Answer: Archimedes go to sleep at 8.32 metres away from the rock.
Step-by-step explanation:
Given that the rock beside which he slept was 5 meters tall
Height h = 5m
Angle Ø = 31 degree
To get distance x away from the rock, we will use trigonometry function. SohCahToa
TanØ = opposite/adjacent
Tan 31 = 5/x
x = 5/tan31
x = 8.32m
To find the distance from the rock where Archimedes went to sleep, we calculate the adjacent side of a right triangle using the tangent function with the given angle of 31 degrees and the rock's height of 5 meters. The result is approximately 8.32 meters.
The student's question involves finding the distance from the rock where Archimedes slept to the point where the sunlight hit the ground at a 31-degree angle.
This scenario forms a right triangle with the rock's height as the opposite side, the distance from the rock as the adjacent side, and the Sun's angle providing information to use trigonometry—specifically, the tangent function since we have the opposite side and are looking for the adjacent side.
To calculate the distance, we use the equation tan(angle) = opposite/adjacent, which can be transformed into adjacent = opposite/tan(angle).
Plugging in the values, we get:
adjacent = 5 meters/tan(31 degrees)
adjacent = 8.32
We find that the adjacent side, which is the distance from the rock, is approximately 8.32 meters.
Therefore, Archimedes went to sleep roughly 8.32 meters away from the rock.
Two less than the product of 3 and x
Answer:
3x-2
Step-by-step explanation:
Answer:
3x-2
Step-by-step explanation:
"Less than" makes the whole expression changed.
If the less than was not there, it would have been 2-3x.
"Product" is multiplication. So it would be 3x.
The "Less than" also has less in it which is subtraction.
Determine the zeroes of 10x2−5=35
Answer:
x = +2, x = -2
Step-by-step explanation:
The equation to solve in this problem is
[tex]10x^2-5=35[/tex]
The first step we do is to subtract 35 on both sides of the equation, so we get:
[tex]10x^2-5-35=0\\10x^2-40=0[/tex]
Now we simplify the equation by dividing both terms by 10:
[tex]\frac{10x^2-40}{10}=0\\x^2-4=0[/tex]
Now we observe that the term on the left is the difference between two squares, so it can be rewritten using the property:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Where here,
a = x
b = 2
So we can rewrite the equation as:
[tex]x^2-4=0\\(x+2)(x-2)=0[/tex]
And this equation is zero when either one of the two factors is zero, so the two solutions are:
[tex]x+2=0\rightarrow x=-2\\x-2=0 \rightarrow x=+2[/tex]
The two cones are congruent
Determine the unknown measures of the cones.
A= units
B = units
C = units
Du units
5.2/B
6.2
V.42 units
Va
units
Answer:
3.1
4.2
5.2
42
Step-by-step explanation: They’re congruent so just copy what the other triangle has all you had to do was find the radius.
(4 × 6) ÷ (2 + 4) ÷ (8 ÷ 4) =
Answer:
2
Step-by-step explanation:
24÷ 6÷ 2=2
An IQ test is designed so that the mean is 100 and the standard deviation is 1414 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 9090% confidence that the sample mean is within 66 IQ points of the true mean. Assume that sigmaσequals=1414 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
Answer:
37
Step-by-step explanation:
The first thing is to calculate critical z factor
the alpha and the critical z score for a confidence level of 90% is calculated as follows:
two sided alpha = (100% - 90%) / 200 = 0.05
critical z factor for two sided alpha of .05 is calculated as follows:
critical z factor = z factor for (1 - .05) = z factor for (.95) which through the attached graph becomes:
critical z factor = 2.58
Now we have the following formula:
ME = z * (sd / sqrt (N) ^ (1/2))
where ME is the margin of error and is equal to 6, sd is the standard deviation which is 14 and the value of z is 2.58
N the sample size and we want to know it, replacing:
6 = 2.58 * (14 / (N) ^ (1/2))
solving for N we have:
N = (2.58 * 14/6) ^ 2
N = 36.24
Which means that the sample size was 37.
temperatures in f can be converted in c using the formula c=5(f-32)/9
Make F the subject of the formula.
give your answer in the form aC+b/c where a, b and c are all positive intergers.
