A square's area an is growing at a rate of 6 cm2 each minute. The side length of the square is increasing at a rate of 2.45 cm/min.
The side length of a square is related to the area of the square by the equation side length = square root of (area). That means, if the area is increasing, the side length of the square is also increasing. To calculate the rate at which the side length is changing, we can take the derivative of the equation side length = square root of (area) with respect to time. This gives us a rate of change of 2.45 cm/min. This means that for every minute the area increases by 6 cm2, the side length of the square will increase by 2.45 cm.
Rate of change = d(side length) / dt
= (1/2) * (d(area) / dt) / (square root of (area))
= (1/2) * (6 cm2/min) / (square root of (area))
= 2.45 cm/min
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find the z-score for the value 62, when the mean is 79 and the standard deviation is 4.
The z-score of the value 62 in the distribution is -4.25
How to determine the z-score of the value?From the question, the given parameters about the distribution are
Mean value of the set of data = 79
Standard deviation value of the set of data = 4
The actual data value = 62
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the known values in the above equation, so, we have the following representation
z = (62 - 79)/4
Evaluate the difference
z = -17/4
Evaluate the quotient
z = -4.25
Hence, the z-score is -4.25
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an airplane travels 5032 kilometers against the wind in 8 hours and 6152 kilometers with the wind in the same amount of time. what is the rate of the plane in still air and what is the rate of the wind?
The rate of the plane in still air is 644 kilometers per hour. The rate of the wind is 72 kilometers per hour.
To calculate the rate of the plane in still air and the rate of the wind, we can use the formula Rate = Distance/Time. To calculate the rate of the plane in still air, we can use the distance of 5032 kilometers and the time of 8 hours to get a rate of 644 kilometers per hour. To calculate the rate of the wind, we can subtract the rate of the plane in still air (644 kilometers per hour) from the rate of the plane with the wind (6152 kilometers per hour) to get a rate of 72 kilometers per hour. Therefore, the rate of the plane in still air is 644 kilometers per hour and the rate of the wind is 72 kilometers per hour.
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Jay has an album that holds 500 stamps. Each page of the album holds 5 stamps. If 21% of the album is empt, how many pages are filled with stamps?
Answer: 79 pages
Step-by-step explanation:
100% - 21% = 79%
So we know that Jay has 79% of the stamps
79% = 0.79
Take 500 times 0.79 = 395 stamps
Then we take 395 divided by 5 = 79 pages
So, 79 pages are filled with stamps
What are the vertex and range of y = |2x 6| 2? (0, 2); 2 < y < [infinity] (0, 2); −[infinity] ≤ y < [infinity] (−3, 2); 2 < y < [infinity] (−3, 2); −[infinity] ≤ y < [infinity]
The vertex of the function is (-3,3) when the function is y=|2x+6|+3 and the range is -∞<y<∞.
Given that,
The function is y=|2x+6|+3
We have to find the vertex and range.
We know that,
What is function?According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. This special sort of relationship is what it is called.
So,
|2x+6|=0
2x=-6
x=-6/2
x=-3
Now,
y=|2(-3)+6|+3
y=|-6+6|+3
y=3
The vertex is (-3,3)
Therefore, The vertex of the function is (-3,3) when the function is y=|2x+6|+3 and the range is -∞<y<∞.
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The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.(a) What proportion of the students scored at least 26 points on this test, rounded to five decimal places? (b)What is the 31 percentile of the distribution of test scores, rounded to three decimal places?
Using z-scores the answers are found to be, part(a) 0.02280 and part(b) = 22.980 points
What is z-score?Z-score is a value that describes the deviation of a value from the standard deviation. Z-score is the number of standard deviations a given data point lies above or below mean.
What is the formula for z-score?The formula for z-score is,
z = (x - µ) / a
where µ is the mean of data set and a is the standard deviation of the data
For part (a),
z = 26-22/2
z = 2.00
P(x>26) = 0.5 - 0.4772
P(x>26) = 0.02280
For part(b),
To find the value of x we first need to find the value of z-score. z-score at 100 - 31 - 50 = 19% = 0.19
At an area of approximately 0.19, the z-score is 0.49
Using above formula, 0.49 = (x -22)/2
x = 22.980
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Calculate the double integral.
(2x)/(1+xy) dA
R = [0, 2]
The double integral of (2x)/(1+xy)dA over the rectangular region R = [0, 2]×[0, 1] give an approximate value of 2.0044.
