If w and v represent integers, which linear equation shown below will pass through the origin?

Answer:

I'm pretty sure the answer is 80.

Step-by-step explanation:

5 × 8 × 2 = 80

Answer:

Let's use "a" to represent the length of the shortest side. The remaining two sides are equal in length and double the length of the shortest side, thus we may represent them as "2a" according to the issue.

Because the perimeter of a triangle is equal to the sum of its sides' lengths, we may solve the following equation:

a + 2a + 2a = 36

We may simplify the left side of the equation as follows:

5a = 36

When we divide both sides by 5, we get:

a = 7.2

Now that we know the length of the shortest side, we can calculate the lengths of the other two sides:

2a = 14.4

As a result, the triangle's sides are 7.2 inches, 14.4 inches, and 14.4 inches.

To ensure that these lengths match the problem's requirements, we may check that the two larger sides are equal in length and twice the length of the shortest side:

14.4 = 2(7.2)

14.4 = 14.4

As a result, x = 7.2 inches and 2x = 14.4 inches is our solution.

The length of the shortest side is 7.2 inches, and the equal sides are each 14.4 inches (2x).The three sides of the triangle are 7.2 inches, 14.4 inches, and 14.4 inches.

Let's use x to represent the length of the shortest side. According to the problem, the other two sides are equal in length and double the shortest side, so they must be 2x each.

To find the perimeter of the triangle, we add up the lengths of all three sides:

x + 2x + 2x = 5x

We know that the perimeter is 36 inches, so we can set up an equation:

5x = 36

To solve for x, we divide both sides by 5:

x = 7.2

Now that we know the length of the shortest side, we can find the lengths of the other two sides:

2x = 2(7.2) = 14.4

So the three sides of the triangle are 7.2 inches, 14.4 inches, and 14.4 inches.

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Answer:

Area: 201.06 cm^2

Circumference: 50.265 cm

Step-by-step explanation:

Area of a circle: A=πr²

π≅3.1415

A=π(8)²

Area≅201.06 cm²

Circumference of a circle: C=2π²

C=2π(8)

C=50.265 cm

Answer:

Area = 50.27cm² , Circumference = 25.13cm

Step-by-step explanation:

First off, to find the area of a circle the formula is [tex]\pi[/tex]r², and in the equation you gave a diameter, so to get a radius divide the diameter by 2.

So therefore [tex]\pi[/tex]4² is your equation and the answer is 50.27cm²

Now to find the circumference. The formula to find circumference is 2[tex]\pi[/tex]r.

Again if you're given a diameter divide it by 2 to get the radius.

So 2[tex]\pi[/tex]4 is the equation, and the answer is 25.13 cm.

Please let me know if you have any more questions, or need any extra assistance!

If triangle has opposite side as "B", adjacent side as "A" and hypotnuse as 10 units, then Sine is B/10 and Cosine is A/10.

The Sine is defined as the ratio of the opposite side to the hypotenuse:

So, sin(θ) = opposite/hypotenuse

In this case, the opposite-side is = B and the hypotenuse is = 10 units,

So we can write : sin(θ) = B/10,

Similarly, cosine is defined as the ratio of the adjacent-side to the hypotenuse : cos(θ) = adjacent/hypotenuse

In this case, the adjacent side is = A and the hypotenuse is = 10 units,

So, we can write : cos(θ) = A/10,

Therefore, the sine of the triangle is B/10 and the cosine of the triangle is A/10.

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The given question is incomplete, the complete question is

Find the Sine and Cosine of a triangle with the opposite side=B, the adjacent side=A and the hypotnuse=10 units.

Answer:

71 is about 72, and 33% is about 1/3, so 33% of 71 is approximately 1/3 × 72 = 24.

.33 × 71 = 23.43, so the approximation is reasonable

The minimum number of fish that a family member caught is 1. Based on the given frequency table, the minimum number of fish that a family member caught can be determined by looking at the lowest "Number of fish" value with a non-zero "Number of family members" value.

Here's a step-by-step explanation:

1. Observe the frequency table:

  Number of fish | Number of family members
  -----------------------------------------
  0              | 0
  1              | 3
  2              | 1
  3              | 0
  4              | 4

2. Identify the lowest "Number of fish" value with a non-zero "Number of family members" value. In this case, it's "1 fish" with "3 family members".

Therefore, the minimum number of fish that a family member caught is 1 fish.

