3 different numbers that have a multiple of 36?

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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The value of the expression 18 + 4(28) will be 130.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 18 + 4(28)

Simplify the expression, then the value of the expression will be

⇒ 18 + 4 x (28)

⇒ 18 + 4 x 28

⇒ 18 + 112

⇒ 130

Thus, the value of the expression 18 + 4(28) will be 130.

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the Answer is C. 367 meters

Answer: 367 meters

Step-by-step explanation:

He will complete his work at 2:45 pm.

First find the total amount of time it will take to go through 5 such work pieces:

= (time taken for cutting + time taken for molding) x total number of work pieces

= (8 + 13) x 5

= 105 minutes

In hours this is:

= 105 / 60

= 1 hour 45 minutes

Add this to the time he started which is 1 pm

= 1pm + 1 hour 45 minutes

= 2:45 pm

He will complete his work at 2:45 pm.

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(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.

Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.

Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.

(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).

Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.

(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.

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Step-by-step explanation:

indicates the level

of uncertainty that people can

tolerate to work efficiently without

experiencing undue stress

Answer:

\(x = \frac{9}{ \sqrt{2} } = \frac{9 \sqrt{2} }{2} \)

The length of the diagonal of the rectangular prism is 14.7 feet to the nearest tenth.

In a three-dimensional space prism is a polyhedron where two ends are similar.

Given:

The dimensions of the right rectangular prism:

Length l = 10cm

Width w = 4cm

Height h = 10cm

The length of the diagonal of the rectangular prism,

= √(l² + w² + h)

= √{(10)² + (4)² + (10)²}

= 14.69

= 14.7 feet.

Therefore, the length of the diagonal is  14.7 feet.

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Answer: Three hundred five hundred fifty one thousand, five hundred twenty eight and ninety four thousandths.

Hope this helps!

Answer:

Three hundred Fifty One Thousand

Five Hundred Twenty Eight

and Nine hundredths Four Thousandths

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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The square of a binomial, when the binomials are subtracted, is defined as follows:

(a - b)² = a² - 2ab + b².

When the two binomials are added, the square is given as follows:

(a + b)².

Expanding the square, we have that:

(a + b)² = (a + b) x (a + b).

(a + b)² = a² + ab + ab + b².

(a + b)² = a² + 2ab + b².

Which is the result presented in this problem.

Now, when the binomial has a minus sign, involving a subtraction, the pattern is obtained as follows:

(a - b)² = (a - b) x (a - b).

(a - b)² = a² - ab - ab + b².

(a - b)² = a² - 2ab + b².

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a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

what's that

Step-by-step explanation:

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

\(x+2y-10=0\)

Step-by-step explanation:

Consider an equation: \(y=mx+c\)

Here, m is the slope of the line and c is the y-intercept.

Given equation is \(y=2x+3.14\)

Here, slope is \(m=2\)

As product of slopes of two perpendicular lines is equal to \(-1\), slope of the required line is \(m_1=\frac{-1}{m}=\frac{-1}{2}\).

Let \((x_1,y_1)=(2,4)\)

Equation of the required line is \(y-y_1=m_1(x-x_1)\)

\(y-4=\frac{-1}{2}(x-2)\\2(y-4)=-1(x-2)\\2y-8=-x+2\\x+2y-8-2=0\\x+2y-10=0\)

The blanks that are missing in the sequence are -3 and 11

from the question, we have the following parameters that can be used in our computation:

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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Answer:

0.5a + 0.75p ≤ 23

Step-by-step explanation:

Cost of a apples: 0.5a

Cost of p pears: 0.75p

The total cost must be $23 or less.

0.5a + 0.75p ≤ 23

Answer:

Present Value A=Rs.52,488

Depreciation rate r=10% per annum

Time t=4 years

Let initial value be P

We know the formula, A=P(1−100r)t

Substituting the given values, we get.

52,488=P[1−10010]4

52,488=P(0.9)4

P=0.656152488

P=Rs.80,000

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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Answer:

the right answer is 18 because 120 divided by 20 is 6 so the you do 6 times 3

Answer:

the answer is 18

Step-by-step explanation:

20:3=workers:casiers

120:x

cross multiply so that means 3 multiplied by 120 which is 360 divided by 20 which is 18

hope this helps :)

Answer:

810 is the number that represents the same amount.

Hope this helps :)

9514 1404 393

Answer:

  A, C, E

Step-by-step explanation:

A. 0.6 • 25 = x . . . . . a direct translation of 60% of 25 (yes)

B. x • 1.6 = 25 . . . no (means 160% of x is 25)

C. 6/10=x/25 . . . . . . the ratio of x to 25 is 60% (yes)

D.60/100 = 25/x . . . no (means 25 is 60% of x)

E. x/25 = 60/100 . . . . . the ratio of x to 25 is 60% (yes)

F.6.0 • 25 = x . . . no (no means 600% of 25)

Answer:

A, C, E

Step-by-step explanation:

Answer:

20% of 60 is 12

Step-by-step explanation:

60 * 0.20 = 12

Hey there!

20% of 60

= 20% * 60

= 20/100 * 60

= 20/100 * 60/1

= 20 ÷ 20/100 ÷ 20 * 60/1

= 1/5 * 60/1

= 1(60)/5(1)

= 60/5

= 60 ÷ 5

= 12

Therefore, your answer is: 12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

47mph

Step-by-step explanation:

divide 141 by 3

Answer: 47

Work: To find the rate of speed, you divide 141 by 3, and you get 47 mph.

The first step to find the area of the hexagon is to find the apothem of it by using the following formula:

Where l is the sidelength and θ is half the central angle:

Now, find the perimeter of the hexagon by multiplying the side length by 6:

Finally, find the area of the hexagon by using the following formula:

The area of the given hexagon is 128√3

Answer:

2

Step-by-step explanation:

the line meets the y axis at (0,2)

Answer:

you need this ?

the y is

y=-x+2

The area on the graph that is not shaded is the region of feasibility. The shape is a triangle and the vertices of the feasible region are: (5,1.5), (.75,.75), (1.5,.5)

The system of inequalities below, We need to determine the shape of the feasible region and find the vertices of the feasible region

x+y<=2

3x+y>=3

x+3y>=3

x>=0

y>=0

Now, we would graph with the following inequalities

x+y>=2

3x+y<=3

x+3y<=3

x<=0

y<=0

Therefore, the area on the graph that is not shaded is the region of feasibility and the shape is a triangle, the vertices of the feasible region are: (5,1.5) (0.75, 0.75), (1.5,.5).

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Answer:

B. -55

Step-by-step explanation:

La resta entre ambas funciones consiste en la sustracción de términos semejantes como demostraremos a continuación:

1) \(f(x) =-2\cdot x ^{2}-6\) Dado

2) \(g(x) = x+4\) Dado

3) \((f-g)(x) = (-2\cdot x^{2}-6)-(x+4)\) Definición de resta de funciones.

4) \((f-g)(x) = (-2\cdot x^{2}-6)+(-1) \cdot (x+4)\)        \((-1)\cdot a = -a\)

5) \((f-g)(x) = (-2\cdot x^{2}-6) + (-x-4)\) Propiedad distributiva/\((-1)\cdot a = -a\)

6) \((f-g)(x) = -2\cdot x^{2}-x+(-6-4)\) Propiedad conmutativa

7) \((f-g) (x) = -2\cdot x^{2}-x-10\) Sustracción de términos semejantes/Resultados.

A continuación, evaluamos la función resultante en \(x = -5\):

\((f-g)(-5) = -2\cdot (-5)^{2}-(-5)-10\)

\((f-g)(-5) =-55\)

Por ende, la respuesta correcta es B.