2400 tiles of 25 cm* 25 cm needed to cover the surface of a rectangular pool with length of 15 meters and width of 10 meters.
The area of a rectangle with length 'L' and Breadth 'B' is given by,
A = L*B
We know that 1 meter = 100 centimeter.
The length of the rectangular pool is = 15 meters = 15*100 = 1500 cm.
The width of the rectangular pool is = 10 meters = 10*100 = 1000 cm.
So the area of the rectangular pool is = 1500*1000 square cm.
Now, the dimensions of a tile is = 25 cm* 25 cm
So the area of each tiles = 25*25 = 625 square cm.
So the number of tiles needed to cover the surface of the pool is given by
= (1500*1000)/625 = 2400.
Hence 2400 tiles are needed to cover the surface of the pool.
To know more about area here
https://brainly.com/question/28020161
#SPJ1
Both of these functions grow as x gets larger and larger. Which function eventually exceeds
the other?
f(x) = 3"
Submit
g(x) = 3x + 12
Step-by-step explanation:
3^x eventually gets larger......it has exponential growth....the other is only linear growth
The graph shows a line of fit for data collected on the value of used cars in a relation to the number of years since they were purchased. The equation of line of fit is y = -750x + 11000. Using the equation of the line of fit, what is the value of a car 5 years after its purchase?
The calculated value of the car 5 years after its purchase is 7250
What is the value of a car 5 years after its purchase?From the question, we have the following parameters that can be used in our computation:
Equation of line of fit is y = -750x + 11000
The value of a car 5 years after its purchase means that the value of x is 5
i.e. x = 5
Substitute the known values in the above equation, so, we have the following representation
y = -750 * 5 + 11000
Evaluate
y = 7250
Hence, the value of a car 5 years after its purchase is 7250
Read more about linear regression at
https://brainly.com/question/26755306
#SPJ1
during the most recent economic recession, the auto industry relied heavily on 0% financing to entice customers to purchase cars. edmonds estimated that 22.4% (0.224) of the car deals involved 0% financing. a random sample of 500 financed car deals found that 98 of them used 0% financing. construct a 95% confidence interval estimate for the population proportion of car deals that used 0% financing. a. (0.1668 , 0.2252) b. (0.1612 , 0.2308) c. (0.1608 , 0.2312) d. (0.1733 , 0.2187)
The 95% confidence interval estimate for the population proportion of car deals that used 0% financing is (0.1612, 0.2308). So, the correct option is (b).
To construct a confidence interval estimate for the population proportion of car deals that used 0% financing, we can use the formula
CI = p ± z√((p(1-p))/n)
where
p = sample proportion = 98/500 = 0.196
n = sample size = 500
z = z-score for the desired level of confidence, which is 95% in this case. From a standard normal distribution table, the z-score corresponding to 95% confidence level is approximately 1.96.
Substituting the values, we get
CI = 0.196 ± 1.96√((0.196(1-0.196))/500)
= (0.1612, 0.2308)
Therefore, the 95% confidence interval estimate is (0.1612, 0.2308).
The correct answer is (b).
To know more about confidence interval:
https://brainly.com/question/29680703
#SPJ4
A hat company wants to create a cylindrical travel case to protect its beach sun hats using the following pattern.
net drawing of a cylinder is shown as two circles with diameters labeled 17 inches and a rectangle with a height labeled 5 inches
How many square inches of leather will be necessary to create the travel case? Approximate using π = 3.14.
2,081.82 square inches
1,174.36 square inches
720.63 square inches
493.77 square inches
Answer:
720.33 square inches.
Step-by-step explanation:
To find the amount of leather needed to create the travel case, you need to find the surface area of the cylinder. The surface area of a cylinder is given by the formula:
SA=2πr2+2πrh
where r is the radius of the base and h is the height of the cylinder. In this case, the radius is half of the diameter, so r = 17/2 = 8.5 inches. The height is given as 5 inches. Using π = 3.14, we can plug in these values and get:
SA=2×3.14×8.52+2×3.14×8.5×5
SA=452.38+267.95
SA=720.33
Therefore, the amount of leather needed is approximately 720.33 square inches. The closest answer is C. 720.63 square inches.
Answer:
720.63 square inches
To find the surface area of the cylindrical travel case, we need to add the areas of the two circular bases and the lateral surface area.
The diameter of the circular bases is given as 17 inches, so the radius is 17/2 = 8.5 inches. Using the formula for the area of a circle, we can find the area of one base:
Area of one base = πr^2 = 3.14 x 8.5^2 = 226.96 square inches
Since there are two circular bases, the total area of both bases is:
Total area of both bases = 2 x 226.96 = 453.92 square inches
The lateral surface area is a rectangle with height 5 inches and length equal to the circumference of the circular base. We can find the circumference using the formula:
Circumference = 2πr = 2 x 3.14 x 8.5 = 53.38 inches
So, the lateral surface area is:
Lateral surface area = height x circumference = 5 x 53.38 = 266.9 square inches
Therefore, the total surface area of the cylindrical travel case is:
Total surface area = 453.92 + 266.9 = 720.82 square inches (rounded to two decimal places)
So, the answer is approximately 720.63 square inches (rounded to two decimal places).
Please HELPPlease HELPPlease HELPPlease HELPPlease HELPPlease HELP
g(x) is a translation of f(x), and it can be written as:
g(x) = f(x + 2)
What transformation of f(x) will produce g(x)?So f(x) is the graphed function and g(x) is the one in the table. We can see that the slopes of both functions are 2, so there is no change in the slope nor any type of reflection.
This means that we have a translation.
Now, comparing values:
f(0) = 1 and g(0) =5
f(1) = 3 and g(1) = 7
and so on.
in any of the values we can see that g(x) is 4 units above f(x), then there are two possible transformations:
g(x) = f(x) + 4
g(x) = f(x + 2)
(The +2 in the argument is equivalent because of the slope of 2, when we take that product we will get a 4)
Thus the correct option is the second one.
Laern moer about translations at:
https://brainly.com/question/24850937
#SPJ1
A group of 450 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries, reality 20 percent, and sci-fi 20 percent
How many middle school students prefer the Documentaries television genre?
24
76
86
108
The number of middle school students prefer the Documentaries television genre is108.
How many middle school students prefer the Documentaries television genre?To get that, we need to multiply the total number of students by the correspondent percentage (in decimal form).
We know that there are 450 students, and 24% (just add the other percentages, and 24% is the amount missing to reach 100%) like the documentaries.
That percentage in decimal form is 24%/100% = 0.24
Then the estimation will be:
450*0.24 = 108
So that is the correct answer.
LEarn more about percentages at:
https://brainly.com/question/843074
#SPJ1
Barry used a number line to simplify a numerical expression on a math test. Which number did Barry add to get a result of 4 on the numerical expression he simplified? –14 −6 4 14
To get a result of 4 on the numerical expression, Barry added 4 to the expression on the number line. So, the correct answer is C).
The expression involves adding up the values at different points on the number line. We can see that the value at the point labeled "x" is the missing value that needs to be found.
By adding up the values at each point, we get the following equation
-5 + (-3) + x - (-7) = 1
Simplifying this equation gives
-5 - 3 + x + 7 = 1
Simplifying further
-x = -4
Solving for x, we get
x = 4
Therefore, the value of x that Barry added to the expression on the number line to get a result of 4 is 4. So, the correct option is C).
To know more about number line:
https://brainly.com/question/16191404
#SPJ1
--The given question is incomplete, the complete question is given
" Barry used a number line to simplify a numerical expression on a math test. Which number did Barry add to get a result of 4 on the numerical expression he simplified? A –14, B −6, C 4, D 14 "--
Variables x and y are related by the equation y = ln(x)/e^x
Show that dy/dx = 1 - x·ln(x)/x·e^x
To show that dy/dx = 1 - x·ln(x)/x·e^x, we shall first find the derivative of y with respect to x using the chain rule and the quotient rule.
