To convert the score of 14 to a z-score, we use the formula:
z = (x - μ) / σ
where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Substituting the given values, we get:
z = (14 - 20) / 2.8
z = -2.14
The z-score of -2.14 indicates that the score of 14 is quite far from the mean of 20, which makes it an unusual score. To determine how unusual it is, we can compare the z-score to the standard normal distribution table.
The table shows that a z-score of -2.14 corresponds to a probability of approximately 0.016. This means that only about 1.6% of contestants would receive a score of 14 or lower in this cooking contest. Therefore, we can conclude that the score of 14 is unusual.
Which data set could be used to create the box plot below
the correct answers are:=4, 11, 8, 12, 1, 6, 14 and 14, 10, 6, 9, 11, 8, 1 for the given data
How to solve the data
The box plot represents the distribution of a dataset using quartiles, median, and outliers. In order to create a box plot, we need to have a dataset with numerical values. Based on the options given, the data sets that can be used to create the box plot are:
4, 11, 8, 12, 1, 6, 14: This data set has all the required numerical values to create a box plot. It contains 7 values which are within the range of values shown on the x-axis of the box plot.
14, 10, 6, 9, 11, 8, 1: This data set also contains all the required numerical values to create a box plot. It has 7 values which are within the range of values shown on the x-axis of the box plot.
The remaining data sets listed are either non-numerical or do not contain values within the range shown on the x-axis. Therefore, they cannot be used to create the box plot.
In summary, the correct answers are:
4, 11, 8, 12, 1, 6, 14
14, 10, 6, 9, 11, 8, 1
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A. 0.2
B. 0.6
C. 0.15
D. 0.65
The probability of the two events, A and B, is given as follows:
C. P(A and B) = 0.15.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the result of a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of the event B happening, given that the event A happened.[tex]P(A \cap B)[/tex] is the probability of both the events A and B happening.P(A) is the probability of the event A happening.The parameters for this problem are given as follows:
P(A|B) = 0.25, P(B) = 0.6.
Hence the probability of the two events is given as follows:
P(A and B) = P(A|B) x P(B)
P(A and B) = 0.6 x 0.25
P(A and B) = 0.15.
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NEED STEP BY STEP ASAP DUE AT 9:00
The equation of the given circle is expressed as: x² + y² - 24x + 14y + 112 = 0
How to find the equation of a circle?The standard form of expression for the equation of a circle is expressed as:
(x - h)² + (y - k)² = r²
where:
(h, k) are coordinates of the center of the circle
r is radius
We are given the parameters:
Coordinates of center = (12, -7)
Diameter = 18
Radius = 18/2 = 9
Thus, equation of circle is:
(x - 12)² + (y - (-7))² = 9²
x² - 24x + 144 + y² + 14y + 49 = 81
x² + y² - 24x + 14y + 112 = 0
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Which expression is equivalent to 9t+4t?
9t + 4t can be simplified by combining the like terms (terms with the same variable and exponent). The coefficients of the two terms (9 and 4) are added to get the coefficient of the simplified term:
9t + 4t = (9 + 4)t = 13t
Therefore, the expression that is equivalent to 9t + 4t is 13t.
A scale drawing of a bedroom is shown below. The scale is 1 : 30. A rectangle is shown. The length of the rectangle is labeled 3 inches. The width of the rectangle is labeled 4 inches. Show your work to determine the area of the room in square feet.
The scale is 1 : 30. A rectangle is shown. The length of the rectangle is labeled 3 inches. The width of the rectangle is labeled 4 inches. Show your work to determine the area of the room in square feet.First, we need to convert the measurements of the rectangle from inches to feet, since the question asks for the area in square feet. 3 inches = 3/12 feet = 0.25 feet 4 inches = 4/12 feet = 0.33 feet Now, we can use the scale to determine the actual dimensions of the room. If 1 inch on the drawing represents 30 inches in real life, then: 1 foot on the drawing represents 30 feet in real life So, the length of the room is: 1 foot on the drawing = 30 feet in real life 3 inches on the drawing = 3/12 feet = 0.25 feet in real life 0.25 feet x 30 = 7.5 feet And the width of the room is: 1 foot on the drawing =
Select the action you would use to solve x-4=16. The select the property that just justifies that action
how many integers between 100 and 999, inclusive, have the property that some permutation of its digits is a multiple of 11 between 100 and 999? for example, both 121 and 211 have this property. (2017amc10a problem 25) (a) 226 (b) 243 (c) 270 (d) 469 (e)
226 integers are present between 100 and 999, inclusive, and have the property that some permutation of its digits is a multiple of 11 between 100 and 999. Hence, option A is the correct option.
The problem statement is to find the number of multiples of 11 between 100 and 999 inclusive, where some multiples may have digits repeated twice and some may not.
To solve this problem, we can first count the number of multiples of 11 between 100 and 999 inclusive, which is 81. Some of these multiples may have digits repeated twice, and each of these can be arranged in 3 permutations. Other multiples of 11 have no repeated digits, and each of these can be arranged in 6 permutations. However, we must account for the fact that switching the hundreds and units digits of these multiples also yields a multiple of 11, so we must divide by 2, giving us 3 permutations for each of these multiples.
Thus, we have a total of 81 × 3 = 243 permutations. However, we have overcounted because some multiples of 11 have 0 as a digit. Since 0 cannot be the digit of the hundreds place, we must subtract a permutation for each of these multiples. There are 9 such multiples (110, 220, 330, ..., 990), yielding 9 extra permutations. Additionally, there are 8 multiples (209, 308, 407, ..., 902) that also have 0 as a digit, yielding 8 more permutations.
Therefore, we must subtract these 17 extra permutations from the total of 243, giving us 226 permutations in total. Hence, option A is the correct option.
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(normal approximation) samples of size 49 are selected from a population with mean 40 and standard deviation 7.5. the standard error of the sampling distribution of sample means is
Samples of size 49 are selected from a population with mean 40 and standard deviation 7.5. the standard error of the sampling distribution of sample means is B. 1.07
The standard error of the sampling distribution of sample means can be calculated using the formula:
Standard Error (SE) = (Standard Deviation of the Population) / sqrt(Sample Size)
In this case, the population mean (μ) is 40, the standard deviation (σ) is 7.5, and the sample size (n) is 49.
To find the standard error, plug the values into the formula:
SE = 7.5 / sqrt(49)
SE = 7.5 / 7
SE = 1.07
Therefore, the standard error of the sampling distribution of sample means is 1.07 (Option B).
The Question was Incomplete, Find the full content below :
(normal approximation) samples of size 49 are selected from a population with mean 40 and standard deviation 7.5. the standard error of the sampling distribution of sample means is
A. 0.30
B. 1.07
C. 7.50
D. 0.82
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Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $350 and $450
Answer:
34.1%.
Step-by-step explanation:
Given: Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50.
This problem tells us that the distribution of weekly wages at the factory is normally shaped.
68.2% of wages fall within the standard deviation of the mean.
Since the mean is $400, this means that 68.2% of wages fall between $400 +/- $50, or between $350-$450.
Instead, we are interested in the probability of a wage being between $350-$400.
Said differently, this is between the mean ($400) and one standard deviation below the mean ($350).
The fact that the wages are normally distributed also means that the shape of the distribution is symmetrical above and below the mean.
So the probability of wages being between $350-$400 is half of 68.2%, or 34.1%.
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the following table is based off a survey of employment from 2018. what is the p-value for testing if the proportion who are unemployed differs between the two groups? give your answer to three decimal places.
The p-value for testing if the proportion who are unemployed differs between the two groups is 0.
To calculate the p-value for testing if the proportion who are unemployed differs between the two groups, we can use a two-sample test of proportions
Let's define
Group 1: High School or Some College
Group 2: Bachelor's or Higher
We want to test if the proportion of unemployed individuals differs between Group 1 and Group 2.
First, we need to calculate the proportion of unemployed individuals in each group
Group 1: 41/601 = 0.06822
Group 2: 14/875 = 0.016
Next, we need to calculate the pooled proportion
Pooled proportion = (41 + 14) / (601 + 875) = 0.043
Now we can calculate the test statistic
Test statistic = (0.06822 - 0.016) / sqrt(0.043 × (1 - 0.043) × (1/601 + 1/875)) = 7.57
Using a two-tailed test with a significance level of 0.05, we can find the critical value from a normal distribution table or calculator. For a two-tailed test with a significance level of 0.05, the critical value is approximately 1.96.
Since the test statistic (7.57) is greater than the critical value (1.96), we reject the null hypothesis that the proportion of unemployed individuals is the same in both groups.
Finally, we can calculate the p-value as the probability of getting a test statistic as extreme or more extreme than the one we observed, assuming the null hypothesis is true. Since this is a two-tailed test, we need to double the area to the right of the test statistic (7.57) under the standard normal curve
p-value = 2 × P(Z > 7.57) = 0
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The given question is incomplete, the complete question is:
The following table is based off a survey of employment from 2018. What is the p- value for testing if the proportion who are unemployed differs between the two groups? Give your answer to three decimal places. Total Unemployed 41 Employed 834 875 High School or Some College Bachelor's or Higher Total 14 587 601 55 1421 1476
3. How many square feet of flooring are needed to
cover the entire floor of Bedroom 1?
Bedroom 1
Scale: 1in. = 4 ft
The gridlines are spaced 1 inch apart.
Answer: The bedroom is 8 gridlines by 10 gridlines.
Step-by-step explanation:
The area of the bedroom is 8 x 10 gridlines, or 80 square gridlines.
Multiply this by 4 to get the number of square feet needed to cover the entire floor of Bedroom 1:
80 x 4 = 320 square feet
when conducting a simple main effects analysis, which of the following is true? select one: you use the ms between value from the original two-factor anova you use the ms within value from the original two-factor anova you use the ms between value from the statistically significant interaction effect you use the ms error value from the original two-factor anova
The true answer for the statement 'When conducting a simple main effects analysis is given by you use the MS within value from the original two-factor ANOVA.
Simple main effects analysis involves,
Examining the effect of one independent variable at each level of the other independent variable.
It allows us to determine the significance of the effect of one independent variable at each level of the other independent variable.
To compute the simple main effects,
We use the residual variability from the original two-factor ANOVA, which is the MS within value.
This is because the variability between the levels of the other independent variable has already been accounted for by the original two-factor ANOVA.
It is required to look only at the variability within each level of the other independent variable.
To determine the significance of the effect of the independent variable of interest.
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5y > 30 slove each inequality
Answer:
y>6
Step-by-step explanation:
5y>30
y>6
therefore, y can be any number that is larger than 6 (e.g. 7, 10 etc)
Max says entire workout consists of 10 minutes of warm up exercises, 25 minutes of Lifting weights, and 15 minutes on the treadmill. What was the ratio of the number of minutes he lifted weights to the total number of minutes of his entire work out?
A) 1:1
B) 1:2
C) 3:10
D) 5:8
the ratio of the number of minutes he lifted weights to the total number of minutes of his entire workout is 1:2 option B is correct.
Ratios can be written in three forms:
A to B
A:B
A/B
Ratios are also simplified by reducing to lowest terms like fractions are.
This problem's ratio is:
minutes lifted weights to total minutes workout
The number of minutes lifting weights is in the question: 25.
To find the total minutes of his workout, add the number of minutes he spent for all of the activities:
Total minutes = warm-up + lifting weights + treadmill
Total minutes = 10 + 25 + 15
Total minutes = 50
The ratio before simplifying is 25÷50.
This ratio can be reduced to lowest terms. Both sides are divisible by 25.
[tex]\frac{25}{25}=1[/tex]
[tex]\frac{50}{25} = 2[/tex]
The ratio in the lowest terms is 1/2.
It can also be written as 1 to 2 or 1:2.
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11. The path of a pirate ship adventure ride at a theme park follows the shape of a parabola. The ship swings back and forth, accelerating to the base and then upwards. The height of a rider above ground level, h m, can be modelled by the equation h = 1.2x² - 12x + 30, where x is the horizontal distance of the rider from where the ride begins. (i) On a sheet of graph paper, using a scale of 2 cm to represent 1 m on the x-axis and 4 cm to represent 10 m on the h-axis, draw the graph of h = 1.2x² 12x + 30 for 0≤x≤ 10. (ii) Explain the meaning of the constant term 30 in - the equation. (iii) When a rider is 19.2 m above ground level, water is splashed on him. Find the horizontal distance a rider travels between the two splashes.
(i) The graph is attached below. (ii) the minimum value of the function is h = 30, when x = 5. (iii) the horizontal distance traveled by the rider between the two splashes is 2 × 9 m = 18 m.
Describe Acceleration?Acceleration is a physical quantity that measures the rate at which the velocity of an object changes over time. It is a vector quantity, meaning that it has both magnitude and direction.
Acceleration is defined as the change in velocity of an object divided by the time interval over which the change occurred. It is typically measured in meters per second squared (m/s²) in the metric system, or in feet per second squared (ft/s²) in the imperial system.
If the velocity of an object is increasing, its acceleration is said to be positive. If the velocity is decreasing, the acceleration is said to be negative or deceleration. If the velocity is constant, there is no acceleration.
(i) Using the given scale, we can plot the graph of h = 1.2x² - 12x + 30 for 0 ≤ x ≤ 10 as follows:
Parabolic graph is attached below.
(ii) The constant term 30 in the equation represents the minimum height of the pirate ship ride above ground level. This is because the equation is in the form of a quadratic function in standard form, y = ax² + bx + c, where the vertex of the parabola is at the point (-b/2a, c - b²/4a). In this case, the vertex is at (5, 0), which means that the minimum value of the function is h = 30, when x = 5.
(iii) We are given that a rider is 19.2 m above ground level, which means that h = 19.2. We can substitute this value into the equation and solve for x:
19.2 = 1.2x² - 12x + 30
1.2x² - 12x + 10.8 = 0
x² - 10x + 9 = 0
(x - 1)(x - 9) = 0
Therefore, the rider is at a height of 19.2 m when he is either 1 m or 9 m away from the starting point. Since the rider swings back and forth, the distance between the two splashes is twice the distance from the starting point to either splash. Therefore, the horizontal distance traveled by the rider between the two splashes is:
2 × 9 m = 18 m
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, Make Sense and Persevere How much
greater is the part of families with 1 or
2 girls than with 0 or 3 girls? Explain.
Families with one or two females make up the same percentage of households as those with three or more girls. These two categories are identical to one another.
What is the probability?Assuming that the probability of having a boy or a girl is equal and independent for each child, there are four possible outcomes for the number of girls in a family: 0, 1, 2, or 3.
To determine the difference in the proportion of families with 1 or 2 girls compared to those with 0 or 3 girls, we need to calculate the probability of each scenario.
The probability of having 0 or 3 girls is the same because there are two ways to achieve this outcome: either all children are boys, or there is exactly one boy and two girls in the family. The probability of each of these outcomes is:
P(0 girls or 3 girls) = P(all boys) + P(1 boy, 2 girls)
[tex]= (1/2)^3 + 3(1/2)^3[/tex]
[tex]= 1/2[/tex]
The probability of having 1 or 2 girls is the complement of the probability of having 0 or 3 girls, which is:
P(1 girl or 2 girls) [tex]= 1 - P[/tex] (0 girls or 3 girls)
[tex]= 1 - 1/2[/tex]
[tex]= 1/2[/tex]
Therefore, the proportion of families with 1 or 2 girls is the same as the proportion of families with 0 or 3 girls. There is no difference between these two groups.
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Can do one please help me with this math homework
The error mason did is he has subtracted 5 from the right side of the inequality.
What is inequality?An inequality is a statement that one value is greater than, less than, or equal to another value. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
According to question:The given inequality is x-5<11.
Solution of the given equation is x<6.
To solve the equation the addition property of inequality is used and 5 is added to both sides of the equation.
a) The error mason did is he has subtracted 5 from the right side of the inequality. Instead of adding the number 5.
So, the error was to subtract 5 from right side.
b) The given inequality is x-5<11.
Add 5 on both the sides
x - 5 + 5 < 11 +5.
After adding we get,
x < 16.
Now plot the point 16 on the number line. Since the inequality conatins < sign, number to the left of 16 are the solution.
The correct solution on the number line is as shown in the figure.
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the extent to which an instrument is consistent within itself (measures the same way every time) is:
The extent to which an instrument is consistent within itself is called reliability.
Reliability refers to the consistency or stability of the measurements obtained using a specific instrument or test. In other words, it is the degree to which a tool or instrument measures the same way each time it is used under the same conditions. If an instrument is reliable, it produces consistent results across repeated trials or measurements.
Reliability is an important aspect of measurement because it determines the accuracy of the results obtained using the instrument. An unreliable instrument can produce inconsistent or inaccurate results, which can lead to erroneous conclusions or decisions.
Therefore, it is crucial to establish the reliability of an instrument before using it to make important decisions or draw conclusions based on the measurements obtained. There are several methods for measuring reliability, including test-retest reliability, inter-rater reliability, and internal consistency reliability.
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the radius of a circle is 3 miles. what is the circumference? give the exact answer in simplest form.
Answer:
18.84 miles
Step-by-step explanation:
Circumference = 2πr
= 2 × 3.14 × 3
= 18.84 miles
The exact circumference of the circle with radius 3 miles is 6π or 18.84 miles (approx).
The radius of a circle is 3 miles. What is the circumference?The formula to calculate the circumference of a circle is given as:
Circumference = 2πr, where r is the radius of the circle and π is a constant value, approximately equal to 3.14. Substituting the given value of r in the formula, we have:
Circumference = 2π(3)
Circumference = 6π
Therefore, the exact circumference of the circle is 6π miles. To simplify this answer in its simplest form, we can use the value of π as 3.14 (approximately).Circumference = 6π = 6(3.14) = 18.84Therefore, the exact circumference of the circle is 18.84 miles (approx).
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Can someone PLEASE help me ASAP it’s due today!! I will give brainliest if it’s all done correctly.
Answer part A, B, and C for brainliest!!
Blake's recorded result of a probability model in a 12 times die roll:
Part A: 0 %
Part B: 25 %
Part C: 41.67 %
How to calculate probability?To complete the probability model
Part A:
To find the experimental probability of rolling a 3, count the number of times 3 appears in the table and divide by the total number of rolls:
Number of 3's rolled: 0
Total number of rolls: 12
Experimental probability of rolling a 3: 0/12 = 0/1 = 0
So the probability of rolling a 3 is 0, or 0/1 as a fraction, 0 as a decimal number, and 0% as a percentage.
Part B:
To find the experimental probability of rolling a 6, we need to count the number of times 6 appears in the table and divide by the total number of rolls:
Number of 6's rolled: 3
Total number of rolls: 12
Experimental probability of rolling a 6: 3/12 = 1/4 = 0.25
So the probability of rolling a 6 is 1/4 as a fraction, 0.25 as a decimal number, and 25% as a percentage.
Part C:
To find the experimental probability of rolling a number less than 4, add the experimental probabilities of rolling a 1, 2, or 3:
Experimental probability of rolling a 1: 2/12 = 1/6 = 16.67%
Experimental probability of rolling a 2: 3/12 = 1/4 = 25%
Experimental probability of rolling a 3: 0/12 = 0/1 = 0
Experimental probability of rolling a number less than 4: 16.67% + 25% + 0 = 41.67%
So the probability of rolling a number less than 4 is 5/12 as a fraction, 0.4167 as a decimal number, and 41.67% as a percentage.
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Image transcribed:
16. For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Blake rolled a die 12 times. He recorded the results in the table below.
Results
6 | 2 | 1 | 4
4 | 3 | 1 | 5
2 | 2 | 6 | 6
Then, Blake created the probability model shown below from the data in the chart. Blake was only able to complete part of the model.
Probability Model
1 | 2 | 3 | 4 | 5 | 6
P(1) 17% | P(2)-25% | ? | P(4) 17% | P(5) 8% | ?
Part A: Help Blake complete the probability model by finding the experimental probability of rolling a 3. Provide your answer as a fraction, a decimal number, and a percent.
Part B: Help Blake complete the probability model by finding the experimental probability of rolling a 6. Provide your answer as a fraction, a decimal number, and a percent.
Part C: Use your probability model to find the experimental probability of rolling a number less than 4. Provide your answer as a fraction, a decimal number, and a percent.
The area of sector AOB is 42.257 cm². Find the exact area of the shaded region.
o 13 cm
a.
(42.25л - 169)cm²
b. (42.25л - 84.5) cm ²
B
с.
(42.257 – 84.5 /2 ) em²
-
d. none of these
A (
в (
с о
DO
The exact area of the shaded region is = 42.25π - 84.50
What do you mean by Radius?
A radius is a line segment that has one endpoint in the circle's centre and the other terminus on the circumference of the circle. Radius = Diameter of circle.
Given that radius OA and OB = 13 cm
Area of sector AOB is 42.25π cm²
now,area of Δ AOB =1/2 ×base×height
= 1/2 × 13 ×13
=1/2 × 169
= 84.5cm²
now area of shaded region
= Area of sector AOB - area of Δ AOB
= 42.25 л cm²- 84.50 cm²
Therefore the area of shaded region is 42.25 л cm²- 84.50 cm²
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15.026 is the same thing as fifteen and twenty-six hundredths.
O True
O False
*
Answer:
False
Step-by-step explanation:
15.026
1 = tens
5 = ones
0 = tenths
2 = hundredths
6 = thousandth
This number is read as fifteen and twenty-six thousandths.
So, the answer is False.
Please Help Iĺl pick your answer as the brainliest.
The measure of angle a for the given rectangular piece of paper folded along ∠a ≅ ∠z is 46.5°.
Give a brief account on linear set of angles.A straight angle has an measure of 180° and looks like a straight line, so it is a mathematical way of representing a straight line. The angle at which the arms extend in opposite directions from the vertex and join to form 180°. Whenever two rays come together they form an angle, and the angle made by two rays in opposite directions is called a right angle.
Given,
∠a ≅ ∠z
∠HMG = 87°
Since all three angles form a straight angle:
∠a + ∠z + ∠HMG = 180°
As, ∠a ≅ ∠z
∠a + ∠z = 2∠a
Now,
2∠a + ∠HMG = 180°
2∠a + 87° = 180°
2∠a = 180° - 87°
2∠a = 93°
m∠a = 46.5°
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The rectangular sheet of paper with the given folds along a and z has an angle of 46.5°.
Briefly describe the linear set of angles.A straight angle is a mathematical representation of a straight line since it has a measure of 180° and seems to be a straight line. the arc formed by the arms joining to form a 180° angle as they extend in opposing directions from the vertex. A right angle is the designation for the angle created by two rays travelling in the opposing directions. Angles are formed whenever two rays come together.
What various angles are there?In geometry, there are primarily six different types of angles. The names of all angles together with their characteristics are:
• Acute Angle: It ranges from 0° to 90°.
• Obtuse Angle: It ranges from 90° to 180°
• Right Angle: The angle that is exactly 90 degrees.
• Straight Angle: The angle that is exactly 180 degrees
• Reflex Angle: The angle that is larger than 180 degrees and less than 360 degrees
• Complete Rotation: the full 360-degree rotation
Given,
∠a ≅ ∠z
∠HMG = 87°
Since all three angles form a straight angle:
∠a + ∠z + ∠HMG = 180°
As, ∠a ≅ ∠z
∠a + ∠z = 2∠a
Now,
2∠a + ∠HMG = 180°
2∠a + 87° = 180°
2∠a = 180° - 87°
2∠a = 93°
m∠a = 46.5°
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Factor 3a2 − 6a − 4a + 8 by grouping.
Step-by-step explanation:
3a² -6a -4a +8
By Grouping method,
= 3a(a-2)-4(a-2)
= (3a-4)(a-2)
Answer:
(3a − 4)(a − 2)
Step-by-step explanation:
i got it on my quiz
Group and factor out the greatest common factor (GCF), then combine.(3a−4)(a−2)
1. a triangle with side lengths of 9, 12 and 15 is a right triangle by the converse of pythagorean theorem. what are the measures of the acute angles of the triangle?
The required measures of the acute angles in the given right triangle with side lengths 9, 12, and 15 is equal to 36.87 degrees and 53.13 degrees approximately.
Right triangle with side lengths of 9, 12 and 15.
Check whether Pythagorean theorem holds true,
which states that the sum of the squares of the two shorter sides equals the square of the hypotenuse.
9^2 + 12^2 = 15^2
Simplifying this equation, we get,
⇒81 + 144 = 225
⇒225 = 225
This implies,
Pythagorean theorem holds for this triangle,
And by the converse of the Pythagorean theorem,
Triangle is a right triangle with the right angle opposite the side with length 15.
The acute angles of a right triangle are complementary.
Which means that their sum is 90 degrees.
Calculate the measures of the acute angles in this triangle,
Use trigonometric functions.
Use the sine function to find one of the acute angles,
sin(θ) = opposite/hypotenuse
= 9/15
= 0.6
Taking the inverse sine function of both sides, we get,
θ = sin^(-1)(0.6)
⇒ θ ≈ 36.87 degrees.
Sum of the acute angles is 90 degrees, the other acute angle is equals to,
90 - 36.87 = 53.13 degrees.
Therefore, the measures of the acute angles of the triangle are approximately 36.87 degrees and 53.13 degrees.
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Determine the graph's end behavior. Find the x-intercepts and y-intercept. Determine whether the graph has symmetry. Determine the graph of the function.
f(x) = x^{3}+3x^{2}-x-3 x
The y-intercept of the function is -3. The function of f(-x) is not equal to f(x) hence, it is not symmetric.
What is Intermediate value Theorem?According to the Intermediate Value Theorem, there must be at least one value c in the interval (a, b) such that f(c) = k if f(x) is a continuous function on the closed interval [a, b] and if k is any number between f(a) and f(b).
The Intermediate Value Theorem in calculus is frequently employed to demonstrate the reality of a function's roots or zeros. The Intermediate Value Theorem may be used to determine that there is at least one value c in the interval (a, b) such that f(c) = 0 if we know that a function is continuous on the interval [a, b] and that f(a) and f(b) have opposite signs.
The given function is: f(x) = x³ + 3x²- x - 3.
Using synthetic division we have:
-1 | 1 3 -1 -3
| -1 -2 3
|___________
1 2 -3 0
The polynomial can be factored as:
f(x) = (x + 1)(x² + 2x - 3)
The quadratic equation can be factored as:
x² + 2x - 3
x² + 3x - x - 3
(x + 3)(x - 1)
Now, set x = 0:
f(0) = 0³ + 3(0)² - 0 - 3 = -3
Therefore, the y-intercept is (0, -3).
For symmetry we have:
Substituting -x for x:
f(-x) = (-x)³ + 3(-x)² - (-x) - 3x = -x³ + 3x² + x - 3x
This is not equal to f(x), so the function is not symmetric about the y-axis.
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How to compare the following ratios
17:23 and 5:9
To compare the ratios 17:23 and 5:9, you can do it by either finding their decimal equivalents or by cross-multiplying.
Finding decimal equivalents:
Divide each part of the ratio by the sum of its parts.
For 17:23:
17 ÷ (17+23) = 17 ÷ 40 = 0.425
For 5:9:
5 ÷ (5+9) = 5 ÷ 14 = 0.3571
Now compare the decimals:
0.425 > 0.3571
So, the ratio 17:23 is greater than 5:9.
Cross-multiplying:
Cross-multiply the two ratios and compare the products.
For 17:23 and 5:9, multiply 17 by 9 and 23 by 5:
17 * 9 = 153
23 * 5 = 115
Now compare the products:
153 > 115
So, the ratio 17:23 is greater than 5:9.
In both methods, the result is the same: 17:23 is greater than 5:9.
Point b has corrdinates (5,1) the x coordinates of point a is -4 the distance between point a and point b is 15 units what are the possible coordinates of point a
The possible coordinates of the point a is (-4, 11.06) and (-4, -9.06).
Given that point, b has coordinates (5,1) and the distance between point a and point b is 15 units, we can use the distance formula to find the possible coordinates of point a.
The distance formula is given by:
distance = [tex]\sqrt({x_{2}-x_{1 })^{2} } +\sqrt({y_{2}-y_{1 })^{2}[/tex]
If we replace with the point b's coordinates, we obtain:
15 = [tex]\sqrt({5}-(-4)})^{2} } +\sqrt({1-y_{1 })^{2}[/tex]
Simplifying the equation, we get:
225 = [tex](9 + y_{1} ^{2} - 2y_{1} )[/tex]
Rearranging and solving for y1, we get:
y₁² - 2y₁ - 216 = 0
Using the quadratic formula, we get:
y₁ = 11.06
y₁ = -9.06
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100 POINTS PLEASE HURRY
The image of a composite figure is shown.
A four-sided shape with the bottom side labeled as 17.4 yards. The height is labeled 6 yards. A portion of the top side from the perpendicular to right vertex is labeled 2.1 yards. The portion of the top from the perpendicular to the left vertex is 15.3 yards.
What is the area of the figure?
91.8 yd2
104.4 yd2
117 yd2
219.24 yd2
The height divides the shape into 2 parts : a trapezoid and a right-angled triangle.
A(trapezoid) = [(a+b)h]/2, where a;b;h are the length, width and height respectively.
-> A(trapezoid) = [(15.3+17.4) x 6]/2 = 98.1 (yd2)
A(triangle) = lh/2, where l is the base.
-> A(triangle) = 2.1 x 6 : 2 = 6.3 (yd2)
So, the area of the figure is 98.1 + 6.3 = 104.4 (yd2)
Find the time required for an investment of 5000 dollars to grow to 7200 dollars at an interest rate of 7.5 percent per year, compounded quarterly
the time required for an investment of $5000 to grow to $[tex]7200[/tex] at an interest rate of [tex]7.5[/tex] percent per year, compounded quarterly, is approximately [tex]3.79[/tex] years.
What is the required for an investment?o find the time required for an investment of $5000 to grow to $7200 at an interest rate of 7.5 percent per year, compounded quarterly, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^(nt)[/tex]
where:
A = the final amount (in this case, $7200)
P = the principal amount (in this case, $5000)
r = the annual interest rate (in decimal form, so 7.5% = 0.075)
n = the number of times the interest is compounded per year (in this case, quarterly, so n = 4)
t = the number of years (which we need to find)
Plugging in the values, we get:
[tex]7200 = 5000(1 + 0.075/4)^(4t)[/tex]
Now we can solve for t by isolating it on one side of the equation.
Dividing both sides by 5000:
Taking the natural logarithm of both sides:
[tex]ln(7200/5000) = ln((1 + 0.075/4)^(4t))[/tex]
Using the property of logarithms that ln(a^b) = b * ln(a):
[tex]ln(7200/5000) = 4t\times ln(1 + 0.075/4)[/tex]
Dividing both sides by [tex]4 \times ln(1 + 0.075/4):[/tex]
[tex]t = ln(7200/5000) / (4 * ln(1 + 0.075/4))[/tex]
Using a calculator, we can find the value of t to be approximately 3.79 years (rounded to two decimal places).
Therefore, the time required for an investment of $5000 to grow to $7200 at an interest rate of 7.5 percent per year, compounded quarterly, is approximately 3.79 years.
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