The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:

A linear model with ordered pairs at 0, 26 and 2, 34 and 4, 34 and 8, 30 and 10, 0 and 12, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet.

Part A: During what interval(s) of the domain is the water balloon's height increasing? (2 points)

Part B: During what interval(s) of the domain is the water balloon's height staying the same? (2 points)

Part C: During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points)

Part D: Use the constraints of the real-world situation to predict the height of the water balloon at 14 seconds. Use complete sentences to support your answer. (3 points)

Hitting a red light three days in a row

Answer:

1. not continuous, as the function definitions deliver different function values at x=1 when approaching this x from the left and from the right side.

2.

2 = a + b

3.

0 = 2a + b

4.

a = -2

b = 4

Step-by-step explanation:

the function is continuous at a specific point or value of x, if the f(x) = y functional value is the same coming from the left and the right side at that point.

1. that means that for x=1

3 - x = ax² + bx

so,

3 - 1 = a×1² + b×1 = a + b

2 = a + b

we have to use a=2 and b=3

2 = 2 + 3 = 5

2 is not equal 5, so the assumed equality is false, so the function is not continuous there.

2. point 1 gave us already the working relationship between a and b.

2 = a + b

only if that is true, is the function continuous at x=1.

3. now for x=2

5x - 10 = ax² + bx

5×2 - 10 = a×2² + b×2 = 4a + 2b

10 - 10 = 4a + 2b

0 = 4a + 2b

0 = 2a + b

4. to find a and b to be continuous at both locations x=1 and x=2 both expressions in a and b must apply.

so, they establish a system of 2 equations with 2 variables.

2 = a + b

0 = 2a + b

a = 2 - b

0 = 2×(2-b) + b = 4 - 2b + b = 4 - b

b = 4

therefore

a = 2 - 4 = -2

5. I cannot draw a graph here.

just use now the function

3 - x, x < 1

‐2x² +4x, 1 <= x < 2

5x - 10, x >= 2

The functions have a range of  \(\(y \in \mathbb{R} \, | \, -\infty < y < \infty\)\) are all function

A. \(\(F(x) = -(x + 1)^2 - 4\)\)

B. \(\(F(x) = 2^x + 3\)\)

C. \(\(F(x) = x^2 + 7x - 9\)\)

D. \(\(F(x) = -4x + 11\)\)

E. \(\(F(x) = \frac{2}{3}x - 8\)\)

A. \(\(F(x) = -(x + 1)^2 - 4\)\)

This function represents a downward-opening parabola, and the term \(\(-(x + 1)^2\)\) ensures that the function's output will not exceed any upper bound as x increases.

Thus, the range is \(\(y \in \mathbb{R}\)\).

B. \(\(F(x) = 2^x + 3\)\)

Exponential functions with positive bases grow without bound as x increases.

Thus, the range of this function is \(\(y \in \mathbb{R}\)\).

C. \(\(F(x) = x^2 + 7x - 9\)\)

This function represents an upward-opening parabola and grows without bound as x increases.

Thus, the range is \(\(y \in \mathbb{R}\)\).

D. \(\(F(x) = -4x + 11\)\)

This function represents a linear equation, and the coefficient of x does not introduce any limiting factor on its output.

Thus, the range is \(\(y \in \mathbb{R}\)\).

E. \(\(F(x) = \frac{2}{3}x - 8\)\)

This function represents a linear equation with a non-zero coefficient of x, and it has a range of \(\(y \in \mathbb{R}\)\).

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The question attached here is in incorrect form, the correct form is:

Select all the correct answers. Which functions have a range of \(\(y \in \mathbb{R} \, | \, -\infty < y < \infty\)\)?

A. \(\(F(x) = -(x + 1)^2 - 4\)\)

B. \(\(F(x) = 2^x + 3\)\)

C. \(\(F(x) = x^2 + 7x - 9\)\)

D. \(\(F(x) = -4x + 11\)\)

E. \(\(F(x) = \frac{2}{3}x - 8\)\)

Answer:

a. €1200;$1667.70

Step-by-step explanation:

a. Number of euros

\(\text{euros} = \$1962 \times \dfrac{\text{1 euro}}{\text{\$1.635}} = \textbf{1200 euros}\)

b. Dollars remaining

Dollars on hand                        = $1962.00

Less 15 % spent = 0.15 × 1962 =   -294.30

Balance remaining                   =  $1667.70

\(\\ \sf\longmapsto \dfrac{5}{12}\)

\(\\ \sf\longmapsto 0.4166\)

\(\\ \sf\longmapsto 0.417\)

\(\\ \sf\longmapsto 0.42\)

Step-by-step explanation:

0.417 round to the nearest hundredth

Answer:

120 millimeters or 0.12 liters

Step-by-step explanation:

To solve this question :

1 liter = 1000 millimeter

2 liters = 2 x 1000 = 2000mm

8 people drank cocoa = 8 x 235 = 1880mm

Amount of cocoa left over = 2000 - 1880 = 120mm or 0.12 liters

Answer:

35%

Step-by-step explanation:

14 green / 40 total

Answer:

\(\boxed {\boxed {\sf \frac{7}{20} \ or \ 35 \% }}\)

Step-by-step explanation:

Probability tells us how likely something is to occur. It is found by dividing the favorable outcomes by the total outcomes.

\(P=\frac{favorable \ outcomes}{total \ outcomes}\)

In this question, a favorable outcome is selecting a green dye. The total outcomes are all the dyes.

\(P(green \ dye)=\frac{14}{40}\)

Reduce the fraction. Both the numerator and denominator can be divided by 2.

\(P(green \ dye) =\frac{14/2}{40/2}\)

\(P (green \ dye)=\frac {7}{20}\)

This is the probabilty as a fraction. It can also be written as a percent. Divide the fraction, then multiply by 100.

\(P(green \ dye)=\frac{7}{20}*100\)

\(P(green \ dye)=0.35 *100\)

\(P(green \ dye)=35 =35 \%\)

The probablity of selecting a green dye is 7/20 or 35%

The solution for x in the equation y = -2cot(3x), restricted to the interval (0, π/3), is x = (1/3) * arctan(1/2), x = (1/3) * arctan(1), and x = (1/3) * arctan(2).

To solve the equation y = -2cot(3x) for x in the interval (0, π/3), we need to find the values of x that satisfy the equation within that interval.

First, let's rewrite the equation using the identity cot(x) = 1/tan(x):

y = -2/tan(3x)

Now, we can take the reciprocal of both sides:

1/y = -tan(3x)/2

Next, we can take the arctangent of both sides to isolate 3x:

arctan(-1/y) = 3x

Now, divide both sides by 3:

x = (1/3) * arctan(-1/y)

Since we are restricted to the interval (0, π/3), we need to make sure that the values of x we obtain from the equation fall within that range.

Let's calculate x using the given equation for different values of y within the interval:

For y = -2, we have:

x = (1/3) * arctan(-1/(-2)) = (1/3) * arctan(1/2)

For y = -1, we have:

x = (1/3) * arctan(-1/(-1)) = (1/3) * arctan(1)

For y = -1/2, we have:

x = (1/3) * arctan(-1/(-1/2)) = (1/3) * arctan(2)

These calculations will give us the corresponding values of x within the specified interval.

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The solution for x in the interval (0, π/3) is:

x = (1/3) * arctan(1/(-2y))

We rewrite the equation using the reciprocal identity for cotangent:

cot(θ) = 1/tan(θ)

y = -2/tan(3x)

We multiply both sides by -1/2:

-2y = 1/tan(3x)

1/(-2y) = tan(3x)

3x = arctan(1/(-2y))

x = (1/3) * arctan(1/(-2y))

In conclusion, reciprocal identities  are described as the reciprocals of the six fundamental trigonometric functions  which are sine, cosine, tangent, secant, cosecant, cotangent.

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Answer:

40

Step-by-step explanation:

\(1600 = 40^{2}\)

\(\sqrt{1600} = \sqrt{40^{2}} = 40\)

The cable connectors that requires pressing a retaining tab to remove the faulty fiber optic network cable is likely an SC (Subscriber Connector) connector.

The cable in question is likely using an SC (Subscriber Connector) connector. The SC connector is a commonly used fiber optic connector that features a push-pull mechanism with a retaining tab. To remove the faulty fiber optic network cable, the technician would need to press the retaining tab on the SC connector, which releases the connector from its mating receptacle.

The SC connector is known for its ease of use and high performance. It has a square-shaped connector body and utilizes a push-pull latching mechanism, which makes it convenient for installation and removal. By pressing the retaining tab, the technician can safely and efficiently disconnect the faulty fiber optic cable.

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Answer:

B) one or more of the conditions have different effects.

The alternative hypothesis evaluated by Fobt in the one-way ANOVA states that one or more of the conditions have different effects. The correct answer is B) one or more of the conditions have different effects.

The one-way ANOVA is a statistical test used to determine if there is a significant difference between the means of three or more groups. The null hypothesis in this test assumes that all of the groups have the same mean, while the alternative hypothesis assumes that at least one group has a different mean.

Fobt (also known as the F statistic) is calculated by dividing the variance between groups by the variance within groups. The value of Fobt is then compared to a critical value to determine if the null hypothesis should be rejected in favor of the alternative hypothesis. Therefore, the correct answer is B) one or more of the conditions have different effects.

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Answer: The solution for w, expressed as a natural logarithm, is:

w = ln(88/3) / 5

Step-by-step explanation: Starting with the given equation:

-3e^(5w) = -88

Dividing both sides by -3:

e^(5w) = 88/3

Taking the natural logarithm of both sides:

ln(e^(5w)) = ln(88/3)

Using the property that ln(e^x) = x:

5w = ln(88/3)

Finally, solving for w by dividing both sides by 5:

w = (1/5)ln(88/3)

So the solution for w, expressed as a natural logarithm, is:

w = ln(88/3) / 5

x = 58.62 feet

y = 85.3 feet

Given that,

The cost of exterior walls is $140 per linear foot.

The cost of interior walls is $100 per linear foot.

  xy = 5000

⇒ y = 5000/x

For the exterior walls, we have 2(x + y)(110)

For the interior wall, we have 100x

The cost function = C

⇒ C = 2(x + y)(110) + 100x

⇒ C = 220(x + y) + 100x

      = 220x + 240y + 100x

      = 320x + 240y

Recall that y = 5000/x

C = 320x + 220(5000/x)

C = 320x + 1100000/x

Differentiate C with respect to x

C'(x) = 320 - 1100000/x²

       = (320x² -1100000) / x²

To minimize cost

C'(x) = 0

(320x² -1100000) / x² = 0

320x² -1100000 = 0

⇒ 320x² = 1100000

⇒ x² = 1100000/320

⇒ x = √1100000/320

⇒ x = 58.62 feet

Recall that y = 5000/x

y = 5000/58.62

y = 85.3 feet

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Answer:

19.26

Step-by-step explanation:

You multiply the cost of the backpack by 1.tax percent.

Answer:

C

Step-by-step explanation:

The electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

To determine the electron domain charge cloud geometry of \(BrF_5\), we need to examine the number of electron domains around the central atom (Br).

\(BrF_5\) consists of one central bromine atom (Br) surrounded by five fluorine atoms (F). Each bond and lone pair of electrons represents an electron domain.

In \(BrF_5\), there are five bonding pairs (Br-F) and no lone pairs around the central bromine atom. Therefore, the total number of electron domains is five.

Based on this information, the electron domain charge cloud geometry of \(BrF_5\) is trigonal bipyramidal.

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Answer:

30+6p

Step-by-step explanation:

6 times p + 6times5

6p+30

Answer: by weighing it and seeing how much lbs it weighs

Step-by-step explanation:

Answer:

\(X = \sqrt{39}\)

Step-by-step explanation:

\(1)\ X^2 + 5^2 = Y^2\ (Y\ is\ the\ hypotenuse\ of\ the\ smaller\ triangle)\)

\(2)\ Y^2 + 6^2 = 10^2\)

\(3)\ X^2 + 25 + 36 = 100\)

\(4)\ X^2 = 39\)

\(5)\ X = \sqrt{39}\)

Answer:

X = \(\sqrt{39}\)

Step-by-step explanation:

if the function is divided and we get the remainder of  zero then  it is said to be a factor of a function

According to the Remainder Theorem, by a factor x − an of that polynomial, then you will get a zero remainder. The point of the Factor Theorem is the turnaround of the Remainder Theorem: On the off chance that you synthetic-divide a polynomial by x = a and get a zero remainder, at that point not as it were is x = a, a zero of the polynomial(for the remainder theorem ) but x − a is additionally a factor of the polynomial according to of the Factor Theorem.

