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The integer solutions of the graph are x = -1, 0, 1, 2, 3 and 4

The complete question is added as an attachment

To determine the solution of f(x) at tthe points where f(x) is more than or equal to 0.

We make use of the positive y-axis

On the positive y axis, the values of x are

x = -1 to 4

This means that the solution is x = -1, 0, 1, 2, 3 and 4

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Yes, these two triangles are similar. these are similar by SAS~ rule of similarity.

When two figures have the same shape but differ in size, they are said to be similar figures. In other words, two figures are said to be comparable when they have many characteristics but aren't necessarily identical.

Similar figures are two shapes with the same dimension or common ratio but a different size or length, such as triangles, polygons, quadrilaterals, etc.

If two triangles are comparable, then any pairs of triangles with the same corresponding angles are also comparable.

Triangles have proportional sides on all matching sides.

In this 20.8/23.4 = 8/9

and angle between these two sides are congruent.

So these triangles are similar by the rule of SAS~ of similarity.

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Answer: Yes

Step-by-step explanation:

So, first of all, convert all the given quantities in the same unit.

6m = 600cm

4m = 400cm

2.5m = 250cm

Now, volume of the garage = 600 x 400 x 250

                                              = 60,000,000cm³

And, volume of a brick = 7 x 22 x 10

                                      = 1,540cm³

Number of bricks needed = 60,000,000 ÷ 1,540

                                           ≈ 39,000

So yes, Natalia's estimate is correct.

The solution to the inequality is -5 <= x <= -3.

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

x^2 + 8x + 15 <= 0

Expand

x^2 + 3x + 5x + 15 <= 0

Factorize the expression

(x + 3)(x + 5) <= 0

Expand

x + 3 <= 0 and x + 5 <= 0

So, we have

x <= -3 and x <= -5

When combined, we have

-5 <= x <= -3.

Hence, the solution is  -5 <= x <= -3.

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The standard deviation is a useful tool in understanding the spread of data and making inferences about the population mean based on sample means.

The standard deviation is a measure of how spread out the data is from the mean.

In this case, the mean recycled material collected per household in other local authorities is 40kg with a standard deviation of 15kg.

In part a, the probability of a randomly selected household recycling less than 30kg in a given week is calculated. In part b, the probability of the sample mean recycled material collected in a given week being less than 30kg for a sample of 100 households is calculated.

In part c, it is explained that finding a sample mean of 30kg for 100 households on a single street does not necessarily mean that the recycling scheme of local authority A is not working.

Finally, in part d, a 95% confidence interval for the mean amount of recycled material per household in local authority A is constructed after an advertising campaign.

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Answer:

40d > 600

Step-by-step explanation:

In order to find the number of days the store needs to sell, you need to determine the number of shirts the store sells in a day, which is 40. If you multiply the number of shirts the store sells in a day (40) with the number of days its open (d), you get 40d. 40d must be greater than 600, since the store needs to sell more than 600 shirts.

The radius of the oil slick as a function of time t is R(t) = √((10/8) × 10000t/π), and after approximately 31.83 hours, the oil slick will have a radius of 1 kilometre.

(a) Let's assume that the oil spread rate is constant. Then, the volume of oil that has leaked into the ocean after t hours is 10000t litres. If this oil forms a circular slick of radius R, then its surface area is given by A = πR². If 8 litres of oil spread out over 10 square meters of the ocean surface, then 1 litre of oil spreads out over 10/8 square meters. Therefore, the surface area of the circular slick is given by

A = (10/8) × 10000t

Equating this to πR², we have:

πR² = (10/8) × 10000t

R² = (10/8) × 10000t / π

R = √((10/8) × 10000t / π)

So, the radius of the oil slick as a function of time t is:

R(t) = √((10/8) × 10000t / π)

(b) To find the time at which the oil slick has a radius of 1 kilometre, we set R(t) = 1 km and solve for t:

1 km = √((10/8) × 10000t / π)

1² km² = (10/8) × 10000t / π

π / (10/8) = 10000t / (1 km)²

π / (10/8) = 10000t / (1000 m)²

π / (10/8) = 10000t / (10⁶ m²)

Solving for t, we find:

t = π / (10/8) × (10⁶ m²) / 10000

t = π / (10/8) × 1000

t = (π × 1000) / (80)

So, after approximately 31.83 hours, the oil slick will have a radius of 1 kilometre.

