The percent decrease in the number of people who went to the pool over these four weeks is 15%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
The number of people by the fourth week will be:
= 1060 - 105 + 145 - 199
= 901
The percentage decrease will be:
= (1060 - 901) / 1060 × 100
= 159/1060 × 100
= 15%
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the volume of an expanding sphere is increasing at a rate of 12 cubic feet per second. when the volume of the sphere is 36 pi cubic feet, how fast, in square feet per second, is the surface area increasing?
Surface are increasing at the rate of 8 square feet per second.
What is a sphere?
A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its centre.
Volume(V) = [tex]4\pi r^3[/tex]
[tex]\frac{dV}{dt} =\frac{4\pi }{3} \times3r^2\times\frac{dr}{dt} =4\pi r^2.\frac{dr}{dt} \\\\\boxed{\frac{dr}{dt} =\frac{1}{4\pi r^2} (\frac{dV}{dt} )}[/tex]
[tex]V=36\pi \\\\\frac{4}{3} \pi r^3=36\pi \\\\r^3=\frac{108}{4} =27\\\\\boxed{r=3}\\\\\boxed{\frac{dV}{dt} =12}[/tex]
Surface area(S) = [tex]4\pi r^2[/tex]
[tex]\frac{dS}{dr} =8\pi r\times\frac{dr}{dt} \\\\\frac{dS}{dt} =\frac{8\pi r}{4\pi r^2} \times\frac{dr}{dt}\\\\ \frac{dS}{dt}=\frac{2}{r} \times \frac{dV}{dt} =\frac{2}{3} \times12=8\\\\\boxed{\frac{dS}{dt} =8}[/tex]
Hence, the surface area increasing at the rate of 8 square feet per second.
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y=(x+5)²-4
Vertex:
Axis of Symmetry:
x-intercepts:
y-intercept:
Is the vertex a maximum or minimum?
on a standardized test with a normal distribution, the mean was 64.3 and the standard deviation was 5.4. what is the best approximation of the percent of scores that fell between 58.9 and 75.1?
the best approximation of the percent of scores that fell between 58.9 and 75.1 is 4.
The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.
Find the difference between these two figures and the mean, divide it by the standard deviation of 5.4, and you will know how many standard deviations 75.1 and 61.5 are above and below the mean:
(75.1−64.3)/5.4
=2sd
According to the empirical rule, 95% of data are within two standard deviations of the mean.
So, the answer is 4.
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Assume that women's weights are normally distributed with a mean given by μ=143 lb and a standard deviation given by σ =29 lb.
b) If 4 women are randomly selected, find the probability that they have a mean weight above 176
c) If 57 women are randomly selected, find the probability that they have a mean weight above 176
Answer:
b) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9332 = 0.0668
c) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9997 = 0.0003
what determined whether college freshmen who had been randomly paired for a welcome week dance liked each other?
Physical attractiveness determined whether college freshmen who had been randomly paired for a welcome week dance liked each other.
What is random pair?Samples with natural or matched couplings are known as paired samples (sometimes referred to as dependent samples). This results in the creation of a data set where each data point from one sample is uniquely linked with a data point from the other sample. In statistics, paired data, also known as ordered pairs, refers to two variables in a population's individuals that are linked together to ascertain their association. We refer to two datasets that are identical in length and in which each observation can be "paired" with an observation from the other dataset as having "paired data." Each observation in one dataset must only be paired with one observation in the other dataset in order for the two datasets to be paired.
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in a nondirectional significance test of a correlation, the null hypothesis states that the population correlation is zero. true false
The given statement is True.
What is the Null Hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is possible to determine the probability that the null hypothesis is correct using statistical tests.
True. In a non-directional significance test of a correlation, the null hypothesis states that the population correlation is zero.
Hence, The given statement is True.
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find an explicit description of nul a by listing vectors that span the null space. a question content area bottom part 1 a spanning set for nul a is
By using the concept of null space of a matrix, it can be calculated that
Nullspace of A = [tex]\{ \begin{bmatrix} 3 \\ 1 \\0 \\ 0\\0 \end{bmatrix} , \begin{bmatrix} 3 \\ 0 \\-4 \\ 1\\0 \end{bmatrix}\}[/tex]
What is Nullspace of a matrix?
Nullspace of a matrix A is the solution of the equation AX= 0 where 0 is the zero matrix
[tex]\begin{bmatrix} 1 & -3 & 0 & -3 & 0 \\ 0 & 0 & 1 & 4 & 0 \\0 & 0 & 0 & 0 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \\z \\w \\t \end{bmatrix}[/tex]
We need to find Ax = 0
[tex]\begin{bmatrix} 1 & -3 & 0 & -3 & 0 \\ 0 & 0 & 1 & 4 & 0 \\0 & 0 & 0 & 0 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \\z \\w \\t \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\0 \end{bmatrix}[/tex]
x - 3y - 3w = 0
x = 3y + 3w
z + 4w = 0
z = -4w
-t = 0
t = 0
[tex]\begin{bmatrix} x \\ y \\z \\w \\t \end{bmatrix} = \begin{bmatrix} 3y + 3w\\ y \\-4w \\ w\\0 \end{bmatrix}\\\\y \begin{bmatrix} 3 \\ 1 \\0 \\ 0\\0 \end{bmatrix} + w \begin{bmatrix} 3 \\ 0 \\-4 \\ 1\\0 \end{bmatrix}[/tex]
Nullspace of A = [tex]\{ \begin{bmatrix} 3 \\ 1 \\0 \\ 0\\0 \end{bmatrix} , \begin{bmatrix} 3 \\ 0 \\-4 \\ 1\\0 \end{bmatrix}\}[/tex]
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Complete Question
The complete question has been attached
of the 2,598,960 different five-card poker hands possible from a deck of 52 playing cards, how many would contain 2 black cards and 3 red cards?
The number of ways to contain 2 black card and 3 red cards are 84,500.
What is card deck?
A piece of specially made card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that has been imprinted with distinctive motifs is what is known as a playing card. Each card frequently has a finish on the front and reverse to make handling simpler.
There are 26 red card and 26 black card in a 52 card deck.
We have to find the number of ways contain 2 black card and 3 red cards.
Initial black card: 26 options
Secondly black card: 25 options
First caution: 26 options
Second warning: 25 options
Three red cards: 24 options
A total of,
26 x 25 x 26 x 25 x 24 = 10,140,000.
But since all orders are equal, we divide by the number of orders for a five card hand:
5 x 4 x 3 x 2 x 1 = 5! = 120
So,
10,40,000 / 120 = 84,500.
Hence, the number of ways to contain 2 black card and 3 red cards are 84,500.
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please help.. just how many times am i gonna have to post the same question over and over again to get an actual answer
The dimensions of the base of box 2 are: width: x; length: 3 width: x; length: 4x â€"" 1 width: x; length: x â€"" 4 width: x; length: 4x 1
Answer: 4x - 1
Step-by-step explanation:
Answer:
4x-2
Step-by-step explanation:
i did it
Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence increases the margin of error will and the confidence interval will be A larger sample size will improve the accuracy of the confidence interval, therefore margin of error will and the confidence interval will be A) Decrease, wider. Increase, narrower B) Decrease, narrower. Increase, wider C) Increase, wider. Decrease, narrower. D) Increase, narrower. Decrease, wider.
For the given statement option C increase, wider and decrease , narrower is correct.
What is confidence interval?
A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used.
When constructing a confidence interval, if the level of confidence increases, the margin of error must Increase and the confidence interval will be Wider.
Hence Increase; wider is the correct answer.
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if two erminette chickens were crossed, what is the probability that: a. they would have a black chick?
Probability of two black Erminette chickens crossed is equal to 1/4.
As given in the question,
Erminette chickens are basically a chicken with a gene of black and white feathers.
There are two groups of chicken black feather chicken and white feather chicken.
