Liliana wants to start a seventh-grade computer club at Hamden Middle School. She surveyed 20 seventh-grade students at the town park. She asked each student how many hours they spend on their computers each week. She obtained the following results.

8, 15, 0, 11, 12, 13, 16, 13, 0, 4, 17, 14, 30, 13, 5, 12, 1, 13, 12, 21

What is the ratio of the total number of students who used their computers to the total number of students surveyed?

Answer:

1) not diverges

2)not diverges

3) diverges

4)not diverges

Step-by-step explanation:

In geometric series, If the |r|<1 then the series is convergent and if |r|>1 then the series is divergent

Where r is the ratio between the consecutive terms of series.

1) 3/5 + 3/10 +3/20 + 3/40 ......

in the above geometric series

r= (3/10) / (3/5)

 = 1/2

 = 0.5

As |r|= 0.5 < 1, so the series will not diverge

2) -10+4-8/5 + 16/25 -......

in the above geometric series

r= (4) / (-10)

 = -2/5

 = -0.4

As |r|= 0.4 < 1, so the series will not diverge

3) ∑ 2/3(-4)^(n-1)

in the above geometric series

r= -4

As |r|= |-4| = 4 > 1, so the series will diverge

4) ∑ (-12)(1/5)^(n-1)

in the above geometric series

r=1/5

 = 0.2

As |r|= 0.2 < 1, so the series will not diverge !

Answer:

Its C!!!!!!!!!!

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

we have the number

[tex]7,027[/tex]

we know that

[tex]7,027=7*1,000+2*10+7*1[/tex]

so

The value of the first 7 is equal to

[tex]7*1,000=7,000[/tex]

The value of the second 7 is equal to

[tex]7*1=7[/tex]

therefore

[tex]7,000/7=1,000[/tex]

The value of the first 7 is one thousand times greater than the second 7

The answer is no

Answer:

x = -7 and x = 3

Step-by-step explanation:

x² + 4x - 21 = 0 factors as follows:  (x + 7)(x - 3) = 0.

Then x = -7 and x = 3.

Answer:

[tex]x = 3\\x = -7[/tex]

Step-by-step explanation:

We have the following quadratic equation

[tex]x^2 + 4x - 21 =0[/tex]

To solve the equation we must factor it.

To factor the equation we must find 2 numbers b and c that when adding them, you obtain as result 4 ([tex]c + b = 4[/tex]) and when multiplying them, you obtain as result -21 ([tex]c * b = -21[/tex]).

Then the polynomial will be factored in the following way:

[tex](x+c)(x + b) = 0[/tex]

You can verify that the numbers that meet this condition are:[tex]b = 7\\c = -3[/tex]

So

[tex]x^2 + 4x - 21 =(x-3)(x + 7)=0[/tex]

Finally the solutions are:

[tex]x = 3\\x = -7[/tex]

since the point (4,13) is on the circle, then the distance from the center to it, is the radius of the circle.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{13})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-2)]^2+[13-5]^2}\implies r=\sqrt{(4+2)^2+(13-5)^2} \\\\\\ r=\sqrt{36+64}\implies r=\sqrt{100}\implies r=10 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-2}{ h},\stackrel{5}{ k})\qquad \qquad radius=\stackrel{10}{ r}\\[2em] [x-(-2)]^2+[y-5]^2=10^2\implies (x+2)^2+(y-5)^2=100[/tex]

Answer:

The graph in the attached figure

The point  (-1,4)  represent a solution

Step-by-step explanation:

we have

[tex]x> -2[/tex]----> inequality A

[tex]y\leq 2x+7[/tex] ----> inequality B

using a graphing tool

The solution is the shaded area

see the attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution of the system of inequalities

The point  (-1,4)  represent a solution

Answer:

(-1,4)

Step-by-step explanation:

The given system of inequalities is:

x>-2:(red region)

[tex]y\le2x+7[/tex]: (blue region)

The graph of the system f inequalities is shown in the attachment.

The points that lies in the intersection of the red and blue region is the solution to the inequality.

From the graph (-1,4) is a solution to the system of inequalities.

They won 14 games. If you subtract 2 ( the ties ) you are left with 22. Subtract 6 ( games more won than loss) you get 16. Then divide by two and get 8. 8 + 6 = 14.

Answer:

14 games.

Step-by-step explanation:

Let x represent number of games lost by Hawks.

We have been given that the Hawks won 6 more games than they lost. So number of games won by Hawks would be [tex]x+6[/tex].

We have been given that they played a total of 24 games and tied in 2 games, so total game won or lost by Hawks would be [tex]24-2=22[/tex].

Now we will equate sum of games won and lost by 22 as:

[tex]x+x+6=22[/tex]

[tex]2x+6=22[/tex]

[tex]2x+6-6=22-6[/tex]

[tex]2x=16[/tex]

[tex]\frac{2x}{2}=\frac{16}{2}[/tex]

[tex]x=8[/tex]

Number of games won by Hawks would be [tex]x+6\Rightarrow 8+6=14[/tex]

Therefore, Hawks won 14 games.

To calculate the new discounted price, $49.95×.60=$29.97

Answer:

The required expression is [tex]0.40\times 49.95[/tex].

Step-by-step explanation:

Consider the provided information.

The price for a pair of sandals is $49.95 in June.

In August the price is 60% less.

After getting 60% discount customer need to pay only 40% of the price.

This can be written as:

[tex]40\% \times 49.95[/tex]

[tex]\frac{40}{100}\times 49.95[/tex]

[tex]0.40\times 49.95[/tex]

Hence, the required expression is [tex]0.40\times 49.95[/tex].

Answer:

Option A true is the answer.

Step-by-step explanation:

The given circle there are two arcs AB and CD.

Angles formed by these arcs at the center arc 30°

Formula of length of arc = r × θ

where r = radius of the circle

and θ = angle formed by arc at the center.

mAB = OA × (30°) [ By formula ]

similarly mCD = DC × (30°)

Since OA = OC = r (radii of the circle )

So mAB = mCD

Therefore, statement is true.

Option A true is the answer.

Answer:true

Step-by-step explanation:

Answer:

radius = circumference / (2 * PI)

radius = 5.8378033126

Circle Area = PI * radius^2

Circle Area = PI * 5.8378033126^2

Circle Area = PI * 34.0799475167

Circle Area = 107.07 square units

Step-by-step explanation:

Answer:

[tex]7\sqrt[3]{x^2}[/tex]

Step-by-step explanation:

The rule of exponents that dictates this to be solved is:

[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}[/tex]

The power of 2/3 is on "x", NOT 7, so we use this property to write it as:

[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a} \\7x^{\frac{2}{3}}=7\sqrt[3]{x^2}[/tex]

third answer choice is right,  [tex]7\sqrt[3]{x^2}[/tex]

Answer:

b or the second one top to botton

Step-by-step explanation:

trust

For this case we make a rule of three to determine the initial amount of euros:

1 euro ----------------> 1.3687 dollars

x ------------------------> 250 dollars

Where "x" represents the amount of euros equivalent to 250 dollars.

[tex]x = \frac {250 * 1} {1.3687}\\x = 182.655074158[/tex]

Thus, Phelan received 182.655074158 euros.

If I spend 150 euros, we have:

[tex]182.655074158-150 = 32.655074158[/tex]

Now, we make the conversion to know the amount of dollars equivalent:

1 euro ----------------> 1.3687 dollars

32,655074158 ------------------------> y

Where "y" represents the amount of dollars:

[tex]y = \frac {32.655074158 * 1.3687} {1}\\y = 44,695[/tex]

So, Phelan has 44,695 dollars

Answer:

$ 44,695

Answer:

Option 3. 360°

Step-by-step explanation:

we know that

The sum of the measures of the interior angles of triangle is equal to 180 degrees

The figure has two triangles

therefore

[tex]2(180\°)=360\°[/tex]

Alternative Method

The formula to calculate the sum of the measures of the interior angles of a polygon is equal to

[tex]S=180(n-2)[/tex]

where

n is the number of sides of the polygon

In this problem we have a a quadrilateral

so

n=4

substitute

[tex]S=180(4-2)[/tex]

[tex]S=180(2)[/tex]

[tex]S=360\°[/tex]

Answer:

360

Step-by-step explanation:

Answer:

j=90 B=34 C=108

Step-by-step explanation:

if you know that the value of B=34 and the value of A= 38 and the sum of angles of the triangle =180 therefore C=180-(34+38)=108

Answer:

The answer is 55.5 sq ft per gift.

