Which of the following are linear measurements?

A) Length and width
B) Depth and height
C) Diameters, clearance, end play, and thickness
D) All of the above

Divide price by quantity:

3.00 / 12 = $0.25 per can.

The (∃E) rule is used to infer P(0) from ∀xP(x), and this conclusion is supported by the existence of an object that satisfies the predicate.

The rule of natural deduction that justifies P(0) from ∀xP(x) is the existential elimination (∃E) rule. This rule allows us to infer a particular instance of an existential quantification based on the existence of an object that satisfies the predicate. In this case, since we have the universal quantification ∀xP(x), we can use (∃E) to conclude P(0) by substituting 0 for x. By doing so, we have shown that there exists an object, namely 0, that satisfies the predicate P(x). Therefore, (∃E) justifies the statement P(0) from the given universal quantification.

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The possible value of QRP is 24^o.

A sine rule is a trigonometric rule which can be used to determine either the angle or length of side of a given triangle that is not a right angle.

sine rule states that;

a/Sin A = b/Sin B = c/Sin C

From the given question, let the measure of angle QRP be represented by R. So that;

9/ Sin 37 = 6/ Sin R

9 Sin R = 6 Sin 37

Sin R = 6 Sin 37/ 9

  = 3.611/ 9

  = 0.4012

R = Sin^-1 (0.4012)

  = 23.65

Thus, QRP is 24^o.

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The number of students received the text message at 10 am is 25 and at 11 am is 125.

Given,

Lets solve this using exponential expressions;-

Number of students received same text message at 9 am = 5¹ = 5

At 10 am each of this 5 students send the same text message to another 5 students;

That is, 5 x 5 = 5² = 25

Now,

At 11 am  each of this 25 students send the same text message to another 5 students;

So, 5 x 5 x 5 = 5³ = 125

Therefore,

The number of students received the text message at 10 am is 25 and at 11 am is 125.

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The efficiency of the pump (in %) is 0.35%. Hence, option (c) is correct.

Efficiency of the pump:

According to the question, a centrifugal pump with a performance curve is given. For H, the performance curve is given as,

H = 340 - 1.2(Q²) in feetAnd for BP, the performance curve is given as,

BP = 0.0521(Q³) + 1.25(Q²) + 11.042(Q) + 134.5 in horsepower (HP)

Where Q is the flow rate in ft³/s.

We have to find the efficiency of the pump which can deliver 8 ft³/s.

The specific weight of water is given as 62.4 lbf/ft³.

Efficiency of the pump,η = (output power/input power)

Where input power = power supplied to the

pump = g × Q × H × w

Where g is acceleration due to gravity, w is the specific weight of the water.

Given, g = 32.2 ft/s², w = 62.4 lbf/ft³ = 32.2 × 62.4 = 2009.28 lbf/ft³'

Using the performance curves,

H = 340 - 1.2(Q²)BP = 0.0521(Q³) + 1.25(Q²) + 11.042(Q) + 134.5

Substituting Q = 8 ft³/s, we get

H = 304 ftBP = 77.87 HP Power supplied to the pump = g × Q × H × w

= 32.2 × 8 × 304 × 2009.28

= 16.57 × 10^6 ft-lbf/s

Output power of the

pump = BP × 746

= 77.87 × 746

= 58.17 × 10^3 ft-lbf/s

Efficiency of the pump,η = (output power/input power)η

= (58.17 × 10³)/(16.57 × 10^6)η

= 0.003509

= 0.3509%.

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\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

In the first sequence,

let's take ratio of the next term with its preceding term, so we will get the common ratio ~

\(\qquad \sf  \dashrightarrow \: \cfrac{4}{16} = \dfrac{1}{4} \)

So, we can imply that The next term of the sequence is 1/4 times the previous term.

hence, the unknown term will be 1/4 times of previous term.

Therefore, the next term here is 1

In the second sequence,

Do the same procedure as above, we will get common ratio as :

\(\qquad \sf  \dashrightarrow \: \cfrac{18}{6} = 3\)

So, the next term is 3 times the preceding term, that is :

Therefore, the next term is 162

Answer:

A, 6

Step-by-step explanation:

\(50=8x+2\)

subtract \(2\) from both sides

\(48=8x\)

divide both sides by \(8\)

\(x = 6\)

plz mark me brainliest ;)

Answer:

C and B

Step-by-step explanation:

Evaluate g(5) then substitute the value obtained into f(x)

g(5) = \(\sqrt{5-1}\) = \(\sqrt{4}\) = 2 , then

f(2) = 3(2) + 1 = 6 + 1 = 7

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

f(x) = \(\frac{x^2+3}{(x-4)(x+8)}\)

the denominator of f(x) cannot be zero as this would make f(x) undefined.

equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

(x - 4)(x + 8) = 0

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 8 = 0 ⇒ x = - 8

the vertical asymptotes are x = 4 and x = - 8

Answer:

Step-by-step explanation:

The perpendicular is equal to 6. That's because the left triangle's missing angle is 180 - 45 -90 = 45

The angle in the right triangle is given as 52.

