the answer is 47 I know because Im in 8th grade
sketch the grapf of each function f(x)=-x^4+2x^2-2x-3
The graph of each function [tex]f(x)=-x^4+2x^2-2x-3[/tex] is attached below.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
A Linear function is a function whose graph is a straight line
We are given the function;
[tex]f(x)=-x^4+2x^2-2x-3[/tex]
If we know that the function crosses x axis at some point, then for the polynomial functions, we have those as roots of the polynomial.
The graph of each function f(x) is attached below.
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The variables x
and y
vary directly. Use the values to find the constant of proportionality, k
. Then write an equation that relates x
and y
pls help due in 12min
An equation that relates x and y is y = kx.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
A proportional relationship between x and y.
That means,
x ∝ y.
y = kx, where k is constant.
y/x = k
When y = 72, x = 3.
That means., k = 24.
The equation is y = kx.
Therefore, the equation is y = kx.
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Each letter of the alphabet is assigned
an integer, starting with A = 0, B = 1, and so on. The
numbers repeat after every seven letters, so that G = 6,
H = 0, and I = 1, continuing on to Z. What two-letter
word is represented by the digits 16? (MT calendar
problem)
The two letter word represented by the digits 16 is given as follows:
in.
How to obtain the two letter word?Considering the pattern, the digits representing each letter are given as follows:
A = 0.B = 1.C = 2.D = 3.E = 4.F = 5.G = 6.H = 0.I = 1.J = 2.K = 3.L = 4.M = 5.N = 6.O = 0.P = 1.Q = 2.R = 3.S = 4.T = 5.U = 6.V = 0.X = 1.W = 2.Y = 3.Z = 4.Hence the first letter can be:
B, I, P or X.
The second letter can be:
G, N, U.
Hence the word is:
in.
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the grades of students in a high school algebra course are approximately normally distributed, with a mean of 75 and a standard deviation of 5 points. of the following, which group is expected to have the greatest percent of students?
The group with the greatest percent of students is expected to be the one with grades between 70 and 80 (inclusive), since this is close to the mean of 75 and encompasses approximately 68% of the data in a normal distribution (according to the empirical rule).
The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
So, in this case, grades between 70 and 80 (75 - 5 and 75 + 5) would contain approximately 68% of the students in the course.
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A) Find the slope of the line passing through the points (−8, -4) and (−8, 8).
B) Find the slope of the line passing through the points (3, 4) and (−3, 4).
The slope of the line passing through the points (−8, -4) and (−8, 8) is undefined.
The slope of the line passing through the points (3, 4) and (−3, 4) is equal to 0.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (8 - (-4))/(-8 - (-8))
Slope (m) = (8 + 4)/(-8 + 8)
Slope (m) = 12/0
Slope (m) = undefined.
For line B, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 4)/(-3 - 3)
Slope (m) = 0/6
Slope (m) = 0.
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4 2⁄3 - 3 2⁄5 ( 22 POINTS IF CORRECT ANSWER! I WILL TAKE DOWN If I FIGUrE T OUT THO SO HURRYYY!)
The subtraction of fraction numbers 4(2/3) and 3(2/5) is, 19/15
What is subtraction?In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.
For example, if we take 4 pencils out of 10 then remaining pencils are 6
so this process is called subtraction.
Given that,
Two fraction numbers,
4(2/3)
And 3(2/5)
Subtraction of both the terms = ?
⇒ 4(2/3) - 3(2/5)
Both the numbers can be written in the simplified form as,
⇒ (12 + 2)/3 = 14/3
⇒ (15 + 2)/5 = 17/5
Now, subtracting both the terms,
⇒ 14/3 - 17/5
Taking LCM of 3 & 5
LCM(3,5) = 15
⇒ Now, for making denominator same we multiply and divide each term 14/3 & 17/5 by 5 and 3 respectively,
⇒ (14/3)x(5/5) - (17/5)x(3/3)
⇒ (14x5)/(3x5) - (17x3)/(5x3)
⇒ 70/15 - 51/15
Now, denominators are same,
So, it can be written as,
⇒ (70 - 51)/15
⇒ 19/15
Hence, the result is 19/15
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4 (a) The nth term of a progression is 3n+ 5. (i) (ii) Determine whether the progression is Arithmetic or Geometric progression
The sequence 3n + 5 because each next term has a constant common difference of 3.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
4. (a). Given, The nth term of a progression is 3n + 5.
Now, Putting some value of 'n' we have,
when n = 1,
a₁ = 8.
when n = 2,
a₂ = 11.
when n = 3,
a₃ = 14.
Now, a₃ - a₂ = a₂ - a₁ = 3.
So, the sequence has a common difference of 3 and hence it is an arithmetic sequence.
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e of x.
2x-4
39
parate answers as needed.)
x+6
24
▪▪▪
The solution to the proportional relationship (2x - 4)/39 = (x + 6)/24 is given as follows:
x = 36.67.
How to solve the proportional relationship?The proportional relationship for this problem is defined as follows:
(2x - 4)/39 = (x + 6)/24
As the measures are proportional, we can apply cross multiplication, hence:
24(2x - 4) = 39(x + 6).
Applying the distributive property to each side of the equality, we have that:
48x - 96 = 39x + 234
Hence, isolating x, the solution is obtained as follows:
48x - 39x = 234 + 96
9x = 330
x = 330/9
x = 36.67.
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Simplify each expression. Write your answer with positive exponents. Assume that all variables represent positive real numbers. Do this in your answer sheet.
The results of the exponents are;
1) n^6
2) 3r^2
3) b
4) b^7/2
5) 1/3x^13/12
6) 8/m^9/2
7) x^1/3y^1/8
8) 5^1/5
9) q^1/2
10) 2x^3/2
What are exponents?Exponents are a mathematical notation used to represent repeated multiplication of a number by itself. The number being multiplied is called the base, and the exponent is a power that indicates the number of times the base is being multiplied by itself.
We can see that in the problems that we have above, we can be able to obtain the exponents by the use of the law of exponents.
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A line has a slope of
–
7 and passes through the point (2,
–
2). Write its equation in slope-intercept form.
The equation of a line in slope-intercept form is y = 7x - 12.
What is slope of a line?A line's slope is defined as the ratio of the change in the y coordinates to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x.
Given the slope of the line is 7
and passes through the point (2, 2)
equation of a line is given by,
y = mx + c
m = slope = 7
y = 7x + c
for c substitute the values of x and y, where x = 2 and y = 2
y = 7x + c
2 = 7(2) + c
c = 2 - 14
= -12
equation is y = 7x - 12
Hence equation of a line is y = 7x - 12.
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In a game of darts, there are 20 sectors on a target, and a smaller circular "bullseye" in the center. In this particular game, a player must correctly call "low,” consisting of the sectors numbered 1–10; "high,” consisting of the sectors numbered 11–20; or "bullseye,” depending on what they are trying to hit. If they hit the section they call, they are a winner. A player will attempt to hit "low" on the first throw, then will attempt to hit "high" on the second throw, then will attempt to hit "bullseye" on the third throw, and so on until hitting the section they called.
Is it appropriate to use the geometric distribution to calculate probabilities in this situation?
Answer: This game of darts involves the player calling the target they aim to hit and the winner is determined by hitting the section they called. The player starts by attempting to hit "low" (sectors 1-10), followed by "high" (sectors 11-20), then "bullseye", and this pattern continues until the player successfully hits the section they called.
Step-by-step explanation:
The diameter of a ball bearing was measured by 12 inspectors, each using two different kinds of calipers. The results are as follows: Inspector Caliper 1 Caliper 2 0.264 1 2 0.265 0.264 0.266 3 4 5 6 0.265 0.265 0.266 0.267 0.267 0.265 0.267 0.267 0.265 0.268 0.267 0.268 0.264 7 8 9 0.265 0.265 0.267 10 11 0.268 0.268 12 0.265 0.269 (a) Is there a significant difference between the means of the population of measurements from which the two sam- ples were selected? Use a = 0.05. (b) Find the P-value for the test in part (a). (c) Construct a 95 percent confidence interval on the differ- ence in mean diameter measurements for the two types of calipers.
The P-value for the test is 1.804 and the 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers is [-0.00147, 0.00347].
a) To determine if there is a significant difference between the means of the population of measurements from which the two samples were selected, we can use a two-tailed t-test. We can calculate the t-statistic as follows:
t = (x1 - x2) / sqrt[((s1^2)/n1) + ((s2^2)/n2)]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
For this example, the sample means are x1 = 0.266 and x2 = 0.267. The sample standard deviations are s1 = 0.0017 and s2 = 0.0015. The sample sizes are n1 = 12 and n2 = 12.
Plugging these values into the formula, we get:
t = (0.266 - 0.267) / sqrt[((0.0017^2)/12) + ((0.0015^2)/12)] = -0.145
The critical t-value for a two-tailed test at a significance level of 0.05 with 11 degrees of freedom is 2.201. Since our calculated t-value of -0.145 is not greater than the critical t-value, we can conclude that there is not a significant difference between the means of the population of measurements from which the two samples were selected.
b) The P-value for the test in part (a) is the probability of obtaining a test statistic as extreme as the one we calculated (or more extreme) if the null hypothesis is true. We can calculate this probability as follows:
P = 2 * P(t <= -0.145)
where P(t <= -0.145) is the cumulative probability of the t-distribution with 11 degrees of freedom at -0.145.
Using the t-distribution table, the cumulative probability of t at -0.145 is 0.902. Thus, the P-value for the test in part (a) is P = 2 * 0.902 = 1.804.
c) To construct a 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers, we can use the following formula:
CI = [x1 - x2 +/- t(alpha/2, df) * sqrt[((s1^2)/n1) + ((s2^2)/n2)] ]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and t(alpha/2, df) is the critical t-value for the two-tailed test at a significance level of alpha/2 with df degrees of freedom.
For this example, the sample means are x1 = 0.266 and x2 = 0.267. The sample standard deviations are s1 = 0.0017 and s2 = 0.0015. The sample sizes are n1 = 12 and n2 = 12. The critical t-value for a two-tailed test at a significance level of 0.025 with 11 degrees of freedom is 2.771.
Plugging these values into the formula, we get: CI = [0.266 - 0.267 +/- 2.771 * sqrt[((0.0017^2)/12) + ((0.0015^2)/12)] ] = [-0.00147, 0.00347]
Thus, the 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers is [-0.00147, 0.00347].
The results of the two-tailed t-test show that there is not a significant difference between the means of the population of measurements from which the two samples were selected. The P-value for the test is 1.804 and the 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers is [-0.00147, 0.00347].
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Can anyone help with the circled questions?
The equation of the given lines in both questions are;
15) y = x + 8
16) y = ¹/₄x - 12
What is the equation of the line?15) The formula for the equation of a line between two coordinates is;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
The coordinates are (-4, 4) and (2, 10) and as such we have;
(y - 4)/(x + 4) = (10 - 4)/(2 + 4)
(y - 4)/(x + 4) = 6/6
y - 4 = x + 4
y = x + 8
16) The slope perpendicular to another line is; -1/m
Thus, slope of new line = -1/(-4) = 1/4
The coordinates are (16, -8). Thus;
Equation of Line is;
y + 8 = (1/4)(x - 16)
y = ¹/₄x - 12
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The volume of a rectangular prism is represented by the expression (2x ^ 3 + 7x ^ 2 - 9) the height of the prism is (2x + 3) what are expressions for the length and width of the prism?
The expression for the volume of a rectangular prism is given as (2x^3 + 7x^2 - 9) and the height of the prism is (2x + 3). But the length and width of the prism are not specified in the given information, so it is not possible to write expressions for the length and width of the prism.
11/3 - 6/7 =
Fractions
Answer:
Step-by-step explanation:
11/3- 6/7 = (77-18)/21
= 59/21
25 POINTS!! PLEASE HELP!! i only need help with the circled answers
The function rule for the table is y = -3x - 1
The graph of the functions are attached
y = -7ˣ
domain (-∞, ∞)range (-∞, 0)y = 3 * 6ˣ
domain (-∞, ∞)range (0, ∞)How to find the function rule for the tableThe function in the table is a linear function which is written as
y = mx + c
where
m = slope
c = y intercept'
From the table c = -1
m = (-1 - -4) / (0 - 1) = -3
the function rule is y = -3x - 1
The function y = -7ˣ and y = 3 * 6ˣ are exponential functions
y = -7ˣ
all real numbers is the domain and the range is all real integers less than zero
y = 3 * 6ˣ
all real numbers is the domain and the range is all real integers greater than zero
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There are 16 flowers in a vase. Four flowers are daisies, 1 is rose, 3 are tulips and the rest are sunflowers. Suppose the probability of randomly choosing a flower is 41. Which of the following flowers could it be?
Choose the TWO correct answers.
Responses
The probability of choosing a sunflower
The probability of choosing a sunflower
The probabilty of choosing a daisy
The probabilty of choosing a daisy
The probability of choosing a daisy or a sunflower
The probability of choosing a daisy or a sunflower
The probability of choosing a rose or a tulip
The probability of choosing a rose or a tulip
The probability of not choosing a rose
Answer:
The probability of not choosing a rose
Step-by-step explanation:
Answer:
yes. sjsksj d djdiodldkdkkdkd
dnsjjs
A newspaper article reported that people spend a mean of 6 hours per day watching TV, with a standard deviation of 1.9 hours. A psychologist would like to conduct interviews with the 10% of the population who spend the most time watching TV. She assumes that the daily time people spend watching TV is normally distributed. At least how many hours of daily TV watching are necessary for a person to be eligible for the interview? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.
?hours
10 hours is the daily watching TV necessary for a person to be eligible for the interview.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The empirical rule states that 68% of the data falls within one standard deviation of the mean (6 - 1.9 to 6 + 1.9 hours)
95% of the data falls within two standard deviations of the mean (6 - 2 ×1.9 to 6 + 2×1.9 hours)
99.7% of the data falls within three standard deviations of the mean (6 - 3 × 1.9 to 6 + 3×1.9 hours)
she wants to find the daily TV watching time that separates the top 10% from the rest of the population.
Since 90% of the data falls within two standard deviations of the mean, the necessary daily TV watching time for a person to be eligible for the interview is 6 + 2 × 1.9 = 9.8 hours.
Hence, 10 hours is the daily watching TV necessary for a person to be eligible for the interview.
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need help, So the question is "write the equation of a line that is perpendicular to the graph y=-4x-9 that passes through the point (16,9) anybody please??
Answer:
Step-by-step explanation:
[tex]m_{2}=\frac{-1}{m_{1} }[/tex]
m2=4
y=mx+c
9=4(16)+c
9=64 +c
c=9-64
c=-55
∴y=4x-55
What point divides the directed line segment AB¯¯¯¯¯ into a 2:3 ratio?
Responses
(6, 1)
begin ordered pair 6 comma 1 end ordered pair
(8, 1)
begin ordered pair 8 comma 1 end ordered pair
(10, 1)
begin ordered pair 10 comma 1 end ordered pair
(12, 1)
Answer:
(8, 1)
Option 2
Step-by-step explanation:
Let C be the point that divides AB in the ratio 2:3
The technique to find individual segments is to note that if a line is 2+3 = 5 units long then one segment will be 2/5 and the other segment will be 3/5
2/5 : 3/5 = 2 : 3
Length of segment AB = 14 - 4 = 10 since the y values are the same and it is a horizontal line
So length of segment AC = 2/5 + 10 = 4
TO find the absolute x-value we add this length to the x-coordinate of A: 4 + 4 = 8
The y-coordinate of C = y-coordinate of A = y-coordinate of B = 1
So the point that divides the line segment AB in the ration 2:3 is (8, 1)
This would correspond to the second option
The cost of 3 pounds of grapes is 6.57$. What is the cost of 2 pounds of grapes? Please help! I’ll give brainly.
please help!!
very detailed explanation and answer please!
Answer:
20 Stickers
Step-by-step explanation:
You cross multiply
[tex] \frac{70 \times 4}{14} [/tex]
[tex] \frac{280}{14} = 20[/tex]
Question 1(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 5 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
70 m2
38 m2
35 m2
19 m2
Question 2(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
An image of a parallelogram is shown.
A parallelogram with a base of 22 and one-half feet and a height of 18 and three-fourth feet.
What is the area of the parallelogram?
four hundred forty-four and three-eighths ft2
four hundred twenty-one and seven-eighths ft2
four hundred twelve and one-half ft2
four hundred five and one-half ft2
Question 3(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 16 feet. The height of the figure is 22 feet. The portion from the vertex to the perpendicular height is 8 feet. The portion from a point to a vertical line created by two vertices is 4 feet.
Which of the following represents the total area of the figure?
44 ft2
400 ft2
440 ft2
484 ft2
Question 4(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 10 and three-fifths inches. The side to the right of the base is 6 inches. The small side parallel to the base is 4 and one-fifth inches. There are two sides that form a point at a right angle. The smaller is 4 inches, and the larger is 5 inches.
What is the area of the shape for the quilt block?
seventy-three and three fifths in2
forty-one and four fifths in2
eighty-three and three fifths in2
one hundred forty-seven and one fifth in2
Question 5(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
An image of a rhombus is shown.
A rhombus with a base of 16 centimeters and a height of 15.5 centimeters.
What is the area of the rhombus?
15.75 cm2
31.5 cm2
124 cm2
248 cm2
Question 6(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A maintenance worker needs to wax a restaurant floor shaped like the image shown.
A six-sided figure. There is a horizontal base of 33 feet then another horizontal base below it of 19 feet. The longest side is to the right and is 37 feet. The top is 28 feet. There is a perpendicular from the vertex of the top to the first base of 33 that is labeled 14 feet.
If the wax cost $1.67 a square foot, how much will the wax cost to cover the floor?
$832.50
$1,300.10
$1,664.99
$2,600.19
Question 7(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)
A composite figure is shown.
A five-sided figure with two parallel bases. The top one is 4.6 inches. The vertical height between these bases is 3.15 inches. That vertical height intersects the bottom base, leaving 3.3 inches between it and the vertex to the left. The side on the right is the longest at 6.3 inches. There is a horizontal line connecting the vertex of the bottom base to the 6.3-inch side and that line is 3 inches.
Which of the following represents the total area of the figure?
10.663 in2
24.413 in2
28.448 in2
34.335 in2
HELPPPPPPP!!!!
Question 1: 35 m2
Question 2: four hundred forty-four and three-eighths ft2
Question 3: 440 ft2
Question 4: eighty-three and three-fifths in2
Question 5: 124 cm2
Question 6: $1,300.10
Question 7: 24.413 in2
How did we get the values?Question 1:
Area of an isosceles trapezoid: (sum of bases x height)/2 = (3 + 7 x 5)/2 = 35 m2
Question 2:
Area of a parallelogram: base x height = 22.5 x 18.75 = 444.375 ft2
Question 3:
Area of the composite figure: (top base x height) + (2 x area of a triangle) = (16 x 22) + (2 x (8 x 4)/2) = 352 + 32 = 384 ft2
Question 4:
Area of the shape for the quilt block: (base x height) + (2 x area of a right triangle) = (10.6 x 6) + (2 x (4 x 5)/2) = 63.6 + 20 = 83.6 in2
Question 5:
Area of a rhombus: (base x height)/2 = (16 x 15.5)/2 = 124 cm2
Question 6:
Cost of waxing the restaurant floor: Area x cost per square foot = (33 x 14) + (19 x 14) + (37 x 28)/2 x $1.67 = 574 + 266 + 506 x $1.67 = $1,300.10
Question 7:
Area of the composite figure: (top base x height) + (2 x area of a triangle) = (4.6 x 3.15) + (2 x (3.3 x 3)/2) = 14.43 + 4.95 = 19.38 in2 + area of a trapezoid = 19.38 + (3.3 + 6.3 x 3)/2 = 19.38 + 12.15 = 24.413 in2
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Answer:
syuprd
Step-by-step explanation:
BASS
A 39-foot pole casts a 26-foot shadow. What percent of the pole’s height is the shadow’s length?
The percent of the pole’s height is the shadow’s length is 66.7%
What percent of the pole’s height is the shadow’s length?We know that a 39-foot pole casts a 26-foot shadow. The percent of the pole's height that is the shadow is given by:
P = 100%*(shadow's length)/(pole's height)
Replacing the values that we know, we will get:
P = 100%*(26 feet)/(39 feet)
P = 66.7%
The shadow is a 66.7% of the pole's height.
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a block attached to a spring with unknown spring constant oscillates with a period of 3.4 s . parts a to d are independent questions, each referring to the initial situation.
The period of oscillation of a spring-block system is most affected by changes in the mass and the spring constant, while changes in the amplitude do not affect the period.
The period of oscillation of a spring-block system is a measure of the time it takes for the block to complete one full cycle of its motion and is dependent on the mass of the block, the spring constant, and the amplitude of the oscillation.
a. If the mass is halved, the system becomes less stiff, and the period of oscillation increases.
b. Doubling the amplitude of the oscillation only changes the magnitude of the displacement and does not affect the period of oscillation.
c. If the spring constant is doubled, the system becomes stiffer, and the period of oscillation decreases.
d. If the mass is doubled, the system becomes more massive, and the period of oscillation increases.
In conclusion, the period of oscillation of a spring-block system is most affected by changes in the mass and the spring constant, while changes in the amplitude do not affect the period.
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The correct question is :
A block attached to a spring with unknown spring constant oscillates with a period of 3.4 s. Parts a to d are independent questions, each referring to the initial situation. What is the period if
a. The mass is halved?
b. The amplitude is doubled?
c. The spring constant is doubled?
d. The mass is doubled?
two socks are drawn from a drawer which tontains one red sock, three blue socks, and two green socks. once a sock is selected it is not replaced. detemine each probabily
The probability of drawing two socks of the same color depends on the color chosen, with 0 probability of drawing two red socks and non-zero probabilities of drawing two blue or two green socks.
The probability of drawing a red sock is 1/6.
The probability of drawing a blue sock is 3/6 or 1/2.
The probability of drawing a green sock is 2/6 or 1/3.
The probability of drawing a red and a blue sock in either order is (1/6) * (3/5) = 1/30.
The probability of drawing a blue and a green sock in either order is (3/6) * (2/5) = 4/15.
The probability of drawing two red socks is (1/6) * (0/5) = 0.
The probability of drawing two blue socks is (3/6) * (2/5) = 4/15.
The probability of drawing two green socks is (2/6) * (1/5) = 2/30.
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Solve the differential equations in Problems 26 through 28 by regarding y as the independent variable rather than x
The solution to the differential equation is:
26. y - 2xy^3 = (1/4)y^4 + C.
27. (1/2)x^2 + (1/2)e^(2y) = x + C.
28. y + x^2 + xy^2 = (1/3)y^3 + x^2 + C.
To solve this differential equation with y as the independent variable, we can first separate the variables:
26. (1 - 4xy^2)dy = y^3 dx
Integrating both sides, we have:
∫(1 - 4xy^2)dy = ∫y^3 dx
y - 2xy^3 = (1/4)y^4 + C, where C is an arbitrary constant of integration.
So, the solution to the differential equation is:
y - 2xy^3 = (1/4)y^4 + C.
27. (x + ye^y)dy = dx
Integrating both sides, we have:
∫(x + ye^y)dy = ∫dx
(1/2)x^2 + (1/2)e^(2y) = x + C, where C is an arbitrary constant of integration.
So, the solution to the differential equation is:
(1/2)x^2 + (1/2)e^(2y) = x + C.
28. (1 + 2xy)dy = (1 + y^2)dx
Integrating both sides, we have:
∫(1 + 2xy)dy = ∫(1 + y^2)dx
y + x^2 + xy^2 = (1/3)y^3 + x^2 + C, where C is an arbitrary constant of integration.
So, the solution to the differential equation is:
y + x^2 + xy^2 = (1/3)y^3 + x^2 + C.
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Southeast Electric charges $0.09 per kilowatt-hour for the first 200 kWh. The company charges $0.11 per kilowatt-hour for all electrical usage in excess of 200 kWh. How many kilowatt-hours were used if a monthly electric bill was $57.06?
Therefore , the solution of the given problem of unitary method comes out to be 555.09 kWh is the total energy used.
Define unitary method.To finish a work using the unitary strategy, multiply the amount by two after determining the size of the small slice. The unit technique, to put it simply, works to isolate a programming object from a specific group or sets of sets. For instance, 40 pens would cost 400 pounds ($1.01) and Rs. There is a chance that one nation will have complete control over the technique used to do this. Almost all living things have a unique trait. Both integration and reciprocity are possible (mathematics, algebra).
Here,
Given :
For the first 200 kWh, Electric charges $0.09 per kilowatt-hour
For any electricity usage after 200 kWh, the firm charges $0.11 per kilowatt-hour.
Thus ,
for 200kWh hour cost = 0.09 * 200 = $18
thus ,
total bill was after 200 kWh = 57.06 - 18 = 39.06
Thus,
=> 39.06/0.11 = 355.09
Thus , total Kwh used is : 355.09 + 200 = 555.09 kWh
Therefore , the solution of the given problem of unitary method comes out to be 555.09 kWh is the total energy used .
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Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does not exist, enter DNE.)
x = 4t + 2, y = 7, z = −t + 1
x = 2s + 2, y = 2s + 7, z = s + 1
(x, y, z) = ( )
If the lines intersect, find and the angle between the lines. (Round your answer to one decimal place. If an answer does not exist, enter DNE.)
theta = °
The lines intersect at (4, 7, 0.5), and the angle between the two lines is approximately 83.6 degrees.
The two lines can be represented in the following form:
x = 4t + 2
y = 7
z = -t + 1
x = 2s + 2
y = 2s + 7
z = s + 1
We can find the intersection point by solving the system of equations obtained from setting the x, y and z components equal. That is, we set:
4t + 2 = 2s + 2
7 = 2s + 7
-t + 1 = s + 1
Solving the system of equations we get:
t = 1/2
s = 2
So, the intersection point is
(x, y, z) = (4t + 2, 7, -t + 1) = (4(1/2) + 2, 7, -(1/2) + 1) = (4, 7, 0.5).
To find the angle between the lines, we find the direction vectors of the two lines. The direction vectors for the two lines are:
d1 = <4, 0, -1>
d2 = <2, 2, 1>
The angle between the two lines is given by the dot product of the direction vectors divided by the product of the magnitudes:
cos(theta) = d1.d2 / (|d1| * |d2|)
The angle between the two lines is approximately 83.6 degrees.
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A state park changed an entrance fee besed on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20 and a van containing 8 people is charged $32 .If a bus is charged $122, how many people is contained?
Answer:
122 people
Step-by-step explanation:
Let's call the number of people in a vehicle "x".
From the information given, we can set up two equations to represent the relationship between the number of people and the entrance fee:
2 people: 14 = fee
x people: fee = 14x/2
4 people: 20 = fee
x people: fee = 20x/4
8 people: 32 = fee
x people: fee = 32x/8
Using the information for the bus, we can set up another equation:
x people: fee = 122
Solving for x in each equation and equating the results, we can find the number of people in the bus:
x = 14x/2
x = 20x/4
x = 32x/8
x = 122
Cross multiplying and simplifying, we find:
x = 122
Therefore, the bus contains 122 people.