All possible outcomes when Erminette chicken crossed each other are:
= { BB , BW, WB, WW}
Total number of outcomes are = 4
Favourable outcomes are ={ BB }
Number of favourable outcomes = 1
Probability of two black Erminette chickens crossed each other
= ( Favourable outcomes) / ( Total number of outcomes )
= 1 / 4
Therefore, probability of two black Erminette chickens crossed each other with the given condition is equal to 1/ 4.
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Expand and simplify if possible (√2+5)(1+√2)
Answer:
7 + 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
note that [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a
([tex]\sqrt{2}[/tex] + 5)(1 + [tex]\sqrt{2}[/tex])
each term in the second factor is multiplied by each term in the first factor, that is
[tex]\sqrt{2}[/tex](1 + [tex]\sqrt{2}[/tex]) + 5(1 +[tex]\sqrt{2}[/tex]) ← distribute parenthesis
= [tex]\sqrt{2}[/tex] + 2 + 5 + 5[tex]\sqrt{2}[/tex] ← collect like terms
= 7 + 6[tex]\sqrt{2}[/tex]
JUST WANT THE ANSWER NO EXPLINATION NEED HELP ASAP!
Answer:
Step-by-step explanation:
11. First option
12. 5p+4 > 14
> symbol is greater than and has an open circle, going right
Answer:
Option A for both questions--------------------------
The first questionThe graph indicates the inequality n ≤ 1, since highlighted part is to the left from the 1 and there is a closed circle.
Double both sides to get 2n:
n ≤ 1 ⇒ 2n ≤ 2And add 5 to both sides to get 7:
2n + 5 ≤ 2 + 5 ⇒ 2n + 5 ≤ 7This is matching the option A.
Question 12The graph indicates the inequality p > 2, since highlighted part is to the right from the 2 and there is a open circle.
Multiply both sides by 5 to get 5p:
p > 2 ⇒5p > 10Add 4 to both sides to get 14:
5p > 10 ⇒5p + 4 > 14This is matching the option A.
Let ????=−5y????+5x????. Use the tangential vector form of Green's Theorem to compute the circulation integral ∫????????⋅???????? where C is the positively oriented circle x2+y2=25
The value of the required integral is 50π where C is the positively oriented circle x2+y2=25
We are given a vector F = -yi + xj. A vector is a quantity with magnitude and direction that is commonly represented by a directed line segment, with length representing magnitude and orientation in space representing direction. We need to use the tangential vector form of Green's Theorem to compute the circulation integral ∫CF⋅dr where C is the positively oriented circle x² + y² = 25
Let the value of the integral be represented by the variable "I".
I = ∫∫[(/x)(x) - (/y)(-y)]dA
I = ∫∫[(1 - (-1)]dA
I = ∫∫2dA
I = 2∫∫dA
I = 2×(Area of the circle)
I = 2*(πr²)
I = 2*(π*25)
I = 50π
Hence, the value of the required integral is 50π.
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a store owner currently sells bags of peanuts that cost $2.2 per pound and bags of almonds that cost $9.1 per pound. the owner wishes to make a 49 pound bag of a mixture of peanuts and almonds that costs $6.85 per pound. how many pounds of peanuts and almonds does the owner need?
To make a 49 pound bag of a mixture of peanuts and almonds that costs $6.85 per pound, the owner needs 15.98 pounds of peanuts and 33.02 pounds of almonds.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x = pounds of peanuts in the mixture
y = pounds of almonds in the mixture
The owner wished to make a total of 49 pounds of mixture of peanuts ang almonds. Hence,
x + y = 49
x = 49 - y (equation 1)
Bags of peanuts cost $2.2 per pound and bags of almonds cost $9.1 per pound, and the mixture should cost $6.85 per pound. Hence,
2.2x + 9.1y = 6.85(49)
2.2x + 9.1y = 335.65
Substitute equation 1 and solve for y.
