find the linear approximation l(x) to y = f(x) near x = a for the function. f(x) = 1 x , a = 9

Answer:

Word. The word name

Step-by-step explanation:

I hope this helps you :)

The answer is 33.

A number is divisible by 9 if and only if the sum of its digits is divisible by 9. We can use this fact to count the number of a_n that are divisible by 9.

For any n, the sum of the digits in a_n is given by:

S_n = 1 + 2 + 3 + ... + n

This is the sum of an arithmetic sequence, which can be computed using the formula:

S_n = n(n+1)/2

Therefore, the sum of the digits in a_n is:

S_n = n(n+1)/2

We want to find the values of n for which S_n is divisible by 9. Since 9 is a factor of 3, we only need to consider the cases where n(n+1) is divisible by 3.

Case 1: n is divisible by 3

In this case, either n or (n+1) is divisible by 3. Therefore, S_n is divisible by 3, and hence by 9.

Case 2: n is not divisible by 3

In this case, neither n nor (n+1) is divisible by 3. Therefore, S_n is not divisible by 3.

Therefore, the only values of n for which S_n is divisible by 9 are those that are divisible by 3. There are 33 such values of n between 1 and 100 (namely, 3, 6, 9, ..., 99), so the answer is 33.

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The example of choosing candy falls under the dignified criteria of Qualitative data. Then the correct option required is Option B.

Qualitative data refers to data that is considered descriptive and conceptual which are collected through questionnaires, observation, and interviews. candy choices in the given question fall under the description of Qualitative data. Due to the  following reasons

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The possible 3rd degree binomial with a constant term of 888 is x^3 + 2x^2 + 3x + 888, for the given one degree of freedom.

To find a 3rd degree binomial with a constant term of 888, we can start by writing the general form of a 3rd degree binomial: ax^3 + bx^2 + cx + d.

Since we want the constant term to be 888, we can set d = 888.

Now, we need to choose values for a, b, and c. We have one degree of freedom, so we can choose any values for a, b, and c as long as they satisfy the condition of being a 3rd degree binomial.

For example, let's choose a = 1, b = 2, and c = 3.

Therefore, a possible 3rd degree binomial with a constant term of 888 is x^3 + 2x^2 + 3x + 888.

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The probability of both events A and B occurring together is 0.2491 or about 24.91%.

The formula for the probability of events A and B occurring together is given by:

P(A and B) = P(A ∩ B)

If events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event. In this case, if events A and B are independent, then we can use the multiplication rule of probability to find the probability of both events occurring together.

The multiplication rule states that the probability of two independent events A and B occurring together is equal to the product of their individual probabilities:

P(A and B) = P(A) * P(B)

In this problem, we are given that events A and B are independent, and we are also given the individual probabilities of each event:

P(A) = 0.47

P(B) = 0.53

Using the multiplication rule, we can find the probability of both events A and B occurring together:

P(A and B) = P(A) * P(B)

= 0.47 * 0.53

= 0.2491

Therefore, the probability of both events A and B occurring together is 0.2491 or about 24.91%.

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Answer: 50 degrees

Step-by-step explanation:

Answer:

Greater than or >

Step-by-step explanation:

Since it is negative the -1/2 is greater than the -3.75

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Convert -3.75 to fractions

\(\\ \rm\rightarrowtail \dfrac{-375}{100}\)

\(\\ \rm\rightarrowtail \dfrac{-75}{20}\)

\(\\ \rm\rightarrowtail \dfrac{-15}{4}\)

\(\\ \rm\rightarrowtail -3\dfrac{3}{4}\)

Answer:

1). g(x) = \(5^{3x}\)

2). g(x) = \(\frac{1}{3}5^{x}\)

3). g(x) = \(3(5)^{x}\)

4). g(x) = \(5^{\frac{1}{3}x}\)

Step-by-step explanation:

Parent function f(x) = \(a^{x}\) when transformed in the form of  \(g(x)=h(a^{\frac{x}{k} })\)

1). If h > 1, function is vertically stretched.

2). If 0 < h < 1, function is vertically compressed.

3). If k > 1, function is horizontally compressed.

4). If 0 < k < 1, function is horizontally stretched.

Parent function of the given functions in the question is f(x) = \(5^{x}\)

g(x)= \(\frac{1}{3}(5^{x})\), parent function is vertically compressed by a factor of \(\frac{1}{3}\).

g(x) = \(5^{3x}\), parent function 'f' is horizontally stretched by a factor of 3.

g(x) = \(5^{\frac{x}{3}}\), parent function 'f' is horizontally compressed by a factor of \(\frac{1}{3}\).

g(x) = \(3(5^{x})\), parent function 'f' is vertically stretched by a factor of 3.

A grain of rice contains about 0.029 milliliters of volume.

A grain of rice is a tiny, ingestible seed that comes from either Oryza sativa (Asian rice) or Oryza glaberrima, two types of grass (African rice). A single grain of rice is round or oval in shape and measures about 3–4 millimeters in length. A grain of rice has a volume of 0.029 milliliters and a mass of approximately 0.05 grams. The type of rice and the method of processing affect the size and form of a single grain of rice. Over half of the world's population relies heavily on rice as a source of nutrition and as a staple food in many different cultures. Sushi, risotto, rice pudding, and many more recipes all use rice as an ingredient.

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The primary tool for determining whether the assumptions made about the regression model are appropriate is residual analysis.

Regression analysis is a collection of statistical techniques used in statistical modelling to estimate the associations between a dependent variable and one or more independent variables. Regression analysis is a mathematical method for determining which of those factors has an effect.

Regression analysis is an effective statistical tool for examining the connection between two or more variables of interest. When the dependent and independent variables are connected in a linear or nonlinear form and the goal variable has a set of continuous values, it is extensively employed. As a result, regression analysis methodologies aid in the establishment of causal links between variables, as well as in the modelling of time series and forecasting.

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Answer:

62-24=38

or 24 + x = 62

Step-by-step explanation:

The equation to determine whether Owen earned $38 or $31 on Saturday afternoon ⇒ $24 + $ x = 62.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

According to the questions,

On Saturday morning, Owen earned $24 raking leaves.

By the end of the afternoon he had earned a total of $62.

The equation to determine whether Owen earned $38 or $31 on Saturday afternoon.

⇒ $62 - $24 = $38

⇒ $24 + $ x = 62

Hence the required equation is $24 + $ x = 62.

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20 different pizzas

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

Explanation:

Consider 3 slots to fill. I'll label them slot A, B, C.

There are 6 choices for slot A, then 5 choices for B, and 4 for C. We count down by one each time since we cannot reuse a topping.

There would be 6*5*4 = 30*4 = 120 permutations if order mattered.

However, order doesn't matter with pizza toppings. So we must divide by 3*2*1 = 6 (this is the number of ways to arrange any group of 3 things)

We get 120/6 = 20 as the final answer

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

Alternatively, you can use the nCr combination formula following these steps.

n C r = (n!)/(r!(n-r)!)

6 C 3 = (6!)/(3!*(6-3)!)

6 C 3 = (6!)/(3!*3!)

6 C 3 = (6*5*4*3!)/(3!*3!)

6 C 3 = (6*5*4)/(3!)

6 C 3 = (6*5*4)/(3*2*1)

6 C 3 = (120)/(6)

6 C 3 = 20 different pizzas possible

As the third to the last line shows, we have 6*5*4 up top and 3*2*1 down below. This matches exactly what was discussed in the previous section.

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

Yet another alternative is to use Pascal's Triangle (see below) and we locate the row that has 1,6,... at the start. We circle the fourth item of this row that corresponds to 6C3 = 20

Answer:

\(\boxed {Vertex = (-7, 2)}\\\boxed {Focus = (0, \frac{49}{8})}\)

Step-by-step explanation:

Completing the square :

x² + 14x - 8y + 65 = 0

x² + 14x + 49 - 49 - 8y + 65 = 0

(x + 7)² - 8y + 16

(x + 7)² = 8y - 16

⇒ x = -7, y = 2 (Vertex)

Finding a :

⇒ x² = 4ay

⇒ (-7)² = 4(2)a

⇒ a = 49/8

Finding the focus :

⇒ (0, a)

⇒ (0, 49/8) (Focus)

Answer:

\( \boxed{Volume \: of \: rectangular \: prism = 2166 \: {ft}^{3}} \)

Explanation:

Volume of rectangular prism is same as volume of cuboid

Length = 19 ft

Width = 6 ft

Height = 19 ft

Volume of rectangular prism = Length × Width × Height

= 19 × 19 × 6

= 19² × 6

= 361 × 6

= 2166 ft³

Answer:

5.76106287

Step-by-step explanation:

Answer: 5.76106287488

Step-by-step explanation:

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Step-by-step explanation:

Let the other endpoint be (x,y)

Since, (1,6) is the midpoint between (9,1) and (x,y)

Therefore,

1=(9+x)/2

=> 2=9+x

=> x= -7

and,

6=(1+y)/2

=>12= 1+y

=> y=11

So, the other endpoint is ( -7, 11)

Answer:

Step-by-step explanation:

Let the coordinates of Endpoint 2 be

(x ,y)

The midpoint of the endpoints is given by

\((1,6) = ( \frac{9 + x}{2} , \frac{1 + y}{2} )\)

Where x and y are coordinates of Endpoint 2

Comparing with the midpoint we have

\(1 = \frac{9 + x}{2} \\ 2 = 9 + x \\ \\ x = 2 - 9 \\ \\ x = - 7\)

\(6 = \frac{1 + y}{2} \\ 12 = 1 + y \\ \\ y = 12 - 1 \\ \\ y = 11\)

Therefore x = - 7 and y = 11

The coordinates of Endpoint 2 are

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From the given information provided, the number of people having brown eyes in town is 180.

If the probability that a person in the town has brown eyes is 2/5, then we can expect that 2 out of every 5 people have brown eyes.

To find the number of people in the survey who would be expected to have brown eyes, we can use the following proportion:

(2/5) = (x/450)

where x is the number of people expected to have brown eyes.

Solving for x, we can cross-multiply:

5x = 2 × 450

5x = 900

x = 180

Therefore, the expected number of people in the survey who would have brown eyes is 180.

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Answer:

d or c

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

Since the formula for grid's are y by x Y=2 X=5 put them as a fraction there you have 2/5 as I think it is

Answer:

k ≤ 7

Step-by-step explanation:

\( \: \: \: \: \: \: \)

\( = \: \: \: \: r = 5\)

Step-by-step explanation:

\(7 + 4(r + 3) = 9r - 6\)

\(7 + 4r + 12 = 9r - 6\)

\(19 + 4r = 9r - 6\)

\(19 + 9r = - 6\)

\(4r - 9 = - 6 - 19\)

\( - 5r = - 6 - 19\)

\( - 5r = - 25\)

\( = \: \: \: \: r = 5\)

The Keith will spend $16 to rent 1 movie and 2 video games from the store.

Let's assume the rental fee for each movie is "m" and the rental fee for each game is "g".

From the given information, we can form the following system of equations:

3m + 2g = 25 (Calvin's rental)

2m + g = 14.75 (Samantha's rental)

We can solve for "m" and "g" by using elimination or substitution method. Here, we will use substitution method.

From the second equation, we can solve for "g" in terms of "m":

g = 14.75 - 2m

Substituting this into the first equation, we get:

3m + 2(14.75 - 2m) = 25

Simplifying this, we get:

3m + 29.5 - 4m = 25

-m + 29.5 = 25

-m = -4.5

m = 4.5

Now that we know the rental fee for each movie is $4.50, we can find the rental fee for each game by substituting "m" into either of the original equations:

2(4.5) + g = 14.75

g = 14.75 - 9 = 5.75

So the rental fee for each game is $5.75.

To find how much Keith will spend to rent 1 movie and 2 video games, we can simply add up the rental fees:

1(4.5) + 2(5.75) = 16

Therefore, Keith will spend $16 to rent 1 movie and 2 video games from the store.

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Answer:

From left to right:

90°  (clockwise or counterclockwise)

45°  (clockwise or counterclockwise)

72°  (clockwise or counterclockwise)

Step-by-step explanation:

360/4 = 90°

360/8 = 45°

360/5 = 72°

The null hypothesis is denoted by the symbol H0, not H1. The null hypothesis is a statement that is typically formulated in terms of population parameters or characteristics, not sample statistics. It states that there is no significant or meaningful effect or relationship between variables or treatments under investigation.

The alternative hypothesis (H1 or Ha) is the complementary statement to the null hypothesis, representing the claim or hypothesis that contradicts the null hypothesis. The alternative hypothesis is often formulated to suggest that there is a significant effect or relationship present.

The null hypothesis, denoted by the symbol H0, is a fundamental concept in hypothesis testing and statistical inference. It is formulated as a statement about the population parameters or characteristics under investigation. The null hypothesis typically assumes that there is no significant effect, difference, or relationship between variables or treatments being studied.

In statistical hypothesis testing, researchers aim to gather evidence to either reject or fail to reject the null hypothesis. If the evidence is strong enough, the null hypothesis is rejected in favor of the alternative hypothesis, suggesting that there is a significant effect or relationship present.

The alternative hypothesis, denoted by H1 or Ha, is the complement to the null hypothesis. It is usually stated as the hypothesis that contradicts the null hypothesis and supports the researcher's claim or hypothesis. The alternative hypothesis asserts that there is a significant effect, difference, or relationship between variables or treatments.

It is important to note that the formulation of the null and alternative hypotheses depends on the research question and the specific context of the study. The null hypothesis is essential in hypothesis testing as it provides a baseline against which the alternative hypothesis can be compared and evaluated using statistical methods.

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The graph of the system of inequalities is attached to the solution.

Given is a system of inequalities, y > -x/3+5 and y ≥ 3,

So, we will simply find the coordinates of both the inequalities, and plot them,

We know that the solution of a system of inequalities is all the part which is common in both the inequalities.

So, here the first inequality,

y > -x/3+5

Finding the coordinates,

y = -x/3+5

Put x = 0

y = 5

(0, 5)

Put y = 0,

x = 15

(15, 0)

Therefore, the inequality will pass from these two lines, and since the sing is > so the shaded part will be above the line and the line will be dotted.

And y ≥ 3,

In this inequality the graph will simply pass by y = 3 and since the sing is ≥ so the shaded part will be above the line and the line will solid line.

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Answer:

Step-by-step explanation:

The determinant is the price of related goods, specifically the price of fuel. The increase in fuel prices would lead to a decrease in the demand for Ford F150 trucks, shifting the demand curve to the left.

The price of related goods is an important determinant of demand.

The drastic increase in fuel prices is likely to shift the demand curve for Ford F150 trucks to the left.

This is because consumers tend to reduce their demand for vehicles with lower fuel efficiency when fuel prices increase.

The determinant of this shift in demand is the price of related goods, specifically, the price of gasoline.

When the price of gasoline increases, it affects the demand for vehicles that are less fuel-efficient, such as trucks.

Therefore, the price of related goods is an important determinant of demand.

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The Area of the composite figure = area of the rectangle + area of the triangle = 148.5 cm².

The figure formed by the arrow can be decomposed into a rectangle and a triangle.

The area of the composite figure = area of the rectangle + area of the triangle.

Find the area of the rectangle:

Length = 12 cm

Width = 11 cm

Area of the rectangle = (length)(width) = (12)(11)

Area of the rectangle = 132 cm²

Find the area of the triangle

Base = 11 cm

Height = 15 - 12 = 3 cm

Area of the triangle = 1/2(b)(h) = 1/2(11)(3)

Area of the triangle = 16.5 cm²

Area of the composite figure = area of the rectangle + area of the triangle = 132 + 16.5 = 148.5 cm².

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Answer:

60cm and 100cm

Step-by-step explanation:

12 parts in total

240/12 is 20

each part is 20

3x20 is 60 and 5x20 is 100

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad N(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +2}{2}~~~ ,~~~ \cfrac{ y -3}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(5~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +2 }{2}=5\implies x+2=10\implies \boxed{x=8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -3 }{2}=1\implies y-3=2\implies \boxed{y=5}\)