how many different positive integers divisible by $4$ can be formed using each of the digits $1,$ $2,$ $3,$ and $4$ at most once, and no other digits? for example, $12$ counts, but $512$ does not.

yes

the two shortest lengths are longer than the longest lenght

when added

5+3=8

8>6

Answer:

The y value of the point (x, y) is known as the ordinate.

Step-by-step explanation:

It represents the vertical or perpendicular distance of the point from the origin or from the x-axis. The point at which a line intercepts the x-axis is called the x-intercept, and the point at which it intercepts the y-axis is called the y-intercept.

The rate of change in feet per minute for each of the balloons, can be found to be :

The rate of change in feet per minute is dependent on the change in altitude given and the change in time in minutes.

For Midnight Express balloon, the change in feet per minute would be:

= Change in altitude / Change in time

= - 2, 700 / 135

= - 20 ft per minute

For Neon Lights balloon, the change in feet per minute is:

= 480 / 30

= 16 ft per minute

For Star Wonder, the change in feet per minute is:

= - 1, 500 / 60

= - 25 ft per minute

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Approximately 34% of observations in a normal distribution lie above one standard deviation below the mean.

In a normal distribution, approximately 68% of observations fall within one standard deviation of the mean. This means that approximately 34% of observations lie below one standard deviation below the mean and 34% of observations lie above one standard deviation above the mean.

The standard normal distribution (also known as the Z-distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. So if you have a normal distribution with a mean of "mu" and a standard deviation of "sigma", you can standardize it by (X - mu)/sigma to obtain the Z-score.

In a standard normal distribution, 34% of observations fall below -1 standard deviation and 34% fall above +1 standard deviation. So, 34% of observations in a normal distribution lie above one standard deviation below the mean.

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The statement without random selection, we cannot appropriately apply the laws of probability to perform inference is true.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

We have to check the given statement without random selection, we cannot appropriately apply the laws of probability to perform inference is true or false.

Random selection is needed to eliminate bias and gives each individual the same probability of being selected.

Hence, the statement without random selection, we cannot appropriately apply the laws of probability to perform inference is true.

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On solving the provided question we can say that by equation of the cost, 96 x 1.46 = $140.16 = total fencing cost

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

one fence is around the perimeter of the garden,

36/4  = 9  by 9  for the inner fence  

6 for the outer fence,  15 by 15

60 + 36 = 96 feet total fence

total fencing cost is 96 x 1.46 = $140.16

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The second graph  represents the function [tex]f(x)=8^{\frac{1}{3} x}[/tex]

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function is

[tex]f(x)=8^{\frac{1}{3} x}[/tex]

At x=0, f(0)=1

At x=1, f(1)=2

At x=2, f(2)=4

The graph of f(x) passing through the points (0,1), (1,2), (2,4),(3,8).

According to these coordinates we can say that the graph of f(x) is represented by option 2.

Therefore correct option is 2.

Hence, the second graph  represents the function [tex]f(x)=8^{\frac{1}{3} x}[/tex]

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1. Line AB is an angle bisector of DAC.

4. Angle ABD is congruent to angle ABC

5. Triangle DAB is congruent to triangle CAB

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, Triangle DAC is isosceles with congruent sides AD and AC.

The statements that are sufficient to for proving triangle DBC is isosceles

are, Line AB is an angle bisector of DAC.

Angle ABD is congruent to angle ABC as the opposite sides are equal.

Triangle DAB is congruent to triangle CAB as they share a common side AB and sides AD and AC are equal in length.

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Answer: Non zero solution : A solution of a set of homogeneous linear equations in which at least one of the variables has a value different from zero.

Step-by-step explanation:

Answer:

At the beginning, the box has 12 ounces of cereal.

Sue eats 1/6 of the box which is 12*(1/6) = 2 ounces.

Glen eats 2/3 of the box which is 12*(2/3) = 8 ounces.

So, the total ounces that they have eaten is 2+8 = 10 ounces.

Therefore, 12-10 = 2 ounces are left in the box.

So on solving the provided question, we can say that 121 and 1221 are palindrome numbers

A number that remains the same even after the digits are switched is known as a palindrome. With regard to the vertical axis, it is mirror symmetric. The word "palindrome" is derived from the word "palindrome," and it describes words whose spelling remains the same when the letters are switched. A palindromic number, also known as a numeric palindrome or numeric palindrome, is a number (such as 16461), in which the value is unaffected by the order of the digits. Therefore, the first palindromes are 0 and 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, which equals 121.

here the numbers are

33, 121, 1221, 23465

121 and 1221 are palindrome numbers

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Answer:

y = 2/3x + 4

Step-by-step explanation:

It intersects at (0, 4)

With the description of the parallel lines and the transversal line, the alternate exterior angles are angle 1 and angle 8 and they are equal

According to the description

angle 1 + angle 2 = 180 degrees (angles of a straight line)

angle 4 + angle 2 = 180 degrees (angles of a straight line)

subtracting will result to

angle 1 - angle 4 = 0

angle 1 = angle 4

the vertical angle theorem

because the line is parallel

angle 1 = angle 5 (corresponding angles)

angle 4 = angle 8 (corresponding angles)

Since angle 1 = angle 4 = angle 8 then applying transitive property

angle 1 = angle 8

This completes the prove that alternate exterior angles are equal.

Another pair of alternate exterior angles are angle 2 and angle 7

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The value of Double integral will be [tex]\mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}[/tex]

A two-dimensional region can be integrated using double integrals. They enable us to, among other things, calculate the volume beneath a surface.

The integrals of a function in two variables over a region in R2, or the real number plane, are referred to as double integrals in mathematics. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as: R f (x, y) d A = R f (x, y) d x d y.

We know that by the property of integral [tex]$\int u \mathrm{udv}=u v-v \int d u$[/tex]

[tex]$$\begin{aligned}& \mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}=\left[\mathrm{x} \ln (1+\mathrm{x})-\int \mathrm{x} \frac{.1}{1+\mathrm{x}} \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4\left[\mathrm{x} \ln (1+\mathrm{x})-\int\left(1-\frac{1}{1+\mathrm{x}}\right) \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4[\mathrm{x} \ln (1+\mathrm{x})-\mathrm{x}+\ln |1+\mathrm{x}|]_0^4 \\& \mathrm{I}=[4 \ln (5)-4+\ln (5)]-[0-0+0] \\& \mathrm{I}=4[5 \ln 5-4] \\& \mathrm{I}=20 \ln 5-16\end{aligned}$$[/tex]

We have to evaluate the given double integral

[tex]$$\iint_{\mathrm{R}} \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dA} \text { where } \mathrm{R}=[0,4] \times[0,1]$$[/tex]

[tex]$$\begin{aligned}& \mathrm{I}=\int_0^4 \int_0^1 \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dydx}=\int_0^4 4 \mathrm{x}\left[\frac{|1+\mathrm{xy}|}{\mathrm{x}}\right]_0^1 \mathrm{dx} \\& \mathrm{I}=\int_0^{44}[\ln |1+\mathrm{x}|-0] \mathrm{dx}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\end{aligned}$$[/tex]

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Answer:

8.15

Step-by-step explanation:

halfway means the middle value. Therefore the mean.

(8 + 8.3)/2

= 8.15

The number of Canadians who are at least 100 years old in 2001 is 3793.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Percentage of Canadians who live in British Columbia are at least 100 years old = 14%

The number of Canadians who live in British Columbia who are at least 100 years old in the 2001 census = 531

This means,

14% = 531

Now,

The number of Canadians who are at least 100 years old.

14% = 531

Multiply 100/14 on both sides.

100% = 100/14 x 531

100% = 3792.8

100% = 3793

Thus,

The number of Canadians who are at least 100 years old is 3793.

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Answer: From the information provided, it can be inferred that the graph represents a piecewise function, which is a function defined by multiple smaller functions that apply to different parts of the domain.

Based on the information given, we can see that the function is constant for an input of 1. So the output value of 2 is not in the domain of the function.

It's also important to note that a function can only have one output value for a given input value, and the value of 2 is not on the graph of the function provided.

Step-by-step explanation:

The radius of the third circle is found out to be as , 1cm.

The radius of 1st circle = 1

radius of second circle = 4

Let XYR be external tangent of the circle which is centered at C,.

Then if we will extend the line PQ to R ,

the result will be , XPR being similar to triangle YQR ,

Therefore,

RQ = x

and length of RP = x   + 5

Therefore, x / x+ 5 = 1/4

=> 4x = x + 5

=> x = 1

So , the length of QR is found out to be as 1cm.

A tangent to a circle is known as a straight line which touches the circle exactly at one point . A circle can have infinite number of tangents.

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Jon is painting a box like a rectangular prism with dimensions of 15 by 8 by 12 inches. Total surface area of the box that he has to paint is 792 square inches.

Let:

w = width of the rectangular prism

l = length of the rectangular prism

h =height of the rectangular prism

Then, the surface area can be calculated as:

surface area = base area + top area + left side area + right side area + front side area + back side area.

surface area = 2 (w x l) + 2 (l x h) + 2 (w x h)

Substitute:

w = 8 inches

l = 15 inches

h = 12 inches

Surface area = 2 (8 x 15) + 2 (15 x 12) + 2 (8 x 12)

                     = 2 x (120 + 180 + 96)

                     = 792

Hence, Jon has to paint 792 sq. in.

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Grace can use the fraction 3 / 5 of the distance from point A and 2 / 5 of the distance from point B to determine the x coordinate of point C.

