The walls of a bathroom 2,5 m long, 2,05 m
wide and 3 m high are to be covered with
tiles, each 15 cm by 15 cm. If a saving of
108 tiles is made on doors and windows,
how many tiles will be needed altogether?
Note that some tiles will have to be cut.)
Answers
Answer:
The number of tiles needed is 1.105.\(\overline 3\) tiles
Step-by-step explanation:
The given data on the dimensions of the bathroom wall are;
The length, l = 2.5 m
The width, w = 2.05 m
The height, h = 3 m
The dimension of the tiles with which the walls are to be covered = 15 cm by 15 cm
The dimensions of the tiles in meters = 0.15 m by 0.15 m
The number of tiles savings made on the doors and windows of the bathroom = 108 tiles
Let 'A' represent the surface area of the bathroom wall, we have;
A = h·w + h·w + l·h + l·h = 2·h·w + 2·l·h = 2·h·(w + l)
∴ A = 2 × 3 m (2.5 m + 2.05 m) = 27.3 m²
The surface area per tile, Tₐ = 0.15 × 0.15 = 0.0225
∴ Tₐ = 0.0225 m²/tile
The number of tiles needed, n = A/Tₐ - 108 tiles
∴ n = 27.3 m²/(0.0225 m²/tile - 108 tiles = \(\left (1105+\dfrac{1}{3} \right )\) tiles = 1.105.\(\overline 3\) tiles
The number of tiles needed, n = 1.105.\(\overline 3\) tiles.
Related Questions
Determine the number of solutions: 3x+2=3x+2
Answers
Answer:
infinite
Step-by-step explanation:
Both sides are equal
can soemone help meee ):
Answers
I don't know the answer but my tip would be to split the shape the way I did it, find the lengths of each side, and then find the area for each individual shape.
Then add all the areas together.
Select the correct answer.
Which function Is represented by this graph?
Answers
If m∠ADB=( 3a + 10)° and m∠BDC= 13a°, find a, m∠ADB, and m∠BDC.
Answers
Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.
What is the numerical value of a, ∠ADB and ∠BDC?When two angles have measures adding to up to 90 degrees, they are called complementary .
Given that;
m∠ADB = ( 3a + 10 )m∠BDC = 13aNumerical value of a = ?For complimentary angles;
m∠ADB + m∠BDC = 90°
Plug in the given values and solve for a.
( 3a + 10 ) + 13a = 90
3a + 10 + 13a = 90
10 + 16a = 90
16a = 90 - 10
16a = 80
a = 80/16
a = 5
Now, find the measure of ∠ADB and ∠BDC.
m∠ADB = ( 3a + 10 ) = 3(5) + 10 = 15 + 10 = 25°
m∠BDC = 13a = 13( 5 ) = 65°
Given that ∠ADB and ∠BDC are complimentary angles, the numerical value of a, ∠ADB and ∠BDC are 5, 25° and 65° respectively.
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A media center specialist wants to make a display of 3 types of fiction books. She has 4 mysteries, 3 adventures, and 6 science fiction books. How many possible combinations are there for a display with one mystery, one adventure, and one science fiction book?
Answers
Answer:
72 possible combinations
Step-by-step explanation:
In order to calculate the total number of possible outcomes of using one of each category we simply need to multiply the total number of books from each category together. Since there are 4 mysteries, 3 adventures, and 6 science fiction books we multiply these values with one another.
4 * 3 * 6 = 72
Finally, we can see that there are a total of 72 possible combinations for displaying one book from each category together.
Find the sum of -4a-3 and 7a-4.
Answers
Answer: 3a - 7
Step-by-step explanation:
(-4a - 3) + (7a - 4)
Combine like terms
-4a + 7a - 3 - 4
3a - 7
Hope this helped!
7 a -4 =30
Move all terms not containing
a
to the right side of the equation.
Tap for more steps...
7
a = 34
Divide each term by
7
and simplify.
Tap for more steps...
a = 34 7
The result can be shown in multiple forms.
