for which value of x does each expression make sense: square root of (x-2) / square root of (x-3)

Answer:

We can say that he used a total of 5/8 gallons of glue

let x - glue to make purple slime

5/8 = 2/5 + 1/5 + x

5/8 = 3/5 + x             (LCD of 5 and 8 is 40)

25/40 = 24/40 + x

25/40 - 24/40 = 24/40 - 24/40 + x    (subtract 24/40 both sides)

x = 1/40

5/8 = 2/5 + 1/5 + 1/40

5/8 = 3/5 + 1/40

25/40 = 24/40 + 1/40

25/40 = 25/40

Therefore, the glue to make purple slime is 1/40 gallons.

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Step-by-step explanation:

There were 37 kisses at the family reunion. Probability is used to make predictions and inform decision-making.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.

To find the number of kisses at the family reunion, you can set up the ratio 4 hugs : 1 kiss as a proportion and solve for the number of kisses. Here's how you can do this:

First, cross-multiply to find the total number of hugs and kisses:

4 hugs * 1 kiss = 148 hugs

4 kisses = 148 hugs

Then, divide both sides of the equation by 4 to find the number of kisses:

4 kisses / 4 = 148 hugs / 4

1 kiss = 37 hugs

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The operations, along with their inverses are given as follows:

The operations are solved applying the inverse operations.

The first operation is solved as follows:

x + 10 = 25

x = 25 - 10

x = 15.

Hence the addition operation was solved applying the subtraction operation, which is the inverse operation of the addition.

The second operation is solved as follows:

2x = 28

x = 28/2

x = 14.

Hence the multiplication operation was solved applying the division operation, which is the inverse operation of the multiplication.

The third operation is given as follows:

4^x = 64.

log4(4^x) = log4(64)

x = 3. (as 4³ = 64, hence log4(64) = 3).

Hence the exponential operation was solved applying the logarithm operation, which is the inverse operation of the exponential.

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The triangle ΔRCD is similar to the triangle ΔRAP. Then the value of the variable 'x' is 28 units.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔRCD is similar to the triangle ΔRAP. Then the equation is given as,

RC / CA = RD / DP

x / 10 = 42 / 15

x / 2 = 14

x = 2 (14)

x = 28

The triangle ΔRCD is similar to the triangle ΔRAP. Then the value of the variable 'x' is 28 units.

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Answer:

x = 28 units

Step-by-step explanation:

As AP is parallel to CD (indicated by the arrows on the line segment), triangle APR is similar to triangle CDR.

In similar triangles, corresponding sides are always in the same ratio.

[tex]\implies \sf AP:CD=PR:DR=AR:CR[/tex]

Given

Therefore:

[tex]\implies \sf PR:DR=AR:CR[/tex]

[tex]\implies \sf 57:42=10+x:x[/tex]

[tex]\implies \sf \dfrac{57}{42}=\dfrac{10+x}{x}[/tex]

[tex]\implies \sf 57x=42(10+x)[/tex]

[tex]\implies \sf 57x=420+42x[/tex]

[tex]\implies \sf 15x=420[/tex]

[tex]\implies \sf x=28[/tex]

The rock will take 10.25 seconds to hit the ground, as the amount determined by the formula h=352-16t^(2).

The given equation is h=352-16t^(2). This equation can be used to calculate the time it will take for a rock to hit the ground after it has been dropped from a tower that is 352 feet high. The equation states that the rock's height (h) is equal to 352 minus 16 times the square of the time (t). To find the time it will take for the rock to hit the ground (h=0), we can rearrange the equation to solve for t. The rearranged equation is t=sqrt((352-0)/16), which simplifies to t=10.25. This means that the rock will take 10.25 seconds to hit the ground. This can also be expressed in tenths of a second as 102.5, which is the same as 10.25 seconds.

t= sqrt((352-0)/16)

t= sqrt(22)/4

t= 10.25

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Answer:

Below

Step-by-step explanation:

Multiplying the equation by -1 will flip it around the x - axis

so    3(x-2)^3

The value of c in the equation A is 7 and the value of d in the equation B is 5

The first equation is

[tex]\sqrt{448x^c}=8x^3\sqrt{7x}[/tex]

Move the term 8x^3 inside the square root

[tex]\sqrt{448x^c}=\sqrt{7x(8x^3)^2}[/tex]

Multiply the terms in the equation

[tex]\sqrt{448x^c} = \sqrt{448x^7}[/tex]

Here the both terms are equal. Therefore the value of x^c and the x^7 will be equal.

Then the value of c = 7

Part 2

The second equation is

[tex]\sqrt[3]{576x^d}=4x \sqrt[3]{9x^2}[/tex]

Move the term 4x inside the square root

[tex]\sqrt[3]{576x^d}=\sqrt[3]{9x^2(4x)^3}[/tex]

Multiply the terms in the equation

[tex]\sqrt[3]{576x^d}=\sqrt[3]{576x^3}[/tex]

Here the both terms are equal. Therefore the value of x^d and the x^5 will be equal

Then the value of d = 5

Therefore, the value of c = 7 and the value of d = 5

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Answer:

D). 27

Step-by-step explanation:

The mass of each bag is 9 kilograms

We have 3 bags

Let's add the mass of all 3 bags to find our answer.

9 kilograms + 9 kilograms  + 9 kilograms = 27 kilograms

The solution is, D). 27  is the total mass, in kilograms, of all of the bags of pebbles.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

A worker has 3 bags of pebbles to use in a garden. The mass of each bag is 9 kilograms.

so, we have,

The mass of each bag is 9 kilograms

We have 3 bags

i.e. total mass = 9 * 3 =27

here, we have to multiply 9 by 3 we get the total mass,

i,e. 27 kg.

similarly, we have,

Let's add the mass of all 3 bags to find our answer.

9 kilograms + 9 kilograms  + 9 kilograms = 27 kilograms

Hence, The solution is, D). 27  is the total mass, in kilograms, of all of the bags of pebbles.

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A formal power series that encodes the coefficients of a sequence of numbers is a generating function.

Here, the coefficients of the sequence {Sₙ} are encoded by the generating function S(x). where Sₙ is the number of lattice paths as described above.

Here we will use the fact that the generating function for a sequence satisfies a functional equation that relates the generating function to the sequence itself to prove that 1 + (x – 1)S(x) + xS(x)² = 0,

Here, the functional equation is

S(x) = 1 + xS(x) + xS(x)²

This equation implies that

The term 1 on the right-hand side corresponds to the fact that to reach the point (0,0) (the starting point), there is exactly one way which is to stay at the starting point.

The term xS(x) corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-1, n-1) we can reach any point (n,n)

The term xS(x)² corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-2, n-2), and then taking another step in the positive x-direction and following a path to (n-1, n-1) we can reach any point (n,n)

Thus, 1 + (x – 1)S(x) + xS(x)² = 0. Hence proved.

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Answer:

120 children

Step-by-step explanation:

c=children

a=adults

c+a=237

1.75c+2a=444

(c+a=237)*2 ==> make a in the equation equal to 2a

       2c+2a=474

- (1.75c+2a=444)  ==> eliminate a from the equation

2c-1.75c + 2a-2a = 474-444

2.00c-1.75c = 30

0.25c = 30

4 * 0.25c = 4 * 30   ==> remove decimals by multiplying each side by 4

c = 120 children

For regression and classification predictive modeling, the Maximum Likelihood Estimation framework can be used as a foundation for estimating the parameters of numerous machine learning models.

The logistic regression model is a part of this.

For species distribution models, maximum likelihood is a common parameter estimation method. A popular species distribution model, the Poisson point process, does not always have maximum likelihood estimates.

At the end of the day, the most extreme probability gauge for p is the mean of the y variable from the N draws. According to the result, p=n1/N=y is the value of p that maximizes the above log-likelihood function.

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The new price of the item is equivalent to $3.25.

Given is that the price of an item has been reduced by 95%. The original price was $65

Assume the new price to be $[x]. So, we can write -

x = 65 - {95% of 65}

x = 65 - {(95/100) x 65}

x = 65 - {6175/100}

x = 65 - 61.75

x = 3.25

Therefore, the new price of the item is equivalent to $3.25.

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The volume of the composite solid that is made up of hemisphere and cylinder will be 7,121.52 cubic feet.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The shape is the combination of the hemisphere and cylinder. Then the volume of the composite solid is calculated as,

V = Volume of hemisphere + Volume of cylinder

V = (2/3) πr³ + πr²h

Simplify the equation, then we have

V = (2/3) π(9)³ + π(9)²(22)

V = 486π + 1782π

V = 2268 x 3.14

V = 7,121.52 cubic feet

The volume of the composite solid will be 7,121.52 cubic feet.

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The depth of the river is 3.192 feet.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Since last year the depth of the river was 4.2 feet deep and year it dropped 24%. The depth will be:

= 4.2 - (24% × 4.2)

= 4.2 - 1.008

= 3.192 feet

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The solution to the given composite functions are;

f(g(x)) = √(x² + 1) + 8

g(f(x)) = [√(x) + 8]² + 1

Composite functions are usually formed when one function is used as the input of another function.

