For the dilation with center (0, 0) shown on the graph, your friend says the scale factor is 4.
Is your friend correct or no? If he is incorrect, What is the correct scale factor? and what mistake did he likely make?

The value of the expression 5^log525⋅2^log28⋅3^log33 is 125.

To justify this answer, let's analyze the expression step by step using the properties of logarithms:

1. Start with the expression: 5^log525⋅2^log28⋅3^log33.

2. We know that log(base a)b = c is equivalent to a^c = b.

3. Applying this property to the expression, we have 5^log525 = 25, since log(base 5)25 = 2.

4. Similarly, 2^log28 = 8, because log(base 2)8 = 3.

5. Lastly, 3^log33 = 3, as log(base 3)3 = 1.

6. Combining these results, the expression simplifies to 25⋅8⋅3.

7. Evaluating the multiplication, we get 25⋅8⋅3 = 600.

Therefore, the value of the expression 5^log525⋅2^log28⋅3^log33 is 125

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Answer:

None. \(24+25+26\) is the only valid answer

Step-by-step explanation:

We can create an expression for the sum of 3 consecutive numbers.

\(S=x+(x+1)+(x+2)\)

Which we can simplify to

\(S=x+x+1+x+2\)

\(S=3x+3\)

In this example we are given a sum of 75.

\(75=3x+3\)

Lets solve for \(x\).

Subtract 3 from both sides.

\(72=3x\)

Divide both sides by 3.

\(24=x\)

To find out what the 3 numbers are we can plug in 24 for x

\(x+(x+1)+(x+2)\)

\(24+(24+1)+(24+2)\)

\(24+25+26\)

Answer:

  4 other ways (5 ways, total).

Step-by-step explanation:

You want to know how many other ways 75 can be written as the sum of consecutive whole numbers other than 24+25+26.

If 75 is written as the sum of an odd number of integers, the middle integer of the set will be 75 divided by the number of integers. The divisors of 75 are {1, 3, 5, 15, 25, 75}. If the numbers in the sum are non-negative, the number of integers involved cannot be more than √(2·75) ≈ 12. Then allowed odd numbers of integers in the sum are 3 and 5.

If 75 is written as the sum of an even number of integers, the quotient when 75 is divided by the number of integers must be 1/2 more than a whole number. Such integer divisors are 2, 6, and 10.

  37 + 38 = 75 . . . . 2 integers

  24 + 25 + 26 = 75 . . . . 3 integers (the given sum)

  13 + 14 + 15 + 16 + 17 = 75 . . . . 5 integers

  10 + 11 + 12 + 13 + 14 + 15 = 75 . . . . 6 integers

  3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 75 . . . . 10 integers

There are 4 other ways to use consecutive non-negative integers to make a sum of 75.

On solving the provided question, we can say that, by solving the equations  that amount is $36.95

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Suppose x be the number of minutes of local calls when cost of plans are the same

Cost of Plan 1is $27.95+.12x

Cost of Plan 2 is $12.95+.32x

\($27.95+0.12x=12.95+.32x \\\)

\($27.95-$12.95+.12x-.12x=$12.95-$12.95+.32x-.12x\\$15.00=.20x\)

x=75 minutes

\(27.95+.12(75)=12.95+.32(75)\\27.95+9.00=12.95+24.00\\36.95=36.95\)

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Answer:

A 3 and 8

Step-by-step explanation:

if a/b=c/d, the extremes are "a" and "d". The means would then be "b" and "c"

The extremes of the proportion are 3 and 8.

To find the extremes of a proportion, we need to identify the numbers that are positioned at the far ends of the proportion. In the given proportion:

3/4 = 6/8

The numerator of the first fraction, 3, and the denominator of the second fraction, 8, are the extremes. These numbers form the far ends of the proportion.

Therefore, the extremes of the proportion are 3 and 8.

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Answer:

someone needs to answer this because i dont know

it.

Step-by-step explanation:

he is correctStep-by-step explanation:

Answer:

Step-by-step explanation:

There are two if you want to answer the question. You have to know the starting value, and you have to know the ending value.

The question asks how many cans were sold. You can't answer that without knowing what you started with and what you ended with.

98 - 10 = 88

The probability that more boys than girls are chosen is approximately 0.171.  

To solve this problem, we can use the binomial distribution. Let X be the number of boys chosen out of the 5 students selected.

Then, X has a binomial distribution with parameters n = 5 and p = 16/(16+19) = 16/35, since there are 16 boys and 19 girls, and we are selecting 5 students at random.

We want to find the probability that more boys than girls are chosen, which is the same as the probability that X is greater than 2. We can compute this probability using the cumulative distribution function (CDF) of the binomial distribution:

P(X > 2) = 1 - P(X ≤ 2)

= 1 - (P(X = 0) + P(X = 1) + P(X = 2))

Using the binomial probability formula, we can calculate each term of the sum:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where (n choose k) = n! / (k! * (n-k)!) is the binomial coefficient.

Thus, we have:

P(X = 0) = (5 choose 0) * (16/35)^0 * (19/35)^5 = 0.107

P(X = 1) = (5 choose 1) * (16/35)^1 * (19/35)^4 = 0.349

P(X = 2) = (5 choose 2) * (16/35)^2 * (19/35)^3 = 0.373

Substituting these values into the formula for P(X > 2), we get:

P(X > 2) = 1 - (0.107 + 0.349 + 0.373) = 0.171

Therefore, the probability that more boys than girls are chosen is approximately 0.171.

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First, we need to convert the given weight to mass. Since we know that gravitational acceleration is 32 ft/s² and the weight is 1 pound, we can calculate the mass.

Weight = Mass × Gravitational acceleration
1 lb = Mass × 32 ft/s²
Mass = 1 lb / 32 ft/s² = 1/32 slugs
Now, we need to find the angular frequency (ω) using the formula ω = sqrt(k/m):
ω = sqrt(100 lb/ft / (1/32 slugs)) = sqrt(3200) = 40 rad/s
The equation of motion will be:
y(t) = A * cos(ωt)

Since the spring is stretched an additional 1 inch (1/12 ft), that will be the amplitude (A): Amplitude = 1/12 ft

Now we can write the complete equation of motion:
y(t) = (1/12) * cos(40t)

In conclusion: Amplitude: 1 inch (1/12 ft)
Period: π/20 seconds

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Step-by-step explanation:

the slope intercept form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

so, we have the equations

y = -2x -5

y = (-1/4)x + 1

y = 2x

Answer:

51

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Since the sectors all meet at the centre of the circle, then

The angles around a point sum to 360° → A

90°... See More

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Answer:

5.26

Step-by-step explanation:

To find the area of a circle, you square the radius and multiply your answer by pi. The radius is half the diameter.

2.6/2=1.3

1.3^2=1.69

1.69*3.14= 5.3066 (approx.)

Finally, round to the nearest hundredth.

5.3066≈5.31

a) The total number of possible outcomes is n = 16 outcomes

b) The probability of selecting an orange ball and a blue ball in either order is given by P = 2/9

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of selecting an orange ball and a blue ball in either order be represented as P

Now , the value of P is

The total number of balls in the bag = 4 balls

The number of blue balls = 2

The number of yellow balls = 1

The number of orange balls = 1

The total number of outcomes S = { ( blue , blue ) , ( blue , orange ) , ( orange , blue ) , ( yellow , blue ) , ( blue , yellow ) , ( yellow , orange ) , ( orange , yellow ) , ( yellow , yellow ) , ( orange , orange ) }

Now , the sample space of selecting 2 balls that are orange and a blue ball is A = { ( orange , blue ) , ( blue , orange ) }

So , the probability of selecting an orange ball and a blue ball in either order is P = 2/9

Hence , the probability is 2/9

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Answer:

Its a right triangle

Step-by-step explanation:

Answer:

It is a right angle.

Step-by-step explanation:

Data set A and B have the same number of data points, but A has a larger standard deviation and a smaller range compared to B.

Assume that,

There are two data sets, A and B, with the same number of data points:

Data Set A: [3, 5, 7, 9, 11]

Data Set B: [6, 7, 8, 9, 10]

In this example, both data sets have five data points, but Data Set A has a larger standard deviation while having a smaller range compared to Data Set B.

Data Set A has a larger standard deviation because the values are more spread out from the mean.

The standard deviation of Data Set A is approximately 3.16, while the range is,

11 - 3 = 8

On the other hand, Data Set B has a smaller standard deviation because the values are closer to the mean.

The standard deviation of Data Set B is approximately 1,

While the range is,

10 - 6 = 4

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Answer:

sqrt(1/m+4)

Step-by-step explanation:

n^2-1/m=4

n^2=1/m+4

n=sqrt(1/m+4)

The value of the equation is n = √ ( 4 + 1/m )

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.

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 data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

n² - 1/m = 4   be equation (1)

On simplifying the equation , we get

Adding 1/m on both sides of the equation , we get

n² = 4 + 1/m

Taking square roots on both sides of the equation , we get

n = √ ( 4 + 1/m )

Therefore , the value of n is √ ( 4 + 1/m )

Hence , the equation is n = √ ( 4 + 1/m )

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Using the theorem of angles of a straight line, the value of x and y are 10 and 41 respectively.

In the given problem, the angle or relationship between them are alternate angles and corresponding angles. The theorem supporting this states that "alternate angles are equal to one another" and " corresponding angles are equal to one another".

(2y - 14) + (2y + 30) = 180

Reason: Angles on a straight line are equal to 180 degrees

2y + 2y + 30 - 14 = 180

4y + 16 = 180

4y = 180 - 16

4y = 164

y = 164 / 4

y = 41

For x;

(13x - 18) + (5x + 18) = 180

Reason: Angle on a straight line are equal to 180 degrees

13x + 5x -18 + 18 = 180

18x = 180

x = 180 / 18

x = 10

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Answer:

b. 31.

Step-by-step explanation:

The other 2 angles in the triangle are congruent so they are:

(180 - 118) / 2

= 31 degrees.

The possible measure of two similar angles in an isosceles triangle could be b. 31 °

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know in an isosceles triangle two sides are equal and angles opposite sides to the equal side are also equal.

We also know that the sum of all the interior angles in a triangle is 180°.

Let, The similar angles be 'x'.

Therefore,

x + x + 118 = 180

2x = 62.

x = 31°.

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The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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\(d = \frac{d(10 {}^{k + p} - 10 {}^{k}) }{(10 {}^{k + p} - 10 {}^{k})} \)

where

Step-by-step explanation:

Greetings !

use the above formula to change any decimal into fraction form

Thus, plug in the value and solve

Hope it helps !

Answer:

\(\large\boxed{\tt x = 2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for x in the given equation.}\)

\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)

\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{How is this possible?}}\)

\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)

\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)

\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)

\(\textsf{of once.}\)

\(\large\underline{\textsf{For our problem;}}\)

\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)

\(\textsf{Property of Equality;}/tex]

\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)

\(\tt - x^{3} = 8\)

\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)

\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)

\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)

\(\underline{\textsf{Evaluate;}}\)

\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)

\(\textsf{*Note;}\)

\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)

\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)

\(\underline{\textsf{We should have;}}\)

\(\tt -x=2\)

\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)

\(\large\boxed{\tt x = 2}\)

So, the formula that we're going to use is:

Compound interest

A = P(1 + r/n)ⁿˣ

Where

A = amount

P = principal = $100

r = rate = 8% = 8 / 100 = 0.08

x = time

In this case, n=4 since it is being compounded quarterly, so:

The answer is $126.82.

The probability of obtaining a mean greater than M = 22 is: a. 0.50

The probability of obtaining a mean greater than 22 for a sample of n = 4 scores can be calculated using the sampling distribution of the sample mean.

The sampling distribution follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

By calculating the z-score for a mean of 22, we can find the corresponding area under the normal curve, which represents the probability.

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Answer:

Step-by-step explanation:

You want to know the amount borrowed at 10%, 12%, and 14% if the total borrowed was $21000, the total interest was $2580, and the total of amounts borrowed at 10% and 14% was double the amount borrowed at 12%.

The relations give rise to three equations. If we let x, y, z represent the respective amounts borrowed at 10%, 12%, and 14%, we have ...

  x + y + z = 21000 . . . . . . total borrowed

  0.10x +0.12y +0.14z = 2580 . . . . . . total interest

  x + y = 2z . . . . . . . . . . . relationship between amounts

Writing the last equation as ...

  x -2y +z = 0

we can formulate the problem as a matrix equation and use a solver to find the solution. We have done that in the attachment. It tells us the amounts borrowed are ...

__

Additional comment

Recognizing that the amount at 12% is 1/3 of the total, we can use that fact to rewrite the other two equations. The interest on the $7000 at 12% is $840, so we have ...

These two equations have the solution shown above. (It is usually convenient to solve them by substituting for x in the second equation.)

<95141404393>

Answer: Isosceles triangle

Step-by-step explanation:

Answer:

Undefined at x = 2 and x = -2

Step-by-step explanation:

(5x²+x+11)/(x²-4)

Function becomes undefined when the denominator goes to zero.

x² - 4 = 0

x = 2, -2

Answer:

In Real numbers: none (defined for all real numbers)

In Complex numbers: not defined for \(x = 2i, -2i\)

Step-by-step explanation:

Fraction becomes undefined when the denominator = 0

\(x^2 + 4 = 0\)

Has no real solutions

The fraction is defined for all real values of x

\(x^2 + 4 = 0\)

\(x^2 = -4\)

\(x = 2i, -2i\)

The fraction is not defined for \(x = \dfrac{+}{-2i}\) (in Complex Numbers)