7 Theodore and Pam are rolling
out modeling clay for an activity in
art class. Theodore rolled out his
clay until it was 5 inches long
Pam rolled hers times as far
Did Pam roll her clay out less
than, more than, or the same as
Theodore?

the quotient of 5 and y:   5÷y

added to 3:   3 + 5÷y

is at least (AKA is greater than or equal to) 5:  3 + 5÷y  ≥ 5

Answer:   3 + 5÷y ≥ 5

Given:

defective units = 29.1

total production = 9,700

Hence:

substituting values in the formula:

ANSWER

0.3 percent of the production is defective.

Answer:

\(y=3x^{2} -18x+15\) is the equation the quadratic as per the given conditions.

Step-by-step explanation:

Let the equation of the quadratic be:

\(y=ax^{2} +bx+c\)

Given that it has zeroes at x = 1 and x = 5 i.e. y = 0 at both the values of x.

Also passes through point (3, -12). i.e. when x = 3, y = -12

Putting x = 1, y = 0:

\(\Rightarrow a\times 1^{2} +b\times 1+c=0\\\Rightarrow a+b+c=0 ....... (1)\)

Putting x = 5, y = 0:

\(\Rightarrow a\times 5^{2} +b\times 5+c=0\\\Rightarrow 25a+5b+c=0 ....... (2)\)

Putting x = 3, y = -12:

\(\Rightarrow a\times 3^{2} +b\times 3+c=-12\\\Rightarrow 9a+3b+c=-12 ....... (3)\)

Equation (2) - Equation (1):

\(24a+4b=0\\\Rightarrow 6a +b=0 ...... (4)\)

Equation (2) - Equation (3):

\(16a+2b=12\\\Rightarrow 8a +b=6 ...... (5)\)

Equation (5) - Equation (4):

\(2a=6\\\Rightarrow a =3\)

Putting value of a in equation (4):

\(6\times 3+b=0\\\Rightarrow b = -18\)

Putting a and b in equation (1):

\(3-18+c=0\\\Rightarrow c= 15\)

So, the quadratic equation is:

\(y=3x^{2} -18x+15\)

Answer:

15) 3(4+r)=-18

3x4+3xr

12+3r= -18

-12        -12

3r= -30

/3    /3

r= -10

Step-by-step explanation:

distribute the 3 to the 4 and the r you should then have 12+3r=-18 and so subtract from both sides 12 and you should have 3r=-30 divide both sides by 3 and you get your answer r=-10

Answer:

(7) n=9

8) x=8

9) m=-7

10) b= -6

11) r=6

12)b=10

13)v=8

14)k=-8

15)r=-10

16)p=20

17)v=10

18)x=21

19)a=28

20)b=10

Step-by-step explanation:

Step-by-step explanation:

4 x^2 - 64 = 0        re-wrire by adding 64 to both sides of the equation

4x^2 = 64               now just divide both sides by 4

x^2 = 16        that is the first part.....now sqrt both sides

x = +- 4

Answer: x^2 = 16, x = ±4

Step-by-step explanation:

Part 1: Starting with 4x^(2) - 64 = 0:

Add 64 to both sides to isolate the x^2 term:

4x^(2) = 64

Divide both sides by 4 to get x^(2) by itself:

x^(2) = 16

So we can rewrite 4x^(2) - 64 = 0 as x^(2) = 16.

Part 2: To solve x^(2) = 16, we take the square root of both sides:

x = ±√16

x = ±4

So the solution set for the equation 4x^(2) - 64 = 0 is {x = -4, x = 4}.

Answer:

8x⁵y⁷

Step-by-step explanation:

4x²y³ × 2x³y⁴ = 8x⁵y⁷

The account balance three years from now will be $13,666.10. So, the correct option is D) $13,666.10.

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The system of Linear Equation has Infinitely Many Solutions

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

To check the numebr we need to find the vaules of

a1/a2, b1/b2, c1/c2

a1/a2 = -3/-6 = 1/2

b1/b2 = 4/8 = 1/2

c1/c2 = -5/-10 = 1/2

Since the values of a1/a2 = b1/b2 = c1/c2

Theerefore, the system of Linear Equation has Infinitely Many Solutions

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The differentiation of the function y = sin(2 sin⁻¹x) is; dy/dx = d√(1 - y²)]/(√1 - x²)

1) We want to differentiate the function;

\(\frac{\sqrt{x + 1} + \sqrt{x - 1}}{\sqrt{x + 1} - \sqrt{x - 1} }\)

Differentiating this gives;

dy/dx = \(\frac{[(\frac{1}{2\sqrt{x + 1}} - \frac{1}{2\sqrt{x - 1}}) * \sqrt{x + 1} + \sqrt{x - 1}]}{(\sqrt{x + 1} - \sqrt{x - 1})^{2} }\)

That can be simplified to get;

dy/dx = \(\frac{\sqrt{x + 1} + \sqrt{x - 1} }{(x - 1)\sqrt{x + 1} + (-x - 1) \sqrt{x - 1}}\)

2) We want to differentiate the function;

y = sin(2 sin⁻¹x)

Differentiating the function gives;

dy/dx = [2cos(2 sin⁻¹x)]/√(1 - x²)

We know from trigonometric identity that;

cos²x = 1 - sin²x

Thus;

1 - sin²(2 sin⁻¹x) = cos²(2 sin⁻¹x)

But sin²(2 sin⁻¹x) = y²cos²(2 sin⁻¹x)

Thus; √(1 - y²) = cos(2 sin⁻¹x)

dy/dx = d√(1 - y²)]/(√1 - x²)

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Answer:

125.

Given:

Step-by-step explanation:

As given in the question that the ratio is already given,

therefore,

1. The ratio of tourist of to locals

the ratio of tourist to local is 4:5

\(\frac{tourist}{locals}\)=\(\frac{4}{5}\)

2. Attendance of locals at the opening

here are 100 tourist at the opening

\(\frac{100}{locals} =\frac{4}{5}\)

locals= 125

locals are 125 in attendance.

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125 is the attendance of locals

The ratio of tourists to locals is 4:5

Tourists / Locals = 4 / 5

There are 100 tourists at the opening of the new museum

100 / locals = 4/5

locals = 500/4

locals = 125

The attendance of locals is 125.

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Answer:

I think it is 90° because on a line it is 180 and and both add up to 360°

Answer:

y= -6

Step-by-step explanation:

The surface area is 72 square inches.

To find the surface area of a square pyramid, we need to calculate the area of the base and the four triangular faces.

Given that the base is 4 inches wide, the area of the square base is:
Base area = side² = 4² = 16 square inches.

The slant height is 7 inches. To find the area of one triangular face, we use:
Triangle area = (base * slant height) / 2

Each triangle has the same base length as the square base, which is 4 inches. Therefore, the area of one triangular face is:
Triangle area = (4 * 7) / 2 = 14 square inches.

Since there are four triangular faces, their total area is:
4 * Triangle area = 4 * 14 = 56 square inches.

Finally, add the base area and the total area of the triangular faces to get the surface area:
Surface area = Base area + Total triangular faces area = 16 + 56 = 72 square inches.

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Operationalization of variables in research involves defining a concept in a way that it can be measured or observed.

It is the process of taking abstract concepts, such as attitudes, beliefs, or behaviors, and defining them in a way that they can be measured using empirical methods. This is done by creating a set of specific and concrete indicators or measures that represent the concept being studied. The operationalization of variables is a critical step in the research process, as it ensures that the data collected is both reliable and valid, and can be used to draw meaningful conclusions and make predictions.

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Answer: Falling

Step-by-step explanation:

Once you rearrange this equation into y-intercept form and you get y = -4x-3, you then graph the line and the line appears to be decreasing down.

The mean or average of the dataset are calculated below by simply taking the average of each dataset.

Mean of a dataset is the average of all the observations present in the table. It is the ratio of the sum of observations to the total number of elements present in the data set. The formula of mean is given by;

Mean = sum the data / total number data

a. 6, 7, 5, 6, 9, 2, 6, 54

The mean can be calculated as;

mean = 6 + 7 + 5 + 6 + 9 + 2 + 6 + 54 / 8

mean = 95/8 = 11.875

b. 3.2, 5.4, 3.2, 3.2, 3.2, 10.8, 4.5, 4.9

mean = 3.2 + 3.2 + 3.2 + 3.2 + 4.5 + 4.9 + 5.4 + 10.8 / 8

mean = 24/5 = 4.8

c. The data set given cannot have a mean

d. 83, 79, 81, 83, 82

mean = 79 + 81 + 82 + 83 + 83 / 5

mean = 408/5 = 81.6

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Let x be the number

40% of x = 8

Multiply both-side of the equation by 100

Divide both-side of the equation by 40

Therefore, 8 is 40% of 20

Answer:not sure

Step-by-step explanation:

I have the same problem

The minimum surface area of the container is: 96.00 cm² in the given case.

Let's call the length and width of the square base "x", and the height of the container "h". Since the container has a volume of 256 cm^3, we can write:

V = \(x^2 * h = 256\)

We want to minimize the surface area of the container, which consists of the area of the base plus the area of the four sides. The area of the base , and the area of each side is xh. Therefore, the total surface area of the container is:

A = \(x^2 + 4xh\)

We can solve for h in terms of x using the volume equation:

h = \(256 / (x^2)\)

Substituting this expression for h into the surface area equation, we get:

A(x) =

To find the minimum surface area, we need to find the critical points of the function A(x).

We can do this by taking the derivative of A(x) with respect to x, setting it equal to zero, and solving for x:

\(dA/dx = 2x - 1024 / x^2 = 0\\2x = 1024 / x^2\\x^3 = 512\\x = ∛512\\x ≈ 8.00 cm\)

To confirm that this is a minimum, we can check the second derivative:

\(d^2A/dx^2 = 2 + 2048 / x^3\)

This is positive, so A(x) has a minimum at x =\(∛512\). Therefore, the minimum surface area of the container is:   96.00 cm²

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The doubling time of a population can be computed by using the exponential growth formula: dt = ln(2)/r.

Exponential growth refers to a situation where the value keeps on increasing at a constant rate relative to the initial value.

The exponential growth function represents this situation and is given as

f(x) =a(1+r)ˣ

f(x) = exponential growth function

a = initial amount or value

r = growth rate

x = period of time

To find the population's doubling time, we can apply the exponential formula for time: dt = ln(2)/r

Where:

dt = the doubling time,

r = the growth rate (expressed as a decimal fraction)

ln(2) = the natural logarithm of 2 (about 0.693)

For instance, when a population has a growth rate of 0.05 (5%) per year, its doubling time is about ln(2)/0.05 = 13.9 years.

Thus, one can calculate the exact doubling time of a population by using the exponential growth equation above, solving for time.

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Answer:

We need to know the rate constant (k), which can be determined experimentally or given in the reaction's rate equation to calculate the half-life of a reaction or decay process.

Once you have the rate constant, you can use the following formula:

\(\bold{t_{\frac{1}{2}}=\frac{ln 2}{k}}\)

Where:

\(t_{\frac{1}{2}}\)

represents the half-life of the reaction or decay process.

ln represents the natural logarithm.

k is the rate constant.

By plugging in the appropriate rate constant into the formula, you can calculate the half-life for a specific chemical reaction or decay process.

Vertical angulation refers to the angle at which the x-ray beam is directed when taking dental radiographs. It is an important factor in obtaining clear and accurate images.

In both the paralleling and bisecting techniques, the group of answer choices remains the same. However, the vertical angulation is generally greater for images taken with the paralleling technique compared to the bisecting technique.

This is because the paralleling technique requires the x-ray beam to be directed more vertically in order to capture the entire tooth structure on the film. On the other hand, the bisecting technique involves angling the x-ray beam downward to intersect the imaginary bisector between the long axis of the tooth and the film.

Therefore, the vertical angulation differs depending on which technique is being used.

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Answer:

using the formula

y -y1 = m(x -x1)

y -6 = 2(x -5)

y -6 = 2x -10

y = 2x -10+6

y =2x -4(equation of the line)

Answer:

>34.88km/h

Step-by-step explanation:

Because we have two unknown values in this question (speed of train and speed of car), we will need two equations to solve it.

Firstly, we can make a big equation for time in terms of the vehicle speeds. Time = distance / speed, so if we use t for the train speed and c for the car speed, we get this equation for speed:

30/c + 90/t = 2.5

Here the 30 is the distance traveled by the car in km and the 90 is the distance traveled by the train in km (120 - 30 = 90).

We also know that the train speed was 20km/h faster than the car speed so our second equation is:

c + 20 = t

So now we can substitute this in the big equation so we only have one variable to solve for:

30/c + 90/(c+20) = 2.5

Now to solve this, this first step is to get rid of the fractions, which we can do by multiplying all the terms by the lowest common factor of the two denominators which is c(c+20):

(30/c)*c(c+20) + (90/c+20)*c(c+20) = 2.5

This simplifies to:

120c+600=2.5c^2+50c

and then into the quadratic equation:

2.5c^2-70c-600=0

This can be solved with the quadratic formula or a solver/calculator, and yields the solutions:

c=−6.88, 34.88 (both to 2dp)

We can eliminate the negative solution because speed cannot be negative meaning that Rosea must drive her car at the speed of at least/greater than 34.88km/h if she wants the total trip to be less than 2.5 hours.

Hope this helped!

Answer:

Iran

Step-by-step explanation:

Answer:

\(x=-20\)

Step-by-step explanation:

\(\frac{x}{5}+7=3\\ \\\frac{x}{5}+7-7=3-7\\ \\\frac{x}{5}=-4\\ \\\frac{x}{5}*5=-4*5\\ \\x=-20\)

Answer:

-20

Step-by-step explanation:

Answer:

The HCF of \(a=2^1 \cdot 3^4 \cdot 5^1\) and \(b = 2^3 \cdot 3^2 \cdot 5^2\) is \(90\).

Step-by-step explanation:

To calculate the HCF of two numbers given their prime factorization, we take the lowest exponent of every prime when comparing the two numbers.

So the HCF of \(a=2^1 \cdot 3^4 \cdot 5^1\) and \(b = 2^3 \cdot 3^2 \cdot 5^2\) is \(2^1 \cdot 3^2 \cdot 5^1 = 90\).

The answer is ,  the transactions just described contribute how much to U.S. GDP for 2014 is $17 million. Option (b) .

Explanation: Gross domestic product (GDP) is a measure of a country's economic output.

The total market value of all final goods and services produced within a country during a certain period is known as GDP.

The transactions just described contribute $17 million to U.S. GDP for 2014. GDP is made up of three parts: government spending, personal consumption, and business investment, and net exports.

The transactions just described contribute how much to U.S. GDP for 2014 is $17 million.

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Answer:

|7| = 7

|-7| = 7

Step-by-step explanation:

Each is 7 numbers away from zero.

Absolute value is always positive.

A. -2/7

B. -8/15

hope it helps...!!!