Answer: Using the two given points (0, 97507) and (5, 225317), we can find the slope:
slope = (225317 - 97507) / (5 - 0) = 25662
Then using the point-slope form of a line with the point (0, 97507):
y - 97507 = 25662x
Simplifying and putting in slope-intercept form:
y = 25662x + 97507
Therefore, the equation in slope-intercept form is y = 25662x + 97507.
Step-by-step explanation:
A meal costs $5.75. You offer a 10% discount. The sales tax is 4%. How much should you charge the customer? $
Answer:
To calculate the final cost of the meal, we need to first calculate the discount and then add the sales tax. Discount = 10% of $5.75 = $0.575 Price after discount = $5.75 - $0.575 = $5.175 Sales tax = 4% of $5.175 = $0.207 Final cost = Price after discount + Sales tax = $5.175 + $0.207 = $5.382 Therefore, you should charge the customer $5.382.
well, let's hmmm apply the 10% discount first
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 5.75}}{\left( \cfrac{10}{100} \right)5.75} ~~ \approx ~~ 0.58~\hfill \stackrel{ 5.75~~ - ~~0.58 }{\approx\text{\LARGE 5.17}}[/tex]
now let's apply the 4% tax to it
[tex]\stackrel{\textit{4\% of 5.17}}{\left( \cfrac{4}{100} \right)5.17} ~~ \approx ~~ 0.21\hspace{5em}\stackrel{ 5.17~~ + ~~0.21 }{\text{\LARGE 5.38}}\qquad \textit{final charge}[/tex]
What is the average rate of change for the function on the interval (2, 3)
A given function or graph is needed to find the average rate of change between an interval
Theo washed 6 cars last week. He washed each car in 34
hour. He washed the same cars this week in 23
hour each using his new pressure sprayer. How much longer did it take Theo to wash all the cars last week than this week?
Answer:
66 hours.
Step-by-step explanation:
6 cars x 34 hours per car = 204
6 cars x 23 hours per car= 138 hours
now subtract:
204 - 138 = 66
therefore, it took Theo 66 hours longer to wash all the cars last week than last week.
Find the surface area of the rectangular prism.
Using the formula, we now know that the surface area of the rectangular prism is 22 in².
What is a rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.
It also goes by the name cuboid.
Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.
Its length, width, and height are its three dimensions.
Rectangular tissue boxes, school notebooks, laptops, fish tanks, and big buildings like freight containers, rooms, storage sheds, etc. are a few instances of rectangular prisms in daily life.
So, the formula for the surface area of the rectangular prism:
A = 2(wl+hl+hw)
Now, insert values as follows:
A = 2(wl+hl+hw)
A = 2·(1·1+5·1+5·1)
A = 22 in²
Therefore, using the formula, we now know that the surface area of the rectangular prism is 22 in².
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a measurement of internal consistency that allows researchers to determine how well the different items/questions within a test measure different aspects of the same topic is:
The higher the value of Cronbach's alpha, the higher the internal consistency reliability of the assessment.
A measurement of internal consistency that allows researchers to determine how well the different items/questions within a test measure different aspects of the same topic is known as reliability.
Reliability refers to the consistency of the results of an assessment. In other words, it refers to the extent to which an assessment yields stable and consistent results. Researchers use various methods to assess the reliability of an assessment.
These include test-retest reliability, inter-rater reliability, and internal consistency reliability.
In this case,
The internal consistency reliability is the method that allows researchers to determine how well the different items/questions within a test measure different aspects of the same topic.
Internal consistency reliability is a method that measures the consistency of the results of an assessment by examining the relationships among the different items/questions within the assessment. It looks at the degree to which the items/questions within an assessment measure the same thing or construct.
If the different items/questions within an assessment are measuring the same thing, then the assessment is said to have high internal consistency reliability. If the items/questions are measuring different things, then the assessment is said to have low internal consistency reliability.
Researchers use various statistical methods to assess internal consistency reliability. One of the most common methods is Cronbach's alpha, which measures the degree to which the items/questions within an assessment are correlated with each other.
The higher the value of Cronbach's alpha, the higher the internal consistency reliability of the assessment.
