Given the inequalities y< 2x-2 and y>-x-4 graphed on the same coordinate
grid, which of the following coordinates gives a true statement?
OA. (4,6)
OB. (2,-6)
O C. (6,4)
OD. None of the above

The unit of the rate of change is (b) dollars per month

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

The table of values

Where we have

y = total amount in dollars

x = number of months

The rate of change is calculated as

Rate  = y/x

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

Rate = total amount in dollars/number of months

So, we have

Unit = dollars per month

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suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is  nλe^(-nλx)

Given fx (x) = λe^λx

Fx (x) = 1 – e^-λx      x…0

To find distribution of Min (X1,….Xn)

By applying the equation

fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)

For minimum j = 1

[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx

= ne^[(n-1) λx] λe^(λx)

= nλe^(-λx[1+n-1])

= nλe^(-nλx)

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Answer:

-3, 3, 0.54545455, 8, 3.14159265..., 0, 2.44948974, 6

these are the real numbers

Answer and Step-by-step explanation:

I think this is correct? The directions aren't very clear/descriptive, so sorry if this is wrong.

A.

1. wins:games

2. wins:losses

3. losses:wins

4. games played:wins

5. losses:games played

B.

1. 8:12, or 2:3

2. 3:7

3. 5:3

4. 12:15, or 4:5

5. 20:25, or 4:5

#teamtrees #PAW (Plant And Water)

For this we use the slope formula, where m is the slope:

If we take (-2, -1) as the first point and (1, -3) as the second point, we have:

The value of the triple integral\(\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}\) by using spherical coordinates \(2\pi(e^{-1}-e^{-9})\).

Given that the triple integral is-

\(\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}\)

E is the region bounded by the spheres which are,

\(x^2+y^2+z^2=1\\\\x^2+y^2+z^2=9\)

In spherical coordinates we have,

x = r cosθ sin ∅

y = r sinθ sin∅

z = r cos∅

dV = r²sin∅ dr dθ d∅

E contains two spheres of radius 1 and 3 () respectively, the bounds will be like this,

1 ≤ r ≤ 3

0 ≤ θ ≤ 2π

0 ≤ ∅ ≤ π

Then

\(\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}\)

\(\int\int\int _{E} \frac{e^{-r^2}}{r}r^2Sin\phi drd\phi d\theta\\\\2\pi \int_{0}^{\pi} \int_1^3 re^{-r^2} dr d\phi\\\\2\pi \int_1^3 re^{-r^2} dr\\\\2\pi(e^{-1}-e^{-9})\)

The complete question is-

Use spherical coordinates to evaluate the triple integral ∭ee−(x2 y2 z2)x2 y2 z2−−−−−−−−−−√dv, where e is the region bounded by the spheres x2 y2 z2=1 and x2 y2 z2=9.

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Answer:

53,000

Step-by-step explanation:

1 ten is 10

So 5,300 x 10 = 53,000

Other ways to say "5,300 tens":

53,000 ones

5,300 tens

530 hundreds

53 thousands

5.3 ten thousands

The number x = 5,300 is regrouped and is renamed as:

53,000 ones

5,300 tens

530 hundreds

53 thousands

5.3 ten thousands

Given data:

To regroup and rename 5,300 tens, we are essentially converting this number into a more manageable form while preserving its overall value.

First, we can recognize that 5,300 tens can be written as 53,000. This is because each "ten" represents a factor of 10, and multiplying by 10 once more shifts the number one place to the left, resulting in 53,000.

Another way to express this number is in terms of hundreds. Since 100 tens make a hundred, we can divide 53,000 by 100 to find that it is equal to 530 hundreds.

Furthermore, we can break it down even further by noting that 10 hundreds make a thousand. Thus, 530 hundreds are equivalent to 53 thousands.

Hence, the number 5,300 is regrouped and renamed.

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For Serenity's lemonade recipe, the lemons being used per cup of lemonade is 0.8

Ratio is a comparison of two quantities that are expressed in relation to each other. Ratios are typically expressed in the form of a fraction, with the numerator representing one quantity and the denominator representing the other quantity.

To find the rate at which lemons are being used in lemons per cup of lemonade, we need to calculate the ratio of lemons used to cups of lemonade.

According to the recipe, 4 lemons are required to make 5 cups of lemonade. So the rate of lemons used is:

4 lemons / 5 cups = 0.8 lemons per cup of lemonade

This means that for every cup of lemonade, 0.8 lemons are used.

Alternatively, we can also express this rate as a fraction, which gives us:

0.8 lemons / 1 cup of lemonade

Either way, the rate of lemons used is 0.8 lemons per cup of lemonade.

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The amount that the home will be worth after 7 years is  $457763.67

The geometric sequence is sometimes called the exponential sequence. The formula for calculating the nth term of an arithmetic sequence is expressed as:

Tn = ar^n-1

where

a is the first term = 120,000

r is the common ratio = 150000/120000 = 1.25

Required

7th term

Substitute

T7 = 120,000(1.25)^7-1
T7 = 120,000(1.25)^6

T7 = 120,000(3.8147)

T7 = $457763.67

Hence the amount that the home will be worth after 7 years is  $457763.67

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Answer:

(c) $457,763.67

Step-by-step explanation:

hope this helps:)

Answer:

10 rows with 6 passengers per row

Step-by-step explanation:

Let x be the number of rows and y the number of passengers per row.

Then we can interpret the story as the following two equations:

xy=60

(x+2)(y-1)=60

Solving these two equations:

y=60/x

(x+2)(60/x-1)=60     (substitute y)

60 - x + 120/x - 2 = 60 (multiply by -x)

x² + 2x - 120 = 0     (factor)

(x-10)(x+12) = 0

x = 10

y = 60/10 = 6

and indeed 10 * 6 = 60 and also 12 * 5 = 60

Answer:

A. y = –5x – 27

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line parallel to  y = − 5 x + 3 .

y = − 5 x − 27                           PARALLEL

...................................................................................................................................................

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  y = − 5 x + 3 .

y = 1 /5 x + 21 /5                    PERPENDICULAR

Answer:

y.

Point B is reflected at from point A at y-axis.

The volume of the given rectangular prism is 14/3 units³ or approximately 4 2/3 units³.

Given:

Rectangular base area = 3 1/3 units²

Height = 1 2/5 units

Convert the mixed number to improper fractions.

The rectangular base area can be written as:

= 3 + 1/3

= 3/1 + 1/3

= 10/3 units².

The height can be written as:

= 1 + 2/5

= 1/1 + 2/5

= 7/5 units.

Multiply the area of the base by the height.

Volume = Base area × Height

Volume = (10/3 units²) × (7/5 units)

Multiply the numerators and denominators separately.

Volume = (10 × 7) / (3 × 5) units³

Volume = 70 / 15 units³

Volume = 14/3 units³

Therefore, the volume of the given rectangular prism is 14/3 units³ or approximately 4 2/3 units³.

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Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

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Okay so you put -6 in where y is then solve and youll get your answer

-8x-7(-6)=-6

Option B, \(\rm y=4^{x-1}\) is the equation the represents this graph.

An equatiοn is a statement in mathematics that states the equality οf twο expressiοns. An equatiοn has twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine which variable(s) must be changed in οrder fοr the equatiοn tο be true.

Simple οr cοmplicated equatiοns, regular οr nοnlinear equatiοns, and equatiοns with οne οr mοre factοrs are all feasible. In the equatiοn "x² + 2x - 3 = 0," fοr example, the variable x is raised tο the secοnd pοwer. Lines are used in a variety οf mathematical disciplines, including algebra, calculus, and geοmetry.

Alsο, the y-intercept is 0 < y < 1.

