Find f. f ''(x) = 4 + 6x + 36x2, f(0) = 2, f (1) = 10

The question relates to a statistical hypothesis test, specifically comparing a sample mean to a known population mean. This involves recognizing null and alternative hypotheses, identifying and calculating a test statistic, deciding a significance level, determining a critical value, and finally comparing the test statistic to this critical value to decide whether to reject or not reject the null hypothesis.

The subject matter posed in the question concerns a statistical hypothesis test.

In these cases, we have two contradictory hypotheses about a population: the null hypothesis, denoted as 'H₀', which generally represents the status quo or a statement of no effect (e.g. a population mean is equal to 50), and the alternative hypothesis, denoted 'H₁', the contrary of the null hypothesis (population mean is not equal to 50). In your specific case, the null hypothesis 'H₀' is that the mean is equal to 50 (μ = 50) and the alternative hypothesis 'H₁' is that the mean is less than 50 (μ < 50).

To test these hypotheses, you could follow these steps:

Identify a test statistic: Since we know the population is normally distributed and we are comparing the sample mean to the population mean, we can use a z-test statistic.

Compare the test statistic to the critical value to decide whether to reject or fail to reject the null hypothesis.

After these steps, interpret the results in terms of the problem.

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[tex] |\Omega|=8\cdot7\cdot6=336\\
|A|=\underbrace{1\cdot6\cdot3}_{\text{8,any,even}}=18\\\\
P(A)=\dfrac{18}{336}=\dfrac{3}{56}=5\% [/tex]

The probability of selecting a black seven or a red three will be 1/13.

What is Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

You randomly select one card from a​ 52-card deck.

Now,

Number of black sevens = 2

Number of red three = 2

So, The probability of selecting a black seven or a red three is;

= (2 + 2) / 52

= 4 / 52

= 1 / 13

Thus, The probability of selecting a black seven or a red three will be 1/13.

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Answer: 300 ft²

Step-by-step explanation:

Answer:

A circle with center at (-3, 6) and a radius of 10 has the following standard form equation

[tex](x+3)^2+(y-6)^2=100[/tex]

Step-by-step explanation:

This is the general standard equation for the circle centered at (h, k) with radius r

[tex](x-h)^2+(y-k)^2=r^2[/tex]

It shows all the important information at a glance: the center (h, k) and the radius r.

A circle with center at (-3, 6) and a radius of 10 has the following standard form equation

Start with:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Put in (h, k) and r

[tex](x-(-3))^2+(y-6)^2=10^2\\(x+3)^2+(y-6)^2=100[/tex]

Answer:

The discontinuity of the function is at x=-8.        

Step-by-step explanation:

Given : Function [tex]f(x)=\frac{x^2+5x+6}{2x+16}[/tex]

To find : What are the discontinuities of the function?

Solution :

Discontinuity of the function is happen when denominator is zero.

First we factor the function,

[tex]f(x)=\frac{x^2+5x+6}{2x+16}[/tex]

[tex]f(x)=\frac{(x+2)(x+3)}{2(x+8)}[/tex]

Denominator = 0

[tex]2(x+8)=0[/tex]

[tex]x+8=0[/tex]

[tex]x=-8[/tex]

The discontinuity of the function is at x=-8.

The conjecture about the sum of the first 15 positive even numbers is 15 * 16

Making a conjecture about the sum of the first 15 positive even numbers.

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

The table of values

Where, we have

2 = 1 * 2

2 + 4 = 2 * 3

2 + 4 + 6 = 3 * 4

And so on

This means that

Sum of first n positive even numbers = n * (n + 1)

So, for the first positive even numbers, we have

n = 15

This gives

Sum of first 15 positive even numbers = 15 * (15 + 1)

Evaluate

Sum = 15 * 16

Sum = 240

Hence, the sum is 15 * 16

Answer:

Assessment value of Henry's home is $50750

Step-by-step explanation:

Henry's home has a market value of $145000 and the assessment rate is 35%.

This means value of home is 35% of the total cost $145000

Now we will solve it by calculating percentage

Assessment = 35% of 145000 = [tex](145000)(\frac{35}{100})=(1450).(35)=50750[/tex]

So the answer is assessment of Henry's home = $50750.

To calculate the perimeter of a rectangle given the area and the width, divide the area by the width to find the length, then use the formula Perimeter = 2(Length + Width), adjusting for scientific notation as necessary. This will provide the perimeter in scientific notation.

To find the perimeter of the rectangle when we have the area and the width, we need to first calculate the length of the rectangle using the formula Area = Length × Width. The width is given as 4.6 x 105 and the area is 2.76 x 1012. To find the length, we divide the area by the width:

Length = Area ÷ Width = (2.76 x 1012) ÷ (4.6 x 105)

After performing the division, we obtain the length in scientific notation. The next step is to use the formula Perimeter = 2(Length + Width). After calculating the sum of the length and width, we multiply by 2 to obtain the perimeter of the rectangle in scientific notation.

Let's assume after performing the calculation that the length is found to be L x 10n where L and n are specific numbers. The perimeter now would be calculated as:

Perimeter = 2((L x 10n) + (4.6 x 105))

Be sure to adjust the exponents so they match before adding the length and width together. This might involve converting one or the other so that you can add them directly. Once that is done, you can multiply by 2 to find the total perimeter of the rectangle and express it in scientific notation.

Answer: [tex]a_n=5+n[/tex]

Step-by-step explanation:

The explicit formula for an arithmetic sequence is given by:-

[tex]a_n=a+d(n-1)[/tex], where a is the first term , di sthe common difference and n is the number of terms.

The given sequence : 6, 5, 4, 3, 2, . .

Common difference  d = 1

First term = 1

Now, the explicit formula for given arithmetic sequence will be:

[tex]a_n=6+1(n-1)\\\\\Rightarrow\ a_n=6+n-1\\\\\Rightarrow\ a_n=5+n[/tex]

Hence, the explicit formula for given arithmetic sequence :  [tex]a_n=5+n[/tex]

Answer:

Option(C)

Step-by-step explanation:

As per histogram, given below

3 students took holidays between 5-10 days.

5 students took holidays between 10-15 days.

5 students took holidays between 15-20 days.

4 students took holidays between 20-25 days.

3 students took holidays between 25-30 days.

therefore, option (C) is correct.

Option B= $23000 is the answer.

Explanation:

Let the bakery's sales for the month be represented by = x

As given, the bakery has total receipts for the month = $24150

Rate of sales tax = 5%

This implies that total monthly sales(x) + sales tax on 'x' = 24150

[tex]x+\frac{5x}{100}=24150[/tex]

[tex]x+0.05x=24150[/tex]

[tex]1.05x=24150[/tex]

x=23000

Hence, the bakery's sale for the month is $23,000

Answer:

C.) 4

Step-by-step explanation:

we are given ABCD is an isosceles trapezoid

AB || CD

AB = m + 6

CD = 3m + 2

BC = 3m

AD = 7m - 16

Since, ABCD is an isosceles trapezoid

so, two sides must be equal

[tex]BC=AD[/tex]

now, we can plug values

[tex]3m=7m-16[/tex]

now, we can solve for m

[tex]3m-7m=7m-16-7m[/tex]

[tex]-4m=-16[/tex]

Divide both sides by -4

and we get

[tex]m=4[/tex]

Answer:

M= 4

Step-by-step explanation:

Answer:

13.

Step-by-step explanation:

No triangles can be constructed from line segments of 4 cm, 5 cm, and 9 cm in length, because the Triangle Inequality Theorem requires the sum of any two sides to be greater than the third side, which is not the case here.

The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters. To determine how many triangles can be constructed with these segments as sides, we need to apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the sum of the two shortest sides, 4 cm and 5 cm, is 9 cm, which is equal to the length of the longest side. Because one condition for the Triangle Inequality Theorem is not strictly being met (the sum must be greater, not equal), we can conclude that no triangles can be constructed using these three segments as sides.

When constructing triangles from three measures of angles or sides, it's important to realize that these conditions determine whether you can create a unique triangle, more than one triangle, or no triangle at all.