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True. This is known as Bayes' theorem, which states that the probability of an event A given the occurrence of another event B can be calculated as the probability of both events A and B occurring divided by the probability of event B occurring. It can be written as: P(A | B) = P(B | A) * P(A) / P(B).

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there is a statistically significant association between the two variables

a) Yes, because 0.01 < 0.05.

In a chi-square test for a 2x2 table, the degrees of freedom is 1. A p-value of 0.01 indicates that the probability of observing a chi-square statistic as extreme or more extreme than the one calculated under the null hypothesis (i.e., assuming no association between the two variables) is very low. Since 0.01 is less than the chosen level of significance of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant association between the two variables

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A matrix is a rectangular array of numbers or other mathematical objects arranged in rows and columns.

(a) To find the inverse of the matrix, we write it in the form I - D. Let A be the given matrix.

A =

[0.7 -0.2 -0.4]

[0.8 0.0 0.0]

[0.0 0.0 1.0]

Let D = 0.3A, then we have:

I - D =

[0.7 - 0.3(0.7) - 0.3(-0.2) - 0.3(-0.4)]

[0.8 - 0.3(0.8) - 0.3(0.0) - 0.3(0.0)]

[0.0 - 0.3(0.0) - 0.3(0.0) - 0.3(1.0)]

=

[0.46 0.06 0.12]

[0.56 0.80 0.00]

[0.00 0.00 0.70]

Using the sum-of-powers method, we have:

(I - D)^(-1) =

[1.131 -0.509 -0.343]

[-0.951 1.509 0.000]

[0.000 0.000 1.429]

To check the accuracy of our answer, we can use the determinant-based formula for the inverse:

A^(-1) = (1/det(A)) * adj(A)

where det(A) is the determinant of A, and adj(A) is the adjugate of A. We have:

det(A) = (0.70.01.0) + (-0.20.00.0) + (-0.40.80.0) - (-0.40.0-0.2) - (0.70.80.0) - (-0.20.01.0) = 0.56

adj(A) =

[0.0 0.8 0.0]

[-0.4 0.0 0.28]

[0.28 -0.2 0.0]

So, we have:

A^(-1) = (1/0.56) *

[0.0 0.8 0.0]

[-0.4 0.0 0.28]

[0.28 -0.2 0.0]

=

[1.131 -0.509 -0.343]

[-0.951 1.509 0.000]

[0.000 0.000 1.429]

which is the same as the answer we obtained using the sum-of-powers method.

(b) To find the inverse of the matrix, we write it in the form I - D. Let A be the given matrix.

A =

[0.6 0.3]

[0.2 0.5]

Let D = 0.2A, then we have:

I - D =

[0.52 -0.12]

[-0.08 0.48]

Using the sum-of-powers method, we have:

(I - D)^(-1) =

[2.058 0.514]

[0.343 2.171]

To check the accuracy of our answer, we can use the determinant-based formula for the inverse:

A^(-1) = (1/det(A)) *

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Interpret the Confidence Interval. Based on the information provided, we have the following data: Population 1 (Rural Voters): 85 surveyed, 21 support gun control, Population 2 (City Voters): 85 surveyed, 57 support gun control

Let's assume you've already calculated the confidence interval in Step 1. The confidence interval will show a range within which the true difference in support for gun control between rural and city voters is likely to fall.

To interpret the confidence interval, consider the following example:

Confidence Interval: (X1, X2)

If the entire interval is positive (X1 > 0 and X2 > 0), it indicates that city voters are more likely to support gun control than rural voters, with a certain level of confidence (usually 95% or 99%).

If the entire interval is negative (X1 < 0 and X2 < 0), it indicates that rural voters are more likely to support gun control than city voters, with the same level of confidence.

If the interval contains 0 (X1 < 0 and X2 > 0), it means there is not enough evidence to conclude that there is a significant difference in gun control support between rural and city voters at the chosen confidence level.

Remember to always provide the actual confidence interval values and the chosen confidence level in your interpretation.

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The differential equation describing the cell phone sales is [tex]\frac{{dy}}{{dt}} = 0.5357 \cdot y(t) \cdot \left(1 - \frac{{y(t)}}{{100}}\right)[/tex].

Based on the given information, the cell phone sales growth is logistic, with a carrying capacity of 100 thousand units. When 28 thousand cell phones have been sold, the rate of sales increase is 10 thousand units per month.

