how many places can you put the lens to form a well-focused image of the candle flame on the wall?

Answer:

6cm

Step-by-step explanation:

Given, the length of two sides of a triangle are 6 cm and 10 cm.

We have to find the length of the third side.

We know that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

Sum of two sides = 6 + 10

= 16 cm

We know that the third side must be greater than the difference between two sides and less than the sum of two sides.

Difference of two sides = 10 - 6

= 4 cm

So, the third side must be greater than 4 cm and less than 16 cm.

Therefore, the third side is 6 cm.

Answer:

Drawf planets orbit the Sun.

Dwarf planets are round.

Pluto is a dwarf planet.

Answer:a,c,d

Step-by-step explanation:

edge 2023

The required value of the given function is (f ⋅ g)(4) = 130.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows:

f(x)=3x+1 and g(x)=x²-6

(f ⋅g)(x) is the composition of the functions f and g, which means f(x) × g(x).

(f ⋅ g)(x) = f(x) × g(x)

So, substituting x = 4:

(f ⋅ g)(4) = f(4) × g(4)

= (3 × 4 + 1)×(4² - 6)

= 13 × 10

= 130

So, (f ⋅ g)(4) = 130.

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The length of something like the curve is 8.083, going per the supplied statement.

Curve, An abstract phrase used to characterize the trajectory of a continually moving point in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a solid line or a collection of connected line segments. The IS curve displays permutations of borrowing costs and production levels where anticipated expenditure and income are equal. The many interest and income configurations along which the commodity is in homeostasis are represented by the IS Curve.

[tex]\begin{aligned}& r(t)=\left\langle 8 t, t^2, \frac{1}{12} t^3\right\rangle \\& r^{\prime}(t)=\left\langle 8,2 t, \frac{t^2}{4}\right\rangle\end{aligned}[/tex]

[tex]\begin{aligned}& \left|\lambda^{\prime}(t)\right|=\sqrt{64+4 t^2+\frac{t^4}{16}}=\sqrt{1 / 16\left(t^2+32\right)^2} \\& \left|r^{\prime}(t)\right|=\frac{1}{4}\left(t^2+32\right)\end{aligned}[/tex]

Length of arc = [tex]\int_a^b\left|r^{\prime}(t)\right| d t[/tex]

[tex]\begin{aligned}& L=\frac{1}{4} \int_0^1\left(t^2+32\right) d t \\& L=\frac{1}{4}\left[\frac{t^3}{3}+32 t\right]_0^1=\frac{1}{4}\left[\frac{1}{3}+32\right]\end{aligned}[/tex]

L = 8.083

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Answer:

3

Step-by-step explanation:

every term is divisible by 3, therefore it is the greatest common factor

Answer: 174

Step-by-step explanation: In the first year, the population of 32 goats increases by 71/10032 = 22.72 goats

So the population after 1 year would be 32+22.72 = 54.72 goats

In the second year, the population of 54.72 goats increases by 71/10054.72 = 38.9792 goats

So the population after 2 years would be 54.72+38.9792 = 93.69 goats

It's important to note that the answer provided (93) is the population after one year, not two years. The population after two years would be 174 goats.

A room classified as a group a-2 occupancy has dimensions of 60 feet by 80 feet and is in a sprinklered building. the minimum required separation distance from the nearest exit door is  r is 50 feet

This is determined by the occupancy type of the room, which is classified as a Group A-2 occupancy. According to the International Building Code, Group A-2 occupancies are those that involve assembly uses with an occupant load of 50 or more and with fixed seating. Therefore, the minimum required separation distance from the nearest exit door is 50 feet.  

To calculate this, I referred to the International Building Code (IBC) Chapter 10, which outlines the requirements for means of egress. Section 1020.1 of the IBC states that the required separation distance between an exit door and the nearest obstruction must be at least half the length of the maximum overall diagonal dimension of the room. Since the room has dimensions of 60 feet by 80 feet, the maximum overall diagonal dimension is 100 feet.

Therefore, half of this distance is 50 feet, which is the minimum required separation distance from the nearest exit door.   In addition, the IBC also requires that Group A-2 occupancies be sprinkled, which the room in question is. This means that there may be additional requirements for separation distances for the egress system depending on the specific type of sprinkler system being used.

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a room classified as a group a-2 occupancy has dimensions of 60 feet by 80 feet and is in a sprinklered building. what is the minimum required separation distance from the nearest exit door?

The exponential equation represented by the table is given as y = 12(2ˣ)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The standard form of an exponential equation is:

y = abˣ

Where b is the rate of change and a is the y intercept.

From the table, at point (0, 12):

y = abˣ

Substituting the values gives:

12 = ab⁰

a = 12

At point (1, 24):

y = abˣ

Substituting the values gives:

24 = ab¹

24 = 12b

b = 2

The exponential equation is given as y = 12(2ˣ)

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Answer:

x = -5

y = -4

Step-by-step explanation:

-2x + 5y = 14

3x - 3y = -3 --divide by 3 --> x - y = -1 --multiply by 2 --> 2x - 2y = -2

-2x + 5y = 14

2x - 2y = -2

Add the two equations

-3y = 12

y = -4

PLUG INTO x - y = -1

x + 4 = -1

x = -5

Hope this helps :)

Have a great day!

Answer:x=3, y=4

sorry if im wrong

Step-by-step explanation:

1.81 value of z should we use when making a 93% confidence interval for p. This can be solved using the concept of z-table.

The difference from the mean is expressed as a z-score in standard deviation units. It is not clear either one agree or disagree with the null hypothesis. The likelihood that a point as severe as their statistic would be seen that under null hypothesis is known as the p-value.

A z-table, sometimes referred to as the standard normal table, gives the area beneath the curve to the left of a z-score. This region indicates the likelihood that z-values will fall inside a particular area of the standard normal distribution.

At 93% confidence level the z is:

α = 1 - 93%

α = 1 - 0.93

α = 0.07

Now, α /2 = 0.035

Next, Z(α /2) = Z(0.035) = 1.81 ( Using z table )

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The limit exists, where limx→+∞ ex=+∞  and  limx→+∞ arctanx=π\2

This problem can be solved by dividing it into smaller parts.

Let f(x)=ex and g(x)=arctan(x)

The range of the function arctan(ex) is equal to the intersection of the ranges of f(x) and g(x).

Since the range of f(x) is [0,∞] and the range of g(x) is [−π/2,π/2], the intersection is [0,∞] ∩ [−π/2,π/2] or [0,π/2]

but the limit as x approaches infinity or limx→∞.

Since the highest number in the possible range is π/2, that is the limit as x approaches infinity.

if x is approaching negative infinity or limx→−∞, the answer would be the lowest value in the function's range. Therefore, it would be 0

So, as x→∞, ex→∞ so that, letting t=ex we have limx→∞ arctan(ex)=limt→∞ arctan(t)=π/2.

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The compound proposition defined by implication is: If 2 · x + 5 = 5, then the value of x is 0.

Propositions are logical constructions that contains a truth value. Proposition can be simple or composite, that is, the result of combination between simple propositions by use of operators. In this case we find a composite proposition formed by two simple propositions and a logic operator (an implication):

α ⇒ β

Where:

If the antecedent is true, then the consequent must be true. If 2 · x + 5 = 5, then we must clear x within the equation to determine a value such as composite proposition becomes true:

2 · x + 5 = 5

2 · x = 0

x = 0

The statement presents several mistakes and is incomplete. Correct form is presented below:

Complete this proposition:

If 2 · x + 5 = 5, then the value of x is ___________.

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For [tex]f(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. Matching with vertex form, we see the vertex of the graph of [tex]f(x)[/tex] has coordinates [tex](4,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=4[/tex].

Similarly, for [tex]h(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. The vertex of the graph of a quadratic function is either the minimum or maximum point (it depends on the leading coefficient of the function). Here, there is a maximum point, which has coordinates [tex](-2,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=-2[/tex].

The double integral. ∫∫R 2x/1 + xy dA, R = [0, 2] × [0, 1] is: 2*(1/2ln(3) - 1/2ln(1))

To calculate the double integral ∫∫R 2x/1 + xy dA, we need to integrate with respect to x and y over the region R = [0, 2] × [0, 1].

We can solve this by using the order of integration.

First we need to fix the limits of integration with respect to y and then integrate with respect to x.

∫∫R 2x/1 + xy dA = ∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy

∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy = ∫(0 to 1) ( 2*ln(1+xy)|x=0 to 2) dy

∫(0 to 1) ( 2ln(1+2y) - 2ln(1+0) ) dy

= 2*∫(0 to 1) ln(1+2y) dy

= 2*[y*ln(1+2y) - ∫(0 to 1) ln(1+2y) dy] |y = 0 to 1

= 2*[yln(1+2y) - (1/2 ln(3) - 1/2* ln(1))] |y = 0 to 1

= 2*(1ln(3) - 0ln(1) - 1/2* ln(3) + 1/2* ln(1))

= 2*(1/2ln(3) - 1/2ln(1))

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The calculator helps to slove an expression. By putting all elements one by one of the expression to get result.

What is a calculator?

A calculator is a device that performs numerical arithmetic operations. Basic calculators can only perform addition, subtraction, multiplication, and division calculations.

To perform basic operations, use the basic operation symbols. Addition (+), subtraction (-), multiplication (), and division () are examples of these operations.

Don't be concerned about the order of operations. A scientific calculator will perform calculations in the correct order.

Using the parentheses keys, you can change the order of operations. The calculator's order of operations will be overridden.

Correct your errors. If you accidentally press the wrong key, press the DEL key. This will remove the last button you pressed, but it will not remove any calculations you've made.

Make a clean sweep of your work. To clear the line, press the CLEAR button. You can probably scroll up to see previous calculations. You can delete these by pressing delete after each line.

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Answer: Answer is 193% or c

Step-by-step explanation: To solve this, we can use algebra. Suppose x represents the percent of increase. 1.37 * x = 4.02. Divide both sides by 1.37 to get x = 2.93. This represents 293% However, since it is asking for the increasing, we need to subtract 100% since we only want to increase, not the total value.

Answer:

b. 393%

Step-by-step explanation:

1.37 + 1.37x% = 4.02

We can rewrite the expressions by using exponent properties:

(225a¹⁰)/(5a²)² =  9a⁶

(x⁵/3)³*81x⁴ = 3x¹⁹

Here we need to use some exponent properties, these are:

(xᵃ)ᵇ = xᵃᵇ

xᵃ/xᵇ = xᵃ⁻ᵇ

Here we have the expression:

(225a¹⁰)/(5a²)²

We can rewrite the denominator as:

(5a²)² = 25a⁴

We can rewrite it as:

(225a¹⁰)/ 25a⁴ = (225/25)*(a¹⁰/a⁴) = 9*a¹⁰⁻⁴ = 9a⁶

The other expression is:

(x⁵/3)³*81x⁴

(x¹⁵/27)*81x⁴ = (x¹⁵*x⁴)*(81/27) = 3*x¹⁵⁺⁴ = 3*x¹⁹

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The treatments of this experiment are the four different concentrations of the fungus mixtures that are given. The four concentrations are 0 ml/l, 1.25 ml/l, 2.5 ml/l, and 3.75 ml/l.

The experimental units are the 20 individual containers, each containing an equal number of the insects.

The response variable of the experiment is the number of insects that are still alive in each container one week after spraying.

The researchers will measure the number of insects that are still alive in each container after one week and this will be used to determine the effectiveness of the fungus mixture.

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The statement that correctly describes the proportion of arm spans that are longer than 170 cm in the stem plot is C.

The proportion of arm spans that are longer than 170 cm is about the same for Class A and Class B.

It should be noted that from the information given, the variability of the arm span shows that they have about the same variability.

Therefore, the statement that correctly describes the proportion of arm spans that are longer than 170 cm in the stem plot is C. The proportion of arm spans that are longer than 170 cm is about the same for Class A and Class B.

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The scatter plot shows the number of hats and scarves each knitter sold at a knitting show. 02 hats did the knitter who sold 9 scarves sell.

Scatterplot:

A scatterplot  is a graph or mathematical graph that displays the values ​​of usually two variables of a data set using Cartesian coordinates. is a kind of Additional variables can be displayed if the points are coded (color/shape/size). The data is displayed as a set of points, where each point has the value of one variable that determines its position on the horizontal axis and the value of another variable that determines its position on the vertical axis.

According to the Question:

I need to find out how many hats were sold when the knitter sold his 09 scarves.

To find this out, in the scatterplot he needs to find the x-values ​​corresponding to the y-values ​​of the 9 scarves.

Corresponding to 9 on the y-axis, there is a point with a corresponding value of 02.

Therefore, when the weaver sold 09 scarves, he sold two(02) hats.

Option B) 02 is correct.

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Answer:

Step-by-step explanation:

To calculate the percent error, we use the formula:

(|(Actual distance - Estimated distance)| / Actual distance) * 100

So for this case:

(|(4.32 - 4.5)| / 4.32) * 100 = (0.18 / 4.32) * 100 = 0.041666666666666664 * 100 = 4.16666667%

Therefore, Kin's percent error is 4.16666667%.

It is important to note that the percent error can be positive or negative depending on whether the estimated value is higher or lower than the actual value.

So the answer is D-0.18%

The statistic is misleading because the sample is biased.

The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.

All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.

A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.

Thus, the statistic is misleading because the sample is biased.

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Answer:

msrk the side BC and DF that way it will be SAS axiom

The main difference between the line segment and the directed line segment is given by line segment has two endpoints and the directed line segment has only one end point.

As given in the question,

Difference between the line segment and the directed line segment is given by following points:

Therefore, different number of endpoints represents the main difference between line segment and the directed line segment  given by :

line segment with two endpoints and directed with one end point.

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Number line of integers from 1 to 30:

   |    5    |    10    |    15    |    20    |    25    |    30

   |    1    2    3    4    5    6    7    8    9    10    11    12

   |    13   14   15   16   17   18   19   20   21   22   23   24

   |    25   26   27   28   29   30

Examples of comparing integers:

5 is less than 10

15 is greater than 10

Examples of querrainging integers:

The square of 9 is 81

The cube of 3 is 27

Examples of counters:

I gained 2 pounds of weight

I lost 3 pounds of weight

Examples of addition of integers:

5 + 10 = 15

-3 + 8 = 5

There are four ways for four kings can be next to each other and four queens can be next to each other.

The first way is by positioning the kings and queens diagonally opposite each other.

The second way is by arranging them in a cross shape, with two kings on the top, two queens on the bottom, two queens on the left, and two kings on the right.

This means that in total, there are four possible ways that four kings and four queens can be placed next to each other.

The kings and queens on a card set are four in number. Hence, the probability of their arrangement next to each other would be four.

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The length of the side XY for the given triangles is 3 units.

Congruent figures and shapes are those that may be reversed or rearranged such that they match up with other figures and shapes. These shapes can be produced by mirroring these forms.

A closed polygon known as a triangle has three line segments that cross at each of its three angles.

Given two triangles,

ΔHIJ and ΔXYZ

and both are congruent,

ΔHIJ ≅ ΔXYZ

for congruent triangles the measure of sides and angles are equal,

we find that,

YZ ║ IJ, HI ║ XY and XZ ║ HJ

so YZ = IH = 4 units

HI = XY = 3 units

XZ = HJ = 5 units

Hence the length of XY is  3 units.

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The kite is flying 23.4ft far of the ground.

as per the details stated above,

the angle of elevation given is 67 degrees

the length at which the string is extended is 20 feet

the spool is 5ft above the ground

so if d is the height of the spool the the actual length of the kite flying will be ( the length of the kite flying + the height of the spool (d) )

according to the question

the hypotenuse side of the triangle or the length of the string is extended is 20 feet

we have to find the opposite side of the triangle using the sine rule

sin [tex]67^0 = \frac{h}{20}[/tex]

=> 20 sin [tex]67^0[/tex] = h

=> h = 18.4 feet

the kite is flying above the spool 5 feet of the ground that is

the kite flying at

h = 18.4 + d

=> 18.4 + 5

=> 23.4 feet

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Answer:

x = 2

Step-by-step explanation:

To solve, you have to get the variable to only be on one side by subtracting from one side.

The solutions for the system of equations is the point (2, 2).

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given are two linear equations,

y = -x + 4 and

y = 2x - 2

First graph the lines.

For that, find two points on each equation and join them.

x = 0, then y = 4

y = 0, then x = 4

We have two points (0, 4) and (4, 0). Join these points to form the line.

x = 0, then y = -2

y = 0, then x = 1

We have two points (0, -2) and (1, 0). Join these points to form the line.

We have two equations, which are equal to each other.

-x + 4 = 2x - 2

-x - 2x = -2 - 4

-3x = -6

x = 2

y = -2 + 4 = 2

So the solution of the system of equations is the intersecting point of the two lines which is (2, 2).

Hence the solution of the system of equations is (2, 2).

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