Exact Form:
a = 34 7
Decimal Form:
a = 4. 857142
Mixed Number Form:
a
=
4 6/ 7
Solve the following problems: 1. In order to build a new warehouse facility, the regional distributor for Valco Multi-Position Valves borrowed $1.6 million at 10% per year interest. If the company repaid the loan in a lump sum amount after 2 years, what was (a) the amount of the payment, and (b) the amount of interest? 2. A sum of $2 million now is equivalent to $2.42 million 1 year from now at what interest rate? 3. In order to restructure some of its debt, General Motors decided to pay off one of its short-term loans. If the company borrowed the money 1 year ago at an interest rate of 8% per year and the total cost of repaying the loan was $82 million, what was the amount of the original loan? 4. How many years would it take for an investment of $280,000 to cumulate to at least $425,000 at 15% per year interest? 5. Valtro Electronic Systems, Inc. set aside a lump sum of money 4 years ago in order to finance a plan expansion now. If the money was invested in a 10% per year simple interest certificate of deposit, how much did the company set aside if the certificate is now worth $850,000 ? 6. Two years ago, ASARCO, Inc. invested $580,000 in a certificate of deposit that paid simple interest of 9% per year. Now the company plans to invest the total amount accrued in another certificate that pays 9% per year compound interest. How much will the new certificate be worth 2 years from now? 7. How many years would it take for money to triple in value at 20% per year simple interest? 8. If Farah Manufacturing wants its investments to double in value in 4 years, what rate of return would it have to make on the basis of (a) simple interest and (b) compound interest? 9. What simple interest rate per year would be required to accumulate the same amount of money in 2 years as 20% per year compound interest? a. 20.5% b. 21% c. 22% d. 23%
Answers
1. The payment amount and the interest on the loan, we need to use the formula for calculating compound interest. The formula is: A = P(1 + r)^n
Where:
A is the total amount after n years,
P is the principal amount (loan amount),
r is the interest rate per period (in this case, 10% per year),
n is the number of periods (in this case, 2 years).
(a) To find the amount of the payment, we need to calculate the total amount (A) and subtract the principal amount (P):
A = P(1 + r)^n
A = $1,600,000(1 + 0.10)^2
A = $1,600,000(1.10)^2
A = $1,600,000(1.21)
A = $1,936,000
Payment amount = A - P = $1,936,000 - $1,600,000 = $336,000
(b) To find the amount of interest, we subtract the principal amount from the total amount:
Interest = A - P = $1,936,000 - $1,600,000 = $336,000
Therefore, the amount of the payment is $336,000 and the amount of interest is also $336,000.
2. To find the interest rate, we can use the formula for compound interest:
A = P(1 + r)^n
Where:
A is the future amount ($2.42 million),
P is the present amount ($2 million),
r is the interest rate per period (unknown),
n is the number of periods (1 year).
We can rearrange the formula to solve for r:
r = (A/P)^(1/n) - 1
r = ($2.42 million / $2 million)^(1/1) - 1
r = 1.21 - 1
r = 0.21
Therefore, the interest rate is 21%.
3. To find the original loan amount, we can use the formula for calculating the future amount with compound interest:
A = P(1 + r)^n
Where:
A is the total cost of repaying the loan ($82 million),
P is the original loan amount (unknown),
r is the interest rate per period (8% per year),
n is the number of periods (1 year).
We can rearrange the formula to solve for P:
P = A / (1 + r)^n
P = $82 million / (1 + 0.08)^1
P = $82 million / 1.08
P ≈ $75.93 million
Therefore, the amount of the original loan was approximately $75.93 million.
4. To find the number of years required for the investment to reach at least $425,000, we can use the formula for compound interest:
A = P(1 + r)^n
Where:
A is the future amount ($425,000),
P is the initial investment ($280,000),
r is the interest rate per period (15% per year),
n is the number of periods (unknown).
We can rearrange the formula to solve for n:
n = log(A/P) / log(1 + r)
n = log($425,000/$280,000) / log(1 + 0.15)
n ≈ 4.61 years
Therefore, it would take approximately 4.61 years for the investment to cumulate to at least $425,000 at a 15% per year interest rate.
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Pedro fills up his truck with gas he paid $2.75 a gallon which of these represents an amount and price of gas that Pedro purchased select all that apply
Answers
The options that represent an amount and price of gas that Pedro purchased are 19 gallons of gas for $52.25, 16 gallons of gas for $44. So options C and D are correct.
To calculate the amount of gas and the total price that Pedro purchased, we need to use the formula:
Price = Cost per gallon * Number of gallons
Dividing the total price by the cost per gallon will give us the number of gallons purchased. We can then compare this with the given options to see which one(s) match.
Using the given cost per gallon of $2.75, we can check each option:
a) 13.75 gallons of gas for $41.25
Price = $2.75/gallon * 13.75 gallons = $37.81
This option does not match the total price of $41.25, so it is not correct.
b) 22 gallons of gas for $71.5
Price = $2.75/gallon * 22 gallons = $60.50
This option does not match the total price of $71.5, so it is not correct.
c) 19 gallons of gas for $52.25
Price = $2.75/gallon * 19 gallons = $52.25
This option matches the total price of $52.25, so it is correct.
d) 16 gallons of gas for $44
Price = $2.75/gallon * 16 gallons = $44
This option matches the total price of $44, so it is correct.
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Complete question is:
Pedro fills up his truck with gas he paid $2.75 a gallon which of these represents an amount and price of gas that Pedro purchased select all that apply.
a) 13.75 gallons of gas for $41.25
b) 22 gallons of gas for $71.5
c) 19 gallons of gas for $52.25
d) 16 gallons of gas for $44
Previous
37
Question
Each side of quadrilateral TVWX is tangent to ⊙Y. Find the perimeter of the quadrilateral.
Answers
keeping in mind that tangent lines to the same circle when intersecting each other outside the circle are the same length, Check the picture below.
Solve the triangle in the figure.
Question options:
A)
BC = 9; m∠A = 53.1°; m∠B = 6.9°; m∠C = 90°
B)
BC = 11; m∠A = 42.8°; m∠B = 47.2°; m∠C = 90°
C)
BC = 19; m∠A = 36.9°; m∠B = 53.1°; m∠C = 90°
D)
BC = 9; m∠A = 36.9°; m∠B = 53.1°; m∠C = 90°
Answers
Answer:
D)
BC = 9; m∠A = 36.9°; m∠B = 53.1°; m∠C = 90°
Step-by-step explanation:
15²-12² = 9²
BC = 9
sin B = 12/15 = 0.8
∠B = 53.1°
The solution will be BC = 9; m∠A = 36.9°; m∠B = 53.1°; m∠C = 90°. The correct option is D.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.
The triangle ABC is a right triangle. The new path is in front of the right angle, therefore it is the hypotenuse. To find the length of the hypotenuse we use the Pythagorean theorem:
H² = P² + B²
The length BC will be calculated as below:-
15²-12² = 9²
BC = 9
The angle B will be calculated as below:-
sin B = 12/15 = 0.8
∠B = 53.1°
Therefore, the solution will be BC = 9; m∠A = 36.9°; m∠B = 53.1°; m∠C = 90°. The correct option is D.
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Find the magnitude and direction of the vector with initial
point P(7,−9) and terminal point Q(−5,1).
→ |u|=________
Round to two decimal places
θ =_______ °
Round to the nearest tenth
Answers
The magnitude of the vector PQ is approximately 15.62. The direction of the vector is approximately -44.10 degrees when measured counterclockwise from the positive x-axis.
To find the magnitude and direction of the vector with initial point P(7,-9) and terminal point Q(-5,1), we can use the following formulas:
Magnitude:
The magnitude or length of the vector u = PQ is given by the distance formula:
|u| = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Direction:
The direction of the vector u = PQ can be found using trigonometry. The angle θ between the positive x-axis and the vector u is given by:
θ = atan2((y2 - y1), (x2 - x1))
Let's calculate the magnitude and direction of the vector.
