what is 1.75 times 1.75?

The new functions are:

(f + g)(x) = 3x - 4

(g - h)(x) = 6x - 4

(f o g)(x) = 2x - 4

(g o h)(x) = -8x - 1

And the value of (f-g)(3) = -2.

To find new functions, we can combine the given functions using arithmetic operations.

(f + g)(x) = f(x) + g(x) = (x - 1) + (2x - 3) = 3x - 4

(g - h)(x) = g(x) - h(x) = (2x - 3) - (1 - 4x) = 6x - 4

(f o g)(x) = f(g(x)) = f(2x - 3) = (2x - 3) - 1 = 2x - 4

(g o h)(x) = g(h(x)) = g(1 - 4x) = 2(1 - 4x) - 3 = -8x - 1

To find (f-g)(3), we need to evaluate the function (f - g) at x = 3:

(f - g)(3) = f(3) - g(3) = (3 - 1) - (2(3) - 3) = 1 - 3 = -2

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The given question is incomplete, the complete question is

If  f(x) = x -1, g(x) = 2x - 3, and h(x) = 1 - 4x, find the following new functions, as well as any values (f-g)(3)

(f + g)(x)

(g - h)(x)

(f o g)(x)

(g o h)(x)

The zoo received 1100 visitors that day

The length of a pendulum with period 8 seconds would be, 316 feet.

What is Period of a simple pendulum?

The formula for the period T of a pendulum is T = 2π Square root of √L/g, where L is the length of the pendulum and g is the acceleration due to gravity.

The equation relating the period T and length L of a pendulum is given by:

T = 2π√(L/32)

We can rearrange this equation to solve for L in terms of T:

L = 32(T/2π)²

To find the length of a pendulum with period 8 seconds, we can substitute T = 8 into the above equation and solve for L:

L = 32(8/2π)²

L ≈ 316 feet

Rounding this value to the nearest foot, we get:

L ≈ 316 feet (to the nearest foot)

Therefore, The length of a pendulum with period 8 seconds would be, 316 feet.

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When you create a dot plot, the operations that you have to do are:

c. Place a dot along a horizontal scale for each observation.

d. "Pile up" dots that are too close to show separately

A dot plot is a simple way of representing numerical data. It consists of a horizontal axis and a series of dots that are placed along it to represent the values of individual observations. Each dot corresponds to one observation, and its position along the axis represents its value.

Option (a) is not correct because a dot plot typically does not have a vertical axis showing frequency of observations. Option (b) is not correct because connecting adjacent dots to create a polygon is not a common practice in dot plots. Instead, each dot represents a single observation, and dots are placed along a horizontal scale to show their value. If multiple observations have the same value, they are "piled up" on top of each other to avoid overcrowding the plot.

Therefore, the correct options are (c) Place a dot along a horizontal scale for each observation and d. "Pile up" dots that are too close to show separately

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Answer:

We can use the following logarithmic identities to simplify the expression:

log a + log b = log (ab)

log a - log b = log (a/b)

n log a = log (a^n)

Using these identities, we can simplify the expression as follows:

1/2(log₂x + log₂y) - 5 log₂(x+6)

= 1/2 log₂(xy) - log₂(x+6)^5 (using the first two identities)

= log₂[(xy)^(1/2)/(x+6)^5] (using the third identity to combine the logarithms)

Therefore, the simplified expression is:

log₂[(xy)^(1/2)/(x+6)^5]

Step-by-step explanation:

Correct statement is that m∠BAD = m∠CAD

A angle bisector is a line that bisects an angle into two equal angles. A bisector means dividing a shape or  object into two equal parts. When we draw a ray that bisects an angle into two equal parts of equal magnitude, it is called angle bisector.

Given,

In triangle ABC,

AD is angle bisector, D lies on BC,

which means, angle BAC is bisected

So,

magnitude of angle BAC will be divided into two equal parts.

m∠BAD = m∠CAD

Hence, m∠BAD = m∠CAD is correct statement given.

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The number of pretzels in the beginning was 44 pretzels solving the equation.

An equation is a mathematical statement containing two expressions on either sides which are connected with an equal to sign.

Either sides of an equation is called as left hand side and right hand side.

Let the total number of pretzels = x

Pretzels has been spilled and lost half of the pretzels.

Remaining pretzels = x - x/2

Jane ate 14 pretzels.

Remaining pretzels = x - x/2 - 14

Her sister then ate one more than half the remaining pretzels.

Remaining pretzels = x - x/2 - 14 - [1/2 (x - x/2 - 14) + 1]

Remaining pretzels is 3.

So we get an equation,

x - x/2 - 14 - [1/2 (x - x/2 - 14) + 1] = 3

Solve for x.

x - x/2 - 14 - (x/2 - x/4 - 7 + 1) = 3

x - x/2 - x/2 + x/4 - 14 + 7 - 1 = 3

x/4 - 7 - 1 = 3

x/4 - 8 = 3

x/4 = 11

x = 44

Hence the total number of pretzels was 44.

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Your question is incomplete. The complete question is as follows.

On a car trip, Jane ate some pretzels. After spilling and losing half of the pretzels, she ate 14. Her sister then ate one more than half the remaining pretzels, after which there was 3 pretzels.

How many pretzels was there?

The total amount of interest that the student paid for the unsubsidized Stafford loan with an interest rate of 6.8%, compounded monthly is,

⇒ $476.24.

Thus, The correct answer is Option C.

A loan is the lending of money by one or more individuals, organizations, or other entities to other individuals, organizations, or other entities in finance.

Given that;

Borrowed money = $2,560

The fixed monthly payment = $84.34

Hence, The total amount that the student paid for 3 years after the grace period is,

= $84.34 × 3 × 12

= $3036.24

Thus, The amount of interest will be;

⇒ Total amount paid - Sum borrowed

Hence, We get;

Interest =  $ 3,036.24- $2,560

            = $ 476.24

Therefore, $476.24 is the total amount of interest the student paid.

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There are a total of 2π Radians in a circle that is equal to 360°.

A circle is the locus of all those points which are at the same distance from a particular point called center in any plane. A radian is basically another unit of measuring the angle, it is equivalent to the standard degrees measures that we use commonly to find an angle.

When we make a circle, the angle it makes is equal to 360°. This is a characteristics property of a circle.

Now, we know,

π Radians = 180°

2 x 180° = 2xπ Radians

360° = 2π Radians

So, the circle will have a total of 2π Radian in it.

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The answer is (A) (11, 4).

Step-by-step explanation:  Given that two vertices of a right-angled triangle are A(5, 12) and B(11, 12).

We can plot the given points on the co-ordinate plane as shown in the attached figure.

We will then see that only the point C(11, 4) will lie exactly below the point B(11, 12). Also, the segment AB and BC are the legs of the triangle, AC is the hypotenuse.

The lengths of the three sides are

[tex]AB = 11 - 5 = 6\\\\BC = 12 - 4 = 8\\\\AC = \sqrt{AB^{2} +BC^{2} } = \sqrt{6x^{2}+8^{2} } = \sqrt{100} = 10[/tex]

Thus, the correct option is (A).

You will earn R450 in interest ($1500 x 0.10 x 3 = $450). Simple interest is calculated by multiplying the principal by the interest rate and the number of years.

The interest earned on a fixed deposit of R1500 at 10% p.a simple interest for 3 years will be R450.

To calculate the interest earned, we need to use the simple interest formula:

where I is the interest earned, P is the principal amount, r is the interest rate and t is the time period.

P = R1500

r = 10%

t = 3 years

I = 1500 * 0.10 * 3

I = R450

The interest rate of 10% per annum is the same for each year, and the interest is calculated on the initial principal, not the accumulated interest from previous years. This is why the formula for simple interest is so simple - the same calculation is applied each year, so the amount of interest earned increases each year, but at a slower rate than with compound interest.

The total amount of interest earned over the 3 years is R450, which is calculated by multiplying the principal by the interest rate and the number of years.

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if f f(x) = ax² + bx + c for all x and if f( -3 ) = 0 and f( 1) = 0 then b + c will be either 1,-5 or 5 depending on value of c.

A relation is a function if it has only One y-value for each x-value.

Given that f(x) = ax² + bx + c for all x and

if f( -3 ) = 0 and

f( 1) = 0

We need to find the value of b+c

f(-3)=a(-3)² + b(-3) + c

f(-3)=9a-3b+c=0

9a-3b+c=0

We need to find the value of b + c, which is equal to -a.

From equation (2), we have:

a = -b - c

Substituting this value of a in equation (1), we get:

9(-b - c) - 3b + c = 0

-12b - 8c = 0

3b + 2c = 0

b = -(2/3)c

Substituting this value of b in equation (2), we get:

a + (-(2/3)c) + c = 0

a = (1/3)c

Therefore, b + c = -(2/3)c + c = (1/3)c

Hence, if f f(x) = ax² + bx + c for all x and if f( -3 ) = 0 and f( 1) = 0 then b + c will be either 1,-5 or 5 depending on value of c.

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For a golf ball with a circumference of 0.170, 1.468, 4.638, 5.872, the number of dimples are 233.8, 12.1, 3.4, 2.3 per square centimeter respectively. By using the formula, Number of dimples per square centimeter ≈ Number of dimples / Surface area

The surface area of a golf ball can be calculated using the formula for the surface area of a sphere:

Surface area = 4πr^2, where r is the radius of the ball.

We don't know the radius of the golf ball, but we do know its circumference, which is:

Circumference = 2πr

Therefore, we can rearrange the formula to solve for the radius:

r = Circumference / 2π = 13.408 cm / 2π ≈ 2.132 cm

Now we can calculate the surface area:

Surface area = 4π(2.132 cm)^2 ≈ 57.11 cm^2

Number of dimples per square centimeter ≈ Number of dimples / Surface area

For a golf ball with a circumference of 0.170 cm:

Number of dimples per square centimeter ≈ 336 / (4π(0.085 cm)^2) ≈ 233.8 dimples/cm^2

For a golf ball with a circumference of 1.468 cm:

Number of dimples per square centimeter ≈ 336 / (4π(0.734 cm)^2) ≈ 12.1 dimples/cm^2

For a golf ball with a circumference of 4.638 cm:

Number of dimples per square centimeter ≈ 336 / (4π(2.319 cm)^2) ≈ 3.4 dimples/cm^2

For a golf ball with a circumference of 5.872 cm:

Number of dimples per square centimeter ≈ 336 / (4π(2.936 cm)^2) ≈ 2.3 dimples/cm^2

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Answer:

1 ≤ x ≤ 9

Step-by-step explanation:

The correlation coefficient ranges from -1 to +1. (option b)

Correlation is a measure that is used in statistics to measure the relationship that exists between two variables. Correlation can either be positive, negative or zero.

Positive correlation exists when two variables move in the same direction. The correlation coefficient usually ranges from 0 to 1. Negative correlation exists when the two variables move in different direction. The correlation coefficient usually ranges from  -1 to 0. Zero correlation is when there is no relationship between the variables.

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Answer:

After performing synthetic division, as the last number in the bottom row is not zero, this indicates that (x + 3) is not a factor of the given polynomial.

Step-by-step explanation:

Given polynomial function:

[tex]2x^3+7x^2+3[/tex]

To determine is (x + 3) is a factor of the given polynomial by the method of synthetic division:

Note: As the x term is missing, place a zero in its place.

[tex]\begin{array}{c|cccc}-3 &2&7&0&3\\\cline{1-1}\end{array}[/tex]

Bring the leading coefficient straight down:

[tex]\begin{array}{c|cccc}-3 &2&7&0&3\\\cline{1-1}&\downarrow&&&\\\cline{2-5}&2&&&\end{array}[/tex]

Multiply the number you brought down with the number in the division box and put the result in the next column (under the 7):

[tex]\begin{array}{c|crrr}-3 &2&7&0&3\\\cline{1-1}&\downarrow&-6&&\\\cline{2-5}&2&&&\end{array}[/tex]

Add the two numbers together and put the result in the bottom row:

[tex]\begin{array}{c|crrr}-3 &2&7&0&3\\\cline{1-1}&\downarrow&-6&&\\\cline{2-5}&2&1&&\end{array}[/tex]

Repeat:

[tex]\begin{array}{c|crrr}-3 &2&7&0&3\\\cline{1-1}&\downarrow&-6&-3&9\\\cline{2-5}&2&1&-3&12\end{array}[/tex]

The bottom row (except the last number) gives the coefficients of the quotient. The degree of the quotient is one less than that of the dividend.  The last number in the bottom row is the remainder.

Therefore, if we divide the polynomial by (x + 3) we get:

[tex]2x^2+x-3+\dfrac{12}{x+3}[/tex]

As the last number in the bottom row is not zero, this indicates that (x + 3) is not a factor of the given polynomial.

The function is given as 6 < x < 15

Assuming that Pass members pay $8 each movie for the first five films, the equation y = 8x will be used to express this. Also, it is stated that after five films, additional films are free up to fifteen films. Thus, y = 40 will be the function used to represent this.

X represents the total number of films, while Y represents the monetary cost.

the function would be:

y = 8x{0 < x < 5}

y = 8 x 5

y = 40 {6 < x < 15}

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This indicates that one solid plastic ball with a radius of one inch requires 4.19 cubic inches of plastic.

The volume of an object or a substance can be calculated using various formulas, depending on the shape and dimensions of the object or substance. For instance, the volume of a cube can be calculated by multiplying the length, width, and height of the cube. Similarly, the volume of a cylinder can be calculated by multiplying the area of the circular base by the height of the cylinder. Volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. In physics, the volume of a material is important in understanding its density and mass. In chemistry, the volume of a gas is related to its pressure and temperature through the ideal gas law. In engineering and architecture, volume is important in designing and constructing buildings, bridges, and other structures.

Here,

The formula for the volume of a sphere is given by:

V = (4/3) * π * r³

where V is the volume of the sphere and r is the radius.

Substituting the given radius of 1 inch and the value of π as 3.14, we get:

V = (4/3) * 3.14 * 1³ = 4.19 cubic inches

This means that it takes 4.19 cubic inches of plastic to make one solid plastic ball with a radius of 1 inch.

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A derivative calculator is an online application or programme that allows you to determine the derivative of a function fast and conveniently without having to complete the calculations by hand.

The derivative of a function tells you how the function is evolving at any given moment, and it is a key topic in calculus. Derivative calculators are important tools for students and professionals that need to rapidly and properly find derivatives.

To use a derivative calculator, enter the function to be differentiated and the calculator will calculate the derivative for you. To find the derivative, the calculator will employ differentiation methods such as the power rule, product rule, and chain rule.

For example, if you wanted to calculate the derivative of the function f(x) = [tex]x^{2}[/tex]+ 2x + 1, you would enter it into the derivative calculator, which would provide the result f'(x) = 2x + 2.

Depending on the amount of detail offered by the calculator, derivative calculators can also provide other information about the function, such as critical points, inflection points, and concavity.

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The regression line can be used to determine the strength of a linear association between two variables, as well as to make predictions about the values of y for a given x-value.

The regression line is a type of mathematical model used to describe the relationship between two variables, typically denoted as x and y. The regression line is a straight line that best fits the data points of the two variables. This line can be used to make predictions about the values of y for a given x-value.

The equation of the regression line is y = mx + b, where m is the slope of the line, and b is the y-intercept. The slope of the line, m, represents the strength of the linear relationship between the two variables. It is calculated by dividing the covariance of the two variables by the variance of the independent variable (x). The y-intercept, b, is the point where the regression line crosses the y-axis. It is calculated by taking the mean of y and subtracting the slope of the line multiplied by the mean of x.

The regression line can also be used to determine the strength of the linear association between two variables. This is determined by calculating the correlation coefficient, which is a measure of how closely two variables are associated. The correlation coefficient is calculated by taking the covariance of the two variables, divided by the product of the standard deviation of each variable. A correlation coefficient of close to 1 indicates a strong positive linear association, while a correlation coefficient of close to -1 indicates a strong negative linear association.

In conclusion, the regression line can be used to determine the strength of a linear association between two variables, as well as to make predictions about the values of y for a given x-value.

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Answer:

Step-by-step explanation:

In this case total surface area of the prism is the sum of each of the areas of the sides of the triangular prism including the base. In order to find out the exact numerical value of the total surface area we can sum up the areas of each of the sides including the base.

the prism has 5 sides as it is triangular, so we have five values of area.

Let A1 and A2 be area of the triangular sides. A1=A2

A3 be the base area

A4 be the slant side's area

A5 be the area of the side with 6cm height

A1=A2=(8*6)/2=24cm^2

A3=8*4=32cm^2

A4=10*4=40cm^2

A5=6*4=24cm^2

A=A1+A2+A3+A4+A5

A=24+24+32+40+24=144cm^2

Randomization in an experiment is important because it ensures that the results achieved are accurate .

Randomization in an experiment refers to a random assignment of participants to the treatment in an experiment .

Randomizing the experiments can help you get the best cause-effect relationships among the variables. It helps in controlling the lurking variables . These variables can affect the results to be different from what they are supposed to be . Randomization prevents biases and makes the results fair.

For ensuring that the information obtained from the experiment is correct, A randomized experiment is perfect to help us .

Researchers control values of the explanatory variable with a randomization procedure. So, if we see a relationship between the explanatory variable and response variables, we can say that it is a causal one.

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With the help of using Pythagoras Theorem, we find out the value of C in this abc right angled triangle. A = 12units, B = 5 units and C = 13 units.

assuming that A and B are the lengths of the legs of a right angled  triangle and we need to find the length of the hypotenuse (c), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Using this theorem, we can write:

c² = a² + b²

Substituting the given values, we get:

c² = 12² + 5²

c² = 144 + 25

c² = 169

c = √169

c = 13

Therefore, the length of the hypotenuse (c) is 13 units. the Pythagorean theorem is a mathematical formula that relates to the sides of a right angled triangle. It states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (legs). The Pythagorean theorem is named after the ancient Greek mathematician Pythagoras and is widely used in geometry and other fields of mathematics. It is a fundamental concept in trigonometry, which deals with the relationships between the angles and sides of triangles.

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The conversion of 20 km in miles is 12.42742 miles.

Kilometer (km) and mile are both units of distance or length, but they are used in different parts of the world.

A kilometer is a metric unit of length used in most countries outside the United States. It is defined as 1,000 meters, or approximately 0.62 miles.

To convert kilometers (km) to miles, you can use the conversion factor of 1 km = 0.621371 miles.

So, to convert 20 km to miles, you can multiply 20 by 0.621371:

20 km * 0.621371 miles/km = 12.42742 miles

Therefore, 20 kilometers is approximately equal to 12.42742 miles.

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"6x - 5" is the expressions that can be subtracted from 9x to give the result in expression 3x+5.

To find the expression that can be subtracted from 9x to result in the expression 3x+5.

Let the expression be (a - b = c),

Here a = 9x

and the result, c = 3x + 5

We have to find out b = ?

Substitute the values of a and b in the above equation then we get;

9x - b = 3x + 5

9x - (3x + 5) = b

b = 6x - 5

Hence the expressions that can be subtracted from 9x to result in the expression 3x+5 is 6x - 5

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The odds of winning the Mega Millions jackpot are approximately 1 in 302 million.

The chances of winning the Mega Millions Jackpot, which requires matching each of the five white balls and the gold Super Ball, are around 1 of every 302 million. The chances of winning any award in Uber Millions, which incorporates matching essentially the Super Ball, are around 1 of every 24. The size of the award relies upon the quantity of matching numbers and the Super Ball, with the big stake being the biggest award. The likelihood of winning the bonanza increments somewhat as the quantity of tickets sold increments, however it stays an exceptionally low likelihood occasion. Notwithstanding the slim chances, a great many individuals play the Uber Millions lottery consistently with expectations of becoming quite wealthy.

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