In order to calculate the confidence Interval, what we need is the t distribution. The population mean number of visits is 11.667 and 19.9928 visits. 95 percent contains true mean while the other 5 does not.
How to solve for the statisticsWe have n = 12
df = n- 1 = 11
a. To compute the confidence interval use a t distribution.
The mean = fx/n
= 15.83
level of significance = 0.05
standard deviation = 6.555
t α/2, df = 2.20
standard error = 6.555 / √ 12 = 1.8922
margin of error , = 2.2 * 1.8922 = 4.1628
barx - E = 15.83 - 4.1628 = 11.6672
barx + E = 15.83 + 4.1628 = 19.9928
With 95% confidence the population mean number of visits is between 11.667 and 19.9928 visits.
c. About 95 percent of these confidence intervals will contain true mean.
about __5__percent will not contain the true population
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Graph the line with a slope of −1 that contains the point (3,6).
Answer:
The equation of the line is y = -1.x + 9
Graph is provided in the attached figure
Step-by-step explanation:
The slope intercept equation of a line in 2D(x,y) coordinates is given by the equation
[tex]y = mx + c[/tex]
where m is the slope of the line and c the y-intercept i.e. where the line crosses the y axis at x = 0
Given slope = -1, we can find c and the equation of the line
Since (3,6) is a point on the graph, these coordinates must satisfy the above equation
Substitute for y = 6 and x = 3
[tex]6 = (-1)3 + c\\\\c = 9\\\\\textrm{Equation of line is }\\y = -1.x + 9 \\y = 9-x[/tex]
In the attached figure you can see that (3,6) is on the line
8v(v+3)(v+3) rewrite the expression factoring out (v+3)
If we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex]
Given an expression 8v(v+3)(v+3).
We are required to rewrite the given expression.
Expression is a combination of numbers, symbols, fraction , determinants,indeterminants, coefficients. They are not mostly found in equal to form. It expresses a relationship of a line or something else.
The expression is 8v(v+3)(v+3). There are three terms in which variable is v.
To rewrite the expression we have to multiply all the three terms with each other which can be done as under:
=8v(v+3)(v+3)
=[tex](8v^{2}+24v)(v+3)[/tex]
=[tex]8v^{3}+24v^{2}+24v^{2}+72v[/tex]
=[tex]8v^{3}+48v^{2} +72v[/tex]
Now divide it by 8.
=[tex]v^{3}+6v^{2} +9v[/tex]
Hence if we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex] .
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Consider the functions f(x) = (four-fifths) Superscript x and g(x) = (four-fifths) Superscript x + 6. What are the ranges of the two functions?
Let the two exponential functions be
[tex]$f(x) = (4/5)^x[/tex] and
[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]
Both of these exist exponential functions with positive bases, we end that the range for both exists: {y| y > 0}.
Therefore, the ranges of the two functions exists {y| y > 0}.
How to find the ranges of the two functions?Let the two exponential functions be
[tex]$f(x) = (4/5)^x[/tex] and
[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]
Both of these exist exponential functions with positive bases, then neither of these can contain negative outcomes, while, as x increases, the outcome will also increase.
Then both the functions exist exponential growths, so the range for both of these exists the set of all real positive values, written in both cases as: {y| y > 0}.
Therefore, the ranges of the two functions exists {y| y > 0}.
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Mitch throws a baseball straight up in the air from a cliff that is 95 ft high. The initial velocity is 95 /ftsec. The height (in feet) of the object after t sec is given by =ht+−19t2+95t95. Find the time at which the height of the object is 114 ft. Round your answers to two decimal places.
The time at which the height of the object is 114 ft rounded to two decimal places is; 5.85 seconds
How to find the height of a projectile?We are given;
Height of cliff = 95 ft
Initial velocity of throw = 95 ft/s
The height (in feet) of the object after t sec is given by;
h(t) = −19t² + 95t + 95.
Now, we want to find the time at which the height of the object is 114 ft. Thus, we will set h(t) = 114 ft to get;
114 = −19t² + 95t + 95.
Subtract 114 from both sides to get;
−19t² + 95t + 95 = 0
Using quadratic formula, we have;
t = [-95 ± √(95² - 4(-19 * 95))]/(2 * -19)
t = [-95 ± √(16245)]/-38
t = (-95 ± 127.4559)/(-38)
t = (-95 - 127.4559)/-38 or (-95 + 127.4559)/-38
t = 5.85 s or -0.85
Time cannot be negative and so t = 5.85 seconds
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integer for 1,440 feet below sea level
12.Find the range, the standard deviation, and the variance for the given samples.
