Find a formula for the tenth term in this arithmetic sequence: a1=28 a2=21 a3=14 a4=7

The terms of the sequence are t1 = 8, t10 = 39.5 and t23 = 85

From the question, we have the following function definition that can be used in our computation:

tn=3.5n+4.5

Using the above as a guide, we have the following equations:

t(1) = 3.5(1) + 4.5 = 8

t(10) = 3.5(10) + 4.5 = 39.5

For 85,, we have

3.5n+4.5 = 85

This gives

3.5n = 80.5

Dvide by 3.5

n = 23

Hence, 85 is the 23rd term of the sequence

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Answer: 1/3

Step-by-step explanation: The only option would be two and that has a 1/3 chance of occuring.

155 degrees

Straight line equals 180 degrees.

180 - 25 = 155 degrees

Answer:

155 degrees

Step-by-step explanation:

A straight angle is 180 degrees. The equation to solve this would be 25+x=180; to solve this, subtract 180-25=x; x=155

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The experimental probability of getting an odd number on the next toss is 51.3%.

Probability is a measure of the likelihood of an event occurring. In the case of the six-sided number cube, the theoretical probability of getting an odd number on any one roll is 3 out of 6, or 1/2, or 50%. However, this is a theoretical value and may not match the actual results obtained from a set of experiments.

The experimental probability of an event is calculated by observing the actual results of a series of trials and comparing it to the number of possible outcomes. In this case, the number cube was tossed 150 times and the results were recorded in the table. The frequency of the odd numbers (1, 3, and 5) was found to be 77.

The experimental probability of getting an odd number on the next toss can be calculated by dividing the frequency of the odd numbers by the total number of tosses, which is 150. 77/150 = 0.513 or 51.3%.

Therefore, the experimental probability of getting an odd number on the next toss of the six-sided number cube is 51.3%.

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254 degrees is the coterminal to 614°

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

To find coterminal angles when given a positive angle, subtract 360 degrees to the given angle until you get an angle between 0 and 360.

614-360=254

254 lies between 0 and 360 degrees.

Hence, 254 degrees is the coterminal to 614°

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The triangle ABC is equal to triangle ADE by Angle-Angle-Side theorem.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In triangle ABC and ADE -

It can be seen that ∠B = ∠E.

Also the line segment AB is equal to line segment AE.

AB = AE

The angles ∠BAC and ∠DAE are vertically opposite to each other.

So, they are also equal.

∠BAC = ∠DAE

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, Δ ABC ≅ Δ ADE according to AAS theorem.

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Answer:

shown below

Explanation:

you can take the y-intercept and plot that right away. The y intercept for this equation is 1, so you plot a point at (0,1). Then you can use the slope to find your next point. You can put the slope, 6, into a fraction form, making it  “6/1” then you use rise/run and go up 6, over 1, and plot your next dot at (7,1). You then take a straight edge and graph the line that intercepts both points. It looks like the picture below.

The value of the expression 2/3 x -4/5 is -8/15.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:
An expression,

2/3 x -4/5.

Here, we have to multiply the fraction.

So,

2/3 x -4/5,

= -8/15

Therefore, -8/15 is the value.

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Expression is; 29 - x = 16 an expression to represent this situation.

Where in mathematics is an expression?

An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

                               Term is a mathematical concept that refers to a constant, a single variable, or a mixture of variables and constants along with multiplication or division. Example of an algebraic expression: 3x + 9; 5x + 10

We are told that at lunchtime, it was 29 degrees Celsius and that by sunset, the temperature had dropped to 16 degrees Celsius.

Let the drop be x.

Thus;

29 - x = 16

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The complete question is -

On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

1). The two adjacent angles are ∠1 and ∠2.

2). The two vertically opposite angles are ∠1 = ∠3.

3). The value of x will be 10.

Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and corresponding angles.

1.) The two adjacent angles will be:-

∠1 and ∠2

The two angles are just next to each other which is why they are adjacent angles.

2). The two vertically opposite angles are ∠1 = ∠3. They are opposite to each other so their values will also be the same.

3). The value of x will be calculated as:-

9x = 90

x = 90 / 9

x = 10

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The original price of the pair of jeans is equals to the $120.

We Jodi wants to buy a pair of jeans.

The purchase price of pair of jeans = $90

Discount on price of jeans = 75%

Let the original price of pair of jeans be equal to "$x". Percent is an important concept of mathematics. It is a number or ratio of fraction of hundred. It is denoted by symbol %. The formula is

% = ( part /whole )×100

Here, it is said that the price of pair of jeans, $90, is only 75% of the original price. So, we can write it as the following way 75% of x = 90

=> (75/100) of x = 90

=> (75/100) × x = 90

=> x = 90× 100/75

=> x = 9000/75

=> x = 120

Hence, required value of x is 120.

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For the significance test given, the error will be a type one error.

The results of tests for statistical significance show whether apparent variations in assessment results are the product of random variation or sampling mistake. The given parts can be answered as -

a) The analysis of the given question was conducted with a likelihood of .05 for a type one error. This is because the level of significance for it is .05 as well. Therefore, such a situation implies that regardless of whether the null hypothesis is correct and accurate there is still a five percent chance that it will be incorrect or will be rejected.

b) The probability that a representative sample will be equally extreme or more intense than the one that was correctly predicted is known as the p-value when the null hypothesis is true. In this case, the p-value is only .03 and drops below the .05 criterion of significance. This reveals that the generic parameter-supported null thesis is categorically rejected. This study would thus, further result in the rejection of the null hypothesis.

c) A decision error from the test could be either a Type I error or a Type II error. While a Type II error happens when the null hypothesis is true but not rejected, a Type I error happens when the opposite is true. Since the null hypothesis was true but was rejected by chance in this situation, any judgement error that the test produced would be of the Type I variety.

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Answer:

[tex]\displaystyle \sqrt{3}\biggr[\cos\biggr(\frac{11\pi}{9}\biggr)+i\sin\biggr(\frac{11\pi}{9}\biggr)\biggr][/tex]

Step-by-step explanation:

Use the nth-root formula for complex numbers in polar form

[tex]\displaystyle \sqrt[n]{r}\biggr[\text{cis}\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr]\\ \\\\\sqrt[2]{3}\biggr[\text{cis}\biggr(\frac{\frac{4\pi}{9}+2\pi(1)}{2}\biggr)\biggr]\\ \\\\\sqrt{3}\biggr[\text{cis}\biggr(\frac{2\pi}{9}+\pi\biggr)\biggr]\\\\\\\sqrt{3}\biggr[\text{cis}\biggr(\frac{11\pi}{9}\biggr)\biggr][/tex]

[tex]\displaystyle \sqrt{3}\biggr[\cos\biggr(\frac{11\pi}{9}\biggr)+i\sin\biggr(\frac{11\pi}{9}\biggr)\biggr][/tex]

Note that this is one of the square roots of the complex number with k = n-1 = 2-1 = 1, but is the only applicable answer to this problem.

Answer:

9.4 ounces of oat meal

Step-by-step explanation:

37.6 x 10 = 376

4 x 10 = 40

we do this to get rid of the decimal

376/40=188/20=94/10=47/5=9(2/5)=9.4 ounces of oat meal

Answer:

18x + 346

Step-by-step explanation:

8(x+12) + 10(x+25)

8x + 96 + 10x + 250

18x + 346

Answer: 132 degrees

Step-by-step explanation: 180 degrees ( the degree of a straight line) - 48 equals 132

Answer:

C. 5 hours

Step-by-step explanation:

We know

One delivery driver can complete a route in 6h

The rate is 1/6

One delivery driver can complete a route in 5h

The rate is 1/5

To solve this, we use the equation

rate + rate = together rate

1/6 + 1/5 = 1/y

10/60 + 12/60 = 1/y

22/60 = 1/y

y =  5 hours

So, the answer is C. 5 hours

Yes, it is possible to relate a given quantity to an indicated amount using more than one symbol because variables are often used to represent unknown quantities and different symbols can be used.

If you want to find the volume of a cylinder, you can use the formula V = πr^2h, where V represents the volume, r represents the radius, h represents the height, and π represents pi. Using different symbols to represent the same quantity can be helpful in different situations and can make the mathematics clearer and more concise.

For example, instead of using the symbol V to represent the volume of a cylinder, you could use the symbol V₁. This can make it clear that the volume being calculated is the volume of a cylinder, and not the volume of some other shape.

In conclusion, using different symbols to represent the same quantity can help to make the mathematics clearer, more concise, and more specific to the problem being solved.

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It is important to use a device like a random number table in a simulation because Option A Chance plays a part in the process being simulated.

In simulations, a random number table is used to incorporate the element of chance into the process being modeled. The reason this is important is that many real-world processes involve uncertainty and randomness, and to accurately simulate these processes, it is necessary to include these elements.

For example, in simulating the stock market, stock prices can be modeled as random variables, because they are influenced by a variety of unpredictable factors such as changes in interest rates, company earnings, geopolitical events, and investor sentiment. To simulate this process, a random number table can be used to generate random numbers that represent these unpredictable factors.

By using a random number table, the simulation can model the uncertainty and randomness inherent in the real-world process, which makes the simulation more accurate and realistic. This is why it is important to use a device like a random number table in a simulation when chance plays a part in the process being simulated.

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The given exponential function represents decay since the base (0.13) is less than 1. And the percentage decrease of 91.68%.

The percentage rate of the decrease can be determined by taking the base and subtracting it from 1 and then multiplying the result by 100. Mathematically, this can be expressed as (1 - 0.13)*100 = 87%. To illustrate this mathematically, let's assume that the initial value of y is 100. We can then calculate the value of y after one time period (t) as follows: y = 64(0.13)t.

Plugging in t = 1, we get y = 64(0.13) = 8.32. This means that the value of y has decreased by (100 - 8.32) = 91.68, or a decrease of 91.68%. Dividing this by the initial value of 100 gives us a percentage decrease of 91.68%/100 = 0.9168 or 91.68%.

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Two details are that support the response:

The oak is revered as a cosmic repository of knowledge represented by its imposing might. It develops at its own pace, gradually yet steadily. Due of its size and longevity, oak is frequently connected with dignity, nobility, and knowledge as well. Since the very beginnings of human interaction with oaks, a highly potent symbolic picture of oaks has emerged, in which these trees have come to be connected with immortality, power, consistency, perseverance, fertility, justice, and honesty.

Two responses are:

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Answer:

6902.97m³

Step-by-step explanation:

volume of a sphere =4/3πr³

=4/3×3.142×13×13×13=9203.965m³

1/4×9203.965=2300.99125m³

9203.965-2300.99125=6902.974

=6902.97m³

Answer:

£ 162

Step-by-step explanation:

Ratio:

    Ratio of money = 2 : 3

Edward receives two parts of the money and Thomas receives three parts of the money.

Edward's share = 2x

Thomas share = 3x

Thomas receives £243 which is three parts. Find 'x'.

           Thomas share = £ 243

                              3x  = 243

         Divide both sides by 3,

                                 x = 243 ÷ 3

                                 x = 81

Now, find Edward's share.

Edward's share = 2x

                          = 2*81

                         = £ 162

Answer:

£ 162

Step-by-step explanation:

Ratio:

   Ratio of money = 2 : 3

Edward receives two parts of the money and Thomas receives three parts of the money.

Edward's share = 2x

Thomas share = 3x

Thomas receives £243 which is three parts. Find 'x'.

          Thomas share = £ 243

                             3x  = 243

        Divide both sides by 3,

                                x = 243 ÷ 3

                                x = 81

Now, find Edward's share.

Edward's share = 2x

                         = 2*81

                        = £ 162

Answer: no

Step-by-step explanation:

jose added the same variable, (n) to the left side that he subtracted from the right side. so the eqation is not correct

Answer: 23

Step-by-step explanation:

This is another parallel line theorem that is important. Over here, we will need to use the concept of corresponding angles (refer to images below). In corresponding angles, they are equal. So we know the corresponding angle to [tex]x + 1[/tex] will be equal to [tex]x + 1[/tex] since corresponding angles are equal.

Now we have to use the fact that angles on a line add up to 180°. Keeping this in mind, we can now solve it like this:

[tex](x + 1) + (7x-5) = 180\\x + 1 + 7x - 5 = 180\\8x - 4 = 180\\8x = 184\\x = 23\\\\[/tex]

Once again, if there is anything you don't understand, please reply back :)

Answer:

Step-by-step explanation:

7+m>5

Answer:

m = -2

Step-by-step explanation:

yes.

Answer: (-8,104)

you have to find the component form of the resultant vector.