A pendulum is a weight attached to a fixed rod, as shown in the figures. Suppose that during an experiment, a pendulum moves back and forth in a periodic manner. At the beginning of the experiment , when the time is t = 0 seconds , the pendulum is at a point halfway between its maximum and minimum distances from the wall, 2.5 m away from the wall (Figure 1) and moving toward the wall. The pendulum first reaches its minimum distance from the wall , 1 m from the wall , when t = 1 second (Figure 2). When t = 4 seconds, the pendulum is back to a point halfway between its maximum and minimum distances from the wall. The pendulum continues to move back and forth so that the distance between the pendulum and the wall over time can be modeled by a sinusoida ! function .

For the given function the intercepts are:

x-intercept: x = -4

y-intercept: y = 12.

Here we have a table that defines a function, and we want to find the intercepts of said function.

We can assume it is linear, then the slope of the function will be given by:

a = (9 - 3)/(-1 + 3) = 6/2 = 3

The linear function is like:

y = 3x + b

To find the value of b we can replace the values of the last point on the table, x = 2 and y = 18.

18 = 3*2 + b

18 = 6 + b

18 - 6 = b = 12

The linear function is:

y = 3x + 12

The x-intercept is the value of x when y = 0

0 = 3*x + 12

-12 = 3x

-12/3 = x = -4

And the y-intercept is the value of y when x = 0.

y = 3*0 + 12

y = 12

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Answer:

The 440-yd race is longer than the 400-m race by 2.336 meters.

Step-by-step explanation:

We can convert the distance of the 440-yd race to meters using the conversion factor 1 yd = 0.9144 m:

440 yd = 440 x 0.9144 m/yd = 402.336 m

Therefore, the 440-yd race is 402.336 meters long.

On the other hand, the 400-m race is already in meters.

Comparing the two distances, we can see that the 440-yd race is longer than the 400-m race.

To find out by how much longer, we can subtract the length of the 400-m race from the length of the 440-yd race:

402.336 m - 400 m = 2.336 m

Therefore, the 440-yd race is longer than the 400-m race by 2.336 meters.

The solutions of the function as required to be determined is; x = 8 or x = -4.

As evident in the task content; the given equation are;

f(x)=9x² - 5x - 58 and

g(x) = 7x² + 3x + 6.

The solution of the equation can be determined as follows;

9x² - 5x - 58 = 7x² + 3x + 6.

2x² -8x - 64 = 0

x² - 4x - 32 = 0

(x - 8) (x + 4) = 0

x = 8 Or x = -4.

Ultimately, the solutions of the equation are; x = 8 or x = -4.

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Answer:

I think the answer is D.) 7/8 mile

Step-by-step explanation:

If you make the mixed numbers improper fractions. 2 and 1/8 is 17/8, 1 and 1/4 (2/8) is 10/8, then you subtract the numerators and keep the denomitators the same to get 7/8 mile (sorry if I spelt something wrong)

Answer:

0.125

Step-by-step explanation:

Answer:

5% of 40 is 2

Step-by-step explanation:

number  = x

25% of x is = 10

25% = 25/100, or 1/4

[tex]\frac{1}{4}x = 10[/tex]

multiply each side by 4

[tex]x = 40[/tex]

5% is 5/100, or 1/20

[tex]\frac{1}{20}x = ?[/tex]

plug-in the known value

[tex]\frac{1}{20}*40 = ?\\\frac{40}{20} = ?\\\frac{4}{2} = ?\\\\? = 2[/tex]

The answers to the questions are in the picture

Answer:

the answer is D

both lines intersect at (2, -3)

hope this helps <3

Answer:

c. 0.29

Step-by-step explanation:

edge

According to given information, A is 50 years old and B is 10 years old.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be evaluated to produce a numerical result or a value.

Let's use algebra to solve the problem.

Let A's current age be x, and B's current age be y.

From the problem, we know that:

x = 5y (A is five times as old as B)

x + 10 = 3(y + 10) (After 10 years, A will be 3 times as old as B)

We can use the first equation to substitute x in the second equation:

5y + 10 = 3(y + 10)

Simplifying this equation gives:

5y + 10 = 3y + 30

2y = 20

y = 10

So B is currently 10 years old. We can use the first equation to find A's current age:

x =5y = 5(10) = 50

So A is currently 50 years old.

Therefore, according to given information, A is 50 years old and B is 10 years old.

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[tex]101 - 99 = 2[/tex]

101 → 200

99 → 100

[tex]200 - 100 = 100[/tex]

⇒ the numbers could be: 99 and 101

other pairs of numbers: (199,201), (299,301) ...

The pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is [tex]175 nm^{-2[/tex].

First, we need tο cοnvert the area οf the blοck's base frοm square meters tο square nanοmeters, since the fοrce is given in newtοn-meters (N m) and we want tο find the pressure in newtοn-meters-squared ([tex]N/m^2[/tex] οr[tex]Nm^{-2[/tex]):

[tex]0.04 m^2 = 0.04 \times 10^18 nm^2 (since 1 m = 10^9 nm)[/tex]

Next, we can use the fοrmula fοr pressure, which is:

pressure = fοrce/area

Substituting the given values, we get:

[tex]pressure = 7 N m / 0.04\times 10^{18} nm^2[/tex]

Simplifying this expressiοn, we get:

[tex]pressure = (7 / 0.04) \times 10^{(-9)} N/nm^2[/tex]

[tex]pressure = 175 \times 10^{(-9)} N/nm{^2[/tex]

[tex]pressure = 175 nm^{-2[/tex]

Therefοre, the pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is[tex]175 nm^{-2[/tex].

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The time needed for the sample size to double is given as follows:

26.3 hours.

The exponential function that models the sample size after t hours is given as follows:

y(t) = y(0)e^(0.0264t).

The parameter y(0) represents the initial population, hence when the population is doubled, we have that:

y(t) = 2y(0).

Then we must solve the exponential function for the variable t, applying the natural logarithm, which is the inverse of the exponential, as follows:

2y(0) = y(0)e^(0.0264t).

e^(0.0264t) = 2

0.0264t = ln(2)

t = ln(2)/0.0264

t = 26.3 hours.

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The sums, differences, product, and quotient of the functions and their domains are;

f(x) = √(16 - x^2), g(x) = √(x + 3)

f + g = √(16 - x^2) + √(x + 3)

Domain; [-3, 4]

f - g = √(16 - x^2) - √(x + 3)

Domain: [-3, 4]

f × g = √(16 - x^2) × √(x + 3) = √(-x³ - 3·x² + 16·x + 48)

f × g = √(-x³ - 3·x² + 16·x + 48)

Domain; [-3, 4]

f/g = √(16 - x^2)/√(x + 3) = √(16 - x^2)/(x + 3))

f/g = √(16 - x^2)/(x + 3))

Domai; [-3, 4] ∪ [1, 4]

f(x) = √(81 - x^q2), g(x) = √(x² - 16)

f + g = √(81 - x^2) + √(x² - 16)

Domain [-9, -4] ∪ [4, 9]

f - g = √(81 - x^2) - √(x² - 16)

Domain: [-9, -4] ∪ [4, 9]

f × g = √(81 - x^2) × √(x² - 16) = √(-x⁴ + 97·x² - 1296)

f × g = √(-x⁴ + 97·x² - 1296)

Domain: [-9, -4] ∪ [4, 9]

f/g = √(81 - x^2)/√(x² - 16)

Domain: [-9, -4] ∪ [4, 9]

The sum of two functions is obtained by adding the values of the functions at each point.

The sum of two functions is obtained by adding the values of the functions at each point. The domain of the sum is the intersection of the domains of the two functions, In this case, the domain of f + g is [-3, 4]

The difference of two functions is obtained by subtracting the functions values at each point. The domain of the difference is the intersection of the domains of the two functions. In this case, the domain of f - g is [-3, 4]

The product of two functions is obtained by multiplying the values of the functions at each point. The domain of the product of the functions is the domain of the intersection of the domains of the two functions. The domain of f × g is  [-3, 4]

The quotient of two functions is obtained by dividing the values of the functions at each point. The domain of the quotient is the same as the domain of the intersection of two functions, excluding any points where the denominators is zero. The domain of f/g is [-3, -1] ∪ [1, 4].

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The area of the circle shown above is equal to: A. 1,520.5 cm².

Mathematically, the area of a circle can be calculated by using the following mathematical expression:

Area of a circle, A = πr²

Where:

r represents the radius of a circle.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of a circle, A = πr²

Area of a circle, A = 3.14 × 22²

Area of a circle, A = 1,520.5 cm².

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Answer:

Step-by-step explanation:

8y-7-4y=

8y-4y= -7

4y=-7

DBS by 4

y=1.75

Answer:

(−∞,∞)

Step-by-step explanation:

The total surface area of a cylinder with a height that was two times greater than its radius is 6πr²

The total surface area of a cylinder is the region occupied by the cylinder. It is given by A = 2πr(r + h) where

Since we want to find which student found the total surface area of a cylinder with a height that was two times greater than its radius.

We proceed as follows.

Since we have that the height that was two times greater than its radius. So, for that cylinder, h = 2r

So, to find the surface area, we substitute the values of the variables into the equation for the total surface area.

So,  A = 2πr(r + h)

Given that h = 2r, we have that

A = 2πr(r + h)

A = 2πr(r + 2r)

A = 2πr(3r)

A = 6πr²

So, the area is 6πr²

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Answer:

a) r = 9.7 m

Step-by-step explanation:

      CD = CE + ED

            = 9 + r +r

            = 9 + 2r

If a tangent and a secant are drawn from a common point outside the circle, then

                     CE * CD = CB *CB

               9 *  ( 9 + 2r) = 16 * 16       {Distributive property}

               9*9 + 9*2r   = 256

                   81 + 18r    = 256

Subtract 81 from both sides,

                            18r   = 256 - 81

                               18r = 175

Divide both sides by 18,

                                  r = 175÷ 18

                                   [tex]\boxed{\bf r = 9.7 \ m }[/tex]

Answer:

Step-by-step explanation:

ntroduction to standard deviation

Standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.

For example, the blue distribution on bottom has a greater standard deviation (SD) than the green distribution on top:

Answer:

146 and 1

Step-by-step explanation:

146+1=147

The equatiοn 9 -3 = 6 can be written in different fοrms, but the correct one is 9 = 3 + 6.

Every cοmbinatiοn οf a number, a variables, and οperatiοn symbοls is cοnsidered an expressiοn. An equatiοn is created by cοmbining twο expressiοns and jοining them with the equal sign.

Cοnditiοns οn the parameters are fοund in simple equatiοns. It is clear frοm an equatiοn that the answer οn the left and right are equivalent. The expressiοn tο the left οf the symbοl "=" is the LHS, while the expressiοn tο the right is the RHS. With the fοrm y = "sοme expressiοn invοlving x," a sοlutiοn invοlving x and y can be expressed, such as y = f. ( x). This final statement, which may be interpreted as "y equals f οf x," denοtes that y is a cοefficient οf x.

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Complete question:

Which answer shows the equation 9-3=6 below written in different forms?

Pearl's mortgage payment would be $678.47 per month.

A mortgage is a type of loan that is used to finance the purchase of real estate, such as a house or a piece of land. When a person takes out a mortgage, they borrow money from a lender (usually a bank or other financial institution) to buy the property, and they agree to pay back the loan over a set period of time, typically 15 to 30 years.

In the given question,

To calculate Pearl's mortgage, we need to first determine the amount of her down payment.

Down payment = 10% x $130,000

Down payment = $13,000

The amount that Pearl needs to finance with her mortgage is:

$130,000 - $13,000 = $117,000

To calculate the mortgage payment, we can use the formula for a fixed-rate mortgage:

Mortgage Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal (amount borrowed)

r = Monthly interest rate (annual rate divided by 12)

n = Number of monthly payments (30 years x 12 months per year)

Monthly interest rate = 6.3% / 12 = 0.00525

Number of monthly payments = 30 years x 12 months = 360

Using these values, we can calculate the monthly mortgage payment:

Mortgage Payment = $117,000 * 0.00525 * (1 + 0.00525)^360 / ((1 + 0.00525)^360 - 1)

Mortgage Payment = $678.47 (rounded to the nearest cent)

Therefore, Pearl's mortgage payment would be $678.47 per month.

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The net that represents this solid figure is diagram D.

A solid figure is a three-dimensional geometric shape that has length, width, and height. It is also called a three-dimensional or 3D figure. Some examples of solid figures include cubes, spheres, cylinders, cones, and pyramids.

Solid figures are different from two-dimensional shapes, which only have length and width. In contrast, solid figures have depth or thickness, making them more complex and interesting.

Solid figures can be classified based on their properties, such as the number of faces, vertices, and edges they have. For example, a cube has six faces, eight vertices, and 12 edges, while a sphere has no faces, vertices, or edges.

In this case, it has 2 squares and 4 rectangles. The appropriate diagram is D

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Answer:6

Step-by-step explanation:

[tex]\frac{a^{b} }{a^{c}} =a^{b-c} \\a^{b} *a^{c} =a^{b+c}\\ \frac{(-4)^{10}}{(-4)^{n}}=(-4)^{2}*(-4)^{2} \\(-4)^{10-n}=(-4)^{4}\\ 10-n=4\\ -n=-6\\n=6[/tex]

Answer:

n = 6

Step-by-step explanation:

[tex]\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2}*(-4)^{2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2+2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{4}[/tex]

If they have the same base which is -4 we can either add or subtracting the exponent.

Add the exponenet when multiplying.

Subtract the exponent when dividing.

[tex](-4)^{10-n}=(-4)^4\\\\10-n=4\\10=4+n\\n= 6[/tex]

[tex]\frac{(-4)^{10}}{(-4)^{6}}=(-4)^{10-6}=(-4)^4[/tex]

The null hypothesis for this study is that there is no significant difference in stress levels between the untreated population and the sample of students who were taught mindfulness meditation.

The null hypothesis states that the mindfulness meditation has no effect on the stress levels of the students.

In terms of the mean stress level (μ), the null hypothesis can be expressed as:

H₀: μ = 30

This means that under the null hypothesis, the mean stress level of the students who were taught mindfulness meditation is equal to the mean stress level of the untreated population (μ = 30).

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Answer:

Answer is B

Step-by-step explanation:

Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10

The correct statement regarding whether (8, √17) lies on the circle is given as follows:

Yes, the distance from the origin to the point (8,√17) is 9 units.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The parameters for this circle are given as follows:

Hence the equation is given as follows:

x² + y² = 81.

For point (8, √17), we have that:

8² + (√17)² = 81

64 + 17 = 81

81 = 81.

Hence the point lies on the circle.

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Answer:

A fully loaded and fueled spacecraft weighing 5.1 million pounds is equivalent to 2550 US tons

Step-by-step explanation:

The Venn diagram needed based on the question is given below:

             __________

            /          \

           /     A      \

          /____________\

          \            /

           \   E ∩ F  /

            \_________/

                 B

In the diagram, the set A represents the event of having an adequate supply of material A, and the set B represents the event of having an adequate supply of material B.

The overlap of A and B represents the event of having an adequate supply of both materials.

The set E represents the event of a shortage in material A, and the set F represents the event of a shortage in material B.

The intersection of E and F, denoted by E ∩ F, represents the event of a shortage in both materials.

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Answ

Step-by-step explanation:

x is equal to -9/2