To make F the subject of the formula in the Celsius to Fahrenheit conversion, multiply by 9, divide by 5, and then add 32, resulting in F = (9/5)C + 32.
Explanation:To make F the subject of the formula when given the Celsius to Fahrenheit conversion formula c = 5(f - 32)/9, we start by isolating Fahrenheit on one side of the equation. Here's a step-by-step process:
Multiply both sides of the equation by 9: 9c = 5(f - 32).Divide both sides by 5: (9/5)c = f - 32.Add 32 to both sides to isolate f: f = (9/5)c + 32.Now the formula for F in terms of C is in the form aC + b with a = 9/5, b = 32, and there's no c as in the denominator since the conversion is direct.
[tex]\( F = \frac{9c + 160}{5} \).[/tex] In form [tex]\( aC + \frac{b}{c} \), \( a = 9 \), \( b = 160 \),[/tex] and [tex]\( c = 5 \).[/tex]
Let's break down the process of rearranging the formula step by step.
Given formula: [tex]\( c = \frac{5(F - 32)}{9} \)[/tex]
We want to isolate [tex]\( F \)[/tex] on one side of the equation.
1. Multiply both sides by [tex]\( \frac{9}{5} \):[/tex]
[tex]\[ \frac{9}{5} \cdot c = \frac{9}{5} \cdot \frac{5(F - 32)}{9} \][/tex]
This cancels out the fraction on the right side.
[tex]\[ \frac{9}{5} \cdot c = F - 32 \][/tex]
2. Add 32 to both sides to isolate [tex]\( F \):[/tex]
[tex]\[ \frac{9}{5} \cdot c + 32 = F \][/tex]
Now, [tex]\( F \)[/tex] is isolated on the right side of the equation.
3. Rewrite [tex]\( F \)[/tex] in the required form [tex]\( aC + \frac{b}{c} \):[/tex]
[tex]\[ F = \frac{9}{5}c + 32 \][/tex]
To express [tex]\( F \)[/tex] in the required form, we can rewrite [tex]\( \frac{9}{5}c \) as \( \frac{9c}{5} \),[/tex]so the form becomes [tex]\( aC + \frac{b}{c} \).[/tex]
So, [tex]\( a = 9 \), \( b = 32 \), and \( c = 5 \).[/tex]
4. Final Form:
[tex]\[ F = \frac{9c + 160}{5} \][/tex]
So, in the form [tex]\( aC + \frac{b}{c} \),[/tex] we have [tex]\( a = 9 \), \( b = 160 \), and \( c = 5 \).[/tex]
What is the value of x when solving the equation Negative 2 x + (negative 8) = 2 x + 8 using algebra tiles?
x = negative 4
x = negative 2
x = 2
x = 4
Answer:
the first option ...-4
Step-by-step explanation:
The solution is Option A.
The value of the equation is x = -4
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = Negative 2 x + (negative 8) = 2 x + 8
Substituting the values in the equation , we get
( -2x ) + ( -8 ) = 2x + 8 be equation (1)
On simplifying the equation , we get
-2x - 8 = 2x + 8
Adding 8 on both sides of the equation , we get
2x + 16 = -2x
Adding 2x on both sides of the equation , we get
4x + 16 = 0
Subtracting 16 on both sides of the equation , we get
4x = -16
Divide by 4 on both sides of the equation , we get
x = -4
Therefore , the value of x is -4
Hence , the value of the equation is x = -4
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Create a list of steps, in order, that will solve the following equation.
