The slower vehicle is the car, and it would take (11.67 - 10.5) = 1.17 minutes longer to travel 7 miles compared to the subway train.
To find out how much longer it would take to travel 7 miles in the slower vehicle, we need to calculate the speed of
each vehicle first.
The car travels 3 miles in 5 minutes, which means it travels at a speed of 3/5 miles per minute.
The subway train travels 4 miles in 6 minutes, which means it travels at a speed of 4/6 miles per minute. Simplifying
this, we get a speed of 2/3 miles per minute.
Now, we can calculate how long it would take each vehicle to travel 7 miles:
The car travels at a speed of 3/5 miles per minute, so it would take (7 / (3/5)) = 11.67 minutes to travel 7 miles.
The subway train travels at a speed of 2/3 miles per minute, so it would take (7 / (2/3)) = 10.5 minutes to travel 7 miles.
Therefore, the slower vehicle is the car, and it would take (11.67 - 10.5) = 1.17 minutes longer to travel 7 miles compared to the subway train.
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A concert ticket costs $65. If 25,300 tickets are available, how much money will be made in concert tickets if every
ticket is sold. Create an equation to represent this situation. Write the equation in function notation. State the
ordered pair for 25,300 tickets and explain your solution.
Answer:
$ 1644500
Step-by-step explanation:
ehat are the roots of the polynominal equation? use a grapghing calculator and make 0=y,and find the x intercepts. x2 + x - 72=0 enter you answers in the boxes.
Therefore, the roots of the polynomial equation x² + x - 72 = 0 are -9 and 8.
What is quadratic equation?A quadratic equation is a type of polynomial equation of the second degree, which means it has one or more terms in which the variable is raised to the power of two, but no higher powers.Quadratic equations can have zero, one, or two real solutions, depending on the values of a, b, and c. These solutions are also called the roots or zeros of the equation.
Here,
To find the roots of the polynomial equation x² + x - 72 = 0, we can set y = 0 and solve for x. This is equivalent to finding the x-intercepts of the graph of the function f(x) = x² + x - 72.
We can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In this case, a = 1, b = 1, and c = -72, so we have:
x = (-1 ± √(1² - 4(1)(-72))) / (2(1))
x = (-1 ± √(1 + 288)) / 2
x = (-1 ± √(289)) / 2
x = (-1 ± 17) / 2
Therefore, the roots of the polynomial equation x² + x - 72 = 0 are:
x = -9 or x = 8
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the die will be rolled 12 times. let x be the number times the die lands on a green square. x has a binomial distribution. what is a trial? a single roll of the 20-sided die what would be considered a success? a green square how many trials? n
The probability of getting 'p' success when a die rolled 12 times with 'x' success that has binomial distribution is equal to ¹²Cₓ pˣ ( 1 - p )¹²⁻ˣ.
Number of times die to be rolled = 12
In this scenario, a trial refers to a single roll of the 20-sided die.
Here , 'x' represents the the number times the die lands on a green square.
A success would be defined as landing on a green square,
And a failure would be landing on any other color.
Since the die will be rolled 12 times, there are 12 trials in total.
This implies, the number of times the die lands on a green square, x, has a binomial distribution.
With parameters n = 12 the number of trials and p the probability of success which is landing on a green square.
Probability = ⁿCₓ pˣ ( 1 - p )ⁿ⁻ˣ
Therefore, the probability of rolling a die 12 times with 'x' success which has binomial distribution and 'p' probability of success is equal to ¹²Cₓ pˣ ( 1 - p )¹²⁻ˣ.
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40000 is divided by the smallest number so that the result is a perfect cube. find the cube root of the resulting number.
The Cube root of the resulting number is 8.
The smallest number that 40000 can be divided by so that the result is a perfect cube, we need to factorize 40000 into its prime factors:
[tex]40000 = 2^6 \times 5^4[/tex]
To make this a perfect cube, we need to ensure that the powers of each prime factor are multiples of 3.
The smallest number we can divide 40000 by so that the result is a perfect cube is:
[tex]40000 = 2^6 \times 5^4[/tex]
Now we can find the cube root of the resulting number:
[tex]3\sqrt (40000 \div 100) = 3\sqrt400 = 8.[/tex]
Factories 40000 into its prime components in order to determine.
The least number that the result may be divided by while still producing a perfect cube.
The powers of each prime factor must be multiples of three in order for this to be a perfect cube.
The least number that 40000 may be divided by to produce a perfect cube is:
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Find the points on the surface z2 = xy +16 closest to the origin. The points on the surface closest to the origin are (Type an ordered triple. Use a comma to separate answers as needed. )
The points on the surface z² = xy + 16 closest to the origin are: (-4,4,0) and (4, -4, 0)
We know that the distance between an arbitrary point on the surface and the origin is d(x, y, z) = √(x² + y² + z²)
Using Lagrange multipliers,
L(x, y, z, λ) = x² + y² + z² + λ(z² - xy - 16)
We have partial derivatives.
[tex]L_x[/tex] = 2x - λy
[tex]L_y[/tex] = 2y - λx
[tex]L_z[/tex] = 2z + 2zλ
[tex]L_\lambda[/tex] = z² - xy - 16
Now we set each partial derivative to zero to find critical points.
[tex]L_x[/tex] = 0
2x - λy = 0
[tex]L_y[/tex] = 0
2y - λx = 0
After solving above equations simultaneously we get (x + y)(x - y) = 0
i.e., x = -y OR x = y
[tex]L_z[/tex] = 0
2z + 2zλ = 0
z = 0 OR λ = 0
Consider [tex]L_\lambda[/tex] = 0
z² - xy - 16 = 0
-xy = 16 ............(as z = 0)
when x = y then -y² = 16 which is not true.
So, consider x = -y
-(-y)y = 16
y² = 16
y = ±4
when y = 4 then we get x = -4
and when y = -4 then we get x = 4
Therefore, the closest points are:(-4,4,0) and (4, -4, 0)
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In the accompanying diagram, m<A=32° and AC = 10. Which equation could be used to find x in ∆ABC?
1. x=10 sin [32°]
2. x=10 cos [32°]
3. x = 10 tan [32°]
4. x=10/cos32
The equation x = 10 tan (32°) could be used to find x in ∆ABC.
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) , where:
[tex]sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse}\\ \\ tan(x)=\frac{sin(x)}{cos(x)} =\frac{opposite\ side}{adjacent\ side}[/tex]
The question gives the value of the two sides and the value of an angle. From the trigonometric ratios presented before, you can write:
[tex]tan(32)=\frac{opposite\ side}{adjacent\ side}=\frac{x}{10} \\ \\ x=10\ tan (32\°)[/tex]
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Verify that the segments are parallel.
10. CD || AB
Answer: Prove that the triangles are similar, and therefore the lines have the same slope and are parallel.
please solve correctly my grade depends on it
Just use the pythagorean theorem to solve the hypotenuse!
(3^2)+(2^2)=x^2
9+4=13^2
[tex]\sqrt{13}[/tex] = [tex]\sqrt{x}[/tex]
[tex]13^{2}[/tex] km
Hope this helps <3
a coin is tossed 10,000 times. what is the chance that the number of heads will be in the range 4850 to 5150?
The chance that the number of heads will be in the range 4850 to 5150 is approximately 0.9973, or about 99.73%.
The number of heads in 10,000 coin tosses follows a binomial distribution with parameters n = 10,000 (the number of trials) and p = 0.5 (the probability of heads on a single toss).
We can approximate this binomial distribution using the normal distribution, with mean μ = np = 5000 and variance σ² = np(1-p) = 2500.
To find the probability that the number of heads is in the range 4850 to 5150, we can use the normal distribution and standardize the range using the z-score formula:
z = (x - μ) / σ
where x is the number of heads in the range we're interested in.
For the lower bound of 4850, we have:
[tex]z_lower = (4850 - 5000) / \sqrt{(2500)}[/tex]
= -3
For the upper bound of 5150, we have:
[tex]z_upper = (5150 - 5000) / \sqrt{(2500)} = 3[/tex]
Using a standard normal distribution table or calculator, we can find the probability of being within 3 standard deviations of the mean:
P([tex]z_lower[/tex] < Z < [tex]z_upper[/tex] ) ≈ P(-3 < Z < 3)
= 0.9973.
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Interpret the probability. In 100 trials of this experiment, it is expected about (Round to the nearest whole number as needed.) to result in exactly 15 flights being on time
Hence, it is expected that 14 flights will arrive on time out of the 100 trials of this experiment.
What is the probability?The probability of an occurrence is a number used in mathematics to describe how likely it is that the event will take place. In terms of percentage notation, between 0% and 100% it is expressed as a number between 0 and 1, or . The higher the likelihood, the more likely it is that the event will take place.
What is the trials?when we refer to an experiment or trial, we mean a random experiment. When difference between a trial and an experiment, think of the experiment as a larger entity created by the fusion of several trials.
Unless otherwise stated,A trial is any specific outcome of a random experiment. In other words, a trial of the experiment is what we call when we conduct an experiment.
according to question, the number of on-time flights in 100 trials as a binomial random variable with parameters n = 100 (the number of trials) and p (the chance of success, i.e., a flight being on time), presuming that the probability of a flight being on time is the same in all trials.
The expected number of on-time flights in 100 trials is E(X) = np if the same of a flight being on time is p. Given that E(X) = 15, we determine p ,
E(X) = n p = 15 n = 100
p = [tex]\frac{E(X)}{n} = \frac{15}{100}[/tex] = 0.15
Therefore, it is probability that 0.15 %of flights will arrive on time.
To determine the expected number of trials from a total of 100
Using the probability mass function of the binomial distribution, we can get the expected probability of trials out of 100 that result in precisely 15 flights departing on time:
[tex]P(X = 15)=(100 choose 15) * 0.15^{15} * 0.85^{85}[/tex]
We can calculate this 0.144 get using a calculator.
therefore it is expected that 14 flights will arrive on time out of the 100 trials of this experiment. It should be noted that while this is an expected value, random fluctuation may cause the actual number of on-time flights in each trial to deviate somewhat from this figure.
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Round the number. Write the result as the product of a single digit and a power of 10.
4,241,933,200
Write the functions in standard form:
h(x)=2(x-3)²-9
h(x)=
p(x) = -5(x + 2)² + 15
p(x)=
Answer:
[tex]h(x)=2x^2-12x+9[/tex], [tex]p(x)=-5x^2-20x-5[/tex]
Step-by-step explanation:
To get to the standard form of a quadratic equation, we need to expand and simplify. Recall that standard form is written like so:
[tex]ax^2+bx+c[/tex]
Where a, b, and c are constants.
Let's expand and simplify h(x).
[tex]2(x-3)^2-9=\\2(x^2+9-6x)-9=\\2x^2+18-12x-9=\\2x^2+9-12x=\\2x^2-12x+9[/tex]
Thus, [tex]h(x)=2x^2-12x+9[/tex]
Let's do the same for p(x).
[tex]-5(x+2)^2+15=\\-5(x^2+4+4x)+15=\\-5x^2-20-20x+15=\\-5x^2-5-20x=\\-5x^2-20x-5[/tex]
Thus, [tex]p(x)=-5x^2-20x-5[/tex]
The table of values forms a quadratic function f(x). X f(x)
−2 48
−1 50
0 48
1 42
2 32
3 18
4 0
What is the equation that represents f(x)?
f(x) = –2x2 – 4x + 48
f(x) = 2x2 + 4x – 48
f(x) = x2 + 2x – 24
f(x) = –x2 – 2x + 24
To form a suitable quadratic equation using the values from the table given in the question also considering the event of forming a equation that represents f(x) is Option A.
In order to find the equation that is represented by f(x), we have to implement the standard form of a quadratic function
f(x) = ax² + bx + c
here a, b and c = constants.
