I have 13 nutcrackers and 14 snowmen on my tree. How many stars are there? Let s repentant the amount of stars.



Hint there is 29 in all.

The 96th term of the given arithmetic sequence is -220

From the question, we are to determine the 96th term of the given arithmetic sequence.

The given arithmetic sequence is

-30, -32, -34

The nth term of an arithmetic sequence is given by

aₙ = a + (n - 1)d

Where a is the first term

and d is the common difference

From the sequence,

a = -30

d = a₂ - a₁ = -32 - (-30)

d = -32 + 30

d = -2

Thus,

The 96th term is

a₉₆ = -30 + (96 -1)-2

a₉₆ = -30 + (95)-2

a₉₆ = -30 + (-190)

a₉₆ = -30 - 190

a₉₆ = -220

Hence, the 96th term is -220

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The required dimensions of the package for maximum volume are radius = 14, height = 44 inches.

A cylinder is round and has a top and base looking like a circle. The top and base are level and consistently a similar size. I figure the most effective way to portray the state of a chamber is to consider a container of soup

We have,

combined length and girth is 132 inches.

So, Girth = 2πr

If length of cylinder is h,

2πr + h = 132

h = 132- 2πr

the dimensions at which the max volume can be sent

Volume of cylinder; V = πr²h

put 132 - 2πr for h to get

V = πr²(132 - 2πr)

V =132πr² - 2π²r³

Differentiating with respect to r ,

dV/dr = 264πr - 6π²r²

For max volume will be when dV/dr = 0

Then,

264πr - 6π²r² = 0

adding 6π²r² to both sides

264πr = 6π²r²

264/6 = (π²r²)/πr

44 = πr

r =44/π = 14 inches

Radius =  14 inches

Put 44/π for r in h = 132 - 2πr to get;

h = 132 - 2π(44/π)

h = 132 -88

h = 44 inches

Thus, required height is  44 inches.

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The required relationship between weight and number of months is given as y = 6x + 90.

As of the given data, assume the relationship on the graph,
Initially ordered pair (0, 90) and instantaneous ordered pair (8, 138)

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The slope of the relationship,

M = (y₂ - y₁) /  (x₂ - x₁)

m = 138 - 90 / 8  - 0
m = 48 / 6
m = 6

Now,
Equation of the relationship,

y - y₁ = m (x - x₁)
y - 90 = m{x - 0}
y = 6x + 90

Thus, y = 6x + 90 is the needed relationship between weight and the number of months.

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Yes, The relation represent a function.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The points are,

{ (- 12, - 21) , (- 21, - 22) , (22, - 12) , (21, 22) , (17, -22) } ​

Now,

Since, The points are,

{ (- 12, - 21) , (- 21, - 22) , (22, - 12) , (21, 22) , (17, -22) } ​

Clearly, All inputs having exactly one output.

Thus, The relation represent a function.

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Check the picture below, so the parabola looks more or less like so.

keeping in mind the vertex is always half-way between the focus point and the directrix, let's also notice the "p" distance.

[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-4\\ k=2\\ p=-1 \end{cases}\implies 4(-1)(y-2)=( ~~ x-(-4) ~~ )^2\implies -4(y-2)=(x+4)^2 \\\\\\ y-2=-\cfrac{1}{4}(x+4)^2\implies {\Large \begin{array}{llll} y=-\cfrac{1}{4}(x+4)^2 + 2 \end{array}}[/tex]

The 91st term in the sequence is 1,1.01,1.02 is 1.9.

An arithmetic sequence is a set of numbers that are ordered and have a common difference between each consecutive term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence. We use the formula for finding the nth term to find a specific term in an arithmetic sequence. Step 1: An arithmetic sequence's nth term is given by a = a + (n - 1)d.

Based on the information given, it should be noted this is an arithmetic sequence.

The formula t calculate the nth term will be:

= a + (n - 1)d

where

a = first term = 1

n = 91

d = common difference = 0.01

The 91st term will be:

= a + (n - 1)d

= 1 + (91 - 1) × 0.01

= 1 + (90 × 0.01)

= 1 + 0.9

= 1.9

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I think that it is true because it is asking for a summary of the data and finding the mean and standard deviation of the speeds and weight would give you the summary of all the data.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.

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[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ t=years\\ \end{cases} \\\\\\ A=20000(1 - 0.1)^{t} \implies A=20000(0.9)^t[/tex]

how long till it's $7000?

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &7000\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ t=\textit{elapsed time} \end{cases} \\\\\\ 7000=20000(1 - 0.1)^{t} \implies \cfrac{7000}{20000}=0.9^t\implies \cfrac{7}{20}=0.9^t[/tex]

[tex]\log\left( \cfrac{7}{20} \right)=\log(0.9^t)\implies \log\left( \cfrac{7}{20} \right)=t\log(0.9) \\\\\\ \cfrac{\log\left( \frac{7}{20} \right)}{\log(0.9)}=t\implies 9.96\approx t \qquad \textit{about 9 years and 11 months}[/tex]

The measure of the angle L in the parallelogram LMNO with the given conditions is equal to 40°.

As given in the question,

In the parallelogram LMNO,

Measure of angle L = (2x)°

Measure of angle O = (4x +60)°

In parallelogram LMNO,

LM is parallel to NO

And LO is the transversal

∠MLO and ∠NOL forms the interior angles

Interiors angles formed by two parallel lines are always supplementary.

m∠L + m∠O = 180°

⇒ (2x)° + (4x + 60)° = 180°

⇒ 6x° = 180° - 60°

⇒ x° = 120°/6

⇒ x° = 20°

Here, m∠L = 2x°

                  = 2(20°)

                  =40°

Therefore, the measure of angle L in the parallelogram is equal to 40°.

The complete question is :

What is the measure of angle L in parallelogram LMNO such that measure of angle L is (2x)° and measure of angle O is (4x + 60)° ?

a. 20°               b. 30°                c.  40°                   d. 50°

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Answer:

c

Step-by-step explanation:

source: trust me bro

The probability of getting a prime number of heads given that heads occurs on at least 6 of the tosses is 0.0078

The number of observations n is 7

Here the success is heads

The probability of heads is 1/2

We need to find the the probability of getting a prime number of heads.

Heads occurs on at least 6 of the tosses

prime number greater than equal to 6 and less than equal to 7 is 7

So, X = 7

P(X = 7) = 7C7(1/2)⁷(1/2)⁰

P(X = 7) =  1 x (1/2)⁷ x

P(X =7 ) = 1/128

= 0.0078

Therefore, the probability of getting a prime number of heads given that heads occurs on at least 6 of the tosses is 0.0078

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Kevin should decrease his prices toward the end of the season to avoid having unsold produce.

What is price?

The price of a product is the amount that customers are willing to spend. While also taking into account supply costs, seasonal discounts, competitor prices, and retail markup, marketers must connect the price to the product's actual and perceived value.

Consider the following,

Price per Pound (dollars)       Quantity Sold (pounds)

            1.00                       ⇔                       5,700

            2.00                      ⇔                       4,100

            3.00                      ⇔                       2,300

Kevin has seen that demand increases when prices decrease.

Hence, Kevin should decrease his prices toward the end of the season to avoid having unsold produce.

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Complete question:

Kevin owns a fruit stand alongside a busy road. For several years, he has kept track of the number of apples that people purchase at different prices. He decides to graph the number of apples sold and the various prices at which he sold them. The graph shows his record of the number of apples sold at different prices.

Fill in the table with the number of apples Kevin sold at each price. Use the graph to estimate approximate quantities of apples.

What is the relationship between the price of apples and the demand for apples among Kevin’s customers?

Based on your answer to part B, should Kevin increase or decrease his prices toward the end of the season to avoid having unsold produce?

Answer: Kevin has seen that demand increases when prices decrease, so he should decrease his prices toward the end of the season to avoid having unsold produce.

Step-by-step explanation: PLATO answer :)

As x and f(x) vary directly when x = 11 , f(x) = 110/3.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and f(x) varies directly, let f(x) be y.

∴ y = kx.

150 = 45k.

k = 150/45.

k = 30/9.

K = 10/3.

Now, when x = 11.

y = (10/3)×11.

y = 110/3.

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z =  -2.114, test statistic used to test the claim that fewer than 90% of the company employees opted to work from home at least one day a week at the 5% significance level.

A result of a statistical test of a hypothesis is a number known as the test statistic. It displays how closely the distribution predicted by your observed data fit the null hypothesis of that statistical test.

The p value of your findings, which aids in determining whether to accept or reject your null hypothesis, is calculated using the test statistic.

P = [tex]\frac{x}{n}[/tex]

= [tex]\frac{36}{41}[/tex]

1 - P₀ = 1 - 0.95 = 0.05

Test statistic= z

=P - P₀ / {√P₀ * (1 - P₀)/ n}

=0.8780 - 0.95 /√(0.95 * 0.05) / 41

z = -2.114

Test statistic used to claim that is, z = -2.114 .

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a) scatter diagram made using the provided data is attached.

b) According to the scatter diagram, the number of defective parts discovered rises with line speed.

c) Y = 27.5 - 0.3 X is the regression model.

What does statistics mean in plain English? a field of mathematics concerned with the gathering, examination, presentation, and interpretation of vast amounts of numerical data. a compilation of numerical data

20 faulty pieces are anticipated to be present when the line speed is 25 feet per minute.

Detailed explanation:

The given information is displayed as follows:

Line Speed;                   20,   20,    30,    30,    40,    40,    50,     50

Number of Defective;   23,    21,     19,     16,     15,     17,     14,       11  

Parts located

a. The scatter diagram made with Microsoft Excel is attached.

b. The scatter figure appears to show a relationship between increased line speed and the quantity of detected defective parts.

c. The following equation is given for linear regression using the least squares approach;

Y = a + b·X

Where;

b= N∑XY - (∑X)(∑Y)/N∑X^2 - (∑X)^2

a= ∑Y - b∑X / N

We have data from Microsoft Excel;

∑X = 280, ∑Y = 136, ∑X² = 10,800, ∑XY = 4,460, (∑X)² = 78,400, N = 8

By entering the values, we obtain;

b = (8×4,460 - 280×136)/(8×10,800 - 78,400) = -0.3

a = (136 - (-0.3)×280)/8 = 27.5

As a result, we have the following linear regression;

Y = 27.5 - 0.3·X

Consequently, we have when the line speed is 25 feet per minute;

Y = 27.5 - 0.3 × 25 = 20

When the line speed is 25 feet per minute, Y = 20 faulty components should be expected to be identified.

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The perimeter of 2nd right isosceles triangle is 16(√2 + 2).

If a is the equal sides of a right isosceles triangle,

Then its hypotenuse is √2 a and perimeter is √2a (√2  + 1 )

The perimeter of 1st right isosceles triangle is 16(√2 + 1)

= √2a (√2  + 1 )

= 16 (√2  + 1 )

a = 8√2

The hypotenuse of 1st triangle = √2  a

= √2 * 8√2

= 16cm

Let A be the equal sides of 2nd right isosceles triangle

Then its hypotenuse is √2 a and perimeter is √2a (√2  + 1 )

According to the question,

A = 16 cm

The perimeter of 2nd right isosceles triangle is √2 * 16(√2 + 1)

= 16(√2 + 2)

Hence, The perimeter of 2nd right isosceles triangle is 16(√2 + 2).

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The confidence interval for the given data be,

(144.83 , 155.17).

On Subtracting 1 from your sample size, we get

150 – 1 = 149.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 149 and α = 0.025

from the table at df = 149 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(150) = 2.28

Now, 2.262 × 2.28 = 5.17

So, the confidence interval be,

(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)

Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17).

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The domain of the given composite f(g(x)) will be (-∞,-√2 - 2)∪(-√2 - 2,√2 - 2)∪(√2 - 2,∞).

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

As per the given phrase,

f(x) = 1/(x-2)

g(x) = (x + 2)²

f(g(x)) = 1/((x + 2)² - 2)

The above function will be defines except (x + 2)² - 2 = 0

(x + 2)² = 2

x + 2 = ±√2

x = √2 - 2 and x = -√2 - 2

Thus, the domain will be  (-∞,-√2 - 2)∪(-√2 - 2,√2 - 2)∪(√2 - 2,∞).

Hence "The domain of the given composite f(g(x)) will be (-∞,-√2 - 2)∪(-√2 - 2,√2 - 2)∪(√2 - 2,∞)".

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a) The minimum number of dogs that could have a mass of more than 26 kg is of: 5.

b) The maximum number of dogs that could have a mass of more than 26 kg is of: 16.

The frequency table shows the number of times that each value, or values in each range, appears in the data-set.

11 weights are between 20 and 30, hence:

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Answer:

m<D = 108

Step-by-step explanation:

m<ACD = 28 degrees. This is because if a transversal cuts through two parallel lines, Alternate Interior Angles are Congruent.

m<CAD = 44 degrees. This is because if a transversal cuts through two parallel lines, Alternate Interior Angles are Congruent. (Same reasoning.)

Now, since the sum of all angles in a triangle is 180 degrees, we can use the two angles that we know as well as angle D to add up to 180 and figure out how much D is. (All of the angles in triangle ADC)

<CAD + <ACD + <D = 180

Substitute the values in.

44 + 28 + <D = 180

72 + <D = 180

Subtract on both sides

<D = 108

The measure of angle D is 108 degrees.

The equation of the line perpendicular to given equation is 3x - y + 2 = 0

what is perpendicular line?

A straight line that forms a right angle of 90 degrees with another line is known as a perpendicular in mathematics. Alternatively stated, two lines are perpendicular to one another if they cross at a right angle.

solution:

The slope for the perpendicular line is - ( 1/m )

Then the given line has the slope y = (1/3)x - 2 is 1/3

substitute 1/3 in perpendicular equation, Then the slope for the perpendicular line is - ( 1/m ) is -3

The line equation is y = mx +c, ( -2, -4 )

Then c = -2

substitute slope for the perpendicular line is - ( 1/m ) is -3 and c = -2 in line equation

then the equation is 3x - y + 2 = 0

Therefore the equation of line perpendicular to given equation is 3x - y + 2 = 0

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Step-by-step explanation:

390 ft² (aka 390 ft. squared)

bh times 1/2

13 times 5 divided by two is 37.5 but sine you have two just skip the division and say 75

and then multiply 12 by 10 for the square and get 120

(120+75)*2=390

so the answer is 390 ft. squared

Answer: 6 and 7

Step-by-step explanation:

Find the square root of 42 = 6.48

Closest whole numbers to 6.48 are 6 and 7

The probability he or she selects a management major is 0.176. This is estimated using empirical probability.

Probability is a branch of mathematics that deals with numerical probabilities of events. It is expressed in a range from 0 to 1, not below or above this range. The probability formula is P(E) = (number of favorable outcomes)÷(total number of outcomes).

a) Here, given the total number of outcomes is 34. The favorable outcome is 6. Therefore, the probability he or she selecting the management major is,

P(E)=6/34=0.176.

b) The empirical probability employs numerous trials to calculate likelihood using real observed frequencies. It is an experimental probability that is based on previous or past data.

In the given question, we used past data to estimate the probability. Therefore, it is empirical.

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The number of total different outcomes are, 7,776.

What is rolling dice?

Every face of a cube known as a dice has a unique number.

By throwing a dice into the air, players can advance in any game by getting a certain number. Typically, this dice or dice has numbers from 1 to 6 written on each face or side of the cube-like shape.

Given:

Discrete 5 dice of different colors are rolled, and the number coming up on each dice is recorded.

Since all the dice are of different colors.

So any combination of the numbers on the dice is unique.

Dice has numbers 1 to 6.

So, for each dice there are 6 possibilities.

Since number coming on a dice is independent to the number coming on the another dice.

So, total different outcomes are = 6 x 6 x 6 x 6 x 6 = 6^5 = 7776.

Hence, the number of total different outcomes are, 7,776.

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The real life example of cartesian coordinate system, is given below.

What is cartesian coordinate system?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

The real life use of cartesian coordinate system is,

In real life, there are many straightforward situations where the Cartesian coordinate plane of x and y works well.

For instance, you can create a two-dimensional grid representing the room and use the appropriate unit of measurement to plan where to place various pieces of furniture in the room.

Define a location as your starting point and choose one direction to be x and the other (perpendicular) direction to be y. (i.e., the zero coordinate on both axes).

For example, (3, 5) would be 3 meters in the x-direction and 5 meters in the y-direction from your selected (0, 0) point. You can specify any position in the room with two numbers in the format (x, y).

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Answer: w = 7

Step-by-step explanation:

Isolate the variables by dividing each side with the constants.

Hope this helps!

The dimension of the rectangular pen that maximizes the area is 61,250ft.

What is a dimension?

Something's size, including its breadth, height, and depth: She took exact measurements of the room's dimensions in one direction, like the distance from the ceiling to the floor. The room was surprisingly small, in terms of length, width, and height.

Here, we have

L+2W = 700

Area = A= LW = (700-2W)W = 700W -2W²

Take the derivative, set it equal to zero, and solve for W

-4W + 700 = 0

W = 175 feet

L = 700-2(175) = 350 feet

350 by 175 ft maximizes area = 61,250 square feet

Hence, the dimension of the rectangular pen that maximizes the area is 61,250ft.

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The required 90% confidence interval for population mean age is (22.35,23.45)

Given,

Sample size, n = 20

Sample mean, μ = 22.9 years

Standard deviation, σ = 1.5 years

Significance level, α = 0.05

We have to find the 90% confidence interval;

Here,

x ± z(critical) σ/√n

Substituting the values;

z(critical) at  α₀.₀₅ = ±1.64

22.9 ± 1.64 (1.5/√20)

= 22.9 ± 0.55

= (22.35, 23.45)

That is,

(22.35,23.45) is the required 90% confidence interval for population mean age.

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The total area will be;

⇒ 7.514 × 10⁷ km²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The area of the Okhotsk Sea is 1.583 × 10⁶ km².

And, The area of the Indian Ocean is 7.3556 × 10⁷ km².

Now,

Since, The area of the Okhotsk Sea is 1.583 × 10⁶ km².

And, The area of the Indian Ocean is 7.3556 × 10⁷ km².

Hence, The total area = 1.583 × 10⁶ + 7.3556 × 10⁷

                                  = 1.583 × 10⁶ + 73.556 × 10⁶

                                  = 75.14 × 10⁶

                                  = 7.514 × 10⁷ km²

Thus, The total area will be;

⇒ 7.514 × 10⁷ km²

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