(5x+30)=7x ??
Can anyone help me

The recursive formula of the linear growth model is Pₙ = Pₙ ₋ ₁ + 5

The explicit formula of the model is P(n) = 7 + 5n

37 cars are sold in the 6th week

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

P₀ = 7

P₁ = 12

So, the common difference is

d = 12 - 7

Evaluate

d = 5

The recursive formula of the linear growth model is

Pₙ = Pₙ ₋ ₁ + d

So, we have

Pₙ = Pₙ ₋ ₁ + 5

Here, we have

P₀ = 7

d = 5

The explicit formula of the linear growth model is

P(n) = P₀ + nd

So, we have

P(n) = 7 + 5n

This means that

n = 6

So, we have

P(6) = 7 + 5 * 6

Evaluate

P(6) = 37

Hence, 37 cars are sold in the 6th week

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Lets call the above set of points \(L\).

The domain is between minimum and maximum of the x-coords points specified,

\(\mathrm{min}(L;x)=0\)

\(\mathrm{max}(L;x)=7\)

So domain is \(D_L=[\mathrm{min}(L;x),\mathrm{max}(L;x)]=[0,7]\).

The range is the same story but you look at y values,

\(\mathrm{min}(L;y)=-8\)

\(\mathrm{max}(L;y)=8\)

So range is \(R_L=[\mathrm{min}(L;y),\mathrm{max}(L;y)]=[-8,8]\).

Hope this helps :)

Answer:

When 2 coins are tossed, the possible outcomes can be {HH, TT, HT, TH}. Thus, the total number of possible outcomes = 4 Getting only one head includes {HT, TH} outcomes. So number of desired outcomes = 2

Step-by-step explanation:

hope this heps :)

Answer:

\((a)\ \bar x_1 - \bar x_2 = 2.0\)

\((b)\ CI =(1.0542,2.9458)\)

\((c)\ CI = (0.8730,2.1270)\)

Step-by-step explanation:

Given

\(n_1 = 60\)     \(n_2 = 35\)      

\(\bar x_1 = 13.6\)    \(\bar x_2 = 11.6\)    

\(\sigma_1 = 2.1\)     \(\sigma_2 = 3\)

Solving (a): Point estimate of difference of mean

This is calculated as: \(\bar x_1 - \bar x_2\)

\(\bar x_1 - \bar x_2 = 13.6 - 11.6\)

\(\bar x_1 - \bar x_2 = 2.0\)

Solving (b): 90% confidence interval

We have:

\(c = 90\%\)

\(c = 0.90\)

Confidence level is: \(1 - \alpha\)

\(1 - \alpha = c\)

\(1 - \alpha = 0.90\)

\(\alpha = 0.10\)

Calculate \(z_{\alpha/2}\)

\(z_{\alpha/2} = z_{0.10/2}\)

\(z_{\alpha/2} = z_{0.05}\)

The z score is:

\(z_{\alpha/2} = z_{0.05} =1.645\)

The endpoints of the confidence level is:

\((\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}\)

\(2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}\)

\(2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}\)

\(2.0 \± 1.645 * \sqrt{0.0735+0.2571}\)

\(2.0 \± 1.645 * \sqrt{0.3306}\)

\(2.0 \± 0.9458\)

Split

\((2.0 - 0.9458) \to (2.0 + 0.9458)\)

\((1.0542) \to (2.9458)\)

Hence, the 90% confidence interval is:

\(CI =(1.0542,2.9458)\)

Solving (c): 95% confidence interval

We have:

\(c = 95\%\)

\(c = 0.95\)

Confidence level is: \(1 - \alpha\)

\(1 - \alpha = c\)

\(1 - \alpha = 0.95\)

\(\alpha = 0.05\)

Calculate \(z_{\alpha/2}\)

\(z_{\alpha/2} = z_{0.05/2}\)

\(z_{\alpha/2} = z_{0.025}\)

The z score is:

