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Answer:

Step-by-step explanation:

1 yard = 3 feet    

1/3          3/3    

1/3 yard = 1 feet

3ft * 5 yards = 15ft

1/3yard * 2 = 2/3yard        1ft * 2/3 = 2ft

15ft+2ft=17ft

The rate of change on the graph is 2, 000 which represents Elizabeth's cost of 1 ton of coffee beans.

The rate of change for Elizabeth's cost per ton of coffee beans can be found by the formula :

= Change in total cost / Change in coffee beans purchased

We shall use the points ( 10, 80 ) and ( 20, 100 ).

The rate of change is :

= ( 100 - 80 ) / ( 20 - 10 )

= 20 / 10

= 2

This is 2, 000 on the graph.

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Answer:

We can break this down:

The student has a one out of five chance of getting a correct answer, and a four out of five chance of an incorrect answer. We can express the students odds of getting one incorrect answer as 4/5. In order to get the odds of two wrong answers, we need to multiply this answer again by the odds of choosing a wrong answer. Therefore:

The odds of one wrong answer = 4/5

The odds of two wrong answers = (4/5) * (4/5) = 16/25 chance of getting both of the questions wrong.

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

The slope of the line perpendicular to another slope is the opposite sign and flipped(reciprocal)

The slope of the line = 1/2

So the perpendicular slope = -2

Answer:

\(x = 9.4\)

\(y = 17.7\)

Step-by-step explanation:

Given: The figure

Required: Find x and y

The relationship between length x, length 15 and angle 32 is as follows:

\(tan \theta = \frac{opp}{adj}\)

So, we have:

\(tan\ 32= \frac{x}{15}\)

Cross multiply:

\(x =15*tan\ 32\)

\(x = 15 * 0.6248693519\)

\(x = 9.3730402785\)

\(x = 9.4\) --- approximated

Similarly:

The relationship between length y, length 15 and angle 32 is as follows:

\(cos \theta = \frac{adj}{hyp}\)

So, we have:

\(cos\ 32= \frac{15}{y}\)

Cross Multiply:

\(y * cos\ 32= 15\)

Solve for y

\(y = \frac{15}{cos\ 32}\)

\(y = \frac{15}{0.84804809615}\)

\(y = 17.6876760506\)

\(y = 17.7\) --- approximated

El número "Novecientos mil cuatrocientos ochenta y nueve" se representa como 900,489 en notación numérica.

Por otro lado, el número "cuarenta mil dos" se representa como 40,002.

Si estamos buscando determinar cuál de estos dos números es mayor, podemos comparar las cifras en cada posición.

Comenzando desde la izquierda, el primer dígito de 900,489 es 9, mientras que el primer dígito de 40,002 es 4.

Dado que 9 es mayor que 4, podemos concluir que 900,489 es mayor que 40,002.

En general, al comparar números, se debe observar cada posición en orden de mayor a menor importancia.

Esto significa que el primer dígito a la izquierda es el más significativo y tiene más peso en el valor total del número.

Si los dígitos en la posición más significativa son iguales, se debe pasar a la siguiente posición hasta que se encuentre una diferencia.

En este caso, dado que el primer dígito de 900,489 es mayor que el primer dígito de 40,002, no es necesario comparar los dígitos en posiciones posteriores.

Por lo tanto, podemos concluir que el número "Novecientos mil cuatrocientos ochenta y nueve" (900,489) es mayor que "cuarenta mil dos" (40,002).

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Answer:

8.46/6 = 1.41

Step-by-step explanation:

Using the principle of alternate angles we can say that the value of x will be 120°.

The intersection of two parallel lines by a transversal produces alternate angles.

The alternate angles are equivalent when a transversal cuts two parallel lines.

The total of all the angles created on a transverse that are inside either of the two parallel lines is always 180 degrees.

Alternate interior angles for non-parallel lines don't have any special characteristics.

Angles of the same size that are found on opposing sides of the transversal line are known as alternate angles.