5(x-3)^2+4=1295(x−3)
2
+4=129
Answer:
subtract 4 from both sides
divide both sides by 5
take the square roots of both sides
add 3 to both sides
Step-by-step explanation:
Jacob wants to enlarge a triangle with sides 7, 12, and 12 inches to create a similar triangle. If the shortest side of the enlarged triangle is 24.5 inches, how long will each of the other two sides be?
Answer:
42
Step-by-step explanation:
If the shortest side is 7 and it is enlarged to be 24.5.
It is enlarged by a scale of 3.5.
so if you scale 12 by 3.5
then you get 42
The first three terms of a geometric sequence are as follows.
-3, 6, -12
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
Answer:
24, -48
Step-by-step explanation:
In this geometric sequence, the previous number is being multiplyed by -2 each time
This said the next number is 24.
-12*-2=24
and the next one is -48.
24*-2=-48
Final answer:
The next two terms of the geometric sequence -3, 6, -12 are 24 and -48, found by repeatedly multiplying with the common ratio of -2.
Explanation:
The first three terms of the given geometric sequence are -3, 6, and -12. To find the next two terms in this sequence, we need to determine the common ratio between the terms. The common ratio (r) is the factor by which we multiply one term to get the next term. In this case, 6 divided by -3 equals -2, and similarly, -12 divided by 6 also equals -2. This confirms that our common ratio is -2.
Now, to find the fourth term of the sequence, we multiply the third term (-12) by the common ratio (-2):
-12 × -2 = 24
To find the fifth term, we multiply the fourth term (24) by the common ratio (-2):
24 × -2 = -48
Therefore, the fourth and fifth terms of the geometric sequence are 24 and -48, respectively.
Paul observes that AB=AC and concludes that AB abd AC must be tangent to the circle. What is wrong with pauls reasoning?
Answer:
C
Step-by-step explanation:
Answer:
The answer should be C
Step-by-step explanation:
we know that
the triangle AOB is congruent with triangle AOC
because
AB=AC
OB=OC-----> the radius of the circle
The OB side is common
but
there is no additional information that allows me to calculate the OBA angle to determine if it is a right angle
therefore
the answer is the option
C.There is no indication that AB and AC are perpendicular to the radii at the points of intersection with the circle.
Thanks (4)
Each wall in Keith's room is 12 meters long and seven and 7 7/8 meters wide. He plans to paint one wall blue. Each can of paint covers 15 square meters. How many cans of paint does kids need to cover the bedroom wall?
Answer:
7 cans
Step-by-step explanation:
6 cans of paint kids need to cover the bedroom wall.
What is area of a rectangle?The formula for calculating the area of a rectangle with dimensions l and w is: A = lw (rectangle). In other words, the length times the width equals the area of a rectangle.
Given
length = 12 m
width = 7.875 m
area = 12 * 7.875 = 94.5 sq. m
area 1 can can fill = 15 sq. m
no. of cans that can fill 94.5 = 6
therefore, 6 cans of paint kids need to cover the bedroom wall.
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What is the measure of
Answer:
C: 107
Step-by-step explanation:
135-28 = 107
Answer:
it would have to be 107 bro
Step-by-step explanation:
Haley bought a 3-pound bag of cat food. She feeds her cat 6 ounces of cat food each day. Will the bag of cat food be enough to feed her cat for 7 days? Use the drop-down menus to explain.
Answer:
a -pound bag of cat food can enough to feed her cat for 7 days
Step-by-step explanation:
Given:
3-pound bag of cat food6 ounces of cat used per dayNumber of cat food used in 7 days (in ounces): 7*6 = 42 ounces
As we know,1 pound (lb) is equal to 16 Ounces (oz)
<=> 42 ounces = 42 /16 = 2.625 pounds < 3-pound bag
So a -pound bag of cat food can enough to feed her cat for 7 days
Hope it will find you well.
Answer:
Yes it will
Step-by-step explanation:
Let's first work with a single unit so that our work will be a lot easier.
We are going to convert pounds to ounces and since 1 pound = 16 ounces, 3 pounds = 16 × 3 = 48 ounces of cat food.
