Answer:
0.15 expressed as a fraction in its simplest form is 3/20.
Step-by-step explanation:
To express a terminating decimal as a fraction:
Step 1Write the decimal as a fraction by dividing it by 1:
[tex]\boxed{\dfrac{0.15}{1}}[/tex]
Step 2Multiply the numerator and denominator by 10 for every number after the decimal point.
As there are two numbers after the decimal point, multiply the numerator and denominator by 100:
[tex]\boxed{\dfrac{0.15 \times 100}{1 \times 100}=\dfrac{15}{100}}[/tex]
Step 3Find the highest common factor (HCF) of the numerator and denominator.
Factors of 15: 1, 3, 5 and 15.Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100.Therefore, the HCF of 15 and 100 is 5.
Divide the numerator and denominator by the HCF to reduce the fraction to its simplest form:
[tex]\boxed{\dfrac{15 \div 5}{100 \div 5}=\dfrac{3}{20}}[/tex]
Conclusion0.15 expressed as a fraction in its simplest form is 3/20.
Answer:
See below, please.
Step-by-step explanation:
Write 0.15 as the fraction 15/100.Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 15 and 100 is 5.Divide both 15 and 100 by 5. This gives 3/20.The resulting fraction 3/20 is in its simplest form, as 3 and 20 have no common factors other than 1.The final answer is 3/20.So the order would be:Write 0.15 as the fraction 15/100.Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 15 and 100 is 5.Divide both 15 and 100 by 5. This gives 3/20.The resulting fraction 3/20 is in its simplest form, as 3 and 20 have no common factors other than 1.The final answer is 3/20.circle project represented in a graph
1. Draw a point at (1,-2).
2. Draw a long radius of 8 units.
3.Using a compass, draw a circle with your point from step one as its center and the point from step two as the side.
4.Using a protractor, draw a 70 degree arc
5. draw a central angle that intersects your arc
6. Draw an inscribed angle that intersects an arc of 40 degrees
7.draw a tangent line
8. draw a secant line
9. write the equation of your circle
Answer:
search up the answers
Step-by-step explanation:
Find the first three terms of the arithmetic series. Given a1 = 11, an = 110 and Sn = 726.
andace had scores of 96, 84, 95, and 82 on her first four exams of the semester. what score must she obtain on the fifth exam to have an average of 90 or better for the five exams
Andace needs to score at least 98 on her fifth exam to have an average of 90 or better for the five exams.
To find out what score Andace needs to get on the fifth exam, we can use the formula for the average (also known as the mean):
Average = (sum of all scores) / (number of scores)
We know that Andace needs an average of 90 or better for the five exams. Therefore, the sum of all five scores must be at least 450 (90 multiplied by 5).
The sum of Andace's first four scores is:
96 + 84 + 95 + 82 = 357
To get an average of 90 or better for the five exams, Andace needs to get a total of:
450 - 357 = 93
on her fifth exam.
Since she has already taken four exams and the maximum score she can get on her fifth exam is 100, we can subtract her first four scores from 93 to find out what she needs to score on her fifth exam:
93 - 96 - 84 - 95 - 82 = -164
Since it's not possible for Andace to score a negative number on her fifth exam, we can conclude that she needs to score at least 98 (93 - 5) to have an average of 90 or better for the five exams.
In conclusion, Andace needs to score at least 98 on her fifth exam to have an average of 90 or better for all five exams.
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housing costs: a government report on housing costs says that single-family home prices nationwide are skewed to the right, with a mean of $235,700. a. we collect price data from a random sample of 50 homes in orange county, california. why is it okay to use these data for inference even though the population is skewed?
It is fine to use these data because the price sample is random so bias will not interfere with the results.
Why is it okay to use this data?Based on the information, we can infer that it is correct to use the data from this sample because it is random, that is, it does not have a defined order. Therefore, it is not necessary to take bias into account because it will not have any influence on the results.
In accordance with the above, it would be incorrect to take the data from a non-random sample because information would be prioritizing and this would cause the results to be blinded.
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Solve the triangle ….?
that the sum of the angles in a triangle is 180 degrees: C = 180 - A - B
C = 180 - 15 - 120
C = 45 degrees.
What is triangle?A triangle is a geometrical shape that consists of three straight sides and three angles. It is a three-sided polygon, which means that it is a closed figure with three-line segments as its sides. The sum of the interior angles of a triangle is always equal to 180 degrees, which is a fundamental property of triangles. Triangles can have different shapes and sizes, and they can be classified based on their side lengths and angle measures. Some common types of triangles include equilateral triangles (where all three sides are equal), isosceles triangles (where two sides are equal), and scalene triangles (where all three sides are different lengths). Triangles are commonly used in mathematics, geometry, and various fields of science and engineering.
by the question.
To solve the triangle, we can use the Law of Cosines, which states that:
[tex]c^{2} = a^{2} + b^{2} -2abcos(c)[/tex]
where c is the length of the third side and C is the angle opposite to it.
Given that one side is 17 and the first angle is 15 degrees, we can use the Law of Sines to find the ratio of the remaining sides:
[tex]a/sin(A) = b/sin(B) = c/sin(C)[/tex]
where A and B are the known angles and a and b are the known sides.
Using this formula, we have:
[tex]a/sin(15) = b/sin(120)[/tex]
or
[tex]b=a/sin(15) = b/sin(120)[/tex]
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the probability of getting heads on a fair coin is 0.50. the probability of getting tails is also 0.50. if you toss the coin three times and get heads all three times, what is the probability of getting tails on the next toss?
The probability of getting tails on the next toss is 0.5 as the coin is a fair coin and doesn't remember the past results.
The probability of getting heads on a fair coin is 0.50.
The probability of getting tails is also 0.50.
If you toss the coin three times and get heads all three times,
The probability of getting tails on the next toss:The probability of getting tails on the next toss is 0.5 as the coin is a fair coin and doesn't remember the past results.
The term 'fair coin' mean:A fair coin is a coin where each of the two faces has the same probability of landing on any coin toss. That is, a fair coin will land on tails and heads equally often.
In other words, the probability of getting heads and tails is 0.5.
The possible outcomes of flipping a fair coin:There are only two possible outcomes of flipping a fair coin.
The two outcomes are heads or tails:The probability of each outcome is 0.5.
This is because a fair coin has two equally likely outcomes.
The probability of getting heads on any flip is 0.5.
The same goes for the probability of getting tails on any flip.
This implies that the probability of flipping a fair coin three times and obtaining three heads is
(0.5 x 0.5 x 0.5) = 0.125
Similarly, the probability of flipping a fair coin three times and obtaining three tails is also 0.125.
As each flip is independent, the outcome of the preceding flips does not affect the next flip, and the probability of getting tails on the next toss is 0.5.
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Becky bought a bag of dog food costing $8.42. If Becky received $1.53 in change, how much money did she give to the cashier?
Answer:9.95
Step-by-step explanation:
Answer: 9.95
Step-by-step explanation:
8.42 +1.53=9.95
A party tent is used for an outdoor event. Ropes of equal length support each tent pole. The angle each rope makes with the ground is 52°.
What is the height of each tent pole?
Therefore, the height of each tent pole is approximately 8.07 meters.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding the length of a side or the measure of an angle. Trigonometry is based on the use of trigonometric functions, which are ratios of the sides of a right triangle.
Here,
We can use trigonometry to solve this problem. Let's call the height of the tent pole "h" and the length of the rope "r". Then, we can use the tangent function to find the height:
tan(52°) = h/r
Rearranging this equation, we get:
h = r * tan(52°)
We know that the length of each rope is equal, so we can choose any arbitrary length for r. For simplicity, let's assume that each rope is 10 meters long. Then, we can plug in the values into the equation:
h = 10 * tan(52°)
Using a calculator, we get:
h ≈ 8.07 meters
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44.0183 rounded to the nearest thousands
the doctor has ordered 1.25 mg/kg of a medication im. it the patient weighs 175 lbs. the drug on hand is available is a vial with 100 mg/2ml. (1) how many mg will be given? (2) calculate the amount to be injected.
1. The amount of medication to be given is 99.25 mg.
2.The amount of 1.985 mL medication should be injected.
To answer the given question, let's follow the steps mentioned below.
Determine the amount of medication to be given:1. Convert the weight of the patient from pounds to kilograms.
175 pounds = 79.4 kilograms
2. Multiply the patient's weight in kilograms by the ordered dosage.
1.25 mg/kg × 79.4 kg = 99.25 mg
Therefore, 99.25 mg of medication is required
Calculate the amount to be injected1. Find the number of milliliters (mL) required to deliver the medication dosage.
The concentration of the drug is 100 mg/2 mL.
100 mg/2 mL ÷ 1 = 50 mg/m
2. Divide the total amount of medication required by the concentration of the drug.
99.25 mg ÷ 50 mg/mL = 1.985 mL
Therefore, 1.985 mL of the medication should be injected.
Note:
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Alia left to go on a camping trip at 12:55. She returned from the trip the following
day at the time shown on the following day at 10:40
How long was she away for?
Give your answer in hours and minutes.
Answer:
Step-by-step explanation: 12:55 she returned at 10:40 12:55 plus 5 minutes is 1:00 plus 9 hours and 40 minutes is 10:40 she was 9 hours and 45 minutes awayThe angles of an irregular pentagon is x, 90, x, 150, x degrees.
Calculate the size of the largest angle.
Answer:
x=130°
Step-by-step explanation:
The sum of the angel of the pentagon is equal to 540°
X+90+x+150+x=540
3x+240=540
3x=540-150
3x=390
X=130
What is 3x+7y=11 equal to
(6,-1)
(1,-2)
(0,4)
The given equation 3x + 7y = 11 is equal to (1,-2).
The given equation is 3x + 7y = 11.
To find the solution of the equation, we need to consider the given options:
(6,-1)(1,-2)(0,4)
Now substitute each value of x and y in the given equation, we get,
If x = 6 and y = -13(3 × 6) + (7 × -1) = 18 - 7 = 11 ≠ 11
If x = 1 and y = -2(3 × 1) + (7 × -2) = 3 - 14 = -11 ≠ 11
If x = 0 and y = 4(3 × 0) + (7 × 4) = 0 + 28 = 28 ≠ 11
Therefore, the given equation 3x + 7y = 11 is equal to (1,-2).
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Given that x = (5,-5) and y = (8,-3), find x•y
If x = (5,-5) and y = (8,-3), x•y is: 55.
How to find the vectors?The dot product (also called scalar product or inner product) of two vectors x = (x1, x2) and y = (y1, y2) is given by:
x•y = x1y1 + x2y2
Using the coordinates of the given vectors:
x = (5, -5)
y = (8, -3)
x•y = (5)(8) + (-5)(-3) = 40 + 15 = 55
Therefore, x•y = 55.
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is there a significant difference in the mean amount of e. coli bacteria detected by the two methods for this type of beef? provide a statistical justification to support your answer
Certainly, there is a significant difference in the mean amount of e.coli bacteria detected by the two methods for this type of beef. This can be supported statistically by conducting a hypothesis test.
The null hypothesis ([tex]H_0[/tex]) is that there is no significant difference in the mean amount of E. coli bacteria detected by the two methods. The alternative hypothesis ([tex]H_a[/tex]) is that there is a significant difference in the mean amount of e.coli bacteria detected by the two methods.
The two-sample t-test can be used to test the hypothesis. The t-test compares the means of two independent groups and determines whether they are significantly different. The t-test assumes that the two samples are normally distributed and have equal variances.
If the sample sizes are large, then the t-test can still be used even if the samples are not normally distributed.
