A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 15, 0, 3, 0, negative 3, 0, 15.
Predict which statements are true about the intervals of the continuous function. Check all that apply.
f(x) > 0 over the interval (−, 3).
f(x) ≤ 0 over the interval [0, 2].
f(x) < 0 over the interval (−1, 1).
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, ).
Answers
The time periods that satisfy the requirement include:
(B) f(x)<=0 over the interval [0,2]
(D) f(x)>0 over the interval (-2,0)
(E) f(x)>=0 over the interval [2,∞)
In the given situation:
The table containing values for x and f(x)
Let's examine the table and determine whether each choice satisfies f(x) or not.
Look at the values of x between -3 and 3, there are both positive and negative values for f(x).
Then, f(x)>0 is false over the interval (-∞,3)
The values of f(x) are 0 and negative between 0 and 2.
Then, f(x)<=0 over the interval [0,2]
F(x) values are both positive and negative over the range (-1, 1).
f(x)<0 is false over the interval (-1,1)
In the interval (-2,0), the f(x) is positive.
f(x)>0 over the interval (-2,0)
When divided by [2, ∞], f(x) is positive.
f(x)>=0 over the interval [2,∞)
Therefore, the time periods that satisfy the requirement include:
(B) f(x)<=0 over the interval [0,2]
(D) f(x)>0 over the interval (-2,0)
(E) f(x)>=0 over the interval [2,∞)
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Related Questions
what number represented by the expanded form shown? Write the number in the place value thirty-six and fourteen hundreds
Answers
The number in expanded form can be written as 1000+400+30+6.Place value of 36 is Tens and place value of 1400 is thousand.
In Mathematics, What does "Place value" refers to?The position or placement of a digit within a number impacts its value, according to the mathematical notion of place value. It is a number-representation system in which the value of each digit is determined by its location in the number.
How to find expanded form of a number?The expanded form of the number can be found by multiplying its Face value with place value.
Let's consider the number 2603. In this number:
3 is in the "ones" place, so its place value is 3.
0 is in the "tens" place, so its place value is 0 multiplied by 10, which is 00.
6 is in the "hundreds" place, so its place value is 6 multiplied by 100, which is 600.
2 is in the "thousands" place, so its place value is 2 multiplied by 1000, which is 2000.
Place value can be detertermined by using, Place value chart as given below,
Th H T O
1 4 3 6
Hence, For given number, the expanded form will be,
[tex]1*1000+4*100+3*10+6 = 1000+400+30+6[/tex]
Number in place value 36 will be
T O
3 6
i.e (3 x 10+6). Place value of 36 is tens
and 1400 will be
Th H T O
1 4 0 0
i.e (1x1000+4x100). Place value of 1400 is thousand.
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Which quadratic regression equation best fits the data set
x1|-2 -1.5 -0.5 0 0.5 1.5 2
y1| 4 0.5 -3.5 -4 -3.5 0.5 4
y=2x2^+0x-4 or y=2x2^-4
y=-4x2^+0x+2 or y=-4x2^+2
y=x2x2^-4x+0 or y=2x2^-4x
Answers
The quadratic regression equation best fits the data set is:
[tex]y=-4x^2+0x+2\ or\ y=-4x^2+2[/tex]
What is quadratic regression ?
Quadratic regression is a statistical method used to determine the relationship between a dependent variable and one or more independent variables.
Given data set:
x1|-2 -1.5 -0.5 0 0.5 1.5 2
y1| 4 0.5 -3.5 -4 -3.5 0.5 4
To determine which quadratic regression equation best fits the data set, we need to calculate the regression equation that has the smallest sum of squared residuals.
Using a calculator or regression software, we can find that the quadratic regression equation that best fits the data set is:
[tex]y = -4x^2 + 0x + 2[/tex]
Therefore, the answer is:
[tex]y=-4x^2+0x+2\ or\ y=-4x^2+2[/tex]
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An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use a=0.05 . Factor A is method of loading and unloading; Factor B is the type of ride.
Type of Ride
Roller Coaster Screaming Demon Long Flume
Method 1 47 51 54
49 43 50
Method 2 51 47 50
53 43 46
Set up the ANOVA table (to whole number, but -value to 2 decimals and value to 1 decimal, if necessary).
