If the nth term of a sequence is n squared - 3. Find the first 3 terms and the tenth term

To match a given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form is y = (3/4)x - 5.

The formula y = mx + b,

where "m" stands for the slope and "b" for the y-intercept, is used to match a given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form.
1. If m = 2 and b = 3, the slope-intercept form of the equation would be y = 2x + 3

2. With m = -1/2 and b = 4, the slope-intercept form of the equation would be: y = (-1/2)x + 4.

3. If m = 0 and b = 2, then the slope-intercept form of the equation is: y = 0x + 2 (or just y = 2).

4. With m = 3/4 and b = -5, the slope-intercept form of the equation is: y = (3/4)x - 5.
Therefore, The equation of the line in slope-intercept form is y = (3/4)x - 5, which may be used to match a given slope (m) and y-intercept (b) with it.

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The area of the figure is 225 ft²

From the figure shown, we have that it is made up of a triangle and a rectangle.

Now, the formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Such that;

Substitute the values

Area = 1/2 × 10 × 15

Multiply the values

Area = 75 ft²

Area of the rectangle is;

Area = length × width

Area = 10(15)

Area = 150 ft²

Total area = 225 ft²

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Answer:

The answer is y>-x+3

Step-by-step explanation:

slope=rise/run

(0,3),(3,0)

m=y2-y1/x2-x1

m=0-3/3-0

m=-3/3

m= -1

y=mx+b

y= -x+b

3=-(0)+b

b=3

y>-x+3

Answer:

  3) an = 8 +13(n -1); a20 = 255

  4) an = 6 -4(n -1); a20 = -70

Step-by-step explanation:

You want the rule and the 20th term for the arithmetic sequences ...

  3)  8, 21, 34, ...

  4)  6, 2, -2, ...

The n-th term of an arithmetic sequence is given in terms of the first term (a1) and the common difference (d) as ...

  an = a1 +d(n -1)

The first term is 8. The common difference is 21 -8 = 13. The rule is ...

  an = 8 +13(n -1)

The 20th term is ...

  a20 = 8 +13(20 -1) = 255

The first term is 6. The common difference is 2 -6 = -4. The rule is ...

  an = 6 -4(n -1)

The 20th term is ...

  a20 = 6 -4(20 -1) = -70

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Answer:

3. 255

4. -70

Step-by-step explanation:

3.

For the arithmetic sequence 8, 21, 34, 47, 60, ...

The common difference between consecutive terms is d =(21-8)= 13. Therefore, the nth term of the sequence can be expressed as:

[tex]\bold{a_n = a_1 + (n - 1) * d}[/tex]

where [tex]\bold{a_1}[/tex] is the first term of the sequence,

n is the term number, and d is the common difference.

Substituting [tex]a_1 = 8[/tex] and d = 13, we get:

[tex]a_n = 8 + (n - 1) * 13\\a_n = 13n - 5[/tex]

To find [tex]a_{20}[/tex], substitute n = 20 in the above formula:

[tex]a_{20} = 13(20) - 5\\a_{20}= 255[/tex]

4.

For the arithmetic sequence 6, 2, -2, -6, -10, ...

The common difference between consecutive terms is d =(2-6)= -4. Therefore, the nth term of the sequence can be expressed as:

[tex]\bold{a_n = a_1 + (n - 1) * d}[/tex]

where [tex]a_1[/tex] is the first term of the sequence,

n is the term number, and

d is a common difference.

Substituting [tex]a_1[/tex]= 6 and d = -4, we get:

[tex]a_n = 6 + (n - 1) * (-4)\\a_n = 10 - 4n[/tex]

To find [tex]a_{20}[/tex], substitute n = 20 in the above formula:

[tex]a_{20} = 10 - 4(20)\\a_{20}= -70[/tex]

Answer:

To find the new balance, we'll start with the initial balance on May 20 and then perform the transactions in chronological order.

Step-by-step explanation:

Initial balance on May 20: $189.75

Deposit on May 22: +$112.45

To calculate the balance after the deposit, we add the deposit amount to the initial balance:

New balance after deposit = $189.75 + $112.45 = $302.20

Check written on May 29: -$75.68

To calculate the balance after writing the check, we subtract the check amount from the previous balance:

New balance after check = $302.20 - $75.68 = $226.52

ATM withdrawal on June 1: -$50.00

To calculate the final balance after the ATM withdrawal, we subtract the withdrawal amount from the previous balance:

Final balance after ATM withdrawal = $226.52 - $50.00 = $176.52

Therefore, the new balance after all the transactions is $176.52.

The correct option is the first one, we need to round down to the nearest whole so we will get:

f(1.4) = 1

Here we have the step function:

f(/x) = [x]

This function rounds down to the nearest whole any input we give (like you can see on the graph).

Then we have:

f(0) = 0

f(0.5) = 0

f(0.7) = 0

f(1.2) = 1

f(1.3) = 1

f(5.2) = 5

And so on.

With that in mind, if we evaluate in 1.4, then we round down to the nearest whole which is 1, then:

f(1.4) = 1

The correct option is the first one.

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x=1/3

33x-1=10

add 1 on both sides

33x=11

divide 33 on both sides

and it should equal 1/3

Answer:

it's is D

This is because equation 1 to 3 results in only a constant but D x will be 1

Answer: 4x - 10 = -2(-2x + 5)

Step-by-step explanation:

An equation has an infinitely many solutions when both sides are equal to each other.

-2(-2x+5) expands to become (-2*-2)*x + 5*(-2) = 4x - 10

Since the other side of the equation is also 4x - 10, both sides of the equation are identical and thus the equation has infinitely many solutions.

For finding a 95% confidence interval:

a) The sample mean is x = 16.13.

The sample standard deviation is s = 6.948.

The degrees of freedom are df = 10.

The critical value of t for a 95% confidence interval is t = 2.228.

The margin of error is ME = t × s/√n = 2.228(6.948)/√11 = 4.263.

The 95% confidence interval is x ± ME = 16.13 ± 4.263 = (11.867, 20.393).

b) The 95% confidence interval is (11.867, 20.393).

This means that we are 95% confident that the true population mean number of visits per physical therapy patient is between 11.867 and 20.393 visits.

c) This is because the confidence interval is a range of values that is likely to contain the true population mean. If many samples of the same size are taken from the same population, then about 95% of the confidence intervals from these samples will contain the true population mean.

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Answer:

8 months

Step-by-step explanation:

[tex]4000=400(\frac{(1+.045)^{n}-1 }{.045})[/tex]

Do what's in parentheses.

[tex]4000=400(\frac{(1.045^{n}-1) }{.045})[/tex]

Multiply 400 by the numerator.

[tex]4000=(\frac{400(1.045^{n})-400 }{.045})[/tex]

Divide both sides by .045.

[tex]180=400(1.045)^{n}-400[/tex]

Add 400 to both sides.

[tex]580=400(1.045)^{n}[/tex]

Divide both sides by 400.

[tex]\frac{29}{20} =1.045^{n}[/tex]

Convert to logarithmic equation.

[tex]log_{1.045}\frac{29}{20}=n[/tex]

8.441=8 months

Hope this helps!!

The positions will be filled in 56,280 ways

There are 11 qualified candidates applying for 7 positions. The order of the positions does not matter. after choosing a position the number of persons drop so we solve as follows

For the position of president

11 combination 1 = 11

For the position of secretary

10 combination 1 = 10

For the position of treasurer

10 combination 1 = 10

For the position of three directors

8 combination 3 = 56 ways

the total number of ways to fill these positions is

11 x 10 x 9 x 56 = 56,280.

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The product of sin B and tan C is c/a.

The product of sin C and tan B is b/a.

Given is a right triangle, ABC, we need to find the product of sin B and tan C and the product of sin C and tan B,

So, we know,

Sine = Opposite ÷ Hypotenuse.

Cosine = Adjacent ÷ Hypotenuse.

Tangent = Opposite ÷ Adjacent.

Therefore,

Sin B = b/a

Tan C = c/b

Sin B x Tan C = b/a x c/b = c/a

And,

Sin C = c/a

Tan B = b/c

Sin C x Tan B = c/a x b/c = b/a

Hence the products are c/a and b/a.

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The complete is attached.

Any situation where there is a relationship between two variables that can be modeled by a linear equation can benefit from the use of a line of fit to make predictions.

There are many other real-world situations where an equation of a line of fit can be useful in making predictions. For instance, a business owner could use data on sales and time to forecast future sales and plan inventory accordingly. A scientist could use data on temperature and precipitation to predict crop yields and plan agricultural strategies. An economist could use data on interest rates and inflation to forecast future economic trends and plan investment strategies. In general, any situation where there is a relationship between two variables that can be modeled by a linear equation can benefit from the use of a line of fit to make predictions.

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Answer:

  A. If you moved the students from the top 25% in Class 1 into Class 2, the Class 2 median would increase.

Step-by-step explanation:

You want to know the effect of changing or combining class data, given the box plots show two classes with the same median.

We can consider the choices:

The medians of the two classes are the same. The maximum value of Class 1 is in the third quartile of Class 2, so the top 25% of Class 1 would be added to the data values currently in the 3rd quartile of Class 2.

In general, one might expect that adding data values above the median will raise the median. Whether this is actually true depends on the details of the distribution and the number of data points added.

It is probably true that the Class 2 median would increase.

The students who did no homework in Class 1 are the reason for the whisker extending to 0. Removing those from the data set will increase the minimum, likely increasing the value of Q1. This will cause the IQR to be reduced, not increased.

The range of the combined data sets will be the difference of the largest maximum (70) and the smallest minimum (0). The combined range will be 70, not 105.

Combining two data sets with the same median will result in a set of data with the same median. The median will not change, as half the combined data will be above it, and half the combined data will be below it.

Choice A is the only one that makes sense.

<95141404393>

Answer:

The large prism is 5 inches taller than the small prism

Step-by-step explanation:

We know that the formula for volume of a rectangular prism is

V = lwh, where

Step 1:  We're given the volume, length, and width for both rectangular prisms, but not the height.  We can find the height of each rectangular prism by rewriting the volume formula in terms of h (i.e., isolate h), which gives us:

V / (lw) = h

Step 2:  To find the height of the small prism, we plug in 100 for V, 5 for l, and 4 for w in the volume formula (in terms of h) and simplify:

100 / (5 * 4) = h

100 / 20 = h

5 inches = height

Optional Confirmation of Step 2:

We can check that our height is correct by plugging in 5 for h in the regular volume formula, with 100 for V, 5 for l, and 4 for w;

100 = 5 * 4 * 5

100 = 20 * 5

100 = 100

Step 3:  To find the height of the large prism, we plug in 200 for V, 5 for l, and 4 for w in the volume formula (in terms of h) and simplify:

200 / (5 * 4) = h

200 / 20 = h

10 inches = height

Optional Confirmation of Step 3:

We can check that our height is correct by plugging in 5 for h in the regular volume formula, with 200 for V, 5 for l, and 4 for w;

200 = 5 * 4 * 10

200 = 20 * 10

200 = 200

Step 5:  

10 - 5 = 5 inches taller

Answer:

17 and 8

Not sure what the underscore is for

Step-by-step explanation:

Answer:

17 and 8

Step-by-step explanation:

10+7 = 17 and 5+3 =8

On July 20, the company recorded a journal entry debiting cash for $4,140, crediting treasury stock for $3,780, and crediting paid-in capital from treasury stock for $360.

To record the reissuance of treasury stock on July 20, the following journal entry should be made:

Date: July 20

Debit: Cash ($46 * 90) $4,140

Credit: Treasury Stock ($42 * 90) $3,780

Credit: Paid-In Capital from Treasury Stock $360

Explanation:

The debit to Cash represents the amount received from the reissuance of 90 shares at $46 per share, totaling $4,140.

The credit to Treasury Stock reduces the balance of the treasury stock account by the cost of the 90 shares, which is $42 per share, totaling $3,780.

The credit to Paid-In Capital from Treasury Stock accounts for the difference between the cost of the treasury stock and the amount received from its reissuance, which is $46 - $42 = $4 per share, totaling $360.

This journal entry properly reflects the increase in cash from the reissuance of the shares, reduces the treasury stock account balance, and recognizes the gain in paid-in capital resulting from the reissuance at a higher price than the repurchase cost.

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The probability that either event will occur is given as follows:

P(A or B) = 0.82 = 82%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of events in this problem is given as follows:

23 + 18 + 9 = 50.

The events are given as follows:

Hence the number of desired outcomes is given as follows:

23 + 18 = 41.

And the probability is of:

p = 41/50 = 0.82 = 82%.

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Answer:

Set your calculator to degree mode.

[tex] {tan}^{ - 1} \frac{15}{36} = 22.62 \: degrees[/tex]

So angle I measures about 22.62°.

Answer:

perimeter = 28 units. area = 45 square units.

Step-by-step explanation:

perimeter = (6 - -3) + (7 -2) + (6 - -3) + (7 - 2)

                = 9 + 5 + 9 +5

                 = 28 units.

area = (6 - -3) X (7 -2)

        = (6 + 3) X 5

         = 9 X 5

         = 45 square units

Check the picture below.

A contradiction in the given clues and it is not possible to find a valid code with the given information.

The code to open the treasure chest can be determined using a few simple steps.
Firstly, we know that the last digit is half of 18, which is 9.

This means that the code ends with the number 9.
Next, we are given the information that the sum of the two middle digits is 10.

This tells us that the two middle digits must be 4 and 6, as they add up to 10.
Thirdly, we know that the third and fourth digits are the same.

Since we already know that the last digit is 9, this means that the third digit must also be 9.
Finally, we are told that the first digit is double the second digit.

Since we know that the second digit is 4, we can determine that the first digit must be 8.
Therefore, the code to open the treasure chest is 8469.

Mr Brainiac can now use this code to unlock the chest and discover the treasures inside.
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Answer: 20.4

Step-by-step explanation:

Answer:

The number line has a closed circle at -2 and a closed circle at -6.

Step-by-step explanation:

|x+4| = 2

x + 4 = 2  or  x + 4 = -2

x = -2  or  x = -6

The number line has a closed circle at -2 and a closed circle at -6.

The conclusion that can be gotten from the dot plot is that the median is 10

A dot plot, also known as a dot chart or dot graph, is a simple type of data visualization that displays individual data points on a number line. It is a way to visually represent the distribution and frequency of a dataset.

In a dot plot, each data point is represented by a dot or a marker placed above the corresponding value on the number line. If there are multiple data points with the same value, the dots are stacked vertically above that value.

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When a circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base, a pair of intersecting lines is formed.

How to know what is formed from a line intersecting a cone?

The right circular cone is intersected by a plane that passes through the cone's vertex and is perpendicular to its base.

This means the intersecting line forms a right angle with the base of the right circular cone.

Therefore, from this interaction is a pair of intersecting lines.

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a) The required down payment = $4,700

b) The amount of the auto loan is = $42,300

c)  The monthly payment is $864.97

Given data ,

Maria plans to purchase a new work truck. The dealer requires a 10% down payment on the $47,000 vehicle

Maria will finance the rest of the cost with a fixed-rate amortized auto loan at 8.5% annual interest with monthly payments over 5 years

(a)

The required down payment is 10% of $47,000, which is:

Down payment = 0.1 x $47,000 = $4,700

(b)

The amount of the auto loan is the total cost of the truck minus the down payment, which is:

Auto loan = $47,000 - $4,700 = $42,300

(c)

To find the monthly payment, we can use the formula for a fixed-rate amortized loan:

PMT = r(PV) / [1 - (1 + r)^(-n)]

where PMT is the monthly payment, r is the monthly interest rate (which is the annual interest rate divided by 12), PV is the present value of the loan (which is the auto loan amount), and n is the total number of payments (which is the number of years multiplied by 12).

Substituting the given values, we get:

r = 0.085 / 12 = 0.00708333 (monthly interest rate)

PV = $42,300

n = 5 x 12 = 60 (total number of payments)

PMT = 0.00708333($42,300) / [1 - (1 + 0.00708333)^(-60)] = $864.97

Hence , the monthly payment is $864.97

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Answer:

Step-by-step explanation:

yea the checks are not correct

Answer:

1,2

4,-1

5,-3

6,-5

Step-by-step explanation:

the question is unclear but if you put it in desmos this is what you get

Answer:

148 in²

Step-by-step explanation:

The box is made up of two triangles and three rectangles.  The formula for the rectangles is length times width.  The formula for the triangles is one-half base times height.

RECTANGLES: (lxw)

7x2=14

12.5x2=25

12.5x2=25

TRIANGLES: (1/2bh)

1/2x12x7=42

1/2x12x7=42

Add together to get the sum of the surface area:

14+25+25+42+42=148 inches squared

The equation of the line is y = 2x - 8.

The equation of a line in slope-intercept form (y = mx + b) is determined by the slope (m) and the y-intercept (b).

Given that the point (3, -2) lies on the line and the slope is 2, we can substitute these values into the slope-intercept form to find the y-intercept.

Using the point-slope formula:

y - y1 = m(x - x1)

Substituting (3, -2) and m = 2:

y - (-2) = 2(x - 3)

Simplifying:

y + 2 = 2x - 6

Rearranging to slope-intercept form:

y = 2x - 8

The equation of the line containing the point (3, -2) with a slope of 2 in slope-intercept form is y = 2x - 8.

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