Revisit Exercise 1.2.18 about the study on Rhesus monkeys. When given a choice between two boxes, 30 out of 40 monkeys approached the box that the human had gestured toward, and 10 approached the other box. The purpose is to investigate whether rhesus monkeys can interpret human gestures better than random chance.
1.3.16 For this study:
a. State the null hypothesis and the alternative hypothesis in the context of the study.
b. Determine the standardized statistic from the data. (Hint: You will need to get the standard deviation of the simulated statistics from the null distribution in an applet.)
c. Interpret the standardized statistic in the context of the study. (Hint: You need to talk about the value of your observed statistic in terms of standard deviations assuming ______ is true.)
d. Based on the standardized statistic, state the conclusion that you would draw about the research question of whether rhesus monkeys have some ability to understand gestures made by humans.

Answer:

The equation |z + 3| = |z - 2| can be solved by first considering two cases:

z + 3 = z - 2

Adding 3 to both sides and subtracting z from both sides gives:

6 = -2

This is a contradiction, so this case has no solution.

z + 3 = - (z - 2)

Adding 3 to both sides and subtracting z from both sides gives:

1 = -2z

z = -1/2

So the only solution to the equation |z + 3| = |z - 2| is z = -1/2.

The results of composition between two functions are listed below:

A: f(g(x)) = 3 · x - 5, Domain: All real numbers.

g(f(x)) = 3 · x - 5 / 2, Domain: All real numbers.

f(f(x)) = 36 · x - 35, Domain: All real numbers.

B: f(g(x)) = x - 3, Domain: All real numbers.

g(f(x)) = √(x² - 3), Domain: x ≤ - √3 and x ≥ √3.

f(f(x)) = x⁴, Domain: All real numbers.

And the components of the composition are listed below:

A: f(x) = x⁵, g(x) = x - 9

B: f(x) = √x, g(x) = 5 - x

In this problem we shall use a special operations between two functions known as composition, consisting in substituting the indepedent variable of the first function (f (x)) for the entire second function (g (x)):

f ° g (x) = f[g(x)]  

Part 3 - Now we proceed to determine a composition between two functions and its domain, that is, the set of x-values such that function exists:

Case A: f(x) = 6 · x - 5, g(x) = x / 2

f(g(x)) = 6 · (x / 2) - 5

f(g(x)) = 3 · x - 5

Domain: All real numbers.

g(f(x)) = (6 · x - 5) / 2

g(f(x)) = 3 · x - 5 / 2

Domain: All real numbers.

f(f(x)) = 6 · (6 · x - 5) - 5

f(f(x)) = 36 · x - 35

Domain: All real numbers.

Case B: f(x) = x², g(x) = √(x - 3)

f(g(x)) = x - 3

Domain: All real numbers.

g(f(x)) = √(x² - 3)

Domain: x ≤ - √3 and x ≥ √3.

f(f(x)) = (x²)²

f(f(x)) = x⁴

Domain: All real numbers.

Part 4 - Now we proceed to separate each function as parts of a composition:

Case A: h(x) = (x - 9)⁵

f(x) = x⁵, g(x) = x - 9

Case B: H(x) = √(5 - x)

f(x) = √x, g(x) = 5 - x

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The required interval notation of the given inequality is (-∞, 2). A graph of the given inequality has been shown.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality x < 2
Since the above inequality shows that the value of x is all real numbers less than 2. A Set of all real numbers less than 2 is given as (-∞, 2)

Thus, the required interval notation of the given inequality is (-∞, 2). A graph of the given inequality has been shown.

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The value of f(g(3)) is   19

f(x)=2x-5

g(x)=4x,

f(g(3))= ?

Solution:

g(3) = 4*3 = 12

f(g(3)) = f(12) = 2*12 - 5 = 24 - 5= 19

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The value of f(g(3)) is 29.

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The equation of the set of algebra tiles is x + 8 = 12.

Algebra tiles are mathematical manipulatives that help students comprehend the principles of algebra and strategies to think algebraically. For introductory algebra pupils at the level of elementary school, middle school, high school, and college, these tiles have been demonstrated to offer solid examples.

Given set,

x 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1

the set has one positive x and eight positive units,

the equation is x + 8.

and on the right side of the equation, there are 12 positive units,

equation is x + 8 = 12

Hence the equation s x + 8 = 12.

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Answer:

x + 8 = 12.

