for which type of function does linear approximation always give the exact value of f ( x ) for x near the starting point? linear quadratic exponential logarithmic linear approximation never gives the exact value.

Answer:

A handtowel costs $2.00 and a bathtowel is $9.00

Step-by-step explanation:

Let h equal the cost of a handtowel. And let b equal the cost of a bathtowel.

In Campbell, they spent:

255 = 6h + 27b

In Lowell, they spent:

343 = 50h + 27b

Solve the system.

see image.

Answer:

Step-by-step explanation:

First, add 7 to all parts of the inequality to isolate x.

-10+7 < 3x-7+7 ≤ 5+7

-3 < 3x ≤ 12

Then divide all sides by 3.

-1 < x ≤ 4

So x is greater than -1 but less than or equal to 4.

This can be written as (-1, 4] in interval notation.

Answer: it will take both the kids 5 hours

Step-by-step explanation: 45+5x5=50   5+9x5=5

9 times 5 is 45 in 5 hours Isaiah will have completed 5 pages and he started at 45 so in 5 hours Brenna will have completed 45 pages and she started at 5

The area of the region between line y =3x -6 and line y=-2x+8 and

the x-axis with the help of integration will be 2.88 sq units.

What exactly is integration?

The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).

Integral Fundamental

A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.

From a to b, use ∫f(x)dx

indefinite integral

Integrals are defined without upper and lower limits. It looks like this:

A indefinite Integral is written as:

∫f(x)dx = F(x) + C

Where C might be any constant and the function f(x) is referred to as the integrand.

Now,

As given in image

Area of the region will be  =∫3x-6 dx from x=2 to 2.8 +∫-2x+8 from x=2.8 to 4.

=(3x²/2-6x) from x=2 to 2.8 + (-2x²/2+8x)  from x=2.8 to 4.

=3*0.8*0.8/2-6*0.8-2*1.2*1.2+8*1.2

=2.88 sq units.

Hence,

           The area of the region between line y =3x -6 and line y=-2x+8 and the x-axis with the help of integration will be 2.88 sq units.

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By Using the Cumulative distributed Function(CDF)m we get:

a) P (x <= 3 ) = 0.36

b) P ( 2.5 <= x <= 3  ) = 0.11

c) P (x > 3.5 ) = 1 - 0.49 = 0.51

d) x = 3.5355

e) f(x) = x / 12.5

f) E(X) = 3.3333

g) Var (X) = 13.8891  , s.d (X) = 3.7268

h) E[h(X)] = 2500

Given:

The cdf is as follows:

F(x) = 0                    x < 0

F(x) = (x^2 / 25)     0 < x < 5

F(x) = 1                   x > 5

Now,

a) Evaluate the CDF given with the limits 0 < x < 3.

So, P (x <= 3 ) = (x^2 / 25) | 0 to 3

P (x <= 3 ) = (3^2 / 25)  - 0

P (x <= 3 ) = 0.36

b) Evaluate the CDF given with the limits 2.5 < x < 3.

So, P ( 2.5 <= x <= 3 ) = (x^2 / 25) | 2.5 to 3

P ( 2.5 <= x <= 3  ) = (3^2 / 25)  - (2.5^2 / 25)

P ( 2.5 <= x <= 3  ) = 0.36 - 0.25 = 0.11

c) Evaluate the CDF given with the limits x > 3.5

So, P (x > 3.5 ) = 1 - P (x <= 3.5 )

     P (x > 3.5 ) = 1 - (3.5^2 / 25)  - 0

    P (x > 3.5 ) = 1 - 0.49 = 0.51

d) The median checkout for the duration that is 50% of the probability:

   So, P( x < a ) = 0.5

         ⇒ (x² / 25) = 0.5

          ⇒ x² = 12.5

          ⇒ x = 3.5355

e) The probability density function can be evaluated by taking the derivative of the cdf as follows:

      pdf f(x) = d(F(x)) / dx = x / 12.5

f) The expected value of X can be evaluated by the following formula from limits - ∞ to +∞:

      E(X) = integral ( x . f(x)).dx          limits: - ∞ to +∞

       E(X) = integral ( x² / 12.5)    

        E(X) = x³ / 37.5                    limits: 0 to 5

        E(X) = 5³ / 37.5 = 3.3333

g) The variance of X can be evaluated by the following formula from limits - ∞ to +∞:

 Var(X) = integral ( x² . f(x)).dx - (E(X))^2          limits: - ∞ to +∞

 Var(X) = integral ( x³ / 12.5).dx - (E(X))^2    

 Var(X) = x⁴/ 50 | - (3.3333)^2                         limits: 0 to 5

 Var(X) = 5⁴/ 50 - (3.3333)^2 = 13.8891

Standard Deviation (s.d) (X) = sqrt (Var(X)) = sqrt (13.8891) = 3.7268

h) Find the expected charge E[h(X)] , where h(X) is given by:

      h(x) = (f(x))^2 = x^2 / 156.25

The expected value of h(X) can be evaluated by the following formula from limits - ∞ to +∞:

E(h(X))) = integral ( x . h(x) ).dx          limits: - ∞ to +∞

E(h(X))) = integral ( x^3 / 156.25)    

E(h(X))) = x^4 / 156.25                      limits: 0 to 25

E(h(X))) = 25^4 / 156.25 = 2500

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The value of the conversion is;

16, 666. 67 minutes

277.78 hours

Conversion of units is described as the conversion between different units of measurement for the same quantity, using the multiplicative factor.

From the information given, we have;

10⁶ seconds

But, we have to take note of;

60 seconds = 1 min

Then 10⁶ seconds = x min

cross multiply

x = 16, 666. 67 minutes

Also,

60 minutes = 1 hour

Then 16, 666. 67 minutes = x

cross multiply

x = 277.78 hours

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The solutions are given in the ordered pairs.

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

We have to choose a value for x to find the corresponding y value to make the equation true.

1)6x=7y

To find x:

divide both sides by 6.

We get, [tex]\frac{6x}{6} =\frac{7y}{6}[/tex]⇒[tex]x=\frac{7y}{6}[/tex]

To find y:

divide both sides by 7.

We get, [tex]\frac{6x}{7} =\frac{7y}{7}[/tex] ⇒ [tex]y=\frac{6x}{7}[/tex]

Therefore solution for the given equation is [tex](\frac{7y}{6} ,\frac{6x}{7})[/tex]

2) 5x+3y=9

To find x:

subtract 3y from both sides,

⇒ 5x=9-3y then divide 5 on both sides,

⇒ [tex]\frac{5x}{5}=\frac{9-3y}{5}[/tex]⇒ [tex]x= \frac{9-3y}{5}[/tex]

To find y:

subtract 5x from both sides.

⇒3y=9-5x, then divide by 3 on both sides we get,

[tex]\frac{3y}{3}=\frac{9-5x}{3}[/tex]⇒[tex]y=\frac{-5x}{3}+3[/tex]

The solution for this equation is [tex](\frac{9-3y}{5},\frac{-5x}{3}+3)[/tex]

3) y+5-(1/3)x =7

To find x:

subtract y-5 from both sides we get,

[tex]-\frac{1}{3}x=2-y[/tex] then multiply both sides by -3,

[tex]\frac{\frac{-1}{3}x }{\frac{-1}{3}}=\frac{2-y}{\frac{-1}{3}}[/tex]⇒x=3y-6

To find y:

Subtract 5 from both sides.[tex]y-\frac{1}{3}x = 7-5[/tex] and add [tex]\frac{1}{3} x[/tex]

we get, [tex]y=2+\frac{1}{3}x[/tex]

The solution for this equation is ([tex](3y-6, 2+\frac{1}{3})[/tex]

Hence, the solutions are given in the ordered pairs.

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The length of segment AC is equal to 9.

Since B is between A and C, we can use the fact that AB + BC = AC. Similarly, since C is between B and D, we can use the fact to state the lengths of the following segments that: CD + BC = BD.

Substituting the given values, we get:

AB + BC = AC

CD + BC = BD

We are given segments BD = 7 and BC = 3, so we can substitute these values:

CD + 3 = 7

Solving for CD, we get:

CD = 7 - 3

CD = 4

Now we can use the fact that AD = AC + CD to solve for the length of segment AC:

AD = AC + CD

13 = AC + 4

AC = 9

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Answer: About 50 lbs

Step-by-step explanation:

Answer:

12.3

Step-by-step explanation:

To find the mean you have to add all the numbers and divide by the number of numbers.

They add up to 74 and divided by the number of numbers(6)

you get 12.333...

Then yiu round up to 12.3

The point of intersection can be found by setting the equations equal, dividing by the same quantity, taking the natural log, and dividing by ln(1.25).

[tex]2500(1.25^t) = 6000(0.3^t)[/tex]

[tex]2500*1.25^t = 6000*0.3^t[/tex]

Divide both sides by 2500:

[tex]1.25^t = 0.3^t * (6000/2500)[/tex]

Divide both sides by[tex]0.3^t[/tex]:

[tex]1.25^t / 0.3^t = (6000/2500) / 0.3^t[/tex]

Take the natural log of both sides:

[tex]t*ln(1.25) = ln((6000/2500) / 0.3^t)[/tex]

Divide both sides by ln(1.25):

[tex]t = ln((6000/2500) / 0.3^t) / ln(1.25)[/tex]

The point of intersection is t = ln((6000/2500) / [tex]0.3^t[/tex]) / ln(1.25).

The point of intersection of two exponential functions can be found algebraically by setting the two equations equal to each other and solving for the variable t. For example, if we want to find the point of intersection of [tex]2500(1.25^t) = 6000(0.3^t)[/tex], we can start by setting the two equations equal to each other and dividing both sides by [tex]2500: 1.25^t = 0.3^t * (6000/2500)[/tex]. Then we can divide both sides by[tex]0.3^t: 1.25^t / 0.3^t = (6000/2500) / 0.3^t[/tex]. We then take the natural log of both sides: [tex]t*ln(1.25) = ln((6000/2500) / 0.3^t)[/tex]. Finally, we divide both sides by ln(1.25): [tex]t = ln((6000/2500) / 0.3^t) / ln(1.25)[/tex]. This means that the point of intersection is[tex]t = ln((6000/2500) / 0.3^t) / ln(1.25).[/tex] In conclusion, the point of intersection of two exponential functions can be found algebraically by setting the two equations equal to each other, dividing both sides by the same quantity, taking the natural log of both sides, and then dividing both sides by ln(1.25).

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The sample space for choosing one card is S={V, S, I, D, I, I, N, O}.

What is a sample space?

A set of potential outcomes from a random experiment is known as a sample space. The sample space is identified by the letter "S". Events are a subset of the potential outcomes of an experiment. The results in a sample area could vary depending on the experiment.

Given that, a set of eight cards were labeled D, I, V, I, S, I, O, and N.

All the possible outcomes should be included in the sample space.

Here, the sample space will be { D, I, V, I,S, I, O, N}

Elements in the order will be

S={V, S, I, D, I, I, N, O}

Therefore, the sample space for the given set of cards is

S={V, S, I, D, I, I, N, O}.

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The total cost of haircuts for Michael's three children, including tip, would be $207.00.

If Michael gave a 20% tip and the haircuts cost $57.50, the tip would be:

Tip = 0.20 * $57.50 = $11.50

The total cost of the haircuts, including the tip, is as follows:

Total cost = haircut cost + tip

The total cost is $57.50 + $11.50.

The total cost is $69.00.

Since Michael took his three children to get haircuts, the total cost for all three children, including tip, would be:

Total cost for three children = three times the total cost

Total cost for three children = three times $69.00

The total cost for three children is $207.00.

As a result, the total cost of haircuts for Michael's three children, including tip, would be $207.00.

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The chance of a series of draws can be calculated while drawing from a collection of things (for instance, a deck of cards) without replacing the items after they are drawn.

Calculate the likelihood of the initial draw while accounting for the sample space's abundance of favourable outcomes. The probability of drawing two consecutive red marbles is 4/25.

Probabilities are always in the 0 to 1 range. Probability = Number of favourable outcomes / Total number of outcomes is the general formula for probability. Or. P(A) = f / N.

On the initial draw, there is a 2/5 chance of getting a red marble.

Out of the five marbles, there are two red ones.

On the second draw, there is still a 2/5 chance of drawing a red marble.

Probability of drawing a red marble on the first draw equals the probability of drawing two red marbles (Probability of drawing a red marble on the second draw)

= (2/5) × (2/5)

= 4/25

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Answer:

x ≈ 40.6

Step-by-step explanation:

using the sine ratio in the right triangle

sin38° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{25}{x}[/tex] ( multiply both sides by x )

x × sin38° = 25 ( divide both sides by sin38° )

x = [tex]\frac{25}{sin38}[/tex] ≈ 40.6 ( to 1 decimal place )

Answer:

x ≈ 40.6 units

(nearest tenth / one decimal place)

Step-by-step explanation:

You can use the law of sines in this situation since you know it is a right triangle because of the right angle, and you have an angle and a corresponding side.

Given this information, you can use the equation:

sin A / a = Sin B / b = Sin C / c

Given: A is 38°, a is 25, C is 90°.

Find: x which is side c

sin A / a = Sin B / b = Sin C / c →

[Substitute the information given]

Sin (38°) / 25 = Sin (90°) / c →

[Use the basic identity of sin(90°)]

Sin (38°) / 25 = 1 / c →

[Use the reciprocal rule]

25 / Sin(38°) = c →

[Rotate the equation]

c = 25 / Sin(38°) →

[Solve]

c = 40.606731137068..

[Reduce to the nearest tenth

(one decimal place) and set c to x]

x ≈ 40.6

Answer: A. Passenger train: 52 mph B. Freight train: 24 mph

Step-by-step explanation:

Considering the definition of pH and pOH, you obtain that:

pH is the Hydrogen Potential. It is a measure of acidity or alkalinity that indicates the amount of hydrogen ions present in a solution or substance.

Mathematically, pH is calculated as the negative base 10 logarithm of the activity of hydrogen ions, that is, the concentration of hydrogen ions:

pH= - log [H⁺]

Similarly, pOH is a measure of hydroxyl ions in a solution and is expressed as the logarithm of the concentration of OH⁻ ions, with the sign changed:

pOH= - log [OH⁻]

The following relationship can be established between pH and pOH:

pOH + pH= 14

In this case, you know that a solution has a pH = 13. So, the pOH can be calculated as:

pOH + 13= 14

pOH= 14 -13

pOH= 1

Then, the concentration of OH⁻ can be calculated as:

1= - log [OH⁻]

[OH⁻]= 10⁻¹

[OH⁻]= 0.1

Finally, a solution with a pH = 13 has 0.1 moles of OH⁻ ions per liter.

On the other side, remembering that pH = 13, the concentration of H⁺ can be calculated as:

13= - log [H⁺]

[H⁺]= 10⁻¹³

[H⁺]= 1×10⁻¹³

So, a solution with a pH = 13 has 1×10⁻¹³ moles of H⁺ ions per liter.

Finally, you have a different solution with an H⁺ concentration of 1.0×10⁻⁴. Replacing in the definition of pH:

pH= - log (1.0×10⁻⁴)

Solving:

pH= 4

Then, a different solution with an H⁺ concentration of 1.0×10⁻⁴ would have a pH= 4.

In summary, you obtain that:

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The cost of one ounce of chocolate cream at Philadelphia according to the cost in pound will be $0.47.

We are aware of the fact that 1 pound is equal to 16 ounces. So, the cost of one pound will be the cost of 16 ounces. Representing this information in ounces and expression -

Cost of 1 pound = 7.52

Rewriting the equation according to ounce

Cost of 16 ounces = 7.52

So, cost of 1 ounce = 7.52/16

Performing division on Right Hand Side of the equation

The cost of one ounce = 0.47

Therefore, the cost of one ounce will be $0.47.

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Raoul and Sven are at an angle of = cos1 (cos a cos 43° + sin a sin 43°). The sled is being moved by a force with a magnitude of [(105 cos a + 122 cos 43°)2 + (105 sin a + 122 sin 43°)2].

The outcome of two vectors is determined by the parallelogram law of vector addition. The resultant vector, R=(A2+B2+2ABcos), follows this law. A and B are the two vectors in this situation, and is the angle between them.

The component in the direction of the sled's path is:

105 cos a

The component perpendicular to the path is:

105 sin a

Similar to this, Sven's force may be broken down into two parts: one that is parallel to the sled's course and one that is perpendicular to it. The element pointing in the sled's direction is:

122 cos 43°

The component perpendicular to the path is:

122 sin 43°

The net force on the sled is the vector sum of these four components:

Net force = (105 cos a + 122 cos 43°) i + (105 sin a + 122 sin 43°) j

The magnitude of the net force is:

|Net force| = √[(105 cos a + 122 cos 43°)² + (105 sin a + 122 sin 43°)²]

To find the angle between Raoul and Sven, we can use the dot product of their forces:

Raoul · Sven = |Raoul| |Sven| cos θ

We can solve for θ as follows:

cos θ = (Raoul · Sven) / (|Raoul| |Sven|)

cos θ = [(105)(122) cos a cos 43° + (105)(122) sin a sin 43°] / (105)(122)

cos θ = cos a cos 43° + sin a sin 43°

θ = cos⁻¹(cos a cos 43° + sin a sin 43°)

a. The angle between Raoul and Sven is θ = cos⁻¹(cos a cos 43° + sin a sin 43°).

b. The magnitude of the force moving the sled is |Net force| = √[(105 cos a + 122 cos 43°)² + (105 sin a + 122 sin 43°)²].

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In a case whereby Jonah has $7,586 in an account that earns 10% interest compounded annually, the amount he will have in 3 years is $10,096.97

The concept that will be used here is counpound interest.

The  amount that will be present in the  account in 3 years can be estimated using the expression beleow which is:

FV = P(1 + r)^n

P represent the  amount in the account which is  $7,586

r  represen the interest rate which is 10/100 =0.01

n represent the number of years

FV  represent the future value

We can input all these values as :

FV =[ 7,586(1 + 0.1)^3]

= (7,586 x 1.1^3 )

= $10,096.97

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complete question:

Jonah has $7,586 in an account that earns 10% interest compounded annually.

To the nearest cent, how much will he have in 3 years?

To mode of given data set of number of days worked in october for 10 programmers of a software company is 7 and 14.

The mode of a data set is the value that appears most frequently. In this case, we can see that both 7 and 14 appear twice, while all other values appear only once. Therefore, there are two modes in this data set: 7 and 14.

To solve mathematically, we can use the mode formula:

mode = value with the highest frequency

In this case, we have two values with the highest frequency, which are 7 and 14. Therefore, the mode of given data set is 7 and 14.

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The value of the expression as a constant is 49.5

From the question, we have the following parameters that can be used in our computation:

3(5x - 1) + b(2x - 7)

For the expression to be a constant, the following must be true

b(2x) = -3(5x)

Divide by x

b(2) = -3(5)

Divide by 2 and remove bracket

b = -7.5

Substitute the known values in the above equation, so, we have the following representation

3(5x - 1) -7.5(2x - 7)

So, we have

15x - 3 - 15x + 52.5

Evaluate the like terms

49.5

Hence, the constant is 49.5

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To find out how many percent of computers have the Microsoft operating system installed, we need to add up the percentage of computers that have Windows XP and Windows 7 installed.

First, let's find out how many percent of computers have both Windows 7 and Linux installed:

85% (Windows 7) - 6% (Windows 7 & Linux) = 79% (Windows 7 only)

Next, let's find out how many percent of computers have both Windows XP and Linux installed:

20% (Windows XP) - 4% (Windows XP & Linux) = 16% (Windows XP only)

Finally, let's add up the percentage of computers that have Windows XP and Windows 7 installed:

79% (Windows 7 only) + 16% (Windows XP only) = 95%

So, 95% of the company's computers have the Microsoft operating system installed.

Answer:

o calculate the percentage of computers with the Microsoft operating system installed, we need to find the total number of computers that have either Windows XP or Windows 7 installed.

Microsoft Windows XP operating system is installed on 20% of the company's computers, so 20% of the computers have Windows XP installed.

Microsoft Windows 7 is installed on 85% of computers, so 85% of the computers have Windows 7 installed.

Linux and Microsoft Windows 7 are installed on 6% of computers, so 6% of the computers have both Windows 7 and Linux installed.

Microsoft Windows XP and Linux on 4% of computers, so 4% of the computers have both Windows XP and Linux installed.

All three programs are installed on 2% of computers, so 2% of the computers have all three programs installed.

To avoid double-counting the computers that have both Windows 7 and Linux installed, we need to subtract 6% from the total number of computers with Windows 7 installed. The same applies to the computers that have both Windows XP and Linux installed, so we need to subtract 4% from the total number of computers with Windows XP installed.

The total number of computers with Windows XP or Windows 7 installed is 20% + (85% - 6%) + (20% - 4%) = 20% + 79% + 16% = 115%.

So, 115% of the company's computers have the Microsoft operating system installed.

Step-by-step explanation:

The value of the missing side of the given triangle would be = 12

To calculate the value of the missing length the Pythagorean formula can be used such as;

c² = a² + b²

where;

C =?

a = 11

b = 5

C² = 11²+5²

= 121 + 25

= 146

C =√ 146

C = 12

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The cost of a pair of pants is $17.

And the cost of a shirt is $31.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

The total cost of 5 shirts and 3 pairs of pants is $206.

The total cost of a shirt and a pair of pants is $48.

Let y be the cost of a pair of pants and x be the cost of a shirt.

That means,

we have the system of equations,

x + y = 48   {equation 1}

5x + 3y = 206   {equation 2}

Multiply 5 to the equation 1 and then subtract equation 2 to equation 1,

we get,

2y = 34

y = 17

And x = 48 - 17 = 31.

Hence, $17 is the cost of a pair of pants.

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To translate the sentence into an equation, we can let c represent the value we want to find. The difference between c and 25 is 75, so we can write this as:

c - 25 = 75

To solve the equation, we can add 25 to both sides:

c - 25 + 25 = 75 + 25

c = 100

So the value of c is 100.

The critical value if the hypothesis is to be tested at the 0.05 level of significance is 1.96 . So, option C is the correct answer.

To test the hypothesis that Woof Chow has a market share of 25%, we need to conduct a hypothesis test with the null hypothesis that the true proportion of dog owners who use Woof Chow is 0.25, and the alternative hypothesis that the true proportion is not 0.25.

Since the sample size n is large (n = 100), we can use the normal distribution to perform this test. The critical value for a two-tailed test at the 0.05 level of significance is given by:

z_critical = ±1.96

This value corresponds to the 2.5th and 97.5th percentiles of the standard normal distribution. The critical value is ±1.96 because we want to be 95% confident that the true proportion of dog owners who use Woof Chow is within a certain range, and the 95% confidence interval corresponds to two standard deviations from the mean.

To determine whether or not to reject the null hypothesis, we would calculate a test statistic (z-score) based on the sample proportion, and compare it to the critical value. If the test statistic falls outside the critical value, we would reject the null hypothesis and conclude that Woof Chow does not have a market share of 25%.

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Answer:

85%

Step-by-step explanation:

well, she missed 3 throws only from all 20's, hmmm if we take 20(origin amount) to be the 100%, what's 3 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 3& x \end{array} \implies \cfrac{20}{3}~~=~~\cfrac{100}{x} \\\\\\ 20x=300\implies x=\cfrac{300}{20}\implies x=15[/tex]

I- uhm, it makes one but, I think that's just an equation...