Expand 2(q+3) please

Answer:

f(2) = 1

x = 0

Step-by-step explanation:

f(2) = 1 since y=1 when x=2.

f(0) = -3 since x=0 when y=-3

we have the function

using a graphing tool

see the attached figure below

The real-world problem involving perimeter is that the perimeter of a rectangle of length 18 units and width 15 units is 66 units

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

2 x 18 + 2 x 15 = 66

The perimeter of a rectangle can be calculated using

Perimeter = 2 x Length + 2 x Width

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

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The calculated value of x at g(x) = 2 is x = 2.5

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

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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The percentile of 6.2 in the given data set is 40%.

To determine the percentile of 6.2 in the given data set, we can use the following steps:

Arrange the data set in ascending order:

4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2

Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.

Calculate the percentile using the formula:

Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100

In this case, the percentile of 6.2 can be calculated as:

Percentile = (4 / 10) × 100 = 40%

The percentile of 6.2 in the sample data set is therefore 40%.

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The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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Answer:

terima kasih atas poin ngratis nya

Annual expenses need to be budgeted for monthly, therefore the statement is false.

A budget is vital for an individual to plan well. It's important for an individual to budget monthly for annual expenses. This will make it easier for the person to pay.

An annual expense can include house rent, paying for a car, etc. Therefore, it's important for one to plan ahead. Ta essential for one.to pay them on time too.

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The answer is 3 cm. A space of 3 cm is left between the edge of the photograph and the frame.

Let x= width of the frame

width of the frame with picture=15+2x

length of frame with picture=24+2x

Area of frame with picture=(24+2x)(15+2x)=(360+78x+4x^2)

Area of picture alone=24*15=360

Area of the frame with picture-Area of picture alone=270

That is:  360+78x+4x^2 - 360 = 270

4x^2+78x-270=0

2x^2+39-135=0

On solving, the solutions are:

x = - 45 / 2 and x = 3

x can't be negative so x = 3 cm

Therefore space of the width of 3 cm is left between the edges of the photograph and the frame.

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Answer:

41

Step-by-step explanation:

Jus replace x with 3 and put it in a calculator.

Answer:

1. (a)  [-1, ∞)

   (b)  (-∞, -1) ∪ (1, ∞)

2. (a)  (1, 3)

    (b)  (-∞, 1) ∪ (3, ∞)

3. (a)  9.6 m and 0.4 m

   (b)  03:08 and 15:42

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

Part (a)

When x < 0, the function is f(x) = x².

Since the square of any non-zero real number is always positive, the range of the function f(x) for x < 0 is (0, ∞).

When x ≥ 0, the function is f(x) = sin(x).

The minimum value of the sine function is -1 and the maximum value of the sine function is 1.  As the sine function is periodic, the function oscillates between these values.  Therefore, the range of function f(x) for x ≥ 0 is [-1, 1].

The range of function f(x) is the union of the ranges of the two separate parts of the function.  Therefore, the range of f(x) is [-1, ∞).

Part (b)

The domain of the function g(x) = ln(x² - 1) is the set of all real numbers x for which (x² - 1) is positive, since the natural logarithm function (ln) is only defined for positive input values.

Find the values of x:

\(\implies x^2-1 > 0\)

\(\implies x^2 > 1\)

\(\implies x < -1, \;\;x > 1\)

Therefore, the domain of function g(x) is (-∞, -1) ∪ (1, ∞).

Part (a)

To determine the interval where f(x) < 0, we need to find the values of x for which the quadratic is less than zero.

First, set the function equal to zero and solve for x:

\(\begin{aligned} x^2-4x+3&=0\\x^2-3x-x+3&=0\\x(x-3)-1(x-3)&=0\\(x-1)(x-3)&=0\\ \implies x&=1,\;3\end{aligned}\)

Therefore, the function is equal to zero at x = 1 and x = 3 and so the parabola crosses the x-axis at x = 1 and x = 3.

As the leading coefficient of the quadratic is positive, the parabola opens upwards. Therefore, the values of x that make the function negative are between the zeros.  So the interval where f(x) < 0 is 1 < x < 3 = (1, 3).

Part (b)
Since the square root of a negative number cannot be taken, and dividing a number by zero is undefined, function f(x) has to be positive and not equal to zero:  f(x) > 0.

As the parabola opens upwards, the values of x that make the function positive are less than the zero at x = 1 and more than the zero at x = 3.

Therefore the domain of g(x) is (-∞, 1) ∪ (3, ∞).

Part (a)

The range of a sine function is [-1, 1]. Therefore, to calculate the maximal and minimal possible water depths of the bay, substitute the maximum and minimum values of sin(t/2) into the equation:

\(\textsf{Maximum}: \quad 5+4.6(1)=9.6\; \sf m\)

\(\textsf{Maximum}: \quad 5+4.6(-1)=0.4\; \sf m\)

Part (b)

To find the times when the depth is maximal, set sin(t/2) to 1 and solve for t:

\(\implies \sin \left(\dfrac{t}{2}\right)=1\)

\(\implies \dfrac{t}{2}=\dfrac{\pi}{2}+2\pi n\)

\(\implies t=\pi+4\pi n\)

Therefore, the values of t in the interval 0 ≤ t ≤ 24 are:

Convert these values to times:

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

Answer:

c is the right answer

Step-by-step explanation:

okk how are u ?

The statement (C) "While long-term bonds have more risks associated with them, they have the potential to bring in higher returns for the initial investment" is correct.

Long-term bonds keep an investor's money locked up for a longer period than a short-term bond, giving the bond's price more time to be impacted by changes in interest rates and inflation.

As we know,

The fact that short-term bonds offer lower interest rates than long-term bonds is a drawback.

Long-term bonds have a larger chance of receiving higher rates since there is a bigger likelihood that interest rates will rise over time.

Bonds with a long term are often those that investors hold for almost ten years.

Thus, the statement (C) "While long-term bonds have more risks associated with them, they have the potential to bring in higher returns for the initial investment" is correct.

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Answer:

Unit rate = 1.25 inches per yard

Length of fence B on the blueprint = 5 inches

Step-by-step explanation:

We are told that Fence A is 1 1/5 yards long but is 1 1/2 inches long on the blueprint.

This means it's 1.2 yards long but 1.5 inches on the blueprint.

Thus, the unit rate for this blueprint will be; 1.5/1.2 = 1.25 inches per yard

fence B is 4 yards long.

Thus, the corresponding blueprint measurement = 4yards × 1.25 inches/yard = 5 inches.

Answer:

A) 192

Step-by-step explanation:

20% = 0.2

240(0.2) = 48

This means $48 will be taken from the original price so:

240 - 48 = 192

Answer:

The easiest way to do these is to plot your known point on a graph. for example #15, you would plot your (-3,-4), then you know m=your slope, so you would go down 9 since it is negative, and left 2 because it's negative. This would make your next point at (-5, -13) and answer what y is

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:

120

Step-by-step explanation:

The total number of medals won is 150, and the circle graph shows that the proportion of medals won as gold is 20 percent, as silver is 30 percent, and as bronze is 50 percent.

To find the number of gold and bronze medals won, we need to calculate the total number of medals won in each category by multiplying the total number of medals by the proportion of medals won in each category.

Gold medals: 150 * 20% = 30

Bronze medals: 150 * 50% = 75

So, a total of 30 + 75 = 105 medals were won as gold and bronze.

Answer:

B

Step-by-step explanation:

Answer:

(2.6,1.8)

Step-by-step explanation:

length of horizontal side = (xB − xA) = 4 units

length of vertical side = (yB − yA) = 2 units

To find the x-coordinate of the point that divides the horizontal side in the ratio 2 : 3, first convert the ratio between the parts into the fraction of the sum that the first part is equal to:    a/a+b= 2/2+3= 2/5

Multiply the length of the horizontal side by the fraction, and then add the result to the x-coordinate of point A:  Xc= Xa  + (a/a+b) (Xb - Xa) = 1+ (2/5 x 4) = 2.6

Multiply the length of the vertical side by the fraction, and then add the result to the y-coordinate of point A:  Yc= Ya  + (a/a+b) (Yb - Ya) = 1+ (2/5 x 2) = 1.8

It follows that point C is located at (2.6, 1.8).

Answer:

The coordinates of point C is (2.6,1.8)

Step-by-step explanation:

Given dimensions of the room:

Length: \(\displaystyle\sf 12.5 \,m\)

Width: \(\displaystyle\sf 9 \,m\)

Height: \(\displaystyle\sf 7 \,m\)

Area of each wall:

\(\displaystyle\sf Area_1 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_2 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_3 = 9 \times 7 = 63 \,m^2\)

\(\displaystyle\sf Area_4 = 9 \times 7 = 63 \,m^2\)

Area of each door:

\(\displaystyle\sf Area_{\text{door}} = 2.5 \times 1.2 = 3 \,m^2\)

Area of each window:

\(\displaystyle\sf Area_{\text{window}} = 1.5 \times 1 = 1.5 \,m^2\)

Total area occupied by doors:

\(\displaystyle\sf Total_{\text{doors}} = 2 \times Area_{\text{door}} = 2 \times 3 = 6 \,m^2\)

Total area occupied by windows:

\(\displaystyle\sf Total_{\text{windows}} = 4 \times Area_{\text{window}} = 4 \times 1.5 = 6 \,m^2\)

Total wall area excluding doors and windows:

\(\displaystyle\sf Total_{\text{wall\,area}} = (Area_1 + Area_2 + Area_3 + Area_4) - Total_{\text{doors}} - Total_{\text{windows}}\)

\(\displaystyle\sf = (87.5 + 87.5 + 63 + 63) - 6 - 6\)

\(\displaystyle\sf = 275 - 6 - 6\)

\(\displaystyle\sf = 263 \,m^2\)

Cost of painting the walls:

\(\displaystyle\sf Cost_{\text{painting}} = Total_{\text{wall\,area}} \times 3.50\)

\(\displaystyle\sf = 263 \times 3.50\)

\(\displaystyle\sf = 920.50 \,Rs\)

Therefore, the cost of painting the walls of the room at Rs. 3.50 per square meter is Rs. 920.50.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Omg what is this? hopefully god helps you.

Step-by-step explanation:

Answer:

- sinu

Step-by-step explanation:

using the difference identity for sine

sin(a - b) = sinacosb - cosasinb

then

sin(u - π )

= sinucosπ - cosusinπ

= sinu(- 1) - cosu(0)

= - sinu - 0

= - sinu

Answer:

It's A.) linear

Step-by-step explanation:

The power of x is equal to one, making it linear [ f(x) = 2x^1 ]

Answer:

y=2x-13

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-7-(-1))/(3-6)

m=(-7+1)/-3

m=-6/-3

m=2

y-y1=m(x-x1)

y-(-1)=2(x-6)

y+1=2(x-6)

y=2x-12-1

y=2x-13

In polar coordinates, the inequality changes to

\(x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta\)

which is a circle of radius 2 and centered at (2, 0). The set D is then

\(D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}\)

The integral is then

\(\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta\)

\(=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta\)

\(=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta\)

\(=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta\)

There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,

\(\sin(2\theta)=2\sin\theta\cos\theta\)

so that the integral is

\(=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta\)

\(=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta\)

Then invoke another double-angle formula,

\(\sin^2\theta=\dfrac{1-\cos(2\theta)}2\)

to change the integral to

\(=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta\)

\(=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}\)

The value οf P(x > 104) is 0.1587 οr apprοximately 15.87%.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο find the prοbability οf P(x > 104) fοr a nοrmal distributiοn with mean οf 98 and standard deviatiοn οf 6, we need tο standardize the value οf 104 using the fοrmula:

z = (x - μ) / σ

where z is the standard scοre, x is the value we want tο find the prοbability fοr, μ is the mean οf the distributiοn and σ is the standard deviatiοn.

Plugging in the values, we get:

z = (104 - 98) / 6 = 1

Nοw we need tο find the area tο the right οf this value οn the standard nοrmal distributiοn table οr calculatοr.

Using a standard nοrmal distributiοn table οr calculatοr, we find that the area tο the right οf z = 1 is 0.1587.

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\( {2}^{ \frac{5}{3} \times \frac{1}{4} } = {2}^{ \frac{5}{12} } \\ \)

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Thus the correct answer is the third one.

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