Therefore, the answer is 2.0044.
By double Riemann sum,
∫∫(2x)/(1+xy) dA ≈ ∑(i = 1 to m)∑(j = 1 to n)f(xij*⁻, yij*⁻)ΔA
R = [0, 2]×[0, 1], that is a = 0, b = 2, c = 0, d = 1
Dividing R into four squares with m = n = 2 and corners of each square chosen (1, 1), (1, 2), ( 2, 1) and (2, 2). So midpoint of the square is (0.5, 0.5), (0.5, 1.5), ( 1.5, 0.5) and (1.5, 1.5)
Δx = (b - a)/m = 1
Δy = (d - c)/ n = 0.5
ΔA = ΔxΔy = 0.5
∫∫(2x)/(1+xy) dA ≈ ∑(i = 1 to 2)∑(j = 1 to 2)f(xij*⁻, yij*⁻)ΔA
= ΔA × ( f(0.5, 0.5) + f(0.5, 1.5) + f( 1.5, 0.5) + f(1.5, 1.5))
= 0.5 × ( (2×0.5)/(1+0.5×0.5) + (2×0.5)/(1+0.5×1.5) + (2×1.5)/(1+1.5×0.5) + (2×1.5)/(1+1.5×1.5))
≈ 0.5 × 4.0088
= 2.0044
--The question is incomplete, answering to the question below--
"Calculate the double integral.
(2x)/(1+xy) dA
R = [0, 2]×[0, 1]"
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A vote for the Best Dancer of the Year was held last week. Patricio received 65% of the votes. A total of 80 people voted. How many votes did Patricio receive?
The number of Patricio votes is 52
How to determine the number of Patricio votes?From the question, we have the following parameters that can be used in our computation:
Number of people = 80
Proportion of votes = 65%
The number of Patricio votes is then calculated as
The number of Patricio votes = Proportion of votes * Number of people
Substitute the known values in the above equation, so, we have the following representation
The number of Patricio votes = 65% * 80
Evaluate
The number of Patricio votes = 52
Hence, the votes is 52
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Emika has a monthly budget for her cell phone bill.
Last month she spent 120% of her budget, and the bill was $60.
What is Emika’s monthly budget?
7/15 * (9/-28)...pls answer fast!!,step by step explanation plsssssssssss
The value of the fraction 7/15 * (9/-28) is - 3/20.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
On the other hand, a fraction appears in the numerator or the denominator of a complex fraction. The value will be:
= 7/15 * (9/-28)
= -63 / 420
= -3/20
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A fish tank that holds 80 gallons of
water is 55% full.
How many more gallons are needed to fill
the tank?
Answer:
36 gals
Step-by-step explanation:
45% more is needed to be 100% full
45% is .45 in decimal
.45 * 80 = 36 gals
What i the value of x? (5 point) A right angle i hown divided into two part. The meaure of one part of the right angle i 30 degree. The meaure of the other part i 4x
The measure of the other part i 4x is 40degrees.
What is right angle measures?
Right angles may be found everywhere around us. The corners of a room, a book, a cube, windows, among other locations, all have right angles. The most typical right angles are those formed by a vertical and a horizontal line. However, right angles are also created when diagonal lines cross one other.
The words "right" and "correct" share the same origin, although "right angle" comes from the second meaning rather than the first. Ancient geometry defined a right angle as the intersection of two straight, or right, lines in relation to dimensional axes.
A right angle measures 90 degrees, so the part labeled 2x measures 90-10 = 80 degrees. If 2x is 80 degrees, x must be 40 degrees.
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the average height of women in the united states is 62 inches with a standard deviation of 2 inches. what is the height of a woman who is 1 standard deviations below the mean?
1) To find a standardized score (z-score), take the individual core minus the mean, then divide by the standard deviation: z = (score - mean)/ SD
Shuri's standardized score would be: z = (69.5 - 65)/2.5 = 1.8
2) First, find the z-score for 62 in: z= (62 - 65) / 2.5 = -1.2
Next, look up -1.2 in a z-table. The corresponding number in the table is .1151.
Multiple this number by 100 to get a percentage: .1151 * 100 = 11.51%
Thus 11.51% of people will be less than 62 inches.
3) Outliers are defined differently dependent on who you ask, often values that are 3 standard deviations (or more) above or below the mean are considered an outlier.
