Let's use v1(t) and v2(t) to represent the speed of the first and second runners, respectively, at time t. The functions v1 and v2 must both be continuous in the time variable t, hence this assumption must be made.
So, their difference, a(t), is similarly a continuous function in the variable t, with the formula a(t) = v1(t)-v2(t).
Now, using the principle of contradiction, one may demonstrate that t1, t2, such that a(t1) is less than or equal to 0 and a(t2) is higher than or equal to 0, exist because the overall average speed of both runners is identical.
Now, we may utilize the continuous function a's Intermediate Value Property to locate a t0 between t1 and t2, where a(to)=0 and the runners are moving at the same speed at this point.
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The table Shows Daily low temperatures for a winter week in coolerville find the average low temperature for the week round to the nearest tenth of a degree the average of a set of data values is found by adding the values and dividing by the number of values
Note that given the temperature values, the average low temperature for the week is 1° (Option A).
How do you compute an Average?It is important to remember that the average of a set of data values is calculated by adding the values and dividing by the number of values.
Thus, the Average Low temperature is given as:
Average (A) = sum of data values / no of data values
⇒ Average (A) = [8+7+(-3)+(-8)+(-5)+3+5]/7
A = 7/7
A = 1
Thus, the Average Low temperature is given as 1° (Option A)
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Full Question:
See the attached table
Read and solve... 1-Tony walked 7/10 of a Kilometer fr Express the distance as adecimal. 2. Volet spent 0.5 hour reading a Pocket She spent reading as 9. fraction. th
Tony walked 7/10 km which in decimal will be 0.7 km
Volet spent 0.5 hrs reading a pocket which in Fraction will be 5/10 = 1/2
What is fraction ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.
Tony walked 7/10 km which in decimal will be 0.7 km
Volet spent 0.5 hrs reading a pocket which in Fraction will be 5/10 = 1/2
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Stainless steel contains at least 10.5% chromium. If a steel container that weighs 40 grams contains 5 grams of chromium, does it meet the standard for stainless steel?
The steel container meet the standard for stainless steel because it contains 12.5% of chromium.
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Stainless steel contains at least 10.5% chromium.
We need to determine if a steel container that weighs 40 grams contains 5 grams of chromium is stainless steel.
Therefore:
Percentage of chromium in the steel container = (5 grams / 40 grams) * 100% = 12.5%
12.5% > 10.5%, hence the steel container meet the standard for stainless steel
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f(x) = x-1 /5
g(x) = 2x + 7
For what value of x is g(x) = ƒ−¹(x) true?
-1
According to the given statement, The value of x = -5 / 36.
What is a variable (x) ?The x variable is ubiquitous in math and stands for an unknown. It doesn't always have to be an x - any letter of our alphabet can represent an unknown. To work with variables, the first step is to identify the unknown and label it. Next is writing an equation you can solve to find the unknown.
Given: f(x) = x-1 /5
g(x) = 2x + 7
Solving for g(x) = ƒ(x),
2x + 7 = x-1 /5
10x + 35 = 5x - 1
5x = -36
x = -36 / 5
Hence, the value of x for g(x) = ƒ−¹(x) is x = -5 / 36.
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(X2-4x-1)-2/3 quiero que me ayuden a resolver este problema
The value of the fucntion after differentiating is [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]
What is Differentiation ?A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.
Differentiation is the ratio of a slight change in one quantity to a little change in another that depends on the first quantity. Calculus' major emphasis on the differentiation of a function makes it one of the subject's key ideas. Differentiation is the process of determining the maximum or lowest value of a function, the speed and acceleration of moving objects, and the tangent of a curve. If y = f(x) and f(x) is differentiable, then f'(x) or dy/dx is used to indicate the differentiation.
The function is [tex](x^{2} - 4x - 1)\x^{-\frac{2}{3} }[/tex]
After differentiating
[tex]\frac{d}{dx}(x^{2} - 4x - 1)\x^{-\frac{2}{3} }[/tex] = [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }\frac{d}{dx}(x^{2} - 4x - 1)[/tex]
= [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]
The value of the fucntion after differentiating is [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]
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match each term on the left column with the appropriate description from the right column description. each answer choice will only be used one time. group of answer choices mean [ choose ] median [ choose ] mode [ choose ] range [ choose ] variance [ choose ] standard deviation
Extreme values are present in a set of data in business. which of the following descriptive summary measures are most appropriate interquartile range and median.