Source of Variation Sum of Squares Degrees of Freedom Mean Square F -value
Factor A
Factor B
Interaction
Error
Total
The -value for Factor A is
What is your conclusion with respect to Factor A?
The -value for Factor B is ________
What is your conclusion with respect to Factor B?
The p-value for the interaction of factors A and B is
What is your conclusion with respect to the interaction of Factors A and B?
What is your recommendation to the amusement park?
Answers
Part 5
Use either loading or unloading methods.
Since the two factors are not significant. So, use either loading or unloading methods.
How to solveThe null and alternative hypotheses can be defined as follows:
The null hypothesis,
H_0: There is no significance difference between two levels of method at 5% level of significance.
Against alternative hypothesis,
H_a: There is significant difference between two levels of method at 5% level of significance.
From the ANOVA table, the P-value for factor A is 0.315.
Since, 0.315 is greater than the level of the significance. So, the null hypothesis fails to be rejected.
Therefore, there is no significant difference between two levels of method of main effect at 5% level of significance.
Part 2
The P-value is 0.315.
There is no significant difference between two levels of method of main effect at 5% level of significance.
Explanation
Since, 0.315 is greater than the level of the significance. So, the null hypothesis fails to be rejected.
Therefore, there is no significant difference between two levels of the method of main effect at 5% level of significance.
Step 3/5
(3)
The null and alternative hypotheses can be defined as follows:
The null hypothesis,
H_0: There is no significance difference between three types of rides at 5% level of significance.
Against alternative hypothesis,
H_a: There is significant difference between three types of rides at 5% level of significance.
From the ANOVA table, the P-value for factor B is 0.687.
Since, 0.687 is greater than the level of the significance. So, the null hypothesis fails to be rejected.
Therefore, there is no significance difference between three types of ride at 5% level of significance.
Part 3
The P-value is 0.687.
There is no significance difference between three types of ride at 5% level of significance.
Since, 0.687 is greater than the level of the significance. So, the null hypothesis fails to be rejected.
Therefore, there is no significant difference between three types of ride at 5% level of significance.
Step 4/5
(4)
The null and alternative hypotheses can be defined as follows:
The null hypothesis,
H_0: There is no significance difference of interaction between method and ride at 5% level of significance.
Against alternative hypothesis,
H_a: There is significance difference of interaction between method and ride at 5% level of significance.
From the ANOVA table, the P-value for integration of factor A and factor B is 0.138.
Since, 0.138 is greater than the level of the significance. So, the null hypothesis fails to be rejected.
Therefore, there is no significant difference that the interaction between loading and unloading method and types of ride at 5% level of significance.
Part 4
The P-value is 0.138.
There is no significant difference that the interaction between loading and unloading method and types of ride at 5% level of significance.
Explanation
Hint for Next Steps
Since, 0.138 is greater than the level of the significance. So, the null hypothesis fails to be rejected.
Therefore, there is no significant difference that the interaction between loading and unloading method and types of ride at 5% level of significance.
Step 5/5
(5)
Since, the two factors are not significant. So, use either loading or unloading methods.
Part 5
Use either loading or unloading methods.
Since the two factors are not significant. So, use either loading or unloading methods.
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PLEASE help 1-4 pls and thank you
Answers
The arithmetic or geometric sequences, common difference (d) or the common ratio (r) include:
Arithmetic: d = 2, an = 2n, Terms: 2, 4, 6, 8, 10, 12Geometric: r = 0.5, a1 = 8, an = 8(0.5)^(n-1), Terms: 8, 4, 2, 1, 0.5, 0.25Arithmetic: d = 1.5, a1 = 7, an = 1.5n + 5.5, Terms: 7, 8.5, 10, 11.5, 13, 14.5Geometric: r = 4, a1 = 5, an = 5(4)^(n-1), Terms: 5, 20, 80, 320, 1280, 5120What is a geometric sequence?A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed number, which is called the common ratio (r). In other words, a geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by the same number.
For example, the sequence 2, 4, 8, 16, 32 is a geometric sequence with a common ratio of 2. To get each term in the sequence, you multiply the preceding term by 2. So, 2 x 2 = 4, 4 x 2 = 8, and so on.
The explicit formula for a geometric sequence is: an = a1 × r^(n-1), where a1 is the first term, r is the common ratio, and n is the term number.
