3 A cake is made of three round layers. The diameters and heights are in the ratio 5:3:2 The cake's bottom layer has a diameter of 30cm and a height of 10cm. Work out the following, giving your answers to the nearest whole number. cm (1 mark ) a

By answering the presented question, we may conclude that As a result,  Pythagorean theorem each side of the square park is exactly [tex]12\sqrt(2)[/tex]feet long.

The Pythagorean Theorem, generally known as Pythagorean Theorem, is the foundational Euclidean arithmetic that links the three points of a right triangle. This rule states that the area of a cube only with hypotenuse side is equal to the total of the areas of triangles that have both two sides. The Pythagorean Theorem states that the square that spans the hypotenuse of a right triangle opposite the right angle is the total of all the squares that span its vertices. It is sometimes represented in broad algebraic notation as a2 + b2 = c2.

Let us solve this problem using the Pythagorean theorem. The diagonal in a square is the hypotenuse of a right triangle, with each side of the square acting as one of its legs. The Pythagorean theorem asserts that the sum of the squares of the two shorter sides of a right triangle equals the square of the hypotenuse.

x² + x² = 24²

2x² = 576

x² = 288

[tex]x = \sqrt (288)\\x = \sqrt(144 * 2)\\x = 12\sqrt (2)\\[/tex]

As a result, each side of the square park is exactly [tex]12\sqrt(2)[/tex]feet long.

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The value of angle 1 , angle 2 and angle 3 are 60°, 30° and 60° respectively

A polygon is called regular if it has equal sides and angles. Thus, a regular triangle is an equilateral triangle, and a regular quadrilateral is a square.

An hexagon is a six sided polygon. This means that;

The sum of angle in an hexagon = (6-2)180 = 180× 4 = 720

Therefore each angle in the hexagon = 720/6 = 120°

The angles are equally bisected

therefore, angle 3 = 120/2 = 60°

angle 1 = 180-(60+60)

= 180-120 = 60°

angle 2 = 180-(90+60)

= 180-150

= 30°

therefore the value of angle 1 , angle 2 and angle 3 are 60°, 30° and 60° respectively

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Answer: x = (-1 + sqrt(85)) / 6, or x = (-1 - sqrt(85)) / 6

Step-by-step explanation:

Let's simplify and solve the equation step by step:

Distribute the -5 and -4 on the left side and combine like terms:

-5x + 10 + 4x = 3x^2 - x - 4x + 8 + x + 2

Simplifying the left side and combining like terms on the right side, we get:

-x + 10 = 3x^2 + 3

Subtract 10 from both sides to isolate the variable on one side:

-x = 3x^2 - 7

Add x to both sides to get the quadratic equation in standard form:

3x^2 + x - 7 = 0

Use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = 1, and c = -7. Substituting these values, we get:

x = (-1 ± sqrt(1^2 - 4(3)(-7))) / 2(3)

Simplifying under the square root, we get:

x = (-1 ± sqrt(85)) / 6

Therefore, the solutions to the equation are:

x = (-1 + sqrt(85)) / 6, or x = (-1 - sqrt(85)) / 6

These are approximate values since sqrt(85) is irrational.

The measure of T in the quadrilateral can be found to be B. 100 degrees.

The two quadrilaterals given are trapeziums and they are similar. This means that they have the same angles meausures.

As this is a quadrilateral, the total measure of the interior degrees would be the value of 360 degrees.

The value of T is the only missing angles and so can be found to be:

T = 360 - 125 - 60 - 75

T = 360 - 260

T = 100 degrees

In conclusion, the measure of T is 100 degrees.

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Some of the features of the quadratic function y = 2(x - 2)² + 3 are

The vertex form of a quadratic equation is

y = a(x - h)² + k

Where

Using the above features, we have the following key features

Quadratic function 1

y = 2(x - 2)² + 3

Quadratic function 2

y = 3(x + 2)² - 2

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Answer:

15/13 OR 1.154

Step-by-step explanation:

2 1/2=5/2

2 1/6=13/6

5/2 / 13/6

=5/2 x 6/13

=30/26

=15/13

=1.15384615385

≈ 1.154

The length x of the similar triangle is 17.3 units.

Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.

Therefore, the triangles are similar to each other. Let's use the similarity to find the side length x.

Therefore,

10 / x = x / 30

cross multiply

30 × 10 = x²

x² = 300

square root both sides of the equation

x = √300

x = 17.3205080757

x = 17.3 units

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On solving the question we have that If you meant "1+1=2, then what is equation 2+2?" the answer is four.

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

"1+1+" is an incomplete expression since it requires another operand or operator to form a valid mathematical statement.

Assuming you meant "1+1=," the answer is two.

If you meant "1+1=2, then what is 2+2?" the answer is four.

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On solving the question we get 2 + 2 = 4 because it is given 1 + 1 = 2 it means it is basic addition.

In addition we perform mathematical operation in which we add two or more no with other numbers to get the desire or final output. Output can be positive or negative it only based on your input values.

Mathematical operation is defined as sentence in which two or more number perform an operation which finally gave us result.

Mathematical operations are addition, Subtraction , Multiplication , Division, Percentage etc.

"1+1+" is an incomplete expression since it requires another operand or operator to form a valid mathematical statement.

It is given that  "1+1=,"  so the answer was two.

it meant  that if "1+1=2, then what is 2+2 =4 .

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The dairy farmer used the relative frequency method of probability to reach his conclusion.

Relative frequency is a method of calculating probability that is based on the observation of how often an event occurs in a sample. The farmer likely observed how often he gets between 12 and 14 gallons of milk in a day and used that data to calculate the probability of it happening.

In contrast, theoretical probability is based on the assumption that all possible outcomes are equally likely. It is calculated by dividing the number of desired outcomes by the total number of possible outcomes.

Therefore, the correct answer is relative frequency.

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Answer:

jiris age is 32

Step-by-step explanation:

39(palma's age)+32(jiris age)=71

By using Pythagorean theorem, the length of the common chord is approximately 4.58 cm.

What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental result in Euclidean geometry that describes the relationship between the three sides of a right-angled triangle.

In equation form, this can be written as:

[tex]c^2 = a^2 + b^2[/tex]

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (also known as the legs) of the right-angled triangle.

Let O1 and O2 be the centers of the circles with radii 5cm and 3cm, respectively, and let A and B be the points of intersection of the circles.

Let O1 and O2 be the centers of the circles with radii 5 cm and 3 cm, respectively, and let A and B be the points of intersection of the circles. Then, by the Pythagorean theorem, we have:

[tex]$$\begin{aligned} AB^2 &= AO_1^2 - BO_1^2 \ &= (5^2 - 2^2) , \text{cm}^2 \ &= 21 , \text{cm}^2 \end{aligned}$$[/tex]

Therefore, the length of the common chord AB is:

[tex]$$AB = \sqrt{21} \approx 4.58 , \text{cm}$$[/tex]

Thus, the length of the common chord is approximately 4.58 cm.

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The polynomials P(x) can be formulized as P(x) =  (1/5)(x-1)²(x)(x+3).

The given problem states that a degree 4 polynomial, P(x), has the following properties:

The degree of the polynomial is 4, so the polynomial can be written as;

P(x) = a(x-1)²(x-0)(x+3)

To find the value of 'a', substitute the given point (5,128) into the equation, P(x);

P(5) = a(5-1)²(5-0)(5+3) = 128

P(5) = a(4)²(5)(8) = 128

Simplifying, we get;

128 = 640a,

a = 1/5

Thus, the formula for P(x) is; P(x) = (1/5)(x-1)²(x)(x+3)

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The probability that the average life of the selected batteries is between 95 and 105 is 0.9292.

The company claims their batteries will last an average of 100 days with a standard deviation of 15 days. If 20 of these batteries are selected, the probability that the average life of the selected batteries is between 95 and 105 can be determined by the central limit theorem. In statistics, the central limit theorem (CLT) states that as the sample size increases, the distribution of the sample means approaches a normal distribution, irrespective of the population's underlying distribution. Therefore, the distribution of the sample means is a normal distribution with a mean equal to the population mean and standard deviation equal to population standard deviation divided by the square root of the sample size. Hence, the probability that the average life of the selected batteries is between 95 and 105 is the probability that the sample mean lies between 95 and 105.Using the z-score formula, z = (x - μ) / (σ / sqrt(n)), the z-scores can be calculated as follows:z1 = (95 - 100) / (15 / sqrt(20)) = -1.79z2 = (105 - 100) / (15 / sqrt(20)) = 1.79From the standard normal distribution table, the probability of z-score between -1.79 and 1.79 is 0.9292.Therefore, the probability that the average life of the selected batteries is between 95 and 105 is 0.9292.

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False, Example 1:4(x-2)=4•x-4•2 and Example 2:4•26 and Example 3: 4•(20+6)=4•20+4•6 are NOT examples of using the "Distributive Property".

The Distributive Property is a fundamental property of algebra that is used to simplify expressions involving multiplication and addition. It states that the product of a number and the sum or difference of two or more numbers is equal to the sum or difference of the products of that number and each of the numbers in the sum or difference.

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After 12 months she replace both the light bulb and the air filter

We can also use the concept of the Least Common Multiple (LCM) to find the answer to the problem.

The LCM of two numbers is the smallest number that is divisible by both of them. To find the LCM of 6 and 4, we can list the multiples of each number and look for the smallest multiple that is common to both lists. Alternatively, we can use the prime factorization of each number and multiply the highest powers of the common prime factors.

Prime factorization of 6: 2 x 3

Prime factorization of 4: 2^2

To find the LCM, we multiply the highest powers of each prime factor:

LCM = 2^2 x 3 = 12

Therefore, the LCM of 6 and 4 is 12. This means that the next time Destanye will replace both the light bulb and the air filter is in 12 months.

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The correct answer is x = 9.

Making use of the logarithm table, Compute the characteristic that the provided integer's whole number component dictates. Using the significant digits of the given number, find the mantissa. Add a decimal point after combining the characteristic and mantissa.

The student's solution has a division by zero error. The wrong step is when ln(x2) = ln(3x) - 0. It would have been better to first simplify the addition of ln(9) - 2ln(3) as follows:

The formula is ln(9) - 2ln(3) = ln(9) - ln(32) = ln(9/32) = ln(1/3).

When we substitute this number into the first equation, we get:

ln(1/3) - ln(3x) = 2ln(x)

ln(3x/1/3) = 2ln(x)

2ln(x) = ln (9x)

If we multiply both sides by their exponential, we get:

E = 2ln(x) + eln (9x)

x^2 = 9x

x^2 - 9x = 0

x(x - 9) = 0

As a result, the solutions are x = 0 and x = 9, but since ln(0) is undefined, we must determine whether x = 0 is a valid solution. So x = 9 is a workable answer.

Hence, the right response is x = 9.

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68% of the sample means fall within 19.32 and 20.98.

By the central limit theorem, we know that the distribution of sample means will approach a normal distribution with a mean equal to the population mean (20.15) and a standard deviation equal to the population standard deviation divided by the square root of the sample size (3.7 / sqrt(20) ≈ 0.828).

To find the interval within which 68% of the sample means fall, we need to find the z-scores corresponding to the 16th and 84th percentiles of the normal distribution (which is the range that encompasses 68% of the data in a normal distribution).

Using a z-table or a calculator, we can find that the z-score for the 16th percentile is approximately -1.0 and the z-score for the 84th percentile is approximately 1.0.

Therefore, the interval within which 68% of the sample means fall is:

20.15 - 1.0(0.828) = 19.32

to

20.15 + 1.0(0.828) = 20.98

So the answer is option A: 19.32 and 20.98.

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Given:

45 rewards points for signing up

11.5 points for each visit

Total Number of Points are:

45 + 11.5 · number of visits he makes

45 + 11.5 · x  ≥ 160 points for a free movie ticket

Where, x is how many visits must Tyler make to earn a free movie ticket

      11.5 · x  ≥ 160 - 45

               x  ≥ 115 / 11.5

                x ≥ 10

Since the number of visits to reach 180 points is 10 then Tyler has to visit the movie theater 10 times or more.

Check our answer:

45 + 11.5 · 10 = 160 will earn him a free movie ticket

Answer:

69

Step-by-step explanation:

2y + x = 180 ( Linear Pair)

As x = 42

2y + 42 = 180

2y = 180- 42

2y = 138

y = 138/2

y = 69

By technicality, he earns 18000*5 which equals 90000, however after his investments, it is 72000.

if lucky got 20 questions correct then lucky had missed 4 tests.

If Lucy got 4 out of 5 questions correct, then the proportion of questions she got correct is:

4/5 = 0.8

We can use this proportion to find the number of questions she got correct in the larger set of 20 questions:

0.8 x 20 = 16

So, Lucy got 16 questions correct out of 20. To find the number of questions she missed, we can subtract the number she got correct from the total number of questions:

20 - 16 = 4

Therefore, Lucy missed 4 questions on the test.

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When the circle's radius is 8 cm and it is shrinking at a rate of 0.4 cm per second, the rate that the area is shrinking is -6.4 cm²/s.

Circle area formula: r² = r. The radius squared is multiplied to find the circumference of the circle. When a circle's radius is specified, its area is equal to r². When the diameter "d" is known, the circle's surface area is equal to d²/4.

90 degrees is equal to a quarter turn. A complete turn is 360 degrees, while a half turn is 180. Moreover, the rotation can be expressed in radians or fraction of pi. Under this system, a complete circle turn is equal to 2 radians, a half circle turn is equal to 1, and so on.

Step 1: Variables involved in the question:

The variables involved in the question are:

The radius of the circle r = 8 cm (constant value)

The rate at which the radius is decreasing (dr/dt) = -0.4 cm/s (negative because it's decreasing)

The rate at which the area of the circle is changing dA/dt = ?

Step 2: Chain rule:

We can use the chain rule to link the three rates:

dA/dt = dA/dr x dr/dt

Step 3:

From the given information, we know that (dr/dt) = -0.4 cm/s.

Step 4: Equation for dA/dr

The formula for the area of a circle is  A = πr², where r is the radius of the circle. We can differentiate both sides of the equation with respect to r to get the following formula for dA/dr:

dA/dr = 2πr

Step 5:

Substituting the given value of r = 8 cm in the equation for dA/dr, we get:

dA/dr = 2π(8) = 16π cm

Step 6: dA/dt:

Now we can use the chain rule to find dA/dt by substituting the values we have found for dA/dr and dr/dt:

dA/dt = dA/dr x dr/dt

dA/dt = 16π cm x -0.4 cm/s

dA/dt = -6.4π cm²/s

Therefore, the rate at which the area of the circle is decreasing when its radius is 8cm and decreasing at -0.4 cm/s is  -6.4π cm²/s.

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Answer:

Answer:$8,890.83

Step-by-step explanation:

The scale factor of dilation is 0.075 and the coordinates of F" are (0.9, 0.375)

A thing must be scaled down or altered during the dilation process. It is a transformation that reduces or enlarges the objects using the supplied scale factor. Pre-image refers to the original figure, whereas image refers to the new figure obtained following dilatation.

Label the triangle D” E” F”.

The label of the triangle is added as an attachment.

From question, we have

DE = 12 units

Then, we have

D"E" = 0.9 units

Using the above, we have the following:

Scale factor = D"E"/DE

Scale factor = 0.9/12

Scale factor = 0.075

Hence, the scale factor of dilation is 0.075.

The coordinates of F"

This is calculated as

F = Scale factor * F

So, we have

F = 0.075 * (12, 5)

F = (0.9, 0.375)

The trigonometry ratios the sine, cosine and tangent are calculated as follow:

sin(D") = EF/DF

cos(D") = DE/DF

tan(D") = EF/DE

So, we have

sin(D") = 0.375/1 = 0.375

cos(D") = 0.9/1 = 0.9

tan(D") = 0.375/0.9 = 0.416

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The probability of X = 44 is approximately 0.087 using the normal approximation to the binomial.

The normal approximation to the binomial is a technique used to estimate probabilities for large binomial distributions when calculating by hand becomes impractical. In this case, we have N = 50, p = 0.8, and we want to find the probability of X = 44.

To use the normal approximation, we need to first check if the binomial distribution is approximately normal. This can be done by checking if the conditions np >= 10 and n(1-p) >= 10 are met. In our case, np = 50 x 0.8 = 40 and n(1-p) = 50 x 0.2 = 10, so the conditions are met.

Next, we calculate the mean and standard deviation of the normal distribution using the formulas μ = np and σ = sqrt(np(1-p)). In our case, μ = 40 and σ = sqrt(50 x 0.8 x 0.2) ≈ 2.83.

Finally, we use the normal distribution with mean μ and standard deviation σ to find the probability of X = 44. We need to standardize X using the formula Z = (X - μ) / σ, which gives Z = (44 - 40) / 2.83 ≈ 1.41.

Using a standard normal table or calculator, we find that the probability of Z being less than 1.41 is approximately 0.921. This means that the probability of X being less than or equal to 44 is approximately 0.921.

Therefore, the probability of X being exactly 44 is approximately the difference between the probability of X being less than or equal to 44 and the probability of X being less than or equal to 43. Using a continuity correction, we adjust 43.5 to 43, which gives us:

P(X = 44) ≈ P(43.5 < X < 44.5) ≈ P(Z < (44.5 - 40) / 2.83) - P(Z < (43.5 - 40) / 2.83) ≈ 0.087.

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The number of 11-inch softballs ordered is 70 and the number of 12-inch softballs ordered  is 50

a + b = 120 equation 1

2.50a + 3.50b = 350 equation 2

Where:

The elimination method would be used to determine the number of each size of softball ordered.

Multiply equation 1 by 2.5

2.5a + 2.5b = 300 equation 3

Subtract equation 3 from equation 2

b = 50

Substitute for b in equation 1

a + 50 = 120

a = 120 - 50

a = 70

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In response to the given question, we can state that Rounding this to the  Pythagorean theorem nearest inch gives an answer of [tex]$\boxed{\textbf{(D) }45}$[/tex]

The Pythagorean Theorem is the foundational Euclidean geometry relationship among a right triangle's three sides. The area of a cube with the velocity vector side is the sum of something like the areas of squares that have the other two sides, according to this rule. The rectangle that spans the slope of a triangular shape across the sharp angle equals the total of the rectangles that span its sides, as defined by the Pythagorean Theorem. In general algebraic notation, it is written as a2 + b2 = c2.

The height of each triangle can be found using the Pythagorean theorem:

[tex]$15^2 - \left(\frac{20}{2}\right)^2 = 225 - 100 = 125$, so the height of each triangle is $\sqrt{125} = 5\sqrt{5}$.[/tex]

The overall height of the kite is the sum of the heights of the two triangles, which [tex]is $2 \cdot 5\sqrt{5} = 10\sqrt{5}$.[/tex]

Rounding this to the nearest inch gives an answer of [tex]$\boxed{\textbf{(D) }45}$[/tex]

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The steps he can use are [tex]x = -\frac{-16 \± \sqrt{16\² - 4 \cdot 8 \cdot 3}}{16}[/tex], (x + 1)² = 5/8 and 8(x² + 2x + 1) = -3 + 8

From the question, we have the following parameters that can be used in our computation:

8x² + 16x + 3 = 0

Assuming he uses the quadratic formula method, which is represented as

[tex]x = -\frac{-b \± \sqrt{b\² - 4ac}}{2a}[/tex]

So, we have

[tex]x = -\frac{-16 \± \sqrt{16\² - 4 \cdot 8 \cdot 3}}{2 \cdot 8}[/tex]

[tex]x = -\frac{-16 \± \sqrt{16\² - 4 \cdot 8 \cdot 3}}{16}[/tex]

If he uses completing the square, then we have

8x² + 16x = -3

So, we have

x² + 2x = -3/8

x² + 2x + 1 = -3/8 + 1

So, we have

(x + 1)² = 5/8

If he factorizes, then the expression is

8(x² + 2x + 1) = -3 + 8

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The value of h of the parallelogram is = 4.2

A parallelogram is a special kind of quadrilateral made up of parallel lines. A parallelogram can have any angle between its adjacent sides, but for it to be a parallelogram, its opposite sides must also be parallel.

If the opposing sides of a quadrilateral are parallel and congruent, the shape will be a parallelogram. Hence, if both sets of opposite sides are parallel and equal, a quadrilateral is said to be a parallelogram.

A parallelogram's area is determined as follows:

Area = base × height

In the given parallelogram, we can note that the base is 8.4 inches, and the corresponding height is 5 inches.

This means that:

Area of parallelogram = 8.4 × 5 = 42 in²

This same area can be calculated using the other base (6 in) and its corresponding height (h)

This means that:

Area of parallelogram = 10 × h

42 = 10 × h

h = 42/10

h = 4.2 inches.

Hence, value of h in the parallelogram is equals to 4.2.

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