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Answer:

  B.  relative maximum of 8.25 at x=2.5

Step-by-step explanation:

A quadratic of the form ax²+bx+c has an absolute extreme at x=-b/(2a). For your quadratic, that is ...

  x = -5/(2(-1)) = 5/2

The value of the extreme is ...

  f(5/2) = (-5/2 +5)(5/2) +2 = 25/4 +2 = 33/4 = 8.25

The negative leading coefficient tells you the graph opens downward, so the extreme is a maximum.

The function has a relative maximum of 8.25 at x = 2.5.

__

A graphing calculator can show this easily.

Answer:

d. y = x + 6

Step-by-step explanation:

Equation of AD can be written in the slope-intercept form, y = mx + b

First, find the slope (m) and y-intercept (b) of line AD.

✔️Slope (m) = change in y/change in x

Using two points on line AD, (-5, 1) and (0, 6):

Slope (m) = (6 - 1)/(0 - (-5))

Slope (m) = 5/5

m = 1

✔️y-intercept (b) is the point where the line cuts across the y-axis = 6

b = 6

✔️To write the equation, substitute m = 1 and b = 6 into y = mx + b

y = 1(x) + 6

y = x + 6

Answer:

hear is your answer in attachment please give me some thanks

Answer:

C. 3/8

Step-by-step explanation:

[tex] - 3x + 8y = 12 \\ \therefore 8y =3x + 12 \\ \therefore \: y = \frac{3}{8} x + 12 \\ equating \: it \: with \\ y = mx + b \: we \: find: \\ m = \frac{3}{8} \\ \therefore \: slope = \frac{3}{8} [/tex]

The answer above is wrong I took the test. It's in the picture below!

Answer:

6

Step-by-step explanation:

=>root(2) x root(3) x root(6)

=>root(2x3) x root(6)

=>root(6) x root(6)

=>6

Answer:

the shortest side is 855 miles long.

Step-by-step explanation:

a + b + c = 3078 miles

a = b - 71

c = b + 371

=>

(b-71) + b + (b+371) = 3078

3b + 300 = 3078

3b = 2778

b = 926 miles

a = 926 - 71 = 855 miles

c = 926 + 371 = 1297 miles

Answer:

6

Step-by-step explanation:

6*9 = 54

6*6 = 36

6*7 = 42

Answer:

yes, this forms a right angle

Answer:

535,095 different samples of size six that contain exactly 2 defective parts.

0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

As the order of the parts is not important, the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

How many different samples are there of size six that contain exactly 2 defective parts?

2 defective from a set of 3, and 4 non-defective from a set of 47. So

[tex]D = C_{3,2}*C_{47,4} = \frac{3!}{2!1!}*\frac{47!}{4!43!} = 535095[/tex]

535,095 different samples of size six that contain exactly 2 defective parts.

What is the probability that a sample contains exactly 2 defective parts?

The total number of samples is:

[tex]T = C_{50,6} = \frac{50!}{6!44!} = 15890700[/tex]

Then...

[tex]p = \frac{D}{T} = \frac{535095}{15890700} = 0.0337[/tex]

0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.

Answer:

The answer is "(0.727, 1.573)".

Step-by-step explanation:

The confidence interval of 98 percent is C.I = (0.727, 1.573). You might disregard the statement of the experts that the genuine average duration in California of earthquakes is 0.5 minutes.

[tex]C.I = \bar{x}\pm t_{\frac{\alpha }{2}}\times \frac{s }{\sqrt{n}}\\\\[/tex]

      [tex]= 1.15 + 3.365 \times 0.12574\\\\= 1.15 + 0.4231\\\\= (0.7269, 1.5731)[/tex]

Answer:

2.3 =x

Step-by-step explanation:

We know the opposite and adjacent sides.

Since this is a right triangle, we can use trig functions

tan 38 = opp/ adj

tan 38 = x/3

3 tan 38 = x

2.34385688= x

To the nearest tenth

2.3 =x

Answer:

x ≈ 3.9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 38°

Opposite Leg = x

Adjacent Leg = 5

Step 2: Solve for x

Answer:

r = 8%

Step-by-step explanation:

Given that,

Interest, I = $24

Principal, P = $1200

Time, t = 90 days = 90/360 = 1/4 years

We need to find the rate.

We know that,

The simple interest is given by :

[tex]I=\dfrac{Prt}{100}[/tex]

Put all the values,

[tex]r=\dfrac{100I}{Pt}\\\\r=\dfrac{100\times 24}{1200\times \dfrac{1}{4}}\\\\r=8\%[/tex]

So, the rate is 8%.

Answer:

x(1+20)=22

21x=22

x= 22/21

x= 1.05

Step-by-step explanation:

Answer:

2!!!

Step-by-step explanation:

the person is wrong.. 2+20=22

The surface area is 150.5 in

Answer:

The surface area of this rectangular prism is 150.5 [tex]inches^{2}[/tex].

Step-by-step explanation:

The formula for finding the surface area of a rectangular prism is this :

A=2(wl + hl + hw)

l = 3.5, w = 9, h = 3.5

Now we substitute those values in and solve for A.

A = 2 · ( 9 · 3.5 + 3.5 · 3.5 + 3.5 ·9) = 150.5

The surface area of this rectangular prism is 150.5 [tex]inches^{2}[/tex].

Hope this helps, please mark brainliest. Have a great day!

Answer:

D

Step-by-step explanation:

We have the quadratic function:

[tex]f(x)=-x^2-4x+5[/tex]

First, the domain of all quadratics is always all real numbers unless otherwise specified. You can let x be any number and the function will be defined.

So, we can eliminate choices A and B.

Note that since the leading coefficient is negative, the parabola will be curved downwards. Therefore, it will have a maximum value. This maximum value is determined by its vertex, which is (-2, 9).

Since it is curving downwards, the maximum value of the parabola is y = 9. It will never exceed this value. Therefore, the range or the set of y-value possible is always equal to or less than 9.

So, the range of the function is all real numbers less than or equal to 9.

Our answer is D.

It is not C because the maximum value is dependent on y and not x.

Answer:

Due to the lower price per kilogram, purchasing the regular size at 720 grams for 60c is more economical.

Step-by-step explanation:

Which is more economical?

Whichever situation has the lowest price per kilogram.

3 kilograms for $3.15

3.15/3 = $1.05 per kilogram.

720 grams for 60c

0.6/0.72 = $0.83 per kilogram.

Due to the lower price per kilogram, purchasing the regular size at 720 grams for 60c is more economical.

Answer:

Answer:

Since i m not sure of the equation i have dont both possible ways :)

Step-by-step explanation:

b)

(5/9) ÷ 5

    [tex]= \frac{5}{9} \div 5\\\\=\frac{\frac{5}{9}}{5}\\\\=\frac{5}{9 \times 5}\\\\=\frac{1}{9}[/tex]

5/(9÷5)

   [tex]=\frac{5}{9 \div5}\\\\= \frac{5}{\frac{9}{5}}\\\\=\frac{5 \times 5}{9}\\\\=\frac{25}{9}[/tex]

Answer:

[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]

The inverse function is to calculate the number of rides; given the amount paid

Step-by-step explanation:

Given

[tex]Admission = 15[/tex]

[tex]Ride = 3[/tex] per ride

Required

Explain the inverse function

First, we calculate the function

Let x represents the number of rides

So:

[tex]f(x) = Admission + Ride * x[/tex]

[tex]f(x) = 15 + 3 * x[/tex]

[tex]f(x) = 15 + 3x[/tex]

For the inverse function, we have:

[tex]y = 15 + 3x[/tex]

Swap x and y

[tex]x = 15 + 3y[/tex]

Make 3y the subject

[tex]3y = x - 15[/tex]

Make y the subject

[tex]y =\frac{x}{3} - 5[/tex]

Replace y with the inverse function

[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]

The above is to calculate the number of rides; given the amount paid

Answer:

a) p = 0.5.

b) s = 0.025.

c) 0.7257 = 72.57% probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

It is known that 50% of the general population has an IQ score exceeding 100. Sample of 400.

This means that [tex]n = 400, p = 0.5, s = \sqrt{\frac{0.5*0.5}{400}} = 0.025[/tex]

(a) Find the mean of p, where p is the proportion of people with IQ scores over 100 in a random sample of 400 people

By the Central Limit Theorem, p = 0.5.

(b) Find the standard deviation of p.

By the Central Limit Theorem, s = 0.025.

(c) Compute an approximation for P(p is greater than or equal to 0.485), which is the probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400.

This is 1 subtracted by the p-value of Z when X = 0.485. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.485 - 0.5}{0.025}[/tex]

[tex]Z = -0.6[/tex]

[tex]Z = -0.6[/tex] has a p-value of 0.2743.

1 - 0.2743 = 0.7257.

0.7257 = 72.57% probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400.

Answer:

47

Step-by-step explanation:

1. #2 and #3 reveal that it must be between 31 to 89

2. #4 and #5 reveals that the answer is one of these numbers:

44, 45, 46, 47, 48, 49

64, 65, 66, 67, 68, 69

84, 85, 86, 87, 88, 89

This is because only 4, 6, and 8 are divisible by 2

3. You must add up all the numbers to see which ones add up to either 11 or 12.

4 + 7 = 11

4 + 8 = 12

6 + 5 = 11

6 + 6 = 12

8 + 4 = 12

This means that these are the following numbers: 47, 48, 65, 66, 84

4. #7 says that you must find the smallest number. The smallest number left is 47.

Answer:

1.894

3.169

2.064

3.690

Step-by-step explanation:

A.) 90% ; sample size = 8

Degree of freedom, df = n - 1

t(1 - α/2, 7) = t0.05, 7 = 1.894

B.) 99% ; sample size = 11

Degree of freedom, df = n - 1

t(1 - α/2, 10) = t0.005, 10 = 3.169

C.) 95% ; sample size = 25

Degree of freedom, df = n - 1

t(1 - α/2, 24) = t0.025,24 = 2.064

(D.) 99.5% and sample size 10.

Degree of freedom, df = n - 1

t(1 - α/2, 9) = t0.0025,9 = 3.690

Answer:

1.4

Step-by-step explanation:

= [(4 x 2) + (2 x 3)] ÷ 2 x 5

= [8 + 6] / 10

= 14 / 10

= 1.4

If you folded the figure up, you would have a prism where the parallel bases are right triangles. Each lateral face is a rectangle.

It might help to imagine a room where the floor and ceiling are triangles (they are identical or congruent triangles). Each wall of this room is one of the rectangles shown.

Answer:

5.313 ft (about 5'3.75")

Answer: hello your question has some missing data attached below is the missing data

answer :

∑ Volume variance = $55272

∑ Sales price variance = $41944 ( F )

Step-by-step explanation:

First step : prepare a flexible budget data for the current year using the formulae below

flexible budget = Actual units * Budgeted rate

and

Sales price variance = Actual - Budgeted data

Attached below is the Table showing the evaluation of sales price variance and volume variance