consider the set of integers from 1 to 20 inclusive. this set has how many 3-element subsets, such that no two consecutive integers are in the subset?

The value of x from the exponential equation is 2.866.

Logarithm:

A logarithm is a power to which a number must be raised to get some other number.

Here we have to find the value of x.

The equation is given:

[tex]6^{x}[/tex] = 170

Taking logarithms on both sides, we have:

log [tex]6^{x}[/tex] = log 170

x log 6 = log 170

x = log 170 / log 6

 = 2.230/ 0.778

 = 2.866

Therefore the value of x is 2.866.

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If solving an equation, put it in standard form with 0 on one polynomial side and simplify.

If you're down to a linear or quadratic equation (degree 1 or 2),

Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.

Put the equation in standard form with 0 on one side to simplify it while solving it.

Know the anticipated number of roots.

If you're left with a linear or quadratic equation of degree 1 or 2, use the quadratic formula or visual inspection to solve it.

Identify one logical cause or source.

Subtract from your factor.

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A line divides the box at 18. Weights of dogs in shelter b which correctly compares the ranges  in shelter a is 11, and the range in shelter b is 4.

The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Given:

For Shelter A: The whiskers range from 8 to 30

The minimum weight of Shelter A is 8 pounds.

For Shelter B: The whiskers range from 10 to 28

The minimum weight of Shelter B is 10 pounds.

Thus, the animal shelter has the dog that weighs the least is Shelter A. The animal shelter has the dog that weighs the least is Shelter A

Infact,  whiskers are plotted are from the minimum to Q1 and from Q2 to the max.

Q1 stands here for low quartile and

Q2 stands here for upper quartile .

Median is the point  between Q1 and Q3 .Interquartile range is the range from Q1 to Q3 .

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The total value of Dan's piggy bank coins is worth 2844 cents.

What is currency?

Currency is defined as a unit of account that is issued by a government and is accepted at face value. Commodities and services can be exchanged using money.

As we know, each penny is worth 1 cent

Then, 14 pennies = 14 cents

And, a nickel worth 5 cents

Then, 12 nickles = 12*5 = 60 cents

And, a dime worth 10 cents

Then, 32 dimes = 32*10 = 320 cents

And, a quarter worth 25 cents

Then, 48 quarters = 48*25 = 1200 cents

And, a half dollar worth 50 cents

Then, 7 half dollars = 7*50 = 350 cents

And, a dollar worth 100 cents

Then, 9 dollars = 9*100 = 900 cents

Now,

Total coins worth = 14 + 60 + 320 + 1200 + 350 + 900

                             = 2844 cents

Hence, the total value of coins is 2844 cents.

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Answer:

Step-by-step explanation:

The conclusion is that the null hypothesis is not true

Yes, the altitude of an isosceles triangle bisect the vertex angle as ∠BAD = ∠CAD (by CPCT) in isosceles triangle ABC.

Given, an isosceles triangle ABC

now, the two sides are equal

AB = AC

now, drawing an altitude AD in the triangle.

So, in triangles ADB and ADC

AB = AC (given)

AD = AD (common)

∠ADB = ∠ADC (90°)

So, by RHS congruence rule

ΔADB ≅ ΔADC

and therefore ∠BAD = ∠CAD (by CPCT)

Hence, Yes the altitude of an isosceles triangle bisect the vertex angle as ∠BAD = ∠CAD (by CPCT) in isosceles triangle ABC.

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Based on the probability values, the value of the probability notation P(B|A) is 9/11

The given parameters from the question are given as

P(A) = 2/3

P(B) = 3/5

P(AB) = 11/15

Before solving the probability notation P(B|A), we start by calculating the probability expression

This is represented as

P(B|A) = P(AB)/P(A)

Substitute the known values in the above equation, so, we have the following representation

P(B|A) = (3/5)/(11/15)

Express the quotient expression as products

So, we have the following representation

P(B|A) = 3/5 * 15/11

Divide 15 and 5 by 5

This gives

P(B|A) = 3/1 * 3/11

So, we have

P(B|A) = 3 * 3/11

Multiply 3 and 3

P(B|A) = 9/11

Hence, the value of the probability is 9/11

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90% confidence interval will have the smallest margin of error.

What is global warming?

Long-term changes in temperature and weather patterns are referred to as climate change. These changes may be organic, but since the 1800s, human activity has been the primary cause of climate change. This is primarily because burning fossil fuels, such as coal, oil, and gas, releases gases that trap heat.

In March 2015, the Public Policy Institute of California (PPIC) surveyed 7,525 likely voters living in California.

In the survey, respondents were asked about global warming. PPIC results show that 47% of adults age 55 and older view global warming as a serious problem, and 65% of adults age 18 to 34 view global warming as a serious problem.

PPIC researchers are interested in the difference in proportions of adults age 55 and over and adults age 18 to 34.

The standard error for the difference in proportions is 0.011.

The correct option is (a).

As the confidence level decreases margin of error decreases.

So 90% confidence interval will have the smallest margin of error.

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By combining like terms, the equivalent of the given expression, [tex]-\frac{2}{3}a + \frac{5}{6}a-\frac{1}{6}[/tex] , is [tex]\frac{a}{6} -\frac{1}{6}[/tex] or [tex]\frac{a-1}{6}[/tex]

From the question, we are to combine like terms to create an equivalent expression of the given expression.

The given expression is

[tex]-\frac{2}{3}a + \frac{5}{6}a-\frac{1}{6}[/tex]

Combining like terms

[tex]\frac{2(-2a) + 1(5a)}{6} -\frac{1}{6}[/tex]

[tex]\frac{-4a + 5a}{6} -\frac{1}{6}[/tex]

[tex]\frac{a}{6} -\frac{1}{6}[/tex]

= [tex]\frac{a-1}{6}[/tex]

Hence, the equivalent expression is [tex]\frac{a}{6} -\frac{1}{6}[/tex] or [tex]\frac{a-1}{6}[/tex].

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Answer:

Did you mean x^2 + 5x + 6?

Step-by-step explanation:

If so, then the answer would be x=-2 or x=-3

Step 1: Factor left side of equation.

(x+2)(x+3)=0

Step 2: Set factors equal to 0.

x+2=0 or x+3=0

x=−2 or x=−3

if you additionally recognize the perimeter of the rectangle, you could use that data to locate possible values for length and width. The area of a rectangle (A) is related to the length (L) and width (W) of its facets by the following relationship: A = L × W

ShapeIn Euclidean aircraft geometry, a rectangle is a quadrilateral with four right angles. it may additionally be defined as an equiangular quadrilateral, given that equiangular method that all of its angles are identical (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with 4 facets of an equal period is a square. The term rectangular is sometimes used to refer to a non-square rectangle. A rectangle with vertices ABCD might be denoted as Rectangle ABCD.

The phrase rectangle comes from the Latin rectangles, which is a mixture of rectus (as an adjective, right, proper) and angelus (attitude).

A crossed rectangle is a crossed (self-intersecting) quadrilateral that consists of two opposite aspects of a rectangle in conjunction with the two diagonals (consequently simplest aspects are parallel). it's miles a special case of an antiparallelogram, and its angles aren't right angles and now not all same, although opposite angles are the same. different geometries, along with spherical, elliptic, and hyperbolic, have so-called rectangles with opposite facets same in the period, and the same angles that aren't right angles.

Rectangles are worried in many tiling issues, including tiling the aircraft by means of rectangles or tiling a rectangle through polygons.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{0}) \implies y +1= -3 (x -0) \\\\\\ y+1=-3x\implies {\Large \begin{array}{llll} y=-3x-1 \end{array}}[/tex]

Last week Bob was paid total of $480 for the items that he produced that week and this week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

Let's start with the simplest case:

he produced 36 or less items this week.

In this case he produced less than 36 items last week too.

So he was paid the same amount of dollar per item. Using assumptions (1) and (2), we have:

$480 + 2X = $510

⇒2X=510-480$

⇒2X=$30

⇒2X=$30/2

⇒X=$15

He was paid $15 per item.

Last week he received his $480.

480/15= 32 items.

This week he received his $510.

510/15=34 items. Other cases have no solution.

seems your question is incomplete., but most probably the complete question was

If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is paid X dollars per item for the first 36 items and 3/2 times that amount for each additional item. How many items did Bob produce last week?(1) Last week Bob was paid total of $480 for the items that he produced that week.(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

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The unknown value x = 2 after substitution for the value y = -5x for y = 2x - 4.

Substitution in mathematics is the process for solving systems of equations that include solving for one variable and using that solution to find the other (or unknown) variable.

For y = 2x - 14 and y = -5x, we substitute the value -5x for y in the equation y = 2x - 4 to find the unknown value x;

-5x = 2x - 14

add 5x to both sides of the equation

5x - 5x= 2x + 5x - 14

0 = 7x - 14

add 14 to both sides of the equation

14 = 7x - 14 + 14

14 = 7x

also 7x = 14 {divide through by 7}

x = 14/7

x = 2.

Thus, the value of the unknown x is 2 after proper substitution.

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In Circles the central angle is the angle measures between two radii of the circle.

As shown in the figure:

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In multiple regression analysis, there can be several independent variables, but only one dependent variable

The link between several independent or predictor variables and one dependent or criterion variable is typically explained using multiple regression. The constant term, along with a number of independent variables and their corresponding coefficients, are used to model a dependent variable. Thus, it refers to a regression model that uses two or more predictor variables.

It is a statistical method that can be used to examine the relationship among a single dependent variable and a number of independent variables. The variables are quantified because an equation is used to represent the model. Although the independent variables are almost always positive, their coefficients occasionally aren't.

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By applying a translation of 5 units down, we will find the translated function:

g(x) = 3x - 7

Here we have the function:

y = f(x) = 3x - 2

And we want to apply a shift (translation) of 5 units downwards.

For any function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N > 0, the translation is upwards.

if N < 0, the translation is downwards.

Here we want to apply a translation of 5 units downwards, so we will write:

g(x) = f(x) - 5

Replacing f(x) we get:

g(x) = 3x - 2 - 5

g(x) = 3x - 7

That is the translated function.

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For the month of November, there has been a depreciation of almost $1,089.60.

By deducting the expected residual value from the cost of the tractor and dividing the result by the total projected operational life in hours, let's first get the depreciation per hour:

A tractor's depreciation per hour is calculated by deducting the residual value from the purchase price, and multiplying the result by the number of hours the tractor will be in use.

[tex]\rm D = \dfrac {136,700 - 14,500} { 18,800}\\D = \$6.81[/tex]

Multiplying the depreciation per hour by the number of hours the tractor was used to get the depreciation for the month of November

[tex]D_m = 6.81 \times 160\\D_m = \$1,089.60[/tex]

Therefore, for the month of November, there has been a depreciation of almost $1,089.60.

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The number square root of 87 which is √87 lies between the two consecutive integers are 9 and 10.

Given that,

The number is square root of 87 which is√87.

We have to find the two consecutive whole numbers does √87 lies.

We know that,

In the category of numbers known as "whole numbers," all natural numbers and 0 are included. They are a subset of "real numbers," which are those that don't contain fractions, decimals, or negative numbers.

The √87 lies between √81 and √100

Which we can write as

√81<√87<√100

9<√87<10

Therefore, The number square root of 87 which is √87 lies between the two consecutive integers are 9 and 10.

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The correct statement will be;

''A multiple is a number that is the product of a given number and some other number.''

What is Greatest common factors?

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The statement is,

A multiple is a number that is the ____ of a given number and some other number.

Now,

We know that;

A multiple is a number that is the product of a given number and some other number.

Thus, The correct statement will be;

''A multiple is a number that is the product of a given number and some other number.''

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Answer:

x=30°

Step-by-step explanation:

Find angles of the triangles:

Angles on a straight line:

180°-120°=60°

Opposite angles(intersection property):

55°= 55°

Sum of angles in a triangle = 180°

So:

------>60°+55°+2x+5=180°

------>120°+2x=180°

------>2x=180°-120°

------>2x=60°

------>x=60/2°

------>x=30°

let an agle be 'a' and 'b' ,

120°+a=180° ( linear pair )

a=120°-180°

a=60°

b=55°(opposite angle )

a+b+2x+5=180°(angle sum property)

60°+55°+2x+5=180°

120°+2x=180°

2x=180-120

2x=60

x=60/2

x=30

hence, the value of x is 30

Answer:

Curtis spent 14 dollars

Step-by-step explanation:

3x-29=13

   +29. +29

3x=42

/3.  /3

x=14

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The percentage of error in the estimation of Alton is:

13.04%

Given:

Alton estimated that 230 people attended the band concert.

The actual count for attendance was 200 people.

we are asked to determine the percent of error = ?

Percent error

Using this formula

Percent error=Actual attendance -Estimated attendance/Actual attendance

Let plug in the formula

Percent error=230-200/230

Percent error=30/230

Percent error=0.1304×100

Percent error=13.04%

Hence we get the percentage error as 13.04%.

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Based on this information and the ratios given in the table, I would say that skull B is most likely a human skull.

Given,

In the question:

A series of measurements were made on four skulls (descriptions of the measurements can be found in the Student Exploration Sheet).

To find the which is most likely a modern human skull?

Now, According to the question:

The cranium/face area ratio relates to the size of the cranium relative to the rest of the skull, and we would expect this ratio to be fairly large for a human. The face angle relates to human faces in relation to primate faces, which are less protruded forwards (i.e., we have relatively flat faces), and the foramen magnum is the hole in the base of the skull through which the spinal column connects to the skull. In bipeds, we would expect this hole to be fairly equally distant from the back of the skull to the front of the skull,

So this ratio would be closer to

Hence, Based on this information and the ratios given in the table, I would say that skull B is most likely a human skull.

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The problem that looks like after that he implifie the factor is 3/5.

A factor is a number that divides another number with no residual. In other words, if multiplying two whole numbers yields a product, then the numbers we are multiplying are factors of the product since they are divisible by the product.

Factors are numbers that can divide a number exactly. As a result, there is no leftover remaining after division. Factors are the numbers that you multiply together to get another number. As a result, a factor is the divisor of another integer.

Given, Yen calculates the product 5/8 times 24/25.

The product 5/8 times 24/25

=(5/8)(24/25)

Now, we have to factor the terms.

=(5/2×2×2)×(2×2×2×2)/(5×5)

=(5×2×2×2×3)/(2×2×2×5×5)

=3/5

The problem that looks like after that he implifie the factor is 3/5.

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The rate of change for the first week is 40%, and it changes values over the time.

Rate is a measurement to determine the change in one quantity with respect to another quantity.

It shows are the changing

The amount deposit by Dora in account = $50.

Also, amount planned  by Dora to deposit each week = $20

The rate of change for first week = (20/50)×100 %

                                                       = 40 %

The rate of change for the first week is 40%.

The rate of change will change the value, as principal amount increases every week, therefore, rate of change will decrease over the time.

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The price level that people expected rise above.

What is the term for price increases?

The rate at which prices rise over a given time is called inflation. A country's cost of living or overall increase in prices are two examples of broad measures of inflation.

What happens when the price level rises above expectations?

The economy's leading indicators are price levels; Inflation occurs when prices rise in response to increased demand, while deflation occurs when prices fall in response to decreased demand.

What happens when the price rises?

The average price of all goods and services sold rises when an economy's price level rises. The percentage increase in a nation's price level over some time, typically a year, is what is used to calculate inflation. This indicates that inflation is taking place during the time when prices rise.

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The required distance that a car can drive in one lap is 1099 ft. Option 2 is correct.

Given that,
A race track has a diameter of 350 ft. how far a car drive if it completes one lap is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
Diameter = 350 ft
Circumference = πD
Circumference = 3.14 × 350 = 1099ft

Thus, the required distance that a car can drive in one lap is 1099 ft. Option 2 is correct.

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The correct answer is the equation of line is y = 7x + 6 when the point is (0,6) and the slope is 7.

We know a point which is (0,6) and a slope which is 7.  It's a unique point, where we have to find its equation. Firstly, it is the y intercept because
x = 0.  We can use the equation for a line in the form of slope-intercept

The required equation of line formula is y= mx+c where m is the slope that is 7 and c is the y intercept that is 6.

where y = 7x + 6

The general equation of a straight line is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

On the y-axis, this value c is referred to as the intercept, it represents the equation of a straight line with gradient m and intercept c on the y-axis.

Hence, the equation of line is y = 7x + 6 when the point is (0,6) and the slope is 7.

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There are a total of 126 ways to distribute the 10 identical candies among the 5 distinct kids.

A combination is also called a selection. A combination corresponds to a selection of things from a given set of things. It is Denoted by

ⁿCᵣ = n!/r!(n-r)!

the number of unique r selections fromaset of n objects.

We have given that,

Total number of candies for distribution = 10

number of kids who take the candies = 5

Candies are distributed among the kids such that each kid has atleast one candy.

Here, candies are identical and kids are distinct.

Number of ways in which 10 identical candies can be divided among 5 kids if each kid must get at least one candy. The problem can be solved using the combination formula with

n = 5, k = 10.

= ⁽ᵏ⁻¹⁾Cₙ₋₁· = ⁹C₄ = 126 ways to do this.

So, there are 126 ways to distribute the candies among the five kids.

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