Find the measure of ∠.

Using the normal distribution, it is found that there is a 0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

In this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 2.8, \sigma = 0.7[/tex].

The probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters is one subtracted by the p-value of Z when X = 4, hence:

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

[tex]Z = \frac{4 - 2.8}{0.7}[/tex]

Z = 1.71

Z = 1.71 has a p-value of 0.9564.

1 - 0.9564 = 0.0436.

0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.

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Answer:

≈4.24x

Step-by-step explanation:

[tex]\sqrt{18} = 4.24[/tex]

Have a nice day! :)

Answer:

18x

Step-by-step explanation:

because itś squared, and the area of a square is always squared, its 18x

Answer: f(y) x g(y) = 1

Step-by-step explanation:

[tex]\frac{2y^3-y^2+2y-1}{y^3-y^2+y-1}\cdot \frac{2y^2-3y+1}{4y^2-4y+1}\\\\= \frac{4y^5-8y^4+9y^3-9y^2+5y-1}{4y^5-8y^4+9y^3-9y^2+5y-1} \\\\= \frac{(y-1)(2y-1)(2y-1)(y^2+1)}{(y-1)(2y-1)(2y-1)(y^2+1)} \\\\= 1[/tex]

Answer:

3

Step-by-step explanation:

2(x + 1) = 3(5 - x) + 2

Distribute,

2(x + 1) = 3(5 - x) + 2

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

Rearrange terms,

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

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

Distribute,

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

2x + 2 = -3x + 15 + 2

Add the numbers,

2x + 2 = -3x + 15 + 2

2x + 2 = -3x + 17

Subtract 2 from both sides,

2x + 2 = -3x + 17

2x + 2 - 2 = -3x + 17 - 2

2x  = -3x + 17 - 2

2x  = -3x + 15

Add 3x to both sides,

2x  = -3x + 15

2x + 3x  = -3x + 3x + 15

5x  = -3x + 3x + 15

5x  =  15

Divide both sides by the same factor (15),

5x  =  15

5x/5 = 15/5

x = 15/5

x = 3

Hence, the answer is 3.

Answer:

x = 3, y = 3

Step-by-step explanation:

x = -5x -18

5x + 18 = -x

6x + 18 = 0

6x = 18

x = 3

The statements which are correct include the following:

The table given shows that:

This therefore results in the conclusion that option 1,3 and 4 are

the most appropriate options.

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Answer:

10 lbs

Step-by-step explanation:

25 is to 5    as   x is to 2

25/5 = x/2

2 * 25/5 = x = 10 lbs

An expression that gives the degree of the polynomial is [tex]\rm ax^2+bx+c=0[/tex].

An irreducible quadratic factor is an irreducible factor that is quadratic or has the highest exponent of 2.

An irreducible quadratic factor is an irreducible factor that is quadratic or has the highest exponent of 2.

A nonlinear equation is one in which the maximum degree of a term is two or more than two. When the polynomial equation is with degree two, then it is called a quadratic equation, and it is represented by a standard expression;

[tex]\rm ax^2+bx+c=0[/tex]

Where a is not equal to 0.

The degree of the polynomial is 2.

A quadratic polynomial can be further divided into linear factors. Now, simplify one of the quadratic expressions by completing the square method, which gives two linear factors.

Hence, an expression that gives the degree of the polynomial is [tex]\rm ax^2+bx+c=0[/tex].

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Answer:

pickup b

Step-by-step explanation:

Unit conversion :

1 kilogram is about 2.20462262 pounds

Solving :

⇒ Let's convert pickup b's mass into pounds

⇒ mass (pickup b) = 685 × 2.20462262

⇒ mass (pickup b) = 1510 pounds (approximately)

Clearly :

⇒ 1500 < 1510

⇒ mass (pickup a) < mass (pickup b)

Hence, pickup b weighs more.

The mean of the number of pets which Spencer has surveyed for five of his friends is number 3.

The mean of the data is the average value of the given data. The mean of the data is the ratio of sum of all the values of data to the total number of values of data.

Spencer has surveyed five of his friends to known that how many pets they have.

His results are shown in the table below.  Cody has 1 Lara has 4 Sam has 5 Ella has 3 Maria has 2. There are total 5 friends. Thus the mean number of pets is:

[tex]\text{Mean}=\dfrac{1+4+5+3+2}{5}\\\text{Mean}=\dfrac{15}{5}\\\text{Mean}=3[/tex]

Thus, the mean of the number of pets which Spencer has surveyed for five of his friends is number 3.

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Step-by-step explanation:

[tex]Another example , when a straight wire is moved up and down rapidly between the two poles of a horseshoe magnet , then an electric current is produced in the wire. This is also an example of electromagnetic induction .

Answer:

2/7 + 7/14 = 11/14

Step-by-step explanation:

7 x -2 = -14 Each seventh is going to be worth 2 fourteenths!

This means 2/7 = 4/14

4/14 + 7/14 = 11/14

Answer:

eleven fourteenths

Step-by-step explanation:

Answer:

5000 multiplied by 0.05 multiplied by 4

Step-by-step explanation:

you should get 1000. :D next you add 1000 to the orginal 5000 to get 6000!

Answer:

A

Step-by-step explanation:

if it is at least -27 it will be greater than or equal to -27

Answer:

1/10

Step-by-step explanation:

Answer:

pls refer to given attachemnt

Answer:

D

Step-by-step explanation:

[tex] \frac{3}{10} = 0.3[/tex]

[tex] \frac{1}{3} = 0.333333333[/tex]

[tex]0.333 = 0.333[/tex]

[tex]33\% = 0.33[/tex]

[tex]0.3 < 0.33 < 0.333 < 0.333333333[/tex]

The algebraic expression of a polynomial with a degree of 4 is 9x⁴ – x³ – x/5

For a polynomial to have a degree of 4, the following must be true:

Using the above highlight, the algebraic expression of a polynomial with a degree of 4 is 9x⁴ – x³ – x/5

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The statement third, “This is voluntary response bias. The result overestimates true support for firing the coach” is correct.

A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.

We have:

A local baseball team is struggling this season, and many fans of the team believe it may be time to replace the head coach.

Number of votes V(n) = 2367

After the value of V(n) 79% of those who responded felt the coach should be fired.

Based on the data given, we can say this is referred to as voluntary response bias. The outcome exaggerates the level of support for firing the coach.

Thus, the statement third “This is voluntary response bias. The result overestimates true support for firing the coach” is correct.

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Answer:

[tex]12x - 3y = 6[/tex]

Step-by-step explanation:

Standard form is written this way: [tex]Ax+By=C[/tex]

However, in this case, we just have to simplify 8x-3y=6-4x, as it is already mostly in standard form.

So, to do this, we have to combine like terms.

The only like terms that can be combined are -4x and 8x.

So, we add 4x to both sides, and we get: [tex]12x - 3y = 6[/tex].

Answer:

5/6

Step-by-step explanation:

The factors of 24 that are on a die are: 1,2,3,4 and 6. This only leaves 5 that isn't a factor of 24. Therefore, since there are 5 possibilities out of the 6 total numbers, the probability of rolling factors of 24 is 5/6.

Answer:

The perimeter of this isosceles trapazoid is 49

Step-by-step explanation:

P = 11 + 14 + 2(12)

Answer:

the answer is 80

Step-by-step explanation:

QR=ST: 7x+3=5x+25

2x=22

x=11

7(11)+3=80      5(11)+25=80

Answer:

C.

Step-by-step explanation:

10^2=100

100 shifts the decimal point 2 places to the right

Answer: P(sum is 5 or lower) = 10/36 (not simplified) = 5/18 (simplified)

Step-by-step explanation: The event is {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1)}

x = 50.5°

In order to solve, get to know about the sine rule:

[tex]\bf Sine \ Rule = \dfrac{A}{sinA} = \dfrac{B}{sinB}= \dfrac{C}{sinC}[/tex]

[tex]\sf \dfrac{BD}{sin(50)} = \dfrac{5.6}{sin(78)}[/tex]

[tex]\sf BD = \dfrac{5.6(sin(50))}{sin(78)}[/tex]

[tex]\sf BD = 4.385686657 \ cm[/tex]

Then find angle D = 180° - 78° = 102°

[tex]\sf \dfrac{4.385686657}{sinC} = \dfrac{9.3}{sin(102)}[/tex]

[tex]\sf C = sin^{-1}(\dfrac{4.385686657sin(102)}{9.3} )[/tex]

[tex]\sf C = 27.37 ^{\circ \:}[/tex]

[tex]\sf B + C + D = 180^\circ[/tex]

[tex]\sf x + 27.37^\circ + 102^\circ = 180^\circ[/tex]

[tex]\sf x = 180^\circ - 102^\circ - 27.37^\circ[/tex]

[tex]\sf x = 50.53^\circ[/tex]

[tex]\sf x = 50.5^\circ \ \ \ (rounded \ to \ nearest \ 3 \ significant \ figure)[/tex]

Answer:

x = 50.5° (3 sf)

Step-by-step explanation:

Sine Rule for side lengths

[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Find BD:

[tex]\implies \sf \dfrac{BD}{\sin BAD}=\dfrac{AB}{\sin BDA}[/tex]

[tex]\implies \sf \dfrac{BD}{\sin 50^{\circ}}=\dfrac{5.6}{\sin 78^{\circ}}[/tex]

[tex]\implies \sf BD=\dfrac{5.6\:sin 50^{\circ}}{\sin 78^{\circ}}[/tex]

[tex]\implies \sf BD=4.385686657...cm[/tex]

Angles on a straight line sum to 180°

⇒ ∠ADB + ∠BDC = 180°

⇒ 78° + ∠BDC = 180°

⇒ ∠BDC = 102°

Sine Rule for angles

[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Find ∠BCD:

[tex]\implies \sf \dfrac{\sin BCD}{BD}=\dfrac{\sin BDC}{BC}[/tex]

[tex]\implies \sf \dfrac{\sin BCD}{4.385...}=\dfrac{\sin 102^{\circ}}{9.3}[/tex]

[tex]\implies \sf BCD=\sin^{-1}\left(\dfrac{4.385...\sin 102^{\circ}}{9.3}\right)[/tex]

[tex]\implies \sf BCD=27.46935172...^{\circ}[/tex]

The interior angles of a triangle sum to 180°

⇒ ∠CBD + ∠BDC + ∠BCD = 180°

⇒ x + 102° + 27.469...° = 180°

⇒ x = 50.53064828...°

⇒ x = 50.5° (3 sf)

Answer: Heyaa!~

Your Answer is... 15/2 in its exact form!

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Hopefully this helps you! ~