The diagram shows a triangle.
3t
2t–50°
2t–50°
What is the value of t?
t =

Explanation:

The rule to use here is log(x)-log(y) = log(x/y)

So,

log(6)-log(3) = log(6/3) = log(2)

Answer:

log(2)

Step-by-step explanation:

As we have,

log(a)−log(b)=log(a/b)

Replace 'a' as 6 and 'b' as 3.

Then we get,

\(\hookrightarrow log(6)-log(3)\\\\\hookrightarrow log(\frac{6}{3} )\\\\\hookrightarrow log(2)\)

Therefore , the solution of the given problem of area comes out to be

A = 16 is the equation that accurately depicts how to calculate the sector's area.

Its total size can be determined by figuring out how much space is required to completely cover the outside. The immediate surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. A cuboid's capacity for internal water is determined by the sum of the borders that link all of it's six rectangle edges.

Here,

The formula for calculating a circle's sector's area is:

=> A = (θ/360) x πr²

where A is the sector's area, is its central angle measurement, and r is the circle's radius.

Since the radius is 8 cm and the central angle is 90 degrees in this instance, we can reduce by plugging in these values:

=> A = (90/360) x π(8²)

=>  A = (1/4) x π(64)

=>  A = π(16)

=>  A = 16π

A = 16 is the equation that accurately depicts how to calculate the sector's area.

The answer will be given in radius squared units, in this case, cm2.

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Option D. The correct calculation of the area of the sector is      \(A=(\frac{90}{360}) * (\pi 8^{2} )\)

An area of the sector is the portion of the area of a circle that is enclosed by two radii and an arc. The area of a sector can be found using the formula:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Given, the radius is 8 cm and the central angle is 90° in this instance, put all these values:

\(A=(\frac{90}{360}) * \pi (8^{2} )\)

or we can write down, \(A=(\frac{90}{360}) * (\pi 8^{2} )\)

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The probability that a randomly chosen student is taking tech given that they are taking art is 50%.

To find the probability that a randomly chosen student is taking tech given that they are taking art, we need to use conditional probability. We can use the formula:

P(Tech | Art) = P(Tech and Art) / P(Art)

We know that 62 students are taking both tech and art, so P(Tech and Art) = 62. To find P(Art), we need to subtract the number of students who are only taking tech or only taking art from the total number of students:

P(Art) = (74 - 62) + (112 - 62) + 62 = 124

Therefore, we have:

P(Tech | Art) = 62 / 124 = 0.5

So the probability that a randomly chosen student is taking tech given that they are taking art is 50%.

In summary, we can use conditional probability to find the probability that a randomly chosen student is taking tech given that they are taking art. We need to find the number of students who are taking both tech and art and the total number of students taking art, and then divide the two numbers to get the probability.

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Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Answer:

The Ball costs 10 cents

Step-by-step explanation:

Hope this helps!

Enjoy the rest of your day!

Answer:

85 girls and 140 boys

Step-by-step explanation:

The displacement vector dW corresponding to the second leg of the student's trip can be expressed as (-0.400, 0) miles.

To find the displacement vector dW for the westward leg of the trip, we need to consider the overall displacement from the starting point.

The student first travels 0.900 miles north, so the displacement vector dN for this leg is (0, 0.900) miles.

Then, the student travels 0.400 miles west. Since this is a westward displacement, the x-component of the displacement vector dW will be negative, and the y-component will be zero. Therefore, the displacement vector dW can be expressed as (-0.400, 0) miles.

Finally, the student travels 0.100 miles south. Since this is a southward displacement, the y-component of the displacement vector dS will be negative, and the x-component will be zero. Therefore, the displacement vector dS can be expressed as (0, -0.100) miles.

To find the overall displacement vector d, we sum the individual displacement vectors:

d = dN + dW + dS

d = (0, 0.900) + (-0.400, 0) + (0, -0.100)

d = (-0.400, 0.900 - 0.100)

d = (-0.400, 0.800) miles

Hence, the displacement vector dW for the westward leg of the trip can be expressed as (-0.400, 0) miles. The x-component represents the westward displacement, which is -0.400 miles, and the y-component represents the northward displacement, which is 0 miles.

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the function should be represented as f(t) = 24,500( 0.88\()^{t}\)

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Given,  f(t) = 24,500 x (0.88)t

Assuming that the value of the car only increases by 88% per year compared to the previous year, the function rule needs to have "t" as the exponent, thus it should be f(t) = 24,500( 0.88\()^{t}\)

Hence, the function should be represented as f(t) = 24,500( 0.88\()^{t}\)

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The decimal number 1490 can be represented as 10111011010 in binary notation.

To represent the decimal number 1490 in binary notation, we need to convert it into its binary equivalent. The binary system uses base 2, where each digit represents a power of 2.

To convert 1490 to binary, we can use the process of successive division by 2. Let's go through the steps:

Step 1: Divide 1490 by 2.

Quotient: 745

Remainder: 0

Step 2: Divide the quotient (745) from Step 1 by 2.

Quotient: 372

Remainder: 1

Step 3: Divide the new quotient (372) by 2.

Quotient: 186

Remainder: 0

Step 4: Divide the new quotient (186) by 2.

Quotient: 93

Remainder: 1

Step 5: Divide the new quotient (93) by 2.

Quotient: 46

Remainder: 0

Step 6: Divide the new quotient (46) by 2.

Quotient: 23

Remainder: 1

Step 7: Divide the new quotient (23) by 2.

Quotient: 11

Remainder: 1

Step 8: Divide the new quotient (11) by 2.

Quotient: 5

Remainder: 1

Step 9: Divide the new quotient (5) by 2.

Quotient: 2

Remainder: 0

Step 10: Divide the new quotient (2) by 2.

Quotient: 1

Remainder: 1

Step 11: Divide the new quotient (1) by 2.

Quotient: 0

Remainder: 1

Now, let's arrange the remainders obtained from the successive divisions in reverse order to get the binary representation:

1490 in binary notation: 10111011010

Therefore, the decimal number 1490 can be represented as 10111011010 in binary notation.

To verify this result, we can convert the binary number back to decimal to see if we obtain the original decimal number.

10111011010 in decimal:

(1 * 2^10) + (0 * 2^9) + (1 * 2^8) + (1 * 2^7) + (1 * 2^6) + (0 * 2^5) + (1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)

= 1024 + 0 + 256 + 128 + 64 + 0 + 16 + 8 + 0 + 2 + 0

= 1490

The resulting decimal number is indeed 1490, which confirms that our binary representation is correct.

In summary, the decimal number 1490 can be represented as 10111011010 in binary notation.

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The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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So there are 23 states that border just a major body of water and 7 states that border just a foreign country.

A Venn diagram consists of one or more circles or ovals, each representing a set of objects or concepts. The circles can overlap, indicating that some objects or concepts belong to more than one set. The non-overlapping parts of the circles represent the objects or concepts that belong to only one set.

Let's first calculate the number of states that border either a major body of water, a foreign country, or both:

Number of states that border a major body of water = 30

Number of states that border a foreign country = 14

Number of states that border both a major body of water and a foreign country = 7

To find the total number of states that border either a major body of water, a foreign country, or both, we can add these three numbers:

30 + 14 + 7 = 51

However, since there are only 50 states in the US, this means that one of these numbers must be incorrect. The only possibility is that the number of states that border both a major body of water and a foreign country is included in both the number of states that border a major body of water and the number of states that border a foreign country. Therefore, we need to subtract the number of states that border both from each of the other two numbers:

Number of states that border a major body of water only = 30 - 7 = 23

Number of states that border a foreign country only = 14 - 7 = 7

So there are 23 states that border just a major body of water and 7 states that border just a foreign country.

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The vertex of the graph is (1, -4). Therefore, the correct option is c. (1, -4) The factored form of the quadratic equation \(x^2 - 2x - 3 = 0\) is (x - 3)(x + 1) = 0. To find the vertex of the graph of \(f(x) = x^2 - 2x - 3\), we need to determine the x-coordinate of the vertex using the formula x = -b/2a.