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somebody helpppppppppppppppppp
Answer: D
Step-by-step explanation:
To narrow it out, Histograms dont have spaces meaning this chart wouldnt work as a histogram, and A and C are just plain incorrect
a bag contains ten black marbles, twenty white marbles, and five grey marbles. you pick one without looking. what is the probability that the marble will be either white or black? show your work.
The probability that the marble drawn from the bag will be either white or black is 2/3 or approximately 0.667.
To calculate this probability, we first need to find the total number of marbles in the bag, which is 10 + 20 + 5 = 35. Then, we need to find the total number of marbles that are either white or black, which is 10 + 20 = 30.
Finally, we divide the number of white or black marbles by the total number of marbles to get the probability:
30/35 = 2/3 ≈ 0.667
Therefore, the probability is approximately 0.667 or 2/3. This means that there is a higher chance of drawing a white or black marble than a grey marble, as there are more white and black marbles in the bag than grey marbles.
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The point P = (-, y) lies on the unit circle shown below. What is the value of y
in simplest form?
P (x, y)
(Note: the figure is not drawn to scale)
(1, 0)
The value οf y fοr pοint P οn the unit circle in the third quadrant with x-cοοrdinate -6/7 is -sqrt(13)/7.
What is the value οf y fοr pοint P οn the unit circle in the third quadrant with x-cοοrdinate -6/7?PWe knοw that the pοint is in the third quadrant and is distance 1 away frοm the οrigin, which is at (0,0). We alsο knοw that there is a pοint at (1,0) οn the x-axis, which is tο the right οf the οrigin.
Tο sοlve fοr y, we can use the Pythagοrean theοrem tο set up an equatiοn based οn the distance fοrmula:
[tex]\sqrt{(x^2 + y^2)} = 1[/tex]
Squaring bοth sides, we get:
[tex]x^2 + y^2 = 1[/tex]
Since we knοw that x = -6/7, we can substitute that in and sοlve fοr y:
[tex](-6/7)^ + y^2 = 1[/tex]
Simplifying, we get:
[tex]36/49 + y^2 = 1[/tex]
Subtracting 36/49 frοm bοth sides, we get:
y^2 = 13/49
Taking the square rοοt -
οf bοth sides yields:
[tex]y = +/- \sqrt{(13)} /7[/tex]
Because P is lοcated in the third quadrant, y must be negative. Therefοre, the value οf y in simplest fοrm is:
[tex]y = - \sqrt{(13)}/7[/tex]
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need help on this asap
Geometry pls help asap
if x = 25, quadrilateral ABCD will be a trapezoid with AB || CD.thus, the answer is (C) 25.
What is trapezoid?
For quadrilateral ABCD to be a trapezoid, it must have a pair of parallel sides. In other words, either AB || CD or AD || BC. We can use the angle measures to determine which condition must be satisfied.
Trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The height of a trapezoid is the perpendicular distance between the bases. The area of a trapezoid can be calculated by taking the average of the lengths of the two bases and multiplying by the height. The formula for the area of a trapezoid is: Area = (base1 + base2) / 2 * height
If AB || CD, then opposite angles must be supplementary, which means that:
A + D = 180°
Substituting the given angle measures, we get:
3x + (5x-20) = 180
Simplifying, we get:
8x - 20 = 180
Adding 20 to both sides, we get:
8x = 200
Dividing both sides by 8, we get:
x = 25
Therefore, if x = 25, quadrilateral ABCD will be a trapezoid with AB || CD.
Thus, the answer is (C) 25.
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At her birthday party, Jayla wants to play a game where team members race through an obstacle course with bean bags on their heads. She bought a box of 100 bean bags in assorted colors to use in the game. She randomly selected 14 bean bags from the box and then put them back. Here are the colors she selected:
red, blue, green, blue, yellow, red, green, blue, red, yellow, red, green, blue, red
Based on the data, estimate how many red bean bags are in the box.
If necessary, round your answer to the nearest whole number.
