consider rolling two dice. which of the following describe two events that are collectively exhaustive? multiple select question. event 1: a value of 6 or more. event 2: a value of 8 or less. event 1: a value of 9 or more. event 2: a value of 7 or less. event 1: a value of 7 or more. event 2: a value of 6 or less. event 1: rolling an even number. event 2: rolling an odd number.

The equation of the circle with center at (8, 2) that passes through (17, 14) in standard form is (x - 8)² + (y - 2)² = 225

In your problem, we are given that the center of the circle is located at (8, 2) and that the circle passes through the point (17, 14). To find the equation of this circle, we need to use the standard form of the equation of a circle, which is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius of the circle.

To find the radius of the circle, we can use the distance formula between the center of the circle and the point on the circle that is given to us. The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) is the center of the circle and (x₂, y₂) is the point on the circle that is given to us.

Plugging in the values we have, we get:

d = √((17 - 8)² + (14 - 2)²) = √(81 + 144) = √(225) = 15

So the radius of the circle is 15.

Now we can plug in the values we have into the standard form of the equation of a circle:

(x - 8)² + (y - 2)² = 15²

which simplifies to:

(x - 8)² + (y - 2)² = 225

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Answer:

0.15 expressed as a fraction in its simplest form is 3/20.

Step-by-step explanation:

To express a terminating decimal as a fraction:

Write the decimal as a fraction by dividing it by 1:

[tex]\boxed{\dfrac{0.15}{1}}[/tex]

Multiply the numerator and denominator by 10 for every number after the decimal point.

As there are two numbers after the decimal point, multiply the numerator and denominator by 100:

[tex]\boxed{\dfrac{0.15 \times 100}{1 \times 100}=\dfrac{15}{100}}[/tex]

Find the highest common factor (HCF) of the numerator and denominator.

Therefore, the HCF of 15 and 100 is 5.

Divide the numerator and denominator by the HCF to reduce the fraction to its simplest form:

[tex]\boxed{\dfrac{15 \div 5}{100 \div 5}=\dfrac{3}{20}}[/tex]

0.15 expressed as a fraction in its simplest form is 3/20.

Answer:

See below, please.

Step-by-step explanation:

The function for the total cost of renting a car for a weekend with a base cost of $45 and a mileage charge of $0.15 per mile can be written as:

Total Cost = 45 + 0.15 * miles driven

where "miles driven" is the number of miles the car is driven over the rental period.

To find out how much it would cost Tara to rent the car if she travels 500 miles, we can substitute "500" for "miles driven" in the function:

Total Cost = 45 + 0.15 * 500

Total Cost = 45 + 75

Total Cost = $120

Therefore, if Tara drives 500 miles over the rental period, the total cost of renting the car for the weekend would be $120.

Hence, the total cost of renting a car for a weekend with a base cost of $45 and a mileage charge of $0.15 per mile can be calculated using the function Total Cost = 45 + 0.15 * miles driven. To find the total cost for a specific number of miles driven, we can substitute that number for "miles driven" in the function.

In this case, if Tara drives 500 miles, the total cost of renting the car would be $120.

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The number of ways a person can toss a coin 15 times so that the number of tails is between 4 and 11 inclusive is the product of the total number of ways and the sum of probabilities for k=4 to k=11 inclusive.

Binomial distribution refers to the issue of tossing a coin 15 times and getting a specific amount of tails. The following gives the binomial distribution formula:

[tex]P(X=k) = C(n,k) (n,k) * p^k * (1-p)^(n-k) (n-k)[/tex]

Where P(X=k) denotes the likelihood that there will be k tails in n tosses, p is the likelihood that there will be one tail in a single toss, and C(n,k) denotes the number of combinations of n objects that will be picked up k at a time.

The total of probability for k=4 to k=11 inclusive must be calculated in order to find the solution. This is,

P (4), P (5), P (6), P (7), P (8), P (9), P (10) and P (11)

We can figure out and add up each of these probability using the technique above. As an alternative, we can compute the probabilities using a statistical software programme or a binomial probability table.

A person can flip a coin 15 times in a total of 32,768 different ways. By calculating the total number of ways by the sum of probabilities for k=4 to k=11 inclusive, one may get the number of ways that the number of tails is between 4 and 11 inclusive.

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Answer: 2+2

Step-by-step explanation: easy thanks :)

The truck must make 2 trips tο deIiver 7 m³ οf sand.

VοIume is the amοunt οf space οccupied by an οbject οr substance. It is typicaIIy measured in cubic units such as cubic meters, cubic centimetres, οr cubic feet.

Tο caIcuIate the number οf trips the truck must make tο deIiver 7 m³ οf sand, we need tο determine hοw much sand the truck can carry per trip.

The vοIume οf the truck bed can be caIcuIated as fοIIοws:

VοIume οf the truck bed = Iength x width x height

= 2.5 m x 1.5 m x 1 m

= 3.75 m3

Therefοre, the truck can carry 3.75 m³ οf sand per trip.

Tο deIiver 7 m³ οf sand, we divide the tοtaI amοunt οf sand by the amοunt οf sand the truck can carry per trip:

Number οf trips = tοtaI amοunt οf sand / amοunt οf sand per trip

= 7 m³ / 3.75 m³ per trip

= 1.87

Since we cannοt make a partiaI trip, we must rοund up tο the nearest whοIe number.

Therefοre, the truck must make 2 trips tο deIiver 7 m³ οf sand.

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The product of the eigenvalues is equal to the determinant of the matrix. In other words, if λ1, λ2, ..., λn are the eigenvalues of a square matrix A, then det(A) = λ1 * λ2 * ... * λn. This relationship also holds true for both matrices A and C.

To enter matrices A and C in MATLAB, we can use the following commands:

A = [6, -1, 0; -1, -2, -1; 0, -1, 2];

C = [1, -1, 1; -1, 2, 0; 0, -1, 2];

To find the trace of A and C, we can use the following commands:

trace_A = trace(A);

trace_C = trace(C);

The trace of matrix A is 6 - 2 + 2 = 6, and the trace of matrix C is 1 + 2 + 2 = 5.

To find the eigenvalues of A and C, we can use the eig() function in MATLAB:

[eig_vec_A, eig_val_A] = eig(A);

[eig_vec_C, eig_val_C] = eig(C);

The eigenvalues of matrix A are -1, 1, and 6, and the eigenvalues of matrix C are 1, 1, and 2.

There is a relationship between the trace of a square matrix and its eigenvalues. Specifically, the sum of the eigenvalues is equal to the trace of the matrix. In other words, if λ1, λ2, ..., λn are the eigenvalues of a square matrix A, then trace(A) = λ1 + λ2 + ... + λn. This relationship holds true for both matrices A and C.

To find the determinant of A and C, we can use the following commands:

det_A = det(A);

det_C = det(C);

The determinant of matrix A is 12, and the determinant of matrix C is 5.

There is also a relationship between the eigenvalues and the determinant of a square matrix. Specifically, the product of the eigenvalues is equal to the determinant of the matrix. In other words, if λ1, λ2, ..., λn are the eigenvalues of a square matrix A, then det(A) = λ1 * λ2 * ... * λn. This relationship also holds true for both matrices A and C.

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Answer: 56448² ft

Step-by-step explanation:

7 x 4 x 18 x 4 x 7 x 4 = 56448 and square it to get 56448² and then add the unit to get  56448 ft² :)

The probability of either die rolling the value 3 or both dice rolling even values is 5/9.

The probability of rolling a 3 on a single die is 1/6, so the probability of either die rolling a 3 is 2/6 or 1/3 (since there are two dice).

The probability of rolling an even number on a single die is 1/2 (since there are three even numbers and three odd numbers on a 6-sided die). The probability of rolling even values on both dice is the product of the probability of each die rolling an even value, which is (1/2) x (1/2) = 1/4.

To find the probability of either die rolling a 3 or both dice rolling even values, we need to subtract the probability of rolling both a 3 and an even value (since we would be double-counting this case). The only way to roll both a 3 and an even value is to roll two 6's, so the probability of this happening is 1/36.

Therefore, the probability of either die rolling 3 or both dice rolling even values is:

P(either die rolling 3 or both dice rolling even) = P(die 1 = 3 or die 2 = 3 or both dice even) - P(both dice = 6)

= (1/3 + 1/3) + (1/4 - 1/36)

= 5/9

Hence, the probability is 5/9.

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Using the idea of comparable ratio, we may determine x:y:z to be 3:16:1, given as x:y=3:4 and y:z=1:4.