In this case, a = 1 and b = -2. Plugging these values into the formula, we get x = -(-2)/(2*1) = 1. Therefore, the x-coordinate of the vertex is 1. To find the y-coordinate of the vertex, we substitute the value of x into the equation \(f(x) = x^2 - 2x - 3\). Evaluating f(1), we get \(f(1) = 1^2 - 2(1) - 3 = -4\). Hence, the vertex of the graph is (1, -4).

The factored form of the quadratic equation helps us determine the x-intercepts, which are the points where the graph intersects the x-axis. By setting each factor equal to zero, we find the solutions x = 3 and x = -1. These values represent the x-coordinates of the x-intercepts, which can be used to find the vertex of the parabola. The x-coordinate of the vertex is the average of the x-intercepts, which in this case is (3 + (-1))/2 = 1. To find the y-coordinate of the vertex, we substitute the x-coordinate into the equation \(f(x) = x^2 - 2x - 3\). The resulting value is -4, so the vertex of the graph is (1, -4). Therefore, the correct option is c. (1, -4).

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The z-score for X = 48, given a population with a standard deviation of 8 and a mean of 40, is 1.

A bell-shaped curve, also known as a normal distribution, is a symmetric curve with a single peak resembling a bell. It is commonly used to represent data that follows a normal distribution pattern.

In the provided graph, the location of the mean (μ) is marked on the bell-shaped curve. Additionally, the numbers corresponding to each standard deviation, which are -1, -2, +1, and +2, are also indicated. These values represent the distance from the mean in terms of standard deviations.

To calculate the z-score for X = 48, we can use the z-score formula: $z = \frac{X - \mu}{\sigma}$, where X is the raw score, μ is the population mean, and σ is the population standard deviation.

Applying the formula to the given values, we have:

$z = \frac{48 - 40}{8} = 1$

Therefore, the z-score for X = 48 is 1.

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Answer:

\( \sf p = \dfrac{i}{rt} \)

Step-by-step explanation:

Solve for p:

\( \longrightarrow \) i = prt

i = prt is equivalent to prt = i:

\( \longrightarrow \) prt = i

Divide both sides by rt:

\( \longrightarrow \) \( \sf \dfrac{prt}{rt} = \dfrac{i}{rt} \)

\( \sf \dfrac{prt}{rt} = p: \)

\( \longrightarrow \) \( \sf p = \dfrac{i}{rt} \)

Answer:

Less Than,Less Than or Equal to,Greater Than,Greater Than or Equal to

Step-by-step explanation:

The line under plays the role of an equal sign and the others are pretty self explanatory

Answer: The first one is a greater sign, the second one is greater than or equal to, the third one is less than, and the last one is less than or equal to.

Step-by-step explanation: hope this helps

Answer:

x = 3

y = 2

Step-by-step explanation:

3x + 2y = 12

-2x + 3y = 5 to find the solution we will use elimination method and for that, multiply second equation with 3 and the first equation with 2

2 * 3x + 2y = 12

6x + 4y = 24

3 * -2x + 3y = 5

-6x + 9y = 15  now find the sum of both equation:

6x + 4y  -6x + 9y = 24 + 15 add like terms

13y = 39 divide both sides by 13

y = 3 now that we found the value of y we can use this to calculate the value of x

3x + 2y = 12 replace y with 3

3x + 2*2 = 12

3x + 4 = 12 subtract 4 from both sides

3x = 9 divide both sides by 3

x = 3

The total amount of pentagons and hexagons that Shari does need altogether is given as follows:

32.

The total amount is obtained applying the proportions and ratios in the context of the problem.

Sheri needs 3 pentagons for every 5 hexagons, hence the equation is:

H = 5P/3.

Sheri needs between 10 and 15 pentagons, hence the possible amounts are given as follows:

Hence the amount is of 12 pentagons and 20 hexagons, thus the amount is:

12 + 20 = 32 pentagons and hexagons altogether.

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Answer:

Steve got 32 points

Step-by-step explanation:

Take the total score and multiply by the percentage received

40 * 80%

Change to decimal form

40 * .80

32

Steve got 32 points

The minimum sample size is  n = 97

The minimum sample size is define as the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power.

We have the information from the question is:

The margin of error is  E = 1.25

The  standard deviation is  s = 7.5

The confidence level is  90% then the level of significance is mathematically represented as:

\(\alpha =100-90\)

\(\alpha =10%\)%

\(\alpha =0.10\)

Now, The critical value of \(\frac{\alpha }{2}\) from the normal distribution table  

The value is \(Z_\frac{\alpha }{2}=1.645\)

The minimum sample size is mathematically evaluated as:

\(n=\frac{Z_\frac{\alpha }{2}(s^2)}{E^2}\)

Plug all the values in above formula:

\(n=\frac{1.645^2(7.5)^2}{1.25^2}\)

After calculation, we get :

n = 97

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The given question is incomplete, complete question is:

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is 1.25? The standard deviation in a pre-selected sample is  7.5

Answer:

$33

Step-by-step explanation:

If each locker costs $6, 33x6=330 (the 33 is from 27+6)

As for whether Z[√-6] is a unique factorization domain (UFD), it depends on whether every non-unit element in Z[√-6] can be uniquely factored into irreducible elements. To justify the answer, one would need to show that Z[√-6] satisfies the necessary conditions for being a UFD, such as the existence of unique factorization and the absence of zero divisors.

1.) Z[√-6] refers to the set of numbers of the form a + b√-6, where a and b are integers. To find the units of Z[√-6], we need to determine which elements have multiplicative inverses. In this case, the units of Z[√-6] are ±1.

2.) To show that 2, 5, 2-√-6, and 2 + √-6 are irreducible in Z[√-6], we need to demonstrate that they cannot be factored into non-unit elements of Z[√-6]. This can be done by assuming a factorization exists and showing it leads to a contradiction.

3.) To determine if 2 or 5 is an associate of 2-√-6 or 2 + √-6 in Z[√-6], we need to check if their ratio is a unit (±1). If the ratio is not a unit, then they are not associates.

4.) As for whether Z[√-6] is a unique factorization domain (UFD), it depends on whether every non-unit element in Z[√-6] can be uniquely factored into irreducible elements. To justify the answer, one would need to show that Z[√-6] satisfies the necessary conditions for being a UFD, such as the existence of unique factorization and the absence of zero divisors. I apologize, but the question you provided seems to involve concepts from abstract algebra, specifically related to the ring of integers extended with the imaginary number √-6 (denoted as Z[√-6]). As an AI language model, I can provide a general overview of the topic, but I may not be able to generate a detailed answer or explanation for each part of the question. Please note that the explanations provided here are general and may not cover all the details and proofs required for each specific part of the question. For a complete and rigorous answer, I would recommend consulting a textbook or a knowledgeable instructor in abstract algebra.

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The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

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The definition of percent helps you write fraction and decimal equivalents by understanding that "per cent" means "per hundred".

For example, if you are asked to write the fraction and decimal equivalent of 25%, you would divide 25 by 100 to get the fractional equivalent of ¼, and divide 25 by 100 to get the decimal equivalent of 0.25.

The decimal equivalent of a fraction or percentage is the numerical value expressed in decimal form. For example, the decimal equivalent of 1/2 is 0.5 and the decimal equivalent of 25% is 0.25. Decimal equivalents are useful for calculations and can be used to convert fractions and percentages into decimal form.

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Answer: 250+3x

Step-by-step explanation: 250 for the bus and the students is $3 each so the students could be x.

Answer:

Step-by-step explanation:

123 X 8000 = 984000

984000/48 = 20500(PUT EURO SIGN)

Answer:

-3y+8z

Step-by-step explanation:

2x-2y+5z-2x-y+3z

you don't need to change their signs just place them accordingly

2x-2x-2y-y+5z+3z

-3y+8z

The standard deviation for the given data is 5

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

Given that,

the data,

X            Xₙ - X₀            (Xₙ - X₀)²

18            -7                      49

21             -4                      16

24            -1                        1

24            -1                        1

25             0                       0

31              6                      36

32            7                     49  

175                                  152

X₀  = 175/7 = 25

Variance  =    (Xₙ - X₀)²/(n-1)

                 =  152/(7-1)

                 =   25.33

Standard deviation =  √Variance

                                =  √25.33

                                =   5.03

Hence, the standard deviation is 5

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