speed of both traveling east that was 112 mile wide and 8 mile per hour. North wind current is 5 miles per hour. what is speed of boat

Answer:

Step-by-step explanation:

4-10(9m-7)

4-90m+70

74-90m

56x+24/8

8(7x + 3)/8

7x + 3

24r + 16

8(3r + 2)

is 2m-3 same as 4(1/2m-3)

2m-3 = 2m-12

: no

-2(10-15x) same as 14x-20+16x

-20+30x = -20+30x

: yes

a. The probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.

b. The probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6

Explain probability

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur, and 1 means the event will definitely occur. Probability is a fundamental concept in mathematics and is used in many fields, including statistics, science, and finance.

According to the given information

a. The total number of brownies sold for a random sample of 56 days, Y, is a normal random variable with mean µ_Y = 56µ_X = 5638 = 2128 and standard deviation σ_Y = √(56)*σ_X = √(56)*6 = 25.21.

We want to find P(Y < 2070). Standardizing Y, we get:

Z = (Y - µ_Y) / σ_Y = (2070 - 2128) / 25.21 = -2.31

Using a standard normal distribution table or calculator, we can find that P(Z < -2.31) is approximately 0.0107. Therefore, the probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.

b. 2X₁ + X₂ + 3X₃ + X₄ is also a normal random variable with mean 2µ₁ + µ₂ + 3µ₃ + µ₄ = 2(3.6) + 0.9 + 3(1.8) + 7.4 = 18.5 and variance 4o² + o² + 9o² + o² = 14o².

We want to find P(2X₁ + X₂ + 3X₃ + X₄ ≤ 17.6). Standardizing the variable, we get:

Z = (17.6 - 18.5) / √(14o²) = -0.5735 / √(o²)

To find P(Z ≤ -0.5735 / √(o²)), we need to know the value of o². If o² = 1, then P(Z ≤ -0.5735) = 0.2831. If o² is a different value, we would need to adjust accordingly.

Therefore, the probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6

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The range is expressed in interval notation as (-1, ∞)

To find the linear function f(x), let us use the table given.

A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):

[tex]g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)[/tex]

Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:

a = -6, g(a) = 16, b = -3 and, g(b) = 10

Therefore g(x)

[tex]g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4[/tex]

now find the (f+g)(x).

[tex](f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\[/tex]

(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1

The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:

[tex](f +g)(x) = 0^{2} - 1 = -1[/tex]

Furthermore, because the coefficient of [tex]x^{2}[/tex] is 1, which is positive, this function indicates a parabola that has been opened upwards.

As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.

The range is expressed in interval notation as (-1, ∞)

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Answer:

29i

Step-by-step explanation:

While multiplying complex numbers we should remember that i^2=−1.

As p=2 and q=5i,

(2−5i)(p+q)i

= (2−5i)(2+5i)i

= (2×2+2×5i−5i×2−5i×5i)×i

= (4+10i−10i−25×i2)×i

= (4+10i−10i−25×(−1))×i

= (4+25)×i

=29i

Answer:

a) To find the exponential growth function, we can use the formula:

P(t) = P0 * e^(rt)

Where:

P(t) = the population at time t

P0 = the initial population (in this case, 5.51 million)

e = the mathematical constant e (approximately 2.71828)

r = the annual growth rate (in decimal form)

t = the number of years

Substituting the given values, we have:

P(t) = 5.51 * e^(0.0382t)

b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:

P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million

Therefore, the estimated population of the city in 2018 is approximately 6.93 million.

c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:

10 = 5.51 * e^(0.0382t)

e^(0.0382t) = 10/5.51

0.0382t = ln(10/5.51)

t ≈ 11.7 years

Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.

d) To find the doubling time, we can use the formula:

T = ln(2) / r

Where:

T = the doubling time

ln = the natural logarithm

2 = the factor by which the population grows (i.e., doubling)

r = the annual growth rate (in decimal form)

Substituting the given value of r, we have:

T = ln(2) / 0.0382 ≈ 18.1 years

Therefore, the doubling time for the population of the city is approximately 18.1 years.

Answer:          To answer these questions using the simple interest formula, we need to know the values of P (the principal or initial investment), r (the interest rate), and t (the time period in years).

In this case, P = $325, r = 0.08 (8% expressed as a decimal), and t = 15.

Using the simple interest formula, I = P ∙ r ∙ t, we can calculate:

I = $325 ∙ 0.08 ∙ 15 = $390

Therefore, Charlie's initial investment will earn $390 in interest over the 15-year period.

To calculate how much money Charlie will have after the 15 years, we need to add the interest earned to the initial investment.

The total amount of money that Charlie will have after the 15 years is:

Total amount = Initial investment + Interest earned

Total amount = $325 + $390

Total amount = $715

Therefore, Charlie will have $715 after 15 years.

Step-by-step explanation:

The probability of drawing a black card is P(draw a black card) = 0.3 or 30%.

Probability is a branch of mathematics that deals with the study of random events and the likelihood or chance of their occurrence. It is the measure of how likely or unlikely it is for an event to happen. The probability of an event is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to occur.

Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if we want to calculate the probability of flipping a coin and getting heads, we divide the number of ways to get heads (1) by the total number of possible outcomes (2), which gives us a probability of 1/2 or 0.5.

Probability is used in many real-world applications, such as in the fields of finance, insurance, and engineering, to make informed decisions based on the likelihood of an event occurring. It is also used in statistical analysis to make inferences about a population based on a sample of data.

The total number of cards in the deck is:

Total number of cards = number of black cards + number of red cards = 33 + 77 = 110

The probability of drawing a black card is given by:

P(draw a black card) = (number of black cards) / (total number of cards) = 33 / 110

Therefore, the probability of drawing a black card is:

P(draw a black card) = 0.3 or 30%

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Answer:

1  17/30.

Step-by-step explanation:

you can find this out by seeing how many 30s go into 47 which is 1.

Then subtract to find how much is leftover still over 30.

47 - 30 = 17

So 1 and 17/30

the solution to the equation  is x = -10.use the distributive property of multiplication over addition to simplify the left-hand side of the equation

what is distributive property ?

The distributive property is a mathematical property that is used to simplify expressions that involve multiplication and addition or subtraction. It states that when you multiply a number (or variable) by a sum or difference,

In the given question,

To solve the equation 3(x+6) = x + 8 + x, you can use the distributive property of multiplication over addition to simplify the left-hand side of the equation, and then combine like terms on both sides of the equation.

Here are the steps:

Distribute the 3 on the left-hand side of the equation:

3(x+6) = 3x + 18

Combine the two x terms on the right-hand side of the equation:

3x + 18 = 2x + 8

Subtract 2x from both sides of the equation:

3x - 2x + 18 = 2x - 2x + 8

Simplifying this expression gives:

x + 18 = 8

Finally, subtract 18 from both sides of the equation:

x + 18 - 18 = 8 - 18

Simplifying this expression gives:

x = -10

Therefore, the solution to the equation 3(x+6) = x + 8 + x is x = -10.

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The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;

1. The vertex point is (50, 630)

2. The solution point are; (20, 0), and (80, 0)

3. Vertex form; f(x) = -0.7·(x - 50)² + 630

4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)

A quadratic equation is an equation of the form f(x) = a·x² + b·x + c

1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)

The vertex point is; (50, 630)

2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;

The solutions are; (20, 0), and (80, 0)

3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

Therefore;

(h, k) = (50, 630)

f(20) = 0 = a·(20 - 50)² + 630

a·(20 - 50)² = -630

a = -630/((20 - 50)²) = -630/900 = -7/10

a = -7/10 = -0.7

The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630

4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)

r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7

The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)

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The measurements for area of Jacobs yard are;

Part A = 6m x 3m = 18m

Part B = 4.5m x 3m = 13 m

Part C = 1/2 x 3m x 3m = 4.5 m²

Total area = 18m² + 13.5m² + 4.5m² = 36m²

To identify sections that would help in calculating area, you need to look for shapes or figures that can be divided into simpler geometric shapes, such as squares, rectangles, triangles, and circles.

Once you have identified the simpler shapes, you can use their formulas to calculate their areas and then add them together to find the total area of the larger shape or figure.

For example, a rectangle can be divided into two triangles or two smaller rectangles, and a circle can be divided into a sector or a ring. Breaking down a larger shape into smaller, simpler shapes can make it easier to calculate their areas accurately.

Jacob is putting tiles on the section of his yard labeled A, B, C. What is the area of the parts that need tiles?

Part A = .............. x ........... = ...........m

Part B = + .............. x ............. = ............ m

Part C = 1/2 x ................. x ............ = ............... m²

Total area = ................... + ..................... + .................. = ..............m

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Answer: Amaterasu

Step-by-step explanation: The sun goddess Amaterasu is considered the most important of the Shinto gods because she is believed to be the ancestor of the Japanese imperial family, and therefore the protector of the Japanese people. She is also associated with agriculture, which was a vital part of Japanese society.

The range in ages for the middle 50% of viewers is the interquartile range (IQR), which is the height of the box in the box plot. The best approximation is C) 20.

The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. It is a useful measure of spread because it is not influenced by outliers.

Range is a statistical measure that represents the difference between the highest and lowest values in a set of data. It provides a simple indication of the spread or variability of the data.

According to the given information:

A box plot is a graphical representation of the distribution of a dataset. The box in the plot represents the middle 50% of the data, with the lower end of the box representing the 25th percentile (Q1) and the upper end of the box representing the 75th percentile (Q3). The distance between Q1 and Q3, which is represented by the height of the box, is called the interquartile range (IQR).

To answer the question, we need to find the best approximation for the range in ages for the middle 50% of viewers. From the box plot, we can see that the height of the box is approximately 20 units, which is the IQR. Therefore, the best approximation for the range in ages for the middle 50% of viewers is option C) 20. This means that 50% of viewers are between Q1-10 to Q3+10, where Q1 is the 25th percentile and Q3 is the 75th percentile.

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Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.

From the label, we see that the serving size contains 3.5g of saturated fat.

To calculate the %DV for saturated fat, we use the equation:

%DV = (amount of nutrient per serving / DV) x 100%

Plugging in the values for saturated fat, we get:

%DV = (3.5g / 19g) x 100%

%DV = 0.1842 x 100%

%DV ≈ 18%

Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

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The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

The basic probability formula of dividing the number of favorable outcomes by the total number of outcomes.

In this case, we are given the percentage of members in each age group, and we need to find the probability of selecting a member with a certain age range.

Here we have

The table shows the age distribution of members of a gym.  

Age -            Under 21      21 -35     36 - 55   Over 55

percentage       12                42            32          14  

a) To find the probability that the selected member is 21 or more,

Add the percentage of members who are 21-35, 36-55, and over 55 since all of these age groups are 21 or more.

Probability (21 or more)

= Percentage (21-35) + Percentage (36-55) + Percentage (Over 55)

= 42% + 32% + 14%

= 88%

b) To find the probability that the selected member is 55 or less,  

Add the percentage of members who are under 21, 21-35, and 36-55 since all of these age groups are 55 or less.

Probability (55 or less)

= Percentage (Under 21) + Percentage (21-35) + Percentage (36-55)

= 12% + 42% + 32%

= 86%

c) To find the probability that the selected member is not in the 21 to 35 age group,

Add the percentage of members who are under 21, 36-55, and over 55 since all of these age groups are not in the 21 to 35 age group.

Probability (not in the 21 to 35 age group)

= Percentage (Under 21) + Percentage (36-55) + Percentage (Over 55)

= 12% + 32% + 14%

= 58%

Therefore,

The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

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After 6 fluid ounces , Naya uses 4 glasses as a result.

A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce .  A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce

In Naya's pitcher, there are three glasses of salted lassi.

She fills each glass with six fluid ounces of lassi.

By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.

8 fluid ounces make constitute a cup.

Consequently, 3 cups equal 24 fluid ounces (3 x 8).

24 divided by 6 results in:

4 glasses are equal to 24/6.

Naya uses four glasses as a result.

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The solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is p > 6 or p > -3.

A compound inequality is a mathematical statement that involves two or more inequalities joined by either the word "and" or "or". The solution set of a compound inequality is the set of all values that satisfy both (in the case of "and") or either (in the case of "or") of the individual inequalities.

Let's solve each inequality separately:

4p + 1 < −11

Subtracting 1 from both sides, we get:

4p < -12

Dividing both sides by 4 (and remembering to flip the inequality because we are dividing by a negative number), we get:

p > -3

So the solution to the first inequality is:

p > -3

Now let's look at the second inequality:

6p + 3 > 39

Subtracting 3 from both sides, we get:

6p > 36

Dividing both sides by 6, we get:

p > 6

So the solution to the second inequality is:

p > 6

Therefore, the solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is:

p > 6 or p > -3

This can be written more simply as:

p > -3

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a. TRUE, b. TRUE, c. TRUE, d. TRUE, e. TRUE, f. FALSE, g. TRUE

a. TRUE: The probability of an event can never be negative, and can at most be equal to 1, which represents certainty.

b. TRUE: The sample space is the set of all possible outcomes of an experiment, and the probability of the sample space is always equal to 1, since one of the outcomes must occur.

c. TRUE: If the events in a sequence are disjoint, then they have no outcomes in common, so the probability of the union of the events is the sum of the probabilities of the individual events.

d. TRUE: If one event is a subset of another event, then the probability of the subset is less than or equal to the probability of the superset. This follows from the fact that the subset contains fewer outcomes than the superset.

e. TRUE: The probability of the union of two events is the probability of the first event plus the probability of the second event, minus the probability of the intersection of the events, which is the probability of both events occurring together. This is known as the inclusion-exclusion principle.

f. FALSE: The formula (P(A ∩ B) = P(A)P(B)) only applies to independent events, but not all independent events are mutually exclusive. For example, if A is the event of rolling a 4 on a die, and B is the event of rolling an even number, then A and B are independent, but not mutually exclusive.

g. TRUE: If two events are mutually exclusive, then they have no outcomes in common, so the occurrence of one event tells us that the other event cannot occur. This dependence means that the events are not independent.

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Using curves, we can find that the value of y at the indicated point on the curve is √3.

What is the definition of curves?

A smooth-drawn figure or line with a bend or turns is referred to as a curve. A circle is an illustration of a curved shape. Geometry is a subfield of mathematics that examines the dimensions, characteristics, and shapes of figures.

Here in the question,

Given equation:

x = y² - 2

As a point (1, y) is on the curve, we can put the value of x coordinate in the equation:

1 = y² - 2.

Adding 2 on both sides:

1 + 2 = y² - 2 + 2

⇒ 3 = y²

⇒ y = √3.

Therefore, the value of y at the indicated point on the curve is √3.

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Answer:

-4 + 8 = 4

-2 + 6 = 4

-1 + 5 = 4

So the three pairs are -4 and 8; -2 and 6; and -1 and 5.

Let x be the distance traveled on the first day. Then, the distance traveled on the second day is 1.1x, on the third day is 1.1(1.1x) = 1.21x, and so on. After 7 days, the total distance traveled is:

x + 1.1x + 1.21x + ... + (1.1)^6 x = 56.923

Using the formula for the sum of a geometric series, we have:

x(1 - (1.1)^7)/(1 - 1.1) = 56.923

x(1 - 1.1^7)/(-0.1) = 56.923

x = 56.923(-0.1)/(1 - 1.1^7) ≈ 4 miles

Therefore, the hiker traveled approximately 4 miles on the first day.

Sn = x(1 - r^n)/(1 - r)

where x is the first term, r is the common ratio (in this case, 1.1), and n is the number of terms.

S14 = x(1 - 1.1^14)/(1 - 1.1)

S14 ≈ 167.63

Therefore, the hiker will travel approximately 167.63 miles in 14 days.

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In the equation 1 over 2 x + y=c, the constant proportionality is defined as c. It displays the line's y-intercept and slope.

If the ratio of one statistic to the other is constant, then there is a proportional relationship between the two variables.

The ratio of y to x is the constant of proportionality if x and y have a proportional connection. At times, we can also say that x is to y.