Use the same formula for finding a z-score: z= (score - mean)/ SD
For the taller height use 3:
3= (x - 65)/2.5
Do a little algebra and you get: 3(2.5) + 65 = x thus x = 72.5 or taller
For the shorter height, use -3:
-3(2.5) + 65 = x thus x = 57.5 or shorter
If you need to use a different value for an outlier, then use that number in place of +/- 3.
Hence we get the desired answer.
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Your question is incomplete. Please find the missing content below.
A sample of 300 adult women finds that their heights are approximately Normally distributed with an average height of 65 inches and a standard deviation of 2.5 inches.
1) Shuri is 69.5 inches tall. What is her standard score for height?
2) How many women in the sample would you expect to be less than 62 inches tall?
3) How tall or short would a woman have to be to be considered an outlier? Show your work.
Please help meeeeee !!????!!!!
Answer: She fills 2 full boxes and has 3 animals left over.
Step-by-step explanation: To find how many full boxes she can fill, we can do 5 x 2, without going over. So, 5 x 2 is 10, so now we subtract 10 from 13 and get 3, so this explains that we that she can fill 2 FULL boxes, yet have 3 animals LEFT OVER. I hoped this helped!
Answer:
2 boxes can be filed completely with 3 stuffed animals left over.
Step-by-step explanation:
Take the number of stuffed animals (13) and dive that by the number that will fit in each box (2). The remainder is how many extra stuffed animals are left.
13 ÷ 2 = 5 remainder 3
g about anova assumptions, which of the following is wrong? group of answer choices samples are selected independently. each population is normally distributed. the variances in the groups are random. samples are randomly selected.
The Anova assumptions are each population is normally distributed and the Types of Assumptions. Brookfield (1995) classifies assumptions into 3 categories: paradigmatic, prescriptive, and causal.
ANOVA assumes that the information is usually distributed. The ANOVA additionally assumes homogeneity of variance, because of this that that the variance many of the organizations must be about equal. ANOVA additionally assumes that the observations are impartial of every other. is primarily based totally on the idea that the populations must have the identical variance and they may be usually distributed.
Also, the pattern must be decided on randomly and independently from the populations. The handiest assumption that isn't required to apply ANOVA is c) All samples are of the identical size.The factorial ANOVA has a numerous assumptions that want to be fulfilled – (1) c programming language information of the based variable, (2) normality, (3) homoscedasticity, and (4) no multicollinearity.
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When viewed from the side, the spire on the top of a building forms an isosceles triangle m
Answer: When viewed from the side, the spire forms an isosceles triangle m, the area of the isosceles triangle is equal to 1/4b√4a²-b².
Step-by-step explanation:
What is isosceles triangle?
A triangle with two equal-length sides is said to be isosceles. The triangle's third side is referred to as the base, while the triangle's two equal sides are known as the legs. The triangle's legs are usually shorter than the base, which is usually the triangle's longest side.
To determine if the spire on top of a building forms an isosceles triangle when viewed from the side, we first need to define the three sides of the triangle. Let's call the two sides that are equal in length "s" and the third side "l".
Next, we need to determine if the triangle satisfies the definition of an isosceles triangle. The two sides "s" of the spire must therefore be of equal length for the spire to create an isosceles triangle.
To confirm this, we can measure the length of the sides "s" and compare them to each other. If they are equal in length, then the spire forms an isosceles triangle. If they are not equal in length, then the spire does not form an isosceles triangle.
For example, if the base of the triangle is 10 feet and the length of the two equal sides is 10 feet, then the triangle is isosceles. Therefore, the spire on the top of the building forms an isosceles triangle when viewed from the side.
Therefore, if the two sides "s" of the spire are equal in length, then the spire forms an isosceles triangle when viewed from the side.
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An isosceles triangle is a triangle with two sides of equal length and two equal angles.
What is isosceles triangle?
An isosceles triangle is a type of triangle that has two sides of equal length and two angles of equal measure. The two sides of equal length are the two legs of the triangle, while the third side is called the base. The angles opposite the two equal sides are equal in measure, while the angle opposite the base is the third angle. Isosceles triangles are classified according to the measure of their angles. An equilateral triangle is an isosceles triangle with all angles equal to 60°. An isosceles triangle with two angles equal to 45° is called an isosceles right triangle. An isosceles triangle with two angles equal to less than 45° is referred to as an acute isosceles triangle, while an isosceles triangle with two angles equal to more than 45° is referred to as an obtuse isosceles triangle. Isosceles triangles have many practical uses in engineering and architecture. For example, buildings and bridges often feature isosceles triangles in their roofs and arches in order to provide strength and stability.
When viewed from the side, the spire on the top of a building forms an isosceles triangle because it has two equal sides (the sides running up the spire) and two equal angles (the angles at the base of the spire).
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Simplify the expression.
-2.2+0.4f-14-6
Simplify your answer. Use integers or decimals for any numbers in the expression
After solving the given expression, the value of obtained for f is equal to 55.5.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. A mathematical operation like reduction, addition, multiplication, or division is used to include terms in an expression.
As per the given information in the question,
The given expression is,
-2.2 + 0.4f - 14 - 6
-2.2 + 0.4f - 20
0.4f - 22.2
0.4f = 22.2
f = 22.2/0.4
f = 55.5
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Which of the following is equivalent to −3(2p − 4q)?
−5p − 7q
−5p + 12q
−6p − 4q
−6p + 12q
Answer:
-6p+12q
Step-by-step explanation:
−3(2p − 4q)
Distribute the -3
-3 * 2p -3 * -4q
-6p+12q
Answer:
[tex] \sf \: d) \: -6p + 12q [/tex]
Step-by-step explanation:
Now we have to,
→ simplify the given expression.
The expression is,
→ -3(2p - 4q)
Let's simplify the expression,
→ -3(2p - 4q)
→ -3(2p) - 3(-4q)
→ (-3 × 2)p - (3 × -4)q
→ -6p - (-12)q
→ -6p + 12q
Hence, answer is -6p + 12q.
if a die is rolled 4 times, what is the probability that a number greater than 3 is rolled at least 2 times? (round your answer to three decimal places.)
1.521 is the probability when the die is rolled at least two times which is greater than 3.
Probability: It is an event that depends upon the number of favorable outcomes and the total outcomes, and also defines the ratio of the number of favorable outcomes to the total outcomes in that sample space.
The general formula for probability is:
P(A)=n/N=outcomes in A/outcomes in sample space.
Here, a number greater than 3 we can take as 4 or 5 so the total number of dies rolled is 4, and the total number of the die is 6 which is rolled 2 times greater than 3.
[tex]P(A)=2-(\frac{5}{6} )^4\\\\P(A)=2-(\frac{625}{1296} )\\\\P(A)=\frac{2592-625}{1296} \\\\P(A)=\frac{1971}{1296} \\\\P(A)=1.5208333[/tex]
Thus, the total probability is 1.521
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the amount of a sum of money in 2 yrs and 5 yrs are rs 2800 and rs 3250 respectively. Find the sum
Answer: 6050
Step-by-step explanation: 2800 + 3250 = 6050
Answer:2500
Step-by-step explanation:
The Amount increases to 2800 after 2 years
it increases 3250 after 5 years
so , in 3 years it increased ( 3250-2800) = 450 rupees.
in 3 years it increased 450
so in 1 it increased 150
according to the problem the sum amounts to 2800 rupees
so in 2 years it increased (150*2)=
300 rupees ,
So the sum was (2800-300) =
2500 rupees
Which number line shows the solution to the inequality -2(3x - 1) < 8?
Answer: B
Step-by-step explanation:
1. multiply (-3x+1) by -2 to get -6x+2 -> -6x+2<8
2. then subtract 2 from both sides, -6x+2 -2 < 8 -2 -> -6x<6
3. divide both sides by -6, when dividing an inequality, the inequality symbol switches so you'd have x > -1
so the answer would be B
a washing machine can hold 3/4 kg of laundry in each load. if randy has . 6 kilograms of laundry, how many loads does he need to do? 5 6 7 d8
Randy needs 8 loads.
To find the answer on the question we have to follow the method of multiplication and division .
A washing machine can hold [tex]\frac{3}{4}[/tex] kg of laundry in each load.
[tex]\frac{3}{4}[/tex] kg of laundry is equal to 1 load.
[tex]\frac{3}{4}[/tex] kg of laundry = 1 load
1 kg of laundry = [tex]\frac{1 * 4}{3}[/tex] load ( following the method of division )
1 kg of laundry = [tex]\frac{4}{3}[/tex] load
Randy has 6kg of laundry.
So, 1kg of laundry i.e [tex]\frac{4}{3}[/tex] load is to be multiplied by 6.
6kg of laundry = [tex]\frac{4 * 6}{3}[/tex] load ( following the method of multiplication)
= 8 loads
Hence, Randy needs 8 loads.
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Solve | x + 5 | - 6 = 7
Answer:
x=8
Step-by-step explanation:
|x+5|−6=7
|x+5|−6+6=7+6
|x+5|=13
|x+5|=13
x+5=13
x+5−5=13−5
x=8
Brainliest Please?
Gievn f(x)=3x+2, find f (-4)
Answer:
-10
Step-by-step explanation:
f(x)=3x+2
f(-4)=3(-4)+2
f(-4)=-12+2
f(-4)=-10
determine the area of the region bounded by the given function, the x -axis, and the given vertical lines. the region lies above the x -axis. f ( x )
the region lies above the x -axis. f ( x )= x2 + x , x = −4, x = 2.The area of the region is (2^2 + 2) - (-4^2 + -4) = 26.
To determine the area of the region bounded by the given function, the x-axis, and the given vertical lines, we must first calculate the area of the region. To do this, we need to find the area of the region above the x-axis. To do this, we must calculate the area under the function between the given vertical lines. The area of the region is the area under the function f(x) = x2 + x between x = -4 and x = 2.
(2^2 + 2) - (-4^2 + -4)
= 26.
This can be calculated by solving the integral of the function from -4 to 2, which gives us the answer of 26.
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Maria is going to make some flapjacks. Here are four of the ingredients that she will use. 175 g butter 175 g syrup 175 g sugar 330 g oats What percentage of these four ingredients is oats? Give your answer correct to 3 significant figures.
Answer:
330/(175 + 175 + 175 +330)
= 330/855
= 0.3859
= 38.59% of the ingredients is oats= 22/57 of the ingredients is oats
CREDITS:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Read the following statement: If meX = mY and mY = meZ, then m2X = m Z. This statement demonstrates:
the substition property.
the refexive property.
the symmetric property.
the transitive property.
If meX = mY and mY = meZ, then meX = meZ. This statement demonstrates
the transitive property.What is transitive property?According to the transitive property, all the quantities are equal to each other if two quantities are equal to the third quantity.
For the given problem, if meX = mY and mY = meZ, then meX = meZ
The two properties that are equal is meX and mY
since mY is also equal to meZ then transitive property says that meX and meZ are still equal
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You earn 15n dollars for mowing n lawns. How much do you earn for mowing 1 lawn? 7 lawns?
Answer:
Step-by-step explanation:
You plug in the number of lawns mowed for "n"
So 1 lawn would be 15(1) (15 times 1)
15(1)=15
15(2)=30
15(3)=45
15(4)=60
15(5)=75
15(6)=90
15(7)=105
15(8)=120
15(9)=135
15(10)=150
and so on
an online retailer determines that people click on a particular advertisement 2\%2%2, percent of the times it appears. let vvv be the number of times the advertisement appears to get the first person to click on it. assume each click is independent. find the probability that a person first clicks on the advertisement the 8^{\text{th}}8 th 8, start superscript, start text, t, h, end text, end superscript time it appears. you may round your answer to the nearest hundredth.
The probability of the event that a person first clicks on the advertisement the 8th time it appears is approximately 0.0177 (rounded to the nearest hundredth).
To find the probability that a person first clicks on the advertisement the 8th time it appears (vvv = 8), we can use the geometric probability formula:
[tex]P(X = k) = (1 - p)^{(k-1)}* p[/tex]
where:
P(X = k) is the probability of the event occurring on the kth trial,
p is the probability of success (clicking on the advertisement) on a single trial, which is 2% or 0.02 in decimal form,
k is the number of trials (number of times the advertisement appears) until the first success (first click).
In this case, k = 8 (the 8th time the advertisement appears) and p = 0.02.
[tex]P(X = 8) = (1 - 0.02)^{(8-1)} * 0.02\\P(X = 8) = (0.98)^7 * 0.02[/tex]
P(X = 8) ≈ 0.0177
So, the probability of the event that a person first clicks on the advertisement the 8th time it appears is approximately 0.0177 (rounded to the nearest hundredth).
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evaluate the function: f(n)=n^2 + 3n; find f(-2)
Answer:
f(-2) = -2
Step-by-step explanation:
Step 1: Substitute -2 for the variable n.
f(-2) = (-2)^2 + 3(-2)
Step 2: Simplify the expression.
f(-2) = 4 - 6
Step 3: Evaluate the expression.
f(-2) = -2
2x2x2x3x3 = ?⁵
does this work or not?
Why?