According to the given information, We will use a right-tailed test. The critical [tex]$z$[/tex]-value is [tex]$z_\alpha = 1.645$[/tex] and the test value is 1.77.
What is right-tailed test?
A right-tailed test, also known as a one-tailed test, is a statistical hypothesis test where the alternative hypothesis is directional and is expressed as an inequality with the greater-than symbol (>), indicating that the parameter being tested is expected to be larger than a specified value.
(a) The null hypothesis [tex]($H_0$)[/tex] and alternative hypothesis [tex]($H_a$)[/tex] are:
[tex]$H_0: \mu = 25$[/tex] (the addition of the mineral does not increase the number of pages read per day)
[tex]$H_a: \mu > 25$[/tex] (the addition of the mineral increases the number of pages read per day)
We will use a right-tailed test because the alternative hypothesis is one-sided (i.e., [tex]$\mu$[/tex] is greater than the hypothesized value).
(b) The critical [tex]$z$[/tex]-value for a one-tailed test with a 5% significance level and 29 degrees of freedom ([tex]df=n-1$, where $n=30$[/tex]) is:
[tex]$z_\alpha = 1.645$[/tex] (from the standard normal distribution table or calculator)
(c) The test value ([tex]$z$[/tex]-value) can be calculated as:
[tex]$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$$[/tex]
where [tex]$\bar{x}$[/tex] is the sample mean, [tex]$\mu$[/tex] is the hypothesized population mean, [tex]$\sigma$[/tex] is the population standard deviation, and [tex]$n$[/tex] is the sample size.
Plugging in the values, we get:
[tex]$z = \frac{25.5 - 25}{\frac{2.4}{\sqrt{30}}} \approx 1.77$$[/tex]
The test value (1.77) is greater than the critical [tex]$z$[/tex]-value (1.645), so we reject the null hypothesis and conclude that the addition of the mineral is effective in increasing the number of pages read per day.
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What would the polar coordinate graph of r^2=81cos2θ like?
The equation of a polar curve r^2 = a cos 2θ describes a limaçon, which is a type of polar curve with a loop. When a is positive, the limaçon has an outer loop and an inner loop. When a is negative, the limaçon has a dimple instead of an inner loop.
In this case, a = 81, which is positive, so the limaçon will have an outer loop and an inner loop.
To graph the limaçon, we can start by considering the behavior of the curve at θ = 0, π/4, π/2, 3π/4, and π.
At θ = 0, r^2 = 81cos(2θ) = 81cos(0) = 81, so r = ±9. This means that there are two points on the curve at θ = 0, one at (9, 0) and one at (-9, 0).
At θ = π/4 and 3π/4, cos(2θ) = cos(π/2) = 0, so r^2 = 0 and r = 0. This means that there are two points on the curve at θ = π/4 and two points at θ = 3π/4, all located at the origin.
At θ = π/2, r^2 = 81cos(2θ) = 81cos(π) = -81, which is negative. Since r is always non-negative, there are no points on the curve at θ = π/2.
At θ = π, r^2 = 81cos(2θ) = 81cos(2π) = 81, so r = ±9. This means that there are two points on the curve at θ = π, one at (9, π) and one at (-9, π).
Based on this information, we can sketch the graph of the limaçon as follows:
There are two points on the x-axis, one at (9, 0) and one at (-9, 0).
There are four points at the origin.
There are two points on the line θ = π, one at (9, π) and one at (-9, π).
The curve passes through the origin at θ = π/4, π/2, and 3π/4, and has a loop that encloses the origin.
Overall, the limaçon has a symmetric, flower-like shape with a loop that encloses the origin.
Answer:
an infinity sign
Step-by-step explanation:
Si tanθ=-1, un posible valor de θ es
If tan θ = - 1, a possible value of θ is C. 135 degrees.
How to find the value of θ?If tanθ = -1, we are looking for an angle where the ratio of the opposite side to the adjacent side is -1. This occurs in the second and fourth quadrants, where either the opposite side is positive and the adjacent side is negative or vice versa.
In the second quadrant, the angle would be (180 - 45)° = 135° or (3π/4) radians.
