The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t,
the time in minutes spent on the Internet.
$0
0 <1≤ 30
f(t)= $5 30 < t < 90
$10
> 90
Which statement is true about the Internet connection cost?
O It costs $5 per hour to connect to the Internet at the gaming store.
O The first half hour is free, and then it costs $5 per minute to connect to the Internet.
O It costs $10 for each 90 minutes spent connected to the Internet at the gaming store.
O Any amount of time over an hour and a half would cost $10.

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

Answer:

No, the answer would be 51755.3 (repeating), so no.

Step-by-step explanation:

The confidence interval is (22.68,29.52).

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

n = 10

x = 26.1

s = 4.2

Two-sided confidence interval :

CI = \((x-\frac{z*s}{\sqrt{n}},x+\frac{z*s}{\sqrt{n} } )\)

    = \((26.1-\frac{2.576*4.2}{\sqrt{10}},26.1+\frac{2.576*4.2}{\sqrt{10}} )\)

    = (26.1−3.42,26.1+3.42)

    = (22.68,29.52)

Hence, the confidence interval is (22.68,29.52).

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Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

Juan rode his bicycle at a rate of 22 feet per second. 79200 is his rate in feet per hour.

Since the International Yard and Pound Agreement of 1959, one foot is precisely equal to 0.3048 meters. One foot equals 12 inches in both customary and imperial measures, whereas one yard equals three feet.

To calculate the rate we have a conversion type:

1 feet per second = 3600 feet per hour

1 feet per second=(exactly)0.3048/(0.3048/36001)

1 feet per second=3600 ft/hr

The SI units are 0.3048 meters per second, for 1 feet per second.

And SI units approximately 8.4666667 × 10⁻⁵ meters per second, for 1 feet per hour.

This shows, that feet per second are bigger units than feet per hour.

Given feet per second=22

Now, for 22 feet per second contain how many feet per hour for this we need to multiply by 3600.

rate=22 × 3600

rate=79200 ft/hr

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Answer:

f(5) = -1

Step-by-step explanation:

f(5) is x = 5.

When x = 5, y = -1.

Therefore, f(5) = -1

Answer:

6 units

Step-by-step explanation:

JK + KL = JL

3x + 5x-6 = 4x+2

8x-6 = 4x+2

subtract 4x from each side to get:

4x - 6 = 2

add 6 to each side to get:

4x = 8

x = 2

JK = 3x and x=2 so JK = (3)(2) or 6

The numerical length of JK = 6

What is Line Segment?

" A line segment is a line section that can link two points. "

We know that point K is divide line JL

Given that JL = 4x+2

                 KL = 5x-6

                JK = 3x

So,  Equation is JK+KL = JL

                           3x+5x-6 = 4x+2

                           8x-6 = 4x+2

                            8x-4x = 2+6

                            4x = 8

                              x = 8/4

                             x = 2

So , numerical length of JK = 3x

                                        JK = 3×2

                                         JK = 6

Hence , length of JK is 6

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Answer:

surface area y is equal to 7cm.

Thus, the part of the trinomial that's equal to the product of p and q is the constant

term!

B: The Constant Term

Step-by-step explanation:

She just run 25 miles in the 4th week

Since the runner wants to have an average of 22 miles per week in 4 weeks, then the total miles that she must run will be:

= 22 × 4

= 88 miles

We will then add the total number of miles for the first 3 weeks. This will be:

= 20 + 22 + 21

= 63 miles

Then, the number of miles needed for the 4th race will be:

= 88 miles - 63 miles

= 25 miles

Therefore, she must run 25 miles in the 4th week.

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The most appropriate method of integration that should be used to solve the integral ∫3x eˣ dx is Integration by parts.

The given integral is,

∫3x eˣ dx

∫3x eˣ dx is the given integral.

This can be written as,

∫3x eˣ dx = 3 ∫x eˣ dx

Here there are two functions x and eˣ to be integrated.

One of them is exponential function.

When we want to integrate two functions especially of which one of them is exponential or logarithmic, then the most appropriate method used to find the integral is integration by parts.

Hence the correct option is Integration by parts.

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Hence, the probability that an aircraft entering the area is detected by more than two radar sets is approximately 0.998816, or about 99.88%.

To calculate the probability that an aircraft is detected by more than two radar sets, we need to consider the different combinations of radar sets that can detect the aircraft.

Let's analyze the possibilities:

If the aircraft is detected by all three radar sets:

Probability = (probability of detection) * (probability of detection) * (probability of detection)

= (0.98) * (0.98) * (0.98)

= 0.941192

If the aircraft is detected by exactly two radar sets:

There are three possible combinations of two radar sets that can detect the aircraft: (1st and 2nd), (1st and 3rd), (2nd and 3rd).

Probability for each combination = (probability of detection) * (probability of detection) * (probability of failure to detect) = (0.98) * (0.98) * (0.02) = 0.019208.

Total probability = 3 * 0.019208 = 0.057624.

Therefore, the probability that an aircraft is detected by more than two radar sets is the sum of the probabilities from the two cases above:

Probability = 0.941192 + 0.057624

= 0.998816

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Bring like terms together

on number line, we will have

The length of a standard basketball court is 94 feet (28.65 meters), and the width is 50 feet (15.24 meters).

A standard basketball court is rectangular in shape and follows certain dimensions specified by the International Basketball Federation (FIBA) and the National Basketball Association (NBA). The length and width of a basketball court may vary slightly depending on the governing body and the level of play, but the most commonly used dimensions are as follows:

The length of a basketball court is typically 94 feet (28.65 meters) in professional settings. This length is measured from baseline to baseline, parallel to the sidelines.

The width of a basketball court is usually 50 feet (15.24 meters). This width is measured from sideline to sideline, perpendicular to the baselines.

These dimensions provide a standardized playing area for basketball games, ensuring consistency across different courts and facilitating fair play. It's important to note that while these measurements represent the standard dimensions, there can be slight variations in court size depending on factors such as the venue, league, or specific regulations in different countries.

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Answer: rectangular prism

Step-by-step explanation:

The polynomial expression given is y=(x−1)³(x−2)²(x−5).This equation can be analyzed using various methods to determine different characteristics such as domain, range, symmetry, end behavior, and turning points. It is possible to factor the expression into linear terms and find out the zeros as well.First, let's determine the domain and range of the function.

The domain of a polynomial function is the set of all real numbers, which means that there are no restrictions on x for this equation. The range of the function, however, depends on the degree of the polynomial. In this case, the degree of the polynomial is odd, which means that its range is all real numbers.

Now let's take a look at the symmetry of the function.A function is symmetric if it remains unchanged when reflected across a line of symmetry. The degree of a polynomial determines whether the function is even, odd, or neither. In this case, the degree of the polynomial is odd, which means that the function is not symmetric about the y-axis or origin.

Next, let's analyze the end behavior of the function.The end behavior of a polynomial function is the behavior of the graph as x approaches positive or negative infinity.

The degree and leading coefficient of a polynomial function determine the end behavior. Since the degree of the polynomial is odd and the leading coefficient is positive, the end behavior of the function is that it rises to the left and falls to the right.Let's now determine the turning points of the function.

A turning point is a point on a curve where the slope changes from positive to negative or vice versa. Turning points can be found by setting the derivative of the function equal to zero. However, in this case, finding the derivative of the polynomial equation is very tedious and not feasible.

Thus, we can use a graphing calculator or software to plot the function and find the turning points.Therefore, the function y=(x−1)³(x−2)²(x−5) has a domain of all real numbers, a range of all real numbers, no symmetry, and end behavior that rises to the left and falls to the right.

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Answer:

y =4x+ 18

Step-by-step explanation:

Slope intercept form: y = mx + b

y -6 = 4(x + 3)

y - 6 = 4x + 12

Add 6 to both side

y = 4x + 12 + 6

y = 4x + 18

______________

\( \: \)

y - 6 = 4(x + 3)

y - 6 = 4x + 12

y = 4x + 12 + 6

y = 4x + 18✔

Answer:

\(\mathrm{C.\:}25\)

Step-by-step explanation:

Notice how each congruent square is divided into four equal parts. Since each square has four parts and there are four squares, there are \(16\) of these parts in total. Because each of these parts make up \(\frac{1}{4}\) of each square, all parts are equal. Therefore, you can count the total number of shaded parts to get your percentage.

The top left and bottom right both have one part shaded each for a total of \(2\) parts.

The top right and bottom left have \(0.5\) and \(1.5\) parts shaded, respectively, for a total of \(2\) parts.

Therefore, in total, there are \(2+2=4\) parts shaded out of \(16\) total parts.

Thus, the percentage of the total area that is shaded is:

\(\frac{4}{16}=\frac{1}{4}=\fbox{$25\%$}\).

Answer:

2.2:1

Step-by-step explanation:

Found the cube root of 1331

\( \sqrt[3]{1331} = 11\)

Reciprocal of 0.2 is

\( \frac{1}{0.2} = 5\)

Our ratio is 11:5. Our right hand number must equal 1 so we divide 5 by both sides.

\(11 \div 5 = 2.2\)

So our n is 2.2

Answer:

2.2:1

Step-by-step explanation:

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

Explanation:

The angle adjacent to the 146 degree angle is 180-146 = 34 degrees.

In other words, the angles 34 and 146 combine to 180. These angles are supplementary.

The tickmarks on this triangle tell us it is isosceles. The angles opposite the congruent sides are congruent angles. So the unmarked interior angles (not marked x) are 34 degrees each.

Now use the fact that any triangle has its interior angles always add to 180

x+34+34 = 180

x+68 = 180

x = 180-68

x = 112

Answer:

(x,y+7)

Step-by-step explanation:

x-side to side

y- up and down

We need to roll a die at least 3 times and a coin should be tossed at least 2 times.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given this, Becca repeatedly tosses a fair coin until she gets a head.

The probability of getting a head P(H) is = 1/2.

The probability of getting a number 3 or higher is,

P(3) + P(4) + P(5) + P(6).

= 1/6 + 1/6 + 1/6 + 1/6.

= 4/6.

= 2/3.

So, to get a number 3 or higher we need at least 3 rolls, and to get a head we need at least 2 tosses.

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Answer:

C = 84

Step-by-step explanation:

14 × 2 = 28

28 × 3 = 84

#CarryOnLearning

\(\large\mathfrak{{\pmb{\underline{\blue{Given}}{\blue{:}}}}}\)

Radius of the circle "\(r\)" = \(14\)

Value of \(π\) = \(3\)

\(\large\mathfrak{{\pmb{\underline{\pink{To\:find}}{\pink{:}}}}}\)

The circumference "\(C\)" of the circle.

\(\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf {C≈ 84}}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

We know that,

\(\sf\green{Circumference\:of\:a\:circle \:=\:2πr }\)

\( = 2 \times 3 \times 14\)

\( = 6 \times 14 \)

\( = 84\)

Therefore, the circumference of the circle is \(\boxed{ 84 }\).

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{❦}}}}}\)

Hence, 10⁵ ÷ 10⁷ equals 1/100.

Hoped this helped.

\(BrainaicUser1357\)

Answer: 1/x^2

Step-by-step explanation:

Cancel the common factor (10 in this case):

\(\frac{x^5}{x^7}\)

Apply the exponent rule for division, subtract the exponents

\(\frac{1}{x^7-5}\)\(= \frac{1}{x^2}\)

These are the equations of the lines in slope-intercept form, as requested: a. y = (9/7)x - 2 b. y = (-2/3)x + 1 c. y = 4x - 8/3 d.  y = (-8/3)x + 28/3

Given slope = 3/5 and y-intercept = 13.

Using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we substitute the given values:

y = (3/5)x + 13

The equation of the line is y = (3/5)x + 13.

Given slope = 9/7 and y-intercept = -2.

Using the slope-intercept form, y = mx + b, we substitute the given values:

y = (9/7)x - 2

Given slope = -2/3 and passes through the point (-6, 5).

Using the point-slope form, y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope, we substitute the values:

y - 5 = (-2/3)(x - (-6))

y - 5 = (-2/3)(x + 6)

y - 5 = (-2/3)x - 4

y = (-2/3)x + 1

Given slope = 4 and passes through the point (1, 4/3).

Using the point-slope form, y - y₁ = m(x - x₁), we substitute the values:

y - (4/3) = 4(x - 1)

y - (4/3) = 4x - 4

y = 4x - 4 + (4/3)

y = 4x - 8/3

Given two points: (7/2, 0) and (5, 4).

Using the two-point form, y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁), where (x₁, y₁) and (x₂, y₂) are the given points, we substitute the values:

y - 0 = (4 - 0)/(5 - 7/2)(x - 7/2)

y = (4/(-3/2))(x - 7/2)

y = (-8/3)(x - 7/2)

y = (-8/3)x + (8/3)(7/2)

y = (-8/3)x + 56/6

Simplifying,

y = (-8/3)x + 28/3

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The directional derivative of f at (2,1,1) in the direction of v is π/4 + (√3/2). The maximum rate of change of f at  (2, 1, 1) point is approximately 5/2 in the direction of v= <tan⁻¹1/5, 2tan⁻¹1/5, 3/10>.

To find the directional derivative of f(x, y, z) = xy^2tan⁻¹z at (2, 1, 1) in the direction of v = <1, 1, 1>, we first need to find the gradient of f at (2, 1, 1)

∇f = <∂f/∂x, ∂f/∂y, ∂f/∂z>

= <y²tan⁻¹z, 2xytan⁻¹z, xy²(1/z²+1)/(1+z²)>

Evaluating this at (2, 1, 1), we get

∇f(2, 1, 1) = <tan⁻¹1, 2tan⁻¹1, 3/2>

Now, we can find the directional derivative of f in the direction of v using the dot product

D_vf(2, 1, 1) = ∇f(2, 1, 1) · (v/|v|)

= <tan⁻¹1, 2tan⁻¹1, 3/2> · <1/√3, 1/√3, 1/√3>

= (√3/3)tan⁻¹1 + (2√3/3)tan⁻¹1 + (√3/2)

= (√3/3 + 2√3/3)tan⁻¹1 + (√3/2)

= (√3/√3)tan⁻¹1 + (√3/2)

= tan⁻¹1 + (√3/2)

= π/4 + (√3/2)

Therefore, the directional derivative is in the direction of v is π/4 + (√3/2).

The maximum rate of change of f at (2, 1, 1) occurs in the direction of the gradient vector ∇f(2, 1, 1), since this is the direction in which the directional derivative is maximized. The magnitude of the gradient vector is

|∇f(2, 1, 1)| = √(tan⁻¹1)² + (2tan⁻¹1)² + (3/2)²

= √(1+4+(9/4))

= √(25/4)

= 5/2

Therefore, the maximum rate of change of f is 5/2, and it occurs in the direction of the gradient vector

v_max = ∇f(2, 1, 1)/|∇f(2, 1, 1)|

= <tan⁻¹1/5, 2tan⁻¹1/5, 3/10>

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Answer:

w+h+10=10wh

Step-by-step explanation: