The rate of change of the distance among the car and the person at that instant is 110,98 m/s.
How do we find the rate of change of distance between two points?To find the average rate of change, we need to divide the change in y (output) by the change in x (input). And visually, all we are doing is calculating the slope of the secant line passing among two points. Finding the average rate of change is particularly useful for determining changes in measurable values like average speed or average velocity.
In this case, consider A as the point where a person is, the intersection (o) and the car from the north form a right triangle. So, based on Pythagoras Theorem:
L^2 = x^2 + y^2
where:
L is the distance between the person and the car.
x is constant since the person does not move.
Now, taking derivatives with respect to time, we will have:
2 * L * dL/dt = 2 * y * dy/dt (1)
where:
x = 15 mts
y = 888
dy/dt = 111 m/s
Now, substitute all the values into the formula:
L^2 = x^2 + y^2
L = √ (15)^2 + (888)^2
L = √ 225 + 788544
L = 888,13 m
So, when we apply to the (1) equation, it will be:
2 * L * dL/dt = 2 * 888 * 111
dL/dt = (888) * 111 / 888,13
dL/dt = 0,99 * 111
dL/dt = 110,98 m/s
Hence, the rate of change of the distance is 110,98 m/s.
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Triangle ABC with D on AC and E on AB
DE is a straight line
AD= 27m, AE=39m, DE=23m, and BC=65m
Calculate the length of CD
Therefore , the solution of the given problem of triangle comes out to be Replace with CD-49.
What does a triangle actually mean?Because triangles have four or more sides, they are considered polygons. Its design is straightforward and geometric. The ABC letters come together to form a triangle with a square angle. Euclidean geometry generates a single rectangle or square when the sides do not coincide. Because they consist of three sides and three corners, triangles are polygons. The corners of a triangle are formed by the junction of its three sides.
Here,
Triangles that are similar may or may not be congruent.
The CD is 49 units long.
The following equivalent ratios can be derived from the triangles that are supplied.
AC: CB = AD: DE
Where:
AC= AD + CD
We thus have:
DE = AD + DC
CB
Replace known values
=>27:23-27+ DC: 65
Describe as a fraction
=> 27+DC
65 x 65 multiplied by both sides yields 27+ DC.
Take 27 away from both sides.
2x65-27 - DC
DC 76-27 - DC 49-DC 27x65-27 = DC 1755-27=DC
Replace with: CD-49
Therefore , the solution of the given problem of triangle comes out to be Replace with CD-49.
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Round each mixed number to the nearest whole number. Then, estimate the product.8 9/10x1 4/5
Answer:
9 × 2 = 18
Step-by-step explanation:
8 9/10 is closer to 9 than it is to 8. So you round 8 9/10 up to 9.
1 4/5 is closer to 2 than to 1. So round it up to 2.
Use the rounded numbers to estimate the product. 9 × 2 is 18
The estimate is 18.
a bag contains 9 blue marbles and 1 green marble. what is the probability of drawing a blue marble (no replacement) followed by a green marble?
The probability of drawing a blue marble (no replacement) followed by a green marble is 2/207
Total marbles: 2 + 9 + 18 + 10 + 7 = 46
In the first scenario, the likelihood of getting a red marble is 2/46=1/23.
Since there are now 45 marbles, the probability of drawing a purple marble in the second scenario is 10/45, or 2/9.
Therefore, the likelihood of taking out a red marble in the first scenario, failing to replace it, and taking out a purple marble in the second scenario is 1/23 * 2/9.
Therefore, the likelihood of removing a red marble in the first scenario, choosing not to replace it and removing a purple marble in the second scenario
=2/46 x 10/45
=1/23 x 2/9
=2/207
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PLS HELP ASAP
D = Drawing
W = Writing
Jordan spends 75 minutes drawing and writing his comic book every day. He draws for 25 minutes longer than he writes.
D + W = 75
W + 25 = D
How much time does Jordan spend writing each day? Show All Work
Is it possible for Jordan to have spent 30 minutes writing if he spends exactly 75 minutes working on his comic book and draws for 25 minutes longer than he writes.
Yes or No?