Answer:
Jayla selected 14 bean bags randomly with replacement from a box of 100 bean bags, and 6 of them were red. To estimate how many red bean bags are in the box, we can use proportion:
Let's call "x" the number of red bean bags in the box. Then we can set up a proportion:
(red bean bags in the box) / (total bean bags in the box) = (red bean bags selected) / (total bean bags selected)
x / 100 = 6 / 14
Simplifying the right side, we get:
x / 100 = 3 / 7
Multiplying both sides by 100, we get:
x = 300 / 7
Rounding to the nearest whole number, we get:
x ≈ 43
Therefore, based on the data, we can estimate that there are approximately 43 red bean bags in the box.
Answer + Explanation:
To estimate how many red bean bags are in the box, we can use a sampling method called "balloting." Balloting is a way of estimating the number of items of a specific type in a larger population by taking a random sample and counting how many of that type are in the sample.
In this case, we have a population of 100 bean bags and a sample size of 14. We can calculate the sample proportion of red bean bags by dividing the number of red bean bags in the sample by the total number of bean bags in the sample, which gives:
(4/14) × 100% ≈ 28.6%
This means that, on average, we would expect 28.6% of the 100 bean bags in the box to be red. To estimate the actual number of red bean bags, we can multiply the sample proportion by the total number of bean bags in the box:
28.6% × 100 = 28.6
So the closest estimate for the number of red bean bags in the box is 29.
Note that this is just an estimate, and the actual number of red bean bags in the box may be higher or lower than the estimated value.
A ball is thrown across the field from point A to point B. It hits the ground at point B. The path of the ball is shown in
the diagram below. The x-axis shows the horizontal distance the ball travels in feet, and the y-axis shows the height of
the ball in feet. Use the diagram to complete parts (a)-(f).
a.
b.
C.
d.
e.
f.
A
C
B
Suppose point A is approximately 6 feet above ground and that at time t=0 the ball is at point A. Suppose
the length of OB is approximately 88 feet. Include this information on the diagram.
Suppose that after 1 second, the ball is at its highest point of 22 feet (above point C) and has traveled a
horizontal distance of 44 feet. What are the approximate coordinates of the ball at the following values of
t: 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, and 2.
Use your answer from part (b) to write two predictions.
What is happening to the ball when it has coordinates (88, 0)?
Why do you think the ball is at point (0, 6) when t = 0? In other words, why isn't the height of the ball 0?
Does the graph allow us to make predictions about the height of the ball at all points?
Based on the information, the height of point A is 6 feet above ground and the length of OB is approximately 88 feet.
How to explain the valueb) At t = 0.25 seconds, the approximate coordinates of the ball are (11, 13.5).
At t = 0.5 seconds, the approximate coordinates of the ball are (22, 12).
At t = 0.75 seconds, the approximate coordinates of the ball are (33, 9).
At t = 1 second, the approximate coordinates of the ball are (44, 6).
At t = 1.25 seconds, the approximate coordinates of the ball are (55, 3).
At t = 1.5 seconds, the approximate coordinates of the ball are (66, 0).
At t = 1.75 seconds, the approximate coordinates of the ball are (77, -3).
At t = 2 seconds, the approximate coordinates of the ball are (88, -6).
The height of the ball will be negative when it reaches point B again after traveling from A to B, assuming it follows the same path.
The time it takes for the ball to reach its maximum height and return to the ground will be approximately 2 seconds.
When the ball has coordinates (88, 0), it has reached the ground at point B, and its horizontal distance traveled is 88 feet.
At t = 0, the ball is at point A, which is 6 feet above the ground. This is because it was thrown from that height, and the time elapsed is not enough for gravity to affect its height yet.
Yes, the graph allows us to make predictions about the height of the ball at all points. However, the accuracy of the predictions may depend on the assumptions and approximations made about the ball's initial velocity, air resistance, and other factors.
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Consider the table of values shown to the right.
a. Write a linear function to model the relationship between
y and x.
b. Explain the meaning of the slope of this problem.
Pls show work
Thank you
Answer: y= 4x+2
Step-by-step explanation: meaning of slope - the amount of bacteria multiplies by 4 as each minute passes
(sorry English isn't my first language)
Please help asap
A summer camp took a survey of how much time their campers spend reading daily. Sixty campers said that they spend between 1 and 2 hours reading daily.
What is the total number of campers that were surveyed?
___ campers
The total number of campers surveyed is 150.
What is percentage?The symbol for percentage is "%". Percentages are commonly used in a wide range of contexts, such as in finance, statistics, and everyday life.
According to question:We can use the information provided about the percentage of campers in each time interval to set up an equation to solve for the total number of campers surveyed.
Let n be the total number of campers surveyed. Then:
15% of n spend more than 3 hours reading daily.
10% of n spend between 2 and 3 hours reading daily.
35% of n spend less than 1 hour reading daily.
40% of n spend between 1 and 2 hours reading daily.
We know that 60 campers spend between 1 and 2 hours reading daily, which represents 40% of the total number of campers surveyed. So we can set up the following equation:
0.4n = 60
Solving for n, we get:
n = 60 / 0.4 = 150
Therefore, the total number of campers surveyed is 150.
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7x^2-34=2x^2+16
solving quadratic equation using square root
According to the given information, the solutions to the equation 7x²-34=2x²+16 are x = √10 and x = -√10.
What is quadratic equation?
A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0 where a, b, and c are constants, and x is the variable.
To solve for x in the equation 7x²-34=2x²+16 using square roots, we can first simplify the equation by moving all the x² terms to one side and all the constant terms to the other side:
7x² - 2x² = 16 + 34
5x² = 50
5x²/5 = 50/5
x² = 10
Finally, we can take the square root of both sides (remembering to include both the positive and negative square root, since x could be positive or negative):
x = ±√10
Therefore, the solutions to the equation 7x²-34=2x²+16 are x = √10 and x = -√10.
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Select all that apply. A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular. The city will pay to have soft pavement made of recycled tires installed in the playground. In the first plan, one side 8 yards longer than the other side. Which equations model the possible dimensions of the playground? x( x + 8) = 256
( x2) - 8 = 256
x2- 8 x - 256 = 0
( x + 4)( x - 4) = 256
x( x - 8) = 256
The equations model the possible dimensions of the playground is option (A) x(x + 8) = 256.
What is equation?A statement that affirms the equality of two expressions connected by the equals symbol "=" is known as an equation. For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
The area of the rectangular playground is given as 256 square yards. Let x be the length of the shorter side of the playground in yards. Then the length of the longer side can be expressed as x + 8 yards, since it is 8 yards longer than the shorter side.
The area of the rectangle is given by the product of its length and width. Therefore, we can write:
x(x + 8) = 256
This equation represents the possible dimensions of the playground, where x is the length of the shorter side and x + 8 is the length of the longer side.
So, the correct equation that models the possible dimensions of the playground is:
x(x + 8) = 256.
Therefore, the equations model the possible dimensions of the playground is option (A) x(x + 8) = 256.
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How long a line can you make using all the 5/8 inch strips?
The length of the line can be made is 5x/8 inch, where 'x' is the number of strips.
Finding the Length of a Line:Length is a measure of the size of an object or distance between two points, usually measured in units such as meters, centimeters, inches, feet, or miles.
In the given problem to find the length of a line we need to multiply the length of each strip by the number of strips
Here we have
The length of the strip = 5/8
The length of the line will depend on the number of strips
Let there be 'x' number of strips
The length of the line can be made = x × 5/8
=> 5x/8
Therefore,
The length of the line can be made is 5x/8 inch, where 'x' is the number of strips.
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Sp
4
A square has an area of 100 sq meters. What is the perimeter of the square?
The area of a square is given by the formula A = s^2, where s is the length of a side of the square. If the area of the square is 100 sq meters, then:
s^2 = 100
Taking the square root of both sides, we get:
s = 10
Therefore, the length of a side of the square is 10 meters. Since all four sides of a square are equal, the perimeter of the square is:
4s = 4(10) = 40 meters
A group of three friends ate dinner at a
restaurant. When they settled the check andtip, Peter paid 4/5 as much as John paid, and
John paid 1/3 as much as Ralph paid. What
fraction of the check and tip did John pay?
The fraction of the check and tip did John pay is 5/24.
What are rational numbers?
It is possible to express rational numbers in the form pq, where p and q are integers and q0. The distinction between fractions and rational numbers is that the numerator or denominator of a fraction cannot be negative. As a result, the numerator and denominator of a fraction are whole numbers (denominator 0), as opposed to integers in the case of rational numbers.
Here, we have
Given: A group of three friends ate dinner at a restaurant. When they settled the check and tip, Peter paid 4/5 as much as John paid, and John paid 1/3 as much as Ralph paid.
we have to find a fraction of the check and tip did John pay.
p, j, r, the fractions that each paid.
p + j + r = 1....(1)
p = (4/5)j and j = (1/3)r
From equation(1), we get
(4/5)j + j + 3j = 1
j(4/5 + 1 + 3) = 1
(24/5)j = 1
j = 5/24
We have
r = 3j
r = 3(5/24)
r = 5/8
Hence, the fraction of the check and tip did John pay is 5/24.
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sarah was selling lemonade. she makes .50 dollars on a small cup, and 1 dollar on a medium cup. She wants to make at least 30 dollars and only has 75 cups. If s represents a small cup, and m represents a medium cup, which system of linear inequalities correctly represetns her situation?
A) linear inequality, 0.5 s + 1 m = 30 < 75 where, 's' represents a small cup, and 'm' represents a medium cup.
We know that Sarah was selling lemonade and she makes 0.50 dollars on a small cup, and 1 dollar on a medium cup but she wants to make at least 30 dollars and only has 75 cups.
We need to show a linear inequality where, 's' represents a small cup, and 'm' represents a medium cup:
Linear inequalities are the expressions where any two values are compared by the inequality symbols ‘<’, ‘>’, ‘≤’ or ‘≥’
Linear equations are a combination of constants and variables.
let number of small cups be s,
therefore, total amount of small cups = 0.5 s
let number of medium cups be m,
therefore, total amount of medium cups = 1 m
with this given information, we can form our equation as:
0.5 s + 1 m = 30 < 75.
Therefore, a linear inequality, 0.5 s + 1 m = 30 < 75 where, 's' represents a small cup, and 'm' represents a medium cup.
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Complete question: Sarah was selling lemonade. she makes .50 dollars on a small cup, and 1 dollar on a medium cup. She wants to make at least 30 dollars and only has 75 cups. If s represents a small cup, and m represents a medium cup, which system of linear inequalities correctly represents her situation?
A. 0.5 s + 1 m = 30 < 75
B. 1s + 3m + 5l
C. $75
D. $93
the acceptance scheme for purchasing lots containing a large number of batteries is to test no more than 75 randomly selected batteries and to reject a lot if a single battery fails. suppose the probability of a failure is 0.001. (a) what is the probability that a lot is accepted? (b) what is the probability that a lot is rejected on the 20th test? (c) what is the probability that it is rejected in 10 or fewer trials?
If the probability of failure is 0.001, then the probability that
(a) lot is accepted is 0.9277,
(b) lot is rejected on 20th test is 0.000981,
(c) lot is rejected in 10 or fewer trials is 0.01.
Let the random-variable "X" represent number of batteries to test to get the first-battery which fails; in other words, to get first success.
Since, the trials are independent, X has a geometric distribution
Part (a) :
Let X = the number of trials,
So, the probability that the lot is accepted is :
⇒ P(X=75) = (0.999)⁷⁵×(0.001)⁰ = 0.9277,
Part (b) :
let Y = the numbers of trials before the first failure (geometric distribution and
So, the probability that lot is rejected on 20th-test is :
⇒ P(Y=20) = (0.001)⁰×(0.999)¹⁹ = 0.000981,
Part (c) :
The probability that it is rejected in 10 or fewer trials is :
⇒ 1- P(no Failures)
⇒ 1 – (0.001)⁰(0.999)¹⁰ = 0.01.
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We are given that angle aob is a central angle of circle o and that angle acb is a circumscribed angle of circle o. we see that ao ≅ bo because . we also know that ac ≅ bc since . using the reflexive property, we see that . therefore, we conclude that △aco is congruent to △bco by the
we conclude that △ACO is congruent to △BCO by the side-angle-side (SAS) congruence theorem.
We are given that angle AOB is a central angle of circle O and that angle ACB is a circumscribed angle of circle O. We see that AO ≅ BO because they are radii of the same circle.
We also know that AC ≅ BC since they are both tangent to the same circle and intersect at point C.
Thus, angle ACB and angle AOB have the same measure, which means that triangle ACO and triangle BCO are isosceles with AC ≅ BC and ∠ACO ≅ ∠BCO.
Using the reflexive property, we see that angle COA is congruent to angle COB since they are both vertical angles.
Therefore, we conclude that △ACO is congruent to △BCO by the side-angle-side (SAS) congruence theorem.
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Solve the expression one-half x (48 ÷ 6) – 2 + 5 using PEMDAS.
7
8
9
10
The value of the expression using PEDMAS is 7.
What is PEDMAS?The acronym PEMDAS, which can alternatively stand for "Please Forgive My Dear Aunt Sally," is a mnemonic tool for remembering the order of operations in mathematical and algebraic formulas. Its acronym is:
P - Parenthesis (operations inside parentheses are done first)
E: Exponents (operations involving exponents are done next)
Divide and multiply is abbreviated MD (these operations are done left to right, whichever comes first)
AS stands for addition and subtraction (these operations are done left to right, whichever comes first). No matter how they approach it or how they understand it, PEMDAS helps to ensure that the same statement is assessed in the same way by various people. In mathematics, it is crucial to understand this idea, especially when working with complicated expressions or formulae.
The given expression is 1/2 x (48 ÷ 6) – 2 + 5.
Simplifying the expressions we have:
1/2 x (48 ÷ 6) – 2 + 5
= 1/2 x 8 - 2 + 5
= 4 - 2 + 5
= 7
Hence, the value of the expression using PEDMAS is 7.
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Andres needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 5.25 hours and charged him $116 for parts. The total was $719.75. Which equation could be used to determine cc, the cost of labor per hour?
assume that the weights of individuals are independent and normally distributed with a mean of 160 pounds and a standard deviation of 30 pounds. suppose that 25 people squeeze into an elevator that is designed to hold 4300 pounds. 2a) what is the probability that the load (total weight) exceeds the design limit?
The probability that a standard normal variable exceeds 2 is approximately 0.0228
To solve this problem, we need to use the central limit theorem, which states that the sum of a large number of independent and identically distributed random variables tends to follow a normal distribution, regardless of the distribution of the individual variables.
In this case, we have 25 independent individuals, each with a normal distribution of weights with mean 160 pounds and standard deviation 30 pounds. The total weight of the 25 individuals is the sum of these 25 random variables.
The mean weight of a single person is 160 pounds, so the mean weight of 25 people is 25 times 160, which is 4000 pounds. The standard deviation of the sum of 25 random variables is the square root of the sum of the variances of the individual variables, which is the square root of 25 times 30 squared, or 150 pounds.
The probability that the total weight of the 25 people exceeds the design limit of 4300 pounds can be calculated using the standard normal distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. We can convert the total weight of the 25 people to a z-score using the formula
z = (x - mu) / sigma
where x is the total weight, mu is the mean weight, and sigma is the standard deviation of the sum of the individual weights.
z = (4300 - 4000) / 150 = 2
The probability that a standard normal variable exceeds 2 is approximately 0.0228.
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Which equation describes the function below (photo below)
The equation y=x²+2 (letter C) describes the given function.
Functions
In math, there are different functions: linear, quadratic, cubic, exponential and others. Each type of function presents its characteristics. See below:
A linear function can be represented by the standard form for the linear equation is: y= mx+b , for example, y=5x+6. Where: m= the slope and b= the constant term that represents the y-intercept.
Since, the quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For answering that the question asks you should test the values of x that represent the value y in the given table.
Equation A: y=-3xFor x=-2 -> y=-3*(-2)=6 . Then, (-2,6) is a point of the function.
For x=5 -> y=-3*(5)=-15. Then, (5,27) is not a point of the function.
Thus, the equation y=-3x does not describe the function.
Equation B: y=5x+16For x=-2 -> y=5*(-2)+16=-10+16=6 . Then, (-2,6) is a point of the function.
For x=5 -> y=5*(5)+16=-25+16=41 . Then, (5,27) is not a point of the function.
Thus, the equation y=5x+16 does not describe the function.
Equation C: y=x²+2For x=-2 -> y=(-2)²+2=4+2=6 . Then, (-2,6) is a point of the function.
For x=5 -> y=(5)²+2=25+2=27. Then, (5,27) is a point of the function.
For x=4 -> y=(4)²+2=16+2=18. Then, (4,18) is a point of the function.
For x=7 -> y=(7)²+2=49+2=51. Then, (7,51) is a point of the function.
Thus, the equation y=x²+2 describes the function.
Equation D: y=2x²-2For x=-2 -> y=2*(-2)²-2=2*4-2=8-2=6 . Then, (-2,6) is a point of the function.
For x=5 -> y=2*(5)²-2=2*25-2=50-2=48. Then, (5,27) is not a point of the function.
Thus, the equation y=2x²-2 does not describe the function.
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At 1:00 p.m., the temperature in Arizona was 87o. Six hours earlier, the temperature was 20o cooler.
What was the temperature at 7:00 a.m?
The temperature at 7:00 a.m. was 67 degrees.
To find the temperature at 7:00 a.m., we need to consider that it was 20 degrees cooler than at 1:00 p.m.
1. Identify the given information: At 1:00 p.m., the temperature was 87 degrees, and it was 20 degrees cooler six hours earlier.
2. We need to find the temperature at 7:00 a.m., which is six hours before 1:00 p.m.
3. Since the temperature was 20 degrees cooler at 7:00 a.m.
we will subtract 20 from the temperature at 1:00 p.m.
4. Perform the subtraction:
87 degrees (1:00 p.m. temperature) - 20 degrees (cooler difference) = 67 degrees.
5. The result, 67 degrees, is the temperature at 7:00 a.m.
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solve[tex]\sqrt{-4=4[/tex]
The radical expression √(-4x) = 4 when evaluated has a value of x = -4
Evaluating the radical expressionFrom the question, the equation is given as
√(-4x) = 4
We can start by squaring both sides of the equation to eliminate the square root:
(√(-4x))^2 = 4^2
So, we have
-4x = 16
Dividing both sides by -4, we get:
x = -4
However, we need to check if this solution satisfies the original equation.
√(-4x) = √(-4(-4)) = √(16) = 4
So, the only solution to the equation is x = -4.
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Forest bought a box of chocolates for himself last week. However, by the time forest got home he had eaten 1/3 of the box. As Forest was putting the groceries away, he at 1/4 of what was left. There are now 12 chocolates left in the box.
How many chocolates were in the box to begin?
Be sure to show and explain all your reasoning.
Answer:
There were 24 chocolates in the box to begin with.
Step-by-step explanation:
Let's use working backwards to solve this problem.
We know that there are 12 chocolates left in the box. Let's call the number of chocolates that were in the box to begin with "x".
After eating 1/4 of what was left, Forest had 3/4 of the chocolates left. So, we can set up an equation:
3/4 (x - 1/3x) = 12
We can simplify this equation by multiplying both sides by 4/3:
x - 1/3x = 16
Multiplying both sides by 3:
2x = 48
x = 24
Therefore, there were 24 chocolates in the box to begin with.
a sphere of radius $10$ inches is inscribed in a cone with a base of radius $15$ inches. in cubic inches, what is the volume of the cone?
The volume of the cone is approximately 2941.6 cubic inches.
To begin with, let's recall the formula for the volume of a cone. The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height of the cone.
We can see that the radius of the base of the cone is 15 inches. However, we do not know the height of the cone yet. To find the height, we can use the fact that the sphere is inscribed in the cone.
We have a right triangle with the height of the cone, the radius of the base of the cone (which is one leg of the triangle), and the diameter of the sphere (which is the hypotenuse of the triangle). Using the Pythagorean theorem, we get:
h² + 15² = 20²
Simplifying this equation, we get:
h² + 225 = 400
h² = 175
h ≈ 13.23
Now that we know the height of the cone, we can plug in the values of the radius and the height in the formula for the volume of the cone. We get:
V = (1/3)π(15²)(13.23) ≈ 2941.6 cubic inches
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