PLEASE HELP ME!!!!
A toy American Eskimo dog has a mean weight of 8 pounds with a standard deviation of 1 pound. Assuming the weights of toy Eskimo dogs are normally distributed, what range of weights would 95% of the dogs have?

a. Approximately 7–9 pounds

b. Approximately 6–10 pounds

c. Approximately 5–11 pounds

d.Approximately 4–12 pounds

Answer:3,380

Step-by-step explanation:

we need to apply cross-multiplication to the ratio of chili preferences in the sample (60) against the total attendance (8450). This gives us:

(60/150) = (x/8450)

where x is the number of people in attendance who would prefer chili on a hot dog.

Simplifying this equation, we get:

x = (60/150) * 8450x = 3,380

Answer:

Option i) At least 64 of the numbers are greater than or equal to 35 must be true

Since the median is 35, we know that there are 63 numbers greater than 35 and 63 numbers smaller than 35. However, since there is an odd number of total numbers (127), the median itself must be included in one of these groups. Therefore, there are at least 64 numbers that are greater than or equal to 35.

Here the  p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.

We have to evaluate null and alternative hypotheses for the scenario .

In this scenario, the null hypothesis is

H0: μ = 5.8

here

μ = true mean pressure produced by the valve.

Now for the alternative hypothesis is

HA: μ > 5.8

here

μ = true mean pressure produced by the valve.

Therefore to  determine if there is sufficient observation at the 0.05 level that the valve performs above specifications,

Here we can utilize a one-tailed z-test with

α = 0.05

Then,  test statistic can be evaluated as

z = (X' - μ) / (σ / √n)

where:

X' = sample mean

μ = hypothesized value concerning the population mean

σ = population standard deviation

n = sample size

Substituting in our values, we get:

z = (5.9 - 5.8) / (1 / √130) = 1.8856



Now utilizing a z-table  we can evaluate that the p-value associated with this test statistic is approximately 0.0292.

Since this p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.

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If a group of friends wanted to rent a cabin for the fourth of July. The number of  friends that were originally in the group is 8.

Let x represent the number of friends in the group

Cost per person =960/x

After   the 4 friends dropped out the remaining number of friends was = x - 4

New cost per person =960/x + 120

New total cost of the cabin rental = (x - 4) * (960/x + 120)

Set the two expressions equal to each other

960 = (x - 4) * (960/x + 120)

960 = 960 - (3840/x) + 120(x - 4)

Simplifying

3840/x = 120x - 480

Multiplying both sides by x

3840 = 120x^2 - 480x

Rearranging

120x^2 - 480x - 3840 = 0

Dividing both sides by 120

x^2 - 4x - 32 = 0

Quadratic equation

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where:

a = 1, b = -4, and c = -32.

Plugin the formula

x = (4 ± √(16 + 128)) / 2

x = (4 ± √(144)) / 2

x = (4 ± 12) / 2

x = 8 or x = -4

Therefore the number of friends  is 8.

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The surface area of the rectangular prism which is given above would be = 130ft²

To calculate the surface area of the rectangular prism the formula that should be used;

=2( wl+hl+wh)

where;

w = 5ft

l = 10ft

h = 1 ft

surface area = 2(5×10+1×10+5×1)

= 2(50+10+5)

= 2×65 = 130ft²

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the width of the previous image is 9.5mm.

     The widthh can be defined as the horizontal measurement or distance measured from side to side.

       In geometry, the shorter side of an object is frequently referred to as its "width". For instance, both of the given rectangles are identical rectangles, but one of them has been rotated to demonstrate that the shorter side of the rectangle is referred to as its width.

In the given problem,

         if the width of the previous image is x,

                            4x=38

                        ⇒x=9.5mm

So, the width of previous image is 9.5mm.

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Using the top number line, p + q and p + (-q) can be located as shown in the attached image.

A number line is a line on which numbers are marked at intervals, used to illustrate simple numerical operations. It is also a pictorial representation of the real numbers.

Since point p has a value of 2 and point q has |q| = 5. We can say:

p + q = 2 + 5 = 7

p + (-q) = 2 + (-5) = -3

Therefore, using the top number line, we can then locate p + q and p + (-q) with their calculated values (Check the green dot in the attached image).

