The lower and upper limit of the 95% confidence interval is 183.2 and 196.0 unit.
What is a confidence interval ?
When you run your experiment again or resample the population in the same way, you can expect your estimate to fall within a certain range of values a certain percentage of the time. This is known as the confidence interval.
Main Body:
Given in question :
x- bar = 189.6
standard deviation = 10
C.I. = 95% =0.95
N=12
so, degree of freedom (D.F) = N-1 = 11
confidence level (α) = (1- C.I.)/2
= 0.025
according to t- distribution table for d.f = 11 and α= 0.025 , my result is 2.201
Now dividing standard deviation by square root of samples, we get
= 10/√12= 2.887
Lower limit = Mean - 2.201*2.887
= 189.6- 6.354
= 183.246
Upper limit = Mean + 2.201*2.887
= 189.6 + 6.354
= 195.954
Hence the result is 183.2 and 196.
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In the acute triangle ABC with angle ACB = 60°, M is the midpoint of side AB. Points D and E are the height points on sides BC and AC, respectively. Show: The triangle MDE is equilateral
An equilateral triangle in geometry is a triangle with three equal-length sides. An equilateral triangle has congruent sides, which means that each side is the same length. The triangle MDE is equilateral only because it is midpoint of ACB
Explain about the Acute triangle?If the square of the longest side is smaller than the sum of the squares of the two smaller sides, the triangle is said to have an acute angle according to Pythagoras's theorem. Given a triangle with sides "a," "b," and "c," with side "a" being the longest, the triangle is steeply angled if "a2" exceeds "b2" plus "c2."
By adding the squares of the triangle's two smaller sides and comparing the result to the square of the largest side, you may determine whether the triangle is acute, right, or obtuse. The triangle is sharp because this total is higher.
Isosceles, equilateral, or scalene acute triangles are all possible. An acute triangle's longest side is located across from its biggest angle.
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The statement 4 less than a number is given w
The equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following statement - "4 less than a number is given w".
Assume the number to be [x].
We can write the equation representing the statement -
"4 less than a number is given w" as a mathematical expression as -
[w] = x where x ∈ (- ∞, 4)
Therefore, the equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
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HELP FOR BRIANLEST
The function will be;
⇒ y = 3x - 1
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The domain and the range is shown in table.
Two points on the line are (2, 5) and (7, 20).
Now,
Since, The equation of line passes through the points (2, 5) and (7, 20).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (20 - 5) / (7 - 2)
m = 15 / 5
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - 5 = 3 (x - 2)
⇒ y - 5 = 3x - 6
⇒ y = 3x - 6 + 5
⇒ y = 3x - 1
Therefore, The function will be;
⇒ y = 3x - 1
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How can the narrator's parents be described in chapters 1-4 of Frankenstein?
A. Poor farmers
B. Distinguished counsellors
C. Military officers
D. Migrant workers
Answer: B)
Step-by-step explanation:
Suppose 57% of the doctors in a hospital are surgeons.
If a sample of 465 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 6%? Round your answer to four decimal places.
The probability that the proportion of surgeons will differ from the population proportion by greater than 6%-22.22%
How to solve for the probabilityP of 6%
= P (p > 0.06)
we would have to use the formula that is given below
[tex]P[z > \frac{p-P}{\sqrt{} \frac{PQ}{n} }[/tex]
where we have n = 465
p = 6%
P = 0.57
Q = 1 - 0.57 = 0.43
We would have to put the values into the equation that we have here as:
0.06 - 0.057 = -0.51
0.57 x 0.43 / 465 = 0.000527
√0.000527 = 0.022956
The probability = -0.51 / 0.022956
= -22.22%
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I dont understand, please help
The slope is 5 and the y-intercept is -2000.
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) The situation can be modeled as y = 5x -200. Here, y= profit per week and x= number of customers per week.
(d) If the state world roller rink reached a maximum capacity of 2,500 customers per week then the weekly profit will be $10,500.
What is meant by slope intercept form?In order to make the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) immediately apparent, a line's equation must be written in the slope-intercept form. This version is frequently known as y = mx + b. the equation of a straight line in the form of y = mx + b, where m is the line's slope and b is its y-intercept. The slope intercept formula y = mx + b is used when you know the line's slope and the provided point is also the line's y-intercept (0, b). y = mx + b, where m represents the line's slope, is the slope-intercept form of a line.