The proportionality constant, or c, in the equation 1 over 2 x + y = c serves as a gauge for how quickly two variables change. The proportionality constant's value doesn't change when the value of one of the variables does.

A linear equation with two variables, x and y, is 1 over 2x + y = c. In the x-y plane, it symbolises a straight line.

If x = 0

Then,

1/2(0) + y = c

y = c

The proportionality constant, c, can be seen in the equation

1 over 2 x + y = c.

This number, which is unrelated to the actual values of the variables, shows the relationship between the two variables x and y.

The slope of the line connecting the two variables is another name for the constant of proportionality.

Two variables, x and y, are included in the equation 1 over 2 x + y = c in addition to the proportionality constant. The two quantities that

are being compared are represented by these variables.

In the equation 1 over 2 x + y=c, the proportionality constant is defined as c. It displays the line's y-intercept and slope.

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The Complete questions as follows-

Explain what the constant of proportionality means in the equation 1 over 2 x + y = c

The probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.

What is fraction?

A fraction is a method of representing a part of a whole or a ratio of two numbers. It is a number that is written in the form of one integer (the numerator) over another integer (the denominator), separated by a line or slash.

The probability of selecting the 3 oldest people in a group of 10 people depends on the assumption that all 10 people are distinct individuals and that the selection process is truly random.

The total number of ways to select 3 people from a group of 10 people is given by the combination formula:

C(10, 3) = 10! / (3! * 7!) = 120

This means that there are 120 possible ways to select a group of 3 people from a group of 10 people.

Since we are interested in selecting the 3 oldest people, we assume that the 3 oldest people are identified and we only need to select them from the group of 10 people. There is only 1 way to select the 3 oldest people out of the group of 10 people.

Therefore, the probability of selecting the 3 oldest people in a group of 10 people is:

P = Number of ways to select the 3 oldest people / Total number of ways to select 3 people from a group of 10 people

P = 1 / 120

P = 0.0083

So, the probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.

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There are 13,800 different recital programs possible.

What is permutation?

In mathematics, a permutation is an arrangement of objects in a specific order. In other words, a permutation is a way of selecting a certain number of objects from a larger set and arranging them in a particular order.

The pianist has 25 choices for the first piece, then 24 choices for the second piece (since one piece has already been played), and 23 choices for the third piece (since two pieces have already been played). Therefore, the number of different recital programs possible is:

25 x 24 x 23 = 13,800

There are 13,800 different recital programs possible.

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Answer:

Step-by-step explanation:

A=1/2(b1+b2)h

=1/2 (11yd+11yd)(7yd)

=1/2(22yd)(7yd)

=(11yd)(7yd)

=77yd

The next entry on the long division would be 0.054, and 0.0054

Long division is a method of dividing two numbers using a step-by-step process. Here's how to perform long division:

Step 1: Write the dividend (the number being divided) and the divisor (the number you're dividing by) in the long division format, with the dividend inside the division symbol and the divisor outside.

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The cost of pizza with no toppings is $6. So correct option is C.

A graph is a visual representation of data or information, typically shown on a coordinate plane or a network of nodes and edges. Graphs are used to help people understand complex information by presenting it in a clear and concise way.

There are many different types of graphs, including bar graphs, line graphs, scatter plots, pie charts, and network graphs. Each type of graph is best suited for representing different types of data. For example, bar graphs are used to represent discrete data or data that can be divided into categories, while line graphs are used to represent continuous data or data that changes over time. Scatter plots are used to represent the relationship between two variables, while pie charts are used to represent percentages or proportions. Network graphs are used to represent complex systems of relationships between objects or people.

Graphs are commonly used in fields such as business, economics, science, and engineering to help people understand trends, patterns, and relationships in data. They can also be used to make predictions, identify outliers or anomalies, and communicate results to others. In addition, graphs can be customized to suit the needs of different audiences, such as by adding labels, titles, and other visual elements to make the data more understandable.

Because when x is 0 ,y is 6. So, the y intercept is the cost of a pizza with no toppings is $6.

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The complete question is:

The effective tax rate for a taxable income of $115,500 is A) 18.71%

The introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).

Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,

= 18%

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