A basis for Col A is (-2,2,0,0) and (4,-6,0,0). A basis for Nul A is (2,1,0,0), (-1,0,1,1/2), and (-2,0,0,1). These bases were found using the row reduced form of A.
Since A is row equivalent to B, they have the same row space, null space, and column space. Thus, we can find the bases for Nul A and Col A using the row reduced form of A, which is
[tex]\left[\begin{array}{cccc}1&-2&1&2\\0&1&1/2&-1\\0&0&0&0\\0&0&0&0\end{array}\right][/tex]
To find a basis for Col A, we can take the columns of A that correspond to the pivot columns in the row reduced form. In this case, the pivot columns are the first and second columns. Therefore, a basis for Col A is
(-2, 2, 0, 0), (4, -6, 0, 0)
To find a basis for Nul A, we need to solve the system of homogeneous linear equations Ax = 0, which is equivalent to solving the system of equations corresponding to the row reduced form. Letting the free variable be t, we have
x¹ - 2x² + x³ + 2x⁴ = 0
x² + (1/2)x³ - x⁴ = 0
Expressing x¹ and x⁴ in terms of x² and x³, we get
x¹ = 2x² - x³ - 2x⁴
x⁴ = (1/2)x³ - x²
Thus, any solution to Ax = 0 can be written as
x = (2x² - x³ - 2x⁴, x², x³, (1/2)x³ - x²) = x²(2, 1, 0, 0) + x³(-1, 0, 1, 1/2) + x⁴(-2, 0, 0, 1)
Therefore, a basis for Nul A is
(2, 1, 0, 0), (-1, 0, 1, 1/2), (-2, 0, 0, 1)
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2㏒_[6](2)+3㏒_[6](3)+㏒_[6](12)
Answer: 4
Step-by-step explanation:
Given:
[tex]2log_62+3log_63+log_612[/tex]
Rewrite using the power property:
[tex]log_62^2+log_63^3+log_612[/tex]
Rewrite by adding the logarithms together (multiplying) since they all have a common base of 6:
[tex]log_6(2^2*3^3*12)[/tex]
Simplify by multiplying:
[tex]log_6(4*27*12)[/tex]
[tex]log_6(1,296)[/tex]
Evaluate the logarithm:
[tex]log_6(1,296)[/tex]
4
*MATH* PLS HELP! THE PROBLEM IS IN THE IMAGE!
(PLEASE show your work or explain how you got that answer)
The scale factor that takes triangle C to triangle D is 3/10.
What is scale factor?Scale factor is a number by which the size a geometrical figure or shape can be changed with respect to its original size.
To find the scale factor that takes triangle C to triangle D, we use the formula below
Formula:
S.F = Length of triangle D/Corresponding Length of triangle CWhere:
S.F = Scale factorFrom the diagram in the question,
Given:
Hypotenus of triangle D = 3.36Hypotenus of triangle C = 11.2Substitute these values into equation 1
S.F = 3.36/11.2S.F = 0.3 = 3/10Hence, the scale factor is 3/10.
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let p(n) be the statement that 1^3 +2^3+ 3^3 ... +n^3 = (n(n 1)2)^2 for the positive integer n. we will have completed the basis step of the proof if we show that
Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.
To complete the basic step of the proof, we need to show that the statement p(n) is true for the smallest positive integer n, which is 1.
Let's plug n = 1 into the statement p(n):[tex]1^3 = (\frac{1(1 + 1))}{2})^2[/tex]
Simplifying the equation, we get:
[tex]1^3 = (1(2)/2)^2\\1^3 = (1^2)^2\\1 = 1[/tex]
Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.
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The statement is true for n=1, and we have completed the basis step of the proof.
To complete the basis step of the proof for the statement p(n), we need to show that it is true for the smallest positive
integer n, which is 1.
Our statement is:
[tex]1^3 + 2^3 + 3^3 + ... + n^3 = (n(n+1)/2)^2.[/tex]
For the basis step, let n = 1:
Left side: [tex]1^3 = 1[/tex]
Right side:[tex](1(1+1)/2)^2 = (1(2)/2)^2 = (1)^2 = 1[/tex]
Since the left side and the right side are equal, we have successfully completed the basis step of the proof for the statement p(n).
Therefore, the statement is true for n=1, and we have completed the basis step of the proof.
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The volume of a volleyball is approximately 113 in ^3. What is its diameter? Round your answer to the nearest whole number.
A. 13 in
B. 6 in
C. 2 in
D. 5 in
will give brainliest
If the volume of a volleyball is approximately 113 in³, then the diameter of the volleyball is approximately option (D) 5 inches.
The formula for the volume of a sphere is
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.
We are given the volume of the volleyball as 113 in³, so we can solve for the radius as follows
113 = (4/3)πr³
r³ = 113 / ((4/3)π)
r³ ≈ 21.50
r ≈ 2.8
To find the diameter, we double the radius:
d = 2r ≈ 5.6
Rounding this to the nearest whole number
d = 5 in
Therefore, the correct option is (D) 5 in
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Find a congruence transformation that maps triangle RST to triangle UVW.
A congruence transformation that maps triangle RST to triangle UVW is a reflection along the line y = 1, followed by a translation 2 units right and down by 1 units.
A congruence transformation that maps triangle RST to triangle UVW is a rotation of 180°, followed by a translation 2 units left and down by 5 units.
What is a transformation?In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.
By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-images underwent a sequence of congruence transformations to produce the images.
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the mean weight of an adult is 62 kilograms with a variance of 144 . if 195 adults are randomly selected, what is the probability that the sample mean would be greater than 59.5 kilograms? round your answer to four decimal places.
The probability is 0.9835 where the sample mean would be greater than 59.5 kilograms.
The central limit theorem can be used to approximate the sampling distribution of the sample mean as a normal distribution.
where the mean equals the population mean (μ = 62 kg) and the standard deviation equals the population standard deviation divided by the square root of sample size (σ/sqrt (n) = sqrt(144 / 195) = 2.4287 kg).
Next, find the probability that the sample mean is greater than 59.5 kilograms.
z = (59.5 - 62) / (2.4287 / square (195)) = -2.1295
Using an ordinary regular table or calculator, we know that the probability of a Z-score less than -2.1295 is 0.0165.
Therefore, the probability that the sample mean exceeds 59.5 kilograms is
1 - 0.0165 = 0.9835
Rounding to four decimal places gives a probability of 0.9835.
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Find the value of ‘x’
x =
Step-by-step explanation:
For intersecting chords, the products of the related segments are equal
8 * 6 = 3x * x
48 = 3x^2
16 = x^2
x = 4 units
can I get some help on this really fast?
The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
The vertex is classified as a maximum or minimum depending on the term a, which multiplies x², as follows:
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The estimated velocity v (in miles per hour) of a car at the end of a drag race is v=234pw−−√3, where p is the horsepower of the car and w is the weight (in pounds) of the car. A car has a horsepower of 1311 and weighs 2744 pounds. Find the velocity of the car at the end of a drag race. Round your answer to the nearest whole number.
Please write out the work for the problem.
we get the velocity of the car at the end of the drag race to be 162 mph.
What is weight?Assuming you meant "weight," weight is the measure of the amount of force that gravity exerts on an object. It is usually measured in units such as pounds or kilograms. The weight of an object can vary depending on the strength of gravity and the mass of the object. For example, an object that has a mass of 10 kilograms on Earth would weigh approximately 98 Newtons (which is about 22 pounds) due to the gravitational force of the Earth.
To find the velocity of the car, we can simply plug in the given values of horsepower and weight into the given formula:
[tex]v = 234 * \sqrt(p / w)[/tex]
Substituting p = 1311 and w = 2744, we get:
[tex]v = 234 * \sqrt(1311 / 2744)[/tex]
[tex]v \approx 162[/tex]
Rounding this to the nearest whole number, we get the velocity of the car at the end of the drag race to be 162 mph.
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A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
Answer: First choice 480t = 300t + 900
Step-by-step explanation:
A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.
Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.
ANS
Let say t is time in hrs for Which Both Assembly line worked
M made 300 toys per hr on Tuesday
Toys made on Tuesday at Assembly line M = 300 × t = 300t toys
N made 480 toys per hr on Tuesday
Toys made on Tuesday at Assembly line N = 480 × t = 480t toys
Toys Made by N on Tuesday = Toys made by M on Tuesday + Toys made by M on Monday
480t = 300t + 900
=> 180 t = 900
=> t = 900/180
=> t = 5 hr
N capacity on tuesday Per hour * t = M capacity on tuesday per hour * t + Toys made by M on Monday
N = N capacity on tuesday Per hour
M = M capacity on tuesday Per hour
=> t (N - M ) = 900
=> t = 900/(N-M)
a man can hit his target 25% of the time if he fires 4 shots in succession what is the probability that he will hit his target
The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.
The probability of missing all 4 shots is (0.75)^4 = 0.3164.
Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:
1 - 0.3164 = 0.6836 or 68.36%.
So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.
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Triangle UVW has vertices at U(−2, 0), V(−3, 1), W(−3, 3). Determine the vertices of image U′V′W′ if the preimage is rotated 90° counterclockwise.
U′(0, −2), V′(−1, −3), W′(−3, −3)
U′(0, −2), V′(1, −3), W′(3, −3)
U′(2, 0), V′(3, −1), W′(3, −3)
U′(−2, 0), V′(−3, 0), W′(3, −3)
Answer:
The vertices of the image after rotating triangle uvw 90 degrees counterclockwise are u′(0, −2), v′(1, −3), w′(3, −3).
Step-by-step explanation:
How do you find the period of a cosine function of the form y = cos bx?
The period of a cosine function of the form y = cos bx is equal to T= 2π/b where 'T' is the period of the cosine function and b is the coefficient of x in the function.
This formula tells us that the period of the cosine function is equal to the length of one complete cycle of the function.
it represents the distance along the x-axis for the cosine function to complete one full oscillation.
The period of a cosine function of the form y = cos bx, first identify the coefficient b.
Use the formula T= 2π/b to calculate the period 'T'.
For example,
Consider cosine function y = cos 2x,
The coefficient of x is 2.
Using the formula above, the period is equal to
Period = 2π/2
= π
So the period of the function y = cos 2x is π.
This implies that the cosine function completes one full oscillation every π units along the x-axis.
Therefore, the formula used to calculate the period of the cosine function y = cos bx is given by T= 2π/b.
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pls help!!! make sure to show ur workkk!! i need this ASAP.
Answer:
a = 2
b = 4
c = 4.47
Step-by-step explanation:
a is 2 units long
b is 4 units tall
To find c, we can use the formula: a^2 + b^2 = c^2
Plug it in:
(2)^2 + (4)^2 = c^2
4 + 16 = c^2
20 = c^2
c = 4.47
Answer:
length a is 2 length b is 4 length c is 4
Step-by-step explanation:
In an expression using the logical operator ____, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. a. OrElse b. Nor c. AndAlso d. Xor
In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.
The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true
. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.
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In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.
This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters
the first false condition since the overall result will definitely be false.
In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing
any further conditions. This is also known as short-circuit evaluation.
In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing
any further conditions. The Nor and Xor operators are less commonly used and have different behavior.
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Solve for all values of x by factoring.
x² + 6x-41 = 6x - 5
The solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.
Solving for all values of x by factoring.To solve for all values of x by factoring x² + 6x - 41 = 6x - 5, we can first simplify the equation by combining like terms:
x² + 6x - 41 = 6x - 5
x² - 41 = -5
Next, we can bring all the terms to one side of the equation:
x² - 41 + 5 = 0
x² - 36 = 0
Now we can factor the left side of the equation:
(x - 6)(x + 6) = 0
Setting each factor equal to zero and solving for x, we get:
x - 6 = 0 or x + 6 = 0
x = 6 or x = -6
Therefore, the solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.
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Please use Triangle Inequality to solve, I'm having a bit of trouble. I'd also appreciate if you just help me.
The value of x for the given triangle through which the perimeter of the given relation is satisfied is 10.
What about perimeter of triangle?
The perimeter of a triangle is the total length of its boundary, which is the sum of the lengths of its three sides. The perimeter can be thought of as the distance around the triangle, and it is measured in units of length such as centimeters, meters, or feet. The perimeter of a triangle is an important geometric property that is used in many practical applications, such as calculating the amount of fencing needed to enclose a triangular-shaped garden or determining the length of wire required to form a triangular circuit.
According to the given information:
The perimeter of triangle is sum of all sides of the triangle
In which,
2x + 4 + 3x - 8 + x - 2 = 54
6x - 6 = 54
6x = 60
x = 10
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[tex]-\frac{7}{8} - - \frac{5}{6} +\frac{1}{3}[/tex]
Answer: 7/24 ≅ 0.2916667
Step-by-step explanation: QUICK MATH
the time it takes to cover the distance between two cities by car varies inversely with the speed of the car. the trip takes hours for a car moving at . how long does the trip take for a car moving at ?
The time takes by car to cover the distance between two cities by car varies inversely with the speed of car. Total 5 hours will consume to complete the trip with a car moving at 40 mph.
Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.
The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as [tex]Speed(s ) = \frac{Distance(d)}{Time(t)}[/tex]
Distance(d) = Speed(r)×Time(t)Time(t) = Distance(d)/Speed(s)Now, Speed of car (s) = 50 miles per hour
Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the speed formula, [tex]50 mph = \frac{ x}{4 \: \: hours}[/tex]
=> x = 4 × 50 miles
=> x = 200 miles
Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the time formula,[tex]time ( t') = \frac{distance (x) }{ speed( s')} [/tex]
=> [tex] time (t') = \frac{ 200 \: miles}{ 40 \: mph}[/tex]
= 5 hours.
Hence, required value of time is 5 hours.
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Complete question :
The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?
The moon has a radius of approximately 1737 km. What is the length of the equator
Therefore, the length of the equator of the moon is approximately 10,921.5 kilometers.
What is the Moon's equatorial length?NASA (opens in new tab) estimates that the moon's diameter is less than one-third that of Earth's. At its equator, the moon is 6,783.5 miles (10,917 km) in circumference.
The following equation can be used to determine the length of the moon's equator:
C = 2πr
where r is the circle's radius (i.e., the moon's radius) and C is the circle's circumference (i.e., the moon's equator).
Inputting the specified number as the moon's radius results in:
C = 2π(1737) km
C ≈ 10921.5 km
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Fruit Smoothle
O E. Talia can use 1
cup orange juice
cup yogurt
8 cup strawberries
8 cup blueberries
cup of ice
Blend all ingredients. Serve cold.
Makes 1 serving.
Which statement about the recipe is true? Mark all that apply.
cup strawberries to double the recipe.
O A. Talia can use
OB. Talia can use
OC. Talia can use
12 cup yogurt to make 3 servings.
cup blueberries to make 4 servings.
OD. Talia can use
1
cups orange juice to make 4 servings.
cup of ice to make 5 servings.
A. Talia can use 1 and 3/4 cup strawberries to double the recipe. B. Talia can use 1 and 1/3 cup yogurt to make 3 servings. D. Talia can use 2 cups orange juice to make 4 servings.
What is proportion?In statistics, a proportion is a fraction or a percentage that reflects the proportion of a population's or sample's members who share a particular attribute to the population's or sample's overall size. It is a kind of ratio where the denominator is the entire population or sample size and the numerator is the number of people who possess a specific trait or attribute.
From the given ingredients and the serving size we can see that the correct statement is:
A. Talia can use 1 and 3/4 cup strawberries to double the recipe.
B. Talia can use 1 and 1/3 cup yogurt to make 3 servings.
D. Talia can use 2 cups orange juice to make 4 servings.
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The complete question is:
i need some help with this problem i don’t really understand it
Answer:
-34x+29
Step-by-step explanation:
[tex]7(5-x)-3(9x+2)=7.5-7x-3.9x-3.2=35-7x-27x-6\\=-34x+29[/tex]
A pre-image has coordinates A(3, -5), B(3, 1) and C(-2, 0). The image has coordinates A'(3, 5), B'(3, -1) and C'(-2, 0). What type of reflection occurred? Explain how you know.
For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the x-axis refection.
Explain about the reflection about x axis:The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
Given data:
pre-image coordinates - A(3, -5), B(3, 1) and C(-2, 0).
Image coordinates A'(3, 5), B'(3, -1) and C'(-2, 0).
As its is clear from the given coordinates that value of x is same while the value of y gets change by negative.
(x,y) ---> (x, -y) , shows the refection about the x axis.
Thus, For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the refection about the x axis.
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4. The radius of a cylinder is 3x-2 cm. The height of the cylinder is x +3 cm. What is the
surface area of the cylinder? Use the formula A=2x²+2xrh.
02x (3x2+10x-8)
O 27(12x+7x-2)
O 27(12x²-2x+13)
O 27(12x²-5x-2)
Answer:
D: 27(12x² - 5x - 2).
Step-by-step explanation:
The formula for the surface area of a cylinder is: A = 2πr² + 2πrh
Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values in the formula and simplify:
A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)
A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)
A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π
A = 24πx² - 10πx - 4π
A = 2π(12x² - 5x - 2)
Therefore, the answer is option D: 27(12x² - 5x - 2).
Answer:
D
Step-by-step explanation:
Which Riemann sum represents the illustration shown?
The highlighted answer was just a misclick, i dont know if its the answer or not
The Riemann sum that represents the illustration on the graph is the second option as i goes from 1 to 4:
[tex]1∑2 {(xᵢ)}^{2} [/tex]
What is the Riemann sumThe Riemann sum is a mathematical concept used to approximate the area under a curve. It is named after the German mathematician Bernhard Riemann.
The idea behind the Riemann sum is to divide the area under the curve into a series of rectangles, where the height of each rectangle is determined by the function being integrated, and the width of each rectangle is determined by the size of the intervals used to divide the domain of the function. The area of each rectangle is then calculated and added together to get an approximation of the total area under the curve.
The Riemann sum is written in the following form:
[tex]∑f(xᵢ)Δxᵢ[/tex]
where f(xᵢ) is the value of the function at the ith point in the interval, Δxᵢ is the width of the ith rectangle, and the sum is taken over all i intervals.
Thus, the Riemann sum that represents the illustration on the graph as i goes from 1 to 4 is:
[tex]1∑2 {(xᵢ)}^{2} [/tex]
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for most stocks, a scatter plot chart of stock returns versus past stock returns will appear as: multiple choice a shotgun pattern centered close to the origin. a random pattern mostly concentrated in the top-right and lower-left quadrants. a random pattern mostly concentrated in the upper-left and upper-right quadrants. none of the options.
A scatter plot chart of stock returns versus past stock returns will typically appear as a random pattern mostly concentrated in the top-right and lower-left quadrants.
Describe your answer more in detail?This pattern indicates that there is a positive correlation between past and current stock returns, but there are also instances where current returns are negative despite past positive returns.
The top-right quadrant represents instances where both past and current returns are positive, while the lower-left quadrant represents instances where both past and current returns are negative.
The random pattern indicates that stock returns cannot be predicted with certainty based on past returns alone.
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The length of one leg of a right triangle is 2 times the length of the other, and the
length of the hypotenuse is 12. What is the length of the longest leg?
Answer:
[tex]\frac{24\sqrt{5} }{5}[/tex]
Step-by-step explanation:
Let's start by assigning one of the unknown legs with the variable x.
We know that the other leg is 2 times the length of x, so we can write:
2x
We also know that the length of the hypotenuse is 12.
From here, we can use the Pythagorean Theorem.
Recall that the Pythagorean Theorem is:
[tex]a^2+b^2=c^2[/tex]
where a is the length of one leg, b is the length of the other leg, and c is the length of the hypotenuse.
Let's substitute the values. We have:
[tex]x^2+(2x^2)=12^2=\\x^2+4x^2=144=\\5x^2=144=\\x^2=\frac{144}{5}=\\x=\frac{12}{\sqrt{5} }[/tex]
Let's rationalize the denominator by multiplying the numerator and denominator by [tex]\sqrt{5}[/tex], like so:
[tex]\frac{12}{\sqrt{5} } =\\\frac{12\sqrt{5} }{5}[/tex]
Therefore, [tex]x=\frac{12\sqrt{5} }{5}[/tex]
Let's solve for 2x:
[tex]2x=\\2(\frac{12\sqrt{5} }{5})=\\ \frac{24\sqrt{5} }{5}[/tex]
So, the length of the longest leg is [tex]\frac{24\sqrt{5} }{5}[/tex]
.
Which equation is a step in solving the equation |5 − 3x| + 2 = 19?
A.
5 − 3x = -17
B.
|5 − 3x| = -17
C.
5 + 3x = -17
D.
|5 + 3x| = 17
Answer:
Step-by-step explanation:
The absolute value (or modulus) | 5 - 3x | of a real number 5 - 3x is the non-negative value of 5 - 3x without regard to its sign.
| 5 - 3x| + 2 = 19
| 5 + 3x | = 19 - 2
| 5 + 3x | = 17
Ans: D
rem (rapid eye movement) sleep is sleep during which most dreams occur. each night a person has both rem and non-rem sleep. however, it is thought that children have more rem sleep than adults (reference: secrets of sleep by dr. a. borbely). assume that rem sleep time is normally distributed for both children and adults. a random sample of n1 5 10 children (9 years old) showed that they had an average rem sleep time of x1 5 2.8 hours per night. from previous studies, it is known that s1 5 0.5 hour. another random sample of n2 5 10 adults showed that they had an average rem sleep time of x2 5 2.1 hours per night. previous studies show that s2 5 0.7 hour. do these data indicate that, on average, children tend to have more rem sleep than adults? use a 1% level of significance.
Yes, indicate that, on average, children tend to have more REM sleep than adults.
How to determine children tend to have more REM sleep than adults?We can determine this by performing a two-sample t-test using the following null and alternative hypotheses:
Using a significance level of 0.01 and the given information, we calculate the t-statistic as follows:
t = ((2.8 - 2.1) - 0) / sqrt((0.5^2 / 10) + (0.7^2 / 10))
t = 2.697
Using a t-distribution table with degrees of freedom equal to 18 (10 + 10 - 2), we find the critical value to be 2.878 (for a one-tailed test at the 0.01 level of significance).
Since our calculated t-statistic of 2.697 is less than the critical value of 2.878, we fail to reject the null hypothesis.
Therefore, we conclude that there is evidence to suggest that children have more REM sleep than adults on average.
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One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 17 feet, a width of 15 feet, and a height of 12 feet? Write your answer as a decimal. Gal
We need at least 3.465 gallons of paint to paint the walls of this room.
The area of the two rectangular faces on either end of the prism is:
length x height = 17 x 12 = 204 square feet
The area of the two rectangular faces on the sides of the prism is:
width x height = 15 x 12 = 180 square feet
The area of the top and bottom faces of the prism is:
length x width = 17 x 15 = 255 square feet
The total surface area of the prism is:
2(204) + 2(180) + 2(255) = 1386 square feet
Now, we divide surface area by coverage of one gallon of paint:
1386 / 400 = 3.465
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