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The antiderivative of 70xe^(7x^2) is 5e^(7x?) + C, where C represents the constant of integration.

To find the antiderivative of the function 70xe^(7x^2), we need to take the derivative of each answer choice and determine which one yields the original function.

Let's evaluate the derivatives of the given answer choices one by one:

5e^(49x^2) + C

The derivative of this function with respect to x is:

d/dx [5e^(49x^2) + C] = 2x * 5e^(49x^2) = 10xe^(49x^2)

5xe^(7x)?

The derivative of this function with respect to x is:

d/dx [5xe^(7x)?] = 5e^(7x?) + 5xe^(7x?) * d/dx [7x?] = 5e^(7x?) + 35xe^(7x?)

5e^(7x)?

The derivative of this function with respect to x is:

d/dx [5e^(7x)?] = 0 + 5xe^(7x?) * d/dx [7x?] = 5xe^(7x?)

10e^(7x^2) + C

The derivative of this function with respect to x is:

d/dx [10e^(7x^2) + C] = 14x * 10e^(7x^2) = 140xe^(7x^2)

Comparing the derivatives of the answer choices to the original function 70xe^(7x^2), we can see that only the second option, 5e^(7x?), yields the correct derivative.

Therefore, the antiderivative of 70xe^(7x^2) is 5e^(7x?) + C, where C represents the constant of integration.

It's important to note that when evaluating the antiderivative, we need to consider the constant of integration, denoted as C. The constant of integration arises because the derivative of a constant is zero, so when we integrate a function, we need to include a constant term to account for all possible antiderivatives.

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Answer:

Subtract 3 from both sides.

Step-by-step explanation:

Doing this will leave 2x by itself.

Answer:

read below

Step-by-step explanation:

2x + 3 = 7

To isolate 2x, subtract 3 from both sides of the equation.

 \(2x + \frac{3}{-3} = \frac{7}{-3}\)

3 - 3 = 0

7 - 3 = 4

\(2x = 4\)

divide both sides by 2

\(x = 2\)

If Ms. Smith and Mr. Jones are each building a house from the same floor plan and Mr. Jones is using brick veneer. The  statements that  is true is: Mr. Jones's foundation plan will be 8 longer and wider than Ms. Smith's because a brick veneer house needs a 4 ledge on all four sides.

Stud wall can be defined as the wall that are often in vertical position and this wall is also known as the wall framing  as they help to   support  home  frame .

Based on the scenario since Mrs smith make use of stud wall and Mr Jone made used of brick veneer which implies that Mr. Jones Foundation will be  more  longer and wider than that of  Ms. Smith's.

Therefore Mr. Jones's foundation plan will be 8 longer and wider than Ms. Smith's because a brick veneer house needs a 4 ledge on all four sides.

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Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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Step-by-step explanation:

16 = 5(6x + 20)/4

6x + 20 = 12.8 (multiply 4/5 on both sides)

6x = -7.2 (subtract 20 on both sides)

x = -1.2.

Answer:

20%

Step-by-step explanation:

Percent Error =  

Vobserved - Vtrue

Vtrue

=  

24 - 20

20

=  

4

20

=  20%

Answer:

20 Percent Increase

Step-by-step explanation:

Trust Me

Answer:

Fraction 3/4 percent 75%

Step-by-step explanation:

.75 in simplest form is 3/4

3x - 3= x + 5

=> 3x - x = 5 + 3

=> 2x = 8

=> x = 8/2

=> x = 4

Answer:

4

Step-by-step explanation:

3x - 3 = x+5

=> 3x = x+5+3            ( transposing method)

=> 3x-x = 5+3

=> 2x = 8

=> x = 8/2

=> x = 4

Answer:

a + b = 50 (Two numbers total 50)

b = a - 6 (one number is 6 less than the other)

Since we have a value, we can use the substitution metod:

a + a - 6 = 50

Simplify:

2a - 6 = 50

From here, you should know how to isolate a variable--add 6 then divide by 2 in this case. That'll give you a, and you'll be able to use that to solve for b.

2(a) -6= 50

2a-6= 50

six goes and adds to 50 on the other side

2a = 56

divide both sides by 2

a= 28

final answer 28

Answer:

18cm = 45km

Step-by-step explanation:

Divide 18 by 4 to get 4.5. Multiply 4.5 by 10 to get 45km.