(a) Consider two points
(x₁, y₁) = (400, 0)
(x₂, y₂) = (500, 500)
The slope is given as
m = (y₂ - y₁)/ (x₂ - x₁)
= (500-0)/(500-400)
= 500/100
= 5
To find y- intercept put (x, y) = (400,0) in y= mx+b (slope-intercept form of a line)
0 = 5(400)+b
0 = 2000 + b
b= - 2000
(b) The slope tells us about the rate of change in weekly profit and the y-intercept tells us about the minimum profit.
(c) Let the number of customers per week = x
And the profit per week = y
Then, the situation can be modeled using slope-intercept form as
y = 5x -200
(d) Put x= 2500 in y = 5x -200
y = 5(2500)-2000
= 12,500-2000
= 10,500
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Use the literal symbols listed at the end of the problem to translate the given statement into an algebraic formula.
In a given weight, the number of grams equals 454 times the number of pounds. (g. p)
Choose the correct formula below.
A. g=454 +p
C. p=454g
E. g=454-p
G. g= 454
——
p
B. p=454 +g
D. p=454-g
F. g=454p
H. g= p
—
454
If the area to the left of x in a normal distribution is 0.193, what is the area to the right of x?
The area to the right of x in the normal distribution is 0.807
What is the normal distribution?The normal distribution is the probability distribution that helps to find the probability for continuous variables.
For a probability x, for a normal distribution, we have that
P(X ≤ x) + P(X ≥ x) = 1
How to find the area to the right of x?Since the area to the left of x in a normal distribution is 0.193, we require the area to the right of x.
Since P(X ≤ x) + P(X ≥ x) = 1 where
P(X ≤ x) = area to the left of x P(X ≥ x) = area to the right of xMaking P(X ≥ x) subject of the formula, we have that
P(X ≥ x) = 1 - P(X ≤ x)
Given that P(X ≤ x) = 0.193
Substituting this into the equation, we have
P(X ≥ x) = 1 - P(X ≤ x)
P(X ≥ x) = 1 - 0.193
P(X ≥ x) = 0.807
So, the area to the right of x is 0.807
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2÷7756
Find the quotient.
77.56 divided by .2 = ?
By division, the following results are obtained
[tex]2 \div 7756\\[/tex] = 0.0025
[tex]77.56 \div 0.2 = 387.8[/tex]
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
The quotients of the two divisions are shown below-
[tex]2 \div 7756\\[/tex] = 0.0025
[tex]77.56 \div 0.2\\7756 \div 20 \\387.8[/tex]
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Can someone please help me solve this, I’m so stressed
Answer:
3a. $8493.42
3b. 139.0 months
4a. 10
4b. 10.2 years
Step-by-step explanation:
Given exponential equations, you want values for specific times, and you want times for specific values.
In part (a), the value is found by substituting an appropriate value for t and doing the arithmetic.
In part (b), logarithms will be involved in solving for t.
3. Investment(a) Use t=12, the number of months in one year. You want the value of ...
S = 8000·1.005^12 ≈ 8493.42
The amount after 1 year is $8493.42.
(b) The time it takes to double the investment is the value of t such that ...
16000 = 8000·1.005^t
2 = 1.005^t . . . . . . divide by 8000
log(2) = t·log(1.005) . . . . . take logarithms
t = log(2)/log(1.005) ≈ 138.976
The investment will double in about 139.0 months.
4. Otters(a) Use t=0 and evaluate.
y = 2500 -2490e^(-0.1·0) = 2500 -2490 = 10
The population of otters was 10 when they were reintroduced.
(b) The time it takes for the population to reach 1600 is the value of t such that ...
1600 = 2500 -2490e^(-0.1t) . . . . use 1600 for y
-900 = -2490e^(-0.1t) . . . . . . . . . subtract 2500
900/2490 = e^(-0.1t) . . . . . . . . . divide by -2490
ln(900/2490) = -0.1t . . . . . . . . . take natural logs
t = ln(900/2490)/-0.1 . . . . . . . . divide by the coefficient of t
t ≈ 10.176 ≈ 10.2
It will be 10.2 years before the otter population reaches 1600.
If India works overtime, she receives an
hourly rate of 1-times her regular hourly 1/2
rate. What is her hourly overtime rate?
