Manufacturers of tires report that tires should be able to last an average of 50,000 miles. A new tire company produces a different type of tread and tests 100 randomly selected tires. This sample of 100 tires lasted an average of 52,000 miles. Assuming the new type of tread does not improve the mileage of the tire, 200 sample means were simulated and displayed on the dotplot.



Using the dotplot and the sample mean mileage, is there convincing evidence that the new type of tread improves the mileage?

Yes, because a mean mileage of 52,000 or more occurred only 7 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
Yes, because a mean mileage of 52,000 or less occurred 193 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 52,000 or less occurred 193 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 52,000 or more occurred 7 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.

Answer:

x=3

Step-by-step explanation:

9x-6=3x+12

6x=18 |:6

x=3

Answer:

y= csc(x)+1

Step-by-step explanation:

A P E X

cosec(X) + 1  has the range (-infinity,-2]U[0,infinity)

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

As, the given range (-infinity,-2]U[0,infinity) well satisfied the cosec(X) + 1

Generally, Range of Cosec x is, (-∞,-1] ∪ [1,∞).

So,

Range of Cosec (x) +1 will be ,

= (-∞,-1+1] ∪ [1+1,∞).

= (-∞, 0] ∪ [2,∞)

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The method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

In order to enhance strong number sense in children, there are various methods that can be used.

In the given scenario, Mme Potatana asked the children to count as a whole class from 1 to 20 while Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count.

Both methods have their own benefits, but the method of counting seeds by touching each can be more effective in enhancing strong number sense in children.

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children because it allows them to experience each number physically.

This helps them in developing a strong sense of numbers. By touching each seed as they count, children can feel and see each number, which helps them in understanding numbers better. Additionally, it helps in developing the concept of one-to-one correspondence and counting by rote.

Here are some appropriate examples for enhancing strong number sense using the method of counting seeds by touching each:

1. Use counters: Provide children with counters such as small objects, blocks, or toys. Ask them to count the number of counters by touching each as they count.

2. Counting on fingers: Encourage children to count on their fingers. This helps them in developing a strong sense of numbers and helps them in understanding the concept of one-to-one correspondence.

3. Counting objects in a pile: Ask children to count objects in a pile by touching each as they count. This helps in developing the concept of counting by rote and helps in enhancing strong number sense.

Overall, the method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

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The two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

The unit circle is rotationally symmetric, meaning that any angle of rotation on the unit circle will take a point to another point on the unit circle with the same distance from the origin. This means that if we rotate point A by 7π/6 radians, we can also rotate it by 19π/6 or 31π/6 radians and end up at the same point B.

The point A has polar coordinates (1, 0). This means that it is located at a distance of 1 unit from the origin and has an angle of 0 radians with the positive x-axis.

The point B has polar coordinates (√3/2, 1/2). This means that it is located at a distance of √3/2 units from the origin and has an angle of 7π/6 radians with the positive x-axis.

If we rotate point A by 19π/6 radians, we get a point with polar coordinates (√3/2, -1/2). This point is located at the same distance from the origin as point B and has the same angle with the positive x-axis.

Therefore, the two other positive angles of rotation that take A to B are 19π/6 and 31π/6.

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The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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(a) √2 · √8. The simplified surd expression is 4.

(b) √80. The simplified surd expression is  4√5.

(c) √5/√20. The simplified surd expression is  1/2.

(d) √20. The simplified surd expression is  2√5.

The given surd expression is simplified as follows;

(a) √2 · √8

we can simplify it as;

√2 · √8 = √(2 x 8) = √16 = 4

(b) √80

we can simplify it as;

√80 = √ (16 x 5) = √16  x √5 = 4√5

(c) √5/√20

we can simplify it as;

√5/√20  x  √20 / √20

= (√5  x √20 ) /(20)

= √100 / 20

= 10/20

= 1/2

(d) √20

we can simplify it as;

√20 = √4  x √5 = 2√5

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Step-by-step explanation:

I think the figure is cuboid

Volume of cuboid = l × b × h

Volume = 8.7 × 5.6 × 3.4

Volume = 165.648 cm³

Answer:

10 square units

Step-by-step explanation:

Answer:

one forty fifth times five equals one ninth

Step-by-step explanation:

In division, the number being divided is the dividend or numerator, the denominator is the number we use to do the division while the result is the quotient and there may be a reminder.

For example, if

a/b = c

then

a = b * c

hence

1/9  ÷ 5

= 1/9 * 1/5

= 1/45

This means that

1/45 * 5 = 1/9

Hence the related multiplication equation related to the division equation one ninth ÷ 5 is one forty fifth times five equals one ninth

Division expression are the expression in which one number is divided by other. Multiplication equation is related to the division equation one ninth divided by five is one forty fifth times five equals one ninth. Thus the option 2 is the correct option.

The given division equation is the fraction 1/9 divided by the number 5. That is,

\(\dfrac{\dfrac{1}{9} }{5} =\dfrac{1}{45} \)

Division expression are the expression in which one number is divided by other

1) Five times one twenty fifth equals one ninth-This can be written as,

\(5\times \dfrac{1}{25} =\dfrac{5}{25} \)

\(5\times \dfrac{1}{25} =\dfrac{1}{5} \)

Which is not equal to the the given division expression.

2) One forty fifth times five equals one ninth-This can be written as,

\(\dfrac{1}{45}\times5 =\dfrac{1}{9} \)

This is equal to the the given division expression.

3) One forty fifth times one fifth equals one ninth-This can be written as,

\( \dfrac{1}{45}\times\dfrac{1}{5} =\dfrac{1}{225} \)

Which is not equal to the the given division expression.

4) Five times one fifteenth equals one ninth-This can be written as,

\(5\times \dfrac{1}{15} =\dfrac{1}{3} \)

Which is not equal to the the given division expression.

Hence multiplication equation is related to the division equation one ninth divided by five is one forty fifth times five equals one ninth. Thus the option 2 is the correct option.

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Explanation:

This problem is a simple percent chage problem. The absoluge change in price was $12−$8=$4. Relative to the original price, it was 412, which is 0.3333 or 33.33%.

The amount that hw must invest to achieve the goal when it will be compounded annualy is $68750

Given Information:

Principal Amount (P) = to be calculated

Rate of Interest (r) = 8 %

Time Period (t) = 6

Amount Received (A) = $110000

Number of times the interest is compounded quarterly (n) = 4

The Formula for the amount received when the principal (P) is compounded is given by,

\(A = P( 1 + \frac{r}{100n} )^{nt}\)

Now, putting the values, we get:

\(110000 =P( 1 + \frac{8}{100*4} )^{4*6}\)

P = $68750

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Answer:

153.86

Step-by-step explanation:

formula - A = π × r2

3.14 x 7^2

= 153.86

Answer: 106.76 Millimeters

Step-by-step explanation:

The radius is 17 millimeters. Replace r by 17 in the formula.

C = 2​r

≈2 x 3.14 x 17

≈106.76

The circumference is about 106.76 millimeters.

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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The answer to question 15 is, an equivalent exposure for 1/125 sec. at f/16 may be 1/60 sec. at f/22. Option A is the correct answer.

In photography, equivalent exposure also means exposure compensation and it means change in the combination of the speed of shutter and that of aperture that produces the same exposure value.

To find an equivalent exposure for 1/125 sec. at f/16,

Adjust either the shutter speed or aperture using exposure triangle but ensure that exposure value is not changed.

If ISO sensitivity is fixed,  double the shutter speed to 1/60 sec. and halve the aperture to f/22. When you do this, you will realize that the exposure value is the same because the amount of light entering the camera is the same in both cases.

Thus, an equivalent exposure for 1/125 sec. at f/16 would be 1/60 sec. at f/22.

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Answer: its 3(3x^3-8)

Step-by-step explanation:

B.. No, because the lines are in the same plane.

Remember to take breaks. It can be really really skew but its going to be their tm. Maybe with more assignments but still. happy learning.

