Write the recursive rule for the 5th term of the sequence: -7, -3, 1, 5, 9

Jakobe sold 150 coffee, 50 tea and 120 donuts at the coffee cart on Monday.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of coffee, y represent the amount of tea and z represent the amount of donuts, hence:

x + y + z = 320    (1)

Also:

1.5x + 2y + 0.75z = 415     (2)

And:

x = 3y     (3)

From the equations:

x = 150, y= 50 and z = 120

Jakobe sold 150 coffee, 50 tea and 120 donuts at the coffee cart on Monday.

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Answer:

b) - 10

Step-by-step explanation:

To find the average rate of change, we have divide the change in y of f(x) , by the change in x(input).

   [tex]\sf \boxed{\text{\bf Average rate of change = $\dfrac{f(b)-f(a)}{b-a}$}}[/tex]

 a = 4 ; f(a) = -17

b = 6 ;   f(b) = -37

     [tex]\sf Average \ rate \ of \ change = \dfrac{-37-[-17]}{6-4}[/tex]

                                         [tex]\sf =\dfrac{-37+17}{2}\\\\=\dfrac{-20}{2}\\\\=-10[/tex]

The point that is on the graph of the function [tex]F(x) = 5^x[/tex] is given by:

D. (1,5).

The function is defined by:

[tex]F(x) = 5^x[/tex]

When x = 0, [tex]F(x) = 5^0 = 1[/tex], hence point (0,1) is on the graph of the function.

When x = 1, [tex]F(x) = 5^1 = 5[/tex], hence point (1,5) is on the graph of the function, which means that option D is correct.

When x = 5, [tex]F(x) = 5^5 = 3125[/tex], hence point (5,3125) is on the graph of the function.

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12 inches

A regular polygon is any 2-D shape where all the sides and angles are congruent.

Regular Hexagon

As denoted by the prefix "hexa-", hexagons have 6 sides and internal angles. The perimeter is equal to all 6 sides added together. However, we know that these sides must be congruent because it is a regular hexagon.

Solving for Perimeter

We can create an equation that describes the perimeter of this shape, with "x" representing the length of one side.

Since all the sides are equal we can use multiplication instead of addition. To solve this equation, divide both sides by 6.

This means that all sides must be 12 inches.

The equation of the line in standard form is 6x - 7y = - 11

The standard form for linear equations in two variables is Ax + By = C.

Therefore, using (-3, -1)(1 / 2, 2)

y = mx + b

where

Hence,

m = 2 + 1 / 1  /2 + 3 = 6 / 7

Hence,

-1 = 6 / 7(-3) + b

- 1 = - 18 / 7 + b

-1 + 18 / 7 = b

b =  -7 + 18/ 7

b = 11 / 7

Therefore,

y = 6 / 7 x + 11 / 7

Using the standard form,

6 / 7 x - y = - 11 / 7

6x - 7y = - 11

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The linear equation in standard form is:

6x - 7y = -11

Which is the last option.

The line in slope-intercept form is written as:

y = a*x + b

We can see that the line passes through the points (-3, -1) and (1/2, 2), then the slope is:

[tex]a = \frac{2 - (-1)}{1/2 - (-3)} = \frac{3}{3.5} = \frac{6}{7}[/tex]

Then we can write:

y = (6/7)*x + b

To find the value of b, we use the first point. It means that when x = -3, the value of y is -1, then we get:

-1 = (6/7)*-3 + b

-1 + 18/7 = b

-7/7 + 18/7 = b

11/7 = b

Then the equation is:

y = (6/7)*x + 11/7

If we multiply both sides by 7 we get:

7y = 6x + 11

Now we move the term with "x" to the left:

7y - 6x = 11

That is the line in standard form.

If we multiply both sides by -1, we get the last option:

6x - 7y = -11

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Parallelogram is the quadilateral  ABCD with vertices A(-1,0), B(4, 0),

C(5, 4), and D(0, 4)

A parallelogram is a quadrilateral whose opposite sides are parallel and equal.

first, find the length of the sides of the quadilateral.

AB = [tex]\sqrt{(4-(-1))^2+0-0^2} \\[/tex]= [tex]\sqrt{5^2+0}[/tex] = [tex]\sqrt{25}[/tex] = 5

BC = [tex]\sqrt{(5-4)^2+(4-0)^2}[/tex] = [tex]\sqrt{1^2+4^2}[/tex] = [tex]\sqrt{1+16} = \sqrt{17}[/tex]

CD = [tex]\sqrt{(0-5)^2+(4-4)^2} = \sqrt{(-5)^2+0} = \sqrt{25-0} = 5[/tex]

DA = [tex]\sqrt{(-1-0)^2+(0-4)^2} = \sqrt{(-1)^2+(-4)^2} = \sqrt{1+16} = \sqrt{17}[/tex]

opposite side length is equal.

so quadilateral is parallelogram.

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The most precise name for quadrilateral ABCD with vertices

A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is parallelogram.

Hence, the most precise name for quadrilateral ABCD with vertices A(-1,0), B(4, 0), C(5, 4), and D(0, 4) is a parallelogram.

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Step-by-step explanation:

solution:

given,

or, 2:5 = 8:x

or, 2/5 = 8/x [ changing into fraction form ]

or, 2x = 40 [ doing cross-multiplication ]

or, x = 20 [ dividing both sides with 2]

Answer:

b, only b

y = -3 has zero slope.

Step-by-step explanation:

Only a horizontal line has zero slope. A horizontal line's equation is given in the form: "y equals a number" So y=-3 is horizontal with zero slope.

Vertical lines have undefined slope. This is not the same as zero. Vertical lines have an equation in the form x= anumber. Above in the answer choices, choice a and d are both vertical with undefined slope and are not the correct answer. Choice c has slope 5, because that is the number beside the x in the form y=mx+b where m is the slope. So choice c is also not the answer.

Only choice b has zero slope.

The number of possible committees from the given list is; 120 committees

From the given list, we can say that;

Number of faculty members = 4

Number of male students = 2

Number of female students = 3

Number of parents = 5

Thus, the number of ways to fill the 4 member committee is calculated from probability combination as;

Number of committees = 4 * 2 * 3 * 5 = 120 possible committees

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[tex]y=9x^2-4\\9x^2=y+4\\x^2=\dfrac{y+4}{9}\\x=\pm\sqrt{\dfrac{y+4}{9}}=\pm\dfrac{\sqrt{y+4}}{3}\\\\\text{inverse: }y=\pm\dfrac{\sqrt{x+4}}{3}[/tex]

The inverse of the function y = 9x² - 4 is y = ±√((x + 4)/9). The correct option is A.

To find the inverse of a function, we need to swap the positions of the input variable (usually x) and the output variable (usually y), and then solve for y. The resulting equation will be the inverse function.

To find the inverse of the function y = 9x² - 4, we need to swap the positions of x and y and then solve for y.

So, starting with y = 9x² - 4:

y = 9x² - 4

x = 9y² - 4 (swapping x and y)

x + 4 = 9y² (adding 4 to both sides)

y² = (x + 4)/9 (dividing both sides by 9)

y = ±√((x + 4)/9) (taking the square root of both sides, plus or minus)

So the inverse of the function y = 9x² - 4 is:

y = ±√((x + 4)/9)

Note that since we have a plus or minus sign in the expression, this means that the inverse is actually two functions: one that gives the positive square root, and one that gives the negative square root.

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The center of the circle is (-5, 4)

The circle equation is given as:

(x + 5)^2 + (y - 4)^2 = 9

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where

Center = (a, b)

By comparing both equations, we have

(a, b) = (-5, 4)

Hence, the center of the circle is (-5, 4)

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Answer: [tex]2\sqrt{2}[/tex]

Step-by-step explanation:

The inradius is given by the area of the triangle divided by the semiperimeter.

The semiperimeter is [tex]\frac{12+12+8}{2}=16[/tex].

Thus, by Heron's formula, the area is [tex]\sqrt{16(16-12)(16-12)(16-8)}=32\sqrt{2}[/tex].

Therefore, the radius is [tex]\frac{32\sqrt{2}}{16}=2\sqrt{2}}[/tex]

1a.The mean is 8.

b. The median is 8.

c. The mode is 8.

2. The shape of the data is: perfectly symmetrical distribution.

To find the mean of the data set given for the difference in weight, 4, 8, 9, 5, 12, 7, 6, 15, 10, 4, 8, 8, 1, add all the values and divide by the number of values given, which is, n = 12.

Mean = (4 + 8 + 9 + 5 + 12 + 7 + 6 + 15 + 10 + 4 + 8 + 8)/12

Mean = (96)/12

Mean = 8

The median is the center of the data when it is ordered.

Ordered data: 4, 4, 5, 6, 7, 8, 8, 8, 9, 10, 12, 15

The center (median) is the average of the two center values = (8 + 8)/2 = 16/2

Median = 8

The mode of the data is 8, because 8 appeared most in the data set.

The mean is 8.

The median is 8.

The mode is 8.

Thus, when the mean, median, and mode of a data set are the same, then it means the data is non-skewed or perfectly symmetrical.

Therefore the shape of the data is: perfectly symmetrical distribution.

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Answer:

Step-by-step explanation:

i didnt do anything bro why u delete my answer

110 postcards Xiulin had at first.

Algebric equation is a mathematical statement in which two equation set equal to each other.

Let the number of postcards belonging to Xiulin and Meifang be x.

Let the number of postcard Meifang gave to Xuilin be 'a'

Number of postcard left with meifang

=> x-a = 72                                                              

=> x = 72+a

Meifang had 76 fewer postcards than Xiulin.

so, (x+a)-72=76

   72+a+a-72=76

   2a = 76

   a = 38

meifang give 38 cards to xuilin

x = 72+38

 = 110

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It is an example of Type I error.

About Type I error

The rejection of a null hypothesis (H0) when it is actually true is a Type I error. It is represented by the following condition,

Failure to reject a null hypothesis when it is true that it is false which is a Type II error.

How is this an example of Type I error?

The given case's hypothesis is described as follows:

H₀: The product has no effect on the plant's height.

Hₐ: The substance causes the plant to enlarge.

The sample claims that the product causes the plant to grow taller, however in reality, it has no effect on the plant's height.

Therefore, the sample recommends rejecting the null hypothesis even though it is true. Consequently, a result, this error is a Type I error.

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Answer: (9, 10800)

Step-by-step explanation:

We will first let x be the number of years and y be the total cost.

In that case, let's plug in the values for each into the equation y=mx+b, where m is the slope and b is the y-intercept.

The y-intercept will be the value we start with before any years pass, so it will be the installation cost. The slope is how fast the total cost will increase. Since the operation costs have to be added on every year, it will be our slope.

With that in mind, let's create both of our equations:

Since y is solved for in the first equation, we can substitute it into the second equation:

[tex]900x + 2700 = 200x + 9000[/tex]

[tex]700x + 2700 = 9000[/tex] [Subtracting 200x from both sides]

[tex]700x = 6300[/tex] [Subtracting 2700 from both sides]

[tex]x = 9[/tex] [Dividing both sides by 700]

We can now substitute 9 for x in any equation and solve for y. Here I substituted it into the first one:

[tex]y = 900(9) + 2700[/tex]

[tex]y = 8100 + 2700[/tex] [Multiplying]

[tex]y = 10800[/tex] [Adding]

Hence, the solution to this linear system is (9, 10800).

The time taken for 3 machines to pack 5000 articles is 8 hours.

It is given that,

A machine can pack 5000 articles in 24 hours. I.e,

1 machine → 5000 articles → 24 hours

3 machines → 5000 articles → 24/3 hours

Thus, 3 of such machines can pack the same number of articles in

24 ÷ 3 = 8 hours.

Therefore, 3 of such machines take 8 hours to pack 5000 articles.

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The null hypothesis is that the proportions are 0.30, 0.20, 0.20, 0.20, 0.10 and the alternative hypothesis is that the proportions are not as given above.

It should be noted that the null hypothesis is the theory that states that there is no statistical relationship between the variables.

In this case, the Chi square test can be run to get the desired information. Therefore, X² was gotten as 19.597. The degree of freedom is 4 and the p value is 0.0006 from the distribution table.

In this case, the critical value of 0.006 is less than the 0.05. Therefore, we need to reject the null hypothesis.

This implies that there's evidence that the distribution doesn't correlate with what we've.

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Considering the similarity of triangles, the corresponding sides are:

[tex]\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}[/tex].

If two triangles have the exact same angles, they are called similar, and the corresponding sides, that is, the sides adjacent to the same angles, have proportional lengths.

In this problem, the corresponding sides have equal ratios given as follows:

[tex]\frac{DE}{AB} = \frac{EF}{BC} = \frac{DF}{AC}[/tex].

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The percent greater of 8 than 6 to the nearest percent is 25%

Percent greater = difference / higher chance value × 100

= 2/8 × 100

= 0.25 × 100

Percent greater = 25%

Therefore, the percent greater of 8 than 6 to the nearest percent is 25%

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The correct equation of 146 ÷ 7 = 20857 is 146.0 ÷ 7.0 = 20.857

The equation is given as:

146 ÷ 7 = 20857

The above equation is wrong.

The equation can be rewritten as:

146.0 ÷ 7.0 = 20857

The significant digits in 146.0 and 7.0 are 3 and 1, respectively.

3 - 1 = 2

This means that

So, the decimal place in the result must be after the second digit.

So, we have:

146.0 ÷ 7.0 = 20.857

Using the above highlights, we have:

146 ÷ 0.7 = 208.57

1.46 ÷ 7 = 0.20857

14.6 ÷ 0.7 = 20.857

1460 ÷ 70 = 20.857

The reasoning behind the above equations is that the decimal position in the results is dependent on the decimal positions in the dividend and divisor

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The maximum amount they can afford to spend on each window is $400

23,150 = 10,350 + 32x

23,150 - 10,350 = 32x

12,800 = 32x

x = 12,800 / 32

x = $400

Therefore, the amount spent on each window is $400

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The equation for the height exists h = 31 sin((8π)t + π/2) + 35.

The model for the height can be emanated from the general formula of the sine function, then

y = A sin(Bt - C) + D

Maximum point = 70 - 4 = 66 at t = 0

Minimum point = 4

Amplitude, A = (66 - 4) ÷ 2 = 31

D = 4 + 31 = 35

At t = 0, we have;

66 = 31 × sin(B × 0 - C) + 35

31 = 31 × sin(- C)

sin(- C) = 1

C = -π/2

1 minute = 60 seconds

1 second = 1 minute/60

15 seconds = (15/60) minutes

Period = 15 seconds = 15/60 minutes

Period = 2π/B

Therefore, 15/60 = 2π/B

1/4 = 2π/B

B = 2π/(1/4) = 8π

y = Height of the function

Let h denote the height of the wristband.

The equation for the height exists h = 31 sin((8π)t + π/2) + 35.

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Answer:

Step-by-step explanation:

First, the y-intercept is -3 so from -3 the slop to the next point is 4/1.

Answer:

1/2

Step-by-step explanation:

[tex]f( - 3) = 4 {(2)}^{ - 3} = \frac{1}{2} [/tex]

Answer:

15/16

Step-by-step explanation:

because 2/3have Becky

The expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]

From the question, we are to determine the expression for a in terms of c

In the given right triangle, we can write that

[tex]c^{2} = a^{2} +3^{2}[/tex] (Pythagorean theorem)

Thus,

[tex]c^{2} = a^{2} +9[/tex]

[tex]a^{2}= c^{2} -9[/tex]

[tex]a^{2}= \sqrt{c^{2} -9}[/tex]

Hence, the expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]

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The spending variance for salaries and wages cost in February would be closest to; $282 F.

The spending variance as the name implies is the difference between the budgeted cost and actual cost paid for an item. It therefore follows from the definition above that for the month of February;

Spending variance = $7,640 - (2850 + (16×317))

Spending variance = $7,640 - (7922)

Spending variance is therefore; $282 F.

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