Step-by-step explanation:

in case you need it (x=4)

Step-by-step explanation:

I assume we're naming the graph

Seeing the situation:

We have $4 for bonus bucks

We have $50 for amount spent

On the bottom we have the 50, so we can put "Amount spent" in that box

On the left, we have 4, so we can put "Bonus bucks" in that box

At the top, the name is your choice, but we can combine the names in a way... "Bonus Bucks per amount spent"... I guess that works

Looking at the graph, it's correct, but it's in reverse. you want your first dot where the 50 and 4 intersect, then you go diagonally upwards

Answer:aw dawd

Step-by-step explanation:awd awdkakwd

The length of side PT by using the ratio of similar triangles is 49/3 or 16 1/3. Option A is correct.

Triangles that are similar to one another in terms of shape but not necessarily size are called similar triangles. In simple words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are also equivalent.

In the event that two triangles are similar with sides P, Q, R and p, q, r, then the pair of their matching sides is also proportional.

From the given figure, using the ratios of similar triangles;

QP/QS = RP/RT

(12+28)/12 = (7 + x)/7

40/12 = (7 +x)/ 7

7(40/12) = 7 + x

70/3 = 7 + x

x = 49/3 o 16 1/3

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Contrapositive represents the implication of conditional statement to the logical statement if p then q to be false where as contradiction we prove that our supposition is false that implies the given condition is true.

Comparison in the proof of contrapositive and contradiction:

Contrapositive represents the hypothesis is true that implies conclusion is also true or the conclusion is false that implies hypothesis is also false.

Example of contrapositive: For any integer a , b a + b ≥ 17 , a≥9 , b≥ 9.

Using contrapositive :

If a < 9 , b < 9 then a + b < 17

a < 9, b < 9 consider a ≤8 , b≤8

a + b = 8 + 8

        = 16

        < 17

It proves a < 9 , b < 9 then a + b < 17 implies ,when  a≥9 , b≥ 9 then

a + b ≥ 17 .

Contradiction : Here we suppose the statement which is against the required statement and prove it wrong which implies our given statement is true.

Example: For any integer a, a²  is even then a is even .

Here we assume a is an odd integer then prove it wrong.

Therefore, comparing contrapositive and contradiction provides contrapositive is conditional to logical and contradiction required to our supposition is wrong.

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Answer:

1) It's a slope

2) It's the x-intercept

3) It's the y- intercept

Answer: 36 problems

Step-by-step explanation:

40% is nothing but 40/100, which is just 4/10. To start, multiply 60 by the fraction 4/10. Cancel out the 10 from the denominator of the fraction to get 4 x 6 = 24. Now, we just found the number of problems that the student solved, but we need to find how many problems still need to be solved. To do that, do 60 - 24 = 36. The student needs to solve 36 more problems.

I hope this helps!

Answer:

[tex]n \leqslant 312[/tex]

Step-by-step explanation:

[tex]45 + 7 \geqslant \frac{1}{6}n - 7 + 7 [/tex]

[tex]52 \times 6\geqslant \frac{1}{6} n \times 6[/tex]

[tex]312 \geqslant n[/tex]

You can multiply by 6 without changing the sign as 6 > 0

Answer:

i don't know

Step-by-step explanation:

The output voltage of an amplifier is 1350mV.

The voltage that a machine, like a voltage regulator or a generator, releases into the air is known as the output voltage. Voltage regulators keep voltage levels steady.

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 the output voltage of an amplifier is calculated by multiplying the input voltage by the voltage gain of the amplifier.

The output voltage will be calculated as:-

Output voltage = 45 x 30

Output voltage = 1350 mV

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A polynomial of degree 3 with real coefficients can be written in the form f(x) = a(x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots of the polynomial. Since the given zeros are -4 and 2 + i, we can write the polynomial as follows: f(x) = a(x + 4)(x - (2 + i))(x - (2 - i)).

What is polynomial of degree?

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using only the operations of addition, subtraction, and multiplication. The degree of a polynomial is defined as the highest power of the variable in the polynomial. For example, the polynomial 3x^2 + 2x + 1 has a degree of 2, since the highest power of x is 2. A polynomial of degree 0 is a constant, a polynomial of degree 1 is a linear function, a polynomial of degree 2 is a quadratic function, and so on.

A polynomial of degree 3 with real coefficients can be written in the form f(x) = a(x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots of the polynomial. Since the given zeros are -4 and 2 + i, we can write the polynomial as follows:

f(x) = a(x + 4)(x - (2 + i))(x - (2 - i))

The third root is the complex conjugate of the second root, and since the coefficients of the polynomial are real, the conjugate must also be included.

