The first equation in the following system gives a company's income, in dollars, for selling x baseball caps. The second equation gives the cost of making x baseball caps. Y = 8x y = -0. 01 x2 4x 3,200 The solution of the system is (400, 3,200). How would you interpret this solution?.

Answer:

Step-by-step explanation:

N = 16.9 ft²

M = 16π/3 = 16.76 ft²

P = 5π = 15.71 ft²

N.   M.   P.      16π/3=16.755   5π=15.707

Answer:

102

Step-by-step explanation:

Let x be the amount of money John spends.

x/2-5=46

x/2=51

x=102

9514 1404 393

Answer:

  $28.14

Step-by-step explanation:

The area of a container will be the sum of the base area and the lateral area. The relevant formulas are ...

  A = πr^2 . . . . . . . . area of the circular base with radius r

  A = 2πrh . . . . . . .  area of the side of the container

The sum of the two areas is ...

  Atot = πr^2 +2πrh = πr(r +2h) = π(7/2 cm)(7/2 cm +2·21 cm) = (π/4)(7)(91) cm^2

  Atot = 159.25π cm^2 = 0.015925π m^2 . . . . metal area per container

__

Then 125 containers will have an area of ...

  Aall = (125)(0.015925π m^2) = 1.990625π m^2 ≈ 6.25373 m^2

The price of this amount of sheet metal will be ...

  (6.25373 m^2)($4.50 /m^2) = $28.14 . . . cost of 125 containers

__

Additional comment

1 cm = 0.01 m, so (1 cm)^2 = (0.01 m)^2 = 0.0001 m^2

To know which girl ate the most, we have to compare the two fractions.

To be able to compare the fractions, we can:

1.- We convert to decimal numbers.

2.- We modify the fractions such that both fractions have the same denominator.

To compare the fraction we will change them in a way that both have the same denominator.

Recall that a fraction represents the same number if we multiply it and divide it by the same number.

Notice that:

Since both fractions are the same, we can conclude that both girls ate the same amount.

Answer: 3/6 is equal to 4/8.

Both girls ate the same amount

In a two-way analysis of variance, a researcher tests for the significance of two main effects and an interaction.

A statistical test called two-way analysis of variance (ANOVA) compares the means of many groups using two independent variables (factors) and one dependent variable.

In a two-way analysis of variance (ANOVA), the researcher tests for the significance of two main effects and an interaction effect between two independent variables (factors) on a dependent variable. The main effects refer to the individual effect of each factor on the dependent variable, while the interaction effect refers to the combined effect of both factors on the dependent variable. Thus, the researcher aims to examine how each independent variable affects the dependent variable separately (main effects) and how their combination affects the dependent variable (interaction effect).

Therefore, in a two-way analysis of variance, a researcher tests for the significance of two main effects and an interaction.

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Step-by-step explanation:

(0.4 x 1.5 )X 18p

(0.6) × 18 p

=10.8 p

The solution to √x-1 = √x-1 is all real numbers.

To solve the equation √x-1 = √x-1, let's start by isolating one of the square roots. We can square both sides of the equation to eliminate the square roots:

(√x-1)² = (√x-1)²

Expanding both sides:

x - 2√x + 1 = x - 2√x + 1

We can observe that the equation simplifies to 1 = 1. This equation is true for all real numbers since any number minus itself equals zero. Therefore, there is no restriction on the value of x, and the solution is all real numbers.

The solution to the equation √x-1 = √x-1 is all real numbers.

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The graph of the inequality 3x - 2y > 2 is attached below.

We are given an inequality. The inequality is given below.

3x - 2y > 2

First of all, we will simplify the inequality. We need to keep the variable "y" on one side of the inequality. The inequality is modified as given below.

3x - 2y > 2

3x > 2 + 2y

3x - 2 > 2y

2y < 3x - 2

y < (3x - 2)/2

Now, to draw the graph of the inequality. We will first find the equation of the straight line corresponding to the given inequality.

y = (3x - 2)/2

We will draw a dotted line according to the above equation. Now, we will shade the area that satisfies the inequality. Hence, the graph is obtained.

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Yes, we can conclude that there is a positive correlation between the success of college students (measured by cumulative grade point average) and the income of their respective families.

For testing whether there is a significant correlation between two variables, we need to calculate the correlation coefficient r.

Given that the sample size (n) is 20, and the correlation coefficient (r) is 0.40. The test statistic value, t can be calculated using the formula:

(\(t = (r * \sqrt{n - 2} /\sqrt{1 - r^2} )\))

Therefore, substituting the values,

(\(t = (0.40 *\sqrt{20 - 2} / \sqrt{1 - 0.4^2} )\))

= 2.53

Using the t-table with 18 degrees of freedom (df = n - 2 = 20 - 2 = 18) at a significance level of 0.01, we find that the critical value of t is 2.878.

Since the calculated value of t is less than the critical value of t, we fail to reject the null hypothesis.

Therefore, we can conclude that there is a positive correlation between the success of college students (measured by cumulative grade point average) and the income of their respective families.

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With no limiting factors to the growth of the plants, the number of  months have passed since the plants were first introduced is 23.1.

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

A type of plant is introduced into an ecosystem and quickly begins to take over.

A scientist counts the number of plants after m months and develops the equation to model the situation, which is given as,

\(p(m)=19.3(1089)^m\)

Most recently, the scientist counted 138 plants.

\(138=19.3(1089)^m\\(1089)^m=7.15\)

Taking log both sides of the equation,

\(\log(1.089)^m=\log7.15\\m\log(1.089)=\log(7.15)\\m=\dfrac{\log7.15}{\log(1.089)}\\m\approx23.1\)

Thus, with no limiting factors to the growth of the plants, the number of  months have passed since the plants were first introduced is 23.1.

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Answer:

With no limiting factors to the growth of the plants, the number of  months have passed since the plants were first introduced is 23.1.

Step-by-step explanation:

the component form of vector v is approximately (-20, 52). Answer choice D is the correct one.

To find the component form of vector v, we first need to find the magnitude and direction of vector u.

The magnitude of vector u is given by the distance between its initial and terminal points:

|u| = √[(5 - 15)^2 + (-4 - 22)^2] = √(100 + 676) = √776

The direction of vector u is given by the angle it makes with the positive x-axis:

θ = tan^(-1)[(-4 - 22)/(5 - 15)] ≈ -1.96 radians (measured counterclockwise from the positive x-axis)

Since vector v points in the opposite direction of vector u and has twice its magnitude, we know that:

|v| = 2|u| = 2√776

The direction of vector v is opposite to that of vector u, so its angle is θ + π radians (180 degrees) measured counterclockwise from the positive x-axis.

Now we can find the component form of vector v:

v = |v| [cos(θ + π), sin(θ + π)]

v = 2√776 [-cos(θ), -sin(θ)]

v ≈ (-20, 52)

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The width of the plywood is 16 inches.

To find out the width of the piece of plywood, let's use the Pythagorean Theorem. It states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Here, the piece of plywood forms a right triangle with the 20-inch cut being the hypotenuse, and the width of the plywood being one of the legs. The other leg is unknown.

We can use the Pythagorean Theorem to solve for the width. Let the width of the plywood be x inches.

Then we have

$x^2 + 12^2 = 20^2$

Simplifying:

$x^2 + 144 = 400$

Subtracting 144 from both sides:

$x^2 = 256$

Taking the square root of both sides:

$x = \pm 16$

Since we're dealing with a physical object that can't have a negative width, the width of the plywood is 16 inches.

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Answer:

2 feet per year

Step-by-step explanation:

The calculated value of x in the triangle is 4.79 feet

From the question, we have the following parameters that can be used in our computation:

X

7 feet

43.2°

The value of x in the triangle can be calcuated using the following sine rule

sin(43.2) = x/7

Make x the subject of the above equation

So, we have

x = 7 * sin(43.2)

Evaluate the products

x = 4.79

Hence, the value of x is 4.79 feet

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The value of the given arithmetic expression will be 36c⁹.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, an expression such as

\(-\frac{1}{4} \sqrt{54c^{6} } (-8\sqrt{6c^{12} } )\)

Simplifying the equation,

=> \(-\frac{1}{4} \sqrt{54c^{6} } (-8\sqrt{6c^{12} } )\\\)

=> \(-\frac{1}{4} \sqrt{6 * 9c^{6} } (-8\sqrt{6c^{12} } )\)

=> \(2 \sqrt{6 * 9c^{6} } (\sqrt{6c^{12} } )\)

=> \(2*3 \sqrt{6*c^{6} } (\sqrt{6c^{12} } )\)

=> \(6* c^{3\\} \sqrt{6*c^{6} } (\sqrt{6c^{6} } )\)

=> 6 * c³ * 6c⁶

=> 36c⁹

Therefore, The value of the given arithmetic expression will be 36c⁹.

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The probability of rolling a 5 and then 6 is 1/36

From the question, we have the following parameters that can be used in our computation:

Number cube rolled twice

The sample space of each number cube is

Sample space = {1. 2. 3. 4. 5. 6}

From the above entries, we have

P(5) =1/6

P(6) = 1/6

Using the above as a guide, we have the following:

P = 1/6 * 1/6

Evaluate

P = 1/36

Hence, the probability is 1/36

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The data collection method in exercise 1.46, 1.47, and 1.50 may introduce bias, impacting the trustworthiness of the results, while the methods used in exercises 1.48 and 1.49 appear to be reasonable and unbiased. In evaluating the trustworthiness of study results, it is important to assess the potential biases in the method of data collection.

1.46 The method of data collection in this study is not biased as it involves asking a random sample of students a straightforward question about their study hours. However, there may be limitations in terms of relying solely on self-reported data.

1.47 The method of data collection in this study may be biased because the question asked is leading and suggests a positive response towards giving teachers a raise. This may result in a higher proportion of people supporting the raise, leading to an overestimation of the true proportion.

1.48 The method of data collection in this study is biased because only 10 apples are selected from the top of the truckload, which may not be representative of the entire load. This method may underestimate or overestimate the average bruising in the whole truckload.

1.49 The method of data collection in this study is not biased as it involves testing each printer of a specific type. However, the results may not generalize to other types of printers, limiting the estimation of the average lifespan of all printers.

1.50 The method of data collection in this study may be biased as it relies on the self-selection of students who choose to reply to the email. This may introduce selection bias, as those who respond may have different views compared to the general population of students, leading to an inaccurate estimation of the proportion of students supporting funding for an ultimate frisbee team.

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In this context, the dependent variable is the height of the ball (in meters).

To complete the table and determine the dependent variable, let's analyze the given information:

a) Completing the table:

The table provided includes time values (in seconds) and the corresponding height values (in meters) of the ball at different time intervals. It also includes the first differences, which represent the change in height between consecutive time intervals.

Using the given information, we can complete the table as follows:

Time (s) | Height (m) | First Differences

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

0.0      | 0          | -

0.5      | 9          | 9

1.0      | 15         | 6

1.5      | 19         | 4

2.0      | 20         | 1

2.5      | 19         | -1

3.0      | 15         | -4

3.5      | 9          | -6

4.0      | 0          | -9

b) Dependent variable:

The dependent variable is the variable that is affected by changes in the independent variable. In this case, the dependent variable is the height of the ball (in meters). The height of the ball is determined by the time at which it is measured and various factors such as the initial velocity, gravitational force, and air resistance.

The reasoning behind the height being the dependent variable is that the height changes depending on the time. As time progresses, the ball moves upwards, reaches its peak height, and then falls back down. The height value is directly influenced by the time at which it is measured, and thus, it is dependent on the independent variable, which is time in this case.

Therefore, in this context, the dependent variable is the height of the ball (in meters).

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Answer:

the answer should be -1

Step-by-step explanation:

-3 + (-2) + (-4) = -9

-9 + 4 = -5

-5 ÷ 5 = -1

Hope this helped :)

Answer:

-1 is your answer,

Step-by-step explanation:

first of all, add all those scores

-3 + 1 + -2 + -4 + 3 = -5

and for average, there is 5 rounds, so divide by 5

hence answer is -5 / 5 - = -1

The true conditional statement in the if-then form for daylight savings time is: If a state is in the United States, then it observes daylight savings time. Here's a step-by-step explanation:

1. A conditional statement consists of two parts: the hypothesis (if part) and the conclusion (then part). In this case, the hypothesis is "a state is in the United States" and the conclusion is "it observes daylight savings time." 2. The hypothesis states the condition that needs to be true for the conclusion to be valid. In this case, the condition is located in the United States. 3. The conclusion states the outcome or action that follows if the condition in the hypothesis is true. In this case, the outcome is observing daylight savings time. 4. The conditional statement expresses the relationship between the hypothesis and the conclusion. It states that if a state is in the United States (hypothesis), then it observes daylight savings time (conclusion). It's important to note that the statement is true because it accurately reflects the observation that all states in the United States, except for Arizona and Hawaii, observe daylight savings time.

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The integral of \(t^3\) from -1 to 4 is 63.75

To find the integral of \(t^3\) from -1 to 4,

-Determine the antiderivative of \(t^3\).

-The antiderivative of \(t^3\) is \(( \frac{1}{4} )t^4 + C\), where C is the constant of integration.

- Apply the Fundamental Theorem of Calculus. Evaluate the antiderivative at the upper limit (4) and subtract the antiderivative evaluated at the lower limit (-1).
\((\frac{1}{4}) (4)^4 + C - [(\frac{1}{4} )(-1)^4 + C] = (\frac{1}{4}) (256) - (\frac{1}{4}) (1)\)

-Simplify the expression.
\((64) - (\frac{1}{4} ) = 63.75\)

So, the integral of \(t^3\) from -1 to 4 is 63.75.

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A. The derivative is negative at x = 1.5 , B. The function is negative at x = -1 , C. The derivative is smallest (most negative) at x = 3 , D. The derivative is zero at x = 2.25. E. The derivative is approximately the same as at x = 2.25 at x = 0.7.

A. To find a point where the derivative of the function is negative, we need to locate a point on the graph where the slope is negative. From the graph, it appears that around x = 1.5, the function has a negative slope. Therefore, x = 1.5 is a point where the derivative of the function is negative.

B. To find a point where the value of the function is negative, we need to locate a point on the graph that lies below the x-axis. By observing the graph, it seems that around x = -1, the function takes negative values. Thus, x = -1 is a point where the value of the function is negative.

C. To find a point where the derivative of the function is smallest (most negative), we need to find a point on the graph where the slope is the steepest in the negative direction. Looking at the graph, it seems that around x = 3, the derivative is the most negative. Hence, x = 3 is a point where the derivative of the function is smallest.

D. To find a point where the derivative of the function is zero, we need to locate a point on the graph where the slope is flat or reaches a maximum/minimum. From the graph, it seems that around x = 2.25, the derivative is zero. Therefore, x = 2.25 is a point where the derivative of the function is zero.

E. To find a point where the derivative of the function is approximately the same as the derivative at x = 2.25 but distinct from x = 2.251, we can choose x = 0.7. It appears that the derivative of the function at x = 0.7 is similar to the derivative at x = 2.25.

In summary: A. The derivative is negative at x = 1.5. B. The function is negative at x = -1. C. The derivative is smallest (most negative) at x = 3. D. The derivative is zero at x = 2.25. E. The derivative is approximately the same as at x = 2.25 at x = 0.7.

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Answer:

D) 39

Step-by-step explanation:

\(||\text{c}\bold{u}||=||3\langle5,12\rangle||=||\langle3*5,3*12\rangle||=||\langle15,36\rangle||=\sqrt{15^2+36^2}=\sqrt{225+1296}=\sqrt{1521}=39\)

Answer:

x = 20

Step-by-step explanation:

You can use Pythagorean theorem which is \(a^2 + b^2 = c^2\)

a = 12

b = 16

and c would be x.

12^2 + 16^2 = c^2

144 + 256 = c^2

400 = c^2

square root

c = 20 or x = 20

The inverse Laplace transform of the function (s-6)/(3s^2+s+6) is (1/9)sinh(2t) + (2/3)e^(-3t), where sinh denotes the hyperbolic sine function.

To determine the inverse Laplace transform of the given function, we need to decompose the expression into partial fractions and then find the inverse transforms of each term.

First, we factor the denominator of (s-6)/(3s^2+s+6) as (3s+6)(s-1). Using partial fraction decomposition, we can express the function as A/(3s+6) + B/(s-1), where A and B are constants.

Next, we find the values of A and B by equating the numerators:

(s-6) = A(s-1) + B(3s+6).

By comparing coefficients, we find A = -1/3 and B = 2/3.

Now, we can take the inverse Laplace transforms of each term:

Inverse Laplace transform of -1/3(1/(3s+6)) = -(1/9)e^(-2t).

Inverse Laplace transform of 2/3(1/(s-1)) = (2/3)e^(3t).

Combining the inverse transforms, we have (1/9)sinh(2t) + (2/3)e^(-3t) as the inverse Laplace transform of (s-6)/(3s^2+s+6).

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Answer:

162 apples

Step-by-step explanation:

Hi there!

Create a proportion:

\(\displaystyle\frac{6\hspace{5}apples}{2\hspace{5}oranges}=\frac{x\hspace{5}apples}{54\hspace{5}oranges}\)

\(\displaystyle\frac{6}{2}=\frac{x}{54}\)

Simplify fraction:

\(3\displaystyle=\frac{x}{54}\)

Multiply both sides by 54 to isolate x:

\(3*54=x\\x=162\)

Therefore, there would be 162 apples in the basket if there was 54 oranges.

I hope this helps!

Answer:

x = 51

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

x² = 45² + 24² = 2025 + 576 = 2601 ( take the square root of both sides )

x = \(\sqrt{2601}\) = 51

Answer:

x = 51.

Step-by-step explanation:

The triple you require is 17-15-8

We have x-45-24

- that is three times each number in the triple.

So x = 3*17 = 51.

Answer:

43

Step-by-step explanation:

180 - 43 = 137

then,

180 - 137 = 43

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. The coefficient of 2\(x^{2}\) is 2. Therefore, the answer is 2 for a. 1 is the coefficient of -x after we add it to the left side. Therefore, b is 1. C is 5, as it is the only whole number.

This means that the answer is a = 2, b =1, c =5.

2. You can simply cancel out both 3s by dividing, which leaves us with  1±9\(\sqrt{5}\).

3.  The answer is c. Unfortunately, I can't explain that, it's just a well known formula.

I hope this helped!

1. The coefficient of 2 is 2. Therefore, the answer is 2 for a. 1 is the coefficient of -x after we add it to the left side. Therefore, b is 1. C is 5, as it is the only whole number.

This means that the answer is a = 2, b =1, c =5.

2. You can simply cancel out both of the 3s by dividing, which leaves us with  1+9.

3.  The answer is c.

I hope this helped!