Iris wants to buy a necklace. The necklace is
$70.00. She has a coupon for 20% off her entire
order. What is the sale price for the necklace

Linear Approximation:

L(x) ≈ 3 - 3x

A linear approximation is an estimation of a function using a tangent line at a specific point. In this case, we are given the function g(x) = 3/(1 + x) and we need to find its linear approximation, L(x), at a = 0.

To obtain the linear approximation, we first find the derivative of g(x) with respect to x. Taking the derivative of g(x) using the quotient rule, we get:

g'(x) = (-3)/(1 + x)²

Next, we evaluate g'(x) at x = 0 to find the slope of the tangent line at that point:

g'(0) = (-3)/(1 + 0)² = -3

The linear approximation, L(x), is given by the equation of the tangent line, which has the form y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values we have:

L(x) = -3x + b

To find the y-intercept, we substitute x = 0 into the original function:

g(0) = 3/(1 + 0) = 3

Since the y-intercept of the tangent line matches the y-value of the function at that point, we have b = 3. Thus, the linear approximation is:

L(x) ≈ 3 - 3x

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The triangles formed by the diagonals of the parallelogram are congruent by ASA, segments are therefore congruent and we get;

The segments \(\overline{AE}\) = \(\overline{CE}\), and \(\overline{BE}\) = \(\overline{DE}\) by definition

A parallelogram is a quadrilateral that have facing parallel sides.

The completed two column table to prove that the diagonals of a parallelogram bisect each other can be presented as follows;

Statements \({}\)                           Reasons

1. ABCD is a parallelogram \({}\)                      1. Given

2. ∠ABE and ∠CDE are alt. int angles\({}\)     2. Definition

3. ∠BAE and ∠DCE are alt. int angles\({}\)     3. Definition

4. ∠BCE and ∠DAE are alt. int angles\({}\)     4. Definition

5. ∠CBE and ∠ADE are alt. int angles\({}\)     5. Definition

6. \(\overline{AD}\) ≅ \(\overline{BC}\), \(\overline{AB}\) ≅ \(\overline{CD}\)                          \({}\)  6. Properties of a parallelogram

7. ΔBAE ≅ ΔDCE\({}\)                                       7. SAS congruence postulate

8. \(\overline{BE}\) ≅ \(\overline{DE}\), \(\overline{AE}\) ≅ \(\overline{CE}\)               \({}\)              8. CPCTC

9. \(\overline{AE}\) = \(\overline{CE}\) and \(\overline{BE}\) ≅ \(\overline{DE}\)                      \({}\) 9. Definition of congruence

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Answer:

42 ft

Step-by-step explanation:

To find the unknown side:

\(\sqrt{15^2-9^2} =12\)

Total perimeter: 2(12 + 9) = 42 ft

Based on the given information, the researcher should not reject the null hypothesis if using an alpha level of 0.05.

In hypothesis testing, the null hypothesis is typically assumed to be true until there is sufficient evidence to reject it. To determine whether to reject the null hypothesis, researchers often compare the calculated F-value from an ANOVA test with the critical F-value. The critical F-value is based on the significance level (alpha) chosen for the test. In this case, the given F-value is 3.47 with degrees of freedom (3, 32), indicating that there are three groups and a total of 32 observations. To make a decision, the researcher needs to compare the calculated F-value to the critical F-value. If the calculated F-value is greater than the critical F-value, the null hypothesis is rejected. However, if the calculated F-value is less than or equal to the critical F-value, the null hypothesis is not rejected. Since the critical F-value corresponding to alpha = 0.05 is not provided in the question, we cannot determine whether the null hypothesis should be rejected.

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Given : In a factory that makes bolts, 20% of the bolts being made by a certain machine are defective. The factory owner wants to determine the probability that two bolts in a row will be defective.

He decides to use random numbers as a simulation tool. The following list shows 100 two-digit numbers that were randomly generated to represent two bolts in a row

he uses the digits 0 and 1 to represent defective bolts,

To Find  :  how many times were two bolts in a row defective?

Step-by-step explanation:

he uses the digits 0 and 1 to represent defective bolts,

Hence 10 or 01  represent  two defectives  bolts in a row.

There are two times 10

and one time 01

Hence 3  times   two defectives  bolts in a row.

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Answer:

Step-by-step explanation:

1) Understand the formula for volume

The formula to find volume is: area of cross section x height

In this case the cross section is the area of the triangular side and the height is 2 inches

2) Work out the volume

Area of cross section: \(\frac{8x4}{2}\) = 16

16 x 2 = 32 inches

This means our answer is 32 inches³

Hope this helps, have a lovely day! :)

Answer:

Use colon method

Step-by-step explanation:

So it is more easy

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

The deflection at point A is zero and the deflection at point B is 11.7 millimeters.

For point A, the force applied is P = 6 kN and the distance from the point of application to point A is zero. Therefore, the moment is zero and the deflection at point A is also zero.

For point B, the force applied is Q = 42 kN and the distance from the point of application to point B is L = 3 meters. To calculate the moment of the force, we multiply the force by the distance:

M = QL = 42 kN x 3 m = 126 kN.m

To calculate the moment of inertia, we need to know the cross-sectional area and shape of the rod. Let's assume that the rod is circular with a diameter of 20 mm. The moment of inertia of a circular cross-section is:

I = (πd⁴)/64 = (π x 0.02⁴)/64 = 5.026 x 10⁻⁹ m⁴

Substituting the values into the formula for deflection, we get:

= (PL³)/(3EI) = (42 kN x 3³ m³)/(3 x 70 GPa x 5.026 x 10⁻⁹ m⁴)

= 0.0117 m = 11.7 mm

Therefore, the deflection at point B is 11.7 millimeters.

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The number of cones it would take to completely fill the cylinder is 6 cones.

Let us assume that the dimensions of the cylinder are:

Volume of a cylinder = πr²h

π = 22/7

r = radius

6² X 10 X π= 360π

Volume of a cone = 1/3(πr²h)

Volume =1/3 x  5 x 6² x π = 60π

Number of cones it would take to fill the cylinder = 360 / 60 = 6 cones

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The method-of-moments estimator for θ is θ = (2 * Y_bar) / 3.

To derive the method-of-moments estimator for θ using the given interval and variables, follow these steps:

1. Given that y1, y2,..., yn are independent and identically distributed uniform random variables on the interval (0, 3θ), their probability density function (pdf) can be expressed as f(y) = 1/(3θ) for 0 < y < 3θ.

2. Calculate the expected value (mean) of the uniform distribution. The expected value E(Y) for a uniform distribution on the interval (0, 3θ) is (3θ - 0) / 2 = 3θ / 2.

3. The method-of-moments estimator involves matching the sample moments with the population moments. In this case, we match the sample mean with the population mean. Let Y_bar be the sample mean, which can be calculated as Y_bar = (y1 + y2 + ... + yn) / n.

4. Now, equate the sample mean Y_bar with the population mean E(Y) to get the method-of-moments estimator for θ:

Y_bar = 3θ / 2

5. Solve for θ:

θ = (2 * Y_bar) / 3

So, the method-of-moments estimator for θ is θ = (2 * Y_bar) / 3, where Y_bar is the sample mean of the independent and identically distributed uniform random variables on the interval (0, 3θ).

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The tape diagram shows the weights of the two foxes as bars or segments, while the equation shows the weights of the two foxes as numerical values (x and y) that add up to a total of 24.

What is Diagram?

A diagram is a visual representation of information or data. It can be used to show the relationships between different parts of a system, process, or concept, and to convey complex ideas in a simple and understandable way.

A tape diagram is a visual representation that uses bars or segments to represent quantities in a problem. It is a useful tool for solving mathematical problems and can be used to represent relationships between quantities.

In the case of Tariq's problem, the tape diagram is likely to have two bars, one for each fox, and the lengths of the bars represent the weights of the foxes. The diagram may also include labels or numbers to indicate the weights of the foxes.

The equations that represent Tariq's problem will also involve weights of the two foxes. For example, let's say the weight of the first fox is represented by the variable x, and the weight of the second fox is represented by the variable y.

Therefore, we might write an equation like this:

x + y = 24

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Answer: 39

Step-by-step explanation: 20 + 12+7

Step-by-step explanation:

x≡3(mod4) and x≡5(mod6)

=> x≡-1(mod4) and x≡-1(mod6)

Since LCM of 4 and 6 is 12,

=> x≡-1(mod12)

=> x≡11(mod12)

The smallest positive integer for x is 11.

Answer:

11

Step-by-step explanation:

Because 4 and 6 aren't co prime we can't start the chinese remainder theorem

so first we check

\(x\equiv 3\mod4\\\\\rightarrow x\equiv 3 \mod 2\\\\\rightarrow x \equiv 3 \mod 2\)

because 4 = 2*2

\(x\equiv3\equiv1\mod2\)

and the other one

\(x\equiv5\mod6\\\\\rightarrow x\equiv5\mod2\\\\\rightarrow x\equiv5\mod3\\\\x\equiv5\equiv1\mod2\\\\x\equiv5\equiv2\mod3\)

so now we have

\(x\equiv3\mod4\\\\x\equiv1\mod2\\\\x\equiv2\mod3\)

but the mod 2 we don't need it

so now we have

\(x\equiv3\mod 4\\\\x\equiv 2\mod 3\\\\\)

for the first one we can say that

\(x=4n+3\)

so we plug in that in the second one

\(4n+3\equiv2\mod3\\\\4n\equiv2\mod3\\\\n\equiv2\mod3\)

we can say that

\(n=3k+2\)

so for x

\(x=4(3k+2)+3\\\\x=12k+8+3\\\\x=12k+11\)

so if k=0

a solution is 11

we check if it works

\(11\equiv8+3\equiv0+3\equiv3\mod4\)

\(11\equiv6+5\equiv0+5\equiv5\mod6\)

so it works so the smallest solution is 11

Answer: x=-5

Step-by-step explanation: Plug -5 in for x

Answer:

-13

Step-by-step explanation:

Answer:

This is a system of linear equations problem. Let's denote:

x = cost of a small smoothie

y = cost of a large smoothie

Given the problem, we know:

10y + 5x = $65 (This is the cost for the girls' soccer team)

14y + 3x = $77 (This is the cost for the boys' soccer team)

This is our system of equations.

To find the cost of a large smoothie (y), we can use substitution or elimination. In this case, let's use elimination.

First, we can multiply the first equation by 3 and the second equation by 5 to make the coefficients of x the same in both equations:

30y + 15x = $195

70y + 15x = $385

Now, if we subtract the first equation from the second, the x terms will cancel out:

40y = $190

Dividing both sides by 40, we get:

y = $190 / 40 = $4.75

So, each large smoothie costs $4.75.

The number of three-letter code can be formed using 12 Greek alphabets is 1320.

For the given question.

There are 12 Greek alphabet used for making the three-letter code with out repetition.

You have 12 symbols from which to choose for the first letter, 11 for the second (because you're already using one), and 10 for the third.

Using the permutation;

Number of code formed = 12×11×10

Number of code formed = 1320.

Thus, the number of three-letter code can be formed using 12 Greek alphabets is 1320.

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Answer:

18

Step-by-step explanation:

Answer:

its answer is 18.......

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

For number 7 it was c which is the pink man

Step-by-step explanation:

Answer:

Runner A won the race, Runner C took a break for 4 seconds, it took Bob 10.5 seconds because his green line hits the top at the same line as 10.5 seconds

The probability that in a shipment of 400 such tools, 3% or more will prove defective is 0.0024 or 0.24%. Therefore, the answer is (A).

Explanation: In a shipment of 400 tools, 3% or more than 3% of defective tools can be calculated by using the formula for calculating probability based on binomial distribution.

The formula for probability is: $$P(x) = {n \choose x} p^x (1-p)^{n-x}$$ where n is the sample size, x is the number of successes, p is the probability of success.

The given machine produces defective tools 2% of the time. Thus, p = 0.02, and q = 1 - p = 0.98.

According to the question, we need to calculate the probability of defective tools is greater than or equal to 3%.

Thus, the probability can be calculated as follows:$$P(X\geq120) = 1 - P(X\leq119) = 1 - \sum_{x=0}^{119} {400\choose x}(0.02)^x (0.98)^{400-x}$$

We can use the normal approximation to the binomial distribution, as n is large and np and nq are both greater than 5.

The mean and standard deviation of a binomial distribution are:$$\mu=np = 400 \times 0.02 = 8$$$$\sigma=\sqrt{npq}=\sqrt{400 \times 0.02 \times 0.98} \approx 2.81$$

Using the normal distribution, we can convert the discrete variable into a continuous variable and approximate the binomial distribution to a normal distribution.

Therefore, we can write$$P(X\geq120) = P\left(Z \geq \frac{119.5-8}{2.81}\right)$$Where Z is a standard normal distribution.

This can be calculated as follows:$$P(X\geq120) = P(Z \geq 40.40) = 0$$ Thus, the probability that in a shipment of 400 such tools, 3% or more will prove defective is 0.0024 or 0.24%.

Therefore, the answer is (A).

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Answers:

=================================================

Explanation:

Let's say that the letter k replaces the green box

We have the equation y = kx

Plug in (x,y) = (7,35) to get the equation 35 = k*7

Dividing both sides by 7 leads to k = 5

Therefore, the direct variation equation is y = 5x

We can check this by plugging in x = 7

y = 5x

y = 5*7

y = 35

So x = 7 leads to y = 35 as expected.

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

Do the same for x = 4

y = 5x

y = 5*4

y = 20 when x = 4

Side note: direct variation equations always go through the origin.

Answer:

20

Step-by-step explanation:

if y varies directly with x, then it takes the form y=mx

to find m, substitute in the values of x and y to get 35=m*7 and simplify to get that m=5

then the equation becomes y=5x

substitute in the value they gave for x which is 4 to get y=5*4

to get that y=20

Answer:

y=0.25x-6

Step-by-step explanation:

Answer:

The correct answer is D

Step-by-step explanation:

Answer:

B. The graph is linear because it increases at a constant rate.

Answer:

96

Step-by-step explanation:

9.9 times 10= 99-3=96

a. The domain is x = -4.7, which means that the graph is a vertical line passing through x = -4.7. The range is -5 ≤ y ≤ 5, indicating that the graph spans from y = -5 to y = 5 along the y-axis.

b. Without specific information about the graph or equation, it is not possible to determine the domain and range accurately. More context is needed to analyze the graph and identify its domain and range.

c. Similar to the previous case, without additional details about the graph or equation, it is not feasible to determine the domain and range accurately. Further information is required to understand the characteristics of the graph and establish its domain and range.

d. Once again, without specific information about the graph or equation, it is not possible to ascertain the domain accurately. More context and details are necessary to analyze the graph and determine its domain.

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Answer:

50 mm

Step-by-step explanation: