The heights of male students are normally distributed with a mean of 160 cm and a standard deviation
of 6 cm.
Find the percentage of male students who are between 154 cm and 166 cm. Round your answers to
the nearest hundredth.

Answer:

3/10

Step-by-step explanation:

i

Answer:

3/10

Step-by-step explanation:

Multiply 1/2 by 5 to reach 5/10 and 1/5 by 2 to reach 2/10. Then subtract 2/10 from 5/10 to achieve the answer 3/10.

The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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Answer:

D

Step-by-step explanation:

\(\frac{1}{2} = \frac{7}{14} \\\)

\(\frac{1}{7} = \frac{2}{14}\)

\(\frac{7}{14} + \frac{2}{14} = \frac{9}{14}\)

5+2=7

\(7 + \frac{9}{14} = 7 \frac{9}{14}\)

The reading that separates the rejected thermometers from the others is given as follows:

1.175 ºC.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for this problem are given as follows:

\(\mu = 0, \sigma = 1\)

The 12% higher of temperatures are rejected, hence the 88th percentile is the value of interest, which is X when Z = 1.175.

Hence:

1.175 = X/1

X = 1.175 ºC.

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The probability of exactly 5 occurrences is (Rounding to three Decimal places), we get P(X ≤ 3) ≈ 0.251.

a) The probability of exactly 5 occurrences is given by the Poisson probability mass function:

P(X = 5) = (e^(-λ) * λ^5) / 5! = (e^(-5.1) * 5.1^5) / 120 ≈ 0.1755

Rounding to four decimal places, we get P(X = 5) ≈ 0.1755.

b) The probability of more than 6 occurrences can be calculated as the complement of the probability of 6 or fewer occurrences:

P(X > 6) = 1 - P(X ≤ 6) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6))

Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:

P(X = 0) ≈ 0.006

P(X = 1) ≈ 0.031

P(X = 2) ≈ 0.079

P(X = 3) ≈ 0.135

P(X = 4) ≈ 0.174

P(X = 5) ≈ 0.1755

P(X = 6) ≈ 0.1493

Substituting these values into the formula, we get:

P(X > 6) ≈ 1 - (0.006 + 0.031 + 0.079 + 0.135 + 0.174 + 0.1755 + 0.1493) ≈ 0.249

Rounding to three decimal places, we get P(X > 6) ≈ 0.249.

c) The probability of 3 or fewer occurrences is given by the cumulative distribution function:

P(X ≤ 3) = ∑ P(X = k), for k = 0, 1, 2, 3.

Using the Poisson probability mass function and the given value of λ, we can calculate each of the probabilities:

P(X = 0) ≈ 0.006

P(X = 1) ≈ 0.031

P(X = 2) ≈ 0.079

P(X = 3) ≈ 0.135

Adding these probabilities, we get: P(X ≤ 3) ≈ 0.251

Rounding to three decimal places, we get P(X ≤ 3) ≈ 0.251.

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At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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Answer:

1532

Step-by-step explanation:

Answer:

9006-7417= 1532

do you know how to work it out?

Answer:

1. 90

2. -12 +5

3. 83

Step-by-step explanation:

90 -12 + 5 = 83

Answer:

so i am sorry but somehow my answer got deleted

Step-by-step explanation:

Answer:2.750

Step-by-step explanation:

Or D

Answer:

You will have 3 apples left because 5 - 2 = 3.

(Hope this helps! Btw, I am the first to answer. Brainliest pls! :D)

Answer:

that look hard

Step-by-step explanation:

1. The volume of the black bag is 1728 cubic inches. 2. The volume of the blue bag is 2700 cubic inches. 3. The black bag will fit in the Check Box. 4. The bigger suitcase is 27 times larger than the smaller suitcase.

Volume, which is commonly expressed in cubic units, is the amount of space occupied by a three-dimensional object. By multiplying an object's length, breadth, and height, as well as other formulas depending on the shape of the object, one can get the volume of the thing. Volume is a key concept in many practical applications, including calculating container capacity, constructing structures, and estimating the amount of material required for a construction project. Volume is utilised in many branches of mathematics, science, and engineering.

For the given dimensions of the bags we have:

1. The volume of the black bag is:

18 x 12 x 8 = 1728 cubic inches

2. The volume of the blue bag is:

18 x 15 x 10 = 2700 cubic inches

3. The black bag will definitely fit in the Check Box because its volume of 1728 cubic inches is less than the volume of the Check Box, which is 2772 cubic inches.

4. The ratio of bigger suitcase to smaller suitcase is:

75 x 20 x 18 = 27000 cubic inches

25 x 8 x 9 = 1800 cubic inches

27000 / 1800 = 27

The bigger suitcase is 27 times larger than the smaller suitcase.

5. Now, if the watermelons is about 10 inches long and 9 inches wide, then its height would be:

720 = 10 x 9 x H

720 = 90H

H = 8 inches

The maximum amount of watermelons that can fit are:

27000 / 720 = 37.5 watermelons = 37 watermelons.

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Answer: 9

Step-by-step explanation: h=2(A/a+b)=2(66.66/4.9+9.9)=9.01

Answer:

21. 2x + 28

22. 18a - 17b

23. He flipped the numerator and denominator, 6.4 with 7.2 and he added the exponents instead of subtracting.

24. 8.8888888888889 × 10^{0}

Step-by-step explanation:

Answer:

\(y = 1\)

Step-by-step explanation:

Given

Attached graph

Required

The graph equation

Pick any two points, we have:

\((x_1,y_1) = (1,1)\)

\((x_2,y_2) = (3,1)\)

Calculate slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{1 - 1}{3 - 1}\)

\(m = \frac{0}{2}\)

\(m = 0\)

The equation is then calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = 0* (x - x_1) + 1\)

\(y = 1\)

Hence, the equation is:

\(y = 1\)

The length οf each side οf the dilated rectangle is 63 cm.

Dilatiοn is a transfοrmatiοn that changes the size οf the οbject withοut affecting its shape. It invοlves stretching οr shrinking an οbject unifοrmly alοng all its dimensiοns by a fixed scale factοr.

(a) Tο find the length οf each side οf the dilated image, we need tο multiply the οriginal dimensiοns by the scale factοr οf 3.5.

The length οf the dilated rectangle wοuld be:

Length = 18 cm x 3.5 = 63 cm

The width οf the dilated rectangle wοuld be:

Width = 8 cm x 3.5 = 28 cm

Therefοre, the length οf each side οf the dilated rectangle is 63 cm fοr the length and 28 cm fοr the width.

(b) Tο draw the new image A'B'D'C, we can use the fοllοwing steps:

Draw a rectangle with a length οf 63 cm and a width οf 28 cm.

Draw a vertical line thrοugh the midpοint οf the rectangle, dividing it intο twο equal halves.

Label the midpοint οf the line as O, which is the center οf dilatiοn.

Draw lines cοnnecting each cοrner οf the οriginal rectangle tο the center οf dilatiοn.

Extend each line tο dοuble its length, passing thrοugh the center οf dilatiοn and ending at A', B', C', and D'.

Cοnnect the endpοints οf each line tο fοrm the dilated rectangle A'B'D'C.

The resulting image shοuld lοοk like a larger rectangle that is centered arοund the midpοint O and is 3.5 times larger than the οriginal rectangle.

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The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

-------------

First determine the interest and then use the formula for ordinary interest.

Calculate the interest:

Use the ordinary interest formula:

Plug in the values and solve for Time:

Isolate the Time variable:

Tara would have to pay back the loan in approximately 120 days.

Answer:

If 63 is added to a number, the result is 43 less than three times the number. Find the number.

Step-by-step explanation:

Answer:

9/8

Step-by-step explanation:

x=(3/4)/2*3=9/8

Answer:9/8

Step-by-step explanation:divide 3/4 by 2/4

The percent of sales tax on the food total is 6%.

We must first determine the 20% of the total amount of food that is the tip:

Tip = 0.2 * $32.50 = $6.50

The total cost of the meal before tax is:

Total cost before tax = food total + tip = $32.50 + $6.50 = $39.00

The cost of the lunch, including the sales tax of $1.95, is

Sales tax and the total cost before taxes = $39.00 + $1.95 =  $40.95.

The final price of the lunch, including tax and tip, is thus $40.95. You can compute the percentage of sales tax on the entire amount of food as follows:

Percent of sales tax on food = (sales tax / food total) * 100%

= ($1.95 / $32.50) * 100%

= 6%

So, the percent of sales tax on the food total is 6%.

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An example of "an enumeration of its range {aξ : ξ < α}" in this case would be the list of natural numbers {0, 1, 2, 3, ...}, which represents the ordinal numbers less than ω^2.

An example of "an enumeration of its range {aξ : ξ < α}" can be found in the context of ordinal numbers.

Let's consider the ordinal number α = ω^2, where ω represents the first infinite ordinal (the set of all natural numbers). In this case, the range {aξ : ξ < α} refers to the collection of all ordinal numbers that are less than α.

The ordinal numbers less than ω^2 can be enumerated as follows:

a0 = 0

a1 = 1

a2 = 2

...

an = n

...

Each natural number n corresponds to an ordinal number less than ω^2. The enumeration continues indefinitely, as there are infinitely many ordinal numbers less than ω^2.

So, an example of "an enumeration of its range {aξ : ξ < α}" in this case would be the list of natural numbers {0, 1, 2, 3, ...}, which represents the ordinal numbers less than ω^2.

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Answer:

c

Step-by-step explanation:

- - - - - - - - - - - - - - - - - - - - - - - -

Heyo! Your explanation is below, if necessary.

- - - - - - - - - - - - - - - - - - - - - - - -

If it's 51 miles per hour, simply multiply the distance by the number of hours.

51 x 6 = 306

51 x 55/60 = 46.75

Now, add the products.

306 + 46.75 = 352.75

- - - - - - - - - - - - - - - - - - - - - - - -

Have a great day/night!

~pinetreee :)

Answer:

linear

Step-by-step explanation:

Where is the picture for this problem???

Answer:

Camille's is linear

Step-by-step explanation:

The weight for Camille's puppy increases in a constant rate(the puppy gains .5 pound per week, every week).

Amit's puppy is non-linear. Observe the table

X 1  2   3   4   5    6    7    8     9   10

Y 4  6  8  12  16  20  22  24  28  32

weeks start out with constant + 2 changes, then at week 3-4 the puppy gains a +4 (no longer linear - your line is no longer straight)

Olivia's puppy is linear

Answer:

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

f(x)=ax²+bx+c

Simplify each term.

f(x)=2x²−8x+8+6

Add 8 and 6.

f(x)=2x²−8x+14

Step-by-step explanation:

Answer:

it is 9

Step-by-step explanation:

adding 79 and 10 and subsequently subtracting 72 and 8 to get 9

The circumference of a circle with diameter 6cm is 18.85 cm.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that diameter of a circle is 6 cm.

We need to find the circumference  of circle with diameter 6 cm.

The formula to find circumference of circle=2πr

Radius=Diameter/2

=6/2=3 cm

Circumference of circle=2×3.14×3

=18.85

Hence, the circumference of a circle with diameter 6cm is 18.85 cm.

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Answer:

Step-by-step explanation:

18.8