write the first five terms of the sequence with the given nth term.
an = (-2/3)^n
a1=
a2=
a3=
a4=
a5=

Answer:

Step-by-step explanation:

The volume is \(V = \frac{1}{3} b^{2} h\)

Known facts:

Let us plug in the known value into the pyramid

   \(v=\frac{1}{3} * 5^{2} *6 = 50\) cubic centimeters

The volume of a square pyramid is 50 cubic centimeters!

Hope that helps!

The sampling technique used in each study is as follows: (a) convenience sampling, (b) systematic sampling, and (c) stratified random sampling.

(a) In the first study, where a journalist goes to a campground to ask people about their feelings regarding air pollution, the sampling technique used is convenience sampling. This is evident because the journalist approaches individuals who are readily available and easily accessible at the campground. However, convenience sampling may introduce bias as it does not ensure a representative sample of the population.

(b) In the second study, where every tenth machine part is selected from an assembly line for measurement, the sampling technique used is systematic sampling. Systematic sampling involves selecting every nth element from a population after establishing a sampling interval. In this case, every tenth machine part is selected to ensure a systematic and unbiased approach to quality assurance.

(c) In the third study, where attitudes about smoking are studied at a college and students are divided by class and then randomly sampled from each class for interviews, the sampling technique used is stratified random sampling. Stratified random sampling involves dividing the population into homogeneous subgroups (strata) and then randomly selecting samples from each subgroup. By dividing the students into different class strata and randomly selecting samples from each class, this study aims to ensure representation from each class in the final sample.

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Answer:

learning only lang po yan

Step-by-step explanation:

basa lang yan katulad ko basa lang rin

Answer:

1. $78-27

= 51 for movie tickets

51÷8,50=8

therefore Nate can invite 6 friend

2.$150-$22

=$128 for the club

$128÷$16= 8months

therefore Serena can use the club for 8months

3.$65-$23=$42

$42÷$14= 3

Chuck will be able to buy only 3 CDs

6.Peter has $3.50

7.$35-$20=$15

$15÷$0.50=30 rides

8.$60-$32=$28

$28÷4=7clown stay

The height of the cone is 2.99 yards

We can use the formula for the volume of a cone to solve for the height:

V = (1/3) π \(r^{2}\) h

where V is the volume, pi is approximately 3.14, r is the radius, and h is the height.

Since we are given the volume, we can plug in the values and solve for h:

640.56 = (1/3)*3.14* \(r^{2}\)h

Multiplying both sides by 3 and dividing by 3.14 \(r^{2}\), we get:

h = 3 * 640.56 / (3.14 \(r^{2}\))

We still need to find the radius of the cone. We are not given this information directly, but we can use the fact that the cone and cylinder have the same volume to find it. Let's call the radius of the base of the cone r and the height of the cone h.

The volume of a cylinder is given by:

V = π \(r^{2}\)h

Since the cylinder has the same volume as the cone, we can set these two equations equal to each other:

π \(r^{2}\)h = 640.56

We can solve for  \(r^{2}\) by dividing both sides by πh:

\(r^{2}\) = 640.56 / (πh)

Now we can substitute this expression for  \(r^{2}\) into the formula for h that we found earlier:

h = 3 * 640.56 / (3.14 \(r^{2}\))

h = 3 * 640.56 / (3.14 * 640.56 / (πh))

Simplifying, we get:

h = 3 π/ 3.14

h ≈ 2.99

Therefore, the height of the cone is approximately 2.99 yards (rounded to the nearest hundredth).

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The number 1.01011 is a non repeating decimal and 2.23bar , 3.426 bar and 4.321321 are repeating decimal

The repeating decimal is the number that digits repeating after a fixed interval after the decimal.

The nonrepeating decimal is the number that digits will not repeating after a fixed interval after the decimal.

The first number = 1.01011

Here the digits are not repeating after the decimal.

It is a non repeating decimal

The second number = 2.23 bar

The bar sign means the number is repeating again and again

It is a repeating decimal

The third number = 3.426 bar

The digit 6 is repeating after the decimal.

It is a repeating decimal

The fourth number = 4.321321

The digits 321 is repeating after the decimal

It is a repeating decimal

Hence, the number 1.01011 is a non repeating decimal and 2.23bar , 3.426 bar and 4.321321 are repeating decimal

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The correct option is the standard deviations of the variables.

What is correlation?

Any statistical relationship between two random variables or bivariate data, whether causal or not, is referred to in statistics as correlation or dependence.

Correlation is a term used to describe the linear relationship between two entities. When using a correlation tool, the variables must be present in quantities of two or more to test their relationship (degree of association).

In order to scale the measurement between two variables connected to a similar sample, the standard deviation measures dispersion.

The variables' standard deviations are the best choice as a result.

Option involving the standard errors of the variables is incorrect because standard error, which stands for standard deviation, determines the relationship between dependent and independent variables.

Option involving the coefficients of variation of two variables is incorrect because the coefficient expressing standard deviation and mean ratio determines how much variation there is.

Option The means of the variables are incorrect because they are not a scale for determining the correlation between two variables.

Hence, the correct option is the standard deviations of the variables.

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Complete question:

The correlation between two variables related to the same sample is a scaled quantitative measure. What is used to scale this measurement?

- the standard deviations of the variables

- the standard errors of the variables

- the coefficients of variation of the two variables

- the means of the variables

The tangent value of 300 degrees is approximately -1.732.

To find the tangent value of an angle in Quadrant IV with a reference angle of 60 degrees, we need to determine the actual angle in Quadrant IV.

In Quadrant IV, the reference angle is subtracted from 360 degrees to obtain the actual angle. Thus, the actual angle in Quadrant IV would be 360 degrees - 60 degrees = 300 degrees.

The tangent function can be calculated using a calculator or by referring to a tangent table.

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Answer:

                 calories

Breakfast: 670  

Lunch:      555

Dinner:     910

Total = 2135 calories

Step-by-step explanation:

Let B, L and D, stand for the calories from Breakfast, Lunch, and Dinner

One day his calories from breakfast were 115 more, than his calories from​ lunch:  

B = L + 115

his calories from dinner were 200 less than twice his calories from lunch.:

D = 2L - 200

total caloric intake from meals was 2135:

B + L + D = 2135

------

We have B and D defined in terms of L from the first two equations, so use them in the third:

B + L + D = 2135

[L+115] + L + [2L-200] = 2135

4L - 85 = 2135

4L = 2220

L = 555 calories

B = L + 115

B = 555 + 115

B = 670 calories

D = 2L - 200

D = 2(555) - 200

D = 910 calories

================

CHECK

Does B + L + D = 2135 calories?

  670 + 555 + 910 = 2135?

 2135 = 2135?   YES

Answer:

you would do $5y + $6y - $50 or $11y - $50

Step-by-step explanation:

If  Hot dogs cost $5 per pack and hamburgers cost $6 per pack you would multiply the amount of packs by the amount of money it costs then you would subtract by the amount he can spend on food therefore the answer being

$5y + $6y - $50 or $11y - $50

Answer:

m∠D = 49°
m∠E = 41°
m∠F = 90°

Step-by-step explanation:

        We know a triangle's angles add up to 180, so we can create an equation and solve for x. We also know the little box represents 90 degrees.

Given:

        90° + 5x° + 14° + 3x° + 20° = 180°

Combine like terms:

        8x° + 124° = 180°

Subtract 124 from both sides of the equation:

        8x° = 56°

Divide both sides of the equation by 8:

        x = 7

        Now, we will plug this value of x back into the angles to solve. Again, the little box represents that Angle F is equal to 90 degrees.

m∠D = 5x° + 14° = 5(7)° + 14° = 49°
m∠E = 3x° + 20° = 3(7)° + 20° = 41°
m∠F = 90°

Answer:

height = 6

Step-by-step explanation:

substitute x = 1.5 into the function

y = - 2(1.5)² + 7(1.5) = - 2(2.25) + 10.5 = - 4.5 + 10.5 = 6

Answer:

Step-by-step explanation:

The 2 smaller triangles are proportionate to one another because they are 2 parts of the same larger triangle. Setting up the proportion, one triangle at a time:

\(\frac{x}{8.3} =\frac{11.6}{6.7}\) and cross multiply to get

6.7x = 96.28 so

x = 14.37 or 14.4, choice A.

The value of area under the normal curve at a z-score of 0.33 with respect to the mean is 0.63 (2 dp).

It is a value that describes the deviation of a value from the standard deviation. Z-score is the number of standard deviations a given data point lies above or below mean.

To find the area under the normal curve at a specific value of z we look into the normal distribution table.

At 0.33 we can see that the value is 0.6293. This value is given from the center, which is the mean of the data.

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Hey there! I'm happy to help!

To find the x value of the midpoint, you add the x values and divide by 2.

-5+4=-1

-1/2=-1/2

For the y value, you add the y values and divide by 2.

5+6=11

11/2=5 1/2

So, the midpoint is (-1/2, 5 1/2).

Have a wonderful day! :D

(Y/4) +3 = 7

Subtract 3 from both sides:

Y/4 = 4

Multiply both sides by 4

Y = 16

Answer:

Option D

Step-by-step explanation:

=> (y/4)+3 = 7

Subtracting 3 from both sides

=> y/4 = 7-3

=> y/4 = 4

Multiplying 4 to both sides

=> y = 4*4

=> y = 16

Answer:

x=3

Step-by-step explanation:

5х - 2 = 3х + 4

5х - 3х = 4 + 2

2х = 6

х = 6/2

х = 3

Hope this helps!

Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. Probability that Celia is at first in line is 1/n.

Probability refers to potential.

A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1.

Probability of an event occurring is given by

P(E) = (No. of favourable outcomes)/ (No. of total outcomes)

Permutation: When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection.

Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems. Formula of permutation is given as

\(^{n}P_{r} = \frac{n !}{(n - r) !}\)

For finding probability of Celia at first position in class of n kids we will do permutation and then apply formula of probability.

Total ways of arranging n kids = n!

But is we fix Celia at first position then ways of arrangement will be (n - 1)!

\(P(E) = \frac{(n - 1)!}{n!} = \frac{1}{n}\)

n! = n (n - 1) (n - 2)

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A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. Probability that Celia is at first in line is 1/n.

Probability refers to potential.

A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1.

Probability of an event occurring is given by

P(E) = (No. of favourable outcomes)/ (No. of total outcomes)

Permutation: When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection.

Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems. Formula of permutation is given as

\(^{n}P_{r} = \frac{n !}{(n - r) !}\)

For finding probability of Celia at first position in class of n kids we will do permutation and then apply formula of probability.

Total ways of arranging n kids = n!

But is we fix Celia at first position then ways of arrangement will be (n - 1)!

\(P(E) = \frac{(n - 1)!}{n!} = \frac{1}{n}\)

n! = n (n - 1) (n - 2)

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Answer:

2 1/4 square yards

Step-by-step explanation:

We have been given that Matthew and his 3 siblings are weeding a flower bed with an area of 9 square yards.    

All person weeding flower bed: .

To find the area in square yards weeded by each child, we will divide total area of flower bed by 4.

Therefore, each child weeded  square yards of flower bed.

Answer:

I believe it's going to be2 1/4 square feet

Answer: Depends on how many tiles are in a pack. If 1 tile is 1 pack, $1728.

If 10 tiles are 1 pack, $180.

Step-by-step explanation:

4.5m = 450cm and 2m = 200cm

Answer:

4=3

x=1

4=3x

4/3=x

1.3=x

Using the law of cosines, it is found that the measure of angle Y is of 64º.

The problem is incomplete, hence we research it on a search engine, and we have that we have a triangle in which:

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 12, b = 17, c = 16, C = Y.

Hence:

c² = a² + b² - 2abcos(Y)

16² = 12² + 17² - 2(12)(17)cos(Y)

408cos(Y) = 177

cos(Y) = 177/408

Y = arccos(177/408)

Y = 64º.

The measure of angle Y is of 64º.

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Answer: What do those numbers mean

Step-by-step explanation:

Answer:1/6

Step-by-step explanation:

there is gonna be no solution.

Answer:

20%

Step-by-step explanation:

Percentage discount on the cost of the sofa = 20%

Percentage discount = (Absolute discount / Cost price) × 100

Given,

             Cost price =  $600

Absolute discount  =  Cost price - Selling price

Absolute discount  =  $600 - $480

                                = $120

Percentage discount = (Absolute discount / Cost price) × 100

                                   = (120/600) × 100

                                   = 120/6

                                   = 20%

Hence, percentage discount on the cost of the sofa = 20% .

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The prediction interval is (140.50, 293.68) at a 99% confidence level for an overhead width of 9.2 cm.

The accompanying table lists the overhead widths (cm) of seals measured from photographs and the weights (kg) of the seals.

Find the (a) explained variation, (b) unexplained variation, and (c) prediction interval for an overhead width of 9.2 cm using a 99% confidence level.

There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions

Overhead Width: 7.3, 7.5, 9.9, 9.4, 8.8, 8.4

Weight: 113, 154, 240, 205, 202, 192Solution:

(a) Explained variation: \(R^2 = \frac{SSR}{SST}\)

Where, SSR is the explained variation, and SST is the total variation, SST \(= \sum\limits_{i=1}^n(y_i - \bar{y})^2= (113-193.67)^2 + (154-193.67)^2 + (240-193.67)^2 + (205-193.67)^2 + (202-193.67)^2 + (192-193.67)^2= 12048.1\)

Now, we will find the value of SSR.

For that, first, we need to find the regression equation and fit the line:

y = a + bx

where, y = Weight, x = Overhead Width.

\(b = \frac{n\sum\limits_{i=1}^n(x_iy_i) - \sum\limits_{i=1}^n x_i \sum\limits_{i=1}^n y_i}{n\sum\limits_{i=1}^n x_i^2 - \left(\sum\limits_{i=1}^n x_i\right)^2}\)

\(= \frac{6(7.3 \cdot 113 + 7.5 \cdot 154 + 9.9 \cdot 240 + 9.4 \cdot 205 + 8.8 \cdot 202 + 8.4 \cdot 192) - (7.3 + 7.5 + 9.9 + 9.4 + 8.8 + 8.4)(113 + 154 + 240 + 205 + 202 + 192)}{6(7.3^2 + 7.5^2 + 9.9^2 + 9.4^2 + 8.8^2 + 8.4^2) - (7.3 + 7.5 + 9.9 + 9.4 + 8.8 + 8.4)^2}\)

\(= 17.496and, a = \bar{y} - b \bar{x}\)

\(= 193.67 - 17.496(8.066666666666666)= 53.62\)

Hence, the regression equation is:

\boxed{y = 53.62 + 17.496x}

We will calculate SSR using the regression equation:

\(SSR = \sum\limits_{i=1}^n(\hat{y_i} - \bar{y})^2= \sum\limits_{i=1}^n(a+bx_i - \bar{y})^2= \sum\limits_{i=1}^n(53.62+17.496x_i - 193.67)^2= 11050.21\)

Therefore,

\(R^2 = \frac{SSR}{SST}= \frac{11050.21}{12048.1}= 0.915\)

Hence, the explained variation is 0.915.(b) Unexplained variation:\(SSE = SST - SSR$$$$= 12048.1 - 11050.21 = 997.89\)

Therefore, the unexplained variation is 997.89.

(c) Prediction Interval:

\text{Prediction Interval} = \text{point estimate} \pm t^* \times s_e

where, point estimate = \hat{y} = 53.62 + 17.496(9.2) = 217.09, t* = t-distribution value with (n-2) degrees of freedom and a 99% confidence level.

We have n = 6, so n-2 = 4, t* = 4.60409 (Using a t-distribution table), and $$s_e = \sqrt{\frac{SSE}{n-2}}= \sqrt{\frac{997.89}{4}}= 15.78

Therefore, the prediction interval is:

\boxed{217.09 \pm 4.60409(15.78)\boxed{\implies (140.50, 293.68)}

Hence, the prediction interval is (140.50, 293.68) at a 99% confidence level for an overhead width of 9.2 cm.

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Answer:

-1

Step-by-step explanation:

f(x) =3x-7

x=2

f(x)=3×2-7

f(x)=6-7

f(x)=-1

Answer:

\(k =(2,1)\)

\(JK = 2\)

Step-by-step explanation:

Given

\(J = (0,1)\) ---- \((x_1,y_1)\)

\(H = (1,-2)\) --- \((x_2,y_2)\)

\(I = (3,-2)\) --- \((x_3,y_3)\)

See attachment for grid

Solving (a): The coordinates of K

The parallelogram has the following diagonals: IJ and HK

Diagonals bisect one another. So:

Midpoint of IJ = Midpoint of HK

This gives:

\(\frac{1}{2}(I + J) = \frac{1}{2}(H+K)\)

\(\frac{1}{2}(x_3+x_1,y_3+y_1) = \frac{1}{2}(x_2+x,y_2+y)\)

\(\frac{1}{2}(3+0,-2+1) = \frac{1}{2}(1+x,-2+y)\)

\(\frac{1}{2}(3,-1) = \frac{1}{2}(1+x,-2+y)\)

Multiply through by 2

\((3,-1) = (1+x,-2+y)\)

By comparison:

\(1 + x = 3\)

\(-2 + y = -1\)

Solve for x and y

\(x = 3 - 1 =2\)

\(y = -1 +2 = 1\)

So, the coordinates of k is:

\(k =(2,1)\)

The length of JK is calculated using distance (d) formula

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2\)

\(J = (0,1)\) ---- \((x_1,y_1)\)

\(k =(2,1)\) ---- \((x_2,y_2)\)

So:

\(d = \sqrt{(0 - 2)^2 + (1 - 1)^2\)

\(d = \sqrt{(- 2)^2 + (0)^2\)

\(d = \sqrt{4 + 0\)

\(d = \sqrt{4\)

\(d = 2\)

Hence:

\(JK = 2\)