The formula for the t-test is:
[tex]t = (x_1 - x_2) / [s^2(1/n_1 + 1/n_2)][/tex]
Where:
[tex]x_1[/tex] = the sample mean for method 1
[tex]x_2[/tex] = the sample mean for method 2
[tex]s^2[/tex] = the pooled variance of the two samples
[tex]n_1[/tex] = the sample size for method 1
[tex]n_2[/tex] = the sample size for method 2
The t-value can then be compared to the critical value of [tex]t[/tex] for the desired level of significance (usually 0.05).
If the t-value is greater than the critical value of [tex]t[/tex], then the null hypothesis can be rejected and it can be concluded that there is a significant difference in the mean amount of E. coli bacteria detected by the two methods.
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A well of 3 cm diameter is dug to a depth of 14 m. Akind of embankment is made by spreading the soil out of it evenly around the well, forming a circular platform (ring) 4m wide. Find the height of this embankment
The height of the embankment will be 1.125. As the embankment is in cylinder shape shown in figure.
The shape of the well will be cylindrical as shown in the figure below in the image section.
Given that :
Depth (h1) of well = 14m
Radius (r1) of the circular end of well = 3/2 m Width of embankment = 4 m
From the figure, it can be observed that our embankment will be in a cylindrical shape having outer radius, (r2) = 4 + 3/2 = 11/2m
Let the height of the embankment be h2 .
Volume of soil dug from well = Volume of earth used to form the embankment
⇒ π × r1² ×h1 = π × (r2-r1)² ×h2
⇒ π × (3/2)² × 14 = π ×[(11/2)² - (3/2)² × h2]
⇒ 9/4 × 14 = 112/4 × h2
⇒ h2 = 9/8
⇒ h2 = 1.115 m
Therefore the height of the embankment will be 1.125m.
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Find the sum of and .2푥+1
Answer:
2*22/7/27+1
Step-by-step explanation:
2*22/7*27+1
2*(594+1)/7
2*595/7
2*85
170 ans..
please help 9 10 ll and 12 need answers i have 1 hour to get answers please
1. The area of the circle with radius r = 4 is 200.96 square cm. 2. The area of the circle is approximately 113.04 square cm.
What is radius and diameter of the circle?A circle's radius is equal to twice its diameter. In other words, if d is the diameter and r is the radius, then d = 2r. On the other hand, a circle's radius is equal to half of its diameter. Finding the circumference or area of a circle are only two examples of computations involving circles for which this connection is crucial.
The area of the circle is given by the formula:
A = πr²
Substituting the value r = 8 we have:
Area = 3.14(8)² = 200.96 square cm
2. For circle with d = 12 cm we have the radius as:
r = 12/2 = 6
A = 3.14(6)² = 113.04 square cm
Hence, the area of the circle with radius r = 4 is 200.96 square cm. 2. The area of the circle is approximately 113.04 square cm.
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Write the slope-intercept form of the equation of the line described.
througt: (2,5), perp,to y=-1/2x-2
The slope-intercept form of the equation of the line described is y = 2x + 1.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.Since the line is perpendicular to the other line that is represented by this equation y = -1/2(x) - 2, we have the following;
Slope (m) = -1/2.
Perpendicular line.
m₁ × m₂ = -1
-1/2 × m₂ = -1
m₂ = 2.
At data point (2, 5), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = 2(x - 2)
y = 2x - 4 + 5
y = 2x + 1
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Select the correct answer. Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina? A. The equation that represents this situation is t − 3 = 18. Tina is 21. B. The equation that represents this situation is t + 3 = 18. Tina is 15. C. The equation that represents this situation is 3 − t = 18. Tina is 21. D. The equation that represents this situation is -3 − t = 18. Tina is 15.
Step-by-step explanation:
A. t-3=18. Tina is 21. Here's your answer.
The correct option is A
The equation that represents this situation is [tex]t-3=18[/tex]. Tina is [tex]21[/tex].
