The areas under the curve of the z-scores are 0.5098, 0.4357 and 0.1254
Calculating the areas under the curve of the z-scoresFrom the question, we have the following parameters that can be used in our computation:
(a) z = -0.69 to 0.69
This is represented as
Area = P(-069 < z < 069)
Using a graphing calculator, we have
Area = 0.5098
(b) z = -1.52 to 0
This is represented as
Area = P(-1.52 < z < 0)
Using a graphing calculator, we have
Area = 0.4357
(c) z = -0.75 to -0.38
This is represented as
Area = P(-1.52 < z < -0.38)
Using a graphing calculator, we have
Area = 0.1254
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foreign direct investment helps improve the economic situation of a recipient country by increasing —- opportunities in the country that the company invests in.
Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.
When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.
Increased employment opportunities result in more individuals having access to income and improved standards of living.
Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.
Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.
Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.
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Which statement is true about this argument?
Premises:
If a parallelogram has a right angle, then it is a rectangle.
Parallelogram PQRS has a right angle.
Conclusion:
Parallelogram PQRS is a rectangle.
Answer:
The argument is valid by the law of detachment.
3rd Grade Math Question
Answer:
∠ 1 = 110° , ∠ 2 = 70°
Step-by-step explanation:
∠ 1 and ∠ 2 lie on a straight line and sum to 180° , that is
6x + 20 + 4x + 10 = 180
10x + 30 = 180 ( subtract 30 from both sides )
10x = 150 ( divide both sides by 10 )
x = 15
Then
∠ 1 = 6x + 20 = 6(15) + 20 = 90 + 20 = 110°
∠ 2 = 4x + 10 = 4(15) + 10 = 60 + 10 = 70°
which is true regarding the sequence below?
5,2,-3,-10,-19
Answer: Its going down by odd numbers
Step-by-step explanation:
5-2=3, 2-(-3)= 5, then it would go on 7, 9, 11, 13...
Answer:
The difference between the numbers does not follow a common pattern; hence, the sequence is not arithmetic.
Step-by-step explanation:
Let's take the 1st two digits, 5 and 2
The difference between the numbers, 5-2 = 3
Following this pattern,
2-(-3) = 5
-3-(-10) = 7 and,
-10-(-19) = 9.
We can see that the differences are 3, 5, 7 and 9 and therefore we can prove that there is no common difference between the numbers.
Hence the sequence does not follow an arithmetic pattern as there is no common difference
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NO LINKS!! URGENT HELP PLEASE!!
a. Discuss the association.
b. Predict the amount of disposable income for the year 2000.
c. The actual disposable income for 2000 was $8,128 billion. What does this tell you about your model?
Answer:
a) See below.
b) $911 billion
c) See below.
Step-by-step explanation:
Linear regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data.
It estimates the slope and y-intercept of a straight line that minimizes the overall distance between the observed data points and the predicted values. The linear regression equation is y = ax + b.
Part aThe association between year and amount of disposable income is indicated by the linear regression equation y = ax + b.
The value of a is the slope of the linear regression line, and represents the average rate of change in disposable income per year. As a = 14.0545, it means that the disposable income increases by approximately $14.0545 billion dollars each year.
As the value of r (correlation coefficient) is very close to +1, it indicates a very strong positive linear correlation between the year and disposable income. This suggests that as the years progress, the disposable income tends to increase.
Part bLinear regression equation:
[tex]\boxed{y=14.05454545x-27198}[/tex]
To predict the amount of disposable income for the year 2000, we can substitute x = 2000 into the linear regression equation:
[tex]y = 14.05454545 \cdot 2000 - 27198[/tex]
[tex]y=28109.0909...-27198[/tex]
[tex]y=911.0909...[/tex]
[tex]y=911[/tex]
Therefore, the predicted amount of disposable income for the year 2000 is approximately $911 billion.
Part cThe predicted value of $911 billion for the year 2000 is significantly lower than the actual value of $8128 billion. This implies that the model is not accurately capturing the increasing trend in disposable income over time, leading to an underestimation of the income level in 2000. This suggests that the model may have limitations or inaccuracies when extrapolating beyond the range of the provided data. It indicates the need for caution and further analysis when using the model to make predictions outside of the given timeframe.
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 23.5 for a sample of size 775 and standard deviation 12.2. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:
[tex]22.6 < \mu < 24.4[/tex]
How to obtain the confidence interval?The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:
[tex]\overline{x} = 23.5, \sigma = 12.2, n = 775[/tex]
Looking at the z-table, the critical value for a 95% confidence interval is given as follows:
z = 1.96.
The lower bound of the interval is then given as follows:
[tex]23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6[/tex]
The upper bound of the interval is then given as follows:
[tex]23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4[/tex]
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A car that averages 22 miles per gallon emits 4.3 metric tons of carbon dioxide per year. A passenger bus emits 9.2 metric tons of carbon dioxide per year and can carry 30 people at a time. How much less carbon dioxide does a commuter who takes a bus emit in a year compared to a commuter who drives everyday?
13.5 metric tons
2.1 metric tons
5.1 metric tons
3.99 metric tons
The answer is 3.99 metric tons.
To calculate the difference in carbon dioxide emissions between a commuter who takes a bus and one who drives a car every day, we need to compare the emissions of each mode of transportation per person.
The car averages 22 miles per gallon, which means it emits 4.3 metric tons of carbon dioxide per year. However, we don't know the number of passengers in the car.
The passenger bus emits 9.2 metric tons of carbon dioxide per year and can carry 30 people at a time. To find the emissions per person, we divide the total emissions by the number of passengers. In this case, each person on the bus emits 9.2 / 30 = 0.3067 metric tons of carbon dioxide per year.
To determine the difference in emissions, we subtract the emissions per person for the bus from the emissions per person for the car. Therefore, the difference is 4.3 - 0.3067 = 3.9933 metric tons of carbon dioxide per year.
Rounding this value to two decimal places, we get 3.99 metric tons.
Therefore, the answer is 3.99 metric tons.
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3. In ∆ JAM, which of the following statement is always TRUE?
The option that shows the missing angles in the triangle is:
Option C: m∠1 < m∠4
How to identify the missing angle?We know that the sum of angles in a triangle is 180 degrees.
Therefore looking at the given triangle, we can say that:
m∠1 + m∠2 + m∠3 = 180°
We also know that the sum of angles on a straight line is 180 degrees and as such we can say that:
m∠3 + m∠4 = 180°
By substitution we can say that:
m∠4 = m∠1 + m∠2
Thus:
m∠1 < m∠4
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The missing options are:
m∠1 > m∠4
m∠2 > m∠4
m∠1 < m∠4
m∠3 = m∠4
PLSSS HELP 13 POINTS
The equation of the line perpendicular to y = 2 / 3 x - 4 and passes through (6, -2) is y = - 3 / 2x + 7.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptThe slopes of perpendicular lines are negative reciprocals of one another.
Therefore, the slope of the line perpendicular to y = 2 / 3 x - 4 is - 3 / 2.
Hence, let's find the line as its passes through (6, -2).
Therefore,
y = - 3 / 2 x + b
-2 = - 3 / 2(6) + b
-2 = -9 + b
b = -2 + 9
b = 7
Therefore, the equation of the line is y = - 3 / 2x + 7.
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The volume of the triangular prism below is 120 cubic units. Solve for X and for the surface area.
Answer:
X=20
Step-by-step explanation:
20 On one side and the other side are mirror so
is 40
120-40=80
Both the top and lower triangles are similar which will be half divided
40 each scare now divide again for 2 parts of x
x=20
60+40[tex]60+40[/tex]
Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2/1/2+2/3/4+3=8/1/4 pounds
The correct total weight of the bags of granola is 8 1/4 pounds.
One thing that can be done to improve Roberto's reasoning is to ensure the accuracy of the calculations.
In his conclusion, Roberto added the weights of the bags of granola (2 1/2, 2 3/4, and 3) and claimed that the total weight was 8 1/4 pounds. However, the sum of these weights does not equal 8 1/4 pounds.
To address this, Roberto should recheck his calculations. Adding mixed numbers involves adding the whole numbers separately and then adding the fractions separately. In this case, 2 1/2 + 2 3/4 + 3 can be calculated as follows:
2 + 2 + 3 = 7 (sum of whole numbers)
1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4 (sum of fractions)
Thus, the correct sum is 7 + 1 1/4 = 8 1/4 pounds.
By double-checking the calculations and providing the accurate sum, Roberto's reasoning would be more precise, reliable, and free from errors.
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The probable question may be:
Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2 1/2+2 3/4+3=8 1/4 pounds.
what is one thing that you could do to Roberto's Reasoning
Tasha used the pattern in the table to find the value of 4 Superscript negative 4.
Powers of 4
Value
4 squared
16
4 Superscript 1
4
4 Superscript 0
1
4 Superscript negative 1
One-fourth
4 Superscript negative 2
StartFraction 1 Over 16 EndFraction
She used these steps.
Step 1 Find a pattern in the table.
The pattern is to divide the previous value by 4 when the exponent decreases by 1.
Step 2 Find the value of 4 Superscript negative 3.
4 Superscript negative 3 = StartFraction 1 Over 16 EndFraction divided by 4 = StartFraction 1 Over 16 EndFraction times one-fourth = StartFraction 1 Over 64 EndFraction
Step 3 Find the value of 4 Superscript negative 4.
4 Superscript negative 4 = StartFraction 1 Over 64 EndFraction divided by 4 = StartFraction 1 Over 64 EndFraction times one-fourth = StartFraction 1 Over 256 EndFraction
Step 4 Rewrite the value for 4 Superscript negative 4.
StartFraction 1 Over 256 EndFraction = negative StartFraction 1 Over 4 Superscript negative 4 EndFraction
The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.
In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.
To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.
Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.
Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.
Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction
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What is the probability that either event will occur?
A
30
8
B
7
P(A or B) = P(A) + P(B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
The probability that either event will occur is 0.33
What is the probability that either event will occur?From the question, we have the following parameters that can be used in our computation:
Event A = 8Event B = 7Other Events = 30Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 8 + 7 + 30
Evaluate
Total = 45
So, we have
P(A) = 8/45
P(B) = 7/45
For either events, we have
P(A or B) = 8/45 + 7/45
P(A or B) = 15/45
Evaluate
P(A or B) = 0.33
Hence, the probability that either event will occur is 0.33
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The price of stock A at 9 a.m. was 12.67. Since then, the price had been increasing at the rate of $
0.06
While this analysis provides a basic understanding of the stock's movement, it should not be regarded as a definitive forecast.
At 9 a.m., the price of stock A stood at $12.67. From that point onwards, the price of the stock has been experiencing a consistent increase of $0.06. This means that for every hour that passes, the price of stock A rises by $0.06.
If we were to track the price of stock A throughout the day, we would observe a gradual ascent in its value. By 10 a.m., the price would reach $12.73, then $12.79 by 11 a.m., and so on.
This pattern continues throughout the day, with the price increasing by $0.06 for each subsequent hour.
If we assume a linear growth pattern, we can calculate the price at any given time after 9 a.m. For instance, after one hour, at 10 a.m., the price would be $12.67 + $0.06 = $12.73. Similarly, after two hours, at 11 a.m., the price would be $12.67 + ($0.06 × 2) = $12.79.
This trend continues, with the price increasing by $0.06 for each hour elapsed. Therefore, at 12 p.m., three hours after the initial price, the price of Stock A would be $12.67 + ($0.06 × 3) = $12.8
It's important to note that this projection assumes a constant rate of increase. However, the actual stock market is subject to various factors that can influence price fluctuations, such as market demand, economic news, and company performance.
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Simplify the expression so there is only one positive power for the base, -5.
Answer:
c
Step-by-step explanation:
it's a property of powers, when the base is the same (-5) , you need to
sum the powers when both terms are multiplyng
subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)
= find the passible values of K if x² + (k-3) x+4 = 0
The quadratic equation is x² + (k - 3)x + 4 = 0.
The values of k are 7 and -1.
Given: The quadratic equation is x² + (k - 3)x + 4 = 0.
Now, we can find the possible values of k.
To find the values of k, we will apply the discriminant formula of quadratic equation which is given by: [tex]$D=b^2-4ac$[/tex] ,where a,b and c are the coefficients of the quadratic equation: ax²+bx+c
Roots of the quadratic equation are given by:
[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]
Now, let's apply these formulas to the given quadratic equation:
x² + (k - 3)x + 4 = 0
Comparing with the standard quadratic equation of the form ax² + bx + c = 0, we get:
[tex]a = 1, b = k - 3, and c = 4$\\D = b^2 - 4ac$= $(k - 3)^2 - 4(1)(4)$= $k^2 - 6k + 9 - 16$= $k^2 - 6k - 7$[/tex]
The roots of the given quadratic equation are given by:
[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]
Substituting the values of a, b, c, and D, we get:
[tex]$x = \frac{-(k - 3) \pm \sqrt{(k - 3)^2 - 4(1)(4)}}{2(1)}$$x = \frac{3 - k \pm \sqrt{k^2 - 6k - 7}}{2}$[/tex]
Now, for the quadratic equation to have real and equal roots, the discriminant must be equal to zero, i.e., [tex]$D = 0$$\ therefore, k^2 - 6k - 7 = 0$.[/tex]
Factoring the quadratic equation, we get:
[tex]$k^2 - 7k + k - 7 = 0$$\\k(k - 7) + 1(k - 7) = 0$$\\(k - 7)(k + 1) = 0$[/tex]
So, the possible values of k are k = 7 and k = -1.
Hence, the values of k are 7 and -1.
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A popular restaurant has 48 tables. On each table are 3 different types of salsa. In one day, all of the tables are used for 9 different sets of customers. Which expression can be used to estimate how many containers of salsa are needed for all the tables in one day?
A 50 × 9
B 16 × 3 × 9
C 50 × 3 × 10
D 40 × 5 × 5
The expression to estimate the number of containers of salsa needed is: 48 × 3 × 9. none of the option is correct.
To estimate how many containers of salsa are needed for all the tables in one day, we need to consider the total number of tables and the number of salsa containers required for each table.
Given that there are 48 tables and each table has 3 different types of salsa, we can estimate the total number of containers needed by multiplying the number of tables by the number of salsa types.
However, we also need to account for the fact that there are 9 different sets of customers throughout the day. Each set of customers will use all the tables, so we need to multiply the estimated number of containers by the number of sets of customers to get an accurate estimation for the day.
Let's analyze the options provided:
A) 50 × 9: This option assumes there are 50 tables, which is incorrect based on the given information.
B) 16 × 3 × 9: This option assumes there are 16 tables, which is incorrect based on the given information.
C) 50 × 3 × 10: This option assumes there are 50 tables and 10 different sets of customers. Although the number of tables is incorrect, this option accounts for the number of salsa types and the number of sets of customers. However, it does not accurately represent the given scenario.
D) 40 × 5 × 5: This option assumes there are 40 tables and 5 different sets of customers. It also considers the number of salsa types. However, it does not accurately represent the given scenario as the number of tables is incorrect.
None of the options provided accurately represent the given scenario. The correct expression to estimate the number of containers of salsa needed for all the tables in one day would be:48 × 3 × 9
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Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 80 degrees and the low temperature of 50 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
To find an equation for the temperature, D, in terms of t, we can use the properties of a sinusoidal function to model the temperature variation over the day.
Given:
High temperature: 80 degrees
Low temperature occurs at 5 AM (t = 5)
t is the number of hours since midnight
Let's assume a sinusoidal function of the form:
D = A * sin(B * t + C) + Dc
where:
A represents the amplitude (half the difference between the high and low temperatures)
B represents the frequency (how many cycles occur over a 24-hour period)
C represents the phase shift (how much the function is shifted horizontally)
Dc represents the vertical shift (the average temperature throughout the day)
We can determine the values of A, B, C, and Dc based on the given information.
Amplitude (A):
The amplitude is half the difference between the high and low temperatures:
A = (80 - 50) / 2
= 30 / 2
= 15 degrees
Frequency (B):
Since we want the temperature to complete one cycle over a 24-hour period, the frequency can be calculated as:
B = 2π / 24
Phase Shift (C):
Since the low temperature occurs at 5 AM (t = 5), the function should be shifted horizontally by 5 hours. To convert this to radians, we multiply by (2π / 24):
C = 5 * (2π / 24)
Vertical Shift (Dc):
The average temperature throughout the day is the midpoint between the high and low temperatures:
Dc = (80 + 50) / 2
= 130 / 2
= 65 degrees
Now we can put all the values together to obtain the equation for the temperature, D, in terms of t:
D = 15 * sin((2π / 24) * t + (5 * 2π / 24)) + 65
Simplifying further:
D = 15 * sin((π / 12) * t + (π / 12)) + 65
Therefore, the equation for the temperature, D, in terms of t is:
D = 15 * sin((π / 12) * t + (π / 12)) + 65.
Which graph best represents the solution to the following pair of equations?
y = 4x + 2
y = x + 5
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair 1, 6.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair 2, negative7.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair negative 1, negative 6.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair negative 2, 7.
The given pair of equations is y = 4x + 2 and y = x + 5, and we are to determine which of the given graphs represents their solution. The first equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Comparing this with the given equation, we see that its slope is 4 and y-intercept is 2.
The second equation is also in slope-intercept form, y = mx + b. Comparing it with the given equation, we see that its slope is 1 and y-intercept is 5.Since we have two lines, we need to find their point of intersection. Substituting y = 4x + 2 into y = x + 5, we have4x + 2 = x + 5Simplifying the equation, we get3x = 3, which gives x = 1.
Substituting this value of x into either of the equations, say y = 4x + 2, we have y = 4(1) + 2 = 6. Hence, the point of intersection is (1, 6). Now, let's examine the given graphs and see which one has (1, 6) as a point of intersection:
Graph 1: The line y = 4x + 2 passes through (0, 2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 1 is not the solution.
Graph 2: The line y = 4x + 2 passes through (-1, -2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 2 is not the solution.
Graph 3: The line y = 4x + 2 passes through (-1, -2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2.
Hence, these two lines cannot intersect at (1, 6). Graph 3 is not the solution.Graph 4: The line y = 4x + 2 passes through (0, 2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 4 is not the solution.
Therefore, none of the given graphs represents the solution to the pair of equations.
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Find x and y . URGENT please help!!
six people want equally share 1 1/2 pizzas. how much pizza does each person get?
Using the Empirical Rule, approximate the following percentages for Parts A - E.
The distribution of weights of newborn babies in one region is bell-shaped with a mean of 3000 grams and standard deviation of 500 grams. For all questions below, show all relevant work.
Part A :Approximately, what percentage of newborn babies weigh more than 3000 grams?
Part B : Approximately, what percentage of newborn babies weigh more than 2000 grams?
Part C : Approximately, what percentage of newborn babies weigh less than 4000 grams?
Part D : Approximately, what percentage of newborn babies weigh between 2000 and 4000 grams?
Part E : What is the range of birth weights that would contain the middle 68% of newborn babies' weights?
Part A: Approximately 50% of newborn babies weigh more than 3000 grams. Part B: Approximately 84.13% of newborn babies weigh more than 2000 grams. Part C: Approximately 84.13% of newborn babies weigh less than 4000 grams. Part D: Approximately 68% of newborn babies weigh between 2000 and 4000 grams. Part E: The range of birth weights that would contain the middle 68% of newborn babies' weights is from 2500 grams to 3500 grams.
1: Calculate the Z-scores for the given weights using the formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
For Part A:
Z = (3000 - 3000) / 500 = 0
Using the Z-table, we find that the percentage of babies weighing more than 3000 grams is approximately 50%.
For Part B:
Z = (2000 - 3000) / 500 = -2
Using the Z-table, we find that the percentage of babies weighing more than 2000 grams is approximately 97.72%. Since we want the percentage of babies weighing more than 2000 grams, we subtract this value from 100% to get approximately 2.28%.
For Part C:
Z = (4000 - 3000) / 500 = 2
Using the Z-table, we find that the percentage of babies weighing less than 4000 grams is approximately 97.72%.
For Part D:
To find the percentage of babies weighing between 2000 and 4000 grams, we subtract the percentage of babies weighing more than 2000 grams from the percentage of babies weighing less than 4000 grams.
Approximately 97.72% - 2.28% = 95.44%
For Part E:
Since the Empirical Rule states that approximately 68% of the data falls within one standard deviation of the mean, we need to find the weights that correspond to the boundaries of this range.
The lower boundary would be the mean minus one standard deviation: 3000 - 500 = 2500 grams.
The upper boundary would be the mean plus one standard deviation: 3000 + 500 = 3500 grams.
Therefore, the range of birth weights that would contain the middle 68% of newborn babies' weights is from 2500 grams to 3500 grams.
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write an equation of the form y=mx for the line shown below (-1,4)
The equation of the Line of the form y = mx is y = -x + 3.
To write an equation of the form y = mx for the line shown below (-1,4), we need to determine the slope (m) of the line first.
Let (x₁, y₁) = (-1, 4) be a point on the line. Now let's find another point on the line. Let's say we have another point (x₂, y₂) = (1, 2).The slope (m) of the line can be calculated using the formula:m = (y₂ - y₁) / (x₂ - x₁)Substituting the values,
we get:m = (2 - 4) / (1 - (-1))= -2 / 2= -1
Now that we know the slope of the line, we can use the point-slope form of the equation of a line to write the equation of the line:y - y₁ = m(x - x₁)Substituting the values, we get:y - 4 = -1(x - (-1))y - 4 = -1(x + 1)y - 4 = -x - 1y = -x - 1 + 4y = -x + 3
Therefore, the equation of the line is y = -x + 3 in slope-intercept form. Since the question specifically asks for the equation of the form y = mx, we can rewrite the equation in this form by factoring out the slope:y = -x + 3y = (-1)x + 3
Thus, the equation of the line of the form y = mx is y = -x + 3.
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Please help!! I don’t understand what to do
Answer:
y = x^2 + 6x +7
y=-x+1
Step-by-step explanation:
To answer this question, we need to find the equation for the line and for the parabola. So, let's do just that!
Line:
The line has a slope of -1 and and y-intercept of 1. This means that the equation for the line is y=-x+1.
Parabola:
To find the vertex form of a parabola, we must first find the vertex form of a parabola. The vertex form of a parabola is y=a(x-h)^2+k, where the vertex is (h,k). Since the vertex of the parabola is (-3,-2), h=-3 and k=-2. Let's plug these values into the vertex form of a parabola.
y=a(x-h)^2+k
y=a(x-(-3))^2+(-2)
y=a(x+3)^2-2
We're not done yet, though, as we still need to find the value of a. To do this, we will take one of the points on the parabola and plug it into the equation. I will be using the point (-1,2).
y=a(x+3)^2-2 [Plug in x and y values]
2=a((-1)+3)^2-2 [Simplify]
2=a(2)^2-2 [Simplify]
2=4a-2 [Add 2 to both sides]
4=4a [Divide both sides by 4]
a=1
Now, we know that the equation of our parabola in vertex form is y=(x+3)^2-2. This isn't what the problem is asking for, though. Instead, they want the standard form of the parabola. To do this, we will need to expand y=(x+3)^2-2.
y=(x+3)^2-2
y=x^2 + 6x + 9 -2
y = x^2 + 6x +7
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please help i dont know how to do this
Answer:
CD: 8.5
m<D: 20.6°
m<C: 69.4°
Step-by-step explanation:
CD:
The first thing it wants us to do is find the length of CD. Since the triangle shown is a right triangle, we can use Pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to solve for the missing length. It's important to remember that when using the Pythagorean theorem, c is the hypotenuse.
[tex]a^{2}+b^{2}=c^{2}\\3^{2}+8^{2}=c^{2}\\9 + 64 = c^{2}\\73 = c^{2}\\\sqrt{73} =c[/tex]
Since our answer is no an integer, we must turn it into a decimal.
[tex]\sqrt{73}[/tex] ≈ 8.544003745 ≈ 8.5
m<D:
Now, they want us to find the measure of <D. To do this, we will need to use trig functions (sine, cosine, tangent). To help us determine which trig function to use, we can remember the acronym SOH CAH TOA. This acronym tells us that sine is equal to opposite divided by hypotenuse, cosine is equal to adjacent divided by hypotenuse, and tangent is equal to opposite divided by adjacent. Since we do the hypotenuse and sides adjacent and opposite of <D, we can choose whichever trig function we want. For this problem, we will use tangent, so we can avoid using a rounded number, 8.5, as one of our sides.
Tan(D) = opposite / adjacent
Tan(D) = 3 / 8 [Take the tan inverse of both sides}
[tex]Tan^{-1}(Tan(D))=Tan^{-1}(3/8)[/tex] [Simplify]
[tex]D=Tan^{-1}(3/8)[/tex] [Solve]
D ≈ 20.55604522
D ≈ 20.6°
m<C:
Lastly, we must find the last unknown angle on the triangle. Since all angles on a triangle total 180°, if know that <C+<D+<E=180°. Let's solve this equation.
<C+<D+<E=180°
<C + 20.6 + 90 = 180 [Add]
<C + 110.6 = 180 [Subtract]
<C = 180 - 110.6 [Solve]
<C = 69.4°
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In a large restaurant, there are 9 times as many chairs as tables. The restaurant is famous for its very spicy chili. If the restaurant has 360 chairs, how many tables are in the restaurant?
Answer:
There are 40 tables.
Step-by-step explanation:
Since we know that there are 9 times as many chairs, then there are tables, all we have to do is divide the number of chairs by 9, and we get the answer 40.
Integrate e^(1-3x) dx with upper limit 1 and lower limit-1
After getting the integration [tex]e^{(1-3x)} dx[/tex] with upper-limit 1 and lower-limit -1, we get [tex]\frac{-1}{3}[e^{-2}-e^{4}][/tex]
We know,
[tex]\int\limits^a_{b} {f(x)} \, dx[/tex] = [tex][F(x)]\limits^a_b[/tex]=F(a)- F(b).
Where,
a⇒Upper limit.
b⇒Lower limit,
f(x)⇒Any function of x.
F(x)⇒ [tex]\int {f(x)}[/tex] gives its antiderivative F(x).
Now here,
a is given as +1, and b is given as -1.
f(x)= [tex]e^{(1-3x)}[/tex].
Suppose, 1-3x =t.
∴ -3dx =dt.[By applying derivative rule]
Now,[tex]\int\limits e^{(1-3x)} dx[/tex]
=[tex]\int e^t.(\frac{-1}{3} ) dt[/tex]
=[tex]-\frac{1}{3} \int {e^t} dt[/tex].
=[tex]-\frac{e^t}{3}dt[/tex]
=[tex]\frac{1}{3}e^{(1-3x)}[/tex]
∴,[tex]\int\limits e^{(1-3x)} dx[/tex] =[tex]\frac{1}{3}e^{(1-3x)}[/tex].
So,[tex]\int\limits^1_{-1} e^{(1-3x)} \, dx[/tex]
=- [tex][\frac{1}{3}e^{(1-3x)}]^1_{-1}[/tex]
=[tex]\frac{-1}{3}[e^{(1-3)}-e^{(1+3)}][/tex]
=[tex]\frac{-1}{3}[e^{-2}-e^{4}][/tex]
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I need help , any of u guys have the answer?
What is the domain of the square root function graphed below?
On a coordinate plane, a curve open up to the right in quadrant 4. It starts at (0, negative 1) and goes through (1, negative 2) and (4, negative 3).
x less-than-or-equal-to negative 1
x greater-than-or-equal-to negative 1
x less-than-or-equal-to 0
x greater-than-or-equal-to 0
Mark this and return
The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.
The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.
From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).
The x-values of these points are 0, 1, and 4.
Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.
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