Answer:
See the explaination
Step-by-step explanation:
Total No. of rolling each side of the 12-sided die= 12 x 12= 144 outcomes
No. of outcomes equals 10 are: (1, 9), (9, 1), (2, 8), (8, 2), (3, 7), (7, 3), (4, 6), (6, 4), (5, 5) = 9 outcomes.
No. of outcomes of rolling a No. >10: 144–9 = 135 outcomes.
Probability, Pr, of rolling a No. >10= 135/144
Pr (No. >10) = 0.9375 (to 4 dec. pl.)
Answer: I think you’re missing something on your question. But I think what your asking is how many numbers greater than 10. It should 2/12 or
Step-by-step explanation:
Mr.Estevez got a new post mounted mail box. He dug out the old one and left a square hole and only measured one side. Mr.Estevez measured a side of 9.75cm's. What is the square area of dirt Mr. Estevez needs to fill up the hole for his new mailbox. (Round to the nearest tenth)* 0 95.1cm2 0 95.06cm2 0 95.1cm O 95.06cm
Answer:
[tex]95.1\ cm^2[/tex]
Step-by-step explanation:
we know that
A square is a quadrilateral that has four equal sides and four equal interior right angles.
The area of the square is given by the formula
[tex]A=b^2[/tex]
where
b is the length side of the square
In this problem we have
[tex]b=9.75\ cm[/tex]
substitute in the formula
[tex]A=(9.75)^2=95.06\ cm^2[/tex]
Round to the nearest tenth
[tex]A=95.1\ cm^2[/tex]
Answer:
95.06cm
Step-by-step explanation:
Hope this helps
The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are semi-circles. What is the volume, in cubic units, of the solid?
Answer:
Option b) [tex]18\pi[/tex] is correct∴ the volume of the solid is [tex]A(x)=18\pi[/tex] cubic unitsStep-by-step explanation:
Given that the base of a solid is the circle [tex]x^2 + y^2 = 9[/tex] and Cross sections of the solid perpendicular to the x-axis are semi-circles.
To find the the volume of the solid in cubic units:We know that the cross sections are semicircles with the diameter in the given circle [tex]x^2 + y^2 = 9[/tex]
That is we have to find the formula for the area of any semicircle perpendicular to x-axis, and integrate it from -3 to 3.
Now the area of a semicircle is
[tex]A=\frac{\pi r^2}{2}[/tex] cubic units
Let r = y and [tex]y^2=9-x^2[/tex]
Then area of the semicircle crossing the x-axis at x is given by
[tex]A(x)=\frac{1}{2}\pi y^2[/tex] cubic units
[tex]=\frac{1}{2}\pi(9-x^2)[/tex]
Now we can find the definite integral of A(x) from x = -3 to x = 3.
Since A(x) is an EVEN function then the definite integral of A(x) from x = -3 to x = 3 is the same as twice the integral of A(x) from x = 0 to x = 3.
We have that
[tex]A(x)=2(\int_0^3 \frac{1}{2}\pi(9-x^2))dx[/tex]
[tex]=2(\frac{\pi}{2}[9x-\frac{x^3}{3}]_0^3)[/tex]
[tex]=\pi[9(3)-\frac{3^3}{3}-9(0)-(-\frac{0^3}{3})][/tex]
[tex]=\pi[27-\frac{27}{3}][/tex]
[tex]=\pi[27-9][/tex]
[tex]=\pi[18][/tex]
[tex]=18\pi[/tex]
∴ option b) [tex]18\pi[/tex] is correct∴ the volume of the solid is [tex]A(x)=18\pi[/tex] cubic unitsThe volume of the solid is 18π cubic units.
The base of the solid is defined by the circle’s equation x² + y² = 9, indicating that the radius of the circle is 3 units. The cross-sections perpendicular to the x-axis are semi-circles.
To find the volume, we need to integrate the area of these semi-circular cross-sections. For a slice at a given x-coordinate, the diameter of the semi-circle is the length of the chord of the circle at that x-coordinate, which is given by 2√(9 - x²). The radius of the semi-circle is then √(9 - x²), and the area of the semi-circle is (1/2)πr².
The area of each semi-circular slice is: A(x) = (1/2)π(√(9 - x²))² = (1/2)π(9 - x²).