The explanation for the correct option:
Option A:
It is given in the question, Tina's age is [tex]t[/tex].Cole's age is [tex]3[/tex] year less than Tina's age, that is [tex]t-3[/tex].It is given that Cole's age is given to be [tex]18[/tex].From the given question:
[tex]t-3=18[/tex]
Adding [tex]3[/tex] both sides in order to solve for [tex]t[/tex]:
[tex]t=18+3[/tex]
[tex]=21 \ years[/tex]
Therefore, the equation to find the age of Tina is [tex]t-3=18[/tex] and the age of Tina is [tex]21[/tex] years.
Hence, Option (A) is the correct option.
Psychologists are concerned that ____ personality tests are not easy to interpret and do not always produce consistent results because they are not standardized.
Psychologists have raised concerns about the accuracy and validity of ____ personality tests, as they are not standardized. This means that the same test administered to two different people can yield different results, making it difficult to interpret. Moreover, results may be inconsistent, meaning the same test administered at different times could produce different results. This lack of consistency can lead to inaccurate interpretations and can render the tests less useful. Furthermore, there is a lack of standardization of criteria and methodologies used to evaluate personality tests, which could lead to misinterpretations of results.
In order to address these issues, it is important to use standardized personality tests, which are tested and validated to ensure consistent and accurate results. This will ensure that the tests yield consistent results and can be interpreted accurately.
Additionally, researchers must adhere to established guidelines and criteria to ensure that the results are reliable and valid. This will enable professionals to confidently use the tests and make accurate interpretations of the results.
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the coefficient of variation is best described as . multiple choice a relative measure of dispersion a relative measure of central location an absolute measure of central location an absolute measure of dispersion
Measure of the dispersion of a dataset relative to its mean.
The coefficient of variation is best described as a relative measure of dispersion. It is a measure of the dispersion of a dataset relative to its mean.
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Right triangle STD has a longer leg measuring exactly 3√5 cm. The altitude from right angle T to hypotenuse
SD cuts the hypotenuse into two segments where the shorter part is 1 less than the longer part. Find the exact
length of each part of the hypotenuse, SU and UD, the exact length of altitude TU and the exact length of ST.
Answer:
Let's call the length of the hypotenuse SD as x.
Since the altitude from T to SD divides SD into two parts, let the length of the shorter part be y. Then the length of the longer part is x-y.
Using similar triangles, we have:
TU/TS = ST/TD
Substituting the values we have:
TU/(3√5) = √5/UD
TU = (3/5)UD
Using the Pythagorean theorem in triangle TUS, we have:
TU² + (3√5)² = TS²
(3/5 UD)² + 45 = ST²
9/25 UD² + 45 = ST²
Using the Pythagorean theorem in triangle TUD, we have:
TU² + UD² = TD²
(3/5 UD)² + UD² = x²
9/25 UD² + UD² = x²
34/25 UD² = x²
UD² = (25/34)x²
Substituting the value of UD² in the equation ST² = 9/25 UD² + 45, we get:
ST² = 9/25 (25/34)x² + 45
ST² = 45/34 x² + 45
Since y = x-y-1, we have y = (x-1)/2.
