At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels at the zoo.
Complete the table.
Original ratio Number in the zoo
Baby camels 5 ?
Adult camels 6 ?
Total camels ? 44

a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

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Hannah's thought that the original photo is congruent and similar to the final image is false

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

Translation creates congruent and similar shapes

However, dilation only create similar shapes,  but not congruent shapes

This means that the shapes are similar, but not congruent

Hence. Hannah is incorrect

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Answer:  8.1 minutes per mile

=======================================================

Work Shown:

40 minutes, 30 seconds = 40 + 30/60 = 40+0.5 = 40.5 minutes

She ran 5 miles in 40.5 minutes

This forms the ratio

5 miles : 40.5 minutes

Divide both sides by 5 to turn "5 miles" into "1 mile" and we get

5/5 miles : 40.5/5 minutes

1 mile : 8.1 minutes

Her minute per mile pace is 8.1 minutes per mile

This means it takes 8.1 minutes to run each mile.

Answer:

1 mile every 8 minutes

Step-by-step explanation:

To classify the equations as separable, linear, exact, can be made exact, Bernoulli, Riccatti, homogeneous, linear combination, or neither, you will need to identify the type of differential equation present.

Below are the classifications of each equation:

1. dy/dx = 5x²

This is a separable differential equation since it can be written as: dy = 5x² dx, and both variables can be separated.

2. y' + 2xy = x²

This is a linear differential equation since it can be written in the form of y' + p(x)y = q(x), where p(x) = 2x and q(x) = x².

3. (2x + 1) dx - (3y + 1) dy = 0

This differential equation is not linear and not separable, so it must be classified using other methods.

4. (2xy - y³) dx + (x² - 3y²) dy = 0

This is an exact differential equation since the partial derivatives of M and N are equal.

5. 3y' + 2ty = t²

This is a linear differential equation that can be solved using an integrating factor.

6. y' - y/x = x³

This is a Bernoulli differential equation since it can be written in the form of y' + p(x)y = q(x)yn, where n ≠ 1 and q(x) = x³.

7. y' = 2xy² + 3x

This is a Riccati differential equation since it can be written in the form of y' = p(x)y² + q(x)y + r(x), where p(x) = 2x, q(x) = 0, and r(x) = 3x.

8. (x² - y²) dx - 2xy dy = 0

This is a homogeneous differential equation since it can be written in the form of M(x,y)dx + N(x,y)dy = 0 and both M and N are homogeneous functions of the same degree.

9. y'' + 2y' + y = x + 1

This is a linear combination of homogeneous solutions and particular solutions since it can be solved using both techniques.

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Answer:

7 2/45

Step-by-step explanation:

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45(v - 7) = 2...divide both sides by 45

v - 7 = 2/45...add 7 to both sides

v = 2/45 + 7

v = 2/45 + 315/45

v = 317/45 or 7 2/45

The width of the round cake needs to be approximately 2 times the radius, or about 15.6 inches, to have the same volume as the rectangular prism cake.

A three-dimensional structure with six rectangular faces that are parallel and congruent together is called a rectangular prism. It has a length, width, and height. By multiplying the length, width, and height together, one may get the volume. Contrarily, a cylinder is a three-dimensional shape with two congruent and parallel circular bases. It has a height and a radius, and you can determine its volume by dividing the base's surface area by the object's height. A cylinder has curved edges and no corners while a rectangular prism has straight edges and corners.

The volume of the rectangular cake is given as:

V = length * width * height

Substituting the values we have:

16 * 12 * 3 = 576 cubic inches

Now, for the cylindrical cake to be of the same volume we have:

V = π * radius² * height

π * radius² * 3 = 576

(3.14) * radius² * 3 = 576

radius = 15.6 inches

Hence, the width of the round cake needs to be approximately 2 times the radius, or about 15.6 inches, to have the same volume as the rectangular prism cake.

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Answer:

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

Find the area between x = 85 and x = 125.

The matching choice is A

Answer:

0.7938

Step-by-step explanation:

The given graph is a normal distribution curve.

If a continuous random variable X is normally distributed with mean μ and variance σ²:

\(\boxed{X \sim \textsf{N}(\mu,\sigma^2)}\)

Given:

\(\text{If \; $X \sim \textsf{N}(100,15^2)$,\;\;find\;\;P$(85\leq X\leq 125)$\;\;to\;3\;s.f.}\)

Therefore, we need to find the area to the left of x = 125 and subtract the area to the left of x = 85.

Method 1

Using a calculator:

\(\begin{aligned}\implies \text{P}(85\leq X\leq 125)&= \text{P}(X\leq 125)-\text{P}(X < 85)\\&=0.9522096477-0.1586552539 \\&=0.7935543938\\&\approx0.7938\end{aligned}\)

Method 2

Converting to the z-distribution.

\(\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}\)

\(x=85 \implies Z_1=\dfrac{85-100}{15}=-1\)

\(x=125 \implies Z_2=\dfrac{125-100}{15}=1.67\)

Using the z-tables to find the corresponding probabilities (see attachments).

\(\begin{aligned}\implies \text{P}(-1\leq Z\leq 1.67)&= \text{P}(Z\leq 1.67)-\text{P}(Z < -1)\\&=0.9525-0.1587\\&=0.7938\end{aligned}\)

The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)

The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.

First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.

Now we'll apply the chain rule. We have:

f'(x) = (derivative of outer function) * (derivative of inner function)

f'(x) = (-1/√(1-u^2)) * (2x)

Since u = x^2, we'll substitute that back into our equation:

f'(x) = (-1/√(1-x^4)) * (2x)

So, the derivative of f(x) = arccos(x^2) is:

f'(x) = -2x / √(1-x^4)

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Answer:

7 dimes and 19 nickels

Step-by-step explanation:

d = dimes

n = nickels

The total amount is

.05n + .1d =1.65

He has 12 more nickels than dimes

12+d = n

Substitute this into the first equation

.05 (12 +d)  + .1d =1.65

.6 + .05d +.1d = 1.65

Combine like terms

.6 + .15d = 1.65

Subtract .6 from each side

.15d = 1.65-.6

.15d = 1.05

Divide by .15

.15d/.15 = 1.05/.15

d = 7

Now find n

12+d = n

12+7 = n

19 = n

Answer:

19 nickels and 7 dimes

Step-by-step explanation:

0.05n + 0.10d = 1.65

d+12=n

0.05(d+12) +0.010d = 1.65

0.05d + 0.6 + 0.10d = 1.65

0.15d = 1.05

d = 7 dimes

d+12=n

7+12=n

n = 19 nickels

4000x32 i think maybei dont know

Answer:

$ 4.20

Step-by-step explanation:

He spent $3.63 on apples

$1.80 on peaches

if you subtract both those numbers from $9.63 you get $4.20

So thats the amount he spent on tomatoes

Answer:

y = 7

z = 1

Step-by-step explanation:

If the triangles are congruent

AB = QR

y+ 34 = 41

Subtract 34 from each side

y = 41-34

y = 7

and QP = BC

38 = z+37

Subtract 37 from each side

38-37 = z

1 =z

Answer:

y = 7

z = 1

Step-by-step explanation:

The triangles are congruent, the length of the sides are equal.

y + 34 = 41

y = 41 - 34

y = 7

z + 37 = 38

z = 38 - 37

z = 1

Answer:

90

Step-by-step explanation:

q

Answer:

\(12\sqrt{8} ^{x}\)

Step-by-step explanation:

The sine of 60° is derived to be √3/2 using trigonometric ratios which makes option C correct.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right triangle from bisecting an equilateral triangle with equal side lengths of 2 units, the hypotenuse will be 2 units and the adjacent side to the angle 60° will be 1 unit

by Pythagoras rule, the opposite side to the angle 60° is derived as;

√(2² - 1² ) = √3

so;

sin 60° = √3/2 {opposite/hypotenuse}

Therefore, the sine of 60 degree is equal to √3/2 using trigonometric ratios.

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Answer:

B) 10 cm

Step-by-step explanation: since DC scaled up to 10 cm and they were both originally 6cm, RU would be 10cm.

Therefore, the equivalent metric length of a 3-inch scar would be 7.62 centimeters.

Explanation: Metric length is a measurement system that uses the metric unit. The metric unit is more common than the customary unit system in the United States. To convert customary unit lengths to metric lengths, a conversion factor is used.3 inches is the measurement of the scar in customary units. To convert 3 inches to metric units, multiply it by the conversion factor. There are 2.54 centimeters in one inch, which is the conversion factor. To find the equivalent metric length of a 3-inch scar, multiply 3 by 2.54. Therefore, the equivalent metric length of a 3-inch scar would be 7.62 centimeters.  The equivalent metric length of a 3-inch scar would be 7.62 centimeters. Metric length is a measurement system that uses the metric unit. The metric unit is more common than the customary unit system in the United States. To convert customary unit lengths to metric lengths, a conversion factor is used. There are 2.54 centimeters in one inch, which is the conversion factor.

Therefore, the equivalent metric length of a 3-inch scar would be 7.62 centimeters.

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Answer:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. ... They may also have been called the input and output of the function.)

In its simplest form the domain is all the values that go into a function, and the range is all the values that come out.

Answer:

No they are not equivalent.

Step-by-step explanation:

2(x - 2) + 3

First distribute the 2. It goes to both the x and also to the - 2

= 2x - 4 + 3

Add - 4 + 3

= 2x - 1

This is not equal to 2x - 7

Answer:

a,c,d

Step-by-step explanation:

Correct answer is C) none

I did the assignment, the other answer is incorrect.

Answer:

The first will be 16.6

The second will be 29

Step-by-step explanation:

Hope this Helped

\(5x + 7 = 90\)

\(3x + 3 = 90\)

Answer:

£40000

Step-by-step explanation:

→ Set up an equation

x × 0.6 = 24000

→ Divide both sides by 0.6

x = 24000 ÷ 0.6 = 40000

Answer:

Find the rectangle's area on the left hand side, using the formula:

A = l x w

Where 'l' represents the length and 'w' stands for the width.

Plug in what you know:-

A = l x w

A = 15 x 5

A = 75 square units is the area of the left rectangle.

Now let's find the rectangle's area on the right hand side, using the formula:

A = l x w

Where 'l' represents the length and 'w' stands for the width.

A = l x w

A = 15 x 4

A = 60 square units is the area of the right rectangle.

Now find the middle small horizontal rectangle's area, using the formula:

A = l x w

Where 'l' represents the length and 'w' stands for the width.

But, let's figure out the length first.

We know that from the left rectangle, the two side lengths beside the unknown length of the middle rectangle area 5 and 7.

The unknown length plus those two lengths (5&7) will have to equal 15 since that is the total length, so;

15 - (5 + 7) = x

15 - 12 = x

3 = x, so the unknown length of the middle rectangle is 3.

Plug in what you know into the formula:

A = l x w

A = 3 x 7

A = 21 square units is the area of the middle rectangle.
Now add up all the areas together:

75 + 60 + 21

= 156 square units is the area of the shape.

The required answers are:

a.  \(f(1) = f(1_R)\) is an ideal of S.

b. i) It is shown that \(\phi\) is onto.

   ii)  \(Ker(\phi)\) = {0}, and it is a principal ideal of \(Q[x]\) generated by the zero                        

       polynomial

iii)  \(Q[x]/Ker(\phi)\) is isomorphic to \(Q[x]\).

a) To show that \(f(1) = f(1_R)\) is an ideal of \(S\), to check two conditions: it is an additive subgroup of \(S\), and for any element s in f(1) and any element r in S, the product \(rs\) and \(sr\) are both in \(f(1)\).

Additive Subgroup:

Since f is an onto homomorphism of rings, it preserves addition. Therefore, \(f(1)\) contains the identity element of S, which is \(f(1_R)\).

For any two elements \(s, t\) in \(f(1)\) , gives \(s = f(r)\)  and \(t = f(t')\) for some elements \(r, t'\) in \(R\).

Then, \(s - t = f(r) - f(t') = f(r - t')\) which belongs to f(1) since \(R\) is an ideal of \(R\).

Ideal Condition:

Let \(s\) be an element in  \(f(1)\)and r be an element in \(S\).

Then, \(s = f(r')\) for some element \(r'\) in \(R\).

Thus, \(rs = f(r')r\), which belongs to \(f(1)\) since \(R\) is an ideal of \(R\).

Similarly, sr = rf(r') also belongs to f(1) since \(R\) is an ideal of \(R\).

Therefore, \(f(1) = f(1_R)\) is an ideal of S.

(b) Now let's consider the substitution homomorphism \(pvz: Q[x] \c- R\) given by \(\phi(p(x)) = p(\sqrt{2} )\).

(i) To show that  \(\phi\) is onto, to show that for any element a in ℝ, there exists an element p(x) in Q[x] such that \(\phi(p(x)) = p(\sqrt{2} ) = a.\)

Let's take \(p(x) = x - a\). Then, \(\phi(p(x)) = (\sqrt{2} - a)\).

Since \(\sqrt{2} - a\) is a real number, Thus shown that \(\phi\) is onto.

(ii) The kernel of φ, denoted by \(Ker(\phi)\), consists of all polynomials p(x) in \(Q[x]\) such that \(\phi(p(x)) = p(\sqrt{3} ) = 0.\)

In other words, \(Ker(\phi)\) is the set of all polynomials in \(Q[x]\) whose root is \(\sqrt{2}\). Since \(\sqrt{2}\) is irrational, the only polynomial in \(Q[x]\) with \(\sqrt{2}\) as a root is the zero polynomial.

Therefore, \(Ker(\phi) =\){0}, and it is a principal ideal of \(Q[x]\) generated by the zero polynomial.

(iii) The Fundamental Homomorphism Theorem (FHT) states that for any homomorphism \(\phi: R \c- S\), the image of \(\phi\) is isomorphic to the quotient ring  \(R/Ker(\phi)\).

In this case, the image of \(\phi\) is \(R\) and the kernel \(Ker(\phi)\) is {\({0}\)}.

Since \(Ker(\phi)\) is the zero ideal, the quotient ring \(R/Ker(\phi)\) is isomorphic to R itself.

Therefore,  \(Q[x]/Ker(\phi)\) is isomorphic to \(Q[x]\).

Hence, the required answers are:

a.  \(f(1) = f(1_R)\) is an ideal of S.

b. i) It is shown that \(\phi\) is onto.

   ii)  \(Ker(\phi)\) = {0}, and it is a principal ideal of \(Q[x]\) generated by the zero polynomial.

iii)  \(Q[x]/Ker(\phi)\) is isomorphic to \(Q[x]\)

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Answer:

8.324

Step-by-step explanation:

The 8 serves as the first digit and the "and " represents a decimal point  the remaining numbers go behind that decimal point therefore 8.324.

Answer:

The Rams scored 7 points.

Step-by-step explanation:

42/6 = 7

since the Coyotes scored 42 points, you would divide that score by however many they would get for every 1 point the Rams would get.