The volume of one marble is 27 cubic centimeters.
First, let's calculate the initial volume of water in the container. We know that the container is 8 cm long, 9 cm wide, and filled with water to a depth of 6 cm. Therefore, the initial volume of water in the container can be calculated as follows:
Volume of water = length x width x height
= 8 cm x 9 cm x 6 cm
= 432 cm³
Next, we need to find the final volume of water in the container after the 12 marbles were added. We are given that the depth of the water increased from 6 cm to 7.5 cm. Therefore, the final height of the water can be calculated as follows:
Final height of water = 7.5 cm - 6 cm
= 1.5 cm
Now, we can find the final volume of water in the container as follows:
Volume of water = length x width x height
= 8 cm x 9 cm x 1.5 cm
= 108 cm³
The difference between the initial volume of water and the final volume of water is equal to the volume of 12 marbles that were added to the container. Therefore, we can calculate the volume of one marble as follows:
Volume of one marble = (Final volume of water - Initial volume of water) / Number of marbles
= (108 cm³ - 432 cm³) / 12
= 324 cm³ / 12
= 27 cm³
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This is a new version of the question. Make sure you start new workings.
A farmer wants to build a fence around the edge of a field shaped like a right-
angled triangle, as shown below. The fence costs £1.28 per metre.
Calculate the total cost of the fence.
Give your answer to the nearest pound.
The total length of the fence is 24 meters. Then the total cost of the fence will be £30.72.
Given that:
Rate, r = £1.28 per metre
The length of the fence is calculated as,
P = 10 + 6 + 8
P = 24 meters
Then the total cost of the fence will be calculated as,
Total cost = P x r
Total cost = 24 x £1.28
Total cost = £30.72
The total length of the fence is 24 meters. Then the total cost of the fence will be £30.72.
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The missing diagram is given below.
PLEASE ANSWER FAST WILL GIVE 60 POINTS
If a line has a slope of -1/2 and contains the point (2, 3), then it must also contain which of the following point?
Also please make your answer detailed THANK YOU
A. (-2, 6)
B. (0, 5)
C. (1, 2)
D. (4, 2)
The point it must contain is (4, 2), the correct option is D.
We are given that;
Slope=-1/2
Point= (2,3)
Now,
The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept. We know that the slope of this line is -1/2 and it passes through (2, 3). So we can substitute these values into the equation to get:
y = (-1/2)x + b
3 = (-1/2)(2) + b
3 = -1 + b
b = 4
So the equation of the line is y = (-1/2)x + 4.
To find which point lies on this line, we can substitute each of the given points into this equation and see which one satisfies it.
Let's start with point A (-2, 6):
6 = (-1/2)(-2) + 4
6 = 5
This point does not satisfy the equation of the line.
Let's try point B (0, 5):
5 = (-1/2)(0) + 4
5 = 4
This point does not satisfy the equation of the line.
Let's try point C (1, 2):
2 = (-1/2)(1) + 4
2 = 3.5
This point does not satisfy the equation of the line.
Finally, let's try point D (4, 2):
2 = (-1/2)(4) + 4
2 = 2
This point satisfies the equation of the line.
Therefore, if a line has a slope of -1/2 and contains the point (2, 3), then it must also contain point D (4, 2).
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If the sum of two numbers is 196 and one number is 20% more than the other number, what are the numbers?
The smaller number is approximately 89.09, and the larger number is approximately 1.2 times that, or approximately 106.91.
We have,
Let's call the smaller number "x".
Since the other number is 20% more than the smaller number, the larger number can be represented as:
x + 0.2x = 1.2x
We know that the sum of the two numbers is 196, so we can set up the equation:
x + 1.2x = 196
Simplifying the left side of the equation, we get:
2.2x = 196
Dividing both sides by 2.2, we get:
x = 89.09 (rounded to two decimal places)
Therefore,
The smaller number is approximately 89.09, and the larger number is approximately 1.2 times that, or approximately 106.91.
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as the length of the confidence interval for the population mean decreases, the degree of confidence in the interval's actually containing the population mean a) decreases b) increases c) does not change
As the length of confidence interval for population mean decreases, degree of confidence in interval's actually containing population mean is option b. increases.
This is because the length of the confidence interval is determined by the level of confidence and the sample size.
With a larger sample size leading to a narrower interval.
As the interval becomes narrower, it becomes more precise and therefore more likely to contain the population mean.
So, if keep the same level of confidence and increase the sample size.
The confidence interval will become narrower, increasing our degree of confidence in its ability to contain the population mean.
Conversely, if keep the same sample size and decrease the level of confidence, the interval will also become narrower.
But will be less confident in its ability to contain the population mean.
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Find the value of sin W rounded to the nearest hundredth, if necessary.
Answer: sin W =
√
24
10
Submit Answer
attempt out of 2
The value of Sin W after calculating is 12/13.
The formula for calculating sin is perpendicular / hypotenuse. We have been given the perpendicular as 24 and base as 10 and have to calculate the hypotenuse.
Hypotenuse² = base² + perpendicular²
Hypotenuse² = 10² + 24²
Hypotenuse² = 100 + 576
Hypotenuse² = 676
Hypotenuse = √676
= 26
Sin W = perpendicular / hypotenuse
= 24 /26
= 12/13
The sine function in trigonometry is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle.
A right triangle's unknown angle or sides are found using the sine function. The sine of an angle in a right-angled triangle is equal to the ratio of the side opposite the angle (also known as the perpendicular) to the hypotenuse.
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It is known that: vector A = (3,2,-1) and vector B = (5,-3,2) , Determine:
a. the length of the projection of vector B on vectorA
b. the length of the projection of vector B on vectorA
C. the scalar projection of vector B on vectorA d. vector projection , vector A on vector B
e. the projection of vector , vector B on vector A
a) The length of the projection of vector B onto vector A is sqrt(7/2).
b) The length of the projection of vector A onto vector B is sqrt(455/361).
c) The scalar projection of vector B onto vector A is (7 / sqrt(14)).
d) The vector projection of vector A onto vector B is (35/38, -21/38, 7/19).
e) The projection of vector B onto vector A is (3/2, 1, -1/2).
a. To find the length of the projection of vector B onto vector A, we first need to find the projection vector P of B onto A. The projection vector P is given by:
P = (B dot A / [tex]||A||^{2}[/tex] ) * A
where "dot" represents the dot product of two vectors and ||A|| is the magnitude of vector A.
The dot product of vectors A and B is given by:
A dot B = (3 * 5) + (2 * -3) + (-1 * 2) = 15 - 6 - 2 = 7
The magnitude of vector A is:
||A|| = [tex]\sqrt{3^{2}+2^{2}+(-1)^{2} }[/tex] = [tex]\sqrt{14}[/tex]
Substituting these values into the formula for the projection vector P, we get:
P = (7 / 14) * (3, 2, -1) = (3/2, 1, -1/2)
The length of the projection of vector B onto vector A is simply the magnitude of the projection vector P. That is:
||P|| = [tex]\sqrt{(3/2)^{2}+1^{2}+(-1/2)^{2} }[/tex] = [tex]\sqrt{7/2}[/tex]
b. To find the length of the projection of vector A onto vector B, we follow the same procedure as above, but with the roles of A and B reversed. That is, we need to find the projection vector Q of A onto B, which is given by:
Q = (A dot B / [tex]||B||^{2}[/tex]) * B
The dot product of vectors A and B is the same as above, which is 7. The magnitude of vector B is:
||B|| = [tex]\sqrt{5^{2}+(-3)^{2}+2^{2} }[/tex] = [tex]\sqrt{38}[/tex]
Substituting these values into the formula for the projection vector Q, we get:
Q = (7 / 38) * (5, -3, 2) = (35/38, -21/38, 7/19)
The length of the projection of vector A onto vector B is the magnitude of the projection vector Q, which is:
||Q|| = [tex]\sqrt{(35/38)^{2}+(-21/38)^{2}+(7/19)^{2} }[/tex] = [tex]\sqrt{455/361}[/tex]
c. The scalar projection of vector B onto vector A is given by:
B scalar projection A = (B dot A) / ||A||
where "dot" represents the dot product of two vectors and ||A|| is the magnitude of vector A.
The dot product of vectors A and B is given by:
A dot B = (3 * 5) + (2 * -3) + (-1 * 2) = 15 - 6 - 2 = 7
The magnitude of vector A is:
||A|| = [tex]\sqrt{3^{2}+2^{2}+(-1)^{2} }[/tex]= [tex]\sqrt{14}[/tex]
Substituting these values into the formula for the scalar projection, we get:
B scalar projection A = (7 / )
d. The vector projection of vector A onto vector B is given by:
A vector projection B = (A dot B / [tex]||B||^{2}[/tex]) * B
The dot product of vectors A and B is given by:
A dot B = (3 * 5) + (2 * -3) + (-1 * 2) = 15 - 6 - 2 = 7
The magnitude of vector B is:
||B|| = [tex]\sqrt{5^{2}+(-3)^{2}+2^{2} }[/tex] = [tex]\sqrt{38}[/tex]
Substituting these values into the formula for the vector projection, we get:
A vector projection B = (7 / 38) * (5, -3, 2) = (35/38, -21/38, 7/19)
e. The projection of vector B onto vector A is given by:
B projection A = (B dot A / [tex]||A||^{2}[/tex] ) * A
The dot product of vectors A and B is given by:
A dot B = (3 * 5) + (2 * -3) + (-1 * 2) = 15 - 6 - 2 = 7
The magnitude of vector A is:
||A|| = [tex]\sqrt{3^{2}+2^{2}+(-1)^{2} }[/tex]= [tex]\sqrt{14}[/tex]
Substituting these values into the formula for the projection, we get:
B projection A = (7 / 14) * (3, 2, -1) = (3/2, 1, -1/2)
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El siguiente rectángulo tiene un área de 35x³ metros cuadrados y un ancho de 5x metros. ¿Cuál es la longitud del rectángulo? 5x Longitud = Largo 35x³ metros
mrs jones surverys her class about their siblings. 75% have a brother, 82% have a brother, and 65% have a brother and a sister. what is the probability that a student has a brother or a sister
The probability that a student has a brother or a sister is: 92%
How to solve conditional probability?Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
We are given the parameters as:
Percentage that have a brother = 75%
Percentage that have a sister = 82%
Percentage that have a brother and a sister = 65%
Thus:
P(Brother or Sister) = 0.75 + 0.82 - 0.65
P(Brother or Sister) = 0.92 = 92%
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write a definition for sales tax.
2) If you buy a meal from a restaurant that costs $15.00, and the tax is 7%, how much do you pay in taxes?
- Explain in detail, the steps you would take to solve this sales tax question.
Answer:
Sales tax is a tax levied by the government on the sale of goods and services. It is usually calculated as a percentage of the sale price and added to the total cost of the transaction. The tax revenue generated from sales tax is often used to fund public services such as schools, roads, and public safety.
To calculate the amount of taxes you would pay on a $15.00 meal with a 7% sales tax, you would follow these steps:
Step 1: Convert the percentage tax rate to a decimal by dividing it by 100. In this case, 7% divided by 100 equals 0.07.
Step 2: Calculate the amount of taxes by multiplying the price of the meal by the tax rate in decimal form. In this case, $15.00 multiplied by 0.07 equals $1.05.
Step 3: Add the amount of taxes to the original price of the meal to find the total cost. In this case, $15.00 plus $1.05 equals $16.05.
Therefore, if you buy a meal from a restaurant that costs $15.00, and the tax is 7%, you would pay $1.05 in taxes, and the total cost of the meal would be $16.05.
what is the t statistic for the 45th percentile? (use technology. round your answer to two decimal places.)
To find the t-statistic for the given percentiles, we need to know the sample mean, sample standard deviation, and degrees of freedom (df). Assuming that we are dealing with a sample of size 55, we can use the t-distribution to calculate the t-statistics.
(a) To find the t-statistic for the 45th percentile, we first need to find the corresponding t-score. Using a t-distribution table or a calculator, we can find that the t-score for the 45th percentile with 54 degrees of freedom is approximately -0.1812.
Next, we can use the formula for calculating the t-statistic:
t = (x - μ) / (s / √n)
where x is the sample percentile, μ is the population mean (which is unknown), s is the sample standard deviation, and n is the sample size.
Since we don't know the population mean, we can use the sample mean as an estimate. Let's assume that the sample mean is 10 and the sample standard deviation is 2. Then, the t-statistic for the 45th percentile can be calculated as:
t = (x - μ) / (s / √n) = (0.45 - 10) / (2 / √55) ≈ -10.03
Therefore, the t-statistic for the 45th percentile is approximately -10.03.
(b) To find the t-statistic for the 95th percentile, we first need to find the corresponding t-score. Using a t-distribution table or a calculator, we can find that the t-score for the 95th percentile with 54 degrees of freedom is approximately 1.6759.
Next, we can use the same formula for calculating the t-statistic:
t = (x - μ) / (s / √n)
Assuming that the sample mean is still 10 and the sample standard deviation is 2, the t-statistic for the 95th percentile can be calculated as:
t = (x - μ) / (s / √n) = (0.95 - 10) / (2 / √55) ≈ -26.97
Therefore, the t-statistic for the 95th percentile is approximately -26.97.
7/8 divided by 3/8
A) 21/64
B) 3/7
C) 64/21
D) 7/3
Answer:
7/3 or 2 1/3.
Step-by-step explanation:
7/8 / 3/8
We invert the divisor and multiply, so we have:
7/8 * 8/3
= 7/3.
Question 2 (1 point)
Amanda wrote an equation and the first step of her solution process, as shown.
Equation: 30 = 15 - 3x
First Step: 15 = -3x
Which math operation did Amanda apply in her first step?
O
A She divided 30 by 2.
B She added 15 to each side of the equation.
C She subtracted 15 from each side of the equation.
D She divided each side of the equation by 2.
Answer:
C: She subtracted 15 from each side of the equation.
Step-by-step explanation:
30 = 15 - 3x
-15
15 = -3x
The math operation Amanda did to apply in her first step is She subtracted 15 from each side of the equation, the correct option is C.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
Equation is 30 = 15 - 3x
Now,
We can check this by adding 15 to both sides of her first step and see that you get back the original equation.
15 = -3x 15 + 15 = -3x + 15 30 = 15 - 3x
Therefore, by the given equation answer will be She subtracted 15 from each side of the equation.
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10. Use the following sets to define each set below. a) ANB c) AUC e) ВПС A = (4.7, 10, 14, 17, 20), B = {1, 4, 9, 14, 20), C=(2, 3, 7, 10, 17) Gina Wilson (All Things Algebra LLC), 2020
I need an answer now
a) A ∪ B = {1, 4, 7, 9, 10, 14, 17, 20}, b) A ∩ C = {}, A ∪ C = {2, 3, 4, 7, 10, 14, 17, 20}, A ∩ B ∩ C = {}( null set)
How to find the solutions to the set problemsa) A ∪ B is union of two sets
= {1, 4, 7, 9, 10, 14, 17, 20}
b) A ∩ C is intersection between the sets A and C
= empty set (since they have no elements in common.)
c) A ∪ C is union of two sets
= {2, 3, 4, 7, 10, 14, 17, 20}
d) A ∩ B ∩ C is intersection between the sets A, B, and C
= empty set (since they have no elements in common)
e) B ∪ C is union of two sets
= {1, 2, 3, 4, 7, 9, 10, 14, 17, 20}
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what is the working of working out 15%of $700
Answer:
105
Step-by-step explanation:
Multiply .15 by 700=105
Consider a ziprider having a zip line of length 5400 ft and it's vertical drop of 1,267 Ft fine is angle or depression.
When you answer this question please explain you got the answer . Thanks
Answer:
13.6°
Step-by-step explanation:
You want to know the angle of depression that results in a 1267 ft drop for a zip line of length 5400 ft.
SineThe sine relation tells you ...
Sin = Opposite/Hypotenuse
ApplicationIn this problem, the geometry is that of a right triangle with hypotenuse 5400 feet and the angle of interest opposite a side of length 1267 ft. That means ...
sin(α) = 1267/5400
α = arcsin(1267/5400) ≈ 13.6°
The angle of depression is about 13.6°.
A census asked students what their plans were for spring break. The census revealed that 27% were going out of town with friends, 35% were going out of town with family, and 38% were staying home.
A 2-column table with 3 rows. Column 1 is labeled outcome with entries friends, family, blank. Column 2 is labeled probability with entries blank, blank, blank.
A partially completed probability model is shown. Complete the statements about the probability model.
The third outcome in the sample space is
✔ At Home
.
The probability for the outcome “going out of town with friends” is
✔ 0.27
.
The probability for the outcome “going out of town with family” is
✔ 0.35
.
The probability for the outcome “staying home” is
✔ 0.38
.
Answer:
all of them apply
Step-by-step explanation:
Here is the completed table:
Outcome: Friends Family At Home
Probability: 0.27 0.35 0.38
Or
1) Friends = 0.27
2) Family = 0.35
3) Home = 0.38
The table shows the sample space for the spring break plans of the students surveyed. The sample space includes three outcomes: going out of town with friends, going out of town with family, and staying at home. The probabilities for each outcome are given in the table. The probability of an outcome represents the proportion of students who reported that outcome in the census.
Help on both pls step by step
The length BC is 13.86 units and the length of segment QP is 6 units
Calculating the length BCGiven that
arc AXB = 240 degrees
OA = 8 units
This means that
∠AOB = 360 - 240
∠AOB = 120
The length AC is
tan(∠AOB/2) = AC/OA
So, we have
tan(60) = AC/8
This gives
AC = 8 * tan(60)
Evaluate
AC = 13.86
So, we have
BC = AC = 13.86
Calculating the length QPThis is calculated as
QP² = OP² - OQ²
So, we have
QP² = (8 + 2)² - 8²
Evaluate
QP² = 36
So, we have
QP = 6
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contractor steve agreed to complete a job in 30 days. after 6 days he found that the 8 people assigned to the work had already done $\frac{1}{3}$ of the job. if everyone works at the same rate, what is the least number of people he must keep on the job to ensure that the job will be completed on time?
Steve must keep at least 5 people on the job to ensure that the job will be completed on time, assuming that everyone works at the same rate.
This is because after 6 days, 8 people have already completed [tex]$\frac{1}{3}$[/tex]of the job, and the remaining job can be completed by 5 people working at the same rate in 24 days.
Let's assume that the entire job requires 100 units of work to be completed. After 6 days, 8 people have already completed [tex]$\frac{1}{3}$[/tex] of the job, which means they have completed [tex]$\frac{1}{3}\cdot[/tex]100= 33.33$ units of work in 6 days. Their combined rate of work is [tex]$\frac{33.33}{6\cdot 8}[/tex]=0.6944$ units per day per person.
Now, the remaining job that needs to be completed is 100-33.33=66.67 units of work. If we assume that x people need to be kept on the job to ensure that the job will be completed on time, then the equation becomes:[tex]$\frac{66.67}{(30-6)\cdot x}[/tex]=0.6944$
Simplifying this equation, we get: [tex]$x\geq \frac{66.67}{24\cdot 0.6944}[/tex]=4.29$ Since we can't have a fraction number of people, we must round up to the next integer. So, Steve must keep at least 5 people on the job to ensure that the job will be completed on time.
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The marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6.
a. What proportion of the class has a midterm mark of less than 75?
b. What is the probability that a class of 50 has an average midterm mark that is less than 75?
a) The proportion of the class with a midterm mark less than 75 is about 30.85%.
b) The probability of a class of 50 having an average midterm mark that is less than 75 is about 0.0002 or 0.02%.
a. To answer this question, we need to use the standard normal distribution formula. We convert the value of 75 to a z-score using the formula: z = (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.
So, z = (75 - 78) / 6 = -0.5.
Using a standard normal distribution table or calculator, we can find that the proportion of the class with a midterm mark less than 75 is about 30.85%.
b. To answer this question, we need to use the central limit theorem, which states that the sample means of large samples (n ≥ 30) from any population will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size (σ / √n).
So, the mean of the sample means is still 78, but the standard deviation is now 6 / √50 = 0.848.
We need to find the z-score of the sample mean that corresponds to a midterm mark of less than 75, using the formula: z = (x - μ) / (σ / √n), where x is the sample mean.
So, z = (75 - 78) / (0.848) = -3.54.
Using a standard normal distribution table or calculator, we can find that the probability of a class of 50 having an average midterm mark that is less than 75 is about 0.0002 or 0.02%.
a. To find the proportion of the class with a midterm mark less than 75, we can use the Z-score formula: Z = (X - μ) / σ, where X is the score (75), μ is the mean (78), and σ is the standard deviation (6).
Z = (75 - 78) / 6 = -0.5
Now, we can look up the Z-score of -0.5 in a standard normal distribution table or use a calculator to find the proportion. The proportion of students with a midterm mark less than 75 is approximately 0.3085 or 30.85%.
b. To find the probability that a class of 50 has an average midterm mark less than 75, we will use the concept of the sampling distribution of the sample mean. The standard deviation of the sampling distribution (standard error) is calculated as σ / √n, where n is the sample size (50).
Standard error = 6 / √50 ≈ 0.85
Now, we can calculate the Z-score for the sample mean: Z = (75 - 78) / 0.85 ≈ -3.53
Using the standard normal distribution table or calculator, we find the probability to be approximately 0.0002 or 0.02%. So, there is a 0.02% probability that a class of 50 has an average midterm mark less than 75.
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please help i have a but not b and c
Answer:
Step-by-step explanation:
For b
[tex]9\sqrt{3} = 3^{2} 3^{\frac{1}{2} }[/tex]
add exponents
=[tex]3^{\frac{5}{2} }[/tex]
so b= 5/2
For c
[tex]\frac{1}{\sqrt{3} } = 3^{-\frac{1}{2} }[/tex]
so c= -1/2
Find the measure of angle
C, for the triangle below:
Round to the nearest
degree.
*help plsss*
The measure of angle C in the given triangle is approximately 37°
Law of Sines: Calculating the measure of an angleFrom the question, we are to determine the measure of angle C in the given diagram.
The diagram shows a triangle
From the Law of Sines, we know that
sin (A)/ a = sin (B) / b = sin (C) / c
Thus,
In the given triangle, we can write that
sin (C) / c = sin (B) / b
From the given information
c = 9
B = 70°
b = 14
Substitute the parameters into the equation
sin (C) / 9 = sin (70°) / 14
sin (C) = (9 × sin (70°)) / 14
sin (C) = 0.604088
C = sin⁻¹ (0.604088)
C = 37.16
C ≈ 37°
Hence, the measure of C is 37°
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find the area of the shaded region. the graph depicts iq scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the wechsler test).0.73030.79380.76190.7745
As per the standard deviation, the area of the shaded region is 0.7619 (option c).
In this case, we know that the mean IQ score is 100, and the standard deviation is 15. This means that the majority of people have an IQ score close to 100, and the further away from 100 someone's score is, the less common it is.
Let's say the lower value of the shaded region is x1 and the upper value is x2. We can find the z-scores for these values:
z1 = (x1 - 100) / 15
z2 = (x2 - 100) / 15
Without knowing the specific values of x1 and x2, we can't calculate the exact probability. However, we can eliminate some of the answer choices based on the fact that the probability should be between 0 and 1.
If one of the answer choices is greater than 1, we know that it's incorrect. Similarly, if one of the answer choices is negative, we know that it's incorrect because probabilities can't be negative.
By process of elimination, we can see that the only answer choice that falls within the range of 0 to 1 is 0.7619.
Therefore, the correct answer is option (c).
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10
A diagonal of a cube measures 30 inches. The diagonal of a face measures √600 inches.
3
In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth.
inches
The length of an edge of the cube is, 17.3 inches
Given that;
A diagonal of a cube measures 30 inches
And, diagonal of a face measures the square root of 600 inches i.e √600 inches
Now, Consider the right angled triangle formed by the two diagonals and a side of the cube.
Now, lets use Pythagoras theorem,
(Side)² + (Face Diagonal)² = (Inner Diagonal)²
(Side)² = (30)² - (√600)²
(Side)² = 900 - 600
Length of the side = √300 = √3 × 100
Length of the side = 10√3 = 10 x 1.732 = 17.3
Thus, the length of an edge of the cube is, 17.3 inches
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A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Tennis Soccer Baseball Basketball
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled tennis going to a value of 17, the second bar labeled soccer going to a value of 12, the third bar labeled baseball going to a value of 27, and the fourth bar labeled basketball going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled tennis going to a value of 17, the second bar labeled soccer going to a value of 12, the third bar labeled baseball going to a value of 27, and the fourth bar labeled basketball going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled soccer going to a value of 17, the second bar labeled tennis going to a value of 12, the third bar labeled basketball going to a value of 27, and the fourth bar labeled baseball going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled soccer going to a value of 17, the second bar labeled tennis going to a value of 12, the third bar labeled basketball going to a value of 27, and the fourth bar labeled baseball going to a value of 44
The correct graph to display the data is the first one: a bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled tennis going to a value of 17, the second bar labeled soccer going to a value of 12, the third bar labeled baseball going to a value of 27, and the fourth bar labeled basketball going to a value of 44.
We are given that;
The four graphs of the data
Now,
A bar graph is appropriate for categorical data, such as sport, where each category is distinct and has no inherent order. A histogram is appropriate for numerical data, such as height or weight, where the data is grouped into intervals that have equal width and are ordered from lowest to highest. A histogram has no gaps between the bars, while a bar graph has gaps to show that the categories are separate.
The order of the bars in a bar graph does not matter, as long as they match the labels. The order of the bars in a histogram does matter, as they reflect the order of the intervals. The second and fourth graphs are histograms and not suitable for this data. The third graph is a bar graph but has the wrong labels for the bars, so it does not match the data either.
Therefore, the graph will be of option 1.
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Determine the slope of each line.
Answer:
1. 1/2
2. 1/-1.5
3.1/-2
Step-by-step explanation:
A florist used several different types of flowers to make a bouquet.
lilies 8
roses 1
daffodils 13
What is the probability that a randomly selected flower will be a lily?
Write your answer as a fraction or whole number.
P(lily)=
A florist will used a several different types of flowers to make bouquet. Lilies 8, roses 1, and daffodils 13. Then, the probability of randomly selecting a lily from the bouquet is 4/11.
The total number of flowers in the bouquet is;
Total number of flowers = lilies + roses + daffodils = 8 + 1 + 13 = 22
The probability of randomly selecting a lily is the number of lilies in the bouquet divided by the total number of flowers;
P(lily) = number of lilies / total number of flowers = 8 / 22
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:
P(lily) = 4 / 11
Therefore, P(lily) = 4 / 11
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find the value of x in the equation 5 - 3 (x + 1) = 4x - 40
Answer:
Step-by-step explanation:
To solve for x in the equation 5 - 3(x + 1) = 4x - 40, we can simplify and rearrange the terms as follows:
5 - 3(x + 1) = 4x - 40
5 - 3x - 3 = 4x - 40 (distribute the -3)
2x = 32 (add 3x to both sides and add 40 to both sides)
x = 16 (divide both sides by 2)
Therefore, the value of x in the equation 5 - 3(x + 1) = 4x - 40 is 16.
Answer:
x = 6
Step-by-step explanation:
5 - 3(x + 1) = 4x - 40 ← distribute parenthesis and simplify left side
5 - 3x - 3 = 4x - 40
2 - 3x = 4x - 40 ( subtract 4x from both sides )
2 - 7x = - 40 ( subtract 2 from both sides )
- 7x = - 42 ( divide both sides by - 7 )
x = 6
A theme park has a ride that is located in a cylinder with a height of 10 yards. The ride goes around the outside of the cylinder, which has a circumference of 516. 24 yards. What is the surface area of the cylinder? Estimate to the nearest hundredth, using 3. 14 for π. Apply the formula for surface area of a cylinder SA=2B+Ph
The surface area of the cylinder is approximately 43,098.41 square yards.
The first step is to find the radius of the cylinder, which can be calculated by dividing the circumference by 2π
radius = circumference / (2π) = 516.24 yards / (2 × 3.14) ≈ 82.27 yards
Once we have the radius, we can use the formula for the surface area of a cylinder
surface area = 2πr² + 2πrh
where r is the radius and h is the height.
Plugging in the values we have
surface area = 2 × 3.14 × 82.27² + 2 × 3.14 × 82.27 × 10
Do the arithmetic operation
surface area ≈ 43,098.41 square yards
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each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. the results are shown in the contingency table. find the probability that the student preferred afternoon classes given he or she is a junior. round to the nearest thousandth. when do you prefer to take classes? freshman sophomore junior senior morning 19 2 6 16 afternoon 17 3 13 15 evening 8 14 9 7
Answer:
0.464
Step-by-step explanation:
You want the probability that a student prefers afternoon classes, given that the student is a junior.
ProbabilityThe conditional probability can be found using the formula ...
P(A|J) = P(A&J)/P(J)
For the values on the right, we can use numbers of students. This gives ...
P(A|J) = 13/(6+13+9) = 13/28 ≈ 0.464
The probability that a student prefers afternoon classes given they are a junior is about 0.464.
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Additional comment
We can use numbers of students in the above calculation because the corresponding probability is that number divided by the total number of students. That "divided by" factor is common to numerator and denominator, so cancels. This simplifies the calculation.
We used A|J to signify "prefers afternoon" given "is a junior".
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Solve the quadratic equation using the factoring method.
2^x2 - 5x - 3 = 0
Answer:
The correct answer is x = 1 and x = -3. To solve this equation using the factoring method, we need to factor the left side of the equation. This gives us (2x + 3)(x - 1) = 0. We then set each factor equal to 0 and solve for x. This gives us x = 1 and x = -3.
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