And she feeds her cat 6 ounces of food each day,that means that in 7 days the cat will only be able to consume just 7 × 6 = 42 ounces,but remember that the amount of cat food bought is equal to 48 pounds.
This here means that the cat food will be enough to feed the cat for 7 days
The equation of a line is y=8x+2 and the point (3,q) lies on this line. What is the value of q?
Answer:
q = 26
Step-by-step explanation:
Given that (3, q ) lies on the line, then the coordinates of the point make the equation true.
Substitute x = 3, y = q into the equation
q = 8(3) + 2 = 24 + 2 = 26
Final answer:
To determine the value of q for the point (3, q) on the line y=8x+2, substitute x with 3 to get y=26. Hence, q is 26, and the point is (3, 26).
Explanation:
To find the value of q for the point (3, q) that lies on the line with the equation y=8x+2, we substitute the x-coordinate of the point, which is 3, into the equation and solve for y. This gives us:
y = 8(3) + 2
y = 24 + 2
y = 26
Therefore, the value of q is 26, and the point is (3, 26). This demonstrates how to use a line's equation to find a specific point on the line. The question illustrates the algebraic relationship between the coordinates of a point on a line and the equation of the line itself.
MaryJo is considering investing in 2 different mutual funds. Option A has an annual interest rate of 7% and requires a principal of $10,000 with monthly deposits of $200 for 10 years. Option B has an annual interest rate of 9% and requires a principal of $10,000 with monthly deposits of $200 for 5 years.
The option A mutual funds will be more effective.
Step-by-step explanation:
Option A:
Principal amount = $10000
Monthly deposit = $200
Time = 10 years
Rate of interest = 7%
Total deposit = (200 x 12 x 10) + 10000
= 24000 + 10000
= $34000
Interest = (34000 x 7 ) /100
= 340 x 7
= $2380
Total amount = 34000 + 2380
= $36380
Option B:
Principal amount = $10000
Monthly deposit = $200
Time = 5 years
Rate of interest = 9%
Total deposit = (200 x 12 x 5) + 10000
= 12000 + 10000
= $22000
Interest = (22000 x 9 ) /100
= $1980
Total amount = 22000+1980
= $23980
The option A mutual funds will be more effective.
Answer:
What is the difference in the final balances of the two mutual funds?
Step-by-step explanation:
The difference is $12,400.
70 points- help ASAP, please.
1. Is a^2 - 39 prime...
a. Over the set of polynomials with rational coefficients?
b. over the set of polynomials with real coefficients?
c. Explain your answers to Parts a and b
2. The Discriminant Theorem Factoring Quadratics applies to quadratics with ___ coeffecients.
Answer:
1) a) yes
b) no
c) a² - 39
(a)² - (sqrt(39))²
(a - sqrt(39))(a + sqrt(39))
This quadratic can be split into real factors, but not rational
sqrt(39) is a real number, but not rational
2) real
students in art class make square tiles that are 5 inches long. They plan to make a row of tiles that is 4 feet 2 inches long. How many tiles will the students need to make?
The required students will need to make 10 tiles to create a row that is 4 feet 2 inches long.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
To solve this problem, we first need to convert the length of the row from feet and inches to inches.
4 feet 2 inches is equal to (4 x 12) + 2 = 50 inches.
Next, we can divide the length of the row by the length of each tile to find the number of tiles needed:
Number of tiles = Length of row / Length of each tile
Number of tiles = 50 inches / 5 inches
Number of tiles = 10 tiles
Therefore, the students will need to make 10 tiles to create a row that is 4 feet 2 inches long.
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*ignore selected answer haha* just need help answering
Answer:
[tex]x^2+8x+15[/tex]
Step-by-step explanation:
[tex]f(x)=x+4\\g(f(x))=g(x+4)\\g(x+4)=(x+4)^2-1\\(x+4)^2-1=x^2+8x+15[/tex]
Researchers studying the acquisition of pronunciation often compare measurements made on the recorded speech of adults and children. One variable of interest is called "voice onset time" (VOT), the length of time between the release of a consonant sound (such as "p") and the beginning of an immediately following vowel (such as the "a" in "pat"). For speakers of English, this short time lag can be heard as a period of breathiness between the consonant and the vowel. Here are the results for some randomly selected 4-year-old children and adults asked to pronounce the word "pat". VOT is measured in milliseconds and can be either positive or negative.
Children: n = 10, mean = 60.67, standard deviation = 39.89
Adults: n = 20, mean = 88.17, standard deviation = 24.74
You are interested in whether there is a difference in the VOT of adults and children, so you plan to test H0:μa−μc=0 against Ha:μa−μc≠0, where μa and μcare the population mean VOT for adults and children, respectively.
A. What additional information would you need to confirm that the conditions for this test have been met?
B. Assuming the conditions have been met, calculate the test statistic and p-value for this test.
C. Interpret the p-value in the context of this study and draw the appropriate conclusion at
α = 0.05.
D. Given your conclusion in part C, which type error, Type I or Type II, is it possible to make? Describe that error in the context of this study.
Answer:
(A) The additional information that is needed to confirm about the conditions for this test have been met is ‘Population is approximately normal.
(B) The test statistic = 1.9965
(C1) P-value = 0.0556
(C2) There is no significant difference between mean VOT for children and adults.
D1) It is possible to make type II error.
(D2) There should be a difference in the VOT of adults and children.
Step-by-step explanation:
Let na be the number of adults = 20
xa mean VOT for adults = 88.17
sa standard deviatiation of VOT for adults = 24.74
Let nc be the number of children = 10
xc mean VOT for children =60.67
sc standard deviatiation of VOT for children = 39.89
(A) From the information the population variances are unknown and the two sample are assumed to be independent and the sample the sample size are smaller that is (n<30).
This indicates that the additional information that is required for the conditions of the test to be satisfied is 'distribution of the population'. the addition assumption to be made is, that the population distribution is normal.
(b) Calculating the test statistics using the formula;
t = (xa -xc)/SE - d
where SE = standard deviation , d= hypothesized difference = 0
But SE = √sa²/na +sc²/nc
= √24.74 ²/20 + 39.89²/10
= √189.72559
= 13.774
Substituting into test statistics equation, we have
t = (xa -xc)/SE - d
= (88.17 - 60.67/13.774
= 1.9965
Therefore the test statistic is 1.9965
(c) Calculating the p-value, we have;
Degree of freedom = na + nc -2
= 10+ 20 -2
= 28
The p-value for t=1.9965 at 28 degrees of freedom and 0.05 level of significance is 0.0556.
The p-value 0.0556 is greater than given level of significance 0.05 hence we fail to reject the null hypothesis and conclude that there is no significant difference between mean VOT for children and adults.
(D1) From the information in part (C) the null hypothesis is not rejected.
Since the null hypothesis is not rejected, there might be a chance that not rejecting null hypothesis would be wrong. In this type of situation the error that can occur would be type II error.
(D2) The type of error describe in the context of this study is obtained by the concept of the type II error which tells that the null hypothesis is not rejected when it is actually false.
what are the two sides of a ray called??
Solve negative 7 over 3, the whole multiplied by x minus 3 equals negative 52.