\(z_{\alpha/2} = z_{0.025} =1.96\)

The endpoints of the confidence level is:

\((\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}\)

\(2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}\)

\(2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}\)

\(2.0 \± 1.96 * \sqrt{0.0735+0.2571}\)

\(2.0 \± 1.96* \sqrt{0.3306}\)

\(2.0 \± 1.1270\)

Split

\((2.0 - 1.1270) \to (2.0 + 1.1270)\)

\((0.8730) \to (2.1270)\)

Hence, the 95% confidence interval is:

\(CI = (0.8730,2.1270)\)

Step-by-step explanation:

First step is to find out if it's arthmetic or geometric:

Minus the second term with the first and then the third with the second. if they have the same difference. it's arthmetic

Divide the terms do the same thing as what I wrote but divide instead. Geometric Sequence

Your teacher didnt provide u with formula, use the long way just add the difference or the ratio u get

Answer:

0.468

Step-by-step explanation:

9514 1404 393

Answer:

  cos(210°) = -(√3)/2

Step-by-step explanation:

The terminal ray of a 210° angle is in the third quadrant. The angle it makes with the -x axis is (210° -110°) = 30°. This is the "reference angle". In the 3rd quadrant, the x-coordinate of the terminal ray's intersection with the unit circle has a negative sign. This will be the sign of the cosine of the angle.

__

The reference angle of 30° tells you that the trig functions of the angle can be found from the side ratios of the "special right triangle" with angles of 30°, 60°, and 90°. The side ratios, shortest to longest, in that triangle are 1 : √3 : 2.

The cosine of the angle is the ratio ...

  Cos = Adjacent/Hypotenuse

In the above special triangle, the side adjacent to the 30° angle is the one that is √3 ratio unis. The hypotenuse is 2 ratio units. So, the cosine of 30° is ...

  cos(30°) = (√3)/2

As we said above, the sign of the adjacent side of the reference angle for 210° has a negative value. (The hypotenuse is always considered to be positive.) Then the desired cosine is ...

  cos(210°) = -cos(30°)

  cos(210°) = -(√3)/2

Answer: 566.55 US dollars

Step-by-step explanation: i think, please give 5 stars

Since opposite angles of a kite are equal, therefore ∠B and ∠D are also equal. So, m∠D = m∠B = 60°.

Right angles are angles that measure exactly 90 degrees. They are formed when two straight lines intersect at a point, creating four equal angles. Right angles are the most common type of angle and can be found in many shapes, including squares, rectangles, and triangles. Right angles are also used in architecture and engineering to create structures that are strong and stable.

In the given figure, we can see that ∠A and ∠C are both right angles, so they are both equal to 90°.

Since opposite angles of a kite are equal, therefore ∠B and ∠D are also equal. So, m∠D = m∠B = 60°.

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Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

Answer:

3+4+12+7=26

Step-by-step explanation:

Answer:

26 hours

Step-by-step explanation:

3+4+12+7=26

Answer:

34 mph

Step-by-step explanation:

Average speed = total distance / total time

Total distance = ( 40 × 2 + 30 × 3 )

= 170 miles

Total time = 5 h

So, avg speed = 170/5 = 34 mph

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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Answer:

Below

Step-by-step explanation:

Given  1 C = 9/5 F      this is also     5/9 C = F

      then 5 °C  change  would be     5 C * 9/5 F = 9 degrees F change

and   25 F change     would be       5/9 * 25 = 13.9° C change

Answer:

110

Step-by-step explanation:

5.5 x 20 = 110

The volume of any cylinder is

V = pi*r^2*h

where r is the radius and h is the height. We are keeping r = 2 the same the entire time, as the first part of the instructions indicate. In contrast, h is allowed to vary or change based on the values shown in the table.

If h = 1, then,

V = pi*r^2*h

V = pi*2^2*1

V = pi*4

V = 4pi

So you'll write "4pi", without quotes of course, in the V column next to h = 1. This first row shows a height of 1 leads to a volume of 4pi.

-------------

Then if h = 2, we have,

V = pi*r^2*h

V = pi*2^2*2

V = pi*8

V = 8pi  ... this is written in the second box

and finally if h = 3, we would say,

V = pi*r^2*h

V = pi*2^2*3

V = pi*12

V = 12pi .... and this is placed in the third box

---------------

The values of V we got were: 4pi, 8pi, 12pi

This is for h = 1,2 and 3 respectively in that order.

The sequence 4,8,12 is linear because we are adding 4 each time. More specifically, it fits the equation y = 4x where x = 1,2,3. Think of y = 4x as y = 4x+0 and that fits the slope intercept form y = mx+b.

Answer:

Carrier B

Step-by-step explanation:

The linear equation that represents Carrier B is y=55x+300. it's a linear equation so 55 represent the monthly fee and 300 represents the initial fee. So the initial fee of carrier B is 300. In case of Carrier A, the total cost increases by $150 as months increases by 3. So The initial fee of Carrier A is 500-150=$350 . Hence, Carrier B has lower initial fee.

Answer:

14400 gallons of gas

Step-by-step explanation:

Answer:

Width = 64.4 feet

Step-by-step explanation:

A scale is a representative faction that can be used to either increase or decrease the dimension of a given object.

scale = \(\frac{nem length}{actual length}\)

But,

1 feet = 12 inches

For the actual MetroPass;

length = 3.4 inches = 0.2033 feet

width = 2.1 inches = 0.175 feet

The MetroPass float has a length of 74.8 feet.

scale = \(\frac{74.8}{0.2033}\)

         = 367.93

So that;

the width of the MetroPass float = 0.175 x 367.93

                               = 64.388

Therefore, the width of the MetroPass float is 64.4 feet.

Answer:

the second option!

Step-by-step explanation:

hope this helps! will appreciate brainliest!

The football is approximately 96.4 feet from the base of the goal post.

The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:

tan(theta) = opposing / adjacent.

When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.

Given, the angle of elevation is 16 degrees 42'.

That is,

Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees

Using tangent function we have:

tan(16.7) = 30/x

x = 30 / tan(16.7)

x = 96.4 feet

Hence, the football is approximately 96.4 feet from the base of the goal post.

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Step-by-step explanation:

There is no proportional relationship between x and y.

No, all ratios yx are not equivalent.

We have,

"Two or more number or variable are said to be in proportion if the ratio between them are equivalent to each other."

According to the question,

Given x : 8 , 10, 12, 14

        y : 5, 7, 9, 11

Ratio between different values of x and y are not equivalent

( 8 /5) ≠ (10 / 7)≠ (12 /9) ≠(14 /11)

We conclude there is no proportional relationship between x and y.

Hence, Option(1) is the correct answer.

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complete question:

Is there a proportional relationship between x and y? Explain.

x 8 10 12 14

y 5 7 9 11

1. No; all ratios yx are not equivalent.

2.Yes; each x value and y value increases by 2.

3.Yes; the difference between each x value and y value is 3.

4.No; all ratios xy are greater than 1.

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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Answer:

can you write this on paper and send me? i have feeling ik this but i don't understand what u need

The surface area of the triangular prism is 313.47 cm².

Given is a triangular prism, we need to find the surface area,

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.

Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.

so, the surface area of a triangular prism =

perimeter × length + 2 × base area

So,

SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9

= 167.67 + 145.8

= 313.47

Hence the surface area of the triangular prism is 313.47 cm².

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Answer: 0.8333

Step-by-step explanation:

Answer:

The interest rate per year is 0.1

Step-by-step explanation:

The equation is A = P(1+rt)

Substitute the numbers

3500 = 2500 (1+4r)

solve for r:

\(3500/2500 = 1+4r\)

\(1.4-1 = 4r\)

\(0.4 /4 = r\)

\(r = 0.1\)