Important Characteristics Quiz The probability of success in each of the 58 identical engine tests is p = 0.92. What is the mean of this binomial distribution?

Answer:

31.67

Step-by-step explanation:

12 2/3 X 2 1/2

we begin by converting this into improper fractions,

= 38/3 * 5/2

= 95/3

= 31.67

Answer:

a relationship ( model equation)

Step-by-step explanation:

the relationship specifies how the dependent variable relies on the independent variable.This helps in manipulating of the variable to see its effect/outcome.The relationship can be mathematical or logical ; it can also be a set of algorithm (program) which can be worked on using the independent variables as inputs. Usually the independent variables influence the dependent variables.

Answer:

Bb

Step-by-step explanation:

Final answer:

After applying a 20% discount and a 10% service fee to a pair of shoes originally priced at $75, Martinez ends up saving 12% from the original price.

Explanation:

Martinez is looking to calculate the final price of a pair of shoes after applying a 20% discount and a 10% service fee. She wants to know the overall percentage saved from the original price. First, let's calculate the discount: $75.00 × 0.20 = $15.00. Thus, the discounted price is $75.00 - $15.00 = $60.00. Next, we add the service fee on the discounted price: $60.00 × 0.10 = $6.00. Therefore, the total cost after the discount and service fee is $60.00 + $6.00 = $66.00.

To find the percent decrease from the original price, we can use the formula 'Percent Decrease = ((Original Price - Final Price) / Original Price) × 100%'. Substituting the respective values, we get: ((75 - 66) / 75) × 100% = 12%. Martinez saved 12% off the original price of the shoes after all the adjustments.

Answer:

A frequency distribution lists the number of occurrences of each category of​ data, while a relative frequency distribution lists the proportion of occurrences of each category of data.

Explanation:

A "frequency distribution" is one of the ways in organizing a data, either by listing the information, putting them in a table or showing them in a graph. The items in the list (distinct values) are then counted when it comes to the number of times they've occurred.

Thus, this explains the first answer, "number."

On the other hand, a "relative frequency distribution" refers to the proportion of the overall number of observations in a particular category.  You can get this by dividing each frequency with the total number of data in a sample.

Thus, this explains the second answer, "proportion."

A frequency distribution lists the number of occurrences for each category of data, whereas a relative frequency distribution provides the proportion of occurrences for each category in relation to the total number of data points. Histograms are a common tool to visualize these distributions, with the heights of bars representing either frequency or relative frequency.

The frequency distribution primarily deals with the number of occurrences of each category of data. For instance, in a class of 20 students, if the question is how many students scored in a particular range, the frequency distribution helps identify this - telling us how many students achieved each possible score.

In contrast, a relative frequency distribution showcases the proportion of the total number of data points that each category represents. So, instead of just telling you how many students achieved each score, it would express these amounts as a ratio or percent of the 20 total students, giving you a relative perspective of the categories.

An example of these principles might be visualized in a histogram: a type of graph that can express either frequency or relative frequency. The horizontal axis represents the categories of data (such as score ranges), while the vertical axis reflects frequency or relative frequency, displaying these values through the heights of bars along the graph.

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Final answer:

To calculate the total number of cherries that the bakery started with, multiply the number of pies by cherries per pie and then add the ones thrown away, resulting in 3026 cherries.

Explanation:

The question asks how many cherries the bakery started with before making the cherry pies. To find the answer, we multiply the number of cherry pies by the cherries used per pie and then add the number of cherries thrown away.

Multiply the number of pies (26) by the number of cherries used for each pie (115).

The result from step 1 gives the number of cherries used to make the pies.

Add the number of cherries thrown away (36) to the result from step 2.

The sum from step 3 is the total number of cherries the bakery started with.

Let's do the calculations:
26 pies × 115 cherries per pie = 2990 cherries
2990 cherries + 36 bad cherries = 3026 cherries

Therefore, the bakery started with 3026 cherries.

Answer:

The number of cookies in each package = 6

Step-by-step explanation:

Given:

Taylor purchased a pack of cookies.

Number of cookies Taylor gave to her friends = 5

Number of cookies she had left = 1

To find the number of cookies 'p' in each package.

Solution:

[tex]p\rightarrow[/tex] Number of cookies in each package.

If Taylor gave away 5 cookies to her friends, then the number of cookies left in the package can be represented as:

⇒ [tex]p-5[/tex]

Number of cookies she had left = 1

So, the equation to solve for [tex]p[/tex] can be given as:

[tex]p-5=1[/tex]

Solving for [tex]p[/tex]

Adding 5 both sides.

[tex]p-5+5=1+5[/tex]

∴ [tex]p=6[/tex]

Thus, number of cookies in each package = 6.

Step-by-step explanation:

Let w be the work of waxing.

Rosita can wax her car in 2 hours or 120 minutes.

Time taken by Rosita = 120 minutes

[tex]\texttt{Rate of Rosita = }\frac{W}{120}[/tex]

Let time taken by Helga be t,

[tex]\texttt{Rate of Helga = }\frac{W}{t}[/tex]

When she works together with Helga, they can wax the car in 45 minutes.

We have

             [tex]\frac{W}{\frac{W}{120}+\frac{W}{t}}=45\\\\120t=45(120+t)\\\\120t=5400+45t\\\\t=72minutes[/tex]

Time taken by Helga to wax the car is 72 minutes

Answer: The area of triangle ΔXYZ is 12 square inches.

Step-by-step explanation:

Since we have given that

RS = 3 inches

XY = 2 inches

Area of ΔRST = 27 in²

Since ΔRST is similar to ΔXYZ.

So, using the "Area similarity theorem":

[tex]\dfrac{\Delta RST}{\Delta XYZ}=\dfrac{RS^2}{XY^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{3^2}{2^2}\\\\\dfrac{27}{\Delta XYZ}=\dfrac{9}{4}\\\\\Delta XYZ=3\times 4=12\ in^2[/tex]

Hence, the area of triangle ΔXYZ is 12 square inches.

The area of triangle XYZ is found by squaring the ratio of the corresponding sides of the similar triangles and multiplying it by the area of the larger triangle RST. With the side length ratio of 2:3, the area ratio is (2/3)², resulting in an area of 12  in² for triangle XYZ.

The student's question involves determining the area of a smaller similar triangle (XYZ) given the area of the larger similar triangle (RST) and the lengths of corresponding sides. To solve, we utilize the property that similar triangles' areas are proportional to the square of the ratio of their corresponding sides.

Given:
Length of RS in triangle RST = 3 inches
Length of XY in triangle XYZ = 2 inches
Area of triangle RST (A1) = 27  in²

We establish the ratio of their sides as 2 inches (XY) / 3 inches (RS), which simplifies to 2/3. The ratio of their areas would then be (2/3)² because the area of similar triangles scales with the square of the ratio of their corresponding linear dimensions. Hence, the Area of triangle XYZ (A2) will be A1 × (2/3)².

A2 = 27 in² × (2/3)2 = 27 × 4/9 = 12 in².

The area of triangle XYZ is 12 in².

Answer:

this is a left tailed test

   Null hypothesis,  [tex]H_{0} :[/tex] σ = 40 seconds

   Alternate hypothesis, [tex]H_{a} :[/tex] σ < 40 seconds.

Step-by-step explanation:

i) the standard deviation of duration times in seconds of the old faithful geyser is less than 40 sec. identify the null hypothesis and alternative hypothesis in symbolic form

ii) this is a left tailed test

   Null hypothesis,  [tex]H_{0} :[/tex] σ = 40 seconds

   Alternate hypothesis, [tex]H_{a} :[/tex] σ < 40 seconds.

The expression to represent the total price of the supplies is 1.29n + 0.79w + 2.39b

Solution:

Let "n" be the number of nails

Let "w" be the number of washers

Let "b" be the number of bolts

Given that ,

Price of nail = $ 1.29 per lb

Price of washers = $ 0.79 per lb

Price of bolts = $ 2.39 per lb

To find: Expression to represent the total price of the supplies.

Total price = number of nails x Price of nail per lb + number of washers x Price of washers per lb + number of bolts x Price of bolts per lb

[tex]Total\ price = n \times 1.29 + w \times 0.79 + b \times 2.39\\\\Total\ price = 1.29n + 0.79w + 2.39b[/tex]

Thus the expression to represent the total price of the supplies is found

Answer:

her weekly allowance is $16

Step-by-step explanation:

Let x represent Joan's weekly paycheck.

Joan spent half of her paycheck going to the movies. This means that the total amount that she spent at the movies is x/2. The amount that she is left with would be

x - x/2 = x/2

She washed the family car and earned 7 dollars. This means that the total amount left with her is

x/2 + 7

if she ended with 18 dollars, it means that

x/2 + 7 = 18

x/2 = 18 - 7 = 11

x = 2 × 11 = $22

Answer:

  about 5.52%

Step-by-step explanation:

If Lucius wants an account value of $2000 after 3 years, she can find the interest rate by solving the polynomial ...

  550x³ +600x² +650x -2000 = 0

This equation has one positive real root. It is irrational, so must be found using the rather complicated cubic solution formula or, more simply, a graphing calculator. The latter shows the root to be near 1.05516.

Lucius needs an interest rate of ...

  (1.05516 -1)×100% = 5.516%

The interest rate needed for a balance of $2000 after 3 years is about 5.52%.

Answer:

Company made 63 rods with the given amount of steel.

Step-by-step explanation:

Given:

Radius of each rod =4 cm

height of each rod = 30 cm

Number of steel company used = 94953.6

We need to find how many rods company can make.

Solution:

First we will find the Volume of each rod.

Since rod is in cylindrical shape.

So we will use Volume of cylinder.

Now Volume of cylinder is given by π times square of the radius times height.

framing in equation form we get;

Volume of each rod = [tex]\pi r^2h= \pi \times4^2\times 30 = 1507.96 \ cm^3[/tex]

So we can say that steel used to make each rod = 1507.96

Number of steel company used = 94953.6 (given)

To find the number of steel rod company made we will divide Number of steel company used by number of steel used to make each rod.

framing in equation form we get;

number of steel rod company made = [tex]\frac{94953.6}{1507.96}= 62.96\approx63[/tex]

Hence Company made 63 rods with the given amount of steel.

The number of rods made using given data is approximately 63 rods .

To find out how many steel rods a company made based on the total volume of steel used, we need to calculate the volume of one rod and then divide the total volume of steel by this.

The volume of a cylinder (which is the shape of the rods) is calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

Given that each rod has a radius of 4 centimeters and a height of 30 centimeters, the volume of one rod can be found as follows:

V = π(4²)(30)

   ≈ 3.14(16)(30)

   = 1,507.2 cm³

Given the total volume of steel used is 94,953.6 cm³, the number of rods made can be calculated by dividing the total volume of steel by the volume of one rod:

Number of rods = 94,953.6 cm³ / 1,507.2 cm³

                           ≈ 63

Therefore, the company made approximately 63 steel rods.

Answer:

see the explanation

Step-by-step explanation:

we know that

To determine the rate per pretzel or unit rate, divide the total paid by the number of pretzel

so

[tex]\frac{126}{42}=\$3\ per\ pretzel[/tex]

Jaimie's error

He subtracted 42 from $126 when he should have divided $126 by 42

Answer:

Leo is 1 year old.

Step-by-step explanation:

Given:

Lily's age = 5

Leo's age = [tex]3x-14[/tex]

we need to find the Leo's age.

Solution:

Leo's age = [tex]3x-14[/tex]

where x ⇒ Lilly age

But Lilly's age = 5 years (given)

So we will substitute the value of x as 2 in Leo's age expression.

On Substituting we get;

Leo's age = [tex]3x-14 = 3\times5-14 = 15-14 = 1\ year[/tex]

Hence Leo is 1 year old.

Final answer:

To find the length of each piece of ribbon, divide the total length of 2.65 feet by 5, resulting in 0.53 feet per piece, or approximately 6 inches after converting to a more convenient measurement.

Explanation:

The student's question involves the division of a length of ribbon into equal pieces. Miss Alvarez has a piece of ribbon that is 2.65 feet long and she cuts it into 5 equal pieces. To estimate the length of each piece, we would divide the total length of the ribbon by the number of pieces.

The calculation would be: 2.65 feet ÷ 5 pieces = 0.53 feet per piece. If we want a more convenient measure, we could convert feet to inches since there are 12 inches in a foot, resulting in approximately 6.36 inches per piece (0.53 feet × 12 inches/foot).

As an estimate and for ease of measurement, we might round this to the nearest whole number, suggesting that each piece of ribbon is approximately 6 inches in length.

ANSWER= 0.9772

STEP-BY-STEP EXPLANATION:

We are assuming that there is an underlying distribution of package weights,even though we don´t speciify the shape of that distribution.

Letting [tex]x_{i}[/tex] denote the ith package weight and S=[tex]x_{1} +....x_{100}[/tex] we are trying to find P(S ≤ 1700)

We know that the distribution of S is approximately normal with mean nцХ and variance по²Х

S≈N( 100 * 15, 100 * 10² ) = N (1500.10000) (note that they gave us the standar deviation aove; variances add, so we need to square this). Finally,

P(S ≤ 1700) = P ([tex]\frac{S-1500}{\sqrt{10000} }[/tex] ≤ [tex]\frac{1700 - 1500}{\sqrt{10000} }[/tex])

≈P (Z≤2) = 0.9772

Answer:

The weight of the seventh linebacker is = 214 lb.

Step-by-step explanation:

Given:

Mean of 7 linebackers = 236 lb

The weights of first 6 linebackers are:

215 lb, 305 lb, 265 lb, 196 lb, 221 lb and 236 lb

To find the weight of seventh linebacker.

Solution:

Let the weight of the seventh linebacker be = [tex]x[/tex]

The mean of 7 line backers will be given as:

⇒ [tex]\frac{215+305+265+196+221+236+x}{7}[/tex]

The mean of the 7 linebackers is given = 236 lb

Thus, the equation to find [tex]x[/tex] will be :

[tex]\frac{215+305+265+196+221+236+x}{7}=236[/tex]

Simplifying.

[tex]\frac{1438+x}{7}=236[/tex]

Multiplying both sides by 7.

[tex]7.\frac{1438+x}{7}=236(7)[/tex]

[tex]1438+x=1652[/tex]

Subtracting both sides by 1438.

[tex]1438-1438+x=1652-1438[/tex]

∴ [tex]x=214[/tex]

Thus, the weight of the seventh linebacker is = 214 lb.

Answer:

Step-by-step explanation:

You swim at 3 km/hr with your body perpendicular to a stream with a current of 5 km/hr.

If your actual velocity is the vector sum of the stream's velocity and your swimming velocity, it means that your actual velocity is the resultant velocity. Let R represent the resultant velocity. It means that

R² = 3² + 5² = 9 + 25

R² = 34

Taking square root of the left hand side and the right hand side of the equation, it becomes

R = √34 = 5.83 km/hr.

Final answer:

To find the swimmer's actual velocity in a stream where the swimmer's velocity is 3 km/hr and the stream's velocity is 5 km/hr, we use the Pythagorean theorem, resulting in an actual velocity of approximately 5.83 km/hr.

Explanation:

The question involves calculating the actual velocity of a swimmer moving in a stream. The swimmer swims at a rate of 3 km/hr perpendicular to the stream, while the stream itself has a current of 5 km/hr.

To find the swimmer's actual velocity when these two vectors are combined, we use the Pythagorean theorem, as the velocities are perpendicular to each other.

Let the swimmer's velocity be represented by Vswimmer = 3 km/hr and the stream's velocity by Vstream = 5 km/hr.

The actual velocity (Vactual) is the vector sum of these two velocities. Since they are at right angles to each other, Vactual can be calculated as [tex]\sqrt{((Vswimmer)^2 + (Vstream)^2)[/tex] .

Substituting the values gives Vactual =[tex]\sqrt{(3^2 + 5^2)} = \sqrt{(9 + 25)} = \sqrt{(34),[/tex] which approximately equals 5.83 km/hr.

Therefore, the actual velocity of the swimmer, taking into account the stream's current, is approximately 5.83 km/hr.

Answer:

(2x-3)/(x+4)

Step-by-step explanation:

Answer:

(x - 4).

Step-by-step explanation:

(x - 4) is common to to top and bottom of the fraction.

The fraction simplifies to (2x+3)/(x+4).

Answer:

x = 6.54 cm

h = 3.27 cm

Step-by-step explanation:

Volume of open top box

V = 140 cm³

Dimensions of the box

It is a base square box then area of the base of side x is

A(b) = x²

And we will call h the height of the box then

V = 140   ⇒    140 = x²*h     ⇒   h = 140/ x²

We have to calculate the area of the 4 sides

Area of one side is  As = x*h        ⇒ total area of 4 sides = 4 x* 140/x²  

Ats  =  560/x

Then Total area of the box is

A(t)  =  Area of the base  +  Total area of sides

A(x)  =   x²  +   560/x

Taking derivatives on both sides of the equation we get:

A´(x)  =  2x   -  560/x²

A´(x)  =  0     ⇒    2x   -  560/x² = 0   ⇒   2x³  -  560  = 0

x³  =  280     ⇒    x  = 6.54 cm

And h      h  =  140/ (6.54)²    ⇒ h =  140/ 42.77    h  = 3.27 cm

Answer:

[tex]\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles[/tex]

Step-by-step explanation:

Given:

The fractions are given as:

[tex]\dfrac{1}{2}\ and\ \dfrac{3}{5}[/tex]

The denominators of the first fraction is 2 and that of the second fraction is 5.

In order to find the common denominator for 2 and 5, we have to find the least common multiple of each of the numbers.

Multiples of 2 = 2, 4, 6, 8, 10, 12,....

Multiples of 5 = 5, 10, 15, 20, 25, 30,....

Therefore, the least common multiple of 2 and 5 is 10. So, the common denominator is 10.

Now, multiply the numerator and denominator of each fraction by the same suitable number such that the denominator becomes 10.

So, for the first fraction, 2 is in the denominator.

So, 2 when multiplied by 5 gives 10.

So, we multiply the numerator and denominator of first fraction by 5. This gives,

[tex]\dfrac{1}{2}=\dfrac{1\times 5}{2\times 5}=\dfrac{5}{10}[/tex]

Now, for the second fraction, 5 is in the denominator.

So, 5 when multiplied by 2 gives 10.

So, we multiply the numerator and denominator of first fraction by 2. This gives,

[tex]\dfrac{3}{5}=\dfrac{3\times 2}{5\times 2}=\dfrac{6}{10}[/tex]

Therefore, the new fractions after making the denominators same are:

[tex]\dfrac{5}{10}\ and\ \dfrac{6}{10}[/tex]

So, the miles covered in fraction with same denominators are:

[tex]\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles[/tex]

Answer:

Last week she work  [tex]3\frac{54}{78}\ hours[/tex].

Step-by-step explanation:

Given:

Last week Stacy earned $24 for baby sitting for hours in her part time job at Burger city she work 12 hours and earned $78.

Now, to find the total hours she work last week.

As, given she work 12 hours and earned $78.

So, to solve by using unitary method:

If she earned $78 in working 12 hours.

So, she earned $1 in working = [tex]\frac{12}{78}\ hour.[/tex]

Thus, she earned $24 in working = [tex]\frac{12}{78} \times 24[/tex]

                                                        [tex]=\frac{288}{78}[/tex]

                                                        [tex]=3\frac{54}{78}\ hours.[/tex]

Therefore, last week she work  [tex]3\frac{54}{78}\ hours[/tex].

Answer:

  d.  300%

Step-by-step explanation:

The given relation is ...

  60%·A = 20%·B

Dividing by 20%, we see that ...

  3·A = B

Of course, 3 = 3×100% = 300%, so B is 300% of A.

First, let's write the given condition in the form of an equation. If 60% of A is 20% of B, it can be written as:

60/100 * A = 20/100 * B

In order to proceed, we begin simplifying the equation by eliminating the fractions. This can be achieved by multiplying both sides of the equation by 100, turning our equation into:

60A = 20B

Following this, we can further simplify by solving for B. This involves dividing the equation through by 20A which yields:

B = 60A / 20

This simplification results in the following expression:

B = 3A

This means that B equals three times the value of A. However, we have been asked to express B in terms of what percent it is of A. Knowing that 'percent' may be understood as 'per hundred', this corresponds to converting the ratio to a percentage.

We can safely say therefore that B is 300% of A which corresponds to choice (d) among our original options.

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Approximately 97.72% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg.

To find the percentage of 18-year-old women with a systolic blood pressure between 96 mmHg and 144 mmHg, we need to calculate the z-scores for the given values using the formula z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

For X = 96 mmHg, z = (96 - 120) / 12 = -2.

For X = 144 mmHg, z = (144 - 120) / 12 = 2.

Using a standard normal distribution table, we can find that approximately 0.9772 (97.72%) of the values fall within 2 standard deviations from the mean. Therefore, approximately 97.72% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg.

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Final answer:

Approximately 95% of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg, as calculated using Z-scores and the standard normal distribution.

Explanation:

The question asks us to determine the percentage of 18-year-old women who have a systolic blood pressure between 96 mmHg and 144 mmHg, given that the systolic blood pressure is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg.

We will use the concept of Z-scores to find this probability. A Z-score represents the number of standard deviations a data point is from the mean. We can calculate the Z-scores for the systolic blood pressure values of 96 mmHg and 144 mmHg and then use the standard normal distribution table to find the percentages. The calculations are as follows:

Z-score for 96 mmHg = (96 - 120) / 12 = -2
Z-score for 144 mmHg = (144 - 120) / 12 = 2

Looking at the Z-score table, we find that the area between Z = -2 and Z = 2 covers approximately 95% of the data under the normal distribution curve. Therefore, about 95% of 18-year-old women will have a systolic blood pressure between 96 mmHg and 144 mmHg.

Answer:

[tex] r =\frac{2437points}{25 years} =97.45 \frac{points}{year}[/tex]

So then we have that Morten Andersen scored on average 97.45 points per year in his career.

Step-by-step explanation:

Assuming the following table on the figure attached.

We see that the career points for Morten Andersen was 2437. That include all the points over alll the years the he played in the NFL.

Since the total years played by Morten Andersen was 25 we can write the following equation:

[tex] 25 r =2437[/tex]

Where [tex] r[/tex] represent the rate of points average per year.

If we solve for r from the last equation we can divide both sides of the equation and we got:

[tex] r =\frac{2437points}{25 years} =97.45 \frac{points}{year}[/tex]

So then we have that Morten Andersen scored on average 97.45 points per year in his career.

Answer:

Mrs. Fowler will get [tex]9[/tex] free pizza. And she needs two more coupon for the next pizza.

Step-by-step explanation:

Given that pizza stand gives a free pizza for every [tex]8[/tex] coupons.

And Mrs. Fowler has [tex]78[/tex] coupons.

Part (a)

How many free pizzas can Mrs. Fowler get if she has [tex]78[/tex]coupons?

We will divide total number of coupons [tex]78[/tex] by [tex]8[/tex] coupons.

[tex]\frac{78}{8}=9\frac{6}{8}[/tex]

When we divide we get quotient as [tex]9[/tex], with a remainder of [tex]6[/tex]. So, Mrs. Fowler will get [tex]9[/tex] free pizza.

Now, part (b)

If  Mrs. Fowler adds two more coupons that will turn remainder [tex]6[/tex] into [tex]6+2=8[/tex].

So, she can have next pizza.

Answer:

Step-by-step explanation:

Using the formula of derivative, it can be easily shown that, [tex]\frac{d f(x)}{dx} = 2[/tex] where [tex]f(x) = x^{2}[/tex].

Here we need to show that as per the instructions in the given table.

Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = [tex](1 + 0.01)^{2} - 1^{2} = 0.0201[/tex].

In the above equation, we have put x = 1 because we need to find the slope of the line tangent at x = 1.

Hence, dividing Δy by Δx, we get, [tex]\frac{0.0201}{0.01} = 2.01[/tex].

Let's examine this taking a smaller value.

If we take Δx = 0.001, then Δy = [tex]1.001^{2} - 1^{2} = 0.002001[/tex].

Thus, [tex]\frac{0.002001}{0.001} = 2.001[/tex].

The more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.

We can see here that the slope of the line tangent to the function at x = 1 is 2.001 ≅ 2.

We can use the formula of derivative: [tex]\frac{df(x)}{dx} = 2[/tex]

Looking at the instructions in the given table, we have:

Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = (1 + 0.01)² - 1² = 0.0201

In the above written equation, x = 1 because we need to find the slope of the line tangent at x = 1.

Thus, Δy divided by Δx, we get, 0.0201/0.01 = 2.01

If we take Δx = 0.001, then Δy = 1.001² - 1² = 0.002001

So, we have: 0.002001/0.001 = 2.001

We can see here that the more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.

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Answer: True.

Step-by-step explanation:

The total number of possible digits in the number system :  10  (from 0 to 9)

If there are 6 randomly selected digits in an automobile license tag, and each digit must be one of the 10 integers (0-9), then the choices for each digit in license tag = 10

Fundamental counting principle , the total number of ways to make 6-digits license tag where the choices for each digit in license tag is 10 will be :

[tex]10\times10\times10\times10\times10\times10=10^6[/tex]

Hence, there are [tex]10^6[/tex] possible license tags.

Therefore , the given statement is correct.

Final answer:

The statement is True because for each of the 6 digits in a license tag, there are 10 possible integers, giving us a total of 10^6 possible combinations.

Explanation:

The question relates to probability and combinatorics, which are branches of mathematics that deal with the likelihood of certain outcomes and the combination of different elements, respectively. If an automobile license tag consists of 6 randomly selected digits and each digit must be one of the 10 integers (0-9), then we must consider every digit independently.

Since there are 10 options for each digit, and there are 6 digits, we calculate the total number of possible license tags by multiplying the number of options for each digit. This is done by raising the number of options (10) to the power of the number of digits (6), which gives us: 10^6. Therefore, the statement is True as there are indeed 10^6 possible license tags.