4. The interior angles of a triangle are 60°, 45° and 75°. The shortest side is 10 cm less than the
longest side. Determine the perimeter of the triangle to the nearest cm.
Answers
Answer:
Step-by-step explanation:
The length of each side corresponds to the sizes of each angle respectively.
To determine the length of each side, we would apply sine rule which is expressed as
a/sinA = b/SinB = c/SinC
The diagram of the triangle is shown in the attached photo. The longest side is c. If the shortest side is 10 cm less than the longest side, it means that the length of the shortest side is c - 10
Therefore,
c/Sin75 = (c - 10)/Sin45
c/0.966 = (c - 10)/0.707
Cross multiplying, it becomes
c × 0.707 = 0.966(c - 10)
0.707c = 0.966c - 9.66
0.966c - 0.707c = 9.66
0.259c = 9.66
c = 9.66/0.259
c = 37.3 cm
The shortest side is
37.3 - 10 = 27.3 cm
Applying the sine rule again,
b/Sin60 = 37.3/Sin75
b/0.866 = 37.3/0.966
Cross multiplying, it becomes
0.966b = 0.866 × 37.3
b = 32.3018/0.966
b = 33.4 cm
The perimeter is
27.3 + 33.4 + 37.3 = 98 cm
Related Questions
Shawna is a member of the swim team. She can swim 3 laps in 3 minutes
and 21 seconds. If Shawna swims at the same pace, how long would it take
her to swim 8 laps?
Answers
Answer:
8 minutes and 53 seconds
Answer:
8 minutes and 56 secondsStep-by-step explanation:
3 laps ⇒ 3 minutes and 21 seconds given1 lap ⇒ 1 minute and 7 laps divide by 3 8 laps ⇒ 8 minutes and 56 seconds multiply by 8Please help me! Geometry! Transition math
Answers
Answer:
total area = 18.28 in.^2
perimeter = 16.28 cm
Step-by-step explanation:
Area:
The total area of the figure is the sim of the area of the rectangle and the area of the semicircle.
total area = LW + (1/2)(pi)r^2
total area = (4 in.)(3 in.) + (1/2)(3.14)(2 in.)^2
total area = 12 in.^2 + 6.28 in.^2
total area = 18.28 in.^2
Perimeter:
The perimeter of the figure is the sum of the lengths of the left side, bottom side, and right side of the rectangle and the circumference of the half circle.
perimeter = 3 cm + 4 cm + 3 cm + (1/2)(pi)d
perimeter = 10 + (1/2)(3.14)(4 cm)
perimeter = 10 + 6.28 cm
perimeter = 16.28 cm
a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 425 gram setting. it is believed that the machine is underfilling the bags. a 18 bag sample had a mean of 416 grams with a standard deviation of 19 . assume the population is normally distributed. a level of significance of 0.01 will be used. find the p-value of the test statistic. you may write the p-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answers
A significant deviation from the expected value of 425 grams for the bag filling machine. The manufacturer should investigate and adjust the machine to ensure that it is distributing the correct amount of chocolate chips in each bag.
Based on the information provided, the manufacturer of chocolate chips is interested in determining if there is a deviation from the expected value of 425 grams for the bag filling machine. They have collected a sample of 18 bags and calculated a mean of 416 grams with a standard deviation of 19. Assuming a normal distribution, they would like to determine the p-value of the test statistic with a significance level of 0.01.
To do this, they would conduct a one-sample t-test using the formula:
t = (x - μ) / (s / √n)
where x is the sample mean, μ is the population mean (expected value), s is the sample standard deviation, and n is the sample size.
Plugging in the values, we get:
t = (416 - 425) / (19 / √18) = -2.21
Using a t-distribution table or calculator with 17 degrees of freedom (n-1), we can find the p-value associated with a t-score of -2.21 and a one-tailed test (since we are interested in whether the bags are underfilled). The p-value is approximately 0.0212, which is less than the significance level of 0.01. Therefore, we reject the null hypothesis and conclude that the bags are likely being underfilled by the bag filling machine at the 425-gram setting.
In summary, the p-value of the test statistic is approximately 0.0212, indicating a significant deviation from the expected value of 425 grams for the bag filling machine. The manufacturer should investigate and adjust the machine to ensure that it is distributing the correct amount of chocolate chips in each bag.
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A significant deviation from the expected value of 425 grams for the bag filling machine. The manufacturer should investigate and adjust the machine to ensure that it is distributing the correct amount of chocolate chips in each bag.
Based on the information provided, the manufacturer of chocolate chips is interested in determining if there is a deviation from the expected value of 425 grams for the bag filling machine. They have collected a sample of 18 bags and calculated a mean of 416 grams with a standard deviation of 19. Assuming a normal distribution, they would like to determine the p-value of the test statistic with a significance level of 0.01.
To do this, they would conduct a one-sample t-test using the formula:
t = (x - μ) / (s / √n)
where x is the sample mean, μ is the population mean (expected value), s is the sample standard deviation, and n is the sample size.
Plugging in the values, we get:
t = (416 - 425) / (19 / √18) = -2.21
Using a t-distribution table or calculator with 17 degrees of freedom (n-1), we can find the p-value associated with a t-score of -2.21 and a one-tailed test (since we are interested in whether the bags are underfilled). The p-value is approximately 0.0212, which is less than the significance level of 0.01. Therefore, we reject the null hypothesis and conclude that the bags are likely being underfilled by the bag filling machine at the 425-gram setting.
In summary, the p-value of the test statistic is approximately 0.0212, indicating a significant deviation from the expected value of 425 grams for the bag filling machine. The manufacturer should investigate and adjust the machine to ensure that it is distributing the correct amount of chocolate chips in each bag.
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Mary analyzed occupancy rates at two community hospitals and obtained the following Excel results.
t-Test for Acue Care Occupancy Rates
MaxHealth HealthPro Mean 62.5462 68.4800 Variance 108.2377 98.3707 Observations 13 10 Hypothesized Diff 0 df 20 t Stat −1.3923 P(T<=t) one-tail 0.0896 t Critical one-tail 1.7247 P(T<=t) two-tail 0.1791 t Critical two-tail 2.0860 Which conclusion is correct in a two-tailed test at α = .05?
Multiple Choice
There appears to be no difference in the mean occupancy rates.
There is a significant difference in the mean occupancy rates.
HealthPro has a significantly higher mean occupancy rate.
Carver Memorial Hospital’s surgeons have a new procedure that they think will decrease the time to perform an appendectomy. A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes. For a right-tailed test for equal means (assume equal variances), the critical value at α = .10 is
Multiple Choice
2.120
2.754
1.746
1.337
Answers
The conclusion that is correct in a two-tailed test at α = .05 is There appears to be no difference in the mean occupancy rates.
How to solveFrom the given values:
Thus, the P-value = 0.1791
Interpret results. Since the P-value (0.1791) is greater than the significance level (0.05), we failed to reject the null hypothesis.
From the above test, we do not have sufficient evidence in favor of the claim that there is a difference in the mean occupancy rates.
Thus, option A is correct.
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100 points and brainlyest
Part 2 - Writing Equivalent Expressions - You will now use mathematical properties to create two expressions that are equivalent to Sara’s expression.
Property Used
Original/Changed Expression
New expression with property used
Commutative Property of Addition (rearrange the added terms in the parentheses to group like terms together.)
5(2j + 3 + j)
Combine Like terms after rearranging them
(put your answer from the previous row here)
Distributive Property of multiplication over addition (multiply the number outside the parentheses)
(put your answer from the previous row here)
(Use this final expression that you write in this box on the next slide.)
Answers
Answer:
Commutative Property of Addition: to change the order of numbers in an addition or multiplication operation does not change the sum or the product.
New expression with property used: 5(2j + j + 3)
Combine like terms: when combining like terms, add their coefficients
The like terms are 2j and j. Add their coefficients: 2 + 1 = 3, which means that the combination of like terms is 3j.
New expression with property used: 5(3j + 3)
Distributive Property of multiplication over addition: multiplying a sum by a number gives the same result as multiplying each added term by the number and then adding the products together.
So 5(3j + 3) = 5 · 3j + 5 · 3 = 15j + 15
New expression with property used: 15j + 15
4/5 x 1/4 Write the answer in simplest form.
Answers
Answer:
0.2 or 1/5 as fraction form
Step-by-step explanation:
Hope this helps?!
:)
Hi!
Given:
\(\frac{4}{5} *\frac{1}{4}\)
First, multiply the numerators.
\(4*1=4\)
Second, multiply the denominators.
\(5*4=20\)
Now we have:
\(\frac{4}{20}\)
Last, simplify. 20 and 4 can both be divided by 4.
\(\frac{4/4}{20/4} =\frac{1}{5}\)
Your answer is \(\frac{1}{5}\)
---------------------------------------------------------------------------------------------
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If you have an independent group design and ordinal data, which test do you use?
Answers
The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test
Given: Independent group and ordinal data. To find which test to use.
What's the Kruskal Wallis test?
The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.
The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.
The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.
How to calculate the Kruskal Wallis test?
The computation of the Kruskal- Wallis statistic requires
Combine the individualities from all the separate samples and rank order the entire group.Regroup the individualities into the original samples and cipher the sum of the species( T) for each sample. A formula is used to cipher the Kruskal- Wallis statistic which is distributed as a ki-square statistic with degrees of freedom equal to the number of samples minus one. The attained value must be lesser than the critical value for ki- forecourt to reject H0 and conclude that there are significant differences among the treatments.Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.
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We can use the Kruskal Wallis test when we have an independent group design and ordinal data.
We are given an independent group design and ordinate data.
We need to tell which test to use on them.
The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.
The null hypothesis for the Kruskal- Wallis test tells us that:
There are no methodical or harmonious differences among the treatments being compared.
Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.
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17. A rectangular prism has a length of 12 cm, a
height of 6/cm, and a width of 4 cm. Use the
formula SA = 2({w) + 2(wh) +2(ehy to find the
surface area of the rectangular prism.
Answers
Answer:
SA = 288 cm
Step-by-step explanation:
l = 12
w = 4
h = 6
SA = 2lw + 2wh + 2lh
SA = (2 x 12 x 4) + (2 x 4 x 6) + (2 x 12 x 6)
SA = 96 + 48 + 144
SA = 288
Rosie is mixing a special green paint which contains 2/3 cups yellow paint 1/3cups white paint 1 and 1/5 cups blue paint and last 1/5 black paint what percentage what percentage of the green paint is blue
Answers
What are the vertices of triangle PQR?
Answers
Answer: D. P, Q and R.
Step-by-step explanation:
The vertices of the triangle PQR - it is P, Q and R.
Question 11
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Simplify the expression x^1/5 • x^5/2 Assume x > 0.
A) The answer can be written in the form x^a where
the exponent a is: Note: enter the exponent as a reduced fraction or integer.
B) The answer can be written in the form 1/x^b where the exponent b is:
Note: enter the exponent as a reduced fraction or integer.
Answers
Answer:
A. x^27/10
B. 1/x^-27/10
Step-by-step explanation:
Mathematically, if we have the same base, we simply add up the index
Thus, we have that;
x^1/5•x^5/2 = x^(1/5 + 5/2) = x^(2 + 25)/10 = x^27/10
A) In the first form, we have that;
x^27/10
a = 27/10
B) We simply negate what we have above in terms of the index according to the indices law below;
a^b = 1/a^-b
Hence, we have that;
1/x^-27/10
−5/6e−2/3e=−24 solve for e
Answers
Answer:
-3e/2
Step-by-step explanation:
Find the 4th term in the sequencewith the following definition:aj = 0an = 2(an-1-3)
Answers
Answer:
-60
Explanation:
To find the 4th term we need to also find the 2nd and 3rd terms as follows:
\(\begin{gathered} a_n=2(a_{n-1}-3) \\ a_2=2(a_{2-1}-3) \\ a_2=2(a_1-3) \\ a_2=2(0-3) \\ a_2=2(-3) \\ a_2=-6 \end{gathered}\)\(\begin{gathered} a_3=2(a_{_2}-3) \\ a_3=2(-6-3) \\ a_3=3(-9) \\ a_3=-27 \end{gathered}\)Finally, we can calculate the value of the 4th term as:
\(\begin{gathered} a_4=2(a_3-3) \\ a_4=2(-27-3) \\ a_4=2(-30) \\ a_4=-60 \end{gathered}\)So, the answer is -60
?
Answer the question below. Type your response in the
space provided.
Does your state have a sales tax?
Answers
Does (9, 0) make the equation y = x + –9 true?
Answers
Answer:
yes it does
Step-by-step explanation:
if y =0,
x=9
if x =0,
y=-9
therefore it makes the equation true.
Answer:
No it doesn't
Step-by-step explanation:
Because substituting Y=9 and x=0 into the equation it won't give the correct answer:
9=0-9
9=-9
this shows that they are not equal
Molly purchased a car for $16,079 at 3.6% add-on rate for 4 years. Determine the amount of interest and the monthly payment for the car loan.
$3,010.16 ; $310.50
$3,010.16 ; $383.22
$2,315.38 ; 310.50
$2,315.38 ; $383.22
Answers
the correct answer to the given question about car loan is option D: $2,315.38; $383.22.
To determine the interest and monthly payment for the car loan, we can use the add-on interest formula:
Total Interest = Principal x Rate x Time
where:
Principal = $16,079 (the amount of the loan)
Rate = 3.6% (the add-on interest rate)
Time = 4 years
Total Interest = $16,079 x 0.036 x 4
Total Interest = $2,315.38
So the total amount of interest on the loan is $2,315.38.
To calculate the monthly payment, we can use the following formula:
Monthly Payment = (Principal + Total Interest) / (Number of Payments)
where:
Principal = $16,079 (the amount of the loan)
Total Interest = $2,315.38 (the total interest on the loan)
Number of Payments = 4 x 12 = 48 (since the loan is for 4 years, and there are 12 months in a year)
Monthly Payment = ($16,079 + $2,315.38) / 48
Monthly Payment = $383.22
Therefore, the amount of interest on the loan is $2,315.38 and the monthly payment for the car loan is $383.22.
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(ross p1.15) consider a group of 20 people. if everyone shakes hands with everyone else, how many handshakes take place?
Answers
190 handshakes take place.
What is Combinations?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. The sequence in which the chosen components are chosen is crucial in permutations, too. For instance, the arrangements ab and ba are distinct in permutations but equivalent in combinations (regarded as one arrangement).
Combinatorics is the study of combinations, although mathematics and finance are two other fields that employ combinations.
EXPLNATION : For a handshake you need two people. Therefore, select two from twenty, that is, 20C2 ways. It is 20*19/2 = 190.
In general, if there are ’n’ number of people there can be nC2 handshakes.
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The top of square table has an area of 24 square feet. What is the length of 1 edge of the tabletop?
Answers
The length of one edge of the tabletop is 4.89 feet.
We know that square is a shape that has all the side equal. Based on this using the formula to find the length of edge of the tabletop.
The area of square table is given by the formula -
Area of square table = side²
We will keep the value of area of square table to find the value of side which will be length of edge
24 = side²
Side = ✓24
Taking square root for the value on right side of the equation
Side = 4.89
Hence, the length of one edge of the tabletop is 4.89 feet.
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What is the ratio of 2,753 to 1,750 as a decimal? ( Rounded to two decimal places)
Answers
Answer:
-0.17
Step-by-step explanation:
The length of a rectangular garden is 20 feet and the width is 15 feet. What is the ratio of length to width?
Answers
Answer:
4:3 because 20 divided by 5 is 4 and 15 divided by 5 is 3.
Can you help me with this? 7
Answers
Answer:
65º
Step-by-step explanation:
The angle of a straight line is 180º, so ∠ABD=180º and ∠ABC=(180-6x)ºThe sum of the interior angles of a triangle is 180, so (x+40)º+(3x+10)º+(180-6x)º=180We can solve from there, x+40+3x+10+180-6x=180Combine like terms, -2x+230=180Subtract 230, -2x=-50Divide by -2, x=25m∠CAB=(x+40)º=(25+40)º=65ºm∠ABC=(180-6x)º=(180-150)º=30ºm∠BCA=(3x+10)º=(75+10)º=85ºFactor x2 + 15x + 50
To receive all 5 points, include the question (+1 point), your work to find the two numbers (+3 points), and the final answer (+1 point).
Answers
Step-by-step explanation:
here's your solution
=> x^2 + 15x + 50
=> By using middle term split
=> x^2 + 10x + 5x + 50
=> taking common from each
=> x(x + 10) + 5(x + 10)
=> (x + 5) (x + 10
hope it helps
Emiko needs to go to the dentist. It takes her 65minutes to get there by riding her bike. This is 5 minutes shorter than twice the time it would takeby bus. How long does it take Emiko to get to the dentist by bus? a.35 min b.40 min c.45 min d.50 min I will brainliest
Answers
65 min by riding her bike
x min by boarding a bus
since the time taken to get to the dentist with a bus is 5min shorter than twice the time taken with a bike, it can be written as
(2x) - 5 = 65
2x = 65 + 5
2x = 70
x = 35 min. (A)
Mrs. Wilson tells you that the next test is worth 100 points and contains 38 problems. Multiple-choice questions are worth 2 points each and word problems are worth 5 points. How many of each type of question are there
Answers
Answer:
30 mcq and 8 word problems
plz mark as brainliest
Which sentence expresses numbers correctly? When the temperaturos fell below Zero degrees Fahrenheit, the employees decided to take public transportation When the temperatures fell below 0 degrees Fahrenheit, the employees decided to take public transportation When the temperatures fell below zero degrees Fahrenheit, the employees decided to take public transportation
Answers
The sentence that expresses numbers correctly is: "When the temperatures fell below zero degrees Fahrenheit, the employees decided to take public transportation."
In the sentence, the number is correctly expressed as "zero degrees Fahrenheit." When referring to temperatures below freezing, it is common to use the term "zero" to indicate the absence of heat. The numerical value of zero is represented by the numeral "0," rather than the word "Zero."
Additionally, the unit of measurement, Fahrenheit, is capitalized as it is a proper noun derived from the name of the scientist who developed the temperature scale.
Therefore, the sentence "When the temperatures fell below zero degrees Fahrenheit, the employees decided to take public transportation" accurately conveys the correct numerical and linguistic representation of the temperature.
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what is the value of a in this equation 2a+3=a-4
Answers
Answer:
a = -7
Step-by-step explanation:
You want to know the value of 'a' in the equation 2a +3 = a -4.
SolutionTo solve a linear equation like this, you want to collect the variable terms on one side of the equal sign, and the constant terms on the other side. In general to remove a term from a place where you don't want it, you subtract it from both sides of the equation.
2a +3 = a -4 . . . . . . given equation
To remove the 'a' term on the right, we subtract 'a' from both sides:
2a -a +3 = a -a -4
a +3 = -4 . . . . . . . . . simplify
Now, we have a constant on the left that we don't want, so we subtract that from both sides:
a +3 -3 = -4 -3
a = -7 . . . . . . . . . . . simplify
The value of 'a' in the equation is -7.
Use the product notation to rewrite the following expression. (t − 6) · (t2 − 6) · (t3 − 6) · (t4 − 6) · (t5 − 6) · (t6 − 6) · (t7 − 6) = π7k = 1
Answers
The expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).
As per the question, we can write the expression as:
(t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9)
Using product notation, we can write this as:
Π⁷k =1 \((t^k - 9)\)
where Π represents the product of terms, k is the index of the product, and the subscript 7 indicates that the product runs from k = 1 to k = 7.
Therefore, the expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).
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Solve for x.
(4x + 7)
(2x + 5)
can someone please help me with this
thanks in advance
Answers
(4x+7)(2x+5) Like this???
4x+7=2x+5 or like this?!!?!
university had enrollments of 40,555 students in 2000 and 44,109 students in 2008 at its main campus. (a) Assuming the enrollment growth is linear, find a linear model that gives the enrollment in terms of the year t, where t=0 corresponds to 2000.
Answers
Linear model for enrollment of a university Assuming that the enrollment growth is linear, we need to find a linear model that gives the enrollment in terms of the year t, where t=0 corresponds to 2000.
A linear equation is represented as y = mx + c where m is the slope and c is the y-intercept. Here, t corresponds to x, and enrollment corresponds to y. Let's calculate the slope of the line: Using the formula for slope: m = (y₂ - y₁) / (x₂ - x₁) = (44,109 - 40,555) / (8 - 0) = 3,554 / 8 = 444.25Substitute the values of m and the coordinates (2000, 40,555) in the formula for the line to get the value of c:40,555 = 444.25(0) + c c = 40,555The linear model that gives the enrollment in terms of the year t, where t = 0 corresponds to 2000 is: y = 444.25x + 40,555 where y is the enrollment and x is the number of years after 2000.
A continuous response variable is portrayed in linear models as a function of one or more predictor variables. They can assist you in analyzing experimental, financial, and biological data, understanding and predicting the behavior of complex systems.
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a book has 136 pages. each page has the same number of words, and each page has no more than 100 words on it. the number of words in the book is congruent to 184, modulo 203. how many words are on each page?
Answers
The words are on each page is 73.
Given:
A book has 136 pages. each page has the same number of words, and each page has no more than 100 words on it.
The number of words in the book is congruent to 184, modulo 203.
136n mod 203 =184,
solve for n
Using CRT + MMI
n =203m + 73, where m =0, 1, 2, 3....
Therefore the words are on each page is 73.
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