A ​$260 suit is marked down by 30​%. Find the sale price.

The function in vertex form is equivalent to \(\rm y = (x + 2/4)^2 + \frac{3}{4}\).

A quadratic equation is an equation of degree 2 in other words.Quadratic equations have the form ax² + bx + c = 0 and are second-degree algebraic expressions.

The standard quadratic function with vertex (h, k) is ;

\(\rm y = a(x - h)^2 + k\)

The general quadratic equation is found as;

\(\rm y = ax^2 + bx + c\)

The value of h is given as;

\(\rm h = \frac{-b}{2a}\)

For the given equation in the problem;

\(\rm y = x^2 + x + 1\)

The value of the k is found by;

\(\rm y =( \frac{-1}{2}) ^2 - \frac{1}{2} + 1 \\\\ y= \frac{1}{4} - \frac{1}{2}+ 1 \\\\ y= \frac{1}{4}- \frac{2}{4}+ \frac{4}{4}\\\\ y= \frac{3}{4}\)

So the vertex is at \(\frac{-2}{4}\) and \(\frac{1}{4}\)  then the vertex form is:

\(y = (x +\frac{2}{4} )^2 + \frac{3}{4}\)

Hence the functions in vertex form are equivalent \(\rm y = (x + 2/4)^2 + \frac{3}{4}\).

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Answer: OPTION 3

Step-by-step explanation:

The maximum value of f(x) = x + 625/x for x in the interval (0, ∞) is 50 at x = 25, and there is no minimum value within the given interval.

To find the critical points, we take the derivative of f(x) with respect to x and set it equal to zero:

f'(x) = 1 - 625/x^2 = 0

Solving this equation, we get x = ±25. However, since x must be positive, we discard the negative solution.

Now we need to check the endpoints of the interval. As x approaches 0, f(x) approaches infinity. Therefore, there is no minimum value at x = 0.

To determine the maximum, we compare the values of f(x) at the critical point and the endpoint:

f(25) = 25 + 625/25 = 50

Since f(25) = 50 is the maximum value, there is no minimum value.

In summary, the function f(x) = x + 625/x has a maximum value of 50 at x = 25, and there is no minimum value within the given interval.

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If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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Answer:

d. 0

Step-by-step explanation:

Given that:

A rational number is multiplied by a irrational number.

And the result is a rational number.

To find:

Such rational number wil be:

a. \(\frac{1}2\)

b. 1

c. \(\frac{1}{10 }\)

d. 0

Solution:

Let us consider the given options one by one.

Let the irrational number be = \(\pi\)

Checking option a.

Multiply \(\pi\) and \(\frac{1}2\).

Result is: \(\frac{\pi}2\) which is again irrational.

So, a. is not correct.

Checking option b.

Multiply \(\pi\) and 1.

Result is: \(\pi\) which is again irrational.

So, b. is not correct.

Checking option a.

Multiply \(\pi\) and \(\frac{1}{10}\).

Result is: \(\frac{\pi}{10}\) which is again irrational.

So, c. is not correct.

Checking option d.

Multiply \(\pi\) and 0.

Result is: 0 which is rational.

So, d. 0 is the correct answer.

The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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The assertion that which shows that P(k + 1) is true provided Pk in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

What is Integer?

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Given that P(n) be the assertion

∑j² = n (n+1)(2n+1)/6

(a) For n = 3, we get

∑j² = 1² + 2²+3² =14

= 3(3+1)(6+1)/6

=14

Hence, P(3) is true.

(b) Expression for P(k) may take the form

∑j² = k (k+1)(2k+1)/6

(c) Expression for P(k + 1) may take the form

∑j² = (k+1) (k+2)(2k+3)/6

(d)Base case:

In base case, we must prove that P(1) is true.

(e) To prove P(n) will be true for every positive integer n, we need to prove that P(k + 1) is true in the inductive step, where k is a positive integer.

(f) In the Inductive step, the Inductive hypothesis is that Pk is true for positive integer k.

(g)Base case:

a) For n=1, we get

RHS= 1(1+1)(2+1)/6

=1

Hence, P(1) is true.

Inductive hypothesis:

Assume P(k) is true:

∑j² = k (k+1)(2k+1)/6

Inductive step:

Now,

∑j² = k (k+1)(2k+1)/6 +(K+1)²

which shows that P(k + 1) is true provided P(k) in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

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Answer:

A+B =2.25

Step-by-step explanation:

x² + 8x+ 4 = 4(1/4 x² + 2x +1)

4(1/4 x² + 2x +1)  = 0

1/4 x² + 2x +1  = 0

Ax² + Bx + 1 = 0

A = 1/4 , B = 2

A+B = 2 1/4 = 2.25

The equation of the parabola in vertex form that passes through the points (-2, 4) and (1, 0):

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

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex is (-1, 2), so we can write the equation as y = -2(x + 1)^2 + 2.

To find the vertex of the parabola, we can take the average of the x-coordinates of the two points, and then take the average of the y-coordinates of the two points. The average of the x-coordinates is (-2 + 1)/2 = -0.5, and the average of the y-coordinates is (4 + 0)/2 = 2. Therefore, the vertex is (-0.5, 2).

Once we know the vertex, we can find the value of a by substituting the vertex coordinates into the vertex form of the parabola. Substituting (-0.5, 2) into the equation y = a(x - h)^2 + k, we get 2 = a(-0.5 - (-1))^2 + 2. Simplifying, we get 2 = a(0.25) + 2. Solving for a, we get a = -2.

Plugging in a = -2 into the vertex form of the parabola, we get y = -2(x + 1)^2 + 2. This is the equation of the parabola in vertex form.

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The equation of the parabola in vertex form that passes through the points (-2, 4) and (1, 0):

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

The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex is (-1, 2), so we can write the equation as y = -2(x + 1)^2 + 2.

To find the vertex of the parabola, we can take the average of the x-coordinates of the two points, and then take the average of the y-coordinates of the two points. The average of the x-coordinates is (-2 + 1)/2 = -0.5, and the average of the y-coordinates is (4 + 0)/2 = 2. Therefore, the vertex is (-0.5, 2).

Once we know the vertex, we can find the value of a by substituting the vertex coordinates into the vertex form of the parabola. Substituting (-0.5, 2) into the equation y = a(x - h)^2 + k, we get 2 = a(-0.5 - (-1))^2 + 2. Simplifying, we get 2 = a(0.25) + 2. Solving for a, we get a = -2.

Plugging in a = -2 into the vertex form of the parabola, we get y = -2(x + 1)^2 + 2. This is the equation of the parabola in vertex form.

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The value of p that makes the given equation true is equal to: B. p = -5

Given the following equation:

To find a value of p that makes the given equation true:

In this exercise, you're required to determine a value of p that satisfies the given equation true such that when substituted into the equation, it has a true result or outcome.

Rearranging the equation by collecting like terms, we have:

\(3p - 8 = -23\\\\3p=-23+8\\\\3p=-15\\\\p=\frac{-15}{3}\)

p = -5

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Answer:

It should be the 2nd one.

Answer: A, C, 57

Step-by-step explanation:

I multiply by 0.40 for the first one, and then multiply by 1.0625. 0.40 = 40% and multiplying by 1.0625 is the same as adding 6.25%. For the second, I multiply by 0.70 because that is 70%. For the last, I multiply by 0.95 for the same reason.

Answer:

-15

-907

Step-by-step explanation:

1. -24 + 18 - 9 = -15

2. 10-7[3+128]

= 10-7(131)

= 10-917

= -907

Answer:

Step-by-step explanation:

Question (1). An alloy contains zinc and copper in the ratio of 7 : 9.

If the weight of an alloy = x kgs

Then weight of copper = \(\frac{9}{7+9}\times (x)\)

                                      = \(\frac{9}{16}\times (x)\)

And the weight of zinc = \(\frac{7}{7+9}\times (x)\)

                                      = \(\frac{7}{16}\times (x)\)

If the weight of zinc = 31.5 kg

31.5 = \(\frac{7}{16}\times (x)\)

x = \(\frac{16\times 31.5}{7}\)

x = 72 kgs

Therefore, weight of copper = \(\frac{9}{16}\times (72)\)

                                               = 40.5 kgs

2). i). 2 : 3 = \(\frac{2}{3}\)

        4 : 5 = \(\frac{4}{5}\)

Now we will equalize the denominators of each fraction to compare the ratios.

\(\frac{2}{3}\times \frac{5}{5}\) = \(\frac{10}{15}\)

\(\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}\)

Since, \(\frac{12}{15}>\frac{10}{15}\)

Therefore, 4 : 5 > 2 : 3

ii). 11 : 19 = \(\frac{11}{19}\)

    19 : 21 = \(\frac{19}{21}\)

By equalizing denominators of the given fractions,

\(\frac{11}{19}\times \frac{21}{21}=\frac{231}{399}\)

And \(\frac{19}{21}\times \frac{19}{19}=\frac{361}{399}\)

Since, \(\frac{361}{399}>\frac{231}{399}\)

Therefore, 19 : 21 > 11 : 19

iii). \(\frac{1}{2}:\frac{1}{3}=\frac{1}{2}\times \frac{3}{1}\)

             \(=\frac{3}{2}\)

     \(\frac{1}{3}:\frac{1}{4}=\frac{1}{3}\times \frac{4}{1}\)

              = \(\frac{4}{3}\)

Now we equalize the denominators of the fractions,

\(\frac{3}{2}\times \frac{3}{3}=\frac{9}{6}\)

And \(\frac{4}{3}\times \frac{2}{2}=\frac{8}{6}\)

Since \(\frac{9}{6}>\frac{8}{6}\)

Therefore, \(\frac{1}{2}:\frac{1}{3}>\frac{1}{3}:\frac{1}{4}\) will be the answer.

IV). \(1\frac{1}{5}:1\frac{1}{3}=\frac{6}{5}:\frac{4}{3}\)

                  \(=\frac{6}{5}\times \frac{3}{4}\)

                  \(=\frac{18}{20}\)

                  \(=\frac{9}{10}\)

Similarly, \(\frac{2}{5}:\frac{3}{2}=\frac{2}{5}\times \frac{2}{3}\)

                       \(=\frac{4}{15}\)                  

By equalizing the denominators,

\(\frac{9}{10}\times \frac{30}{30}=\frac{270}{300}\)

Similarly, \(\frac{4}{15}\times \frac{20}{20}=\frac{80}{300}\)

Since \(\frac{270}{300}>\frac{80}{300}\)

Therefore, \(1\frac{1}{5}:1\frac{1}{3}>\frac{2}{5}:\frac{3}{2}\)

V). If a : b = 6 : 5

     \(\frac{a}{b}=\frac{6}{5}\)

        \(=\frac{6}{5}\times \frac{2}{2}\)

        \(=\frac{12}{10}\)

  And b : c = 10 : 9

  \(\frac{b}{c}=\frac{10}{9}\)

 Since a : b = 12 : 10

 And b : c = 10 : 9

 Since b = 10 is common in both the ratios,

 Therefore, combined form of the ratios will be,

 a : b : c = 12 : 10 : 9

So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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The expression for P(x) is -3x³ - 4.

To find the expression for P(x), we need to subtract C(x) from R(x).

Given that R(x) = 2x² - 3x³ + 2x - 1 and C(x) = x² - x² + 2x + 3, we can substitute these values into the equation P(x) = R(x) - C(x):

P(x) = (2x² - 3x³ + 2x - 1) - (x² - x² + 2x + 3)

Simplifying, we can combine like terms:

P(x) = 2x² - 3x³ + 2x - 1 - x² + x² - 2x - 3

The x² terms cancel each other out, and the 2x and -2x terms also cancel each other out:

P(x) = -3x³ - 1 - 3

Simplifying further:

P(x) = -3x³ - 4

Therefore, the expression for P(x) is -3x³ - 4.

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By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

From the given figure, KR=9 units, RL=15 units, MT=7.5 units and TL=12.5 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Consider ΔKML and ΔRTL, we get

RL/KL =15/(15+9)

= 15/24

= 5/8

TL/ML =12.5/(12.5+7.5)

= 12.5/20

= 5/8

Here, RL/KL=TL/ML

Here, ∠KLM≅∠RLT

By SAS similarity, ΔKML and ΔRTL are similar triangles

So, ∠KMT≅∠RTL

By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

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Answer:

a

Step-by-step explanation:

got it right in edmentum

Answer:

Translation

Step-by-step explanation:

Not completely sure.

Can I have Brainliest?

Answer:

Translation

Step-by-step explanation:

The square is just moved to another side, its not rotted or reflected (if it were reflection it would be in the -x side)

An equation to represent the relationship between miles driven (y) and gallons of gas (x) used is \(28=ky\)

Given the following data:

Distance = 28 miles

To write an equation to represent the relationship between miles driven (y) and gallons of gas (x) used:

In this exercise, we would assign a variable to the parameters stated in the question in order to write an equation to represent the relationship between miles driven (y) and gallons of gas (x) used by Weston’s car during the trip.

Also, the amount of gas used up by a car is directly proportional to the distance traveled by the car. Mathematically, this is given by this expression:

\(x\; \alpha \;y\\ \\ x=ky\)

Substituting the given parameters into the formula, we have;

\(28=ky\)

Note: k is the constant of proportionality.

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Answer:

Step-by-step explanation:

C the probability that a customer buys a hat given that the customer has bought a sweater.

The length of side AB is 15 units.

Given that triangles ADE and ABC are similar, and the length of side AC is 12, the length of side AE is 8 and the length of side AD is 10.

We need to find out the length of side AB.Since triangles ADE and ABC are similar, the corresponding sides are proportional.

Therefore, we have the proportion:AD / AB = AE / AC

So, we can find the length of AB by rearranging the proportion:

AB = AD × AC / AE

Since triangles ADE and ABC are similar, we can use the similarity property to indicate that corresponding sides of similar triangles are proportional.

Let x be the length of side AB.

Knowing the ratio of the corresponding sides, we can establish the ratio:

AE / AB = DE / BC

Substitute the given values:

8 / x = 10 / 12

To solve for x can do cross multiplication.

Solve the resulting equation:

8 * 12 = 10 * x

96 = 10x

Divide both sides by 10:

96 / 10 = x

x = 9.6

Taking the given values:

AB = 10 × 12 / 8AB

= 15

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Answer:

-64

Step-by-step explanation:

Start by moving everything to the left side making the equation equal 0. Then combine like terms.

Answer:

565656÷8=p

So the answer is 637:D

Answer:

A

Step-by-step explanation:

We add 4 on both sides

-1 + 4 < -4 + 4 + d

= 3 < d

Flip it and we get d > 3

The answer is A

Answer:

233

Step-by-step explanation:

2=33=2=

Answer:

D.

Step-by-step explanation:

Both have a slope or "rate of change" of 1/2 because going from (0,5)-->(2,6) on the first one you go right 2 units and up 1 and slope is rise over run or y/x values in this case it would be 1/2 and on the bottom function you can see it goes from (0,-2)-->(4,0) and this goes right 4 units and up 2 units same principal applies you get 2/4 which is equal to 1/2 also it being negative or not doesn't change whether the two functions have the same rate of change.

Answer: 3 gallons < 11.37 liters

Step-by-step explanation:

First you want to convert gallons to liters (or liters to gallons).

3 gallons is equivalent to 11.356 liters.

As you can see, all digits up to the hundredths digit are equal, while the hundredths digit of 11.37 is greater than the hundredths digit in 11.356(3 gallons), meaning that 11.37 liters is greater than 3 gallons.

I hope this helps.

Answer:

5 and 13

Step-by-step explanation:

Answer:

13

is the answer

Hope it help u

1. y=6

2. y=3/2 alternate form y=1 1/2, y=1.5

2. 3. and 4. the same answer

Step-by-step explanation:

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