To support your answer
_ + _ _ 75
Jordan spend 25 minutes writing each day
No
How much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:
D + W = 75
W + 25 = D
So, we have
W + W + 25 = 75
Evaluate
W = 25
This means that Jordan spends 25 minutes on writing
is it possible?Based on the answer in (a), the truth statement is No
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Karla will select 2 different side dishes from the following list at a restaurant.
•French fries
•Salad
•Onion rings
•Beans
Which list shows all the possible outcomes of 2 different side dishes from this list?
a quick quiz consists of 5 5 multiple choice problems, each of which has 6 6 answers, only one of which is correct. if you make random guesses on all 5 5 problems, (a) what is the probability that all 5 5 of your answers are incorrect? answer: (b) what is the probability that all 5 5 of your answers are correct? answer
(a) The probability of getting all 5 answers incorrect is [tex](5/6)^{5}[/tex] = 0.327.
(b) The probability of getting all 5 answers correct is [tex](1/6)^{5}[/tex] = 0.00013.
Probability: Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a value between 0 and 1, with 0 meaning that an event is impossible and 1 meaning that an event is certain to happen. Probabilities can also be expressed as percentages, with 0% meaning impossible and 100% meaning certain. Probability is used in many fields, including statistics, finance, and game theory, to make predictions and decisions based on uncertain information.
The quiz has 5 multiple choice questions with 6 options each, and only one of the options is correct.
(a) The probability of getting one answer incorrect is 5/6, so the probability of getting all 5 answers incorrect is [tex](5/6)^{5}[/tex], which is equal to 0.327.
(b) The probability of getting one answer correct is 1/6, so the probability of getting all 5 answers correct is [tex](1/6)^{5}[/tex], which is equal to 0.00013.
So, The probability of getting all 5 answers incorrect is 0.327 and the probability of getting all 5 answers correct is 0.00013.
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The point where the lines containing the altitudes are concurrent is called the _____ of a triangle.
The point where the lines carrying the elevations intersect is the orthocenter of a triangle.
What is a triangle?A polygon with three edges and three vertices is called a triangle.
It is one of the fundamental geometric shapes.
The symbol for a triangle having vertices A, B, and C is ABC.
In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space).
In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.
All triangles are enclosed in a single plane if all of the geometry is the Euclidean plane, however, this is no longer true in higher-dimensional Euclidean spaces.
The orthocenter of a triangle is the intersection of the lines that carry the elevations.
Therefore, the point where the lines carrying the elevations intersect is the orthocenter of a triangle.
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i need someone to talk to plssssssssssssss
Answer:
oh hi buddy if your lonely I'm always here for you
Find the degree of this polynomial. 4q
The degree of the polynomial is 9
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of terms, variables, constants, coefficients, and factors.
They are also made up of some mathematical operations, such as;
AdditionSubtractionMultiplicationDivisionBracketParentheses, etcTo determine the degree of a polynomial which is also an example of algebraic expressions, we need to take note of the sum of the exponents.
From the information given,we have that
4q^2rs^6
The degree would be;
= 2 + 1 + 6
Add values
= 9
Hence, the value is 9
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The complete question:
Find the degree of this polynomial. 4q^2rs^6
complete the equation describing how x and y are related
The equation represents the relationship between x and y is y = 5x + 3
How to determine the equationFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table of values, we can see that
y is 3 more than five times x
When represented as an equation, we have
y = 5x + 3
Hence, the equation is y = 5x + 3
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A lorry is travelling at 13.5 m/s along a stretch of road where the speed limit is 50 km/h. 1 kilometre = 1000 metres 1 hour = 3600 seconds Show that the lorry is travelling below the speed limit.
The lorry is travelling below the speed limit.
What is Unit of measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that A lorry is travelling at 13.5 m/s along a stretch of road where the speed limit is 50 km/h
We know that 1 kilometre = 1000 metres
1 hour = 3600 seconds
It will do a lot more than that in an hour
13.5×3600 m/h
13.5×3600 / 1000 km/hour
= 48.6km/hour
That is definitely less than 50km/h
Hence, the lorry is travelling below the speed limit.
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what is the number of distinct proper subsets of a set with n elements is
A number of Appropriate Subsets of the Set: There are 2n - 1 appropriate subsets of the set for every n element in the set.
What are sets?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.
A set is a mathematical model for a collection of various things.
A set with a single element is a singleton, while a set with no elements is an empty set.
A set can either be infinite or have a finite number of elements.
If all of the elements in two sets are identical, then the sets are equal.
The number of subsets of a set is 2n if the set has 'n' items.
A number of Appropriate Subsets of the Set: If a set has 'n' items, then 2n - 1 is the number of appropriate subsets of the set.
Therefore, a number of Appropriate Subsets of the Set: There are 2n - 1 appropriate subset of the set for every n element in the set.
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Correct question:
The number of distinct proper subsets of a set with n elements is ____.
a company has given you the task to research the amount of snowfall in cleveland from december to february. would you be more interested in looking at the mean, median, or mode?
The number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.
The mean, median, and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February. The mean is calculated by adding up all of the snowfall measurements and dividing that by the number of measurements. For example, if there were 4 snowfall measurements of 10, 20, 30 and 40 inches, the mean would be 25 inches (10+20+30+40 / 4). The median is the middle value of the snowfall measurements when they are arranged from least to greatest. In this example, the median would be 25 inches as well. The mode is the most frequently occurring value among the snowfall measurements. In this example, the mode is also 25 inches.
The mean, median and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February, with the mean and median being calculated by adding up all of the snowfall measurements and dividing that by the number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.
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The satellite Space Explorer flies 30400 miles in 19 hours. Find the rate of change.
Helga buys a packet of 68 chocolates and decides to
share them with herself and the other twelve people on her soccer team.
One of Helga's team mates, Sasha, says "63 ÷ 13 = 4.846, therefore we
can have 5 chocolates each".
Create your own question where people might make the mistake of rounding to the nearest whole number if they didn't think about the context.
Answer:
This dosen't make anysense to me
i am trying really hard
Step-by-step explanation:
PLEEASE HELPP
The volume of a cylinder can be expressed as V=πr2h, where r is the radius, and h is the height of the cylinder. Use the tools provided to complete the formula for the volume of a cylinder when solved for the radius, r.
r=?
Answer:
r = [tex]\sqrt{\frac{V}{h\pi } }[/tex]
Step-by-step explanation:
V = πr²h ( isolate r² by dividing both sides by hπ )
[tex]\frac{V}{h\pi }[/tex] = r² ( take square root of both sides )
[tex]\sqrt{\frac{V}{h\pi } }[/tex] = r
Why do you think it is important to consider both salary and benefits when applying for a job? Dave Ramsey video notes
Answer:
Ramsey Solutions pays an average salary of $84,233 and salaries range from a low of $72,978 to a high of $96,811. Individual salaries will, of course, vary depending on the job, department, location, as well as the individual skills and education of each employee.
Match the terms to their definition. 1. numerator a number with an integer part and a fraction part 2. mixed number a fraction with a whole number for the numerator and a whole number other than zero for the denominator 3. denominator the number above the fraction line; tells how many parts of the whole exist 4. common fraction a fraction in which the numerator is larger than the denominator 5. like denominators the number under the fraction line; tells how many equal parts the whole was broken into 6. improper fraction
Answer:
numerator - the number above the fraction line; tells how many parts of the whole exist
mixed number - a number with an integer part and a fraction part
denominator - the number under the fraction line; tells how many equal parts the whole was broken into
common fraction - a fraction with a whole number for the numerator and a whole number other than zero for the denominator
like denominators - two fractions with the same denominator
improper fraction - a fraction in which the numerator is larger than the denominator
Triangle ABC is shown. A 40 m B 10 m 26 m What is the length of AC, in meters?
Answer:
42 m AC
Step-by-step explanation:
\sqrt{26^{2}-10^{2}}= 24 DB
\sqrt{40^{2}-24^{2}}= 32 AB
32 + 10 = 42 AC
a marketing research company records the consumer habits of a sample of families from a certain community. the table below summarizes the number of gallons of milk consumed by these families during the last month. number of families gallons of milk for these families, what is the mean number of gallons of milk consumed last month? round your answer to at least one decimal place.
Answer:
The mean is 11.3 to one decimal place.
Step-by-step explanation:
the number $r$ can be expressed as a four-place decimal $0.abcd$, where $a$, $b$, $c$, and $d$ represent digits, any of which could be zero. it is desired to approximate $r$ by a fraction whose numerator is 1 or 2 and whose denominator is an integer. the closest such fraction to $r$ is $\frac{2}{7}$. what is the number of possible values of $r$?
The number of possible values regarding the given fraction situation of $r$ is 8.
To find the possible values of $r$ that can be approximated by [tex]$\frac{2}{7}$[/tex], we need to determine the range of values for $r$ that is closest to [tex]\frac{2}{7}$[/tex]. This can be done by finding the two closest fractions with numerator 1 or 2 to [tex]$\frac{2}{7}$[/tex] and determining the range of values for $r$ between those two fractions. The two closest fractions are [tex]$\frac{1}{3}[/tex] and[tex]\frac{2}{5}[/tex].
If $0.abcd$ is between[tex]\frac{1}{3}[/tex] and [tex]$\frac{2}{5}[/tex], it will be closest to [tex]$\frac{2}{7}$[/tex]. The decimal representation of [tex]\frac{1}{3}$[/tex] is 0.3333..., and the decimal representation of [tex]$\frac{2}{5}$[/tex] is 0.4. Thus, the possible values of $r$ that can be approximated by [tex]\frac{2}{7}$[/tex] are [tex]$0.3333... \leq r \leq 0.4$[/tex] , which have 8 possible values, including both endpoints.
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A survey of statistics undergraduate at prosperity university completed a survey that asked for their verbal and math sat scores. they wanted to predict the verbal score based on the math score. interpret the slope12.78% of the variability of verbal score can be explained by the variation in the math score.A.12.78% of the variability of math score can be explained by the variation in the verbal score.B.As the math score increases by 1 point, the verbal score increases by 12.78 points on average.C.As the verbal score increases by 1 point, the math score increases by 12.78 points on average.D.As the math score increases by 1 point, the verbal score increases by 0.3480 points on average.E.As the verbal score increases by 1 point, the math score increases by 0.3480 points on average.
The correct option: A. 12.78% of the variability of verbal score that can be explained by the linear regression on the math score.
Correlation coefficient: What is it?A "Statistical measurement" that determines the strength of the correlation between the relative movements for two variables is the correlation coefficient. R is used to denote it, and its range is somewhere between (-1 , 1).Students majoring in statistics at Prosperity University responded to a survey that requested their Verbal as well as Math SAT scores. Depending on the math score, they sought to anticipate the verbal score.
Stated values:
R-Squared was initially 12.78%.The verbal score increases up 12.78 points on average for every point in math scored higher, and vice versa.We must first comprehend what a correlation coefficient is, claims the assertion.
Here, depending on the survey results, they seek to determine the verbal score using the math number (independent variable).
The dependent variable is verbal score.Score in math is an independent variable.r² = 0.1278
r = √0.1278
Statement(1): - 12.78% of the verbal score variability that the linear regression on the mathematics score can account for.
TRUE. The provided model accounts for 12.78% of the variability and the verbal and mathematical scores.
Statement #2: A linear regression just on verbal score can account for 12.78% of the variance in math scores.
FALSE, Since the verbal score rather than the numerical score is the dependent variable.
Statement 3: The verbal significant dimension by 12.78 points for every 1 point improvement in math scores.
FALSE, the determination coefficient does not accurately capture the slope of the a linear model.
Statement (4): A math score increases up 12.78 points for every 1 point that the verbal score goes up on average.
FALSE—the determination coefficient does not accurately capture the slope of the a linear model.
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The correct question is-
A survey of Statistics undergraduate at Prosperity University completed a survey that asked for their Verbal and Math SAT scores. They wanted to predict the verbal score based on the math score. The value of R-Squared was 12.78%. Interpret R-squared.
Group of answer choices
A. 12.78% of the variability of verbal score that can be explained by the linear regression on the math score.
B. 12.78% of the variability of math score that can be explained by the linear regression on the verbal score.
C. As the math score increases by 1 point on average, the verbal score increases by 12.78 points.
D. As the verbal score increases by 1 point on average, the math score increases by 12.78 points.
Olivia's family took a road trip to the Grand Canyon. Olivia fell asleep after they had travelled 243 miles. If the total length of the trip was 900 miles, what percentage of the total trip had they travelled when Olivia fell asleep?
The percentage of the total trip had they travelled when Olivia fell asleep is 73%.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Olivia's family took a road trip to the Grand Canyon.
Olivia fell asleep after they had travelled 243 miles.
If the total length of the trip was 900 miles,
then they had travelled when Olivia fell asleep,
= (900 - 243) x 100 /900
= 73%
Therefore, the percentage is 73%.
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to what decimal place should each answer be rounded? how many significant figures does the rounded answer have?
The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.
Rounding a number is important when providing an answer to a calculation or question. The number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required.
To calculate the number of decimal places and significant figures the answer should be rounded to, the general rule is to round to one more decimal place than the least accurate measurement. For example, if the least accurate measurement used in the calculation is rounded to two decimal places, the answer should be rounded to three decimal places.
The significant figures of the rounded answer can be determined by counting the number of digits in the number, excluding the decimal point. For example, the number 6,782 would have four significant figures, as there are four digits in the number.
In conclusion, the number of decimal places and significant figures the answer should be rounded to depends on the accuracy of the answer that is required. The number of decimal places should be one more than the least accurate measurement, and the number of significant figures can be determined by counting the digits in the number, excluding the decimal point.
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PLEASE HELP I DONT UNDERSTAND
Answer:
18
Step-by-step explanation:
X= -6 which is x≤2
So,
f(-6) = -2(-6)+6
= 18
qualitative research relies on numerical data and statistical tests as the bases for reporting results. true or false
The statement "qualitative research relies on numerical data and statistical tests as the bases for reporting results." is False.
Qualitative research does not rely on numerical data and statistical tests as the bases for reporting results.
Qualitative research is a type of research that focuses on understanding and describing the experiences, behaviors, and motivations of individuals and groups.
This type of research typically involves collecting numerical data through methods such as surveys, experiments, and statistical analyses, and using statistical tests to analyze the data and make inferences about the population being studied.
Therefore, it is false that qualitative research relies on numerical data and statistical tests as the bases for reporting results.
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on the sldt, why is a standard score of 89 considered below average if the mean is 100 with a standard deviation of 15?
A standard score of 89 is considered below average because it is 11 points lower than the mean, which is a deviation of more than 0.7 standard deviations below the mean.
A standard score of 89 is considered below average because it falls below the mean score of 100. This is because it is 11 points lower than the mean, which is a deviation of more than 0.7 standard deviations below the mean. The standard deviation is a measure of the spread of the data, where higher values indicate more spread out data. In this case, the mean score of 100 has a standard deviation of 15, which means that any score lower than 85 (100 - 15) is considered below average. A score of 89 is 11 points below the mean, which is a deviation of more than 0.7 standard deviations. This indicates that it is lower than the average score, and therefore considered below average.
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which algebraic expression is represented by the model
The algebraic expression that is represented by the model is 3x + 2y + 5
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
From the model:
Each yellow box, represent x, each blue box represent y and each maroon box represent 1. Hence:
The expression = (x + x + x) + (y + y) + (1 + 1 + 1 + 1 + 1) = 3x + 2y + 5
The algebraic expression is 3x + 2y + 5
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Both trapezoids are similar. The area of the larger trapezoid is 61 ft? Which is the best approximation for the area of the smaller trapezoid?
The area of the smaller trapezoid is 39 ft².
What is Similarity?Two figures are said to be similar if they share the same shape. Congruent objects are those that are precisely the same size and shape.
Given:
The area of the larger trapezoid is 61 ft².
and, side of smaller trapezium, a = 24 feet
side of larger trapezium, b = 30 feet
So, Area of the larger trapezoid / Area of the smaller trapezoid = b² /a²
61 / Area of the smaller trapezoid = 30² / 24²
Area of the smaller trapezoid = 39 ft²
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Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.
I think there is only one solution which is (0,2), I believe. However, I'm not sure if that is correct. How would I correctly answer this question?
The solution to the two equations will be (0,2).
What is a system of equations?A finite set of equations for which we searched for common solutions is referred to in mathematics as a system of equations, also known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized.
Given that there are two equations:-
g(x) = 3x + 2
f(x) = | x - 1 | + 1
The solution of the equations can be calculated as:-
- ( x - 1 ) + 1 = 3x + 2
-x + 1 + 1 = 3x + 2
4x = 2 - 2
x = 0
The value of the dependent variable is:-
y = 3x + 2
y = 0 + 2
y = 2
Hence, the solution of the system of equations will be ( 0, 2 ).
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