Answer: The 90% confidence interval for the population mean of the length of text messages is a range of values that is likely to contain the true population mean with a probability of 0.90 (or 90%). Based on the given information, we can calculate the confidence interval as follows:
Standard error of the mean (SE) = σ / sqrt(n)
where σ is the population standard deviation, n is the sample size, and sqrt denotes the square root.
SE = 3 / sqrt(22) ≈ 0.639
Margin of error (ME) = t(α/2, df) × SE
where t(α/2, df) is the critical value from the t-distribution with df degrees of freedom, and α is the level of significance (1 - confidence level).
For a 90% confidence level and 21 degrees of freedom (df = n - 1), the critical value is approximately 1.717.
ME = 1.717 × 0.639 ≈ 1.098
The confidence interval can be calculated as:
CI = sample mean ± ME
= 31 ± 1.098
= (29.902, 32.098)
Therefore, we can say that we are 90% confident that the true population mean of the length of text messages falls between 29.902 and 32.098 characters. In other words, if we were to repeat the sampling process many times and construct a 90% confidence interval for each sample, we would expect 90% of the intervals to contain the true population mean. Additionally, we can interpret the margin of error as the maximum amount that the sample mean is expected to differ from the true population mean, with a probability of 90%.
Step-by-step explanation:
What is the volume of a rectangle prism with a length of 24 1/2 feet a width of 14 feet and a height of 11 feet
Answer:
19,322 cubic feet.
Step-by-step explanation:
Volume = Length × Width × Height
Given the measurements provided:
Length = 24 1/2 feet
Width = 14 feet
Height = 11 feet
We need to convert the mixed number for the length, 24 1/2 feet, into a single fraction.
24 1/2 feet = 24 + 1/2 feet = 48/2 + 1/2 feet = 49/2 feet
Now we can substitute the given values into the formula for volume:
Volume = (Length) × (Width) × (Height)
= (49/2 feet) × (14 feet) × (11 feet)
Next, we can multiply the lengths, widths, and heights together:
Volume = (49/2 feet) × (14 feet) × (11 feet)
= 49 × 14 × 11 cubic feet / 2
Finally, we can calculate the volume by dividing the product by 2:
Volume = 49 × 14 × 11 cubic feet / 2
= 19,322 cubic feet
Help me on the questions please and thank you.
The lateral surface area of the rectangular prism is 308 units² and the total surface area is 398 units²
What is the lateral and total surface area of the rectangular prismThe formula of lateral surface area of the rectangular prism is given as;
LSA = 2(l +b)h
l = length b = breath or widthh = heightsubstituting the values into the formula;
LSA = 2(5 + 9) * 11
LSA = 308 units²
The total surface area is given by
TSA = 2(lb + bh + lh)
TSA = 2[(5*9) + (9*11) + (11*5)
TSA = 398 units²
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to estimate the percentage of all their customers that would buy a new flavor, an ice cream shop surveys the first five customers that place an order.will this likely give an accurate estimate of this percentage?select from the drop-down menus to correctly complete the statement.this method is choose... to give an accurate estimate of the percentage since it choose... from a large enough randomly selected sample of customers
This method is unlikely to give an accurate estimate of the percentage since it chooses only 5 customers from a small sample size, which may not be representative of the entire population of customers.
In statistical terms, the sample size of 5 is considered very small and may not be large enough to capture the variability in customers' preferences. A larger sample size would increase the precision and accuracy of the estimate of the percentage of customers who would buy a new flavor.
A small sample size may lead to unreliable estimates and may not be representative of the population, highlighting the importance of using appropriate sample sizes in statistical analysis.
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Could Someone Please Explain What This Parallelogram Answer Is?
The area of the parallelogram is[tex]39\sqrt(15)[/tex] square units.
How to deal with Parallelogram?In the preceding diagram, we must determine the height of the parallelogram in order to determine its area. The length of the perpendicular line segment drawn from vertex A to side BC determines the parallelogram's height. We'll refer to this line segment as AD. Since AD is perpendicular to BC, we can calculate its length using the Pythagorean theorem:
[tex]AD^2 = AC^2 - CD^2[/tex]
[tex]AD^2 = 12^2 - 3^2[/tex]
[tex]AD^2 = 135[/tex]
[tex]AD = \sqrt(135) = 3\sqrt(15)[/tex]
Now that we know the height of the parallelogram, we can use the formula for the area of a parallelogram:
Area = base x height
The base of the parallelogram is the length of side AB, which is 13 units. Therefore, the area of the parallelogram is:
[tex]Area = 13 \times 3\sqrt(15)[/tex]
[tex]Area = 39\sqrt(15) square units[/tex]
Therefore, the area of the parallelogram is [tex]39\sqrt(15)[/tex] square units.
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a right circular cylinder is inscribed in a sphere of radius r. find the largest possible surface area of such a cylinder
For a inscribed right circular cylinder in sphere of radius r, largest possible surface area of such a cylinder is equals to the [tex]= πr²( 1 + \sqrt{5}) [/tex].
The maximum or minimum value of a continuous function can be determined by derivatives of the function. If y= f(x) is a continuous function, Then slope of function at extreme points( maximum or minimum) is zero, [tex]\frac{dy}{dx} =0[/tex]. Let's consider r be the radius of the sphere and is a constant. Let R and h be the radius and height of the cylinder that can be inscribed in a sphere of radius r as shown in the above figure. By Pythogoras Theorem, base radius of cylinder as,[tex]R =\sqrt{ r²-\frac{h²}{4}}[/tex]
Surface area of cylinder, S = 2πRh + 2πR²
=> [tex]S= 2πh\sqrt{ r²- \frac{h²}{4}} + 2π(r²- \frac{h²}{4}) \\ [/tex]. We need to calculate height of cylinder such that surface area is maximum. For surface area to be maximum, [tex] \frac{dS}{dh} =0[/tex]
[tex]2πh \frac{1}{2\sqrt{ r² - \frac{h²}{4}}}( \frac{ - 2h}{4} ) + 2π\sqrt{ r² - \frac{h²}{4}} + 2π \frac{(-2 )h}{4} = 0 \\ [/tex]
=>[tex] \frac{- h²}{4\sqrt{ r² - \frac{h²}{4}} } + \sqrt{ r² - \frac{h²}{4}} - \frac{h}{2} = 0[/tex]
=> [tex]- h² + 4 ( r² - \frac{h²}{4} ) - 2h\sqrt{ r² - \frac{h²}{4}} = 0 \\ [/tex]
[tex]- 2h² + 4r² - 2h\sqrt{ r² - \frac{h²}{4}} = 0[/tex]
=>[tex]- 2h²+ 4r² = 2h\sqrt{r²- \frac{h²}{4}}[/tex]
Squaring on both sides, [tex]4h^{4} + 16r⁴ - 16r²h² = 4h² ( r² - \frac{h²}{4}) = 0 \\ [/tex]
[tex]h^{4} + 4r⁴ - 4r²h² = h² r² - \frac{h⁴}{4} = 0 \\ [/tex]
=> [tex]5h^{4} + 4r⁴ - 5r²h² = 0 [/tex]
which is Quadratic equation with h² variable, so using quadratic formula for determining the values of h², [tex]=4r^{2} ( \frac{5 ± \sqrt{5}}{10})[/tex]. Since we need largest possible surface area, we will consider, [tex]h² = 4r²( \frac{ 5 - \sqrt{5}}{10})[/tex]
=> [tex]r² - \frac{h²}{4} = r²( \frac{ 5 + \sqrt{5}}{10})[/tex]
Substituting the values in the surface area equation, [tex]S= 2πh\sqrt{ r² - \frac{h²}{4}} + 2π(r² - \frac{h²}{4}) \\ [/tex]
[tex]= 4πr²(\sqrt{ \frac{5 - \sqrt{5}}{10}})(\sqrt{ \frac{ 5 + \sqrt{5}}{10}} )+ 2πr²( \frac{ 5 + \sqrt{5}}{10}) \\ [/tex]
[tex]= 2πr²( \frac{ 4\sqrt{5}}{10} + \frac{ 5 + \sqrt{5}}{10} ) \\ [/tex]
=> [tex]= πr²( 1 + \sqrt{5}) [/tex]
Hence, required area is [tex]= πr²( 1 + \sqrt{5}) [/tex].
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216,36,6,... Find the 8th term. Find the 8th term.
Answer:
t8 term is
[tex] \frac{ 1}{1296} [/tex]
Use limits to determine if
x+3
f(x) = is continuous at x = 3.
The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).
To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.
First, we can check the limit as x approaches 3 from the left:
lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞
Next, we can check the limit as x approaches 3 from the right:
lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞
Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.
Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.
The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).
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Electric utility poles in the form of right cylinders are made out of wood that costs $25. 97 per cubic foot. Calculate the cost of a utility pole with a diameter of 1. 5 ft and a height of 45 ft. Round your answer to the nearest cent
Rounding to the nearest cent, the cost of the utility pole is $2,061.33 with a diameter of 1. 5 ft and a height of 45 ft.
To calculate the cost of a utility pole, we first need to find its volume, which is the product of its height and the cross-sectional area of its base. Since the pole is in the form of a right cylinder, the cross-sectional area of its base is a circle with radius equal to half the diameter, which is 0.75 ft. Therefore, the cross-sectional area is:
Area = πr^2 = π(0.75)^2 = 1.767 ft^2
The volume of the pole is then:
Volume = Area x Height = 1.767 x 45 = 79.515 ft^3
Finally, we can calculate the cost of the pole by multiplying its volume by the cost per cubic foot of wood:
Cost = Volume x Cost per cubic foot = 79.515 x $25.97 = $2,061.33
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A rock brought back from the moon contained 1/8 of the radioactive substance that was present when the rock was formed. If the half-life of this substance is 1.5 billion years, how old in the moon rock?
PLS anser quick
Answer:
4.5 billion years
Step-by-step explanation:
Answer: We can use the formula for radioactive decay:
N = N0 * (1/2)^(t/T)
where N is the current amount of the radioactive substance, N0 is the original amount, t is the time that has passed, T is the half-life.
Let's assume that the original amount of the substance in the rock was 8 units. If the current amount is 1 unit, then:
1 = 8 * (1/2)^(t/1.5 billion)
Taking the natural logarithm of both sides, we get:
ln(1) = ln(8) - (t/1.5 billion)*ln(2)
Simplifying:
0 = ln(8) - (t/1.5 billion)*ln(2)
t/1.5 billion = ln(8)/ln(2)
t = 1.5 billion * (ln(8)/ln(2))
t ≈ 3.91 billion years
Therefore, the moon rock is about 3.91 billion years old.
Step-by-step explanation:
Calculate the size of angle edc
Answer:
64 degrees
Step-by-step explanation:
Corresponding angles are equal so angle BAF = 133 degrees. Supplementary angles add to 180 degrees so angle AFC = 47 degrees.
Angles on a straight line add to 180 degrees so angle CFE = 180 - 47 = 133 degrees.
Angles in a quadrilateral add to 360 degrees so angle EDC = 360 - (133 + 101 + 62) = 64 degrees.
Therefore angle EDC = 64 degrees
In the picture below Pac-Man, from the video game PAC-MAN, is shown eating ghosts. In the picture his mouth is open 60° and the radius of the circle is 13 mm. What is the area of the Pac-Man, to the
nearest tenth mm²?
The area of Pac-Man to the nearest tenth mm² is 11.4 mm².
What is area of circle?A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius.
To find the area of Pac-Man, we need to calculate the area of the sector that corresponds to the angle of his open mouth and subtract the area of the isosceles triangle formed by the two radii of the sector and the chord that represents the straight edge of his mouth.
First, we need to calculate the angle in radians that corresponds to the 60° angle given:
angle in radians = (60/360) x 2π = π/3 radians
Next, we can use the formula for the area of a sector:
Area of sector = (angle in radians / 2π) x πr²
where r is the radius of the circle.
Area of sector = (π/3 / 2π) x π(13mm)² ≈ 84.95 mm²
Now, we need to calculate the area of the triangle. We can use the formula for the area of an isosceles triangle:
Area of triangle = (1/2) x base x height
where the base is the chord that represents the straight edge of Pac-Man's mouth, and the height is half the length of the chord times the sine of half the angle of the mouth opening.
The base of the triangle is given by the formula:
base = 2r x sin(angle/2)
base = 2(13mm) x sin(30°) ≈ 22.52 mm
The height of the triangle is given by the formula:
height = (base / 2) x sin(angle/2)
height = (22.52 mm / 2) x sin(30°) ≈ 6.53 mm
Therefore, the area of the triangle is:
Area of triangle = (1/2) x base x height ≈ 73.5 mm²
Finally, we can subtract the area of the triangle from the area of the sector to get the area of Pac-Man:
Area of Pac-Man ≈ 84.95 mm² - 73.5 mm² ≈ 11.4 mm²
Therefore, the area of Pac-Man to the nearest tenth mm² is 11.4 mm².
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The Normal model is a goodâ first-choice to model data if the data are suspected to be
The Normal model is a good first-choice to model data if the data is normally distributed or approximately normally distributed
Normally distributed or approximately Normally distributed. The Normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is widely used in statistical modeling due to its mathematical properties and practical applications in many fields.
When the data is Normally distributed, the Normal model provides a good approximation of the underlying distribution of the data. This means that the parameters of the Normal distribution can be estimated from the data using methods such as maximum likelihood estimation, and the resulting model can be used to make predictions and conduct statistical inference.
However, it is important to note that the Normal model may not be appropriate for all types of data, particularly if the data exhibits significant departures from Normality. In such cases, other distributional models or non-parametric methods may be more appropriate.
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Identify scale factor in scale drawings
The scale factor in scale drawing from figutre A to figure B is 4
Identifying the scale factor in scale drawingsIn a scale drawing, the scale factor represents the ratio of the size of an object in the drawing to the size of the corresponding object in real life.
In the given scale drawing, the object is scaled up from 7 cm to 28 cm.
Therefore, the scale factor can be calculated as follows:
scale factor = size of object in drawing / size of corresponding object in real life
scale factor = 28 cm / 7 cm
scale factor = 4
So, the scale factor in this scale drawing is 4.
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What is the approximate solution to the equation 6e^4x — 3 = 21? a) 0.7945 b) 0 c) 0.1505 d) 0.3466
Answer: the answer is d) 0.3466.
Step-by-step explanation:
Starting with the equation:
6e^(4x) - 3 = 21
Add 3 to both sides:
6e^(4x) = 24
Divide both sides by 6:
e^(4x) = 4
Take the natural logarithm of both sides:
ln(e^(4x)) = ln(4)
Use the property of logarithms that ln(e^y) = y:
4x ln(e) = ln(4)
Simplify:
4x = ln(4)
Solve for x by dividing both sides by 4:
x = (1/4) ln(4)
Using a calculator, we get:
x ≈ 0.3466
Therefore, the answer is d) 0.3466.
I need some help please
Answer:
x+2
hope this helps ;)
and cute pfp
Answer:
Step-by-step explanation:
x-1, because 3 fits the criteria, x>=1
what is the equation in point slope form equation for line (-3,5) and (1,-1)
Considering the expression of a line, the equation of the line that passes through the pair of points (-3,5) and (1,-1) is y=-1.5x +0.5.
Definition of linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope and the value of one of the points, the value of the ordinate to the origin can be obtained.
Equation in this caseIn this case, being (x₁, y₁)= (-3, 5) and (x₂, y₂)= (1, -1), the slope m can be calculated as:
m= ( -1 -5)÷ (1 - (-3))
m= ( -1 -5)÷ (1 + 3)
m= (-6)÷ 4
m= -1.5
Considering point 2 and the slope m, you obtain:
-1= -1.5×1 + b
-1= -1.5 +b
-1 + 1.5= b
0.5= b
Finally, the equation of the line is y=-1.5x +0.5.
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How many flowers, spaced every 3 in., are needed to surround a circular garden with a 175-ft radius? Use 3.14 for pi.
First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:
[tex]\text{C}=2\pi \text{r}[/tex]
If we substitute 175 ft for [tex]\text{r}[/tex] and use 3.14 to approximate [tex]\pi[/tex] we get a circumference of:
[tex]\text{C}=2\times3.14\times175 \ \text{ft}[/tex]
[tex]\text{C}=6.28\times175 \ \text{ft}[/tex]
[tex]\text{C}=1099 \ \text{ft}[/tex]
We can now convert the circumference in feet to inches:
[tex]1099 \ \text{ft}\times \dfrac{12 \ \text{in}}{1 \ \text{ft}} \implies[/tex]
[tex]1099\times12 \ \text{in}\implies[/tex]
[tex]=13188[/tex]
To find how many flowers we need we can divide the circumference in inches by the 3 inches between flowers giving:
[tex]13188 \ \text{in}\times\dfrac{1 \ \text{flower}}{3 \ \text{in}}\implies[/tex]
[tex]13188 \ \text{in}\times\dfrac{1 \ \text{flower}}{3 }\implies[/tex]
[tex]\dfrac{13188 \ \text{flower}}{3 }\implies[/tex]
[tex]=4396 \ \text{flower}[/tex]
You would require 4,396 flowers
show your work i need it
The expression representing the width of the garden is given as follows:
6w + 2.
An equivalent expression is given as follows:
2(3w + 1).
How to obtain the expression?The width of the rectangle is represented as follows:
w.
Six times the width of the rectangle is represented as follows:
6w.
Two feet plus six times the width of the rectangle is represented as follows:
6w + 2.
6 = 2 x 3, hence the simplified expression can be given as follows:
2(3w + 1).
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3 Marcus has 500 g of flour. He uses 200g to bake
bread and 120g to make biscuits.
Work out the percentage of the flour:
A he uses for bread
B he uses for biscuits
C he does not use
Answer:
40% , 24% , 36%
Step-by-step explanation:
first express each as a fraction then multiply the fraction by 100%
A
[tex]\frac{200}{500}[/tex] × 100% = 0.4 × 100% = 40% used for bread
B
[tex]\frac{120}{500}[/tex] × 100% = 0.24 × 100% = 24% used for biscuits
C
percentage not used = 100% - (40 + 24)% = 100% - 64% = 36%
Solve for x. Type your answer as a number in the blank without "x=".
Answer:
17
Step-by-step explanation:
The midpoint theorem states that “The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
therefore 2(x+5) = 3x-7
distribute
2x+10 = 3x-7
subtract 2x from both sides
2x+10 -2x = 3x-7 -2x
x-7 = 10
add 7 to both sides
x- 7 +7 = 10 + 7
x = 17
Answer:
Step-by-step explanation:
I think you are in 11th grade
we can use the theorem midpoint theorem.
as the mid-point theorem,
2(x+5)=3x-7
2x+10=3x-7
x=17
I really love your profile picture, is it real?
Please help me , ASAP thank you
Answer:
(x - 4)² + (y + 3)² = 4
Remember the circle formula:
(x - h)² + (y - k)² = r²
h = X center point
k = Y center point
In this case your center point is (4,-3) and your radius is 2
If u plug everything in and simplify you should get this:
(x - 4)² + (y - (-3))² = 2²
(x - 4)² + (y + 3)² = 4
I need help converting 20000 lb into tons please
Answer:
10
20,00/2000=10
Step-by-step explanation:
Hope this helps! =D
Mark me brainliest! =D
Answer: 10 tons.
Step-by-step explanation: There are 2000 pounds in one ton. Hence:
20000 lb ÷ 2000 lb/ton = 10 tons
why does an angle formed by a tngent and a chord have the same measure as an insribed angle that intercepts the same arc
An angle formed by a tangent and a chord in a circle is called an "angle between tangent and chord" while an inscribed angle is an angle whose vertex is on the circle and whose sides intersect the circle at two distinct points.
When a tangent line and a chord intersect at a point on the circle, the tangent line is perpendicular to the radius drawn to the point of intersection.
This means that the angle between the tangent and the chord is equal to the angle between the radius and the chord.
Now, consider an inscribed angle that intercepts the same arc as the chord.
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that it intercepts.
Thus, the measure of the inscribed angle is equal to the measure of the arc that the chord intercepts.
Since the angle between the tangent and the chord is equal to the angle between the radius and the chord, and the inscribed angle intercepts the same arc as the chord, it follows that the angle between the tangent and the chord is equal to the inscribed angle that intercepts the same arc.
Therefore, an angle formed by a tangent and a chord has the same measure as an inscribed angle that intercepts the same arc.
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What are the possible values of x if 52 ÷ (|x|+8) = 4?
O {-21, 21}
O {-13, 13}
O {-11, 11}
O {-5,5}
Answer:
First, we can multiply both sides of the equation by the absolute value of x plus 8, to get rid of the fraction:
52 = 4(|x| + 8)
Now we can solve for the absolute value of x:
| x | + 8 = 13
| x | = 5
This means that x could be either positive 5 or negative 5. Therefore, the possible values of x are {-5, 5}.
So the answer is option D: {-5, 5}.
a ladder leans against a wall so that its slope is 1.60. the top of the ladder is 8 vertical feet above the ground. what is the approximate horizontal distance from the base of the ladder to the wall? (assume that the positive direction points from the base of the ladder toward the wall.)
Answer: We can use the trigonometric function tangent to solve this problem. Let x be the horizontal distance from the base of the ladder to the wall. Then we have:
tan(1.60) = x / 8
Multiplying both sides by 8, we get:
x = 8 tan(1.60)
Using a calculator, we find:
x ≈ 8 × 1.518 = 12.14
Therefore, the approximate horizontal distance from the base of the ladder to the wall is 12.14 feet.
Step-by-step explanation:
Let f be the function defined by f(x)=xlnx for x>0. On what open interval is f decreasing?
The function f(x) = xlnx is decreasing on the open interval (0, e^-1).
To find the interval on which the function f(x) = xlnx is decreasing, we need to find the intervals where the first derivative f'(x) is negative.
Using the product rule of differentiation, we can find the first derivative of f(x) as
f'(x) = x × (1/x) + ln(x) × 1 = 1 + ln(x)
Now, we need to find the values of x where f'(x) < 0
1 + ln(x) < 0
ln(x) < -1
x < e^-1
Therefore, f(x) is decreasing on the interval (0, e^-1).
Note that we exclude x = 0 from the interval because the function is not defined for x ≤ 0.
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Which choice shows (4+9)+11 correctly rewritten using the associative property and then correctly simplified ?
o 11+(4+9)=11+13=24
o 4+(9+11)=4+20=24
o 4+(91+1)=4+92=96
o 11+(9+4)=11+13=24
The associative property of addition:
[tex](a + b) + c = a + (b + c)[/tex]
We now apply the associative property of addition to the expression in this problem.
[tex](4+9)+11=4+(9+11)[/tex]
Now we follow the correct order of operations by adding the numbers inside the parentheses first.
[tex]= 4 + 20[/tex]
[tex]= 24[/tex]
Answer: B
Find the values of c that make f continuous everywhere: x² – ² f(x) CX + 9 smaller c = if < 15 if x > 15 larger c = Use at least 3 decimal places in your answers. Submit Question 2 -5 4 -3 -2 1 2 3 4 5 1 -2 3 -4 -5+ Use the graph of f(x) above to estimate the value of f'(-2) to one decimal place. f'(-2) = Question Help: P Viden 1 d. 6+ 5 4 3 2 1 -6 -5 -4 -3 -2 2 3 4 5 -Z -1 5 6 -2 ده -4 -5 -6+ a In the graph above the slope of the tangent at 2 is
To find the values of c that make f continuous everywhere, Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.
For x < 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c = 201 - 15c
Solving for c, we get c = 13.4 (rounded to 3 decimal places).
For x > 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c ≤ 15 Solving for c, we get c ≥ 12.9 (rounded to 3 decimal places).
Therefore, the values of c that make f continuous everywhere are 13.4 ≤ c ≤ 12.9.
To estimate the value of f'(-2), we can look at the slope of the tangent line at x = -2 on the graph. From the graph, it looks like the slope of the tangent at x = -2 is around -2.5. Rounding to one decimal place, we estimate f'(-2) to be -2.5.
Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.
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If 68 colored pencils are split evenly between 4 students, how many pencils does each student get?
Each person will get 17 pencils.
What is Division?
Division is the opposite of multiplication. For example, If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division.
The main goal of dividing is to see how many equal groups are formed or how many are in each group when sharing fairly.
In the problem given above, to divide 68 colored pencils to 4 students each, you will have to put 68 colored pencils for each student. So, 68 divided by 4 will give the result 17.
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Solve 2x^2+x-3=0 by factoring.
Answer:
To solve the quadratic equation 2x^2 + x - 3 = 0 by factoring, we follow these steps:
Step 1: Write the equation in standard quadratic form, which is ax^2 + bx + c = 0. In this case, the equation is already in standard form: 2x^2 + x - 3 = 0.
Step 2: Factor the quadratic expression on the left-hand side of the equation. We look for two numbers that multiply to give us the constant term (c) and add to give us the coefficient of the linear term (b). In this case, c = -3 and b = 1.
The two numbers that satisfy these conditions are -3 and 1, as -3 * 1 = -3 and -3 + 1 = -2.
Step 3: Use the factored form to set each factor equal to zero and solve for x.
2x^2 + x - 3 = 0
(2x - 3)(x + 1) = 0 (factored form)
Setting each factor equal to zero:
2x - 3 = 0
2x = 3
x = 3/2
x + 1 = 0
x = -1
So the solutions to the equation are x = 3/2 and x = -1.