a plane left kennedy airport on tuesday morning for a 595-mile, 5-hour trip. for the first part of the trip, the average speed was 110 mph. for the remainder of the trip, the average speed was 125 mph. how long did the plane fly at each speed? first part of trip h second part of trip h

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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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

We can see that the triangle is equilateral, thus, the value of x is 13.

We can see that it is a right triangle, and we know the value of one of the catheti and one of the angles.

Remember that the sum of the interior angles must be equal to 180°.

So if we have a right angle and a 45° angle, then the measure of the remaining angle is:

a = 180° - 90° - 45° = 45°

So we have an equilateral triangle, thus, the measure of x must be 13 units.

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Answer: 13

Step-by-step explanation: Just took the test

Answer: MHT = 125; AHM = 55

Step-by-step explanation:

(2x + 11) + (6x - 7) = 180 since they are supplementary angles

8x + 4 = 180 ---- subtract 4 on both sides

8x = 176 ---- divide by 8 on both sides

x = 22

MHT = 6x - 7

6(22) - 7 = 132 - 7 = 125

AHM = 2x + 11

2(22) + 11 = 44 + 11 = 55

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.

Answer:

Step-by-step explanation:

(227-127)/4=x

"/" means divide.

The expected student population of the school will be N(t) = 15000*(1+3%)6=17910.78.

The term "population" refers to all citizens who are either permanently residing in a country or who are just passing through.  Growth rates are the population changes that occur each year as a result of births, deaths, and net migration. The world population clock maintained by the US Census Bureau indicated that there were 7,922,312,800 people on the planet as of September 2022, and that number would rise to 8 billion by mid-November. China and India will have the two largest populations in the world in 2022, followed by the United States, the European Union, Indonesia, and Pakistan.

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Answer: 2x + 12

Step-by-step explanation:

The system of equations that correctly represents the situation of Lina and Sarika's ages are:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations is called simultaneous equations.

The sum of Lina and Sarika's ages = 31

Lina's age > Sarika's by 5 years

Let Lina's age = L

Let Sarika's age = S

L + S = 31... Equation 1

L - S = 5... Equation 2

2L = 36

L = 18.

Substituting L = 18 into either Equation 1 or 2:

18 + S = 31

S = 31 - 18

S = 13

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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)

[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 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.

In the beginning, Sita had Rs. 64 to start with.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

From the given information the equation can be formed as,

4ˣ + 128 = 3.2⁽ˣ⁺³⁾.

2²ˣ + 2⁷ = 3.2⁽ˣ⁺³⁾.

Putting some arbitrary values of 'x' we gey at x = 3,

64 + 128 = 3.64.

So, In the beginning, she had 4³ rs which is 64 rs.

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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

Answer:

B

Step-by-step explanation:

given a line parallel to a side of a triangle and intersecting the other 2 sides, then it divides those sides proportionally , that is

[tex]\frac{32}{x}[/tex] = [tex]\frac{20}{30}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

2x = 3 × 32 = 96 ( divide both sides by 2 )

x = 48

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 percentage of people with blood pressure between 115 and 165 mm is 68.27% (closest to option e). The percentage of people with blood pressure between 140 and 165 mm is 89.4% (closest to option b). The percentage of people with blood pressure over 165 mm is 10.6% (closest to option a).

To solve this problem, we can use the properties of the normal distribution, which is a continuous probability distribution that is often used to model real-world data. In particular, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentages of people with blood pressure within certain ranges. The empirical rule states that, for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean. Approximately 95% of the data falls within two standard deviations of the mean. Approximately 99.7% of the data falls within three standard  deviations of the mean. Using this rule, we can estimate the following  percentages: The percentage of people with blood pressure between 115 and 165 mm: First, we need to find the z-scores for the lower and upper limits of the range: z_lower = (115 - 140) / 20 = -1.25.

z_upper = (165 - 140) / 20 = 1.25

We can then use a standard normal distribution table or a calculator to find the areas under the curve corresponding to these z-scores:

P(-1.25 < Z < 1.25) = 0.7887 - 0.1056 = 0.6831

So, approximately 68.31% of people have blood pressure between 115 and 165 mm.

The percentage of people with blood pressure between 140 and 165 mm: In this case, the lower limit is equal to the mean, so we only need to find the z-score for the upper limit: z_upper = (165 - 140) / 20 = 1.25

Using the same approach as before, we get:

P(Z < 1.25) = 0.8944

So, approximately 89.44% of people have blood pressure between 140 and 165 mm. The percentage of people with blood pressure over 165 mm:

In this case, we only need to find the area to the right of the upper limit:

P(Z > 1.25) = 0.1056

So, approximately 10.56% of people have blood pressure over 165 mm.

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Complete Question

The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.

a. 10.6%

b. 89.4%

c. 39.4%

d. 78.8%

e. 68.27%

___ The percentage of people with blood pressure between 115 and 165 mm.

___ The percentage of people with blood pressure between 140 and 165 mm.

___ The percentage of people with blood pressure over 165 mm.

melody had 120 stamps.

and she gave Jeremy 30 stamps .

so she had 90 stamps now.

after she gave Jeremy 30 stamps,she had twice as much as him.

so 90 is 45+45 .other way 45 is half of 90.

so Jeremy had 45 stamps now.

they have altogether 90+45=135 stamps.

the answer is 135

By creating and solving an algebraic equation, we learn that Jeremy started with 60 stamps and Melody started with 180 stamps. Therefore, they originally had 240 stamps combined.

We'll use algebra to solve this. Let's let Jeremy's number of stamps be represented by J. According to the information, Melody had 120 more stamps than Jeremy before she gave him 30, so she had J + 120 stamps. After transferring the 30 stamps, she has J + 120 - 30 stamps, which simplifies to J + 90 stamps. According to the problem, this amount is twice the amount Jeremy has after receiving the 30 stamps (J + 30). So, we can set up this equation: 2(J + 30) = J + 90.

Solving this equation gives J = 60. That means Jeremy started with 60 stamps. Therefore, Melody started with 60 + 120 = 180 stamps. The total number of stamps both had originally is 60 + 180 = 240 stamps.

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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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The liquid should be in the cooler less than 10 minutes. Therefore, option C is the correct answer.

A thermometer can be used to measure the degree of hotness or coolness that is present. It also expresses the rate of motion of a substance's atoms and molecules. The Fahrenheit, Celsius, and Kelvin thermometers measure temperature in degrees.

Given that, the temperature of a liquid must stay above 60° F.

The starting temperature of the liquid is 90° F.

Difference in temperature = 90-60

= 30

It is placed in a cooler, which lowers its temperature 3° F each minute.

= 30/3

= 10° F

Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

For an experiment, the temperature of a liquid must stay above 60°F. The starting temperature of the liquid is 90°F . It is placed in a cooler, which lowers its temperature 3°F each minute. Let m represent the number of minutes the liquid is in the cooler. Which statement determines how many minutes the liquid can stay in the cooler?

A) The liquid must be in the cooler fewer than 10 minutes.

B) The liquid must be in the cooler fewer than 15 minutes.

C) The liquid must be in the cooler fewer than 30 minutes.

D) The liquid must be in the cooler fewer than 60 minutes.

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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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]

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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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 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 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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