We are given the functions;

f(x) = √(x) + 8

g(x) = x² + 1

1) f(g(x)); This simply means we will put the entire g(x) function for x in f(x) to get;

f(g(x)) = √(x² + 1) + 8

2) g(f(x)); This simply means we will put the entire f(x) function for x in g(x) to get; g(f(x)) = [√(x) + 8]² + 1

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The amount after 20 years is $662.04.

The interest does she earn is $240.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the addition of interest to the loan or deposit principal.

One plus the annual interest rate raised to the number of compound periods minus one is multiplied by the initial loan amount, or principal, to determine compound interest.

Given:

Jessica puts away $200 a month for 20 years.

P = $200

t = 20 years

r = 6% = 0.06

n = 12 (compounded monthly)

Consider the compound interest formula,

[tex]A = P(1+\frac{r}{n})^n^t[/tex]

Plug the values of P, r, n and t in the above equation.

⇒

[tex]A = 200(1+\frac{0.06}{12})^1^2^*^2^0\\ A = 200(1+0.005)^2^4^0\\A = 200(1.005)^2^4^0\\A = 662.04089\\A = 662.04[/tex]

Hence, the amount after 20 years is $662.04.

Now to find the interest does she earn.

Interest = Principle x time x rate

             = 200 x 20 x 0.06

Interest = $240

Hence, the interest does she earn is $240.

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Step-by-step explanation:

-3x² - 6x + 24

this is an expression, not an equation.

for an equation this would have to look like e.g.

-3x² - 6x + 24 = 0

anyway, yes, we can factor this expression :

-3x² - 6x + 24 = -3(x² + 2x - 8) = -3(x + 4)(x - 2)

why ?

x² + 2x - 8 corresponds to

(x + a)(x + b) = x² + (a+b)x + ab

so which factors a and b multiply to ab = -8 and add to (a+b) = 2 ?

-8 has the factors

4, -2

-4, 2

8, -1

-8, 1

only (4, -2) covers the both criteria.

therefore, the correct factorization is

-3(x + 4)(x - 2)

The number of cubical boxes that can contain in the rectangular box is 36.

Volume is defined as the space occupied by an object.

The volume of a cuboid is (length×width×height).

Given, Length of the rectangle box is 16 cm and the width of the box is

12 cm.

We know the volume of a cube is (side)³.

Therefore, given that the volume of a cubical 64 cm³ and we know (4)³ is 64.

Hence the height of the rectangular box is 3 layers so (4×3) = 12 cm

So, the volume of the rectangular box is (16×12×12) cm³ = 2304 cm³.

Therefore, The maximum number of boxes that can be contained is

= (2304/64)

= 36.

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In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 in.

[tex]\boxed{\bold{= > (39)^2=(15)^2+(QN^2}}\\\boxed{= > QN=\bold{\sqrt{(39)^2-(15)^2}} }\\\boxed{= > QN=\bold{36}}[/tex]

Now we have to determine the side RN.

Now put all the values in the above expression, we get the value of side RN.

[tex]\boxed{\bold{= > (17)^2}=(15)^2+(RN)^2}\\\boxed{= > RN=\bold{\sqrt{(17)^2-(15)^2} }}\\\boxed{= > RN=\bold{8}}[/tex]

Therefore,  In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 inches.

[tex]\text{The correct answer is QR is, 44 in.}[/tex]

Using Pythagoras theorem in ΔPNQ:

[tex]\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PQ)^2=(PN)^2+(QN)^2}}[/tex]

[tex]\boxed{(39)^2=(15)^2+(QN)^2}\\\boxed{\bold{QN=\sqrt{(39)^2-(15)^2} }}\\\boxed{QN=\bold{36}}[/tex]

[tex]\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PR)^2=(PN)^2+(QN)^2}}[/tex]

[tex]\boxed{\bold{(17)^2=(15)^2+(RN)^2}}\\\boxed{\bold{RN=\sqrt{(17)^2-(15)^2} }}\\\boxed{RN=\bold{8}}}[/tex]

Adding the numbers:

36 + 8 = 44

[tex]\text{Hence, The correct answer is QR is, 44 in.}[/tex]

To find the probability that Y1 = 71 and Y2 = y2, we can write G(y1, y2) = P(Y1 = 71, Y2 = y2).

To find the probability that Y1 = 71 and Y2 = y2, we need to consider the possible values of X1 and X2 that could lead to these values of Y1 and Y2. The probability density functions (PDFs) of an exponential distribution with mean 1000 is f(x) = 1/1000 * e^(-x/1000). Therefore, the probability of this event is

Another possibility is that X1 = y2 and X2 = 71. The probability of this event is

Since these two events are mutually exclusive and exhaust all possible ways that Y1 can equal 71 and Y2 can equal y2, the probability of these events occurring is the sum of these probabilities. Therefore,

Note that this expression is only valid when 0 < 71 < y2 < ∞ since these are the conditions under which Y1 can equal 71 and Y2 can equal y2.

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Using the given provided probability value of getting three heads, The statement which best follow the given condition is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close to 12.5%.

What do you mean by probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

According to the given question:

Assume you have a fair coin, which means it will likely land tails up 50% of the time and heads up 50% of the time. Let's say you flip it three times, each time independently. What is the likelihood that it will land heads up first, followed by a tails up landing?

The solution is 1/8, or 12.5%.

coin flipped = 3 times.

probability of getting three heads = 0.125

Since, This probability explains the chances of landing three heads which is 0.125 which in terms of percentage is 12.5% .

So, The statement is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.

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We calculated sample mean 14 and standard deviation 1.32

A sample mean refers to the average of all values included in the data list.

When we have a list of data set, we can calculate the mean value of the data set by adding all the values and divided by the amount of data.

We are given, 8 packages of ground chuck

 number of samples, N = 8

fat contents (%) for 8 packages, X= 12, 15, 16, 13, 15, 13, 15, 13

Sum of X= ∑X= 112

sample mean= sum of all data values/ number of data items in the sample

   X= ∑X/N

  sample mean X = 112/8 =14

we calculate   X² for 8 sample = 144, 225, 256, 169, 225, 169, 225, 169

∑X² = 1582

standard deviation is calculated by using the formula bellow

√[∑X²/N-(∑X/N)²] = √[1582/8-(112/8)²]  

standard deviation = 1.32

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To find the Fourier cosine series of the function f(x), we first need to find the Fourier coefficients of f(x).

The Fourier coefficients of f(x) are given by:

a0 = (2/L) * integral of f(x) from x=0 to x=L

an = (2/L) * integral of f(x) * cos(npix/L) from x=0 to x=L

bn = (2/L) * integral of f(x) * sin(npix/L) from x=0 to x=L

Using the result from part a) and the fact that the series can be integrated term by term, we can find the Fourier cosine series of f(x) as follows:

F(x) = a0/2 + sum from n=1 to infinity of an * cos(npix/L)

Therefore, the Fourier cosine series of the function f(x) is:

F(x) = (1/L) * integral of f(x) from x=0 to x=L + sum from n=1 to infinity of (2/L) * integral of f(x) * cos(npix/L) from x=0 to x=L

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Answer:

4.9

Step-by-step explanation:

Answer:

you multiply to find common denominators. in the example below you multiply the denominators by themselves, and then individually. 1/2 and 1/3 are the fractions your working with. (2x3)=6 and then (1x3)=3 and (1x2)=2 (2+3)=5 and so (5/6)

Step-by-step explanation:

example: 1½+1⅓=2⅚

Answer: You have to find a common denominator.

Step-by-step explanation: Look at this attachment to understand: (Directions included)

I hoped this helped! If you can, may you PLEASE mark me brainliest?

Answer:

To find x and y intercept .... y = 4, and x = -2

Step-by-step explanation:

y-2x=4

y = 4

-2x=4

-2x/-2 = 4/-2

x = -2

Is this equation for solving y and x

The type of function is it is C . Exponential growth .

Given :

For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value .

If  for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.

Option B is incorrect because  because y is not decreasing

Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.

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Answer:

so (-5.2,-2) and (4.2,-2) are 9.4 units apart  away from each other

Step-by-step explanation:

so (4.2,-2) and (-5.2,-2) add together and get 9.4

400 square feet of carpet area for $240 is the best deal among the given option.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).

The carpets were sold for the following prices:

1) $67 for 100 square feet.

2) $130 for 200 square feet.

3) $240 for 400 square feet

4) $504 for 800 square feet.

For each of them, we would calculate the unit cost per square foot. It develops

1) The price per square foot is 67÷100 = $0.67

2) The price per square foot is 130÷200 = $0.65.

3) The price per square foot is 240÷400 = $0.6.

4) The price per square foot is 504÷800 = $0.63.

Comparing the unit costs per square foot the best deal costs $0.6 per square foot per unit, which is 400 square feet of carpet for $240.

400 square feet of carpet area for $240 is the best deal among the given option.

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