Answer:
x= [tex]\frac{135}{7}[/tex]
Step-by-step explanation:
1. [tex]-\frac{7}{3} (x-3)=-52[/tex]
2. combine -7/3(x - 3)
= [tex]-\frac{7}{3}x-7 = -52[/tex]
3. Do combine like terms on both sides
= -52 + -7 = -45
4. left with, [tex]-\frac{7}{3}x = -45[/tex]
5. divide -45 by -7/3
6. left with, [tex]x = \frac{135}{7}[/tex]
Answer:
21
Step-by-step explanation:]
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Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 38 hours and a standard deviation of 5.8 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries.a. What can you say about the shape of the distribution of the sample mean?
b. What is the standard error of the distribution of the sample mean? (Round your anser to 4 decimals places.)
c. What proportion of the samples will have a mean useful life of more than 39.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places)
d. What proportion of the sample will have a mean useful life greater than 37.5? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Answer:
a) For this case we select a sample size of n=9. And we know that the distribution of X is normal so then the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
b) [tex] SE = \frac{\sigma}{\sqrt{n}} =\frac{5.8}{\sqrt{9}} =1.9333[/tex]
c) [tex] P\bar X >39.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 39.5 we got:
[tex] z = \frac{39.5-38}{\frac{5.8}{\sqrt{9}}}= 0.78[/tex]
And using the complement rule we got:
[tex] P(z >0.78) =1-P(Z<0.78) = 1-0.7823= 0.2177[/tex]
d) [tex] P\bar X >37.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 37.5 we got:
[tex] z = \frac{37.5-38}{\frac{5.8}{\sqrt{9}}}= -0.26[/tex]
And using the complement rule we got:
[tex] P(z >-0.26) =1-P(Z<-0.26) = 1-0.3974= 0.6026[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the life of batteries of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(38,5.8)[/tex]
Where [tex]\mu=38[/tex] and [tex]\sigma=5.8[/tex]
Part a
For this case we select a sample size of n=9. And we know that the distribution of X is normal so then the distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
Part b
The standard error is given by:
[tex] SE = \frac{\sigma}{\sqrt{n}} =\frac{5.8}{\sqrt{9}} =1.9333[/tex]
Part c
We want this probability:
[tex] P\bar X >39.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 39.5 we got:
[tex] z = \frac{39.5-38}{\frac{5.8}{\sqrt{9}}}= 0.78[/tex]
And using the complement rule we got:
[tex] P(z >0.78) =1-P(Z<0.78) = 1-0.7823= 0.2177[/tex]
Part d
We want this probability:
[tex] P\bar X >37.5)[/tex]
And we can use the z score given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 37.5 we got:
[tex] z = \frac{37.5-38}{\frac{5.8}{\sqrt{9}}}= -0.26[/tex]
And using the complement rule we got:
[tex] P(z >-0.26) =1-P(Z<-0.26) = 1-0.3974= 0.6026[/tex]
The distribution of the mean life of Batteries produced by Power+, Inc. follows Normal distribution. The standard error is calculated to be 1.9333. Using Z scores, it's discovered that approximately 21.77% of samples will have a mean life more than 39.5 hours while around 60.26% samples will have a mean useful life more than 37.5 hours.
Explanation:Understanding the Distribution of the Mean Life of Batteries
a. The distribution of the sample mean should approximate a normal distribution because we know the distribution of the population (life of the batteries) is normal. The expectation is that the sample mean should also follow normal distribution, based on the Central Limit Theorem.
b. The standard error of the distribution of the sample mean, is calculated as the standard deviation divided by the square root of the number of samples. Therefore, the standard error is 5.8 / sqrt(9), that is approximately 1.9333.
c. To find the proportion of samples with a mean useful life of more than 39.5 hours, we first find the Z score for 39.5. The Z score is calculated by (sample mean - population mean) / standard error. Therefore, Z = (39.5 - 38) / 1.9333 = approximately 0.78 (rounded to 2 decimal places). Looking this up on a Z table gives us 0.7823. However, because we want the proportion where it is more than 39.5 hours, we need to subtract this from 1. So, 1-0.7823 = 0.2177 (i.e., 21.77% samples will have a mean useful life more than 39.5 hours).
d. Following the same procedure, the Z score for a sample mean of 37.5 is approx negative -0.26 (rounded to 2 decimal places) using the same calculation as above. Looking this up on a Z table gives us 0.3974. But, because we want the proportion greater than 37.5 hours, we need to subtract this from 1. So, 1-0.3974 = 0.6026 (i.e., 60.26% samples will have a mean useful life more than 37.5 hours).
