A line passes through (-3, 6) and has a slope of -5.
What is an equation of the line?

a) the study has been done by controlling the groups hence it is an experiment.

b) The persons are assigned randomly o each group hence it is a randomized design.

c) the explanatory and response variables. are:

Effect of listening to music by Mozart

IQ of the person

What are an experiment and observational study?

In observational research, participants are measured or surveyed without any attempt to influence them. In a controlled experiment, participants or objects are divided into groups, and one group is given treatment while the other is not.

What are randomized or block designs?

An experimental design known as a randomized block design divides the experimental units into units known as blocks. The experimental units inside each block are assigned the treatments at random. We have a fully randomised block design when each block has at least one instance of each treatment.

a. Is this an experiment or an observational study?

Since the study has been done by controlling the groups hence it is an experiment

b. If it is an experiment, is it randomized or block design?

Since the persons are assigned randomly o each group hence it is a randomized design

c. If it is an experiment, identify the explanatory and response variables.

explanatory variable = effect of listening to music by Mozart

response variable =  IQ of the person

(d)Three levels of the treatment  effect of listening to music by Mozart

level 1: listen to Mozart's music

level 2: told to relax

level 3: no instructions

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Answer:

A scale model of a house uses a scale of 14 inches = 3 feet, this means that for every 14 inches in the model, it represents 3 feet in the actual house.

If the model is 4.25 inches tall, we can use this proportion to find the actual height of the house:

4.25 inches / 14 inches = x / 3 feet

To find the actual height of the house, we can cross-multiply and then divide:

(4.25 inches * 3 feet) / 14 inches = x

x = 1.5 feet

So the actual height of the house is 1.5 feet

The zeros of the polynomial are: x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).We have found all three real zeros of the polynomial, which confirms that there are no complex zeros.

f(x) = 2x³ - 112x² + 27x - 41x + 15

To find the zeros and their multiplicities of this polynomial, we can begin by using Descartes' Rule of Signs. Let's consider the sign changes in the coefficients:

There are 2 sign changes in the coefficients (from 2x³ to -112x² and then to 27x, and finally to -41x and 15), which means there are either 2 or 0 positive real zeros.

There are no sign changes when we replace x with -x, which means there are either 0 or 2 negative real zeros.

Thus, there can be either 0, 2, or 4 real zeros, but we cannot determine their exact number or location with Descartes' Rule of Signs alone.

Next, we can use the Upper and Lower Bound Theorem to limit our search for rational zeros. According to this theorem, any rational zero of the polynomial must be of the form p/q, where p is a factor of the constant term (15 in this case) and q is a factor of the leading coefficient (2 in this case). Therefore, the possible rational zeros of the polynomial are:

±1/2, ±1, ±3/2, ±5, ±15/2, ±30

We can use synthetic division or long division to check these possible rational zeros and see which ones are actually zeros of the polynomial. Doing so, we find that the rational zeros of the polynomial are:

x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).

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\( {6x}^{2} - 24 = 0 \\ = > 6( {x}^{2} - 4) = 0 \\ = > 6 {((x)}^{2} - {(2)}^{2} ) = 0 \\ = > 6(x - 2)(x + 2) = 0 \\ = > 6(x - 2) = 0 \: \: \: or \: \: 6(x + 2) = 0 \\ = > 6x - 12 = 0 \: \: \: or \: \: \: 6x + 12 = 0 \\ = > x = 2 \: \: \: or \: \: \: x = - 2\)

Hope you could get an idea from here.

Doubt clarification - use comment section.

The total of a hexagon's internal angles is 720 degrees.

The internal angles of a hexagon may be calculated using the formula "180 - (360/n)," where n is the number of sides. When you enter 6 for a hexagon, the response is 120 degrees.

We might begin by imagining a hexagon to better comprehend the notion. It is a basic design made up of six distinct straight lines that join to form a closed shape. The internal angles are the angles on the inside of the form.

The above-mentioned formula may be used to compute the internal angles of a hexagon. For each inner angle of a hexagon, the computation yields a value of 120 degrees. Hence the total of a hexagon's internal angles is 720 degrees.

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Answer:

Step-by-step explanation:

(f-g)(x) = f(x)- g(x)

= (3x + 7) - (3x)

= 7

Therefore (f-g)(x) = 7

Answer:

(f - g)(x) = 7

Step-by-step explanation:

Here, we should subtract the two functions:

f(x) = 3x + 7  and g(x) = 3x

(f - g)(x) = 3x + 7 - 3x

            = 3x - 3x + 7

           = 7

Hence, (f - g)(x) = 7

The average rate of change of the function f(x) = \(2x^2-11\) over the interval [-3, 3] is 0

The function is

f(x) = \(2x^2-11\)

The average rate of change = \(\frac{f(b)-f(a)}{b-a}\)

First we have to find each values and substitute the values in the equation.

The interval = [-3, 3]

The value of a = -3

The value of b = 3

To find the value of f(-3), substitute the value of x = -3 in the given function

f(-3) = \(2(-3)^2-11\)

= 2×9 - 11

= 18-11

= 7

The value of f(b) = \(2(3)^2-11\)

= 2×9 - 11

= 18-11

= 7

The average rate of change = \(\frac{7-7}{3--3}\)

= 0/6

= 0

Hence, the average rate of change of the function f(x) = \(2x^2-11\) over the interval [-3, 3] is 0

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The system of equation that has one solution is: (d) –2x+ 7y = –5  and 2x +7y = –9

This is a group of equations which may have none, one or more solutions.

From the list of given options, the system of equations that has one solution is:

–2x+ 7y = –5  and 2x +7y = –9

This is so because, the solution is (-1,-1)

However, the other systems have infinite many solutions

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Answer:

D. -2x + 7y = -5 and 2x + 7y = -9

Step-by-step explanation:

Edge 2023

To decide the power of 10 multiplies an equation with repeating digits; Round the equation to the required significant numbers.

when the numerator of an equation is divided by the denominator and the result is not a whole number ( i.e. number with some decimals)and sometimes the decimal places are unending. to present the result properly we have to round off the number to the nearest significant number, then you can multiply the equation with the power of 10, in relation to the number of significant places you rounded off.

Example :

5/200 = 0.025

To express this answer with the power of 10

0.025 = 2.5 * 10 ^-2

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Answer:

Step-by-step explanation:

(3a-7)²=(3a-7)(3a-7)

= 9a²-21a-21a+49

= 9a²-42a+49

Therefore the error in that answer is -42a was replaced with -21a.

Answer:

(3a-7)²=(3a-7)(3a-7)

= 9a²-21a-21a+49

= 9a²-42a+49

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given quadratic function is,

f(x) = -x² - 4x + 5

Leading term of the quadratic function is 'x²'

Coefficient of this leading term is (-1).

Now we will convert this standard equation into vertex form,

f(x) = -x² - 4x + 5

     = -(x² + 4x) + 5

     = -[x² + 2(2x) + 4 - 4] + 5

     = -[x² + 2(2x) + 2²] + 4 + 5

     = -(x + 2)²+ 9

f(x) = -(x + 2)² + 9

Since, coefficient of the leading term is negative the parabola will open downwards.

Vertex form of the function is given by,

g(x) = -(x - h)² + k

(h, k) is the vertex.

By comparing the equation of the function 'g' with the function 'f',

(-2, 9) will be the vertex of the function which is the maximum point of the function.

1. C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

2. B. Type Ia supernovae

3. D. Downwards; towards the center of the Sun

The interpretation of the equations and the correct options for the given questions are as follows:

Question 1:

The equation interpretation is related to gravity. The equation states a relationship between gravity and distance. The correct option is:

C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

Question 2:

To test how the constant G (gravitational constant) has changed over the evolution of the Universe, certain phenomena or objects are used. The correct option is:

B. Type Ia supernovae

Question 3:

Based on the excerpt, the direction of gravity from the Sun is described. The correct option is:

D. Downwards; towards the center of the Sun

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The total number of possible choices that John had for making baked goods for the party is 8.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

\(^nC_r = \dfrac{n!}{r!(n-r)!}\)

where,

n is the number of choices available,

r is the choices to be made.

We know that the number of choices with John for his baked goods is only two which are muffins or bread, therefore, the choices of the baked good can be written as \(^2C_1\).

Also, the number of choices with John for flavors is four which are blueberries, bananas, apples, or chocolate chips, therefore, the choices of the flavor can be written as \(^4C_1\).

Now, the total possible choices that John had

= The choices of the baked good x The choices of the flavor

\(=\ ^2C_1 \times ^4C_1\\\\=\ 8\)

Hence, the total number of possible choices that John had for making baked goods for the party is 8.

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Answer:

C (x = 2)

Step-by-step explanation:

Since x is a non-negative number, A and B are eliminated.

This leaves C and D.

C: x = 2,

2 + 3 < 2^2

5 < 4 is false.

So C would be a counterexample.

Hope this helps!

The value of x is a counterexample to the student's conjecture (x = 2). The correct option is C.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that x is a non-negative number, a student conjectured that x + 3 < x².

Since x is a non-negative number, A and B are eliminated.

This leaves C and D at the value of x = 2,

2 + 3 < 2²

5 < 4 is false.

Therefore, the value of x is a counterexample to the student's conjecture (x = 2). The correct option is C.

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Answer:

x = 67

y = 23.5

Step-by-step explanation:

Sum of angles in a triangle is supplementary,

x + 90 + 23 = 180

x + 113 = 180

x = 180 - 113

x = 67

y = ?

180 - 67 / 2

= 133 / 2

= 66.5

y + 66.5 = 90

y = 90 - 66.5

y = 23.5

The time to calculate her rate along the summit Rate = 1.5 mph

Rate = Distance / Time

To solve this problem, we will first need to calculate the time it took Jane to reach the peak. Since she rode 40 miles uphill, we can use the rate of 5 mph slower than when she reached the peak to calculate this time.

Time = Distance / Rate

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5)

Time = 8 hours

Since Jane spent 2 hours exploring the mountain, the total time it took her to reach the peak was 8 hours. We can now use this time to calculate her rate along the summit.

Rate = Distance / Time

Rate = 12 miles / 8 hours

Rate = 1.5 mph

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The truth value of the conditional statement is false, and the counterexample of this statement is corresponding angles

The conditional statement is given as:

If two angles are congruent, then they are vertical angles.

The above statement is false because not all congruent angles are vertical angles

A counterexample of this statement is a corresponding angle

i.e. corresponding angles are congruent angles, but they are not vertical angles

Hence, the truth value of the conditional statement is false, and the counterexample of this statement is a corresponding angle

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Answer:

The type of number that represents -4/2 is:

Choice B) Integer

Choice C) Rational

Step-by-step explanation:

The number -4/2 is an integer because it represents a whole number (-2) and it is also a rational number because it can be expressed as a fraction of two integers.

-4/2 is an :

Solution:

Before we make any decisions about the type of number -4/2 is, let's simplify it first.

It's the same as -2. Now, let's familiarize ourselves with the sets of numbers out there. Where does -2 fit in?

______________

This set incorporates only positive numbers and zero. So -2 doesn't belong here.

This set incorporates whole numbers and negative numbers. So -2 belongs here.

This set has integers, fractions, and decimals. So -2 does belong here too.

This is a set for numbers that cannot be written in fraction form (a/b, where b ≠ 0). So -2 doesn't belong here.

-4/2 belongs in the integer and rationals set.

The exact duplication of elements on either side of a central axis is called symmetry. Symmetry refers to the property of an object or system where it exhibits a precise duplication of elements on either side of a central axis or plane.

This duplication can occur in various forms, such as shapes, patterns, or structures. Symmetry is a fundamental concept in mathematics, art, design, and science. It is often studied and utilized to create aesthetically pleasing compositions, identify patterns, and analyze the properties of objects.

Symmetry can be classified into different types, such as bilateral symmetry (reflectional symmetry) where the object is identical on both sides of a vertical axis, or radial symmetry where the object is identical around a central point.

The concept of symmetry plays a significant role in diverse fields, including geometry, biology, crystallography, and physics.

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Yes, the measure of angle 1 is equal to the measure of angle 2 because Option a. they both intercept the same arc on the circle.

Measure of ∠1 is equal to the measure of ∠2 using the inscribed angle theorem.

Which states that an angle formed by two chords that intersect on a circle is half the measure of the intercepted arc.

The length of the sides of an angle is not a factor in determining its measure.

So the fact that the sides of ∠2 are longer than those of ∠1 is irrelevant in this case.

Also, the fact that they intercept the circle at different points is also not a relevant factor.

As it is the measure of the intercepted arc that determines the measure of the inscribed angle, not the position of the points on the circle.

Therefore, the measure of angle1 is equal to the measure of ∠2 is the only relevant factor given by option a. they intercept the same arc.

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The above question is incomplete, the complete question is:

Is the measure of angle1 equal to the measure of angle 2? why?

a. yes, because they intercept the same arc.

b. no, because the sides of ∠ 2 are longer

c. no, because they intercept the circle at different points

Answer:

×=-51/2, x=-5.5

Step-by-step explanation:

hshshshdh:))

Answer:

The answer is 1

Step-by-step explanation:

The answer is 1 because if you multiply -2 x 5 then you get -10

11 - 10 = 1

The answer is 1

Answer:

(- 1, 1 ) and (2, 4 )

Step-by-step explanation:

Given the 2 equations

y = x + 2 → (1)

y = x² → (2)

Substitute y = x² into (1)

x² = x + 2 ( subtract x + 2 from both sides )

x² - x - 2 = 0 ← in standard form

(x - 2)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x + 1 = 0 ⇒ x = - 1

Substitute these values into (1) for corresponding values of y

x = 2 → y = 2 + 2 = 4 ⇒ (2, 4 )

x = - 1 → y = - 1 + 2 = 1 ⇒ (- 1, 1 )

We reject the null hypothesis. Therefore, the hypotheses (i) and (ii) are rejected.

a)The equation for the Ordinary Least Square is given by:

Yi = a0 + a1Xi + εi

Where, Yi represents the dependent variable (percentage grade points in this case) and Xi represents the independent variable (hours spent studying).

