviation is 0.033, X-bar is called the sampling distribution of the sample mean
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.
The bigger the deviation within the data collection, the more the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.
Processor chips = 35
Let the x-bar be the sample mean
x-bar = 1 mm
Size of the processor chips = 0.2 mm
n = 35
Standard deviation = Size of the processor chips/\(\sqrt{n}\)
= 0.2/\(\sqrt{35}\)
= 0.2/5.9160
= 0.033
Standard deviation = 0.033
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What is the solution to the system of equations in the graph?A. (5.5, 0)B. (2, 0)C. (5, -2)D. (-2, 5)
The solution is where both lines cross each other:
Correct option: C (5,-2)
4. a survey of customers who shop at a designer clothing store found the average number of t-shirts they own costing at least $30 (designer t-shirt was 3.61 with a standard deviation of 1.18 t-shirts. a histogram of the data shows a skewed-right distribution. (a) should we expect the mean to be less than, greater than, or approximately the same as the median? explain. (b) at least what percent of customers would we find on the interval between 1.30 t-shirts and 5.92 t-shirts? (c) what is the smallest interval guaranteed to capture at least 71% of all customers?
In a survey of customers who shop at a designer clothing store, the average number of t-shirts they own costing at least $30 is expected to be approximately the same as the median. The distribution of t-shirt ownership exhibits a skewed-right pattern.
(a) Skewed-right distributions are characterized by a tail that extends towards the right side. In this case, the distribution of the number of designer t-shirts owned by customers is skewed-right. As a result, the mean is typically greater than the median. However, in skewed-right distributions, the mean is less affected by the tail on the right side compared to the median. Since the distribution is skewed-right, but not extremely so, we can expect the mean to be roughly equal to the median.
(b) To determine the percentage of customers falling within a given interval, we need to convert the values to z-scores. The z-score formula is (x - mean) / standard deviation. For the interval between 1.30 t-shirts and 5.92 t-shirts, we calculate the z-scores for both values using the mean of 3.61 and the standard deviation of 1.18. Then we consult a standard normal distribution table or use statistical software to find the percentage of values between those two z-scores. By finding the corresponding probabilities, we can estimate the percentage of customers falling within that interval.
(c) To find the smallest interval guaranteed to capture at least 71% of all customers, we need to calculate the z-score that corresponds to the cumulative probability of 0.71. Using the standard normal distribution table or statistical software, we can find the z-score associated with a cumulative probability of 0.71. From this z-score, we can determine the corresponding values in the original scale using the mean and standard deviation. This will give us the smallest interval that captures at least 71% of all customers.
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select the appropriate formula for the surface area of the given figure
Answer:
The answer is A
Step-by-step explanation:
This figure is a cylinder and the surface area formula of a cylinder is 2 pi rh + 2pi r^2
С E A B G 77° D plz help.me
In a study of the fertility of married women, conducted by Martin O'Connell and Carolyn C. Rogers for the Census Bureau in 1979, two groups of married women between the ages of 25 and 29 were randomly selected and without children, and each was asked if she planned to have a child at some point. A group of women married less than two years and another of women married five years were selected. Suppose that 240 of 290 women married less than two years plan to have a child someday, compared to 292 of 400 women married five years. We can conclude that the proportion of women married less than two years who plan to have a child children is significantly greater than the proportion of women married for five years who also plan to have children? Use a p-value.
The appropriate null hypothesis for this study is that there is no significant difference in the proportion of women married less than two years who plan to have children someday and the proportion of women married five years who plan to have children someday.
The alternative hypothesis states that there is a significant difference in the proportion of women married less than two years who plan to have children someday and the proportion of women married five years who plan to have children someday.
The hypothesis can be expressed in terms of population proportions as follows:H0: p1 = p2 (there is no significant difference in the proportion of women married less than two years who plan to have children someday and the proportion of women married five years who plan to have children someday)p1 - proportion of women married less than two years who plan to have children someday.