13. A data set has a mean of x=3905 and a standard deviation of 110.Find the z-score for each of the following
Answer:
12. standard deviation =6.22972...
. variance = 38.80952...
Find the savings plan balance after 18 months with an APR of 5% and monthly payments of $200.
The savings plan balance after 18 months is $3,730.38
What is an ordinary annuity?
An ordinary annuity means that periodic savings are made at the end of each period unlike an annuity due where payments are made at the beginning of each period.
To determine the savings plan balance after 18 months, we need to make use of the future value formula of an ordinary annuity provided below:
FV=monthly payment*(1+r)^N-1/r
FV=future value after 18 months=unknown
monthly payment=$200
r=monthly interest rate=5%/12=0.00416666666666667
N=number of monthly payments in 18 months=18
FV=$200*(1+0.00416666666666667)^18-1/0.00416666666666667
FV=$200*(1.00416666666666667)^18-1/0.00416666666666667
FV=$200*(1.07771621094479000-1)/0.00416666666666667
FV=$200*0.07771621094479000/0.00416666666666667
FV=$3,730.38
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what is a1 of the arithmetic sequence for which a3=126 and a64= 3,725
If the third term of the aritmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.
Given the third term of the aritmetic sequence is 126 and sixty fourth term is 3725.
We are required to find the first term of the arithmetic sequence.
Arithmetic sequence is a series in which all the terms have equal difference.
Nth term of an AP=a+(n-1)d
[tex]A_{3}[/tex]=a+(3-1)d
126=a+2d--------1
[tex]A_{64}[/tex]=a+(64-1)d
3725=a+63d------2
Subtract second equation from first equation.
a+2d-a-63d=126-3725
-61d=-3599
d=59
Put the value of d in 1 to get the value of a.
a+2d=126
a+2*59=126
a+118=126
a=126-118
a=8
[tex]A_{1}[/tex]=a+(1-1)d
=8+0*59
=8
Hence if the third term of the arithmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.
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The cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks. The property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle. What is the square footage of the cheetahs' habitat? Round to the nearest hundredth.
1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle. This can obtained by using the formula of Area of a Triangle with 2 Sides and Included Angle.
Find the area of the cheetah area at the zoo:Area of a triangle is obtained using the formula of Area of a Triangle with 2 Sides and Included Angle.
If in a triangle ΔABC,
1/2 × bc × sin(A), if b and c are two sides of a triangle and angle A is the included angle1/2 × ac × sin(B), if a and c are two sides of a triangle and angle B is the included angle1/2 × ab × sin(C), if a and b are two sides of a triangle and angle C is the included angleHere it is given that,
67 feet and 48 feet are the sides of the triangular space and angle 72° is the included angle.
By using the formula of Area of a Triangle with 2 Sides and Included Angle,
Area of the cheetah area = 1/2 × bc × sin(A)
Area of the cheetah area = 1/2 × (67)(48) × sin(72°)
sin(72°) = 0.951056516
Area of the cheetah area = 1608 × 0.951056516
Area of the cheetah area = 1529.29888 ≈ 1529.3 square unit
Hence 1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle.
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Maria had a seven square-foot piece of construction paper. She used four square feet of the paper to make a large greeting card for a friend. Which operation would help to find the amount of paper she could use for another card? O division O addition subtraction multiplication
Answer:
subtraction
Step-by-step explanation:
If she had 7 sqft and used up 4 sqft, she no longer has that 4 sqft. It's used up, gone, taken away. We remove it from her total. That is "take away" this means subtraction.
7 - 4
= 3 she has 3sqft of construction paper left.
– 30% OF THE CELL PHONE USERS TODAY USE A MOTOROLA
PHONE. DETERMINE THE PROBABILITY THAT IF SIX CELL PHONE USERS
ARE SELECTED AT RANDOM, EXACTLY FOUR OF THEM USE A MOTOROLA CELL
PHONE.
Using the binomial distribution, there is a 0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are given by:
p = 0.3, n = 6.
The probability that exactly four of them use a Motorola cell phone is given by P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
P(X = 4) = C(6,4) x (0.3)^4 x (0.7)² = 0.0595
0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
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What is the common denominator of x+5/x+8=1+6/x+1?