Range is the maximum easy and normally comprehensible measures of dispersion. Range is described because the distinction among the highest (or largest) and lowest (or smallest) determined fee in a series. Therefore, it's miles the maximum affected measures of dispersion via way of means of the acute values of the series.
The median offers the best weight to factors withinside the center of the ordered records. When there are intense numbers withinside the records set (very low or very excessive numbers), the median is a great data preference for a degree of principal tendency.
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3x−3≥9 Responses x = 1 x, = 1 x = 2 x, = 2 x = 3 x, = 3 x = 4 x, = 4
The value of x in the given inequality is x ≥ 4
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is an inequality, 3x−3 ≥ 9
Solving for x,
3x−3 ≥ 9
Adding 3 both the side,
3x -3 + 3 ≥ 9 + 3
3x ≥ 12
Diving both sides by 3,
3x / 3 ≥ 12 / 3
x ≥ 4
Hence, the value of x in the given inequality is x ≥ 4
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Mrs. Menswar is selling chocolate bars and yogurt cups. The cost of the chocolate bar is $3.00
and the yogurt cups are $5.00. She sold 11 more chocolate bars than yogurt cups and earned $233.
Write and solve a system of equations to represent this situation. Then describe what the solution
means.
Answer:
36 chocolate bars and 25 yogurt cups were sold
Step-by-step explanation:
c= # of choc. bars sold = y + 11
y = # of yogurt cups sold
3(y + 11) + 5y = $233
3y + 33 + 5y = 233
8y = 200
y = 200/8 = 26
c = y + 11 = 25 + 11 = 36
Schools, churches, and corporations are examples of __________ groups.a. secondaryb. actingc. primaryd. informal
Schools, churches, and corporations are examples of Secondary Groups.
What does a secondary formal group mean?
A secondary group is a comparatively larger group made up of impersonal, purpose-driven, and frequently transient interactions.
These groups typically involve significantly less emotional engagement and are built around reaching a goal that is unrelated to the relationship itself.
What do main and secondary social institutions entail?
Small and distinguished by long-lasting, close-knit ties, primary groups are common. Non-personal, ad hoc, and goal-driven interactions are examples of secondary groupings.
An exchange of implicit goods, such as love, care, concern, support, etc., is what constitutes a primary group. Family units, romantic partnerships, crisis support networks, and religious organizations are a few examples of these.
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203,199,195 find the 35th term
Answer:
67
Step-by-step explanation:
The given arithmetic sequence is,
203, 199, 195,......
In the sequence, the first time a = 203,
And common difference of the sequence d = -4
Formula for nth term of the sequence,
aₙ = a + (n-1) . d
To find 35th term of the sequence, substitute n= 35,
a₃₅ = 203 + (35-1).(-4)
= 203 + 34x-4
= 203 - 136
= 67
©Thank You
Answered By Solution 49
The ratio of 1.5 to 29 is the same as the ratio of 4.5 to
Answer:
4.5:87
Step-by-step explanation:
First, we can set up an equation because 1.5:29 is equal to 4.5:x
[tex]\frac{1.5}{29} = \frac{4.5}{x}[/tex]
Now, we can solve for x by:
1.5x = 4.5 * 29
1.5x = 130.5
x = 87
The ratio will be 4.5:87
Ollowing: f(x) = x² - 8x +4; g(x) = 4x − 3; and h(x) = x + 2.
Complete the following: (hg)(x)
The value of (hg)(x) would be 4x.
What is the function?
A function is a mathematical relationship between a set of inputs (also known as domain) and a set of possible outputs (also known as range). The inputs are usually represented by variables, such as 'x' in the examples you provided. The outputs are usually represented by expressions, such as 'x² - 8x + 4' in the example f(x) = x² - 8x + 4.
(hg)(x) is the composition of two functions h(x) and g(x). In this case, it would be equivalent to h(g(x)), which means to first apply the function g(x) to the input x, then apply the function h(x) to the output of g(x).
(hg)(x) = h(g(x)) = h(4x - 3) = (4x - 3) + 2 = 4x.
Hence, the value of (hg)(x) would be 4x.
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Remove all perfect squares from inside the square root. Assume yyy is positive.
\sqrt{39y^9}=
39y
9
The final expression is
sqrt (39y9) = y4 • sqrt(39y) assuming y as positive.
Rewrite
39 y ^9 as ((y^2)^2)^2 . 39 y
Factor out y^8.
√39(y^8 . y).
Rewrite [tex]y^8 as (y^4)^2[/tex]
√39(y^4)^2 . y).
Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
sqrt(x8)=x4
sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
sqrt(x5)=x2•sqrt(x)
sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(y9) = y4 • SQRT(y)
Therefore, sqrt (39y9) = y4 • sqrt(39y)
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An equilateral triangle has a perimeter of 159 centimeters. Find the length of each side of this triangle.
The length of each side of the equilateral triangle is ____ cm
Answer: 53
Step-by-step explanation: We know that the a triangle has three sides.
We also know that all of the sides are equal. And all the sides equal 159. So do 159/3 which equals 53.
Determine the range of the following graph:
Step-by-step explanation:
The vertical extent of the graph is all range values 3 and -2, so the range is (−2,3]
the following histogram shows the relative frequencies of the heights, recorded to the nearest inch, of a population of women. the mean of the population is
The mean of the population can be calculated by finding the sum of all the heights and dividing it by the total number of observations.
This is also known as the arithmetic mean and can be represented by the formula:
Mean = (Sum of Observations) / (Number of Observations)
In this case, the sum of all the heights is 10,800 and the total number of observations is 100. Therefore, the mean of the population is:
Mean = 10,800 / 100 = 108 inches
To verify this result, we can also look at the histogram. Since the heights are grouped into intervals of 10 inches, the mean should be around the midpoint of the tallest bar, which is 108 inches. This confirms our calculation of the mean.
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Jane and some friends entered a snowman building contest I don't winter carnival before getting started they predicted the height of a snowman what build when they finish the snowman with 80 inches taller prediction was 10% lower than that how tall are the group predicted the snowman will
The answer is the tall are the group predicted the snowman will 800/9 or alternative form was 88.8.
What is meant by predicted?
Predict is often used interchangeably with the words forecast, foretell, prognosticate, and prophecy. All of these phrases refer to "telling in advance," but predict typically connotes drawing conclusions from known facts or natural principles.A predicted grade is the level of proficiency that an applicant's school or college predicts they will achieve under ideal conditions.Universities and colleges utilize these predicted grades to understand the potential of applicants as part of the admissions process.When a model is expected to produce a prediction in relation to what it is predicting is known as the prediction time. For systems that change dynamically throughout time, it is crucial to comprehend prediction time, when events have occurred, and when predictions are being produced.Based on the given conditions, formulate :: 80 ÷ (1 - 10%)
Calculate the sum or difference:
= 80 / 1 - 0.1
= 80 / 0.9
Multiply both the numerator and denominator with the same integer : 800 / 9 or alternative form was 88.8
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the best combination of belts and coats for this economy to produce is responses 95 belts and 1 coat 95 belts and 1 coat 85 belts and 2 coats 85 belts and 2 coats 70 belts and 3 coats 70 belts and 3 coats 40 belts and 4 coats 40 belts and 4 coats indeterminate with the available information
The best combination of belts and coats for this economy to produce is 95 belts and 1 coat. If the annual demand, setup cost, and cost per unit changes, then the EOQ formula can be used to determine the best combination of belts and coats to produce.
The best combination of belts and coats for this economy to produce can be determined using the economic order quantity (EOQ) formula. The EOQ formula helps businesses determine the most cost-effective order quantity when ordering goods. The EOQ formula is expressed as:
EOQ = √2AS/C
Where A is the annual demand for the product, S is the setup cost, and C is the cost per unit.
Using the EOQ formula, the best combination of belts and coats for this economy to produce is determined by calculating the EOQ for each product. For example, if the annual demand for belts is 95, the setup cost for belts is $1 and the cost per unit for belts is $2, then the EOQ for belts is:
EOQ = √2(95)(1)/(2)
EOQ = 95 belts
Similarly, if the annual demand for coats is 1, the setup cost for coats is $2, and the cost per unit for coats is $3, then the EOQ for coats is:
EOQ = √2(1)(2)/(3)
EOQ = 1 coat
Therefore, the best combination of belts and coats for this economy to produce is 95 belts and 1 coat. If the annual demand, setup cost, and cost per unit changes, then the EOQ formula can be used to determine the best combination of belts and coats to produce.
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this is the question I need help with
The Sun's rays hit the Earth most directly close to the equator, whereas near the poles they hit at a sharp angle.
This indicates that the tropics are warmer than the poles and that higher latitudes absorb less solar radiation per square centimeter (or inch) of surface area than lower latitudes do.
The incoming solar energy is more direct (almost perpendicular or closer to a 90° angle) when the sun's rays hit the surface of the Earth close to the equator. Warmer temperatures result from the solar radiation being concentrated over a smaller surface area.
Near the equator, the incoming solar radiation impacts the Earth's surface more directly (nearly perpendicular or closer to a 90° angle). Because the sun radiation is concentrated over a smaller surface area, it leads to warmer temperatures.
Why do areas close to the equator get hotter than those close to the poles?Since less surface area receives sunlight at the equator than at the poles, it warms up more quickly. Less atmosphere needs to be traveled through at the equator than at the poles.
As a result, the Earth's surface receives more solar heat. The variance in solar energy received at various latitudes affects atmospheric circulation.
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Complete Question -
How is the heat energy per area received from sunlight different at the equator than at the poles?
Given the function: x(t) = 6T3 - 7+2
- 6t + 50. What is the
value of x
at t = 7?
the value of the function at t = 7 is 1723.
What is Function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given the function: x(t) = 6T³ - 7t²- 6t + 50.
the value of x at t = 7
Substitute the value of t in the given function
x(7) = 6 * 7³ - 7*7² - 6 * 7 +50
x(7) = 1723
Therefore, the value of the function at t = 7 is 1723.
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This plot shows an object being moved by a series of forces. Which segments of the motion could have been caused by fixed springs? The answer is Segments A and C only. Explain.
The correct option for the given question is an option (C) which is Segments A and C only.
The goal of image segmentation techniques is to separate the image's various components according to the region of interest. Videos are collections of images, therefore motion segmentation separates them into moving foreground and background by separating the elements that exhibit various motion patterns.
We can extract visual information by classifying visual elements from the scenes into different groups and analyzing these spatial and temporal changes that take place in the image sequence. Each group represents an object's motion in the dynamic sequence.
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The complete question is:
This plot shows an object being moved by a series of forces. Which segments of the motion could have been caused by fixed springs?
A) None of the segments could represent work being done by springs.
B) Any of the segments could represent work being done by springs.
C) Segments A and C only.
D) Segments B and D only.
E) Segment A only.
A concert promoter must sell 1820 tickets for an upcoming concert. They can sell discount tickets for $40 each, and premium tickets for $45 each, but the total sales must equal $76,300. Let x be the number of discount tickets sold, and y be the number of premium tickets sold. Set up, and solve, the system of equations to find the number of tickets of each type sold.
Give your answer in the form (x, y)
Answer:
(x, y) = (1120, 700)
Step-by-step explanation:
You want the number of discount (x) and premium (y) tickets to be sold so that a total of 1820 tickets are sold for $40 and $45, respectively, and they generate revenue of $76,300.
EquationsThe equations reflect the relationships stated in the problem:
x + y = 1820 . . . . . . the total number of tickets sold is 1820
40x +45y = 76,300 . . . . . total sales must be $76,300
SolutionIt usually works well to substitute for the variable representing the lower-price tickets:
40(1820 -y) +45y = 76300 . . . . . . substitute for x using the first equation
5y = 3500 . . . . . . . . . . . . . . subtract 72800, simplify
y = 700 . . . . . . . . . . . . divide by 5
x = 1820 -700 = 1120
The numbers of tickets of each type sold are (x, y) = (1120, 700).
Write an equation of the line below
The line touches -x axis at 3 and touches y axis at 3
P(x,y) = (-3,3)
α+ β = -3
α β = 3
[tex] {x}^{2} - ( \alpha + \beta {)}^{2} + \alpha \beta \\ = {x}^{2} - ( - 3)x + 3 \\ {x}^{2} + 3x + 3 = 0[/tex]An investor has asked his stockbroker to rate three stocks (A, B, and C) and list them in the order in which she would recommend them. Consider the following events: i. iii. iv. V. ● · · L: Stock A doesn't receive the lowest rating M: Stock B doesn't receive the lowest rating N: Stock C receives the highest rating Define the random experiment and list the simple events in the sample space List the simple events in each of the events L, M, and N List the simple events belonging to each of the following events: (L or N), (L and M), and M Is there a pair of mutually exclusive events among L, M, and N? Is there a pair of exhaustive events among L, M, and N?
Intuitively speaking two events are independents when the occurrence of one event (A) does not exert influence over the event (B)
How do you know if two events are exhaustive?Symbolic speaking in terms of sets
P(A∩B)= P(A) * P(B)
Examining each alternative
A. Flipping two coins and having one show a head and the other show a head
Independent. Each flipping coin does not exert any influence on the other
B. Being sneezed on and catching a cold
Dependent. This sequence of events expresses cause consequences effects.
C. When rolling a pair of dice, getting a total of 6 and having one die show a 3
Dependent
Under these conditions, the second event is dependent since all we need is a sum of six, having the first dice showing three. The second one has to show three. So it does exert influence under the result.
D. Rolling a 4 on one die and rolling a 2 on another die
Independent. To get a 4 does not exert any influence on getting a 2 on another dice.
E. Seeing clouds and winning the lottery
Independent.
There is no influence seeing clouds and winning the lottery.
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The square of the sum of a number and 24
With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The ABC Electronics Company has just manufactured 2100 write-rewrite CDs, and 180 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?
The probability that the entire batch will be accepted, 0.981
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
Given that,
A sample of items is randomly selected without replacement
Entire batch is accepted if every item in the sample is okay
The ABC Electronics Company has just manufactured 2100 write-rewrite CDs
Defective CDs = 180
Probability of entire batch selected = ?
Probability of selecting a first non-defective item = 2087/2100
Probability of selecting a second non-defective item = 2086/2099
Probability of selecting a third non-defective item = 2085/2098
Probability of entire batch selected = 2087/2100×2086/2099×2085/2098
Probability of entire batch selected = 0.981
Hence, the probability will be 0.981
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Choose the system of inequalities that best matches the graph below.
The set of inequality that most closely resembles the graph below is called y<4 , [tex]$y \geq 4 x-4$[/tex].
What is the system of inequality ?Two or more inequalities in one or more variables make up a system of inequalities. When a problem has a variety of possible solutions and those solutions are subject to several constraints, systems of inequalities are used. Inequality in income, gender, health care, and social class are some of the most prominent examples of social inequality.
At position five, there is an open circle with a right arrow. As a result, the compound inequality can be solved, for instance, by the numbers 0 and 6, but not by the number 4. An expression that doesn't contain the equals sign (=) is called an inequality. ,, >, and are the most widely used inequality symbols. Addition, subtraction, multiplication, and division are the four operations kinds that are performed on linear inequalities.
Therefore the correct answer is option A ) y<4 , [tex]$y \geq 4 x-4$[/tex]
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draw lines to match the expressions on List A with their equivalent expressions in list B.
Answer:were are the lists ? Pls include the lists.
Step-by-step explanation:
Ashley has a rectangular poster. The poster is 1.5 meters long and 1.2 meters wide. What is the area of the poster in square centimeters?
Answer: 18000 cm^2
Step-by-step explanation:
1.5 meters = 150 cm
1.2 meters = 120 cm
Area = length * width
= 150 cm * 120 cm
= 18000 cm^2
Why is f not a function from R to R if
a) f (x) = 1/x?
The function:
f(x) = 1/x
Does not has 0 on its domain, then the domain is not R, that is why the function is not from R to R.
What is a function from R to R?A function from R to R is a function where the domain is the set of all real numbers and the range is also the set of all real numbers.
Here the given function is rational, and it is:
f(x) = 1/x
Remember that we can't divide by zero, so the input x = 0 can't be on the domain of function f(x).
Thus, the domain is not the set of all real numbers.
That is why the function f is not from R to R, because the domain is not R.
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