After solving, 50% is her hourly overtime rate.
In the given question,
India works overtime, she receives an hourly rate of 1-times her regular hourly 1/2 rate.
We have to find her hourly overtime rate.
India is working overtime so her regular hourly rate is 1/2.
Evaluating the expression
We find her hourly overtime rate in percentage.
She receive overtime rate for 1 time is 1/2 rate.
We can write 1/2 as 0.5.
To express it as percentage we multiply and divide by 100.
= 0.5 × 100/100
= 50%
Hence, 50% is her hourly overtime rate.
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Raise the powers of all variables and numbers indicated, and then turn the following expressions in radical form into exponential expressions in rational form. You do not need to evaluate or solve any of the expressions, just put them in simplest exponential form. [All sets of similar base variables and numbers are meant to be under the same radical sign]
The radical expression [tex]\sqrt[5]{x^3}^8.x^4[/tex] simplifies to [tex]x^\frac{44}{5}[/tex].
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, [tex]\sqrt[5]{x^3}^8.x^4[/tex].
= [tex]x^3(^\frac{8}{5}).x^4[/tex].
= [tex]x^\frac{24}{5}.x^4[/tex].
= [tex]x^\frac{24}{5}^{+4}[/tex].
= [tex]x^\frac{24 + 20}{5}[/tex].
= [tex]x^\frac{44}{5}[/tex].
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The scale on a map states that 1 centimeter corresponds to 15 kilometers Find how far apart two cities are if their corresponding points on the map are 13 centimeters apart
In this case, they are both centimetres, so they remain constant. The true size, 15km, is then multiplied by 13/ 1. Then, 20 × 13 = 195. As a result, the answer is 195 kilometres.
What is scale?The term scale refers to the relationship that exists between a measurement on a model and the corresponding measurement on the actual object. A scale of 1:5 means that the size of one unit in the drawing represents five units in reality. A scale of 1:5 is used, for example, if a giraffe with a real-world height of 150 inches is represented as 30 inches on the drawing. A ratio, such as 1:100, is used to represent a scale.A drawing at a scale of 1:100 indicates that the object is 100 times smaller than it would be in real life. You could also say that one unit in the drawing equals one hundred units in real life.Therefore,
The map has a scale = 1 cm
Corresponds to = 15 kilometers
Map centimeters apart = 13 cm
Then you simply multiply the true size
= 15km, by 13/ 1.
Then, 20 x 13 = 195.
Hence, the answer is 195 kilometers.
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NEED HELP ASAPPPPPPPP
1) In figure 4, the area of the square os 16cubes. The shaded part is 7cubes, being one less than 4^2 or 4*4. The formula is n+n-1. This can be put in for 5 too. 5+5-1=9.
2) Using the formula, 50+50-1=99. Therefor, the shaded squares in the 50th figure would be 99.
Complete sentence:
1) The formula for the number of shaded squares in the Nth figure is n+n-1.
2) There would be 99 shaded squares in the 50th figure.
explanation: Knowing that the area of a square is length*width, in this case because the figures are squares, the length and the width are both the same number. From this, we can tell that for figure 45, the length is 45 and so this the width. The one square in the corner is both the length and the width so this is why we take 1 away or -1.
Solve The Problem
All the students in grades 3, 4 and 5 are going on a field trip to Coney Island
Each grade has 125 students. The cafeteria needs to pack lunches. About how
many students are going on the trip? Represent the exact amount of student
in all three grades using an array, How many students are there altogether?
The number of Students going on the trip is 375.
In the question,
It is given that:
There are 125 students in Grade 3.
There are 125 students in Grade 4.
There are 125 students in Grade 5.
So, Total number of students going on trip = Number of students in Grade 3 + Number of students in Grade 4 + Number of students in Grade 5
= 125 + 125 + 125 = 375.
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Alisha used her bank card to buy a bus pass 3 times. Each time she bough
a pass it cost her $13.75. She then deposited $30 into her bank account. Write
an expression to find the change in Alisha's bank account in dollars as a result
these transactions. Also, evaluate the expression to find the change in the
account balance.
The answer will be A-3*13.75+30 using arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Alisha used her bank card to buy a bus pass 3 times.
Each time she bought a pass it cost her $13.75,
She then deposited $30 into her bank account.