2.2x + 9.1y = 335.65
2.2(49 - y) + 9.1y = 335.65
107.8 - 2.2y + 9.1y = 335.65
6.9y = 227.85
y = 33.02
pounds of almonds in the mixture = 33.02
Using equation 1, solve for x.
x = 49 - y
x = 49 - 33.02
x = 15.98
pounds of peanuts in the mixture = 15.98
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3. Se tiene un auto pesado y un auto ligero, Ex-
plica qué ocurrirá en los siguientes casos:
a. Si los dos carros aceleran igualmente en el
arranque, ¿cuál gana?
b. Si ambos desaceleran igual, ¿cuál se detie-
ne en menos tiempo?
Answer:
a. El auto pesado ganará, ya que debido a su mayor masa tendrá una mayor fuerza de arrastre.
b. El auto ligero se detendrá en menos tiempo, debido a que su masa es menor, lo cual significa que tendrá una menor resistencia al movimiento.
Step-by-step explanation:
A boat is heading towards a l, whose beacon-light is 113 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 11 ∘ ∘ . What is the ship’s horizontal distance from the lighthouse (and the shore)?
113 % = 1893per capacity
Step-by-step explanation:
first you have to calculate the 113 feet with its equation then calculate the quation with the number 69 divisible by it then divide it and your answer is there
eacher: ""the first triangle is an isosceles triangle. the second triangle is an isosceles triangle. the third triangle is not an isosceles triangle. based on your observations alone what should be the definition of an isosceles triangle?""what does this question illustrate about the geometry teacher’s questioning techniques?
We have demonstrated the definition of an isosceles triangle.
What is an isosceles triangle?
An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.
The isosceles triangle has both two equal sides and two equal angles. The name derives from the Greek iso (same) and Skelos (leg). A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle.
The given diagram shows an isosceles triangle.
Hence, we have demonstrated the definition of an isosceles triangle.
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Which ordered pair would make this set a function when it replaces (x, y)?
{(0, 1), (2, 6), (1, 7), (5, 7), (x, y)}
ANSWER CHOICES
(2, 4)
(5, 9)
(1, 6)
(4, 8)
Hence, the ordered pair which replace [tex](x,y)[/tex] is [tex](4,8)[/tex].
What is the function?
Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.
Here given function is
[tex]{(0, 1), (2, 6), (1, 7), (5, 7), (x, y)}[/tex]
So, the value which replace [tex](x,y)[/tex] is [tex](4,8)[/tex], because for the function every element have a single image.
Hence, the ordered pair which replace [tex](x,y)[/tex] is [tex](4,8)[/tex].
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if the video is shot at 190 frames per second, how many wing beats does the dragonfly perform per second?
After solving, 41.67 Hz wing beats the dragonfly performs per second.
In the given question, if the video is shot at 190 frames per second, then we have to find how many wing beats the dragonfly performs per second.
From the given question,
Frames per one wing beat = 6 frames
Video shot at = 250 frames per second
We firstly find the time period
So, Time period (T) = 6/250
T= 0.024 s
Snce we have to find how many wing beats the dragonfly performs per second.
Per second number of wing beats = 1/T
Per second number of wing beats = 1/0.024
Per second number of wing beats = 41.67 Hz
Hence, 41.67 Hz wing beats the dragonfly performs per second.
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The right question is;
A frame by frame analysis of a slowmotion video shows that a hovering dragonfly takes 6 frames to complete one wing beat.
If the video is shot at 190 frames per second, how many wing beats does the dragonfly perform per second?
Casey’s bedroom is shaped like a square. The distance between opposite corners is 12√2 feet. How long is each side of the bedroom?
Answer:
12 feet
Step-by-step explanation:
You want the length of the side of a square with a diagonal length of 12√2.
Diagonal of a squareThe diagonal of a square is the hypotenuse of a right triangle with equal-length sides. Such an isosceles right triangle has side lengths in the ratio ...
1 : 1 : √2
That is, the hypotenuse is √2 times the side length.
The given hypotenuse is 12√2, so the side length is 12.
Each side of the bedroom is 12 feet.
What is this answer? Please do it for me fast!
After a dilation by a scale factor of (3/2) the vertices are A'(- 3, - 3), B'(6, - 3) and
(3/2, 3/2).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
A triangle has coordinates A(- 2, - 2), B(4, - 2) and C(1, 1).