The cos(52) = adjacent side (which we just found to be 6) / y

Multiply both sides by y

y cos(52) = 6

cos(52) = 0.6157

Divide by sides by cos(52)

y = 6 / cos(52)

y = 6 / 0.6157

y = 9.76

The sum of the first 7 terms of the series is,

⇒ S = 14.91

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The series is,

8, 6, 9/2, …

Now, We can find the common ratio as;

Common ratio = 6 / 8 = 3 / 4

And, 9/2 ÷ 6 = 3/4

Hence, The series is geometric series.

So, The sum of nth term of geometric series is,

S = a₁ (1 - rⁿ) / (1 - r)

Where, 'a₁' is first term and 'r' is common ratio.

Here, a = 8, r = 3/4

Hence, The sum of 7th term of geometric series is,

S = a₁ (1 - rⁿ) / (1 - r)

S = 8 (1 - (3/4)⁷) / (1 - 3/4)

S = (8 (4096 - 2187) / 4096 ) / (1/4)

S = 8 × 1909 × 4 / 4096

S = 14.91

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Answer:

Step-by-step explanation:

7.

n=5 (given)

3n=15

3n-7=8

-10(3n-7)=-80

Check:

-10(3(5)-7)=-80

-10(15-7)=-80

-10(8)=-80

-80=-80

For 8 you can create your own descriptions of the next step (i.e Multiply both sides by 2) and just build a different equation from there.

Answer:

Using the banker's method, we can use the following formula to find the interest:

Interest = (Principal x Rate x Days) / 360

Where,

Principal = $16,400

Amount = $16,851

Days = 180

We know that the interest plus the principal equals the amount, so we can set up the following equation:

Interest + Principal = Amount

Substituting the values:

(16,400 x Rate x 180) / 360 + 16,400 = 16,851

Multiplying both sides by 360:

16,400 x Rate x 180 + 5,904,000 = 6,066,360

16,400 x Rate x 180 = 162,360

Rate = 162,360 / (16,400 x 180)

Rate = 0.055 or 5.5%

Therefore, the interest rate of the loan is 5.5%.

Answer:
He can waste 4,575 a month

Step-by-step explanation:

The TRUE statement about a New England Journal of Medicine study about twins and cancer is d) Environment played a dominant role compared to genetics in cancer likelihood amongst twins.

When a factor or person plays a dominant role, it implies that its role is decisive or overwhelming.

For instance, in the study about twins and cancer by the New England Journal of Medicine, environment decides whether twins will be predispose to cancer.

The role of environment overwhelms the role played by genetics in predisposing twins to cancer.

Thus, the true statement about the factor playing the dominant role is Option D.

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Which statement is true about a New England Journal of Medicine study about twins and cancer?

a) There was about a 70% chance if one twin contracted cancer, that the other twin would also get that same cancer.

b) Fraternal and identical twins have about the same chance of contracting cancers.

c) There was no significant correlation concerning cancer from one twin to another.

d) Environment played a dominant role compared to genetics in cancer likelihood amongst twins.

e) Environment was judged to have played a relatively small role in inherited cancer likelihood.

f) None of these statements is correct.

Answer:

The million dollar cube will be 10.79 cm tall

Step-by-step explanation:

Let the sides of the gold cube representing the tallness of the cube  be s

volume of the gold cube V = s³

Then :

\(\mathbf{s = \sqrt[3]{V} }\)  --- (1)

Similarly; we know that , density ρ = mass m/Volume V

making volume the subject of the formula, then ;

V = m/ρ

Replacing that into (1) above , we have:

\(\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }\)

Given that:

At the time, gold is selling for $1282 per troy ounce

∴ In a million-dollar cube of gold, the number of troy ounce that can be bought with a million dollar = 1000000/1282 = 780.03 troy ounce

Since 1.0000 troy ounce equals 31.1035 g

∴ 780.03 troy ounce = 780.03  × 31.1035 g

= 24261.66 g

From the tables 12.1 of Gold , the density of Gold is obtained as 19.3 g/cm³

∴

\(\mathbf{s = \sqrt[3]{\dfrac{m}{\rho}} }\)

\(\mathbf{s = \sqrt[3]{\dfrac{24261.66}{19.3}} }\)

\(\mathbf{s = \sqrt[3]{1257.080829} }\)

\(\mathbf{s = 10.79 \ cm }}\)

The million dollar cube will be 10.79 cm tall

The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.

The random variable b's expected value is then calculated as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X)  = 2.404 books.

Thus, the expected value of discrete probability distribution is 2.404 books.

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The graph for the question is attached.

The surface area of the pyramid is 980  in²

The surface area of the pyramid is given by A = 4A' + A" where

Now, A' is a triangle. So, A' = 1/2bh where

Now using Pythagoras' theorem h = √(H² + (b/2)²) where H = height of pyramid and b = base of triangular face.

So, A' = 1/2bh

= 1/2b√(H² + (b/2)²)

Also, since A" is a square is A" = b²

So, A = 4A' + A"

= 4[1/2b√(H² + (b/2)²)] + b²

= 2b√(H² + (b/2)²) + b²

Given that

Substituting the values of the variables into the equation, we have that

A = 2b√(H² + (b/2)²) + b²

= 2(20 in)√((10.5in)² + (20 in/2)²) + (20in)²

= 40 in√((110.25 in² + 100 in²) + 400in²

= 40 in√((210.25 in²) + 400in²

= 40 in(14.5  in) + 400in²

= 580  in² + 400in²

= 980  in²

The surface area is 980  in²

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The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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The error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.

The right option will be: No, she made an error in step 2. She should have found y = 0. 5.

Given the system of linear equations:

-3x + 2y = 8 ---> eqn. 1

3x + 2y = -6 ---> eqn. 1

First add both equations together:

Step 1: 4y = 2

Next, divide both sides by 4:

Step 2: y = 2/4

y = 0.5

Therefore, the error made by Kaitlyn when solving the system of equations is in step 2. Her solution will be incorrect.

The right option will be: No, she made an error in step 2. She should have found y = 0. 5.

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Given data:

The principal is

The time is

The interest is

Concept:

The formula to calculate interest rate (R) is given below as

By substituting the values in the formula above, we will have

Hence,

The final answer is 5%

Answer:

7.2

Step-by-step explanation:

Apply Law of Cosines, given that b is 13.5, c is 8.9, and Angle a is 29.

\( {a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos(a) \)

\( {a}^{2} = {13.5}^{2} + {8.9}^{2} - 2(13.5)(8.9) \times \cos(29) \)

\( {a}^{2} = 182.25 + 79.21 - 240.3 \times 0.8746\)

\( {a}^{2} = 182.25 + 79.21 - 210.1711\)

\(a = 7.2\)

Answer:

\(a\approx7.2\)

Step-by-step explanation:

The given problem presents one with the following information:

To solve this problem, one can use the law of cosines. The law of cosines is a property that can apply to any triangle. This property comes in the form of a formula, which is as follows:

\(a^2=\sqrt{b^2+c^2-2bc(cos(A))}\)

Where (a), (b), and (c) are sides of the triangle, and (<A) is the angle opposite the side (a).

Substitute the given information into the formula and solve for the unknown side (a):

\(a=\sqrt{b^2+c^2-2bc(cos(A))}\)

\(a=\sqrt{(13.5)^2+(8.9)^2-2(13.5)(8.9)(cos(29))}\)

Simplify,

\(a=\sqrt{(13.5)^2+(8.9)^2-2(13.5)(8.9)(cos(29))}\)

\(a=\sqrt{182.25+79.21-240.3(cos(29))}\)

\(a=\sqrt{261.46-240.3(cos(29))}\)

\(a=\sqrt{261.46-210.1711}\)

\(a=\sqrt{51.2889}\)

\(a\approx7.2\)

Answer:

137

Step-by-step explanation:

Add 80 and 57.

Answer:

yes because it can be equal to it

Answer:

14 months, that is, if that's your answer. You didn't ask it, just sgave information. ;(

Step-by-step explanation:

Answer: its for an assignment

Step-by-step explanation:

Answer:

WXZ, ZXW, 1

Step-by-step explanation:

Answer:

Using the Pythagorean theorem for isosceles right triangle, the length of  the hypotenuse is sqrt( 2 x 10^2) = ~14.1 in

Hope this helps!

:)