The critical value tₕ for a confidence level of 0.99 and a sample size of 22 is approximately 2.831.
To find the critical value tₕ for a given confidence level and sample size, we can use a t-distribution table or a statistical software.
For a confidence level of 0.99, we need to determine the critical value tₕ such that the area under the t-distribution curve to the right of tₕ is equal to (1 - c) / 2. In this case, (1 - c) / 2 = (1 - 0.99) / 2 = 0.005.
Since the sample size is 22, we have n - 1 degrees of freedom, which is 22 - 1 = 21. We need to find the critical value tₕ with 21 degrees of freedom that corresponds to an area of 0.005 in the upper tail of the t-distribution.
Using a t-distribution table or a statistical software, we find that the critical value tₕ is approximately 2.831.
Therefore, the critical value tₕ for a confidence level of 0.99 and a sample size of 22 is approximately 2.831.
It is important to note that the critical value may vary slightly depending on the specific t-distribution table or statistical software used. However, the value obtained above is a reasonable approximation based on commonly used tables or software.
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what is da rate to question
The calculated value of the rate of the graph is 0.8
How to determine the rate of the graphfrom the question, we have the following parameters that can be used in our computation:
The graph
Where, we have
(0, -16) and (20, 0)
The rate of the graph is calculated as
Rate = Change in y/x
using the above as a guide, we have the following:
Rate = (0 + 16)/(20 - 0)
Evaluate
Rate = 0.8
Hence, the rate is 0.8
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Mathematical Literacy/Term 2 Assignment 6 NSC Grade 12 RTB/MAY 2023 QUESTION 4 Ms Lerato bakes rusks and sells them in 500 g packs, at R55,00 per pack. Table 3 shows the main ingredients of the rusks. TABLE 3: MAIN INGREDIENTS TO BAKE 800 g OF RUSKS 2 500 g Self-raising flour 10 cups Bran flour 200 g Raisins 1 000 g Butter Use the information above to answer the questions that follow. 4.1 Convert the mass of the self-raising flour to kg. 4.2 Determine the number of cups of bran flour needed to bake 400 g of rusks. 4.3 Write, in simplified form, the ratio of raisins to butter. 4.4 The rusks were placed in the oven to bake at 14:40. Write down, in words, the time the rusks were placed in the oven. (2) (2) (2) (2) [8]
[tex]{\huge{\blue{\tt{Step\:by\:step\:solution}}}}[/tex]
4.1 To convert the mass of the self-raising flour to kg, we can divide the mass by 1000, since there are 1000 grams in a kilogram:
2 500 g ÷ 1000 = 2.5 kg
So the mass of the self-raising flour is 2.5 kg.
4.2 To determine the number of cups of bran flour needed to bake 400 g of rusks, we can use a proportion:
800 g of rusks requires 10 cups of bran flour
400 g of rusks requires x cups of bran flour
We can set up the proportion as:
800 g ÷ 10 cups = 400 g ÷ x cups
Cross-multiplying, we get:
800 g x cups = 10 cups x 400 g
Simplifying, we get:
x = 5 cups
So 5 cups of bran flour are needed to bake 400 g of rusks.
4.3 To write the ratio of raisins to butter in simplified form, we can divide both quantities by their greatest common factor. The greatest common factor of 200 g and 1 000 g is 200 g, so we can divide both by 200 g:
200 g ÷ 200 g = 1
1 000 g ÷ 200 g = 5
So the simplified ratio of raisins to butter is 1:5.
4.4 The rusks were placed in the oven to bake at 14:40. In words, this time is "twenty to three in the afternoon" (assuming that the time is given in a 12-hour clock format).
Find the area of
the parallelogram.
8
11
7
Use the
formula:
a = bh
area = base x height.
b = 11
h = 7
a = [?]
Answer:
77 units^2
Step-by-step explanation:
Since the formula for the area of a parallelogram is Area = Base x Height, you can multiply the Base (11) by the Height (7)
So, A = (7) x (11) = 77 units^2
The 8 in this case is not necessary. You only need the base and height. Hope this helps!
Make sure to maximize the question window to get the best view of this problem.
Give the formulas for the piecewise function graphed below.
Make sure the top row is for the left piece, the second row is
for the middle plece, and the bottom row is for the right piece.
f(x) =
The formulas for the piecewise function graphed below are:
f(x) = x + 3 for -2 ≤ x < 0, 3 for 0 ≤ x < 2, -2x + 7 for 2 ≤ x ≤ 4.
The piecewise function graph provided consists of three distinct pieces.
To give the formulas for each piece, we can break it down as follows:
For the left piece:
The left piece of the graph starts at x = -2 and ends at x = 0. It appears to be a linear function with a positive slope. Let's call this function f₁(x).
The formula for the left piece, f₁(x), can be written as:
f₁(x) = mx + b
To find the slope (m) and y-intercept (b), we can use two points on the graph.
From the graph, we can see that when x = -2, y = 1. And when x = 0, y = 3.
Using the formula for slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 1) / (0 - (-2))
m = 2 / 2
m = 1
Substituting the values of m and one of the points (x, y) into the equation, we can solve for the y-intercept (b):
1 = 1(-2) + b
1 = -2 + b
b = 1 + 2
b = 3
Therefore, the formula for the left piece is:
f₁(x) = x + 3
For the middle piece:
The middle piece of the graph starts at x = 0 and ends at x = 2. It appears to be a horizontal line.
Let's call this function f₂(x).
The formula for the middle piece, f₂(x), can be written as:
f₂(x) = c
To find the value of c, we can observe that the y-values of this piece are all equal to 3.
Therefore, the formula for the middle piece is simply:
f₂(x) = 3
When x = 2, y = 3. And when x = 4, y = -1.
Using the formula for slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
m = (-1 - 3) / (4 - 2)
m = -4 / 2
m = -2
Substituting the values of m and one of the points (x, y) into the equation, we can solve for the y-intercept (b):
3 = -2(2) + b
3 = -4 + b
b = 3 + 4
b = 7
Therefore, the formula for the right piece is:
f₃(x) = -2x + 7
To summarize, the formulas for the piecewise function graphed below are:
f(x) =
x + 3 for -2 ≤ x < 0
3 for 0 ≤ x < 2
-2x + 7 for 2 ≤ x ≤ 4
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you ran 4 1/2 times around a quarter mile track. how far did you run?
Answer:
1 1/8 of a mile.
Step-by-step explanation:
The distance around the track is one quarter of a mile. Therefore, if you run around the track 4 times, you will have ran 1 mile, as 4 * 1/4 = 1. You would also run the other 1/2 of the lap, and to find that distance, you would multiply 1/2 * 1/4, because you only ran 1/2 of a lap and not one whole lap, which would come out to 1/8 of a mile. So, your final answer would be 1 + 1/8 of a mile, which comes out to 1 and 1/8 of a mile.
See picture dfown below for refgerecnce
The value of the quadratic function y = x² - 4x + 3 is determined by substituting the given value of x into the equation and performing the necessary calculations.
1. Start with the quadratic function: y = x² - 4x + 3.
2. Determine the value of x for which you want to find the value of y.
3. Substitute the given value of x into the equation.
4. Perform the necessary calculations to simplify the expression.
5. Evaluate the expression to find the value of y.
For example, let's find the value of y when x = 2:
1. Start with the quadratic function: y = x² - 4x + 3.
2. We want to find the value of y when x = 2.
3. Substitute x = 2 into the equation: y = (2)² - 4(2) + 3.
4. Simplify the expression: y = 4 - 8 + 3.
5. Perform the necessary calculations: y = -1.
6. Therefore, when x = 2, the value of the quadratic function y = x² - 4x + 3 is -1.
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9 ft
4.7 ft
6.5 ft
6.5 ft
Find the area of the triangle.
Answer: 21.15 ft²
Step-by-step explanation:
We can use the formula for the area of a triangle:
(b×h)/2
In this case, the base is 9 and the height is 4.7.
So, we substitute the variables with the numbers in this problem.
(9 × 4.7)/2
9 × 4.7 = 42.3
42.3/2 = 21.15
So, our final answer is 21.15 ft²
A 25-foot tree casts a 10-foot shadow. At the same time, a nearby cell tower casts a 30 -foot shadow. How tall (in feet) is the cell tower?
give me a solution just the answer
Answer:
If the tickets are priced at $20 each, the total amount of money taken in would be $88,000.
Step-by-step explanation:
To write the number of tickets sold, n, as a function of the ticket price, p, we can use the given information that for every $1 increase in price, 200 tickets go unsold.
Let's define the slope of the line as the decrease in tickets per dollar increase in price. Since 200 tickets go unsold for every $1 increase, the slope of the line is -200.
Now, let's find the equation of the line through the given points: (12, 6000), (13, 5800), (14, 5600), and so on.
Using the point-slope form of a linear equation, we have:
n - 6000 = -200(p - 12)
Simplifying the equation, we get:
n - 6000 = -200p + 2400
Rearranging the equation to solve for n, we have:
n = -200p + 8400
This equation represents the number of tickets sold, n, as a function of the ticket price, p.
To find how much money will be taken in if the tickets are $20 each, we substitute p = 20 into the equation:
n = -200(20) + 8400
n = -4000 + 8400
n = 4400
If the tickets are $20 each, the number of tickets sold would be 4400. To calculate the total amount of money taken in, we multiply the number of tickets sold by the ticket price:
Money taken in = Number of tickets sold * Ticket price
Money taken in = 4400 * $20
Money taken in = $88,000
Hope this helps.
Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
Each pair of figures is similar. Find the value of the missing side (x). Round your answer to the nearest tenth if necessary.
Answer:
4.9 in
Step-by-step explanation:
6/11 = x/9
6/11 times 9 = x
x = 4.9
If GE is the angle bisector of
quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 62
minutes with a mean life of 606
minutes.
If the claim is true, in a sample of 99
batteries, what is the probability that the mean battery life would be greater than 619
minutes? Round your answer to four decimal places.
Answer:
Step-by-step explanation:
What change do you have to make to the graph of f (x) = 7x in order to graph the function g (x) = 7x+10?
To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.
To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.
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Which graph shows a dilation? On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 4, 3), (0, 3), (2, 0), and (negative 2, 0). The smaller quadrilateral has points (negative 2, 2), (0, 2), (0.5, 0), and (negative 1.5, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0). On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 0.5, 0), (negative 1, 2), (1, 2), (1.5, 0).
Celeste is planting a rectangular flower garden in which the width will be 4 feet less than its length. She has decided to put a birdbath within the garden that will occupy a space 3feet by 4 feet how many feet are now left for planting? Express your answer on factored form
Answer:
(L-6)(L+2)
Step-by-step explanation:
Let L be the length of the flower garden.
Then the width will be L-4.
The area of the flower garden = L*(L-4) =L²-4L
The area of the birdbath is 3*4 = 12 ft²
The area of the remaining space for planting is
= Area of flower garden - area of birdbath
L² - 4L - 12We can factor the expression as follows:
L² - 4L - 12 L²-(6-2)L-12L²-6x+2x-12taking common frome each two terms
L(L-6)+2(L-6)(L-6)(L+2)Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.
Which linear equation shows a proportional relationship?
y equals negative one sixth times x
y equals one sixth times x minus 8
y = −6x + 1
y = 6
Answer:
y = (-1/6)x represents a proportional relationship.
write y+4=-2(x-1) in slope intercept form
Answer:
y=2x-6
Step-by-step explanation:
y+4=-2(x-1)
Since the slope intercept form is in the form of:
y=mx+c
Making above equation in this form.
y+4=-2(x-1)
opening bracket
y+4=2x-2
subtracting both side by 4.
y+4-4=2x-2-4
y=2x-6
This equation is the slope intercept form.
14Y - 7y = 35. solve for y
Answer:
y = 5
Step-by-step explanation:
[tex]14y-7y=35\\7y=35\\y=5[/tex]
14 minus 7 is 7
7Y is equal to 35
divide both sides by 7 is equal to 5
A green grocer buys a box of 150 grapefruit for $12. He sells them for 12 cents each. What is the profit percent
The profit percent made by the green grocer on the sale of the grapefruits is 50%.
To calculate the profit percent, we need to determine the profit made on the sale of the grapefruits.
The grocer buys a box of 150 grapefruits for $12, which means the cost of each grapefruit is $12/150 = $0.08.
The grocer sells each grapefruit for 12 cents, which is $0.12.
The profit made on each grapefruit is the selling price minus the cost price: $0.12 - $0.08 = $0.04.
Now, we can calculate the total profit by multiplying the profit per grapefruit by the number of grapefruits: $0.04 * 150 = $6.
To find the profit percent, we divide the profit by the cost price and multiply by 100: ($6 / $12) * 100 = 50%.
Therefore, the profit percent is 50%.
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Shireen had a nap for 2 h. After her nap, she played badminton for 1/2h and swam for 1/5h.
(a) How long did Shireen exercise?
(b) How much more time did Shireen spend on her nap than on
her exercise?
A study was completed in Georgia. In northern Georgia, the study involved 3,000 patients; 84% of them experienced flulike symptoms during the month of December. The study had a margin of error of 1.7% What does that mean for the study?
Simplify 3r^4 • (-4r^0)
A ____ is just another way of saying what we want to count by on our graph.
Answer:
A scale is just another way of saying what we want to count by on our graph.
Step-by-step explanation:
A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.
what is the result of converting 2.3 miles into yards ? remenber that 1 mile=1760 yards.
4048 yards is the answer
Step-by-step explanation:
2.3 × 1760
In simplest radical form, what are the solutions to the quadratic equation 0 =-3x² - 4x + 5?
-b± √b²-4ac
2a
Quadratic formula: x =
O x= -2±√19
3
Ox=-
2+2√19
3
0 x= 2+√15
3
0 x = 2+2√/19
3
Answer:
To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula:x = (-b ± √(b² - 4ac)) / (2a)In this case, a = -3, b = -4, and c = 5. Plugging these values into the formula, we get:x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))Simplifying further:x = (4 ± √(16 + 60)) / (-6) x = (4 ± √76) / (-6) x = (4 ± 2√19) / (-6)We can simplify the expression further:x = -2/3 ± (√19 / 3)Therefore, the solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are:x = (-2 ± √19) / 3The solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are x = (-2 + √19) / 3 and x = (-2 - √19) / 3.
To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).
Comparing the equation to the standard quadratic form ax² + bx + c = 0, we have a = -3, b = -4, and c = 5.
Plugging these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))
= (4 ± √(16 + 60)) / (-6)
= (4 ± √76) / (-6)
= (4 ± 2√19) / (-6)
= -2/3 ± (1/3)√19
Therefore, the solutions to the quadratic equation are:
x = -2/3 + (1/3)√19 and x = -2/3 - (1/3)√19
In simplest radical form, the solutions are:
x = (-2 + √19) / 3 and x = (-2 - √19) / 3.
These expressions cannot be further simplified since the square root of 19 is not a perfect square.
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Which value is equilivent to x+4/4+x
Answer:
It's 1
Step-by-step explanation:
any number or expression divided by itself is 1
Answer:
1
Step-by-step explanation:
The expression (x + 4) / (4 + x) simplifies to 1 because no matter what value you choose for x, when you add 4 to it and add the same value to 4, you always get the same result in the numerator and denominator, making them cancel out and equal to 1.
Factorise the formula y = 4x² + 16x +15 in the form y = (2x +...)(2x + ...). help
Answer:
y = (2x + 5)(2x + 3)
Step-by-step explanation:
y = 4x² + 16x + 15
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 15 = 60 and sum = + 16
the factors are + 10 and + 6
use these factors to split the x- term
y = 4x² + 10x + 6x + 15 ( factor the first/second and third/fourth terms )
y = 2x(2x + 5) + 3(2x + 5) ← factor out (2x + 5) from each term
y = (2x + 5)(2x + 3)
since multiplication is commutative , then could be
y = (2x + 3)(2x + 5)
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.
For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).
Applying this transformation to each vertex of triangle NMO, we get:
N' = (2(-1) - (-5), 2) = (5, 2)
M' = (2(-1) - (-2), 1) = (2, 1)
O' = (2(-1) - (-3), 3) = (3, 3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
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Plot axis of symmetry H(x) = -(x+2)2 + 8
The x-coordinate of the vertex is given by h = -2 and the equation of the axis of symmetry is x = -2.
Given function is H(x) = -(x + 2)² + 8.
The axis of symmetry of a quadratic function y = ax² + bx + c is defined by x = -b/2a.
So, let's solve the problem as follows:
To find the axis of symmetry, we need to convert the given function into standard form y = a(x - h)² + k.
We can do this by completing the square.
For that, we have
H(x) = -(x + 2)² + 8H(x)
= -1(x² + 4x + 4) + 8H(x)
= -1(x + 2)² + 8
The standard form is y = a(x - h)² + k, so the given function is y = -1(x + 2)² + 8.
The vertex form of a quadratic equation is y = a(x - h)² + k
Where(h, k) is the vertex.
The vertex form of the given function H(x) = -(x + 2)² + 8 can be calculated as follows:
y = a(x - h)² + k
The vertex form is y = a(x - h)² + k.
Where the vertex form of the given function is:
y = -1(x + 2)² + 8.
Since the vertex form is y = a(x - h)² + k the vertex form of the given function is y = a(x + 2)² + 8 and (h, k) = (-2, 8).
Vertex is given by h = -2.
Axis of symmetry is x = -2.
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1. Obtener el área del siguiente rectángulo.
13
2
74
The area of the given rectangle is determined by multiplying its length of 13 units by its width of 2 units, resulting in an area of 26 square units.
To find the area of the rectangle, we need to multiply its length by its width. The length of the rectangle is given as 13 units and the width is given as 2 units.
The formula to calculate the area of a rectangle is: Area = Length × Width.
Using the given measurements, we substitute the values into the formula:
Area = 13 × 2 = 26 square units.
Therefore, the area of the given rectangle is 26 square units.
To provide a more detailed explanation, the area of a rectangle represents the total amount of space enclosed by its four sides. In this case, the rectangle has a length of 13 units and a width of 2 units. When we multiply the length by the width, we are essentially finding the product of the two dimensions, which gives us the total area.
The resulting area of 26 square units implies that within the boundaries of the rectangle, there are 26 square units of space. It is important to note that the unit of measurement used for the length and width should be consistent to ensure the accuracy of the area calculation.
In summary, the area of the given rectangle is determined by multiplying its length of 13 units by its width of 2 units, resulting in an area of 26 square units.
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