Let’s calculate the OLS estimators of a and a1. We know that,

n = 15, Σx = 350, Σx² = 15500, Σy = 12575, Σxy = 10500.

The formula for OLS estimator of a1 is given by:

a1 = Σxy/Σx²

=10500/15500

=0.6774.

The formula for OLS estimator of a0 is given by:

a0 = ȳ − a1x¯

where,x¯ = Σx/n = 350/15

= 23.33.

Also, ȳ = Σy/n

= 12575/15

= 838.33

Substituting these values in the above formula,

a0 = 838.33 − (0.6774 * 23.33)

a0 = 822.55.

b) R² is given by,

R² = SSR/SST

= Σ(ŷi − ȳ)²/Σ(yi − ȳ)²

where, ŷi represents the predicted value of Yi and SST (total sum of squares) and SSR (sum of squares of residuals) are given by:

SST = Σ(yi − ȳ)²

= 4187.14

SSR = Σ(ŷi − yi)²

= 1283.04

Now, let's calculate the R² value,

R² = SSR/SST

= 1283.04/4187.14

= 0.3063

c)The formula for the sample correlation coefficient between Y and X is given by:

r = Σxy/√(Σx² Σy²)

= 10500/√(15500* [12575/15]²)

= 0.5533

d)We need to test the hypotheses that (i) a0 = 1 and (ii) a1 = 3, at the 5% level of significance. The formula for the t-statistic for the coefficient of determination (t) is given by,

t = (ai − β0)/SE(ai)

where, SE(ai) is the standard error of ai and is given by:

SE(ai) = √[σ²/Σ(xi − x¯)²]

where, σ² is the variance of the error term (ε) and is given by:

σ² = SSR/(n − 2)

Now, substituting the respective values,

σ² = SSR/(n − 2)

= 1283.04/13

= 98.69

SE(a0) = √[σ²/Σ(xi − x¯)²]

= √[98.69/15500]

= 0.017SE(a1)

= √[σ²/Σ(xi − x¯)²]

= √[98.69/15500]

= 0.017

For a two-tailed test at the 5% level of significance, the critical t-value for 13 degrees of freedom is 2.160.

Now, let's calculate the t-value for each hypothesis,

(i) H0: a0 = 1t

= (a0 − 1)/SE(a0)

= (822.55 − 1)/0.017

= 47936

Reject H0 if |t| > 2.160 |47936| > 2.160

Hence, we reject the null hypothesis.

(ii) H0: a1 = 3t

= (a1 − 3)/SE(a1)

= (0.6774 − 3)/0.017

= -153.94

Reject H0 if |t| > 2.160 |−153.94| > 2.160

Hence, we reject the null hypothesis. Therefore, the hypotheses (i) and (ii) are rejected.

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Answer:

0

Step-by-step explanation:

I hope this helps!

Answer:

Its the same so.. 0???????

Answer: \(14w+28y-7\)

Step-by-step explanation:

multiply everything by -7

Answer:

Step-by-step explanation:

14w+28y-7

Answer:

Well this question is actually a piece of cake. Just pick your favorite number. Multiply it by 10. Then do whatever operation you want with the 2,300. For the exponent part of this. Lets say we do it this way y times z equals 2,300. Exponents are letters used in mathematical terms. So any letter can be used to represent any number.

Step-by-step explanation:

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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Answer:

$2.16

Step-by-step explanation:

if the store sells 9 cm for $0.72

they are selling 27 cm now which is 3 times the amount of 9

so if 27 is 3 x the amount of cm than we need to triple to amount of the cost to.

and 0.72 x 3 is 2.16.

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Answer:

Step-by-step explanation:

Mistake in step 3 the (2x+1) and the (x-1) both cancel out but the other binomials (x + 3) and (x - 3) are different so don't cancel out.

Step 3 should be 3(x-3) / 4(x+3)

3 should not be an excluded value.

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Keep on crossing off the dots. One for the left, one for the right. At the end, you will be left with two dots over the #2. Add those and divide by 2. You will get 2.