In an isosceles triangle, measure of one of the angles is 30o. What are the measures of the other two angles? Select all that apply. Note that more than one option may be correct.
A. 30o, 120o
B. 40o, 110o
C. 75o, 75o
D. 50o, 100o

Answer:

40 and 45

Step-by-step explanation:

let the 2 numbers be x and y with y the larger of the two, then

x + y = 85 → (1)

x = y + 5 → (2)

substitute x = y + 5 into (1)

y + 5 + y = 85

2y + 5 = 85 ( subtract 5 from both sides )

2y = 80 ( divide both sides by 2 )

y = 40

substitute y = 40 into (2)

x = 40 + 5 = 45

the two numbers are 40 and 45

Answer:

[tex]\dfrac{2x^3-x^2+5x}{(x^2+1)^2}\equiv \dfrac{2x-1}{(x^2+1)}+\dfrac{3x+1}{(x^2+1)^2}[/tex]

Step-by-step explanation:

As the denominator has a repeated irreducible quadratic factor, and the degree of the denominator is greater than the degree of the numerator, the partial fraction form is:

[tex]\boxed{\dfrac{N(x)}{(x^2+c)^2} \equiv\dfrac{Ax+B}{(x^2+c)}+\dfrac{Cx+D}{(x^2+c)^2}}[/tex]

Therefore, the given algebraic fraction can be written as partial fractions of the form:

[tex]\dfrac{2x^3-x^2+5x}{(x^2+1)^2}\equiv \dfrac{Ax+B}{(x^2+1)}+\dfrac{Cx+D}{(x^2+1)^2}[/tex]

Add the partial fractions:

[tex]\dfrac{2x^3-x^2+5x}{(x^2+1)^2}\equiv \dfrac{(Ax+B)(x^2+1)+Cx+D}{(x^2+1)^2}[/tex]

Cancel the denominators from both sides of the original identity, so the numerators are equal:

[tex]2x^3-x^2+5x = (Ax+B)(x^2+1)+Cx+D[/tex]

Expand the right side of the equation:

[tex]2x^3-x^2+5x=Ax^3+Ax+Bx^2+B+Cx+D[/tex]

Group elements according to the powers of x:

[tex]2x^3-x^2+5x=Ax^3+Bx^2+(A+C)x+B+D[/tex]

Equate the coefficients of the terms in x³ and x² to solve for A and B:

[tex]\implies A=2[/tex]

[tex]\implies B=-1[/tex]

Substitute the found values of A and B into the equation:

[tex]2x^3-x^2+5x=2x^3-x^2+(2+C)x-1+D[/tex]

Equate the coefficients of the terms in x and the constant to solve for C and D:

[tex]\implies 5=2+C \implies C=3[/tex]

[tex]\implies 0=-1+D \implies D=1[/tex]

Replace A, B, C and D in the original identity:

[tex]\dfrac{2x^3-x^2+5x}{(x^2+1)^2}\equiv \dfrac{2x-1}{(x^2+1)}+\dfrac{3x+1}{(x^2+1)^2}[/tex]

Answer=30 I think

Step-by-step explanation:

Blue card chances: 5/25=%20 Afterwards: 4/25=%16/2=%8

Red card chances: 12/25=%48 Afterwards: 11/25=%44/2=%22

Green card chances: 8/25=%32

Red and Blue card chances: %68

Answer=30 I think

Since the triangles are similar, the value of x is equal to: C. 18 units.

In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;

AC/RS = AB/RT

By substituting the given side lengths into the above equation, we have the following:

x/24 = 24/32

By cross-multiplying, we have the following;

32x = 24(24)

32x = 576

x = 576/32

x = 18 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

11

Step-by-step explanation:

15 - (p + 1)

Let p=3

15 - (3 + 1)

Parentheses first

15 - (4)

11

Answer:

11

Step-by-step explanation:

Given that,

p = 3

So, to find the value of the expression you have to solve it by replacing p with 3.

15 - ( p + 1 )

15 - ( 3 + 1 )

15 - 4

11

The least likely event from given events is Option B: A randomly selected student who is freshmen owns a skateboard.

The event whose occurence is minimum is least likely event.

Suppose there are finite elementary events in sample space of considered experiment and all are equally likely.

Then, we want to find the probability of an event E.

Then, its probability is given as

P(E) = Number of favourable cases/ Number of total cases = n(E)/n(S)

where favorable cases are the elementary events who belong to E, and total cases are size of sample space.

For two events A and B, by chain rule, we have:

P(A∩B) = P(B)P(A|B) = P(A)P(A|B)

How to find the conditional probability:

Suppose that there are two events A and B. Then suppose the conditional probability are:

P(A|B) = probability of occurrence of A given B has already occurred.

P(B|A) = probability of occurrence of B given A has already occurred.

We can then use the chain rule to find them, or Bayes theorem also helps in finding these probabilities.

We are given the table of joint relative frequency:

We take events as A, A' and B and B'

Important probabilities which will be used are evaluated as:

P(A) = n(A)/n(S) = 150/1200 = 1/8

P(B) = n(B)/n(S) = 250/1200 = 5/24

P(A') = 1 - P(A) = 7/8

P(B') = 1 - P(B) = 1 - 5/24 = 19/24

P(A∩B) = n(A∩B) / n(S) = 40/1200 = 1/30

P(A'∩B') = n(A'∩B') / n(S) = 840/1200 = 7/10

P(A'∩B) = n(A'∩B) / n(S) = 210/1200 = 7/40

Evaluating probabilities of choices given, we get:

Case 1: E = A random selected student who owns skateboard is freshmen

P(E) = ?

P(E) = P(B|A) = P(A∩B) / P(A) = 1/30 ÷ 1/8 = 4/15

Case 2: E = A random selected student who is freshmen owns skateboard:

P(E) = P(A|B) = P(A∩B) / P(B) = 1/30 ÷ 5/24 = 4/25

Case 3: E = A random selected student who doesn't owns skateboard is freshmen

P(E) = P(B|A') = P(A'∩B) / P(A') = 7/40 ÷ 19/24 = 21/95

Case 4: E = A randomly selected student who doesn't owns skateboard is not freshmen

P(E) = P(B'|A') = P(A'∩B') / P(A') = 7/10 ÷ 19/24 = 84/95

So, the least probability is for second case.

Question - Seth is analyzing number of students in class and high school who own skateboards. He puts the data in table shown. Given information in table, which event is least likely?

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There are a total of 32 different possible footwear choices that we can make.

Given, The number of pairs of socks = 4

The number of pairs of shoes = 4

We are to find out the number of possible footwear choices we can make if we can wear any combination of socks and shoes, including mismatched pairs.

So, We can wear any pair of socks with any pair of shoes including a mismatch.

Thus, for each pair of socks, there are 4 possible pairs of shoes.

And for each pair of shoes, there are 4 possible pairs of socks.

Therefore, we can form,

Total number of possible footwear choices = 4 pairs of socks * 4 pairs of shoes * 2 (considering the case of mismatched pairs) = 32 pairs.

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The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.

Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.

1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is:   8+4+4+4+4=24 units.

2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.

The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.

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Answer:

See below.

Step-by-step explanation:

to find the change in temperature from 2:00 PM to 10:00 PM, you need to subtract the final temperature from the initial temperature. In other words,

Change in temperature = Final temperature - Initial temperature

In your problem, the final temperature is -9°F and the initial temperature is 18°F. Therefore,

Change in temperature = -9°F - 18°F

Change in temperature = -27°F

So, the change in temperature from 2:00 PM to 10:00 PM is -27°F.

Architects often create scale models before the actual building is constructed. if a scale model has a length of 24 inches and a width of 36 in., 2:3 the dimensions are geometrically similar to the model buildings

Geometrically similar to the model buildings are those whose ratio of corresponding dimensions are the same as those of the model.

The ratio of the dimensions of the scale model is:

length:width = 24:36 = 2:3

There are two ratios to compare in a building with dimensions L and W:

length : width = L:W and

width : length = W:L

The ratio of the dimensions of a building must be in proportion to the ratio of the dimensions of the scale model for geometric similarity.

Since the dimensions of the model are 2:3, the dimensions of the building must also be in a 2:3 ratio.

Therefore, we have: L : W = 2:3

L = (2/3)W

The ratio of the length to the width of the building is 2:3.

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Scaling up, David has 220 coins in his collection with 5% of 11 of the coins kept in his box.

A scale up represents an increase or growth.

Scale factors are ratios comparing two quantities or values.

Proportionately, if 5% represent 11 coins, 100% will be 220 coins.

The number of coins David keeps in his box = 11

The percentage of the coins kept in the box = 5%

Thus, proportionately, 11 = 5%; therefore, 100% = 220 (11 ÷ 5%).

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The expected value (the mean of the distribution) for someone who buys a ticket can be calculated by adding up the total amount of money in the raffle and then dividing that by the number of tickets sold, which in this case in $6.68.

In this scenario, a ticket costs $5. The prize for winning the raffle is $1400 plus the cost of the ticket, which is $5.

The total value of the raffle is equal to the sum of the prize and the total amount of money raised from the tickets. The amount raised from the tickets is the number of tickets sold multiplied by the cost of the ticket.

Therefore, the total value of the raffle is equal to: $1400 + ($5 × 833) = $1400 + $4165 = $5565

The expected value of a ticket is the total value of the raffle divided by the number of tickets sold.

Therefore, the expected value of a ticket is:$5565 / 833 = $6.68

Therefore, the expected value (the mean of the distribution) for someone who buys a ticket is $6.68.

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The margin of error of the 98.4% confidence interval for snapdragons  is 3.71.

The midpoint of the range is calculated by adding the upper and lower bounds and then dividing by two. So, the sample mean is `(20.91 + 38.43) / 2 = 29.67`.

The margin of error is calculated by multiplying the critical value of z* (1.96 for a 98.4% confidence level) by the standard error of the mean. The formula for calculating the margin of error is:

`Margin of error z*(standard deviation/√n`).

The formula is `range/4 = 1.96 * standard deviation/√n`.Now, solve for the standard deviation:

`standard deviation = (range/4) * √n / 1.96`

Substituting the values: `(38.43 - 20.91)/4 = 1.96 * standard deviation/√n`

Simplifying the equation: `4.26 = (1.96*standard deviation)/√n`

Squaring both sides: `4.26^2 = 3.8416 = (1.96^2 * standard deviation^2)/n`

Substituting the value of the standard deviation: `3.8416 = (1.96^2 * ((38.43 - 20.91)/4)^2) / n`

Solving for n: `n = ((1.96^2 * ((38.43 - 20.91)/4)^2) / 3.8416) = 31.54`

Now that we know the sample size, we can calculate the standard error of the mean:

`standard error = standard deviation/√n = ((38.43 - 20.91)/4)/√31.54 = 1.89`.

The margin of error is `1.96 * 1.89 = 3.71`.

The 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). The margin of error of this confidence interval is 3.71.

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Born: 582 BCE

Died: 497 BCE

582-497= 85

Answer: 85 years old

The time necessary for the cell cycle for cancerous cells is significantly shorter compared to normal cells.

This implies that cancerous cells reproduce faster and therefore are able to spread more quickly. Doctors should be aware of this accelerated process so that they can provide more effective treatment options to their patients.

Explanation: In Model 1, the length of the arrow represents the time necessary for a cell to complete its cell cycle. For cancerous cells, the cell cycle is significantly shorter compared to normal cells.

This implies that cancerous cells can reproduce more quickly, and therefore spread more quickly. It is important for doctors to be aware of this so that they can make more informed decisions when it comes to treating cancer patients.

They should have an understanding of the accelerated process of cancerous cells, and use this to create better treatment plans for their patients.

This may include more aggressive methods of treatment such as chemotherapy and radiation, in order to try and stop the rapid spread of cancerous cells.

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Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50. The problem can be solved using a system of equations.

Let's use a system of equations to solve this problem:

Let x be the number of shirts that Siona bought, and y be the number of pairs of shorts that she bought. Then we have:

Equation 1: x + y = 10 (Siona bought 10 outfits in total)

Equation 2: 3.50x + 4.00y = 36.50 (The total cost of the outfits is $36.50)

To solve for x and y, we can use substitution or elimination. Let's use substitution:

From Equation 1, we can solve for x in terms of y:

x = 10 - y

Substitute this expression for x into Equation 2:

3.50(10 - y) + 4.00y = 36.50

Simplify and solve for y:

35 - 3.50y + 4.00y = 36.50

0.50y = 1.50

y = 3

Now we can substitute y = 3 back into Equation 1 to solve for x:

x + 3 = 10

x = 7

Therefore, Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50.

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Thus, total garden area calculated in square meters is found to be 40  sq. m.

If the degree n in the equation is equal to 1, then a linear equation only contains ONE variable. The highest exponent a single variable can have is referred to as the equation's degree. Any arbitrary variable, such as x, y, or z, may be used as long as the linear equation is homogeneous.

Given data:

Let x be the total area of land.

Area of planted flowers : 2/5 x

Remaining area = 24 sq. m.

Thus,

Total area = Area of planted flowers + Remaining area

x = 2/5 x + 24

x - 2/5 x = 24

(5 -2)/5 x = 24

3x/5 = 24

x = 24*5 / 3

x = 8*5

x = 40

Thus, total area of the garden calculated in square meters is found to be 40  sq. m.

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The approximate probability that the actual proportion requiring aid will exceed 0.08 is 0.5 (or 50%) rounded to four decimal places.

Given: The number of members in town = 400

The number of members requiring aid = 32

The proportion of members requiring aid = (number of members requiring aid) / (total number of members) = 32 / 400 = 0.08

To find the approximate probability that the actual proportion requiring aid will exceed this value, we need to assume a distribution for the proportion of members requiring aid. Assuming a normal distribution, we can use the Central Limit Theorem to approximate the sampling distribution of the sample proportion.

The standard error of the sample proportion is given by:

SE = √[p(1-p)/n]

where p is the population proportion and n is the sample size.

Substituting the values, we get:

SE = sqrt [(0.08 × 0.92) / 32] = 0.043

To find the probability that the actual proportion requiring aid will exceed 0.08, we can standardize the distribution using the z-score formula:

z = (x - p) / SE

where x is the value of the proportion we are interested in, p is the population proportion, and SE is the standard error of the sample proportion.

Substituting the values, we get:

z = (0.08 - 0.08) / 0.043 = 0

The probability that the actual proportion requiring aid will exceed 0.08 is equal to the probability of observing a z-score greater than 0, which is 0.5 (or 50%).

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The question is -

The towing service in town contracts with the club to come to the aid of up to 32 members in the next 12-month period. What proportion is that of the 400 members in town? .08 What is the approximate probability that the actual proportion requiring aid will exceed that value? (Round your answer to four decimal places.)

the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two  without neighbors regard to whether they are right or left neighbors is:5!6⋅2=10.6⋅25! = 10

There are $(6-1)! = 5! = 120$ ways to seat six people around a circular table if the seatings are considered distinct. However, we must divide this number by $6$ to account for the fact that rotations of the same seating arrangement are considered the same. We also must divide by $2$ to account for the fact that reflections (i.e., reversing the order of people) of the same seating arrangement are also considered the same.

Therefore, the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors is:

5!6⋅2=10.6⋅25! = 10

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Answer: The answer is 60.

Step-by-step explanation:

Using the fact that OP || RS, we know that∠RWV = 180° − 130° 1.  ∠RWV = 50° We know that,∠PWQ = ∠RWV = 50° (Since, opposite angles of intersecting lines are equal) Also, for line OP∠OQP + θ = 180° θ = 180° − ∠OPQ = 180° − 110° 2.  θ = 70° 

Answer:

The measure of ∠OPQ is 110°.

Step-by-step explanation:

Draw a line parallel to OP from point Q. Label a point on the line T. (See attached diagram).

Angles SRQ and TQR are alternate interior angles, and so according to the Alternate Interior Angles Theorem, they are congruent.

⇒ m∠TQR = m∠SRQ = 130°

Given m∠PQR = 60° and m∠TQR = 130° then:

⇒ m∠TQP + m∠PQR = m∠TQR

⇒ m∠TQP + 60° = 130°

⇒ m∠TQP = 70°

Angles OPQ and TQP are same-side interior angles, and so according to the Same-side Interior Angles Theorem, they are supplementary (sum to 180°).

⇒ m∠OPQ + m∠TQP = 180°

⇒ m∠OPQ + 70° = 180°

⇒ m∠OPQ = 110°

Therefore, the measure of ∠OPQ is 110°.

Answer:

true

Step-by-step explanation:

3rd quadrant sine is (-)

4th quadrant sine is (-)

The dimensions of the rectangle are 6 ft by 5.5 ft, and n = 6.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

We know that the area of a rectangle is given by:

Area = Length x Width

Since the problem does not specify the shape of the rectangle, we cannot assume that it is a square. Therefore, we need to find two numbers whose product is 33.

The factors of 33 are 1, 3, 11, and 33. None of these factors is equal to 3, so we cannot simply multiply 3 by a factor of 33 to get the length of the rectangle. Therefore, we need to use a different approach.

One way to find two numbers whose product is 33 is to start with the square root of 33 and round up and down to the nearest integer. The two resulting integers will be close to the factors of 33 and will multiply to give 33.

The square root of 33 is approximately 5.74. Rounding up and down to the nearest integer gives:

Length = 6 ft

Width = 33 ÷ 6 = 5.5 ft (approximately)

The product of these two numbers is:

6 ft x 5.5 ft ≈ 33 sq ft

Therefore, the dimensions of the rectangle are 6 ft by 5.5 ft, and n = 6.

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The type of average that can be found is the median. The median is the middle value of the data set when the values are arranged in order. In this case, the median is 11, as shown by the line inside the box.

Value is the relative worth, merit, or importance of something. It is subjective and can be determined by a variety of factors, including personal preferences, beliefs, and economic forces. Value is a concept that can be applied to many different aspects of life, including economic goods, personal relationships, and objects. Value is determined by how much someone is willing to pay for something or how much someone needs something. In economics, value is determined by the market, which is based on supply and demand. In personal relationships, value is determined by the mutual respect, trust, and understanding between two people. In objects, value is determined by the sentiment and meaning it holds for the owner. Ultimately, value is a perception of worth, and its true value is subjective.

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Answer:

3.6 miles

Step-by-step explanation:

hope this helps!

The length of the chord is approximately 7.62 inches.

Let's call the center of the circle point O, the radius of the circle 5 inches, the point where the chord intersects the radius point A, and the point where the chord intersects the circle point B.

Since the chord is perpendicular to the radius, we know that angle AOB is a right angle. Also, since OA is 5 inches and AB is 2 inches, we can use the Pythagorean theorem to find the length of OB

OB^2 = OA^2 + AB^2

OB^2 = 5^2 + 2^2

OB^2 = 25 + 4

OB^2 = 29

OB = sqrt(29) ≈ 5.39 inches

Now that we know the length of OB, we can use it to find the length of the chord. Let's call the length of the chord CD, where C and D are the points where the chord intersects the circle. Since OB is perpendicular to CD, we can use the Pythagorean theorem again to find the length of CD

CD^2 = 2OB^2

CD^2 = 2(29)

CD^2 = 58

CD = sqrt(58) ≈ 7.62 inches

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As per the standard deviation, the cutoff salary for teachers in the top 10% of earners in this country is approximately $43,120.

Now, we need to determine the cutoff salary for teachers in the top 10% of earners in this country. To do this, we need to find the salary that corresponds to the 90th percentile of the distribution.

The 90th percentile represents the point below which 90% of the data falls. In other words, if we arrange all the salaries in ascending order, the 90th percentile is the value that is greater than 90% of the salaries.

We can use a standard normal distribution table or a calculator to find the z-score that corresponds to the 90th percentile. The z-score represents the number of standard deviations away from the mean that corresponds to a particular percentile.

Using the standard normal distribution table, we can find that the z-score for the 90th percentile is approximately 1.28. This means that the cutoff salary for teachers in the top 10% of earners is:

Cutoff salary = Mean + (Z-score x Standard deviation)

Cutoff salary = $38,000 + (1.28 x $4,000)

Cutoff salary = $43,120

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Answer:

6.3 miles

Step-by-step explanation:

11-4.7 = 6.3 hope this helps

He requires to travel 6.3 miles more to reach work.

Distance is the measure of how far apart two points are. It is a scalar quantity that is typically measured in units such as meters, kilometers, miles, feet, or inches.

Since the total distance required to be traveled by Chang is 11 miles.

Let  S = total distance = 11

given distance traveled is 4.7 miles

take this traveled distance of 4.7 miles as x

now let S = x+y

replacing the given values where S = 11, x = 4.7

11= 4.7+y

y=11-4.7

y= 6.3

hence the remaining distance required to be traveled by Chang is 6.3 miles.

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The probability that the weight of a randomly selected steer is between 1279 and 1609 lbs is 0.2288.

Given that the weights of steers in a herd are distributed normally.

The standard deviation is 300 lbs and the mean steer weight is 1100 lbs.

We are required to find the probability that the weight of a randomly selected steer is between 1279 and 1609 lbs.

Here, it is given that the mean weight of the herd is 1100 lbs and the standard deviation is 300 lbs.

We need to find the probability of the weight of a randomly selected steer between 1279 lbs and 1609 lbs.

It can be written as;

P (1279 ≤ X ≤ 1609)

We can standardize this distribution by subtracting the mean and dividing it by the standard deviation.

The standardized form is given by

Z = (X-μ)/σ

where X is the given value, μ is the mean and σ is the standard deviation.

Substituting the values we get,

for X = 1279

[tex]Z_1[/tex] = (1279 - 1100)/300 = 0.5967 and

for X = 1609

[tex]Z_2[/tex]  = (1609 - 1100)/300 = 1.6967

We are required to find the probability of Z between [tex]Z_1[/tex] and [tex]Z_2[/tex].

P([tex]Z_1[/tex] ≤ Z ≤ [tex]Z_2[/tex]) To find this probability,

we use the standard normal distribution table,

We get P(Z ≤ 1.70) = 0.9545 and P(Z ≤ 0.60) = 0.7257

Now, P ([tex]Z_1[/tex] ≤ Z ≤ [tex]Z_2[/tex]) = P(Z ≤ 1.70) - P(Z ≤ 0.60) = 0.9545 - 0.7257 = 0.2288.

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Number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.

To find the percent of wolves that are neither female nor hunt in medium-sized packs, follow these steps:
1. Determine the total number of wolves.
2. Identify the number of female wolves and those that hunt in medium-sized packs.
3. Subtract the number of wolves that fit into either category from the total number of wolves.
4. Divide the remaining number of wolves by the total number and multiply by 100 to get the percentage.
Please provide the necessary data (total number of wolves, number of female wolves, and number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.

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