Eliminate option a and d.

The graph is extended towards -x

so, eliminate option c

Now we are left option e and b

But as the origin is (1, 1), The value of x is 1

x = 1

x - 1 = 0

Thus, the correct option is b. \(\rm y=4^{x-1}\).

Lets graph  \(\rm y=4^{x-1}\) to check, see attachment.

Thus,  \(\rm y=4^{x-1}\) is the equation the represents this graph.

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Answer:

V = pi 36 units^3

V =113.04 units^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = pi ( 2) ^2 *9

V = pi 36

Letting pi = 3.14

V =113.04

Answer:

Angles 2, 3 and 6,7 are acute angles

Answer:

∠2≅∠3

∠6≅∠7

∠3≅∠6

∠2≅∠7

Step-by-step explanation:

Hello There!

Acute angles have to have an angle that measures less then 90 degrees. This can simply be determine by looking at the angle and seeing if it makes a smaller angle or a larger angle

∠2 and∠3 are vertical angles which have congruent measures

∠6 and∠7 are also vertical angles

∠3 and∠6 are alternate interior angle which are can be known for being congruent

∠2 and ∠7 are alternate exterior angles which are also congruent

so angles 2, 3, 6 and 7 are all congruent

The domain of the equation include the following: D. all real numbers.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-4, ∞}

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Answer:

$0.30

Step-by-step explanation:

The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.

After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.

However, Caesar, true to his word, had the pirates crucified on his own authority.

This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.

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The length of the two segments, written as radicals, are:

AB = √117

PQ = √244

Remember that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the length of the segment is:

L = √( (x₂ - x₁)² + (y₂ - y₁)²)

First, for the segment AB the endpoints are:

A = (-4,  -4)

B = (2, 5)

Then the length is:

L =  √( (-4 - 2)² + (-4 - 5)²)

L = √117

For the segment PQ the endpoints are:

P = (-6, 8)

Q = (6, -2)

The length is:

L =  √( (-6 - 6)² + (8 + 2)²)

L = √244

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The value of 14.5% of 1,800 is 261 by using the concept of percentage.

In mathematics, a percentage is a value or ratio expressed as a fraction of 100.

The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.

A % is a relative figure that indicates one-tenth of a quantity. One percent (symbolized 1%) is the one-hundredth part; consequently, 100 percent denotes the complete amount, and 200 percent specifies twice the supplied amount.

Given,

14.5% of 1,800

=(14.5/100)×1800

=261

Therefore, the answer is 261.

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Answer: Yes this equation is true.

How Do I know? Well, let's graph this and the answer is (0,32)

Answer:

Yes, it's true

The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

Given:

\($&\overline{A B} \cong \overline{D E} \\\) and

\($&\overline{A C} \cong \overline{D F}\)

According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

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We can expand

\(f(x,y,z) = xy\ln(yz) = xy \ln(y) + xy\ln(z)\)

Then using the product and chain rules,

\(\dfrac{\partial f}{\partial x} = y\ln(y) + y\ln(z) + \boxed{y\ln(yz)}\)

\(\dfrac{\partial f}{\partial y} = x\ln(y) + \dfrac{xy}y + x\ln(z) = \boxed{x\ln(yz) + x}\)

\(\dfrac{\partial f}{\partial z} = \boxed{\dfrac{xy}z}\)

Answer:

CDC and DCD

Step-by-step explanation:

4,6,8,10 are in A.P

\(\\ \rm\Rrightarrow a_n=a+(n-1)d\)

\(\\ \rm\Rrightarrow a_20=4+(20-1)2\)

\(\\ \rm\Rrightarrow a_20=4+19(2)\)

\(\\ \rm\Rrightarrow a_20=4+38\)

\(\\ \rm\Rrightarrow a_20=42\)

Step-by-step explanation:

Just :    5,8374

Answer:

2 4/7

Step-by-step explanation: