Answers
The solution is, the simplification of the equation is :
4x^2 - 4 = (2x -2 ) (2x+2)
Here, we have,
given that,
the expression is:
4x^2 - 4
now, we have to simplify this.
we know that ,
The a^2 - b^2 formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.
It is one of the algebraic identities.
It is used to factorize the binomials of squares.
The a^2 - b^2 formula is given as:
a^2 - b^2 = (a - b) (a + b).
so, we have,
4x^2 - 4
= (2x)^2 - 2^2
= (2x -2 ) (2x+2)
Hence, The solution is, the simplification of the equation is :
4x^2 - 4 = (2x -2 ) (2x+2)
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Related Questions
please help me yalll
Answers
Answer:
13
Step-by-step explanation:
210+50 is the total number of miles that can be driven. This adds up to 260. 260 divided by 20 is miles per gallon, which equals 13.
The entries in Table I are the probabilities that a random variable having the standard normal distribution will take on a value between 0 andz. They are given by the area of the gray region under the curve in the figure. TABLET NORMAL-CURVE AREAS 2 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.5 0.0000 0.0398 0.0793 0.1179 0.1554 0.1915 0.0080 0.0478 0.0871 0.1255 0.1628 0.1985 0.0120 0.0517 0.0910 0.1293 0.1664 0.2019 0.2357 0.2673 0.2967 0.3238 0.3485 0.0160 0.0557 0.0948 0.1331 0.1700 0.2054 0.2389 0.2704 0.2995 0.3264 0.3508 0.0199 0.0596 0.0987 0.1368 0.1736 0.2088 0.0239 0.0636 0.1026 0.1406 0.1772 0.2123 0.0279 0.0675 0.1064 0.1443 0.1808 0.2157 0.0319 0.0714 0.1103 0.1480 0.1844 0.2190 0.0359 0.0753 0.1141 0.1517 0.1879 0.2224 0.2549 0.2852 0.3133 0.3389 0.3621 0.2257 0.0040 0.0438 0.0832 0.1217 0.1591 0.1950 0.2291 0.2611 0.2910 0.3186 0.3438 0.3665 0.3869 0.4049 0.4207 0.4345 0.4463 0.4564 0.4648 0.4719 0.4778 0.6 0.7 0.8 0.9 1.0 0.2580 0.2881 0.3159 0.3413 0.2324 0.2642 0.2939 0.3212 0.3461 0.2422 0.2734 0.3023 0.3289 0.3531 0.2454 0.2764 0.3051 0.3315 0.3554 0.2517 0.2823 0.3106 0.3365 0.3599 0.2486 0.2794 0.3078 0.3340 0.3577 0.3790 0.3980 0.4147 0.4292 0.4418 1.1 1.2 1.3 1.4 1.5 0.3749 0.3944 0.4113 0.4265 0.4394 0.3770 0.3962 0.4131 0.4279 0.4406 0.3810 0.3997 0.4162 0.4306 0.4429 0.3643 0.3849 0.4032 0.4192 0.4332 0.4452 0.4554 0.4641 0.4713 0.4772 0.3686 0.3888 0.4066 0.4222 0.4357 0.4474 0.4573 0.4656 0.4725 0.4783 0.3708 0.3907 0.4082 0.4236 0.4370 0.4484 0.4582 0.4664 0.4732 0.4788 0.3729 0.3925 0.4099 0.4251 0.4382 0.4495 0.4591 0.4671 0.4738 0.4793 0.3830 0.4015 0.4177 0.4319 0.4441 0.4545 0.4633 0.4706 0.4767 0.4817 1.6 1.7 1.8 1.9 2.0 0.450S 0.4599 0.4678 0.4744 0.4798 0.4515 0.4608 0.4685 0.4750 0.4803 0.4525 0.4616 0.4692 0.4756 0.4808 0.4535 0.4625 0.4699 0.4761 0.4812 2.1 2.2 2.3 2.4 2.5 0.4826 0.4864 0.4896 0.4920 0.4940 0.4830 0.4868 0.4898 0.4922 0.4941 0.4834 0.4871 0.4901 0.4925 0.4943 0.4850 0.4884 0.4911 0.4932 0.4949 0.4854 0.4887 0.4913 0.4934 0.4951 0.4857 0.4890 0.4916 0.4936 0.4952 0.4821 0.4861 0.4893 0.4918 0.4938 0.4953 0.4965 0.4974 0.4981 0.4987 0.4838 0.4875 0.4904 0.4927 0.4945 0.4959 0.4969 0.4977 0.4984 0.4988 0.4842 0.4846 0.4878 0.4881 0.4906 0.4909 0.4929 0.4931 0.4946 0.4948 0.4960 0.4961 0.4970 0.4971 0.4978 0.4979 0.4984 0.4985 0.4989 0.4989 2.6 2.7 2.8 2.9 3.0 0.4955 0.4966 0.4975 0.4982 0.4987 0.4956 0.4967 0.4976 0.4982 0.4987 0.4957 0.4968 0.4977 0.4983 0.4988 0.4962 0.4972 0.4979 0.4985 0.4989 0.4963 0.4973 0.4980 0.4986 0.4990 0.4964 0.4974 0.4981 0.4986 0.4990 Also, for 3 - 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999. ^ The entries in Table II are values for which the area to their right under the 1 distribution with given degrees of freedom (the gray area in the figure) is equal toa. TABLE II VALUE OF d.f. Fo.050 os 0.005 d.. 63.657 9.925 1 2 3 4 6.314 2.920 2.353 2.132 2.015 12.706 4.303 3.182 2.776 2.571 0.010 31.821 6.965 4.541 3.747 3.365 1 2 3 4 5.841 4.604 4.032 S S 6 7 6 7 8 1.943 1.895 1.860 1.833 1.812 2.447 2.365 2.306 2.262 2.228 3.143 2.998 2.896 2.821 2.764 3.707 3.499 3.355 3.250 3.169 8 9 9 10 10 11 12 1.796 1.782 1.771 1.761 1.753 13 14 15 2.201 2.179 2.160 2.145 2.131 2.718 2.681 2.650 2.624 2.602 3.106 3.055 3.012 2.977 2.947 11 12 13 15 16 16 17 18 19 20 1.746 1.740 1.734 1.729 1.725 2.120 2.110 2.101 2.093 2.086 2.583 2.567 2.552 2.921 2.898 2.878 2.861 2.845 17 18 19 2.539 2.528 20 21 22 23 24 25 1.721 1.717 1.714 1.711 1.708 2.080 2.074 2.069 2.064 2.060 2.518 2.508 2.500 2.831 2.819 2.807 2.797 2.787 21 22 23 24 25 2.492 2.485 2.056 2.052 26 27 28 29 Inf. 1.706 1.703 1.701 1.699 1.645 2.479 2.473 2.467 2.462 2.326 2.779 2.771 2.763 2.048 26 27 28 29 Inf. 2.045 2.756 2.576 1.960 Question 2 (20 marks) A tutorial school has been running IELTS mock examination for many years. Below is the summary presented by the tutorial school related to the IELTS mock examination in one of the many online classes selected randomly in year 2022. IELTS score in mock examination Number of students <4 0 5 2 6 7 5 15 8 10 3 9 A report presented by this tutorial school 5 years ago indi that the population mean score of IELTS mock examination was 7.05 points and the population proportion of students got 7 points or above was 0.67. (a) Construct a 95% confidence interval estimate of population mean score a student get in the IELTS mock examination in 2022. (b) Test, at 1% level of significance, if the population proportion of students get 7 points or above in 2022 is higher than that in year 2017. (The report must include the (i) null hypothesis and alternative hypothesis, (ii) rejection region(s), (iii) calculation of test statistics, and (iv) conclusion.) (c) If the confidence interval estimate in part (a) is constructed at 99% instead of 95%, would the interval be (1) wider, (II) narrower, or (III) no change in width? (State your answer, no explanation is needed in part (C).)
Answers
From the table, the area between 0 and 2 under the standard normal distribution curve is 0.4772. Therefore, the probability that a random variable having the standard normal distribution will take on a value between 0 and 2 is 0.4772.
X squared minus 14 minus 4x
Answers
The factor form of the given expression is [tex]x^2 - 14 - 4x = (x - 4)(x - 14).[/tex]
To factor the expression x^2 - 14 - 4x, we can use the technique of grouping.
First, we can rearrange the terms as:
x^2 - 4x - 14
Next, we can factor out a common factor of x from the first two terms:
x(x - 4) - 14
Then, we can factor out a negative 1 from the last two terms:
x(x - 4) - 1(14)
Finally, we can write the expression as the product of two binomials:
(x - 4)(x - 14)
Therefore, the factored form of x^2 - 14 - 4x is (x - 4)(x - 14).
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Of the people who fished at Clearwater Park today, 72 had a fishing license, and 8 did not. Of the people who fished at Mountain View Park today, 63 had a license, and 27 did not. (No one fished at both parks.)
Answers
| | Fishing License | No Fishing License |
| ------------- | -------------- | ------------------ |
| Clearwater | 72 | 8 |
| Mountain View | 63 | 27 |
To find the total number of people who fished at both parks, we can add up the number of people with a fishing license at each park:
72 + 63 = 135
Therefore, a total of 135 people fished at both parks today.
-4/3, 1, -4/5, -2/3, -4/7
what is the explicit rule for this sequence
Answers
The explicit rule for the sequence -4/3, 1, -4/5, -2/3, -4/7 is -4(2 + n)
Finding the explicit rule for the sequenceFrom the question, we have the following parameters that can be used in our computation:
-4/3, 1, -4/5, -2/3, -4/7
In the above sequence, we can see that 1 is added to the denomiator of the previous term to get the new term
Take for instance
2nd = -4/(3 + 1) = -1
3rd = -4/(3 + 2) = -4/5
4th = -4/(3 + 3) = -4/6 = -2/3
4th = -4/(3 + 7) = -4/7
Hence, the explicit rule is -4(2 + n)
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Find the area and perimeter of the figure. (Hint: Don't forget your units!)
8cm
1
1
5cm
6cm
Answers
Answer:
Area of parallelogram:
8 × 5 = 40 square centimeters
Perimeter of parallelogram:
2(8 + 6) = 2 × 14 = 28 centimeters
18.What is the perimeter of a rhombus if the length of one side is 8cm?
Answers
The perimeter of a rhombus is the sum of the lengths of all four sides. Since all sides of this rhombus are 8cm, the perimeter is:
4 x 8cm = 32cm
Therefore, the perimeter of the rhombus is 32cm.
Probability Skill Check
DOOR Numbers
1
2
3
4
5
Coloured Blue, Red, Yellow and Green
What is the probability you will sit in a yellow seat? Give your answer as a fraction.
1/4
But what is the probability you will enter using an odd numbered door and sit in a green seat? Give your answer as a fraction.
Answers
The probability you will sit in a green seat is 1/4, since there is one green seat out of a total of four seats.
To find the probability of both events occurring, you can multiply the two probabilities:
3/5 x 1/4 = 3/20
So the probability you will enter using an odd numbered door and sit in a green seat is 3/20.
please help me with this
Answers
Answer: okay ill help
Step-by-step explanation:
find sin 75 without using a calculator
Answers
The value of sin 75 without using a calculator is 1/4(√2 +√6)
Finding sin 75 without using a calculatorFrom the question, we have the following parameters that can be used in our computation:
sin(75)
This can be expanded as
sin(75) = sin(45 + 30)
Using the sine rule, we have
sin(75) = sin(45)sin(30) + cos(45)cos(30)
Evaluate the trigonometry ratios
So, we have
sin(75) = √2/2 * 1/2 + √2/2 * √3/2
So, we have
sin(75) = √2/4 + √6/4
Evaluate the sum
sin(75) = 1/4(√2 +√6)
Hence, the value is sin(75) = 1/4(√2 +√6)
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Find the mean absoulute deviation for the following data 6,7,10,12,13,4,8,12
Answers
Answer:
2.75
Step-by-step explanation:
To find the mean absolute deviation for a set of data, we first need to find the mean (average) of the data set. Then, for each data point, we find the absolute value of the difference between the data point and the mean. Finally, we take the mean of those absolute differences.
Step 1: Find the mean
Mean = (6+7+10+12+13+4+8+12)/8 = 72/8 = 9
Step 2: Find the absolute differences
|6-9| = 3
|7-9| = 2
|10-9| = 1
|12-9| = 3
|13-9| = 4
|4-9| = 5
|8-9| = 1
|12-9| = 3
Step 3: Find the mean of the absolute differences
Mean absolute deviation = (3+2+1+3+4+5+1+3)/8
Mean absolute deviation = 22/8
Mean absolute deviation = 2.75
Therefore, the mean absolute deviation for the given data set is 2.75.
Ferrese
2. (errencer feld acceed
rest
As and ove rect
The x-coordinate of 4s recex is 45
The x-ceerdinate of is rectex is
The coordinate os recex 45
he rease othe reser at
Answers
The true statements are
Its x-intercepts are (0,0) and (11,0)The x-coordinate of its vertex is 5.5How to find the true statementsTo find the true statements about the graph that represents y = -2x(x - 11), we need to analyze the equation and its properties.
x-intercepts by setting y = 0 and solving for x:
form the equation we have y = -2x(x - 11)
0 = -2x(x - 11)
0 = x(x - 11)
x = 0
x = 11
The x-intercepts are at (0,0) and (11,0).
Now let's find the vertex of the parabola. The vertex is located at the x-coordinate x = -b / 2a,
y = -2x^2 + 22x
given that
a = -2,
b = 22
x coordinate of the vertex is found by
= -22 / (2 * -2)
= 22 / 4
= 5.5
so we can say that the true statement is: The x-coordinate of its vertex is 5.5
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Val's whole-house central air conditioner uses 4,000 watts when running. Val runs the AC 7 hours per summer day. Electricity costs (10 cents)/(1 kilowatt-hour). How much does Val's AC cost to run for a summer month of 30 days?
Answers
The electricity cost for the Val's AC to run for a summer month of 30 days is $84.
Given that,
Val's whole-house central air conditioner uses 4,000 watts when running.
Val runs the AC 7 hours per summer day.
Electricity costs (10 cents)/(1 kilowatt-hour).
Total electricity used for the whole house = 4000 watts = 4 kilowatts
Number of hours that the AC runs = 7 hours
Cost of electricity = (10 cents)/(1 kilowatt-hour).
Cost of electricity for 4 kilowatts for 1 hour = 10 × 4 = 40 cents
Cost of electricity for 4 kilowatts for 7 hours = 40 × 7 = 280 cents
= $2.80
Cost of electricity for a summer month of 30 days = $2.80 × 30
= $84
Hence the total cost for the electricity is $84.
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What does the song reveal about the goals of the Nazi Party?
Answers
Adolescents who loved jazz and were drawn to American, British culture in general, as well as conformity and discipline in the army, made up the swing youths in Nazi Germany.
Germany saw significant turmoil in politics in the late 1930s as a result of Hitler's ascension to power and the real-world consequences of his virulent anti-Semitism.
He described how in the Nazi era, there were groups of young people in Vienna who would get together in private, dancing to American bounce music, and express opposition to the brutal Nazi reality through their behavior and attire.
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The question is incomplete, Complete question probably will be:
What does the song Swing Heil reveal about the goals of the Nazi Party?
A virus takes 18 days to grow from 160 to 240. How many days will it take to
grow from 160 to 600? Round to the nearest whole number.
Answers
The virus will thus increase from 160 to 600 in around 10 days.
What is virus ?
A virus is a submicroscopic infectious agent that only reproduces inside of an organism's live cells.
We can resolve this issue using a proportion. Let x be the period of time needed for the virus to multiply from 160 to 600. Then: (240 - 160) / 18 = (600 - 160) / x
This equation may be written as
80/18 = 440/x.
Cross-multiplying:
80x = 18 * 440
80 divided by both sides yields x = 9.9
We obtain x = 10 by rounding to the next full value.
Therefore, The virus will thus increase from 160 to 600 in around 10 days.
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Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answers
As per the given percentage, the value of the loan 10 years after it starts is £4506.32.
We know the values of P and A for the first two years. So, we can use these values to find the value of r. Let's use the formula for the first year:
2645 = 2500(1 + r/1)¹ˣ¹
Simplifying the equation, we get:
1 + r = 2645/2500
1 + r = 1.058
r = 0.058 or 5.8%
Therefore, the interest rate per annum is 5.8% (to 1 decimal place).
Now, let's move on to finding the value of the loan after 10 years. We can use the same formula for compound interest, but we need to substitute the values of P, r, n, and t accordingly. Here's the formula:
A = P(1 + r/n)ⁿˣ
Where:
P = 2500
r = 0.058
n = 1 (as the interest is compounded annually)
x = 10
Substituting these values, we get:
A = 2500(1 + 0.058/1)¹ˣ¹⁰
A = 2500(1.058)¹⁰
A = 4506.32
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URGENT STATISTICS AND PROBABILITIES
Answers
Answer:
the expected point value is -1/5, so it is not advantageous to guess.
Step-by-step explanation:
1(1/5)+(-1/2)(4/5)
1/5-2/5
-1/5
The table below shows information about the thickness of each of the books on a shelf. Work out an estimate for the mean book thickness. Give your answer as a decimal. Thickness, x (mm) 0< x≤2 2< x≤4 4< x≤6 Frequency 4 9 7
Answers
Answer:
3.2mm
Step-by-step explanation:
Answer:
3.2mm
Step-by-step explanation:
A figure has a area of 25 units^2. what will the new area be after a dilation with a scale factor of 4 ?
Answers
The new area of the figure after the dilation with a scale factor of 4 will be 400 units²
We have,
When a figure is dilated by a scale factor of k, its area is multiplied by k².
So,
If the original area of the figure = 25 units²
Dilated by a scale factor = 4
The new area.
= (4²)(25 units²)
= 16(25 units²)
= 400 units²
Therefore,
The new area of the figure after the dilation with a scale factor of 4 will be 400 units².
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100 POINTS!!! PLS ANSWER ASAP
The number of toys owned by eight classmates is shown below:
4, 3, 4, 5, 6, 6, 8, 4
Part A: What is the mean of the data? Show your work. (4 points)
Part B: Use your answer from Part A to calculate the mean absolute deviation for the data. Show your work. (6 points)
Answers
Answer:
the answer for part A is. 5
the absolute deviation is. 1
Step-by-step explanation:
to find the answer for part A add all numbers and divide it by 8
4+3+4+5+6+6+8+5/840/85 is the answersFor part B
4-5= |-1|= 1
3-5= |-2|= 2
4-5= |-1| =1
5-5= |0| =0
6-5= |1 | =1
6-5= |1 | =1
8-5= |3| =3
5-5= |0| =0
Then add all the number and divided them by 8
1+2+1+0+1+1+3+0/89/89/8 is the answerMAY I GET BRAINLIEST
The large solid below is made from small cubes. Each has a side length of 1/5. Answer the questions below. Write your answers in simplest form. (c) What is the volume of the large solid?
Answers
The volume of the large solid is equal to 8/25 cm³.
How to calculate the volume of a cube?In Mathematics, the volume of a cube can be calculated by using the following formula:
V = m³
Where:
V represents the volume of a cube.m is the side lengths of a cube.By substituting the given points into the formula for the volume of a cube, we have the following;
Volume of cube, V = m³
Volume of cube, V = (1/5)³
Volume of cube, V = 1/125 cm³.
For the volume of the large solid, we have:
Volume of large solid = 5 × 2 × 4 × 1/125
Volume of large solid = 8/25 cm³.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
a doctor has 7 patients to visit how many different ways can she make her rounds if she visits each patient only once
Answers
There is only one way for the doctor to visit all seven patients exactly once.
A combination is a way of selecting items from a larger set, where the order of the items is not important. In this problem, we need to select seven patients out of a larger set of seven patients, so we can use the formula for the number of combinations of n items taken r at a time:
C(n,r) = n! / (r!(n-r)!)
where n is the total number of items, r is the number of items to be selected, and the exclamation mark represents the factorial function.
In this case, we need to find the number of combinations of 7 patients taken 7 at a time, which can be written as:
C(7,7) = 7! / (7!(7-7)!) = 7! / (7!0!) = 1
The order in which she visits the patients does not matter since each patient is visited only once.
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PLEASE HELP (WILL GIVE BRAINLIEST
Answers
Answer:
cm^3 can be used to represent volume.
diego is buying a pumpkin that weighs 12.8 pounds. pumpkins cost $0.60 per pound. how much will diego pay for his pumpkin
Answers
As pumpkins cost $0.60 per pound Diego will pay $7.68 for his pumpkin.
To find out how much Diego will pay for his pumpkin, we need to multiply the weight of the pumpkin by the cost per pound:
Cost = weight × cost per pound
In this case, the weight is 12.8 pounds and the cost per pound is $0.60:
Cost = 12.8 pounds × $0.60/pound
Simplifying the expression, we get:
Cost = $7.68
Therefore, Diego will pay $7.68 for his pumpkin.
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Pls help me understand this
Answers
The radius of the circle is 36 centimetres.
The circumference of the circle is 75.36 centimetres.
How to find radius and circumference of a circle?Let's find the radius of the circle with 20 degrees arc and length of 4π centimetres.
Length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleTherefore,
Length of an arc = 20 / 360 × 2 × π × r
4π = 40πr / 360
4π = 1 / 9 πr
cross multiply
πr = 36π
divide both sides by π
r = 36 centimetres
radius = 36 centimetres
b.
The equilateral triangle is inscribed in the circle. Therefore, the circumference of the circle can be found as follows:
The radius of the circle can be found using trigonometric ratios as follows:
The radius is an angle bisector. Hence,
sin 30 = opposite / hypotenuse
0.5 = 6 / r
cross multiply
r = 6 / 0.5
r = 12 centimetres
Lets' find the circumference,
circumference of the circle = 2πr
circumference of the circle = 2 × π × 12
circumference of the circle = 24 × 3.14
circumference of the circle = 75.36 cm
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Jonna is sewing a front cover for a circular pillow. The pillow has a diameter of 15 inches. To sew the front cover, she must cut the fabric two inches wider than the pillow all the way around. What is the minimum area, in square inches, of the piece of fabric she will use?
Answers
Answer:
Step-by-step explanation:
To determine the minimum area of the piece of fabric Jonna needs, we need to calculate the diameter of the circle after adding 2 inches to the radius.
The radius of the pillow is half its diameter, which is 15/2 = 7.5 inches.
When Jonna adds 2 inches to the radius, the new radius becomes 7.5 + 2 = 9.5 inches.
The diameter of the circle with the new radius is 2 x 9.5 = 19 inches.
Therefore, Jonna needs to cut a circular piece of fabric with a diameter of 19 inches.
To calculate the minimum area of the fabric, we need to use the formula for the area of a circle:
Area = π x (radius)^2
The radius is 9.5 inches, so:
Area = π x (9.5)^2
Area = π x 90.25
Area ≈ 283.77 square inches
Therefore, Jonna needs a piece of fabric with a minimum area of approximately 283.77 square inches.
What is the density of a billiard ball with a radius 1.5 inches and a mass of 250g?
Answers
Answer: The density of the billiard ball is 6.67 g/cm^3.
Step-by-step explanation:
A bag has 4 brown marbles and 12 yellow marbles. Half of the yellow marbles are made of glass. A marble is selected at random from the bag. What is the
probability that it is a yellow, glass marble?
Write your answer as a fraction in simplest form.
9
Answers
Answer: 3/8.
Step-by-step explanation: f 4 + 12 = 16, 12 / 2 = 6, 6 / 16 = 3 / 8
Which of the following table represents probability distribution
Answers
Answer:
b
Step-by-step explanation:
wo ships, the Queen Elizabeth and the Queen Mary, are parallel to the shore and 35 km apart. How far is each ship from a lighthouse if the Queen Elizabeth is at an angle of 68° and the Queen Mary is at an angle of 45° to the lighthouse
Answers
tan(68°) = x/d, where d is the distance from the lighthouse to the Queen Elizabeth.
tan(45°) = y/d, where d is the distance from the lighthouse to the Queen Mary.
To solve for x and y, we need to eliminate d. We can do this by solving the second equation for d and substituting into the first equation:
d = y/tan(45°)
tan(68°) = x/(y/tan(45°))
Simplifying this expression, we get:
x = y * tan(68°) / tan(45°)
Now we can substitute the given distance between the ships to solve for y:
y + y * tan(68°) / tan(45°) = 35
Solving for y, we get:
y = 35 / (1 + tan(68°) / tan(45°)) = 12.6 km
Now we can use the equation for x to find the distance from the lighthouse to the Queen Elizabeth:
x = y * tan(68°) / tan(45°) = 18.2 km
Therefore, the Queen Elizabeth is 18.2 km from the lighthouse, and the Queen Mary is 12.6 km from the lighthouse.