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation wherein two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)

Given that y is present in both ratios, we may begin by determining its value:

y = (4/1) * (y/z), multiplied by 4, which is the reciprocal of 1/4.

y = 4(y/z)

y/z = 1/4

z/y = 4/1

We can now find x by using the value of y:

x/y = 3/4 (given)

x = (3/4) * y x = (3/4) * 4(z/y) (simultaneously inserting y/z)

x = 3z

As a result, x:y:z = 3z: 4 is the ratio of x:y:z.

y : z\s= 3 : 4(4) : 1\s= 3 : 16 : 1

So, x:y:z = 3:16:1 is the solution.

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Answer:5

Step-by-step explanation:

angle h and k are equal (because alternate exterior angles are equal)

2x+7=5x-8

8+7=5x-2x

15=3x

15/3=x

5=x

h=2x+7=2*5+7=17degrees

Sarah was charged $54 for parts after the store's technician worked on the computer for 4.25 hours. The cost came to $585.25. The value of x is $125.

Let's use the variable x to represent the cost of the labor per hour.

The technician worked on the computer for 4.25 hours, so the cost of the labor would be:

4.25x

The technician also charged Sarah $54 for parts. So the total cost of the repair is:

4.25x + 54

We know that the total cost of the repair was $585.25. Therefore, we can write the following equation:

4.25x + 54 = 585.25

To solve for x, we need to isolate the variable on one side of the equation. First, we can subtract 54 from both sides:

4.25x = 531.25

Next, we can divide both sides by 4.25:

x = 125

Therefore, the cost of the labor per hour is $125.

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Answer:

In summary, the correct statements are:

The domain is the set of all integers from 0 to 43.

The range is the set of all multiples of 3 from 0 to 129.

this is the best i could do, make what you want of it, good luck

Step-by-step explanation:

he domain of this function is the set of all possible inputs, which in this case is the number of watermelons the farmer can sell. Since the farmer has 43 watermelons and cannot sell a fraction of a watermelon, the domain is the set of all integers from 0 to 43. So, the first statement is correct.

The second statement is incorrect because the farmer cannot sell a fraction of a watermelon, so the domain cannot include all real numbers from 0 to 43.

The range of this function is the set of all possible outputs, which in this case is the total sales in dollars. Since the farmer sells each watermelon for $3, her total sales will be a multiple of 3. The minimum sales value is $0 (if she sells no watermelons) and the maximum sales value is $129 (if she sells all 43 watermelons). So, the range is the set of all multiples of 3 from 0 to 129. Therefore, the fourth statement is correct.

The third statement is incorrect because not all integers between 0 and 129 are possible values for the farmer’s total sales. For example, she cannot make $2 in sales because her sales will always be a multiple of 3.

The fifth statement is incorrect because it implies that the farmer can only make sales in multiples of 43, which is not true since she sells each watermelon for $3.

In summary, the correct statements are:

The domain is the set of all integers from 0 to 43.

The range is the set of all multiples of 3 from 0 to 129.

The number of distinct sequences of letters is 8 × 26⁷.

How many distinct sequences of letters can you make if each sequence is ten letters long and contains the subsequence die?

We have to find the number of distinct sequences of letters that can be made. Here, the word 'die' can occur in any position of the ten-letter sequence. Therefore, we have to find the number of distinct sequences of seven letters that can be formed, which are not related to the word 'die'. The number of distinct sequences of seven letters that can be formed with no restrictions is:

26 × 26 × 26 × 26 × 26 × 26 × 26 = 26⁷

The word 'die' has three letters, and it can be placed in any of the eight positions of the seven-letter sequence (that is not related to the word 'die'). We have a total of 8 possibilities to choose where to put the word 'die'.Thus, the number of distinct sequences of letters is:

8 × 26⁷ (or) 703, 483, 260, 800.

The number of distinct sequences of letters is 8 × 26⁷.

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The difference between the lengths of the radii is approximately 4.70 cm.

What is circle ?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are at a given distance (called the radius) from a given point (called the center). It can also be defined as the locus of all points that are equidistant from a given point. A circle is a closed curve and its circumference is the distance around the circle.

We know that the formula for the circumference of a circle is:

C = 2πr

Where C is the circumference and r is the radius.

For circle A, we have:

21.99 = 2πr

Dividing both sides by 2π, we get:

r = 3.5

For circle B, we have:

51.52 = 2πr

Dividing both sides by 2π, we get:

r = 8.2

The difference between the radii is:

8.2 - 3.5 = 4.7

Rounding to the nearest hundredth, we get:

4.7 ≈ 4.70

Therefore, the difference between the lengths of the radii is approximately 4.70 cm.

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Answer: s = ∛125 in^3

Step-by-step explanation:

To find the edge length "s" of a cube with volume "V", we use the formula:

s = ∛V

For a cube with a volume of 125 cubic inches, we can find the edge length as:

s = ∛125

s = 5

So the edge length of a cube with a volume of 125 cubic inches is 5 inches.

[tex]=\frac{1}{15} +2\\[/tex]

⇒We can only add the numbers if they have the same denominator, to do so we can first convert 2 into a fraction

[tex]=\frac{1}{15} +\frac{2(15)}{1(15)} \\=\frac{1}{15} +\frac{30}{15} \\=\frac{31}{15} \\[/tex]

Answer:

d=-3

Step-by-step explanation:

d^3=-27

d=[tex]\sqrt[3]{-27} \\[/tex]

d=-3

Answer:

d=-3

Step-by-step explanation:

You must that 3rd root of -27, which is -3

Answer:

a) 640 ml

b) 40 ml

Step-by-step explanation:

The ratio of lime to lemonade for the fizzy drink is 5 : 3 or as a fraction that would be

[tex]\dfrac{\text{Lime juice}}{\text{Lemonade}}= \dfrac{5}{3}[/tex]

[tex]\text{Therefore the ratio of lemonade to lime }\\\\ = \text{reciprocal of $ \dfrac{5}{3} $} }\\\\= \dfrac{3}{5}[/tex]

Part a)

For  all 400 ml of  lime juice we would need
[tex]\dfrac{3}{5} \times 400 \;ml = 3 \times 80 = 240 \;ml[/tex]  

Total amount of fizzy drink that can be maade
= amount of lime juice + amount of lemonade

= 400 + 240

= 640 ml

This is the answer to Part a)

Part b)

If Gianni has only 280 ml and is using all 400 ml of lime juice then the amount of lemonade used as calculated in part 1) is 240ml

That means the amount of lemonade left over = 280 - 240 = 40 ml

Answer:

True

Step-by-step explanation:

I did it

The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is [tex]\frac{7}{12}[/tex] , where 7 and 12 are relatively prime positive integers. The answer is 7+12=19.

The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is 1 minus the probability that no diameter of the circle has two girls sitting on opposite ends of the diameter.

There are

[tex]{10\choose5}[/tex] =252

ways to seat the five girls and five boys.

There are 5 ways to choose a diameter of the circle.

Once this diameter is fixed, there are [tex]{5\choose2}[/tex] = 10 ways to choose a pair of seats on the diameter to place two girls (in the order in which they appear counterclockwise).

There are 5!=120 ways to seat the remaining 3 girls and 5 boys such that no two girls sit on the same diameter.

Hence, there are [tex]5\cdot10\cdot120[/tex] =6000 valid seatings that satisfy the condition in the question.

Thus, the desired probability is 1 - [tex]\frac{6000}{252}[/tex] = [tex]\frac{7}{12}[/tex], as stated above.

Thus, the answer is 7+12 = [tex]\boxed{19}[/tex]

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Answer:

[tex]\boxed{\mathtt{10x^{2}-x-16}}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to simplify the given expression.}[/tex]

[tex]\textsf{Consider noting that this expression has like terms, meaning we can combine them.}[/tex]

[tex]\large\underline{\textsf{What are Like Terms?}}[/tex]

[tex]\textsf{Like terms are 2 or more terms that share similarity. They aren't different in a major way.}[/tex]

[tex]\textsf{Like terms are terms with the same type of number, variable, and or exponent.}[/tex]

[tex]\large\underline{\textsf{Combine Like Terms:}}[/tex]

[tex]\mathtt{2x+6x^{2}-10+4x^{2}-3x-6}[/tex]

[tex]\boxed{\mathtt{10x^{2}-x-16}}[/tex]

Answer:

cylinder

Step-by-step explanation:

A cylinder has 2 circular faces and no vertices.

The longest piece of wood we need is the bottom left piece, which requires a board of at least 15 inches in length

Based on the dimensions provided in the image, we can see that Yeidalis needs a board that is at least as long as the longest piece of wood required.

The longest piece of wood required is the diagonal of the rectangle with dimensions 12 inches and 9 inches.

Using the Pythagorean theorem, we can calculate the length of this diagonal as:

sqrt(12^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15 inches

So Yeidalis needs a board that is at least 15 inches long to create her artwork.

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The bottom of the ladder is moving at a rate of 1.333 ft/sec when the top is 8 ft from the ground

The bottom of the ladder is moving at a rate of 6 ft/sec when the top is 8 ft from the ground. This can be found by using the equation v = d/t, where v is the velocity, d is the distance, and t is the time. The distance is 8 feet (from the top of the ladder to the ground) and the time is 1/6 seconds (since the ladder is sliding down at a rate of 6 ft/sec). Therefore, the velocity of the bottom of the ladder when the top is 8 ft from the ground is 8/1/6 = 8/6 = 4/3 = 1.333 ft/sec.

To understand this concept more clearly, imagine a ball rolling along the ground. Its velocity is constant until it hits a slope and begins to move down the slope. At this point, its velocity increases as it moves further down the slope, and its velocity is higher when it is further down the slope.

This is the same concept as the ladder sliding down the wall; the bottom of the ladder is moving faster than the top, so the velocity of the bottom of the ladder increases as the top of the ladder gets closer to the ground.

In conclusion, the bottom of the ladder is moving at a rate of 1.333 ft/sec when the top is 8 ft from the ground. This can be found using the equation v = d/t, where v is the velocity, d is the distance, and t is the time. The distance is 8 feet and the time is 1/6 seconds since the ladder is sliding down at a rate of 6 ft/sec.

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Answer:

56

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

the answer is 56

Larger sample sizes typically result in more precise population mean estimates with lower sampling variability. Thus, when calculating population metrics like the mean, it is frequently preferable to utilize larger sample numbers.

The variability of the sampling distribution of the mean reduces with an increase in the number of observation units. The central limit theorem refers to this.

According to the central limit theorem, the sampling distribution of the mean gets more normal as the sample size grows, and its standard deviation (i.e., the standard error of the mean) drops. Particularly, the square root of the sample size has an inverse relationship with the standard error of the mean.

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Answer:

y=4

Step-by-step explanation:

2y+4=12

2y=8

y=4

answer: y=4

Answer:

y=4

Step-by-step explanation:

2y+4=12

2y=8

y=4

 π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .

When variables and coefficients are combined using arithmetic procedures like addition, subtraction, multiplication, and non-negative integer exponents, the result is a mathematical expression known as a polynomial. Any numerical value may be represented by the variables, and the expression's coefficients are constants that combine the variables.

given

A =  πr², where r is the circle's radius, is the method for calculating a circle's surface area. The area of one circle can be expressed as follows if the radius of each circle is (4a–6):

A₁ = π(4a-6)²

If we condense this phrase, we get:

A₁ = π(16a² - 48a + 36)

A₂ = π(4a-6)²

A₂ = π(16a² - 48a + 36)

A₃ = π(4a-6)²

A₃ = π(16a² - 48a + 36)

A₄ = π(4a-6)²

A₄ = π(16a² - 48a + 36)

We can add up the areas of each of the four circles to determine their combined area:

A1 + A2 + A3 + A4 Equals A total

A total is equal to π (16a2 - 48a + 36) +  π(16a2 - 48a + 36) +  π(16a2 - 48a + 36).

 π(64a2 - 192a + 144) = A total

 π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .

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The probability of x being exactly 48 when it is uniformly distributed between 45 and 150 is 1/105

Since x is uniformly distributed between 45 and 150, the probability of x taking any particular value in this range is the same. Let this probability be denoted by P(x).

To find P(x = 48), we need to first check if 48 lies within the range of values that x can take. In this case, 48 lies within the range of 45 and 150, so it is a possible value for x.

Since the distribution is uniform, the probability of x taking any particular value between 45 and 150 is given by

P(x) = 1 / (150 - 45) = 1 / 105

Therefore, the probability of x being exactly 48 is

P(x = 48) = 1 / 105

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The given question is incomplete, the complete question is:

A random variable x is uniformly distributed between 45 and 150. what is the probability of x = 48?