Solve for the missing length and the other two angles in the triangle below.
Answers
By law of cosine, the triangle has a side of 1.348 units and two angles of 129.852° and 35.148°, respectively.
How to find missing lengths and angles in a triangle
In this problem we find the representation of a triangle, in which we must determine the value of a missing side and two missing angles. This can be done by law of cosine. First, find the missing side:
x = √(3² + 4² - 2 · 3 · 4 · cos 15°)
x = 1.348
Second, find the missing angles:
4² = 3² + 1.348² - 2 · 3 · 1.348 · cos α
cos α = - 0.641
α = 129.852°
β = 180° - 15° - 129.852°
β = 35.148°
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Related Questions
Last week Deion ran a total of 32 miles. This week, he increased his running distance by 6. 4 miles. By what percentage did he increase the distance he ran? Please help waaaaaa
Answers
Deion increased the distance he ran by 20%.
To discover the percentage increase within the distance Deion ran, we need to first calculate the amount of increase.
The increase in distance that Deion ran this week compared to final week is:
6.4 miles
To find the proportion increase, we need to divide the increase by means of the original value (the distance he ran last week),
Then multiply by using a hundred to express the result as a percent.
The original price (last week's distance) is:
32 miles
Therefore, the percentage increase within the distance he ran is:
(6.4 miles / 32 miles) x 100% = 20%
So, Deion increased the distance he ran by 20%.
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Cory and Dalia like to buy fruit at the farmers’ market on Sundays. One Sunday, Cory bought 4 apples and 6 oranges and paid $5.10. Dalia bought 2 apples and 5 oranges and paid $3.65.
What is the cost of 2 oranges?
Write the answer as a decimal to 2 places
Answers
The cost of two oranges is 1.1 dollars.
How to find the cost of two oranges?One Sunday, Cory bought 4 apples and 6 oranges and paid $5.10. Dalia bought 2 apples and 5 oranges and paid $3.65.
Therefore, using equation,
let
x = cost of each apples
y = cost of each oranges
Hence,
4x + 6y = 5.10
2x + 5y = 3.65
Multiply equation(ii) by 2
4x + 6y = 5.10
4x + 10y = 7.3
4y = 2.2
y = 2.2 / 4
y = 0.55 dollars
Therefore,
cost of 2 oranges = 0.55(2) = 1.1 dollars
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Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1). Determine the image coordinates of K′ if the preimage is translated 6 units up.
A. K′(−10, 0)
B. K′(−4, −6)
C. K′(−4, 6)
D. K′(2, 0)
Answers
The coordinates of the images after the translation are K' (-4, 6).
Finding the coordinates of the image of points K'To find the image coordinates of K', we need to translate the coordinates of K 6 units up.
This can be done by adding 6 to the y-coordinate of K.
So, the y-coordinate of K' will be:
y-coordinate of K' = y-coordinate of K + 6
= 0 + 6
= 6
To find the x-coordinate of K', we just need to keep the x-coordinate of K the same, since the translation is only in the vertical direction.
Therefore, the image coordinates of K' are (-4, 6).
So, the correct answer is C. K′(−4, 6).
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Sara drops a tennis ball and lets it bounce. She records the height of the ball after each of its bounces as an ordered pair, where x represents the number of bounces and y represents the height of the ball in inches. The ordered pairs she records are (1,8), (2,6), (3,2) and (4,1)
Answers
We can plot the points (1,8), (2,6), (3,2), and (4,1) on a graph by using a coordinate plane and the x and y-coordinates of each point.
To plot these points, we will use a coordinate plane, which is a two-dimensional graph with an x-axis and a y-axis. The x-axis represents the horizontal position, and the y-axis represents the vertical position. We will use the x-coordinate to determine the horizontal position of the point and the y-coordinate to determine the vertical position of the point.
For the first point, (1,8), we will start at the origin of the graph, which is the point (0,0). We will then move 1 unit to the right along the x-axis and 8 units up along the y-axis to plot the point.
For the second point, (2,6), we will start again at the origin and move 2 units to the right along the x-axis and 6 units up along the y-axis to plot the point.
We will repeat this process for the remaining points, (3,2) and (4,1), to plot all four points on the graph. Once all four points are plotted, we can connect them with a line to visualize the pattern of the ball's bounces.
