Which of the following equations represents the graph shown?

A.)f( x) = - x - 2
B.)f( x) = x + 2
C.)f( x) = - x + 2

Answer: The answer is 15

Answer:

15 is the solution.

Step-by-step explanation:

Finding the value of expression,

→ 12 + |7 - 10|

→ 12 + |-3|

→ 12 + 3 = 15

Hence, the value is 15.

Answer:

-4.5. 2.75+(2)+(-5.25) = -4.5. hope this helps

Step-by-step explanation:

- Zombie

39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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Answer:

x=18

Step-by-step explanation:

Answer:

\(f(x) = (x+1)(x-2)(x+4)\)

        \(= (x^{2} +x-2x-2)(x+4)\\\\= (x^{2} -x-2)(x+4)\\\\= x^{3}-x^{2}-2x+4x^{2} -4x-8\\\\= x^{3} +3x^{2} -6x-8\)

The answer is 13.5 gallon, using arithmetic operation

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

A family drinks 3 gallons of milk in two weeks.

in one week the family will drink is 3/2.

So in 9 week they going to drink = 3/2 * 913.5  galllons of milk.

Hence the family will drink 13.5 gallons of milk in 9 weeks.

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Answer:

120°

Step-by-step explanation:

∠A+∠C = 180°

Or, 60° +∠C = 180°

Therefore, ∠C = 120°

Answer:

120

Step-by-step explanation:

hope that helps

Answer:

What do you need help with?

Step-by-step explanation:

There is no question

Answer:Holly drank 12 bottles in a week.

Step-by-step explanation:

First change the fraction 1 2/5 litre into a decimal, by doing this, we can know how many litres are there in 2/5.

So= 1 2/5

= 2 ÷5 = 0.4

= 1 + 0.4 = 1.4 liters

1.4 liters is the amount of water in a bottle.

Next, also change the fraction 2 2/5 litres into a decimal.

So=2 2/5

= 2÷5 = 0.4

= 2 + 0.4 = 2.4 liters

She drinks 2.4 liters a day.

To find how many bottles she drank in 1 week, we must multiply the amount of water she drinks in a day to the days in a week.

So= 1 week= 7 days

= 1 day= 2.4 liters

So= 2.4 × 7 = 16.8

She drinks 16.8 in a week.

To find how much bottles she drank in a week, we must divide the amount of liters she drank in one week to the amount of liters are there in a bottle.

So= 16.8 ÷ 1.4= 12 bottles

Holly drinks 12 bottles in a week.

I hope this helps! I'm sorry if it's wrong and complicated.

Answer:

(a).   y'(1)=0  and    y'(2) = 3

(b).  \($y'(t)=kb2t\cos(bt^2)$\)

(c).  \($ b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$\)

Step-by-step explanation:

(a). Let the curve is,

\($y(t)=k \sin (bt^2)$\)

So the stationary point or the critical point of the differential function of a single real variable , f(x) is the value \(x_{0}\)  which lies in the domain of f where the derivative is 0.

Therefore,  y'(1)=0

Also given that the derivative of the function y(t) is 3 at t = 2.

Therefore, y'(2) = 3.

(b).

Given function,    \($y(t)=k \sin (bt^2)$\)

Differentiating the above equation with respect to x, we get

\(y'(t)=\frac{d}{dt}[k \sin (bt^2)]\\ y'(t)=k\frac{d}{dt}[\sin (bt^2)]\)

Applying chain rule,

\(y'(t)=k \cos (bt^2)(\frac{d}{dt}[bt^2])\\ y'(t)=k\cos(bt^2)(b2t)\\ y'(t)= kb2t\cos(bt^2)\)  

(c).

Finding the exact values of k and b.

As per the above parts in (a) and (b), the initial conditions are

y'(1) = 0 and y'(2) = 3

And the equations were

\($y(t)=k \sin (bt^2)$\)

\($y'(t)=kb2t\cos (bt^2)$\)

Now putting the initial conditions in the equation y'(1)=0

\($kb2(1)\cos(b(1)^2)=0$\)

2kbcos(b) = 0

cos b = 0   (Since, k and b cannot be zero)

\($b=\frac{\pi}{2}$\)

And

y'(2) = 3

\($\therefore kb2(2)\cos [b(2)^2]=3$\)

\($4kb\cos (4b)=3$\)

\($4k(\frac{\pi}{2})\cos(\frac{4 \pi}{2})=3$\)

\($2k\pi\cos 2 \pi=3$\)

\(2k\pi(1) = 3$\)  

\($k=\frac{3}{2\pi}$\)

\($\therefore b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$\)

The y'(1) =0, y'(2) = 3, and the  \(\rm y'(t) = kb2t \ cos(bt^2)\)  and value of b and k are \(\pi/2\)  and  \(3/2\pi\) respectively.

It is given that the curve  \(\rm y(t) = ksin(bt^2)\)

It is required to find the critical point, first derivative, and smallest value of b.

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have a curve:

\(\rm y(t) = ksin(bt^2)\)

Given that the first critical point of y(t) for positive t occurs at t = 1

First, we have to find the first derivative of the function or curve:

\(\rm y'(t) = \frac{d}{dt} (ksin(bt^2))\)

\(\rm y'(t) = k\times2bt\times cos(bt^2)\)   [ using chain rule]

\(\rm y'(t) = kb2t \ cos(bt^2)\)

y(0) = 0

y'(0) = 0

The critical point is the point where the derivative of the function becomes 0 at that point in the domain of a function.

From the critical point y'(1) = 0 ⇒  \(\rm kb2 \ cos(b) =0\)

k and b can not be zero

\(\rm cos(b) = 0\)

b = \(\rm \frac{\pi}{2}\)

and y'(2) =3

\(\rm y'(2) = kb2\times 2 \times cos(b\times2^2) =3\\\\\rm 4kb \ cos(4b) =3\)(b =\(\rm \frac{\pi}{2}\))

\(\rm 4k\frac{\pi}{2} \ cos(4\frac{\pi}{2} ) =3\\\\\rm2 \pi kcos(2\pi) = 3\)

\(\rm2 \pi k\times1) = 3\\\rm k = \frac{3}{2\pi}\)

Thus, y'(1) =0, y'(2) = 3, and the  \(\rm y'(t) = kb2t \ cos(bt^2)\)  and value of b and k are \(\pi/2\)  and  \(3/2\pi\) respectively.

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Probability that the vaccine will be developed = \(\frac{99363}{100000}\)

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here,

Team 1 has an 86 % chance of success of developing a new vaccine

Team 1 has 100 - 86 = 14% chance of failure of developing a new vaccine

Team 2 has an 87 % chance of success of developing a new vaccine

Team 2 has 100 - 87 = 13% chance of failure of developing a new vaccine

Team 3 has an 65 % chance of success of developing a new vaccine

Team 3 has 100 - 65 = 35% chance of failure of developing a new vaccine

Probability that the vaccine will not be developed =

                                                                                     \(\frac{14}{100} \times \frac{13}{100}\times \frac{35}{100}\\\frac{637}{100000}\\\)

Probability that the vaccine will be developed =

                                                                            \(1 - \frac{637}{100000}\\\\\frac{100000-637}{100000}\\\\\frac{99363}{100000}\)

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Answer:

Step-by-step explanation:

Remember that

Area of Circle = \(\pi r^2\)

\(\pi = pi \\r = radius\)

They told us that for this circle, the area is \(144\pi m^2\)

If you put it back into the formula for area of a circle we get:

Area of Circle = \(\pi r^2\)

\(144\pi = \pi r^2\)

Divide both sides by \(\pi\).

144 = \(r^2\)

Now we want to solve for r (r = radius).

You need to square root each side

\(\sqrt{144} = \sqrt{r^2}\)

\(12 = r\)

So now we know the radius, \(r = 12\) metres

Also remember that

Diameter = \(2r\)

So,

Diameter = 2 times 12 = 24 metres

The required diameter of the given circle is 24 meters.

The area of the circle is given by the pie times square of the radius.

Area of circle = πr^2

Here,
The given area of the circle is 144π m²
And we know that,
Area = πr²

substitute the value of the area in the above expression,

144π = πr²
r² = 144
r = √144
r = 12 meters

Since,
Diameter = 2 × radius
Diameter = 2 × 12 = 24 meter

Thus, the required diameter of the given circle is 24 meters.

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Answer:

\(x=15/2=7.5\)

Step-by-step explanation:

So we have the function:

\(f(x)=2x+1\)

And we want to find x such that:

\(f(x)=16\)

To do so, substitute 16 for f(x):

\(f(x)=2x+1\\16=2x+1\)

Subtract 1 from both sides. The right side cancels:

\((16)-1=(2x+1)-1\\2x=15\)

Divide both sides by 2. The left side cancels:

\((2x)/2=(15)/2\\x=15/2=7.5\)

The value of x is 7.5

Answer:

\(x=\frac{15}{2}\)

Step-by-step explanation:

We are given the value of f(x). Insert this value into the original equation:

\(f(x)=16\\\\16=2x+1\)

Solve for x. Subtract 1 from both sides:

\(16-1=2x+1-1\\\\15=2x\)

Divide both sides by 2 to isolate x:

\(\frac{15}{2} =\frac{2x}{2} \\\\\frac{15}{2}=x\)

When f(x) equals 16, x is equal to \(\frac{15}{2}\)

The number of basket Kathy will make out of 60 tries is 23 basket.

She keeps track of the number of basket she makes while practicing her free throw shots.  

She makes 7 baskets out of 18 tries.

This is when quantities have the same ratios. Therefore,

18 tries = 7 baskets

60 tries = ?

cross multiply

number of basket = 60 × 7 / 18

number of basket = 420 / 18

number of basket = 23.3333333333

number of basket = 23 basket.

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Answer:

-1/4 is the slope.

Step-by-step explanation:

To find the slope of the given points, we can use the formula:

y2-y1/x2-x1

So, in this case, subtract 5 and 7, and subtract 9 and 1.

5-7=-2

9-1=8

-2/8

Now, simplify.

-1/4 is the slope.

The amount Sandra will have in the account after 12 years is b. $140,181.30 if she deposits $3,000 at the end of each semiannual period

We can determine the amount she will have in the account after 12 years by using the formula for future value as follows;

FV = P(1+i)×{ (1+i)^n - 1 } / i

Here;

FV = future value of the money after n periods

P = deposit per period

i = interest rate per period

n = the number of periods

Substituting the values in this equation to find the amount after 12 years as follows;

FV = 3000(1+0.05)×( (1+0.05)^24 - 1 ) / 0.05

FV = 3000(1+0.05)×( (1+0.05)^23 ) / 0.05

FV = 140,181.296 = 140,181.30

Hence the amount after 12 years is calculated to be $140,181.30

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Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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Given the word problem, we can deduce the following information:

1. The diameter of the circle is 3 meters.

2. The side length of the square is 3 meters.

To determine the difference in area between a circle and a square, we note first the formulas of a circle with a diameter d and the area of a square with side length d:

where:

d=diameter

where:

d=side length

The figures are shown below:

Based on this, the difference of areas would be:

Next, we plug in d=3:

Therefore, the difference in areas is:

Answer:

\(x = 5016\)

\(y = 1008\)

Step-by-step explanation:

Given

Let:

\(x \to Elephant\ seal\)

\(y \to Bennet\)

From the first statement, we have:

\(x + y = 6024\)

From the second, we have:

\(2x - y = 9024\)

Required

Find x and y

Add both equations to eliminate y

\(x +2x + y - y = 6024 + 9024\)

\(3x = 15048\)

Divide both sides by 3

\(x = 15048/3\)

\(x = 5016\)

Substitute \(x = 5016\) in \(x + y = 6024\)

\(5016 + y = 6024\)

Solve for y

\(y = 6024 - 5016\)

\(y = 1008\)

Answer:

Step-by-step explanation:

y - 7 = 2(x - 1)

y - 7 = 2x - 2

y = 2x + 5

Part a:  What quantity order size would minimize the total annual inventory cost? Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost At minimum Total Annual Inventory Cost, the formula for the Economic Order Quantity (EOQ) is used. EOQ formula is given below: EOQ = sqrt((2DS)/H)Where, D = Annual DemandS = Ordering cost

The company should place an order for 168 boxes at a time in order to minimize the total annual inventory cost.Part b: Determine the minimum total annual inventory cost.Using the EOQ, the company can calculate the minimum total annual inventory cost. The Total Annual Inventory Cost formula is:Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying CostAnnual Ordering Cost = (D/EOQ) × S = (16,800/168) × $60 = $6,000Annual Carrying Cost = (EOQ/2) × H = (168/2) × $30 = $2,520Total Annual Inventory Cost = $6,000 + $2,520 = $8,520Therefore, the minimum Total Annual Inventory Cost would be $8,520.Part c: Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes)

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Answer:

a) 21, 24, 29

b) 5 terms in the sequence are less than 50

Step-by-step explanation:

\(t_n = n^2+20\\t_1 = 1^2+20 = 1+20= 21\\t_2 = 2^2+20 = 4+20= 24\\t_3 = 3^2+20 = 9+20= 29\\\\\\t_5 = 5^2+20 = 25+20= 45\\\\\\t_6 = 6^2+20 = 36+20= 56\\\)

Since, 5th term is less than 50 and 6th term exceeds 50, therefore 5 terms in the sequence are less than 50.

Answer:

30

Step-by-step explanation:

Based on the directions we know that  both figures are similar, meaning there is a dilation factor changing the overall size of the figures. In order to find this dilation factor we can give it the value of x and multiply it to the various lengths of the smaller figure. Once this is done, we make these values equal to their the corresponding counterparts on the larger figure.

32x=40

x=5/4

Now that the dilation factor is found substitute its value for x

24(5/4)=30

Equations for common surfaces:

1. Plane: Ax + By + Cz + D = 0

2. Sphere: (x - h)² + (y - k)² + (z - l)² = r²

3. (Elliptic) Paraboloid: z = ax² + by² + c

4. Hyperbolic Paraboloid: z = ax² - by² + c

5. (Circular) Cylinder: (x - h)² + (y - k)² = r²

6. Half Cone: z = √(x² + y²)

For each surface:

1. Plane: The easiest coordinate system to express the equation is the Cartesian coordinate system (x, y, z) since the equation involves linear terms in all three variables.

2. Sphere: The Cartesian coordinate system (x, y, z) is most suitable for expressing the equation of a sphere because it directly relates to the distance between the center of the sphere and any point on its surface.

3. (Elliptic) Paraboloid: The Cartesian coordinate system (x, y, z) is most convenient for expressing the equation of a (elliptic) paraboloid because it allows a direct representation of the quadratic terms in x and y.

4. Hyperbolic Paraboloid: Similar to the (elliptic) paraboloid, the Cartesian coordinate system (x, y, z) is best suited for expressing the equation of a hyperbolic paraboloid due to its direct representation of the quadratic terms.

5. (Circular) Cylinder: The cylindrical coordinate system (ρ, φ, z) is easiest to express the equation of a (circular) cylinder because it naturally separates the radial distance from the axis (ρ) and the angle in the xy-plane (φ).

6. Half Cone: The Cartesian coordinate system (x, y, z) is most suitable for expressing the equation of a half cone since it provides a direct representation of the relationship between the coordinates and the square root of the sum of their squares.

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Answer: it is 98

Step-by-step explanation:

Answer:

800

Step-by-step explanation:

Answer:

Volume of the cylinder is 1521π in³

Step-by-step explanation:

Hello,

To find the volume of a cylinder, we need the know the formula used for calculating it.

Volume of cylinder = πr²h

r = radius

h = height

Data,

Radius = 13in

Height = 9in

Volume of a cylinder = πr²h

Now we need to substitute the values into the formula

Volume of a cylinder = π × 13² × 9

Volume of a cylinder = 169 × 9π

Volume of a cylinder = 1521π in³

Therefore the volume of the cylinder is 1521π in³

Answer:

1521

Step-by-step explanation:

Answer:

The temperature is now -16°C.

Answer:

180 pounds

Step-by-step explanation:

In six months Bill's weight will be increased by 60 pounds

10 pounds*6 months=60 pounds

120+60=180

In six months Phil will lose 24 pounds decreasing his weight from 204 to 180

4 pounds*6 months=24 pounds

204-24=180

Answer:

180 lbs

Step-by-step explanation:

204-24= 180

120+60=180

multiply each by 6  

The solution to the equation x² + 5x = 0 is x = 0 or x = -5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

x² + 5x = 0   be equation (1)

Now , on simplifying the equation , we get

On factorizing the equation , we get

Taking the common factor x ,

x ( x + 5 ) = 0

Now , x can take 2 values which will satisfy the given equation

when x = 0 or ( x + 5 ) = 0

when x = 0

Substitute the value of x in the equation , we get

0 ( 0 + 5 ) = 0

0 = 0

The equation is true when x = 0

And ,

when ( x + 5 ) = 0

Subtracting 5 on both sides of the equation , we get

x = -5

when x = -5

-5 ( -5 + 5 ) = 0

-5 x 0 = 0

0 = 0

The equation is true when x = -5

Hence , the solution is 0 , -5

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