A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution. [You may find it useful to reference the t table.] a. Construct the 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to at least 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)
To construct a 90% confidence interval for the average number of customers who visit the salon on weekdays, calculate the sample mean and standard deviation, determine the critical t-value, and use the confidence interval formula to find the range.
Explanation:To construct a 90% confidence interval for the average number of customers who visit the salon on weekdays, we first calculate the sample mean and the sample standard deviation. The sample mean is the average of the seven data points (40, 30, 28, 22, 36, 16, and 50), which is 32. The sample standard deviation is the measure of variability in the data, which is calculated to be approximately 12.11.
Next, we determine the critical t-value for a 90% confidence interval with 6 degrees of freedom (7 data points minus 1). We can find this value in the t-distribution table or use statistical software, and it is approximately 1.943.
Finally, we can calculate the confidence interval using the formula: Confidence interval = sample mean ± (t-value * standard deviation / square root of sample size). Plugging in the values, we get the confidence interval as (23.52, 40.48). Therefore, we can be 90% confident that the average number of customers who visit the salon on weekdays falls within this range.
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Help with this question, please!!
Answer:
[tex]\large\boxed{C=22\pi y\ ft}[/tex]
Step-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
We have the area of a circle
[tex]A=121y^2\pi ft^2[/tex]
Substitute to the formula and solve for r:
[tex]\pi r^2=121y^2\pi[/tex] divide both sides by π
[tex]r^2=121y^2\to r=\sqrt{121y^2}\\\\r=11y\ ft[/tex]
Put the value of r to the formula of a circumference:
[tex]C=2\pi(11y)=22y\pi ft[/tex]
Write and equation of the translated or rotated graph in general form (picture below)
Answer:
The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
xy = -8
∵ A = 0 , B = 1 , C = 0
∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0
∴ B² - 4AC > 0
∴ The graph is hyperbola
* The equation xy = -8
∵ We have term xy that means we rotated the graph about
the origin by angle Ф
∵ Ф = π/4
∴ We rotated the x-axis and the y-axis by angle π/4
* That means the point (x' , y') it was point (x , y)
- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ
∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)
∴ x' = x/√2 - y/√2 = (x - y)/√2
∴ y' = x/√2 + y/√2 = (x + y)/√2
* Lets substitute x' and y' in the 1st answer
∵ (x')² - (y')² - 16 = 0
∴ [tex](\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=[/tex]
( [tex]\frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0[/tex]
* Lets open the bracket
∴ [tex]\frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0[/tex]
* Lets add the like terms
∴ [tex]\frac{-4xy}{2}-16=0[/tex]
* Simplify the fraction
∴ -2xy - 16 = 0
* Divide the equation by -2
∴ xy + 8 = 0
∴ xy = -8 ⇒ our equation
∴ Answer (a) is our answer
∴ The answer is hyperbola; (x')² - (y')² - 16 = 0
* Look at the graph:
- The black is the equation (x')² - (y')² - 16 = 0
- The purple is the equation xy = -8
- The red line is x'
- The blue line is y'
Answer:
a. hyperbola;
A circle has an area of 100 π square inches. What is the circumference of the circle?
A. 10 π inches
B. 20 π inches
C. 2.5 π inches
D. 5 π inches
I think it’s Cnincouod be wrong
given the two sets: A = {1, 2, 3}
B = {3, 2, 1}
which of the following is a true statement?
Answer:
[tex]\large\boxed{A\subseteq B}[/tex]
Step-by-step explanation:
[tex]A=\{1,\ 2,\ 3\},\ B=\{3,\ 2,\ 1\}\\\\4\in A-FALSE,\ \text{because only}\ 1\in A,\ 2\in A\ \text{and}\ 3\in A\\\\A\subseteq B-TRUE,\ \text{because any elements of A are the elements of B.}\\\\A\ \text{is infinite set}-FALSE,\ \text{because set A has a finite number of elements}\\\text{(three elements)}\\\\\O\notin B-FALSE,\ \text{because the empty set is subset of any set.}[/tex]
please answer this TY
Answer:
the limit is 1/16
Step-by-step explanation:
At x=4, the function is indeterminate: 0/0, so l'Hopital's rule can be used to find the limit. Differentiating numerator and denominator, you get ...
lim = (1/√x) / (2x)
Evaluating this at x=4 gives (1/2)/8 = 1/16.
