Part a determine the correct sketches for v=100cos(ωt+ϕ) versus ωt for ϕ=90∘, 45∘, 0∘, −45∘, and −90∘.
The temperature in Fairbanks, Alaska, fell 10 degrees in 2 hours.
Explain why the average temperature change was –5ºF per hour.
The temperature fall can be represented by −10. To find the average change per hour, divide −10 by 2. −10 divided by 2 is −5.
A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]\frac{y}{x}=k[/tex] or [tex]y=kx[/tex]
In this problem we have
Points [tex](2,14)[/tex] and [tex](4,28)[/tex]
so
Find the value of k
First point
[tex]\frac{14}{2}=k[/tex]
[tex]k=7[/tex]
Second point
[tex]\frac{28}{4}=k[/tex]
[tex]k=7[/tex]
the function is
[tex]y=kx[/tex] --------> substitute the value of k
[tex]y=7x[/tex]
therefore
the answer is
[tex]y=7x[/tex]
In this problem with a single point was sufficient to calculate the equation, since in a direct variation the line passes through the origin, it is not necessary to use the formula of the slope
In a 4 x 3 factorial design, there are how many levels of the first grouping factor?
Find the specified element in the inverse of the given matrix
Write an equation of the line in the figure.
The sale price of an item is $45 after a 40% discount is applied. What is the original price of the item?
The original price of the item is $75.
Suppose the original price of the item =x
Discount =40%
What is the percentage?The percentage is the value per hundred.
Given discounted price or sale price of the item =$45
This means [tex]x-\frac{x*40}{100} =45[/tex]
[tex]\frac{60x}{100} =45[/tex]
[tex]\frac{3x}{5} =45[/tex]
[tex]x=75[/tex]
So, the original price of the item =$75
Hence, the original price of the item is $75.
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Bryson hopes to win a three-day vacation in a drawing that is being held at his office. He purchased 40 raffle tickets. There were 500 raffle tickets sold. What is the theoretical probability of Bryson winning the trip?
A-2/25
B-1/5
C-4/5
D-500/40
What is the mean of the high temperatures, in degrees Fahrenheit, for the week? Show your work.
Determine whether each of these sets is the power set of a set, where a and b are distinct elements.
a.∅
c.{∅,{a},{∅,a}}
Consider the equation y = 14 – 2x. with y on the vertical axis and x on the horizontal axis, the horizontal intercept of this line is
For the box shown, the total area is 94 cm2. determine the value of x
The three tools the Federal Reserve uses to enact monetary policy are:
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Why do you round 117290 up to 120000
Please help badly I cannot answer
Lenny uses two pieces of yarn for a craft project. The first piece is 5.89 meters long. The second piece is 2.147 meters long. What is the total length of the two pieces of yarn? Enter your answer in the box. M__
Answer: 8.04 meters
Step-by-step explanation:
length of first piece of yarn = 5.89 meters
length of second piece of yarn = 2.147 meters
Total length of of the two pieces of yarn = length of first piece of yarn + length of second piece of yarn = 5.89 meters + 2.147 meters = 8.037 meters
The rule apply for the addition and subtraction is :
The least precise number present after the decimal point determines the number of significant figures in the answer.
Thus the answer will be 8.04 meters as least precise number 5.89 contains two decimal places.
5x-3 (2x-4)=7x+16. solve for x
I an a factor of 28. the other factor is 4. what number am i
A backpack that normally sells for 39 is on sale for 34% off. Find the amount of the discount and the sale price.
Which pair of measurements is not equivalent?
24 feet, 8 yards
24 inches, 2 feet
10 feet, 120 inches
3 miles, 15,480 feet
The pair of measurements that is not equivalent is 3 miles and 15,480 feet. All other pairs are equivalent when converted to the same units. This determines which measurements do not match in the same units.
To determine which pair of measurements is not equivalent, we need to convert them into the same units and compare them:
24 feet, 8 yards: 1 yard = 3 feet, so 8 yards = 8 * 3 = 24 feet. Therefore, 24 feet is equivalent to 8 yards.24 inches, 2 feet: 1 foot = 12 inches, so 2 feet = 2 * 12 = 24 inches. Therefore, 24 inches is equivalent to 2 feet.10 feet, 120 inches: 1 foot = 12 inches, so 120 inches = 120 / 12 = 10 feet. Therefore, 10 feet is equivalent to 120 inches.3 miles, 15,480 feet: 1 mile = 5280 feet, so 3 miles = 3 * 5280 = 15,840 feet. Therefore, 3 miles is not equivalent to 15,480 feet.Thus, the pair of measurements that is not equivalent is 3 miles, 15,480 feet.
Unfortunately, arsenic occurs naturally in some ground water†. a mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. a well in texas is used to water cotton crops. this well is tested on a regular basis for arsenic. a random sample of 36 tests gave a sample mean of x = 6.8 ppb arsenic, with s = 2.9 ppb. does this information indicate that the mean level of arsenic in this well is less than 8 ppb? use α = 0.01. (a) what is the level of significance? 0.01 state the null and alternate hypotheses. h0: μ = 8 ppb; h1: μ > 8 ppb h0: μ = 8 ppb; h1: μ < 8 ppb h0: μ > 8 ppb; h1: μ = 8 ppb h0: μ < 8 ppb; h1: μ = 8 ppb h0: μ = 8 ppb; h1: μ ≠ 8 ppb (b) what sampling distribution will you use? explain the rationale for your choice of sampling distribution. the standard normal, since the sample size is large and σ is known. the student's t, since the sample size is large and σ is unknown. the student's t, since the sample size is large and σ is known. the standard normal, since the sample size is large and σ is unknown. what is the value of the sample test statistic? (round your answer to three decimal places.) -2.483 (c) estimate the p-value. p-value > 0.250 0.125 < p-value < 0.250 0.050 < p-value < 0.125 0.025 < p-value < 0.050 0.005 < p-value < 0.025 p-value < 0.005 sketch the sampling distribution and show the area corresponding to the p-value. webassign plot webassign plot webassign plot webassign plot (d) based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? are the data statistically significant at level α? at the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) interpret your conclusion in the context of the application. there is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. there is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.