Ayo whats good

the answer's C Line p must be drawn so that it can lie in the same plane as line l.

explination

Answer:

-50

Step-by-step explanation:

25 * -2 = -50

Answer:

The change of temperature of the milk after 25 minutes will be -50 degrees because a rate of -2 per minute would be 25 times -2   Have a nice day! :)

Answer:

b. 1.69

Step-by-step explanation:

So to solve this problem we need to simply find the percentage increase from 11.8 to 12 =>

to solve this we would do 12 - 11.8 = 0.2 --> 0.2 is our "difference in the increase" -->

now we divide this by our amt. which is 11.8 --> 0.2/11.8 = approx. 0.0169

--> finally multiply that by 100 which is simply moving the decimal places 2 places right giving us the final answer of 1.69

Hope this helps!

Answer:

B. 1.69%

Step-by-step explanation:

If Ross calculated the countertop for a laundry room to be 12 square feet but turns out to be actually 11.8 square feet, we need to find out how much percentage error Ross has made!

In order to solve this question,

1) We need to create proportions:

Ross' calculations              x

______________ =   _________

   actual area                   100

x represents the percentage error.

100 is the total percentage.

2) Now we plug in the numbers:

We plug in 12 for Ross' calculations. We plug in 11.8 for the actual area. So, it will look like this:

   12                x

______ = _______

   11.8           100

3) Time for cross multiplication:

12 times 100 is 1,200

11.8 times x is 11.8x

So,

1,200 = 11.8x

4) Now we divide:

1,200 divided by 11.8 equals to 101.69 %

5) We are not done! We still have to subtract:

101.69

-100.00

_______

    1.69

Finished!!

Our answer is 1.69%, which is B.

Hope this was helpful !!!

The solution for the quadratic equation is -5/2, 2/3

Given,

The equation: 18a² - 30 = -33a

We have to solve this equation

We can convert this equation into a quadratic equation:

18a² + 33a - 30 = 0

Now lets solve this quadratic equation with quadratic formula:

Quadratic formula = \(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\)

Here,

a = 18, b = 33 and c = -30

Now we can solve:

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\)

= \(\frac{-33(+-)\sqrt{33^{2} -4(18)(-30)} }{2(18)}\)

=  \(\frac{-33(+-)\sqrt{1089-(-2160)} }{36}\)

= \(\frac{-33(+-)\sqrt{1089+2160} }{36}\)

= (- 33 ± √3249) / 36

= (- 33 ± 57) / 36

Solve for:

(- 33 + 57) / 36 = 24/36 = 2/3

Solve for:

(- 33 - 57) / 36 = - 90/36 = - 30/12 = -10/4 = -5/2

That is, the solution for the quadratic equation is -5/2, 2/3

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Answer:

2^5

Step-by-step explanation:

The base is the same

2^3 * 2^2

We are multiplying, so we can add the exponents

2^3 * 2^2 = 2^(3+2) = 2^5

Answer: \(2^{5}\)

Explanation: I have written this problem on the whiteboard.

For the problem on the board, since our two powers have like bases of 2, we can multiply them together by simply adding their exponents.

So 2³ · 2² is just \(2^{5}\).

A common mistake in this problem would

be for students to say that  2³ · 2² is \(4^{5}\).

It's important to understand however that when applying your

exponent rules, your base in this case 2 will not change.

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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The mean of a data-set is obtained as follows:

Mean = Sum of all observations/number of observations.

The mean of a data-set is given by the sum of all the observations in the data-set divided by the number of observations in the data-set, hence the equation is defined as follows:

Mean = Sum of all observations/number of observations.

According to the question on the commentary, the problem asks how to obtain the mean of a data-set.

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Answer:

9

Step-by-step explanation:

6.4(x)+2.8y=44.4

6.4(3)+2.8y=44.4

19.2+2.8y=44.4

2.8y=25.2

y=9

Answer:

y=9

Step-by-step explanation:

plus in the 3 into x and move the constant to the right. go ahead and calculate then divide by both sides. you should end up with y=9

Answer:

See below.

Step-by-step explanation:

The system of equations graphed are parallel lines, therefore have no solutions.

-hope it helps

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

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Answer:

192.50

Step-by-step explanation:

500-340.50 = 192.50

159.5

Step-by-step explanation:

take 340.50 away from 500, you will have 159.50 left

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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