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Answer:

f(x-1) = [tex]\sqrt{-3x+3}+7[/tex]

Step-by-step explanation:

if f(x) = [tex]\sqrt{x-3}[/tex] + 3

then f(x-1) = [tex]\sqrt{(x-1)-3}+7[/tex]

after expanding its f(x-1) = [tex]\sqrt{-3x+3}+7[/tex]

If sin(4x-8)=cos36°, the value of X is 15.5 since sin x =cos(90-x).

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. A mathematical statement made up of two expressions joined by an equal sign is known as an equation.

Here,

90-(4x-8)=36

4x-8=54

4x=62

x=15.5

The value of X if sin(4x-8)= cos36° is 15.5 as sin x =cos(90-x).

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Answer:

6xy is the answer

Step-by-step explanation:

Dog's position= p

Distance =  rate*time

Dog distance= 720T

The fox position= p+60

Distance= rate*time

d=  750t-60 (Subtract 60 since the fox is already ahead of the dog)

We want to know if their distances are the same. So set  up an equation.

720t=750t-60

-750t   -750t

-30t/-30= -60/-30

t=2(Time)

d= 720(2)= 1440

d= 750(2)-60= 1440

In one minute 0.6 sq meters of land will be cut with machete.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Direct Variation

When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. For instance, a rise in the quantity of commodities will result in higher costs.

Additionally, a guy working alone will accomplish less than a man working with a group of men. Therefore, if we add more men, there will be more labor.

Indirect Variation

It is the direct variation's opposite. If we enhance one quantity, another item's value decreases. For instance, if we speed up, it will take us less time to travel a distance. Therefore, the distance traveled will be shorter as the speed increases.

In 90 minutes 54 meters of land is cut with machete.

In one minute 54/90 = 0.6 sq meters  of land will be cut with machete.

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All the required relationship is given below.

Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.

Given:

A linear function: y = mx + b,

and an exponential function : y = a(b)ˣ

In a linear function,

y = mx + b.

m is the slope or rate of change and b is the y-intercept.

In an exponential function: y = a(b)ˣ,

a is the initial value and r is the rate of change.

When the x-values rise by a certain amount, the y-values change in different ways for linear and exponential relationships:

The y-values in a linear connection differ by an equal amount.

The y-values have identical ratios in an exponential relationship.

Because both linear and exponential equations must rise at the same pace as they began, they are similar.

Therefore, the required relationship is given above.

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The answers to each part of the question is given below.

Given is that Kumiko has $50 gift card for a website.

{ 1 }

We can write the inequality as -

2.5g + 1.5a ≤ 50

{ 2 }

The graph of the inequality is plotted. The shaded region represents the possible set of solutions.

{ 3 }

We can write the combinations as -

Therefore, the answers to each part of the question is given above.

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Step-by-step explanation:

just look at the graph ! what answer options can be possible, when you look at the first and the last point ?

the position km are 40 and 15.

the first answer option is the right one.

Jose's height is 1 standard deviation above the mean height for 7-year-olds and Jamal's height is 0.67 standard deviations above the mean height for 12-year-olds.

Standard deviation is a mathematical term used to measure how far away a data point is from the mean of a set of data.

To determine the number of standard deviations, we use the following formula:

(Jose's height - mean height for 7-year-olds) / standard deviation

(130 - 120) / 10 = 1

So, Jose's height is 1 standard deviation above the mean height for 7-year-olds.

Now, let's look at Jamal. Let's assume that the mean height for 12-year-olds is 150 cm and the standard deviation is 15 cm. Jamal's height is 160 cm.

Using the same formula,

(Jamal's height - mean height for 12-year-olds) / standard deviation

(160 - 150) / 15 = 0.67

So, Jamal's height is 0.67 standard deviations above the mean height for 12-year-olds.

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The required solutions of the situation of the function are  x = 3/4  or x = -1/4.

A unique connection where each input only produces one output. A common notation for it is "f(x)," where x denotes the input value. as in f(x) = x/2 ("f of x equals x divided by 2") Since there is only one output ("x/2") for each input ("x"), it is a function: • f(2) = 1.

We have,

f(x)=2x-1

g(x)=3/8x

To find the value of x for f(x) = g(x).

f(x) = g(x)

2x-1 = 3/8x

16x² - 8x = 3

16x² - 8x - 3 = 0

16x² - 12x + 4x - 3 = 0

4x(4x - 3) + (4x - 3) = 0

(4x - 3)(4x + 1) = 0

x = 3/4  or x = -1/4

Thus, required solution are  x = 3/4  or x = -1/4.

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No such vector exists because the directional cosines must be unit vector, with a magnitude of 1.

The directional cosines of a vector are ratios of the components of the vector in the x, y, and z directions. Each directional cosine is a unit vector, meaning it has a magnitude of 1. Therefore, if the directional cosines of a vector are 5 and 6, as in the question, the magnitude of the vector would be the square root of (5^2 + 6^2), which is 7.81. Similarly, if the directional cosines are 2 and 3, the magnitude of the vector will be the square root of (2^2 + 3^2), which is 3.61. Therefore, the magnitude of the vector would be neither 5 nor 6, so no such vector exists.

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The solution to the system of equations in this problem is given as follows:

(4.5, -1.5).

The intercept of the system of equations is equivalent to the solution of the system of equations.

The system in this problem is defined as follows:

On the second equation, we isolate y, as follows:

y = 7.5 - 2x.

Replacing on the first equation, the value of x is obtained as follows:

-0.4x + 0.25(7.5 - 2x) = -2.175

0.9x = 4.05

x = 4.05/0.9

x = 4.5.

Hence the solution for y is given as follows:

y = 7.5 - 2(4.5)

y = 7.5 - 9

y = -1.5.

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The square root of a negative number is not defined in the real numbers, r cannot be found. This means that y = x^r is not a solution for any real r.

What is square root ?

A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.

x(r^2 x^(r-2)) - rx^(r-1) = 0

Expanding the powers of x and collecting terms, we have:

r^2 x^r - rx^r + x^r = 0

Dividing through by x^r, we have:

r^2 - r + 1 = 0

This is a quadratic equation that can be solved using the quadratic formula:

r = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -1, and c = 1.

Plugging in the values, we get:

r = (-(-1) ± √((-1)^2 - 4 * 1 * 1)) / 2 * 1

r = (1 ± √(1^2 - 4 * 1 * 1)) / 2 * 1

r = (1 ± √(1 - 4)) / 2

r = (1 ± √(-3)) / 2

The square root of a negative number is not defined in the real numbers, r cannot be found. This means that y = x^r is not a solution for any real r.

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The average probability of earning $2 for any given roll of the dice is 8/9, or approximately 0.889.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

There are a total of 36 possible combinations when rolling two six-sided dice (6 possible outcomes for the first die and 6 possible outcomes for the second die).

The number of combinations that will result in a win (earning $2) are 32: (1,1), (1,2), (1,3), ..., (6,5), and (6,6).

The number of combinations that will result in a loss (losing $4) are 4: (2,2), (4,4), and (10,10).

The probability of earning $2 is the number of favorable outcomes (earning $2) divided by the total number of possible outcomes:

P(earning $2) = 32/36 = 8/9

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The selling price of the article that makes 15% of the profit will be Rs 13,800.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A loss of 15% is incurred by selling an article at Rs 10,200. The cost price of the article is given as,

⇒ Rs 10,200 / (1 - 0.15)

⇒ Rs 10,200 / 0.85

⇒ Rs 12,000

The selling price of the article that makes 15% of profit is given as,

⇒ Rs 12,000 x (1 + 0.15)

⇒ Rs 12,000 x 1.15

⇒ Rs 13,800

The selling price of the article that makes 15% of the profit will be Rs 13,800.

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The number of gallons in  64 fluid ounces would be 0.5.

While fluid ounce, denoted by the sign "fl oz," is an imperial measurement system in the US systems volume unit, gallon is a volume unit in the US Customary measurement systems. Thirty-eight fluid ounces make up a gallon of water. It takes 128 fluid ounces to make up a fluid gallon.

Despite the fact that they are very different, ounces and fluid ounces both serve as units of measurement. As the name suggests, fluid ounces are designed to measure volume (generally of liquid ingredients like water), whereas ounces measure weight, typically of solid materials like all-purpose flour.

In a gallon, there are 128 fluid ounces. However, it can change depending on whether the unit system is in use for liquid or dry gallons. There are 148.94545 ounces in a dry US gallon. There are 153 fluid ounces in an Imperial gallon if you measure using the British Imperial method.

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The sum of vectors a and b where a = <3, 2> and b = <-1, 4> is <2, 6>.

The sum of vectors a and b is found by adding the corresponding components of each vector. In this circumstance, the vectors a and b are given as follows:

a = <3, 2>

b = <-1, 4>

The sum of a and b is simply:

a + b = <3, 2> + <-1, 4> = <3 + (-1), 2 + 4> = <2, 6>

So, the sum of vectors a and b is equal to the vector <2, 6>.

Geometrically, the sum of vectors a and b can be represented as the displacement from the tail of vector a to the head of vector b or vice versa. This displacement is the result of adding the vectors, and it starts at the tail of either vector and ends at the head of the other vector.

The sum of vectors is a fundamental concept in linear algebra and is used to describe changes in position, velocity, or any other physical quantities that can be represented as vectors.

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The final answer is 886.1485297964202.

To evaluate the integral, we can use partial integration.

Let u = 17z³

dv = e^z dz

Then du = 51z² dz

v = e^z

Using partial integration, we have:

∫ 17z³ e^z dz = 17z³ e^z - ∫ 51z² e^z dz

= 17z³ e^z - 51 * ∫ z² e^z dz

= 17z³ e^z - 51 * (z² e^z - 2 * ∫ z e^z dz)

= 17z³ e^z - 51z² e^z + 102 * ∫ e^z dz

= (17z³ - 51z² + 102) * e^z + c

So the definite integral from 0 to 2 is equal to

∫_0² 17z³ e^z dz = (17 * 2³ - 51 * 2² + 102) * e^2 - (17 * 0³ - 51 * 0² + 102) * e^0

= (17 * 8 - 51 * 4 + 102) * e²

= (17 * 8 - 51 * 4 + 102) * 7.389056098930649

= (17 * 8 - 51 * 4 + 102) * 7.389056098930649

= 886.1485297964202

Therefore, the answer is 886.1485297964202.

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The data that is considered univariate is, Shoe size, salary, height, sports played in high school, years of experience, favorite color.

Data that just has one variable is said to be univariate data. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis. The analysis's primary goal is to explain the data and identify any patterns in it; it does not deal with causes or correlations. Height is an example of a univariate data.

We know that univariate data only has one variable thus the data that can be represented with a single variable is:

Shoe size, salary, height, sports played in high school, years of experience, favorite color.

Hence, the data that is considered univariate is, Shoe size, salary, height, sports played in high school, years of experience, favorite color.

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Therefore , the solution of the given problem of angles comes out to be

YZ || UV  by following given equality.

Euclidean geometry defines an angle as a shape made up of two rays, referred to as the angle's extremities, that come together at a vertex in the middle. Two rays may combine to form an angle in the surfaces where they are positioned. When two planes collide, an angle too is created. They are referred to as dihedral angles. The shape that two rays and lines with a similar termination can adopt in plane geometry is called an angle. The word "angle" in English is derived from the Latin word "angulus," which meaning "horn."

Here,

Given :

=> m∠1 + m∠5 = 180°

=> m∠1 + m∠4 = 180°

To prove :

YZ || UV

Since,

=> m∠1 + m∠5 = m∠1 + m∠4

=> m∠5 = m∠4 (are equal)

and

=> m∠1 = m∠1  (given)

So, by the following we can say

=> YZ || UV

Thus , YZ || UV .

Therefore , the solution of the given problem of angles comes out to be

YZ || UV  by following given equality.

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It has a time complexity   is 1 as n is a constant.

Time complexity

The time complexity is the number of operations an algorithm performs to complete its task . The algorithm that performs the task in the smallest number of operations is considered the most efficient one in terms of the time complexity.

The number of operations in the best case is constant. The best-case time complexity would therefore be Θ (1). Most of the time, we perform worst-case analysis to analyze algorithms. In the worst analysis, we guarantee an upper bound on the execution time of an algorithm which is good information.

A simple way of quantifying complexity on a structural basis would be to count the number of components and/or interactions within a system.

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The slope of the regression line connecting X and Y is represented by the regression coefficient bxy, which is -7/3.

The linear relationship between two variables, X and Y, is measured by the regression coefficient bxy. The regression coefficient bxy in this instance is -7/3. By rearranging the provided equation to take the form y = mx + b, which is the equation of a straight line, it is possible to determine this coefficient. The equation is rearranged to give us y = (-7/3)x + 28.10. The slope of the line, which is -7/3, is the coefficient bxy. The negative sign shows that X and Y have an inverse relationship, which means that when one goes up, the other goes down. Regression coefficient, which in this case is -7/3, is a useful indicator of the strength of the linear relationship between two variables.

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