Answer:
(x+8) (x+1)
Step-by-step explanation:
To find the common denominator, we need to find the least common multiple of the terms in the denominator
(x+8) from the first term
(1) from the second term
(x+1) from the third term
The least common denominator is
(x+8) (1)(x+1)
Simplifiying
(x+8) (x+1)
Hi, please help me me by demonstrating how to solve these 2 questions step by step :)
The given height of the shape is calculated to be 1,895.04 inches.
How to solve for the heightWe have the following details required to solve this problem
The distance b1 = 800 m
The angle of elevation β1 = 50°
distance b2 = 1450 m
- The new angle of elevation α = 33°
We first have to find the height of h1
800 x tan 50 degrees
= 953.40
The height of h2
1450 x tan 33
= 941.641
The height of the shape is the sum of the heights of h1 and h2
953.40 + 941.641
= 1,895.04
Hence the height of the shape is given as 1,895.04 inches.
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5. Based on your data, what is the experimental probability that the family has two dogs or
two cats?
Answer:
2 dogs
Step-by-step explanation:
Find the range for the set of data 24, 30, 17, 22, 22
Answer:
13
Step-by-step explanation:
The range of the data set can be defined as: max-min, and in a sorted data set, the min should be the first value, and the max should be the last value. We don't necessarily need to sort the data here, since we're just looking for two values which we can easily compare to other numbers without having them in order. Although it's important to note when looking for stuff like the median, first, and third quartile you should sort the data.
With that being said, let's look for the min and max! So by looking at the data set, you should be able to determine that the min (minimum) value is 17, and that the max (maximum) value is 30.
This means the range is defined as: 30 - 17 = 13
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\text{Find the range for the set of data 24, 30, 17, 22, 22}[/tex]
[tex]\huge\textbf{What does \boxed{range} mean in math?}[/tex]
[tex]\boxed{Range}\rightarrow\text{is the DIFFERENCE between the biggest number and the}\\\text{smallest number.}[/tex]
[tex]\huge\textbf{How do you find the \boxed{range}?}[/tex]
[tex]\text{You find the biggest number \& subtract it from the smallest number.}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\text{24, 30, 17, 22, 22}[/tex]
[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{biggest}}} number }\huge\boxed{\downarrow}[/tex]
[tex]\text{30}[/tex]
[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{smallest}}} number }\huge\boxed{\downarrow}[/tex]
[tex]\text{17}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\rm{30 - 17}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\large\text{Start at 30 and go DOWN 17 spaces to the \boxed{left} and you will}\\\large\text{have your answer. }[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{13}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]How many three-digit positive integers have three different digits and at least one prime digit?
The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.
The only two components in prime numbers are 1 and the number itself.
Any whole number greater than one is a prime number.
It has exactly two factors—1 and the actual number.
There is just one 2-digit even prime number.
Every pair of prime numbers is always a co-prime.
The product of prime numbers can be used to represent any number.
Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960
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Find the product. Write your answer in exponential form. 8^-2•8^-9
Answer:
8 ^-11
Step-by-step explanation:
It should be noted that in this case, since it's the product that we want to get, it's important to add the power together. This will be:
8^-2 × 8^-9
= 8^(-2 + -9)
= 8^-11
Can you tell which 3-D shape this would make?
The three dimensional shape formed by the net shown below is a cube.
What is a three dimensional shape?A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.
A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.
The cube is a a three-dimensional solid object bounded by six square faces.
The three dimensional shape formed by the net shown below is a cube.
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laura spends 4 hours reading a book that is 76 pages long. what is the average number of pages she read per hour?
The average number of pages she reads per hour is 19 pages per hour
How to determine the average number of pages she read per hour?The given parameters are:
Number of pages = 76 pages
Number of hours = 4 hours
The average number of pages she reads per hour is calculated using the following formula
Average = Number of pages/Number of hours
Substitute the known values in the above equation
Average = 76 pages/4 hours
Evaluate the quotient
Average = 19 pages per hours
Hence, the average number of pages she reads per hour is 19 pages per hours
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Need help please...
Step-by-step explanation:
Here! ●□●□●□●□● THIS IS THE ANSWER BRO
In a student club, the probability that a randomly selected member volunteered for a recent activity was 24/43. What is the probability that a randomly selected member did not volunteer for the recent activity?
The probability that a randomly selected member did not volunteer for the recent activity is 19/43.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability that a randomly selected member did not volunteer for the recent activity = 1 - ratio of randomly selected members that volunteered
1 - 24/43
(43/43) - (24/43) = 19/43
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need heeeelp please
Answer:
x = 1.086
Step-by-step explanation:
Formula
6^x = 7 Take the log of both sides.