To determine the value of the coefficient a, we can use synthetic division or long division to divide (x + 4) into (x^3 + bx^2 + cx + d). To get the cubic polynomial:

x^3 + bx^2 + cx + d = (x + 4)(x - (2 + i))(x - (2 - i))

Expanding the right side of the equation, we get:

x^3 + bx^2 + cx + d = x^3 - 4x^2 + (4 + 4i)x^2 - (4 - 4i)x + 16

Comparing the coefficients of like terms on both sides of the equation, we get:

b = -4

c = 4 + 4i

d = -16

So the polynomial is:

f(x) = a(x + 4)(x - (2 + i))(x - (2 - i)) = a(x^3 - 4x^2 + (4 + 4i)x^2 - (4 - 4i)x + 16)

Since the coefficient a is arbitrary, we can set it to 1 for convenience:

f(x) = (x + 4)(x - (2 + i))(x - (2 - i))

= x^3 - 4x^2 + (4 + 4i)x^2 - (4 - 4i)x + 16

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The required number of flour cups does he need to make the muffins are 7.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

We have,

Ratio of 3.5 cups of flour for every 1.75 cups of sugar.

cups of flour/ cups of sugar = 3.5/1.75

= 2:1

So, for every two cups of flour, there is one cups of sugar.

The number of cups of flour for 3.5 cups of sugar.

= 2(3.5)

= 7 cups.

Thus, there are 7 cups of flour required.

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For any value of k and h = -18, the system will have infinitely many solutions.

Hence, option (b) is the correct choice.

A coefficient matrix in linear algebra is a matrix made up of the coefficients of the variables in a group of linear equations. In order to solve systems of linear equations, the matrix is employed.

The system will have infinitely many solutions when the determinant of the coefficient matrix is equal to 0.

The determinant can be calculated from the upper triangular matrix as the product of the diagonal elements, which is 0 * (-20) * (h + 18) = 0.

Therefore, the system will have infinitely many solutions when h + 18 = 0,

or h = -18.

This means the answer is (b) any value of k and h = -18.

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Answer:

s - 37 = 73

Step-by-step explanation:

We already have the end result which is 73.

We also know that the sale on Sunday is $37 less than Saturday's sales. This means we'll need to take away the 37 from s (Saturday).

Two angles are considered to be supplementary angles if their sum of measurements is 180 degrees and the required angle B in the given situation is 142°.

When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Subtract the specified angle from 180 degrees to determine the angle that is supplementary to another angle.

If one angle is 60 degrees, for instance, the next angle will be 180 - 60 = 120 degrees.

The pair of angles known as supplementary angles always add up to 180 degrees.

These two perspectives are known as each other's supplements.

So, we have angle A which is 38°.

Now, calculate angle B as follows:

A + B = 180

38 + B = 180

B = 180 - 38

B = 142°

Therefore, two angles are considered to be supplementary angles if their sum of measurements is 180 degrees and the required angle B in the given situation is 142°.

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Answer:

The slope of the line through the points (12, 10) and (24, 20) is 0.5

Step-by-step explanation:

To graph the line, use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept. For this particular line, the equation would be y = 0.5x + b. To find the y-intercept, use one of the given points, (12, 10) in this case, to solve for b. So, 10 = 0.5(12) + b, thus b = 0. So, the equation of the line is y = 0.5x + 0. If graphed, the line should go through the points (12, 10) and (24, 20).

Mosaic Tile Company produces two kinds of tiles, that:

We will solve this problem using the linear programming concept.

From the given case, we know that:

x --> larger tiles

y --> smaller tiles

molding: 0.45x + 0.30y ≤ 75

baking: 0.40x +0.60y ≤ 105

glazing: 0.15x + 0.25y ≤ 60

materials: 30x + 20y ≤ 6,000

Profit: 190x + 240y

We need to find each functions respective constraints and construct a graph containing all of these function constraints.

0.45x + 0.30y = 75

(x = 0)

0.45(0) + 0.30y = 75

y = 250

(y = 0)

0.45x + 0.30(0) = 75

x = 166

0.4x + 0.6y = 105

(x = 0)

0.4(0) + 0.6y = 105

y = 175

(y = 0)

0.4x + 0.6(0) = 105

x = 262

0.15x + 0.25y = 60

(x = 0)

0.15(0) + 0.25y = 60

y = 240

(y = 0)

0.15x + 0.25(0) = 60

x = 400

30x + 20y = 6000

(x = 0)

30(0) + 20y = 6000

y = 300

(y = 0)

30x + 20(0) = 6000

x = 200

We can construct the graph of these constraints such as the attached graph below. From the graph we know that the contraints of molding and baking are intersecting with each other under all of the given constraints. We need to find the intersection point:

0.4x + 0.6y = 105 | x 1| 0.4x + 0.6y = 105

0.45x + 0.3y = 75 | x 2| 0.9x + 0.6y = 150

                                       -0.5x          = -45

                                              x   = 90

0.45(90) + 0.3y = 75

40.5 + 0.3y = 75

0.3y = 34.5

y = 115

The intersection point is (90,115)

We have 3 possible scenario points, their position and each possible profit are:

(0, 175) --> P = 190(0) +240(175) = $42,000

(90, 115) --> P = 190(90) + 240(115) = $44,700

(166,0) --> P = 190(166) + 240(0) = $31,540

The optimum scenario is producing 90 larger tiles and 115 smaller tiles.

By producing the optimum scenario tiles, the baking resources will have:

Baking: 0.40x + 0.6y ... 105

              0.40(90) + 0.6(115) = 105 --> no left over resources

If Mosaic add another hour for Molding, there will be some additional profit, which is can be calculated by trying to create a new equation:

0.45x + 0.30y =< 75+1

0.45x + 0.30y =< 76

0.45x + 0.30y = 76

(y = 0)

0.45x + 0.30(0) = 76

x = 168

We can compare with the initial condition of available molding resources of 75 by producing 166 larger tiles:

Additional profit = (168 x 190) - (166 x 190)

Additional profit = $31,920 - $31,540

Additional profit = $380

Mosaic Tile should not accept the supplier offer because the most critical bottleneck at the time is the molding and baking capacities. Both lines are below the other resources lines and acting as the direct constraint on deciding the optimum possible output. If Mosaic wants to increase its profit, it should look for a solution to increase either or both molding and baking capacities.

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Answer:

Step-by-step explanation:

slope intercept form is

y=mx+b

where m is the slope and b is the y-intercept.

In your equation m = 5/4 so this is your answer.

Answer:

Answer B

Step-by-step explanation:

See graph below

1,-1    and    1,1   are both on Andres' graph....which shows TWO y values for ONE x value....does not pass the 'vertical line test' <====it is not a function

Based on the information, it can be inferred that the correct answer is option A. Qualitative-ordinal since this variable would yield categories with an order.

An ordinal qualitative variable is a term that refers to a type of variable that is characterized by representing non-numerical modalities, in which there is an order.

According to the above, the level of allergens (low, medium, high) is a non-numeric variable that has an order because each one represents a specific value that is organized in a certain order.

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Answer:

B, D, and F

Step-by-step explanation:

The inequality is x< -3, which pretty much says, on the (x,y) function, any x that is less than -3 is valid.

B, D, F are correct because the x value is less than negative 3

C, and G are incorrect because the value of x is greater than negative 3

A, and E are incorrect because the value of x is the same as 3

Answer: 16 grasses, 41 weeds, and 51 trees

Step-by-step explanation:

You can use a variable for the different pollen sources. Use g for grass, w for weeds, and t for trees. w=3g-7.  t=3g+3.  g+w+t=108. In that last equation, you can substitute other values for w and t. g+(3g-7)+(3g+3)=108. combine like terms to get, 7g-4=108. This equation simplifies to g=16. Substitute 16 for g in the first 2 equations, and find that w=41, and t=51.

(Sorry if my explanation didn't make sense)

Your daughter is 7 years old.

Let "x" be your age.

According to the statement, your age is 34. Thus, x= 34.

Let "y" be the age of your daughter.

According to the statement, your daughter's age is given by the following equation:

[tex]2y+20=x\\ \\2y+20=34[/tex]

[tex]2y+20-20=34-20\\ \\2y=14[/tex]

[tex]\frac{2y}{2} =\frac{14}{2} \\ \\y=7[/tex]

Let's see if number 7 makes the original condition be true.

So, you are 20 years older than twice your daughter's age. Let's multiply your daughter○s age by 2 and add 20, it should return your age (34).

[tex]2(7)+20=\\ \\14+20=\\ \\34[/tex]

That's correct, it means that 7 is the correct answer.

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