5.2 Given that cos 20° = p Without using a calculator, write EACH of the following in terms p: 5.2.1 5.2.2 5.2.3 cos 200° sin(-70°) sin 10°​

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

#95141404393

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:

Set your calculator to degree mode.

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

So angle I measures about 22.62°.

Answer:

The average cost is 4400

Step-by-step explanation:

c=800+40x

where x=number of items

c=800+4x;when x=90

c=800+40(90)

c=800+3600

c=4400

Answer:

4400

Step-by-step explanation:

The proportion that shows the relationship is h/4 = 8/h

The values of a, h and b are a = 16√3, b = 16√6 and h = 4√2

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

The similar triangles

Using the right triangle/altitude similarity theorem, we have

h/4 = 8/h

Calculating the values of a, h and b

In (a), we have

h/4 = 8/h

This means that

h² = 32

So, we have

h = 4√2

For the value of (a), we have

a² = h² + 4²

So, we have

a² = 32 + 4²

a² = 48

Evaluate

a = 16√3

Next, we have

b² = 32 + 8²

b² = 96

So, we have

b = 16√6

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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.

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

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:

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!!

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:

-7

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find the value of t, we can use the formula for the slope of a line:

m = (y2 - y1) / (x2 - x1)

Given that the slope of the line is 0, we have:

0 = (-7 - t) / (5 - 3)

To solve for t, we can cross-multiply:

0 * (5 - 3) = -7 - t

0 = -7 - t

To isolate t, we can add 7 to both sides:

7 = -t

Dividing both sides by -1, we get:

t = -7

Therefore, the value of t is -7.

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.

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:

  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>

The description of the difference between the graph of g(x) and f(x), based on the equation relating the functions is the option C.

A function is a definition or rule that maps an input on to an output.

The possible function, obtained from a similar function on the internet can be presented as follows;

f(x) = 2ˣ

g(x) = 2·f(x) = 2·(2ˣ)

Therefore;

The graph of g(x) can be obtained from the graph of f(x), by a transformation of vertical stretch by factor of 2 and the correct option therefore is option C.

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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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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 probability that the respondent has a pet given that the respondent has had a pet is  32/85  or 0.38

We are given the following results below;

Let event B = respondent has a pet now

Now, Probability that the respondent has had a pet = P(A) = 0.88

Probability that the respondent has a pet now and has had a pet =   0.32

So, Probability that the respondent has a pet given that the respondent has had a pet is given by = P(B/A)

This conditional probability is solved as ;

    P(B/A)  =  32/85

                =   0.3764705882

                ≈ 0.38

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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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The correct equation is:

39 × 3 = 30 × 3 + 9 × 3

This equation shows that multiplying 39 by 3 is equal to the sum of multiplying 30 by 3 and multiplying 9 by 3.

Therefore, the answer is:

39 × 3 = 30 × 3 + 9 × 3

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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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:

(-1, 3 1/4) and (3, 12 3/4)

Step-by-step explanation:

These are the only two pairs that will work for the graph.

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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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

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:

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:

[tex]\sqrt[2]{(m)^1}[/tex]

Step-by-step explanation:

denominator = the root number ___

numerator = to the power of ___

If you start at (0,0) and increase 2 units in the x-direction on both lines, Line B goes up 2 units in the y-direction, while Line A only goes up 1 unit in the y-direction.

Put another way, if you started at the origin and were walking up either line (pretend their two hills), your elevation on Line B increases more quickly because it's a steeper hill.

So Line B has a great rate of change.  The rise compared to the run is greater.

Answer:

A, the line is shorter, therefore the result is faster. Hence - change for the greater!

But not necessarily when I’m terms of God Almighty. Change can take longer and God uses it for His glory all the meanwhile He’s teaching, loving and correcting people. That’s Gods endless unconditional love!

John 3:16!!

Step-by-step explanation:

Answer:

The value of y is -5, so the ordered pair is (9, -5).

Step-by-step explanation:

To determine the value of y for the ordered pair (9, y) on the line AC, we first need to find the equation of the line AC.

To find the slope of the line AC, substitute the points A and C into the slope formula:

[tex]\textsf{Slope}\;(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y_C-y_A}{x_C-x_A}=\dfrac{-3-1}{4-(-6)}=\dfrac{-4}{10}=-\dfrac{2}{5}[/tex]

To determine the equation of line AC, substitute the found slope and one of the points into the point-slope formula:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\\y-1&=-\dfrac{2}{5}(x-(-6)\\\\y-1&=-\dfrac{2}{5}x-\dfrac{12}{5}\\\\y&=-\dfrac{2}{5}x-\dfrac{7}{5} \end{aligned}[/tex]

Now we have found the equation of the line AC, to determine the value of y for the ordered pair (9, y), substitute x = 9 into the equation:

[tex]\begin{aligned}y&=-\dfrac{2}{5}(9)-\dfrac{7}{5}\\\\&=-\dfrac{18}{5}-\dfrac{7}{5}\\\\&=\dfrac{-18-7}{5}\\\\&=\dfrac{-25}{5}\\\\&=-5\end{aligned}[/tex]

Therefore, the value of y for the ordered pair is y = -5.

So the ordered pair is (9, -5).

The result to the equation is x = 7.

To find the results of the equation √( 2x- 5) 4 = 1, we can break it step by step

Abate 4 from both sides of the equation

√( 2x- 5) = 1- 4

√( 2x- 5) = -3

Square both sides of the equation to exclude the square root

√( 2x- 5))² = (- 3)²

2x- 5 = 9

Add 5 to both sides of the equation

2x = 9 + 5

2x = 14

Divide both sides of the equation by 2

x = 14/2

x = 7

Thus, the result to the equation is x = 7.

Checking the extraneous result

Substituting x = 7 back into the original equation

√(2(7)-5)+4=1

√(14-5)+4=1

√9+4=1

3+4=1

7 = 1

This equation isn't true, which means that x = 7 is an extraneous result.

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