The limit as x approaches 4 is 1/16.
If sinA=3/5 and cosB=5/13 and if A and B are measures of two angles in Quadrant I, find the exact value of the following functions.
cotB =
sin2A=
3)cos(5pi/6 + B) =
tan(A - pi/4) =
Answer:
1. [tex]\cot B=\frac{5}{12}[/tex]
2. [tex]\sin2A=\frac{24}{25}[/tex]
3. [tex]\cos(\frac{5\pi}{6}+B )=-\frac{5}{26}(\sqrt{3}+1)[/tex]
4. [tex]\tan(A-\frac{\pi}{4} )=-\frac{1}{7}}[/tex]
Step-by-step explanation:
If [tex]\sin A=\frac{3}{5}[/tex] and [tex]\cos B=\frac{5}{13}[/tex], then we can use the Pythagorean identity to find [tex]\cos A[/tex] and [tex]\sin B[/tex].
[tex]\sin^2A+\cos^2A=1[/tex]
[tex](\frac{3}{5} )^2+\cos^2 A=1[/tex]
[tex]\frac{9}{25}+\cos ^2A=1[/tex]
[tex]\cos^2 A=1-\frac{9}{25}[/tex]
[tex]\cos^2 A=\frac{16}{25}[/tex]
[tex]\cos A=\pm \sqrt{\frac{16}{25}}[/tex]
Since A is in quadrant I,
[tex]\cos A=\sqrt{\frac{16}{25}}[/tex]
[tex]\cos A=\frac{4}{5}[/tex]
Also;
[tex]\sin^2B+\cos^2B=1[/tex]
[tex](\frac{5}{13} )^2+\sin^2 B=1[/tex]
[tex]\frac{25}{169}+\sin ^2B=1[/tex]
[tex]\sin^2 B=1-\frac{25}{169}[/tex]
[tex]\sin^2 B=\frac{144}{169}[/tex]
[tex]\sin B=\pm \sqrt{\frac{144}{169}}[/tex]
Since A is in quadrant I,
[tex]\sin B=\sqrt{\frac{144}{169}}[/tex]
[tex]\sin B=\frac{12}{13}[/tex]
This implies that;
[tex]\cot B=\frac{\cos B}{\sin B}[/tex]
[tex]\cot B=\frac{\frac{5}{13} }{\frac{12}{13} }[/tex]
[tex]\cot B=\frac{5}{12}[/tex]
[tex]\sin2A=2\sin A \cos A[/tex]
[tex]\sin2A=2\times \frac{3}{5} \times \frac{4}{5}[/tex]
[tex]\sin2A=\frac{24}{25}[/tex]
[tex]\cos(\frac{5\pi}{6}+B )=\cos(\frac{5\pi}{6})\cos(B )-\sin(\frac{5\pi}{6})\sin(B)[/tex]
This implies that;
[tex]\cos(\frac{5\pi}{6}+B )=\cos(\frac{5\pi}{6})\times \frac{5}{13}-\sin(\frac{5\pi}{6})\times \frac{5}{13}[/tex]
[tex]\cos(\frac{5\pi}{6}+B )=-\frac{\sqrt{3}}{2}\times \frac{5}{13}-\frac{1}{2})\times \frac{5}{13}[/tex]
[tex]\cos(\frac{5\pi}{6}+B )=-\frac{5}{26}(\sqrt{3}+1)[/tex]
[tex]\tan(A-\frac{\pi}{4} )=\frac{\tan A-\tan \frac{\pi}{4} }{1+\tan A \tan \frac{\pi}{4}}[/tex]
But; [tex]\tan A=\frac{\sin A}{\cos A}[/tex]
[tex]\tan A=\frac{\frac{3}{5} }{\frac{4}{5} }=\frac{3}{4}[/tex]
[tex]\tan(A-\frac{\pi}{4} )=\frac{\frac{3}{4}-\tan \frac{\pi}{4} }{1+\frac{3}{4} \tan \frac{\pi}{4}}[/tex]
Simplify;
[tex]\tan(A-\frac{\pi}{4} )=\frac{\frac{3}{4}-1 }{1+\frac{3}{4}}[/tex]
[tex]\tan(A-\frac{\pi}{4} )=-\frac{1}{7}}[/tex]
7 is what percent of 20?