Herein we find the case of a point partitioning a line segment by observing a given ratio. The equation that observes this fraction is shown below:

AC / BC = 2 / 3

AC / AB = 2 / 5

Vectorially speaking, this is equivalent to the following equation:

C(x, y) - A(x, y) = (2 / 5) · [B(x, y) - A(x, y)]

C(x, y) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)

If we know that A(x, y) = (3, 2) and B(x, y) = (6, 11), then the coordinates of point C are, respectively:

C(x, y) = (3 / 5) · (3, 2) + (2 / 5) · (6, 11)

C(x, y) = (9 / 5, 6 / 5) + (12 / 5, 22 / 5)

C(x, y) = (21 / 5, 28 / 5)

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The 95% confidence interval for the population proportion is (0.88, 0.98).

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally employed. The confidence interval is the range of values within which you expect your estimate to fall a given proportion of the time if you repeat your experiment or re-sample the population in the same manner.

Here,

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.93.

The standard error of the proportion is:

σ=√(p(1-p)/n)

=√((0.93*7)/100)

=0.0255

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

=1.96*0.0255

=0.05

Then, the lower and upper bounds of the confidence interval are:

LL=0.93-0.05

=0.88

UL=0.93+0.05

=0.98

The population proportion's 95% confidence interval is (0.88, 0.98).

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The markup from cost to sale price is $108.

The pricing system in which a commodity's (goods or services) price is lower than its listed price is referred to as a "discount." Simply put, "discount" refers to a percentage of the advertised price. A discount is a type of price reduction on products that are seen in consumer transactions.

Given,

the selling price of an item = $520

Markdown = 10% = discount

markdown  ​=  percent markdown * selling price

= 10%*520

=  0.10*520

markdown = $52

To find the sale​ price, subtract the markdown from the selling price.

sale/price ​=  selling price - markdown

= 520 - 52

sale price = $468

to find the markup.

cost of item after markdown = $360

mark up cost  ​=  sale price - cost

mark up = 468 - 360

mark up = $108

Therefore,  the markup from cost to sale price is ​$108.

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Answer:

Step-by-step explanation:

a. The area between -z and z is 0.2206, so we want to find the value of z such that P(-z < Z < z) = 0.2206.

The standard normal distribution is symmetric, so P(-z < Z < z) = 0.5 - P(Z < -z) = 0.5 - P(Z < -z) = 0.5 - 0.2206 = 0.2794

We can use a standard normal table to find the z-value such that P(Z < z) = 0.2794 which is z = 0.68.

b. The area to the left of z is 0.9951, so we want to find the value of z such that P(Z < z) = 0.9951.

We can use a standard normal table to find the z-value such that P(Z < z) = 0.9951 which is z = 2.33.

Given the equation t = -0.0069d + 7.35, where t is the time of sunrise in hours after midnight and d is the number of the day in the year, To find the time of sunrise on December 25th, the 359th day of the year, we need to substitute 359 for d in the equation.

t = -0.0069(359) + 7.35

t = -2.4471 + 7.35

t = 4.9029

This means that the time of sunrise on December 25th is 4.9029 hours after midnight. To convert this to minutes, we can multiply 4.9029 by 60 (since there are 60 minutes in an hour).

4.9029 x 60 = 294.174

So the sun rose on December 25th at 294.174 minutes after midnight, which is equivalent to 4 hours and 54 minutes (294 minutes) after midnight. To the nearest minute, the sun rose on December 25th at 4:54 AM.

The balloons reached the same altitude after 30 seconds.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. 

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

Purple balloon altitude = 2.5 t+0 m = 2.5 t

Starting at a height of 15 meters above sea level, the gold balloon rose 2 meters every second.

Altitude of the gold balloon: 2 t + 15 m

Hence , The balloons reached the same altitude after 30 seconds.

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The equation statement 2(3 + 5x) = 6 + 5x is false

The statement is true if the values in the left hand side of the equation is equal to the value in the right hand side of the equation

The left hand side of the equation is simplified as follows

= 2(3 + 5x)

expanding to open the parenthesis

= 6 + 10x

6 + 10x is not equal to 6 + 5x hence we say that the sides are not equal

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A function f for f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3.

Function:

In mathematics, a function from a set X to a set Y assigns each element of X to exactly one element of Y.  The set X is called the domain of the function and the set Y is called the codomain of the function

As a set of inputs with one output for each, a function is defined as a relationship between them. A function, expressed simply, is an association between inputs where each input is connected to one and only one output.

when it says something like f(1) = 0 it means that when x = 1, y = 0

so we know one point on the graph is (0,0)

When it says something like f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3

Complete Question:

Sketch the graph of a function f for which f(0)=0, f'(0)=3, f'(1)=0, f'(2)=-1

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