There are 95,040 different ways for the first five cars to go through the toll booth.
The first car can be chosen in 12 ways. After the first car has been chosen, the second car can be chosen in 11 ways. This process continues, so the third car can be chosen in 10 ways, the fourth car can be chosen in 9 ways, and the fifth car can be chosen in 8 ways.
So the total number of ways to choose the first five cars is as follows:
12 x 11 x 10 x 9 x 8 = 95,040
Therefore, there are 95,040 different ways for the first five cars to go through the toll booth.
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Ross goes on a hiking trip. He hikes 2000 feet before stopping to rest. He turns around and hikes back 1050 feet and rests again. After some time, he hikes the rest of the way back to his starting point. Sketch the graph to show the distance from his starting point compared to time. Use the graph to find the total distance that Ross hiked.
Helpp!
The total distance that Ross hiked is 4000 feet.
How to determine the total distance hikedFrom the question, we have the following parameters that can be used in our computation:
He hikes 2000 feet before stopping to rest. He hikes back 1050 feet After some time, he hikes the rest of the way back to his starting pointThis means that the total distance travelled is
Total distance = 2 * Initial distance hiked
Substitute the known values in the above equation, so, we have the following representation
Total distance = 2 * 2000
Evaluate
Total distance = 4000
Hence, the total distance hiked is 4000 feet
See attachment for the graph
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The manager of a local radio station wants to find out what type of music people in
the area like the most. She surveys every 10th person leaving a country music
concert held near the radio station.
Is this sample likely to be representative of the population? Explain.
Answer:
No, this sample is not likely to be representative of the population. The sample only includes people who attended a country music concert, which means it does not include people who prefer other genres of music. Therefore, the survey results would likely be biased towards country music, and not necessarily reflective of the general population's music preferences.
justin had 3 rolls of ribbon. he used 1/5 of a roll of ribbon to tie a parcel and 2/5 of another roll of ribbon to tie a present. how many rolls of ribbon did he use in all?
Justin used average two rolls of ribbon in total, using 1/5 of one and 2/5 of another.
Justin had 3 rolls of ribbon before he started tying parcels and presents. He used 1/5 of a roll of ribbon to tie a parcel, and then used 2/5 of another roll of ribbon to tie a present. This means that he used two rolls of ribbon in total, with 1/5 of one and 2/5 of the other. He still has one roll of ribbon remaining, meaning that he didn't use all three rolls of ribbon. To calculate the total amount used, you would need to multiply 1/5 and 2/5 by the length of the ribbon, or alternatively multiply the two fractions together to get 2/5 of a roll of ribbon used. This means that he used two rolls of ribbon in total, with 1/5 of one and 2/5 of the other.
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Bob had $300 in his bank account. He wrote 3 checks for exactly $20, then deposited $50. What is the overall change to his bank account?
Answer: He has 290 dollars.
Step-by-step explanation:
3 x 20 is 60
300-60 is 240
240 + 50 is 290.
The overall change is 110 dollars.
Cherry tomatoes are sold at the store. a 12 pack costs $3, a 16 pack costs $4, and a 24 pack costs $6. write an equation to model the price based on the size of the pack. let t be the number of tomatoes. let p be the price per pack
The equation to model the price based on the size of the pack can be written as p = 0.25t, where p is the price and t is the size of the pack.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that the cost of cherry tomatoes as,
Cost of 12 pack = $3
Cost of 16 pack = $4
Cost of 24 pack = $6
......
Cost of 1 pack = 3/12 = 4/16 = 6/24 = $0.25
Let t be the size of the pack and p be the price.
p = 0.25t
Hence the equation representing the price is p = 0.25t.
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what is 8 x 3 7/9
cuz i dont know
Step-by-step explanation:
hdhfjojfbnx zvcmbbczABMM CXFHEWT
what is a requirement for two sample means in order to conduct a hypothesis test for the difference between the two means? select all that apply!
The two samples must be independent, which means that the results of one sample should not influence the results of the other.
To lead a hypothesis test for the contrast between two examples implies, certain prerequisites should be met. The examples, right off the bat, should be free, implying that the two examples ought to be arbitrarily chosen and the people in a single example ought not to be available in another example.
Furthermore, the examples should be typically dispersed, which can be tried by plotting the information in a histogram.Also, the two examples ought to have equivalent differences, which can be tried by utilizing Levene's test.At long last, the two example sizes ought to be adequately huge to have stable outcomes, generally no less than 30 perceptions.Learn more about hypothesis tests:
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jennifer has three more dimes than nickels and three times as many quarters as nickels. if she has $7.50, how many quarters does she have? www.wyzant
Jennifer has 48 nickels, which means she has 144 quarters.
Let's call the number of nickels Jennifer has "n".
Since Jennifer has three more dimes than nickels, she has n + 3 dimes.
And since she has three times as many quarters as nickels, she has 3n quarters.
We can start by figuring out the total value of the nickels and dimes in terms of cents:
n * 5 cents + (n + 3) * 10 cents = 750 cents
Expanding the right side of the equation and solving for n:
5n + 10n + 30 cents = 750 cents
15n + 30 cents = 750 cents
15n = 720 cents
n = 48
So Jennifer has 48 nickels, which means she has 3 * 48 = 144 quarters.
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What is seventy five divided by four
Answer:
18.75
Step-by-step explanation:
Order these numbers from least to greatest.
4 7/11, 37/8, 4.427, 4.42
The order of given numbers is 4.42<4.427<4.625<4.64.
How to compare to decimals?Comparing decimals involves starting with the digits having the highest place value, just like when comparing other whole numbers. We begin the comparison by putting the provided decimal numbers in a place value table. We move on to the digits in the next place to the right if the digits on the biggest place value match. Up till the digits that are different are reached, we continue comparing digits.
The given numbers are [tex]4\frac{7}{11}[/tex] =4.64, 37/8 =4.625, 4.427, 4.42
From least to greatest is
4.42<4.427<4.625<4.64
Therefore, the order of numbers is 4.42<4.427<4.625<4.64.
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Use the Distributive Property to rewrite each expression in its equivalent form. 5x (2x + 6)
Answer:
10x+30x
Step-by-step Explanation:
Multiply 5x by 2x, which gives you 10xMultiply 5x by 6, which gives you 30xSolved! 10x+30xHelp, will rate brainlist if correct!!
y = x4 - 5x2
A.) What is the y-intercept of this graph? How do you know? (1 point)
B.) What are the x-intercepts/roots/zeros? Show your work. (4 points)
C.) Describe the end behavior of this function (2 points)
D.) Draw a graph of this function, carefully labeling your intercepts and showing the end behavior.
A. The y-intercept is at the point (0, 0).
B. The zeros are x = 0 or x = ±√5
C.
How to solve the expressionA) The y-intercept of this graph is the point where x = 0.
When x = 0, the value of y
= 0^4 - 5*0^2
= 0.
Therefore, the y-intercept is at the point (0, 0).
B) The x-intercepts/roots of the function are the values of x that make y = 0.
To find these values, we need to set y = 0 and solve for x:
x⁴ - 5x² = 0
x⁴ = 5x²
x² = x⁴/5
x = ±√(x⁴/5)
We can simplify this expression by factoring x² out of both sides:
x²(x² - 5) = 0
x² = 0 or x² - 5 = 0
x = 0 or x = ±√5
hence the x-intercepts are at x = 0 and x = ±√5.
C) The end behavior of this function refers to how the graph of the function approaches the x-axis as x approaches positive infinity and negative infinity.
x → ∞ f(x) → ∞
x → -∞ f(x) → -∞
D) The graph is attached
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One of the sides of a parallelogram has a length of 5 in. Can the diagonals
have the following lengths?
4 in. and 3 in.
with explanation, please !
Answer:
No, the diagonals of a parallelogram cannot have lengths of 4 in. and 3 in. The diagonals of a parallelogram bisect each other and have equal length. Therefore, if one diagonal has a length of 4 in., the other diagonal must also have a length of 4 in. and cannot have a length of 3 in.
Step-by-step explanation:
Yes, I know you pretty much
help asap will give briniest
Match the correlation coefficient with the correct association:
Question 8 options:
0.52
-0.86
-0.01
0.93
-0.66
1.
Strong association
2.
Weak association
3.
Moderate association
Answer:
strong:0.93
moderate:0.52
weak:-0.01
Step-by-step explanation:
a certain forest coavers an area of 3900 km^2 suppose that each year this area decreases by 3.25% what will be the aera after 6 years
The solution is, the area after 6 years is 3198.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
Rate of reduction = 100 - 3.25 = 96.75%
After 6 years, the reduction in trees =0 .9675^6
=0.820
Area after 6 years = 3900 x 0.820
= 3198
Hence, The solution is, the area after 6 years is 3198.
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There were 50% more apples picked this year than last. If there were 230 pounds of apples picked this year, how many pounds were picked last year?
Answer:
115 apples were picked last year
Step-by-step explanation
It says there are 50% more apples picked this year than last year. So, we divide 230 by 2 because 50% is half of 100%. 230÷2 = 115
115 apples
pls help plssssss
it would really help
The measure of angle Y is given as follows
m < XYZ = 72.9º.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For angle Y, we have that:
The adjacent side length is of 4 cm.The opposite side length is of 13 cm.Applying the tangent function, the measure is obtained as follows:
tan(Y) = 13/4
Y = arctan(13/4)
Y = 72.9º.
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45 points!
The graph of $y = 2x^2 - 8x + 7$ is identical to the graph of $y = a(x-h)^2 + k$ for some real numbers $a, h, k$.
What is the value of $k$?
The value of k is 3.
What are Quadratic Functions?Quadratic functions are polynomial functions of second degree.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a quadratic function,
y = 2x² - 8x + 7
This function is identical to some function y = a(x - h)² + k
We have to write the given quadratic function in the form y = a(x - h)² + k.
2x² - 8x + 7 = (2x² - 8x) + 7
= 2(x² - 4x) + 7
= 2(x² - 4x + 4) + 7 - 4
We have the algebraic identity, (a - b)² = a² - 2ab + b²
= 2 (x - 2)² + 3
a = 2, h = 2 and k = 3
Hence the value of k is equal to 3.
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the distance between the two curves changes for 0
The distance between the two curves, with respect to the curves changing can be calculated as follows:
3-(3-2sin(2θ))
[tex] \frac{dx}{dθ} 2 \sin(20) [/tex]
2cos(20)
4cos(20)
[tex]4 \cos(2 \frac{\pi}{3} ) = - 2[/tex]
The Fréchet distance is a mathematical metric for comparing the similarity of curves that takes into account the position and arrangement of curve points. Maurice Fréchet is honored by having his name used. The pairs of points that make up the Fréchet distance sweep continuously along their respective curves, so the Fréchet metric takes the flow of the two curves into account. As a result, the Hausdorff distance and other similarity measures for arbitrary point sets are inferior to the Fréchet distance for curves. Two curves might have a small Hausdorff distance but a large Fréchet distance.
Note that the full question is:
The distance between the two curves changes for 0<θ<π/2. Find the rate at which the distance between the two curves is changing with respect to θ when θ = π/3.
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a boat is traveling east across a river that is 112 meters wide at 8 meters per second. If the river has a northeast current of 5 meters per second, what is the resultant speed of the motorboat rounded to the nearest tenth?
Resultant speed of the motorboat is 9.4 m/s.
What is Pythagorean Theorem?Pythagorean theorem states that the squared value of longest side in an right angle triangle will be equal to the addition of the squared value of two smaller sides. Thus, the resultant speed of the boat is 9.4 m/s
This is the concept of application of the pythagorean theorem.
The boat is traveling in the east direction at a speed of 8 m/s but the river has a northward current of 5 m/s. We know than both the directions (East and North) are perpendicular to each other. The bend tending toward east but the river slows down the speed and makes the boat tending toward north-east.
Thus, by applying Pythagorean theorem, the resultant speed can be calculated as:
c² = a² + b²
c² = 8² + 5²
c² = 64 + 25
c² = 89
c = [tex]\sqrt{89}[/tex]
c = 9.4 m/s
Hence, the resultant speed of boat is 9.4 m/s.
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Answer:
9.4
Step-by-step explanation:
just took the quiz
Shanti packs 4689 jelly beans equally into 15 bags and there are some jelly beans left. How many jelly beans are there left?
Answer:
hi !!
Step-by-step explanation:
you have to do an Euclidean division :
4689/15 = 312
the quotient is 312 so there will be 312 jelly beans per bags . The rest is 9 so there are 9 jelly beans left
mrs peery is sharing 18 biscutes between gemma and zak in the ratio 1:2
Answer:
gemma gets 6 and zac gets 12
Step-by-step explanation:
zac gets double the about
a sample of 4 different calculators is randomly selected from a group containing 47 that are defective and 29 that have no defects. what is the probability that all four of the calculators selected are defective? round to four decimal places.
The probability of selecting 4 defective calculators is 0.0009.
The probability of selecting 4 defective calculators out of a group containing 47 defective and 29 non-defective calculators can be calculated using the formula for a combination. The formula is n!/r!(n-r)! where n is the total number of items and r is the number of items being selected. In this case, n is 76 (47 defective + 29 non-defective) and r is 4. Therefore, the probability of selecting 4 defective calculators is 0.0009. To round this answer to four decimal places, the answer is 0.0009.
To calculate this answer, the first step is to calculate the total number of combinations that can be made using 4 items out of 76 items. This is calculated using the formula n!/r!(n-r)!. The numerator, n!, is equal to 76! which is equal to 5.43e+102. The denominator, r!(n-r)!, is equal to 4!(76-4)! which is equal to 5.90e+09. By dividing the numerator by the denominator, the probability of selecting 4 defective calculators is 0.0009. To round this answer to four decimal places, the answer is 0.0009.
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how to find measurements
Answer:
-50 (Hopefully I gave the right answer. If I didn't, I'm sorry)
step-by-step explanation:
ABD= 2x-3 and DBE= 3x+8
2x-3=3x+8
Add 3 to both sides.
2x=3x+11
Now subtract 3x from both sides
-1x=11
Now divide both sides by -1
x=-11
Plug -11 in for x
2(-11)-3 and 3(-11)+8
-22-3 and -33+8
-25 and -25
-25+-25=-50
2.01 Quiz Polygons and Symmetry 1
What is the value of x?
X= ___
Answer:
Step-by-step explanation:
112+120+133+128+100+x=720
593+x=720
x=720-593
x=127
Naomi had a blast at the water park, even though she was 3 inches too short to ride the biggest slide, The Water Slinger. Naomi is 49 inches tall.
Let h represent the minimum height for The Water Slinger. Which equation models the problem?
Which inequality is a true statement?
Select each correct answer.
Responses
−3≤−1
negative 3 less than or equal to negative 1
−3<−1
negative 3 less than negative 1
−3=−1
negative 3 equals negative 1
−3≥−1
negative 3 greater than or equal to negative 1
−3>−1
The following inequalities are correct ,
1. −3 ≤ −1
2. −3<−1
So, Option A & B is correct
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
The inequalities,
Statement 1: negative 3 less than or equal to negative 1
−3 ≤ −1
It is correct
Statement 2: negative 3 less than or equal to negative 1
−3 < −1
It is also correct
Statement 3: negative 3 equals negative 1
−3 = −1
It is Incorrect because -3 is less than -1
Statement 4: negative 3 greater than or equal to negative
−3 ≥ −1
It is also Incorrect because -3 is less than -1
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8 grades, help please!!!
Answer:
Step-by-step explanation:
no it isnt
Directions: Based on the information given in the following problem, compute the gross pay.
Regular salary: $1,100 per month
Overtime rate: $10.38 per hour (20 hours overtime to be paid)
Round your answers to two decimal places.
gross pay: $
The gross pay for the given service is $1307.6.
What is gross pay?Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages.
Given that, the regular salary of some service is $1100, we need to calculate the gross payment with over time rate, which is $10.38 per hour (20 hours overtime to be paid)
Therefore,
To find, gross payment, we will multiply by 10.38 by 20, and add to regular salary,
Gross payment = 10.38 × 20 = 207.6 + 1100
= 1307.6
Hence, the gross pay is $1307.6
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A line has a slope of – 9 and includes the points ( – 9,1) and ( – 10,q). What is the value of q?
To find the value of q, we can use the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) is a second point on the line.
In this case, we have the slope of the line as -9 and the point ( -9, 1), so we can plug in the values:
y - 1 = -9 (x - (-9))
Expanding and solving for y, we get:
y = -9x + 90
Next, we want to find the value of y when x = -10. Substituting this value into the equation:
q = -9(-10) + 90
Solving for q:
q = -90 + 90 = 0
So, the value of q is 0.