Solve this question without using any algebra (variables) and solely by using numbers
Assume the large circle is decreased in size, but it is still larger than the middle circle. Which is true? Answers in the pic
Answer:
haha I just answered a question kind of like this one. The answer would be 4.
Step-by-step explanation:
Although the 2 point circle is still the largest, the rim is skinnier now and the rim of the 4 point is now the biggest area avalible for the dart to be thrown at
Answer:
The answer is (a) The probability of scoring 0 is more likely.
Step-by-step explanation:
find the product of this question down below
Answer:
[tex]\large\boxed{D)\ \dfrac{8}{7}}[/tex]
Step-by-step explanation:
[tex]8\left(-\dfrac{2}{7}\right)\left(-\dfrac{1}{2}\right)\\\\\text{the product of two negative numbers is positive}\\\\8\cdot\dfrac{2\!\!\!\!\diagup^1}{7}\cdot\dfrac{1}{2\!\!\!\!\diagup_1}=8\cdot\dfrac{1}{7}\cdot\dfrac{1}{1}=\dfrac{8}{7}[/tex]
Help please:
Find the product of (3x − 7y)2. (2 points)
9x2 − 42xy + 49y2
9x2 + 42xy + 49y2
9x2 − 49y2
9x2 + 49y2
The product of (3x - 7y)^2 is found by squaring the binomial using the FOIL method, which leads to 9x^2 - 42xy + 49y^2.
To find the product of (3x \\- 7y)^2, you must square the binomial. This means you will multiply the binomial by itself. When you square a binomial, you use the FOIL method (First, Outer, Inner, Last) to multiply the terms.
First: (3x)(3x) = 9x^2
Outer: (3x)(-7y) = -21xy
Inner: (-7y)(3x) = -21xy
Last: (-7y)(-7y) = 49y^2
Combine like terms (the Outer and Inner terms in this case).
9x^2 - 21xy - 21xy + 49y^2 = 9x^2 - 42xy + 49y^2
Thus, the product of (3x - 7y)^2 is 9x^2 - 42xy + 49y^2.
explain this if you can i struggle with Discrete and Continuous Data
Answer:
option A
{1, 2, 4, 7, 9}
Step-by-step explanation:
The domain of a function is the complete set of possible values of the independent variable. Mostly it is 'x' values.
In the figure the tail of arrow represent values of domain and head of arrow represent values of range.
So,
{1, 2, 4, 7, 9} is the domain of G(x) and {3, 5, 8} is the range
What is the greatest common factor (GCF) of 32 and 48?
the answer is 16 :)))))
Answer: Choice B.
Step-by-step explanation: The correct answer is choice B - 16. 16 is the largest number that can evenly be divided into both 32 and 48.
The cheetah traveled 1.75 times faster for the first 8 minutes than it did for the second 8 minutes. Was the distance traveled during the first 8 minutes 1.75 times greater than the distance traveled during the second 8 minutes? Show the calculation to justify your answer.
Answer:
yes, distance travel in first 8 minute is 1.75 time higher than second 8 minutes
Step-by-step explanation:
Given data:
speed in first 8 minute is 1.75 faster than 2nd 8 minutes.
from the above information we can say that time remain same in both situation and we know that speed is given as
speed = distance / time
since time remain same in both case. Therefore speed is directly proportional distance having time as constant
As speed is 1.75 times higher in first 8 minutes than second 8 minutes therefore distance also behave in the same way i.e distance travel in first 8 minute is 1.75 time higher than second 8 minutes
2 fields of a state park are 1,200 meters from each other. On a map the 2 fields are 8 cm apart what scale is the map using
Answer: 150
Step-by-step explanation: a scale of 150 because 150 times 8 is 1,200.
Answer:
150
Step-by-step explanation:
An experiment consists of rolling a die, flipping a coin, and spinning a spinner divided into 4 equal regions. The number of elements in the sample space of this experiment is
3
48
6
12
Answer:
The correct answer option is 48.
Step-by-step explanation:
In the given experiment, three events take place which include rolling a die, flipping a coin and spinning a spinner.
The possible outcomes of each of these events are as follows:
Rolling a die - 6
Flipping a coin - 2
Spinning a spinner - 4
Therefore, by multiplying their possible outcomes, we can find the number of elements in the sample space of this environment.
Number of elements = 6 × 2 × 4 = 48
HELP!!! PLEASE!!!! 70 POINTS AND WILL MARK BRAINLIEST!!!!!
Answer:
41
Step-by-step explanation:
Answer:
41
Step-by-step explanation:
Find the surface area of a cylinder that has a raius of 13.5 cm., and a height of 90 cm. Show all work without using a calculator.
[tex]\bf \textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=13.5\\ h=90 \end{cases}\implies SA=2\pi (13.5)(90+13.5) \\\\\\ SA=27\pi (103.5)\implies SA=2794.5\pi \implies SA\approx 8779.18[/tex]
well, the last part will be with a calculator, but you can simply use the area in π terms.
Whats the original price of a pair of shoes in the sale price is $27 after a 25% discount
the original price would have been $36
Final answer:
The original price of a pair of shoes on sale for $27 after a 25% discount is calculated by dividing the sale price by 0.75, which gives us $36 as the original price.
Explanation:
To find the original price of a pair of shoes if the sale price is $27 after a 25% discount, we need to reverse the discount process. A 25% discount means that the sale price is 75% of the original price, since 100% - 25% = 75%. We can represent the original price with the variable 'P', and the equation we use is 0.75P = $27.
To find P, we divide both sides of the equation by 0.75:
P = $27 / 0.75
P = $36
Therefore, the original price of the pair of shoes was $36.
Rosa is painting two murals.The small mural has an.Area of 2.5 square meters.The Large mural has an area 1.5 times greater than the area of the small mural.What is the are of the large mural
Answer:
6.25 m²
Step-by-step explanation:
The area of the small mural is 1.5 times greater than that of the small mural.
That means the area of the large mural is 2.5 times the area of the small mural.
Area = 2.5 × 2.5 m² = 6.25 m²
The area of the large mural is 6.25 m².
Segments WK, XL, and YJ are medians of triangle WXY.
What is the length of segment WK?
A. 1
B. 6
C. 9
D. 18
What additional information is needed to prove triangle LMN is congruent to triangle KMN using the HL theorem?
∠LMN is a right angle
Step-by-step explanation:If we want to prove that two right triangles are congruent by knowing that the corresponding hypotenuses and one leg are congruent, we begin as follows:
Since two legs are congruent and we know this by the hash marks, then the triangle ΔLKN is isosceles.By definition LN ≅ NKIf ∠LMN is a right angle, then MN is the altitude of triangle ΔLKNAlso MN is the bisector of LK, so KM ≅ MLSo we have two right triangles ΔLMN and ΔKM having the same lengths of corresponding sides In conclusion, ΔLMN ≅ ΔKMNleg MN of both triangle is equal.
Step-by-step explanationHL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called 'legs', or 'base' and 'height'.
It means we have two right-angled triangles with
the same length of hypotenuse the same length for one of the other two legsSince ∠ LMN and ∠KMN are right angle , the hypotenuse LN and and one leg LN of one right-angled triangle LMN are equal to the corresponding hypotenuse KN and leg MN of another right-angled triangle MKN, hence the two triangles are congruent.
i need hep with this ape question plz
Answer:
A
Step-by-step explanation:
The first "circle" is the "domain", which is the set of x values of the function.
The second "circle" is the "range", which is the set of y values of the function.
The range is 4, 7, 9. There are a few x values that match to same y-values but the range is basically the three numbers, 4, 7, and 9.
Option A, {4,7,9} is the correct answer.
Determine the nature of the roots:
Answer:
A. 2 distinct roots.
Step-by-step explanation:
2x^2 + 8x + 3 = 0
Finding the discriminant:
b^2 - 4ac = 8^2 - 4 * 2 * 3
= 64 - 24
= 40
The discriminant is positive but not a perfect square
So there are 2 distinct ,real, irrational roots.
find the area of the sector where the radius is 6 meters and the central angle is 78°
Answer:13
Step-by-step explanation:you have to divide it
The area of a sector is found using the formula :
Area = πr^2(angle/360)
R is given as 6 meters and the angle is given as 78 degrees.
Area = π * 6^2 * (78/360)
Area = π * 36 * 0.21666
Area = π * 7.8
Area = 7.8π square meters. ( Exact area in terms of PI)
or using 3.14 for PI: Area = 24.492 square meters.
Round the decimal area as needed.
Find the limit if it exists.
Answer:
b. 27
Step-by-step explanation:
When finding the limit of a function with no domain restrictions, just plug in the value and evaluate the function
2(2)³ + 2² + 7
2(8) + 4 + 7
16 + 4 + 7
27
Answer:
the value of the given limit is 27
Step-by-step explanation:
[tex]\lim_{x \to 2} (2x^3+x^2+7)[/tex]
To find out the limit , we directly plug in 2 for x inside the given expression
[tex]\lim_{x \to 2} (2x^3+x^2+7)[/tex]
[tex]2(2)^3+(2)^2+7[/tex]
Evaluate the expression
[tex]2(8)+4+7[/tex]
[tex]27[/tex]
So, the value of the given limit is 27
complete the square to determine the minimum or maximum value of the function defined by the expression -x^2-4x+15
[tex] - {x}^{2} - 4x + 15 \\ = - {x}^{2} - 4x - 4 + 15 + 4 \\ = - ( {x}^{2} + 4x + 4) + 19 \\ = \underbrace{- {(x + 2)}^{2}}_{ \leqslant 0} + 19 \\ \Rightarrow - {(x + 2)}^{2} + 19 \leqslant 19 \\ \Rightarrow Maximum \: value \: is \: 19 \: as \: x=-2
[/tex]
(a) What is a sequence? A sequence is the sum of an unordered list of numbers. A sequence is the product of an ordered list of numbers. A sequence is an unordered list of numbers. A sequence is an ordered list of numbers. A sequence is the sum of an ordered list of numbers. (b) What does it mean to say that lim n → ∞ an = 8? The terms an approach -infinity as 8 approaches n. The terms an approach infinity as n become large. The terms an approach 8 as n becomes small. The terms an approach 8 as n becomes large. The terms an approach infinity as 8 approaches n. (c) What does it mean to say that lim n → ∞ an = ∞? The terms an become large as n becomes large. The terms an become small as n becomes large. The terms an become small as n becomes small. The terms an approach zero as n becomes large. The terms an become large as n becomes small.
Answer:
A) A sequence is an ordered list of numbers; B) The terms an approach 8 as n becomes large; C) The terms an become large as n becomes large.
Step-by-step explanation:
A) A sequence is an ordered list of numbers, letters, colors, or other objects. It is essentially a pattern.
B) [tex]n \to \infty (a_n) = 8[/tex] shows n approaching infinity. This means n, the term numbers of [tex]a_n[/tex], get large. The fact that it equals 8 means that the terms of the sequence approach 8 as n gets large.
C) [tex]n \to \infty (a_n) = \infty[/tex] shows n approaching infinity. This means n, the term numbers of [tex]a_n[/tex], get large. The fact that it equals infinity means that the terms of the sequence become large as n becomes large.
A right triangle has legs of length 10 feet and 13 feet. What is the area of the triangle?
A) 65 ft^2
B)100 ft^2
C) 130 ft^2
D) 150 ft^2
Answer:
Option A. [tex]65\ ft^{2}[/tex]
Step-by-step explanation:
we know that
In a right triangle the legs are perpendicular
so
the area is equal to multiply the two legs and divide by two
[tex]A=\frac{1}{2}(10)(13)=65\ ft^{2}[/tex]
Final answer:
To find the area of a right triangle with legs of length 10 feet and 13 feet, you multiply the lengths and divide by 2. The calculated area is 65 square feet, making option A the correct answer.
Explanation:
The question is asking about the area of a right triangle. To find the area of any triangle, you use the formula A = (base × height) / 2. Since a right triangle has two legs that are perpendicular to each other, these legs can be considered as the base and the height of the triangle. In our case, we have legs of lengths 10 feet and 13 feet, so applying the formula:
A = (10 ft × 13 ft) / 2
= (130 ft²)/2
= 65 ft²
So, the area of the right triangle is 65 square feet, which corresponds to option A.
The following figure has rotational symmetry.
True
False
Answer:
The correct answer is false.
Step-by-step explanation: