Help. Please!!! 30 points

We have the following:

The first thing is to calculate the ratio between both paintings.

After finding the ratios, it can be calculated for any value using a proportionality rule.

for example, for 5 cups of blue paint, should be for yellow paint:

therefore, should be 25 cups of yellow paint

Answer: 34 in^3

Step-by-step explanation:

Surface area of triangle = 1/2 x  3.4 x 2.5 = 4.25

To find the volume of the prism, multiply the surface area of the triangle by length.

So 4.25 x 8 = 34 in^3

The axial force in the rails if the temperature were to rise to T3 = 110 ∘F is approximately 84 kips.

Given data: Length of A-36 steel rails = 40 ft

Cross-sectional area of each rail = 6.00 in².

The temperature of the steel rails increases from T₁ = 68°F to T₃ = 110°F.Multiply the coefficient of thermal expansion, alpha, by the temperature change and the length of the rail to determine the change in length of the rail:ΔL = alpha * L * ΔT

Where:L is the length of the railΔT is the temperature differencealpha is the coefficient of thermal expansion of A-36 steel. It is given that the coefficient of thermal expansion of A-36 steel is

\(6.5 x 10^−6/°F.ΔL = (6.5 x 10^−6/°F) × 40 ft × (110°F - 68°F)= 0.013 ft = 0.156\)in

This is the change in length of the rail due to the increase in temperature.

There is a small gap between the steel rails to allow for thermal expansion. The change in the length of the rail due to an increase in temperature will be accommodated by the gap. Since there are two rails, the total change in length will be twice this value:

ΔL_total = 2 × ΔL_total = 2 × 0.013 ft = 0.026 ft = 0.312 in

This is the total change in length of both rails due to the increase in temperature.

The axial force in the rails can be calculated using the formula:

F = EA ΔL / L

Given data:

\(E = Young's modulus for A-36 steel = 29 x 10^6 psi = (29 × 10^6) / (12 × 10^3)\)ksiA = cross-sectional area = 6.00 in²ΔL = total change in length of both rails = 0.312 inL = length of both rails = 80 ftF = (EA ΔL) / L= [(29 × 10^6) / (12 × 10^3) ksi] × (6.00 in²) × (0.312 in) / (80 ft)≈ 84 kips

Therefore, the axial force in the rails if the temperature were to rise to T3 = 110 ∘F is approximately 84 kips.

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To evaluate the integral 10) ∫ (2x-1) ln(3x) dx, we will use integration by parts, which involves the formula ∫udv = uv - ∫vdu, where u and dv are differentiable functions.

Step 1: Choose u and dv:
u = ln(3x), so du = (1/x) dx
dv = (2x - 1) dx, so v = x^2 - x
Step 2: Apply integration by parts formula:
∫ (2x-1) ln(3x) dx = uv - ∫vdu
= (x^2 - x)ln(3x) - ∫(x^2 - x)(1/x) dx
Step 3: Simplify the integral:
= (x^2 - x)ln(3x) - ∫(x - 1) dx
Step 4: Integrate the simplified integral:
= (x^2 - x)ln(3x) - (x^2/2 - x).                                                                                                                                                      Step 5: Add the constant of integration, C:
= (x^2 - x)ln(3x) - (x^2/2 - x) + C
So, the evaluated integral is ∫ (2x-1) ln(3x) dx = (x^2 - x)ln(3x) - (x^2/2 - x) + C.

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Answer: 25

Step-by-step explanation:

they are corresponding angles

By solving for the density of the two metal cubes, we can determine that the two metal cubes are not made from the same material.

Density, denoted by ρ, is a property of any substance that is defined as the ratio between the mass and volume of the substance.

ρ = m/v

where ρ = density

m = mass

v =  volume

Solving the density of each cube.

Cube 1 :

ρ = m/v

ρ = m/e^3

ρ = 43. 63 g/(3. 2 cm)^3

ρ = 1.3315 g/cm^3

Cube 2 :

ρ = m/v

ρ = m/e^3

ρ = 683. 5 g/(8. 34 cm)^3

ρ = 1.1783 g/cm^3

If two objects have the same density, then they are made from the same material. Since the density of the two cubes are not equal, then they are not made form the same material.

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490

472 <490<500

it fits the criteria

Answer:

x and y can be any two numbers greater than zero such that y is also greater than x

D.no more than 45

C.50 miles per hour

Step-by-step explanation:

Let the two numbers be such that x< y because we have been given y/x>1 and x/y< 1 .

Suppose we take y= 9 and x= 3 then

9/3 > 1

3>1

Also

3/9 < 1

1/3 < 1

x and y can be any two numbers greater than zero such that y is also greater than x

2. Total weight that can be carried is 3000 pounds.

The big machine is 300 pounds. The weight that the truck can carry beside the big machine is 3000-300= 2700 pounds.

The smaller machines weigh 60 pounds

The number of smaller machines that can be carried is 2700 ÷ 60= 45 other than the big machine.

3. Total distance = Speed * time

                           = 48 * (40/60) = 32 miles

New distance = 32+ 8= 40 miles

New time = 48 minutes

Speed = distance / time = 40/ 48/60=  50 miles per hour

Answer:

x=−6

Step-by-step explanation:

Answer:

C. x = -6

Step-by-step explanation:

\(2(3x + 7) = -22.\\Step -1: Multiply-through-by-two\\6x + 14= -22\\Collect -like-terms.\\6x= -22-14\\6x =-36\\Divide-both-sides-of-the-equation-by 6\\ = x= -6\)

Answer:

\(\boxed{2x-3}\)

Step-by-step explanation:

\(f(x)=3x-1\\ g(x)= x+2\)

\((f-g)(x)\\f(x)-g(x)\)

\((3x-1)-(x+2)\\ 3x-1-x-2\\2x-3\)

The pharmacy should send two pills marked  for the patient to take.

To answer this question, we can use the formula below;

Dosage = (Amount of Drug x Patient's Weight) / Time

Since we don't have any information about the patient's weight or the time, we can't calculate the dosage.

However, we can calculate the number of pills required.

So, let's proceed with the calculation.

Each pill contains 2.5 mg of the pain reliever.

We need to administer a low dose, so let's assume the dose required is 5 mg.

To administer this dose, we need to give two pills, i.e., 2 x 2.5 = 5mg.

However, the question asks us to round the answer to the nearest tenth of a pill.

Since we can't divide a pill into parts, we need to round the answer up or down to the nearest whole pill.

In this case, since we need two pills, the answer is 2 pills.

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Answer:

The distance is 7 units between point D and point E

We can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:

A parabola refers to the shape that traces the equation of the form ax² + bx + c.

A parabola's directrix is a vertical or horizontal line that never contacts the parabola and is located at p distance from the vertex and 2p distance from the focus.

The parabola created when the directrix is on the y coordinate called a vertical parabola.

If the directrix value is greater than the corresponding focus or vertex, there will be a negative p and the parabola will face downhill.

If the directrix value is less than the corresponding focus or vertex, there will be positive p and the parabola will face up.

From the given definition of the directrix, we can find the value of p;

2p = y coordinate of focus - equation of the directrix

2p = 1 - (-1)

2p = 2

p = 1

Vertex, v(h, k) compared with f(h, k + p), we will get;

k + p = 1

k = 0

Therefore, the vertex is (-8, 0).

Thus, we can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:

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Answer:

$3.40

Step-by-step explanation:

"A bill" = "1 bill"

Possibile bills = $1, $5, $10, $20, $50, $100

4 × 1.65 = 6.6

$6.60 is more than $5, but less than $10

Since the student is only using a single bill, it must be the $10 bill

10 - 6.6 = 3.4

$3.40

The first Epistle of John was written about AD of between 95 and 110 . So, by this our option should be 97 AD, which is true.

The Fourth of the Catholic Epistles, The First Epistle of John[a] is the first of the Johannine epistles in the New Testament. The authorship of the Johannine writings is disputed among academics. The First Epistle's author is identified as John the Evangelist, who most scholars do not consider to be the same person as John the Apostle. The three Johannine epistles are thought to have been written by the same person by the majority of scholars, however it is unclear if the same person wrote the Gospel of John.

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Answer:

c=1t

Step-by-step explanation:

Answer:

-44

Step-by-step explanation:

-2|6 * -3 - 4|

-2|-18-4|

-2|-22|

-2 * 22

-44

Answer:

Step-by-step explanation: There are 8 people in the gym.

An hour later, there are double that number.

How many people are in the gym now?

Answer:

To convert 2 Bigha into Kattha:

If 1 Bigha = 20 Kattha:

2 Bigha = 2 * 20 Kattha = 40 Kattha

If 1 Bigha = 16 Kattha:

2 Bigha = 2 * 16 Kattha = 32 Kattha

graphed below:

\(\sf f(x)=3x^2-6x+5\)

Answer:

Given function:    \(f(x)=3x^2-6x+5\)

Vertex form:  \(y=a(x-h)^2+k\)  

(where \((h, k)\) is the vertex)

Expand vertex form:

\(y=ax^2-2ahx+ah^2+k\)

Compare coefficients of given function with expanded vertex form

Comparing coefficient of \(x^2\):

\(3=a\)

Comparing coefficient of \(x\):

\(\ \ \ \ \ -6=-2ah\\\implies-6=-2 \cdot 3h\\\implies -6=-6h\\\implies h=1\)

Comparing  constant:

\(\ \ \ \ \ \ 5=ah^2+k\\\implies5=3(1)^2+k \\\implies 5=3+k\\\implies k=2\)

Therefore, the vertex is (1, 2)

As the leading coefficient is positive, the parabola will open upwards.

Additional plot points:

\(f(0)=3(0)^2-6(0)+5=5\)

\(f(2)=3(2)^2-6(2)+5=5\)

(0, 5) and (2, 5)

Answer:

I think it stays the same.

Step-by-step explanation:

Answer:

1) m = h - w/8

Subtract h from both sides.

m - h = -w/8

Subtract m from both sides.

-h = -m - w/8

Divide all terms by -1.

h = m + w/8.

2) m = h - w/8

Get rid of the denominator 8 by multiplying 8/1 to all terms.

8m = 8h - w

Add w on both sides and subtract 8m from both sides.

w = 8h - 8m

3) w = x + y/z

Get rid of the denominator z by multiplying it to all terms.

wz = xz + y

Subtract xz from both sides of the equation.

wz - xz = y OR y = wz - xz

4) w = x + y/z

Subtract x from both sides.

w - x = y/z

Get rid of the denominator by multiplying it to all terms.

wz - xz = y

Now factor the expression wz - xz.

z(w - x) = y

Divide both sides by w - x.

z = y / w - x

This is read as z equals to y divided by w minus x.

5) The area of a triangle is A = 1/2bh

First, get rid of the denominator by multiplying both sides by 2.

2A = bh

To find b, divide both sides by h.

2A/h = b

6) P = kt/v

Multiply both sides by v.

Pv = kt

Divide both sides by t.

Pv/t = k OR k = Pv/t.

Step-by-step explanation:

The  value of the given equation is, (6m⁸n⁹) (4mn⁷) =\($$=24 m^9 n^{16}$$\)

Simplify\($\left(6 m^8 n^9\right)\left(4 m n^7\right): \quad 24 m^9 n^{16}$\)

steps

\($$\left(6 m^8 n^9\right)\left(4 m n^7\right)$$\)

Apply exponent rule: \($a^b \cdot a^c=a^{b+c}=0^{\prime}=$\)

\(& m^8 m=m^{8+1} \\\)

\(& =6 n^9 \cdot 4 m^{8+1} n^7\)

\end{aligned}

Add the numbers: \($8+1=9$\)

\(=6 n^9 \cdot 4 m^9 n^7\)

Apply exponent rule: \($a^b \cdot a^c=a^{b+c}$\)

\(& n^9 n^7=n^{9+7} \\\)

\(& =6 \cdot 4 m^9 n^{9+7}\)

Add the numbers: \($9+7=16$\)

\($$=6 \cdot 4 m^9 n^{16}$$\)

Multiply the numbers: 6 - \($4=24$\)

\($$=24 m^9 n^{16}$$\)

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Answer:

Step-by-step explanation:

a² - b² = (a +b)(a - b)

a = 525  & b  = 475

525² - 475² = (525 + 475) (525 - 475)

                   =1000 * 50

                   = 50,000

The value of (525)² - (475)² using the identity (a²- b²) = (a+b) (a-b) is 50000.

The expression given is:

(525)² - (475)²

The above expression looks similar to the expression (a²- b²).

The simplified form of the expression (a²- b²) is (a+b) (a-b).

So, (525)² - (475)² can be written as:

(525)² - (475)² = (525+475) (525-475)

(525)² - (475)² = 1000 * 50

(525)² - (475)² = 50000

Therefore, the value of (525)² - (475)² using the identity (a²- b²) = (a+b) (a-b) is 50000.

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Therefore, there are 53,248 different super subs that can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from at Sandwich Station.

The super sub at Sandwich Station consists of 4 different toppings and 3 different condiments. The question is asking how many different super subs can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from.

To solve this problem, we can use the multiplication principle of counting. The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

Let's use the multiplication principle to solve this problem. There are four different toppings, and we can choose any of the eight toppings for each of the four spots.

Using the multiplication principle, there are

8 x 8 x 8 x 8 = 4096

ways to choose the toppings. Similarly, there are

6 x 6 x 6 = 216

ways to choose the condiments. Lastly, there are 6 different types of homemade bread to choose from. Using the multiplication principle again, there are

4096 x 216 x 6 = 53,248,

which means there are 53,248 ways to make the super subs.

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Answer:127.5

Step-by-step explanation:

15% of 150 = 22.5

150-22.5=127.5

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

2 units

Step-by-step explanation:

Using the given formula

P = 2(l + w)

  = 2(\(\frac{2}{3}\) + \(\frac{1}{3}\) )

   = 2(1)

   = 2 units

According to exponent rules, when we multiply terms with the same base add the exponents. Hence, the correct answer is option D.

Exponent rules are a set of rules that dictate how exponents (numbers written as a superscript) can be manipulated in mathematical operations. Some of the most commonly used exponent rules include:

        For example, \(x^4 * x^5 = x^{4+5} = x^9\)

       For example, \(x^7 / x^3 = x^{7-3} = x^4\)

        For example,\((x^3)^5 = x^{3*5} = x^{15}\)

        For example,\((xy)^3 = x^3 * y^3\)

       For example,\((x/y)^3 = x^3 / y^3\)

According to the product of the power rule, we get that we add the exponents when we multiply terms with the same base.

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