6. A shop keeper has 56 pens. He
soid them for 280 dollars. How
much did the shopkeeper charge
for each pen?

Answer:

hi

Step-by-step explanation:

A distribution is a way of displaying data, consisting of three primary components: shape, center, and spread. The shape is the overall pattern of the distribution, while the center is the point where the distribution is balanced. The spread is the range of values of the data, often measured by the standard deviation or the interquartile range (IQR). The distribution can be visualized through graphs like histograms, box plots, or scatter plots.

A brief description of a distribution should include its shape, center, and spread. The spread is the term that should be included in the blank space.A distribution can be described as a way of displaying data. It gives us an idea about how the data are spread out.

The three primary components of any distribution are the shape, center, and spread. Shape refers to the overall pattern of the distribution. It tells us whether the data are symmetric or skewed. The symmetry means that the left half of the distribution is a mirror image of the right half, whereas a skewed distribution is not symmetrical. The tail of a distribution describes the spread of a skewed distribution. It refers to the parts of the distribution that extend out from the center of the graph.The center refers to the point where the distribution is balanced. In symmetric distributions, the center is the same as the mean and median. However, in a skewed distribution, the mean and median differ from each other.

The spread refers to the range of values of the data. It tells us how much the data are scattered or spread out. A small spread indicates that the data points are close to each other, while a large spread suggests that the data points are far from each other. It is often measured by the standard deviation or the interquartile range (IQR).The distribution of data can be visualized through different graphs like histograms, box plots, or scatter plots.

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Answer:

\(\sqrt{89}\)

Step-by-step explanation:

You want to use the distance formula which is \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

So if you just plug in the numbers correctly and solve correctly then you should get \(\sqrt{89}\)

Answer:

$8.33

Step-by-step explanation:

$14.69                                                                  50.00

+ $20.99                                                            -  41.67

=35.68                                                                =   $8.33

+5.99

=$41.67

\(\textbf{ Heya !}\)

Your Answer Is:-

\(\sf{9x\div6}\)

because,

               it has a coefficient of 9 (a number that comes before a variable)

`hope that was helpful to u ~

To calculate the required exit size, we need to first determine the total valuation of the company at the time of exit. Assuming a 50% dilution before exit, the post-money valuation would be $20M (50% of $40M).

To justify a $10M investment for a 28% ownership, the pre-money valuation would need to be $25M ($10M / 0.28). This means the total valuation at exit would need to be $45M ($25M + $20M).

Next, we need to calculate the probability-weighted expected return. Given a 20% probability of success, the expected return would be 20% x $45M = $9M.

Finally, we can use the expected return and the required return of 15% to determine the exit size needed to justify the investment. Using the formula: Exit size = expected return / (1 - required return), we get:

Exit size = $9M / (1 - 15%) = $10.59M

Therefore, the exit size would need to be at least $10.59M to justify a $10M investment for a 28% ownership with the given parameters.
Hi, I'd be happy to help with your question. To determine how large an exit has to be to justify a $10M investment for a 28% ownership, we'll need to consider the following terms: investment amount, ownership percentage, time horizon, dilution, probability of success, and required return for limited partners. Here's a step-by-step explanation:

1. Calculate the initial post-money valuation: Divide the investment amount ($10M) by the ownership percentage (28%).
  Initial post-money valuation = $10M / 0.28 ≈ $35.71M

2. Account for the 50% dilution before exit: Multiply the initial post-money valuation by 2.
  Post-dilution valuation = $35.71M * 2 = $71.43M

3. Adjust for the probability of success: Divide the post-dilution valuation by the probability of success (20%).
  Adjusted valuation = $71.43M / 0.20 = $357.14M

4. Determine the future exit valuation based on the required return for limited partners: Use the formula Future Value (FV) = Present Value (PV) * (1 + r)^n, where r is the required return (15%) and n is the time horizon (use the midpoint of 5-7 years, so n = 6).
  Future exit valuation = $357.14M * (1 + 0.15)^6 ≈ $906.53M

So, to justify a $10M investment for a 28% ownership with the given parameters, the exit has to be approximately $906.53M.

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Each of the measurements made must contain the correct number of significant figures, in order to provide more accurate values.

Significant figures, as their name mentions, are those figures that have meaning or validity for the type of measurement that is made. Although in large elements they may not be too necessary, in small elements they are crucial.

Due to the aforementioned, if the measurements are being taken from elements of small sizes, it is possible that all the significant figures available are required, so that the measurement and subsequent calculations are as accurate as possible.

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The library is 8 kilometres away from Bree's residence.

1. The equation represents the total travel time of 2 hours.

2. Bree's speed on her way to the library is 6 mph, so the time taken for this part is x/6 hours.

3. Bree's speed on her way home is 12 mph, so the time taken for this part is x/12 hours.

4. Adding the time taken for both parts, we get the equation: x/6 + x/12 = 2.

5. This equation can be solved to find the value of x, which represents the distance from Bree's house to the library.

6. Simplifying the equation further, we have (2x + x)/12 = 2.

7. Combining like terms, we get 3x/12 = 2.

8. Multiplying both sides by 12, we have 3x = 24.

9. Dividing both sides by 3, we find that x = 8.

10. Therefore, the distance from Bree's house to the library is 8 miles.

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The position of the object at time t is given by s(t) = 10 + 70t - 16t²/2, and the velocity of the object at time t is given by v(t) = 70 - 32t.

The rate of change of the displacement of an object is known as its velocity. It is a vector quantity and is measured in meters per second.

To find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial position, we can use the equations of motion.

The equations of motion are:

v(t) = v(0) + ∫[a(t)] dt

s(t) = s(0) + ∫[v(t)] dt

where v(t) represents the velocity at time t, a(t) represents the acceleration, s(t) represents the position, v(0) is the initial velocity, and s(0) is the initial position.

Given:

a(t) = -32 (acceleration)

v(0) = 70 (initial velocity)

s(0) = 10 (initial position)

Let's find the velocity v(t) first:

v(t) = v(0) + ∫[a(t)] dt

v(t) = 70 + ∫[-32] dt

v(t) = 70 - 32t + C

where C is the constant of integration.

Now, let's find the position s(t):

s(t) = s(0) + ∫[v(t)] dt

s(t) = 10 + ∫[70 - 32t + C] dt

s(t) = 10 + (70t - 16t²/2 + Ct) + D

where D is the constant of integration.

To determine the values of the constants C and D, we can use the initial conditions:

v(0) = 70 and s(0) = 10.

Using the initial velocity condition:

v(0) = 70 - 32(0) + C = 70 + C

Given that v(0) = 70, we can solve for C:

70 + C = 70

C = 0

Now, using the initial position condition:

s(0) = 10 + (70(0) - 16(0)²/2 + 0) + D = 10 + 0 + D

Given that s(0) = 10, we can solve for D:

10 + D = 10

D = 0

So the constants C and D are both equal to 0.

Now we can substitute the values of C and D back into the equations for v(t) and s(t):

v(t) = 70 - 32t

s(t) = 10 + 70t - 16t²/2

Therefore, the position of the object at time t is given by s(t) = 10 + 70t - 16t²/2, and the velocity of the object at time t is given by v(t) = 70 - 32t.

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The equation y = -2x +12 in slope - intercept form.

Find the slope of the line that is parallel to y = -2x +3

Slope (m) = -2

Substitute and calculate ;

m = -2, x = 8 ,y = -4 into y = mx + b

-4 = -2 x 8 + b

Calculate the product :

-4 = -16 + b

Calculate the sum or difference:

-b = -12

b = 12

Again, Substitute m = -2 , b = 12 into y = mx +b :

y = -2x + 12

Rewrite the equation y = -2x + 12 in slope - intercept form:

y = -2x + 12

Hence, The equation y = -2x +12 in slope - intercept form.

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Answer:

3 cups

Step-by-step explanation:

If one needs one cup then three needs three cups.

Answer:

B

Step-by-step explanation:

I like to put inequalities in the form y ≤ or ≥ mx + b. It makes it easier to tell which line is which on the graph. So x + y ≥ 5 can be put as y ≥ -x + 5. Next, -3x + 2y ≤ -2 can be put as 2y ≤ 3x -2. This should be further simplified by dividing everything by 2, isolating y, to y ≤ \(\frac{3}{2}\)x - 1. Now since b is the y-intercept, we know that the first inequality (x + y ≥ 5 or y ≥ -x + 5) is represented by the blue line. Since in the new form we put that inequality in (y ≥ -x + 5), the shaded part must be above the line. This means that graph A is not the answer. Next, we know that the second inequality is represented by the red line. We also know that the shaded part must be below the line, which means that it cannot be graph C. It is cannot be graph D because the shaded parts must satisfy BOTH (hence, AND. If it said OR it would be different) inequalities. This leaves B as the only correct answer.

Answer:

3.5*10^3=3,500

3,500+ 575,900=579,400

Step-by-step explanation:

Answer:

Mr. Pham  with 2/7

Step-by-step explanation:

2/7 = 0.286

1/4= 0.25

so 2/7 is ur correct answer.

This scenario demonstrates the behavior of a string under tension and highlights how a specific point on the string can be deflected perpendicular to its resting position when the string is stretched.

In the given scenario, a string of length 15 cm is stretched between two points, and we have a specific point P on the string. Point P is located 5 cm away from point B along the string. When the string is in its resting position, point P is deflected perpendicular to the string by a distance of 5 cm.

This situation can be visualized as follows: imagine a straight line segment representing the string, with points A and B as the two endpoints. Point P lies on this line segment, 5 cm away from point B. When the string is at rest, point P is displaced 5 cm in a direction perpendicular to the line segment AB.

The perpendicular deflection of point P indicates that there is tension in the string. When the string is stretched, the tension causes point P to move away from its original position. The magnitude of the deflection (5 cm) indicates the amount of displacement from the position of rest.

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Correct question:

A string of length 15 cm is stretched between two points as shown in A point P on the string 5 cm from the point B is deflected a distance 5 cm from its position of rest perpendicular to AB and released with zero velocity. What are the initial conditions and boundary conditions for the problem? [Hint: initial conditions = u(x,0) and up(x,0), boundary conditions = u(0,t) and u(L, t)). w Provided that the wave equation model for the problem mentioned above is utt = 3ux for (0 0). Compute the general displacement u(x, t) of any point at any time, t in seconds, for all cases using method of separation of variables.

Answer:

-5

Step-by-step explanation:

subtract -3 with 2

= -3-2

= -5

Answer:

by looking in the copy and learning the tips or step how to do it

Answer:

For example, we could use y = price in dollars, x = gas in gallons, and a constant of proportionality k to represent the amount of money you have to pay at the gas station y = kx. In other words, the price you pay is in direct proportion to the gallons pumped.

Step-by-step explanation:

Hope this helped you understand it better

~Heaven~

Answer:

x> y-300/12

Step-by-step explanation

1. Subtract 300 from both sides

2.  Divide both sides by -12

3. Switch the sides

Answer:

Step-by-step explanation:

The base of the prism is triangle with base of 6 yd and hight of 6 yd.

The hight of the prism is 10 yd.

Therefore, the volume of the prism:

\((\frac12\cdot8\cdot6)\cdot10=240\ yd^3\)

Answer:

Check below:

Step-by-step explanation:

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs so that you can factor out a common factor from each pair.

3x² + 6x + 4x + 8

(3x² + 6x) + (4x + 8)

Step 2: Factoring out the common factors

Factor out the common factors from each pair separately.

3x(x + 2) + 4(x + 2)

Step 3: Factoring out the common factor from the resulting expression

Notice that we have a common factor, (x + 2), in both terms.

(x + 2)(3x + 4)

Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).

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According to the corrosion-resistance, the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the specification has not been met.

Based on the provided information, we can analyze whether the steel conduits meet the corrosion-resistance specification. The sample average penetration is 52.7 mils, with a sample standard deviation of 4.8 mils. The specification states that the true average penetration should be at most 50 mils. To make a conclusion, we need to state the appropriate null and alternative hypotheses, calculate the test statistic, and determine the p-value using α = 0.05.

The null hypothesis (H0) states that the true average penetration of the steel conduits is equal to or less than 50 mils. The alternative hypothesis (H1) states that the true average penetration exceeds 50 mils. Therefore, the hypotheses are as follows:

H0: μ ≤ 50 (where μ represents the true average penetration)

H1: μ > 50

To test these hypotheses, we can use a one-sample t-test since we have the sample mean, sample standard deviation, and a sample size of 45. With α = 0.05, we will reject the null hypothesis if the p-value is less than 0.05.

To calculate the test statistic, we can use the formula:

t = (x - μ₀) / (s / √n)

Plugging in the values:

x = 52.7 (sample average penetration)

μ₀ = 50 (specified maximum average penetration)

s = 4.8 (sample standard deviation)

n = 45 (sample size)

Calculating the test statistic, we find:

t = (52.7 - 50) / (4.8 / √45) ≈ 3.551

Using the t-distribution table or statistical software, we can determine the p-value associated with this test statistic. The p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

Since the p-value is not provided in the question, we cannot determine the exact value. However, if the calculated p-value is less than 0.05 (our chosen significance level), we would reject the null hypothesis and conclude that there is sufficient evidence to demonstrate that the specification has not been met. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the specification has not been met.

In summary, to make a conclusive statement about whether the specification for the steel conduits has been met, we need to calculate the p-value associated with the test statistic.

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The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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In 2015, the cost of a complete bathroom package represented D.  14% of the monthly average household expenditures for the bottom 40% of the poorest population.

This means that out of the total monthly expenses of these households, 14% was spent on bathroom packages. This percentage highlights the financial burden that bathroom expenses placed on these families, as they had to allocate a significant portion of their limited resources towards this essential facility.

Among the given answer choices - a. 40%, b. 5%, c. 27%, and d. 14% - the correct answer is d. 14%, as this is the percentage mentioned in the question. The other percentages do not apply to the context of the question and therefore can be disregarded.

In summary, the cost of a complete bathroom package in 2015 accounted for 14% of the monthly average household expenditures of the bottom 40% of the poorest population. This percentage reflects the financial strain on these households to meet their basic needs, including essential facilities like bathrooms. Therefore the correct option is D

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a. The graph of g(x) is a curve that starts at (0, 4), approaches negative infinity as x approaches negative infinity, and approaches positive infinity as x approaches positive infinity. b. Domain: [0, +∞); Range: (-∞, +∞). c. Increasing: (0, +∞); Decreasing: [-2, 0). d. Concave up: [-2, 0) and (0, +∞).

a. To sketch the graph of the function g(x) = x²√x - x + 4, we can start by analyzing its behavior and key points.

First, let's find the x-intercepts by setting g(x) = 0:

0 = x²√x - x + 4

Unfortunately, this equation cannot be easily solved analytically. However, we can still determine the behavior of the function by analyzing the leading terms. As x approaches negative infinity, x²√x dominates the other terms, and since x²√x approaches negative infinity, we can infer that the graph will approach negative infinity as x approaches negative infinity.

Similarly, as x approaches positive infinity, x²√x dominates the other terms, and since x²√x approaches positive infinity, we can infer that the graph will approach positive infinity as x approaches positive infinity.

Next, let's find the y-intercept by setting x = 0:

g(0) = 0²√0 - 0 + 4 = 4

Therefore, the function g(x) has a y-intercept at (0, 4).

Now, let's find the critical points by taking the derivative of g(x) and setting it equal to zero:

g'(x) = d/dx (x²√x - x + 4)

      = 2x√x + x^(3/2) - 1

Setting g'(x) = 0:

0 = 2x√x + x^(3/2) - 1

Unfortunately, this equation also cannot be easily solved analytically. However, we can still determine the behavior of the function by analyzing the leading terms. As x approaches negative infinity, x^(3/2) dominates the other terms, and since x^(3/2) approaches negative infinity, we can infer that the graph will be decreasing as x approaches negative infinity.

Similarly, as x approaches positive infinity, x^(3/2) dominates the other terms, and since x^(3/2) approaches positive infinity, we can infer that the graph will be increasing as x approaches positive infinity.

From this analysis, we can sketch a rough graph of g(x) as follows:

        ^

        |

    +---|---+

    |   |   |

    |   |   |

    |   |   |

-----|---|---|---|--->

    |   |   |

    |   |   |

    +---|---+

        |

        v

b. Domain: The domain of g(x) is determined by the values of x for which the function is defined. In this case, the function involves square roots, so the radicand (x) must be non-negative.

Therefore, the domain of g(x) is [0, +∞).

Range: To determine the range of g(x), we need to analyze the behavior of the function. As x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches positive infinity.

Hence, the range of g(x) is (-∞, +∞).

c. Increasing and Decreasing Intervals: To determine the intervals on which g(x) is increasing or decreasing, we need to analyze the behavior of the derivative g'(x).

For -2 ≤ x < 0:

g'(x) < 0 for all x in this interval, indicating that g(x) is decreasing on the interval [-2, 0).

For 0 < x < 4:

g'(x) > 0 for all x in this interval, indicating that g(x) is increasing on the interval (0

, 4).

For x > 4:

Since we know g(x) approaches positive infinity as x approaches positive infinity, we can infer that g(x) continues to increase on this interval.

Therefore, g(x) is decreasing on the interval [-2, 0) and increasing on the interval (0, +∞).

d. Concave Up and Concave Down: To determine the intervals on which g(x) is concave up or concave down, we need to analyze the behavior of the second derivative g''(x).

g''(x) = d/dx (2x√x + x^(3/2) - 1)

      = 2√x + (3/2)x^(1/2)

For -2 ≤ x < 0:

Since x is negative in this interval, the term 2√x is undefined. However, the term (3/2)x^(1/2) is well-defined and positive, indicating that g(x) is concave up on the interval [-2, 0).

For 0 < x < 4:

Both terms 2√x and (3/2)x^(1/2) are well-defined and positive, indicating that g(x) is concave up on the interval (0, 4).

For x > 4:

Since we know g(x) is increasing on this interval, we can infer that g(x) continues to be concave up.

Therefore, g(x) is concave up on the intervals [-2, 0) and (0, +∞).

e. To solve g(x) = 0, we need to find the x-values where the graph of g(x) intersects the x-axis. From the graph, we can see that there are two such points, which correspond to the x-intercepts:

x ≈ -1.7 and x ≈ 0.9

f. To determine the number of solutions to the equation g(x) = 2, we need to examine the graph of g(x) and see how many times it intersects the horizontal line y = 2. From the given information, we don't have enough details to accurately determine the number of solutions without the graph or additional information.

g. To calculate the average rate of change of g(x) on the interval [1, 4], we can use the formula:

Average Rate of Change = (g(4) - g(1)) / (4 - 1)

Calculate g(4) and g(1) by substituting the values into the function:

g(4) = 4²√4 - 4 + 4 ≈ 20.31

g(1) = 1²√1 - 1 + 4 = 4

Average Rate of Change = (20.31 - 4) / (4 - 1) ≈ 5.77

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Answer:

21.3

Step-by-step explanation:

15 of 710 dollars is 7.1 dollars and 7.1x3=21.3 dollars commission

and the store earned 689.7 dollars

Answer:

Quadratic

Step-by-step explanation:

The principle can makes 4 groups with 7 girls and 8 boys.

The biggest number that divides each of the two or more numbers is known as the HCF, or highest common factor. The Greatest Common Measure (GCM) and Greatest Common Divisor are further names for HCF (GCD). The least common multiple, or LCM, is used to determine the smallest common multiple of any two or more numbers. LCM and HCM are two separate approaches.

According to the given statement ;

We are given that 28 girls and 32 boys volunteer to plant at a school.

The principle divided the girls and boys into identical groups that have girls and boys in each group.

We have to find that how much the principle can make greatest number of groups.

We will find HCF of 28 and 32

28= 2X2X7

32= 2X2X2X2X2

Highest common factor of 28 and 32 =2X2=4

Therefore, the principle can makes 4 groups with 7 girls and 8 boys.

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By applying Boolean algebra rules and De Morgan's theorem, the simplified form of the Boolean expression f(w, x, y) = wxy + wx + wy + wxy is obtained as f(w, x, y) = wx + wy.

To simplify the given Boolean expression f(w, x, y) = wxy + wx + wy + wxy, we can use Boolean algebra rules and laws, including the distributive property and De Morgan's theorem.

Applying the distributive property, we can factor out wx and wy from the expression:

f(w, x, y) = wx(y + 1) + wy(1 + xy).

Next, we can simplify the terms within the parentheses.

Using the identity law, y + 1 simplifies to 1, and 1 + xy simplifies to 1 as well.

Thus, we have:

f(w, x, y) = wx + wy.

This is the simplified form of the original Boolean expression, obtained by applying Boolean algebra rules and De Morgan's theorem.

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Given half-cup of milk. if we find how many  milliliters are there in this cup we get it approximately equal to 120 milliliters.

In cooking and baking, cup measurements are commonly used. However, it's important to note that cup measurements can vary slightly depending on the country or region. In the United States, a standard cup measurement is equal to 240 milliliters.

A half-cup is exactly half of this measurement, which means it would be approximately equal to 240/2 = 120 milliliters. Therefore, option C, 120, is the closest approximation to the number of milliliters contained in a half-cup of milk. It's worth noting that for more precise measurements, it's always advisable to use a kitchen scale or measuring cup with milliliter markings.

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