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Image transcribed:
For the following problems:
Determine whether the sequence is arithmetic or geometric. ⚫ Find the common difference (d) or the common ratio (r).
Write the explicit formula for the sequence.
Find the next 3 terms of the sequence.
1) 2,4,6,...
Arithmetic or Geometric
OR r =
an=
Terms:
2) 8,4,2
Arithmetic or Geometric
d=
OR r =
1
e
an=
Terms:
3) 7,8.5, 10, 11.5
4) 5, 20, 80, 320,
Arithmetic or Geometric
Arithmetic or Geometric
d=
d =
OR r =
an
Terms:
OR r=
an=
Terms:
An office manager needs to cover the front face of a rectangular box with a label for shipping. The vertices of the face are (–5, 8), (3, 8), (–5, –4), and (3, –4). What is the area, in square inches, of the label needed to cover the face of the box?
96 in2
48 in2
40 in2
20 in2
Answers
The area of rectangle is 96in2 which is option A.
Area of rectangle calculation.
To find the area of the rectangular face, we need to find the length and width of the rectangle, and then multiply them together.
The length of the rectangle is the distance between the points (-5,8) and (3,8), which is 8 - (-4) = 12 inches.
The width of the rectangle is the distance between the points (-5,8) and (-5,-4), which is 3 - (-5) = 8 inches.
Therefore, the area of the rectangular face is 12 x 8 = 96 square inches.
So the answer is 96 in².
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THERE ARE 2 CORRECT ANSWERS FOR THS ONE !!!HELP
Answers
The two correct answers for the dot plot on the First and Second Period is A. the first period is right skewed while the second period is symmetrical.
How do we know the skew ?To determine the skewness of a distribution, we need to look at the shape of the data. In a right-skewed distribution, the tail of the data is longer on the right side and the mode (peak) of the data is lower than the mean.
In a symmetrical distribution, the data is evenly distributed around the mean and the mode and the tail lengths on both sides are equal.
So, based on the given information that the dot plot for the first period is right-skewed while the second period is symmetrical, we can infer that the first period has a longer tail on the right side and the mode is lower than the mean, indicating a right-skewed distribution.
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24x -27 -15 +18 -21x + 27
Answers
Answer:
3x + 3
Step-by-step explanation:
The given expression is 24x - 27 - 15 + 18 - 21x + 27.
To simplify this expression, we can combine like terms. Like terms are terms that have the same variable(s) and exponent(s). In this expression, we have two terms that have x: 24x and -21x. These terms can be combined by subtracting 21x from 24x to get 3x.
The other terms without any variables are -27, -15, 18, and 27. We can combine these terms by adding them together to get 3.
Therefore, the simplified expression is 3x + 3.
Answer:
3x+3
Step-by-stepStep-by-step explanation:
Combine like terms:
(24x+(−21x))+(−27+(−15)+18+27)
3x+3
URGENT !
What effect does replacing x with - 4 have on the graph for the function f( x)?
f(x)= |x-6| +2
A. The graph is shifted 4 units up.
B. The graph is shifted 4 units right.
C. The graph is shifted 4 units left.
D.The graph is shifted 4 units down.
Answers
Answer: D
Step-by-step explanation:
Years Balance
0 $40
1 $42
2 $44
3 $46
What is the interest rate of the account? What is the balance after 10 years?
Answers
By using simple interest we get after ten years balance is **$60**.
what is a simple interest?Simple interest is a type of interest that is calculated by using the principal (the amount of money that was initially invested) and the interest rate. Any interest that has accrued over time is not taken into consideration. For simple interest, use the formula:
I = Prt
where I = interest earned, P = principal, r = interest rate (in decimal form), and t = time (in years).
The interest rate can be calculated using the following basic interest formula:
I = Prt
where P is the principal (the starting balance), r is the interest rate (in decimal form), and t is the duration, and I is the interest earned. (in years).
The information in the table can be used to calculate the interest rate:
$42 - $40 equals $2 in interest over a year.
$2 / $40 equals 0.05 percent, or 5% interest.
Therefore, the account's interest rate is **5%**.
We can apply the formula to determine the balance after ten years:
A = P(1 + rt)
where P is the principle (the starting balance), r is the interest rate (in decimal form), and t is the period of time, and A is the balance after t years. (in years).
The information in the table allows us to determine that:
P = $40
r = 0.05
t = 10
A = $40(1 + 0.05 × 10) = **$60**
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A sports writer wants to see if a football filled with helium travels farther, on average, than a football filled with air. 14 footballs were filled with helium to the recommend pressure and 12 footballs were filled with air to the recommended pressure. The mean yardage for the helium filled footballs was 281 yards with a standard deviation of 3 yards. The mean yardage for the air filled footballs was 233 yards with a standard deviation of 4 yards.
Construct a 80% confidence interval for the mean difference in yardage for the two types of footballs. Assume the populations are normal with equal variances. Round your answers to three decimal places, and use four decimal places for any interim calculations.
We are 80% confident that the interval ( , )contains the true mean difference in yardage between the two types of footballs
Answers
we can say with 80% confidence that the true mean difference in yardage between the two types of footballs is between 46.224 and 49.776 yards.
How to solve the question ?
To construct the confidence interval for the mean difference in yardage between the two types of footballs, we first need to calculate the pooled standard deviation and the standard error of the mean difference. Since the sample sizes are large and the populations are assumed to be normal with equal variances, we can use the following formulas:
Pooled standard deviation:
s_p = √[((n1-1)*s₁² + (n2-1)*s₁²)/(n₁+n₂-2)]
s_p = √[((14-1)*3² + (12-1)*4²)/(14+12-2)]
s_p = 3.517
Standard error of the mean difference:
SE = s_p√(1/n₁ + 1/n₂)
SE = 3.517√(1/14 + 1/12)
SE = 1.416
Next, we can calculate the margin of error by multiplying the standard error by the t-value for the 80% confidence level with degrees of freedom equal to n1+n2-2=24. Using a t-table or calculator, we find that the t-value is 1.329.
Margin of error:
ME = tSE
ME = 1.3291.416
ME = 1.776
Finally, we can construct the confidence interval by adding and subtracting the margin of error from the sample mean difference in yardage.
Confidence interval:
(281-233) +/- ME
48 +/- 1.776
(46.224, 49.776)
Therefore, we can say with 80% confidence that the true mean difference in yardage between the two types of footballs is between 46.224 and 49.776 yards. This means that, on average, the football filled with helium travels 46.224 to 49.776 yards farther than the football filled with air.
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PLS HELP ME
PLS SHOW YOUR WORKING OUT
Answers
Answer:
Step-by-step explanation:
it is really easy
Jermaine is riding his bicycle across his state. At times, Jermaine stops and explores the local scenery or attractions. At other times, especially on the open road, Jermaine likes to travel at a constant speed.
Jermaine decides to travel at a constant speed and travels 50 miles in 5 hours.
Graph the line that represents the relationship between the time, in hours, that Jermaine rides his bicycle, and the distance, in miles, that he travels based on the given data.
Answers
The equation of the graph is y = 10x and the visual representation of the graph is given in the picture.
Graphing the line:To graph, the line that represents the relationship between the time Jermaine rides his bicycle and the distance he travels use the slope-intercept form of a linear equation.
This form of the equation is used to represent a straight line on a graph, where the slope represents the rate of change of the dependent variable with respect to the independent variable, and the y-intercept represents the initial value of the dependent variable when the independent variable is 0.
Here we have
Jermaine decides to travel at a constant speed and travels 50 miles in 5 hours.
To graph the line that represents the relationship between the time and the distance he travels, we can use the formula for the slope-intercept form of a linear equation:
y = mx + b
We know that Jermaine travels 50 miles in 5 hours
Slope (m) = (change in y) / (change in x) = (50 - 0) / (5 - 0) = 10
This tells us that for every 1 hour that Jermaine rides his bicycle, he travels 10 miles.
Hence, the equation of the line y = 10x + b
Take x = 0 and y = 0 [ Since the line passes through (0, 0)
=> 0 = 10(0) + b
=> b = 0
This tells us that the y-intercept of the line is 0.
Hence, the equation of the line, y = 10x
Now draw the graph of y = 10x as shown below
Therefore,
The equation of the graph is y = 10x and the visual representation of the graph is given in the picture.
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volumes of two separate solids are 15 cm and 45 cm what is the ratio of their surface areas
1:3
1:9
1:27
15.3
Answers
The ratio of their volumes is 1:3.
What is volume?
Volume is a physical quantity that measures the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be calculated by multiplying its length, width, and height or by measuring the amount of substance it contains, such as in the case of a liquid or a gas. Volume is an important concept in physics, chemistry, and engineering, and is used to describe a wide range of phenomena, including the size of objects, the amount of material required for a given task, and the capacity of containers
The ratio of the volumes of two solids can be found by dividing the larger volume by the smaller volume.
Let's assume that the volume of the smaller solid is 15 cm and the volume of the larger solid is 45 cm.
The ratio of the volumes of the larger solid to the smaller solid is:
45 cm / 15 cm = 3
Therefore, the ratio of the volumes of the two solids is 3:1.
So the ratio is 1:3.
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Correct question is "volumes of two separate solids are 15 cm³ and 45 cm³ what is the ratio of their volumes -
1:31:91:2715.3"The ratio of Brilliant Blue shampoo is 1 part shampoo to 4 parts water.
How much shampoo will be needed if we use 28 cups of water?
Answers
Answer: 7
Step-by-step explanation:
The ratio is 1:4 so 1/4. Plug in the numbers for the water, 1:4, X:28.
Then divide to find X.
28/4= 7
So your answer is 7. Check your work with multiplication
1:4 = 7:28
Let v = 9j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane. Find the maximum and minimum values of the length of the vector u × v.
maximum
minimum
Incorrect: Your answer is incorrect.
Answers
Therefore , the solution of the given problem of coordinates comes out to be the vector u v's length can be as long as 27, and it can be as short as -27.
What exactly is coordinate plane mean?A parameter can accurately detect position using a variety of attributes or coordinates when used in conjunction with specific other algebra elements on this location, such as Euclidean space. When travelling in reflected space, coordinates, which look as groups of numbers, can be used to pinpoint specific locations or objects. Finding an object over both surfaces can be done using the y & x measurements.
Here,
We can use the knowledge that the length of the cross product of the vectors u and v is equal to the sum of the lengths of u and v multiplied by the sine of the angle between them to determine the maximum and minimum values of the length of the vector u v:
=> |u × v| = |u| |v| sin(θ)
We have |v| = 9 since v = 9j. Additionally, since u rotates on the xy plane and has a length of 3, we can write u as u = (3 cosθ) i + (3 sinθ) j.
This happens when = /2, and sin() has a minimum value of 1, which happens when = 3/2.
Therefore, |u v| has the following maximum value:
=> |u × v| = |u| |v| sin(π/2) = 3(9)(1) = 27
And |u × v| has the following minimum value:
=> |u × v| = |u| |v| sin(3π/2) = 3(9)(-1) = -27
Thus, the vector u v's length can be as long as 27, and it can be as short as -27.
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TimeRyte is a company that manufactures highly accurate stopwatches for sporting events. The company has two manufacturing facilities, one on the east cost and one on the west coast. Some stopwatches are assembled with components manufactured at the east coast facility, some are assembled with components manufactured at the west coast facility, and some are assembled with components manufactured at both facilities. TimeRyte have recently started a new advertising campaign that claims their stopwatches are accurate to a thousandth of a second 98% of the time. An independent research company is investigating the reliability of TimeRyte's stopwatches and the honesty of their claim. Their testing revealed that stopwatches assembled with components from the east coast facility are accurate to one thousandth of a second 96% of the time, stop watches assembled with components from the west cost are accurate to one thousandth of a second 99% of the time, and that stopwatches assembled with components from both facilities are accurate to the thousandth of a second 98% of the time. This a fair and honest ad campaign because .
Answers
The ad campaign by TimeRyte claiming that their stopwatches are accurate to a thousandth of a second 98% of the time is fair and honest based on the information provided. The independent research company's findings support this claim.
According to the research, stopwatches assembled with components from the east coast facility are accurate to a thousandth of a second 96% of the time. This implies that the assembly process at the east coast facility may introduce a slight deviation from the claimed accuracy.
Stopwatches assembled with components from the west coast facility, on the other hand, are accurate to a thousandth of a second 99% of the time. This suggests that the assembly process at the west coast facility is more reliable in achieving the claimed accuracy.
Stopwatches assembled with components from both facilities, which accounts for some of the products, are accurate to a thousandth of a second 98% of the time. This suggests that the combined efforts of both facilities maintain the claimed accuracy.
Considering the overall findings and the accuracy percentages provided, it can be concluded that the ad campaign's claim of 98% accuracy to a thousandth of a second is fair and honest, given the performance of the stopwatches across different assembly scenarios.
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Question 3
A group of 5 people went to the movies and spent $44 on food and drink. The total amount spent, including
tickets, was $98.50.
What was the price, in dollars, of one ticket?
Answers
Answer:
One ticket cost $10.90.
Step-by-step explanation:
The total spent was $98.50--food, drinks, admission--everything.
$44.00 was for food and drinks.
We can take the 44 away from the total.
98.50 - 44.00
= 54.50
They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.
54.50 ÷ 5 = 10.90
The price of one ticket was $10.90
To make this look like algebra class...
let x = the price of one ticket
5x = the price of 5 tickets
5x + 44 = 98.50
subtract 44
5x = 54.50
divide by 5
x = 10.90
Pls help. ASAp. Im confused
Answers
need answer right nowwwww
Answers
Answer:
CAN YOU SHOW THE QUESTION SO I CAN HELP YOU?????????Step-by-step explanation
4. Factors that influence a hypothesis test with the t statistic
Suppose you conduct a hypothesis test about a population mean when the standard deviation is unknown by calculating a t statistic and determining whether to reject the null hypothesis. Assume that your t statistic is a positive value and that you will reject the null hypothesis when t is very large. For each of the potential changes to the components of your study design or the results listed below, determine the change to the t statistic, and then select “Increases,” “Decreases,” or “Stays the same” from the dropdown menu in the right-hand column.
Change in Study Design or Results
The t statistic
A switch from using a one-tailed test to a two-tailed test
An increase in the sample standard deviation (s)
A decrease in the significance level (such as using α = .01 instead of α = .05)
A decrease in the sample size (n)
Answers
The t statistic: Stays the same
A switch from using a one-tailed test to a two-tailed test: Increases
An increase in the sample standard deviation (s): Decreases
A decrease in the significance level (such as using α = .01 instead of α = .05): Increases
A decrease in the sample size (n): Decreases
What is the t statistic?The t statistic: Stays the same
The t statistic itself is calculated based on the sample mean, the population mean, and the sample standard deviation.
Therefore, changing the study design or results in ways that do not affect these values will not change the t statistic.
A switch from using a one-tailed test to a two-tailed test: Increases.
An increase in the sample standard deviation (s): Decreases
A decrease in the significance level (such as using α = .01 instead of α = .05): Increases
A decrease in the sample size (n): Decreases
As the sample size decreases, the standard error of the mean increases, meaning that there is more variability in the sample means. Therefore, the t statistic will be smaller, making it less likely to reject the null hypothesis.
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A man deposited GH¢14100.00 at 8% per annum compound interest. If at the end of 4
years he transfers the total amount to another bank offering 12% compound interest per
annum.
a. How much interest did he get at the end of 7 years?
b. Calculate the total amount he received at the end of seven years.
Answers
a. the man received GH¢26062.23 in interest at the end of 7 years.
b. the man received a total of GH¢40162.23 at the end of 7 years.
What is compound interest?The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest. It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest.
a. Tο find the amοunt οf interest the man received at the end οf 7 years, we need tο first calculate the amοunt οf mοney he wοuld have at the end οf 4 years at 8% cοmpοund interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
where A is the amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.
In this case, P = GH¢14100.00, r = 0.08, n = 1 (compounded annually), and t = 4. Plugging these values into the formula, we get:
[tex]A = GH¢14100.00(1 + 0.08/1)^{(1*4)[/tex]
[tex]A = GH¢14100.00(1.08)^4[/tex]
A ≈ GH¢19792.11
So at the end of 4 years, the man would have GH¢19792.11. We can now use this as the principal and calculate the amount he would have at the end of 7 years at 12% compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
where P = GH¢19792.11, r = 0.12, n = 1, and t = 7.
Plugging these values into the formula, we get:
[tex]A = GH¢19792.11(1 + 0.12/1)^{(1*7)[/tex]
A ≈ GH¢40162.23
So at the end of 7 years, the man would have GH¢40162.23. To find the amount of interest he received, we subtract the original principal of GH¢14100.00:
Interest = GH¢40162.23 - GH¢14100.00
Interest = GH¢26062.23
Therefore, the man received GH¢26062.23 in interest at the end of 7 years.
b. To calculate the total amount the man received at the end of 7 years, we add the interest received to the original principal plus the amount earned from compound interest:
Total amount = GH¢14100.00 + GH¢26062.23
Total amount = GH¢40162.23
Therefore, the man received a total of GH¢40162.23 at the end of 7 years.
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In a scale drawing, the length of a rectangular room is 6 inches, and the width is 3 inches. The actual length of the room is 18 feet. a. What is the scale of the drawing? b. In a new scale drawing of the same room, the length of the room measures 4 inches. What is the scale of the new drawing? Explain. Question content area bottom Part 1 a. The scale of the drawing is 1 in. enter your response here ft. (Type an integer or a decimal.) Part 2 b. The scale is 1 in. = enter your response here ft. In the new scale drawing, a length of 4 inches represents an actual length of enter your response here feet. So, a length of 1 inch represents an actual length of enter your response here feet. (Type integers or decimals.) Enter your answer in each of the answer boxes.
Answers
a) The scale of the drawing is 1 inch represents 216 inches or 1 inch represents 18 feet. b) The scale of the new drawing is 1 inch represents 72 inches or 1 inch represents 6 feet.
What is ratio?A ratio is a comparison between two quantities, often expressed as a fraction. It represents the relative size of two or more values, and can be used to compare, scale, or measure different quantities.
According to question:a. To find the scale of the drawing, we can use the ratio of the length in the drawing to the actual length.
The length in the drawing is 6 inches and the actual length is 18 feet, which is equivalent to 216 inches (since 1 foot = 12 inches).
So the scale of the drawing is:
1 inch in the drawing = 216 inches in reality
Therefore, the scale is:
1 inch : 216 inches
Simplifying this ratio, we get:
1 : 216
Therefore, the scale of the drawing is 1 inch represents 216 inches or 1 inch represents 18 feet.
b. In the new scale drawing, the length of the room is 4 inches. We need to find the scale of this new drawing.
Let x be the scale of the new drawing, such that:
1 inch in the new drawing = x feet in reality
We can set up the proportion:
6 inches in the old drawing : 18 feet in reality = 4 inches in the new drawing : y feet in reality
Simplifying this proportion, we get:
6 : 18 = 4 : y/x
Dividing both sides by 2, we get:
3 : 9 = 2 : y/x
Cross-multiplying, we get:
3x = 18
Dividing both sides by 3, we get:
x = 6
Therefore, the scale of the new drawing is:
1 inch in the new drawing = 6 feet in reality
Simplifying this ratio, we get:
1 : 72
Therefore, the scale of the new drawing is 1 inch represents 72 inches or 1 inch represents 6 feet.
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The ratio of teachers to students in one district is 2 to 47. if the number of teachers in the district is 130, how many student are there?
Answers
Answer:
3055
Step-by-step explanation:
We can rewrite this in fraction form
2/47=130/x
Cross multiply:
47×130=2x
6110=2x
x=3055
3. A rhombus has side lengths of 4 centimeters and an area of 12 square centimeters. What is the height of the rhombus?
O 6 cm
O 4 cm
O 3 cm
O 8 cm
Answers
Answer:
3cm
Step-by-step explanation:
Using the formula A=b×h, if b=4cm and A=12cm²,
h=12/4=3cm.
Hope this helps!
Select the correct difference.
-3z 5 - (-7z 5)
4 z
4 z5
-10 z5
-4 z5
Answers
The correct difference of the expression -3z^5 - (-7z^5) is -4z^5
Evaluating the difference in the expressionThe given expression is -3z^5 - (-7z^5).
When subtracting a negative number, we can change it to addition of the opposite.
So, we can rewrite the expression as -3z^5 + 7z^5.
To simplify the expression, we can combine like terms. The only like terms in the expression are the terms with z^5, so we can add their coefficients:
-3z^5 + 7z^5 = 4z^5
Therefore, the correct difference is 4z^5.
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Drag the tiles to the correct boxes. Not all tiles will be used.
What are the domain and the range of function f?
f(x) = x - 6 / x^2 - 3x - 18
range ---> ??
domain ---> ??
Answers
The Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞) and Range: (-∞, 0) ∪ (0, ∞).
What is domain?
The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.
According to question:
In this case, the denominator of the function is a quadratic expression, and we know that dividing by zero is undefined. Therefore, we need to find the values of x that make the denominator equal to zero, and exclude those values from the domain.
To find the values that make the denominator equal to zero, we can factor it as follows:
x² - 3x - 18 = 0
(x - 6)(x + 3) = 0
So, the denominator is equal to zero when x = 6 or x = -3. Therefore, the domain of the function is all real numbers except x = 6 and x = -3.
Domain: (-∞, -3) ∪ (-3, 6) ∪ (6, ∞)
The range of a function consists of all possible output values of the function, given the domain of the function.
To find the range of this function, we need to analyze the behavior of the function as x approaches positive or negative infinity.
As x approaches positive infinity, both the numerator and denominator of the function approach positive infinity. Therefore, the function approaches zero.
As x approaches negative infinity, both the numerator and denominator of the function approach negative infinity. Therefore, the function approaches zero.
Since the function approaches zero as x approaches positive or negative infinity, we can say that the range of the function is all real numbers except zero.
Range: (-∞, 0) ∪ (0, ∞).
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.
Describe the location of the point in relation to the origin.
(-2, 4, -1)
answer
2 left, 4 right, 1 down
2 left, 4 up, 1 back
2 back, 4 up, 1 left
2 back, 4 right, 1 down
Answers
Answer: The correct answer is: 2 left, 4 up, 1 back.
Step-by-step explanation: The location of the point (-2, 4, -1) in relation to the origin is best described as 2 units to the left, 4 units up, and 1 unit down. This is because each coordinate represents a direction and a distance from the origin, which is the point (0,0,0) in 3-dimensional space. The first coordinate (-2) represents the distance and direction in the x-axis, the second coordinate (4) represents the distance and direction in the y-axis, and the third coordinate (-1) represents the distance and direction in the z-axis. Therefore, we can conclude that the point is located 2 units to the left of the origin in the x-axis, 4 units up from the origin in the y-axis, and 1 unit down from the origin in the z-axis.
TOPIC
13 Vocabulary Review
Understand Vocabulary
Write always, sometimes, or never.
1. An octagon has 6 sides. Vet
2. A right angle forms a square corner.
3.
Quadrilaterals are squares.
4. A square divided into 3 equal parts shows thirds.
Answers
An octagon has 6 sides. Never
A right angle forms a square corner. Always
Quadrilaterals are squares. Sometimes
A square divided into 3 equal parts shows thirds. Always
How to explainAn octagon has 6 sides. Never
An octagon is a polygon with 8 sides, not 6. A polygon with 6 sides is called a hexagon.
A right angle forms a square corner. Always
A right angle is an angle that measures exactly 90 degrees. It forms a square corner, which is often used to describe the corners of a square or rectangle.
Quadrilaterals are squares. Sometimes
A quadrilateral is a polygon with four sides. A square is a specific type of quadrilateral with four equal sides and four right angles. However, not all quadrilaterals are squares; other examples of quadrilaterals include rectangles, parallelograms, rhombuses, and trapezoids.
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100 POINTS PLEASE HURRY MY MOM IS GOING TO GROUND ME
Scale Factor HC)
Sam has a pool deck that is shaped like a triangle with a base of 15 feet and a height of 9 feet. He plans to build a 3:5 scaled version of the deck next to his horse's water trough.
Part A: What are the dimensions of the new deck, in feet? Show every step of your work. (4 points)
Part B: What is the area of the original deck and the new deck, in square feet? Show every step of your work. (4 points)
Part C: Compare the ratio of the areas to the scale factor. Show every step of your work. (4 points)
Answers
Answer:
Step-by-step explanation:
The base of the new deck will be 3/5 times the base of the original deck, and the height will also be 3/5 times the height of the original deck. Therefore, the dimensions of the new deck are 9 feet for the base and 5.4 feet for the height.
Somebody please help me ITS URGENT
Answers
Answer:
Equation: 4I + 25 = 175
Ticket: $37.50
Step-by-step explanation:
4I + 25 = 175
4I + 25 - 25 = 175 -25
4l = 150
4l = 150/4
I = $37.50
✧☆*: .｡. Hope this helps, happy learning! (*✧×✧*) .｡.:*☆✧