Suppose in a market for iTune cards demand is Qd = 1500 - 250P, and supply is Qs = 850P. Find the equilibrium P* and Q*.
What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?
It can be convenient to subtract the right side of the inequality from both sides.
... 2(3x -1) -(4x -6) ≥ 0
... 2x +4 ≥ 0 . . . . . . . . . collect terms
... x +2 ≥ 0 . . . . . . . . . . divide by the coefficient of x
... x ≥ -2 . . . . . . . . . . . . add the opposite of the constant
Any value of x that is at least -2 will be in the solution set.
True or false, the decimal form of 3 3/8 is 3.38
A flag in the shape of a right triangle is hung over the side of a building as shown below. The total weight of the flag is 250 pounds and it has uniform density. a = 15 and b = 39.
Answer:
(a) The density of flag is [tex]\dfrac{25}{27}[/tex] Pounds per square foot
(b) The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex] Pounds
(c) The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds
(d) The exact work by roof is 1250 foot-pounds
Step-by-step explanation:
(a) We are given a flag in the shape of a right triangle.
The total weight of flag is 250 pounds and Uniform density.
Base of the flag [tex]=\sqrt{b^2-a^2}[/tex]
[tex]=\sqrt{39^2-15^2}=36[/tex]
Area of the flag [tex]=\dfrac{1}{2}\times 36\times 15 = 270[/tex]
Weight of flag = 250 pounds
[tex]Density =\dfrac{Weight}{Area}=\dfrac{250}{270}=\dfrac{25}{27}[/tex]
Hence, The density of flag is [tex]\dfrac{25}{27}[/tex]
(b) Weight of strip which is h feet below the roof.
Length of strip [tex]=\dfrac{36}{15}(15-h)[/tex]
Width of strip [tex]\Delta h[/tex]
Weight = Density x area
[tex]=\dfrac{25}{27}\times \dfrac{36}{15}(15-h)[/tex]
[tex]=\dfrac{20}{9}(15-h)\Delta h[/tex]
Hence, The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex]
(c) Work slice to move h feet above to the roof
work[tex]=Weight\times displacement[/tex]
[tex]=\dfrac{20}{9}(15-h)\Delta h\times h[/tex]
[tex]=\dfrac{20}{9}(15-h)h\Delta h[/tex]
Hence, The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds
(d) Exact work on the roof by hanging flag
[tex]W=\int_0^{15}\dfrac{20}{9}(15-h)hd h[/tex]
[tex]W=\dfrac{20}{9}(\dfrac{15h^2}{2}-\dfrac{h^3}{3})|_0^{15}[/tex]
[tex]W=1250-0[/tex]
[tex]W=1250[/tex]
Hence, The exact work by roof is 1250 foot-pounds
Final answer:
The weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.
Explanation:
To find the centroid of a right triangle, we can use the following formulas:
[tex]\[ x_c = \frac{b}{3} \][/tex]
[tex]\[ y_c = \frac{a}{3} \][/tex]
Where:
[tex]- \( x_c \)[/tex] is the x-coordinate of the centroid.
[tex]- \( y_c \)[/tex] is the y-coordinate of the centroid.
[tex]- \( a \)[/tex] is the length of the side perpendicular to the base (height).
[tex]- \( b \)[/tex] is the length of the base.
Given \( a = 15 \) and \( b = 39 \), we can calculate the centroid as follows:
[tex]\[ x_c = \frac{39}{3} = 13 \][/tex]
[tex]\[ y_c = \frac{15}{3} = 5 \][/tex]
So, the centroid of the triangle is located at the point (13, 5).
Now, regarding the weight distribution, if the flag has uniform density, the center of mass (or centroid) would be the point where the total weight is concentrated. Since the total weight of the flag is 250 pounds, and the centroid is the point of concentration of mass, the entire weight of the flag, 250 pounds, can be considered to act at the centroid.
Therefore, the weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.
Its number 15. Thank you
Explain how to solve 2x + 7 = 15
If one score is randomly selected from a normal distribution with m = 100 and s = 20, the probability of obtaining a score between x = 90 and x = 100 is p = 0.3085.
a. True
b. False
James covers a distance of 8 meters in the first second of a 100 meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started? a. 11 c. 28 b. 20 d. 80
Answer:
Option b. 20 meters
Step-by-step explanation:
James covers a distance of 8 meters in the first second of 100 meter race.
Then, he sprints at a speed of 9 meters per second.
We have to find how far is James from the finish line 9 seconds after the start of the race.
James covers distance in first second = 8 meters.
Time remaining in 9 seconds after running 8 meter = 9 - 1 = 8 seconds.
In another 8 seconds James covers the distance = speed × time
= 9 × 8 = 72 meters
Total distance covered in 9 seconds = 8 + 72 = 80 meters
Distance remaining in 100 meter race after 9 seconds = 100 - 80 = 20 meters.
James is 20 meters far from the finish line 9 seconds after the race has started.
Option b. 20 meters is the answer.
find the product. List the units. 8 h $9/h
The product is equivalent to $72.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a rate of $9 per hour for 8 hours.
Now, for 1 hour, the cost is $9. Therefore, for 8 hours, we can write -
x = 9 x 8
x = $72
Therefore, the product is equivalent to $72.
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