Using the Pythagorean theorem in triangle TUD, we have:
(1/4) (x-1)² + UD² = x²
(1/4) (x² - 2x + 1) + (25/34)x² = x²
(1/4)(x²) + (25/34)x² - (1/2)x + (1/4) = 0
(59/68)x² - (1/2)x + (1/4) = 0
Using the quadratic formula, we get:
x = [1/2 ± √(1/4 - 4(59/68)(1/4))]/(2(59/68))
x = [1/2 ± (3√34)/17]/(59/34)
x = 17/59 ± 6√34/59
Since x is the hypotenuse SD, we have:
UD² = (25/34) x²
UD² = (25/34) [(17/59 ± 6√34/59)²]
UD² = 136/59 ± 204√34/295
Therefore, the exact lengths of the two parts of the hypotenuse are:
SD = x = 17/59 ± 6√34/59
SU = x-y = (x-1)/2 = 8/59 ± 3√34/59
UD = y = (x-1)/2 = 8/59 ± 3√34/59
TU = (3/5) UD = (3/5) [8/59 ± 3√34/59] = 24/295 ± 9√34/295
ST² = 45/34 x² + 45 = 45/34 [(17/59 ± 6√34/59)²] + 45
ST = √[45/34 [(17/59 ± 6√34/59)²] + 45]
triangle ABO has been rotated 80° about point O. Choose all statements that are true
Be aware that the other claims are untrue as 80 degrees is the angle B'OA and Triangles ABO and A'B'O are similar triangles are true .
what is triangle ?A closed triangle is a two-dimensional plane shape with three angles and three straight sides. Three non-collinear points are connected with straight line segments to create one of the fundamental shapes in geometry. The lengths of the sides can vary depending on the type of triangle, but the sum of the interior angles of a triangle is always 180 degrees. Triangles with all three sides equal, such as equilateral triangles, isosceles triangles, and scalene triangles, are examples of frequent triangle types (where no sides are equal).
given
According to the diagram, the following claims are accurate:
80 degrees is the angle B'OA.
Triangles ABO and A'B'O are similar triangles.
Angle A'B'O and angle ABO are equivalent.
Line segment AB and line segment A'B' are congruent.
Be aware that the other claims are untrue as 80 degrees is the angle B'OA and Triangles ABO and A'B'O are similar triangles are true .
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A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points)
Answer:
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
Given the diameter of both the cylinder and the cone is 8 inches, the radius is 8/2 = 4 inches.
The volume of the cylinder is Vcyl = π(4)²(3) = 48π cubic inches.
The formula for the volume of a cone is V = (1/3)πr²h.
The volume of the cone is Vcone = (1/3)π(4)²(18) = 96π/3 = 32π cubic inches.
Therefore, the relationship between the volume of the cylinder and the cone is that the volume of the cone is exactly two-thirds of the volume of the cylinder.
We can see this by dividing the volume of the cylinder by the volume of the cone:
Vcyl/Vcone = (48π) / (32π) = 3/2
So, the volume of the cylinder is 1.5 times greater than the volume of the cone.
of the 36 students in richelle's class, 12 prefer chocolate pie, 8 prefer apple, and 6 prefer blueberry. half of the remaining students prefer cherry pie and half prefer lemon. for richelle's pie graph showing this data, how many degrees should she use for cherry pie?
Richelle should use 50 degrees for cherry pie in her pie chart.
The total number of students is 36.
The number of students who prefer chocolate pie is 12.
The number of students who prefer apple is 8.
The number of students who prefer blueberry is 6.
Half of the remaining students prefer cherry pie and half prefer lemon.
So we can calculate the number of students who prefer cherry pie by doing is 1/2 × (36 − 12 − 8 − 6) = 5
The number of students who prefer cherry pie is 5.
The number of students prefer lemon pie is also 5.
The formula for calculating the degrees of an angle in a pie chart is given by the formula given below:
Number of degrees is,
= (number of students who prefer cherry pie / total number of students) × 360°
= (5/36) × 360°= 50°
Thus, Richelle should use 50 degrees for cherry pie in her pie chart.
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A club sponsor collects and analyzes data to estimate the number of students, y
, in attendance at a club meeting x
weeks after the start of the school year. The linear model y=11x+41
can be used to represent the data when x≥0
.
Which two best describe the value 41
?
Responses
change in number of students in attendance per week
change in number of students in attendance per week
initial number of students in attendance when x=0
initial number of students in attendance when x = 0
slope
slope
x
-intercept
x -intercept
y
-intercept
y -intercept
Since the linear model y = 11x + 41 can be used to represent the data when x≥0, the two statement which best describe the value 41 include the following:
B. initial number of students in attendance when x = 0.
E. y-intercept.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.Based on the information, an equation that models the line is given by this mathematical expression;
y = mx + c
y = 11x + 41
By comparison, we have the following:
mx = 11x
Slope, m = 11.