So, do not observe the given image:
We know that it is the pair of alternate angles that is equal.

Then, x = 120°.

Therefore, using the principle of alternate angles we can say that the value of x will be 120°.

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Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Answer:

Decrease; narrower.

Step-by-step explanation:

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

A confidence interval can be defined as a measure of the number of times that a population parameter would be within a given set of data. Thus, it is an estimate of the uncertainty of a given statistical data.

When constructing a confidence interval, if the level of confidence decreases, the margin of error will decrease and the confidence interval will be narrower.

Consequently, when constructing a confidence interval, if the level of confidence increases, the margin of error will increase and the confidence interval will be wider.

Hence, for an estimator to be consistent it must have both a small bias and small variance.

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

There exist integers x and y that satisfy the equation ax by m = gcd (a,b) and p, q are integers that satisfy mp + nq = 1.

The equation ax + by = c is a linear Diophantine equation, where a, b, c, x, and y are all integers.

If a and b are not both 0, then we can use the Euclidean algorithm to find the greatest common divisor (GCD) of a and b. Let d be the GCD of a and b, then we have:

a = dmb = dn

where m and n are coprime integers.

Now, we can multiply both sides of the equation ax + by = c by d:

adx + bdy = cd

Substituting a = dm and b = dn, we get:

dmx + dny = cd

Dividing both sides by d, we get:

mx + ny = c/d

Since m and n are coprime, there exist integers p and q such that:

mp + nq = 1

Multiplying both sides by c/d, we get:

mp(c/d) + nq(c/d) = c/d

Substituting mx + ny = c/d, we get:

mx(c/d) + ny(c/d) = c/d

So, we have:

x = pc/d

y = qc/d

Therefore, the integers x and y that satisfy the equation ax + by = c are:

x = pm/gcd(a,b)

y = qm/gcd(a,b)

where m = gcd (a,b) and p, q are integers that satisfy mp + nq = 1.

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Answer:

Step-by-step explanation:

\(\text{Given that:}\)

\(y = 1+ sec(x) \ \ y =3\)

\(\text{we draw the graph and the curves intersect at:}\)

\(x = - \dfrac{\pi}{3} \ and \ x = \dfrac{\pi}{3}\)

\(\text{Applying washer method;}\)

\(f(x) _{outer} - g(x) _{inner} --- (1)\)

\(V= \int ^b_a A(x) \ dx --- (2)\)

\(\text{outer radius = 3 - 1 = 2}\)

\(\text{inner radius =}\) \(( 1 + sec(x) ) - 1 = sec (x)\)

\(A(x) = \pi ((2)^2 -(sec(x)^2) \\ \\ A(x) = \pi (4 - sec^2 (x)) ---- (3)\)

\(\text{The volume V =}\int ^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ A(x) \ dx\)

\(V = \int ^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ \pi (4- sec^2 (x) ) \ dx\)

\(V = 2 \pi \int ^{\dfrac{\pi}{3}}_{0}( 4 - sec^2 (x)) \ dx\)

\(V = 2 \pi \int ^{\pi/3}_{0} 4 . \ dx - 2 \pi \int ^{\pi/3}_{0} sec^2 (x) \ dx\)

\(V = 2 \pi(4) \int ^{\pi/3}_{0} 1 . \ dx - 2 \pi \Big( tan (x)\Big )^{\dfrac{\pi}{3}}_{0}\)

\(V = 8 \pi(x)^{\dfrac{\pi}{3}}_{0} - 2 \pi \Big( tan \dfrac{\pi}{3} -tan (0)\Big )\)

\(V = 8 \pi({\dfrac{\pi}{3}}-{0}) - 2 \pi \Big( tan \sqrt{3}-(0)\Big )\)

\(V = 8 \pi({\dfrac{\pi}{3}}) - 2 \pi \Big( \sqrt{3}\Big )\)

\(\mathbf{V = 2 \pi \Big(\dfrac{4\pi}{3}- \sqrt{3} \Big)}\)

Answer:

x = 9

Step-by-step explanation:

To solve the equation 2x - 7 + 3x = 4x + 2 for x, you can follow these steps:

Combine like terms on both sides of the equation. Add the x terms together and move the constant terms to one side of the equation:

2x + 3x - 4x = 2 + 7

Simplifying the left side: x = 9

Simplify the right side of the equation:

x = 9

Therefore, the solution to the equation is x = 9.

Answer:

The function which has a slope of 4 will be that function or line which is going through the points (2, 0) and (3, 4).

What is a linear function?

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

In another word, a linear function is a function that varies linearly with respect to the changing variable.

In the given question is saying for the second case the line goes through points  (2, 0) and (3, 4) so the slope will be

(4 - 0)/(3 - 2) = 4 hence, it will be the correct answer because it is the only line that has a slope of 4.

Answer:

On a coordinate plane, a line goes through points (2, 0) and (3, 4).

Step-by-step explanation:

The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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Answer:

Factors: (x²y+6)(y²-11)

Step-by-step explanation:

Here's the original equation.

x²y³ - 11x²y + 6y² - 66

Let's separate it into two groups to make it easier.

(x²y³ - 11x²y) + (6y² - 66)

Let's take a look at (x²y³ - 11x²y) first. Do we notice anything that can be removed from the parentheses?

Yes, x²y can be taken from both polynomials to simplify the contents of the parentheses.

Both polynomials have x² and both have at least one y. Combine that to get x²y. That means that within the parentheses y² and - 11 will be left.

So  (x²y³ - 11x²y) becomes x²y (y²-11)

This works because if we multiply x²y * (y² - 11) we get (x²y³ - 11x²)

Let's apply this same idea to (6y² - 66).

6 is the only thing in common between the two polynomials.

If we follow the same steps we get 6 (y²-11).

Notice how when we simplified both groups they each had something on the outside and (y² - 11) in the parentheses?

So lets combine the things that were on the outside of both (y² - 11).

What was on the outside of each? x²y was on the outside for the first one, and 6 for the outside of the second one.

This means that if we combine everything and simplify, the factors we have are (x²y+6)(y²-11).

If you want to confirm, work your way backwards using the distributive property. You'll find that when you multiply (x²y+6) * (y² -11) you'll get = x²y³ - 11x²y + 6y² - 66. That was the original equation, so we know that these are the factors.

Hope that helps!

Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

The order of operations (PEMDAS) states that we should perform multiplication and division before addition and subtraction. Using this order, we get:

244 - (33456 / 3456) * 345 + 13.55 - 2

= 244 - 97.02 * 345 + 13.55 - 2

= 244 - 33494.1 + 13.55 - 2

= -33238.55

Therefore, 244-33456/3456*345+13.55-2 = -33238.55.

The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.

To determine the time interval of the water in the pool the following is carried out.

At 0 hour, the water is at the level of = 40 gallons

At 1 hour, the water decreased to = 25 gallons.

At 2 hours, the water decreased to = 10 gallons.

The water remained at a constant level till 4 hours.

Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.

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Clearly, the most effective graph could be a time series graph.

He could do something like this:

That's an example of how the graph could be.

Answer:

Yes

Step-by-step explanation:

R-2 < 9; when R=8

8-2 < 9

because

6 < 9 (reads as "6 is less than 9")

The number 2/5 is both a ratio and a fraction.

The number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.

The expression is also a ratio because it indicates the quantitative relationship between the figures.

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An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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If in a certain large population of adults. the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.

Given data:

Mean = 122

Standard deviation = 5

Sample size = 200

Now let find the the standard deviation of the sampling distribution of the mean sample using this formula

Distribution of sample mean = Standard deviation/√Sample size

Let plug in the formula

Distribution of sample mean = 5 /√ 200

Distribution of sample mean = 5/14.14

Distribution of sample mean = 0.35

Therefore the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.

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Answer: it is (c)

i hope this helped :)