Verify that the function f(x) = -4x2 + 12x - 4 In x attains an absolute maximum and absolute minimum on [1, 2]. Find the absolute maximum and minimum values. Hint: In 2 ~0.7, In į = -0.7.

Answer: i think

Step-by-step explanation: -9.8 m/s^2 is not the force of gravity, it is the free fall acceleration due to gravity on Earth. According to Newton's second law, F = ma. Which means that Weight = mass * gravitational

The standard normal distribution of Z is calculated using the standard normal table. The required probabilities are calculated and rounded to four decimal places. The values for 0 ≤ Z ≤ 2.43, -2.10 ≤ Z ≤ 0, -1.25 ≤ Z, -1.10 ≤ Z ≤ 2.00, 1.26 ≤ Z ≤ 2.50, 1.10 ≤ Z, and |Z| ≤ 2.50 are rounded to four decimal places. The symmetry property of the standard normal distribution allows for the calculation of the required probabilities.

Given, Z is a standard normal random variable(a) P(0 ≤ Z ≤ 2.43)Using standard normal table, we can find P(0 ≤ Z ≤ 2.43) = 0.4929 (rounded to four decimal places)(b) P(0 ≤ Z ≤ 2)Using standard normal table, we can find P(0 ≤ Z ≤ 2) = 0.4772 (rounded to four decimal places)(c) P(-2.10 ≤ Z ≤ 0)Using standard normal table, we can find P(-2.10 ≤ Z ≤ 0) = 0.4821 (rounded to four decimal places)(d) P(-2.10 ≤ Z ≤ 2.10)Using standard normal table, we can find P(-2.10 ≤ Z ≤ 2.10) = 0.8192 - 0.1808 = 0.6384 (rounded to four decimal places)(e) P(Z ≤ 1.26)Using standard normal table, we can find P(Z ≤ 1.26) = 0.8962 (rounded to four decimal places)(f) P(-1.25 ≤ Z)

Using standard normal table, we can find

P(Z ≤ -1.25)

= 1 - P(Z > -1.25)

= 1 - 0.8944

= 0.1056 (rounded to four decimal places)

(g) P(-1.10 ≤ Z ≤ 2.00)

Using standard normal table, we can find

P(Z ≤ 2.00)

= 0.9772P(Z ≤ -1.10)

= 1 - P(Z > -1.10)

= 1 - 0.8643

= 0.1357P(-1.10 ≤ Z ≤ 2.00)

= 0.9772 - 0.1357

= 0.8415 (rounded to four decimal places)(h) P(1.26 ≤ Z ≤ 2.50)

Using standard normal table, we can find

P(Z ≤ 2.50)

= 0.9938P(Z ≤ 1.26)

= 0.8962P(1.26 ≤ Z ≤ 2.50)

= 0.9938 - 0.8962

= 0.0976 (rounded to four decimal places)

(i) P(1.10 ≤ Z)Using standard normal table, we can find

P(Z ≤ 1.10)

= 0.8643P(1.10 ≤ Z)

= 1 - 0.8643

= 0.1357 (rounded to four decimal places)(j) P(|Z| ≤ 2.50)

Using symmetry property of standard normal distribution, we can write

P(|Z| ≤ 2.50)

= P(-2.50 ≤ Z ≤ 2.50)

= 0.9938 - 0.0062

= 0.9876 (rounded to four decimal places).

Hence, the required probabilities have been calculated and values have been rounded to four decimal places.

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When s = 0, it will take 20 units of time for the account to double to 2X.

(a) When s = 0, it means the deposit is made at time t = 0. We want to find the time it takes for the account to double to 2X.

To find this time, we need to solve the equation a(t) = 2, where a(t) is the accumulation function.

1 - 0.05t = 2

Simplifying the equation, we have:

-0.05t = 1

Dividing both sides by -0.05, we get:

t = -1 / (-0.05)

t = 20

Therefore, when s = 0, it will take 20 units of time for the account to double to 2X.

(b) When s = 5, it means the deposit is made at time t = 5. We want to find the time it takes for the account to double to 2X.

Using the same equation a(t) = 2 and substituting t = 5, we have:

1 - 0.05(5) = 2

1 - 0.25 = 2

0.75 = 2

This equation is not satisfied, which means the account will not double to 2X when the deposit is made at time t = 5.

(c) The answer in (a) is greater than the answer in (b) because when the deposit is made at time t = 0, the account has more time to accumulate interest and grow compared to when the deposit is made at time t = 5. As time progresses, the effect of compounding becomes more significant, and starting earlier allows for more growth and a shorter time to double the account.

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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The probability of x having a value between 80 to 95 is 0.75.

The probability of x having a value between 80 to 95 can be determined by calculating the proportion of the total range of x that falls within that interval. Since x is uniformly distributed between 70 and 90, the probability can be obtained by dividing the width of the desired interval (15) by the width of the entire range of x (90 - 70 = 20).

Using the formula for probability in a uniform distribution, we have:

Probability = (width of interval) / (width of range)

Probability = 15 / 20

Probability = 0.75

Therefore, the probability of x having a value between 80 to 95 is 0.75.

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The random variable x is known to be uniformly distributed between 70 and 90. the probability of x having a value between 80 to 95 is group of answer choices (a)0.05 (b)0.5 (c)0.75 (d)1

A) y intercept is (0,3)

C) Axis of symmetry is x = -1

D) Vertex is (-1, 4)

So basically everything but choice B is true.

========================================

Explanation:

Choice A is true because plugging in x = 0 leads to y = 3. Effectively, anything with an x goes away when x = 0 leaving that 3 behind. So finding the y intercept in this form is fairly fast.

-------------------

To check choices B through D, let's convert the equation into vertex form.

y = -1x^2 - 2x + 3 is in the form y = ax^2 + bx + c where

a = -1

b = -2

c = 3

The vertex is located at (h,k) such that h = -b/(2a)

Plug the values of 'a' and 'b' into the equation below

h = -b/(2a)

h = -(-2)/(2*(-1))

h = 2/(-2)

h = -1

The x coordinate of the vertex is x = -1

Then use this to find the y coordinate of the vertex

y = -1x^2 - 2x + 3

y = -1(-1)^2 - 2(-1) + 3

y = 4

The y coordinate of the vertex is 4, meaning k = 4

The vertex overall is (h,k) = (-1, 4)

This shows choice D is true, meaning choice B has to be false.

Choice C is true because the axis of symmetry is the x coordinate of the vertex. This is the vertical line that cuts the parabola into two mirrored halves. This vertical line always goes through the vertex.

The option D.15 + 40 = 5(3 + 8); demonstrates the distributive property.

From the given options;

Consider option D; 15 + 40 = 5(3 + 8).

It is the case of distributive addition.

where

5(3 + 8) = 5×3 + 5×8

5(3 + 8) = 15 + 40

Thus, the option D is the correct representation of the distributive law.

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An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.

The solution is 21.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;

7n + 16 = 163

7n = 163 - 16

7n = 147

n = 147/7

n = 21.

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Given:

5) The expressions are

\(16x+24y+32\)

\(8(2x+3y+4)\)

\(4(4x+24y+8)\)

7) The expression is

\(7(3-x)+15x\)

To find:

5) Whether the given expressions are equivalent.

7) simplified form of given expression.

Solution:

5)

First expression is

\(16x+24y+32\)

Second expression is

\(8(2x+3y+4)\)

\(=8(2x)+8(3y)+8(4)\)

\(=16x+24y+32\)

Third expression is

\(4(4x+24y+8)\)

\(=4(4x)+4(24y)+4(8)\)

\(=16x+96y+32\)

Therefore, the simplified forms of given expressions are \(16x+24y+32,\ 16x+24y+32,\ 16x+96y+32\) respectively. It means only first and second expressions and equivalent.

7)

We have,

\(7(3-x)+15x\)

\(=7(3)+7(-x)+15x\)

\(=21-7x+15x\)

\(=21+8x\)

Therefore, the simplified form of given expression is \(21+8x\).

Given:

5) The expressions are

7) The expression is

To find:

5) Whether the given expressions are equivalent.

7) simplified form of given expression.

Solution:

5)

First expression is

Second expression is

Third expression is

Therefore, the simplified forms of given expressions are  respectively. It means only first and second expressions and equivalent.

7)

We have,

Therefore, the simplified form of given expression is .

Answer:

Step-by-step explanation:

G

The type of sampling used by the BLS (Bureau of Labor Statistics) for its National Compensation Survey, where employers are divided by size in the second stage of sampling, is known as stratified sampling.

Stratified sampling involves dividing the population into subgroups or strata based on certain characteristics or criteria. In this case, the BLS divides the employers into different size categories. Within each stratum, a sample is then randomly selected to represent that specific subgroup. This approach allows for a more precise estimation of employment costs within each size category. By using stratified sampling, the BLS ensures that the sample is representative of the different employer sizes and allows for more accurate and reliable estimates of employment costs at a national level.

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The point estimators in your list are b. μ (estimated by the sample mean) and c. s (which is an estimator for σ, the population standard deviation).

A point estimator is a statistic that is used to estimate a population parameter. Out of the options provided, the following are point estimators:

b. μ (mu) - This symbol represents the population mean, which is a measure of central tendency for the entire population. A point estimator for μ would typically be the sample mean (x), calculated from a random sample taken from the population.

c. s - This symbol represents the sample standard deviation, which is a measure of how dispersed the data is from the sample mean. The sample standard deviation (s) is a point estimator for the population standard deviation (σ).

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2500 cheers were there when there were only 10 fans whose jubilation factor was 20.

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12. A positive integer greater than 1, or an algebraic expression, that has only two factors (i.e., itself and 1) is termed prime; a positive integer or an algebraic expression that has more than two factors is termed composite. The prime factors of a number or an algebraic expression are those factors which are prime.

suppose c =K F \(J^{2}\) ( k is a parameter )

According to the question

1000 = k× 100×\(4^{2}\)

k = \(\frac{1000}{1600}\) = 0.625

so 0 = 0.625 F \(J^{2}\) (equation )

when F equal to 10 , J = 20

k= 0.625 × 10 ×\(20^{2}\) = 2500

2500 cheers were there when there were only 10 fans whose jubilation factor was 20.

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The proportion of cranberries required for the muffins is 4 pounds x 16 ounces/pound = 64 ounces of cranberries. Therefore, to make the muffins for the party, you will need 64 ounces of cranberries.

To calculate the amount of cranberries needed for the muffins at a party of 12 people, making 11/2-ounce muffins and assuming each person will have three muffins, we need to convert the measurements and quantities.

Given that each muffin weighs 11/2 ounces, and each person will have three muffins, we can calculate the total weight of muffins needed. 11/2 ounces is equivalent to 1.5 ounces, so each person will consume 1.5 ounces x 3 muffins = 4.5 ounces of muffins.

For a party of 12 people, the total amount of muffins required is 4.5 ounces/person x 12 people = 54 ounces of muffins.

Now, to determine the amount of cranberries needed for the muffins, we need to consider the recipe's proportion. The recipe makes 15 pounds of dough and calls for 4 pounds of cranberries. To convert pounds to ounces, we know that 1 pound is equal to 16 ounces.

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Answer:7 is the exponent

Step-by-step explanation:

Answer:

\(6^7\)

Step-by-step explanation:

Exponents can be expressed through repeated multiplication, meaning that the amount of times one number is being repeated, would be the same amount as put in an exponent. Therefore :

6 * 6 * 6 * 6 * 6 * 6 * 6

6 is being repeated, therefore it's the constant.

6 is repeated 7 times, therefore the exponent is 7.

\(6^7\)

Answer:

The sets of values that correctly completes the t-chart are:

7, -1, 7

Hence, option B is true.

Step-by-step explanation:

Given the equation

y = 2x² - 1

FOR x = -2

substitute x = -2 in the equation

y = 2x² - 1

y = 2(-2)² - 1

y = 8 - 1

y = 7

FOR x = 0

substitute x = 0 in the equation

y = 2x² - 1

y = 2(0)² - 1

y = -1

FOR x = 2

substitute x = 2 in the equation

y = 2x² - 1

y = 2(2)² - 1

y = 8 - 1

y = 7

Thus, the t-chart becomes:

x              y

-2            7

0             -1

2              7

Thus, the sets of values that correctly completes the t-chart are:

7, -1, 7

Hence, option B is true.

Answer:

B.

Step-by-step explanation:

Answer:

si cardo bahyanbayansusb

Answer:

Angle Z = Angle V (as it is already said that ZY = VY and their ending points are Z and V respectively

Step-by-step explanation:

angle z = angle v​ can be proved by the SAS (Side angle side) Property

XZ = TV (Given)

Angle Z = Angle V (as it is already said that ZY = VY and their ending points are Z and V respectively

ZY = VY ( Given )

The best unbiased estimate for μ is \($\bar{x}$\), the confidence interval for the population mean is (14.5044, 17,2956).

The best unbiased estimate for μ is \($\bar{x}$\).

 Sample standard mean \($\bar{x}$\) is the best unbiased estimate of population mean μ.

\($$\begin{aligned}& \mathrm{SE}=\sigma / \sqrt{n} \\& =6 / \sqrt{100}=0.6 \\& \alpha=0.02\end{aligned}$$\)

The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean.

From Table, critical values of \($Z=\pm 2.326$\)

Confidence interval:

\($$\begin{aligned}& \bar{x} \pm \text { Z SE } \\& =15.9 \pm(2.326 \times 0.6) \\& =15.9 \pm 1.3956 \\& =(14.5044,17,2956)\end{aligned}$$\)

Therefore, the confidence interval for the population mean is (14.5044, 17,2956).

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Answer:

looks right

Step-by-step explanation:

The mode is the value that appears most frequently in a dataset. In this case, the mode is 4, as it has the highest frequency of occurrence.

The median is the middle value when the data is arranged in ascending or descending order. Since there are an odd number of families (21 in total), the median will be the value of the 11th observation when the data is sorted. Arranging the data in ascending order, we find that the median is also 4, as it is the middle value.

The mean is the average value and is calculated by summing up all the values and dividing by the total number of observations. In this case, we can calculate the mean by multiplying each number of pets by its corresponding frequency, summing up these products, and dividing by the total number of families (21). Using this approach, the mean can be calculated as:

Mean = (0*2 + 1*1 + 2*8 + 3*1 + 4*9 + 5*0) / 21 ≈ 2.76

Therefore, based on the provided data, the mode, median, and mean number of pets owned by the families are all approximately 4.

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The measure of each exterior angle in a regular pentagon is 72 degrees, indicating that the sum of all exterior angles in the pentagon is 360 degrees.

A regular polygon is a polygon with all sides and angles equal. In the case of a pentagon, it has five sides and five angles. To find the measure of each exterior angle, we can use the formula:

Exterior Angle = 360 degrees / Number of Sides.

In this case, for a pentagon, the formula becomes:

Exterior Angle = 360 degrees / 5 sides = 72 degrees.

Therefore, each exterior angle of a pentagon measures 72 degrees. This means that if you were to extend any side of the pentagon outward, the angle formed between that extended side and the adjacent side would measure 72 degrees.

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Answer:

Shift the graph of y = x2 left 13 units and then up 6 units.

Step-by-step explanation:

Answer:

You start with the graph y=x^2, you shift the graph right 13 units to get y=(x-13)^2, then you shift the graph up 6 units to get y=(x-13)^2+6. Hope this helps!

Answer:

A.)*ೃ: 6f + 3g
B.) *ೃ: -8f +10g
C.) *ೃ: 4fg

Step-by-step explanation:

A.) F x 6 + g x 3 (combined like terms)
     6f + 3g
B.) f(-8)=-8f
    g(-10)=-10g
     -8f-(-10g)

     -8f + 10g
C.) (-2)(-2)=4
    f x 4g = 4fg  

Answer:

• =multiplication

question 7:

1/2•5•x=20

x=8cm

question 8:

answer:y=10cm.

Answer:

1. 25cm² x

2. 36cm² y

3. 18cm² z

Answer:

p + (3p - 5) + (4p +6)        Correct

p + (5 - 3p) + (6 + 4p)       Not Correct

p + 11                                 Not correct

8p + 1                                Correct

7p - 1                                 Not correct

Step-by-step explanation:

p + (3p - 5) + (4p +6)

simplified = 8p +1