Select the correct order for the following numbers. Numbers should be ordered from smallest to largest.

a. 871,290,899,213
b. 871,291,899,213
c. 871,091,899,312
d. 871,190,899,123

Answer:

[tex]P(A\:or\:B)=\frac{7}{11}[/tex]

Step-by-step explanation:

If the two events are disjoint, then P(A or B)=P(A)+P(B).

We were given that:

[tex]P(A)=\frac{4}{11}[/tex]

and

[tex]P(B)=\frac{3}{11}[/tex]

This implies that:

[tex]P(A\:or\:B)=\frac{4}{11}+\frac{3}{11}[/tex]

We simplify the right hand side to obtain:

[tex]P(A\:or\:B)=\frac{4+3}{11}[/tex]

[tex]P(A\:or\:B)=\frac{7}{11}[/tex]

Answer:

5/11

How I got my answer:

For overlapping events, you would subtract P(A and B) from the sum of P(A) and P(B).

In this case, you would do 4/11 + 3/11, which equals 7/11 minus 2/11, which equals 5/11.

Answer:

[tex]y=\dfrac{3}{2}\cdot 2^x[/tex]

Step-by-step explanation:

The general equation of the exponential function is

[tex]y=a\cdot b^x[/tex]

If the graph of the exponential function passes through the points (-2, 0.375) and (7, 192), then their coordinates satisfy the equation:

[tex]0.375=a\cdot b^{-2}\\ \\192=a\cdot b^7[/tex]

Divide the second equation by the first:

[tex]\dfrac{192}{0.375}=\dfrac{a\cdot b^7}{a\cdot b^{-2}}=\dfrac{b^7}{b^{-2}}\\ \\512=b^9\\ \\b=\sqrt[9]{512}=2[/tex]

Substitute it into the second equation:

[tex]192=a\cdot 2^7\\ \\192=a\cdot 128\\ \\a=\dfrac{192}{128}=\dfrac{96}{64}=\dfrac{48}{32}=\dfrac{6}{4}=\dfrac{3}{2}[/tex]

So, the equation of the exponential function is

[tex]y=\dfrac{3}{2}\cdot 2^x[/tex]

The formula for volume of a sphere is V = 4/3 x PI x r^3

r is 1/2 the diameter = 9 inches.

Volume = 4/3  x  3.14 x 9^3 = 3,052 cubic inches.

Answer:

3052 cubic inches

Step-by-step explanation:

1.

Solution here,

let the both planes covers same distance x while over taking.

For the small plane, let time be t.

speed= 240 mph

now,

distance covered by it,

x=240t--------(1)

For jet plane,let the time be t'.

speed=36mph

since it is flewed after 30 mins, it can be written as,

t'=t-30 min=t-0.5 hr

now distance covered by it,

c=360t'=360(t-0.5)=360t-180----------(2)

equating (1) and (2)

240t=360t-180

or, -120t=-180

or, t=1.5 hr

therefore two planes wiil meet after 1.5 hrs.

putting the value of t in (1)

x=240×1.5=360 m

therefore they travel through 360 m from the airport whlie over taking.

2.

For the first car,

speed=50 Kmph

let it covers x distance at time t

so,diatance x=50t--------(1)

For the second car,

speed=45 Kmph

according to the question, in time t, it will covers the distance (x-20)Km

so, distance(x-20)=45t

or, x=45t+20---------(2)

equating (1) and (2),

50t=45t+20

or, 5t=20

or, t=4 hrs.

therefore cars will be apart of 20 km after 4 hrs.

The jet will overtake the small plane in 1 hour, and they will be 360 miles from the airport. Two cars traveling at 50 kmph and 45 kmph will be 20 km apart after 4 hours.

To solve for the time it takes for the jet to overtake the small plane, we can use the relative speed between the two planes.

First, we calculate the distance the small plane has traveled in the 30 minutes (0.5 hours) head start:

Next, we set up the equation to find the time (t) it takes for the jet to catch up:

Solving for t:

The jet will catch up to the small plane in 1 hour.

To find the distance from the airport when they meet:

For the two cars traveling at different speeds, let's use algebra to determine when they will be 20km apart:

The two cars will be 20 km apart after 4 hours.

Answer:

83.28

Step-by-step explanation:

i did 668-85 and got 583 and i / it by 7

Answer:

Step-by-step explanation:

Given that there are only 7 days left until the launch of our new product and we only have 668.00 left in our promotion budget. We need to spend 85.00 on the last day.

Hence amount left for remaining 6 days = [tex]668-85 = 583[/tex]

This can be spent for the remaining 6 days

If equal amount to be sent then we get

[tex]\frac{583}{6} =97.17[/tex]

But we can round off and send in integral values means we can spread as

each day 100 dollars for first 5 days and on 6th day 83 dollars.

Answer:

x=2.4

Step-by-step explanation

Lets take the info already given. 20 is on the larger triangle and 8 is on the smaller. So the side that matches with X is 6. The relationship between 20 and 8 is 2.5. How? 20/8=2.5. then you divide 6 by 2.5. That equals 2.4. So x=2.4. Hope that helps !

Answer:

x=2.4

Step-by-step explanation:

Take the big one and divide it by the small one then you take the answer and divide it by the other side.

1. A<10

2. H> or equal to 55

3. D>85

Answer:

[tex]8\ units < x < 28\ units[/tex]

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x---->the possible lengths for the third side

Applying the triangle inequality theorem

Analyze two cases

 case 1)

[tex]10+18 > x[/tex]

[tex]28 > x[/tex]

Rewrite

[tex]x < 28\ units[/tex]

case 2)

[tex]10+x > 18[/tex]

[tex]x > 18-10[/tex]

[tex]x > 8\ units[/tex]

therefore

The inequalities that describe the values that possible lengths for the third side are

[tex]x > 8\ units[/tex]

[tex]x < 28\ units[/tex]

The compound inequality is

[tex]8\ units < x < 28\ units[/tex]

The possible lengths for the third side of a triangle with sides of lengths 10 and 18 can be found using the triangle inequality theorem. These lengths are denoted by 'x', and must satisfy the inequalities: 8 < x < 28. This rule applies to all triangles, not just right-angled ones.

The question relates to the rules governing triangle side lengths. Specifically, the question draws from the triangle inequality theorem, which states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference of those lengths. Hence, for a triangle with sides of lengths 10 and 18, the possible lengths of the third side (denoted 'x') must satisfy the inequalities: 8 < x < 28.

These inequalities come from the principle that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side: 10 + 18 > x and 18 - 10 < x. Otherwise, the lengths would not meet to form a closed three-sided figure.

It's also worth noting that these rules hold true for any triangle, not just right triangles. Hence, this problem doesn't involve the Pythagorean theorem, which specifically relates the sides of a right-angled triangle.

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The mean is the sum of the elements, divided by the number of the elements:

[tex]\text{mean} = \dfrac{21+32+16+27+22+19+10}{7} = 21[/tex]

The median is the element in the middle of the dataset, once you sort it:

[tex] 10,\ 16,\ 19,\ 21,\ 22,\ 27,\ 32[/tex]

So, the middle element is 21

Finally, the mode is the element that appears more often in the dataset. Since every number appears only once in the dataset, there is no mode.

Answer:

Mean: 10 + 16 + 19 + 21 + 22 + 27 + 32 = 147/7 = 21

Median: 21

Mode: there are no mode in the following data set.

Answer:

E

Step-by-step explanation:

[tex]

y+8=4(x-5)

[/tex]

Put the the E coordinates.

[tex]

-8+8=4(5-5) \\

0 = 4\cdot 0 \\

\boxed{0=0\Longrightarrow E\in y+8=4x-20}

[/tex]

Hope this helps.

r3t40

By simplifying the given equation y + 8 = 4(x - 5) to y = 4x - 28 and substituting the points' coordinates, it is determined that Point B (5, 0) is the correct point that lies on the line described by the equation.

To determine which point lies on the line described by the equation y + 8 = 4(x - 5), we need to verify which of the given options, when substituted into the equation, will satisfy it. First, we will simplify the equation to its standard line equation form y = mx + b (where m is the slope and b is the y-intercept):

Now we can substitute the x and y values from each of the points into this equation and check which one holds true.

Thus, Point B (5, 0) is the point that lies on the line described by the equation.

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Answer:

volume is 15 in cubed

Surface area is 43 in squares

Answer:

c

Step-by-step explanation:

Mean=7/3

median=2

mode=2

rnge=4

2 1/3 is closer to 3 than 2

Answer:

Step-by-step explanation:

Answer:

The common difference is -1/2

Step-by-step explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant and is called the common difference

we have

a1=2/3

a2=1/6

a3=-1/3

a4=-5/6

so

a2-a1=1/6-2/3=-1/2

a3-a2=-1/3-1/6=-1/2

a4-a3=-5/6-(-1/3)=-5/6+1/3=-1/2

therefore

The common difference is -1/2

Answer:

Usual, because the result is between the minimum and maximum usual values.

Step-by-step explanation:

To identify if the value is usual or unusual we're going to use the Range rule of thumbs which states that most values should lie within 2 standard deviations of the mean. If the value lies outside those limits, we can tell that it's an unusual value.

Therefore:

Maximum usual value: μ + 2σ

Minimum usual value: μ - 2σ

In this case:

μ = 153.1

σ = 18.2

Therefore:

Maximum usual value: 189.5

Minimum usual value: 116.7

Therefore, the value of 187 lies within the limits. Therefore, the correct option is D.  Usual, because the result is between the minimum and maximum usual values.

Answer:

D. Usual, because the result is between the minimum and maximum usual values

Step-by-step explanation:

3(2y - 4) = 8y + 9 - 9y

Distribute 3:

6y - 12 = 8y + 9 - 9y

Combine like terms:

6y - 12 = -y + 9

Add y to both sides:

7y - 12 = 9

Add 12 to both sides:

7y = 21

Divide both sides by 3:

y = 3

Answer:

Y = 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]n-number,\ n>0\\\\9n^2+8=44\qquad\text{subtract 8 from both sides}\\\\9n^2+8-8=44-8\\\\9n^2=36\qquad\text{divide both sides by 9}\\\\\dfrac{9n^2}{9}=\dfrac{36}{9}\\\\n^2=4\iff n=\pm\sqrt4\\\\n=\pm4[/tex]

There are 479,001,600 different combinations of songs that can be played without repeating a song

An MP3 player with a playlist of 12 songs can be played in 479,001,600 different orders.

An MP3 player with a playlist of 12 songs can play each song in random order without repetition.

To calculate the number of different orders the songs can be played, we can use the concept of permutations.

In this case, we have 12 songs and want to find the number of different ways they can be arranged.

The formula for permutations is n! / (n - r)!, where n is the total number of items and r is the number of items being arranged.

In this case, n is 12 and r is also 12 (since we want to arrange all the songs).

So the formula becomes 12! / (12 - 12)!. Since 12 - 12 is 0, the denominator becomes 0!.

The value of 0! is defined as 1, so we can simplify the formula to just 12!.

Using a calculator or factorial table, we can calculate that 12! (12 factorial) is equal to 479,001,600.

Therefore, there are 479,001,600 different orders in which the songs can be played on the MP3 player.

ANSWER

[tex] 3840 {m}^{3} [/tex]

EXPLANATION

The total amount of space is the volume of the composite solid.

We find the volume of the rectangular prism and add it to the volume of the triangular prism.

The total amount of space inside the museum is:

[tex] =l \times b \times h + \frac{1}{2} \times base \times height \times height \: of \: triangular \: prism [/tex]

[tex] = 30 \times 12 \times1 0 + 0.5 \times 12 \times 4 \times 10[/tex]

[tex]= 360 0 + 240[/tex]

[tex] = 3840 {m}^{3} [/tex]

Therefore,the total amount of space inside the museum is 3,840 cubic meters.

Answer:

Step-by-step explanation:

Answer:

9 proper fractions:

3/5,3/8,5/8,3/40,5/24,8/15,3/13,5/11,2/8

9 improper fractions:

8/3,8/5,5/3,24/5,40/3,15/8,11/5,13/3,8/2

Step-by-step explanation:

Proper fraction:

Proper fraction are the fractions in which the numerator is less than the denominator and the value of proper fractions is less than 1.

x/y is proper fraction if x<y and x/y<1

Improper fraction:

Improper fraction are the fractions in which the numerator is greater than the denominator and the value of proper fractions is more than 1.

x/y is improper fraction if x>y and x/y>1

Given numbers: 3,5,8

Making 9 proper and improper fractions with above given numbers with condition to use each number only once within a fraction.

nine proper fractions: (x/y is proper fraction if x<y and x/y<1)

3/5

3/8

5/8

3/(5)(8)= 3/40

5/(3)(8) = 5/24

8/(3)(5) = 8/15

3/(5+8) = 3/13

5/(3+8) = 5/11

(5-3)/8 = 2/8

nine improper fractions: (x/y is improper fraction if x>y and x/y>1)

8/3

8/5

5/3

(8)(3)/5 = 24/5

(8)(5)/3 = 40/3

(5)(3)/8 = 15/8

(3+8)/5 = 11/5

(5+8)/3 = 13/3

8/(5-3) = 8/2 !

Final answer:

To create proper and improper fractions using the numbers 3, 5, and 8, proper fractions must have a smaller numerator than the denominator, and improper fractions must have a larger numerator than the denominator. Nine examples of each type are provided using the given numbers and additional integers as necessary.

Explanation:

When creating proper fractions and improper fractions using the numbers 3, 5, and 8, a proper fraction has a numerator (top number) that is smaller than its denominator (bottom number), whereas an improper fraction has a numerator that is larger than its denominator.

Here are nine proper fractions using 3, 5, and 8:

Here are nine improper fractions using 3, 5, and 8:

Answer:

[tex]y=3/x[/tex]  or [tex]yx=3[/tex]

The graph in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

so

in this problem we have

y=0.75 when x=4

Find the value of k

[tex]y*x=k[/tex]

[tex]k=0.75*4=3[/tex]

The equation is equal to

[tex]y=3/x[/tex]

using a graphing tool

see the attached figure

Answer:

Y=3/x is the correct answer

-6

To find the slope of the perpendicular line, start with the original slope, 1/6.

The slope of a perpendicular line is the opposite and inverse of the slope of the original line. So, start by finding the inverse. This is done by simply flipping the numerator and the denominator to get 6/1, which is simplified to 6.

Finally, find the opposite of 6. You can find the opposite of a number by multiplying or dividing it by -1. If it is a positive number, just add a negative sign, and if it is already a negative number, take away the negative sign. So, the opposite of 6 is -6, which is out final answer.

Check the picture below.

so we have two parallel lines, notice, the 115° are corresponding angles and thus equal,  the 65° and 55° angles are linear angles to 115° and 125° respectively.

that leaves us with a triangle with 65° and 55°, and since all interior angles in a triangle sum up to 180°, then the last angle must be 60°, which has a twin vertical angle across the junction.

since a full revolution or a full circle go-around is 360°, the other two twin vertical angles next to the green 60° angles must be 360° - 60° - 60° = 240°, and since they're twins, each takes half of 240°.

Answer:

1) 9/cos(θ)

2)4[tex]\sqrt{3}[/tex](cos(198) +isin(198))

3)z= cos(π/3) +isin(π/3)

Step-by-step explanation:

x=9

i.e. x= 9 +i0

θ= tan^-1 (0/9)

θ= tan^-1 (0)

=0

hence z= r(cosθ +i sinθ)

            = 9(cos 0 + isin 0)

            = 9

As cos (0) = 1 hence polar form of x=9 is 9/cos(θ) where θ=0

2)

Given

z1=2[tex]\sqrt{3}[/tex]( cos(116)+isin(116))

z2=2(cos(82)+isin(82))

As per the product formula od complex polar numbers:

z1.z2= r1.r2(cos(θ1+θ2) +isin(θ1+θ2) )

Putting the values

          = 4[tex]\sqrt{3}[/tex](cos(198) +isin(198))

3)

z= 1/2 + i[tex]\sqrt{3}[/tex]/2

r= [tex]\sqrt{(1/2)^{2}+(\sqrt{3}/2) ^{2}  }[/tex]

r = [tex]\sqrt{1/4 +3/4} \\\sqrt{4/4}\\\sqrt{1}[/tex]

r=1

θ= tan^-1 [tex](\sqrt{3}/2 ) / (1/2)[/tex]

= tan^-1[tex]\sqrt{3}[/tex]

=60

=π/3

hence

z= cos(π/3) +isin(π/3) !

ANSWER

[tex]x = 22 \: \: units[/tex]

EXPLANATION

The line from the center of the circle to the upper chord meets it at right angles, this means that, this line bisects the upper chord.

Hence the length of the upper chord is 2(11)=22 units.

Since the distance from the upper chord to the center is 12 units and the distance from the lower chord to the center is also 12 units, the two chords must be equal.

[tex] \therefore \: x = 22 \: units[/tex]

Answer:

2

Step-by-step explanation:

7 ( 2 e - 1 ) - 3 = 6 + 6 e

Expand brackets

14 e - 7 - 3 = 6 + 6 e

Simplify

14 e - 10 = 6 + 6 e

Minus 6 e from both sides

8 e - 10 = 6

Add 10 on both sides

8 e = 16

Divide by 8 from both sides

e = 2

The value of e from the given expression is e = 2.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given expression is;

7 ( 2 e - 1 ) - 3 = 6 + 6 e

Expand brackets;

14 e - 7 - 3 = 6 + 6 e

Simplify;

14 e - 10 = 6 + 6 e

Minus 6 e from both sides;

8 e - 10 = 6

Add 10 on both sides;

8 e = 16

Divide by 8 from both sides;

e = 2

Hence, the value of e from the given expression is e = 2.

Learn more about equations here;

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Answer:

False

Step-by-step explanation:

The equation in slope-intercept form of a line is y=mx+b, where x and y can represent a point on the line by using the coordinates (x,y), m is the slope, and b is the y intercept.

To double check this equation, plug in the coordinates of the point (3,6) to make sure both sides of the equation equal to each other.

6 = -5(3) + 7

6 = -15 + 7

6 = -8

[tex]6 \neq -8[/tex]

Because the equation is invalid, the line does not pass through these points.

The statement is false because the equation y = -5x + 7 does not satisfy the point (3,6).

To determine if the equation y = -5x + 7 is the equation of a line that passes through the point (3,6) and has a slope of -5, we can plug the coordinates of the point into the equation to see if it satisfies the equation.

Substituting x = 3 and y = 6 into the equation gives us:
6 = -5(3) + 7,
which simplifies to:
6 = -15 + 7,
6 = -8, which is not true.

Therefore, the point (3,6) does not lie on the line with the equation y = -5x + 7. The equation y = -5x + 7 does, however, represent a line with a slope of -5, but since it does not pass through the point (3,6), the initial statement is false.

hari was 7 then which would mean that Anushka was 2. now he is ten and she is five

because you add three more years to each to get present ages

Answer:  The present age of Hari is 10 years and that of Anushka is 5 years.

Step-by-step explanation:  Given that three years ago, Hari was 5 years older than Anushka  and he is now twice as old as she is.

We are to find their present ages.

Let x years and y years represents the present ages of Hari and Anushka respectively.

Then, according to the given information, we have

[tex](x-3)-5=y-3\\\\\Rightarrow x-8=y-3\\\\\Rightarrow x=y+5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]x=2\times y\\\\\Rightarrow y+5=2y\\\\\Rightarrow 2y-y=5\\\\\Rightarrow y=5.[/tex]

From equation (i), we get

[tex]x=5+5=10.[/tex]

Thus, the present age of Hari is 10 years and that of Anushka is 5 years.

Answer:

interest earned= 292.878

the future value of an annuity= 892.878

Step-by-step explanation:

Given Data:

Interest rate= 5%

time,t = 8 years

Quarterly payment, P= 600

n= 4 as quarterly

At the end of 8 years, final investment A= ?

As per the interest formula

A= P(1+r/n)^nt

= 600(1+0.05/4)^32

= 892.878

Interest earned = A-P

                          = 892.878-600

                          = 292.878 !

Answer:

5.832 in³

Step-by-step explanation:

The volume (V) of a cube is

V = s³ ← s is the length of the side

here s = 1.8, thus

V = 1.8³ = 1.8 × 1.8 × 1.8 = 5.832 in³

formula is a^3

a=edge

1.8^3=5.83in^3

volume = 5.832

Answer:

The perimeter of question #1 is 36. The second one is 24 then the third is 19 then 28 then 54

Step-by-step explanation:

Answer:

The perimeter of one is 36. The second one is 24. The third is 19. The fourth is 28. The last is 54.

Step-by-step explanation: Adding all the sides is how you find perimeter. Use πr + 2r, where r is the radius minus the side of the semicircle that touches the other shape since that is inside the shape.