The volume V of the solid is obtained by integrating this area from x = -3 to x = 3:
V = ∫[from x = -3 to x = 3] (1/2)π(9 - x²) dx
This simplifies to:
V = (π/2) ∫[from x = -3 to x = 3] (9 - x²) dx
We solve the integral:
V = (π/2) [9x - (x³ / 3)] (from x = -3 to x = 3)
Evaluating this, we get:
V = (π/2) [(9×3 - (3³ / 3)) - (9×(-3) - ((-3)³ / 3))]
V = (π/2) [(27 - 9) - (-27 + 9)]
V = (π/2) [18 + 18]
V = (π/2) 36
V = 18π
Thus, the volume of the solid is 18π cubic units.
Coll
4/15 version of 4/7 version of M4T2 Test Review
Created by Meena Frazier
Q1: What is the distance between (2, 3) and (-2, 7)? Round to the nearest tenth, if necessary.
Answer:
The answer to your question is 5.7
Step-by-step explanation:
Data
Point A = (2, 3)
Point B = (-2, 7)
Process
To find the distance between points A and B use the formula of the distance between two points, substitute and simplify.
Formula
dAB = [tex]\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2}}[/tex]
-Identify wich is the value of x1, y1, x2, y2
x1 = 2 y1 = 3 x2 = -2 y2 = 7
-Substittion
dAB = [tex]\sqrt{(-2 - 2)^{2} + (7 - 3)^{2}}[/tex]
-Simplification
dAB = [tex]\sqrt{(-4)^{2} + (4)^{2}}[/tex]
dAB = [tex]\sqrt{16 + 16}[/tex]
dAB = [tex]\sqrt{32}[/tex]
-Result
dAB = 5.65 ≈ 5.7
Which function shows a fabric with a price of $1.25 per square yard?
Answer:
x(1.25)
Step-by-step explanation:
x is the yards.
so for example if you need 2 yards of fabric replace x with 2.
Answer:
x=1.25
Step-by-step explanation:
edgu
Given triangle EFG shown below, state the value of the cosine of angle G the hypotenuse which is also side EG = 53 side EF = 45 side GF = 28 F is a right triangle
Answer:
[tex]cos(G)=\frac{28}{53}[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
In the right triangle EFG
[tex]cos(G)=\frac{GF}{EG}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(G)=\frac{28}{53}[/tex]
Suppose that $2000 is loaned at a rate of 11%, compounded semiannually. Assuming that no payments are made, find the amount owed after 5 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
The final value owed will be $3416.29.
Step-by-step explanation:
Since this is a compound interest problem we should use the apropriate formula given bellow:
M = C*(1 + r/n)^(n*t)
Where M is the final amount, C is the initial amount, r is the interest rate, t is the total time and n is the rate at which it is compounded. Since it's semiannually the value of n is 2 and we can use the formula to find the desired value.
M = 2000*(1 + 0.11/2)^(2*5)
M = 2000*(2/2 + 0.11/2)^(10)
M = 2000*(2.11/2)^(10)
M = 3416.29
The final value owed will be $3416.29.
A truck that can carry no more than 6600 lbs is being used to transport refrigerators and upright pianos. each refrigerator weighs 300 lbs and each piano weighs 425 lbs. what is an equation that shows how many refrigerators and how many pianos the truck could carry. will 10 refrigerators and 8 pianos overload the truck?
Answer:
(a). 300r + 425p ≤ 6,600
(b). No, it’s not considered overweight
Step-by-step explanation:
In this question, we are to write an equation that shows the number of refrigerators and pianos the truck could carry.
Let the number of refrigerators be r and the number of pianos be p
By using their individual weights, the equation is as follows;
300r + 425p ≤ 6,600
To the second question, we want to consider if 10 refrigerators and 8 pianos are overload.
To get this, we simply multiply the number of each by their individual weights;
That would be;
300(10) + 425(8) = 3000 + 3,400 = 6,400 lbs
This is not considered overweight as it is less than 6,600 lbs
In a race that consisted of three parts the cycling part was 12 1/2 miles long the running part of the race was won for the distance of the cycling parking asking part of the race was won half the distance of the running part what was the entire distance in miles of the raie
Complete question is;
In a race that consisted of three parts, the cycling part was 12 1/2 miles long. The running part of the race was 1/4 the distance of the cycling part. The kayaking part of the race was 1/2 the distance of the running part. What was the entire distance, in miles of the race?
Answer:
Total distance of race = 17.1875 miles
Step-by-step explanation:
The 3 parts of the race are; cycling, running and kayaking.
The cycling distance was; 12½ miles
We are told that the running part was ¼ of the cycling distance. Thus;
Running distance = ¼ x 12½ = ¼ x 25/2 = 25/8 miles
Lastly, we are told that the kayaking part was ½ the distance of the running part. Thus;
Kayaking distance = ½ x 25/8 = 25/16
Thus,total distance of race = cycling distance + running distance + kayaking distance = 12½ + 25/8 + 25/16 = 17.1875 miles
The current cost of gourmet coffee Is $14 per pound At the corner market the cost has increased 10% Per year over the past few years What did the coffee cost 2 years before ?
Answer:
$11.57
Step-by-step explanation:
Let's call the price of the coffee two years ago by X.
The price increased 10% per year (that is, the price is multiplied by 1+0.1=1.1) over two years, so the current price is:
X * 1.10 * 1.10 = X * 1.21
If the current price is $14, we have that:
X * 1.21 = 14
X = 14/1.21 = 11.57
The price of the coffee two years ago was $11.57
NEED HELP
8x + √1 - √9y - √9x^2
5x + 3√y + 1
5x - 3√y - 1
5x - 3√y + 1
Answer:
Last one: 5x - 3√y + 1
Step-by-step explanation:
8x + √1 - √9y - √9x^2
8x + 1 - 3√y - 3x
5x + 1 - 3√y
5x - 3√y + 1
Answer:Answer:
Last One: 5x - 3√y + 1
Step-by-step explanation:
8x + √1 - √9y - √9x^2
8x + 1 - 3√y - 3x
5x + 1 - 3√y
5x - 3√y + 1
Step-by-step explanation:
You are planning to use PERT for planning of your project. A task has pessimistic estimate of 24 days, most likely estimate of 15 days and optimistic estimate of 12 days. What is the mean using the PERT technique?
a.18 days
b.25.5 days
c.15 days
d.16 days
Answer: d.16 days
Step-by-step explanation:
Hi, using PERT technique we can calculate the mean by applying the next formula:
Mean = (a + 4m + b)/6
Where:
a = optimistic time
m = most likely time
b = pessimistic time
Replacing with the values given:
Mean = (12 +4 (15) + 24)/6
Solving
m = (12+ 60+24)/6
m= 96/6
m = 16 days
Feel free to ask for more if needed or if you did not understand something.
Scientists can measure the depths of craters on the moon by looking at photos of shadows. The length of the shadow cast by the edge of a crater is 500 meters. The angle of elevation of the rays of the Sun is 55∘. Estimate the depth d of the crater to the nearest tenth.
Answer:714.1
Step-by-step explanation:
500 times tan(55)
We can use the tangent function from trigonometry to estimate the depth of the crater. The depth is approximately 714.1 meters when the length of the shadow is 500 meters and the angle of sun elevation is 55 degrees.
Explanation:To solve this problem, we can use trigonometry, specifically the tangent function. The tangent function of an angle in a right triangle is equal to the ratio of the opposite side over the adjacent side. Here, the shadow length of the moon's crater functions as the adjacent side, and the depth of crater is the side opposite to the angle.
So tangent(55°) = depth / 500 meters.
To find the depth, rearrange the equation to multiply both sides by 500: depth = 500 * tangent(55°).
Using a calculator, you'll find that the tangent of 55° is approximately 1.4281. So then your final depth equation would look like: depth = 500 meters * 1.4281. By doing this calculation, we find depth ≈ 714.05 meters, and rounding this to the nearest tenth, we have 714.1 meters. So the estimated depth of the crater is 714.1 meters.
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How many faces dose a triangular prisim have?
Answer:
the answer is 5
Step-by-step explanation:
YW
Answer:
There are 5 faces in a triangular prism
I hope this help. If I'm wrong/made any mistakes please let me know so that I can learn from it!
(a)Nicole has a box of candies and will randomly choose one piece. The odds against choosing a lemon-flavored piece are . What is the probability of choosing a lemon-flavored piece?
Since the odds against choosing the lemon-flavored piece wasn't included, let us now assume that it is 2/5
Answer:
The Probability of choosing a lemon-flavored piece is 5/7
Step-by-step explanation:
Please kindly see the attached files for explanation
The coastline of Canada stretches about 202 080 km. The British Columbia portion of the coastline is about 2/15 of the total coastline of Canada. How long is the coastline of British Columbia?
Given Information:
Coastline of Canada = 202080 km
Coastline of British Columbia = 2/15 of Coastline of Canada
Required Information:
How long is the coastline of British Columbia = ?
Answer:
Coastline of British Columbia is 26944 km long
Step-by-step explanation:
We are given the length of Coastline of Canada that is 202080 km
We also know that Coastline of British Columbia is 2/15 of the Coastline of Canada.
So,
Coastline of British Columbia = (2/15)*202080
Coastline of British Columbia = 26944 km
Therefore, the Coastline of British Columbia is about 26944 km.
Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be 27 .
Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine.
25,30,50,50,50,50,56,n,250
What is the value of n that will make the IQR of the data set equal to 27?
N equals 78
The equation: (56+n)/2 - 40=27
Add 40 to 27=67
Multiply everything by 2 leaving you with 56+n=134
Subtract 56 from 134
Leaves you with n=78
If you plug it in you would get 67-40, which equals 27
3x ^ 3 - x ^ 2 Determine if the expression is polynomial or not . If it is a polynomial , state the type and degree of the polynomimal . The given expression a polynomial
The expression
[tex]3x^{3} -x^{2}[/tex]is a polynomial. Its type is cubic and the degree is 3.
Explanation:The given mathematical expression
[tex]3x^{3} -x^{2}[/tex]is a polynomial. A polynomial is an expression that is made up of variables and coefficients, using only the operations of addition, subtraction, and multiplication and non-negative integer exponents. The type of this polynomial is cubic, because the highest power of the variable (the degree) is 3. In this case, the highest degree is the highest exponent of the variable 'x', which is 3. Hence the given polynomial is cubic, with degree of 3.
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Find the solution by elimination method.
Please Help.
Answer:
I'm newbie here
Step-by-step explanation:
Elimination Method.
4x + 6/y = 15 → step 1
6x - 8/y = 14 → step 2
so,
4x + 6/y = 15 |×6|
6x - 8/y = 14 |×4|
24x + 6/y(6) = 90
24x - 8/y(4) = 56
24x + 36/y = 90
24x - 32/y = 56
____________ _
68/y = 34
68 = 34y
34y = 68
y = 2
subsitution y = 2 to..
4x + 6/y = 15
4x + 6/2 = 15
4x + 3 = 15
4x = 12
x = 3
So, for x is 3, and for y is 2
Answer:
x = 3, y = 2
Step-by-step explanation:
Multiply equation 1 by -6
-24x - 36/y = -90
Multiply equation 2 by 4
24x - 32/y = 56
Add the two equations:
-36/y - 32/y = -34
-68/y = -34
y = -68/-34
y = 2
4x + 6/2 = 15
4x = 15 - 3
4x = 12
x = 3
What is the slope of the line that passes through the points (1, 2) and (-2, -13)?
Answer:
5
Step-by-step explanation:
To find the slope given two points, we use the formula
m= (y2-y1)/(x2-x1)
= (-13-2)/(-2 -1)
= -15/-3
=5
Answer:
The slope is 5
Step-by-step explanation:
Δ means the change in
slope = m = Δy/Δx = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{2-(-13)}{1-(-2)}[/tex] = 15/3 = 5/1 = 5
Slope = 5
12.6 is what percent of 42?
If you were to flip a coin 140 times, how many times would you expect the coin to land on tails?
Answer: 70 times
Step-by-step explanation:
If you were to flip a coin 140 times you would expect it to land on tails 70 since 140 divided by 2 is 70 although coins are normally not evenly weighed meaning that it most likely not going to land evenly on both sides.
what is the percent change of 10 feet to 6 feet
Answer:It would be a decrease of 40 percent
Step-by-step explanation:You go from 10/10 to 6/10 meaning you decrease by 4/10 and 4/10 is the same as 40/100 and anything over 100 is its percent value so you would be going down by 40%
Answer:
40 % decrease or -40%.
Step-by-step explanation:
The decrease is 10 - 6 = 4 feet.
% decrease = (4/10) * 100
= 0.4 * 100
= 40 % decrease.
What is the result of adding 17 to its opposite
The answer is zero (0), when you add any number to it's opposite you always get zero
4) A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is walking away from the pole at a rate of 2 ft/sec. a. At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole? b. At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole?
Final answer:
The rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec. The rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.
Explanation:
To solve for the rates at which the tip of the shadow is moving away from the pole and from the person, we can use similar triangles and related rates. Let's solve each part step by step:
a. Rate the tip of the shadow is moving away from the pole:
We have a right triangle formed by the pole, the person, and the tip of the shadow. Let x be the distance between the person and the tip of the shadow.
Since the person is moving away from the pole at a rate of 2 ft/sec, dx/dt = 2 ft/sec.
Using the similar triangles, we have:
(12 ft + 5.5 ft) / x = 12 ft / (x + 25 ft)
Simplifying the equation gives:
17.5x + 437.5 = 12x + 300
5.5x = 137.5
x = 25 ft
Now, let's differentiate both sides of the equation with respect to time t:
17.5 (dx/dt) = 12 (dx/dt) + 0
17.5 (dx/dt) - 12 (dx/dt) = 0
5.5 (dx/dt) = 0
dx/dt = 0 ft/sec
So, the rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec.
b. Rate the tip of the shadow is moving away from the person:
Using the similar triangles, we have:
(12 ft + 5.5 ft) / x = 5.5 ft / 25 ft
Simplifying the equation gives:
17.5x = 137.5
x = 7.857 ft
Now, let's differentiate both sides of the equation with respect to time t:
17.5 (dx/dt) = 5.5 (dx/dt) + d(7.857)/dt
12 (dx/dt) = d(7.857)/dt
dx/dt = (d(7.857)/dt) / 12
dx/dt = (0 ft/sec) / 12
So, the rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.
Sam and Janet each have a whole number of dollars, and $\frac13$ of Sam's money equals $\frac12$ of Janet's money. Together, they have more than $\$10$. What is the least number of dollars they could have combined?
Answer:
$15
Step-by-step explanation:
Let Sam's Money =s
Let Janet's Money =j
[tex]$\frac13$[/tex] of Sam's money equals [tex]$\frac12$[/tex] of Janet's money.
Let n be the number of dollars held by Sam and Jane respectively
Therefore: [tex]$n=\frac13s=\frac12j$[/tex]
s=3n
j=2n
s+j=3n+2n=5n
Together, they have more than $10
Therefore:
5n>10
n>2
The least sum they could have is at n=3
At n=3
s+j=5n=5X3=$15
The least number of dollars they could have combined is $15.
Express in the form 1 : n 6 : 24
Answer: n=4
Step-by-step explanation: 1:4 = 6:24
Martin has a shoe box with the dimensions 4 inches, by 6 inches, by 10 inches. He wants to determine if a relay baton inches will fit in the box. What is the longest length that the relay baton can be and still fit in the box? (Round to the nearest tenth if needed.) Your answer: 10 inches 12.3 inches 10.8 inches 7.2 inches
Answer:
10 inches.
Step-by-step explanation:
First we need to find what is the bigger dimension of the box, because the relay baton will occupy the box, and the larger dimension of the relay baton (that is, it's length) need to be less or equal than the larger dimension of the box.
The dimensions of the box are: 4 inches, 6 inches and 10 inches.
The larger dimension of the box is 10 inches. So, If we want the relay baton to fit in the box, the maximum length it can have is 10 inches.
Flaky pastry can be made using flour and fat in the ratio 4 : 3. Jake makes some flaky pastry using 90 grams of fat. What weight of flour does he use?
Answer:
He use 120 grams of flour.
Step-by-step explanation:
Given:
Flaky pastry can be made using flour and fat in the ratio 4 : 3. Jake makes some flaky pastry using 90 grams of fat.
Now, to find the weight of flour he use in making flaky pastry.
Let the weight of flour be [tex]x.[/tex]
Weight of fat = 90 grams.
The ratio of flour and fat used in making flaky pastry is 4 : 3.
As, 4 is equivalent to 3.
Thus, [tex]x[/tex] is equivalent to 90.
Now, to solve using cross multiplication method:
[tex]\frac{4}{3} =\frac{x}{90} \\\\By\ cross\ multiplying\ we\ get:\\\\360=3x\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\120=x\\\\x=120\ grams.[/tex]
Therefore, he use 120 grams of flour.
x² - 12x + 27? what is the factored form of this polynomial
Answer:
( x - 9 )( x - 3 )
Step-by-step explanation:
plz give brainliest
Write 0.06 as a fraction in
simplest form.
Answer:
[tex]\frac{3}{50}[/tex]
Step-by-step explanation:
Answer: 6/10
Step-by-step explanation:
the 6 is in the tenth place which means it is by ten