2. The hamster, x, walked 20 feet. The guinea pig walked 1/4 less than that. The guinea
pig walked
feet

a. The probability that the amount of collagen is greater than 60 grams per mililiter is 0.5398

b. The probability that the amount of collagen is less than 90 grams per mililiter is 0.9985.

c. Approximately 68% of the data falls within 1 standard deviation of the mean for a normally distributed dataset.

a. To find the probability that the amount of collagen is greater than 60 grams per milliliter, we'll use the z-score formula:
z = (X - μ) / σ
where X is the value we're interested in, μ is the mean, and σ is the standard deviation.
z = (60 - 61) / 9.8 ≈ -0.1
Now, we'll use a z-table or calculator to find the probability corresponding to this z-score.

A z-score of -0.1 corresponds to a probability of approximately 0.4602.

Since we're looking for the probability that the amount of collagen is greater than 60 grams per milliliter, we need to find the area to the right of this z-score:
P(X > 60) = 1 - P(X ≤ 60) = 1 - 0.4602 ≈ 0.5398
b. To find the probability that the amount of collagen is less than 90 grams per milliliter, we'll again use the z-score formula:
z = (90 - 61) / 9.8 ≈ 2.96
A z-score of 2.96 corresponds to a probability of approximately 0.9985.

Since we're looking for the probability that the amount of collagen is less than 90 grams per milliliter, we'll use this probability directly:
P(X < 90) ≈ 0.9985
c. To find the percentage of compounds formed from the extract of this plant that fall within 1 standard deviation of the mean, we'll use the empirical rule (68-95-99.7 rule), which states that approximately 68% of the data falls within 1 standard deviation of the mean for a normally distributed dataset.

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Answer:well if a ice cub melts its probally gonna be 0

Step-by-step explanation:

im not so good sorry

The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,

(x - h)² + (y - k)² = r²

The area of the circle is 9π. Then the radius of the circle is given as,

A = π

πr² = π

r² = 1

The center of the circle is at (-7, -15). Then the equation of the circle is given as,

(x + 7)² + (y + 15)² = 1

The equation of the circle into the standard form will be (x + 7)² + (y + 15)² = 1.

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Answer:

y=1/3x-3

Step-by-step explanation:

slope = (y2-y1)/(x2-x1)

Use the two points: (0,-3) (3,-2)

slope = (-3+2)/(0-3)

slope = -1/-3 = 1/3

y intercept = -3

Equation: y=1/3x-3

The component form of two vectors 2u - v is (10, 0), no magnitude in the second direction.

A vector is a quantity that has both magnitude and direction.

Given are two vectors u = (4, - 1) and v = (-2, - 2).

∴ The value of 2u - v in component form is 2(4, - 1) - (-2, - 2).

2u - v = (8, - 2) - (-2, - 2).

2u - v = (8+2, - 2+2).

2u - v = 10

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Answer:

1/2 > 3/8

Step-by-step explanation:

To compare the answers, we need to change them to the same denominator.

2x4=8

So we can create an equivent fraction of 1/2 by dividing both numbers by 4:

1x4=4

2x4=8

1/4=4/8

Now we are comparing 4/8 and 3/8, and we can see clearly that 4/8 is greater than 3/8 because 4 is greater than 3.

Hope this helped!

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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The interior angles of a regular polygon can be found using the formula:

interior angle = (n-2) x 180 / n

where n is the number of sides of the polygon.

If we let n = 12,

then the interior angle is:

interior angle = (12-2) x 180 / 12 = 150 degrees

If we let n = 7,

then the interior angle is:

interior angle = (7-2) x 180 / 7 = 128.57 degrees

If we let n = 4,

then the interior angle is:

interior angle = (4-2) x 180 / 4 = 90 degrees

Therefore, the interior angles of regular polygons with 12, 7, and 4 sides are 150 degrees, 128.57 degrees, and 90 degrees, respectively.

Answer:

After 4 minutes

Step-by-step explanation:

After 1 min: Ant 1 is 9.75 mm underground. Ant 2 is 14.5 mm underground.

After 2 min: Ant 1 is 9.5 mm under. Ant 2 is at 14 mm under.

After 3 min: Ant 1 is 9.25 mm under.

After 4 min: Ant 1 is 9 mm under. Ant 2 is 13.5 mm under.

Ant 2 is now closer to the surface than Ant 1.

Answer: A.

Step-by-step explanation:

Slinky A is 26 inches there are 24 inches in two feet so slinky B isn’t longer. Then they are obviously not equal because we figured out they have different lengths

Answer:

Step-by-step explanation:

Given 3x-4y=65

Y=4

So 3x-4×4=65

3x-16=65

3x=65+16

X=81/3

X=27

So value of X is 27

Answer:

4 pounds of granola

Step-by-step explanation:

1.76p = 7.04

p = 7.04/1.76 = 4

Answer:

8*x^2

Step-by-step explanation:

Let x be the number

Expression is, 8*x^2

The Euclidean Parallel Postulate is proven from the Converse of the Alternate Interior Angle Theorem in Hilbert's plane and vice versa. To prove this statement, it is necessary to show that the alternate interior angle theorem's converse is valid, which implies that Hilbert's parallel postulate is true.

That is, two lines, l and m, in the Euclidean plane are parallel if they do not intersect, and given a point P that is not on l, there is a unique line m that goes through P and is parallel to l. That is, given two lines cut by a transversal such that a pair of congruent alternate interior angles is formed,

the lines are parallel. We will prove this statement by contradiction.Assume two lines, l and m, intersected by a transversal, t, have a pair of congruent alternate interior angles (i.e., ∠1 ≅ ∠2 and ∠3 ≅ ∠4 in the figure below) such that l and m are not parallel.

Draw a line through P that intersects m and n at C and D, respectively. Then, by the Exterior Angle Theorem, ∠BPC ≅ ∠DPC and ∠CPA ≅ ∠DPB. Hence, ∠CPA ≅ ∠DPB, which is impossible since CP is not collinear with PD by construction. Thus, this case cannot occur, and m = n. Therefore, there is only one line through P that is parallel to l, and Hilbert's Euclidean parallel postulate holds.

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Answer:

1.   70

Step-by-step explanation:

2.  105

Answer:

A: 70.311 repeat

B: 105.53

Step-by-step explanation:

im not sure if im correct but hope this helps

Step-by-step explanation:

13) 4x-22+x+11+10x-4 =180

15x=195

x=13

<P=(10(13)-4)=126

<Q=(4(13)-22)=30

<R=13+11=24

Answer:

Step-by-step explanation:

9≤2(3a−3)≤24

9≤6a−6≤24(Simplify all parts of the inequality)

9+6≤6a−6+6≤24+6(Add 6 to all parts)

15≤6a≤30  (Divide all parts by 6)

6    6      6

Answer:

5 ≤a≤5

2

(the computer won't do fractions so when you see this 5 it means fraction/division                                                                  9)

Answer:

#1 - y (0, 5) x (1, 8)

#2 - y (0, -2) x (1, 1)

(things in brackets are coordinates for the line)

Step-by-step explanation:

hope that helps :)

Answer:

No

Step-by-step explanation:

Linear equations, when graphed, look like straight lines.

Examples include:

y= mx + b

y = 3

x + 2 = 0

y + 6 = 0

y = 7x +2

Answer:

Step-by-step explanation:

x/4 - 3 = 0

x/4 = 3

x = 12

Answer:

12

Step-by-step explanation:

x/4-3 =0 /×4

x - 12 =0

x=12

Answer:

I think its 900 square feet

Step-by-step explanation:

SA formula for triangular prism

SA=p×H+2B

p is perimeter

h is height

B is area of the base (Base times height)

perimeter is 9+12+15 which is 36

height is 20

area of one of the base is 108

now plug it in and calculate

36×20+2(108)

this is 936

you round down to 900 obviously

and there you go

Answer:

y = 3x + 6

Step-by-step explanation:

Since the line is parallel, it has the same slope -- 3

y = 3x + b, sub point (1, 9)

9 = 3(1) + b

9 = 3 + b

b = 9 - 3

b = 6

y = 3x + b -- y = 3x + 6

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

The Median of the data shown on the line plot is 6.5.

The median of a line plot The median is the central value in a data set that is arranged in numerical order from least to greatest. In other words, the median is the middle number of a set of data. To find the median of a set of data on a line plot, follow the steps below:

Step 1: Arrange the data in numerical order from least to greatest. In the line plot provided above, the data is already arranged in order from least to greatest. It ranges from 4 to 12.

Step 2: Determine the total number of data points. In this case, there are 8 data points.

Step 3: Identify the middle value in the data set. This is done by dividing the total number of data points by 2 (the middle point). If the number of data points is even, the median is the average of the two middle values. If the number of data points is odd, the median is the middle value itself. Since there are 8 data points in the line plot above, we have an even number of data points. The two middle values are 6 and 7, so the median is the average of these two values.

Step 4: Calculate the median. Add the two middle values (6 and 7) together and divide by 2:6 + 7 = 13 13/2 = 6.5

Therefore, the median of the data shown on the line plot is 6.5.

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There will be 48 blocks in 6 rows, with 8 blocks in each row.

Multiplication is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and division. A product is the outcome of a multiplication operation. In mathematics, multiplying implies adding equal groups. The number of items in the group grows as we multiply. A multiplication issue includes the two elements and the product. Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilize every day.

Here,

number of rows=6

number of blocks in row=8

total number of blocks,

=6*8

=48

There will be 48 blocks in 6 rows with each row having 8 blocks.

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Answer:

60

Step-by-step explanation:

Plug in 4 for y

3(4)² + (4) + 8

3(16) + 4 + 8

48 + 12

60

The impulse response function (IRF) h12(t ,T) of the cascaded system S12S2 with inputs x(t) and T(t) and output w(t) is given by h12(t ,T) = h1(t) × h2(t+T+3), where h1(t) and h2(t) are the IRFs of systems S1 and S2, respectively.

To find the IRF h12(t ,T) of the cascaded system S12S2, we first need to find the IRFs of systems S1 and S2. The system S1 can be described by the differential equation y(t) + 4y'(t) + 4y''(t) = x(t), with the initial conditions y(0) = 0 and y'(0) = 0.

Taking the Laplace transform of both sides and solving for Y(s)/X(s), we get Y(s)/X(s) = 1/(s² + 4s + 4) = 1/((s+2)²). Using partial fraction decomposition, we can write this as Y(s)/X(s) = A/(s+2) + B/(s+2)², where A = 1 and B = -1. Taking the inverse Laplace transform, we get the IRF h1(t) = (t+1)e^(-2t)u(t), where u(t) is the unit step function.

The system S2 can be described by the differential equation y'(t) + 3y(t) = w(t), with the initial condition y(0) = 0. Taking the Laplace transform of both sides and solving for Y(s)/W(s), we get Y(s)/W(s) = 1/(s+3). Taking the inverse Laplace transform, we get the IRF h2(t) = e^(-3t)u(t).

Now, we can use the formula h12(t ,T) = h1(t) × h2(t+T+3) to find the IRF of the cascaded system S12S2. Therefore, h12(t ,T) = (t+1)e^(-2t)u(t) × e^(-3(t+T+3))u(t+T+3).

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Answer:

805.92

Step-by-step explanation:

Answer:

if you're talking 20 cents, then 4, if you're talking dollars, then 400.

tell me pls if you want an explanation.

Answer:

400 nickels

Step-by-step explanation:

How many nickels to make $20?

1 nickel = 5 cents ($0.05)

? nickels = $20

How many nickels make $1?

0.05x = 1

/0.05  /0.05

x = 20 <== 20 nickels make $1

How many nickels make $20?

20x = $20

20(20) = $20

400 = $20

This means that 400 nickels make $20

Hope this helps!