the table above shows shipping charges for an online retailer that sells sporting goods. there is a linear relationship between the shipping charge and the weight of the merchandise. which function can be used to determine the total shipping charge f( )x , in dollars, for an order with a merchandise weight of x pounds?

The correct answer is: -2x > 6!

-2x > 6

-2x / -2 > 6 / -2

x > -3

Answer:

39

Step-by-step explanation:

First, we change 8x +7 to 8(4) + 7

Then, 8 x 4 = 32

Lastly, 32 + 7 = 39

When the radius of a sphere is 5cm and its surface area is decreasing at a rate of 1 cm/min, the rate of change of the volume is -25π cm³/min.

The surface area of a sphere is given by the formula A = 4πr², where 'A' is the surface area and 'r' is the radius. We are given that the surface area is decreasing at a rate of 1 cm/min, which means dA/dt = -1 cm²/min.

To find the rate of change of the volume, we can differentiate the volume formula with respect to time. The volume of a sphere is given by the formula V = (4/3)πr³, where 'V' is the volume and 'r' is the radius. Differentiating with respect to time, we get dV/dt = (4/3)π(3r²)(dr/dt).

Substituting the given values, we have dA/dt = -1 cm²/min and r = 5 cm. We can find dr/dt by rearranging the surface area formula: dr/dt = dA/dt / (4πr²). Substituting the values, we have dr/dt = -1 / (4π(5)²) = -1 / (100π) cm/min.

Now, we can substitute the values of dr/dt and r into the rate of change of volume formula to find dV/dt. We have dV/dt = (4/3)π(3(5)²)(-1 / (100π)) = -25π cm³/min.

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Answer:

cannot be factored

Step-by-step explanation:

I plugged into calculator

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its Denominator, or to eliminate denominators from a radical expression.

To rationalize the denominator 1/7 + 3√2,

A rational number is a number that can be expressed as a ratio of two integers, with the denominator not equal to zero. The fraction 4/5, for example, is a rational number since it can be expressed as 4 divided by 5.

Step-by-Step SolutionTo rationalizes the denominator 1/7 + 3√2, we'll need to follow these steps.

Step 1: First, we need to create a common denominator for the two terms. The common denominator is 7. Thus, we can convert the expression to the following form:(1/7) + (3√2 × 7)/(7 × 3√2).

Step 2: Simplify the denominator to 7. (1/7) + (21√2)/(21 × 3√2).

Step 3: The numerator and denominator can now be simplified. (1 + 21√2)/(7 × 3√2).Step 4: Simplify further. (1 + 21√2)/(21√2).We have successfully rationalized the denominator!

The final answer is (1 + 21√2)/(21√2).

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its denominator, or to eliminate denominators from a radical expression.

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Answer:

4 x 4 x 4 = 64 , so 4^3 = 64

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Given equation,

→ x³ = 64

Now the value of x will be,

→ x³ = 64

→ x = ³√64

→ [ x = 4 ]

Hence, the value of x is 4.

Answer: -2.2

Step-by-step explanation:

Answer:

-3/5 which is the third line between 0 and -1 if you're going back from 0.

Probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).

As given,

Insurance protection system recovered of a car=91%

p=0.91

q=1-p

 =1-0.91

 =0.09

n=6

x=5

Using Binomial theorem ,probability of 5 of 6 stolen cars will be recovered is:

ⁿCₓ(p)ˣ(q)ⁿ⁻ˣ

=⁶C₅(0.91)⁵(0.09)⁶⁻⁵

=[6!/(6-5)!5!] × (0.91)⁵× (0.09)

=6×(0.91)⁵×0.09

=0.3369

Therefore, probability that 5 of 6 stolen cars will be recovered with insurance records a car with a certain protection system will be recovered 91% of the time is equal to P(x=5)=0.3369 (approximately).

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Explanation

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

From the given question

Also

Therefore, the answer is Reflexive Property; Given

There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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Answer:

He rented 82 games

Step-by-step explanation:

296=3x+50

246=3x

x=82

Answer:

spent on game rented

= $296 - $50

= $246

games rented

= $246 ÷ $3

= 82

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Answer: True

Step-by-step explanation: When you need to analyze the data presented in PivotTables and PivotCharts, use a trendline to select the data to display and summarize.

True, before adding a trendline to a chart, it is essential to determine the data series that you want to analyze.

A trendline is a graphical representation of a pattern or direction within a given set of data, which can help in predicting future data points or understanding relationships between variables. By selecting the appropriate data series, you can effectively evaluate the trends and correlations within that specific dataset.

When creating a chart, you'll often work with multiple data series representing different variables or measurements. Identifying the relevant data series to analyze is crucial in order to obtain meaningful insights from the trendline. Once you have determined the data series of interest, you can then proceed to add a trendline that best fits the data points and provides a clear understanding of the underlying patterns.

In summary, it is true that determining the data series to analyze is an important step before adding a trendline to a chart, as it allows you to gain valuable insights and make informed decisions based on the observed trends.

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Answer:

\(\pm i\sqrt{38}\)

Step-by-step explanation:

Given radical is \(\pm \sqrt{-38}\)

We can rewrite the radical as,

\(\pm\sqrt{-38}=\pm(\sqrt{-1}\times \sqrt{38})\)

            \(=\pm(i\sqrt{38})\)

(Since, i = \(\sqrt{-1}\))

Therefore, simplified form of the given radical will be,

\(\pm \sqrt{-38}=\pm i\sqrt{38}\)

Answer:

1) A rectangular shape

2) Point  (30, 50)

3) (x - 30)² + (y - 50)² = 10²

4) Yes, the swimming pool will touch the flower beds

5) Point (45, 25)

Step-by-step explanation:

1) Given the number of shapes that are rectangles (4) and the number of circular shapes (1) to conserve more space Kylee should drw the swimming pool with a rectangular shape

2)  So as to avoid touching the flowerbeds which are 20 feet apart, the center of the swimming pool will be moved slightly up to (30, 50)

3) The equation that will draw the swimming pool is the equation of a circle, given as follows

(x - h)² + (y - k)² = r²

Where (h, k) is the coordinate of the center of the circle, and r is the radius of the circle,

Given that the diameter, D, of the circle = 20 feet, the radius, r = D/2 = 20/2 = 10 feet

The equation of the circle is therefore;

(x - 30)² + (y - 50)² = 10²

4) The coordinates of the center of the flower bed is (30, 45) which gives

(x - 30)² + (y - 45)² = 10²

Where the coordinates of the side of the flower pot is (20, 45), we have;

(20 - 30)² + (45 - 45)² = 10²

(-10)² = 10² = r²

Hence, point (20, 45) is on the circle

The other flower bed side has coordinates (40, 45) which gives

(40 - 30)² + (45 - 45)² = 10²

10² = r² = 10²

Point (40, 45) is also on the circle

Therefore, the swimming pool will touch the flower beds

5) At point (45, 25), we have;

(x - 45)² + (y - 25)² = 10²

The closest point is the patio with coordinates (40, 15) which gives;

(40 - 45)² + (15 - 25)² = 10² = 100

(-5)² + (-10)² = 125 > 100

Therefore, point (40, 15), is not on the circle.

Answer:

Word problems with linear equations (that is, with straight-line models) almost always work this way: the slope is the rate of change, and the y-intercept is the starting value.

Step-by-step explanation:

In this problem, we are given data on the wear of two types of tyres, Type A and Type B, mounted on a sample of lorries.

We want to estimate the 95% confidence interval for the difference between the means of the populations of the wear of the two types of tyres and test the hypothesis of a significant difference at the 5% level. This will help us make a conclusion about the choice of tyres.

To estimate the confidence interval for the difference between the means of the wear of Type A and Type B tyres, we can use a two-sample t-test. Given the sample data and assuming the data is approximately normally distributed, we can calculate the sample means, standard deviations, and sample sizes for Type A and Type B tyres.

From the given data, the sample mean wear for Type A tyres is 9.8, and for Type B tyres is 9.8 as well. We can also calculate the sample standard deviations for each type of tyre.

Using statistical software or a calculator, we can perform the two-sample t-test to estimate the confidence interval and test the hypothesis. Assuming equal variances, we calculate the pooled standard deviation and the t-value for the difference in means.

Based on the calculated t-value and the degrees of freedom (which depends on the sample sizes), we can find the critical value from the t-distribution table or using statistical software.

With the critical value, we can calculate the margin of error and construct the 95% confidence interval for the difference between the means of the wear of the two types of tyres.

To test the hypothesis, we compare the calculated t-value with the critical value. If the calculated t-value falls outside the confidence interval, we reject the null hypothesis and conclude that there is a significant difference between the means of the wear of the two types of tyres. Otherwise, if the calculated t-value falls within the confidence interval, we fail to reject the null hypothesis.

Finally, based on the results of the hypothesis test and the confidence interval, we can make a conclusion about the choice of tyres. If the confidence interval does not contain zero and the hypothesis test shows a significant difference, we can conclude that there is a significant difference in wear between the two types of tyres. However, if the confidence interval includes zero and the hypothesis test does not show a significant difference, we cannot conclude a significant difference between the wear of the two types of tyres.

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The displacement vector dW corresponding to the second leg of the student's trip can be expressed as (-0.400, 0) miles.

To find the displacement vector dW for the westward leg of the trip, we need to consider the overall displacement from the starting point.

The student first travels 0.900 miles north, so the displacement vector dN for this leg is (0, 0.900) miles.

Then, the student travels 0.400 miles west. Since this is a westward displacement, the x-component of the displacement vector dW will be negative, and the y-component will be zero. Therefore, the displacement vector dW can be expressed as (-0.400, 0) miles.

Finally, the student travels 0.100 miles south. Since this is a southward displacement, the y-component of the displacement vector dS will be negative, and the x-component will be zero. Therefore, the displacement vector dS can be expressed as (0, -0.100) miles.

To find the overall displacement vector d, we sum the individual displacement vectors:

d = dN + dW + dS

d = (0, 0.900) + (-0.400, 0) + (0, -0.100)

d = (-0.400, 0.900 - 0.100)

d = (-0.400, 0.800) miles

Hence, the displacement vector dW for the westward leg of the trip can be expressed as (-0.400, 0) miles. The x-component represents the westward displacement, which is -0.400 miles, and the y-component represents the northward displacement, which is 0 miles.

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Let $C$ be the event that the camera gets a 10% discount, $G$ be the event that the game gets a 25% discount, and $N$ be the event that neither item gets a discount. Then the probability of each event is:

\begin{align*}

P(C) &= 0.35\cdot 0.1 = 0.035 \\

P(G) &= 0.05\cdot 0.25 = 0.0125 \\

P(N) &= 0.6\cdot 1 = 0.6

\end{align*}

The amount saved on the camera is $0.1\cdot 200=20$, and the amount saved on the game is $0.25\cdot 80=20$. So, we want to find the probability that either event $C$ or $G$ occurs. Since the events are mutually exclusive, we can use the addition rule:

$$

P(C\text{ or }G) = P(C) + P(G) = 0.035 + 0.0125 = 0.0475

$$

The amount saved in dollars at the cash register is $X = 20 + 20 = 40$. To find the probability that the total amount saved is $20$, we need to sum the probabilities of all the ways to get $X=20$. There are two ways to do this: either the camera gets a 10% discount while the game gets no discount, or the game gets a 25% discount while the camera gets no discount. Using the multiplication rule and the probabilities above, we have:

\begin{align*}

P(\text{camera gets 10% discount, game gets no discount}) &= P(C)\cdot P(N) = 0.035\cdot 0.6 = 0.021 \\

P(\text{game gets 25% discount, camera gets no discount}) &= P(G)\cdot P(N) = 0.0125\cdot 0.6 = 0.0075

\end{align*}

Therefore, the probability that the total amount saved is $20$ is:

$$

P(X=20) = P(\text{camera gets 10% discount, game gets no discount}) + P(\text{game gets 25% discount, camera gets no discount}) = 0.021 + 0.0075 = 0.0285

$$

So the chance you save a total of $20$ is $\boxed{0.0285}$.

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Answer:

The statement that is true is:

A debt of $17 is a larger value than a debt of $20.

Step-by-step explanation:

Let us look at the statements one after the other to determine if they are true or not:

1) A debt of $17 is a larger value than a debt of $20: This is true because when measuring debts, we will consider the values in the negative sense (-). Therefore, a debt of $17 has a value of (-17) and a debt of $20 has a value of (-20). -17 is larger than - 20 on a number line, hence, a debt of $17 has a larger value for the debtor, than a debt of 20$

2) One half an apple is equivalent to 8 fourths apples:

one half an apple = \(\frac{1}{2}\ of\ an\ apple\)

8 fourths of an apple = \(\frac{8}{4} = \frac{2}{1}\ of\ and\ apple\). Therefore, one half of an apple is not equivalent to 8 fourth of an apple.

3) 8.01 is a smaller increase in sales than 8.001: This statement is false because 8.001 is counted before 8.01, and the difference between 8.01 and 8.001 is:

8.01 - 8.001 = +0.009, hence, 8.01 is larger than 8.01 by a magnitude of 0.009

4) \(\frac{2}{3}\ below\ zero\) is a lower temperature than 6 below zero:

\(\frac{2}{3}\ below\ zero\ = (-\frac{2}{3})^\circ\)

6 below zero = - 6°

On the number line, -6 is smaller than \(-\frac{2}{3}\) hence the statement is false.

A rhombus has two pairs of parallel sides.

A rhombus is a quadrilateral with four sides of equal length. A rhombus's opposite sides are parallel to one another. It has 2 diagonals that bisect each other at a 90-degree angle. In a rhombus, all sides are the same length. The opposite angles are congruent, but the adjacent angles are not. The adjacent angles have a sum of 180 degrees, as with all quadrilaterals.

A rhombus is a special type of parallelogram. A parallelogram is a four-sided figure with two pairs of parallel sides. A rhombus has two pairs of parallel sides because it is a type of parallelogram. However, all sides of a rhombus are of the same length. Furthermore, a rhombus's opposite angles are equal. This implies that if the diagonal of the rhombus bisects each other at a 90-degree angle, the diagonals are perpendicular.

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Mario can place 36 ornaments along the window.

To find the number of ornaments Mario can place along the window, we need to divide the length of the windowsill by the length of each ornament. The length of each ornament is given as 5 1/3 inches.
To calculate this, we first need to convert the mixed fraction into an improper fraction. 5 1/3 can be written as (5*3 + 1)/3 = 16/3 inches.
Now, we can divide the length of the windowsill, which is 192 inches, by the length of each ornament, which is 16/3 inches:
192 / (16/3) = 192 * (3/16) = 36 ornaments.

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Answer:

  line QR

Step-by-step explanation:

Plane QRB is the front face. Plane TSR is the top face. The planes intersect at the top front edge, line QR.

The equivalent ratios are: (1, 2), (2, 4), and (3, 6)

The graph can be plotted on a coordinate grid as shown in the diagram attached below.

Recall:

Let x = number of books

y = cost (dollars)

Using any of the ordered pairs from the table, say, (7, 14), find k:

k = y/x = 14/7 = 2

Write the equation by plugging in the value of k into y = kx

y = 2x

Using the equation, y = 2x, find the equivalent ratios when x = 1, x = 2, and x = 3:

When x = 1:

y = 2(1) = 2 --> (1, 2)

When x = 2:

y = 2(2) = 4 ---> (2, 4)

When x = 3:

y = 2(3) = 6 ---> (3, 6)

The graph for the three equivalent ratios, (1, 2), (2, 4), and (3, 6) can be plotted on a coordinate grid as shown in the diagram attached below.

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The height of the tree is 15 feet if Scott is 6 feet tall and casts a shadow that is 8 feet long.

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

It is given that:
Scott is 6 feet tall and casts a shadow that is 8 feet long. a nearby tree casts a show that is x+5 feet long

By using scale factor:

Let x be the height of the tree

x/6 = = (x + 5)/8

8x = 6(x + 5)

8x = 6x + 30

2x = 30

x = 15 feet

Thus, the height of the tree is 15 feet if Scott is 6 feet tall and casts a shadow that is 8 feet long.

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Answer:

(-2,-1) i am pretty sure this is the answer because the 1/3 gives a big hint

The Discriminant of the quadratic equation "2x + 5x² = 1" is 24  .

The Discriminant(D) of the Quadratic Equation ax² + bx + c can be calculated using the formula ; D = b² - 4ac .

the quadratic equation is given as 2x + 5x² = 1 ;

after rearranging the terms ,

the equation can be written as :

⇒ 5x² \(+\) 2x - 1 = 0  ;

Substituting the values in the discriminant formula ,

we get ;

D = (2)² - 4×5×(-1)

Simplifying further ,

we get ;

D = 4 + 20

D = 24 .

Therefore , the value of the Discriminant is 24 .

The given question is incomplete , the complete question is  

What is the discriminant of the quadratic equation 2x + 5x² = 1  ?

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Answer:

I would say 6

Step-by-step explanation:

Difference is subtraction.

Using the concepts of weighting, we got that demographic groups helps in fixing  difference between the levels of different people if there are many or too few people in the sample from that group, compared to the population as a whole.

Demographic segmentation examples actually explain how researchers divide a market into the smaller groups according to age, gender, family income, race and ethnicity, qualification, marital status, nature of the  employment, etc.  

It is an extremely tedious task to the accommodate customers belonging to different demographics and develop the exhaustive marketing plan. Demographic examples ease creating the strategy for a marketer. Thus, they are one of  most commonly implemented marketing segmentation methods compared to the other techniques such as geographic segmentation, behavioral segmentation, or the psychographic segmentation.

Hence, certain demographic groups might end up being under or over-represented means that  there are too many or too few people in the sample from that group, compared to the population as a whole, in that case weighting can therefore potentially helps in fixing the difference in the levels of different people.

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