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wyatt bought a jacket that cost 12 dollers and a scarf that costs 18 dollers he recived a discount at the counter if he only paid 21 dollers total how many dollers was the discount?
Answer:
$9
Step-by-step explanation:
12 + 18 = $30 Total
30 - 21 = $9 Discount
30 - 9 = $21 After discount
The area of a regular polygon is 216cm2. The perimeter is 48cm, what is the
length of the apothem?
Answer:
The answer to your question is Apothem = 9 cm
Step-by-step explanation:
Data
Area = 216 cm²
Perimeter = 48 cm
Formula
Area = Perimeter x apothem / 2
Perimeter = length of the side x number of sides
Process
Substitute the values in the area formula and simplify it.
1.- Substitution
216 = 48a/2
-Solve for a
216 x 2 = 48a
432 = 48a
a = 432 / 48
-Result
a = 9 cm
2.6-,2.061,2.601,2.34,2.7 order the following from least to greatest
Answer:
2.061, 2.34, 2.6, 2.601, 2.7
Step-by-step explanation:
Hello!
This is a bit hard to explain! If you want me to try, just comment.
I have arranged the sequence in ascending order below:
[tex]2.061,\:2.34,\:2.6,\:2.601,\:2.7[/tex].
Hope this helps!
Answer:
2.061, 2.34, 2.6, 2.601, 2.7
Step-by-step explanation:
Because the numbers all have a 2 in the ones place, you need to evaluate the numbers in the tenths place and the numbers with the lowest go first and so on :)
Who knows the answer?
Answer:
t
Step-by-step explanation:
Line [tex] \purple{\boxed{\bold{t}}} [/tex] is the transversal.
Solve for a and d
6x^2+14x+4=(ax+b)(cx+d)
b=1 and c=2
Answer:
a = 3
d = 4
Step-by-step explanation:
6x^2+14x+4 = (ax+1)(2x+d)
6x^2+2x+12x+4
2x(3x+1)+4(3x+1)
(3x+1)(2x+4)
3 = a
4 = d
Answer:
Step-by-step explanation:
a=3, d=4
select all of the ratios that are equivalent to 4 to 7.
5/8
12/10
8.14
5 to 10
16/28
9 to 16
Answer:
[tex]\frac{16}{28}[/tex]
Step-by-step explanation:
Question asked:
Select all of the ratios that are equivalent to 4 to 7.
1) 5/8
2) 12/10
3) 8.14
4) 5 to 10
5) 16/28
6) 9 to 16
Solution:
To know the ratios are equivalent to [tex]\frac{4}{7}[/tex] or not, we have to check each by cross multiplication:-
1) [tex]\frac{5}{8}[/tex]
[tex]\frac{4}{7} =\frac{5}{8} \\ \\[/tex]
By cross multiplication:
[tex]4\times8=5\times7\\ \\ 32=35[/tex]
Not equivalent.
2) [tex]\frac{12}{10}[/tex]
[tex]\frac{4}{7} =\frac{12}{10} \\ \\[/tex]
By cross multiplication:
[tex]4\times10=12\times7\\ \\ 40=84[/tex]
Not equivalent.
3) 8.14 = [tex]\frac{814}{100} \ eliminating\ decimal[/tex]
[tex]\frac{4}{7} =\frac{814}{100} \\ \\[/tex]
By cross multiplication:
[tex]4\times100=814\times7\\ \\ 400=5698[/tex]
Not equivalent.
4) [tex]\frac{5}{10}[/tex]
[tex]\frac{4}{7} =\frac{5}{10} \\ \\[/tex]
By cross multiplication:
[tex]4\times10=5\times7\\ \\ 40=35[/tex]
Not equivalent.
5)[tex]\frac{16}{28}[/tex]
[tex]\frac{4}{7} =\frac{16}{28} \\ \\[/tex]
By cross multiplication:
[tex]4\times28=16\times7\\ \\ 112=112[/tex]
Yes, this is equivalent.
6) [tex]\frac{9}{16}[/tex]
[tex]\frac{4}{7} =\frac{9}{16} \\ \\[/tex]
By cross multiplication:
[tex]4\times16=9\times7\\ \\ 64=63[/tex]
Not equivalent.
Thus, only [tex]\frac{16}{28}[/tex] is equivalent.
Find the area of the region enclosed by f(x) and the x axis for the given function over the specified u reevaluate f(x)=x^2+3x+4 x<3 f(x)=4x+10 x greater than or equal to 3 on -3,4
Answer:
A = 68 unit^2
Step-by-step explanation:
Given:-
The piece-wise function f(x) is defined over an interval as follows:
f(x) = { x^2+3x+4 , x < 3
f(x) = { x^2+3x+4 , x≥3
Domain : [ -3 , 4 ]
Find:-
Find the area of the region enclosed by f(x) and the x axis
Solution:-
- The best way to tackle problems relating to piece-wise functions is to solve for each part individually and then combine the results.
- The first portion of function is valid over the interval [ -3 , 3 ]:
[tex]f(x) = x^2+3x+4[/tex]
- The area "A1" bounded by f(x) is given as:
[tex]A1 = \int\limits^a_b {f(x)} \, dx[/tex]
Where, The interval of the function { -3 , 3 ] = [ a , b ]:
[tex]A1 = \int\limits^a_b {x^2+3x+4} \, dx\\\\A1 = \frac{x^3}{3} + \frac{3x^2}{2} + 4x |\limits_-_3^3 \\\\A1 = \frac{3^3}{3} + \frac{3*3^2}{2} + 4*3 - \frac{-3^3}{3} - \frac{3(-3)^2}{2} - 4(-3)\\\\A1 = 9 + 13.5 +12 + 9-13.5+12\\\\A1 =42 unit^2[/tex]
- Similarly for the other portion of piece-wise function covering the interval [3 , 4] :
[tex]f(x) = 4x+10[/tex]
- The area "A2" bounded by f(x) is given as:
[tex]A2 = \int\limits^a_b {f(x)} \, dx[/tex]
Where, The interval of the function { 3 , 4 ] = [ a , b ]:
[tex]A2 = \int\limits^a_b {4x+10} \, dx\\\\A2 = 2x^2 + 10x |\limits_3^4 \\\\A2 = 2*(4)^2 + 10*4 - 2*(3)^2 - 10*3\\\\A2 = 32 + 40 - 18-30\\\\A2 =26 unit^2[/tex]
- The total area "A" bounded by the piece-wise function over the entire domain [ -3 , 4 ] is given:
A = A1 + A2
A = 42 + 26
A = 68 unit^2
To find the area enclosed by f(x) and the x-axis from x = -3 to x = 4 for the given piecewise function, calculate the integral of each piece separately and then sum the areas. The area is divided into two parts due to the function having different expressions before and after x = 3.
Explanation:The student is asking to find the area under the curve of a given piecewise function f(x) on the interval from x = -3 to x = 4. Since the function is defined differently for x < 3 and x ≥ 3, the area calculation involves two parts:
Calculating the area under [tex]f(x) = x^2 + 3x + 4[/tex] from x = -3 to x = 3.Calculating the area under [tex]f(x) = 4x + 10[/tex] from x = 3 to x = 4.The first part can be calculated using the integral of [tex]f(x) = x^2 + 3x + 4[/tex]from x = -3 to x = 3. The second part is the integral of [tex]f(x) = 4x + 10[/tex] from x = 3 to x = 4. The total area is the sum of these two areas. For this function, the areas are bounded above by the function and below by the x-axis, so all areas are considered positive.
Learn more about Area Under a Curve here:https://brainly.com/question/31849536
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