After a dilation by a scale factor of (3/2) it will be A'(- 3, - 3), B'(6, - 3) and
(3/2, 3/2).
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determine the type ii error if the null hypothesis, h0, is: the percentage of college students that will graduate with debt is no more than 65%.and, the alternative hypothesis, ha, is: the percentage of college students that will graduate with debt is more than 65%.
We know that in statistics, the Type II error happens when the null hypothesis is false but fails to get rejected.
Type II error in this scenario will be when the researcher claim 65% of college students will graduate with debt is false but fails to be rejected.
A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one fails to reject a null hypothesis that is actually false. A type II error produces a false negative, also known as an error of omission.
For example, a test for a disease may report a negative result when the patient is infected. This is a type II error because we accept the conclusion of the test as negative, even though it is incorrect.
A Type II error can be contrasted with a type I error is the rejection of a true null hypothesis, whereas a type II error describes the error that occurs when one fails to reject a null hypothesis that is actually false. The error rejects the alternative hypothesis, even though it does not occur due to chance.
Given : The null hypothesis, , is: researchers claim that 65% of college students will graduate with debt.
Then , Type II error in this scenario will be when the researcher claim 65% of college students will graduate with debt is false but fails to be rejected.
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A number a is more than 6. An inequality that represents this word sentence is..
Answer:
x>
Step-by-step explanation:
x>
A number a:
a
is more than 6
< 6
Solution:a < 6I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
a farmer collected some eggs from his farm and found b eggs broken. he packed the remaining eggs in c egg cartons. each egg carton can hold a dozen eggs and no eggs were leftover. write an algebraic expression for the number of eggs he collected initially in terms of b and c.
The algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.
What is an algebraic expression?
In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.).
The total number of eggs he collected = 12c + b.
Because 12 eggs are a dozen multiplied by unknown, you get a multiple of twelve then you add your broken eggs for the total.
Hence, the algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.
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Donald reads 1000 words in five minutes what is the unit rate of words per minute
Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 100x2 + 49y2 = 1
On solving tthe question, we got by double integration [tex]\int\limits^0_1 \int\limits^1_2{100x^2+49y^2} \, dx dy = x(\frac{100x^2 + 147y^2}{3} )[/tex]
What is double integration?A function in two variables over a region in R2, or the real number plane, is referred to in mathematics as a double integral. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as follows: ∬ R f ( x , y ) d A = ∬ R f ( x , y ) d x d y.
g[tex]\int\limits^0_1 \int\limits^1_2{100x^2+49y^2} \, dx dy \\ At first,\\ \int\limits^{} \,100x^2 dx = 100\int\limits^ {} \,x^2 dx \\ \int\limits^ {} \,x^2 dx = \frac{x^3}{3} \\[/tex]
[tex]the result - \frac{100x^3}{3}\\ now,\\\int\limits \, 49y^2dx = 49xy^2\\\\result - \frac{100x^3}{3} + 49xy^2\\\\On simplyfing-\\[/tex]
[tex]x(\frac{100x^2 + 147y^2}{3} )[/tex]
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59 tanya prepared 4 different letters to be sent to 4 different addresses. for each letter, she prepared an envelope with its correct address. if the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address? a) 24 1 b) 8 1 c) 4 1 d) 3 1 e) 8
There is a 1 in 4 probability, or 25%, that the envelope will contain just one letter with the proper address.
Tanya wrote four distinct letters that she was going to send to four different addresses. She prepared an envelope with the correct address for each letter. The probability that only 1 letter will be placed into the envelope with the correct address if the 4 letters are randomly placed into the 4 envelopes is
1 in 4, or 25%
(4c4/4c1).
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In a school, 105 students are sixth graders. If 35% of the students in the school are sixth graders, how many students are there in the school?
The total number of schools such that 35% of it is 105 will be 300.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
Suppose the total number of students is x.
35% of x = 105
(35/100)x = 105
x = 105(100/35)
x = 300 students
Hence "The total number of schools such that 35% of it is 105 will be 300".
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