Magnitude:|u| = sqrt((-5 - 7)^2 + (1 - (-9))^2)
|u| = sqrt((-12)^2 + (10)^2)
|u| = sqrt(144 + 100)
|u| = sqrt(244)
|u| ≈ 15.62 (rounded to two decimal places)
Direction:θ = atan2((1 - (-9)), (-5 - 7))
θ = atan2(10, -12)
θ ≈ -0.7697 radians
To convert radians to degrees, we multiply by 180/π:
θ ≈ -0.7697 * (180/π)
θ ≈ -44.10 degrees (rounded to the nearest tenth)
Therefore, the magnitude of the vector u is approximately 15.62 and the direction is approximately -44.10 degrees.
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it has been observed that some persons who suffer colitis, again suffer colitis within one year of the first episode. this is due, in part, to damage from the first episode. the performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. in order to do this two groups of people suffering a first episode are selected. there are 55 people in the first group and this group will be administered the new drug. there are 45 people in the second group and this group will be administered a placebo. after one year, 11% of the first group has a second episode and 9% of the second group has a second episode. conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode? select the [alternative hypothesis, value of the test statistic].
Answers
The value of the test statistic is 0.
The alternative hypothesis states that there is a difference between the true percentage of the first group who suffer a second episode and the true percentage of the second group who suffer a second episode.
The null hypothesis states that there is no difference between the true percentage
of the first group who suffer a second episode and the true percentage of the second group who suffer a second episode. Let us compute the value of the test
statistic
First, let us determine the proportion of people in each group who suffer a second episode:First group: p1 = 11/55 = 0.2Second group: p2 = 9/45 = 0.2
The sample proportion
of both groups is 0.2. Let us now calculate the standard error of the difference of proportions:SE(p1 - p2) = sqrt{ [p1(1 - p1) / n1 ] + [ p2(1 - p2) / n2 ] }= sqrt{ [0.2(0.8) / 55] + [0.2(0.8) / 45] }= sqrt{ 0.0029 + 0.0044 }= sqrt{ 0.0073 }= 0.0853
Now we can calculate the test statistic:Z = [(p1 - p2) - 0] / SE(p1 - p2)Z = [(0.2 - 0.2) - 0] / 0.0853Z = 0 / 0.0853Z = 0
The value of the test statistic is 0. The alternative hypothesis states that there is a difference between the true percentage of the first group who suffer a second episode and the true percentage of the second group who suffer a second episode. However, the test statistic is 0.
Therefore, there is no evidence to support the alternative hypothesis. The value of the test statistic is 0.
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To calculate the test statistic, we can use the formula (p1 - p2) / sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2)), where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.
Given that p1 = 0.11, p2 = 0.09, n1 = 55, and n2 = 45, we can substitute these values into the formula to find the test statistic:
Test statistic = (0.11 - 0.09) / sqrt((0.11*(1-0.11)/55) + (0.09*(1-0.09)/45))
To conduct a hypothesis test, we need to define our null and alternative hypotheses. In this case, our null hypothesis (H0) states that the true percentage of those in the first group who suffer a second episode is the same as the true percentage of those in the second group who suffer a second episode. Our alternative hypothesis (Ha) states that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode.
Next, we calculate the test statistic, which is the difference between the sample proportions of the two groups. The sample proportion for the first group is 11% (or 0.11), and for the second group is 9% (or 0.09). The test statistic can be calculated as (p1 - p2) / sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2)), where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.
Substituting the values, the test statistic is (0.11 - 0.09) / sqrt((0.11*(1-0.11)/55) + (0.09*(1-0.09)/45)).
Finally, we compare the test statistic to the critical value at the significance level of 0.1. If the test statistic falls outside the critical value range, we reject the null hypothesis and conclude that there is reason to believe that the true percentages are different. Otherwise, we fail to reject the null hypothesis.
In this case, the alternative hypothesis is that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode. The value of the test statistic can be calculated using the formula provided above.
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Solve for x
-2/5x - 8/15x + 1/3x = -54
x=?
Answers
Answer:
x=0
Step-by-step explanation:
solve for x by simplifying both sides of the equation, then isolating the variable. which got me x=0
Answer:
x = 1/90
or
x = 90^-1
Step-by-step explanation:
-2/5x - 8/15x + 1/3x = -54
-9/15x = -54
-3/5x = -54
3x = 270x
270x = 3
x = 1/90, x ≠ 0
This is a similar triangle please find the missing length. (?)