So the expression A-3*13.75+30
A is the initial value.
Hence this will be the expression A-3*13.75+30
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Find the average rate of change.
The average rate of change = 1.59 ≈ 2
The average rate of change can be calculated by
1) The first one = [tex]\frac{3 + 0}{2}[/tex] = 1.5
2 ) the second can also be solved by ; 8 + 2/ 2 = 5
3 ) the third one will be 20 + 6 / 2 = 13
4) 8.5
5) 12.5
To calculate the average rate of change
we will first add all the distance
Adding all the distance we will get the sum = 3 + 8 + 20 + 10 + 10 = 51
The total time = 2 + 6 + 9 +15 = 32
Thus the average rate of change = 51 / 32 = 1.59
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A rectangular patio has a length of 9 2/5 feet and an area of 81 3/8 square feet. What is the width of the patio?
Step-by-step explanation:
81 3/8 ÷ 9 2/5
81*8+3 = 651
651/8
9 2/5 = 9*5+2=47
47/5
651/8 ÷ 47/5 =
651/8 * 5/47 = 3255/376 =
8.65691489362
The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given
by the function D(h) = 111.7√/h. Find the height that would allow a person to see 40 kilometers.
h=km
(Round to two decimal places as needed.)
...
Answer:
0.13 km
Step-by-step explanation:
Rearrange the formula to solve for [tex]h[/tex]:
[tex]D(h)=111.7\sqrt{h}[/tex]
[tex]\frac{D(h)}{111.7}=\sqrt{h}[/tex]
[tex](\frac{D(h)}{111.7})^2=(\sqrt{h})^2[/tex]
[tex](\frac{D(h)}{111.7})^2=h[/tex]
Then, substitute the distance of 40 km:
[tex](\frac{40}{111.7})^2=h[/tex]
[tex]0.13\approx{h}[/tex]
50. WATER HOSES A water hose can spray water at an
initial velocity of 40 feet per second. Use the formula
h(t) = vot – 16t², where h(t) is the height of the water
in feet, vo is the initial velocity in feet per second, and
t is the time in seconds.
-
a. How long will it take the water to hit the
nozzle on the way down?
b. Assuming the nozzle is 5 feet up, what is
the maximum height of the water?
It will take 2.5 seconds for the water to hit the nozzle on the way down if the initial velocity is 40 feet per second. The maximum height of the water is 30 feet if the nozzle is 5 feet up.
a) Given equation
h(t) = v₀t - 16t^2
Substitute v₀ = 40, h(t) = 0 in the given equation
40t - 16t^2 = 0
Solve for t
⇒ 16t^2 = 40t
⇒ 16t = 40
⇒ t = 40/16
⇒ t = 2.5 seconds
Hence, water will take 2.5 seconds to hit the nozzle on the way down.
b) The function that represents the given condition
h(t) = -16t^2 + 40t + 5
The maximum value of the function is the y-coordinate of the vertex.
The x-coordinate of the vertex
= -40/2(-16) = 5/4
Find the y-coordinate of the vertex by substituting t = 5/4
⇒ h(5/4) = -16(5/4)^2 + 40(5/4) + 5
⇒ h(5/4) = -25 + 50 + 5
⇒ h(5/4) = 30
Hence, the maximum height of the water is 30 ft.
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The graph below shows the relationship between the number of ounces and the number of calories in steak.
Which equation best represents this relationship?
Responses
Answer:
??
Step-by-step explanation:
where are the equations ?
Answer:
Step-by-step explanation:
Please help :(
Solve each equation for x. Show all steps.
1) log base4 (x^2 -12x+48) =2
2) 27^(4x-6) = (1/9)^(2x-7)
The values of x in the equations are as follows:
1. x = 8 or 4
2. x = 2
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Therefore, let's solve the equation as follows:
log₄ x² - 12x + 48 = 2
using law of logarithm
4² = x² - 12x + 48
16 = x² - 12x + 48
x² - 12x + 48 - 16 = 0
x² - 12x + 32 = 0
x² - 4x - 8x + 32 = 0
x(x - 4) - 8(x - 4) = 0
(x - 8)(x - 4) = 0
Therefore,
x = 8 or x = 4
[tex]27^{(4x-6)}=(\frac{1}{9})^{2x-7}[/tex]
[tex]27^{(4x-6)}=(3^{-2} )^{2x-7}[/tex]
[tex]3^{3(4x-6)}=3^{-4x+14}[/tex]
[tex]3^{12x-18} =3^{-4x+14}[/tex]
Cancel the base
Therefore,
12x - 18 = - 4x + 14
12x + 4x = 14 + 18
16x = 32
x = 32 / 16
x = 2
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if the selling price for a shirt is $39.98 and the tax rate is 4.5% what is the sales tax
Answer:
8.25 % I got this answer right.