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Complete Question

Check the attached image

The total amount paid to the finance company if the loan is repaid in 40 years is $317,376.00 (option c).

First, we need to find out how much money the couple borrowed. Since they got financing for 80% of the $150,000 purchase price, they borrowed $120,000 ($150,000 x 0.8 = $120,000).

Next, we need to find the monthly interest rate. Since the interest rate is 6% per year, the monthly interest rate is 0.06/12 = 0.005.

Now we can use the table to find the monthly payment per $1000 of mortgage for a 40-year loan with a 6% interest rate. Looking at the fifth column of the table, we find the entry that corresponds to a 6% interest rate and a 40-year loan, which is 5.86. This means that for each $1000 borrowed, the monthly payment is $5.86.

To find the monthly payment for the couple's $120,000 loan, we multiply the monthly payment per $1000 by 120 (since they borrowed $120,000). So the monthly payment is 5.86 x 120 = $703.20.

Finally, we need to calculate the total amount paid to the finance company over the 40-year period. Since the couple will make 12 payments per year for 40 years, the total number of payments will be 12 x 40 = 480. So the total amount paid will be the monthly payment ($703.20) multiplied by the total number of payments (480). This gives us a total of $317,376.

Therefore, the correct option is (c).

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The Median and IQR are most appropriate to describe the measures of center and variability of distribution. The histogram depicts the distribution of time is positively skewed. So, option(b) is right one.

We have a graph present in above figure, which showes the amount of time in hours spent on homework per week for a sample of students. We have to select correct measures of center and variability. The graph is a histogram. From the graph we can see that the data is positively skewed. Now for skewed distribution we prefer median over mean as mean is more sensitive to the outliers. As the data(time) is in ratio scale we can use any of the measures of dispersion; but for skewed distribution IQR is preferred because of its robustness. In a word both median and IQR can handle outliers. Thus the appropriate answer is Median and IQR, option (c).

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Complete question :

The above figure complete the question

the graph below displays the amount of time to the nearest hour spent on homework per week for a sample of students. which measures of center and variability would be most appropriate to describe the given distribution? group of answer choices

a) mean and standard deviation

b) mean and iqr

c) median and standard deviation

d) median and iqr

e) median and range

Answer:

A triangle with side lengths of 38, 38, and 104 is an isosceles triangle. This is because it has two sides of equal length (the two sides that are both 38 units long).

Step-by-step explanation:

The statement that is not true of unnormalized data is option (d) unnormalized data is multivalued data.

Unnormalized data refers to raw data that has not been organized or processed in any way. It may contain redundancies, inconsistencies, and other issues that make it difficult to work with. However, it does not necessarily involve multivalued data.

Multivalued data refers to data that has multiple values for a single attribute. For example, if a customer can have multiple phone numbers, that data would be considered multivalued. Unnormalized data may or may not have multivalued data, depending on the nature of the data itself.

Therefore, the correct option is (d) unnormalized data is multivalued data

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The coordinates of point D on the graph are (2,-2). the square has a surface area of 25 square units. The perimeter of the square p is 20 units.

A (2,3), B (-3, 3), and C (-3, -2) are the given points.

In the graph below, the points are plotted.

The coordinates of point D on the graph are (2,-2).

In this case, AB = 5 units [from the graph].

The square's area = side * side

ABCD's square area = AB *AB

= 5×5

= 25 square units.

As a result, the square has a surface area of 25 square units.

The perimeter of the square p = 4 * side

                                               p = 4 *5 = 20 units.

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Similar question:

The three vertices of a square are A (2,3), B(-3, 3), and C (-3, -2). Plot these points on graph paper and

hence use it to find the coordinates of the fourth vertex. Also, find the area and perimeter of the square.

The remainder of the f(x) = 3x³ + 6x² - 3x + 2 and divisor x + 3 applying synthetic division is equal to -16.

Use synthetic division and the remainder theorem to find the remainder of f(x) when divided by x- c,

Set up the synthetic division table with c on the left side, and the coefficients of f(x) on the top row.

Bring down the first coefficient of f(x) into the first box below the horizontal line.

Multiply c by the number in the first box and write the result in the second box.