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Complete Question:
Sara drops a tennis ball and lets it bounce. She records the height of the ball after each of its bounces as an ordered pair, where x represents the number of bounces and y represents the height of the ball in inches.
The ordered pairs she records are (1,8), (2,6), (3,2) and (4,1).
Plot the ordered points on the graph.
this table shows incidence rates (per 100,000) of groups exposed to neither risk factors or to one or two risk factors for lung cancer. what is the expected value of incidence rate x on asbestos exposure group among smokers in multiplicative scale?
Answers
The correct response is 12, as finding the predicted smoking and asbestos exposure group requires finding x, and in that case, the ratios in the rows and columns are equal.
4/2 = x/6 Or 6/2= x/4
This suggests that x = 12.
Smoking refers to the act of inhaling and exhaling the smoke produced by burning tobacco or other substances such as marijuana or hookah. It is a highly addictive habit that poses significant health risks to both smokers and those exposed to secondhand smoke. Smoking can lead to a variety of illnesses and diseases, including lung cancer, heart disease, stroke, chronic obstructive pulmonary disease (COPD), and various other cancers. It is estimated that smoking is responsible for nearly 8 million deaths globally each year.
The chemicals in tobacco smoke can also harm the environment, contributing to air pollution and litter. Despite the well-known risks associated with smoking, many people continue to smoke due to addiction, peer pressure, or a lack of understanding about the long-term consequences.
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Franklin is helping his aunt sew a lace border onto 2 quilts. Each quilt is 2. 2 meters wide by 2. 7 meters long. At the craft store, they buy a 20-meter roll of lace. To their surprise, they use up almost all of it. How many millimeters of lace do they have left after finishing the quilts?
Answers
The amount in millimeters of lace they have left after finishing the quilts is 400 millimeters.
Determine how much lace is needed for each quilt. Each quilt has a perimeter that we need to cover with lace. The perimeter is the sum of all sides of a rectangle, which is (2 x width) + (2 x length).
Each quilt is 2.2 meters wide and 2.7 meters long. So, the perimeter of one quilt is (2 x 2.2) + (2 x 2.7) = 4.4 + 5.4 = 9.8 meters.
Since there are 2 quilts, the total lace needed for both quilts is 9.8 meters x 2 = 19.6 meters.
They bought a 20-meter roll of lace. To find out how much lace is left, subtract the total lace used from the initial length of the roll: 20 meters - 19.6 meters = 0.4 meters.
To convert this to millimeters, multiply by 1,000: 0.4 meters x 1,000 = 400 millimeters.
So, Franklin and his aunt have 400 millimeters of lace left after finishing the quilts.
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RO Consider the convergent series (-1)" its sum s, and its partial sums n+1 84. That is, (-1)" and 8μ -Σ (-1)" n+1 RO NO 1. Is s - 85 going to be positive or negative? 2. Use the Alternating Series
Answers
The value of s - 85 cannot be determined based on the given information as we do not know the value of s.
Alternating Series Test states that if a series satisfies three conditions, namely the terms alternate in sign, the absolute value of the terms decreases as n increases, and the limit of the terms approaches zero as n approaches infinity, then the series converges.
The given series (-1)^n satisfies the first two conditions as the terms alternate in sign and the absolute value of the terms is decreasing. To check the third condition, we take the limit of the terms as n approaches infinity: lim n→∞ |(-1)^n+1/n+1| = lim n→∞ 1/(n+1) = 0.
Since all three conditions are satisfied, the series converges. We can also see from the given partial sums that the sum s lies between 83 and 85. Therefore, s - 85 is negative or zero.
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Kira paid $15. 60 for 19. 5 centimeters of wire.
Find the unit price in dollars per centimeter.
If necessary, round your answer to the nearest cent.
HELP PLEASE!!! ASAP!!!
Answers
The unit price in dollars per centimeter is 80 cents.
:: Total wire length = 19.5 cm
:: Total amount paid = $15.60
Per unit price = [ (total amount paid) / (total wire length) ]
Per unit price = (15.60 / 19.5) $/cm
Per unit price = 0.8 ($/cm)
And as we know, $1 = 100 cents,
So,
$0.8 = 0.8 x 100 cents = 80 cents.
Therefore, the unit price in dollars per centimeter is 80 cents.
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Y’all pls help this is due tmrwww
Answers
Step-by-step explanation:
1kL = 100 dal
x = 470 dal .... you will criss cross it
1 kl × 470 dal = x ×100dal
470 dal kl = 100dal x ... then you will divide 100 dal from both side
4.7 kl = x
x = 4.7 kl
so our result is 4.7kl which is equal to 470 dal
Step-by-step explanation:
470 dal = 4.7 kl
because 1 kl = 100 dal
[tex] \frac{1}{x} = \frac{100}{470} \\ \\ 100x = 470 \\ x = \frac{470}{100} \\ x = 4.7[/tex]
#CMIIWFor the differential equation
s′′+bs′+6s=0,
find the values of b that make the general solution overdamped, underdamped, or critically damped.
(For each, give an interval or intervals for b for which the equation is as indicated. Thus if the the equation is overdamped for all b in the range −1
If the equation is overdamped, b∈
If the equation is underdamped, b∈
If the equation is critically damped, b∈
Answers
- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.
To determine the behavior of the solution for the given differential equation s′′ + bs′ + 6s = 0, we need to analyze the roots of the characteristic equation:
r^2 + br + 6 = 0
For this quadratic equation, the discriminant Δ is given by:
Δ = b^2 - 4(1)(6) = b^2 - 24
The behavior of the solution depends on the value of Δ:
1. Overdamped: If Δ > 0, the solution will be overdamped.
2. Underdamped: If Δ < 0, the solution will be underdamped.
3. Critically damped: If Δ = 0, the solution will be critically damped.
Now, we find the intervals of b for each case:
1. Overdamped (Δ > 0):
b^2 - 24 > 0
This inequality holds for b ∈ (-∞, -2√6) ∪ (2√6, ∞).
2. Underdamped (Δ < 0):
b^2 - 24 < 0
This inequality holds for b ∈ (-2√6, 2√6).
3. Critically damped (Δ = 0):
b^2 - 24 = 0
This equation holds for b = -2√6 and b = 2√6.
In conclusion:
- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.
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The two-way frequency table shows the results of a survey of middle school students.
Find the probability that a randomly chosen student is a male who enjoys reading. Round
to the nearest thousandth.
Totals
Enjoys Reading
Female
Male
Enjoyment of Reading
Yes
No
40
30
15
30
55
60
70
45
Totals
115
Answers
The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261
To calculate the probability that a randomly chosen student is a male who enjoys reading, you need the number of males who enjoy reading divided by the total number of students.
The probability that a randomly chosen student is a male who enjoys reading can be found by dividing the number of males who enjoy reading by the total number of students.
From the table, we see that there are 30 males who enjoy reading and a total of 115 students. Therefore, the probability is:
P(male and enjoys reading) = 30/115
Rounding to the nearest thousandth, we get:
Therefore, The probability that a randomly chosen student is a male who enjoys reading P(male and enjoys reading) ≈ 0.261
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12 16 10 find d surface area of d solid
Answers
To find the surface area of a solid, we need to add up the area of each face.
For a rectangular solid with dimensions 12, 16, and 10, the surface area would be:
- The area of the top and bottom faces: 2 x (12 x 16) = 384 square units
- The area of the front and back faces: 2 x (12 x 10) = 240 square units
- The area of the left and right faces: 2 x (16 x 10) = 320 square units
Adding these areas together, we get a total surface area of:
384 + 240 + 320 = 944 square units.
Therefore, the surface area of the solid with dimensions 12, 16, and 10 is 944 square units.
In milling operations, the spindle speed S (in revolutions per minute) is directly related to the cutting speed C (in feet per minute) and inversely related to the tool diameter D (in inches). A milling cut taken with a 3-inch high-speed drill and a cutting speed of 70 feet per minute has a spindle speed of 88.2 revolutions per minute. What is the spindle speed for a cut taken with a 4-inch high-speed drill and a cutting speed of 30 feet per minute?
Answers
The spindle speed for a cut taken with a 4-inch high-speed drill and a cutting speed of 30 feet per minute is approximately 35.1 revolutions per minute.
Speed is a measure of how fast an object is moving. It is usually measured in units of distance per unit time, such as miles per hour or meters per second. Speed is an important concept in physics, engineering, and everyday life
We can use the formula for spindle speed that relates spindle speed to cutting speed and tool diameter:
S = (C × 12) / (π × D)
where S is spindle speed, C is cutting speed in feet per minute, D is tool diameter in inches, and π is the mathematical constant pi.
We know that for a 3-inch high-speed drill with a cutting speed of 70 feet per minute, the spindle speed is 88.2 revolutions per minute. We can use this information to solve for the constant of proportionality k:
88.2 = (70 × 12) / (π × 3)
k = 88.2 × (π × 3) / (70 × 12)
k ≈ 0.0039
Now we can use the value of k to find the spindle speed for a 4-inch high-speed drill with a cutting speed of 30 feet per minute:
S = k × C × 12 / D
S = 0.0039 × 30 × 12 / 4
S = 35.1
Therefore, the spindle speed for a cut taken with a 4-inch high-speed drill and a cutting speed of 30 feet per minute is approximately 35.1 revolutions per minute.
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Arturo has completed 27 math problems, which is 75% of the assignment. How many problems total did he have to complete?
I need help!
Answers
The total number of problems he solved is 36 if after completion of 27 problems he has completed 75% of the assignments.
Percentage of completion = 75 % of the work
The percentage can be converted to decimal by dividing the percentage by 100.
Thus, the part that has been completed = 75% = 0.75 of the work
The number of questions done = 27
Let the total number of questions be x
Thus, 75% of x is given as 27
75% of x = 27
0.75 * x = 27
0.75x = 27
x = 27/0.75
x = 36
Thus, the total number of questions is 36.
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A spotlight is mounted on the eaves of a house 20 feet above the ground. A flower bed runs between the house and the sidewalk, so the closest the ladder can be placed to the house is 15 feet. How long a ladder is needed so that an electrician can reach the place where the light is mounted
Answers
Answer:
Step-by-step explanation:
We can use the Pythagorean theorem to solve this problem. Let's call the length of the ladder "L". The ladder, the wall of the house, and the ground form a right triangle. The distance between the ladder and the house is the base of the triangle, which is 15 feet. The height of the triangle is the distance from the ground to the spotlight, which is 20 feet. The length of the ladder is the hypotenuse of the triangle.
Using the Pythagorean theorem, we have:
L^2 = 15^2 + 20^2
L^2 = 225 + 400
L^2 = 625
L = sqrt(625)
L = 25
Therefore, a ladder of at least 25 feet is needed for the electrician to reach the place where the light is mounted.
Two straight lines cross at a point.
b+c+d=280°
Work out the sizes of angles a, b, c and d.
a
b
d.
C
Not drawn accurately
Answers
Answer:
a = c = 80°b = d = 100°Step-by-step explanation:
You want the measures of the angles where lines cross if the sum of three of them is 280°.
Linear pairAngle b and c form a linear pair, so ...
b + c = 180°
Substituting that into the given equation, we have ...
b + c + d = 280°
180° + d = 280°
d = 100°
Vertical anglesAngles in this figure that do not share a side are vertical angles, hence congruent.
b = d = 100°
c = 180° -b = 180° -100° = 80° . . . . using the linear pair relation
a = c = 80°
A bicycle mechanic wants to put a strip of plastic between the tube and tire of a 26-in. diameter bicycle tire. to the nearest inch, how long should the strip of plastic be?
Answers
The bicycle mechanic should cut a strip of plastic approximately 82 inches long to place between the tube and tire of the 26-inch diameter bicycle tire.
To calculate the length of the strip of plastic needed, we first need to determine the circumference of the tire. The formula for the circumference of a circle is C=2πr, where C is the circumference, π is approximately 3.14, and r is the radius of the circle.
In this case, the tire diameter is 26 inches, so the radius is 13 inches (half of the diameter). Therefore, the circumference of the tire is: C = 2πr = 2π(13) = 81.64 inches (rounded to two decimal places)
To ensure that the strip of plastic fits snugly between the tube and tire, it should be the same length as the circumference of the tire. Therefore, the strip of plastic should be 82 inches long (rounded to the nearest inch).
In summary, the bicycle mechanic should cut a strip of plastic that is 82 inches long to fit between the tube and tire of the 26-inch diameter bicycle tire.
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What is the approximate volume of the cylinder? (Use 3. 14 as an approximation of pi. )
Answers
The approximate volume of the cylinder with a diameter of 14cm and height of 49cm is 10780.78 cubic centimeters, calculated using the formula V=πr²h.
To calculate the volume of a cylinder, we use the formula
Volume = πr²h
where π is pi, r is the radius of the cylinder, h is the height of the cylinder.
We are given the diameter of the cylinder, which is 14 cm. The radius of the cylinder is half of the diameter, so
radius = diameter / 2 = 14 cm / 2 = 7 cm
The height of the cylinder is given as 49 cm.
Now we can use the formula to find the volume of the cylinder
Volume = πr²h = 3.14 x 7² x 49 = 10780.78 cubic centimeters (rounded to two decimal places)
Therefore, the approximate volume of the cylinder is 10780.78 cubic centimeters.
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--The given question is incomplete, the complete question is given
" What is the approximate volume of the cylinder? when diameter is 14cm height is 49cm (Use 3. 14 as an approximation of pi. )"--
NEED ASAP!
MATH I NEED TO PASS!!
Answers
Answer:
Step-by-step explanation:
Find area of all shapes and add
A(biggest rectangle) = Lw = 6*3 =18 there are 2 of those A=36
A(long skinny rectangle = Lw = 2*6 =12 there are 2 of those A=24
A(smallest) = Lw = 2*3=6 there are 2 of those A=12
Add it all up
A=36+24+12 = 72
I checked it 5 times. I keep getting 72
Select the correct answer.
Using long division, what is the quotient of 3z + 20z³ + 14x² + 17x + 30 and +6?
OA 32:³ 2x² + 2x - 5
О в.
OC.
OD. 3z² + 2x + 2
22³ + 142² + 17z + 30
3z³ + 2z² + 2x + 5
Reset
Next
Answers
The quotient of the division 3x⁴ + 20x³ + 14x² + 17x + 30 ÷ x + 6 is 3x³ + 2x² + 6x - 19
Evaluating the long division expressionsThe quotient expression is given as
3x⁴ + 20x³ + 14x² + 17x + 30 ÷ x + 6
The long division expression is represented as
x + 6 | 3x⁴ + 20x³ + 14x² + 17x + 30
So, we have the following division process
3x³ + 2x² + 6x - 19
x + 6 | 3x⁴ + 20x³ + 14x² + 17x + 30
3x⁴ + 18x³
--------------------------------
2x³ + 14x² + 17x + 30
2x³ + 12x²
-------------------------------------
6x² + 17x + 30
6x² + 36x
-------------------------------------
-19x + 30
-19x - 114
-------------------------------------
134
Hence, the quotient of the long division is 3x³ + 2x² + 6x - 19
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The answer should be
2x³ + 14x² + 17x + 30
Which expression is equivalent to (3√27)^4
A-12
B-9^2
C-81^4
D-27^3/4
Answers
Answer:
Step-by-step explanation:
(3√27)^4 = (3^1/3 * 3^3/2)^4 = (3^5/2)^4 = 3^10 = 59049
So the equivalent expression is not listed among the given options.
Consider the function f(x) = 1/z on the interval (5,9). (A) Find the average or mean slope of the function on this interval, Average Slope =?
(B) By the Mean Value Theorem, we know there exists a c in the open interval (5,9) such that f'(c) is equal to this mean slope. Find all values of c that work and list them separated by commas) in the box below
Answers
Therefore, the only value of c that works is 6√5.
(A) To find the average slope of the function f(x) = 1/x on the interval (5, 9), we use the formula:
Average Slope = (f(9) - f(5)) / (9 - 5)
Plugging in the values, we get:
Average Slope = (1/5 - 1/9) / 4 = -1/180
Therefore, the average slope of the function on the interval (5, 9) is -1/180.
(B) By the Mean Value Theorem, we know there exists a c in the open interval (5, 9) such that f'(c) is equal to this mean slope.
The derivative of f(x) = 1/x is f'(x) = -1/x^2.
Setting f'(c) = -1/180, we get:
-1/c^2 = -1/180
Solving for c, we get:
c = ±6√5
Since c must be in the open interval (5, 9), the only value that works is:
c = 6√5
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Consider two coordinates given by P(−2, 0) and Q(4, 3).
Find the equation of the straight line connecting these points in the form
y = mx + c
Answers
The equation of the straight line connecting these points in the form of y = mx + c is given as y = (1/2)x + 1.
The line in the slope-intercept equation is given as,
y = mx + c
where:
m = the slope of the line
c = the y-intercept
The slope m of the line connecting two points (x1, y1) and (x2, y2) is given by the formula
= (y₂ - y₁) / (x₂ - x₁)
Substituting the coordinates values of P and Q into this formula, we get
[tex]m = (3 - 0) / (4 - (-2))[/tex]
= 3/6
= 1/2
Therefore, the value of the m is 1/2
We can find the value of c by substituting the m and x values in the equation. using the point P and Substituting x and y values in the equation we get
x = - 2
y = 0
[tex]0 = (1/2) × (-2) + c[/tex]
c = 1
Therefore, the value of c is 1.
By substuting the m and c values in the standard slope-intercept formula we get y = (1/2)x + 1.
Therefore, the equation of the line connecting points P and Q is y = (1/2)x + 1.
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Complete parts a rough for the given function f(x) = -4°-x+2:1-4,4) A. The critical point(a) is(ro) ot x - (Simplify your answer. Use a comma to separate wwers as needed) B. The function does not have a critical point b. Use the First Derivative Test to locate the local maximum and minimum values Select the correct choice below and recessary in the answer box to complete your choice (Simplify your answer. Use a comma to separate arvwers as needed) BA The local maximum/maximal/are at OD. The local minimumiminimais/are OC. The local minimumin nima infare at and the local maximum maxima are at OD. There is no local munimum and there is no local maximum e Identify the absolute maximum and minimum values of the function on the given interval (when they st) Select the correct the below and the web.com your choice (Simplify your answer Uses comma to separato answers as needed) A The absolute maxim is al and the absolute minimumis More 8 10
Answers
The critical point is x = -1/2, the function has a local minimum at x = 1 and an absolute maximum at x = 4, and the absolute minimum is at x = -1/2.
How to find critical point?a. The critical point is x = -1/2.
To find the critical point(s), we need to find where the derivative of the function is equal to zero or undefined. In this case, we have:
f(x) = -4x - x^2 + 2
f'(x) = -4 - 2x
Setting f'(x) equal to zero, we get:
-4 - 2x = 0
-2x = 4
x = -2/2
x = -1
However, we need to check if this value is in the given interval (1-4, 4). Since -1 is not in the interval, it is not a critical point.
Next, we check the endpoints of the interval.
When x = 1, f(x) = -4 - 1^2 + 2 = -3.
When x = 4, f(x) = -4 - 4^2 + 2 = -22.
So the function has a local minimum at x = 1, and an absolute maximum at x = 4, and no local maximum.
How to find local maxima and minima?b. The local maximum is at x = 4, and the local minimum is at x = 1.
We can use the First Derivative Test to locate the local maximum and minimum points. If the derivative changes sign from positive to negative at a point, then it is a local maximum. If the derivative changes sign from negative to positive at a point, then it is a local minimum.
In this case, we have f'(x) = -4 - 2x. It is negative for x < -2 and positive for x > -2. Therefore, the function is decreasing for x < -2 and increasing for x > -2. Since the interval is (1-4, 4), the critical points are -2 and 4.
For x = 4, we have f'(4) = -4 - 2(4) = -12, which is negative, so x = 4 is a local maximum.
For x = 1, we have f'(1) = -4 - 2(1) = -6, which is negative, so x = 1 is a local minimum.
Therefore, the local maximum is at x = 4, and the local minimum is at x = 1.
How to found absouloute maxima and minima?c. The absolute maximum is at x = 4, and the absolute minimum is at x = -1/2.
To find the absolute maximum and minimum, we need to evaluate the function at the critical points and endpoints of the interval, and choose the largest and smallest values, respectively.
We have already found that the local maximum is at x = 4, and the local minimum is at x = 1. We also found that x = -1/2 is a critical point, but it is not in the given interval, so we can ignore it.
Evaluating the function at the endpoints of the interval, we get:
f(1) = -3
f(4) = -22
Therefore, the absolute maximum is at x = 4, and the absolute minimum is at x = 1/2.
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(co 4) from a random sample of 85 teens, it is found that on average they spend 31.8 hours each week online with a population standard deviation of 5.91 hours. what is the 90% confidence interval for the amount of time they spend online each week?
Answers
The 90% confidence interval for the amount of time that teens spend online each week is (30.761, 32.839) hours
To find the 90% confidence interval for the amount of time that teens spend online each week, we can use the following formula
CI = x ± z*(σ/√n)
where
x is the sample mean
σ is the population standard deviation
n is the sample size
z is the z-score associated with the desired confidence level
In this case, we have
x = 31.8 hours
σ = 5.91 hours
n = 85
z = 1.645 (for a 90% confidence level, using a z-table or calculator)
Plugging in these values, we get
CI = 31.8 ± 1.645*(5.91/√85)
Simplifying, we get
CI = 31.8 ± 1.039
We can interpret this interval as saying that if we were to take many random samples of 85 teens and compute the confidence interval for each sample, about 90% of these intervals would contain the true population mean.
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Which is a solution to 2n = 16?
Answers
Answer:
3
Step-by-step explanation:
2x2=4
4x2=8
8x2=16
Josh lit a 14-inch candle. She noticed that it was getting an inch shorter every 30 minutes. Let x be the number of hours and y be the total height of the candle
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The height of the candle after x hours is given by the equation y = 2x + 14.
Let's first convert the time interval to hours. There are 60 minutes in an hour, so 30 minutes is equivalent to 0.5 hours.
After x hours, the candle will have burned down by 2x inches (since it burns 1 inch every 0.5 hours).
If y is the total height of the candle, then we can write the equation:
y - 2x = 14
We can solve for y:
y = 2x + 14
So the height of the candle after x hours is given by the equation y = 2x + 14.
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A jewelry company purchases a necklace for $24. If they mark it up 36% to sell it at their store, what is the selling price of the necklace?
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The selling price of the necklace at the store is $32.64.
To calculate the selling price of the necklace, we will first find the markup amount and then add it to the original cost.
Markup = (Original Cost) x (Markup Percentage)
Markup = $24 x 36% = $24 x 0.36 = $8.64
Now, add the markup amount to the original cost to find the selling price:
Selling Price = Original Cost + Markup
Selling Price = $24 + $8.64 = $32.64
So, the selling price of the necklace at the store is $32.64.
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HELP match each one with either 1-4
Answers
Answer:
(4),(3),(1),(2),(2),(1)
Step-by-step explanation:
Mnemonic to memorize trigonometric ratios: SOH CAH TOA
(S=O/H C=A/H T=O/A)
Sine, Cosine, Tangent, Opposite to x, Adjacent to x, Hypotenuse
Cosecant = 1/Sine, Secant = 1/Cosine, Cotangent = 1/Tangent
A study is designed to test the hypotheses h0: m $ 26 versus ha: m , 26. a random sample of 50 units was selected from a specified population, and the measurements were summarized to y 5 25.9 and s 5 7.6. a. with a 5 .05, is there substantial evidence that the population mean is less than 26
Answers
The p-value for a t-score of -0.92 is approximately 0.18 and since it is greater than the significant level, the null hypothesis is rejected.
The first step in testing this hypothesis is to calculate the test statistic, which in this case is a t-score. The formula for the t-score is (y - mu) / (s / sqrt(n)), where y is the sample mean, mu is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
In this case, the sample mean is 25.9, the hypothesized population mean is 26, the sample standard deviation is 7.6, and the sample size is 50. Plugging these values into the formula, we get a t-score of -0.92.
Next, we need to find the p-value associated with this t-score. We can use a t-table or a calculator to do this. Using a t-table with 49 degrees of freedom (since we have a sample size of 50 and one parameter estimated from the sample), we find that the p-value for a t-score of -0.92 is approximately 0.18.
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. In other words, we do not have substantial evidence to conclude that the population mean is less than 26. However, it is important to note that the sample mean is slightly below the hypothesized population mean, and the p-value is relatively close to the significance level. Therefore, it may be worthwhile to conduct additional studies with larger sample sizes or different populations to further investigate this question.
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