Answer:
54 times
Step-by-step explanation:
1 yard = 3 feet
[tex]9/2 * 3 = 27/2 ft = 13.5 ft[/tex]
1 ft = 12 inches
[tex]13.5*12=162[/tex] inches
162 / 3 = 54 times
B is the answer.
survey found that 68 % of callers complain about the service they receive from a call center. State the assumptions and determine the probability of each event described below. (a) The next three consecutive callers complain about the service. (b) The next two callers complain, but not the third. (c) Two out of the next three calls produce a complaint. (d) None of the next 10 calls produces a complaint.
Answer:
(a) 0.3144
(b) 0.1497
(c) 0.654
(d) [tex]1.125\times 10^{-5}[/tex]
Step-by-step explanation:
It is given that in a survey 68% of callers complain about the service.
So the probability that a caller complaint about the service = 0.68
Therefore probability that caller does not complain for the service = 1-0.68 = 0.32
(a) Probability of next three caller complain about service [tex]=0.68\times 0.68\times 0.68=0.3144[/tex]
(b) Probability that next two caller complain but not third
[tex]=0.68\times 0.68\times 0.32=0.1497[/tex]
(c) Two out of three calls produce a complaint
[tex]=^3C_20.68^2\times 0.32=0.654[/tex]
(d) None of the 10 calls produce a complaint
[tex]=0.32^{10}=1.125\times 10^{-5}[/tex]
The probability of individual and consecutive complaints from a call center are calculated using the given percentage of complaints. These calculations are based on the assumption of a consistent 68% complaint rate and that each complaint is an independent event.
Explanation:The subject of this question is probability, a concept in mathematics. To answer your question, we need to make some assumptions. We must assume that each caller's complaint is an independent event - that is, whether one caller complains does not affect whether the next caller will complain. We also need to assume that the 68% complaint rate is consistent, meaning it does not vary with time or for any other reason.
(a) The probability of three consecutive callers complaining would be (0.68)^3 = 0.314432.
(b) The probability of the next two callers complaining, but not the third would be (0.68)^2* (1-0.68) = 0.147456.
(c) Two out of the next three calls producing a complaint could occur in three ways (CCN, CNC, NCC where C is a complaining caller and N is a non-complainer). So, it would be 3*(0.68)^2* (1-0.68) = 0.442368.
(d) The probability of none of the next 10 calls producing a complaint would be (1 - 0.68)^10 = 0.0000040859.
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ow much fencing is required to enclose a circular gardan whose radius is 14m used 22 / 7 for pi
To enclose a circular garden with a radius of 14m, you would need 88 meters of fencing.
Explanation:To find the amount of fencing required to enclose a circular garden, you need to calculate the circumference of the garden. The formula for circumference is given by C = 2πr, where r is the radius of the garden.
Given that the radius is 14m, you can use the value of π as 22/7. So, the circumference is C = 2 * (22/7) * 14 = 88m.
Therefore, you would need 88 meters of fencing to enclose the circular garden.
Find x, y, z, and w.
[x 6 (2x-1) y 9 9y] = [(2x-3) z 5 7 (w+1) (8y+7)]
Answer:
(x, y, z, w) = (3, 7, 6, 8)
Step-by-step explanation:
Your list equation seems to resolve to 6 equations:
x = 2x -36 = z2x -1 = 5y = 79 = w +19y = 8y +7The first equation tells you ...
0 = x -3 . . . . . subtract x
3 = x . . . . . . . add 3
We can check this in the third equation:
2(3) -1 = 5 . . . true
The fifth equation tells you ...
8 = w . . . . . . . subtract 1
We can check the value of y in the last equation:
9(7) = 8(7) +7 . . . true
The variable values are ...
(x, y, z, w) = (3, 7, 6, 8)
Find the coordinates of the fourth vertex that completes the construction of the rectangle on the coordinate plane.
A(3,-7)
B(7,-3)
C(-3,7)
D(-7,3)
Answer:
The correct answer would be C (-3, 7)
Step-by-step explanation:
The first coordinate is the x (-3) and the second is the y (+7); therefore, the coordinate of the fourth vertex on the plane is (-3, 7).
Answer:
your answer should be C (-3, 7)
Step-by-step explanation:
brainliest pls
Have a nice day
Your total FICA contribution which includes Social Security and Medicare is 15.3% of your salary. 12.4% of your FICA contribution is for Social Security. Your annual income is $67,525. What will be the total deduction be for you and your employer for Medicare?
Answer:
$1,958.23
Step-by-step explanation:
Annual income = $67,525
Total FCIA = 15.3% of salary
Since my annual income is $67,525 the FCIA contribution = 15.3%.
But 12.4% is for Social Security.
The remaining 2.9%(15.3% - 12.4%) will be for Medicare taxes.
The total deduction for I and my employer for medicare taxes will be:
2.9% * $67,525
= $1,958.225
The total deduction for medicare would be: $1,958.23
Note: Assuming we were asked to calculate only employee's medicare, the deduction would be 50% of $1,958.23.
Answer:
1958
Step-by-step explanation:
A bag of chips is 24 ounces. A serving size is 3/4 ounce. How many servings are in the bag of chips?
Answer:
The correct answer to the following question will be "32 servings".
Step-by-step explanation:
The given values are,
A bag of chips = 24 ounces
Serving size = 3/4 ounces
Servings = ?
Now,
On dividing "24 ounces" by "3/4 ounce", we get
⇒ [tex]\frac{24}{\frac{3}{4}}[/tex]
⇒ [tex]24\times \frac{4}{3}[/tex]
⇒ [tex]8\times 4[/tex]
⇒ [tex]32[/tex]
Thus, the bag of chips contains "32" servings.
Final answer:
To determine the number of servings in a 24-ounce bag of chips with a serving size of 3/4 ounce, divide the total weight by the serving size, resulting in 32 servings.
Explanation:
The student has asked a question about how to calculate the number of servings in a bag of chips given its total weight and the size of each serving. This is a mathematics problem involving division.
To find out the number of servings in a 24-ounce bag of chips where each serving is 3/4 ounce, you divide the total weight of the bag by the weight of a single serving:
Number of servings = Total weight of the bag / Weight of one serving
Number of servings = 24 oz / (3/4 oz)
To divide the fractions, you multiply by the reciprocal of the serving size, which is:
Number of servings = 24 oz × (4/3)
Number of servings = 32
Therefore, there are 32 servings in the 24-ounce bag of chips.
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 400 babies were born, and 340 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective? nothingless than pless than nothing (Round to three decimal places as needed.) Does the method appear to be effective? Yes, the proportion of girls is significantly different from 0.5. No, the proportion of girls is not significantly different from 0.5.
Answer:
(a) 99% confidence interval for the percentage of girls born is [0.804 , 0.896].
(b) Yes, the proportion of girls is significantly different from 0.50.
Step-by-step explanation:
We are given that a clinical trial tests a method designed to increase the probability of conceiving a girl.
In the study 400 babies were born, and 340 of them were girls.
(a) Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of girls born = [tex]\frac{340}{400}[/tex] = 0.85
n = sample of babies = 400
p = population percentage of girls born
Here for constructing 99% confidence interval we have used One-sample z proportion statistics.
So, 99% confidence interval for the population proportion, p is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99
P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
99% confidence interval for p = [[tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]
= [ [tex]0.85-2.58 \times {\sqrt{\frac{0.85(1-0.85)}{400} } }[/tex] , [tex]0.85+2.58 \times {\sqrt{\frac{0.85(1-0.85)}{400} } }[/tex] ]
= [0.804 , 0.896]
Therefore, 99% confidence interval for the percentage of girls born is [0.804 , 0.896].
(b) Let p = population proportion of girls born.
So, Null Hypothesis, [tex]H_0[/tex] : p = 0.50 {means that the proportion of girls is equal to 0.50}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.50 {means that the proportion of girls is significantly different from 0.50}
The test statistics that will be used here is One-sample z proportion test statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of girls born = [tex]\frac{340}{400}[/tex] = 0.85
n = sample of babies = 400
So, the test statistics = [tex]\frac{0.85-0.50}{\sqrt{\frac{0.85(1-0.85)}{400} } }[/tex]
= 19.604
Now, at 0.01 significance level, the z table gives critical value of 2.3263 for right tailed test. Since our test statistics is way more than the critical value of z as 19.604 > 2.3263, so we have sufficient evidence to reject our null hypothesis due to which we reject our null hypothesis.
Therefore, we conclude that the proportion of girls is significantly different from 0.50.
To construct a 99% confidence interval for the percentage of girls born, calculate the sample proportion and use it to construct the confidence interval. The method appears to be effective.
Explanation:To construct a 99% confidence interval for the percentage of girls born, we first need to calculate the sample proportion. In this case, the sample proportion of girls is 340/400 = 0.85. Using this proportion, we can construct the confidence interval using the formula.
Confidence Interval = sample proportion ± z x √((sample proportion x (1 - sample proportion)) / sample size). Calculating the confidence interval, we find that it is 0.808 to 0.892. Since this interval does not include the value of 0.5, the method appears to be effective.
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ILL GIVE YOU BRAINLIST !! *have to get it right ! *
Find the slope of the line represented in the table.
Answer:
2/3
Step-by-step explanation:
To find the slope take the difference of the y's over the difference of the x's
(8-6)/ (12-9)
2/3
Three points of a function are graphed.
Which statement describes the function through the points?
The function is a direct variation function with a constant
of variation of 1.5.
The function is a direct variation function with a constant
of variation of 1.8.
The function is linear but is not a direct variation
function.
The function is not a linear function,
. (18, 30)
. (14, 24)
• (10, 18)
4
8
12
16 20 24 28 32 36
x
Answer:
The answer is C.
Step-by-step explanation:
I just took the test on edg and got a 100
The function is linear but is not a direct variation.
What is Direct Variation?Direct variations are defined as the functions of the form y = kx, where k is a constant.
Here when y increases, x increases and if y decreases, x also decreases.
Given is a function that passes through three points (18, 30), (14, 24) and (10, 18).
If the function is linear, the the slope must be constant.
Slope = Change in y coordinates / Change in x coordinates
Consider (18, 30) and (14, 24).
Slope = (24 - 30) / (14 - 18) = -6 / -4 = 3/2
Consider (14, 24) and (10, 18).
Slope = (18 - 24) / (10 - 14) = 3/2
Since slope is constant, function is linear.
Let y = mx + c be the equation of the function, where m is the slope and c is the y intercept.
If the function is direct variation, c = 0.
Substitute (10, 18) in to the equation.
18 = (3/2 × 10) + c
⇒ c = 3
It is not direct variation.
Hence the function is linear but is not a direct variation.
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At a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean serve speed of a particular player was 101 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was bell shaped. What proportion of the player's serves are expected to be between 116 mph and 146 mph? Round to four decimal places.
Answer:
0.1574 = 15.74% of the player's serves are expected to be between 116 mph and 146 mph
Step-by-step explanation:
Problems of normally distributed(bell-shaped) samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 101, \sigma = 15[/tex]
What proportion of the player's serves are expected to be between 116 mph and 146 mph?
This is the pvalue of Z when X = 146 subtracted by the pvalue of Z when X = 116. So
X = 146
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{146 - 101}{15}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a pvalue of 0.9987
X = 116
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{116 - 101}{15}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.9987 - 0.8413 = 0.1574
0.1574 = 15.74% of the player's serves are expected to be between 116 mph and 146 mph
To find the proportion of the player's serves between 116 mph and 146 mph, calculate the z-scores and use a z-table.
Explanation:To find the proportion of the player's serves between 116 mph and 146 mph, we need to calculate the z-scores for these values and then use a z-table.
The formula for calculating the z-score is z = (x - mean) / standard deviation. So, for 116 mph: z = (116 - 101) / 15 = 1; and for 146 mph: z = (146 - 101) / 15 = 3.
The z-score of 1 corresponds to a cumulative proportion of 0.8413 and the z-score of 3 corresponds to a cumulative proportion of 0.9987. So, the proportion of serves between 116 mph and 146 mph is 0.9987 - 0.8413 = 0.1574, rounded to four decimal places.
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2 x + 5 = 10
what is x =?
Answer:
x=[tex]\frac{5}{2}[/tex]
Step-by-step explanation:
First, subtract 5 on both sides since when you subtract 5 from 5, it will give you 0.
Basically we are trying to get rid of the +5.
2x+5-5=10-5
2x=5
Divide by 2 to get rid of the 2 that is combined with the x.
2x/2=5/2
x=[tex]\frac{5}{2}[/tex]
Answer:x=5/2
Step-by-step explanation:
2x+5=10
Subtract 5 from both sides
2x+5-5=10-5
2x=5
Divide both sides by 2
2x/2=5/2
x=5/2
A circle has it's radius as 3.7 inches. What is the area, in square inches, of the circle? *
Answer:
A =42.9866 in^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
The radius is 3.7
A = pi (3.7)^2
Approximating pi by 3.14
A = 3.14 (3.7)^2
A =42.9866
Answer:
The area, in square inches, of the circle is 43.01.
You have two jobs. One job pays nine dollars per hour and the other job pays $7.50 per hour. You worked 18 hours last week and earned $145.50. How many hours did you work at each job?
Answer:
[tex] Y =\frac{16.5}{1.5}= 11[/tex]
[tex] X = 18-11=7[/tex]
And then we conclude that for the first job he works 7 hours and for the second job 11 hours
Step-by-step explanation:
We can define the following notation:
[tex]X[/tex] represent the number of hours worked for one job
[tex]Y[/tex] represent the number of hours worked for the other job
[tex]p_x = 9[/tex] represent the hourly payment for the first job
[tex]p_y = 7.50[/tex] represent the hourly payment for the other job
And we can define the following equations:
[tex] X+ Y= 18[/tex] (1) represent the toal number of hours worked
[tex] 9X +7.5 Y = 145.50[/tex] (2) represent the total amount earned
From equation (1) if we solve for X we got:
[tex] X = 18-Y[/tex] (3)
Replacing equation (3) into equation (2) we got:
[tex] 9(18-Y) +7.5 Y =145.50[/tex]
And after solve the equation we can find the value of Y:
[tex] 162 -9Y +7.5 Y =145.50[/tex]
[tex]16.5 = 1.5 Y[/tex]
[tex] Y =\frac{16.5}{1.5}= 11[/tex]
And solving for X from equation (3) we got:
[tex] X = 18-11=7[/tex]
And then we conclude that for the first job he works 7 hours and for the second job 11 hours
When a number is decreased by 17% the result is 15 what is the original number to the nearest tenth
Answer:
The original number was 18.1.
Step-by-step explanation:
This question can be solved using a simple rule of three.
When a number is decreased by 17% the result is 15.
So 15 is 100-17 = 83%. The original number is 100%. Then
15 - 0.83
x - 1
[tex]0.83x = 15[/tex]
[tex]x = \frac{15}{0.83}[/tex]
[tex]x = 18.1[/tex]
The original number was 18.1.
Suppose that the function g is defined for all real numbers as follows
Answer:
-9
0
3
Step-by-step explanation:
-(-2-1)^2
-(1-1)^2
x>2 , so g(x) = 3
A trapezoid on a square. The square has side lengths of 12 feet. The trapezoid has a base of 6 feet, height of 3 feet, and top side length of 4 feet. Tariq is a swimming-pool designer. He is known for his irregular-shaped swimming pools. The bottom of this pool will be covered in tile. The area of the pool that is covered in tile is ft2.
Answer:
159
Step-by-step explanation:
Answer:
159
Step-by-step explanation:
0.80 (80 repeating) as a fraction
Answer:
80/99
Step-by-step explanation:
When the repeat starts at the decimal point, put the digits over an equal number of 9s.
[tex]0.\overline{80}=\boxed{\dfrac{80}{99}}[/tex]
This fraction cannot be reduced.
Final answer:
To convert the repeating decimal 0.80 (with 80 repeating) to a fraction, set up an equation where x equals the repeating decimal, then multiply by 10 and subtract the original equation to eliminate the repeating part, and solve for x to get 8/9.
Explanation:
The number 0.80 with 80 repeating is often represented as 0.8 with a line over the 8, indicating that the 8 is repeating indefinitely. To convert 0.80 repeating to a fraction, we can use the following method:
Let x equal the repeating decimal: x = 0.888...
Multiply both sides by a power of 10 to move the decimal point to the right of the repeating digits. Here, we multiply by 10: 10x = 8.888...
Subtract the original equation from this new equation to get rid of the repeating decimal: 10x - x = 8 (9x = 8).
Now solve for x: x = 8/9.
Thus, 0.80 with 80 repeating as a fraction is 8/9.
What is the discriminant of the quadratic equation 0 = -x -4x -2
Answer:
search on google
Step-by-step explanation:
As a salesperson, you are paid $52 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Answer:
s≥16
Step-by-step explanation:
3s+52≥100
3s≥100-52
3s≥48
s≥48/3
s≥16
The solution to the inequality is x ≥ 16.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Let x be the number of sales you need to make.
The total pay you receive will be $52 + $3x.
Since you want your pay to be at least $100, we can write the inequality:
52 + 3x ≥ 100
Solving for x, we get:
3x ≥ 48
x ≥ 16
Therefore,
The solution to the inequality is x ≥ 16.
This means that you need to make at least 16 sales to earn at least $100 this week.
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During a walk a thin Noah’s time in hours, t, and distance in miles, d, are related by the equation 1/3d = t. A graph of the equation includes the point (12, 4)
1. Identify the independent variable
2. What does the point (12, 4) represent in this situation
3. What point would represent the time it too to walk 7 1/2 miles
Answer:
Step-by-step explanation:
The independent variable is time (t), determining the distance covered.
The point (12, 4) means Noah walks for 12 hours, covering 4 miles.
To find time for 7[tex]\frac{1}{2}[/tex] miles, [tex]\frac{1}{3}d = t \),[/tex] Substitute 7.5 for d, yielding [tex]\( \frac{1}{3} 7.5 = t \) = 2.5 hour[/tex]. So, (2.5, 7.5) represents Noah taking 2.5 hours to walk 7[tex]\frac{1}{2}[/tex] miles.
1. **Identify the independent variable**:
In the equation [tex]\( \frac{1}{3}d = t \),[/tex] the independent variable is time (t). The independent variable is the one that stands alone and is not dependent on other variables. In this case, time (t) is independent as it determines the distance covered (d).
2. **What does the point (12, 4) represent in this situation**:
The point (12, 4) represents a specific instance in the relationship between time and distance. In this case, it means that when Noah walks for 12 hours, he covers a distance of 4 miles. This point is a solution to the equation [tex]\( \frac{1}{3}d = t \),[/tex] where 12 hours corresponds to the time (t) and 4 miles corresponds to the distance (d).
3. **What point would represent the time it took to walk 7 1/2 miles**:
To find the point representing the time it takes to walk 7 1/2 miles, we substitute 7.5 miles into the equation and solve for time (t). First, we rewrite the equation without fractions to make the calculation simpler:
[tex]\[ \frac{1}{3}d = t \][/tex]
[tex]\[ \frac{1}{3} \times d = t \][/tex]
[tex]\[ \frac{1}{3} \times 7.5 = t \][/tex]
Now, we simply multiply 1/3 by 7.5:
[tex]\[ t = \frac{1}{3} \times 7.5 \][/tex]
[tex]\[ t = 2.5 \][/tex]
So, the time it takes to walk 7[tex]\frac{1}{2}[/tex] miles is 2.5 hours. Therefore, the point representing this situation is (2.5, 7.5), indicating Noah takes 2.5 hours to walk 7.5 miles. This point satisfies the equation [tex]\( \frac{1}{3}d = t \)[/tex], where 2.5 hours corresponds to the time (t) and 7.5 miles corresponds to the distance (d).
In summary, the independent variable in this situation is time (t), the point (12, 4) represents Noah walking for 12 hours and covering 4 miles, and the point (2.5, 7.5) represents Noah taking 2.5 hours to walk 7[tex]\frac{1}{2}[/tex] miles.
What is the growth or decay and the percentage rate of Y=23(0.292)^x
Answer:
So the decay percentage rate is of 70.8%
Step-by-step explanation:
An exponentil function has the following format:
[tex]y = ca^{x}[/tex]
In which c is a constant.
If a>1, we have that a = 1 + r and r is the growth rate.
If a<1, we have that a = 1 - r and r is the decay rate.
In this problem:
a = 0.292
A is lesser than 1, so r is the decay rate.
1 - r = 0.292
r = 1 - 0.292
r = 0.708
So the decay percentage rate is of 70.8%
Simplify 64 x 3 y 3 z 2 24 x y 4 z 4
Answer:
88x+4y+7z+6
Step-by-step explanation:
depends on how u write it take a pic next time please
Put the fraction in order from least to greatest 1/8, 1/3, 1/6
Answer:
You have to make them equal first. Start with that.
1/8 --> 3/24
1/6 ---> 4/24
1/3 --> 8/24
Now, order them.
1/8, 1/6. 1,3
-11+___=15 i think it’s -26 but I don’t know.
answer is POSITIVE 26,
Step-by-step explanation:
because when you add positive 11 to get zero, you just need to add positive 15 to get POSITIVE 15
What is the length of segment TV?
Answer:
38 units
Step-by-step explanation:
VS = TS
39 = 6x – 3
39 + 3 = 6x
42 = 6x
X = 7
TV = 2(VR)
TV = 2 ( 2(7) + 5)
TV = 38 units
Brainiest please?
What is one tenth of 75
Answer:
the answer is 7.5. hope this helps
Answer:
7.5
Step-by-step explanation:
x ^2 +y ^2 −4x+12y−24=0 What is the center of this circle ?
(2, -6) is the center of the circle.
To find the center of the circle, we need to rewrite the given equation in standard form:
[tex]x^2 - 4x + y^2 + 12y = 24[/tex]
We can complete the square to put it into the standard form:
[tex]x^2 - 4x + 4 + y^2 + 12y + 36 = 24 + 4 + 36\\\\(x - 2)^2 + (y + 6)^2 = 64[/tex]
Now we can see that the center of the circle is (2, -6).
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The center of the circle represented by the equation x^2 + y^2 −4x +12y−24=0 is (2, -6), which is determined by completing the square for both x and y terms.
To determine the center of a circle given by the equation x^2 + y^2 −4x +12y−24=0, we need to complete the square for both the x and y terms.
Step 1: Rearrange the equation by grouping x terms and y terms together: x^2 −4x + y^2 +12y = 24.
Step 2: Complete the square for the x terms and y terms: (x^2 −4x + 4) + (y^2 +12y + 36) = 24 + 4 + 36.
Step 3: Simplify the equation: (x − 2)^2 + (y + 6)^2 = 64.
Step 4: In the standard form of a circle equation, (x − h)^2 + (y − k)^2 = r^2, the center is at (h, k). Therefore, the center of the given circle is (2, -6).
What is the rate of change of the following function?
Answer:
You did not provide any function...therefore, i cant give you a proper answer.
Step-by-step explanation:
The recycling bin in the shape of a rectangular prism is 15.5 inches long, 8 inches wide and 7 inches high. The recycling bins need to be emptied when it is 80% full. What is the total amount needed, to the nearest cubic inch, before the recycle bin is ready to empty?
Answer:
694 cubic inches
Step-by-step explanation:
Dimension of prism
Length = 15.5 inches
width = 8 inches
height = 7 inches
Volume of regular prism is given by area of base * height
area of base = length * width ( as bin is rectangular)
area of base = 15.5 * 8 square inches = 124 square inches
Volume of regular prism = area of base * height
= 124 * 7 cubic inches = 868 cubic inches
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868 cubic inches is the full capacity of the recycling bin
it is given that recycling bins need to be emptied when it is 80% full
so we need to find the 80% capacity of recycling bin
80% capacity of recycling bin = 80/100 * full capacity of the recycling bin
= 0.8 * 868 cubic inches = 694.4 cubic inches
694.4 cubic inches is the amount needed before the recycle bin is ready to empty .
But question says answer should in nearest cubic inch
hence answer is 694 cubic inches
There are 20 flowers. I have 10 how many are there
Answer: 10
Step-by-step explanation: because you subtract it by 10
20-10= 10