show that f is continuous on (−[infinity], [infinity]). f(x) = 1 − x2 if x ≤ 1 ln(x) if x > 1

The resulting sampling technique is Stratified sampling.

As in the concept of statistical study, sampling methods refer to how we select members from the population to be in the study and if a sample isn't randomly selected, it will probably be biased in some way and the data may not be representative of the population.

Here we need to find the type of sampling method.

Here the Stratified random sampling involves classifying the units of the population into different strata.

And the give units in each stratum should possess similar characteristics which then allows the researcher to pick a sample from each.

Then the stratified sampling approach can be divided into proportionate stratified sampling and disproportionate stratified sampling

Therefore, these method is employed in cases where the population is heterogeneous.

So, option (b) is correct.

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The first quartile of miles driven is 218 miles.

Quartiles are three values ​​that divide the sorted data into four parts, each of which has the same observation value.

The four quarters that divide the dataset into quartiles are:

Let's arrange the data in an order:

211,212,218,223,231,233,245,261,278,299

Since the data has 10 observation, for which the median will be simply the average of two middle terms i.e.5th and 6th term dividing the data in two halves.

Median: 232

First half: 211,212,218,223,231

Second half: 233,245,261,278,299

As, quartiles are the medians of each half,

First quartile: 218

Third quartile: 261

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Answer:

38 full batch with a remainder of 3

Step-by-step explanation:

18*7 + 15*7 = 231

231/6 = 38 r3

Answer:

the anwser is b

Step-by-step explanation:

Your answer would be x = 2 ± √2

Step-By-Step Solution:

Step one:

9x² - 36x + 32 = 14

Step two:

9x² - 36x + 32 - 14 = 14 - 14

9x² - 36x + 18 = 0

Now we use the quadratic formula.

Step three:

Plug the numbers into the quadratic formula.

x = [tex]\frac{-b±\sqrt{b^{2} - 4ac } }{2a}[/tex]

x = [tex]\frac{-(-36 ± \sqrt{(-36^{2})-4(9)(18 } )}{2(9)}[/tex]

x = [tex]\frac{36 ± \sqrt{648} }{18}[/tex]

x = 2 + √2 or x = 2 - √2

Answer:

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

Given equation:

Solve it in below steps:

Answer:

To prove that 16^5+16^4 is divisible by 17 using factoring, first rewrite the expression 16^5+16^4 using the distributive law as 16^4*(16+1). Then, note that 16+1 is divisible by 17. Since 16^4 is also divisible by 17, the expression 16^4*(16+1) is also divisible by 17. Therefore, 16^5+16^4 is divisible by 17.

Answer:

10 Guests

Step-by-step explanation:

200 - 75 = 125 (We need to find a number that will spend 125 dollars)

125 / 12.50 = 10

12.50 x 10 = 125

So the answer is 10

The domain of the function y = 2x + 5 is [-4, 1), and the range of the function is  [5, 7). The graph is also attached below.

A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.

Given:

As you can see from the graph, the coordinates of the line are (0, 5) and (1,7),

Calculate the equation of the line as shown below,

y - 5 = (7 - 5) / (1 -0) (x-0)

y - 5 = 2 (x +0)

y = 2x + 5

The domain of the above equation can be determined from the graph,

Domain = [-4, 1)

Range = [5, 7)

The graph is also attached below.

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The equation of the line is y = x. Then the rule of reflection is (x, y) ⇒ (y, x).

It is the image of the point which is located in the opposite direction of a given point.

The rule of the refection is given will be

Firstly, the rule for reflecting a point about the line y = x is;

While reflecting on the line y = x, we get the reflected points by swapping the coordinates.

The equation of the line that passes through (0, 0) and (1, 1) is given as,

y - 0 = [(1 - 0) / (1 - 0)](x - 0)

y = x

The equation of the line is y = x. Then the rule of reflection is given as,

(x, y) ⇒ (y, x)

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Answer:

The answer is ab32

Step-by-step explanation:

ab x 8 x 4 = ab32

Answer: a^4b^32

Step-by-step explanation: (ab^8)^4 = (ab^8)(ab^8)(ab^8)(ab^8) = a^4b^32

The Valdez family left at noon for a 4-hour trip to visit relative. They topped 1 hour time for lunch and 2 hour to visit an amusement park.The Valdez family would have arrived at their relative's house at 5 pm.

1. The Valdez family left at noon, so they had 12 hours to get to their relative's house.

2. They stopped for 1 hour for lunch, so they had 11 hours left.

3. They then stopped for 2 hours at the amusement park, so they had 9 hours left.

4. 9 hours later would be 9 pm.

5. However, since it is summer, the clocks are set to daylight savings time and it is currently one hour ahead, so the time is actually 5 pm.

