In an arithmetic sequence, the first term, a1, is equal to 10, and the fourth term, a4,
is equal to 19. Which number represents the common difference of the arithmetic
sequence?
d=3
d=5
d=4
d=6

The distance of the end of the trip from the starting point is 193.1321 km.

The ship goes 180 kilometers on bearing after 70 km of subsequent journey.

The starting point in this case is A, and the ending point is C.

We now discover distance AC:

As we can see, a right-angled triangle results.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides that make up the right angle is equal to the square of the hypotenuse. This can be expressed mathematically as a^2 + b^2 = c^2, where a and b are the two sides that make up the right angle, and c is the hypotenuse.

Use Pythagoras's principle.

c = √a² + b²

The distance in the Hypotenuse in our case is now.

c = √(70)² + (180)²

c = √4900 + 32400

c = √37,300

c = 193.1321 km

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The complete question is:

A ship travels 70 km on a bearing of 27 degrees, and then travels on a bearing of 147 degrees for 180 km. Find the distance of the end of the trip from the starting point.

Equation:

89.50=2.35c+5.50d

If theres 22 dogs and cats in total you can plug in number less than 22 for c(# of cats) and d(# of dogs).

So we try pats numbers 8 cats and 14 dogs so

89.50=2.35(8)+5.50(14)

89.50=18.8+77

89.50=95.8

So pats numbers were wrong so we try different numbers

So i started pluging in numbers from under 22 so i got c is 10 and d is 12 lets try it with the equation

89.50=2.35(10)+5.50(12)

89.50=23.5+66

89.50=89.50 so it works the answer to how many number of dogs and cats is 12 dogs and 10 cats

Alyssa and Caleb ate 5/6 of the nachos together.

To calculate the fraction of nachos that Alyssa and Caleb ate together, add the fractions representing the portions that they each ate. However, because the fractions have different denominators, we must first find a common denominator.

2 and 3 share a common denominator of 6. With a denominator of 6, we can rewrite 1/2 and 1/3 as follows:

1/2 = 3/6

1/3 = 2/6

We can now add these fractions:

3/6 + 2/6 = 5/6

As a result, Alyssa and Caleb shared 5/6 of the nachos.

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If there are 14 people in a club organizing a spaghetti dinner, there can be 364 ways to select 3 people to be ticket takers.

A combination is a selection of things taken from a larger group, where the order in which things are selected is unimportant. A combination is distinct from a permutation, which is a method of organizing objects in which order matters. A combination is a method of selecting things in which order does not matter. In general, the combination formula can be used to determine the number of possible combinations that exist for a given set of things.

Suppose we have to select 3 people out of 14 people. The number of possible combinations can be found using the combination formula, which is given byC(n,r) = n!/(n-r)!r!where n is the total number of objects, and r is the number of objects selected.C(14,3) = 14!/(14-3)!3!C(14,3) = (14 × 13 × 12)/(3 × 2 × 1)C(14,3) = 364Therefore, there are 364 ways to select 3 people to be ticket takers from a group of 14 people.

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Answer:

0

Step-by-step explanation:

-2(-3)+27÷(-3)+3

6-9+3

0

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:

a)30

b)25

Step-by-step explanation:

ratio of red socks and total sock is 1:6 so, lets show this as,

1k and 6k.

1k-------5

6k------x

x=30

a)total socks = 30

b)black socks =total-red socks=30-5=25

Answer: The longest side is on the opposite of the largest angle and the shortest side is on the opposite of the shortest angle.

Step-by-step explanation:

Answer:

376 inches

Step-by-step explanation:

Answer:

Here is a Venn diagram that represents the given:


     F       B

      \     /

       \   /

        \ /

        / \

       /   \

      /     \

     G       B

In this diagram, F represents the set of students who study French, G represents the set of students who study German, and B represents the set of students who study both French and German.

The information given tells us that 13 students study French, 5 study only German, and 6 study both French and German. Therefore, we can place 13 in the region for F, 5 in the region for G, and 6 in the overlapping region for B. The total number of students is 18, so we can calculate the number of students who study only French as 13 - 6 = 7, and the number of students who study only German as 5 - 6 = -1 (which doesn't make sense in this context, so we can ignore it).

Answer:

To create a line plot for this data, we can first convert all the fractions to a common denominator, such as eighths:

Monday: 6/8 of an hour

Wednesday: 4/8 of an hour

Friday: 2/8 of an hour

Sunday: 4/8 of an hour

Then, we can draw a number line with tick marks representing each day of the week and plot a dot for each amount of time spent working out:

0         1         2         3         4

|---------|---------|---------|---------|   <- Number line

         .     .

