]
D
5²
25
2) A two-dimensional preimage is dilated by a scale factor to result in a new image. Fill in the
blanks with the number needed to calculate the area of the new image compared to the area
of the preimage.
25
1
If the scale factor is , then the area of the preimage is multiplied by or to calcu-
late the area of the new image.
()'

Answer: 54 in

Step-by-step explanation:

Since the altitude drawn from the vertex of the isosceles triangle forms two congruent right triangles and divides the base into two equal segments, we can work with one of the right triangles to find the length of the other side of the isosceles triangle.

Let's denote the length of the altitude as a, the length of half the base as b, and the length of the other side of the isosceles triangle as c. From the problem, we know that a = 18 inches and b = 15 inches / 2 = 7.5 inches.

We can use the Pythagorean theorem to find the length of c:

a² + b² = c²

Substitute the known values:

18² + 7.5² = c²

324 + 56.25 = c²

380.25 = c²

Now, take the square root of both sides to find the length of c:

c = √380.25

c ≈ 19.5 inches

Since the isosceles triangle has two sides with equal length, the perimeter is:

Perimeter = base + 2 * c

Perimeter = 15 + 2 * 19.5

Perimeter = 15 + 39

Perimeter = 54 inches

Thus, the perimeter of the isosceles triangle is approximately 54 inches.

From the given sample space the probability of P(at least 2 tails) is 68.75%.

Probability is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the occurrence. Probability is a key idea in mathematics, statistics, and many other disciplines. It is used to describe uncertain events. Many techniques, such as counting techniques, probability distributions, and simulations, can be used to determine probability. Many uses for it include risk analysis, making decisions, and statistical inference.

From the given sample space the outcomes with at least 2 tails are:

{TTTT, TTT H, TT HT, T H TT, H TTT, H HTT, HT HT, HTTH, THHT, THTH, THH H}

Now,

P(at least 2 tails) = 11/16 = 0.6875 ≈ 68.75%

Hence, from the given sample space the probability of P(at least 2 tails) is 68.75%.

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Answer: x=23

Step-by-step explanation:

Set the two equal to each other:

5x=3x+46

2x=46

x=23

Answer:

[tex] \frac{a - 3}{a + 2} [/tex]

Step-by-step explanation:

[tex] \frac{ {a}^{2} - 7a + 12 }{ {a}^{2} - 2a - 8} = \frac{(a - 3)(a - 4)}{(a + 2)(a - 4)} = \frac{a - 3}{a + 2} [/tex]

Answer: $25.41

Step-by-step explanation:

I think this is right, please correct me if I'm wrong

The sample size necessary such that the margin of error of the estimate for a 90% confidence interval for the mean age of all residents is at most 3.4 years is 59.56.

What is a confidence interval?

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

Given: A city official would like to estimate the mean age of all residents of Stuart. The standard deviation of the ages of all residents of Stuart is known to be 16 years.

σ = 16 ..Population SD

The margin of error, E = 3.4

c = 90% = 0.90 ...confidence level

a = 1 - c = 1 - 0.90 = 0.1

a/2 = 0.1/2 = 0.05

Using the Z table,

z = 1.64

Now, sample size (n) is given by,

= (za/E)²

= (1.64×16/3.4)²

=59.56

Hence, the sample size necessary such that the margin of error of the estimate for a 90% confidence interval for the mean age of all residents is at most 3.4 years is 59.56.

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The minimum amount of cloth Carl needs to cover the entire box is 272 square inches.

A prism is a three-dimensional geometric shape that consists of two identical polygonal bases that are connected by a set of parallelogram faces. The shape of the prism is determined by the shape of its bases. For example, if the bases are triangles, the prism is called a triangular prism. Similarly, if the bases are squares, the prism is called a square prism, and so on.

Prisms have a number of interesting properties. The faces that connect the bases are always parallelograms, and the opposite faces are congruent and parallel. The altitude of a prism is the perpendicular distance between its bases, and its lateral faces are all rectangles or parallelograms. The volume of a prism can be calculated by multiplying the area of its base by its altitude. The formula for the volume of a prism is V = Bh, where V is the volume, B is the area of the base, and h is the altitude.

Given:

Length of the rectangular prism, l = 12 in

Height of the rectangular prism, h = 2 in

Width of the rectangular prism, w = 8 in

Carl needs to cover the total surface area of the prism, which is minimum he needs to cover.

Total surface area of rectangular prism= 2(lh+hw+lw)

TSA= 2(12 × 2 + 2×8 + 12 × 8)

      = 2(24 + 16 + 96)

      = 272 square inches

Minimum cloth required = 272 square inches.    

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The complete question is:

The volume of one ice cube produced by this ice machine is 27/64 cubic inches.

The volume of a cube refers to the amount of space that is contained within the cube.A cube is a three-dimensional geometric shape that has six equal square faces and all its edges have equal length. The volume of a cube can be found by multiplying the length of its sides together, using the formula:Volume of cube = (length of side)³

The volume of a cube is given by the formula V = S³ where s is the length of one side of the cube.

In this case, the length of one side of the ice cube is 3/4 inch. Therefore, the volume of one ice cube is:

V = (3/4)³ = 27/64 cubic inches.

So, the volume of one ice cube produced by this ice machine is 27/64 cubic inches.

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The volume of one ice cube produced by this ice machine is 27/64 cubic inches. The correct option is D. 27/64.

In cubic inches, of one ice cube produced by an ice machine with each side measuring 3/4 inch.

Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a

closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Volume is also termed as capacity,

sometimes.

To find the volume, use the formula for the volume of a cube:

[tex]V = side^3.[/tex]

Determine the side length, which is given as 3/4 inches.

Apply the formula for the volume of a cube:

[tex]V = (3/4)^3[/tex]

Calculate the volume by cubing the side length:

V = (3/4) × (3/4) × (3/4) = 27/64 cubic inches

The volume of one ice cube produced by this ice machine is 27/64 cubic inches.

The correct option is D. 27/64.

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A triangular prism whose length is l units, and whose right triangular cross section has base b units and height h units, the volume(V) of the triangular prism 31.5 cubic inches.

Since this figure represents the triangular Prism, it is given in the figure:

Length of triangular prism is 4.5 in.

In the right triangular cross-section,

Base (b) = 2 in and the height (h) = 7 in.

Volume of triangular prism formula: - A triangular prism whose length is l units, and whose right triangular cross section has base b units and height h units, then:

Volume(V) of the right triangular prism is given by V = 1/2xbhl cubic unit

Using the above values; solve for V;

V = Axl, where A is the area of right triangle, or we can write it as:

V = 1/2bhl

⇒ V = 1/2 x 2 x 7 x 4.5 cubic inches.

On simplifying we get, V = 31.5 inches³

Hence, the volume of the triangular Prism is, 31.5 cubic inches.

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True. This is because a two-tailed test evaluates both the extreme lower and upper ends of the distribution, allowing for the possibility of a significant difference in either direction.

In a two-tailed test, we can reject the null hypothesis on either side of the hypothesized value of the population parameter.

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Answer:

please see the attached I put the answer.

Step-by-step explanation:

I put the steps I did, to graph it.

Based on this information, we can conclude that the measured mean values of vcom,1 and vcom,2 are not significantly different from each other and fall within the range of experimental error.

Assuming that the mean value of vcom,1 is 5.2 m/s with an experimental uncertainty of 0.1 m/s, and the mean value of vcom,2 is 5.5 m/s with an experimental uncertainty of 0.2 m/s, we can calculate the difference between the two mean values and compare it with the combined experimental uncertainty.

The difference between the two mean values is 0.3 m/s, which is greater than the combined experimental uncertainty of 0.22 m/s (calculated as the square root of (0.1² + 0.2²)). Therefore, we can conclude that the two mean values are different and outside the range of experimental error.

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The complete question is :

What is the experimental uncertainty of the mean values of vcom,1 and vcom,2, and is the difference between them significant? Can we conclude that the two mean values are the same, or are they within the range of experimental error?

Therefore , the solution of the given problem of expressions comes out to be  (x+y) is the LCM of (x+y, x-y).

Utilizing shifting integers that may prove rising, minimizing, or blocking is preferable to using approximations generated at random. Sharing resources, knowledge, or answers to problems was the only way they could assist one another. An equation for a declaration of truth may contain the justifications, components, and mathematical comments for methods like additional disagreement, manufacture, and mixture.

Here,

We must factor each polynomial into its irreducible factors and then take the sum of the highest powers of each irreducible factor to determine the LCM of two polynomials.

Here are the facts:

=> x+y = (x+y)

=> x-y = -(y-x)

We don't need to include the second component separately in the LCM because it is simply the negation of the first factor.

The LCM is just (x+y) because x+y is already indivisible.

Consequently, (x+y) is the LCM of (x+y, x-y).

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Khalil's cat weighed 8 1/2 pounds more than Sophia's cat.

In mathematics, any integer that can be written as p/q where q  0 is considered a rational number. Additionally, any fraction that has an integer denominator and numerator and a denominator that is not zero falls into the group of rational numbers.

To find out how much more Khalil's cat weighed than Sophia's cat, we need to subtract the weight of Sophia's cat from the weight of Khalil's cat.

Khalil's cat weighed 18 5/6 pounds.

Sophia's cat weighed 10 1/3 pounds.

Subtracting the weights:

18 5/6 - 10 1/3

To subtract mixed numbers, we need to find a common denominator. In this case, the least common multiple of 6 and 3 is 6. So, we can convert the fractions to have a denominator of 6:

18 5/6 - 10 1/3 = 18 5/6 - 10 2/6

Now, we can subtract the whole numbers and the fractions separately:

18 - 10 = 8

5/6 - 2/6 = 3/6

Putting it back together:

8 3/6

We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3 in this case:

8 3/6 = 8 1/2

So, Khalil's cat weighed 8 1/2 pounds more than Sophia's cat.

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Answer:

Answer:

YES!!!

Step-by-step explanation:

The probability that the random variable has a value between 0.1 and 3.3 is 0.0256. Option b is correct answer.

Since the area under the density curve represents the total probability, we need to find the area between the vertical lines at x = 0.1 and x = 3.3, and under the curve.

First, we need to find the y-coordinates of the two horizontal lines. The line passing through (0, 125) and (8, 125) is parallel to the x-axis, so it has a constant y-coordinate of 125. The line passing through (8, 0) and (8, 125) is parallel to the y-axis, so it has an undefined slope and is a vertical line.

Therefore, we do not need to find its y-coordinate.

Next, we need to find the equation of the density curve. Since it is a uniform density curve, the height of the curve is constant over its entire length.

To find the height, we need to find the total area under the curve, which is given by the rectangle formed by the vertical lines at x = 0 and x = 8, and the horizontal lines at y = 0 and y = 125.

The width of the rectangle is 8, and the height is 1/125 (since the total area is 1 and the width is 8). Therefore, the height of the curve is 1/125 over its entire length.

Now, we can find the area between the vertical lines at x = 0.1 and x = 3.3, and under the curve.

The width of this area is 3.3 - 0.1 = 3.2, and the height of the curve is 1/125. Therefore, the area is:

3.2 × (1/125) = 0.0256

Therefore, the probability that the random variable has a value between 0.1 and 3.3 is 0.0256.

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The question is -

Using the following uniform density curve,

What is the probability that the random variable has a value between 0.1 and 3.3?

A) 0.5875 B) 0.0256 C) 0.3750 D) 0.2125

To find the percent change, we need to use the formula:

percent change = (new value - old value) / old value * 100%

In this case, Max's old value is 73 and his new value is 96. So:

percent change = (96 - 73) / 73 * 100%

percent change = 23 / 73 * 100%

percent change = 0.3151 * 100%

percent change = 31.51%

Therefore, Max's percent change is 31.51%, rounded to the nearest whole percent, it is 32%.

Answer:

A

Step-by-step explanation:

Since this is a rectilinear angle, we can find x:

x = 180° - 98° = 82°

Answer:

D

Step-by-step explanation:

y = x² - 4x - 5 → (1)

y = x - 9 → (2)

substitute y = x² - 4x - 5 into (2)

x² - 4x - 5 = x - 9 ( subtract x - 9 from both sides )

x² - 5x + 4 = 0 ← in standard form

(x - 1)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 4 = 0 ⇒ x = 4

substitute these values into (2) for corresponding values of y

x = 1 : y = 1 - 9 = - 8 ⇒ (1, - 8 )

x = 4 : y = 4 - 9 = - 5 ⇒ (4, - 5 )

The solution to the trigonometric equation with sine function is x = 2.5.

Starting with 3√2 sin π/3 (x − 2) + 4 = 7:

First, we can simplify 3√2 sin π/3 to 3, since sin π/3 = √3/2 and 3√2 = 3 x √2 x √2 = 3 x 2 = 6.

6(x - 2) + 4 = 7

6x - 12 + 4 = 7

6x - 8 = 7

6x = 15

x = 2.5

A particular solution to a trigonometric equation is one that is valid for a particular value or range of values of the variable, as opposed to a general solution, which is valid for all conceivable values of the variable.

Finding the general solution, which entails locating all feasible solutions to the equation within a specific range or domain, is frequently necessary while solving trigonometric equations. In order to simplify the problem and describe the answers in a compact form that can be applied to every value of the variable, one often applies a variety of trigonometric identities and algebraic operations to get the general solution.

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Given that ABCD is a parallelogram:

Opposite sides of a parallelogram are parallel and congruent. Therefore, AB = DC.

Diagonals of a parallelogram bisect each other. Therefore, the midpoint of AC is the same as the midpoint of BD. Let M be the midpoint of AC, and N be the midpoint of BD.

By the midpoint theorem, BM = DM and BN = AN.

Since BM = DM and BN = AN, we can conclude that quadrilateral ABCD is a parallelogram in which BC || AD and CD || AB.

Therefore, we have shown that AB = CD and BC = AD in parallelogram ABCD.

Step-by-step explanation:

Because a cube has   6    sides ...and a cube has equal side lengths so the area of each side is s x s = s^2    

   then the total is   6 s^2

To find the product of this expression, we can use the distributive property:

3√5 - √2 = 3√5 * 1 - √2 * 1

= 3√5 * (√2/√2) - √2 * (3√5/3√5)

= (3√10/√2) - (3√10/5)

= 15√10/5√2 - 3√10/5

= (15 - 3√2)√10/5√2

So the product is (15 - 3√2)√10 / 5√2.

Simplifying this expression by rationalizing the denominator, we get:

= (15 - 3√2)√10 / 5√2 * √2 / √2

= (15√2 - 3 * 2)√10 / 10

= (15√2 - 6)√10 / 10

= (3√2(5 - 2√10)) / 10

Hence, the product is (3√2(5 - 2√10)) / 10.

The product of expression 3√5-√2 is ( 15√2 - 2)√10 / 10

An expression is combination of variables, numbers and operators.

To find the product of this expression

Apply the distributive property:

3√5 - √2 = 3√5 × 1 - √2 × 1

= 3√5 × (√2/√2) - √2 × (3√5/3√5)

= (3√10/√2) - (√10/5)

= 15√10/5√2 - √10/5

= (15 - √2)√10/5√2

So the product is (15 - √2)√10 / 5√2.

Simplifying this expression by rationalizing the denominator, we get:

= (15 - √2)√10 / 5√2 × √2 / √2

= (15√2 - 2)√10 / 10

Hence, the product of expression 3√5-√2 is ( 15√2 - 2)√10 / 10

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Step-by-step explanation:

We are given:

Sample size (n) = 35

Sample mean ($\bar{x}$) = 36 seconds

Population standard deviation ($\sigma$) = 8 seconds

Confidence level = 95%

We can find the margin of error using the formula:

Margin of Error = z*(σ/√n), where z is the z-score for the given confidence level, σ is the population standard deviation, and n is the sample size.

For a 95% confidence level, the z-score is 1.96 (from the z-table or calculator).

Putting the values in the formula, we get:

Margin of Error = 1.96*(8/√35) ≈ 2.68

The confidence interval is given by:

Lower Limit = $\bar{x}$ - Margin of Error

Upper Limit = $\bar{x}$ + Margin of Error

Substituting the values, we get:

Lower Limit = 36 - 2.68 ≈ 33.32

Upper Limit = 36 + 2.68 ≈ 38.68

Therefore, the 95% confidence interval for the mean time that all half-hour local TV news broadcasts devote to U.S. foreign policy is (33.32, 38.68).

Since the Lear Center's claim of the average time being 38 seconds falls within this interval, we can say that the sample data supports the Lear Center's claim at a 95% confidence level.

The equation represented by the graph is: y = x² - x - 6. We can solve it in the following manner.

The vertex of the parabola is at (0, -6). We can calculate it in the following manner.

Yes, the equation represented by the graph is: y = x² - x - 6

This is a quadratic equation in standard form, where the coefficient of the x² term is positive, which means that the parabola opens downwards. The equation has a y-intercept of -6 and crosses the x-axis at x = -1 and x = 3. The vertex of the parabola is at (0, -6).

A parabola is a symmetrical plane curve that results from the intersection of a cone with a plane parallel to its side. It is a type of conic section, along with circles, ellipses, and hyperbolas.

A parabola can also be defined as the graph of a quadratic equation, which is a second-degree polynomial. The general form of a quadratic equation in one variable is:

ax² + bx + c = 0

Where a, b, and c are constants and x is the variable. When graphed, a quadratic equation in one variable produces a parabolic curve. The direction and shape of the parabola depend on the sign and value of the coefficient a.

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20.4 seconds separate the lowest 24% of the means.

Look up the z-scores for the given percentages (24% and 76%) using the z-table.

Since the green lights' lengths are normally distributed with a mean of 45 seconds and a standard deviation of 15 seconds, calculate the number of seconds corresponding to the z-scores.

For the highest 76%, the number of seconds is 45 + (0.68 * 15) = 45 + 10.2 = 55.2 seconds.
Now, subtract the lowest 24% of the means (34.8 seconds) from the highest 76% (55.2 seconds) to find the difference in seconds.

So, 20.4 seconds separate the lowest 24% of the means from the highest 76% in the state transportation study's sampling distribution of 75 traffic lights.

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Therefore, the equation of the line is 5x - 3y = -15 and the equation of the line passing through E(4,-3) can be expressed using the point-slope form as y = (5/7)x - (20/7).

a) We can rewrite the provided line in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, to determine the slope.

y + 1 = (5/7)(x - 4) (x - 4)

y = (5/7)x - (20/7) - 1

y = (5/7)x - (27/7)

This line and the one we're looking for are parallel, thus their slopes are the same (5/7). Hence, the equation of the line passing through E(4,-3) can be expressed using the point-slope form:

y - (-3) = (5/7)(x - 4) (x - 4)

y = (5/7)x - (20/7)

b) The intercept form of the equation of a line with an x-intercept of 3 and a y-intercept of 5 is:

x/(-3) + y/5 = 1

The result of multiplying both sides by -15 (the least frequent multiple of -3 and 5) is as follows:

5x - 3y = -15

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The eighth term of the sequence is -14

What is common ratio?

The common ratio between consecutive terms in a geometric sequence is constant. Let's denote this common ratio by 'r'. To find 'r', we can divide any term by the preceding term,

r = -448/896 = -1/2

Now we can use the formula for the nth term of a geometric sequence,

[tex]a_n = a_1 \times p^{n - 1}[/tex]

where '

[tex]a_1[/tex] is the first term and 'n' is the index of the term we want to find.

Substituting the values we have,

[tex]a_8 = 896 (-1/2)^{8-1} \\ = 896 \times (-1/2)^{7} = -14[/tex]

Therefore, the eighth term of the sequence is -14.

So, option A is the correct answer.

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Correct question is "Write an equation for the nth term of the geometric sequence 896,-448, 224,.... Find the eighth term of this sequence.

A) -14

B) -18

C) -19

D) 18"