What transformations of the graph of (x)=|x| are applied to graph the function g?

Answer:

x = -1

Step-by-step explanation:

x−3=4−2(x+5)

x - 3 = 4 - 2x - 10

x - 3 = -2x - 6

3x = -3

x = -1

The maximum area is, A = 10.392

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. LHS = RHS is a common mathematical formula.

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:

y = 9-x²

first, Area = x × y

Area = x(9-x²)

Now,

the Domain: (0, 3)

Also, differentiating

A' = 0

9 - 3x² = 0

x²= 9/3

x =±3

So, the maximum area is

A= 1.732 x 6

A = 10.392

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On solving the provided question, we can say that Rounding to the nearest tenth of a square unit, the area of the circle is approximately 25.1 square units.

A circle seems to be a two-dimensional component defined as such collection of the all points in a jet that become equidistant from the hub. A circle is commonly portrayed with the capital "O" for centre and the lower section "r" for the radius, which is the distance from the origin to any point on the circle. Girth (the distance from around circle) is given by the formula 2r, where (pi) is a proportionality constant roughly equal to 3.14159. The formula r2 calculates the circle's circumference, which refers to the amount of room inside of the circle.

We can use the distance formula to find the radius of the circle, which is the distance between the center C(2, 5) and point D(4, 3):

\($r = \sqrt{(4-2)^2 + (3-5)^2} = \sqrt{8} = 2\sqrt{2}$\)

The area of the circle is given by the formula\($A = \pi r^2$\), so substituting in the radius we just found, we get:

\($A = \pi (2\sqrt{2})^2 = 8\pi \approx 25.1$\\\)

Rounding to the nearest tenth of a square unit, the area of the circle is approximately 25.1 square units.

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The percentage is used to denote the fraction of a quantity present.

The number of athletics students are 4. The correct answer is option A.

The percentage is defined as the portion of quantity present.

It is converted into fraction by dividing it by 100.

The percentage of students in athletics are 48%.

Total number of students in the class is 25.

The number of students in athletics is given as,

N = 48% of 25

=> N = 48 / 100 × 25

=> N = 48 / 4

=> N = 12.

Hence the number of athletics students in Mrs. Cano's class is 12.

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Answer:

push-up = 1 second

sit-up = 3 seconds

Step-by-step explanation:

let p represent the # of push-ups

let s represent the # of sit-ups

System of equations:

19p+8s=43

12p+12s=48

i'll eliminate s by multiplying the top equation by 3 and the bottom equation by -2

57p+24s=129

-24p-24s=-96

33p=33

p=1 second

now solve for s (i'll plug p into the 2nd equation)

12(1) + 12s=48

12s=36

s=3 seconds

Answer:

Ok so I kind of want you to learn how to do this because its really easy. You add up all of the numbers then you count how many numbers there are and you divide of all of the numbers that you added up  and the sum of how many numbers there are for example if I had 34,65, 75, 85, 14, and 23 It would be 34+65+75+85+14+23= 269. There are 6 numbers so 269 divided by 6 and you get 44.8 IF THIS HELPS!!

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

The maximum amount of salt ever in the tank will be lb / (1 +  \((gal/min) * e^{t + C}\) ), where t approaches infinity.

(a) To find the amount of salt in the tank after t minutes, we need to consider the rate at which brine enters the tank and the rate at which the solution leaves the tank.

Let's denote the amount of salt in the tank at time t as S(t).

Brine enters the tank at a rate of lb/gal, and the solution leaves the tank at a rate of gal/min. Therefore, the rate of change of the amount of salt in the tank is given by the following equation:

dS/dt = (lb/gal) - (gal/min) * (S(t) / gal)

This equation represents the rate of change of salt in the tank. It takes into account the incoming brine and the outflow of the solution.

To solve this differential equation, we can separate the variables and integrate them:

\(\int dS / [(lb/gal) - (gal/min) * (S / gal)] = \int dt\)

Integrating both sides gives:

\(ln |(lb/gal) - (gal/min) * (S / gal)| = t + C\)

Where C is the constant of integration.

By exponentiating both sides, we have:

\(|(lb/gal) - (gal/min) * (S / gal)| = e^{t + C}\)

Since the absolute value is always positive, we can drop the absolute value signs:

\((lb/gal) - (gal/min) * (S / gal) = e^{t + C}\)

Simplifying further:

\(S = (gal/lb) * [(lb/gal) - (gal/min) * (S / gal)] * e^{t + C}\)

Simplifying the expression inside the brackets:

\(S = lb - (gal/min) * S * e^{t + C}\)

Rearranging the equation:

\(S + (gal/min) * S * e^{t + C}= lb\)

Factoring out S:

S * (1 + (gal/min) * e^{t + C}) = lb

Solving for S:

\(S = lb / (1 + (gal/min) * e^{t + C})\)

(b) To find the maximum amount of salt ever in the tank, we need to consider the behavior of the expression \((gal/min) * e^{t + C}\) as t approaches infinity.

As t approaches infinity, the exponential term  \(e^{t + C}\) will dominate the expression, making it significantly larger. Therefore, the maximum amount of salt in the tank will occur when the term  \((gal/min) * e^{t + C}\)  is maximized.

Since the exponential function is always positive, the maximum value of  \((gal/min) * e^{t + C}\)  will occur when \(e^{t + C}\) is maximized. This occurs when t + C is maximized, which happens as t approaches infinity.

Therefore, the maximum amount of salt ever in the tank will be lb / (1 +  \((gal/min) * e^{t + C}\) ), where t approaches infinity.

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Answer:

110°F

Explanation:

The temperature on the thermometer is taken at the point where the red ends as highlighted in the diagram below:

At this point, the value is 110.

Therefore, the temperature shown on the thermometer is 110°F.

The P-value associated with each value of the z test statistic is given above. We round our answers to four decimal places.

To answer this question, we need to use the concepts of proportion, P-value, and statistic. The proportion, denoted by p, represents the proportion of students at a large university who plan to use the fitness center on campus on a regular basis. The null hypothesis, H0, states that the proportion is equal to 0.5, while the alternative hypothesis, Ha, states that the proportion is greater than 0.5.
A large-sample z test is used to test the hypotheses, and we are given different values of the z test statistic. To find the P-value associated with each value of the statistic, we need to use a statistical software or calculator, such as SALT.
The P-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed statistic, assuming the null hypothesis is true. A small P-value indicates strong evidence against the null hypothesis, while a large P-value indicates weak evidence against the null hypothesis.
Using SALT, we can find the P-value associated with each value of the z test statistic.
(a) z = 1.10: P-value = 0.1357
(b) z = 0.92: P-value = 0.1788
(c) z = 1.95: P-value = 0.0256
(d) z = 2.44: P-value = 0.0073
(e) z = -0.12: P-value = 0.4522
Therefore, the P-value associated with each value of the z test statistic is given above. We round our answers to four decimal places.

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Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.

Given statement;

Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.

→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.

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Answer:

B.

Step-by-step explanation:

it's the only one that all the angles add up to 180

It is proved that the two properties of the Jacobi symbol:

(a) if a ≡ b (mod n), then (na) = (nb),

(b) (na)(nb) = (nab), demonstrating the relationships between the Jacobi symbol, congruence, and the product of integers.

(a) To prove the first property, let's assume that a and b are congruent modulo n, i.e., a ≡ b (mod n).

We need to show that (na) = (nb). By the definition of the Jacobi symbol, we have (na) = (3a)e3⋅(5a)e5⋅(7a)e7⋯ and (nb) = (3b)e3⋅(5b)e5⋅(7b)e7⋯. Since a ≡ b (mod n), it follows that for each prime factor p of n, we have ap ≡ bp (mod p).

Therefore, the exponents in both (na) and (nb) corresponding to the prime factors of n will be the same, resulting in (na) = (nb).

(b) To prove the second property, we need to show that (na)(nb) = (nab). By expanding the Jacobi symbols using their definition, we have (na)(nb) = (3a)e3⋅(5a)e5⋅(7a)e7⋯(3b)e3⋅(5b)e5⋅(7b)e7⋯.

By the laws of exponents, this can be simplified to (3ab)e3⋅(5ab)e5⋅(7ab)e7⋯, which is equivalent to (nab) based on the definition of the Jacobi symbol.

Therefore, we have proved the two properties of the Jacobi symbol: (a) if a ≡ b (mod n), then (na) = (nb), and (b) (na)(nb) = (nab), demonstrating the relationships between the Jacobi symbol, congruence, and the product of integers.

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Answer:

false

Step-by-step explanation:

The nonstationary penalty function approach for the iteration is:

\(x=\left[\begin{array}{c}\sqrt{2} &0&\sqrt{2} \end{array}\right] ,x=\left[\begin{array}{c}\sqrt{2}&0&\sqrt{3}\end{array}\right] ,x=\left[\begin{array}{c}\sqrt{3}&0&1\end{array}\right]\)

F = x³ -6x₁² + 11x₁ + x₃

Constraints given x₁² + x₂² - x₃² ≤ 0 , 4 - (x₁² + x₂² - x₃²) ≤ 0

we need to check,

\(x=\left[\begin{array}{c}0&\sqrt{2} &\sqrt{2} \end{array}\right]\)

is solution or not by Tagrange multiplier.

The method of multiplies allows us to maximize or minimize functions with the Constraint that point or a certain surface. we only consider points of a certain surface.

To find critical points of a function f(₁, x₂, x₃)  on a level surface g(₁, x₂, x₃) = ((or rubject to constraints) g(₁, x₂, x₃)  = C

we must votre the following system of simultaneous eqⁿ

Δf(₁, x₂, x₃)  = λ g(₁, x₂, x₃)  

g(₁, x₂, x₃) = c

remembering that of is A ΔG this as a Collection of are vectors we can write four equations in the four unknown.

fx₁(₁, x₂, x₃) = λ gx₁(₁, x₂, x₃)

Variable is a dummy called a Lagiange multipliers, only really care about the values x₁, x₂, x₃.

Δfx₁ = (3x² - 12x₁ + 11)  +  Δf = <3x² - 12x₁ + 11>

given x₃ ≤ 5

4-x₁²-x₂²-x₃² ≤0

0≤x₃≤5

-x₁²-x₂²≤21.

1=λ (-2x₃) = -2λ x₃ = 1

x₂ = 0

x₁ = \(\sqrt{2}\) , x₁ = 1 , x₁ = \(\sqrt{3}\)

x₃ = \(\sqrt{2}\), x₃ = \(\sqrt{3}\), x₃ = 1

Therefore, the possible iteration are:

\(x=\left[\begin{array}{c}\sqrt{2} &0&\sqrt{2} \end{array}\right] ,x=\left[\begin{array}{c}\sqrt{2}&0&\sqrt{3}\end{array}\right] ,x=\left[\begin{array}{c}\sqrt{3}&0&1\end{array}\right]\)

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Albert have left 7/4 cups of cheese left.

Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, a specific value, or a thing.

Given,

Amount of cheddar = 2/3 cup

Amount of mozzarella = 5/6 cup

Amount of parmesan = 3/4 cup

Total cups of cheese

= cheddar + mozzarella + parmesan

= 2/3 + 5/6 + 3/4

= 8 + 10 + 9 /12

= 27/12

= 9/4

He puts 1/2 cup of cheese in pizza

Cheese left = 9/4 - 1/2 = 9 - 2 / 4 = 7/4

There is 7/4 cups of cheese left.

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Answer:

Option (3)

Step-by-step explanation:

Given expression in this question represents the partial sum of an infinite geometric series in the sigma notation.

\(S_{n}=\sum_{n=1}^{\infty}6(2)^{n-1}\)

First term of this series 'a' = 6

Common ratio 'r' = 2

We have to find the sum of 4 terms of this infinite series (n = 4).

Sum of n terms of a geometric series is,

\(S_n=\frac{a(r^n-1)}{(r-1)}\)

\(S_4=\frac{6(2^4-1)}{(2-1)}\)

    \(=\frac{6(16-1)}{(1)}\)

    \(=90\)

Therefore, sum of 4 terms of the given series will be 90.

Option (3) will be the answer.

Answer:

31.5 kg om

Step-by-step explanation:

Esto se calcula como:

12 trabajadores = 42 kg

9 trabajadores = x kg

Cruz Mulitiply

12 trabajadores × x kg = 9 trabajadores × 42 kg

x kg = 9 trabajadores × 42 kg / 12 trabajadores

x kg = 31.5 kg

Por tanto, 9 trabajadores consumirán 31.5 kg de arroz al mismo tiempo.

Answer:

31.5 kg de arroz consumirán 9 obreros en el mismo tiempo.

Step-by-step explanation:

Dos cantidades son directamente proporcionales si cuando una de ellas se multiplica o se divide por un número, la otra se multiplica o se divide por el mismo número.

La “regla de tres” es un procedimiento que se aplica para resolver problemas de proporcionalidad en el que se conocen tres de los cuatro datos que componen las proporciones y se requiere calcular el cuarto.

En este caso aplicamos la siguiente regla de tres: si 12 obreros consumen 42 kg, 9 obreros ¿Cuántos kg de arroz consumirán?

\(kg de arroz=\frac{9 obreso*42 kg}{12 obreros}\)

kg de arroz= 31.5

31.5 kg de arroz consumirán 9 obreros en el mismo tiempo.

Answer:

7

Step-by-step explanation:

g(x) = -3x - 5

g(-4) = -3(-4) - 5

g(-4) = 12 - 5

g(-4) = 7

Best of Luck!

240 homes in the county are between $175,000 and $225,000.

The image attached is associated with this question and m in it refers to the mean value which is $225000 here and d refers to the standard deviation which is $25000 here.

Now since m= $225000

and $175000= $225000-$50000= $225000-(2* $25000)= m-2d

Thus, as per the image area covered between m and m-2d=  $225000

and $175000 is (34%+14%)of 500 homes= 68% of 500= 240 homes, is the answer.

A random variable X is said to follow a normal distribution if its parameters are mean and standard deviation. Every other distribution can be reduced to a normal distribution.

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Answer:

You can draw a model for your teacher if your teacher approves

Step-by-step explanation:

Try drawing a model

Answer:

-16r^2 - 10r

Step-by-step explanation:

all you got to do is distribute

The coordinates of the endpoints of rs are r(1,11) and s(6,1). point t is on rs and divides it such that rt:st is 4:1.

the coordinates of the point t are (5, 3)

We may utilise the notion of section formula to get the coordinates of point T, which states that if we have two points A(x1, y1) and B(x2, y2) and a point P splitting the line segment AB in the ratio m:n, then the coordinates of point P can be calculated using the following formula:

P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))

In this situation, we have the coordinates of points R and S, as well as the ratio of T divided by RS. So, let's enter the following values into the formula to determine T's coordinates:

Let the coordinates of point T be (x, y), and the ratio of T to RS be 4:1, implying that RT:ST = 4:1. This means that RT = 4/5 (RS length) and ST = 1/5. (length of RS).

RS length =\(sqrt((6-1)^2 + (1-11)^2)\) = \(sqrt (146)\)

RT=\((4/5) * sqrt(146)\) = \((4/5) * 12.083\) = 9.666

ST =\(1/5* sqrt(146)\) = \(1/5* 12.083\) = 2.4166

We get the following using the section formula:

x = (4×6 + 1×1)/(4+1) = 5

y = (4×1 + 1×11)/(4+1) = 3

T = (5, 3)

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For the function f(x) , the statement based on limit has following answer,

a. For all f(x) , if  lim x→a f(x) does not exist, then lim x→a⁺ f(x) does not exist is false statement.

b.  For all f(x) , if  lim x→a f(x) does not exist, then lim x→a⁻ f(x) does not exist is false statement.

For the function f(x),

If the limit of the function f(x) does not exist then,

(a) lim x→a⁺ f(x) does not exist is a false statement.

If lim x→a⁺ f(x) or lim x→a⁻ f(x) exists.

it is still possible for lim x→a f(x) to not exist.

For example, consider the function f(x) = 1/x and a = 0.

The limit of f(x) as x approaches 0 from the right (i.e., lim x→0⁺ f(x)) does not exist.

But the limit of f(x) as x approaches 0 from the left (i.e., lim x→0⁻ f(x)) does exist.

(b) lim x→a⁻ f(x) does not exist is a false statement.  

Considering same function f(x) = 1/x and a = 0 .

The limit of f(x) as x approaches 0 from the left (i.e., lim x→0⁻ f(x)) does not exist.

But the limit of f(x) as x approaches 0 from the right (i.e., lim x→0⁺ f(x)) does exist.

Therefore, function f(x) represents the following statement as,

a. If  lim x→a f(x) does not exist, then lim x→a⁺ f(x) does not exist is false statement.

b.  If  lim x→a f(x) does not exist, then lim x→a⁻ f(x) does not exist is false statement.

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The above question is incomplete , the complete question is:

Determine whether each statement is true or false. you have one submission for each statement.

(a) for every function f(x), if lim x→a f(x) does not exist, then lim x→a⁺ f(x) does not exist.

(b) for every function f(x), if lim x→a f(x) does not exist, then lim x→a⁻ f(x) does not exist.

Answer:

270 miles

Step-by-step explanation:

if 1 gallon = 18 miles

then 15 gallons = x miles

cross multiply

1 × x = 15×18miles

x = 270 miles

so it travels 270 miles on 15 gallons of gasoline

Using Cosine law,

the angle between two shortest sides of triangle is 85.1°..

We have provided that,

A garden has triangular shape.

let "AB" , "BC" , "CA" be sides of triangular shape garden and

we have the sides of triangle are 475 feet , 595 feet and 401 feet i.e AB = 475 , AC = 595 ,

BC= 401

we have to measure of angle between two shortest sides i.e angle between side AB and BC

let x degree be an angle between two shortest sides of triangle .

Using cosine rule ,

(AC)² = (BC)² + (AB )² - 2 AB×BC Cosx

=> (595)² = (401)² + ( 475)² - 2× 475 ×401 Cosx

=> 2(475×401) Cosx = (401)² + (475)² - (595 )²

=> 2 ( 475×401) Cosx = 32401

=> Cosx = 0.085

=> x = cos⁻¹(0.085) = 85.1°

Hence, the angle between two shortest sides of triangle is 85.1°

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The statement is false. The correct formula to find the size of the union of two sets is |a ∪ b| = |a| + |b| - |a ∩ b|. Substituting the values given in the question, we get |a ∪ b| = n + m - |a ∩ b|.

We don't know anything about the intersection of sets a and b, so we cannot directly calculate |a ∩ b|.

However, we do know that |a ∩ b| is less than or equal to the minimum of |a| and |b|, which is min(n,m). Therefore, we can say that |a ∩ b| ≤ min(n,m).

Substituting this inequality into the formula for |a ∪ b|, we get:

|a ∪ b| = n + m - |a ∩ b|
≥ n + m - min(n,m)

We can simplify this expression by observing that if n ≤ m, then min(n,m) = n. If n > m, then min(n,m) = m. Therefore:

|a ∪ b| ≥ n + m - n = m
or
|a ∪ b| ≥ n + m - m = n

In either case, we have shown that |a ∪ b| is greater than or equal to the larger of |a| and |b|. Therefore, the given formula, |a ∪ b| = nm - nm, cannot be correct. The correct answer is b. false.

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Answer:

Replace y with f−1(x) f - 1 ( x ) to show the final answer. Verify if f−1(x)=x3+73 f - 1 ( x ) = x 3 + 7 3 is the inverse of f(x)=3x−7 f ( x ) = 3 x - 7

Step-by-step explanation:

By using the formula for mean and variance, it can be calculated that

Mean of X = 25

Variance of X = 51.67

What is mean and variance?

Suppose there is a data set. Mean gives the average of the values of the data set

Variance is the square of the sum of deviation from mean.

Let x be the total; of the numbers on the two card

Possible values of X= 15, 20, 25, 30, 35

P(X = 15) = \(\frac{2}{12}\)

P(X = 20) = \(\frac{2}{12}\)

P(X = 25) = \(\frac{4}{12}\)

P(X= 30) = \(\frac{2}{12}\)

P(X = 35) = \(\frac{2}{12}\)

Mean of X =

\(15 \times \frac{2}{12} + 20 \times \frac{2}{12} +25 \times \frac{4}{12} + 30 \times \frac{2}{12} + 35 \times \frac{2}{12}\\\\\frac{300}{12}\\\\25\)

Variance of X =

= \((225 \times \frac{2}{12} + 400 \times \frac{2}{12}+625 \times \frac{4}{12}+900 \times \frac{2}{12}+1225 \times \frac{2}{12}) - (25)^2\\\\\frac{8000}{12} - 625}\\\\666.67 - 625\\\\51.67\)

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Complete Question

In a box are four cards numbered 5, 10, 15, 20. two cards are taken out at random without replacement, and X is the total; of the numbers on the two card. Find the mean and variance of X .

Answer:

The numbers you are looking for would be:

12, 14, and 16

Step-by-step explanation:

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

12,14,16

Step-by-step explanation:

Let x be the first even integer

x+2 is the second even integer

x+4 is the third even integer

x+ x+2 + x+4 = 42

Combine like terms

3x+6 = 42

3x+6-6 = 42-6

3x = 36

Divide by 3

3x/3 = 36/3

x = 12

x+2 = 14

x+4 = 16