There are 40 ducks in a pond. The next spring there is a 40 percent increase. How many ducks are in the pond?

Answer:

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Sum of normal variables:

When normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.

The mean values are 20, 15, and 30 min, respectively:

This means that [tex]\mu = 20 + 15 + 30 = 65[/tex]

The standard deviations are 1, 2, and 1.5 min, respectively.

This means that [tex]\sigma = \sqrt{1^2 + 2^2 + 1.5^2} = 2.6926[/tex]

What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component?

Mean and standard deviation are in minutes, so this is the pvalue of Z when X = 60.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{60 - 65}{2.6926}[/tex]

[tex]Z = -1.86[/tex]

[tex]Z = -1.86[/tex] has a pvalue of 0.0314

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

Answer:

C) 84 cm²

Step-by-step explanation:

The question is asking for the surface area of the square pyramid. So we need to get the area of all the surfaces, then add them together.

6 cm × 6 cm = 36 cm²

1/2(6 cm × 4 cm) = 12 cm² (There are 4 of these sides)

12 cm² + 12 cm² + 12 cm² + 12 cm² + 36 cm² = 84 cm²

Answer:

(1,5)

Step-by-step explanation:

x:

6-5=1

y:

7-2=5

Answer:

isosceles triangle

Step-by-step explanation:

2 sides the same

Answer:

The value of x is 25.83.

Step-by-step explanation:

Vertical angles:

If two angles are vertical, they have the same measure.

In this question:

Angle A has measure 5x + 6

Angle B has measure 6.2x - 25

Since they are vertical:

[tex]A = B[/tex]

[tex]5x + 6 = 6.2x - 25[/tex]

[tex]1.2x = 31[/tex]

[tex]x = \frac{31}{1.2}[/tex]

[tex]x = 25.83[/tex]

The value of x is 25.83.

Answer:

-1 and 1/3

Step-by-step explanation:

Answer:

Answer:

-1 and 1/3

Step-by-step explanation:

Step-by-step explanation:

The magnetic flux of the following options are; 0.072, 0.062, 0.

The magnetic flux can be calculated by the given formula;

Flux = magnetic field B x area A x cos(angle between B and normal of A)

Given;

Magnetic field B = 2.25 T

The length ℓ = 0.420 m

Flux = 2.25 * 0.42^2 * cos(angle)

Flux = 0.072 * cos(angle)

a) The perpendicular to the magnetic field Wb

So, angle = 0°, flux = 0.072 Wb

b) 60.0° from the magnetic field Wb

So, angle = 30°,

flux = 0.072*cos(30) = 0.062 Wb.

c) parallel to the magnetic field Wb

So, angle = 90°, flux = 0

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Answer:

x = 28°

I hope it's helps you

Answer:

X=28

Step-by-step explanation:

(4x+3)+(2x+9)=180

6x+12=180

6x=168

X=28

Answer:

0.32

Step-by-step explanation:

Equation: 16/(2(25)) = ?

Simplify: 16/50

Solve: .32

There are 0.32 ounces of chocolate in each cookie.

There were 0.64 pounds of Choco chips in each cookie.

Unit rate is a rate with 1 as the denominator. A rate is a ratio used to compare different amounts of different quantities that are somehow related.

Given that, Darla made 25 cookies with 16 pounds of Choco chips, we need to find the amount of Choco chips used in each cookie,

So,

16 pounds for 25 cookies

Therefore,

1 cookie = 16/25 pounds

1 cookie = 0.64

Hence, there were 0.64 pounds of Choco chips in each cookie.

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Answer: Expanded Notation Form:

300 + 70 + 2 + 0.3= 372.3

Step-by-step explanation:

Answer:/Step-by-step explanation:

We would apply pythagorean theorem to find the variable in each triangle.

Pythagorean theorem is given as: c² = a² + b², where c is the hypotenuse length or longest leg while a and b are the two other legs.

Thus:

a. h² = (√20)² + 4²

h² = 20 + 16

h² = 36

h = √36

h = 6 units

b. t² = 9² - (√17)²

t² = 81 - 17

t² = 64

t = √64

t = 8 units

c. h² = (√8)² + (√8)²

h² = 8 + 8

h² = 64

h = √64

h = 8

Answer:x=-2

Step-by-step explanation:

3 x -2^2

3 x -4 = -12

Answer:

[tex]3 {x}^{2} = - 12 \\ {x}^{2} = - 12 \div 3 \\ {x}^{2} = - 4 \\ x = \sqrt{ - 4 } \\ x = \frac{ + }{} 2[/tex]

Option D, hope it helps!

Step-by-step explanation:

Sum is addition

1015+119 = 1134

Answer:

n = 6

Step-by-step explanation:

Represent the unknown number by n.  Then 8 - n/3 = 6.

Consolidate the constants on the left side:  2 - n/3 = 0, or n/3 = 2.

Multiplying both sides by 3 results in:  n = 6

Answer:

the area of the triangle ABC is ,then value of a is 27cm.

Solution:

Given Data:

Area of the triangle ABC is

To Find:

Value of a?

Step 1:

Step 2:

By Law of Sines

Simplify the above expression

--- eqn 1

Step 3:

Step 4:

Substitute the A, B and C value from the given Data.

Apply the Sin theta respective value.

From the above we finally got the value of "a" which is 27 cm.

Step-by-step explanation:

Answer:

The answer is 4

A. 43.96in?

Answer:

9 pounds and 3 ounces

Step-by-step explanation:

Althea needs 9 pounds and 3 ounces of cold cuts for her party.

To convert ounces to pounds, divide the number of ounces by 16 since there are 16 ounces in one pound.

147 divided by 16 is equal to 9.1875, which can be rounded to 9.

Then, to find the remaining ounces, multiply the decimal part of the result (0.1875) by 16.

This is equal to 3 ounces.

Therefore, 147 ounces is equal to 9 pounds and 3 ounces.

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Answer:

[tex]\dfrac{17}{13}[/tex]

Step-by-step explanation:

Given that,

r(x) = 3x - 1 and s(x) =  2x + 1

We need to find an expression equivalent to [tex]\dfrac{r}{s}(6)[/tex].

We know that,

[tex]\dfrac{r}{s}(6)=\dfrac{r(6)}{s(6)}[/tex]

Put x = 6 in the above expression

[tex]=\dfrac{3(6)-1}{2(6)+1}\\\\=\dfrac{18-1}{12+1}\\\\=\dfrac{17}{13}[/tex]

So, the equivalent expression is equal to [tex]\dfrac{17}{13}[/tex].

Answer:

80

Step-by-step explanation:

The area of a pyramid is given by the formula 1/3Bh.

We get the B from the area of the base of the pyramid, which is 1/2(6)(8) which is 24 inches. The height given is 10.

1/3(24)(10) is 80 inches cubed.

Answer:

The regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".

Step-by-step explanation:

Given:

Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε ...........(1)

Since there can be only one of spring, summer,fall, and winter at a point in time or in a season, we will have the following when there are winter rainy days:

Spring = 0

Summer = 0

Fall = 0

Rain = 1

Substituting all the relevant values into equation (1) and equating ε also to 0, a reduced form of equation (1) can be obtained as follows:

Humidity = β0 + β1Temperature + (β2 * 0) + (β3 * 0) + (β4 * 0) + (β5 * 1) + 0

Humidity = β0 + β1Temperature + 0 + 0 + 0 + β5 + 0

Humidity = (β0 + β5) + β1Temperature

Therefore, the regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".

The regression equation for winter rainy days is  

Humidity = β0 + β5 + β1Temperature

The regression model is given as:

Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε

To determine the regression equation for winter rainy days, we consider that:

[tex]Rain = 1[/tex]

This also means that:

[tex]Spring = 0[/tex]

[tex]Summer = 0[/tex]

[tex]Fall = 0[/tex]

ε = 0

Because each of these seasons can only happen one at a time, and the current season is winter

So, the regression equation becomes

Humidity = β0 + β1Temperature + (β2 * 0) + (β3 * 0) + (β4 * 0) + (β5 * 1) + 0

Evaluate the products

Humidity = β0 + β1Temperature + 0 + 0 + 0 + β5 + 0

The sum of 0 is 0. So, we have:

Humidity = β0 + β1Temperature + β5

Rewrite as:

Humidity = β0 + β5 + β1Temperature

Hence, the regression equation for winter rainy days is  

Humidity = β0 + β5 + β1Temperature

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from the pic above, hope it helps you

Answer:

B

Step-by-step explanation:

Divided 20 by .50 and got this

Answer:

2) 49

3) 8

4) 85

Hope you still need them and that they are correct!

Answer:

P= -3

X= -18

Y= -7

S= -70

B= -9

M= -5

N= 0

Q= -22

The second slide's answers are attached to this message as a pic ;)

Step-by-step explanation:

Hope it was helpful dear ;)

Answer:

C. 0.10

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Goes to the city playoffs

Event B: Goes to the state playoffs.

In Littletown, the probability that a baseball team goes to the city playoffs is 0.20.

This means that [tex]P(A) = 0.2[/tex]

The probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.50.

This means that [tex]P(B|A) = 0.5[/tex]

What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?

This is [tex]P(A \cap B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(A)*P(B|A) = 0.2*0.5 = 0.1[/tex]

The correct answer is given by option C.