In the fourth quadrant, the angle would be (360 - 45)° = 315° or (7π/4) radians. Both of these angles have a tangent of -1.
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The full question is:
If tan θ = - 1, a possible value of θ is:
A. 0 degrees B. 30 degrees C. 135 degrees D. 60 degreesDraw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The slope of the line is 2/5 and to represent the "rise" and "run" on the line, a vertical line and a horizontal line are drawn to show the change in y and x, respectively.
To find the slope of the line, we can choose two points on the line and use the formula:
slope = (change in y)/(change in x)
Let's choose the points (-2, 3) and (3, 5) on the line. The "rise" is the change in y and the "run" is the change in x between these two points:
Rise = change in y = 5 - 3 = 2
Run = change in x = 3 - (-2) = 5
So the slope of the line is:
slope = (change in y)/(change in x) = 2/5
Therefore, the slope of the line in simplest form is 2/5.
To represent the "rise and run" on the line, we can draw a vertical line going from the point (-2, 3) to the point (-2, 5) to represent the "rise" of 2 units, and a horizontal line going from the point (-2, 5) to the point (3, 5) to represent the "run" of 5 units.
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11. An ultralight airplane tracked monarch
butterflies migrating to Mexico during
the month of September. There are
30 days in September. How many miles
did the ultralight travel in September?
The ultralight airplane traveled a total of 1350 miles in September while tracking the monarch butterflies migrating to Mexico.
How do we get the number of miles?A mile is unit of distance on land in English-speaking countries equal to 5280 feet, or 1760 yards.
The ultralight airplane tracked monarch butterflies migrating to Mexico for 30 days in September, with a flight mile of 45 miles each day. To find the total miles traveled by the ultralight airplane in September, we can do the following:
Multiply flight mile per day by the number of days
= 45 miles/day x 30 days
= 1,350 miles.
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in presenting the findings of an independent samples t-test, which is the correct order of presentation for results?
The correct order of presentation of sample distribution should include the introduction, method, results, discussion, and conclusion.
The correct order of presentation for results of an independent samples t-test is as follows:Introduction: Introduction should include the aim of the research, the hypothesis, and the data collection method. Method: The method should include the sample size, the type of sample, the data collection method, and the statistical analysis techniques used. Results: The results should include descriptive statistics for each group, the t-test result, the degree of freedom, and the p-value. Discussion: The discussion should include the interpretation of the results, the significance of the findings, and the limitations of the study.Conclusion: The conclusion should summarize the findings and provide suggestions for future research.
Explanation In research, presenting the findings of an independent samples t-test involves comparing the means of two independent groups to determine if there is a significant difference between the two groups. The independent t-test is used when the data are independent, and it assumes that the samples have a normal distribution with equal variances.The results of the t-test can be presented using tables, graphs, or charts.
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A recipe uses 3/4 teaspoon of baking soda and 3 teaspoons of salt write the ratio of baking soda to salt then find the value of the ratio
The value of the ratio of baking soda to salt is 3/4 : 1.
Explain fractionA fraction is a number that represents a portion of a whole or a ratio of two quantities. It consists of two integers arranged one above the other and divided by a horizontal line known as a vinculum or fraction bar.The ratio of baking soda to salt in the recipe can be written as:
Baking soda : Salt = 3/4 : 3
To simplify the ratio, we can first convert the fraction 3/4 to an equivalent fraction with a denominator of 12
3/4 = 9/12
So the ratio becomes:
Baking soda : Salt = 9/12 : 3
We can simplify this ratio further by dividing both the numerator and denominator of the first fraction by 3:
Baking soda : Salt = 3/4 : 1
Therefore, the value of the ratio of baking soda to salt = 3/4 : 1.
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Aria used 1/6 teaspoon of vanilla to make 2/12 containers of pudding. How much vanilla is in one container of pudding
Answer:
1
Step-by-step explanation:
Answer: The answer is 1 tablespoon of vanilla.
Step-by-step explanation:
Based on the given conditions, formulate:
[tex]\frac{1}{6}[/tex] ÷ [tex]\frac{2}{12}[/tex]
Simplify fraction(s): [tex]\frac{1}{1}[/tex]
Any fraction with a denominator of 1 is equal to its numerator, which is 1.
I hope this helped you! A brainilist is highly appreciated and helpful! <3
Help me please, it’s an algebra question
Answer:
Step-by-step explanation:
Sea bass can grow up to a maximum l eights of 23 inches how much more would the longest fish caught need to grow in order to reach the maximum length
The longest fish caught needs to grow an additional 4 inches in order to reach the maximum length of 23 inches.
The longest fish caught needs to grow an additional 4 inches in order to reach the maximum length of 23 inches. This can be calculated using the formula:
Maximum length - Current length = Amount of growth required
In this case, we substitute the values as follows:
23 inches - 19 inches = 4 inches
Therefore, the longest fish caught needs to grow an additional 4 inches in order to reach the maximum length.
To help visualize this, we can consider the scales of the fish. To reach the maximum length, the longest fish caught would need to add 4 scales, which is a relatively small amount. This is conceivable, as the fish can continue to grow as long as it has access to enough food and a suitable environment.
In summary, the longest fish caught needs to grow an additional 4 inches in order to reach the maximum length of 23 inches. This can be calculated using the formula: Maximum length - Current length = Amount of growth required. To help visualize this, the fish needs to add 4 scales which is a relatively small amount.
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If two lines intersect, the four angles created by the intersecting lines all share the same ______, but they are _____ only if they are nonadjacent.
linear pairs
vertical angles
supplementary
sides
vertex
Step-by-step explanation:
vertex vertical angles
Maria is making a rectangular quilt. She starts with a square of fabric with side length x cm.
She adds some fabric to one side of the square and a different amount of fabric to an adiacent side of the square. Her final quilt has an area of x2 + 13x + 30 cm?. How much longer is the long dimension of the quilt than the short dimension?
Therefore, the long dimension of the quilt is (26x + 60)/(x + 6) cm longer than the short dimension.
What is area?Area is the measure of the extent of a 2-dimensional surface or region, usually measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²). It is the amount of space inside the boundary of a flat shape or the surface of an object.
Here,
The area of the original square is x^2 cm². Maria adds some fabric to one side of the square, which increases the length of the rectangle by a certain amount, and adds a different amount of fabric to the adjacent side, which increases the width of the rectangle by a certain amount. Let's say Maria adds y cm of fabric to one side and z cm of fabric to the other side. Then the length of the rectangle is x + y cm and the width is x + z cm. The area of the rectangle is given by:
(x + y)(x + z) = x^2 + xy + xz + yz
We know that the area of the rectangle is x² + 13x + 30 cm². So we can set these two expressions equal to each other:
x² + xy + xz + yz = x² + 13x + 30
Simplifying this equation, we get:
xy + xz + yz = 13x + 30
We want to find the difference between the length and the width of the rectangle, which is (x + y) - (x + z) = y - z. To solve for y - z, we need to express yz in terms of y - z. We can do this by factoring the left side of the equation above:
xy + xz + yz = y(x + z) + xz = (y - z)(x + y + z)
Substituting this expression for yz in the equation above, we get:
(y - z)(x + y + z) = 13x + 30
We want to solve for y - z, so let's focus on the left side of the equation:
(y - z)(x + y + z) = y(x + y + z) - z(x + y + z)
= xy + y² + yz - xz - z² - yz
= y² - z² + xy - xz
Substituting the expression we found earlier for xy - xz, we get:
(y - z)(x + y + z) = y² - z² + (y - z)(x + z)
(y - z)[x + y + z - (x + z)] = y² - z²
y - z = (y² - z²)/(y - z) = y + z
= (13x + 30)/(x + 6)
So the difference between the length and the width of the rectangle is:
y - z = (13x + 30)/(x + 6)
Therefore, the long dimension of the quilt is (x + y) = x + (13x + 30)/(x + 6) cm, and the short dimension is (x + z) = x + (30 - 13x)/(x + 6) cm. The difference between the long and short dimensions is:
[x + (13x + 30)/(x + 6)] - [x + (30 - 13x)/(x + 6)]
= (13x + 30)/(x + 6) - (30 - 13x)/(x + 6)
= (26x + 60)/(x + 6)
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Select the two values of x that are roots of this equation.
x^2 +1 = 5x
Answer:
options C and D is the answer
Let us suppose we have data on the absorbency of paper towels that were produced by two different manufacturing processes. From process 1, the sample size was 10 and had a mean and standard deviation of 130 and 15, respectively. From process 2, the sample size was 4 with a mean and standard deviation of 310 and 50, respectively. Find a 95% confidence interval on the difference in the towels' mean absorbency produced by the two processes. Assume the standard deviations are estimated from the data. Round your answers to two decimal places (e.g. 98.76). SH1 – H2= i e Textbook and Media
A 95% confidence interval on the difference in the towels' mean absorbency produced by the two processes is between -295.36 and -104.64
We can use the two-sample t-test formula to find the confidence interval for the difference in means:
t = (x1 - x2 - d) / √(s1²/n1 + s2²/n2)
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, d is the hypothesized difference in means (usually 0 in a two-sided test), and t follows a t-distribution with degrees of freedom given by:
df = (s1^2/n1 + s2^2/n2)^2 / (s1^4/n1^2(n1-1) + s2^4/n2^2(n2-1))
Plugging in the given values, we have:
x1 = 130, s1 = 15, n1 = 10
x2 = 310, s2 = 50, n2 = 4
d = 0 (since we are testing for a difference of means)
t(0.025, df) = 2.306 (using a t-table or calculator)
Substituting these values into the formula, we get:
t = (130 - 310 - 0) / sqrt(15^2/10 + 50^2/4) = -4.156
df = (15^2/10 + 50^2/4)^2 / (15^4/10^2(10-1) + 50^4/4^2(4-1)) = 7.38 (rounded to 2 decimal places)
The 95% confidence interval for the difference in means is given by:
(x1 - x2) ± t(0.025, df) * sqrt(s1^2/n1 + s2^2/n2)
= (130 - 310) ± 2.306 * sqrt(15^2/10 + 50^2/4)
= (-200 ± 95.36)
= (-295.36, -104.64)
Therefore, we can be 95% confident that the true difference in mean absorbency between the two processes is between -295.36 and -104.64. Since the interval does not contain 0, we can conclude that the means are significantly different at the 5% level.
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(20) The images below show a picture of Ricoffy tin container with no dimensions indicated. The container is 2,5 times smaller than what it is in reality. QUESTION 1 ета NESCAFE Ricoffy Share the fresh, smooth taste Solable Chicory and Coffee Granules qane Diameter of the tin on the picture = ? Height of the tin on the picture = ? Actual weight of coffee = 750 g 1.1 Measure the diameter of the tin in mm and write down the real diameter in mm (3)
Answer:21
Step-by-step explanation:
A basic set of drawing pencils costs $8. 98. A professional set of drawing pencils costs $27. 49. How much more does the professional set cost than the basic set?
The professional set of drawing pencils costs $18.51 more than the basic set. This is a significant difference in price and may be worth the additional cost depending on the user's needs.
First, we need to calculate the difference in price between the professional set and the basic set of drawing pencils. To do this, we will subtract the cost of the basic set ($8.98) from the cost of the professional set ($27.49).
We can write this difference as an equation:
Difference = Professional Set Cost - Basic Set Cost
Difference = 27.49 - 8.98
Next, we can solve for the difference in price by subtracting the two values.
Difference = 18.51
Therefore, the professional set of drawing pencils costs $18.51 more than the basic set. This is a significant difference in price and may be worth the additional cost depending on the user's needs.
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Simplify the expression below. Determine the value of the exponent for y.
After answering the provided question, we can conclude that Therefore, the simplified expression is [tex](y / x) * (1 / z^5)[/tex] and the value of the exponent for y is 1.
what is expression ?An expression in mathematics is a collection of manifestations, digits, and transnational corporations that resemble a significant correlation or regimen. A square root, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, pervasiveness, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
To simplify the expression,
[tex]x^0xy^2z(^-3) = xy^2z(^-3)\\xy^2z(^-3) / x^2yz^2\\= (xy^2 / x^2y) * (1 / z^5)\\= (y / x) * (1 / z^5)[/tex]
Therefore, the simplified expression is [tex](y / x) * (1 / z^5)[/tex] and the value of the exponent for y is 1.
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helppppp algebra 2 problem
Therefore, the football team scored 4 touchdowns, 2 field goals, and 1 safety in the game.
What is equation?An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on. An equation is often written with an equal sign (=) between the two expressions. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used extensively in mathematics, physics, engineering, and many other fields to describe relationships between different quantities.
by the question.
Let's denote the number of touchdowns scored by "T", the number of field goals scored by "F", and the number of safeties scored by "S".
From the problem, we know:
[tex]T + F + S = 8 (they scored points 8 times)\\7T + 3F + 2S = 38 (the total score was 38 points)\\T = F + S[/tex] (they scored as many touchdowns as they did field goals and safeties combined)
Substituting the third equation into the first, we get:
[tex]F + S + F + S = 8\\2F + 2S = 8\\F + S = 4[/tex]
We now have a system of three equations:
[tex]T + F + S = 8\\7T + 3F + 2S = 38\\T = F + S[/tex]
Substituting the third equation into the first two, we get:
[tex]7(F + S) + 3F + 2S = 38\\8(F + S) = 21[/tex]
Solving for F + S, we get:
[tex]F + S = 21/8[/tex]
However, we also know that F + S = 4, so there must be a mistake somewhere. Looking back at the problem, we see that the statement "they scored as many touchdowns as they did field goals and safeties combined" implies that T = F + S + 1 (since a touchdown is worth 7 points and a field goal and safety combined are worth 4 points). Substituting this into the first two equations, we get:
[tex](F + S + 1) + F + S = 8\\7(F + S + 1) + 3F + 2S = 38[/tex]
Simplifying, we get:
[tex]2F + 2S = 6\\10F + 9S = 31[/tex]
Solving for F and S, we get:
[tex]F = 2\\S = 1[/tex]
Substituting these values back into the equation T = F + S + 1, we get:
[tex]T = 4[/tex]
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Your boss hands you a memo with a summary of the monthly data. The number of imports is shown as f(x), and the number of exports is shown as g(x). Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents. Use complete sentences.
Month f(x) = No. of imports g(x) = No. of exports
January (1) 3 1
February (2) 4 3
March (3) 5 5
April (4) 6 7
x²+ 5/4x = 3/2
please help with answer
SteSteAnswerAnswer:
x = 3/4 and -2
Step-by-step explanation:
If x²+ 5/4x = 3/2, x²+ 5/4x - 3/2 = 0
Multiply by 4 to get 4x²+ 5x - 6 = 0
Factor it to get (4x - 3)(x + 2) = 0
anything times 0 = 0, so x = 3/4 and -2
Yu Sano downloaded 10 songs and 4 movies for $22. Francois downloaded 20 songs and 2 movies for $26. Create a system of equations.
The system of equations- 4x-22=0
26y-2=0.
What is an equation?A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.
It demonstrates the equality of the relationship between the printed statements on the left and right unknowable quantities, you can solve equations.
A statement is not an equation if it lacks the equals sign.
Left side equals right side in all formulas.
To find the values of unknowable variables, which stand in for
When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.
Hence, The system of equations- 4x-22=0,
26y-2=0.
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(b) Carl, Dina and Eva share 100 oranges. The ratio Carl's oranges : Dina's oranges = 3:5. The ratio Carl's oranges: Eva's oranges = 2:3. Find the number of oranges Carl receives.
Using ratios, Carl will receive 24 oranges, while Dina will get 40 oranges, and Eva will receive 36 oranges.
What is a ratio?A ratio shows the relative size of one quantity compared to another quantity or value.
Ratios are expressed in standard ratio forms using the colon (:), in decimals, fractions, or percentages.
The total number of oranges shared between Carl, Dina, and Eva = 100
The ratio Carl's oranges to Dina's oranges = 3:5
The ratio Carl's oranges to Eva's oranges = 2:3
Based on the above ratios, for every 2 oranges that Carl receives, Eva receives 3.
For Carl to receive 3 oranges, Eva will receive 4.5 oranges (3 x 3/2)
The ratios among the three friends are 3: 5: 4.5
The sum of ratios = 12.5 (3 + 5 + 4.5)
Carl's share = 24 (3/12.5 x 100)
Dina's share = 40 (5/12.5 x 100)
Eva's share = 36 (4.5/12.5 x 100)
Thus, based on the ratios, the number of oranges Carl receives is 24.
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The list price of a commodity is RM 120 and the percentage profit is 60%. If the commodity is sold at a discount of 30%. The profit is
Answer: RM 86.40
Step-by-step explanation:
The profit can be calculated as follows:
Selling price = List price + Profit
Profit = (Percentage profit/100) x List price
Discount = (Discount percentage/100) x Selling price
Selling price after discount = Selling price - Discount
Let's plug in the given values into these formulas:
List price = RM 120
Percentage profit = 60%
Profit = (60/100) x 120 = RM 72
Discount percentage = 30%
Selling price = 120 + 72 = RM 192
Discount = (30/100) x 192 = RM 57.60
Selling price after discount = 192 - 57.60 = RM 134.40
To calculate the profit after discount, we need to subtract the cost price from the selling price after discount:
Profit after discount = Selling price after discount - Cost price
Cost price = List price - Profit = 120 - 72 = RM 48
Profit after discount = 134.40 - 48 = RM 86.40
Therefore, the profit after the discount is RM 86.40.
Bree has 100mg of caffeine in her system at 8am, at 2p, 28.24mg left. What is the hourly decreasing rate the caffeine leaves the body?
The caffeine is leaving Bree's body at a rate of approximately 11.96 mg per hour.
What is the rate?
Rate is a measurement of the speed of change or the amount of change that occurs per unit of time or per unit of some other quantity. It is a ratio between two different measurements, typically expressed in units of distance, time, weight, volume, or currency.
The caffeine in Bree's system is decreasing linearly over the course of 6 hours (from 8am to 2pm).
We can use the information given to find the hourly decreasing rate by calculating the slope of the line connecting the two data points.
The change in caffeine over 6 hours is:
100 mg - 28.24 mg = 71.76 mg
So the hourly decreasing rate can be calculated as:
Hourly decreasing rate = Change in caffeine / Time
Hourly decreasing rate = 71.76 mg / 6 hours
Hourly decreasing rate = 11.96 mg/hour (rounded to two decimal places)
Therefore, the caffeine is leaving Bree's body at a rate of approximately 11.96 mg per hour.
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Triangle JKL has vertices J(3,1),K(7,-5), and L(5,7). Determine the coordinates of the vertex L^(`) after the triangle is rotated by 180degrees clockwise about the origin.
Answer:
(-5, -7)
Step-by-step explanation:
To rotate a point (x,y) by 180 degrees about the origin, we can multiply its coordinates by the matrix:
-1 0
0 -1
So, to rotate the triangle JKL by 180 degrees about the origin, we can apply this transformation to each of its vertices. We have:
J(3,1) -> J^`(−3,−1)
K(7,−5) -> K^`(−7,5)
L(5,7) -> L^`(−5,−7)
Therefore, the coordinates of the vertex L^(`) after the triangle is rotated by 180 degrees clockwise about the origin are (-5, -7).
2.an electric clothes dryer has a power rating of 4000w. assume that a family does five loads of laundry each week for 4 weeks. further assume that each load takes one hour. a.find the energy used in both j and kwh b.if the cost of electricity is $.075/kwh, find the cost of operating the dryer for a month (4 weeks).
The cost of operating the dryer for a month is $6.
An electric clothes dryer has a power rating of 4000W. Assume that a family does five loads of laundry each week for 4 weeks. Further assume that each load takes one hour. A. Find the energy used in both J and kWh.
1J = 1W.s
Energy used = Power x time= 4000W x (5 x 4) x 1h= 80000Wh= 80 kWh
Thus, the energy used in kWh is 80 kWh.1kWh = 1000Wh
1kWh = 3.6 x 10^6 J
Thus, the energy used in J is 80 x 3.6 x 10^6 = 288 x 10^6 J.B. If the cost of electricity is $.075/kWh, find the cost of operating the dryer for a month (4 weeks).
The energy used by the dryer for a month is 80 kWh.
Cost of operating the dryer for a month = Energy used x Cost per kWh= 80 kWh x $0.075/kWh= $6
Therefore, the cost of operating the dryer for a month is $6.
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The x-value for this situation represents time in minutes. So, what does the x-vaule of the point of intersection rrepresent??
The point of intersection of the graph (2,9), means that at 2 minutes, the altitude was 9 thousand feet.
The y-axis in the presented graph denotes altitude in thousand feet, while the x-axis in the graph denotes time in minutes. The point of intersection, (2,9), indicates that the height was 9000 feet at 2 minutes.
The moment when the height was 9000 feet is indicated by the x-value, which in this instance is 2. It identifies the precise point in time when the height was displayed on the graph as 9000 feet.
It is crucial to understand the x-value of the point of contact because it enables precise computations and predictions about the height at various times.For example, if we want to know the altitude at 5 minutes, we can use the slope of the graph and the point of intersection to determine the altitude accurately.
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Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The statements that are true about the quadratic function and its graph include the following:
The value of f(–10) = 82The graph of the function is a parabola.The graph contains the point (20, –8).How to determine the true statements about this function and its graph?In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive i.e when the value of "a" is greater than zero.
Next, we would determine the statements about the quadratic function and its graph that are true:
At point (-10, 82), we have:
[tex]f(x) = \dfrac{1}{5} \ x^2 - 5x + 12[/tex]
[tex]f(x) = x^2/5 - 5x + 12[/tex]
[tex]f(-10) = -10^2/5 - 5(-10) + 12[/tex]
[tex]f(-10) = 82[/tex]
At point (20, -8), we have:
[tex]f(x) = \dfrac{1}{5} \ x^2 - 5x + 12[/tex]
[tex]f(x) = x^2/5 - 5x + 12[/tex]
[tex]f(20) = 20^2/5 - 5(20) + 12[/tex]
[tex]f(20) = -8[/tex]
In conclusion, the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.
Find the gradient of the tangent to the graph:
y = 3x^2 – 7x – 5
at (2, - 7)
Step-by-step explanation:
Take the derivative of this function using the power rule
[tex] \frac{d}{dx} ( {x}^{n} ) = nx {}^{n - 1} [/tex]
Since the terms are serpated using addition or subtraction we can take the derivative of this function separately
So our derivative end up becoming
[tex]6x - 7[/tex]
Plug in x=2
[tex]6(2) - 7 = 5[/tex]
So the gradient of the tangent line at 2,-7 is 5
The equation x2 - 9 = 0 has ___
real solution(s).
By answering the presented question, we may conclude that Because equation both of these answers are real values, the solution to the equation x2 - 9 = 0 is that it has two real solutions.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation [tex]"x^2 + 2x - 3 = 0,"[/tex]for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
(x-3)(x+3) = 0 is a rewrite of the equation [tex]x^2 - 9 = 0.[/tex] This suggests that the equation's solutions are x = 3 and x = -3.
Because both of these answers are real values, the solution to the equation x² - 9 = 0 is that it has two real solutions.
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Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.
y>3x-4
y>-1/2+3
The intersection points between the two lines y > (3x-4) and y > -(1/2)x+3, from the graph is (x, y) = (2, 2)
What is inequalities?To graphically solve the system of inequalities, we will first graph the two boundary lines, which are the lines obtained by replacing the inequality symbols with equality symbols in each of the given inequalities:
y > 3x - 4 (red dotted line)
y > -(1/2)x + 3 (blue dotted line)
When we plug (0, 0) into y > 3x - 4, we get:
⇒ 0 > 3(0) - 4
⇒ 0 > -4
This inequality is true, so we shade the half-plane above the solid line,
y = 3x - 4
When we plug (0, 0) into y > -(1/2)x + 3, we get:
⇒ 0 > -(1/2)(0) + 3
⇒ 0 > 3
This inequality is not true, so we shade the half-plane below the dashed line, y = -(1/2)x + 3
The solution set is the region that is shaded in both half-planes, which is the triangular region above the solid line and below the dashed line.
Now, we have to determine the intersection points between the two lines y > (3x-4) and y > -(1/2)x+3, from the graph, we get; (x, y) = (2, 2)
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Graph of the solution-