Initial number or y-intercept, c = 41.
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A student has a rectangular bedroom. If listed as ordered pairs, the corners of the bedroom are (21, 18), (21, −7), (−12, 18), and (−12, −7). What is the perimeter in feet?
116 feet
58 feet
33 feet
25 feet
The perimeter of the rectangular bedroom is 116 feet.
How to get the perimeter?We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √( (x₂ - x₁)² + (y₂ - y₁)²)
Here the corners of the room are at: (21, 18), (21, −7), (−12, −7) and (−12, 18)
Let's find the distances between these points:
d₁ = √( (21- 21)² + (18 + 7)²) = 25
d₂ = √( (21 + 12)² + (-7 + 7)²) = 33
d₃ = √( (-12 + 12)² + (-7 - 18)²) = 25
d₄ = = √( (-12 - 21)² + (-7 + 7)²) = 33
The perimeter is the sum of these distances so we will get:
d₁ + d₂ + d₃ + d₄ = 25 + 33 + 25 + 33 = 116
The correct option is the first one.
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how much work does it take to pump all the water over the top edge of a cylindrical tank of radius 6 meters and height 14 meters that is filled with water to a depth of 5 meters? round to the nearest kilojoule.
The work required to pump all the water over the top edge of the cylindrical tank is approximately 83,500 kJ.
To calculate the work required to pump all the water over the top edge of the cylindrical tank, we need to determine the volume of the water in the tank and the force required to lift it to the top edge.
The volume of water in the tank can be found by multiplying the cross-sectional area of the tank by the depth of the water. Since the tank is cylindrical, the cross-sectional area is given by πr^2, where r is the radius of the tank. Therefore, the volume of water in the tank is:
V = πr^2h = π(6m)^2(5m) = 540π m^3
To lift the water to the top edge of the tank, we need to overcome the force of gravity acting on the water. The force required to lift an object of mass m against gravity is given by F = mg, where g is the acceleration due to gravity (9.81 m/s^2).
The mass of the water in the tank can be found by multiplying its volume by its density. The density of water is approximately 1000 kg/m^3. Therefore, the mass of the water in the tank is:
m = ρV = (1000 kg/m^3)(540π m^3) = 1.7 x 10^6 kg
The force required to lift the water to the top edge of the tank is:
F = mg = (1.7 x 10^6 kg)(9.81 m/s^2) = 16.7 x 10^6 N
To find the work required to lift the water, we need to multiply the force by the distance over which it acts. The distance is equal to the height of the water in the tank, which is 5 m.
Therefore, the work required to pump all the water over the top edge of the tank is:
W = Fd = (16.7 x 10^6 N)(5 m) = 83.5 x 10^6 J
Rounding to the nearest kilojoule, the work required is approximately 83,500 kJ.
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When we say that liquid water is unstable on Mars, we mean that
Therefore, liquid water is considered to be unstable on Mars due to the cold temperatures, low atmospheric pressure, and the UV radiation. All of these environmental factors make it difficult for liquid water to persist.
Liquid water is unstable on Mars due to its cold, dry environment. Because the atmospheric pressure is too low to hold liquid water, the water on Mars quickly evaporates, sublimates, and/or is broken down by the ultraviolet radiation in the atmosphere.
The average temperature of the surface of Mars is −63 °C, which is well below the freezing point of water. Because of this, liquid water cannot exist on the surface of Mars. When temperatures are slightly higher, water can exist as a liquid, but it cannot stay in this state for very long.
The atmosphere on Mars also does not contain enough pressure to sustain liquid water. Even when water vapor is present, it will quickly evaporate in the low-pressure environment. Additionally, the UV radiation in the Martian atmosphere will break down water molecules quickly.
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