Add the number in the second box to the coefficient in the second column, and write the result in the third box.

Repeat steps 3 and 4 until you reach the last box. The number in the last box is the remainder.

Check if the remainder is zero. If it is zero, then x -c is a factor of f(x),

and g(x) = (x- c) is a factor of f(x).

Dividend is equal to,

f(x) = 3x³ + 6x² - 3x + 2

Divisor is equal to,

g(x) = x + 3

Synthetic division is attached in the figure.

Expressed in remainder theorem

3x² -3x + 6 + ( -16 / x + 3 )

Therefore, the remainder of the synthetic division for the given dividend and divisor is equal to -16.

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Answer:

It can be deduced that the set of fractions that is an example of reciprocal fractions include, 1/2, 3/1, and 1/6.

Step-by-step explanation:

The values of the positive intergers a and b is 2 and 3 respectively and the value of 2a+3b is 13.

An algebraic expression are the expression which consist the variables, coefficients of variables and constants. In the given problem, a and b are positive integers.  The given expression in the problem is: ^2b^3=108.

Let us the hit and trial method to make both the equation equal. For a=1 and b= 1 the expression will be equal to 1. For a =2 and b=3,

(2)^2(3)^3 = 108

(4)(27) = 108

108 = 108

Here, left hand side of the expression is equal to the right hand side of the expression for a =2 and b=3. Thus the value of a and b are,

a = 2

b = 3

The value of the expression we have to find is, 2a+3b. Put the values of a and b in the above expression, we get,

2a+3b = 2^(2)+3^(3)

2a+3b = 4+9

2a+3b = 13

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1/ 3 is the difference in the gierls that have blue eyes and brown eyes

Let's first find the difference in fractions between the number of girls with brown eyes and the number of girls with blue eyes.

Brown eyes: 7/12

Blue eyes: 1/4

To subtract these fractions, we need to find a common denominator, which in this case is 12. So, we'll convert the fractions to have the same denominator:

7/12 - (3/3)*(1/4) = 7/12 - 3/12

Now, subtract the fractions:

(7 - 3)/12 = 4/12

Simplify the fraction:

4/12 = (1/3)*(4/4) = 1/3

So, 1/3 more girls have brown eyes than blue eyes.

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13) The best prediction is that the college will need about 480 cookies.

14) The correct answer is Bus 47, with a median of 16.

For Question 13:

The total number of students surveyed is 225. Out of these, 27 students prefer cookies. So, we can estimate that approximately (27/225) * 4000 = 480 students will prefer cookies.

Therefore, the best prediction is that the college will need about 480 cookies.

For Question 14:

The correct graph for displaying the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.

For Question 15:

We can see that the median for Bus 18 is (10+12)/2 = 11 and the median for Bus 47 is (16+16)/2 = 16. Therefore, Bus 47 typically has the faster travel time.

The correct answer is Bus 47, with a median of 16.

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Answer:162.1

Step-by-step explanation:We know that the sum of supplementary angles is 180°Let the unknown angle be xThus,100° + x = 180°X = 180° – 100°X = 80°Hence, the unknown angle is 80 …I did it my own way ok…

The percent increase in the cost of the uniform from last year to this year is 25%.

To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.

The difference between this year's price and last year's price is:

$65 - $52 = $13

The original price (last year's price) is $52.

So the percent increase in the cost of the uniform is:

percent increase = (difference / original price) x 100

percent increase = ($13 / $52) x 100

percent increase = 0.25 x 100

percent increase = 25%

Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.

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the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation is 0.1, or 10%.

Let A be the event that Jim's vacation was in Alaska, and let S be the event that Jim went surfing during the vacation. We want to find P(A|S), the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation.

By Bayes' theorem, we have:

P(A|S) = P(S|A) * P(A) / P(S)

We can calculate each term as follows:

P(S|A) = 0.1: the probability that Jim went surfing during the vacation given that he was in Alaska.

P(A) = 0.5: the probability that Jim's vacation was in Alaska, since he tosses a fair coin to decide between Hawaii and Alaska.

P(S) = P(S|A) * P(A) + P(S|H) * P(H) = 0.1 * 0.5 + 0.9 * 0.5 = 0.5: the total probability of Jim going surfing during the vacation, since he either went surfing in Alaska with probability 0.1 or went surfing in Hawaii with probability 0.9.

Therefore, we have:

P(A|S) = P(S|A) * P(A) / P(S) = 0.1 * 0.5 / 0.5 = 0.1

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The probability of passing the true/false test of 60 questions if the minimum passing grade is 60% and all responses are random guesses is approximately 0.9802 or 98.02%.

Assuming that all responses are random guesses, we may describe this issue using a binomial distribution, where the number of right responses follows a binomial distribution with [tex]n = 60[/tex] and [tex]p = 0.5.[/tex]

If X represents the total number of accurate responses, it will follow a binomial distribution with[tex]n = 60[/tex] and [tex]p = 0.5[/tex] as its parameters.

If the passing grade is [tex]60%[/tex], then there must be a minimum of [tex]36[/tex]accurate responses [tex](0.6 * 60 = 36).[/tex]

The normal-approximation can be used to calculate the likelihood of receiving at least [tex]36[/tex] correct responses. We must determine the mean and variance of the binomial distribution in order to utilise the normal approximation.

The variance of a binomial distribution is

[tex]2 = np(1-p)[/tex]

[tex]= 60 * 0.5 * 0.5[/tex]

[tex]= 15[/tex]

and the mean is

[tex]= np[/tex]

[tex]= 60 * 0.5[/tex]

[tex]= 30.[/tex]

To calculate the probability of passing, we can use the normal distribution with mean 30 and variance 15 to approximate the binomial distribution with continuity correction.

[tex]P(X \geq 36) = P(Z \geq (36 + 0.5 - 30) / \sqrt{15})[/tex]

where Z is a standard normal random variable.

[tex]P(Z \geq 2.08) = 1 - P(Z \leq 2.08)[/tex]

[tex]= 1 - 0.0198[/tex]

[tex]= 0.9802[/tex]

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the probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

How to solve the question?

To calculate the probability that a randomly selected part-time student has a gym membership, we need to use conditional probability. Specifically, we need to use Bayes' theorem:

P(Gym Membership | Part-Time) = P(Part-Time | Gym Membership) * P(Gym Membership) / P(Part-Time)

Where:

P(Gym Membership | Part-Time) is the probability that a student has a gym membership given that they are part-time.

P(Part-Time | Gym Membership) is the probability that a student is part-time given that they have a gym membership.

P(Gym Membership) is the overall probability of a student having a gym membership (regardless of whether they are full-time or part-time).

P(Part-Time) is the overall probability of a student being part-time (regardless of whether they have a gym membership).

Let's start by filling in the values we know from the table:

P(Part-Time) = (40 + 25) / 155 = 0.5484

P(Gym Membership) = (30 + 25) / 155 = 0.3226

P(Part-Time | Gym Membership) = 25 / (30 + 25) = 0.4545

To find P(Gym Membership | Part-Time), we need to calculate P(Part-Time and Gym Membership). We can use the formula:

P(Part-Time and Gym Membership) = P(Part-Time | Gym Membership) * P(Gym Membership)

Plugging in the values we know, we get:

P(Part-Time and Gym Membership) = 0.4545 * 0.3226 = 0.1463

Now we can use this value, along with P(Part-Time) and P(Gym Membership), to calculate P(Gym Membership | Part-Time):

P(Gym Membership | Part-Time) = 0.1463 / 0.5484 ≈ 0.2667

Therefore, the probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

It's worth noting that this result is based on the assumption that the sample of 155 students is representative of the larger population of the university. If there are any biases or other factors that make this sample unrepresentative, then our calculated probability may not be accurate. Additionally, the results could be affected by other factors, such as the cost of gym membership or the availability of on-campus fitness facilities.

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By quadratic formula the equation that has the same solution(s) as X² − 12x + 49 = 22 is M. (x − 6)² = 9 since it has solutions x=3 and x=9 which are also solutions to X² − 12x + 49 = 22

The quadratic equation ax² + bx + c = 0 can be resolved using the quadratic formula.

that uses the constants (a, b, c) and the numerical coefficients.