The logistic growth differential equation is given by:

[tex]\frac{dy}{dt} = k \cdot y(t) \cdot \left(1 - \frac{y(t)}{M}\right)[/tex]

where dy/dt is the rate of change in sales, y(t) is the number of cell phones sold after t months, k is the growth rate, and M is the carrying capacity.

In this case, y(t) = 28, dy/dt = 10, and M = 100. To find k, we can plug these values into the equation:

10 = [tex]$k \cdot 28 \cdot \left(1 - \frac{28}{100}\right)$[/tex]

Solving for k:

k ≈ 0.5357

Therefore, the differential equation describing the cell phone sales is:

[tex]\frac{{dy}}{{dt}} = 0.5357 \cdot y(t) \cdot \left(1 - \frac{{y(t)}}{{100}}\right)[/tex]

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The coordinates of the image point A after the dilation is (-1/4, -1/4)

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

ABC with vertices at A(-1, -1), B(1, 1), C(0, 1).

The scale factor is given as

Scale factor  = 1/4

So, we have

Image = A * Scale factor  

Substitute the known values in the above equation, so, we have the following representation

Image = (-1, -1)/4

Evaluate

Image = (-1/4, -1/4)

Hence, the image = (-1/4, -1/4)

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Answer: 777 Meters

Step-by-step explanation:asa

To use the comparison test or limit comparison test, we need to find a known series that either diverges or converges and is similar to the given series.

Using the comparison test, we can compare the given series to the series 1/n^2, which is a p-series with p=2 and converges.

To see if our series is smaller or larger than 1/n^2, we can simplify the given series by canceling out k^4 from the numerator and denominator:

k^4 / (16k^6 5) = 1 / (16k^2 5)

Now, we can compare 1 / (16k^2 5) to 1/n^2:

1 / (16k^2 5) < 1/n^2 for all k > 1

Therefore, since our series is smaller than a convergent series, it must also converge.

Alternatively, we can use the limit comparison test by finding the limit of the ratio of the given series to 1/n^2 as n approaches infinity:

lim (n→∞) [k^4/(16k^6 5) / (1/n^2)] = lim (n→∞) (n^2 / (16k^6 5))

This limit is zero for all k > 1, which means the given series and the series 1/n^2 have the same behavior and both converge.

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Answer:

C

Step-by-step explanation:

The distance between the two points can be found using the distance formula, which is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the two points are located at (15, -10) and (15, 22), so:

x1 = 15

y1 = -10

x2 = 15

y2 = 22

Substituting these values into the formula, we get:

d = √((15 - 15)^2 + (22 - (-10))^2)

= √(0 + 32^2)

= √1024

= 32

Therefore, the distance between the two points is 32 units.

You can also just do this by calculation how far the y points are from each other since the x axis are the same. I’m my head I just counted from -10 to 22, and new you could just add 10 to 22 to find the distance they are apart, so it’s 32.

Answer:

PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It's a helpful mnemonic device to remember the order of operations in arithmetic and algebraic equations. When solving a mathematical expression or equation, it's important to follow PEMDAS to ensure that the solution is accurate and consistent.

Answer:

by Paige Faber, ACDC Peer Advisor. Remember in seventh grade when you were discussing the order of operations in math class and the teacher told you the catchy acronym, “PEMDAS” (parenthesis, exponents, multiplication, division, addition, subtraction) to help you remember?

Step-by-step explanation:

HI

To rework problem 27 in section 6.3 with the given data, we need to use the same approach as in the textbook. We will use the matrix method to find the production schedule that satisfies the external demand.

Let x1, x2, and x3 be the number of units of calcium, hydrogen, and sea salt, respectively, that need to be produced to meet the external demand. Then the production constraints can be written as:

0.3x1 + 0.8x2 + 0.3x3 >= 57 (for calcium)
0.2x1 + 0.2x2 + 0x3 >= 32 (for hydrogen)
0.5x1 + 0.4x2 + 0.6x3 >= 13 (for sea salt)

We can write these constraints in matrix form as:

| 0.3  0.8  0.3 |   | x1 |   | 57 |
| 0.2  0.2  0   | * | x2 | >= | 32 |
| 0.5  0.4  0.6 |   | x3 |   | 13 |

Solving this system of inequalities, we get:

x1 = 150
x2 = 40
x3 = 25

Therefore, the production schedule that satisfies the external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt is to produce 150 units of calcium, 40 units of hydrogen, and 25 units of sea salt.
To find the production schedule that satisfies the external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt, we can set up a system of linear equations.