Solution
log 6^x = log 7 Bring the power down You are now dealing with log 6
x * log 6 = log 7 Divide by log 6
x = log 7/log 6
x = .8451 / .7782 Divide
Answer
x = 1.086
A total of 646 tickets were sold. They were either adult ticket or student tickets. There were 54 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
350
Step-by-step explanation:
Let the number of adult tickets be x, then the number of student tickets sold would be (x–54).
We now have
x+(x–54)=646
2x=700
x=350
Therefore, 350 adult tickets were sold.
You plan to make a new fenced area in your back yard for your dog. The length of each side of the new dog area is
shown in meters in the diagram below. What is the perimeter of the new dog area?
20 meters
23 meters
29 meters
26 meter
Toenails grow at an average rate of about 0.05 mm per day, and the average toenail is about 3/4 inch long. About how many months does it take for a toenail to completely regenerate itself?
The number of months taken for the toenail to completely regenerate itself is 13 months
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
We have,
Toenail grows:
0.05 mm per day
0.05 mm = 1 day
[ 1 inch = 25.4 mm ]
So,
1 mm = 1/25.4 inch
0.05 x 1/25.4 inch = 1 day
0.0019 inch = 1 day
Divide both sides by 0.0019
1 inch = 1/0.0019 day
1 inch = 526.32 days
Multiply 3/4 on both sides.
3/4 inch = 3/4 x 526.32 days
3/4 inch = 395 days _____(1)
We can assume,
1 month = 30 days
Multiply 395/30 on both sides.
395/30 months = 395 days
13 months = 395 days _____(2)
From (1) and (2) we get,
3/4 inch = 13 months
Thus,
The number of months taken for the toenail to completely regenerate itself is 13 months.
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Solve for exponential the value of X
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The two triangles are right angled Triangles and they have one common angle. so the two triangles are similar to each other.
By using similarity, ratio of their corresponding sides must be equal as well~
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2 + 1} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{3} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 3 \times 3[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 9 \: \: units[/tex]
If you borrow $100 for 5 years at an annual interest rate of 8%, how much will you pay all together
Answer:
$140
Step-by-step explanation:
interest = 8x5 = 40
total = time + interest
total = 100 + 40 = $140
Useing graph paper draw a array for 237×43
The attached figure represents the array for 237 x 43
How to draw the array?The array is given as:
237 x 43
An array is represented as:
Row x Column
This means that:
Row = 237
Column = 43
i.e. the array has 237 rows and 43 columns
The numbers are large, so the cells would be small when the arrays are drawn
See attachment for the array
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If f ( x ) = 3x 2 - 6x + 2 and g ( x ) = 2x 2 + 2x - 11,
then find f ( x ) + g ( x ).
Answer:
[tex]5x^{2} -4x-9[/tex]
Step-by-step explanation:
f(x)+g(x)
[tex](3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\[/tex]
combine like terms --
[tex]5x^{2} -4x-9[/tex]
The sum of the given two functions f(x) = 3x² -6x + 2 and g(x) = 2x²+ 2x -1 is: f(x) + g(x) = 5x² - 4x - 9
Given that:
Functions, f ( x ) = 3x² - 6x + 2
And g ( x ) = 2x² + 2x - 11.
Then find f ( x ) + g ( x ).
To find the sum of two functions, f(x) + g(x), simply add the corresponding terms together.
To find f(x) + g(x), add the coefficients of the corresponding terms:
f(x) + g(x) = (3x² + 2x²) + (-6x + 2x) + (2 - 11)
Now, combine like terms:
f(x) + g(x) = 5x² - 4x - 9
So, the sum of the two functions is:
f(x) + g(x) = 5x² - 4x - 9
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A tower that is 114 feet tall casts a shadow 121 feet long. Find the angle of elevation of the sun to the
nearest degree
Answer:
43 degrees
Step-by-step explanation:
First, notice that we can draw a right triangle to represent this situation. The vertical leg of the triangle corresponds to the tower, and the horizontal leg corresponds to the shadow. The height of the tower, 114, is OPPOSITE, and the length of the shadow, 121, is ADJACENT to the angle of elevation to the top of the tower. Remember SOH CAH TOA, we can use TAN to find the angle since we know the values of O and A.
TAN(x) = O/A
TAN(x) = 114/121
x = ARCTAN(114/121)
x = 43
