Sketch the graph of each function.
1)f(x)= -2 x-1, & ,x≤2
-x+4,x>2

The correct equation is t = 5 seconds.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Let me mention first that there is an error in the statement that the gravitational pull of the Earth is 16 ft/s^2. It is in fact 32 ft/s^2, and the actual equation uses half of the acceleration multiplied by the square of the variable time, so it gives as final expression :

y(t) = -16t² + 0t + 400

and we want to find the value/s for "t" that make this equation equal zero (when it reaches the ground and the object just touches the ground. This makes the equation we want to solve:

0 = -16t² + 0t + 400

16t² + 0t - 400 = 0

which solving for "t" becomes:

16t² - 400 = 0

16t² = 400

t² = 25

t = √25

t = ± 5

So we adopt the positive answer (positive time) since the negative value has no physical meaning for this problem.

That is: t = 5 seconds

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Using the Normal Distribution , the probability of landing in the circle on ground 10 times or less is 85.32 % , the correct option is (d) None of these   .

The term Normal Distribution is defined as a continuous probability distribution where the values lie in a symmetrical fashion mostly situated around mean .

it is given that ,probability(p) of landing marble on ground is 25% = 0.25

game is played for 30 rounds (n) = 30 ; q = 1 - 0.25 = 0.75 .

we know the mean (μ) = n×p = 30 × 0.25 = 7.5  ;

the standard deviation is (σ) = √n×p×q = √30×0.25×0.75  

= √5.625 = 2.38

By using Normal Distribution , X follows N(μ,σ²)

that is X follows N(7.5 , 2.38²) ;

we have to find P[X<10] = P[ (x-μ)/σ < (10 - 7.5)/2.38]

= P[ z < 2.5/2.38] = P[ z < 1.05 ] = 0.85314094 = 85.32 %

Therefore , the required probability is 85.32 %  .

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The value of c in the interval (-4 , -3) is -√12 such that f'(c) = 0 as

f'(-√12) = 0, so c = -√12.

Given, the function below satisfies Rolle's Theorem on the specified interval.

we have to find the value of c in the interval (-4 , -3) such that

f'(c) = 0.

the function given is,

f(x) = x + 12/x

First we have to find the derivative of the given function f(x).

f(x) = x + 12/x

f'(x) = 1 - 12/x²

Now, equating the derivative with 0 we get

f'(x) = 0

1 - 12/x² = 0

1 = 12/x²

x² = 12

x² - 12 = 0

(x + √12)(x - √12) = 0

x = √12 or x = -√12

we have two values of x be, ±√12.

but only -√12 lie in the interval (-4 , -3).

So, the value of c be -√12.

Hence, the value of c be -√12.

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Differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from [tex]x_{0}[/tex] to [tex]x_{0}[/tex] + dx is [tex]$$d S=\left(12 x_0\right) d x$$[/tex]

As per the given data:

The surface area is given by

[tex]$$S = 6 x^2$$[/tex]

Differentiate both sides with respect to  f(x)

[tex]$$S^{\prime}(x)=\frac{d}{d x}\left(6 x^2\right)\\\\=6(2) x^{2-1}$$[/tex]

= 12 x

The estimated change in surface area is given by

[tex]$$d S=S^{\prime}(x) d x= > d S\\\\$$[/tex]

= (12 x) dx

The change in surface area at [tex]$x=x_{0} $[/tex] is

[tex]$$d S=\left(12 x_0\right) d x$$[/tex]

Therefore the answer is [tex]$$d S=\left(12 x_0\right) d x$$[/tex]

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Write a differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from [tex]x_{0}[/tex] to [tex]x_{0}[/tex] + dx

Answer:

[tex]7.6 \times 10^7[/tex]

Step-by-step explanation:

[tex]1.5 \times 10^8-7.4 \times 10^7 \\ \\ =10^7 (15-7.4) \\ \\ =7.6 \times 10^7[/tex]

The difference between (1.5 x 10⁸) and (7.4 x 10⁷) is 7.6 x 10⁷.

The mathematical operation is subtraction. It is employed to eliminate words or expression's objects.

To find the difference between (1.5 x 10⁸) and (7.4 x 10⁷) :

We subtract both the numbers,

(1.5 x 10⁸) - (7.4 x 10⁷)

To solve further, we take the common term outside the bracket.

(1.5 x 10⁸) - (7.4 x 10⁷)

= 10⁷ (15 - 7.4)

= 7.6 x 10⁷

Therefore, the difference is 7.6 x 10⁷.

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The lengths of the sides of the quadrilateral are:

WX = 7 units

XY = 11 units

YZ = 7 units

WZ = 11 units

A quadrilateral is any polygon that has four sides and four interior angles.

Part A: The quadrilateral WXYZ has the following vertices,

W(-4, 5)

X(3, 5)

Y(3, -6)

Z(-4, -6)

Each of these vertices of quadrilateral WXYZ have been plotted in the graph that is attached below (see attachment).

Part B: To find the length of each of the sides of the quadrilateral, count the number of square boxes between two points on the graph, given that a square is equal to 1 unit.

Length of WX = 7 boxes = 7 units

Length of XY = 11 boxes = 11 units

Length of YZ = 7 boxes = 7 units

Length of WZ = 11 boxes = 11 units

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Answer:GIVE A BETTER DETAILED QUESTION sorry for caps

Step-by-step explanation:

Answer:

Step-by-step explanation:

We calculated 3-month weight moving average forecast = 0.417

It is a statistical expression of calculating average forecast that allows to keep heavier weight with the most recent data.

Given, weights for the 3 months are 0.6, 0.3 and 0.1 where the first weight is used for the most recent month and the last weight is used for the least recent month.

the weighing factor will be n, n-1 and n-2

n is the number of periods and n=3

now, weight moving average = [W1 × n +W2 × (n-1) × W3 × (n-2)]/ [n+(n-1)+(n-2)]

         [0.6 x 3 +0.3 x 2 + 0.1 x 1]/ [3+2+1] = 0.417

hence, weight moving average is 0.417

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We have to find a problem at the 5% significance level.

Sample size = 10.

If the Significant value is between five and ten, we lose one till the test. W. C. has a critical value of 44. We must perform a one-tailed analysis of the test. What tail is that?

If one is more efficient than the other, we are asked.

Here, almost everything is positive, and we discover what our values are. Mhm. The following data set, High bromide, was employed to get more sleep for 10 patients who used love level high school.

That's the control group minus the other one.

The control group is made up of people. I'm not sure if it's a left or right tail, so we'll just calculate the two ends.

The right tail will be 44, the other tail will be divided by two, and 55 minutes will equal 44. It's extremely useful. Okay. It won't reject if it's less than 11, and it will if it's more than 44. Is the music good? There were 10 pupils in our class, and their scores were 1.9 plus 0.8 plus 1.1 plus 0.1. The value of our nut is 23.4. Okay. Critical value takes us directly to the center. This was only a right tail test because we were unable to rule out the null hypothesis. The results would change to 50 if we ran it again at the 1% significance threshold. ten tons and eleven

We failed to reject the hypothesis again.

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The value of x in the kite is 32 (option B)

Polygons are defined as plane (two-dimensional) and closed shapes that are formed by joining three or more line segments with each other.

A polygon can be categorized as regular and irregular polygon based on the length of its sides.

Given figure of kite is a polygon,

Three angles of kite are given as 100° , 101° and (4 + 3x)°

It is given that sides opposite sides are equal to each other

Therefore, opposite angles are also equal

=> 4 + 3x = 100

=> 3x = 96

=> x = 96 / 3

=> x = 32

Hence , Value of x in the kite is 32

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Answer:

40.8 miles.

Step-by-step explanation:

To solve this problem, we need to know the distance that the airplane traveled in the air from the point of descent until it touched the ground. This distance is determined by the glide angle and the altitude of the airplane.

In general, the distance traveled in the air is equal to the altitude of the airplane divided by the sine of the glide angle. In this case, we are given the altitude and the glide angle, so we can calculate the distance traveled in the air as follows:

Distance = Altitude / sin(glide angle)

Plugging in the values from the problem, we have:

Distance = 20.42 miles / sin(30 degrees)

The sine of 30 degrees is 0.5, so the distance traveled in the air is:

Distance = 20.42 miles / 0.5

This simplifies to:

Distance = 40.84 miles

Rounded to the nearest tenth mile, the distance traveled in the air is 40.8 miles. This is the answer to the problem.

For the given height and distance  the answer of the following questions are:

a. Change in distance between the camera to the rocket at that moment is equal to 540ft/sec.

b. Change in the angle of elevation is equal to 0.144rad/sec.

As given in the question,

Let 'α' be the angle of elevation

'h' be the height of the rocket

'x' be the distance between the camera and the rising rocket.

a. Relation between x , h, and 4000 ft during launching pad is given by Pythagoras theorem:

x² = h² + 4000²

Differentiate with respect to time 't' we get,

2xdx/dt = 2hdh/dt + 0 __(1)

When h = 3000ft

x² = 3000² + 4000²

⇒x = 5000ft

dh/dt = 900ft/s

Substitute all values in (1) we get,

2(5000)dx/dt= 2(3000)(900)

⇒dx/dt = 5,400,000/ 10,000

⇒dx/dt = 540ft/sec.

b. tanα = h/4000 __(2)

when h = 3000ft

tanα = 3/4

⇒α = 0.6435

Differentiate (2) with respect to t we get,

sec²α dα/dt = (1/4000) dh/dt

⇒sec²(0.6435) dα/dt = (1/4000)(900)

⇒dα/dt = (0.225)/ 1.5625

⇒dα/dt = 0.144 rad/ sec.

Therefore, for the given height and distance the answer of the following questions are:

a. Change in distance between the camera to the rocket at that moment is equal to 540ft/sec.

b. Change in the angle of elevation is equal to 0.144rad/sec.

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The sum of geometric series is 12.34 and the series is converges

According to the question,

Geometric series is  100/81 + 10/9 + 1 + 9/10 + 81/100 + 729/1000 + . . .

The given series looks like to be in geometric progression with constant ratio r

r = 2nd term/1st term = a2/a1

= (10/9) / (100/81)

=> 9/10

We know that if the ‘r’ is less than 1 then it is convergent

Here 9/10 < 1, it is convergent.

Clearly, this is the sum of an infinite geometric series.

Sum of infinite series in GP = a/(1 - r)

Where a is the first term, 9/10 is the common ratio.

Sum of the geometric series = (100/81) / (1 - 9/10)

=> (100 / 81) / ( 1 / 10)

=> 100 / 8.1

=> 12.34

Therefore, the given series is convergent and its sum is 12.34

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Answer: 27/100

Step-by-step explanation:

Answer: In the below pic attached

Answer:

(10 * 312) + (10 * 612) + (10 * 812)

Step-by-step explanation:

To find the total amount of shampoo that Christa purchased in ounces, we can use the expression (10 * 312) + (10 * 612) + (10 * 812), which is equivalent to the expression that Christa used. This expression is also equivalent to 3120 + 6120 + 8120, which can be simplified to 3120 + 6120 + 8120 = 3120 + 6150 + 8100 = 9280 + 6150 = 15,430. Therefore, the expression (10 * 312) + (10 * 612) + (10 * 812) is equivalent to 15,430.

Answer:

2(x + 1)

Step-by-step explanation:

x is the unknow number.  Add 1 to that and then take that expression (x+1) and multiply it by 2.

Linda enrolls in two semesters for a total of 20 credits at a cost of $550 per credit hour (tuition and fees), plus $350 for each semester's textbooks. $488 is the total cost for one month. The right response in this case is option A.

In economics, the total cost is the total of all expenses a company incurs in order to produce a particular level of production.

The total cost is the sum of all the expenses a firm has expended to create a specific level of output. Product managers can assess their overall profit margin by adding together their fixed and variable costs. The sum of the fixed and variable expenses is the total cost.

The total cost for one semester = 10(550) + 350

= 5850

Total cost for one month = 5850/12

= 487.5 = $488

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To model the data with a linear function, we can use the two data points for ages 32 and 35 to find the slope and y-intercept of the line. Since the cost of life insurance for a female non-smoker at age 32 is $172 and the cost at age 35 is $182, the slope of the line is given by the formula:

$m = \frac{\text{cost at age 35} - \text{cost at age 32}}{\text{age 35} - \text{age 32}} = \frac{182 - 172}{35 - 32} = \frac{10}{3} = 3.33$

We can then use the point-slope formula to find the y-intercept of the line:

$y - y_1 = m(x - x_1)$

$y - 172 = 3.33(x - 32)$

To find the y-intercept, we can set $x = 0$ and solve for $y$:

$y - 172 = 3.33(0 - 32)$

$y - 172 = -105.76$

$y = 66.24$

Therefore, the equation of the line that models the data is given by:

$y = 3.33x + 66.24$

To predict the cost of life insurance for a female non-smoker of age 40, we can substitute 40 for $x$ in the equation above:

$y = 3.33(40) + 66.24$

$y = \boxed{239.44}$

Therefore, the predicted cost of life insurance for a female non-smoker of age 40 is $239.44.

Refer to the photo taken. Please rate :)

Answer:

The width of the rectangle is 32cm and the length is 37cm.

Step-by-step explanation:

On solving the provided question we can sat that, the geometric series' total is 12.34, and they care convergent.

An infinite series in mathematics known as a geometric series has the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. One straightforward illustration is the geometric series with a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, totaling 2 (or 1 if the first term is locked out).

The answer to the query is

The geometric series is made up of the numbers 100/81, 10/9, 1, 9/10, 81/100, 729/1000, and so on.

The provided series appears to be moving forward geometrically with a fixed ratio r.

r = second term, first term, or a2, a1.

[tex]= (10/9) / (100/81)[/tex]

[tex]= > 9/10[/tex]

We are aware that convergence occurs when 'r' is smaller than 1.

In this case, 9/10 1 is convergent.

This sums up an endless geometric sequence, without a doubt.

Infinite series' sum in GP equals a. (1 - r)

The usual ratio is 9/10, where an is the first word.

The geometric series' sum is equal to (100/81) / (1 - 9/10).

[tex]= > (100 / 81) / ( 1 / 10)\\ = > 100 / 8.1\\ = > 12.34[/tex]

The given series is therefore convergent, and its total is 12.34.

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There are four possible  values of C if there exist distinct complex numbers.

A complex number is an element of a number system that extends the real numbers with a specific element denoted i is called the imaginary unit . the equation every complex number can be expressed as,

             a + bi

where a and b are real numbers.

Let p(z) denote the cubic on the left-hand side; the right-hand side is then c3p(z/c). Write p(z)=z3+Az2+Bz+C so

z3 + Az2 + Bz + C ≡  z3+ cAz2 + c2Bz + c3C

⟹ (c−1)A =  (c2−1)B = (c3−1)C = 0.

Solving this we can find the possible values of C.

A real number can be said as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. continuous means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion.

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Question is incomplete. The complete question is:

Let c be a complex number. Suppose there exist distinct complex numbers r, s, and t such that for every complex number z, we have

    (z−r) (z−s) (z−t) = (z−c r) (z−c s) (z−c t).

Compute the number of distinct possible values of c.

Answer:

the answer that ur looking for is Aisha she has read more than David

Step-by-step explanation:

55% of 240=132

Answer:

Step-by-step explanation:

Ashia read more

A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line.

What is number line

A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line. It is assumed that each real number on the number line corresponds to a point on the number line, and vice versa.

Pencil. Edges of a ruler Edges of a paper

Pencil.

Edges of a ruler.

Edges of a paper.

Horizontal Line, Vertical Line, Perpendicular line, Intersecting lines.

Oblique Lines, Divergent lines, Convergent Lines, and Parallel Lines.

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The Time taken for David and Amy to be exactly 23 miles apart is 1.014 Hours.

Let [tex]t[/tex] be the time taken to reach 23 miles apart from a single point.

David and Amy start at same point and move towards different directions, making them move at perpendicular to each other.

According to Pythagoras theorem, and distance = Speed x time.

[tex](17t)^2 + (15t)^2 = 23^2[/tex]

[tex]289t^2 + 225t^2 = 529[/tex]

[tex]\therefore 514t^2 = 529[/tex]

[tex]t^2 = \frac{529}{514}[/tex]

[tex]t^2 = 1.029[/tex]

[tex]\therefore t = \sqrt{1.029} = 1.014 \text{ hours}[/tex]

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Answer: The difference in minutes between 2 hours 35 minutes and 1 3/4 hours is 30 minutes.

Step-by-step explanation:

To find the difference in minutes between 2 hours 35 minutes and 1 3/4 hours, we can first convert 1 3/4 hours to minutes.

There are 60 minutes in 1 hour, so 1 3/4 hours is equal to 1 + 3/4 = 1 3/4 hours = 1.75 hours.

Since there are 60 minutes in 1 hour, 1.75 hours is equal to 1.75 * 60 = 105 minutes.

Then, we can subtract 105 minutes from 2 hours 35 minutes to find the difference in minutes:

2 hours 35 minutes - 105 minutes = 135 minutes - 105 minutes = 30 minutes

So, the difference in minutes between 2 hours 35 minutes and 1 3/4 hours is 30 minutes.

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The mother will give the child $3 for each dot on the upside of the die. the greater expected value is Mother's Offer

The expected value of father's offer is $10, since the probability of getting heads is 50% and the reward for getting heads is $20.

The expected value of mother's offer is $3, since the probability of getting any number is 1/6 and the reward for getting any number is $3.

Therefore, the mother's offer has a greater expected value than the father's offer.

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Answer:

See Attached Images

Step-by-step explanation:

First, draw the lines without < or > signs, just use equals signs:

3x + y = -3

y = -3x - 3 (slope of -3, y-intercept at (0,-3) )

x + 2y = 4

2y = -x + 4

y = -(1/2)x + 4

Now shade the region above and including line (1) and below and including line (2).

Note for similair problems: If you have to multiply or divide by a negative number when solving for y, remember to flip the < or > sign to the other one when determining where to shade on the graph.