The survey of study habits and attitudes (ssha) is a psychological test that measures the motivation, attitude, and study habits of college students. scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation 25. you suspect that incoming freshmen at your school have a mean μ which is different from 115 because they are often excited yet anxious about entering college. to test your suspicion, you decide to test the hypotheses h0: μ = 115 versus ha: μ ≠ 115. you give the ssha to 25 incoming freshmen and find their mean score to be 116.2. what is the value of the test statistic?

Answer:

Important information like the common difference, 1st term, the # of terms; the last term must be included to find the sum of a series.

Answer:

The value of x is 1.6

Step-by-step explanation:

We have been given that triangle CDF ∼ triangle MKP.

Therefore, the ratio of the corresponding sides are equal.

Hence, we have

[tex]\frac{DC}{MK}=\frac{CF}{MP}[/tex]

Plugging the known values, we get

[tex]\frac{9}{1.8}=\frac{8}{0.x}[/tex]

Cross multiplying, we get

[tex]9x=8\times1.8[/tex]

Divide both sides by 9

[tex]x=\frac{8\times1.8}{9}[/tex]

Simplifying, we get

[tex]x=8\times10.2\\\\x=1.6[/tex]

The value of x is 1.6

In scientific notation, 0.00001 is equal to 1 × 10⁻⁵.

Scientific notation is a way of expressing very big or very small numbers conveniently and with the appropriate number of significant figures.  The general expression for the scientific notation is shown below:

M × 10ⁿ

M is a number that is greater than or equal to 1 but less than 10 and n is the number of times you have to multiply M by 10 to get the number.

The value of n can be easily determined by looking at the decimal point and counting the number of times it is moved to the left or to the right until a proper value of M is obtained.

The steps are as follows:

        NOTE: If the decimal point was moved to the left, then the

                    exponent n  will be written as positive (+x).

                    If the decimal point was moved to the right, then the

                   exponent  n will be written as negative (-x).

Applying the steps to the problem:

STEP 1: 0.00001

The decimal point is four places away from the digit 1.

STEP 2:  To get a number M that is greater than or equal to 1 but less than 10, the decimal point must be moved five places to the right and placed after the digit 1. (000001 or 1)

STEP 3: Since the decimal point was moved five places to the right, the exponent should have a magnitude of 5 and a negative sign. (1 × 10⁻⁵)

Keywords: scientific notation, exponential notation

Scientific notation is a form that can be used to represent very large or very small numbers

The option that gives the correct representation of 0.00001 is scientific notation (standard form) is the option;

Reason:

Required: To convert 0.00001 to a power of 10

Solution:

The method to convert a decimal to a scientific notation is given by moving the decimal point to the right of the first significant digit then multiply the result by 10 raised to the negative of the number of places the decimal point is moved

Where;

a = The number having only one digit to the left of the decimal point

b = The number of places the decimal point is moved (b is positive moving left and negative for moving right)

The given decimal number is 0.00001

Therefore, the decimal can be moved 5 places to the right to give;

0.00001 = 1.0 × 10⁻⁵ = 10⁻⁵

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D is the correct answer.

Step-by-step explanation:

D. Glenda chooses to check 300 monitors.

A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Now, to know about the defects through binomial experiment Glenda must choose a number of computers or trials. So, option D is correct.

The statement that will make this process into a binomial experiment is that,

⇒ Glenda checks the monitors until she has 300 non-defective monitors."

Hence, Option C is correct.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Glenda checks the computer monitors made at her company for defects. It has been shown that 0.5% of the monitors are defective.

Since, A binomial experiment is defined as a statistical experiment which consists of n repeated trials.

Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Hence, For check several monitors and record if they are defective,

Glenda checks the monitors until she has 300 non-defective monitors."

Learn more about the mathematical expression visit:

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It’s a little surprising that this question didn’t come up earlier.  Unfortunately, there’s no intuitive way to understand why “the energy of the rest mass of an object is equal to the rest mass times the speed of light squared” (E=MC2).  A complete derivation/proof includes a fair chunk of math (in the second half of this post), a decent understanding of relativity, and (most important) experimental verification.

[tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  shows the correct step that is from the simplification from the given expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex]. Option d is correct.

Simplification is defined as the solution making tendency to expressions.

Here,  expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex]

Multiply the whole power 3 in the square bracket.
Gives,
⇒[tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  

Thus, [tex]\frac{x^{-3}y^{12}}{x^{15}y^{-15}}[/tex]  shows the correct step that is from the simplification from the given expression [tex][\frac{xy^4}{x^{-5}y^5}]^3[/tex].

Learn more about simplification here:
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Answer:

Step-by-step explanation:

n=sample size =200

Mean = x bar = 55 hours

Std deviation (Population) = 7 hours

For 99% confidence level

Z critical value = 2.58

Margin of error = ±2.58(std error)

Std error = [tex]\frac{7}{\sqrt{n} } =0.495[/tex]

Hence margin of error = ±0.495(258)=1.28

Confidence interval = (55-1.28, 55+1.28) = (53.72, 56.28)

~(53.73, 56.27)

Hence option A

Answer:

ΔABP is congruent to ΔBAQ

ΔABP ≡ ΔBAQ

Explanation:

We are given two triangles; ΔABP and ΔABQ

In these two triangles, we have:

AB as a common side

∠ABP = ∠BAQ

AQ = BP

We can conclude that these two triangles are congruent by SAS (side-angle-side) postulate which states that:

"When two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle, then the two triangles are congruent"

Note that when writing congruency statements, the order of the letters is critical as each angle/side in the first triangle must be congruent to its corresponding angle/side in the second triangle.

Based on the above, the congruency statement would be:

ΔABP is congruent to ΔBAQ

Hope this helps :)

Answer: So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 0.64 feet.

Step-by-step explanation:

Since we have given that

Area of Pam 's picture frame which is square in shape = 3 sq. ft.

As we know the formula for "Area of square ":

[tex]Area=Side^2\\\\3=Side^2\\\\\sqrt{3}\ ft=Side[/tex]

So, Perimeter of square frame would be

[tex]Perimeter=4\times side\\\\Perimeter=4\times \sqrt{3}\\\\Perimeter=6.93\ ft[/tex]

Radius of Meg's circular frame = 1 foot

So, Circumference of circular frame would be

[tex]2\pi r\\\\=2\times \dfrac{22}{7}\times 1\\\\=\dfrac{44}{7}\\\\=6.29\ ft[/tex]

So, The circumference of Meg's picture frame is smaller than the perimeter of Pam's picture frame by 6.93-6.29=0.64 feet.

Answer:

(the square root of 2 minus the square root of 6) / 4

Final answer:

The probability of drawing a red or blue marble from a bag containing 25 marbles (10 black, 13 red, 2 blue) is 3/5. This is calculated by dividing the total number of red and blue marbles (15) by the total number of marbles (25).

Explanation:

The question involves calculating the probability of drawing a red or a blue marble from a bag containing 25 marbles: 10 black, 13 red, and 2 blue. To find the probability of an event happening, we divide the number of ways that event can happen by the total number of outcomes. Here, the total number of marbles is 25.

The total ways to get a red or a blue marble is the sum of red and blue marbles, which is 13 (red) + 2 (blue) = 15. Therefore, the probability of drawing a red or blue marble is 15/25. Simplifying that fraction gives us 3/5.

The correct answer is 3/5. This calculation shows how to approach problems involving the probability of one event or another happening, especially when dealing with specific quantities.

Answer:

0.75

Step-by-step explanation:

Final answer:

To sketch the polynomial graph without plotting points beyond intercepts, identify the x-intercepts from the factors, note the behavior at these points due to the powers, and connect them considering the end behavior akin to y = x^13.

Explanation:

To sketch a possible graph of the given polynomial f(x) = (x + 8)^3(x + 6)^2(x + 2)(x - 1)^3(x - 3)^4(x - 6), we can use its intercepts and the behavior near these intercepts. The intercepts are the x-values for which f(x) = 0. These are at x = -8, x = -6, x = -2, x = 1, x = 3, and x = 6.

Since these factors are raised to different powers, the graph will behave differently at each intercept. Also, since the highest power in the polynomial is 13 (3+2+1+3+4+1), the end behavior of f(x) as x approaches positive or negative infinity will resemble that of y = x^13.

Here's a step-by-step guide for sketching the graph:

Plot the x-intercepts on the x-axis: (-8, 0), (-6, 0), (-2, 0), (1, 0), (3, 0), (6, 0).

For each intercept, note that if the factor has an odd power, the graph crosses the x-axis, and if it has an even power, the graph touches the x-axis and turns back.

At x = -8, since the power is 3 (odd), the graph crosses the axis and behaves similarly to y = x^3, starting from the bottom.

At x = -6 and x = -2, the powers are 2 (even), so the graph will just touch the axis and turn back.

At x = 1, the power is 3 (odd), so the graph will cross the axis with the behavior of y = x^3.

At x = 3, the power is 4 (even), hence the graph touches the axis and turns back.

At x = 6, as the factor is raised to the first power (odd), the graph crosses the x-axis.

Finally, connect these points with smooth curves, keeping in mind the end behavior of the graph will rise on both ends because the degree is 13, an odd number.

Remember that the final graph should show the pattern of rising and falling appropriately between these intercepts based on the powers of each factor.

Answer:

Option A is correct.

Step-by-step explanation:

We are given that, the model for the depreciating value of a semi-truck is,

[tex]y = A_{O}(0.83)^x[/tex]

1. It is required to find the value of the truck initially i.e. when x= 0.

So, substituting x= 0, we have,

[tex]y = A_{O}(0.83)^0[/tex]

i.e. [tex]y = A_{O}\times 1[/tex]

i.e. [tex]y = A_{O}[/tex]

Since, the graph passes through the point (0,70,000).

Thus, we get, [tex]A_{O}=70,000[/tex]

Hence, the initial value is 70,000.

2. It is required to find the value of the truck initially i.e. when x= 50,000

That is, when x= 0, the value of y= 50,000.

Graphically, it means that the graph would cut y-axis at the point (0,50,000).

Thus, the y-intercept would be at 50,000.

Change in the initial value will not have any affect on the rate of the graph.

So, from the above, we get,

Option A is correct.