Answer:
y² -5y = 750750 -y(y -5) = 0(y +25)(y -30) = 0Step-by-step explanation:
You want three equations that can be used to solve for the length (y) of a room that is whose width is 5 feet less than its length and whose area is 750 square feet.
AreaThe area of the room is the product of its length and width. We are given that the length is y, so the width is (y-5) and that product is ...
A = LW
750 = y(y -5)
This equation can be rearranged into several different forms:
y² -5y = 750 . . . . . . . multiply it out
750 -y(y -5) = 0 . . . . . subtract the right side expression
(y +25)(y -30) = 0 . . . . factor it
x^2+y^2+6x+2y-6=0 what is the center of this circle? what is the radius of this circle?
Answer:
center : (-3, -1) radius : 4
Find the critical value t
The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.
What is Critical value?In statistics, the critical value is a value that is used to determine whether to reject the null hypothesis in a hypothesis test. It is based on the chosen level of significance, which is the maximum probability of making a Type I error (rejecting a true null hypothesis). The critical value is determined by the sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.
To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.
Using a t-distribution table with 21 degrees of freedom (n-1), we find that the critical value for a 99% confidence level is approximately 2.819.
Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).
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which of these is another way to write the function g(x)= 3x
Answer:
y=9 (3x/9-2) + 18=3x
Step-by-step explanation:
What are the answers to these questions?
absolute maximum is ? and it occurs at x = ?
absolute minimum is ? and it occurs at x = ?
The absolute maximum value of f(x) is 4.5 and it occurs at x = -0.5, and the absolute minimum value of f(x) is -0.241 and it occurs at x = 0.833
Calculating the absolute maximum and minumum of the functionTo find the absolute maximum and minimum of the function f(x) = 4x^3 - 2x^2 - 5x + 3, we need to take the derivative of the function and set it equal to zero to find the critical points.
f(x) = 4x^3 - 2x^2 - 5x + 3
f'(x) = 12x^2 - 4x - 5
Setting f'(x) = 0, we get:
12x^2 - 4x - 5 = 0
Using the quadratic formula, we get:
x = -0.5 or x = 0.833
Now we need to check the values of f(x) at the critical points and the endpoints of the interval
f(-0.5) = 4(-0.5)^3 - 2(-0.5)^2 - 5(-0.5) + 3 = 4.5
f(0.833) = 4(0.833)^3 - 2(0.833)^2 - 5(0.833) + 3 = -0.241
So the absolute maximum it occurs at x = -0.5, and the absolute minimum occurs at x = 0.833
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The wholesale cost of a dining room table is $1,315,80. The selling price of the table is $1,776.33. What is the markup for the table?
A 10%
B 35%
C 65%
D 90%
well, the markup is 1,776.33 - 1,315,80 = 461.33.
now, if we take 1315.80(origin amount), what is 461.33 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1315.80 & 100\\ 461.33& x \end{array} \implies \cfrac{1315.80}{461.33}~~=~~\cfrac{100}{x} \\\\\\ 1315.8x=46133\implies x=\cfrac{46133}{1315.8}\implies x\approx 35[/tex]
Ian has a deck that measures 20 feet by 10 feet. He wants to increase each dimension by equal lengths so that its area is tripled. By how much should he increase each dimension?
Answer:
10 feet
Step-by-step explanation:
Let's start by finding the current area of the deck:
Area = length x width = 20 ft x 10 ft = 200 sq ft
If Ian increases each dimension by the same amount, let's call this amount "x", then the new dimensions of the deck will be:
Length = 20 ft + x
Width = 10 ft + x
The new area of the deck will be:
New Area = (20 ft + x) x (10 ft + x)
We know that Ian wants the new area to be triple the original area of 200 sq ft, so:
New Area = 3 x 200 sq ft
New Area = 600 sq ft
Substituting this into the equation above and solving for "x", we get:
(20 ft + x) x (10 ft + x) = 600 sq ft
200 + 30x + x^2 = 600
x^2 + 30x - 400 = 0
(x + 40) (x - 10) = 0
We discard the negative solution, and we get:
x = 10 ft
Therefore, Ian should increase each dimension by 10 feet to triple the area of his deck.
To confirm, we can check the original area of the deck which is 20 ft x 10 ft = 200 sq ft.
If Ian increases each dimension by 10 feet, the new dimensions of the deck will be 30 ft x 20 ft. The new area of the deck will be 30 ft x 20 ft = 600 sq ft. This is triple the original area of the deck (200 sq ft), which is what we wanted to achieve.
Therefore, increasing each dimension by 10 feet will triple the area of the deck as required.
Ian should increase both the sides by 10 feet each.
This is a simple mathematics problems related to the topic of mensuration.
Firstly we calculate the current area of the deck:
Area of the deck (rectangle) = l x b
Area of the deck (rectangle) = 20 x 10
Area of the deck (rectangle) = 200 square feet
Since Ian wants to triple the area of the deck, the required area is 600 square feet.
We now look at pairs of numbers multiplying which will give us 600:
(1,600) (2,300) (3,200) (4,150) (5,120) (6,100) (8,75) (10,60) (12,50) (15,40) (20,30) (25,24)
Out of the above pairs only one pair fulfils Ian's criteria to increase the length and breadth of the deck by equal measure, i.e., (20,30). So, Ian should increase the length and breadth of his deck by 10 feet each.
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Working with Actual Interest Earned
Debrorah puts $300 in a CD that earns 3.0% APR, compounded
quarterly, for 1 year. She is taxed at a rate of 20% on the interest she
earns. She takes her money out after 9 months and pays the penalty
fee of 1 quarter's interest.
Deposit
PENALTY
7. What is the total amount of interest that Deborah earns, after taxes?
Type answer here.
The account has an annual interest rate of 6.80%, compounded continuously.
What is interst rate?Interest is the cost associated with the boring money or to return on for lending money it is typically expressed as a percent of the principal amount borrowed or lent and usually the paid periodically over the life of loan interest can also be on from investment such as saving account bonds and the other financial instrument.
The interest rate of the account can be calculated as follows:
Rate = ln(1,698.49/1,051)/(8×ln(1))
Rate = 0.0680 or 6.80%
This means that the account has an annual interest rate of 6.80%, compounded continuously.
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the temperature at 8 a.m. was -8.7 F. At 1 p.m. it was 9.3 F. What integer represents the change in the temperature from morning to afternoon?
The integer that represents the change in temperature from morning to afternoon is 18.
What is integer?The group of counting numbers that can be written without a fractional component includes zero and both positive and negative integers. An integer can, as was already established, be either positive, negative, or zero.
To find the change in temperature from morning to afternoon, we need to subtract the morning temperature from the afternoon temperature:
9.3 F - (-8.7 F) = 9.3 F + 8.7 F = 18 F
Therefore, the integer that represents the change in temperature from morning to afternoon is 18.
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Triangle PQR is rotated 180 degrees clockwise about the origin to produce the image Triangle P’Q’R’. Which of the following statements is TRUE abóyate Triangle P’Q’R’.
Answer:
Step-by-step explanation:
We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.
Given the figure below .find X and Y to three significant digits.Write your answer in the answer box provided below
Check the picture below.
Make sure your calculator is in Degree mode.
[tex]\cos(25^o )=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{12}}\implies 12\cos(25^o)=x\implies \boxed{10.876\approx x} \\\\[-0.35em] ~\dotfill\\\\ \sin(25^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{12}}\implies 12\sin(25^o)=z \\\\[-0.35em] ~\dotfill\\\\ \sin(50^o )=\cfrac{\stackrel{opposite}{z}}{\underset{hypotenuse}{y}}\implies y=\cfrac{z}{\sin(50^o)}\implies y=\cfrac{12\sin(25^o)}{\sin(50^o)}\implies \boxed{y\approx 6.62}[/tex]
how can you tell if a quotient is less than 1'.
Answer:
Step-by-step explanation:
Okay so when a smaller number is divided by a larger number, the quotient is less than 1. Hope this helps Bye sisters slay.
A student attempted to solve the system 5x + 2y = 10 and 10x + 2y = 1 by graphing. The graph and the conclusion are
below. What can you say about the student's work?
y
-10x + 2y = 1
5x + 2y = 10
The soluion is ().
O The solution is incorrect because the student did not correctly identify the intersection.
O The solution is correct and the lines are graphed correctly.
O The solution is correct, but the lines were graphed incorrectly.
O The solution is incorrect because the lines are not graphed correctly.
Answer:
Option A: The solution is incorrect because the student did not correctly identify the intersection.
Step-by-step explanation:
Solve by elimination method.
5x + 2y = 10; -10x + 2y = 1
Multiply the second equation by -1, then add the equations together.
(5x + 2y = 10)
-1 (-10x + 2y = 1)
Forms:
5x + 2y = 10
10x - 2y = -1
Add these equations to eliminate y.
15x = 9
Then solve 15x = 9 for x:
15x = 9
15/15 = 9/15 (Divide both sides by 15)
x = 3/5
Now that we've found x let's plug it back in to solve for y.
Write down the original equation:
5x + 2y = 10
Substitute 3/5 for x in:
5x + 2y = 10:
5(3/4)+2y=10
2y+3=10
2y+3-3=10+-3
2y=7
2y/2 = 7/2
y = 7/2
x = 3/5 and y = 7/2.
Comparing the identified answers to the one found by the students, it can be concluded that Option A: The solution is incorrect because the student did not correctly identify the intersection.
The table below shows the numbers of two to five bedroom houses in the Belmont Neighborhood. What is the mean number of bedrooms in a house in this neighborhood?
Number of bedrooms Frequency
2 7
3 35
4 56
5 27
The mean number of bedrooms in a house in this neighborhood will be: 3.824.
How to determine the mean number of bedroomsIn order to find the mean number of bedrooms in a house in the Belmont Neighborhood, we need to calculate the weighted mean by multiplying each number of bedrooms by their respective frequency.
Next, we will add the products, and then divide by the total frequency. So we can start as follows:
(2 * 7) + (3 * 35) + (4 * 56) + (5 * 27) = 14 + 105 + 224 + 135 = 478
Total frequency = 7 + 35 + 56 + 27 = 125
Therefore, the mean number of bedrooms = 478 / 125 approximately 3.824
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FIND THR CIRCUMFERENCE OF A CD THAT HAS A RADIUS OF 6 CENTIMETERS
___cm
Answer:
Hm
Step-by-step explanation:
The formula to find the circumference of a circle is:
Circumference = 2πr
Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of radius, we get:
Circumference = 2 x π x 6
Circumference = 12π
Circumference ≈ 37.7 cm (rounded to one decimal place)
Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.
Chef Lori uses 1 1/4 cup of milk for every 3/4 cup of broth in her soup recipe. This recipe will feed 4 people. Lori is making soup for a banquet that will feed 120 people. How many gallons of milk and broth combined does she need.
Answer: To make soup for 4 people, Lori needs 1 1/4 cups of milk for every 3/4 cup of broth. Therefore, the ratio of milk to broth is:
(1 1/4 cups milk) / (3/4 cup broth) = (5/4 cups milk) / (3/4 cups broth) = (5/3) cups milk per cup of broth
To make soup for 120 people, Lori needs to multiply the ratio by 30 (120/4) to get the total amount of milk and broth needed:
(5/3 cups milk per cup of broth) * 30 = 50 cups of milk per 30 cups of broth
To convert cups to gallons, we divide by 16 (since there are 16 cups in a gallon):
50/16 = 3.125 gallons of milk
30/16 = 1.875 gallons of broth
Therefore, Lori needs a total of 3.125 + 1.875 = 5 gallons of milk and broth combined.
Step-by-step explanation:
Question 1 of 10 What is the area, measured in square centimeters, of the green shape pictured below? Do not include units in your answer. Icm 1cm Answer here
21 is the area, measured in square centimeters, of the green shape pictured below.
What is square?
Square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).
the area of a parallelogram, we can split this shape up into a rectangle and two right triangles.
The rectangle:
The rectangle has dimensions of 4 by 3 centimeters therefore the area would be 4*3=12 cm squared
two right triangles:
The area of a triangle is 1/2 base * height, but since there are two triangles it would just be the base times the height. The base is 3 cm and the height is 3 so 3*3=9
Next, we add the two areas together: 12+9 = 21
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Matt can save $225 per month that he puts into a savings
account earning 5% annual interest. How much will he have
saved after 2 years?
Answer:
FV ≈ $5,673.56
Step-by-step explanation:
To calculate the total amount that Matt will have saved after 2 years of saving $225 per month at an annual interest rate of 5%, we can use the formula for the future value of an annuity:
FV = P * (((1 + r/12)^(n*12) - 1) / (r/12))
where:
FV is the future value of the annuity
P is the periodic payment (in this case, $225 per month)
r is the interest rate per year (in this case, 5%)
n is the number of years (in this case, 2)
Substituting the given values, we get:
FV = $225 * (((1 + 0.05/12)^(2*12) - 1) / (0.05/12))
Using a calculator, we get:
FV ≈ $5,673.56
Therefore, after 2 years of saving $225 per month at an annual interest rate of 5%, Matt will have saved approximately $5,673.56.
Is a measure of 30 inches "far away" from a mean of 15 inches? As someone with knowledge of statistics, you answer "it depends" and request the standard deviation of the underlying data.
(a) Suppose the data come from a sample whose standard deviation is 3 inches. How many standard deviations is inches from 15 inches?
(b) Is 30 inches far away from a mean of 15 inches?
(c) Suppose the standard deviation of the underlying data is 10 inches. Is 30 inches far away from a mean of 15 inches?
Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.
what is standard deviation ?The standard deviation of statistics is a measurement of how much a group of data values deviate from their mean (average) value. While a significant standard deviation suggests that the pieces of information are dispersed throughout a broader range of values, a low standard deviation suggests that the data points are generally close to the mean.
given
a) If the sample's standard deviation is 3 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:
z = (30 - 15) / 3 = 5
b) The context of the data and the standard deviation will determine whether 30 inches is distant from a mean of 15 inches.
A departure of 15 inches from the mean, meanwhile, can be viewed as being significantly off the mean if the standard deviation is minimal.
c) If the underlying data's standard deviation is 10 inches, then the number of standard deviations from the mean of 15 inches that are 30 inches is:
z = (30 - 15) / 10 = 1.5
Hence, 30 inches deviate by 1.5 standard deviations from the 15-inch mean as the underlying data's standard deviation is 10 inches.
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Spring Basketball Tournament Expenses and Income Guidelines:
1. A permit for the event is required and costs $75.60. It takes 8 hours to run a tournament for 8 teams.
2. Each player will be charged a $32 entry fee.
3. There will be exactly 8 players on each team.
4. The rent for a gym in a high school is $62.50 an hour.
5. A caretaker must be present for a Saturday permit and earns $56 an hour.
Will your Spring Basketball Tournament fundraiser make money? What adjustments might you make to this tournament to ensure that it is more profitable? Show your work and explain your thinking below.
If you are performing a left-tailed z-statistic test with a sample size n = 85 and a 0.01 significance level, what is the critical value?
If your calculated value of the z-statistic is z = −1.95, what is your conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis)?
This null hypothesis prompt is actually straight forward. Note that where the above conditions exist, we must NOT reject the null hypothesis due to the values of the z-statistics and the significance level.
What is a nyll hypothesis?The idea that there is no influence on the population is known as the null hypothesis. We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no impact in the population (p≤α ).
So to determine whether or not to accept or reject the null hypothesis, we must determine dthe z-score.
To find the the critial value for a left-tailoed test, where the signifiance level is 0.01, note that we must find the z-score that leaves 1% of the area in the left tail.
Using the standard distribution table, the z-score for 0.01 left tail is about -2.33.
Since
z-satistics which is equal to -1.95 (as given) is greater than the z-score, we must NOT reject the null hypothesis.
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It costs $350 to spend 4 nights at the Econo Motel. It costs $475 to spend 6 nights at the Bluebird Inn. Which of these statements is true?
Answer: A
Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.
What number increased by 3.5% of itself equals 621?
Answer:
Step-by-step explanation:
We need to find a number which increased by 3.5 of itself equals 621.
Let that number be x.
x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.
x(1+3.5) = 621
x(4.5) = 621
x = 621/4.5
x = 138
Therefore the required number is 138.
Answer: 138
Step-by-step explanation:
We need to find a number which increased by 3.5 of itself equals 621.
Let that number be x.
x increased by 3.5 of itself equals 621 implies x+ 3.5x = 621.
x(1+3.5) = 621
x(4.5) = 621
x = 621/4.5
x = 138
Therefore the required number is 138.
If you horizontally…
Check the picture below.
so following the template below, a shift 2 units to the left, means C=2
[tex]G(x)=\sqrt{x+2}[/tex]
Christine is reviewing her credit scores form the three major credit bureaus. Her experian score is 765 her equifax score is 748, and her transunion score is 758 what is Christine’s median credit score? (Round to the nearest whole point if applicable)
Answer: To find the median credit score, we need to arrange the three scores in order from lowest to highest:
748, 758, 765
The median is the middle value in this ordered list. Since there are three scores, the median is the second score, which is 758.
Therefore, Christine's median credit score is 758.
Step-by-step explanation:
20. The volume of a large crate is 84 yd³. It is 23 yd wide and 4 yd high. What is the length of the crate?
Brenda is fishing from a small boat. Her fishing hook is 12 feet below her, and a fish is swimming at the same depth as the hook, 16 feet away. How far away is Brenda from the fish?
Answer:
We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:
x^2 + 12^2 = 16^2
Simplifying:
x^2 + 144 = 256
x^2 = 112
Taking the square root of both sides:
x ≈ 10.6 feet
Therefore, Brenda is approximately 10.6 feet away from the fish.
f(x) = x2 + 4; interval [0, 5]; n = 5; use left endpoints
Therefore, the Left Riemann Sum for this function, interval, and number of subintervals is 50.
The left endpoint rule is what?The top-left corner of these rectangles touched the y=f(x) curve. In other words, the value of f at the subinterval's left endpoint determined the height of the rectangle over that subinterval. This technique is called the left-endpoint estimate because of this.
With left endpoints and n = 5 subintervals, we may use the Left Riemann Sum formula to approximate the area under the curve of f(x) = x2 + 4 over the range [0, 5]:
Left Riemann Sum = ∑[i=1 to n] f(x_i-1) Δx
In this case, a = 0, b = 5, n = 5, and we will use the left endpoints, so:
Δx = (5 - 0)/5 = 1
Using the left endpoints, the subintervals and their left endpoints are:
[0,1],[1,2],[2,3],[3,4],[4,5]
[tex]so,\; x_0 = 0, x_1 = 1, x_2 = 2, x_3 = 3, x_4 = 4.[/tex]
Now we can calculate the Left Riemann Sum:
Left Riemann Sum= [tex]f(x_0)\Delta x + f(x_1)\Deltax + f(x_2)\Deltax + f(x_3)\Deltax + f(x_4)\Deltax[/tex]
= f(0)×1+f(1)×1+f(2)×1+f(3)×1 + f(4)×1
= 4+5+8+13+20
= 50
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Which is NOT the same as asking:
What is the logarithm of 1,296 if the base is 6?
There is a 25% chance that a vowel is drawn from a bag of random letter tiles. what is the probability of drawing a vowel, placing it back in the bag, and then drawing a consonant
The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.
The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.
The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:
P(vowel and consonant) = P(vowel) x P(consonant)
= 0.25 x 0.75
= 0.1875
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In ΔHIJ, h = 33 cm, i = 61 cm and j=39 cm. Find the area of ΔHIJ to the nearest square centimeter.
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
Explain about the Heron's formula:Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)
where s = half the perimeter,
s = (a + b + c)/2.
given data:
In ΔHIJ,
h = 33 cm, i = 61 cm and j =39 cm.semi -perimeter s = (i + j + h) / 2
s = (33 + 61 + 39) / 2
s = 66.5
Now,
s - h = 66.5 - 33 = 33.5
s - i = 66.5 - 61 = 5.5
s - j = 66.5 - 39 = 27.5
area of ΔHIJ = √s(s - h)(s - i)(s - j)
area of ΔHIJ = √66.5*33.5*5.5*27.5
area of ΔHIJ = √336947.1875
area of ΔHIJ = 580.47
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
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