A rectangle has a perimeter of 24 units. If the rectangle is dilated so that its new perimeter is 12 units, what is true about the dilation?

The dilation is an enlargement.
The dilation has a translation factor of 2.
The dilation has a scale factor of 2.
The dilation has a scale factor of 0.5.

The scientific notation of the given number is 1.24×10⁻⁶.

The given number is 0.00000124.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Here, 0.00000124=1.24×10⁻⁶.

Therefore, the Scientific notation of the given number is 1.24×10⁻⁶.

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1) In the first quantity reasoning, the next logical pattern that should follow if it is repeated is E.

2) In the second quantity reasoning, the next logical pattern is D.

A logical pattern is logical sequence of numbers, words, objects, pictures, etc., that follows a related sequence.

Logical patterns are used on quantitative reasoning to understand and communicate mathematical principles.

We can identify three types of logical pattern as follows:

The arrow pointing down without an enclosed circle follows the arrow point up with an enclosed circle in the bigger circle.

Similarly, for the second question, the inner circle at the angles matches the pattern with Option D.

Thus, for the first question, the next logical pattern is Option E while it is Option D for question two.

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The mean of the sampling distribution (p) and The standard error of the mean (o)  are 56 and 2 respectively.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

(a) The mean of the sampling distribution (p) is equal to the population mean, which is 56.

(b) The standard error of the mean (o) is calculated as the standard deviation of the population divided by the square root of the sample size. So for a sample of 36 participants:

o = 12 / √36 = 2

(c) The distribution of the sample means (p) will be approximately normal with a mean of 56 and a standard deviation of 2. To sketch this distribution with M ± 3 SEM, we would plot a normal distribution with mean 56 and standard deviation 2, and shade the region that is 3 standard errors away from the mean on either side.

This region would capture approximately 99.7% of the data if the samples were selected randomly and independently from the population.

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This occurs when the number of $5 price increases is approximately 10.82 or 15.32.

The function given is P(x) = −6x2 + 156x + 1,000, where x is the number of $5 price increases for each solar panel. We are to identify the approximate value of the x-intercept and explain what the x-intercept means in terms of the problem scenario.

The x-intercept is a point where the graph of the function crosses the x-axis. At this point, the value of the function is zero.

We can find the x-intercept by setting P(x) = 0 and solving for x.0 = −6x2 + 156x + 1,0006x2 - 156x - 1000 = 0Dividing by 6, we get:x2 - 26x - 166.67 = 0Solving using the quadratic formula,

we get:x ≈ 10.82 or x ≈ 15.32So, the x-intercepts are approximately 10.82 and 15.32. In terms of the problem scenario, the x-intercept represents the point at which the company breaks even, i.e., the point at which the daily profit is zero.

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Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.

To determine which package is the better buy, we need to compare the cost per hook for each package.

For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:

Cost per hook = $9.95 / 25 = $0.398

Rounding to the nearest cent, the cost per hook is $0.40.

For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:

Cost per hook = $13.99 / 40 = $0.3498

Rounding to the nearest cent, the cost per hook is $0.35.

Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.

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Answer:

0.12

Step-by-step explanation:

This is the answer because:

1) First, rewrite the expression including the x value

1.2(0.1)

2) Next, we know 1.2 x 1 is 1.2, but since we have one decimal point in 0.1, we have to move the decimal point in 1.2 once to the left. This will make the answer 0.12

Hope this helps! :D

The exponential function is used to determine that:

1. A 0.5 percent.

b) 940.

bacteria (9000)

The substitution method entails substituting the values of the function's variables to arrive at the function's value. The system of linear equations is solved using the replacement approach.

Modeling an exponential function involves:

n(t) = n (0)ekt

that where:

The initial value is n(0).

The constant growth rate is k.

The model in this issue is:

n(t) = 940 e^ 0.5 t

Hence, k= 0.5, 940  and

a) 45 percent.

b) 940.

So 9000 bacteria.

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D. I and IV are the quadrants the cosine function is positive

To determine in which quadrants the cosine function is positive, we need to consider the signs of cosine in different quadrants of the Cartesian coordinate system.

The unit circle is a useful tool to understand the behavior of trigonometric functions. In the unit circle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value. The cosine function is positive in the quadrants where the x-coordinate is positive.

Quadrant I is the top-right quadrant, where both the x and y coordinates are positive. In this quadrant, cosine is positive because the x-coordinate is positive.

Quadrant II is the top-left quadrant, where the x-coordinate is negative, but the y-coordinate is positive. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant III is the bottom-left quadrant, where both the x and y coordinates are negative. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant IV is the bottom-right quadrant, where the x-coordinate is positive, but the y-coordinate is negative. In this quadrant, cosine is positive because the x-coordinate is positive.

Based on this analysis, we can conclude that cosine is positive in Quadrant I and Quadrant IV. Therefore, the correct answer is D. I and IV.

It's important to note that this applies to the standard unit circle and the principal values of cosine. When considering periodicity and multiple revolutions around the unit circle, the positive regions of cosine will repeat every 360 degrees or 2π radians.

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Answer:

it is correct I think it's right

Step-by-step explanation:

Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.

A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.

The area of the rectangular patio is given by multiplying its length by its width, so the area is:

A = (1 + 2x)(2 - 3x)

Now using distributive property we get,

A = 2 - 3x + 4x - 6x²

Simplifying further, we get:

A = -6x² + x + 2

Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.

To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:

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

Simplifying this expression, we get:

P = 2 + 4x + 4 - 6x

P = 6 - 2x

Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.

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Answer:

1

Step-by-step explanation:

Answer:

2 units

Step-by-step explanation:

5 and 4 are 1 unit away

-7 and -8 are also 1 unit away

1 + 1 = 2

Hope this helped!

A cruise ship travelled 84 km in 3.5 h. 3.5 h 43.75h It will take 43.75h to travel 1050 km.

Given:

The complex number is:

\(z=1+i\sqrt{3}\)

To find:

The argument of the given complex number.

Solution:

If a complex number is \(z=x+iy\), then the argument of the complex number is:

\(\theta=\tan^{-1}\dfrac{y}{x}\)

We have,

\(z=1+i\sqrt{3}\)

Here, \(x=1\) and \(y=\sqrt{3}\). So, the argument of the given complex number is:

\(\theta =\tan^{-1}\dfrac{\sqrt{3}}{1}\)

\(\theta =\tan^{-1}\sqrt{3}\)

\(\theta =\tan^{-1}\left(\tan \dfrac{\pi}{3}\right)\)

\(\theta =\dfrac{\pi}{3}\)

Therefore, the argument of the given complex number is \(\theta =\dfrac{\pi}{3}\).

Answer:

1/3

Step-by-step explanation:

You can rewrite the equation like so:

2/3 + (-1/3)

2/3 - 1/3

The denominators are the same so you don't need to worry about that:

2/3 - 1/3 = 1/3

1/3 is your answer

Hope this helps!

Answer:

2/3+(-1/3)= 0.333

Step-by-step explanation:

Because I know math

Based on the cost of the pounds of meal and the pounds of grain, the number of pounds of meal that should be mixed to produce the mixture is 300 pounds

Assuming the pounds of meal that needs to be mixed with the 450 lb of grain is denoted as x, the formula would be:

(450 x 1.70) + ( 0.80 × x) = (450 + x) x 1.34

Solving gives:

(450 x 1.70) + ( 0.80 × x) = (450 + x) x 1.34

765 + 0.80x = 603 + 1.34x

765 - 603 = 1.34x - 0.80x

162 = 0.54x

0.54x = 162

x = 162 / 0.54

x = 300 pounds

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9514 1404 393

Answer:

Step-by-step explanation:

Let n represent the number of necklaces Rosaria ordered. Then the total cost of the order is ...

  10(120 -n) +11(n) = 1270

  n = 70 . . . . . . . . . . . . . simplify, subtract 1200

  120 -70 = 50 . . . . . . . the number of bracelets

Rosaria purchased 70 necklaces and 50 bracelets.

Answer:

The p-value of the test is of 0.0086 < 0.01, which means that there is sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 431 gram setting. It is believed that the machine is underfilling the bags.

At the null hypothesis, we test if they are at the correct weight, that is:

\(H_0: \mu = 431\)

At the alternative hypothesis, we test if they are underfilled, that is:

\(H_1: \mu < 431\)

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used to solve this question

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

431 is tested at the null hypothesis:

This means that \(\mu = 431\)

A 26 bag sample had a mean of 421 grams with a standard deviation of 20.

This means that \(n = 26, X = 421, s = 20\)

Value of the test statistic:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{421 - 431}{\frac{20}{\sqrt{26}}}\)

\(t = -2.55\)

P-value of the test and decision:

Using a t-distirbution calculator, the p-value is found using a left-tailed test(test if the mean is less than a value), with 26 - 1 = 25 df and t = -2.55. This p-value is of 0.0086.

The p-value of the test is of 0.0086 < 0.01, which means that there is sufficient evidence to support the claim that the bags are underfilled

In linear equation, No of Adults = 2,179, No of Children = 3,221 .

What in mathematics is a linear equation?

Let Number of Adult admission be x

    Number of children's admission be y

Total tickets were sold = 5400

so x+y= 5400  ....... eq 1

One adult ticket costs $5.50 ,so total Adult ticket costs = 5.50x

One Child ticket costs $ 3.50, so total Children tickets cost= 3.50 y

receipt totaled = $23,258

so 5.50x+3.50y= $23,258....... eq 2

multiply 5.50 to the  eq 1, we get,

5.50x +5.50y = 29,700...... eq 3

subtract eq 2 from eq 3, we get,

5.50y-3.50y = 29,700- 23,258

2y= 6,442

divide by 2 both sides ,we get, y= 3,221

substitute the value of y in eq 1, we get,

x+ 3,221 =5400

x= 5400- 3221

x= 2,179

No of Adults = 2,179, No of Children = 3,221

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Answer:

a) 34

b) 17

c)46

Step-by-step explanation:

55-21 = 34

count

The correct answer is Graph 1: y = cos(x/4)Graph 2: y = cos(x/2)

Based on the given descriptions of the graphs and the patterns they follow, the correct pairs are:

Graph 1: y = cos(x/4) ⟶ This graph has a period of 8 units and matches the pattern described.Graph 2: y = cos(x/2) ⟶ This graph has a period of 4 units and matches the pattern described.

Graph 3: y = cos(x) ⟶ This graph has a period of 2π (or approximately 6.28 units) and matches the pattern described.

Graph 4: (Not used)

Graph 5: (Not used)

Please note that without visual representation, it's difficult to provide a definitive answer. The pairs are based on the descriptions provided and may vary depending on the actual shapes of the graphs.

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You could shade in the faces of the prism or add labels to identify different parts of the drawing.

What is Pentagonal ?

"Pentagonal" is an adjective that describes something that has five sides or angles. In geometry, a pentagon is a two-dimensional shape with five straight sides and five angles.

To draw a pentagonal prism, you'll need to follow these steps:

Draw identical pentagonal bases: Start by drawing two identical pentagons. Make sure they have the same size and shape. You can use a ruler and a protractor to help you draw the lines.

Draw five vertical lines: Connect each vertex of one pentagon to its corresponding vertex on the other pentagon using straight lines. These lines should be perpendicular to the base and have the same length. You should end up with five evenly spaced vertical lines.

Change any hidden lines to dashed lines: Identify any lines that won't be visible in the final drawing and change them to dashed lines. This will help to make the drawing easier to read and understand.

Add any additional details: Once you've completed the basic shape of the pentagonal prism, you can add any additional details or shading to make the drawing more realistic or interesting.

Therefore,  You could shade in the faces of the prism or add labels to identify different parts of the drawing.

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The radical form is  \((5x)^\frac{2}{3}=\sqrt[3]{(5x)^2}\)

Given,

In the question:

Write 5x^2/3 in radical form​.

Let's Know,

What is Radical Form?

An expression that uses a root, such as a square root, cube root is known as a radical notation. Therefore, 33/2 in radical form is √33 = √27. ​​​​Example 2: Solve the radical: 3√x = 8 using the radical formula. Therefore, Thus, the value of x for 3√x x 3 = 8 is 512.

Now, According to the question:

\((5x)^\frac{2}{3}\)

Convert in Radical form:

Apply the rule :

\(x^\frac{m}{n} = \sqrt[n]{x^m}\)

To rewrite the exponential as a radical .

=> \((5x)^\frac{2}{3}=\sqrt[3]{(5x)^2}\)

Hence, The radical form is  \((5x)^\frac{2}{3}=\sqrt[3]{(5x)^2}\)

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The surface area of a right square pyramid if the area of the base is 169 cm² and the slant height of the pyramid is 13 cm is 507 cm².

We know that the area of the square base is 169 cm², so we can solve for the length of one side.

To find the length, we use the formula for the area of a square:

Area = length x length

169 = length²

Taking the square root of both sides, we get:

length = √169

        = 13 cm

Now we can use the formula for the surface area of a square pyramid:

Surface area = area of base + (1/2)perimeter of base x slant height

The perimeter of the base is 4 times the length of one side, so it is:

perimeter of base = 4 x length = 4 x 13 cm = 52 cm

Plugging in the values we have:

Surface area = 169 cm² + (1/2)(52 cm)(13 cm)

Surface area = 169 cm² + 338 cm²

Surface area = 507 cm²

Therefore, the surface area of the right square pyramid is 507 cm².

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Answer:

21x^4+56x^3+49x^2

Step-by-step explanation:

You need to multiply 7x^2 to each side (aka 7x^2*3x^2) and once you have each multiple you will add them all together. <3

PART A:

The linear form of a vector is given by:

Where i indicates the horizontal direction and j indicated the vertical direction.

To find the values of a and b, let's find the horizontal and vertical distances between the points.

For vector u, we have:

For vector v, we have:

PART B:

To find the trigonometric form, we need the magnitude and angle of each vector:

PART C:

Calculating the given operation, we have:

Answer:

2⁸ and 2²⁴

Step-by-step explanation:

Pic attached..

Answer:

Step-by-step explanation:

X=-2 hope this helps

Answer:

Step-by-step explanation:

120-72 = 48

x ≤ 48

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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