If the coefficient of kinetic friction between tires and dry pavement is 0.89, what is the shortest distance in which you can stop an automobile by locking the brakes when traveling at 24.0 m/s ?

Answer:

\(40^{\circ},\:40^{\circ},\: 100^{\circ}\)

Step-by-step explanation:

The interior angles of any triangle always add up to \(180^{\circ}\). In an isosceles triangle, (at least) two sides are congruent and therefore their base angles are also congruent. We can then form the following equation:

\(2x+2x+5x=180\), where \(x\) is some constant.

Solving, we get:

\(9x=180,\\x=20\)

Therefore, plugging our constant back in, our angles are:

\(2(20),\: 2(20), \: 5(20), \\\fbox{$40^{\circ},\:40^{\circ},\: 100^{\circ}$}\).

Note this is only one group of possible angles. We could've also set the angle represented by \(5x\) to be the pair of angles that are congruent, and depending on your definition of isosceles, each angle measure could be \(60^{\circ}\) (equilateral).

Answer:

100, 40, 40

Step-by-step explanation:

First, do 2x+2x+5x because an isosceles triangle has two equal angles. We know that a triangle's total angle is 180 degrees so we do 180/9=20 x=20. Then multiply 2 by 20 to get 40. Then multiply 5 by 20 to get 100. So you get 40 40 100.

Answer:

The salesman sold 120 kg in the morning and 2 times 120 = 2402⋅120=240 kg in the afternoon.

By collecting a random sample of countries in 2010 and using a one-sided t-test for the difference in means, we can determine if there is enough evidence to reject the null hypothesis and conclude that there is a difference in mean CO₂ emissions between the two years.

To formulate the hypotheses, we need to state our null hypothesis and alternative hypothesis. The null hypothesis (H0) is the statement that there is no difference between the mean CO₂ emissions in 2004 and 2010. The alternative hypothesis (Ha) is the statement that there is a difference between the mean CO₂ emissions in 2004 and 2010.

In symbols, we can write the hypotheses as:

H₀: μ₂₀₁₀ - μ₂₀₀₄ = 0

Hₐ: μ₂₀₁₀ - μ₂₀₀₄ < 0

where μ₂₀₁₀ is the true mean CO₂ emissions per capita in 2010, μ₂₀₀⁴ is the true mean CO₂ emissions per capita in 2004, and < 0 indicates that we are testing for a decrease in mean CO₂ emissions.

To test these hypotheses, we can use a one-sided t-test for the difference in means. We would collect a random sample of countries in 2010 and calculate the mean CO₂ emissions per capita for that sample.

We would then use this sample mean and the sample standard deviation to calculate a t-statistic, which measures how far the sample mean is from the null hypothesis mean of 0.

If the t-statistic is large enough, we can reject the null hypothesis and conclude that there is enough evidence to show that the mean CO₂ emissions in 2010 are lower than in 2004.

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Answer:

785

Step-by-step explanation:

Plug Each of the Numbers given in for their associated variable

(25-10)^2 + 10(56)

(15)^2 + 560

225 + 560

so 785

The statement that is false is: m∠D = 100

As  ΔABC ≅ ΔDEF then

∠B ≅ ∠F (given that),

and m∠F = 23,

So, m∠D= m <F is also 23.

Therefore, the statement m∠D = 100 cannot be possible.

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Answer:

-45, -2.5, -1.1, 0.8, 95

Answer:

your answer would be -45, -2.5, -1.1, 0.8, 95

Step-by-step explanation:

if you put the listed numbers out on a number line you would start with the negative numbers on the left side going up to the positive numbers on the right side. -45 is the smallest number in this sequence so it will be the first number. then if you go further right on the number line you'll hit -2.5, then -1.1, then 0.8, then 95. these numbers are large so a number line wouldn't be logical but it always helps to visualize it. hope this helps!

Answer:

1) yes  2) no  3) yes

Step-by-step explanation:

The lengths of the two shorter sides must be greater than the length of the longest side.

1) 8 + 9 > 10    yes

2) 1 + 1 = 2      no

3)  6 + 8 > 9    yes

The lengths which can be side of triangle are:

Apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

1. 8, 9, 10:

The sum of the lengths of the two smaller sides is 8 + 9 = 17 > 10

Therefore, these numbers can be the lengths of the sides of a triangle.

2. 1, 1, 2:

The sum of the lengths of the two smaller sides is 1 + 1 = 2.

No, 2 is equal to the length of the longest side.

So these numbers cannot be the lengths of the sides of a triangle.

3. 6, 9, 8:

The sum of the lengths of the two smaller sides is 6 + 8 = 14 > 10

Therefore, these numbers can be the lengths of the sides of a triangle.

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Answer:

The answer is 2 different angles, 53° and 127°.

