Please help with this! The problem I need help with is problem 7.

C) f is decreasing for x<0 because f′(x)<0 for x<0. , we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of f is f′(x)=x2−a2=(x−a)(x+a).

This implies that f′(x)<0 when x<−a or x>a. From the derivative, we can deduce that f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of the function f is f′(x)=x2−a2=(x−a)(x+a), where a is a positive constant. This means that the derivative is negative when x<−a or x>a. We can use this information to determine the behavior of the function. Since the derivative is negative when x is less than zero, we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

Learn more about function here

https://brainly.com/question/29633660

#SPJ4

Probability calculations are performed for random variables including normal distribution, luxury hotel rates, and sample means of highway drivers' speeds.

In the given problems, different scenarios involving random variables are analyzed using probability concepts. The first scenario deals with a random variable following a normal distribution with a mean of 137 and a standard deviation of 24. The probability of selecting a value between 119 and 150 is calculated by standardizing the values using the z-score formula and referring to the standard normal probability table. Similarly, the probability of selecting a value between 139 and 180 is determined.

In the second scenario, the daily rates of luxury hotels are considered. The average daily rate is $239.89 with a standard deviation of $21.65. The probability of selecting a hotel with a rate less than $260 is calculated by standardizing the value and referring to the standard normal probability table. Similarly, the probability of selecting a hotel with a rate more than $268 is determined.

In the third scenario, a study on highway drivers' speeds is discussed. The average speed of the population is 59.9 MPH with a standard deviation of 5.3 MPH. The probabilities of sample means less than 58 MPH for two different sample sizes, 30 and 45 drivers, are calculated. These probabilities indicate the likelihood of obtaining sample means below the given values based on the population parameters.

Lastly, in the fourth scenario, a survey on home purchases is examined. The proportion of first-time buyers is 43%, and a random sample of 185 people who recently purchased homes is selected. The standard b of the proportion is calculated, representing the variability of the sample proportion compared to the population proportion. Additionally, the probability of less than 84 people in the sample being first-time buyers is determined, which provides insight into the likelihood of observing a specific number of first-time buyers in the sample.

For more information on distribution visit: brainly.com/question/33175925

#SPJ11

The logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

The exponential function in this problem is defined as follows:

8e^x-5 = 0.

The equation can be sorted isolating the exponential as follows:

8e^x = 5.

e^x = 5/8.

The natural logarithm(symbolized by the ln) is the opposite of the exponential function, hence the logarithmic form of the equation is presented as follows:

ln(e^x) = ln(5/8).

As stated above, the natural logarithm and the exponential functions are inverse functions, meaning that:

ln(e^x) = x.

Thus the logarithmic form of the exponential equation 8e^x-5 = 0 is given as follows:

x = ln(5/8).

More can be learned about exponential functions and logarithms at https://brainly.com/question/25537936

#SPJ1

Answer:

i cant see the pic, its too blurry can you re-upload another ? x

Step-by-step explanation:

The two triangles called congruent if two sides the associated angle in one triangle is congruent with two sides and the contained angle in the other triangle.

According to the Side-Angle-Side theorem of congruency, two sides and the angle they produce are congruent if they are equivalent to two sides as well as the angle of another triangle.

Thus, two triangles are termed to be comparable if their two sides are in the same ratio as the two sides of some other triangle and their two sides' angles inscribed in both triangles are equal.

To know more about the Side-Angle-Side (SAS), here

https://brainly.com/question/22472034

#SPJ4

The equilibrium price and quantity for each pair of demand and supply functions are as follows:

a. Q = 10 - 2P

To find the equilibrium, we set the quantity demanded equal to the quantity supplied:

10 - 2P = P

By solving this equation, we can determine the equilibrium price and quantity. Simplifying the equation, we get:

10 = 3P

P = 10/3 ≈ 3.33

Substituting the equilibrium price back into the demand or supply function, we can find the equilibrium quantity:

Q = 10 - 2(10/3) = 10/3 ≈ 3.33

Therefore, the equilibrium price is approximately $3.33, and the equilibrium quantity is also approximately 3.33 units.

b. Q = 1640 - 30P

Setting the quantity demanded equal to the quantity supplied:

1640 - 30P = P

Simplifying the equation, we have:

1640 = 31P

P = 1640/31 ≈ 52.90

Substituting the equilibrium price back into the demand or supply function:

Q = 1640 - 30(1640/31) ≈ 51.61

Hence, the equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In summary, for the demand and supply functions given:

a. The equilibrium price is approximately $3.33, and the equilibrium quantity is approximately 3.33 units.

b. The equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In the first paragraph, we summarize the steps taken to determine the equilibrium price and quantity for each pair of demand and supply functions. We set the quantity demanded equal to the quantity supplied and solve the resulting equations to find the equilibrium price. Substituting the equilibrium price back into either the demand or supply function allows us to calculate the equilibrium quantity.

In the second paragraph, we provide the specific calculations for each pair of functions. For example, in case a, we set Q = 10 - 2P equal to P and solve for P, which gives us P ≈ 3.33. Substituting this value into the demand or supply function, we find the equilibrium quantity to be approximately 3.33 units. We follow a similar process for case b, setting Q = 1640 - 30P equal to P, solving for P to find P ≈ 52.90, and substituting this value back into the function to determine the equilibrium quantity of approximately 51.61 units.

Learn more about functions here:

https://brainly.com/question/31062578

#SPJ11

According to the question Rounded to four decimal places, the probability is approximately 0.00001385, or approximately 0.0014%.

To calculate the probability of obtaining a straight flush in a five-card poker hand, we need to determine the number of possible straight flush hands and divide it by the total number of possible five-card hands.

A straight flush consists of five consecutive cards of the same suit. There are four suits in a standard deck of cards (hearts, diamonds, clubs, and spades), and for each suit, there are nine possible consecutive sequences (Ace, 2, 3, 4, 5, 6, 7, 8, 9; 2, 3, 4, 5, 6, 7, 8, 9, 10; etc.). Therefore, there are \(\(4 \times 9 = 36\)\) possible straight flush hands.

The total number of possible five-card hands can be calculated using the concept of combinations. In a standard deck of 52 cards, there are \(\({52 \choose 5}\)\) different ways to choose five cards. The formula for combinations is \(\({n \choose k} = \frac{n!}{k!(n-k)!}\), where \(n\)\) is the total number of items and \(\(k\)\) is the number of items being chosen.

Using the formula, we have \(\({52 \choose 5} = \frac{52!}{5!(52-5)!} = 2,598,960\).\)

Therefore, the probability of obtaining a straight flush in a five-card poker hand is:

\(\[\frac{\text{{number of straight flush hands}}}{\text{{total number of five-card hands}}} = \frac{36}{2,598,960} \approx 0.00001385\]\)

Rounded to four decimal places, the probability is approximately 0.00001385, or approximately 0.0014%.

To know more about probability visit -

brainly.com/question/17085484

#SPJ11

The required coordinates of point B will be (2/9, -14/9).

Point A is at ( -3,4) and Point C is at ( 2,-6 )

Given that point B on line, AC suck as the ratio of AB to AC is 4:5

The coordinates of point B will be,

{[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}

Breaking it down, the x coordinate is (mx2+nx1)/(m+n) and the y coordinate is (my2+ny1)/(m+n)

As per the question, m = 4 and n = 5

The coordinates of point B :

⇒ {[(4×-3+5×2)/(4+5)],[(4×4+5×-6)/(4+5)]}

⇒ {[(-12+10)/(9)],[(16-30)/(9)]}

⇒ (2/9, -14/9)

Thus, the required coordinates of point B will be (2/9, -14/9).

Learn more about the distance between two points here:

brainly.com/question/15958176

#SPJ1

Answer:

-10*F at 7pm

Step-by-step explanation:

Answer:

Step-by-step explanation:

factored form of x^2 - 12x + 36

(x - 6)(x - 6) or (x - 6)^2

answer is D

The speed is:

Work/explanation:

To find the train's speed, we use the formula:

\(\large\textsl{$Speed=\dfrac{distance}{time}$}\)

In our case, the distance is 400 miles, and the time is 2 hours.

So, I plug in the data:

\(\large\text{$Speed=\dfrac{400}{2}$}\)

\(\large\text{$Speed=200\:mph$}\)

Hence, the train's speed is 200 mph.

Answer:

200 mph (321.87 km/h)

Explanation:

If a train travels 400 miles in two hours, it would travel half of that in one hour (\(400\) ÷ \(2\)) which is 200 miles. To convert mph to km/h, just multiply by 1.61 (to be exact, 1.60934).

The distance that she runs from one corner of the field to another is given as follows:

147.1 yards.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The distance in this problem is the diagonal of a rectangle, which is the hypotenuse of a right triangle in which the length and the width are the sides, hence:

d² = 85² + 120²

d = sqrt(85² + 120²)

d = 147.1 yards.

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

64

x=154(vertically opposite angle)

d =p

then mpn =154-90 = 64

angle epm is straight angle

Answer:

0.296 square km or 296000 square meters

Step-by-step explanation:

first of all to find the area you multiply 0.74 and 0.4 to get 0.296 square kilometers then you multiply by 1 million to convert it to square meters

would be amazing if you marked this as brainliest

\((x^{-6}/x^{2} )^{3}\) = \(1/x^{24}\) is expression is equivalent to (start fraction x superscript negative 6 baselines over x squared end fraction) cubed.

Given:

\((x^{-6}/x^{2} )^{3}\)

Determine the equivalent expression

\((x^{-6}/x^{2} )^{3}\)

First, we need to evaluate the expression in the bracket:

Indices are used to show numbers that have been multiplied by themselves. They can also be used to represent roots, such as the square root, and some fractions. The laws of indices enable expressions involving powers to be manipulated more efficiently than writing them out in full.

So, apply the following law of indices:

\(w^{x} /w^{y} = w^{x-y}\)

So,

\((x^{-6}/x^{2} )^{3}\) becomes:

=> \(x^{(-6-2)^{3}\)

=> \(x^ {(-8 )^{3}\\\)

Again apply the following law of indices:

\((w^m)^n = w^m^n\)

Open the bracket

=> \(x^{-8 * 3}\)

=> \(x^{-24}\)

Convert the above expression to a fraction:

= \(1/x^{24}\)

Hence, \((x^{-6}/x^{2} )^{3}\) = \(1/x^{24}\)

To learn more about the law of indices: https://brainly.com/question/27432311

#SPJ4

Answer:

S.I=$3375

Step-by-step explanation:

S.I=PRT/100

S.I=750×15×3/100

S.I=33750/10

S.I=$3375

The location of the treasure on the treasure map is (b) (7.6,8.8)

The ratio is given as:

\(m : n = 5 : 9\)

The coordinates of the rock and the tree are:

\(Rock =(3,2)\)

\(Tree = (16,21)\)

The x and y coordinates of the location of the treasure are:

\((x,y) = (\frac{mx_2 + nx_1}{m + n},\frac{my_2 + ny_1}{m + n})\)

So, we have:

\((x,y) = (\frac{5 \times 16 + 9 \times 3}{5 + 9},\frac{5 \times 21 + 9 \times 2}{5 + 9})\)

\((x,y) = (\frac{107}{14},\frac{123}{14})\)

\((x,y) = (7.6,8.8)\)

Hence, the location of the treasure is (b) (7.6,8.8)

Read more about line segment ratios at:

https://brainly.com/question/14382744

Answer:

p and m or A. and D.

Step-by-step explanation:

Answer:

D. isosceles triangle

Step-by-step explanation:

The two angles are equal but the third angle will not be. Therefore, a triangle with two equal angles and one not is isosceles.

Answer:

The answer is C if i get it wrong then who ever gave you that is oof

Step-by-step explanation:

Answer:

19.5625

Step-by-step explanation:

To find the mean, you add all of your values together and divide by the number of values you have.

Here are the values in the dot plot listed:

12, 12, 15, 15, 15, 15, 16, 18, 20, 20, 22, 25, 25, 25, 29, 29

To find the mean:

(12 + 12 + 15 + 15 + 15 + 15 + 16 + 18 + 20 + 20 + 22 + 25 + 25 + 25 + 29 + 29)/16 = 19.5625

The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

Learn more about Regression line at:

https://brainly.com/question/14984940

#SPJ4

Answer:

24

Step-by-step explanation:

0.2 * 120 = 24

also, 120% of 20 = 24

Hey ! there

Answer:

Step-by-step explanation:

In this question we are asked , What is 20% of 120 . That means we are provided with a number which is 120 and we've to find out its 20% .

Solution : -

\( \quad \dashrightarrow \qquad \: \: 20\% \: of \: 120\)

Where ,

Now ,

\( \quad \dashrightarrow \qquad \: \: (20 \times \dfrac{1}{100} ) \times 120\)

\( \quad \dashrightarrow \qquad \: \: \dfrac{20}{100} \times 120\)

Cancelling zero :

\( \quad \dashrightarrow \qquad \: \: \dfrac{2 \cancel{0}}{1 \cancel{0} \cancel{0} } \times 12 \cancel{0}\)

We get ,

\( \quad \dashrightarrow \qquad \: \: 2 \times 12\)

\( \quad \dashrightarrow \qquad \: \: \green{\underline{\boxed{\frak{ 24}}}} \quad \bigstar\)

The directional derivative of h at (2, 2, 2) in the direction of the vector v is 24sqrt(2).

To find the directional derivative of the function h(r, s, t) = ln(3r^6s^9t) at the point (2, 2, 2) in the direction of the vector v = 8i + 24j + 12k, we need to first find the gradient of h at that point:

∇h(2, 2, 2) = (∂h/∂r, ∂h/∂s, ∂h/∂t)|_(2,2,2)
= (18/2, 54/2, 36/2)
= (9, 27, 18)

Next, we normalize the vector v to get a unit vector u in the direction of v:

||v|| = sqrt(8^2 + 24^2 + 12^2) = sqrt(800) = 20sqrt(2)
u = (1/||v||) v = (1/20sqrt(2))(8i + 24j + 12k) = (1/sqrt(50))(i + 3j + k)

The directional derivative of h in the direction of v is then given by the dot product of the gradient of h at (2, 2, 2) and the unit vector u:

D_v h(2, 2, 2) = ∇h(2, 2, 2) · u
= (9, 27, 18) · (1/sqrt(50))(i + 3j + k)
= (9/sqrt(50)) + (81/sqrt(50)) + (18/sqrt(50))
= (108/sqrt(50))
= 24sqr

To learn more directional derivative go to:

https://brainly.com/question/29451547

#SPJ11

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer:

(x + 7)(x - 4) = x2 - 4x + 7x - 28 = x2 + 3x - 28

Step-by-step explanation:

Volume of Washing machine = Volume of Rectangle

= Length x Width x Height

= 5 x 6 x 6

\( = 180ft^{3} \)

The alternative hypothesis would be: The proportion of people who own cats is smaller than 90%.

The null hypothesis for this test would be: The proportion of people who own cats is equal to or greater than 90%.

To conduct the hypothesis test, we would need to collect a random sample of 1400 individuals and determine how many of them own cats. Based on this information, we could calculate the sample proportion of cat owners and use this to test the claim that the population proportion is smaller than 90%.

We would use a one-tailed hypothesis test with a significance level of 0.005. If the p-value for our test is less than 0.005, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90%.
Hi! I'd be happy to help you with this question. You want to test the claim that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.

To do this, we will set up our null and alternative hypotheses as follows:

Null Hypothesis (H0): The proportion of people who own cats is equal to 90% (p = 0.90)
Alternative Hypothesis (H1): The proportion of people who own cats is smaller than 90% (p < 0.90)

Here's a step-by-step explanation of how to test this claim:

1. Determine the sample size (n) and the number of cat owners in the sample (x): In this case, n = 1400, and x = 615.

2. Calculate the sample proportion (p-hat): p-hat = x/n = 615/1400 ≈ 0.439.

3. Determine the significance level (alpha): In this case, alpha = 0.005.

4. Calculate the standard error (SE) of the sample proportion: SE = sqrt[p*(1-p)/n] = sqrt[0.9*(1-0.9)/1400] ≈ 0.008.

5. Calculate the z-score: z = (p-hat - p)/SE = (0.439 - 0.9)/0.008 ≈ -57.63.

6. Find the critical z-value for a one-tailed test at the 0.005 significance level: z-critical = -2.576 (from a standard normal distribution table).

7. Compare the calculated z-score with the critical z-value: Since the calculated z-score (-57.63) is less than the critical z-value (-2.576), we reject the null hypothesis.

In conclusion, based on this analysis, we have enough evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.

Learn more about alternative hypothesis at: brainly.com/question/27335001

#SPJ11

Answer:

I'm not sure but I believe it is "Three plus one-half times x."