When factoring cannot be utilized to solve the quadratic expressions, this approach of solving a quadratic equation is typically used.

x = √(b² - 4ac) / (-b √(b²) / (2a)

We must solve each of the preceding equations to determine which one has the same solution(s) as X²- 12x + 49 = 22 in order to determine which equation has the same solution(s) as X²- 12x + 49 = 22.

Let's start by figuring out X²- 12x + 49 = 22:

X² − 12x + 49 = 22

X² − 12x + 27 = 0

The quadratic formula can then be used to find the value of x:

x = √(b² - 4ac) / (-b√(b²) / (2a)

where a=1; b=-12; and c=27.

x = (-(-12) ±√((-12)² - 4(1)(27))) / (2(1))

x = (12 ±√(144 - 108)) / 2

x = (12 √(36))/ 2

x = (12 6) / 2

x = 6,3

So x = 6,3 is the answer to the equation X²- 12x + 49 = 22.

Let's now resolve each of the provided equations:

M. (x − 6)² = 9 (x -6)² -9=0

(x-6+3)(x-6-3)=0

(x-3)(x-9)=0, where x=3 or x=9

P. (x − 7)² = 22 (x-7)²-22=0

(x-7+√(22))=0

(x=7+√(22))

or (x=7-√(22))

R. (x + 7)² = 4.7 (x+7)²-4.7=0

(x+7+√(4.7))(x+7-√(4.7))=0

No effective remedies

S. (x − 12)²= −27 (x-12)²+27=0

No effective remedies

Therefore, the equation that has the same solution(s) as X² − 12x + 49 = 22 is M. (x − 6)² = 9

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The value of  51. 2 divided by 6. 4 using long division is 8.0

To find the value of 512 divided by 64, we can use long division. We start by dividing 5 (the first digit of 512) by 6 (the first digit of 64). Since 5 is less than 6, we bring down the next digit (1) to form the new dividend, 51. We then add a decimal point to the quotient and bring down the next digit (2) to form 512.

We repeat the process of dividing 51 by 6, which gives us 8 with a remainder of 3. We write the quotient (8) above the next digit of the dividend (2) and bring down the next digit (0) to form the new dividend, 30. We continue this process until we have brought down all the digits of the dividend.

At the end of the process, we get a quotient of 8.0, which is the value of our original expression, 51.2 divided by 6.4.

Therefore, 512 divided by 64 is equal to 8.0.

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First, let's calculate the monthly interest rate (i), which is the APR divided by 12 months:

i = APR / 12 months

i = 5.3% / 12

i = 0.00442 or 0.442%

Next, let's calculate the number of months (n) for the mortgage, which is 15 years multiplied by 12 months:

n = 15 years x 12 months/year

n = 180 months

Now, let's calculate the monthly payment (PMT) using the following formula:

PMT = P * i / [tex](1 - (1 + i)^(-n)[/tex])

where P is the principal amount, i is the monthly interest rate, and n is the number of months.

PMT = $325,000 * 0.00442 / (1 - [tex](1 + 0.00442)^(-180)[/tex]

PMT = $2,613.67 (rounded to the nearest cent)

Now, let's create the amortization table for the first two months:

Month | Payment | Interest | Principal | Remaining Balance

1 | $2,613.67 | $1,431.25 | $1,182.42 | $323,817.58

2 | $2,613.67 | $1,428.60 | $1,185.07 | $322,632.51

For each month, the Payment column shows the fixed monthly payment, the Interest column shows the calculated interest based on the remaining balance multiplied by the monthly interest rate, the Principal column shows the portion of the payment that goes towards reducing the principal, and the Remaining Balance column shows the remaining balance after subtracting the principal payment from the previous remaining balance.

The amortization table will continue in this manner for the remaining months until the mortgage is paid off.

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The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

To complete the two-month amortization table, we need to calculate the monthly payment, as well as the principal and interest amounts for each payment.

The formula for calculating a fixed-rate mortgage payment is:

[tex]Payment = P * r * (1 + r)^n / [(1 + r)^n - 1][/tex]

Where:

P = Principal amount borrowed

r = Monthly interest rate

n = Total number of payments

First, let's calculate the monthly interest rate.

Since the APR is an annual rate, we need to divide it by 12 to get the monthly rate:

Monthly interest rate = 5.3% / 12 = 0.0044167

Next, we need to calculate the total number of payments.

Since this is a 15-year mortgage, and we're completing a two-month amortization table, the total number of payments is:

Total number of payments = 15 years * 12 months per year = 180

Number of payments for two months = 2

Now we can plug these values into the formula to calculate the monthly payment:

Payment = [tex]$325,000 * 0.0044167 * (1 + 0.0044167)^180 / [(1 + 0.0044167)^180 - 1][/tex]

= $2,549.67

So the monthly payment is $2,549.67

Now we can use this value to complete the two-month amortization table:

Payment Interest Principal Balance

Month 1 $1,426.25 $1,123.42 $323,876.58

Month 2 $1,420.47 $1,129.20 $322,747.38

To calculate the interest and principal amounts for each payment, we use the following formulas:

Interest = Balance * Monthly interest rate

Principal = Payment - Interest

Balance = Balance - Principal

We start with the initial balance of $325,000 and apply the formulas for each payment.

The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

And so on, for each subsequent payment.

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Therefore , the solution of the given problem of volume comes out to be ceramic mug has a 5 inch height.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The indications for cubic measurements are litre and in3. However, you have to be cognizant of an object's volume in order to calculate its dimensions. Converting an object's weight into metric units like iii . and kilogrammes is a standard technique.

Here,

The following formula determines a cylinder's volume:

=> V = π * r² * h

where r is the cylinder's radius and h is its height, and is roughly equivalent to 3.14.

For the mug made of stainless steel:

1.5 inches is the radius (r).

Height in inches (h) is 8.5

With these values entered into the formula, we obtain:

=> V = 3.14 * (1.5)² * 8.5

=> V ≈ 3.14 * 2.25 * 8.5

=> V ≈ 60.14

The stainless steel mug has a 60 cubic inch volume, rounded to the nearest whole number.

Regarding the mug:

Radius (r) equals two inches

Given that it has the same volume as the stainless steel mug, its volume (V) is equal to 60 cubic inches.

=> 60 = 3.14 * (2)²* h

=> h = 60 / (3.14 * 4)

=> h ≈ 4.77

The ceramic mug has a 5 inch height.

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Answer:

Step-by-step explanation:

$10,008.61

Thus, the function has a minimum value of -2 at x = -1.

There are "hills and valleys" in functions, or points where their value reaches a minimum or maximum.

Locally, it may not be the lowest or maximum for the entire function.

Stated function:

g(x) = 2x² + 4x

Differentiate the function to find the critical points with respect to x.

g'(x) = 4x + 4  ...eq 1

Put g'(x) = 0

4x + 4 = 0

4(x + 1) = 0

x = - 1 (critical point)

Again Differentiate the function to check for maxima or minima:

g'(x) = 4x + 4

g''(x) = 4

g''(x) > 0 (minimum function)

At x = -1 , the function will be minimum.

Minimum value : Put x = -1 in function.

g(x) = 2(-1)² + 4(-1)

g(x) = 2 - 4

g(x) = -2

Thus, the function has a minimum value of -2 at x = -1.

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Answer:

D

Step-by-step explanation:

Look at the graph and find the lowest x value and the highest x value. We don't use y in the inequality because it is not a range question. Domain relates to x-values and range relates to y-values.

When you have found the lowest and highest x-values, look at their dots. If it is shaded, then the answer would contain a less than sign between the number and variable. If it shaded, then it would contain a less than or equal to sign.

Both of the dots with the lowest and highest values are shaded. And the lowest and highest values are -4 and 4 respectively.

Therefore, the answer is D.

The measurement of the angle labeled (3x)° include the following: 120°.

In Mathematics and Geometry, corresponding angles postulate simply refers to a theorem which states that corresponding angles are always congruent (equal) if the transversal intersects two parallel lines.

This ultimately implies that, the corresponding angles would always be congruent (equal) if a transversal intersects two (2) parallel lines.

60 + y = 180

y = 180 - 60

y = 120°

By applying corresponding angles postulate to both lines a, b, and w, we can reasonably infer and logically deduce that the following angles are congruent:

3x = 120°

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