We can utilize the given table of values to evaluate these constants.
Now, we have to place each x value into f(x) to get the concerning y value. Then we can utilize these points to create three equations with three undetermined (a, b and c).
Evaluating these equations will give us the values of a, b and c.
Now, the table of values given in the question is
f(-2) = 48 = 4a - 4b + c
f(-1) = 50 = a - b + c
f(0) = 48 = c
f(1) = 42 = a + b + c
f(2) = 32 = 4a + 4b + c
f(3) = 18 = 9a + 3b + c
f(4) = 0 = 16a + 4b + c
Calculating these equations
a = -2
b = -4
c = 48
Hence, the equation that represents f(x) is f(x) = -2x² - 4x + 48.
The correct option for the given question after considering the given conditions is Option A.
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The complete question is
The table of values forms a quadratic function f(x). X f(x)−2 48
f(−1) = 50
f(0) = 48
f(1) = 42
f(2) = 32
f(3) = 18
f(4) = 0
What is the equation that represents f(x)?
a) f(x) = –2x² – 4x + 48
b) f(x) = 2x² + 4x – 48
c) f(x) = x² + 2x – 24
d) f(x) = –x² – 2x + 24
PLEASE HELP AND EXPLAIN AND SHOW WORK ON HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST. PLEASE EXPLAIN HOW YOU GOT THE ANSWER!!!
The terms arranged in order from smallest to biggest are: (-2)³, -√25, √11, 10, and 4² after comparing the values of the final numbers.
How to arrange the terms of numbers in ascending orderWe shall first simplify the numbers to get their final values and then compare to which is smaller as follows:
4² = 4 × 4 = 16
-√25 = -5
10 = 10
√11 = 3.3166
(-2)³ = -2 × -2 × -2 = -8
In conclusion, we have by comparing the final values of the numbers the terms arranged from smallest to the biggest as: (-2)³, -√25, √11, 10, and 4².
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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 12 people took the trip. She was able to purchase coach tickets for $190 and first class tickets for $980. She used her total budget for airfare for the trip, which was $4650. How many first class tickets did she buy? How many coach tickets did she buy?
Sarah then purchased 9 coach seats as by increasing the first equation by 190 and deducting it from the second equation.
what is equation ?An equation is a logical statement that utilises the equal sign to demonstrate the equality of two expressions. Factors, constants, and mathematical like addition, reduction, multiply, division, and exponentiation can all be found in it. Equations are utilised to find solutions for problems in both mathematics and the real world.
given
Let's use the letters "c" for the quantity of coach tickets and "f" for the quantity of first-class tickets. We are aware that there were 12 travellers in all, so
c + f + 1 = 12
We also know that the entire cost of the airfare was $4650, with coach tickets costing $190 and first-class tickets costing $980. With this knowledge, we can construct the equation shown below:
[tex]190c + 980f = 4650 - 980[/tex]
When we simplify this equation, we obtain:
[tex]190c + 980f = 3670[/tex]
Elimination can now be used to find either "c" or "f." By increasing the first equation by 190 and deducting it from the second equation, let's get rid of "c":
[tex]190c + 190f + 190 = 2280[/tex]
-190c - 980f = -3670
-790f = -1390
f = 1.76
We can round "f" up to 2 because we cannot have a fractional number of persons.
c + 2 + 1 = 12
c = 9
Sarah then purchased 9 coach seats as by increasing the first equation by 190 and deducting it from the second equation.
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I need help please I will give brainliest to the best answer...
The value of x in the intersecting chords that extend outside circle is 5
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
intersecting chords that extend outside circle
Using the theorem of intersecting chords, we have
4 * (x + 6 + 4) = 6 * (x - 1 + 6)
Evaluate the like terms
So, we have
4 * (x + 10) = 6 * (x + 5)
Using a graphing tool, we have
x = 5
Hence. the value of x is 5
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Write your answer as an integer or decimal.
please help
The value of angle GFH is 18°
What is circle geometry?A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
A theorem in circle geometry starts that angle in the same segment are equal. In triangle EFG, angle F and G are on the same segment, this means that angle F and G are equal.
Represent angle F as x
therefore 144+2x = 180° ( sum of angle in a triangle)
2x = 180-144
2x = 36
x = 36/2 = 18°
Therefore the measure of angle GFH is 18°
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Questions three and four please
The 'footprint' of CO2 emissions for a person in 1830 would be 818,199 tons of CO2 emissions per person.
What is the 'footprint' of CO2 emissions for a person in 1830??"To find the 'footprint' of CO2 emissions for a person in 1830, we need to substitute the value of x = 1830 - 1800 = 30 into the given function C(x) = 0.0365 (1.758)^x.
Plugging in x = 30 into the function, we get:
C(30) = 0.0365 * (1.758)^30
Substituting this value back into the function, we get:
C(30) = 0.0365 * 22416413.1381
C(30) = 818199.079541
C(30) ≈ 818,199.08
Answered question "Scientists studying the 'footprint' of carbon dioxide (CO2) emissions attributed to the average person for each decade from 1800 to 1910 used the function C(x) = 0.0365 (1.758)*, where x is the number of decades since 1800 and C is the number of tons of CO2 emissions per person. What is the 'footprint' of CO2 emissions for a person in 1830??"
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you roll a 6-sided dice. what is the probability that you rolled a 5, given that the number rolled was greater than 3?
The probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.
We need to find the probability that you rolled a 5, given that the number rolled was greater than 3. Let's break this down step by step:
1. Identify the total number of outcomes: Since it is a 6-sided dice, there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).
2. Determine the number of outcomes greater than 3: The outcomes greater than 3 are 4, 5, and 6. There are 3 possible outcomes that satisfy this condition.
3. Identify the number of outcomes that result in rolling a 5: There is only 1 outcome that results in rolling a 5.
4. Calculate the probability: To find the probability, divide the number of outcomes that result in rolling a 5 (1) by the total number of outcomes greater than 3 (3).
Probability = (Number of outcomes with a 5) / (Number of outcomes greater than 3) = 1/3
So, the probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.
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The probability that the number rolled was a 5, given that it was greater than 3, is [tex]$\frac{1}{3}$[/tex].
The number rolled was greater than 3, it must be either a 4, 5, or 6.
The probability that the number rolled was a 5, given that it was greater than 3.
Let [tex]$A$[/tex] be the event that the number rolled is a 5 and let [tex]$B$[/tex] be the event that the number rolled is greater than 3.
Then, we want to find. [tex]$P(A|B)$[/tex], the probability of [tex]$A$[/tex] given [tex]$B$[/tex].
By Bayes' theorem, we have:
Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event.
The risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately by conditioning it relative to their age, rather than simply assuming that the individual is typical of the population as a whole.
One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference.
The probabilities involved in the theorem may have different probability interpretations.
Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence.
Bayesian inference is fundamental to Bayesian statistics, being considered by one authority as; "to the theory of probability what Pythagoras's theorem is to geometry."
[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$[/tex]
[tex]$P(A) = \frac{1}{6}$[/tex], since there is only one way to roll a 5 on a 6-sided die.
[tex]$P(B) = \frac{3}{6} = \frac{1}{2}$[/tex], since there are three outcomes (4, 5, or 6) that satisfy. [tex]$B$[/tex], out of a total of six possible outcomes.
[tex]$P(B|A)$[/tex], the probability of rolling a number greater than 3, given that the number rolled is a 5, note that. [tex]$B$[/tex] is true only if the number rolled is a 4, 5, or 6.
Since there is only one way to roll a 5, and only one of these three outcomes satisfies. [tex]$A$[/tex], we have:
[tex]$P(B|A) = \frac{1}{1} = 1$[/tex]
Substituting these values into Bayes' theorem, we get:
[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)} = \frac{1 \cdot \frac{1}{6}}{\frac{1}{2}} = \frac{1}{3}$[/tex]
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Help please? I just need an answer. A clear explanation earns brainliest.
the simplified form of expression is: -(x² + 2x - 2)/((x+2)*(x+4))
what is expression ?
In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that represents a mathematical quantity or relationship. Expressions can be simple or complex
In the given question,
To evaluate the expression 1/(x+2) - (x+1)/(x+4), we need to find a common denominator for the two terms. The least common multiple of (x+2) and (x+4) is (x+2)(x+4).
So, we can rewrite the expression as:
(1*(x+4) - (x+1)(x+2))/((x+2)(x+4))
Expanding the brackets, we get:
(x+4 - x² - 3x - 2)/((x+2)*(x+4))
Simplifying the numerator, we get:
(-x² - 2x + 2)/((x+2)*(x+4))
Therefore, the simplified expression is:
-(x² + 2x - 2)/((x+2)*(x+4))
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Kiran swims z laps in the pool. Clare swims 18 laps, which is 9/5
times as many laps as Kiran. How many laps did Kiran swim?
Equation:
Solution: z=
we use linear equation in one variable to solve the problem. Kiran swam 10 laps in the pool.
Let's represent the number of laps Kiran swam as "z".
We know that Clare swam 18 laps, which is 9/5 times as many laps as Kiran. We can represent this relationship with the following equation:
18 = (9/5)z
To solve for z, we can isolate it by multiplying both sides of the equation by the reciprocal of 9/5, which is 5/9:
18 * (5/9) = (9/5)z * (5/9)
10 = z
Therefore, Kiran swam 10 laps in the pool.
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a p-value a. can be positive or negative. b. is a probability. c. can be smaller than 0 but no larger than 1. d. can be larger than 1 but no smaller than 0. e. can only range in value from -1 to 1.
A p-value is a probability.
A p-value is the probability of obtaining a test statistic as extreme or more extreme.
The observed value, assuming the null hypothesis is true.
It ranges in value from 0 to 1 and represents the strength of evidence against the null hypothesis.
A p-value cannot be negative, as it is a probability and probabilities are always between 0 and 1.
A p-value also cannot be larger than 1, as it represents a probability.
A probability cannot exceed 1.
Finally, a p-value cannot be smaller than 0, as it represents a probability.
A probability cannot be negative.
the correct option is b. is a probability.
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What happens to the value of the function as the number of iterations increases? Be specific with the value.
Without knowing which specific function you're referring to, the answer to this question may depend on the type of function and the nature of the iterative process applied to it. In some cases, the function value may converge towards a limiting value as the number of iterations increases, while in other cases it may oscillate or diverge.
For example, in the case of the fixed-point iteration method used to find the root of a function, the value of the function typically converges towards the root as the number of iterations increases. More specifically, if we have a function f(x) and a starting guess x0 for its root, we can use the iterative formula x(+1)=g(x()), where g(x) is some function that we set based on f(x), to generate a sequence of increasingly accurate approximations to the root. As the number of iterations increases, this sequence of approximations typically converges towards the root of the function, unless some conditions are not met (e.g., the method is not well-suited for some functions, or the iteration formula is not properly set.)
In the case of other types of iterative methods or other functions, however, the behavior of the function value as the number of iterations increases may differ. For instance, in some cases, the function value may oscillate between two or more values or diverge to infinity as the number of iterations increases.
Therefore, the specific behavior of the function value as the number of iterations increases may depend on the specific function being evaluated and the iterative method used.
Find unknown sides and angle of the triangle
The sides and the angle of the right triangle are a = 10√2, b = 10√2 and B = π / 4.
How to find the missing information of a right triangle
In this problem we need to determine the values of two sides and an angle of the right triangle. This can be done by means of the following properties:
A + B + C = π
sin A = a / c
cos A = b / c
tan A = a / b
Where:
A, B, C - Angles of the right triangle, in radians.a, b, c - Sides of the right triangle.If we know that A = π / 4, C = π / 2 and c = 20, then the missing angle and missing sides are, respectively:
B = π - π / 4 - π / 2
B = π / 4
cos (π / 4) = b / 20
b = 20 · cos (π / 4)
b = 10√2
sin (π / 4) = a / 20
a = 20 · sin (π / 4)
a = 10√2
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Slope-intercept (0, -2) , (9,1)
Using the graph, determine the coordinates of the x-intercepts of the parabola.
Answer:
x = -5, x = 1
As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).
Step-by-step explanation:
The x-intercepts are the x-values of the points at which the curve crosses the x-axis, so when y = 0.
From inspection of the given graph, we can see that the parabola crosses the x-axis at x = -5 and x = 1.
Therefore, the x-intercepts of the parabola are:
x = -5x = 1As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).
Eddie Clauer sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 17 sales receipts for mail-order sales results in a mean sale amount of $84. 80 with a standard deviation of $19. 25. A random sample of 12 sales receipts for internet sales results in a mean sale amount of $77. 10 with a standard deviation of $26. 25. Using this data, find the 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.
Step 1 of 3 :
Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Step 2 of 3
Find the Staandard error of the sampling distrbution to be used in constructing the confidence interval
Step 3 of 3
you were to ask to construct the 90% confidence interval, given the following information
The 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is approximately [-6.62, 22.02].
The critical value that should be used in constructing the confidence interval.
Since we are looking for a 90% confidence interval, we need to find the critical value associated with a 5% level of significance in a two-tailed test.
Using a t-distribution with (n1-1) + (n2-1) degrees of freedom and a significance level of 0.05, we find the critical value to be:
t-critical = 1.717 (using a t-distribution table or a calculator)
Step 2 of 3:
Next, we need to find the standard error of the sampling distribution to be used in constructing the confidence interval.
Since the population variances are not equal, we need to use the Welch-Satterthwaite equation to calculate the standard error:
SE = sqrt[([tex]s1^2[/tex]/n1) + ([tex]s2^2[/tex]/n2)]
where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Substituting the given values, we get:
SE = sqrt[([tex]19.25^2[/tex]/17) + ([tex]26.25^2[/tex]/12)]
SE ≈ 8.35
Step 3 of 3:
To construct the 90% confidence interval, we can use the formula:
(mean1 - mean2) ± t-critical * SE
where mean1 and mean2 are the sample means, and t-critical and SE are the values calculated in steps 1 and 2.
Substituting the given values, we get:
= (84.80 - 77.10) ± 1.717 x 8.35
= 7.70 ± 14.32
Therefore,
The 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is (approx) [-6.62, 22.02].
We can be 90% confident that the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases falls within this interval.
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what is 72% written in a deciamal
dora drove east at a constant rate of 75 kph. one hour later, tim started driving on the same road at a constant rate of 90 kph. for how long was tim driving, before he caught up to dora? a. 5 hours b. 4 hours c. 3 hours d. 2 hours
Tim was driving for 5 hours before he caught up to Dora.
The answer is (a) 5 hours.
To solve this problem, we can use the formula:
distance = rate × time
Let's denote the time Tim drove as t hours.
Since Dora started driving one hour earlier, her driving time would be (t + 1) hours.
Dora's distance: 75 kph × (t + 1)
Tim's distance: 90 kph × t
Since Tim catches up to Dora, their distances will be equal:
75(t + 1) = 90t
Now we can solve for t:
75t + 75 = 90t
75 = 15t
t = 5.
The answer is (a) 5 hours.
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What is an equation of the line that passes
through the points (-1, -6) and (6, 1)?
Answer:
y = x - 5
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-1, -6) and (6, 1)
We see the y increase by 7, and the x increase by 7, so the slope is
m = 7/7 = 1
Y-intercept is located at (0, -5)
So, the equation is y = x - 5
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-1)}}} \implies \cfrac{1 +6}{6 +1} \implies \cfrac{ 7 }{ 7 } \implies 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{(-1)}) \implies y +6 = 1 ( x +1) \\\\\\ y+6=x+1\implies {\Large \begin{array}{llll} y=x-5 \end{array}}[/tex]