Answer:4 mph
Step-by-step explanation:
how many ways can a dinner patron select appetizers and vegetables if there are appetizers and vegetables on the menu?
The number of ways a dinner patron can select appetizers and vegetables will depend on the number of options available for each course.
Let's say there are "m" appetizer options and "n" vegetable options on the menu.
Then, the patron has m options for the appetizer course and n options for the vegetable course. To find the total number of ways the patron can select both courses, you would multiply the number of options for each course:
m x n ways
So, if the patron has 4 options for appetizers and 3 options for vegetables, the total number of ways the patron can select both courses would be 4 x 3 = 12.
Therefore, the number of ways a dinner patron can select appetizers and vegetables will depend on the specific number of options available for each course.
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Given that P=1.80 and Q=2.91, find ghe relative error in the computation of 1/P-1/Q
Answer:
±1.007%
Step-by-step explanation:
You want the relative error in the computed value of 1/P -1/Q when P=1.80 and Q=2.91.
Maximum and minimumEach of P and Q is specified to the hundredths place, so the errors in each of P and Q will be half of a hundredth, or 0.005. The maximum value of P or Q will be 0.005 more than the given value, and the minimum will be 0.005 less.
The maximum and minimum of the computation will be had when P and Q are at their opposite extremes: one is a maximum when the other is a minimum.
Max difference = 1/1.795 -1/2.915 ≈ 0.21404
Min difference = 1/1.805 -1/2.905 ≈ 0.20978
Relative errorThe relative error in the computed value can be found a couple of ways. One is to compare the maximum and minimum computed values with the nominal computed value.
Here, we choose to compare half the difference in the computed values to the average of the computed values. That way, we can describe the error as symmetrical about that average;
((0.21404 -0.20978)/2) / ((0.21404 +0.20978)/2) = relative error
= (0.21404 -0.20978) / (0.21404 +0.20978) ≈ 0.01007
The relative error is about ±1.007%.
__
Additional comment
Another way to compute the error is by looking at the derivatives. The relative error found that way is ...
RE = -∆P(Q/P(Q -P)) +∆Q(P/Q(Q -P))
where ∆P and ∆Q are ±0.005.
The maximum relative error found this way is about ±1.00686% compared to the ±1.00685% computed above.
If you compare the possible error to the nominal value, it is not symmetrical: -1.00532% to 1.00841%.
Looking at the above expression for RE, you see that the multiplier of the relative error in P is Q/(Q-P), while the multiplier of the relative error in Q is P/(Q-P). That is, errors in P have a much larger effect than errors in Q.
73.
ILLUSTRATION 7
Find a. the length and b. the diameter of the shaft in
In the illustration given above, the length and the diameter of the shaft would be = 21.8 in and 7/8 in respectively.
How to calculate the total length of the shaft?The total length of the shaft can be calculated through the addition of the various given lengths along the shaft such as follows:
= 5⅛ + 5 + 7⅝ + 4 1/16
First convert all the mixed fraction into single fraction;
= 41/8 + 5/1 + 61/8 + 65/16
= 82+80+122+65/16
= 349/16
= 21.8 in.
The diameter of the shaft can be calculated as follows;
= 7¼ - (3 3/16 + 3 3/16 )
First convert all the mixed fraction into single fraction;
= 29/4 - (51/16 + 51/16)
= 29/4 - 102/16
= 116-102/16
= 14/16
= 7/8 in.
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a researcher uses an anonymous survey to investigate the study habits of american college students by sending surveys to a randomly selected set of students. based on the data she obtains, the researcher finds that these students spend an average of 4.1 hours each week working on course material outside of class. for this study, the set of 56 students who returned surveys is an example of a . group of answer choices
In the given case the set of 56 students who returned surveys is an example of a sample
A sample would be the 56 students who responded to the surveys. A sample is a portion of the population that is chosen for a study in research. American college students would be the population in this scenario. The 56 students who returned the surveys were chosen at random for the sample by the researcher.
The researcher is attempting to guarantee that the sample is representative of the greater population of American college students by utilising a random selection process. The researcher discovered that these students spend an average of 4.1 hours per week working on course material outside of class based on the data collected from the sample. This is an example of a descriptive statistic that provides a summary of the information gleaned from the sample.
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write an equation for the exponential growth of the population in the us if in 1970 the population was 203 million and ten years later, 1980, the population was 226 million.
The exponential function for the population is X = 203.[tex]e^{0.0107.t}[/tex]
The formula for an exponential function is f (x) = ax, where x is a variable and a is a constant that serves as the function's base and must be greater than 0.
Let be supposed that population can be modelled by means of the following exponential function:
X = A.[tex]e^{Bt}[/tex]
Where:
t - Time, measured in years. Where t = 0 for 1970.
A - Initial population, in millions inhabitants.
B - Exponential rate constant, in years.
X - Population, in millions inhabitants.
Each constant is found hereafter:
X = A.[tex]e^{Bt}[/tex]
203 = A.[tex]e^{B*0}[/tex]
203 = A[tex]e^{0}[/tex]
A= 203
X = A.[tex]e^{Bt}[/tex]
X = 203[tex]e^{B.10}[/tex]
226 = 203[tex]e^{B.10}[/tex]
B = 1/10(ln(226/203))
B = 0.0107
The exponential function for the population is:
X = 203.[tex]e^{0.0107.t}[/tex]
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you need to have a password with 4 letters followed by 4 even digits between 0 and 9 , inclusive. if the characters and digits cannot be used more than once, how many choices do you have for your password?
The number of choices for all the possible passwords are 43,056,000
Given, we have to make a password which includes 4 characters and 4 even digits. And none of the characters or digits can be used more than once. So, For the first character we have 26 choices as we can use any character from the alphabet. For the 2nd character we get 25 choices as we cant choose the first character already twice. Similarly, for 3rd character we get 24 choices and for 4th character we get 23 choices.
Now for the digits, we can only use even digits 0,2,4,6,8 with no repetition allowed. Therefore, for first digit we can choose any digit so we get 5 choices. For the 2nd digit we get 4 choices. For the 3rd digit we get 3 choices. For the 4th digit we get 2 choices.
Noe, to find all the possible combinations , we just need to multiply all the choices :
⇒ 26 x 25 x 24 x 23 x 5 x 4 x 3 x 2
⇒ 43,056,000
Therefore, the total number of all the possible combination of passwords according to the given condition is 43,056,000.
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A bag contains 2 red marbles and 3 black marbles. If Abby picks a marble without looking, returns it to the bag, and then draws a second marble, what is the probability that both marbles are red? Write your answer as a fraction.
Answer:
hope this helps!
Step-by-step explanation:
The band Leeward charges different prices for its concert tickets based on a concert-goer's age. The total cost, in dollars, of tickets for a adults and c children is 12a+6c. Edgar bought tickets for 4 adults and 6 children.
How much did Edgar pay for tickets?
Answer:
I believe Edgar payed $84 for the tickets.
Step-by-step explanation:
12(4)=48
6(6)=36
48+36=84
The problem on card I is presented to a Math 2 class. Below are two
of the students' responses. Provide feedback for each student. Offer
feedback in the manner you wish to receive feedback yourself.¹
Line RS is parallel to Line TU.m/7=3r-10, and m/3 = 2x+5.
What is m/1?
The measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.
What are parallel lines?Parallel lines are those straight lines that are always the same distance apart from each other.
Given that, two lines RS and TU are parallel, and ∠ 7 = 3x-10 and ∠ 3 = 2x+5,
We need to find ∠ 1
Since, ∠ 7 and ∠ 3 are corresponding angles between two parallel lines therefore, both are congruent,
Therefore,
3x-10 = 2x+5
x = 15
Now, ∠ 1 = ∠ 3 as they are vertically opposite angles,
Therefore,
∠ 1 = 2(15)+5
∠ 1 = 35°
Hence, the measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.
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The figure was not given so the figure is attached.
Find the area of the shaded region in each of the following figures:
The area of the shaded region in each of the following figures are the same, that is, 94.5cm²
(i) Area of the shaded region in the first figure:
= (Area of the square with side 21m) - (Area of the circle with diameter 21m)
we know the diameter of the circle is 21 cm, therefore we can say that the radius of the circle is 10.5 cm
we need to find the area of the shaded region = (21 × 21)
([tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex]) cm² = 441 - 346.5
= 94.5cm²
(ii) Area of the shaded region in the second figure:
(Area of the square with side 21 cm) - (4×Area of the sector)
= (21 - 21) - (4×[tex]\frac{90}{360}[/tex]×[tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex])
(21 - 21) = (4 - [tex]\frac{1}{4}[/tex]×[tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex])
= (441−346.5) cm²
=94.5 cm²
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Four friends plan to rent a car to go on a camping trip. At the campground the friends sign up to go on a mountain bike tour
The algebraic expression G x C, where G represents the total number of gallons needed and C represents the cost per gallon.
In mathematics, an expression is a combination of one or more numbers, variables, and/or operators that represent a quantity or a mathematical relationship.
To calculate the total cost of gasoline, we first need to determine how many gallons of gasoline will be needed for the entire trip. This can be done by dividing the total distance traveled by the car's miles per gallon (MPG) rating. Let's use "G" to represent the total number of gallons needed.
G = Total Distance Traveled / MPG
To find the total cost of gasoline, we can multiply the number of gallons needed by the cost per gallon. Let's use "T" to represent the total cost of gasoline.
T = G x C
Using the expression we developed earlier, we can now find the total cost of gasoline for the full-size car:
=> T = G x C
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Complete Question:
Four friends plan to rent a car to go on a camping trip. They will drive a total of 450 miles. The cost of gasoline is $2.20 per gallon Type of Car SUV Full size Compact Rental Cost $283 $215 $183 Insurance Cost $120 $108 $95 Miles per Gallon 24 25 33 Total Gas Cost $ $ $ Cost per Person.
Write an algebraic expression for the total cost of the gasoline.
Select the angle that correctly completes the law of cosines for this triangle.
82 +1722(8) (17)cos ____ = 15²
-
28°
17
15
62°
90°
8
The angle that completes the law of cosines is 62°.
Option D is the correct answer.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
The law of cosines in a triangle states that,
c² = a² + b² - 2ab cos C
Where c is the side opposite to ∠C.
Similarly,
a² = b² + c² - 2bc cos A
b² = a² + c² - 2ac cos B
Now,
289 + 64 - 272 cos __ = 15²
17² + 8² - 2 x 17 x 8 cos 62 = 15²
289 + 64 - 272 cos 62 = 15²
Thus,
The angle that completes the law of cosines is 62°.
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The complete question.
289 + 64 - 272 cos __ = 15²
Find the value that makes the proportion true
5/6= ?/180
Answer:
150
Step-by-step explanation:
5/6= ?/180
We can use cross-products to solve.
5 * 180 = 6 * ?
Divide each side by 6.
5 * 180/6 = ?
5 * 30 = ?
150
The missing number is 150.
Answer:
150/180
Step-by-step explanation:
Solution by Cross Multiplication;
The equation:
[tex]\frac{5}{6} = \frac{x}{180}[/tex]
The cross-product is:
5(180) = 6(x)
Solving for x:
x = [tex]\frac{5(180)}{6} \\[/tex]
x = 150
Pls show your work thank you will mark the Brainliest
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: (3 {m}^{5} )(4m {}^{9} )[/tex]
[tex]\qquad \sf \dashrightarrow \: (3 \times 4)(m {}^{5} \times m {}^{9} )[/tex]
[tex]\qquad \sf \dashrightarrow \: 12m {}^{(5 + 9)} [/tex]
[tex]\qquad \sf \dashrightarrow \: 12m {}^{14} [/tex]
So, The correct choice is B.) 12 m¹⁴
Please, I need the answer to this question:
A goldsmith takes 2 hours to make a wedding ring and 3 hours to make a necklace. He can only work for a maximum of 12 hours a day. In a day, he has an order for at least 2 rings and 2 necklaces. On each wedding ring, he makes a profit of $50; on each necklace, he makes a profit of $60.
Assuming he makes x-rings and y-necklaces:
A) Write down all the inequalities correcting x and y
B) Show by shading the Region, R which satisfies all the inequalities in no.A above
C) How many rings and necklaces should the goldsmith make to maximize the profit?
2. For the function f(x)=x² + 3x +4, find f(5). f(-3), f(0).
Answer: 44, -14, 4
Step-by-step explanation:
plug the f(x) into the x and solve itself.
(5)^2 + 3(5) + 4 = 44
(-3)^2 + 3(-3) + 4 = -14
(0)^2 + 3(0) + 4 = 4
pls help will give brainliest??
which statement best describes the association between variable X and Y?
you do not give the answer choice in this picture, but I assume it is along the lines of this
The scatter plot shows a negative association between variable X and Y
Colton is flying a kite, holding his hands a distance of 3 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 32 . If the string from the kite to his hand is 90 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
The height of the kite above the ground is; approximately 50.69 feet.
What are trigonometric identities?
Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
The height of his hands above the ground, h is given by 3 feet
Angle of elevation of the string (above the horizontal), θ = 32°
Length of the string, l is given as 90 feet
The height of the kite above the ground is given by trigonometric ratios as ;
Sin∅ =h /90
Sin 32°= h/90
0.52 =h /90 (Sin32°= 0.52)
so h= 47.69 feet
Then height from ground is (H) = 3 +47.69
H = 50.69 feet
The height of the kite above the ground , ≈ 50.69 feet
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Step-by-step explanation:
Find the sides marked with the letters in Question 9
The value of the lettered sides of the triangle are n=4, m=3
What is congruent triangles?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry
From the Triangles, <BAC = <DBC given
⇒ΔBAD ≅ ΔDBC (SAS)
/BA/ =/BD/ = 3 units
Also, /BC/ = /AD/ = 4 units
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The key on a stem-and-leaf plot shows that 1|9 represents 19. How would the number 402 be represented?
The number 402 would be represented as 4|02.A stem-and-leaf plot is a graphical representation of a data set that is used to show its distribution.
The number 402 would be represented as 4|02. A stem-and-leaf plot is a way of organizing data into numerical order. It separates the numbers into two parts, the stem, which is the first digit or digits, and the leaf, which is the last digit or digits. The stem is listed on the left side and the leaf is listed on the right side. In this case, the stem would be 4 and the leaf would be 02, so the number 402 would be represented as 4|02.
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Answer:4l02
Step-by-step explanation: mark me brainiest ;]
(5×-1)(6×2+3×+8) box method
The final result is: 30x^3 - 6x^2 + 15x^2 - 3x + 40x - 8 = 30x^3 + 9x^2 + 40x - 8
What is the Box method?The box method, also known as the FOIL method, is a way of multiplying two polynomials by using the distributive property.
Given the expression (5x - 1)(6x^2 + 3x + 8), we can use the box method to multiply the terms as follows:
First terms: (5x - 1) * 6x^2 = 30x^3 - 6x^2Outer terms: (5x - 1) * 3x = 15x^2 - 3xInner terms: (5x - 1) * 8 = 40x - 8Last terms: (5x - 1) * 8 = 8Therefore., the final result is:
30x^3 - 6x^2 + 15x^2 - 3x + 40x - 8 = 30x^3 + 9x^2 + 40x - 8
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If m∠HZJ = 38°, what is m∠FZG
Answer: 38 degrees
Step-by-step explanation:
HZJ and FZG are congruent angles so then that means that they are the same 38 degrees.
please help and explain
What are the zeros and a -intercepts for the function below?
f(x) = 2x² + 14x + 20
Step-by-step explanation:
the zeros are the x-intercepts. because these are x values, when y (= f(x)) = 0.
a quadratic equation has 2 zeros (even if they are equal or complex numbers).
a quadratic equation
ax² + bx + c = 0
can always be solved by
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-14 ± sqrt(14² - 4×2×20))/(2×2) =
= (-14 ± sqrt(196 - 160))/4 =
= (-14 ± sqrt(36))/4 = (-14 ± 6)/4
x1 = (-14 + 6)/4 = -8/4 = -2
x2 = (-14 - 6)/4 = -20/4 = -5
these are the 2 zeros (x-intercepts).
if you need the explicit points :
(-5, 0) and (-2, 0)
the y-intercept is the y-value when x = 0
y = 2×0² + 14×0 + 20 = 20
the explicit point : (0, 20)
Cameron has a bag of 24 letter tiles. Some are vowles and some are consonants. He randomly chooses a letter tile and places it back in the bag. He chose 4 vowels and 2 consonants. How many vowels are likely in the bag?
In all, Cameron removed 6 tiles (3 consonant vowels and 4 vowel consonants). Take that amount, 6, then divide it by the 24 vowels in total. 24/6=4. It provides you four. Then you multiply that number, 4, by the number of consonant vowels he removed, which is 3, for a total of 6, or 4*2. your response is six vowels.
The five distinct vowel letters are A, E, I, O, and U. The English language has vowels in practically every word and phrase, making them incredibly prevalent. Any letter of the alphabet that isn't a vowel is referred to as a consonant (a, e, i, o, u).All of the non-vowel sounds in the English alphabet are consonants. Vowels, the loud sounds that make up each syllable's core and are separated by consonants. Letters A and O stand in for vowels, whereas B, C, D, F, J, K, M, N, P, Q, S, T, V, X, and Z stand in for consonants.
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if we are given a right-tail probability (or area) a and want a measurement m, which function in excel should we use? assume that the mean of the distribution is mu and the standard deviation is sigma.
The function in Excel that we should use to find a measurement M given a right-tail probability (or area) A is = NORM.INV(1-A, mu, sigma)
In order to find a measurement M given a right-tail probability A in Excel, we can use the NORM.INV function. The NORM.INV function in Excel returns the inverse of the normal cumulative distribution for a given probability.
The formula for NORM.INV function is:
= NORM.INV(1-A, mu, sigma)
where:
A is the right-tail probability (or area)
mu is the mean of the distribution
sigma is the standard deviation
The function returns the measurement M such that the right-tail area from M to infinity under the normal curve is equal to A.
Note - In some versions of Excel, the function may be called NORM.INV.RT instead of NORM.INV.
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For a game you roll a dice. If you get a 1-3 you get nothing.
If you get 4 or 5 you break even and if you roll a 6 you win
$20. If the game costs $5 to play what is the expected value
For a game you have a 15% chance to get nothing a 25%
Is that all of the question?
An herbalist has 15 oz of herbs costing $3 per ounce. How many ounces of herbs costing $2 per ounce should be mixed with these 15 oz of herbs to produce a mixture costing $2.50 per ounce?
15 ounces of herbs should be mixed to produce a mixture of costing $2.50 per ounce.
What is meant by addition?
In mathematics, addition is the process of fusing two or more integers. The numbers being added are known as addends, while the outcome of the addition process, or the final response, is known as the sum. It is one of the fundamental mathematical operations we employ on a daily basis. We add numbers in many different contexts.
Given that, an herbalist has 15 ounces of herbs costing $3 per ounce.
Let the ounces of herbs costing $2 per ounce that should be added to the above herbs be 'x'
Cost of total mixture is 15*3 + x*2 = (x+15)*2.5
15*(3-2.5) = x*(2.5-2)
15*0.5 = x*0.5
x = 15
Therefore, 15 oz of herbs for $2 should be added.
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some identical cylinders each have a radius of 5cm and a length of 3cm. helena has enough paint to cover 2500cm squared. how many of these cylinders can helena paint completely
Answer:
Helena can paint approximately 32 of these cylinders complete
Step-by-step explanation:
The surface area of a cylinder can be found using the formula:
Surface Area = 2πr(r + h), where r is the radius and h is the height (or length) of the cylinder.
For a cylinder with a radius of 5 cm and a length of 3 cm, the surface area is:
Surface Area = 2π x 5 x (5 + 3) = 2π x 5 x 8 = 80π cm²
So, the surface area of one cylinder is 80π cm². To find the number of cylinders that Helena can paint, we can divide her total paint coverage by the surface area of one cylinder:
2500 cm² ÷ 80π cm² = 31.83 (approximately 32 cylinders).
So, Helena can paint approximately 32 of these cylinders completel
jack bought a bike that was 35% off the original price let p represent the original price. what expressions can be used to calulate the sale price
The expression used to calculate the sale price is given as follows:
S(p) = 0.65p.
How to obtain the sale price?The expression used to calculate the sale price is obtained applying the proportions in the context of the problem.
The price was 35% off, meaning that there was a discount of 35%, meaning that a percentage of 100 - 35 = 65% of the total price was paid, hence the expression used to calculate the sale price is given as follows:
S(p) = 0.65p.
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