       .             .

   .                     .

.                             .

To find out how much time June should work out each day to spend an even amount of time working out, we can first find the total amount of time she spent working out:

6/8 + 4/8 + 2/8 + 4/8 = 16/8 = 2 hours

Since there are four days she worked out, to find out how much time she should work out each day, we can divide the total time by four:

2 hours ÷ 4 = 0.5 hours

Therefore, June should work out for 0.5 hours, or 30 minutes, each day to spend an even amount of time working out.

it will take Bob approximately 47.3 years to save $200,000 for his retirement.

How to find?

To determine the time it will take Bob to reach his retirement goal of $200,000, we can use the formula for compound interest:

A = P(1 + r/n)²(nt)

where:

A = the final amount

P = the initial principal (deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = $400 (monthly deposit)

r = 1.8% (annual interest rate, compounded monthly)

n = 12 (compounded monthly)

A = $200,000

We can solve for t by substituting the given values and solving for t:

200,000 = 400(1 + 0.018/12)²(12t)

500 = (1 + 0.0015)²(12t)

log(500) = 12t log(1.0015)

t = log(500) / (12 log(1.0015))

t ≈ 47.3

Therefore, it will take Bob approximately 47.3 years to save $200,000 for his retirement.

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Answer:

[tex] - 50 + 8i[/tex]

Step-by-step explanation:

[tex]1. \: - 35 - 15i + 21i - 9 - (6 - 2i) \\ 2. \: - 35 - 15i + 21i - 9 - 6 + 2i \\ 3. \: ( - 35 - 9 - 6) + ( - 15i + 21i + 2i) \\ 4. \: - 50 + 8i[/tex]

The garden would require 84 plants, which is the same number of plants as the garden's surface area.

The area of the garden can be determined using the formulas below if it is shaped like a right triangle and has sides that are 7 and 24 yards long.

Area of the garden = (1/2) x Base x Height

Area of the garden = (1/2) x 7 x 24

Area of the garden = 84 square yards

Since there is one square yard of area for each plant, the number of plants needed for the garden would be equal to the area of the garden, which is 84 plants.

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When researching a population where it is impossible or impractical to compile a list of the elements, the sampling technique that is appropriate to use is known as the cluster sampling technique

Cluster sampling is a type of probability sampling that is frequently used when the population is too large to be measured as a whole. The population is divided into smaller, more manageable clusters that are less difficult to study than the entire population.Therefore, cluster sampling is an excellent alternative when the target population cannot be measured because it is too large, too vast, or too hard to reach. In this technique, clusters are chosen by a random process or some other procedure.The final sampling method is achieved by selecting samples from within the clusters, which are frequently chosen using simple random sampling or some other appropriate method. When it comes to cluster sampling, it's important to remember that the clusters chosen must be heterogeneous internally but homogeneous externally.

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The expression for the total amount of shoes for both people is 4X + 2.

As a result, total cost is the sum of fixed and variable costs, or TC = FC + VC = Kr+Lw.

Say Person 1 owns X pairs of shoes. So, Person 2 has two to three times as much as Person 1. This can be said as follows:

Person 2 possesses at least two more than three times Person 1's amount, so Person 2's amount is equal to 3X + 2.

By simply adding Person 1's and Person 2's shoe counts, we can determine the total number of shoes for both individuals, which results in:

Total equals the sum of the amounts given by Persons 1 and 2.

When we replace the value of Person 2's contribution, we obtain:

Amount total = X + (3X + 2)

If we simplify, we get:

Total = 4X plus 2

Hence, 4X + 2 is the total number of shoes for both individuals.

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Answer:

perimeter = 10 mm

Step-by-step explanation:

the perimeter is the sum of the 3 sides.

given perimeter = 24 , that is

w + 6 + 8 = 24

w + 14 = 24 ( subtract 14 from both sides )

w = 10 mm

The probability that Mark selects a car key or door key from the key ring is 0.3 or 30%.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory provides a framework for understanding random events and the laws of chance, and it is an important tool for modeling and simulating complex systems.

Calculating the probability that he selects a car key or door key :

In this context, we are asked to find the probability of Mark selecting a car key or door key from the key ring. To calculate this probability, we need to first determine the total number of keys on the key ring and then count the number of car keys and door keys.

Total number of keys = 10

Number of car keys = 2

Number of door keys = 1

The probability of selecting a car key or door key can be found by adding the probability of selecting a car key to the probability of selecting a door key. Since there is only one door key and two car keys, the probability of selecting a car key is higher, and we can simplify the calculation by finding the probability of selecting a car key and then adding the probability of selecting a door key that hasn't already been selected.

Probability of selecting a car key = 2/10 = 0.2

Probability of selecting a door key = 1/9 (since one key has already been selected) = 0.1111...

Therefore, the probability of Mark selecting a car key or door key from the key ring is 0.2 + 0.1111... ≈ 0.3 or 30%.

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The volume of the triangular prism is 24 cm³.

A triangular prism is a three-dimensional geometric shape that has two parallel, congruent triangular bases and three rectangular faces connecting the bases. The rectangular faces are perpendicular to the bases and to each other. The height of the prism is the perpendicular distance between the two parallel bases

the Pythagorean theorem to find the length of the third side:

a² + b² = c²

where a and b are the lengths of the two equal sides, and c is the length of the third side (the base of the triangle).

Since we know that the base has a length of 75 cm and the area is 30 cm², we can solve for one of the equal sides using the formula for the area of a triangle:

Area = (base × height) / 2

30 cm² = (75 cm×height) / 2

height = 0.8 cm

Now we can use the formula for the volume of a triangular prism:

Volume = Base Area× Height

Volume = 30 cm² ×0.8 cm

Volume = 24 cubic centimeters (cm³)

Therefore, the volume of the triangular prism is 24 cm³.

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Answer:

1. x = -4

y = 3

2.

[tex]x = 3 \frac{7}{13} [/tex]

[tex]y = \frac{9}{13} [/tex]

3. x = 3

y = -4

Step-by-step explanation:

I added a photo of my solution

The probability that a randomly selected loan application takes longer than 11 days to process is 0.1587.

The time taken to process a loan application is uniformly distributed between 5 and 17 days.

We need to determine the probability that a random loan application takes longer than 11 days to process.

To compute the probability, we'll first determine the distribution's parameters;

we have:  a = 5 (minimum value)b = 17 (maximum value)

Mean: μ = (a+b) / 2 = (5+17) / 2 = 11

Variance: σ2 = (b-a)2/12

                     = (17-5)2/12

                     = 12.3333Standard deviation:  

                 σ = 3.516

For the problem, we want to find the probability of a loan application taking more than 11 days to be processed.

In other words, we want to find the probability of the application taking more than one standard deviation from the mean, that is, P(X > μ + σ).

Since the distribution is symmetric, we can also find the probability by calculating P(X < μ - σ) and subtracting the result from 1, since the total probability must be 1.

Using the above formula, we have:

P(X > μ + σ) = P(X > 11 + 3.516)

                  = P(X > 14.516)

To standardize the value of 14.516, we'll convert it to a z-score, which is z = (X - μ) / σ.

Therefore, we have z = (14.516 - 11) / 3.516 = 1

Since we are dealing with a standard normal distribution, we can use the standard normal distribution table to find the probability associated with z = 1.

From the table, we find that the probability of z being less than 1 is 0.8413;

thus, the probability of z being greater than 1 is 1 - 0.8413 = 0.1587.

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Answer:

the measure of ∠D is 8°.

Step-by-step explanation:

Since ∠C and ∠D are vertical angles, they have equal measure. So we can set their measures equal to each other and solve for x:

x + 16° = 4x - 5°

6x = 21°

x = 3.5°

Now we can find the measure of ∠D:

∠D = 4x - 5°

∠D = 4(3.5°) - 5°

∠D = 8°

Therefore, the measure of ∠D is 8°.

The answer to subtracting the two polynomials is 2x2 - 10x - 7.  The process of subtracting polynomials is like that of subtracting any other type of numerical expression.

Polynomials are mathematical expressions consisting of variables, coefficients, and exponents. They are used to represent a variety of functions, such as polynomial equations, rational equations, and trigonometric functions.

In this case, our like terms are 2x2 and 4x2, and -6x and -4x, and -4 and +3. We begin by subtracting the coefficients of the like terms. We subtract the coefficient of the term with the highest power first. In this case, that is 2x2 and 4x2, we subtract 2 from 4 to get 2. Next, we subtract the coefficients of the terms with the second highest power. This is -6x and -4x, so we subtract -6 from -4 to get -2. Thus, our answer now reads 2x2 -2x.

Finally, we subtract the coefficients of the terms with the lowest power. This is -4 and +3, so we subtract -4 from 3 to get -7. Thus, our answer now reads 2x2 -2x -7.

This answer can then be placed in the proper position on the grid.

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The value of p from the given equation is 4.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign [tex]=\\[/tex].

The given equation is [tex]0.5p-3.45=-1.2[/tex]

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The equation can be solved as follows

[tex]0.5p-3.45=-1.2[/tex]

[tex]0.5p= -1.2+3.45[/tex]

[tex]0.5p= 2.25[/tex]

[tex]p= 2.25\div0.5[/tex]

[tex]p= 4.5[/tex]

Therefore, the value of p is 4.5.

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According to a histogram that displays the percentage of replies over time, an April Gallup poll indicated that 55% of Americans think autonomous cars would be widely used in the next ten years.

Whether completely automated "driverless automobiles" would be widely deployed in the United States was the subject of a Gallup Poll conducted in April, which polled Americans ages 18 and older.

How soon, in your opinion, do you believe autonomous cars will be widely used in the US? According to the survey, 55% of Americans think autonomous cars will become commonplace over the next ten years.

The survey's results were displayed as a histogram, displaying the proportion of replies at various time intervals. This indicates how many respondents indicated that driverless cars will be widely utilised within a particular time period (e.g., within 5 years, within 10 years, etc.).

This survey reveals how people feel about autonomous cars in the future and how soon they believe they will be a common sight on the roads.

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The question is -

A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.

If the amount of jen's monthly phone bill is normally distributed with a mean of $86 and standard deviation of $9, Between the values of $77 and $95 inclusive, 68.26% of Jen's phone bills are expected to fall.

To find the values between which 68.26% of Jen's phone bills lie, we need to use the properties of the normal distribution and the empirical rule.

The empirical rule states that for a normal distribution, approximately 68% of the data lie within one standard deviation of the mean. Therefore, we can find the values between which 68.26% of Jen's phone bills lie by calculating the range of values that are one standard deviation away from the mean.

Using the given population mean of $86 and population standard deviation of $9, we can calculate one standard deviation as follows:

One standard deviation = population standard deviation = $9

To find the lower and upper bounds for 68.26% of Jen's phone bills, we can subtract and add one standard deviation from the mean, respectively:

Lower bound = population mean - one standard deviation = $86 - $9 = $77

Upper bound = population mean + one standard deviation = $86 + $9 = $95

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Answer:

(10, - 1 )

Step-by-step explanation:

x - y = 11 → (1)

2x + y = 19 → (2)

adding (1) and (2) term by term will eliminate y

(x + 2x) + (- y + y) = 11 + 19

3x + 0 = 30

3x = 30 ( divide both sides by 3 )

x = 10

substitute x = 10 into either of the 2 equations and solve for y

substituting into (2)

2(10) + y = 19

20 + y = 19 ( subtract 20 from both sides )

y = - 1

solution is (10, - 1 )

The value of x and y for the given set of values in triangle are 8√3 units and 12 units.

A triangle is a polygon with three sides and three angles. It is the simplest polygon that can exist in Euclidean geometry. The sum of the three interior angles of a triangle is always 180 degrees. Triangles can be classified according to the length of their sides and the measure of their angles. The most common classifications are:

Scalene triangle: A triangle with all three sides of different lengths.

Isosceles triangle: A triangle with two sides of equal length.

Equilateral triangle: A triangle with all three sides of equal length.

Acute triangle: A triangle in which all angles are less than 90 degrees.

Obtuse triangle: A triangle in which one angle is greater than 90 degrees.

Right triangle: A triangle in which one angle is exactly 90 degrees.

Here,

Using the given information:

side1 = 8√3

angle1 = 60°

We can use trigonometric ratios to find the values of x and y:

sin(60°) = y / side1

Simplifying:

y = side1 * sin(60°)

y = 8√3 * sin(60°)

y = 8√3 * (√3 / 2)

y = 12

Therefore, x = 8√3 and y = 12.

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Answer:

13.5 would be the answer

Answer: We can use a proportion to solve the problem:

17 gallons / 355 miles = x gallons / 284 miles

Cross-multiplying, we get:

17 * 284 = 355 * x

4844 = 355x

x = 13.66 (rounded to two decimal places)

Therefore, Mai would need approximately 13.66 gallons of gas to drive 284 miles at the same rate.

Step-by-step explanation: