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Francisco v
O GRAPHING. FUNCTIONS, AND LINEAR SYSTEMS
Solving a word problem involving a sum and another basic...
A textbook store sold a combined total of 432 physics and biology textbooks in a week. The number of physics textbooks sold was 60 more than the number of
biology textbooks sold. How many textbooks of each type were sold?

Answer:

here you go............

Step-by-step explanation:

I hope it helped

Answer:n

Step-by-step explanationaa:

Answer:

Option B is correct

Step-by-step explanation:

Given data

We are given the expression

-4x + 2y > 12

We want to substitute y=4 into the expression

-4x + 2(4) > 12

-4x + 8 > 12

-4x> 12-8

-4x> 4

divide both sides by -4

x> 4/-4

x>-1

Hence option B is correct

Step-by-step explanation:

f(g(x))

f(x-1)

(x-1)^2

x^2 -2x + 1

Answer:

Step-by-step explanation:

The answer is TRUE

True

Answer:

a) 2x + 8 = 2(x + 4) has infinite solutions because it simplifies down to x = x. Here is the work where this equation is solved.

2x + 8 = 2(x + 4)

2x + 8 = 2(x) + 2(4)

2x + 8 = 2x +8

2x + 8 - 8 = 2x + 8 -8

2x = 2x

2x/2 = 2x/2

x = x

So, because the equation ends in x = x, you can substitute any value for x and the equation will remain true.

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b) 3x + 7 = 3(x + 7) has no solutions because it simplifies down to an untrue statement. The equation is simplified below.

3x + 7 = 3(x + 7)

3x + 7 = 3(x) + 3(7)

3x + 7 = 3x + 21

3x + 7 - 7 = 3x + 21 - 7

3x = 3x + 14

3x/3 = 3x/3 +14

x = x + 14

However, this is false. x cannot be equal to itself plus 14.

x ≠ x + 14

The simplification of this equation is untrue, so there is no solution to it.

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I hope this is helpful :) Good luck

Answer:

1 / 36 ft³

Step-by-step explanation:

Length = 1/2 ft

Width = 1/6 ft

Height = 1/3 ft

The volume of the tank can be obtained using the relation :

Volume = Length * width * height

Volume = (1/2 * 1/6 * 1/3) ft³

Volume = 1 / 36 ft³

Answer:

A right circular cone

Step-by-step explanation:

Answer:

0.3372 = 33.72% probability of having a sample mean of 116.8 or less for a random sample of this size

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean IQ score of its members is 118, with a standard deviation of 17.

This means that [tex]\mu = 118, \sigma = 17[/tex]

Sample of 35:

This means that [tex]n = 35, s = \frac{17}{\sqrt{35}}[/tex]

What is the probability of having a sample mean of 116.8 or less for a random sample of this size?

This is the pvalue of Z when X = 116.8. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{116.8 - 118}{\frac{17}{\sqrt{35}}}[/tex]

[tex]Z = -0.42[/tex]

[tex]Z = -0.42[/tex] has a pvalue of 0.3372

0.3372 = 33.72% probability of having a sample mean of 116.8 or less for a random sample of this size

Answer:

(x-2)(x-2) or (x+2)(x+2)

Step-by-step explanation:

since you are squaring it, technically the terms are negative, but the product will be positive. when you multiply two negative factors, you get a positive answer. so either both can be negative or both can be positive.

Answer:

a) The total engine volume is 30.3265 in³

b) the mass of air contained in the engine is 0.00129 lbm

c) The efficiency of the engine is 55.6%

Step-by-step explanation:

Given the data in the question;

The configuration is in line with four-stroke, four-cylinder engine.

Bore ( d ) = 3.17 in

Stroke ( L ) = 3.48 in

compression ratio ( r ) = 10.6 : 1

First, we calculate the swept Volume V₁ = π/4 × d²L

we substitute

V₁ = π/4 × (3.17 )² × (3.48) = 27.4655 in³

Now, Compression Ration; r = Vs + Vc / Vc

r = (V₁ + V₂) / V₂

we substitute

10.6 = (27.4655 + V₂) / V₂

10.6V₂ = 27.4655 + V₂

10.6V₂ - V₂ = 27.4655

9.6V₂ = 27.4655

V₂ = 2.861 in³

So

a) total engine volume

[tex]V_{BDC[/tex] = V₁ + V₂

we substitute

[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³

[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³

[tex]V_{BDC[/tex] = 30.3265 in³

Therefore, The total engine volume is 30.3265 in³

b) The mass of air

given that; T = 540°R, P = 14.7 psia

we know that; PV = mRT   { R is constant }

we solve for m

m = PV / RT

we substitute

m = (14.7 × 30.3265)  / ( 0.3704 × 1728 )540

m = 445.79955 / 345627.648

m = 0.00129 lbm

Therefore, the mass of air contained in the engine is 0.00129 lbm

c) The efficiency

from table { properties of air}

At 540°R; u₁ = 92.04 BTu/lbm, u[tex]_r[/tex]₁ = 144.32

Now process 1 - 2 ( Isentropic )   u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂  = V₁/V₁ = r

so,  u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂ = r

144.32  / u[tex]_r[/tex]₂ = 10.6

u[tex]_r[/tex]₂ = 144.32/10.6

u[tex]_r[/tex]₂ = 13.61

Thus, at u[tex]_r[/tex]₂ = 13.61, u₂ = 235 BTU/lbm, T₂ = 1340°R

Now, we know that;

P₁V₁/T₁ = P₂V₂/T₂  ⇒ (P₁/V₁)r = P₂/T₂

⇒ ( 14.7 / 540 )10.6 = P₂/1340

P₂ = 386.664 psia  

process 2 - 3; constant volume heat addition;

Now, At T₃ = 3600°R, u₃ = 721.44 BTU/lbm, u[tex]_r[/tex]₃ = 0.6449

so, [tex]q_{in[/tex] =  u₃ -  u₂

we substitute

so, [tex]q_{in[/tex] =  721.44  -  235  = 486.44 BTU/lbm

Next, process 3 - 4; Isentropic  

u[tex]_r[/tex]₄/u[tex]_r[/tex]₃ = V₄/V₃ = r

u[tex]_r[/tex]₄ / 0.6449  = 10.6

u[tex]_r[/tex]₄ = 6.8359

At u[tex]_r[/tex]₄ = 6.8359; u₄ = 308 BTU/lbm

∴

Heat Rejection [tex]q_{out[/tex] = u₄ - u₁ = 308 - 92.04 = 215.96 BTU/lbm

so, [tex]W_{net[/tex] = [tex]q_{in[/tex] - [tex]q_{out[/tex]

[tex]W_{net[/tex] = 486.44 - 215.96

[tex]W_{net[/tex] = 270.48 BTU/lbm

so the efficiency; η[tex]_{thermal[/tex] = ([tex]W_{net[/tex] / [tex]q_{in[/tex] ) × 100%

η[tex]_{thermal[/tex] = ( 270.48 / 486.44  ) × 100%

η[tex]_{thermal[/tex] = ( 0.55604  ) × 100%    

η[tex]_{thermal[/tex] = 55.6%

Therefore, The efficiency of the engine is 55.6%

Answer:

The answer is 7/20 miles.

Step-by-step explanation:

Just multiply 7/6 x 2/5, then you have the answer

Answer:

List all the factors of 40

Step-by-step explanation:

The solid from the net is a cube

Answer: Cube

A cube has 6 faces, which makes this net accurate.

Answer:

Area of cardboard required = 468 cm²

Step-by-step explanation:

Area of the cardboard required = Surface area of the triangular prism

Surface area of the triangular prism = Area of the lateral sides + Area of the triangular sides

Area of the one triangular side = [tex]\frac{1}{2}(\text{Base)}(\text{Height})[/tex]

                                                    = [tex]\frac{1}{2}(12)(9)[/tex]

                                                    = 54 cm²

Area of lateral sides = Perimeter of the triangular base × Height

Perimeter of the triangular base = 9 + 12 + 15

                                                     = 36 cm

Now area of the lateral sides = (36) × 10

                                                = 360 cm²

Surface area of the prism = 360 + 2(54)

                                          = 360 + 108

                                          = 468 cm²

Therefore, area of cardboard required for each box = 468 cm²

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

Let's use CAH  1st  , on the Lenovo building,  b/c we  have they Hypotenuse (Hyp)  and an angle and we want to know the other side of the Lenovo building

Cos(30) = x/294

294*Cos(30) = x

254.611 = x

Sin(30) = y / 294

294*Sin(30) = y

147 = y

perimeter = 147+254.611+294

perimeter Lenovo = 695.611 feet

For Asus building

hyp = sqrt [ ( 144.5*[tex]\sqrt{2}[/tex])^2 +  144.5*[tex]\sqrt{2}[/tex])^2 )]

hyp = 289

perimeter = 289+144.5*[tex]\sqrt{2}[/tex]+144.5*[tex]\sqrt{2}[/tex]

perimeter Asus = 697.7077

The difference of the two buildings is

697.7077 -  695.611 =2.09671 feet

the difference is 2.10 feet ( rounded to nearest 100th)

Answer:

-6(-2/3+2x)

=12/3+12x

=4+12x

4(1+3x)

Answer:

c is correct

Step-by-step explanation:

Answer:

c is right answer

Step-by-step explanation:

HOPE IT HELPS U

FOLLOW MY ACCOUNT PLS PLS

Answer:

C and E

Step-by-step explanation:

Expressions does not contain any equal or less than greater than sign

So C and E are the right answers

Answer:

4.9:13.1

Step-by-step explanation:

V=4/3*pi*r^3

Answer:

Step-by-step explanation:

Answer:

70kilometers

Step-by-step explanation:

first we must find how much one half of a centimeter is

well, its easy, theres already a half for the distance, and the representation is an even number, so cut it in half.

20-10 is 10

and now the multiplication

20x3=60

60+10=70

70 kilometers

Answer:

See Annex ( Tree diagram )

Step-by-step explanation:

1) Attached

2) Probability of the second ball is yellow is

P(2nd ball is yellow ) = Probability 2nd ball s yellow (if the first one was black) + Probability 2nd ball s yellow (if the first one was Yellow)

P(2nd ball is yellow ) = 0,204 + 0,045

P(2nd ball is yellow ) = 0,249

Answer:

30% ywww

Step-by-step explanation:

Answer:

Step-by-step explanation:

A' (2,-3)

B' (5,-5)

C' (7,-3)

D' (5,-2)

Answer:

A' (2,-3)

B' (5,-5)

C' (7,-3)

D' (5,-2)

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

just done the assignment

Linear regression line is a algebraic model to show the relationship between the two models by putting the value of the one variable to get the value of other.. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels. Therefore the option B is the correct option.

The equation of the experiment to know the relationship between the amount of nitrogen added to a cornfield and the number of bushels of corn produced is,

[tex]y=0.43x+28.5[/tex]

Linear regression line is a algebraic model to show the relationship between the two models by putting the value of the one variable to get the value of other.

Linear regression line can be represent as,

[tex]y=Ax+B[/tex]

Here x is the explanatory variable and y is the dependent variable. A is the slope of the line and B is the intercept.

In the given equation there are two variable given.

Variable x represent the amount of nitrogen added, and the variable y, represents the number of bushels of corn produced.

As putting the value of x the y increases with value of number 0.43. Thus as we are increasing the value of the nitrogen with unit 1 the number of bushels of corn produced is increased by unit 0.43.

Hence for every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels. Therefore the option B is the correct option.

Learn more about the linear regression here;

https://brainly.com/question/25311696

Answer:

625/100,000,000 or 6.25 out of one million

Step-by-step explanation:

(0.005)^4 = .000000000625  =  625/100,000,000

The probability that all four computers fail on one day is =6.3*[tex]10^{-10}[/tex].

It is a branch of mathematics that deals with the occurrence of a random event.

The probability that a computer fails on any single day is 0.005.

Let X denotes no. of computers fail on day

So, n = 4 , p = 0.05, q= 1-0.05=0.995

P (X = x) = [tex]^{n} C_x \;p^{x} \;q^{n-x}[/tex]

P (X = 4)

= [tex]^{4} C_4 \;(0.005)^{4} \;(0.995)^{4-4}[/tex]

=1* 0.00000000063*1

=0.00000000063

=6.3*[tex]10^{-10}[/tex]

Hence, the probability that all four computers fail on one day is

=6.3*[tex]10^{-10}[/tex].

Learn more about probability here:

https://brainly.com/question/15055443

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Answer:

|x-8| = 7

Step-by-step explanation:

The following equation would make x=15 when solved.

|x-8| = 7

This is because if we substitute 15 for x we would have to subtract 8 from 15 which would give us 7 and the absolute value of 7 is 7 which would ultimately make the equation true.