Answers
Find the value of X. Round to the nearest tenth.
Answers
Answer:
x = 4.1 cm
Step-by-step explanation:
The chord is divided into two equal parts. A right angle is formed, therefore, to find x, apply pythagorean theorem.
c² = a² + b²
Where,
c = 8.8 cm
a = x
b = 15.6/2 = 7.8 cm
Plug in the values
8.8² = x² + 7.8²
8.8² - 7.8² = x²
16.6 = x²
√16.6 = x
x = 4.1 (to nearest tenth)
After paying $3 for a sandwich, Trevor has $9.How much money did he have before buying the sandwich?
Answers
Answer:
$12
Step-by-step explanation:
add 3 to 9 and get 12
Please help due in ten minutes
Answers
180- (80-10x)
180-80+10x
100+10x
Answer: 100+10x
a random sample of 380 found that 67% of the readers owned a personal computer. find the value of the test statistic. round your answer to two decimal places.
Answers
The value of the test statistic is 6.51.
The test statistic for this problem can be calculated using the formula:
z = (p - P) / √(P * (1 - P) / n)
Where p is the sample proportion (0.67 in this case), P is the hypothesized population proportion (we don't know this value, so we assume it to be 0.5 for a two-tailed test), n is the sample size (380), and z is the standard normal distribution value corresponding to the level of significance.
Plugging in the values, we get:
z = (0.67 - 0.5) / √(0.5 * (1 - 0.5) / 380) = 6.51
So the value of the test statistic is 6.51.
The test statistic is a measure of how far the sample proportion deviates from the hypothesized population proportion under the null hypothesis. In this case, we assume that the population proportion is 0.5 (since we have no reason to believe otherwise), and we calculate the probability of observing a sample proportion of 0.67 or greater assuming this null hypothesis is true.
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consider a decomposition of relation r (a, b, c, d) into r1 (a, b, d) and r2 (c, d). this decomposition is lossless (non-additive) if c → d.
Answers
Decomposing relation R(a, b, c, d) into R1(a, b, d) and R2(c, d) may or may not be lossless solely based on the functional dependency c → d. The condition R1 ∩ R2 → R2, which implies R2 is functionally dependent on the intersection of R1 and R2, does not guarantee losslessness.
To determine the losslessness of the decomposition, we need to consider all the functional dependencies that hold in the original relation R. If the decomposition satisfies the lossless join property for all possible functional dependencies in R, then it can be considered lossless.
In this case, we have the functional dependency c → d. This means that for any two tuples in R with the same value for c, they must also have the same value for d. However, this functional dependency alone does not provide sufficient information to determine if the decomposition is lossless.
To assess losslessness, we need to examine other functional dependencies in R that involve attributes not present in R1 or R2. If there are additional functional dependencies in R involving attributes not present in R1 or R2, then the decomposition is likely to be lossy, as important dependencies are not preserved.
Therefore, it is essential to analyze all the functional dependencies in R to determine the losslessness of the decomposition. If the decomposition satisfies all the functional dependencies present in R, including those not mentioned in the given question, then it can be considered lossless. Failure to preserve any functional dependency may result in loss of information during the decomposition process.
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The decomposition of relation R(a, b, c, d) into R1(a, b, d) and R2(c, d) is not necessarily lossless (non-additive) based solely on the functional dependency c → d. The condition R1 ∩ R2 → R2 (R2 is functionally dependent on the intersection of R1 and R2) does not guarantee losslessness.
To determine whether the decomposition is lossless or not, we need to examine all functional dependencies that hold in the original relation R. If the decomposition satisfies the lossless join property for all possible functional dependencies in R, then it can be considered lossless.
HELPPPPPPPPPPP ASAP!!!
In the figure below, quadrilateral GHKL is a rectangle, and triangle HJK is isosceles, with HJ KJ.
If mHJK = 38°, what is mJKL?
A.
161°
B.
71°
C.
142°
D.
171°
Answers
Answer:
Answer is A= 161°
Step-by-step explanation:
Since ∡HJK = 38° and ∡HKJ = ∡JHK = (180-38)/2 =71
Therefore ∡JKL = 71+90 = 161°
3. If A and B are complements, P(A)= a, and P(B)=b, which of the following must be true?
(1) a=b+1
(3) a=1-b
(2) a = 1/b
(4) a=b-1
Answers
The statement that must be true if A and B are complements is a = 1 - b
Identifying which of the statement that must be true?From the question, we have the following parameters that can be used in our computation:
A and B are complements
Also, we have
P(A)= a, and P(B)=b
As a general rule, the sum of complement probabilities is 1
using the above as a guide, we have the following:
P(A) + P(B) = 1
substitute the known values in the above equation, so, we have the following representation
a + b = 1
So, we have
a = 1 - b
Hence, the statement that must be true is a = 1 - b
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8th grade volume escape room spheres
Answers
Answer:
Step-by-step explanation:
First: pay attention in class
Next: do what the teacher says
a manager receives 9 applications for a specific position. she wants to narrow it down to 4. in how many ways can she rank 4 applications?
Answers
The number of ways that can she rank 9 applications should be 126.
What is the definition of combination in math?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.
Calculation of the number of ways:
Since A manager receives 9 applications for a specific position. She wants to narrow it down to 4.
So here we do apply the permutation here:
9*8*7*6/ 4*3*2
=126
Hence, The number of ways that can she rank 4 applications should be 126
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Explain how the tangents of complementary angles are related.
Answers
Answer:
tan(α) = 1/tan(90°-α)
Step-by-step explanation:
The tangent of one is the reciprocal of the tangent of the other.
__
In a right triangle, ...
tan = opposite/adjacent
For the two complementary acute angles in such a triangle, opposite and adjacent are swapped. That is the tangent of one is the inverse of the tangent of the other. (That inverse is also known as the cotangent.)
tan(α) = cot(90°-α) = 1/tan(90°-α)
If y = 35 when x = 140, what is the value of y when x = 70?
Answers
Answer:
17.5
Step-by-step explanation:
x and y are in the ratio: 1 : 4
which means that if y is 35 x is 4 times y equating to 140
hence if x is 70 then y is 17.5
The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books. Choosing which 2 books describes a pair of dependent events?
A. one of the nonfiction books on the bottom shelf, and a second nonfiction book from the bottom shelf
B. one of the fiction books on the top shelf, and then one of the nonfiction books on the top shelf
C. one of the fiction books on the top shelf, and then one of the nonfiction books on the bottom shelf
D. one of the fiction books on the top shelf, and then a second fiction book from the bottom shelf
Answers
When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events. The correct option is B.
Which pair of events are called independent events?When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.
Symbolically, we have:
Two events A and B are said to be independent if we have:
\(P(A \cap B) = P(A)P(B)\)
Comparing it with the chain rule will give
\(P(A|B) = P(A)\\P(B|A) = P(B)\)
Thus, showing that whether one occurred or not, the other one doesn't care about it (independence).
The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelves, there are 3 fiction and 5 nonfiction books.
When Choosing 2 books that describe a pair of dependent events, one of the fiction books should be chosen from the top shelf, and another one should be a nonfiction book from the top shelf itself.
Hence, the correct option is B.
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Answer: One of the nonfiction books on the bottom shelf, and a second nonfiction book from the bottom shelf
Step-by-step explanation: Answer on Edmentum
What is the length of the diagonal from B to D of this rectangle? Round your answer to the nearest tenth of a metre.
Answers
Answer:
2√97
Step-by-step explanation:
BD² = BC² + DC²
⇒ BD = √BC² + DC²
= √(18)² + (8)²
= √324 + 64
= √388
Rewrite 388 as 2² · 97.
Factor 4 out of 388.
√4(97)
Rewrite 4 as 2².
√2² · 97
Pull terms out from under the radical.
2√97
The result can be shown in multiple forms.
Exact Form:
2√97
Decimal Form:
19.69771560...
