For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 12 N acts on a certain object, the acceleration
of the object is 4 m/s². If the acceleration of the object becomes 10 m/s², what is the force?
ON

The value of secant theta is 29/20

First, it is important to note the different trigonometric identities and their ratios, we have;

sin θ= opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

sec θ = hypotenuse/adjacent

From the information given, we have that;

tan θ = 21/20

Adjacent = 20

Opposite = 21

Using the Pythagorean theorem, we have;

x² = 21² + 20²

find the squares

x² = 441 + 400

add the values

x² = 841

Find the square root

x = 29

Then, sec θ = 29/20

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Answer:

(-1, 2)

Step-by-step explanation:

1.) The way to use elimination is to add or subtract both of the equations together to eliminate a variable. If we add the two equations together, the -6x and 6x cancel out. Since we added the equations together, -12y and 10y would add up to -2y, and -18 and 14 would add up to -4

2.) Now, we have the equation -2y = -4. By dividing by -2 on both sides, we get y=2.

3.) Next, we need to substitute y back in to get the x value. If you use the first equation, we get -6x - 12 * 2 = -18.

4.) By simplifying, you get that -6x - 24 = -18. If you add 24 on both sides, you get -6x = 6, and by dividing by -6 on both sides, you get x = -1.

5.) Finally, you have to put the answer in form of a point. -1 would be the x-coordinate and 2 would be the y-coordinate. Therefore, the point is (-1, 2)

Step-by-step explanation:

This is kinda like the Pythagorean Theorem with THREE dimensions instead of two

diagonal^2 = 3^2 + 4^2  +  2^2

diagonal = sqrt ( 29) = 5.39 ft

Answer:

144 sq. units

Step-by-step explanation:

Area of Square =[tex][side] ^{2}[/tex]

There are 26.24 cubic feet of sand in the rectangular container based on volume.

We must determine the volume of sand in the rectangular container in order to determine how much is there.

Let's start by determining the container's volume:

Container volume equals length, width, and height

Container volume: 6.5 feet by 3.2 feet by two feet

Container volume is 41.6 cubic feet.

The amount of sand in the container's volume must then be determined. We can determine the volume of sand by using the following formula because it fills the container to a depth of 1.3 feet:

Sand volume is determined by its length, width, and depth.

Sand volume = 6.5 feet by 3.2 feet by 1.3 feet

Sand volume = 26.24 cubic feet

As a result, the container contains 26.24 cubic feet of sand.

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Answer:

To solve this problem, we can use the equations of motion for a vertically launched object. First, we need to find the initial velocity of the snowball when it is kicked off the ground. We know that its speed is 24 feet per second, but we also need to take into account the angle at which it is kicked. Let's assume that Max kicks the snowball at a 45-degree angle. Using trigonometry, we can find that the horizontal velocity of the snowball is also 24 feet per second, and the vertical velocity is 24 feet per second times the sine of 45 degrees, which is approximately 16.97 feet per second. Now we can use the following equation to find the time it takes for the snowball to hit the ground: h = vi*t + 0.5*a*t^2 where h is the maximum height, vi

Answer:

[tex] \sqrt{(22 - 4.25)^{2} +(6.25 - 6.25) ^{2} } \\ [/tex]

[tex] \sqrt{(15.75)^{2} } [/tex]

=15.75 units

The book that weighs 3/4 pounds is greater than 1/2 pounds.

To compare the weights of the two books with 1/2 pound, we need to convert 1/2 pound into a fraction with a common denominator as the given weights. The common denominator of 8 and 4 is 8. So, we can convert 1/2 pound to 4/8 pound.

Now we can compare the weights of the two books with 4/8 pounds. The weight of the first book is 3/8 pounds, which is less than 4/8 pounds. The weight of the second book is 3/4 pounds, which is greater than 4/8 pounds.

Therefore, the book that weighs 3/4 pounds is greater than 1/2 pound.

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Answer:

older than those found in shallower layers of sediment. This is because sedimentary rock layers form over time, with the oldest layers at the bottom and the newest layers at the top. As sedimentary rocks form, they often trap the remains of plants and animals, which then become fossils. The deeper layers have been buried for a longer period of time, so they contain older fossils. This principle is known as the law of superposition and is an important tool for dating fossils and determining the relative ages of different rock layers.

Answer:

  7467 ft 1 in = 89605 inches on a side

Step-by-step explanation:

You want the dimensions of a square with an area of 2 square miles, to the nearest inch.

The area of a square is given by ...

  A = s² . . . . . . where s is the side length

For an area of 2 mi², the side length is ...

  2 mi² = s²

  √(2 mi²) = s = √2 mi

You want the distance to the nearest inch, so we need to convert this to inches.

  √2 mi = (√2 mi) × (5280 ft/mi) × (12 in/ft) ≈ 89604.57 in

Rounded to the nearest inch, this is

  89605 inches

In feet and inches, this is

  89605/12 ft = 7467 1/12 ft = 7467 ft 1 in.

Answer:

21 - 8 = x

21 - 8 = 13

Step-by-step explanation:

because you send a total of 21, and you send 8, just do 21 - 8 and thats how many text messages she sends

we have expressed log146 - log14 3 2 as a single logarithm in terms of natural logarithms, which is ln (2/3) / ln 14.

Using the properties of logarithms, we can simplify the given expression as follows:

[tex]log_{14}[/tex](6) = [tex]log_{14}[/tex](4) - [tex]log_{14}[/tex]([tex]3^{2}[/tex])

= 1 - 2[tex]log_{14}[/tex](3)

So the expression log146 − log1432 can be written as [tex]log_{14}[/tex](6) = 1 - 2[tex]log_{14}[/tex](3).

The first step used the property [tex]log_{a}[/tex] (b/c) =  [tex]log_{a}[/tex](b) -  [tex]log_{a}[/tex](c), and the second step used the property  [tex]log_{a}[/tex](b^c) = c [tex]log_{a}[/tex](b).

In simpler terms, we can say that the given expression is equivalent to subtracting the logarithm of [tex]3^{2}[/tex] from the logarithm of 4, both to the base 14. We can then use the rules of logarithms to simplify the expression into a single logarithm of 6 to the base 14, with a coefficient of -2 in front of the logarithm of 3 to the base 14.

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k is equal to 2, and the function g(x) is obtained by shifting the graph of f(x) two units to the left.

A function in mathematics is a relationship between a set of inputs (also known as the domain) and a set of outputs (also known as the range), where each input is connected to each output inexactly.

It can be compared to a machine that processes inputs and outputs in accordance with predetermined rules or algorithms.

In order to model real-world scenarios, carry out calculations, and examine mathematical relationships, functions are used.

They are frequently depicted through graphs or algebraic equations.

Since g(x) = f(x + k), we need to find the value of k that will shift the graph of f(x) to the graph of g(x). To do this, we can use the fact that g(x) = f(x + k) and the values in the table to determine the value of k.

When x = -1, g(x) = 5 = f(-1 + k). Since f has a point at (-1, 3), we know that f(-1) = 3.

Therefore, we have:

5 = f(-1 + k) = f(-1) + k = 3 + k

Solving for k, we get:

k = 5 - 3 = 2

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Answer:

A

Step-by-step explanation:

given the x- intercepts x = a and x = b then the corresponding factors are

(x - a) and (x - b)

the equation of the quadratic is then the product of the factors , that is

y = a(x - a)(x - b) ← a is a multiplier

here the x- intercepts are x = 4 and x = 8 , then factors are

(x - 4) and (x - 8 ) , so

y = a(x - 4)(x - 8)

to find a substitute any other point on the graph into the equation

given vertex = (6, - 4 ) , then

- 4 = a(6 - 4)(6 - 8)

- 4 = a(2)(- 2) = - 4a ( divide both sides by - 4 )

1 = a , then

y = (x - 4)(x - 8) ← expand using FOIL

y = x² - 12x + 32

Answer:

  B. 1/4(x-5) = 13

Step-by-step explanation:

You want to know which number sentence has one solution.

Typically, an inequality has an infinite set of solutions. The inequalities here are linear inequalities in one variable, so will have an infinite solution set consisting of numbers greater than, or less than, some boundary value.

If the equation can be arranged to be in general form, ax +b = 0, where a ≠ 0, then it will have exactly one solution: x = -b/a.

The set of number sentences contains exactly one equation. That is the number sentence that has exactly one solution:

  B. 1/4(x-5) = 13

From given volume, length of each section is 18 inches.

In mathematics, ‘Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Let's call the length, width, and height of each section l, w, and h, respectively.

Since both sections are the same size, we can set up the following equation for their combined volume:

2(lwh) = 2640

Simplifying this equation, we get:

lwh = 1320

Now we need to find the length of each section, which is represented by the variable l. We can solve for l by dividing both sides of the equation by wh:

l = 1320/wh

We don't have enough information to determine w and h individually, but we do know that the two sections are identical, which means they have the same proportions. This means that w and h must be equal.

Let's call this common value x. Then we can rewrite the equation for l as:

[tex]l = 1320/x^2[/tex]

We can simplify this equation by multiplying both sides by [tex]x^2[/tex]:

[tex]lx^2 = 1320[/tex]

Now we can solve for x:

[tex]x^2 = 1320/l\\\\x = \sqrt{(1320/l)}[/tex]

Since w = h = x, the length of each section is:

[tex]l = 2x = 2 \sqrt{(1320/l)}[/tex]

We can simplify this expression by multiplying both sides by l:

[tex]l^2 = 4*1320/l \\l^3 = 5280\\l = 18[/tex]

Therefore, the length of each section is 18 inches.

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Use circumcenter to draw a circle through three non-collinear points.

a) Draw diameter, construct equilateral triangle with one vertex at center and other two on circle.

b) Draw diameter, construct regular hexagon with one vertex at center and other vertices on circle.

Step 1: To construct a circle through three points not on a line, we can use the circumcenter of a triangle. We first construct the perpendicular bisectors of any two sides of the triangle. The point where these two lines intersect is the circumcenter of the triangle. We can then draw a circle with this point as the center, which passes through all three vertices of the triangle.

Step 2:

a) To construct an equilateral triangle inscribed in a circle, we can draw a diameter of the circle and then construct an equilateral triangle with one of the endpoints at the center of the circle and the other two endpoints on the circle itself.

b) To construct a regular hexagon inscribed in a circle, we can draw a diameter of the circle and then construct a regular hexagon with one of the vertices at the center of the circle and the other vertices on the circle itself.

c) To construct a square inscribed in a circle, we can draw a diameter of the circle and then construct a square with one of the vertices at the center of the circle and the other vertices on the circle itself.

Step 3:

a) To construct a tangent to a circle through a point on the circle, we can draw a radius of the circle to the point of tangency, and then construct the perpendicular bisector of this radius. The line where the perpendicular bisector intersects the circle is the tangent line.

b) To construct a tangent to a circle through a point outside the circle, we can draw a line from the point to the center of the circle, and then construct the perpendicular to this line at the point of tangency. The line where the perpendicular intersects the circle is the tangent line.

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Answer:

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}x&y\\\cline{1-2}\vphantom{\dfrac12}-2&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}-1&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}0&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}1&-1\\\cline{1-2}\vphantom{\dfrac12}2&0\\\cline{1-2}\end{array}[/tex]

Step-by-step explanation:

Given equation:

[tex]y=\log_2x-1[/tex]

To fill out the given x-y chart, substitute each given value of x into the given log equation.

The argument of a log function can only take positive arguments, so when x = -2, x = -1 and x = 0, the y-values are undefined.

The values of y for x = 1 and x = 2 are:

[tex]\begin{aligned}x=1 \implies y&=\log_21-1\\&=0-1\\&=-1\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies y&=\log_22-1\\&=1-1\\&=0\end{aligned}[/tex]

Therefore, the completed x-y chart for the equation y = log₂x - 1 is:

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}x&y\\\cline{1-2}\vphantom{\dfrac12}-2&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}-1&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}0&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}1&-1\\\cline{1-2}\vphantom{\dfrac12}2&0\\\cline{1-2}\end{array}[/tex]

Note: I have used DNE for does not exist.

As the degrees of freedom increase, the Student's t distribution becomes more like the standard normal (z) distribution. Correct option is C.

The Student's t distribution is a probability distribution that is used to estimate the mean of a population when the sample size is small or when the population standard deviation is unknown. It is similar to the standard normal distribution, but it has heavier tails and more spread out.

As the degrees of freedom increase, the t-distribution approaches the normal distribution because the shape of the t-distribution becomes more and more similar to the normal distribution.

This is due to the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches the normal distribution.

When the degrees of freedom is large, the t-distribution becomes less variable, and the tails become less heavy, approaching the normal distribution. Therefore, the standard normal (z) distribution is the limiting distribution of the Student's t distribution as the degrees of freedom increase.

Therefore, Correct option is C.

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complete question is:

As the degrees of freedom increase, what distribution does the student's t distribution become more like?

a) uniform

b) chi-square

c) standard normal (z)

d) binomial

Vertex of h(x) is (-2, 0), and the axis of symmetry is the line x = -2, vertex of g(x) is (3, 0), and the axis of symmetry is the line x = 3, vertex of j(x) is (3, 2), and the axis of symmetry is the line x = 3.

What is axis of symmetry?

In mathematics, the axis of symmetry is a line that divides a given shape into two symmetrical parts, such that each part is a mirror image of the other.

We can use the standard form of a quadratic function, which is given by:

[tex]F(x) = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola and the axis of symmetry is the line x = h.

For [tex]h(x) = (x + 2)^2[/tex], we have:

h = -2 (since x + 2 = 0 when x = -2)

k = 0 (since the square of any real number is non-negative)

Therefore, the vertex of h(x) is (-2, 0), and the axis of symmetry is the line x = -2.

For [tex]g(x) = (x - 3)^2[/tex], we have:

h = 3

k = 0

Therefore, the vertex of g(x) is (3, 0), and the axis of symmetry is the line x = 3.

For [tex]j(x) = (x - 3)^2 + 2[/tex], we have:

h = 3

k = 2

Therefore, the vertex of j(x) is (3, 2), and the axis of symmetry is the line x = 3.

To find the y-intercept of each function, we can simply plug in x = 0:

For h(x):

[tex]h(0) = (0 + 2)^2 = 4[/tex]

Therefore, the y-intercept of h(x) is 4.

For g(x):

[tex]g(0) = (0 - 3)^2 = 9[/tex]

Therefore, the y-intercept of g(x) is 9.

For j(x):

[tex]j(0) = (0 - 3)^2 + 2 = 11[/tex]

Therefore, the y-intercept of j(x) is 11.

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Hence inverse of the function h is

h⁻¹ :x→  2/(x-1)  -1

An inverse function is a function that "undoes" the action of another function. In other words, if a function f(x) takes an input x and produces an output y, then its inverse function, denoted as f⁻¹(y) or sometimes as g(y), takes the output y and produces the input x such that f(x) = y.

 A function is a rule that associates each element of a set (called the domain) with a unique element of another set (called the range or codomain).

Given function

f(x)=1+1/x for x>0

g(x)=(x+1)/2  for x>0

Given: h=fg

h=f(g(x))

h=1+1/(x+1)/2

Now, taking the inverse of the function h,

h=1+1/(x+1)/2

h-1=1/(x+1)/2

1/(h-1)=(x+1)/2

2/(h-1)=x+1

x=2/(h-1) -1

Hence inverse of the function h is

h⁻¹:x→ 2/(x-1) -1

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Using quantitative techniques in the context of The New York Times has both advantages and disadvantages.

The advantages  are:

accuracy:

Quantitative techniques can provide more precise and accurate data, which can lead to more accurate reporting and analysis of news articles.

Data-Driven Insights:

Quantitative techniques help identify trends and patterns in data and help journalists make informed decisions about what to report on.

Objectivity:

Quantitative techniques help reduce bias and subjectivity in reporting by relying on data rather than personal opinions or interpretations.

The disadvantages include:

Lack of context:

Quantitative methods can oversimplify complex issues, resulting in misleading or inaccurate reporting.

Data limit:

Quantitative methods are data-dependent and results may not be reliable if data are incomplete or inaccurate.

Overall, it is very useful for the journalists in the New York Times to use  quantitative techniques

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(a) margin of error; sample statistic.

The center of the confidence interval is determined by the sample statistic, and the width of the confidence interval is determined by the margin of error.

Therefore, the correct option is (a) margin of error; sample statistic.

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Answer:

35

Step-by-step explanation:

Answer:

104

Step-by-step explanation:

You add 65+ 39 and that gives you 104

Answer: B: (7, -4)

Step-by-step explanation:

To solve for x and y, we can use either substitution or elimination method. Here, we'll use the elimination method to solve for x and y:

2x - 4y = 36 (Equation 1)

4x + 3y = -5 (Equation 2)

To eliminate y, we can multiply Equation 1 by 3 and Equation 2 by 2, and then add the two resulting equations:

6(2x - 4y) = 6(36) (Multiplying Equation 1 by 3)

2(4x + 3y) = 2(-5) (Multiplying Equation 2 by 2)

Simplifying, we get:

12x - 24y = 216

8x + 6y = -10

Adding the two equations, we get:

20x = 206

Dividing both sides by 20, we get:

x = 10.3

Now, substituting x = 10.3 into Equation 1 or Equation 2, we can solve for y. Let's use Equation 1:

2x - 4y = 36

2(10.3) - 4y = 36

20.6 - 4y = 36

-4y = 15.4

y = -3.85

Therefore, the solution to the system of equations is (x,y) = (10.3,-3.85).

Rounded to the nearest integer, the solution is approximately (x,y) = (10,-4).

So, the answer is option B: (7, -4).

Answer:

D. (4, 7)

Step-by-step explanation:

2x - 4y = 36

4x + 3y = -5

2(4) - 4(-7) = 36

4(4) + 3(-7) = -5

When a voltage is applied across a copper wire or conductor, the electric field generated by the voltage pushes the free electrons in the copper atoms, causing them to move in the direction of the electric field.

This creates an electric current that flows through the wire or conductor.

Copper is a popular material used for transmitting electrical currents because of its excellent properties.

How copper transmits electrical currents:
Conductivity:

Copper has high electrical conductivity, which means it allows the flow of electrons with minimal resistance.

This property enables it to transmit electrical currents efficiently.
Ductility:

Copper is a ductile material, making it easy to form into thin wires without breaking.

This property allows for the creation of long and flexible copper cables that can be installed in various environments for transmitting electrical currents.
Low electrical resistance:

The low resistance of copper minimizes energy loss in the form of heat when transmitting electrical currents.

This helps to maintain the efficiency and performance of electrical systems.
Availability:

Copper is a relatively abundant material, making it an accessible and cost-effective choice for transmitting electrical currents in various applications.
Durability:

Copper is resistant to corrosion and wear, which means it can maintain its performance over time.

This makes it a reliable material for transmitting electrical currents in both short-term and long-term installations.
In summary, copper transmits electrical currents effectively due to its high conductivity, ductility, low electrical resistance, availability, and durability.

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The distribution will exhibit symmetry. The solution has been obtained by using the histogram.

What is a histogram?

A graph known as a histogram uses rectangles to show the frequency of numerical values. The vertical axis of a rectangle's height (which represents the distribution frequency of a variable) (the amount, or how often that variable appears).

The given histogram's form demonstrates that the distribution's shape exhibits symmetry (i.e. the shorter bars are to the left and to the right while the longer bars are in the middle).

Sales of vehicles under $5,000 and those between $45,000 and $50,000, with expected sales of 200 vehicles each, will be added, resulting in bars at both ends of the histogram that are the same size as the shortest bar.

Due to the distribution's continued symmetry, this won't change the histogram's initial shape of the distribution.

Hence, the first option is the correct answer.

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The complete question and the figure is attached below.

Question: A salesman sells cars with prices ranging from $5,000 to $45,000. the histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.

How would the shape of the distribution change if the salesman decides to also deal in cars priced under $5,000 and in cars priced from $45,000 to $50,000 and projects sales of 200 cars in each category?

a. the distribution will exhibit symmetry.

b. the distribution will exhibit a positive skew.

c. the distribution will exhibit a negative skew.

d. the distribution will uniform throughout.