Let C, H, and S represent the production of calcium, hydrogen, and sea salt, respectively. We have:

1. 0.3C + 0.2H + 0.5S = 57 (calcium requirements)
2. 0.8C + 0.2H + 0.4S = 32 (hydrogen requirements)
3. 0.3C + 0H + 0.6S = 13 (sea salt requirements)

Solving this system of linear equations will give us the production schedule for calcium, hydrogen, and sea salt. Using a matrix solver or similar tool, we find the solutions:

C = 40
H = 20
S = 30

So, to satisfy the external demand, the production schedule should include 40 units of calcium, 20 units of hydrogen, and 30 units of sea salt.

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To express x and y in terms of trigonometric ratios of θ, we need to use the definitions of sine, cosine, and tangent ratios.

Let's assume that θ is an acute angle in a right triangle with hypotenuse of length 1. Then, we have:

sin θ = opposite/hypotenuse = y/1 = y
cos θ = adjacent/hypotenuse = x/1 = x
tan θ = opposite/adjacent = y/x

Therefore, we can express x and y in terms of trigonometric ratios of θ as follows:

x = cos θ
y = sin θ

Alternatively, if we are given the value of one trigonometric ratio and we need to find the others, we can use the Pythagorean identity:

sin^2 θ + cos^2 θ = 1

From this, we can derive:

cos^2 θ = 1 - sin^2 θ
sin^2 θ = 1 - cos^2 θ

And then use the definitions of tangent and cotangent ratios:

tan θ = sin θ/cos θ
cot θ = cos θ/sin θ = 1/tan θ

Hope this helps!
To express x and y in terms of trigonometric ratios of θ, we will use the basic trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). In a right-angled triangle, we have:

1. sin(θ) = opposite side / hypotenuse
2. cos(θ) = adjacent side / hypotenuse
3. tan(θ) = opposite side / adjacent side

Assuming x is the adjacent side and y is the opposite side in relation to angle θ, and the hypotenuse is denoted by r, we can express x and y in terms of trigonometric ratios of θ as follows:

Step 1: Solve for x using the cosine ratio:
x = r * cos(θ)

Step 2: Solve for y using the sine ratio:
y = r * sin(θ)

So, x and y are expressed in terms of trigonometric ratios of θ as x = r*cos(θ) and y = r*sin(θ).

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If events A and B are independent, then P(A and B) = P(A) * P(B). Also, from Bayes' theorem we have P(A | B) = P(A and B) / P(B).

Given that P(A | B) = 0.35 and P(B) = 0.5, we can solve for P(A and B) as follows:

P(A and B) = P(A | B) * P(B) = 0.35 * 0.5 = 0.175

Since events A and B are independent, we have P(A and B) = P(A) * P(B). Solving for P(A), we get:

P(A) = P(A and B) / P(B) = 0.175 / 0.5 = 0.35

Therefore, P(A) = 0.35.

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According to the figure the value of B is

The value of B is solved using the principles of segments of chords secants and tangents

The principle is such that

10^2 = 5 * (5 + b)

100 = 25 + 5b

gathering like terms

5b = 100 - 25

5b = 75

isolating b

b = 75 / 5

b = 15

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b) To find the joint density of the minimum and maximum of the U_i's, we can use the following approach:

Let M = min(U_1, U_2, U_3, U_4, U_5) and let X = max(U_1, U_2, U_3, U_4, U_5). Then we have:

P(M > m, X < x) = P(U_1 > m, U_2 > m, U_3 > m, U_4 > m, U_5 > m, U_1 < x, U_2 < x, U_3 < x, U_4 < x, U_5 < x)

Since the U_i's are independent and uniformly distributed on (0,1), we have:

P(U_i > m) = 1 - m, for 0 < m < 1

P(U_i < x) = x, for 0 < x < 1

Substituting these expressions, we get:

P(M > m, X < x) = (1 - m)^5 * x^5

Therefore, the joint density of M and X is:

f(M,X) = d^2/dm dx (1-m)^5 * x^5 = 30(1-m)^4 * x^4, for 0 < m < x < 1.

c) To find P(R > 0.5), we need to find the probability that the distance between the minimum and maximum of the U_i's is greater than 0.5. We can use the following approach:

P(R > 0.5) = 1 - P(R <= 0.5)

Now, R <= 0.5 if and only if the difference between the maximum and minimum of the U_i's is less than or equal to 0.5. Therefore, we have:

P(R <= 0.5) = P(X - M <= 0.5)

To find this probability, we can integrate the joint density of M and X over the region where X - M <= 0.5:

P(R <= 0.5) = ∫∫_{x-m<=0.5} f(M,X) dm dx

The region of integration is the triangle with vertices (0,0), (0.5,0.5), and (1,1). We can split this triangle into two regions: the rectangle with vertices (0,0), (0.5,0), (0.5,0.5), and (0,0.5), and the triangle with vertices (0.5,0.5), (1,0.5), and (1,1). Therefore, we have:

P(R <= 0.5) = ∫_{0}^{0.5} ∫_{0}^{m+0.5} 30(1-m)^4 * x^4 dx dm + ∫_{0.5}^{1} ∫_{x-0.5}^{x} 30(1-m)^4 * x^4 dm dx

Evaluating these integrals, we get:

P(R <= 0.5) ≈ 0.5798

Therefore,

P(R > 0.5) = 1 - P(R <= 0.5) ≈ 0.4202.

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a. H: δ>100 is a legitimate statistical hypothesis because it is a statement about a population parameter (δ) and it is testable using statistical methods.
b. H: x=45 is a legitimate statistical hypothesis because it is a statement about a population parameter (x) and it is testable using statistical methods.
c. H: s<.20 is a legitimate statistical hypothesis because it is a statement about a population parameter (s) and it is testable using statistical methods.
d. H: δ1/δ2 <1 is a legitimate statistical hypothesis because it is a statement about a population parameter (δ1 and δ2) and it is testable using statistical methods.
e. H: X-Y=5 is a legitimate statistical hypothesis because it is a statement about a population parameter (X and Y) and it is testable using statistical methods.
f. H: גּ<.01 is a legitimate statistical hypothesis because it is a statement about a population parameter (λ) and it is testable using statistical methods, with the parameter being the rate parameter of an exponential distribution used to model component lifetime.

Here are the answers for each assertion:

a. H: δ>100 - This is a legitimate statistical hypothesis because it states a specific direction for the population parameter (delta).

b. H: x=45 - This is not a legitimate statistical hypothesis because it refers to a sample statistic (x) rather than a population parameter.

c. H: s<.20 - This is not a legitimate statistical hypothesis because it refers to a sample statistic (s, sample standard deviation) instead of a population parameter.

d. H: δ1/δ2 <1 - This is a legitimate statistical hypothesis because it specifies a relationship between two population parameters (delta1 and delta2).

e. H: X-Y=5 - This is not a legitimate statistical hypothesis because it refers to sample statistics (X and Y) rather than population parameters.

f. H: λ<.01 - This is a legitimate statistical hypothesis because it states a specific direction for the population parameter (lambda) related to the exponential distribution for component lifetime.

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The most basic distinction between types of data is that some data are quantitative while other data are qualitative. Quantitative data consists of numerical information that can be measured or counted, allowing for statistical analysis and objective comparisons. This type of data can be further classified into two subcategories: continuous data and discrete data.

Continuous data represent measurements that can take on any value within a specified range, such as height, weight, temperature, or time. These measurements can be represented using fractions or decimals and are typically collected using precise instruments like rulers or thermometers.

Discrete data, on the other hand, consist of distinct, separate values that can be counted or categorized. Examples of discrete data include the number of students in a class, the number of cars in a parking lot, or the number of books sold in a month. Discrete data is often collected through surveys or counting processes.

In contrast, qualitative data are non-numerical and describe attributes, characteristics, or experiences. This type of data is typically obtained through observation, interviews, or open-ended survey questions. Examples of qualitative data include feelings, opinions, beliefs, or descriptions of events.

In summary, the primary distinction between types of data lies in their nature: quantitative data is numerical and allows for objective measurement, while qualitative data is descriptive and explores subjective aspects. Understanding the difference between these two types of data is essential for conducting accurate and meaningful research.

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Answer:

x = 4, -10

Step-by-step explanation:

(x + 3)² = 49

[tex]\sqrt{(x + 3){2} }[/tex] = [tex]\sqrt{49}[/tex]

x + 3 = ± 7

x + 3 = 7

x = 4

x + 3 = -7

x = -10

So, the answer is x = 4, -10

Answer:

Step-by-step explanation: Since ABCD is a rhombus, all sides are equal in length, and opposite angles are equal. Let's denote the length of each side as "s". We know that the area of a rhombus can be calculated as (diagonal1 * diagonal2)/2.

Using the given information, we can create the following diagram:

css

Copy code

       A

      / \

     /   \

    /     \

   /       \

  /         \

 P-----------B

  \         /

   \       /

    \     /

     \   /

      \ /

       C

We know that AC and BD are diagonals of the rhombus, and their lengths are in a 4:3 ratio. Let's denote the length of AC as 4x and the length of BD as 3x.

We also know that the length of side PA is equal to the length of side PB, and the length of side PC is equal to the length of side PD. Therefore, we can use the Pythagorean theorem to calculate the value of s:

s^2 = PA^2 + AP^2 = (4x)^2 + (s/2)^2

s^2 = PB^2 + BP^2 = (3x)^2 + (s/2)^2

s^2 = PC^2 + CP^2 = (4x)^2 + (s/2)^2

s^2 = PD^2 + DP^2 = (3x)^2 + (s/2)^2

We can simplify these equations to:

16x^2 + s^2/4 = s^2

9x^2 + s^2/4 = s^2

16x^2 + s^2/4 = s^2

9x^2 + s^2/4 = s^2

Combining like terms, we get:

s^2 = 64x^2/3

s^2 = 36x^2/5

Setting these two expressions equal to each other and solving for x, we get:

64x^2/3 = 36x^2/5

320x^2 = 108x^2

x^2 = 0

This result indicates that our assumption of a rhombus with given side length and diagonal ratio is not valid. Therefore, there is no unique solution for the area of ABCD.

(a) For an area of 0.5 to the left of the z-score under the standard normal curve, z = 0. This is because the standard normal curve is symmetric, and the area to the left of the mean (which is also the median and mode in this case) is 0.5.
(b) For an area of 0.9826 to the left of the z-score under the standard normal curve, you can look up the corresponding z-score in a standard normal (z) table, or use a calculator or software with an inverse cumulative distribution function. The z-score is approximately z = 2.13.

(c) For an area of 0.1423 to the right of the z-score under the standard normal curve, you first find the area to the left (1 - 0.1423 = 0.8577). Then, look up the corresponding z-score in a standard normal (z) table or use a calculator. The z-score is approximately z = 1.08.
(d) For an area of 0.9394 to the right of the z-score under the standard normal curve, find the area to the left (1 - 0.9394 = 0.0606). Then, look up the corresponding z-score in a standard normal (z) table or use a calculator. The z-score is approximately z = -1.55.

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The correct answer is: z-test statistic = 3.41, p-value = 0.0003. To find the standardized test statistic (z-test statistic) and corresponding p-value, we will use the following formula: z = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))


To find the standardized test statistic, we use the formula:

z = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

Plugging in the values given, we get:

z = (78 - 75) / (5.9 / sqrt(45))
z = 3.41

To find the corresponding p-value, we can use a standard normal distribution table or calculator. The p-value represents the probability of getting a z-score as extreme or more extreme than the one we calculated. Since our z-score is positive, we are interested in the area to the right of it on the standard normal distribution. This gives us a p-value of 0.0003.

Therefore, the correct answer is: z-test statistic = 3.41, p-value = 0.0003.
To find the standardized test statistic (z-test statistic) and corresponding p-value, we will use the following formula:

z = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

Plugging in the given values:

z = (78 - 75) / (5.9 / sqrt(45))

z = 3 / (5.9 / 6.708)

z = 3 / 0.880

z ≈ 3.41

Using a standard normal distribution table or a calculator, we find the area to the right of the z-score (since we're testing if the braking distance is greater than the hypothesized mean):

p-value ≈ 0.0003

Therefore, the correct answer is:

z-test statistic = 3.41, p-value = 0.0003

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Answer:

1/

Step-by-step explanation:

A standard dice has 6 equally likely outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Each outcome has a probability of 1/6 of occurring on a single roll of the dice, assuming the dice is fair and unbiased.

Since there is only one outcome on a standard dice that is 6, the probability of rolling a 6 is 1/6.

Therefore, the probability of a dice that is 6 as a fraction is 1/6.

The answers to all parts are shown below.

1. 5a + 3 -4a² + 2a³

writing into standard form of polynomial

2a³- 4a² + 5a +3.

2. 7xy + x³ - y³ -5x²y²

writing into standard form of polynomial

= x³ - y³ - 5x²y² + 7xy

3. The degree of the polynomials are

3x+1 = 1 degree

5x² - 2 degree

10- 0 degree

3x³ -2x² + 10= 3 degree

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