Challenge Question Sally's bank account balance was $50 on Monday. On Tuesday, she bought a new pair of shoes for $45. On Thursday evening she earned $25 babysitting her neighbor's children. On Friday she spent $42 on pizza for her friends. She earned $20 dollars on Saturday raking leaves. What is her bank account balance on Sunday? ?
Answers
Answer:
$8
Step-by-step explanation:
After the shoe purchase, her balance was $50 -45 = $5.
After depositing her babysitting earnings, her balance was $5+25 = $30.
After buying pizza, her balance was $30 -42 = -$12.
Assuming no overdraft charge, her balance after depositing her earnings was ...
-$12 +20 = $8
Sally's balance on Sunday was $8.
Given a normal distribution with u = 100 and o= 10, complete parts (a) through (d).
a. What is the probability that X> 85? The probability that X> 85 is_____(Round to four decimal places as needed.) b. What is the probability that X<80? The probability that X < 80 is ____(Round to four decimal places as needed.) c. What is the probability that X<90 or X> 130? The probability that X<90 or X> 130 is ____ (Round to four decimal places as needed.) d. 99% of the values are between what two X-values (symmetrically distributed around the mean)? 99% of the values are greater than __ and less than _(Round to two decimal places as needed.)
Answers
To solve the given problems, we'll use the properties of the normal distribution with mean μ = 100 and standard deviation σ = 10.
a. Probability that X > 85:
To find this probability, we need to calculate the area under the normal curve to the right of 85. We can use the standard normal distribution table or a calculator to find the corresponding z-score and then use the z-table to find the probability.
First, let's calculate the z-score:
z = (X - μ) / σ
z = (85 - 100) / 10
z = -15 / 10
z = -1.5
Using the z-table or a calculator, we find that the probability of Z > -1.5 is approximately 0.9332.
Therefore, the probability that X > 85 is 0.9332 (rounded to four decimal places).
b. Probability that X < 80:
Similarly, we'll calculate the z-score for X = 80:
z = (X - μ) / σ
z = (80 - 100) / 10
z = -20 / 10
z = -2
Using the z-table or a calculator, we find that the probability of Z < -2 is approximately 0.0228.
Therefore, the probability that X < 80 is 0.0228 (rounded to four decimal places).
c. Probability that X < 90 or X > 130:
To calculate this probability, we'll find the individual probabilities of X < 90 and X > 130, and then subtract the probability of their intersection.
For X < 90:
z = (90 - 100) / 10
z = -10 / 10
z = -1
Using the z-table or a calculator, we find that the probability of Z < -1 is approximately 0.1587.
For X > 130:
z = (130 - 100) / 10
z = 30 / 10
z = 3
Using the z-table or a calculator, we find that the probability of Z > 3 is approximately 0.0013.
Since these events are mutually exclusive, we can add their probabilities:
P(X < 90 or X > 130) = P(X < 90) + P(X > 130)
P(X < 90 or X > 130) = 0.1587 + 0.0013
P(X < 90 or X > 130) = 0.1600
Therefore, the probability that X < 90 or X > 130 is 0.1600 (rounded to four decimal places).
d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?
To find the two X-values, we need to find the corresponding z-scores for the cumulative probabilities of 0.005 and 0.995. These probabilities correspond to the tails beyond the 99% range.
For the left tail:
z = invNorm(0.005)
z ≈ -2.576
For the right tail:
z = invNorm(0.995)
z ≈ 2.576
Now we can find the corresponding X-values:
X1 = μ + z1 * σ
X1 = 100 + (-2.576) * 10
X1 = 100 - 25.76
X1 ≈ 74.24
X2 = μ + z2 * σ
X2 = 100 + 2.576 * 10
X2 = 100 + 25.76
X2 ≈ 125.76
Therefore, 99% of the values are greater than 74.24 and less than 125.76 (rounded to two decimal places).
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15 EASY POINTS.............
Answers
Answer:
x³+7x²+14x+8
Step-by-step explanation:
distribute!
(x³+3x²+2x)+(4x²+12x+8)
add the similar values
x³+7x²+14x+8
Answer:
do math
Step-by-step explanation: