(5 pts) interpolation is used to determine values beyond a given set of data points. a) true b) false

The coordinates of Casper which lies exactly in the middle of Denton and Beacon are (-4, -1).

Coordinates are defined as the set of points in a coordinate plane or space, which describes the position of that point in that plane or space.

In a coordinate plane, the midpoint of two points (x₁, y₁) and (x₂, y₂) is the point (x, y) such that their measures are,

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

First, we can write the given measures.

Coordinates of Albion = (5, 5)

Coordinates of Denton = (-7, -3)

Given that, Beacon is lying exactly in the middle of Albion and Denton.

Let the coordinates of Beacon be (x, y).

Using the formula above,

x coordinate of Beacon = (5 + -7) / 2 = -1

y coordinate of Beacon = (5 + -3) / 2 = 1

Coordinates of Beacon are thus (-1, 1).

Casper is lying exactly in the middle of Denton(-7, -3) and Beacon (-1, 1).

Let (x' , y') be the coordinates of Casper.

Using the same formula,

x' = (-7 + -1) / 2 = -4

y' = (-3 + 1) / 2 = -1

Hence the coordinates of Casper are (-4, -1).

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Answer:

Nick is 6

Andrea is 18

Step-by-step explanation:

Sounds like a system of equations

Letting...

a = Andrea

n = Nick

Since she's 3 times the age, the first equation will be

a = 3n

Since in 10 years, Andrea will be 12 years older than Nick, we can write

a = n + 12

Since we have two a = ,we can set them equal to each other

3n = n + 12

Subtracting n

3n - n = 12

Now combining the n's (n is the same as 1n)

2n = 12

And last but not least, we can divide by 2

n = 6... so Nick is 6 right now.

Going back to our first equation of a = 3n, if we plug 6 in

a = 6(3) = 18.

Making Andrea 18 right now

Answer:

x = 72

Step-by-step explanation:

x : 4 = 54 : 3

express the ratios in fractional form

[tex]\frac{x}{4}[/tex] = [tex]\frac{54}{3}[/tex] = 18 ( multiply both sides by 4 to clear the fraction )

x = 4 × 18 = 72

Answer:

(-2, -6, -6)

Step-by-step explanation:

The center of the sphere, O, and point A, are located on the same diameter of the sphere, AB. Thus, the line segment joining these two points is the radius of the sphere. Therefore, the length of the line segment, OA = OB = r, where r is the radius of the sphere.

We can find the length of the line segment, OA, using the distance formula:

√((5 - 2)^2 + (1 + 3)^2 + (1 - 5)^2) = √(3^2 + 4^2 + (-4)^2) = √49 = 7

Since OA = OB = 7, the coordinates of B can be found by subtracting the radius, 7, from the x, y, and z-coordinates of point A:

B = (5 - 7, 1 - 7, 1 - 7) = (-2, -6, -6)Therefore, the coordinates of B are (-2, -6, -6).

Answer:

Step-by-step explanation:

10, 20, 30, 40, 50

The null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population

The appropriate null and alternative hypothesis that tests whether the proportion of college students who believe in extraterrestrial life is greater than the general population can be expressed as follows:

Null hypothesis: The proportion of college students who believe in extraterrestrial life is equal to or less than the general population, or

H0: p <= 0.47

Alternative hypothesis: The proportion of college students who believe in extraterrestrial life is greater than the general population, or

Ha: p > 0.47

where p is the true proportion of college students who believe in extraterrestrial life.

In other words, the null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population (i.e., there is no difference between the two populations), while the alternative hypothesis assumes that the proportion of college students who believe in extraterrestrial life is higher than the general population.

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The length of the segment NT is  4.5  units

What is isosceles triangle?

An isosceles triangle is one that has two sides of equal length.

The angles opposite to equal sides are equal.

Let RM=x, then  MS=RN=NT=x  ( because RS = RT )

RS=RT =2x

RST and RMN are two similar triangles

So, we have

ST/MN = RT/NT

=>  ST/3.5 = 2x/x

=> ST/3.5 = 2

=> ST = 2*3.5 = 7

Given , perimeter = 25

=> RS+ST+RT = 25

=> 2x+ST+ 2x = 25

=>  4x + 7 = 25

=> 4x= 25-7 = 18

=> x=18/4 = 4.5

NT=x= 4.5  units

The length of the segment NT is  4.5  units

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Answer: 41 degrees

Step-by-step explanation:

121-39=82

82/2=41

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

According to graph, the value of p(x) = 8, when x = -2, as this point lies on the curve ~

Now, put the value of x in each of the choices provided to check if its equal to 8.

[tex]\qquad \sf  \dashrightarrow \: p( x) = (0.35) {}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = (0.35) {}^{ - 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = \dfrac{1}{(0.35 ){}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = \dfrac{1}{0.1225} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = 8.1632[/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) \approx 8[/tex]

Since the value satisfy the first equation, the correct choice will be (A)

The power in a significance test is the probability of detecting a true effect, while the probability of making a type II error is the complementary probability of power.

A significance test is a statistical method used to determine whether an observed difference or effect is statistically significant or simply due to chance.

Power is defined as the probability of detecting an effect in a significance test if an effect truly exists. In other words, it is the probability of correctly rejecting the null hypothesis (H0) when the alternative hypothesis (Ha) is true. The null hypothesis assumes that there is no significant difference between two groups, while the alternative hypothesis states that there is a significant difference.

Mathematically, power is calculated using the following formula:

Power = 1 - β

Where β is the probability of making a type II error, which is the probability of failing to reject the null hypothesis when the alternative hypothesis is true. In other words, it is the probability of not detecting an effect when an effect truly exists.

Therefore, power and β are complementary probabilities. If power is high, β is low, and vice versa. A significance test with a low power has a higher chance of making a type II error, meaning that it can fail to detect a real effect. Conversely, a test with a high power has a lower chance of making a type II error, meaning that it can detect a real effect more accurately.

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Answer:

[tex]g^6[/tex]

Step-by-step explanation:

When multiplying exponents, for example

[tex]x^2 * x^5[/tex]

Their power values are added together to get

[tex]x^2 * x^5 = x * x * x* x* x* x* x = x^7[/tex]

Answer:

[tex]g^6[/tex]

Step-by-step explanation:

because, [tex]g^3*g^3[/tex] is basically [tex]g^(^3^+^3^)[/tex] which is [tex]g^(^6^)[/tex] = [tex]g^6[/tex]

From the following, a panel data set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time is the difference between panel and pooled cross-sectional data.

Panel data refers to samples of the same cross-sectional units observed at multiple points in time.

For example we will follow the same set of households X, Y and Z, for each time period we collect data i.e. in 1990 and we will also interview the same households in 1995.

Pooled data occur when we have a “time series of cross sections,” but the observations in each cross section do not necessarily refer to the same unit.

For example we will take household income data on households X, Y and Z, in 1990. And then we will take the same income data on households G, F and A in 1995. Although we are interested in the same data, we are taking different samples (using different households) in different time periods.

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The functions are matched with their periods as follows:

The period of a trigonometric function is the smallest positive value of "T" for which the function repeats itself.

Note that to determine the period of a function, we need to identify how the function changes over one cycle. The period can then be obtained by dividing the length of the cycle by the number of complete cycles in the full range of the function.

1) y = - 3 ⁢ tan ⁡ 3 ⁢ x: The period of the tangent function is π/b, where b is the coefficient of x. So, the period of y = - 3 ⁢ tan ⁡ 3 ⁢ x is π/3.

2) y = 6 ⁢ sin ⁡ 3 ⁢ x: The period of the sine function is 2π/b, where b is the coefficient of x. So, the period of y = 6 ⁢ sin ⁡ 3 ⁢ x is 2π/3.

3 )y = - 4 ⁢ cot ⁡ x 4: The period of the cotangent function is π/b, where b is the coefficient of x. So, the period of y = - 4 ⁢ cot ⁡ x 4 is π.

4) y = 2 ⁢ cos ⁡ 2 ⁢ x 3: The period of the cosine function is 2π/b, where b is the coefficient of x. So, the period of y = 2 ⁢ cos ⁡ 2 ⁢ x 3 is 3π.

5 )y = - 2 3 ⁢ sec ⁡ x 5: The period of the secant function is 2π/b, where b is the coefficient of x. So, the period of y = - 2 3 ⁢ sec ⁡ x 5 is 2π/5.

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The percent error in the specified situation is 2%.

The actual length of the metal is 30 centimeters, and the measured length is 29.4 centimeters. The difference between the actual and measured lengths is:

30 - 29.4 = 0.6 centimeters

The absolute error is the magnitude of this difference:

|0.6| = 0.6 centimeters

To find the percent error, we divide the absolute error by the actual value and multiply by 100:

percent error = (absolute error / actual value) x 100%

= (0.6 / 30) x 100%

= 2%

Therefore, the percent error is 2%.

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The mean for the number of students who work full-time in

samples of size 16 are 3.5.

We understand The expected value, also known as the expected average in the field of probability theory, is a generalization of the weighted average.

Given, 22% of all students work full-time, per a college poll.

Now, If we choose a sample of 16 students the mean number of students working full-time is,

= 16(22/100)

= 16×0.22

= 3.5.

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112.8 is the the total sound power, when three drill presses are operating

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

Given that a function P(n) = 108 + 10 log(n) gives the total sound power in decibels when n drill presses are operating in a factory.

We need to find the total sound power, to the nearest decibel, when three drill presses are operating

We have to consider n as 3

P(3) = 108 + 10 log(3)

=108+10×0.477

=108+4.77

=112.77

Hence, 112.8 is the the total sound power when three drill presses are operating

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The percentage for the markup for the wheelbarrow is 40%.

It is important to note that the percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100

In this case, the retailer sells wheelbarrows for $21 that were acquired at a cost of $15. The markup will be:

= Selling price - Cost price

= $21 - $15

= $6

Markup percentage will be:

= Markup / Cost price × 100

= [tex]\frac{6}{15}[/tex]× 100%

=0.4*100%

= 40%

Therefore, the percentage for the markup is 40%.

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Using the fractional value of blue paint to white paint, the number of pints of blue paint Fatina used to paint her bedroom walls is 3.12 pints.

A fractional value is a proportional quantity of the whole value.

Fractional values are depicted in decimals, fractions, or percentages.

The total quantity of white and blue paints used on the bedroom walls = 7.8 pints

The fraction of the white paint = 3/5

The fraction of the blue paint = 2/5 (1- 3/5)

2/5 of 7.8 = 3.12 pints

Thus, proportionately, we can conclude that the blue paint Fatina used was 3.12 pints.

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Kathy uses 3.12 pint of white paint to paint her bedroom walls

Total amount of paint ( Blue and white paint)= 7.8 pints

Amount of  blue paint=3/5 x 7.8 = 4.68Pints

amount of white paint = Total amount of paint - amount of blue  paint

= 7.6 pints - 4.68 pints

=3.12 pint of white paint

In conclusion, she uses 3.12 pint of white paint  to paint her bedroom walls

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there are 10 short answer questions on the test, we get this answer after solving.

Let's assume that the number of multiple choice questions on the test is "m", and the number of short answer questions is "s".

From the given information, we can set up a system of equations:

m + s = 30 (The total number of questions on the test is 30)

1m + 3s = 50 (The total number of points on the test is 50)

To solve for "s", we can use the first equation to find "m" in terms of "s":

m = 30 - s

Then we can substitute this expression for "m" into the second equation:

1(30 - s) + 3s = 50

Simplifying and solving for "s", we get:

30 - s + 3s = 50

2s = 20

s = 10

Therefore, there are 10 short answer questions on the test.

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Complete Question

Diego’s history teacher writes a test for the class with 30 question. The test is worth 50 points and has two types of questions: multiple choice worth 1 points each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning.

Answer:

  x = 11

Step-by-step explanation:

You want to know the measure of x in a square marked with one portion of the bisected corner angle as being (6x -21)°.

We presume quadrilateral PQRS is a square, so each of the corner angles is 90°, and each of the diagonals bisects the corner angles. That mean ...

  (6x -21)° = 90°/2

  6x = 66 . . . . . . . . . . divide by °, add 21

  x = 11 . . . . . . . . . . . divide by 6

Answer: b1 = [tex]\frac{2A}{h} -b2[/tex]

Step-by-step explanation:

Algebra my friend...Algebra

So:

A = 0.5h(b1+b2)

A/(0.5h) =b1+b2

.: A/(0.5h) - b2 = b1

In other words:

b1 = [tex]\frac{A}{0.5h} -b2[/tex]

The 0.5 in the denominator can be rearranged to get the final answer:

b1 = [tex]\frac{2A}{h} -b2[/tex]

Answer: An incline, a slant up or down.

Step-by-step explanation:

When given expression (4x⁴-7x³+7x²-12x+15)/(x-1) is solved, result in the form q(x)+r(x)/b(x) will be -7x² + 4 + 19/(x-1).

Expressions in mathematics are mathematical statements that are made up of at least two sentences that contain numbers, variables, or both, and are connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations. For example, x + y is an equation that separates the terms x and y by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 times larger than another number, x. This statement may be expressed mathematically as x/2 + 6. Complex issues are solved using mathematical expressions.

Now,

Given expression to solve is (4x⁴-7x³+7x²-12x+15)/(x-1)

then dividing this

=4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1

=4x³-3x²+4x-8+7/x-1  in form of  q(x)+r(x)/b(x)

= 4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1

= -7x² + 4 + 19/(x-1)

hence,

          When given expression (4x⁴-7x³+7x²-12x+15)/(x-1) is solved, result in the form q(x)+r(x)/b(x) will be -7x² + 4 + 19/(x-1).

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The rays that are opposite are:

TX and TL

A ray is a line that points in one direction. It has one starting point and no end point.

It is important that we know the difference between a line and a ray.

A line has no endpoints or a starting point.

We have,

From the figure,

The rays are:

TS

TL

TV

TZ

All have a common starting point, T.

We see that,

TX and TS are perpendicular rays.

TS and TL are perpendicular rays.

TX and TL are opposite rays.

Now,

The rays that are opposite are:

TX and TL.

Thus,

TX and TL are opposite rays.

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Answer:

y = 2x + 10

Step-by-step explanation:

y = 2x + 10  

y is the total number of loaves of bread.

x is the number of days.

If the baker baked for ten days, he would have 30 loaves of bread

y = 2x + 10

y = 2(10) + 10

y = 20 + 10

y = 30

If he baked for 50 days, he would have baked 110 loaves

y = 2x + 10

y = 2(50) + 10

y = 100 + 10

y = 110

And so on and so on...

The measure of the vertex angle is 53.3degrees, the equation is 3x+20=180.

It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. The triangles on either side of the diagonals are isosceles and congruent.

Given;

Each base angle in an isosceles triangle is 10 degrees larger then the vertex angle.

The addition of the internal angles of triangle is 180

So, let vertex angle be x

The other two sides will be x+10,

x+x+10+x+10=180

3x+20=180

x=160/3

x=53.3

Therefore, the vertex angle of the triangle will be 53.3degrees.

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