Explanation:

As you subtract 180° from the given angle to find the other angle, you will get only 2 angles either 53° or 127°.

To determine the number of units the entrepreneur had to sell in order to turn an economic profit, we need to consider her expenses and the selling price of each unit.

The entrepreneur had a monthly job income of $6,000 but took a one-month unpaid leave. Her expenses included $2,500 in kiosk rent and the cost of purchasing water at $1.48 per gallon. The selling price per gallon was $2.22.

By calculating the difference between the selling price and the total expenses per gallon, we can determine the number of units she needed to sell to cover her expenses and start making a profit.

The entrepreneur's total expenses can be calculated by summing the kiosk rent and the cost of purchasing water:

Total expenses = Kiosk rent + (Cost per gallon * Number of gallons)

Total expenses = $2,500 + ($1.48 * Number of gallons)

To determine the number of units she needed to sell to cover her expenses and start making a profit, we need to find the breakeven point where her revenue equals her expenses:

Total revenue = Selling price per gallon * Number of gallons

Total revenue = $2.22 * Number of gallons

Setting the total revenue equal to the total expenses:

$2.22 * Number of gallons = $2,500 + ($1.48 * Number of gallons)

Simplifying the equation, we can solve for the number of gallons:

$0.74 * Number of gallons = $2,500

Number of gallons = $2,500 / $0.74

By calculating the value, we can find the number of units (gallons) she needed to sell in order to turn an economic profit.

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Answer:

130=monthly charge

119=one time installation fee

Step-by-step explanation:

119 is the y-intercept and in problems like these, it is always the one time fee. 130 is the monthly payment because it has an x, which could account for the number of months. For example , say six months passed, you could multiply 130 * 6 to get the monthly fee for six months. I hope that makes sense!

9514 1404 393

Answer:

  use the transitive property and the congruence of vertical angles

Step-by-step explanation:

First of all, look at the figure and the given information, and see how that relates to the question being asked.

Here, you're given several angles between the lines of interest, all of which are congruent, and you're asked to show the lines are parallel. Two of the given angles (1 and 4) are "alternate interior angles", so the theorem relating those to parallel lines is useful.

Statement . . . . Reason

1. ∠1 ≅ ∠2, ∠3 ≅ ∠4 . . . . 1. Given

2. ∠2 ≅ ∠3 . . . . 2. Vertical angles are congruent

3. ∠1 ≅ ∠3 . . . . 3. transitive property of congruence*

4. ∠1 ≅ ∠4 . . . . 4. transitive property of congruence

5. k ║ l . . . . 5. Converse of alternate interior angles theorem**

_____

* The transitive property tells you if a ≅ b and b ≅ c, then a ≅ c.

** The alternate interior angles theorem says the alternate interior angles at a transversal crossing parallel lines are congruent. The converse says if those angles are congruent, then the lines are parallel.

The value of n that makes a system of equations with a solution that has a y-value of 2 is n = 5

A system of equations is a pair of equation that contain two unknowns.

Given the system of equations

5x+6y= 32  (1)

2x + ny = 18  (2)

We desire the value of n where the value of y is 2

First, we make x subject of the formula from equation (1)

So, x = (32 - 6y)/5

Substituting x into equation (2), we have that

2x + ny = 18  (2)

2(32 - 6y)/5 + ny = 18  (2)

(64 - 12y)/5 + ny = 18

Multiplying through by 5, we have

64 - 12y + 5ny = 90

We now make n subject of the formula.

64 - 12y + 5ny = 90

- 12y + 5ny = 90 - 64

(- 12 + 5n)y = 26

-12 + 5n = 26/y

5n = 26/y + 12

n = 26/5y + 12/5

Since y = 2, substituting y into the equation, we have

n = 26/5(2) + 12/5

n = 26/10 + 12/5

n = (26 + 24)/10

n = 50/10

n = 5

So, the value of n = 5

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The sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

A random sample is drawn from a population with mean μ=73 and standard deviation σ=6.1. To determine if the sampling distribution of the sample mean with n=18 and n=46 is normally distributed, we need to calculate the standard error for each sample size.

For n=18:
The standard error (SE) is calculated using the formula:

     SE = σ / √n
SE = 6.1 / √18

          ≈ 1.441 (rounded to 3 decimal places)

For n=46:
SE = 6.1 / √46 ≈ 0.901 (rounded to 3 decimal places)

To determine if the sampling distribution of the sample mean is normally distributed, we need to consider the Central Limit Theorem (CLT). According to the CLT, when the sample size is sufficiently large (typically n > 30), the sampling distribution of the sample mean tends to be approximately normally distributed, regardless of the shape of the population distribution.

Since both n=18 and n=46 are larger than 30, we can conclude that the sampling distribution of the sample mean with these sample sizes is approximately normally distributed.

Therefore, the sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

The sampling distribution of the sample mean with n=18 and n=46 is normally distributed.

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The four criteria that can be used to prove triangles are congruent and can be used to prove the triangles are congruent.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. These triangles can be moved around, rotated, flipped, and turned to have a same appearance. They match up with one another when moved.

The four criteria that can be used to prove triangles are congruent are SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and SSS (Side-Side-Side). Additionally, CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can be used to prove the triangles are congruent.

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(b+1)/2b

quotient = divided by

we're dividing a number that is 1 more than b (b + 1), with a number twice as large as b (2b).

Answer:

x = -6

y = 2

Step-by-step explanation:

y = (1/3)x + 4

x = (-3)y

We replace the x in the first equation with -3y, since the second equation states that x=-3y.

y=(1/3)(-3y) + 4

y= -y+4

y+y = 4

2y = 4

y=2

then we substitute the y in the second equation by 2.

x=-6

Answer: Addition I think

Answer:

2,172

Step-by-step explanation:

not too sure sorry

Answer:

184

Step-by-step explanation:

y + j + p + a = 1026

y - 60 = j/4 -------> y =  (j/4) + 60

p + 150 = j/2 -----> p = (j/2) - 150

2a = j -------> a = j/2

y = ?

y + p + j + a = 1026

(j/4) + 60 + (j/2) - 150 + j + (j/2) = 1026

(j/4) + j + j - 90 = 1026

(j/4) + 2j = 1116

9j/4 = 1116

9j = 4464

j = 496

y = (496/4) + 60 = 184

The value of the ratio will be a / b = 2 / 3.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

In the given figure there are two lines intersecting the three parallel lines and making the segments a and b. The values of the segment on both sides will be similar.

The value of the ratio will be calculated as,

a / b = 4 / 6

a / b = 2 / 3

Therefore, the ratio a / b is 2 / 3.

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Answer: five groups of seven. 5 times 7

five split into seven groups. 5 divided by 7

Five more than seven. 7 plus 5

Five less than seven. 7 subtracted by 5

Step-by-step explanation:

five groups is multiplying

Five slit is dividing

Five more than is adding

Five less than is subtracting

The specific heat shows that Substance Y has more atoms per gram than substance W.

Specific heat:

Specific heat is a property of a substance that describes how much heat energy is required to raise the temperature of a certain amount of that substance by one degree. It is typically measured in units of joules per gram per degree Celsius (J/g°C).

Different substances have different specific heats. For example, water has a relatively high specific heat of 4.18 J/g°C, which means that it takes a lot of heat energy to raise the temperature of water by one degree. This is why water is often used as a coolant or in air conditioning systems, as it can absorb a large amount of heat energy without experiencing a significant temperature change.

Therefore, the specific heat shows that Substance Y has more atoms per gram than substance W.

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The probability that randomly selected mechanical component weighs: more than 11.5 lbf is 0.0099, less than 8.7 lbf is 0.3208,  less than 5.0 lbf is 0.0228, between 6.2 lbf and 7.0 lbf is 0.1314, between 10.3 lbf and 14.0 lbf is 0.0436, between 6.8 lbf and 8.9 lbf is 0.3464.

We can use the standard normal distribution and z-scores to answer these questions:

P(X > 11.5) = P(Z > (11.5 - 8) / 1.5) = P(Z > 2.33) = 0.0099

Therefore, the probability that a randomly selected mechanical component weighs more than 11.5 lbf is 0.0099, or about 1%.

P(X < 8.7) = P(Z < (8.7 - 8) / 1.5) = P(Z < 0.47) = 0.3208

Therefore, the probability that a randomly selected mechanical component weighs less than 8.7 lbf is 0.3208, or about 32%.

P(X < 5.0) = P(Z < (5 - 8) / 1.5) = P(Z < -2) = 0.0228

Therefore, the probability that a randomly selected mechanical component weighs less than 5.0 lbf is 0.0228, or about 2%.

P(6.2 < X < 7.0) = P((6.2 - 8) / 1.5 < Z < (7 - 8) / 1.5) = P(-1.2 < Z < -0.67) = 0.1314

Therefore, the probability that a randomly selected mechanical component weighs between 6.2 lbf and 7.0 lbf is 0.1314, or about 13%.

P(10.3 < X < 14.0) = P((10.3 - 8) / 1.5 < Z < (14 - 8) / 1.5) = P(1.53 < Z < 2.67) = 0.0436

Therefore, the probability that a randomly selected mechanical component weighs between 10.3 lbf and 14.0 lbf is 0.0436, or about 4%.

P(6.8 < X < 8.9) = P((6.8 - 8) / 1.5 < Z < (8.9 - 8) / 1.5) = P(-0.47 < Z < 0.60) = 0.3464

Therefore, the probability that a randomly selected mechanical component weighs between 6.8 lbf and 8.9 lbf is 0.3464, or about 35%.

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____The given question is incomplete, the complete question is given below:

Suppose that the weight of a mechanical component is normally distributed with mean p = 8.0 Ibf and standard deviation = 1.5 lbf. Answer the following questions: 1. If you randomly select a mechanical component, what is the probability that it weighs more than 11.5 lbf? 2. If you randomly select a mechanical component, what is the probability that it weighs less than 8.7 lbf? 3. If you randomly select a mechanical component, what is the probability that it weighs less than 5.0 lbf? 5. If you randomly select a mechanical component, what is the probability that it weighs between 6.2 lbf and 7.0 lbf? 6. If you randomly select a mechanical component, what is the probability that it weighs between 10.3 lbf and 14.0 lbf? 7. If you randomly select a mechanical component, what is the probability that it weighs between 6.8 lbf and 8.9 lbf?

Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants.

The sampling method described in the scenario is called systematic sampling.

Systematic sampling involves selecting every nth element from a population after randomly selecting a starting point. In this case, the store manager randomly chooses a shopper entering the store as the starting point and then proceeds to interview every 20th person after that initial selection.

Systematic sampling offers several advantages. It is relatively easy to implement and eliminates bias that may arise from the subjective selection of participants. By ensuring a regular interval between selections, systematic sampling provides a representative sample from the population.

However, it's important to note that systematic sampling can introduce a form of bias if there is any periodicity or pattern in the population. For example, if the store experiences a peak in customer traffic during specific time periods, the systematic sampling method might overrepresent or underrepresent certain groups of shoppers.

To minimize this potential bias, the store manager could randomly select the starting point for the systematic sampling at different times of the day or on different days of the week. This would help ensure a more representative sample and reduce the impact of any inherent patterns or periodicities in customer behavior.

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Answer:

15 - 3x

Step-by-step explanation:

3 X 5 = 15

3 X -x = -3x

answer is 15-3x

Answer:

3x - 15

Step-by-step explanation:

3(5 + -x) is equivalent to 3(5 - x)

3(5 + -x)

3(5) + 3(-x)

15 + -3x

15 - 3x

3x - 15

Hope this helps!

Answer:

226.19

Step-by-step explanation:

Since there are two blue blocks and four total blocks, the probability of pulling a blue block is 2/4 or 1/2. Since you replace the block each time, the probability of pulling a blue block remains constant for each trial.

Using the formula for the expected value of a binomial distribution, where n is the number of trials and p is the probability of success:

Expected value = n * p

Expected number of blue blocks pulled in 12 trials = 12 * (1/2) = 6

Therefore, you would expect to pull 6 blue blocks if you try 12 times, assuming the blocks are replaced each time.

Answer: Check out the graph below

The graph is a straight line through the points (0,6) and (1,8)

====================================

Explanation:

Plug in x = 0 to find that...

y = 2x+6

y = 2(0)+6

y = 0 + 6

y = 6

The point (0,6) is on the line

---------

Repeat for x = 1

y = 2x+6

y = 2(1)+6

y = 2 + 6

y = 8

The point (1,8) is also on the line

---------

Now plot the two points together on the same xy grid.

Draw a straight line through the two points. Stretch the line as far as you can in either direction. See below. I used GeoGebra to make the graph. It's a free graphing app.

Desmos is another useful free graphing tool. There are many options if you don't have a graphing calculator.

Answer:

40(1.25-t)

Step-by-step explanation:

There are 3 components to consider; time, speed and distance

Time and Speed are given.

The distance has to be calculated.

Speed to work = 55 miles per hour

Time to work = 1.25-T

Speed to home = 40 miles per hour

Time to home = 1.25-t

Total Time = T + t = 1.25

Distance for trip to home

Speed = Distance/Time

40 = Total Distance/1.25-t

Total Distance = 40(1.25-t)

Therefore, 40(1.25-t) is the correct answer.

!!

Answer:

1). x = 0

2). Option 3

Step-by-step explanation:

1). If the two triangles are similar,

   Their corresponding sides will be proportional.

   \(\frac{5x+2}{6}=\frac{x+4}{12}\)

   12(5x + 2) = 6(x + 4)

   60x + 24 = 6x + 24

   60x - 6x = 24 - 24

   54x = 0

   x = 0

2). Option 1

   2(x - 6) + 3 - 5x = -3x - 9

   2x - 12 + 3 - 5x = -3x - 9

   -3x - 9 = -3x - 9

   True.

   Option 2

   4(2x - 5) + 10 - 5x = 3x - 10

   8x - 20 + 10 - 5x = 3x - 10

   3x - 10 = 3x - 10

   True

   Option 3  

   5x + 4 = 3x + 4

    False

    Option 4

    8x + 3 - 2 = 8x + 1

    8x + 1 = 8x + 1

    True.

Therefore, option 3 is False.