Answers
Answer:
x=31
Step-by-step explanation:
you just have to add the two equations to equal 180 because it's they're supplementary angles.
(25+x)+4x=180
25+x+4x=180
25+5x=180
5x=155
x=31
Answer:
(25+x)+4x=180°
25+x+4x=180°
5x=180-25
5x=155
x=155/5
x =31
Related Questions
In the past, the mean running time for a certain type of flashlight has been 9.2 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. They hypotheses are as follows. Explain a type 2 error.
Answers
Answer:
what are the hypotheses?
Step-by-step explanation:
you said the hypotheses are as folows its not there
The mean height of a Clydesdale horse is 72 inches with a standard deviation of 1.2 inches. What is the probability that a Clydesdale is greater than 75 inches tall?
Answers
Answer:
0.0062
Step-by-step explanation:
Given that:
Mean (μ) = 72 inches, Standard deviation (σ) = 1.2 inches.
The z score is a measure in statistics is used to determine by how many standard deviation the raw score is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean, the z score is negative.
The z score is given as:
\(z=\frac{x-\mu}{\sigma}\)
For Clydesdale is greater than 75 inches tall, x = 75 inches, the z score is:
\(z=\frac{x-\mu}{\sigma}=\frac{75-72}{1.2} =2.5\)
The probability that a Clydesdale is greater than 75 inches tall = P(X > 75) = P(Z > 2.5) = 1 - P(Z < 2.5) = 1 - 0.9938 = 0.0062 = 0.62%
The probability that a Clydesdale is greater than 75 inches tall is 0.62%
94.3 is what percent 143.3? Round to the Nearest tenth
Answers
Answer:
65.8%
Step-by-step explanation:
94.3x100/143.3=65.8
please help it'll mean a lot :) <33
Answers
Tom is buying a $4,500 tv on a deferred payment plan. there is no down payment and no interest for two years, provided he makes every payment and pays off the full balance before the end of two years. tom must make a minimum payment of $150 a month. to avoid a retroactive apr of 21%; he must pay the balance in full before the 2 years has passed. tom decides to pay $150 each month until the final month in which he will pay the balance. how much will tom owe the last month to avoid the interest charges?
Answers
Step 1
Tom will owe $900 in the last month.
Step 2:
What is the remaining balance to avoid interest charges?
Step 3:
To avoid paying interest charges on his $4,500 TV purchase, Tom must make sure he pays off the full balance before the end of the two-year deferred payment plan. The plan stipulates that Tom needs to make a minimum monthly payment of $150. He decides to pay $150 each month, except for the final month, when he plans to pay off the remaining balance to avoid any retroactive APR charges.
Given that Tom will be making 24 monthly payments of $150 each, the total amount he will have paid over the two years will be $150 x 24 = $3,600. To calculate the remaining balance, we subtract the total amount paid from the original TV price: $4,500 - $3,600 = $900.
Therefore, in the last month, Tom will owe $900 to avoid any interest charges. By paying off this remaining balance, he fulfills the requirement of paying off the full balance before the end of the two-year period, ensuring that he won't incur any retroactive APR charges.
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evaluate 1 1/3 - 2 1/6
Answers
Answer:
3/2 or 1.5
Step-by-step explanation:
1) Convert 2 1/6 into improper fraction
2) Find the LCM which is 6
3) Subtract like a normal fraction
Answer:
-5/6Step-by-step explanation:
=1×3+1/3 - 2×6+1/6=1×3+1/3 - 2×6+1/6=3+1/3- 12+1/6=1×3+1/3 - 2×6+1/6=3+1/3- 12+1/6=4/3 - 13/6=1×3+1/3 - 2×6+1/6=3+1/3- 12+1/6=4/3 - 13/6=4×6/6×3 - 13×3/6×3 =1×3+1/3 - 2×6+1/6=3+1/3- 12+1/6=4/3 - 13/6=4×6/6×3 - 13×3/6×3 =24/18 - 39/18 =1×3+1/3 - 2×6+1/6=3+1/3- 12+1/6=4/3 - 13/6=4×6/6×3 - 13×3/6×3 =24/18 - 39/18 = -15/18 =1×3+1/3 - 2×6+1/6=3+1/3- 12+1/6=4/3 - 13/6=4×6/6×3 - 13×3/6×3 =24/18 - 39/18 = -15/18 = -5/6dave is 15 years old and his uncle rob is three times as old. when dave will be 32 years old, his uncle rob will be
Answers
By considering ages and equations we have,
Uncle Rob will be 62 years old when Dave is 32.
Dave is listed as being 15 years old, while his uncle Rob is listed as being three times Dave's age. Rob's age as of right now may be calculated using the formula below:
Age of Rob is Dave times three.
Using Dave's age as a plug-in, we obtain following equations,
Rob's age is equal to 15 + 3 = 45.
Rob is currently 45 years old, according to this.
We need to know how many years it will be before Dave turns 32 in order to calculate Rob's age at that time. By deducting Dave's present age from his anticipated age, we may determine this:
Years from now = Dave's age in the future minus Dave's age currently
By entering the specified values, we obtain:
The number of years from now is equal to 32 - 15 = 17 years.
Dave will turn 32 in 17 years, according to this.
We may multiply Rob's current age by the number of years from now to determine his age at that point:
When Dave reaches the age of 32, Rob will be that age plus the number of years.
When we enter the calculated values, we obtain:
When Dave is 32 years old, Rob will be 45 + 17 years old, or 62 years old.
So, Dave uncle rob 's age will be 62 years old.
As a result, when Dave's age is 32, his uncle Rob's age will be 62.
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Dominic needs 0.6 ounces of fish food to feed his fish for a month. Dominic wants to know how many ounces he needs to feed his fish for 7 months. Which is the correct proportion you could use to solve this problem?
Answers
Answer:
The answer is 0.6*7=4.2ounces of fish food.
Step-by-step explanation:
If 0.6 ounces of fish food will suffice for Dominic's fish for a month, then for 7 months he would need 7 times the food he requires for 1 month.
7*0.6=4.2 ounces of fish food.
uke has blue and red balls. Every day, he wins 2 blue balls and loses 3 red ones. After 5 days, he has the same amount of blue as red. After 9 days, he has twice as many blues as reds. How many red balls did he have at the beginning? Question not Showing?
Answers
A. The number of red balls he had was 8 at the beginning.
Duke's starting red ball total can be found by setting up a system of equations. First, let x represent the number of red balls and y represent the number of blue balls.
After 5 days, the equation is x-15=y+10. This equation states that after 5 days, the number of red balls (x) minus 15 will equal the number of blue balls (y) plus 10. After 9 days, the equation is x-27=2y+20.
This equation states that after 9 days, the number of red balls (x) minus 27 will equal twice the number of blue balls (y) plus 20. To solve for x, both equations can be set equal to each other and solved. This results in x=8. Therefore, Duke had 8 red balls at the beginning.
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Which of the following statements are true? Select all that apply.
Answers
Answer:
a,d
Step-by-step explanation:
Using the net below, find the surface area of the triangular prism.
Answers
160 i believe. to find the area of a triangle act like its a square and divide in half. for squares multiply base by height.
take the area of each shape and add it up
Use the formula for the sum of a geometric sequence to write the following sum in closed form.
63 + 64 + 65 + + 6k
where k is any integer with
k ≥ 3.
Answers
The sum of the sequence 6³ + 6⁴ + 6⁵ + ... + 6^k, where k is any integer with k ≥ 3, can be written in closed form as:
\(S = 216 \times (6^k - 1) / 5.\)
The sum of a geometric sequence can be calculated using the formula:
\(S = a \times (r^k - 1) / (r - 1),\)
where S is the sum of the sequence, a is the first term, r is the common ratio, and k is the number of terms.
In this case, the first term (a) is 6³ = 216, and the common ratio (r) is 6. We need to find the sum of the terms from 6³ to \(6^k\).
Let's calculate the sum using the formula:
\(S = 216 \times (6^k - 1) / (6 - 1)\)
\(= 216 \times (6^k - 1) / 5.\)
Therefore, the sum of the sequence 6³ + 6⁴ + 6⁵ + ... + 6^k, where k is any integer with k ≥ 3, can be written in closed form as:
\(S = 216 \times (6^k - 1) / 5.\)
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I NEED THIS ASAP PLEASE!!!
Find the area of the triangle A = in²
Answers
The length of a rectangle is 19 centimeters less than its width. Its area is 20 square centimeters. Find the dimensions of the rectangle.
Answers
The dimensions of the rectangle are width = 20 centimeters and length = 1 centimeter.
Let's denote the width of the rectangle as "w" centimeters. According to the problem, the length of the rectangle is 19 centimeters less than its width, so the length can be expressed as "w - 19" centimeters.
The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 20 square centimeter
Area = Length × Width
20 = (w - 19) × w
To solve this equation, we can expand it:
20 = \(w^2\) - 19w
Rearranging the equation to bring everything to one side:
\(w^2\) - 19w - 20 = 0
Now, we can factor the quadratic equation:
(w - 20)(w + 1) = 0
Setting each factor equal to zero and solving for "w":
w - 20 = 0 --> w = 20
w + 1 = 0 --> w = -1
Since a negative width doesn't make sense in this context, we discard w = -1.
Therefore, the width of the rectangle is 20 centimeters (w = 20).
To find the length, we substitute this value back into the expression for length:
Length = w - 19
Length = 20 - 19
Length = 1 centimeter
So, the dimensions of the rectangle are width = 20 centimeters and length = 1 centimeter.
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suppose a population was normally distributed with a mean of 10 and standard deviation of 2 . What proportion of the scores are below 12.5? Choose the correct answer 75% 77.8% 92% 89.44% Cannot be calculated
Answers
The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.
The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.
Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.
In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.
The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.
Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.
Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.
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An old cannon hits the target with 0.15 probability. How many shots are needed to hit the target with probability greater than 0.90 ?
Answers
You would need at least 23 shots to hit the target with a probability greater than 0.90.
To determine the number of shots needed to hit the target with a probability greater than 0.90, we can use the concept of probability complement.
Let's assume that the probability of hitting the target with a single shot is p = 0.15. The probability of missing the target with a single shot is then q = 1 - p = 1 - 0.15 = 0.85.
Now, let's calculate the probability of missing the target for a certain number of shots in a row. If we want to calculate the probability of missing the target for n shots in a row, we multiply the probabilities of missing the target for each shot:
P(missing target in n shots) = \(q^n\)
To find the number of shots needed to hit the target with a probability greater than 0.90, we need to find the smallest value of n for which the complement of the probability of missing the target (the probability of hitting the target) is greater than 0.90:
1 - P(missing target in n shots) > 0.90
Since we know that P(missing target in n shots) = \(q^n\), we can rewrite the equation as:
1 - \(q^n\) > 0.90
Now, let's solve this equation for n:
\(0.90 < 1 - q^n\)
\(q^n\) < 0.10
n * log(q) < log(0.10)
n > log(0.10) / log(q)
Plugging in the values, we have:
n > log(0.10) / log(0.85)
Using a calculator, we find:
n > 22.95
Since the number of shots must be an integer, we round up to the nearest whole number:
n = 23
Therefore, you would need at least 23 shots to hit the target with a probability greater than 0.90.
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An equation is blank =540
Answers
A jar contains 18 strawberry, 24 cherry, and 19 lime-flavored candies. The rest of the candys are chocolate there are 82 candys in all. If n represents the number of chocolates in the jar, what equation could you use to find n?
Answers
The equation which is used to find the number of chocolates candy in the jar is given by 18 + 24 + 19 + n = 82 , the number of chocolate candy in the jar is equal to 21.
Number of strawberry candy in the jar = 18
Number of cherry candy in the jar = 24
Number of lime flavored candies = 19
Let 'n' be the number of chocolate candy in the jar
Total number of candy in the jar = 82
Equation used to represent the given condition is :
18 + 24 + 19 + n = 82
⇒ 61 + n = 82
⇒ n = 82 - 61
⇒ n = 21
Therefore, the equation required to represent the number of chocolate candy is 18 + 24 + 19 + n = 82 and the value of n is equal to 21.
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Otis has saved $18,500 so far to buy a
house. He can put this amount into an
account that earns 5.1% simple interest,
or another with 5.1% compounded
annually. Which method of earning
interest should he choose, simple or
compound, and how much more interest
will the account earn using that method
after 4 years?
F Compound interest; $15,106.30
G Simple interest; $15,106.30
H Simple interest; $298.65
J Compound interest; $298.65
no
Answers
9514 1404 393
Answer:
J Compound interest; $298.65
Step-by-step explanation:
Interest compounding pays interest on the interest. For the same annual rate, any amount of compounding will earn more interest.
For short time periods, the effect of compounding is not great. In general, it will be a fraction of the equivalent simple interest rate. Here, the effective multiplier for annual compounding is ...
1.051^4 = 1.22024337
and the effective multiplier for simple interest is ...
1 +0.051·4 = 1.204
Then the difference in interest rate multiplier for the 4-year period is ...
1.22024337 -1.204 = 0.01614337
That fraction of the $18500 principal is $298.65.
Compound interest earns $298.65 more than simple interest in this scenario.
Amy bought a new car for $29,000. She paid a 10% down payment and financed the remaining balance for 60 months with an APR of 5.5%. Assuming she makes monthly payments, determine the total interest Amy pays over the life of the loan. Round your answer to the nearest cent, if necessary.
Answers
Amy will pay a total of approximately $30,007.20 in interest over the life of the loan.
Amy bought a car for $29,000, making a 10% down payment and financing the remaining balance for 60 months with an APR of 5.5%. The question asks for the total interest Amy will pay over the life of the loan.
To calculate the total interest paid, we need to determine the monthly payment amount and then multiply it by the number of months. The monthly payment can be calculated using the formula for a fixed-rate loan: P = (r × PV) / (1 - (1 + r)⁽⁻ⁿ⁾)
where P is the monthly payment, r is the monthly interest rate, PV is the present value or loan amount, and n is the number of months.
First, we calculate the loan amount after the down payment: $29,000 - ($29,000 × 10%) = $26,100.
Next, we calculate the monthly interest rate: 5.5% / 12 = 0.00458.
Using the formula, we can find the monthly payment amount: P = (0.00458 × $26,100) / (1 - (1 + 0.00458)⁽⁻⁶⁰⁾) ≈ $500.12.
Finally, we multiply the monthly payment by the number of months: $500.12 × 60 = $30,007.20.
Therefore, Amy will pay a total of approximately $30,007.20 in interest over the life of the loan.
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Find the difference 10.091-9.987
Answers
Answer: D:104 is the answer
Step-by-step explanation:substract
Given the definitions of f(x) and g(x) below, find the value of g (f(5)).
f(x) = x² - 6x + 14
g(x) = x +14
PLEASE HELP!
Answers
g(x)= 23
Explanation:
f(x)=5^2 - 6(5) + 14
25 - 30 + 14
-5 + 14 = 9
g(x) = 9 + 14
g(x) = 23
A number m is formed by writing all the prime numbers between 0 and 10 in ascending order. another number n is formed by writing all the square numbers between 0 and 10 in descending order: a)find m -n b)express(m-n) as a product of its prime factors
Answers
Answer:
(a) 1416
(b) 2 × 2 × 2 × 3 × 59
Step-by-step explanation:
The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357
The square numbers between 0 and 10 are 1, 4, 9 and in descending order 9,4.1so n = 941
m - n = 2357 - 941 = 1416
Unique prime factors of 1416 are 2,3,59
1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59
In science class, Clare and Lin estimate the mass of eight different objects that actually weigh 2,000 grams each.
Answers
Answer:
Lin was better than Clare
Step-by-step explanation:
GivenClare
mean: 2,000 grams MAD: 275 grams median: 2,000 grams IQR: 500 gramsLin
mean: 2,000 grams MAD: 225 grams median: 1,950 grams IQR: 350 gramsQuestionWhich student was better at estimating the mass of the objects?SolutionComparing data for both Clare and Lin, we can see that:
mean - is same 2000 grams for bothmedian - almost same, 2000 grams vs 1950 gramsMAD - 275 grams vs 225 gramsIQR - 500 grams vs 350 gramsConclusion
Lin was better at estimating than ClareReason
Both students had measures of center (mean and median) very close to 2000 gramsLin got less variable responses as both the MAD and IQR were lower than Clare gotJoe had 5 dollars how much does he have now
Answers
Answer:
5 dollars
Step-by-step explanation:
Find the Area of the figure below, composed of a rectangle and one semicircle, with
another semicircle removed. Round to the nearest tenths place.
Answers
Answer:
56
Step-by-step explanation:
Simple just move the semicircle into the empty spot and there you go.
you toss a coin four times. what's the probability of tossing tails exactly once? is this an unusual event?
Answers
Step-by-step explanation:
Four tosses of the coin result in 2^4 = 16 possible outcomes of which FOUR
will have ONE tails :
HHHT
HHTH
HTHH
THHH so 4 out of 16 = 4/16 = 1/4 Not very unusual
In a certain city, Third A venue runs west to east. Main Stret runs south to north. They
eventually intersect. A library, city hall, and a school are alt on Third Avenue. The library is 400
yards west of Main Street. City Hall is 300 yards west of the library. The school is 200 yards east
of city hall. Describe the location of the school with respect to Main Street.
Answers
Answer:
300 yards west of the library. The school is 200 yards east
Step-by-step explanation:
a bake shop sells twenty different kinds of pastries. twelve of them were chocolate. zack randomly buys eight kinds of pastries. what is the chance that four of them will be chocolate? use the hypergeometric distribution.
Answers
The probability that Zack randomly selects 4 chocolate pastries out of 8 pastries from a population of 20 pastries, of which 12 are chocolate, is approximately 0.206 or 20.6%.
The hypergeometric distribution can be used to calculate the probability of selecting a certain number of objects with a specific characteristic from a population of objects with and without the characteristic, without replacement.
The probability of Zack selecting 4 chocolate pastries out of 8 randomly chosen pastries from a population of 20 pastries, of which 12 are chocolate.
The probability mass function of the hypergeometric distribution is:
\(P(X = k) = (C(N_1,k) \times C(N_2,n - k)) / C(N,n)\)
where:
X is the random variable representing the number of pastries that are chocolate in the sample of 8
k is the number of chocolate pastries in the sample of 8 (in this case, k = 4)
N₁ is the number of chocolate pastries in the population (in this case, N₁ = 12)
N₂ is the number of non-chocolate pastries in the population (in this case, N₂ = 20 - 12 = 8)
n is the sample size (in this case, n = 8)
N is the total number of pastries in the population (in this case, N = 20)
Plugging in the values, we get:
\(P(X = 4) = (C(12,4) \times C(8,8 - 4)) / C(20,8)\)
\(P(X = 4) = (495 \times 70) / 167,960\)
P(X = 4) ≈ 0.206
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A line has slope 2/3 and y intercept -2. Which answer is the equation of the line?
Answers
Answer:
y=2/3x-2
Step-by-step explanation:
All of the given options are in slope intercept form.
Slope intercept form is y=mx+b
This is where m is the slope fo the line and b is the y intercept
That said, we can simply plug the given values into the form.
y=(2/3)x+(-2)
Simplify
y=2/3x-2
Answer:
A. y= 2/3x-2
Step-by-step explanation:
The slope of a line is written in slope-intercept form, which is:
y= mx+b
where m is the slope and b is the y-intercept.
The line has a slope of 2/3 and a y-intercept of -2. Therefore,
m= 2/3
b= -2
Substitute these values into the slope intercept form.
y= mx+b
y=2/3x+(-2)
Adding a negative number (+-) can be simplified to just a negative(-)
y= 2/3x-2
Therefore, the equation of the line is A. y= 2/3x-2