What is the quotient rule?According to the Quotient Rule, the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
Given the equation: y = ln(x)/e^x
First, apply the quotient rule to differentiate y = ln(x)/e^x
dy/dx = [(e^x)(d/dx)(ln(x)) - (ln(x))(d/dx)(e^x)] / (e^x)^2
Next, differentiate ln(x) using the chain rule
(d/dx)(ln(x)) = 1/x
Next, differentiate e^x using the chain rule
(d/dx)(e^x) = e^x
Then, substitute the derivatives of ln(x) and e^x back into the quotient rule expression
dy/dx = [(e^x)(1/x) - (ln(x))(e^x)] / (e^x)^2
Simplify the expression:
dy/dx = (e^x/x - ln(x)e^x) / e^(2x)
Next, multiply the numerator and denominator by x
dy/dx = (xe^x/x^2 - ln(x)e^x/x) / (xe^(2x)/x^2)
Then, simplify the expression
dy/dx = (e^x/x - ln(x)e^x/x) / (xe^(2x)/x^2)
And multiply the numerator and denominator by x^2
dy/dx = (xe^x - xln(x)e^x) / (xe^(2x))
Next, factor out e^x from the numerator
dy/dx = e^x (x - xln(x)) / (xe^(2x))
And simplify the numerator
dy/dx = e^x (x(1 - ln(x))) / (xe^(2x))
Next, simplify further
dy/dx = (x - xln(x)) / (xe^(x))
Finally, rearrange the terms
dy/dx = 1 - xln(x) / xe^(x)
Therefore, the derivative of y with respect to x is given by dy/dx = 1 - xln(x)/xe^(x).
Read more about the Quotient Rule at brainly.com/question/30278964
#SPJ1
Phone numbers consist of a three-digit area code followed by seven digits. If the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, how many different phone numbers are possible? How did you come up with your answer?
a.
8 times 10 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 6,400,000,000
b.
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 1,280,000,000
c.
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 = 128,000,000
d.
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 times 10 = 12,800,000,000
Please select the best answer from the choices provided
If the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, 1 280 000 000 different ways are possible.
Therefore option B is correct.
How do we calculate?In this scenario we apply our knowledge of probability to find the phone number, so:
We can establish the following facts:
The first slot cannot start with 0 or 1, which leaves us 2, 3, 4 ..., 9 to fill which means that we have 8 different arrangements for the first slot.The second slot have a 0 or 1 for the second digit, which leaves us with 2 different arrangements.There are no restrictions for the third slot, so we would have 10 different arrangements.Therefore, if we calculate the possibilities of occurrence, we have:
8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 1,280,000,000
Learn more about probability at:
brainly.com/question/795909
#SPJ1
Find an orthogonal matrix A where the first row is a multiple of (3,3,0). A=
Putting it all together, we get:
A:
[-3 0 0]
[ 0 1 0]
[ 0 0 -1]
which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).
An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.
Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:
(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)
Note that this vector has length 3, so we can divide it by 3 to get a unit vector:
(-3/3, 0/3, 0/3) = (-1, 0, 0)
So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).
To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.
Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):
v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)
= (0, 1, 0) - 0 / 9 * (-3, 0, 0)
= (0, 1, 0)
We can then normalize this vector to get a unit vector:
v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)
So, the second row of the orthogonal matrix A is (0, 1, 0).
To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:
(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)
We normalize this vector to get a unit vector:
v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)
So, the third row of the orthogonal matrix A is (0, 0, -1).
Putting it all together, we get:
A:
[-3 0 0]
[ 0 1 0]
[ 0 0 -1]
To know more about orthogonal matrix,
https://brainly.com/question/31629623
#SPJ11
Find the slope of the line: (4,2) and (0,3)
Answer:
The slope of the line is -1/4. To find the slope of the line, we can use the formula m = (y2 - y1)/(x2 - x1). In this case, y2 = 2, y1 = 3, x2 = 4, and x1 = 0. Plugging these values into the formula gives us m = (2 - 3)/(4 - 0) = -1/4.
Match the transformations to the functions
f(x) =
= e to the graph of g(x) = e*+5 +1
f(x)=e
to the graph of g(x) = -e - 4
f(x)=e to the graph of g(x) = e*+5 +1
f(x)=e
to the graph of g(x)=-e² - 4
1.
2.
3.
Vertical
shift
down by
4
Vertical
shift up
by 1
Horizontal
shift left
by 5
Vertical
reflection
(reflect
over x-
The transformations are matched as follows
f(x) = eˣ to the graph of g (x) = [tex]e^{x + 5} + 1[/tex]
Vertical shift up by 1 unit and Horizontal shift left by 5f(x) = eˣ to the graph of g(x ) = -eˣ - 4
Vertical shift down by 4 and Vertical reflection (reflection over x-axis)f(x) = eˣ to the graph of g (x) = [tex]e^{x + 5} + 1[/tex]
Vertical shift up by 1 unit and Horizontal shift left by 5f(x) = eˣ to the graph of g(x ) = -eˣ - 4
Vertical shift down by 4 and Vertical reflection (reflection over x-axis)What is translation transformation?Translation transformation refers to the movement of an object or figure in a straight line without rotation or distortion in this transformation all points of an object or shape move parallel and in the same direction
The negative sign in g(x) = -eˣ - 4 lead to reflection while the -4 is a translation 4 units downwards.
For the graph of g (x) = [tex]e^{x + 5} + 1[/tex]
The +1 represents a vertical shift up by 1 unit and Horizontal shift left is represented by +5
Learn more about transformation at
https://brainly.com/question/4289712
#SPJ1
Miss Anna needs ⅔ cup of sugar to make peanut biscuits. She used a tablespoon to measure. One tablespoon is equivalent to ⅓ of a cup. how many tablespoon of sugar that she used
Miss Anna needs ⅔ cup of sugar, and one tablespoon is equivalent to ⅓ of a cup.
What might an equivalent look like?
The entire amount of water distributed is roughly comparable to 35 inches of rainfall. Being a noble meant you were barred from holding public office, which effectively disfranchised the whole noble order.
What in academics is equivalent?
The terms "or equivalent" may occasionally be used in conjunction with educational requirements. This means that you may be able to fulfil some or all of the educational prerequisites using your work experience or other experiences in the same or a closely related field.
Therefore, we can find out how many tablespoons of sugar she needs by dividing ⅔ by ⅓.
⅔ ÷ ⅓ = 2
So Miss Anna needs 2 tablespoons of sugar to make peanut biscuits.
To know more about equivalent visit:
https://brainly.com/question/24734894
#SPJ1
Vince's front porch is 8 feet wide and 12 feet long. Vince wants to stain the wood on the porch next weekend. The stain costs $0.69 per square foot. How much will it cost to buy enough stain for the whole porch?
Answer:
$66.24
Step-by-step explanation:
The area of Vince's porch is:
8 feet x 12 feet = 96 square feet
To find the cost of the stain, we need to multiply the area of the porch by the cost per square foot:
96 square feet x $0.69 per square foot = $66.24
So it will cost $66.24 to buy enough stain for the whole porch.
Keisha's paint store brought in $4914 in
paint sales last weekend. She sells premium
paint for $40.50 per gallon and standard
paint for $24.50 per gallon. If the number of
standard paint gallons sold was four less
than twice as many premium gallons sold,
how many gallons of each type of paint did
Keisha sell last weekend?
Keisha sold 48 gallons of basic paint and 92 gallons of premium paint last weekend.
Let's denote the number of premium paint gallons sold by "x" and the number of standard paint gallons sold by "y".
According to the problem statement, we have:
[tex]x = 2y - 4[/tex] (the number of standard paint gallons sold was four less than twice as many premium gallons sold)
The total sales revenue from paint sales can be expressed as:
[tex]40.5x + 24.5y = 4914[/tex]
We can substitute x in the second equation with 2y - 4:
40.5(2y - 4) + 24.5y = 4914
Simplifying and solving for y, we get:
[tex]81y - 162 + 24.5y = 4914\\105.5y = 5076\\y = 48[/tex]
Substituting y in the equation [tex]x = 2y - 4[/tex], we get:
[tex]x = 2(48) - 4\\x = 92[/tex]
Therefore, last weekend, Keisha sold 48 gallons of normal paint and 92 gallons of premium paint.
Learn more about ratios here:
https://brainly.com/question/13419413
#SPJ1
Which geometer developed the deductive reasoning method for geometric proofs that is used today?
1: Euclid
2: Pythagoras
3: Girard Desargues
4: Rene Descartes
Answer: Euclid
Step-by-step explanation:
Answer: 4
Which geometer developed the deductive reasoning method for geometric proofs that is used today?
1. Rene Descartes
2. Pythagoras
3. Girard Desargues
4. Euclid
Deductive reasoning, unlike inductive reasoning, is a valid form of proof. Euclid using his definitions, common notions and postulates as an axiomatic system, was able to produce deductive proofs of a number of important geometric propositions.
Step-by-step explanation:
Triangle ABC with vertices at A(-3, -3), B(3, 3), C(0, 3) is dilated to create triangle A'B'C' with vertices at A'(-1, -1),
B(1, 1), C(0, 1). Determine the scale factor used.
The scale factor used. in the dilation is 1/3
Determining the scale factor used.From the question, we have the following parameters that can be used in our computation:
ABC with vertices at A(-3, -3), B(3, 3), C(0, 3) A'B'C' with vertices at A'(-1, -1), B(1, 1), C(0, 1).The scale factor is calculated as
Scale factor = A'/A
substitute the known values in the above equation, so, we have the following representation
Scale factor = (-1, -1)'/(-3, -3)
Evaluate
Scale factor = 1/3
Hence, the scale factor = 1/3
read more about scale factor at
https://brainly.com/question/29229124
#SPJ1
What is the measure of angle G?
Round only your final answer to the nearest tenth.
17.6°
29.0°
43.4°
O133.4°
Answer:133.4
Step-by-step explanation:
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials..
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a brown marble from the bag.
The theoretical probability, P(brown), is 50%, and the experimental probability is 25%.
The theoretical probability, P(brown), is 50%, and the experimental probability is 22.5%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 13.0%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
Answer:
Step-by-step explanation:
The correct answer is:
The theoretical probability of pulling a brown marble from the bag is 10/40 or 1/4, which is equivalent to 25%. This is because there are 10 brown marbles out of 40 total marbles in the bag.
The experimental probability of pulling a brown marble is 13/40 or 0.325, which is equivalent to 32.5%. This is because the student pulled a brown marble 13 times out of 40 total trials.
Therefore, the correct answer is: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
Please help! Very urgent!!
Step-by-step explanation:
we know the area A = B
10(6 + x) = A
5(15.5 + x) = B
A = B
10(6 + x) = 5(15.5 + x)
solve for x to get
x = 3.5
Add up to get the perimeter is 80
Mark Me Brainliest!
Tom throws some coins on the table. His twin, Joe, throws coins worth twice as much on the table. The total value of coins on the table $5.22 How much money did Tom throw on the table?
Answer: $1.74 worth of coins
Step-by-step explanation:
Let's say Tom throws x amount of money in coins on the table. Then Joe throws twice as much, which is 2x.
The total value of coins on the table is $5.22, so we can write an equation:
x + 2x = 5.22
Simplifying the equation, we get:
3x = 5.22
Dividing both sides by 3, we get:
x = 1.74
Therefore, Tom threw $1.74 worth of coins on the table.
PLEASE HELP
Brian deposited $9,808 into a savings account for which interest is compounded daily at a rate of 3.78%. How much interest will he earn after 12 years? Round answer to the hundredths place. If answer does not have a hundredths place then include zeros so it does. Do not include units in the answer. Be sure to attach your work for credit.
Brian deposited $9,808 into a savings account that compounds interest on a daily basis, at a rate of 3.78%. If we want to find out how much interest he will earn after 12 years, we can use the formula:
A = P(1 + r/n)^(nt)
where A is the amount of money after t years, P is the principal amount (which is $9,808 in this case), r is the annual interest rate (3.78% in this case), n is the number of times the interest is compounded per year (which is 365 since it compounds daily), and t is the number of years (which is 12).
So, plugging in the values we get:
A = $9,808(1 + 0.0378/365)^(365*12)
A = $9,808(1.000103972)^4380
A = $9,808(1.496812899)
A = $14,682.54
Therefore, the interest Brian will earn after 12 years is $14,682.54 - $9,808 = $4,874.54. When we round this answer to the hundredths place, we get $4,874.54.
Prove the identity of sinx+tanx/sinx=1+secx
The proof of trigonometric identity (sin(x) + tan(x))/sin(x) = 1 +secx is given below.
The given trigonometric identity is,
(sin(x) + tan(x))/sin(x).
We know that tan(x) = sin(x)/cos(x), so we can substitute that in:
sin(x)/ sin(x) + sin(x)/cos(x) / sin(x)
We can simplify the fraction in the numerator:
sin(x)/ sin(x) + sin(x)/sin(x)cos(x)
We know that sin(x)/sin(x) = 1, so we can simplify further:
1+ 1/cos(x)
We know that 1/cos(x) = sec(x), so we can substitute that in:
1 + sec(x).
Now we have the same expression as the right-hand side of the identity, so we have proven that:
sin(x) + tan(x)/sin(x) = 1 + sec(x)
Therefore, (sin(x) + tan(x))/sin(x) = 1 +secx.
To learn more about trigonometric identities;
https://brainly.com/question/24377281
#SPJ1
A recipe calls for 6 cups of flour and 4 cups of water. If the recipe decreased to use 2 cups of water, how much flower should be used?
The original recipe requires 6 cups of flour and 4 cups of water. If the water is reduced to 2 cups, then 3 cups of flour should be used, found by setting up a proportion.
The recipe calls for 6 cups of flour and 4 cups of water.
To decrease the amount of water used to 2 cups, we can set up a proportion
(flour)/(water) = (6)/(4) = (x)/(2)
where x is the amount of flour needed when 2 cups of water are used.
Simplifying this proportion, we get
4x = 12
Dividing both sides by 4, we get
x = 3
Therefore, when the recipe uses 2 cups of water, 3 cups of flour should be used.
To know more about amount of water:
https://brainly.com/question/26211317
#SPJ1
Find the p-value for this test based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table)
a. xยฏxยฏ = 380; s = 39; n = 18
The p-value for this test is 0.012, which is the probability of observing a sample mean as extreme as 380 (or more extreme) if the null hypothesis were true.
If the significance level of the test was α = 0.05, for example, we would reject the null hypothesis since the p-value (0.012) is less than the significance level.
To find the p-value for this test, we first need to determine the appropriate test statistic. Since we do not know the population standard deviation, we will use a t-test. The test statistic is calculated as:
t = (X - μ) / (s / √n)
Where X is the sample mean, μ is the null hypothesis population mean, s is the sample standard deviation, and n is the sample size.
In this case, the null hypothesis might be that μ = 400 (for example, if we were testing whether the mean weight of a certain type of fruit was 400 grams). Using the given sample information, we can calculate the t statistic as:
t = (380 - 400) / (39 / √18) = -2.82
Next, we need to find the corresponding p-value from the t-distribution table. Looking at the table with 17 degrees of freedom (since n - 1 = 18 - 1 = 17), we find that the p-value for a two-tailed test with a t-value of -2.82 is approximately 0.012.
To learn more about probability visit;
https://brainly.com/question/30034780
#SPJ11
Algebra 1 - please help!:)
Answer:
[tex]v(t) = 10500( {.86}^{t} )[/tex]
If the volume of a cone is 36л cm³ and the radius is 3 cm,
what is the height?
A. 108 cm
B. 12 cm
C. 14 cm
D. 4 cm
The height of the cone is 4cm
How to calculate the height of the cone?The parameters given in the question are
volume= 36
radius= 3
The formula for calculating the height of a cone is
height= 3(v/πr²)
= 3(36/3.14×3²)
= 3(36/28.26)
= 3(1.273)
= 3.8
⇒4
Hence the height of the cone is 4 cm
Read more on height here
https://brainly.com/question/27695078
#SPJ1
Math question I need help with:
Answer:
197
Step-by-step explanation:
What is the distance between the points (8 , 35) and (8 , 20) in the coordinate plane
The distance between the given points in the coordinate plane is equal to 15 units.
In the coordinate plane ,
Let us consider the points in the coordinate plane is represented by
( x₁ , y₁ ) = ( 8 , 35 )
( x₂ , y₂ ) = ( 8 ,20 )
Using the distance formula between two points ( x₁ , y₁) and ( x₂ , y₂ ) we have,
Distance = √( y₂ - y₁)² + ( x₂ - x₁ )²
Substitute the values we have in the formula,
⇒ Distance = √( 20 - 35)² + ( 8 - 8 )²
⇒ Distance = √ (-15)² + ( 0)²
⇒ Distance = √225
⇒ Distance = 15
Because distance cannot be negative.
Therefore, the distance between the two points (8 , 35) and (8 , 20) is equal to 15 units.
Learn more about distance here
brainly.com/question/31628069
#SPJ4
I NEED HELP ON THIS ASAP!!!! I WILL GIVE BRAINLIEST!!
Answer:
Step-by-step explanation:
I haven't answered because I'm thrown off by (x-1) in exponent but typically the ratio is the base.
The exponent is base with exponent (here not sure if it's from parent or with(x-1 ) depends on professor.
and y int comes from plugging in x=0
Exponential Function Ratio y-int
A [tex]3^{x-1}[/tex] 3 -2/3
B [tex]2^{x-1}[/tex] 2 45/2
C [tex].1^{x-1}[/tex] .1 or 1/10 12340
D [tex](1/2)^{x-1}[/tex] 1/2 -10
I'm positive about y-int and pretty sure about ratio and iffy about ex. function.
Hope this helps.
