Use the figure to find the measures of the numbered angles.
4

Answer:

S∞ = 96

Step-by-step explanation:

a) The probability that at most one is a six is 5/6.

b) The probability that at most one is a six is 2/3.

In the question two dice are rolled in a random experiment and we have to find what is the probability that at most one is a six and if the two faces are different, what is the probability that at most one is a six.

a) The probability that at most one is a six is 5/6. There are only 6 possible outcomes when rolling two dice, and 5 of those outcomes involve at most one six: (1,2), (1,3), (1,4), (1,5), (2,5).

b) The probability that at most one is a six is 2/3. If the two faces are different, there are only 3 possible outcomes: (1,2), (2,3), (3,4). 2 of those outcomes involve at most one six: (1,2), (2,3). Thus, the probability is 2/3.

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The expression for the amount of money Eric has after he pays his brother back is x- 17.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given:

Eric owes his brother $17.

let x be the amount of money Eric got for his birthday.

If Eric gave the money back to his brother then he left with

= x - 17

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Let's call the original number of students in the group "n". Each student contributed $2.50, so the total amount the original group of students collected is $2.50 * n.

When 5 more students join the group, the new total number of students is n + 5, and each student contributes $2.50 - $0.50 = $2.00. So the total amount the new group collects is $2.00 * (n + 5) = $2.00n + $10.

Since the total amount collected remains the same, we can set the two expressions for the total amount equal to each other:

$2.50n = $2.00n + $10

Solving for n, we have:

$0.50n = $10

n = 20

So, there were originally 20 students in the group. To find out how much they plan to spend on the gift, we can multiply the original number of students by the original contribution amount:

$2.50 * 20 = $50.00

Therefore, the students plan to spend $50.00 on the gift.

The probability that at most four of the M&M are yellow is  0.3357 and the probability that at least two of the four of the M & M are yellow is   0.6622

The probability that at most two of the four M&M's are yellow can be calculated using the cumulative distribution function (CDF) of the binomial distribution. The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success. In this case, the number of trials is 4, and the probability of success (getting a yellow M&M) is 0.13.

The cumulative distribution function of the binomial distribution can be expressed as:

P(X <= k) = SUM[i=0 to k] (n choose i) * p^i * (1-p)^(n-i)

Where n is the number of trials, k is the value we want to find the probability for, p is the probability of success, and (n choose i) is the number of combinations of n items taken i at a time, which can be calculated as n! / (i! * (n-i)!).

For this problem, we want to find the sum of probabilities for X = 0, 1, and 2, so we have:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

= (4 C 0) * (0.13)^0 * (0.87)^4 + (4 C 1) * (0.13)^1 * (0.87)^3 + (4 C 2) * (0.13)^2 * (0.87)^2

= 0.3357

NB: "C" represent combination.

So the probability that at most two of the four M&M's are yellow is approximately 0.3357.

b. The probability that at least two of the four M&M's are yellow can be found by subtracting the probability of getting 0 or 1 yellow M&M's from 1. So:

P(X >= 2) = 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - ((4 C 0) * (0.13)^0 * (0.87)^4 + (4 C1) * (0.13)^1 * (0.87)^3)

= 0.6622

So the probability that at least two of the four M&M's are yellow is approximately 0.6622.

The mean of the distribution is given by n * p = 4 * 0.13 = 0.52, and the standard deviation is given by sqrt(n * p * (1-p)) = sqrt(4 * 0.13 * 0.87) = 0.9304.

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Using the log, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].

The power to which a number must be increased in order to obtain another number is known as a logarithm.

For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.

So, solve using a log as follows: (1/243) ^-x/3 = 4

[tex]\begin{aligned}& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4\end{aligned}[/tex]

[tex]\begin{aligned}& 3 \cdot \frac{\left(\frac{1}{243}\right)^{-x}}{3}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4\end{aligned}[/tex]

[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=3 \cdot 4 \\& \left(\frac{1}{243}\right)^{-x}=12\end{aligned}[/tex]

[tex]\begin{aligned}& \left(\frac{1}{243}\right)^{-x}=12 \\& -x=\log _{\frac{1}{243}}(12) \\& \frac{\left(\frac{1}{243}\right)^{-x}}{3}=4 \\& -x=\log _{\frac{1}{243}}(12)\end{aligned}[/tex]

Therefore, using the log, the answer to (1/243) ^-x/3 = 4 is [tex]-x=\log _{\frac{1}{243}}(12)[/tex].

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If carpeting cost AED 12 per square meters for the bedroom of 75m by 50m, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

To calculate the cost of laying carpet for Linda's bedroom, we need to know the area of the bedroom and the cost per square meter of the carpeting.

Linda's bedroom is a rectangle with a length of 75 meters and a width of 50 meters. To calculate the area of the bedroom, we multiply the length by the width:

Area = length x width = 75 meters x 50 meters = 3750 square meters

Now that we know the area of the bedroom is 3750 square meters, we can find the total cost of the carpeting by multiplying the area by the cost per square meter. The cost per square meter is given as AED 12, so:

Total cost = area x cost per square meter = 3750 square meters x AED 12/square meter

Multiplying the area by the cost per square meter gives us:

Total cost = AED 45,000

Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.

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The probability that an orange weighs more than 17 oz is 0.1587.

The probability that an orange weighs more than 17 oz is 0.1587. This value can be calculated using the Z-score formula, which is used to calculate the probability of an event occurring. The formula is as follows:

Z = (x - μ) / σ

where x is the data point, μ is the mean, and σ is the standard deviation.

In this case, the Z-score is (17 - 14) / 2 or 1.5. We can find the probability using the Z-score table, which gives us 0.1587, the probability that an orange weighs more than 17 oz.

The Z-score formula is useful for determining the probability of an event occurring when the data follows a normal distribution. Knowing the mean and standard deviation, we can calculate the likelihood of a certain outcome occurring. In this case, the probability that an orange weighs more than 17 oz is 0.1587.

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100% of the number is: the number x ÷ 0.8 × 1 = the number If 80% of a number is x, then the number can be found by dividing x by the percentage as a decimal.

To convert a percentage to a decimal, divide the percentage by 100.

So, if 80% of the number is x, then:

x ÷ 0.8 = the number

In other words, to find the whole number, we need to divide the part (x) by the percentage as a decimal (0.8).

Once we have the whole number, we can find 100% of it by simply multiplying the whole number by 1.

So, 100% of the number is:

the number x ÷ 0.8 × 1 = the number

In conclusion, if 80% of a number is known, the whole number can be found by dividing the part by the percentage as a decimal, and 100% of the number can be found by simply multiplying the whole number by 1. Understanding the concept of percentage and the ability to convert between percentages, decimals, and whole numbers is an important skill in various areas of life and work.

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Answer:

C = $24 + 0.45x

Step-by-step explanation:

If we let total amount spent by a guest to the park as $C and number of tickets bought is x then the algebraic expression to represent the total amount spent by a guest is

C = $24 + 0.45x

Answer: 8x^2 + xy - 15y^2

Step-by-step explanation:

first do the FOIL method than add 3xy to the equation after

Answer:

[tex]8x^2+xy-15y^2[/tex]

Step-by-step explanation:

[tex](4x+5y)(2x-3y)+3xy\\\\=(4x)(2x)+(4x)(-3y)+(5y)(2x)+(5y)(-3y)+3xy\\\\=8x^2-12xy+10xy-15y^2+3xy\\\\=8x^2+xy-15y^2[/tex]

Answer: 2x + 12

Step-by-step explanation:

Answer:a=3, d=common difference=3, a2=7, a3=9

Step-by-step explanation:

firstly we have given a,d  (using the arithmetic progression formula)

                                          (  an=a+(n-1) )

so we have made a sequence a2=a+d=7  

                                                   a3=a+2d=9

The size of angle BCA is 45 degrees

A quadrilateral called a kite has two pairs of sides that are each the same length and are next to one another.

Where the two uneven sides meet, the two angles are equal. It can be thought of as two congruent triangles sharing a base. It has two diagonals that right-angle intersect with one another.

Given:

From the Figure we can see that

AB = BC and AD = DC = AC

and, ABC = 90 degrees

Now, In triangle ABC using Angle sum Property

A + B + C = 180

So,  A + 90 + C = 180

A + C = 90

As, AB = BC

Then, 2C = 90

C = 45

Hence, the angle is 45 degrees

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The Question attached here seems to be incomplete/ inappropriate. The complete Question is:

ABCD is a kite with AB = BC and AD = DC = AC, What is the size of angle  BCA

Sselecting A, B, and C is the same as selecting B, C, and A, so = 720/(3*2*1) = 120 combinations

When the decision's order is unimportant, a combination is a choice made in mathematics from among a group of distinct elements. A pear and an orange, an apple and an orange, or a trio of fruits—an apple, an orange, and a pear—can be paired into one of three pairs. An official definition of a k-combination of a set S is a subset of S's k unique items. Consequently, two combinations are considered to be same if and only if they both contain the same elements. If a collection contains n elements, a combination is any set of n objects taken k at a time without repetition.

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The price of gasoline and oil will be equal in price after 4 years when the price of gasoline is $2.27 per gallon and decreases at the rate of $0.03 every two months.

To find out when the price of gasoline and oil will be equal, we have to set the two prices equal to each other and solve for time. The price of gasoline decreases at the rate of $0.03 every two months and the price of oil increases at a rate of $0.05 every six months.

We can start with the initial prices and solve for the time when they are equal:

$2.27 - 0.03t = 0.45 + 0.05t

where t represents the time in years.

Solving for t, we get:

$2.27 - 0.03t = 0.45 + 0.05t

$1.82 = 0.08t

t = 22.5

Since t is in months, we have to divide by 12 to convert it to years:

t = 22.5 / 12 = 1.875

So the price of gasoline and oil will be equal in price after approximately 4 years.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

According to given information ~

[tex]\qquad \sf  \dashrightarrow \: g(x) = 11(1.2) {}^{x} [/tex]

if x = 1;

[tex]\qquad \sf  \dashrightarrow \:g(1) = 11(1.2)[/tex]

[tex]\qquad \sf  \dashrightarrow \:g(1) = 11(1 + 0.2)[/tex]

[tex]\qquad \sf  \dashrightarrow \:g(1) = 11 + (0.2 \times 11)[/tex]

[tex]\qquad \sf  \dashrightarrow \:g(1) = 11 + ( \frac{20}{100} \times 11)[/tex]

[tex]\qquad \sf  \dashrightarrow \:g(1) = 11 + ( {20}\% \: \: of \: \: 11)[/tex]

So, there's an increase of 20% in insect population each month.

The expression 1000m ÷ 100n in the form of 10z is 10m/10n, which simplifies to m/10n.

What is an expression?

In mathematics, an expression is a combination of one or more numbers, variables, and operations such as addition, subtraction, multiplication, division, exponentiation, and so on.

We can simplify the expression 1000m ÷ 100n as follows:

1000m ÷ 100n = (1000 ÷ 100) × (m ÷ n)

= 10 × (m ÷ n)

= 10m/n

To write this in the form of 10z, we need to find a value of z that makes 10z equal to 10m/n. Since 10z is equal to 10 times z, we can set 10 times z equal to 10m/n and solve for z as follows:

10z = 10m/n

Dividing both sides by 10, we get:

z = m/10n

Therefore, the expression 1000m ÷ 100n in the form of 10z is 10m/10n, which simplifies to m/10n.

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The volume of a cylinder can be calculated as π * radius^2 * height. In this case, the radius is 0.5 ft and the height is 25 ft, so the volume is:

π * 0.5^2 * 25 = 19.63 cubic feet

So the cost of the utility pole would be 19.63 * $25.81 = $509.24

Rounding to the nearest cent, the cost of the utility pole would be $509.24, which can be rounded to $509.00.

The ordinary numbers for the expressions will be

a. 3.25*10⁴ = 32500

b. 6.04*10⁻³= 0.00604

c. 2400000 = 2.4*10⁶

d. 0.00147 = 1.47*10⁻³

What are expressions exactly?

In mathematics, expressions are mathematical assertions made up of at least two sentences that contain numbers, variables, or both and are linked by an operator. Mathematical operations include addition, subtraction, multiplication, and division. For example, x + y is an equation that uses an addition operator to separate the components x and y. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is six times the size of another number, x. This sentence is mathematically stated as x/2 + 6. Mathematical expressions are used to address complex problems.

Now,

Given expressions/Numbers are a. 3.25*10⁴  then ordinary form is

3.25*10000

=32500

b. 6.04*10⁻³ then ordinary numbers is

=6.04/1000

=0.00604

c. 2400000 then standard from is

=2.4*1000000

=2.4*10⁶

d. 0.00147  then standard form is

=1.47/1000

=1.47*10⁻3

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Part A: The greatest common factor of [tex]10x2 + 25x − 15[/tex]  is 5.

Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex].

Part C: The factoring from Part B is correct, as multiplying the two binomials in the parentheses yields [tex]2x2 + 5x − 3[/tex].

Part A: The greatest common factor of [tex]10x2 + 25x − 15[/tex] is 5. The greatest common factor (GCF) of a set of numbers is the largest number that is a factor of all numbers in the set. To find the GCF, first list all the factors of each number. The common factors among the numbers are the ones that are found in each list of factors. The largest number in the list of common factors is the GCF.

Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex]. To factor this expression, first identify the GCF, which is 5. Then divide the expression by 5 and factor the result. Since the result is a binomial, use the difference of squares formula, (x + a)(x − a). The resulting expression is then[tex]5(2x2 + 5x − 3[/tex]).

Part C: To check the factoring from Part B, multiply the two binomials in the parentheses. The result is [tex]2x2 + 5x − 3[/tex], which is the same as the original expression. To multiply, use the FOIL method. Multiply the First terms [tex](2x2 and 2x2)[/tex], the Outer terms[tex](2x2 and -3)[/tex], the Inner terms (5x and 2x), and the Last terms [tex](5x and -3)[/tex]. The resulting expression is [tex]2x2 + 5x − 3.[/tex]

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A residual plot that shows clear patterns or trends in the residuals suggests that the line of best fit is not a good model.

Here are some characteristics of a residual plot that suggest that the line of best fit is a poor model,

The residuals show a clear pattern or trend, such as a curve or a U-shape.

The residuals are not evenly distributed above and below zero.

There are one or more outliers or extreme values that stand out from the rest of the data.

The variability of the residuals changes across the range of the predictor variable.

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A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

If the ratio is 7: 5 (oranges to apples) we can use this equation to solve the problem:

We multiply by 0.714285714 because we can see that 7 is being multiplied by 0.714285714 to get 5.

Therefore, if the ratio stays proportional, you will need 120 litres of apple juice for every 168 litres of orange juice.

The dimensions of Yura's picture 10×7 square units. The length of Yura's picture 10 units and the width of 7 units.

What is a rectangle?

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.

The number of lines along the length is 11.

The length of the frame is 10 units.

The number of lines along the width is 8.

The width of the frame is 7 units

The dimension of an object is length × width.

The dimension of the frame is 10 units × 7 units.

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Answer:

Step-by-step explanation:

(227-127)/4=x

"/" means divide.

Answer:

4 : 2 = 10 : 5.

Step-by-step explanation:

Let's put this in a fraction way. 4/2 = 2, and 10/5 = 2. Likewise, we can keep going and putting things that equal to 2. (e.g. 42 : 21)

Answer:

C. P = 30

Step-by-step explanation:

Parallelogram opposite (or parallel) sides are equal,

so:

2x = x + 2

5y - 9 = 2y + 3

For x:

2x = x + 2

2x - x = 2

x = 2

For y:

5y - 9 = 2y + 3

5y - 2y = 3 + 9

3y = 12

y = 4

the smallest sides are equal 2x and x + 2 => 2 * 2 = 4

the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11

P = 2 * (a + b)

P = 2 * (4 + 11)

P = 2 * 15

P = 30