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two cars drive from town a to town b at a constant speed. The blue car travels 25 miles per hour and the red car travels 60 mph. The blue car leaves at 9:30am and the red car leaves at noon. The distance between the two towns is 150 miles on a graph
By answering the presented questiοn, we may cοnclude that As a result, expressiοn the red autοmοbile will catch up tο the blue car abοut 1:28 p.m.
What is expressiοn ?A cοllectiοn οf symbοls, numbers, and numbers that are grοuped tοgether tο simulate a statistical cοrrelatiοn οr regularity is knοwn as an expressiοn in mathematics. A real number, mοdifiable, οr a cοmbinatiοn οf the three can be used as an expressiοn.
The οperatiοns οf additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn are all examples οf mathematics. Math, accοunting, and fοrm frequently emplοy expressiοns. They wοrk in the representatiοn οf mathematical fοrmulas, the sοlutiοn οf equatiοns, and the simplificatiοn οf mathematical relatiοnships.
The red autοmοbile gοes at 60 mph, thus it will take 2.5 hοurs tο traverse the same 150-mile jοurney.
Let us nοw cοmpute the distance travelled by the blue autοmοbile frοm 9:30 a.m. till the red car departs at nοοn:
The blue vehicle departs at 9:30 a.m., giving it a 2.5-hοur head start οver the red car, which departs at nοοn.
During this periοd, the blue autοmοbile will have travelled 25 x 2.5 = 62.5 miles (since distance Equals speed x time).
As a result, when the red autοmοbile sets οut at nοοn, the distance between the twο vehicles is 150 - 62.5 = 87.5 miles
As a result, the red autοmοbile will catch up tο the blue car abοut 1:28 p.m
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Find the volume of the rectangular prism?
Write your answer in simplest form.
M
- (5x + 10)~
(6x + 3)º
Answer:
B) Solve the equation for x: 5X-10+X 8290. 6x-18=90. +18 +18. 60x = 108 ... angle measure of each: Angle A. 524. 3x-35. 3(24)-35. 72-35. 37 m ZA = NM M.:
All of the following are equivalent to 1.75 except _____. 14/8, 1 75/100, 1 3/4, 4/7
» The planet Venus is on average
2.5 x 107 kilometers from Earth. The
planet Mars is on average 2.25 x 108
kilometers from Earth. What is the
average distance from Venus to Mars?
Answer:
4.443*10^9
Step-by-step explanation:
pls heart and give brainliest much appreciated
PLSS HELPP
Explain the steps you would take to solve 82.28 ÷ 22.
Answer:
3.74
Step-by-step explanation:
First I would put the equation in a long division form.
Then, I would find the multiples for 22 to get the amount of 82.28.
At first we got 88, 88 isn't the factor of 22 so I find the closest one which is 22×3=66. Then, we would subtract 66 from 82 getting us the difference of 16. Then you bring down the two to be able to divide once again. To remember these steps I use DMSB and R meaning Dangerous monkey swipes bananas this also means divide, multiply, subtract, bring down and repeat. To use these steps I restart meaning I do the whole process all over again. In this case I will find if 22 is a factor of 162 and it isn't so, I find the closest one which is 154= 22×7=154 this is the part I would do division. Then, I would multiply 22×7 to get 154 and subtract it with 162 equaling 8. Like the process says I bring the next number down which is 8. Then I repeat, now that I know 22 is a factor of 88 we put the multiple in the top which is 4 then, we multiply 22×4=88. At last we subtract 88 by 88 getting 0 meaning the end of the process. And also we pull the decimal point on the uppper top in the middle of the quotient.
I would use long division to solve this :)
3.74
22/ 82.28
-66 ↓↓
162 ↓
-154 ↓
088
-88
0
I hope this helps and if you didn't notice I also answered your other question with long division too :D
Use the box-and-whisker plots to determine which statements are true.
The true statements are :
the average monthly temperatures of New Orleans are not as varied as that of Indianapolis.
The median of the average monthly temperatures of New Orleans is equal to the upper quartile of the average monthly temperature of Indianapolis.
What are the true options?A box plot is used to study the distribution and level of a set of scores. The box plot consists whiskers and a box. The whiskers represents the minimum and maximum scores. The difference between the minimum and maximum scores is the range.
On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.
Range for New Orleans = 85 - 50 = 35
Range for Indianapolis = 75 - 25 = 50
Median for New Orleans = 70
Upper quartile for Indianapolis = 70
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What are the vertex and range of y = |x + 1| + 3?
(0, 4); −∞ < y < ∞
(0, 4); 3 ≤ y < ∞
(−1, 3); −∞ < y < ∞
(−1, 3); 3 ≤ y < ∞
According to the given function the Vertex: (-1, 3), Range: 3 ≤ y < ∞.
What is function?In mathematics, a function is a rule that assigns each element in one set, called the domain, to a unique element in another set, called the range. The elements in the domain are the input values, and the elements in the range are the output values.
According to the given information:the vertex and range of the function y = |x + 1| + 3, we need to remember that the absolute value function has a vertex at the point where the input (x) is 0, and the range of the function is always non-negative.
The function y = |x + 1| + 3 is a translation of the absolute value function y = |x| by one unit to the left and three units up. So, the vertex of the function y = |x + 1| + 3 is at the point (-1, 3).
The range of the function y = |x + 1| + 3 is all non-negative values, since the absolute value function always returns non-negative values.
According to the given function the Vertex: (-1, 3), Range: 3 ≤ y < ∞.
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\(3q + 2p + 7\)
A cone has a height of 11 yards and a radius of 5 yards. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Work Shown:
\(V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*5^2*11\\\\V = \frac{1}{3}\pi*275\\\\V = \frac{275}{3}\pi \ \text{ ... exact volume in terms of pi}\\\\V \approx \frac{275}{3}(3.14)\\\\V \approx 287.83333\\\\V \approx 287.83\\\\\)
The units for the volume are in cubic yards which can be abbreviated to the notation \(\text{yd}^3\)
how do you Multiply fractions? could you explain with a few examples?
The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. For example
\(\begin{gathered} \frac{2}{3}\cdot\frac{5}{6}=\frac{2\cdot5}{3\cdot6}=\frac{10}{18} \\ \text{ Now simplify} \\ \frac{10}{18}=\frac{2\cdot5}{2\cdot9}=\frac{5}{9} \\ \text{Then} \\ \frac{2}{3}\cdot\frac{5}{6}=\frac{5}{9} \end{gathered}\)In other words, multiply linearly and simplify
If you have to multiply mixed fractions, first you transform the fraction from mixed to improper and then multiply, for example
\(\begin{gathered} 3\frac{1}{4}\cdot-\frac{8}{5}=\frac{3\cdot4+1}{4}\cdot-\frac{8}{5}=\frac{12+1}{4}\cdot-\frac{8}{5}=\frac{13}{4}\cdot-\frac{8}{5} \\ \text{ Apply the law of signs of the multiplication} \\ 3\frac{1}{4}\cdot-\frac{8}{5}=\frac{13}{4}\cdot-\frac{8}{5}=\frac{13\cdot-8}{4\cdot5}=\frac{-104}{20} \\ \text{Simplify} \\ \frac{-104}{20}=\frac{2\cdot-26}{2\cdot10}=\frac{-26}{10} \\ \text{Then} \\ 3\frac{1}{4}\cdot-\frac{8}{5}=\frac{-26}{10} \end{gathered}\)The law of signs for multiplication is
\(\begin{gathered} +\cdot+=+ \\ +\cdot-=- \\ -\cdot+=- \\ -\cdot-=+ \end{gathered}\)Multiplying fractions starts with the multiplication of the given numerators, followed by the multiplication of the denominators. ...
Example: Multiply the following fractions: 1/3 × 3/5.
Solution: We start by multiplying the numerators: 1 × 3 = 3, then, multiply the denominators: 3 × 5 = 15.
Help please the image is the question