Answers
The value of side x in the triangle is 18.1.
What is sine rule?In trigonometry, sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
To find the length of side x in the triangle, we use sine rule formula below.
Formula:
SinA/a = SinB/b..................... Equation 1From the diagram in the question,
Given:
A = 53°a = xB = 180-(95+53) = 32°b = 12Substitute these values into equation 1
sin53°/x = sin32°/12Make x the subject of the equation
x = 12sin53°/sin32°x = 18.1Hence, the value of x is 18.1
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Related Questions
Evaluate 1/2x^4 – 3/4x² for x = 2.
Answers
Answer:
\(-\frac{5}{32}\)
Step-by-step explanation:
\(\frac{1}{2(2)^4}-\frac{3}{4(2)^2} \\\frac{1}{32} - \frac{3}{16} = -\frac{5}{32}\)
It is a well-defined group of objects called elements that share common characteristics.
Answers
The term "element" refers to a well-defined group of objects or substances that share common characteristics.
In the context of chemistry, elements are the fundamental building blocks of matter, consisting of atoms that possess a specific number of protons in their nucleus. Each element is unique, with distinct physical and chemical properties that distinguish it from other elements.
The periodic table of elements is a widely recognized tool for organizing elements based on their atomic structure and properties. The periodic table displays the elements in order of increasing atomic number, with elements that share similar properties arranged in the same vertical column, or group.
The properties of elements can be studied and manipulated in various ways, leading to their use in a wide range of applications, from medicine to electronics to energy production. By understanding the unique characteristics of each element, scientists can better understand the natural world and develop new technologies that benefit society.
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Find parametric equations that describe the intersection of the cone z=x^2+y^2 and the plane =2z
Answers
Answer:
hhrhrthrtht
Step-by-step explanation:
Look at this set of 5 numbers:
1 2 2 2 8
By how much would the mean increase if the number 9 were added to the set?
Answers
adding 9 would make the mean 4 (24/6)
therefore the mean would increase by 1
pooled variance =a. SS1 + SS2 / df1 + df2b. SS1 + SS2 / n1 + n2
Answers
The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.
The formula for pooled variance is:
pooled variance = (SS₁+ SS₂) / (df₁ + df₂)
where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.
Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in
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Amy is 1 year older than Ben. The sum of their ages is greater than 33 and less than 45 Find all possible ages of Ben
Answers
Answer:
17, 18, 19, 20, 21
Step-by-step explanation:
anyone help me asap no bots and no being rude try to answer them (:
Answers
Step-by-step explanation:
A: (1½hours×60min)+(¾×60)+45min
B: (2¼×60)+45min+(½×60)
subtract the answer of A from the answer of B to find how much more time she worked on it the second week.
PLEASE HELP I WILL GIVE 100 POINTS!
stanley's friend knitted him a wool blanket. the blanket is 84 inches long and 60 inches wide. what is the total area of the blanket?
Answers
Answer:
5040 inches long
Step-by-step explanation:
how to solve the area for something you do the length times the width. so 84 times 60 is 5040.
Answer:
The answer to your problem is, 5040
Step-by-step explanation:
We can do this formula:
L x W = A
By using this formula we can find the answer.
Lets substitute some of the letters.
L = 84
W = 60
A = ? ( We are trying to find that )
Lets do the problem:
84 x 60 = ?
? = 5040. Which is our answer
Thus the answer to your problem is, 5040
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Philippa threw some darts. Her minimum score was 5 and
her maximum score was 53. What was the range of her
scores?
Min = 5
Max = 53
Range = ?
Answers
Dr.Osborne has scheduled Anita Blanchette for a spirometry test and wants you to telephone her the day before the test to prepare her so that optimal results are obtained.
1.) What information do you give Anita before her spirometry so that the best test results can be obtained?
2.) How would you explain the rationale for the performance of this procedure?
Answers
To ensure the best test results, Anita should be provided with the following information before her spirometry:
1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.
2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.
3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.
4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.
The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.
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Samarium-146 has a half-life of 103.5 million years. after 1.035 billion years, how much samarium-146 will remain from a 205-g sample?
Answers
Answer: 0.200 g
Given: Half life of Sm-146 = t1/2 = 103.5 million years
Time period, t = 1.035 billion years = 1035 million years
The original mass of the sample, [A]₀ = 205 g
To determine:
Amount of sample after t = 1035 million years
Explanation:
The rate of radioactive decay is given as:
Answer:
A: 0.200 g.
Step-by-step explanation:
Which expression represents the same solution as (4) (negative 3 and StartFraction 1 over 8 EndFraction? (4) (negative 3) + (4) (StartFraction 1 over 8 EndFraction) (4) (negative 3) + (4) (StartFraction negative 1 over 8 EndFraction) (4 + negative 3) times (4 + StartFraction 1 over 8 EndFraction) (4 + negative 3) times (4 + StartFraction negative 1 over 8 EndFraction)
Answers
Answer:
Option B.
Step-by-step explanation:
The given expression is
\((4)(-3\dfrac{1}{8})\)
We need an expression Which represents the same solution as the given expression.
It can be written as
\((4)[-(3+\dfrac{1}{8})]\)
\((4)[-3-\dfrac{1}{8}]\)
\((4)(-3)+(4)(-\dfrac{1}{8})\)
Since \((4)(-3)+(4)(-\dfrac{1}{8})\) is equivalent to given equation, therefore this equation represents the same solution as the given expression.
Hence, option B is correct.
Answer:
B
Step-by-step explanation:
Six standard 6-sided dice are rolled, and the resulting numbers are multiplied together. What is the probability that the product is divisible by 125?
Answers
Answer:
1453/23328
Step-by-step explanation:
Since we are going to have at least three 5's to obtain a number divisible by 125, the number of ways we can combine exactly three 5's is ⁶C₃. The number of ways we can combine the remaining dice without containing a five is 5³, since there are 3 remaining dice. So, for exactly three 5's , we have ⁶C₃ × 5³. Similarly, for exactly four 5's, we have ⁶C₄ × 5² (5² since there are two dice left). Also, for exactly five 5's, we have ⁶C₅ × 5¹ (5¹ since there are one die left). Finally, for exactly six 5's, we have ⁶C₆ × 5⁰(5⁰ since there are no dice left without a five).
So, for at least three 5's, we have ⁶C₃ × 5³ + ⁶C₄ × 5² + ⁶C₅ × 5¹ + ⁶C₆ × 5⁰
= 20 × 125 + 15 × 25 + 6 × 5 + 1 × 1
= 2500 + 375 + 30 + 1
= 2906 ways
The total number of ways of combining the six dice is 6⁶
So, the probability of obtaining a product divisible by 6 is thus P = 2906/6⁶ = 2906/46656
= 1453/23328
Using the binomial distribution, it is found that there is a 0.0536 = 5.36% probability that the product is divisible by 125.
The product will be divisible by 125 in two outcomes:
3 of the dices result in 5, as \(5^3 = 125\)6 of the dices result in 5, as \(5^6 = 5^3 \times 5^3\)For each dice, there are only two possible outcomes, either the result is 5, or it is not. The results of the dices are independent, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
Six dices are rolled, hence \(n = 6\).Each number is equally as likely, hence the probability of a 5 being rolled, that is, a success, is \(p = \frac{1}{6} = 0.1667\).The probability that the product is divisible by 125 is:
\(p = P(X = 3) + P(X = 6)\)
Hence:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 3) = C_{6,3}.(0.1667)^{3}.(0.8333)^{3} = 0.0536\)
\(P(X = 6) = C_{6,6}.(0.1667)^{6}.(0.8333)^{0} \approx 0\)
Then:
\(p = P(X = 3) + P(X = 6) = 0.0536 + 0 = 0.0536\)
0.0536 = 5.36% probability that the product is divisible by 125.
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what else would need to be congruent to show that Δ ABC ≅ Δ DEF by SAS ?
A. AC ≅ DF
B. ∠ A ≅ ∠ D
C. ∠ C ≅ ∠ F
D. BC ≅EF
Answers
Answer:
A is the answer because it is right
For each expression, write an equivalent expression that uses only addition. 4x−7y−5z+6
Answers
Answer:
Step-by-step explanation:
x + x + x + x - y - y - y - y - y - y - y - z - z - z - z - z + 1 + 1 + 1 + 1 + 1 + 1
There are 18 boys and 12 girls in a math class . What is the ratio of girls to total students
Answers
12:30
Answer:
The ratio of girls to total students is 12:30, which can be simplified to 2:5.
Step-by-step explanation:
You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.
Find the product of 32 and 46. Now reverse the digits and find the product of 23 and 64. The products are the same!
Does this happen with any pair of two-digit numbers? Find two other pairs of two-digit numbers that have this property.
Is there a way to tell (without doing the arithmetic) if a given pair of two-digit numbers will have this property?
Answers
Let's calculate the products and check if they indeed have the same value:
Product of 32 and 46:
32 * 46 = 1,472
Reverse the digits of 23 and 64:
23 * 64 = 1,472
As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.
To find two other pairs of two-digit numbers that have this property, we can explore a few examples:
Product of 13 and 62:
13 * 62 = 806
Reversed digits: 31 * 26 = 806
Product of 17 and 83:
17 * 83 = 1,411
Reversed digits: 71 * 38 = 1,411
As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.
For example, let's consider the pair 25 and 79:
A = 2, B = 5, C = 7, D = 9
The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.
Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.
suppose that the annual rainfall in ferndale, california, is known to be normally distributed, with a mean of 35.5 inches and a standard deviation of 2.5 inches. what is the probability that the rainfall in a given year will exceed 31.5 inches in ferndale? (you may need to use the standard normal distribution table. round your answer to three decimal places.)
Answers
The probability that the rainfall in a given year will exceed 31.5 inches in Ferndale is 0.9452.
How to calculate the value?It is vital to know that the requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.
In this case, the mean is 35.5 inches and a standard deviation of 2.5 inches
We want to find P(x > 31.5)
Z = X - U/ SD
where
SD = standard deviation
U = mean
Z = (31.5 - 35.5( / 2.5
Z = -1.6
P(x > 31.5) = P(z > -1.6)
= 0.9452
The probability is 0.9452.
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A loan of 1400 is to be repaid with quarterly payments at the end of each quarter for 3 years. If the rate of interest charged on the loan is 8% convertible semiannually, find the amount of each quarterly payment. (nearest cent)
Answers
The amount of each quarterly payment is approximately $146.73.
To calculate the amount of each quarterly payment, we can use the formula for the quarterly payment of an annuity
P = \(A * (1 - (1 + r)^(-n)) / r,\)
where P is the quarterly payment, A is the loan amount, r is the quarterly interest rate, and n is the number of quarters.
First, we need to convert the semiannual interest rate of 8% to a quarterly interest rate. Since there are two quarters in each semiannual period, the quarterly interest rate would be 8% divided by 2, which is 4%.
Next, we substitute the values into the formula
P = \(1400 * (1 - (1 + 0.04)^(-12)) / 0.04\),
= \(1400 * (1 - (1.04)^(-12)) / 0.04,\)
≈\(146.73.\)
Therefore, the amount of each quarterly payment is approximately $146.73.
An annuity is a series of regular payments made over a specific period of time. In this case, the loan of $1400 is to be repaid with quarterly payments. The interest on the loan is charged at a rate of 8% convertible semiannually, which means the interest is compounded twice a year. To determine the amount of each quarterly payment, we use the annuity formula and the quarterly interest rate, which is obtained by dividing the semiannual interest rate by 2. By substituting the values into the formula, we find that each quarterly payment amounts to approximately $146.73.
An annuity payment consists of both principal and interest components. In the beginning, a larger portion of each payment goes towards paying off the interest, while the remaining portion is applied towards the principal. As the loan is gradually repaid, the interest portion decreases, and the principal portion increases. The formula allows us to determine the fixed amount required for each payment, ensuring that the loan is fully repaid within the specified period.
It's important to note that the calculated amount of $146.73 is an approximation, and the actual payment may differ slightly due to rounding or any additional fees associated with the loan.
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ill give brainliest to CORRECT ANSWER and 50 points! <3
Answers
Answer:
B:8
A:10
B:19
Step-by-step explanation:
I first did the pedmas equation to then divide, subtract, add etc.. it by the constant.
3x2 = 6
6+4=10
10-2=8
Answer is 8
Next question
3+ 12= g+5
15= g+5
15-5=10
Next question
36/2 = 18
18+9 = 27
= 19
Hope it helps!! Pls give brainliest :)) Have a good dayy
Identify the segments that are parallel, if any, if
Answers
Answer:
The answer is C
Step-by-step explanation:
it is C because parallel lines don't intercept the go up or across but they don't touch, just imagine it isn't graphed.
What 8.1+2.53 with shown work
Answers
Answer:
10.63
Step-by-step explanation:
6) Which list shows how many equal-sized groups of 18 students Ms. Lee can make?
1, 2, 3, 4, or 6
7, 9, 14, 18, or 28
1, 2, 3, 6, 9, or 18
1, 2, 4, 7, 14, or 28
Answers
Answer:
1,2,3,6,9
Step-by-step explanation:
Got it right
this is distance & midpoint formulas I don’t know how to solve this can anyone help?
Answers
Answer:
midpoint formula: (x₁ + x₂)/2, (y₁ + y₂)/2
distance: √[(x₂ - x₁)² + (y₂ - y₁)²]
Step-by-step explanation:
What points are you trying to calculate the distance and the midpoint for?
the cost c in dollars of producing v video games is represented by c=6.8v^2 how many video games are produced if the cost is $979.20
Answers
Answer:
12 video games
Step-by-step explanation:
\(6.8 {v}^{2} = 979.20\)
\( {v}^{2} = 144\)
\(v = 12\)
Quick easy question
Answers
Answer:16
Step-by-step explanation:
144^0.5 = 12
400^0.5 = 20
a^2=b^2+c^2
20^2 = 12^2 +x^2
x^2 = 400-144= 256
x =16
Answer:
16
Step-by-step explanation:
If y=-1/3x-7, then find the output if the input is 12.
Answers
Answer:
-11
Step-by-step explanation:
input=x
output=y
Replace x with 12.
\(y=-\frac{1}{3}(12) -7\)
Solve.
Answer:
Step-by-step explanation:
a paddle wheel on a boat is 4 feet in diameter. the fins along the outer edge travel at a speed of 1.3 feet per second. how long does it take the paddle wheel to complete 100 full revolutions ? round to the nearest second.
_ minutes and _ seconds.
Answers
Answer: To find out how long it takes the paddle wheel to complete 100 full revolutions, we need to calculate the circumference of the paddle wheel and divide that by the speed at which the fins along the outer edge are traveling.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius of the circle.
The radius of the paddle wheel is 2 feet (the diameter of 4 feet divided by 2), so the circumference is:
C = 2π * 2 = 8π feet
To find out how long it takes the paddle wheel to complete 100 full revolutions, we divide the number of feet traveled in one revolution (the circumference of 8π feet) by the speed at which the fins are traveling (1.3 feet per second):
100 * 8π feet / 1.3 feet per second = 615.38 seconds
Rounded to the nearest second, it takes approximately 615 seconds for the paddle wheel to complete 100 full revolutions.
Not really how to do this, but I need some help
Answers
Given a polynomial of the form:
\(x^2+bx+c\)The method of completing the square give us another expression for that polynomial:
Where k is given by:
\(k=c-\frac{b^2}{4}\)So first we have to identify b and c:
\(\begin{gathered} x^2+14x=-69 \\ x^2+14x+69=0 \\ x^2+14x+69=x^2+bx+c \end{gathered}\)Then b=14 and c=69. This means that by completing the square we get:
\(\begin{gathered} x^2+14x+69=(x+\frac{b}{2})^2+c-\frac{b^2}{4} \\ x^2+14x+69=(x+\frac{14}{2})^2+69-\frac{14^2}{4} \\ (x+\frac{14}{2})^2+69-\frac{14^2}{4}=(x+7)^2+69-49 \\ (x+7)^2+69-49=(x+7)^2+20 \end{gathered}\)So we have:
\(\begin{gathered} x^2+14x+69=(x+7)^2+20 \\ \text{And} \\ x^2+14x+69=0 \end{gathered}\)Which means that:
\(\begin{gathered} (x+7)^2+20=0 \\ (x+7)^2=-20 \\ x+7=\pm\sqrt[]{-20}=\pm i\sqrt[]{20}=\pm2i\sqrt[]{5} \\ x=-7\pm2i\sqrt[]{5} \end{gathered}\)Which means that the answer is the second option.
Write the rational number 36/5 as a decimal
Answers
Answer:
36/5 as a decimal is 7.2
Step-by-step explanation:
In the fraction 36/5, 36 is the numerator and 5 is the denominator, the fraction bar means "divided by". Therefore, the fraction 36/5 is same as "36 divided by 5" or "36 ÷ 5".
When we calculated 36 divided by 5, we found that 36/5 in decimal form is:
36 ÷ 5 = 7.2
Therefore, the decimal form of 36/5 is 7.2