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Answer:

7.4 mins

Step-by-step explanation:

135 -----> 1 min

1000 ----> x

1000/135 mins = x

= 7.4 mins

Answer:

To determine how long it will take to fill 1000 containers at a rate of 135 containers per minute, you can use the formula: time = number of containers / filling rate. In this case, the filling rate is 135 containers per minute, and the number of containers you want to fill is 1000. Plugging these values into the formula, we get: time = 1000 / 135 = 7.41 minutes.

Answer:

3900 is decreased.$74100 is new value

Step-by-step explanation:

5% of 78000 subtracted by 78000...

The distance between two buoys by the trigonometric function will be 175.48 feet.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

As per the given situation is making a right angle triangle.

By tan trigonometric function,

tan21.3° = BC/450

BC = 175.48 feet

Hence "According to the trigonometric function, there will be 175.48 feet between two buoys.".

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The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.

Given that,

The expression is -4(5+(-2))

We have to find what is the solution for the given numerical expression.

We know that,

Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Take the numerical expression

-4(5+(-2))

Adding 5+(-2)

Multiply + - we get -

So,

5-2=3

-4(5-2)=-4(3)

Multiply 4 to 3

-4(3)=-12

Therefore, The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.

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Answer:

l = 2.55 meters

Step-by-step explanation:

Tunnels are usually in cylinder shape

Surface Area of Cylinder:

l = s/(2πr)

l = 48/(2π(3))  ==> plug in known values

l = 48/(6π)

l = 8/π  

l = 2.546 meters

l = 2.546 meters

l = 2.55 meters

Three of the seven phases of the impulse purchase cycle. The other phases include antecedent, search, and selection.

The impulse purchase cycle is a model that describes the process of making an impulsive purchase. It is typically divided into seven phases:

Antecedent: This phase is characterized by a need or desire for something. It can be triggered by a variety of factors, such as boredom, hunger, or a sudden craving for a particular product.

Search: In this phase, the consumer begins to actively search for a product that will satisfy their need or desire. They may search online or in physical stores, and they may consider various options before deciding on a product.

Selection: In this phase, the consumer narrows down their options and selects a specific product that they want to purchase. They may consider factors such as price, quality, and convenience when making their decision.

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The answer is 11(a - b), To solve this expression, we need to perform the subtraction operation on the terms inside the parentheses. First, we subtract the term "a + 6b" from "12a - 5b". This gives us 11a - 11b. Then, we can simplify this expression by combining the like terms 11a and -11b to get 11a - 11b = 11(a - b). This is the final answer.

Answer:

i believe its 5+n ≤ -7

Step-by-step explanation:

the sum of 5 and a number(n) would be 5+n, and no more woukd be the  ≤  sign, which would lead to -7

The centroid of the region in the first quadrant bounded by the given curves is (81/170, 81/170).

In the given question, we have to find the centroid of the region in the first quadrant bounded by the given curves.

The given curves are:

y = x^8, x = y^8

We can write the curves as

y = x^8...........................(1)

y = x^{1/8}.......................(2)

Now putting the value of y from equation 1 in equation 2, we get

x^8 = x^{1/8}

Now simplifying,

x^{64} = x

x^{64}-x = 0

x(x^{63} - 1) = 0

After equating equal to zero,

x = 0, x = 1

My = [tex]\int_{a\rightarrow b}x[f(x)-g(x)]dx[/tex]

My = [tex]\int_{0}^{1}x[x^{1/8} - x^{8}]dx[/tex]

My = [tex]\int_{0}^{1}[x^{9/8} - x^{9}]dx[/tex]

My = [tex][(8/17)x^{17/8} - (1/10)x^{10}]_{0}^{1}[/tex]

My = (8/17)-(1/10)

My = 63/170

Mx = 1/2[tex]\int_{a\rightarrow b}[(f(x))^2-(g(x))^2]dx[/tex]

Mx = 1/2[tex]\int^{1}_{0}[x^{1/4} - x^{16}]dx[/tex]

Mx = 1/2 [tex][(4/5)x^{5/4} - (1/17)x^{17}]^{1}_{0}[/tex]

Mx = (1/2)[(4/5)- (1/17)]

Mx = 63/170

M = [tex]\int_{a\rightarrow b}[f(x)-g(x)]dx[/tex]

M = [tex]\int^{1}_{0}[x^{1/8} - x^{8}] dx[/tex]

M = [tex][(8/9)x^{9/8} - (1/9)x^{9}]^{1}_{0}[/tex]

M = [(8/9) - (1/9)]

M =7/9

Center of mass(x',y') = (My/M, Mx/M)

Center of mass(x',y') = ((63/170)/(7/9), (63/170)/(7/9))

Center of mass(x',y') = (81/170, 81/170)

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We can identify a correct system of equations after draw the graph of the system. The point of intersection indicates the correct solution of the system.

Two or more equations which have the same variables, and we can use these all together. The equations are called a set of equations. We get the solution from the system while plotting in the XY coordinate system.

Such as we have two or more linear equations, and we solve each equation and draw a graph for each. We will notice a point of intersection of the straight lines and that refers the solution of the system of equation.

There are many sets or system of equation. Some systems have infinity many solutions and graph of the equations never intersect each other. In the next, there are system of equations such as a set of linear function from where we get a point of intersection after plotting the graphs together. The line of intersection is the correct solution of the system.

On the other hand, there are some sets which have no solution, and they are called inconsistent.

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The equation of the transformed function is g(x) = -x² - 2

From the question, we have the following function that can be used in our computation:

f(x) = x² -- parent root function

When the graph is examined (see attachment), we have the transformation to be

g(x) = reflect f(x) across the x-axis and a downward shift of 2 units.

Mathematically, this can be represented as

g(x) = -f(x) - 2

Substitute the known values in the above equation, so, we have the following representation

g(x) = -x² - 2

Hence, the transformed function is g(x) = -x² - 2

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On integrating the function f(x), we get - (x³/45) + (3x²) - (2x³) + C.

        [tex]$\int_a^b \! f(x) \, \mathrm{d}x.[/tex]

Given is the function, as follows -

f(x) = (x²/15 + 6x - 9x²/{3/2})

The given function is -

f(x) = (x²/15 + 6x - 9x²/{3/2})

∫f(x) = ∫(x²/15 + 6x - 9x²/{3/2}) dx

∫f(x) = ∫(x²/15)dx + ∫(6x)dx - ∫(6x²)dx

∫f(x) = (1/15)(x³/3) + C₁ + (6)(x²/2) + C₂ - (6)(x³/3) + C₃

∫f(x) = (x³/45) + (3x²) - (2x³) + {C₁ + C₂ + C₃}

∫f(x) = x³/45) + (3x²) - (2x³) + C                  (C = C₁ + C₂ + C₃)

Therefore, on integrating the function f(x), we get (x³/45) + (3x²) - (2x³) + C.

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We are given that the probability of selecting a yellow card is 3 times the probability of selecting a blue card, so we can write the following equation:

yellow = 3 * blue

We also know that the sum of the probabilities of selecting a red, yellow, or blue card must be equal to 1, so we can write the following equation:

red + yellow + blue = 1

Substituting the expression for yellow from the first equation into the second equation, we get:

red + 3 * blue + blue = 1

Combining like terms, we get:

red + 4 * blue = 1

We are given that the probability of selecting a red card is 1/9, so we can substitute this value into the equation:

1/9 + 4 * blue = 1

Solving for blue, we get:

blue = (1 - 1/9) / 4

blue = (8/9) / 4

blue = 2/9

Therefore, the probability of selecting a blue card on the first try is 2/9.

-5 + 13x = 60

13x = 65

x = 5

CHECKING:

-5 + 13(5) = 60

-5 + 65 = 60

60 = 60

Step-by-step explanation:

Total no of racks in the store is 30 and grocery item is maximum.

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Divide the amount by the total value to get the percentage, then multiply the resulting number by 100.

Racks of confectionery items = 10

Racks of bread items = 5

Racks of grocery items = 15

The total no of racks in the departmental store is 30

Using the percentage formula we will calculate the percentage of each item

percentage of confectionery items rack =no. of confectionery racks/total no. of racks  x100

=10/30x100=33.33%

percentage of bread items rack = no. of bread racks/total no. of racks x 100

= 5/30x 100=16.66%

percentage of grocery items rack = no. of grocery racks/total no. of racks x 100

= 15/30 x 100 = 50%

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At any point p(x, y), the tangent line to a particular curve has an x-intercept of 3 4 x. The point is also traversed by this curve (1, 16). The equation of the curve is y - 16 = (3/4)(x - 1)^2

To find the equation of the curve, we first need to find the equation of the tangent line at point P(x, y).

Since the x-intercept is 3/4x, the equation of the tangent line is

y - y_p = (3/4)(x - x_p).

We substitute the given point (1, 16) in the equation to find the value of y_p and x_p which are 16 and 1 respectively.

y - 16

= (3/4)(x - 1).

This equation is the equation of the curve.

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Answer:

x weigh of ball

2x+40=160

2x=120

x=60g

The solution is 60 grams

The size of each of the balls is given by the equation x = 60 grams

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the size of the balls be represented as = x

The number of balls = 2

So , the total size of the balls = 2x

Now , the equation will be

The weight of all the elements = 160 grams   equation (1)

The weight is balanced by = 40 grams + 2x   equation (2)

Now , equation (1) = equation (2)

Substituting the values in the equation , we get

160 = 2x + 40

On simplifying the equation , we get

Subtracting 40 on both sides of the equation , we get

2x = 120

Divide by 2 on both sides of the equation , we get

x = 60 grams

Therefore , the value of x is 60 grams

Hence , the size of the ball is 60 grams

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