Abe digs a hole at a steady rate of (meaning negative) 1.2 feet every hour.
Consider ground level to be 0.
What value represents the elevation of the hole relative to ground level after digging for 2.5 hours?
Enter your answer in the box.
A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
How much langer is the pygmy rabbit than the
wase?
Pygmy rabbit is 22.61-10 meters longer than the wasp.
Given:
A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
Pygmy rabbit longer than the wasp = size of pygmy rabbit - size of wasp.
= (24 - 1.39)-10meters
= 22.61-10 meters.
Therefore pygmy rabbit is 22.61-10 meters longer than the wasp.
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write 10 forms for 1 over 8 as you can think of, be creative and use positive and negative powers or other forms of number.
Answer:
No entendí porfavor puedes ponerlo en Español
which statement explains why ABC is congruent to A’B’C’?
The distance of all the side of ΔABC and ΔA'B'C' are equal which makes them congruent triangles.
What is congruent triangles?
When all 3 corresponding sides and every one 3 corresponding angles area unit equal in size, 2 triangles area unit aforementioned to be congruent.
Main Body:
First let us find the co-ordinates of both the triangles.
A= (3,5)
B = (-2, 3)
C= (-4,-1)
A' =(10,-5)
B'= (5, -3)
C' =(3,1)
Distance between two points = d=√((x₂ – x₁)² + (y₂ – y₁)²).
In ΔABC
Distance of side AB = √((3 –(-2) )² + (5 –3 )²)
= √5² +2²
= √29
Distance of side BC = √((-2-(-4) )²+ (3 -(-1 )²)
= √20
Distance of side CA = √((3-(-4) )² + (5-(-1) )²)
= √7² + 6²
= √85
Distance of side A'B' = √((10 -5)² + (-5-(-3))²
= √(5² +2²)
= √29
Distance of side B'C' = √ ((5-3)² + (-3 -1)² )
= √ (2)² +4²
= √20
Distance of side C'A' = √((10-3)² + ( -5-1)²)\
= √(7)² + 6²
= √85
This shows each side of ΔABC is equal to side of ΔA'B'C'.
hence the triangles are congruent.
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Jose hopes to earn $600 in interest in 4.8 years time from $30,000 that he has available to invest. To decide if it's feasible to do this by investing in an account that compounds annually, he needs to determine the annual interest rate such an account would have to offer for him to meet his goal. What would the annual rate of interest have to be? Round to two decimal places.
Answer
The annual rate of interest have to be 3.87%.
How to determine the annual rate of interest?Mathematically, compound interest can be calculated by using this formula:
A = P(1 + r/n)^{nt}
Where:
A represents the future value.P represents the principal.r represents the interest rate.n represents the number of times compounded.T represents the time measured in years.Making the interest rate (r) the subject of formula, we have:
r = n[(A/P)^{1/nt} - 1]
Note: A = SI + P = 600 + 30,000 = $36,000
Substituting the given parameters into the formula, we have;
Interest rate, r = 1[(36,000/30,000)^{1/1 × 4.8} - 1]
Interest rate, r = [(1.2)^{0.20833333333} - 1]
Interest rate, r = [1.0387 - 1]
Interest rate, r = 0.0387
Interest rate, r = 3.87%.
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4.
The sum of two odd consecutive integers is 88. Find the integers.
Answer:
43 and 45
Step-by-step explanation:
→ State an expression for 2 odd consecutive numbers
2x + 1 and 2x + 3
→ Find the sum
4x + 4
→ Equate to 88
4x + 4 = 88
→ Minus 4 from both sides
4x = 84
→ Divide both sides by 4
x = 21
→ Substitute into original expressions
43 and 45
Find m/1 and m/2
1
95°
2
m<1 =
m<2=
Answer: 85
Step-by-step explanation: