Answer:
The value of angle α is 18 degree.
Step-by-step explanation:
Given information: Angles α and β are the two acute angles , α < β.
Given equation is
[tex]\sin (2x-8)=\cos (6x-6)[/tex]
[tex]\cos (90-(2x-8))=\cos (6x-6)[/tex] [tex][\because \sin (90-x)=\cos x][/tex]
Equating both sides.
[tex]90-2x+8=6x-6[/tex]
[tex]98+6=6x+2x[/tex]
[tex]104=8x[/tex]
[tex]13=x[/tex]
The value of x is 13.
The measure of angles is
[tex]2x-8=2(13)-8=18[/tex]
[tex]6x-6=6(13)-6=72[/tex]
Since 18<72, therefore the value of angle α is 18 degree.
Answer:
A
Step-by-step explanation:
Factor 2x2 - 11x - 21.
A) (2x + 3)(x - 7)
Eliminate
B) (x + 3)(2x - 7)
C) (2x - 3)(x + 7)
D) (2x + 7)(x - 3)
Find the lateral area for the regular pyramid.
L. A. =
Every year, 50 million flea collars are thrown away. How many flea collars are thrown away per day, rounded to the nearest thousand
Mrs. Jones Algebra 2 class scored very well on yesterday's quiz. With one exception, everyone received an A. Within how many standard deviations from the mean do all the quiz grades fall?
91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97
A. 1
B. 2
C. 4
D. 3
Given that the values in the table represent the graph of a continuous function, y has at least how many zeros? HELLLLP!!!!!!!!!
Adriana's water bottle contains 2 quarts of water she wants to add a drink to mix into it but the directions for the treatments gives a amount of water fluid ounces how many fluid ounces are in her bottle
Someone please help me?
Which expressions are equivalent to the one below? Check all that apply.
16^x/4^x
A. 16^x
B. (16-4)^x
C. 4^x * 4^x/ 4^x
D. (16/4)^x
E. 4^x
F. 4
There are 25 counters is a bag 6 red, 4 white, 7 blue, and 8 yellow. you choose one counter at random. which color you least likely to choose
By calculating the probability of choosing a counter at random, we find that we are least likely to choose a white counter as it has the least probability.
What is probability?Probability is simply how likely something is to happen.
Probability of choosing a red counter = 6/25 = 0.24
Probability of choosing a white counter = 4/25 = 0.16
Probability of choosing a blue counter = 7/25 = 0.28
Probability of choosing a yellow counter = 8/25 = 0.32
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2. The height of one square pyramid is 24 m. A similar pyramid has a height of 8 m. The volume of the larger pyramid is 648 m3. The surface area of the smaller pyramid is 124 m^2. Determine each of the following, showing all your work and reasoning: find the surface area of the larger pyramid
Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
Factor this expression.
3x2 – 6x
A. 3(x – 2)
B. 3(x2 – 2)
C. 3x(x2 – 2)
D. 3x(x – 2)
Answer:
D.3x(x-2)
Step-by-step explanation:
i already did this
A climber is standing at the top of mount kazbek, approximately 3.1 miles above sea level. the radius of the earth is 3959 miles. what is the climber's distance to the horizon? enter your answer as a decimal in the box. round only your final answer to the nearest tenth. mi
The nearest tenth, the climber's distance to the horizon is approximately 156.6 miles.
The climber's distance to the horizon can be calculated using the Pythagorean theorem, where the Earth's radius and the climber's height above sea level form a right-angled triangle.
[tex]\[ d^2 + R^2 = (R + h)^2 \][/tex]
Expanding the right side of the equation gives us:
[tex]\[ d^2 + R^2 = R^2 + 2Rh + h^2 \][/tex]
Subtracting [tex]\( R^2 \)[/tex] from both sides, we get:
[tex]\[ d^2 = 2Rh + h^2 \][/tex]
Since [tex]\( h^2 \)[/tex] is very small compared to [tex]\( 2Rh \)[/tex] (because [tex]\( h \)[/tex] is much smaller than [tex]\( R \))[/tex], we can neglect [tex]\( R^2 \)[/tex] in our calculation for a more practical approximation. This leaves us with:
[tex]\[ d^2 \approx 2Rh \][/tex]
Taking the square root of both sides to solve for [tex]\( d \)[/tex], we have:
[tex]\[ d \approx \sqrt{2Rh} \][/tex]
Now, plugging in the values for [tex]\( R \) and \( h \):[/tex]
[tex]\[ d \approx \sqrt{2 \times 3959 \times 3.1} \][/tex]
[tex]\[ d \approx \sqrt{2 \times 3959 \times 3.1} \][/tex]
[tex]\[ d \approx \sqrt{24516.8} \][/tex]
[tex]\[ d \approx 156.6 \text{ miles} \][/tex]
Rounding to the nearest tenth, the climber's distance to the horizon is approximately 156.6 miles.
Karl and his dad are building a playhouse for karl's younger sister. the floor of the playhouse will be a rectangle that is 6 by 8 1/2 feet. how much carpeting do karl and his dad need to cover the floor.
The playhouse floor is a rectangle with dimensions of 6 by 8.5 feet. To determine the amount of carpet needed, multiply the length and width to calculate the area, which is 51 square feet.
Karl and his dad need to know the amount of carpeting required to cover the floor of a playhouse, which is a practical mathematics problem involving area calculation. To find out how much carpet they need, they have to calculate the area of the rectangular floor, which is the product of its length and width.
The floor measures 6 feet in length and 8.5 feet in width. Multiplying these two dimensions gives us the area:
Area = Length times Width
Area = 6 ft times 8.5 ft
Area = 51 square feet
Therefore, Karl and his dad would need to purchase 51 square feet of carpeting to cover the playhouse floor.
A jar contains 133 pennies.A bigger jar contains 1 2/7 times as many.What is the value of the pennies in the bigger jar?
Factor 1/2 out of 1/2z+9
1/2(z+18) is the expression of 1/2z+9 when 1/2 is factored out.
What is Fraction?A fraction represents a part of a whole.
Given,
The expression is 1/2 z+9
A factor is a number that divides another number, leaving no remainder.
The given expression is one by two times of z plus nine.
1/2 z+9
Now we need to take 1/2 as common from the expression
1/2(z+18)
Hence, 1/2(z+18) is the expression of 1/2z+9 when 1/2 is factored out.
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Can someone help me solve 2√x−4=10 I'm confused.
a quarterback for the seattle seahawks completes 54% of his passes. let the random variablle x be the number of passes completed in 20 attempts. conduct a stimulation of the 20 attempts using the following random digits. be sure to state how your assign your didgits
a) What proportions of passes were completed?
b) How does this compare with what “should have happened” theoretically?"
First, take 100 numbers, i.e. from 00 to 99, and set that the first 54% are completed passes, therefore from 00 to 53, and the remaining 46% are not completed passes, therefore from 54 to 99.
Now, divide the random digits until you compose 20 numbers: 98, 72, 61, 09, 83, 56, 23, 94, 20, 42, 76, 52, 06, 82, 76, 58, 23, 94, 87, 29.
Then, divide the numbers into the two set categories:
completed: 09, 23, 20, 42, 52, 06, 23, 94, 87 = 9 outcomes
not completed: 98, 72, 61, 83, 56, 94, 76, 82, 76, 58, 29 = 11 outcomes
A) Therefore, from the random digits you get 9/20 = 45% of completed passes and 11/20 = 55% of not completed passes.
B) Using the random digits, the simulation gave an outcome exactly opposite to what we expected.
Find the fifth term of the arithmetic sequence in which
t1 = 3 and tn = tn-1 + 4.
A) 5
B) 7
C) 19
D) 23
n a study of 250 adults, the mean heart rate was 70 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 12 beats per minute. What is the 99% confidence interval for the mean beats per minute?
A sample of 16 from a population produced a mean of 85.4 and a standard deviation of 14.8. a sample of 18 from another population produced a mean of 74.9 and a standard deviation of 16.0. assume that the two populations are normally distributed and the standard deviations of the two populations are equal. the null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is different than the mean of the second population. the significance level is 1%.
Solution: The test statistic under the null hypothesis is:
[tex]t=\frac{\bar{x_{1}}-\bar{x_{2}}}{s_{p}\sqrt{(\frac{1}{n_{1}})+(\frac{1}{n_{2}})}}[/tex]
Where:
[tex]s_{p} = \sqrt{\frac{(n_{1}-1)s^{2}_{1}+(n_{2}-1)s^{2}_{2}}{n_{1}+n_{2}-2} }[/tex]
[tex]s_{p} = \sqrt{\frac{(16-1)14.8^{2}+(18-1)16^{2}}{16+18-2} }[/tex]
[tex]=15.45[/tex]
[tex]\therefore t=\frac{85.4-74.9}{15.45\sqrt{(\frac{1}{16})+(\frac{1}{18})}}[/tex]
[tex]=\frac{10.5}{5.31}[/tex]
[tex]=1.98[/tex]
Now, to find the critical values, we need to use the t distribution table at 0.01 significance level for [tex]df=n_{1} + n_{2} -2 = 16+18-2=32[/tex] and is given below:
[tex]t_{critical}=-2.738,2.738[/tex]
Since the t statistic is less than the t critical value, we therefore fail to reject the null hypothesis and conclude that the two population means are equal.
What are the x intercepts of this function f(x) =2x^2-7x-4?
. (06.02)
The table below shows data for a class's mid-term and final exams:
Mid-Term Final
96 100
95 85
92 85
90 83
87 83
86 82
82 81
81 78
80 78
78 78
73 75
Which data set has the smallest IQR? (1 point)
They have the same IQR
Mid-term exams
Final exams
There is not enough information
2. (06.02)
The box plots below show student grades on the most recent exam compared to overall grades in the class:
two box plots shown. The top one is labeled Class. Minimum at 74, Q1 at 78, median at 85, Q3 at 93, maximum at 98. The bottom b
Which of the following best describes the information about the medians? (1 point)
The exam median is only 1–2 points higher than the class median.
The exam median is much higher than the class median.
The additional scores in the second quartile for the exam data make the median higher.
The narrower range for the exam data causes the median to be higher.
3. (06.02)
The box plots below show attendance at a local movie theater and high school basketball games:
two box plots shown. The top one is labeled Movies. Minimum at 60, Q1 at 65, median at 95, Q3 at 125, maximum at 150. The botto
Which of the following best describes how to measure the spread of the data? (1 point)
The IQR is a better measure of spread for movies than it is for basketball games.
The standard deviation is a better measure of spread for movies than it is for basketball games.
The IQR is the best measurement of spread for games and movies.
The standard deviation is the best measurement of spread for games and movies.
4. (06.02)
The box plots below show the average daily temperatures in April and October for a U.S. city:
two box plots shown. The top one is labeled April. Minimum at 50, Q1 at 60, median at 67, Q3 at 71, maximum at 75. The bottom b
What can you tell about the means for these two months? (1 point)
The mean for April is higher than October's mean.
There is no way of telling what the means are.
The low median for October pulls its mean below April's mean.
The high range for October pulls its mean above April's mean.
5. (06.02)
The table below shows data from a survey about the amount of time high school students spent reading and the amount of time spent watching videos each week (without reading):
Reading Video
5 1
5 4
7 7
7 10
7 12
12 15
12 15
12 18
14 21
15 26
Which response best describes outliers in these data sets? (2 points)
Neither data set has suspected outliers.
The range of data is too small to identify outliers.
Video has a suspected outlier in the 26-hour value.
Due to the narrow range of reading compared to video, the video values of 18, 21, and 26 are all possible outliers.
6. (06.02)
Male and female high school students reported how many hours they worked each week in summer jobs. The data is represented in the following box plots:
two box plots shown. The top one is labeled Males. Minimum at 0, Q1 at 1, median at 20, Q3 at 25, maximum at 50. The bottom box
Identify any values of data that might affect the statistical measures of spread and center. (2 points)
The females worked less than the males, and the female median is close to Q1.
There is a high data value that causes the data set to be asymmetrical for the males.
There are significant outliers at the high ends of both the males and the females.
Both graphs have the required quartiles.
7. (06.02)
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:
High Low Q1 Q3 IQR Median Mean σ
College 50 6 8.5 17 8.5 12 15.4 11.7
High School 28 3 4.5 15 10.5 11 10.5 5.8
Which of the choices below best describes how to measure the spread of this data? (2 points)
Both spreads are best described with the IQR.
Both spreads are best described with the standard deviation.
The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
1. The dataset with the smallest IQR is the Mid-term exams. 2. The exam median is only 1–2 points higher than the class median. 3. The standard deviation is the best measurement of spread for games and movies.
Explanation:1. The dataset with the smallest IQR is the Mid-term exams. To find the IQR, first, calculate the first quartile (Q1) and the third quartile (Q3). Then, find the difference between Q3 and Q1. By comparing the IQR values for the Mid-term and Final exams, it can be determined that the Mid-term exams have the smallest IQR.
2. The exam median is only 1–2 points higher than the class median. The box plot's median represents the middle value of the dataset. By comparing the medians of the exam and class data, it can be determined that the exam median is only 1–2 points higher than the class median.
3. The standard deviation is the best measurement of spread for games and movies. While the IQR can measure spread, the standard deviation is a more precise measurement. Comparing the spread of the data, the standard deviation is the best measurement for both games and movies.
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Various statistical measures such as IQR, Standard Deviation, Median and Mean were used to interpret the given data in numerous scenarios. Outliers were identified and impacts on datasets were evaluated.
Explanation:To answer these questions, we need to understand few key statistical terms: 'Mean' is the simple average of data, 'Median' is the middle score of data, 'IQR' (Inter Quartile Range) is the difference between the upper quartile (Q3) and the lower quartile (Q1), which helps in understanding the spread and '.'Standard Deviation' measures the absolute variability of a dataset.
Question 1: IQR for the mid-term exams is Q3 (92) - Q1 (82) = 10. IQR for the final exams is Q3 (85) - Q1 (78) = 7. So, the final exams have the smallest IQR.
Question 2: The boxes showing median indicates that the exam median is only 1–2 points higher than the class median.
Question 3: Since the spread of the data at basketball games and local movie theaters demonstrates varied distributions, both the IQR and the standard deviation should be used to evaluate the data spread.
Question 4: Box plots do not provide direct information on the mean. So, there is no way of telling what the means are.
Question 5: For the video hours, we see that values 18, 21, and 26 lie far from the main part of the data, thus they can be considered as possible outliers.
Question 6: The male data set shows a high data value, which causes the data set to be asymmetrical. This could affect statistical measures like the mean and standard deviation.
Question 7: The spread of the college data, having a large standard deviation and IQR, is best described by the standard deviation. The high school data, with smaller numbers, is best described by the IQR.
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A tank holds 1,000 gallons of syrup. Danielle filled 65 5-gallon cans with syrup. How much syrup was left in the tank when she finished? 3. Draw a picture or a chart that shows the information and the question.
675 gallons
935 gallons
325 gallons
350 gallons
Answer:
the answer is 675
Step-by-step explanation:
1. there is a tank with 1000 gallons, and we have 65 cans with a capacity of 5 gallons, so if we multiply the 65 cans with the capacity we would have as result
65 x 5 = 325
2- already having the value of gallons used (325) we can subtract this difference to the 1000 gallons that were in the tank at first.
1000 - 325 = 675
A soccer league has 170 players. Of those players 60% are boys. How many boys are in the soccer league
The domain of f(x)=2logx+3 is x > 3.
true.
false.
The length of a rectangle is four times its width. if the width is 15, what is the area?
Please help! Math question
What is the gcf of 3x^2 and 7y
Need help with these 2 questions please and thanks