Step-by-step explanation:

1,332 square feet in all.

If there is 24 gifts then you divide 1,332 by 24.

1,332 divided by 24 is 55.5.

I hope this helps. :)

Final answer:

Regan used 55.5 square feet of wrapping paper for each gift after dividing the total square feet of wrapping paper by the number of gifts.

Explanation:

Regan wrapped 24 gifts using 1,332 square feet of wrapping paper in total. To find out how much wrapping paper she used for each gift, we need to divide the total square feet of wrapping paper by the number of gifts.

The calculation would be 1,332 sq ft ÷ 24 gifts = 55.5 sq ft per gift. Therefore, Regan used 55.5 square feet of wrapping paper for each gift.

Answer:

The equation is equal to

[tex]x^{2}=2x+8[/tex]

Step-by-step explanation:

Let

x -----> the number

we know that

The equation that represented the problem is equal to

[tex]x^{2}=2x+8[/tex]

[tex]x^{2}-2x-8=0[/tex]

Solve the quadratic equation by graphing

The solution are x=-2 and x=4

see the attached figure

therefore

The number can be -2 or 4

Answer:

Check attached graph

Step-by-step explanation:

Given equation is .

Now we need to graph the given equation .

To graph that we can find two points then join them by a straight line.

We are free to plug any number for x say x=0 and x=2

plug x=0

Hence first point is (0,-2).

plug x=2

Hence first point is (2,0).

Now graph both points and joint them to get final graph as shown below.

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Answer:

arctan(2.6) = 68.96

Step-by-step explanation:

To find the arctan of 2.6, we are going to use calculator:

Then, we have that arctan(2.6) = 68.96.

The principal value of arctan(2.6) is 1.231 radians or approximately [tex]70.43^o[/tex].

The arctan function, also known as the inverse tangent function, is the inverse of the tangent function. It is denoted as arctan(x), atan(x), or tan^(-1)(x).

The arctan function takes a real number as input and returns the angle whose tangent is equal to that number. In other words, if y = arctan(x), then tan(y) = x.

In other words, the principal value of arctan refers to the primary angle within a specific range for which the tangent function yields a given value. In the case of arctan(2.6), we are seeking the principal angle whose tangent is equal to 2.6.

We can determine the principal value of arctan(2.6) to be approximately 1.231 radians or approximately [tex]70.43^o[/tex]. It is important to note that the angle can be expressed in either radians or degrees, depending on the desired unit of measurement.

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Answer:

its will just add 25 to the total amount of money she got in the cards.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

In the right triangle with hypotenuse of 10 use the sine ratio to find x

sin20° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]

Multiply both sides by 10

10 × sin20° = x, hence

x ≈ 3.4 ( to the nearest tenth ) → B

Answer:

7

Step-by-step explanation:

2 + 5=7

The answer is 7 duhhhhhh

43785 is not divisible by 2 because it's not an even number, and this also means it's not divisible by 10 because 10 = 2*5.

The sum of its digits is 4 + 3 + 7 + 8 + 5 = 27, which is divisible by 3 since 27 = 3*9, so 43785 is divisible by 3. We have 43785 = 3*14595.

It would be divisible by 9 if 14595 were also divisible by 3. That number has digital sum 1 + 4 + 5 + 9 + 5 = 24, which is divisible by 3, so 14595 is too and 14595 = 3*4865. So 43785 = 9*4865, and it is indeed divisible by 9.

14595 is clearly divisible by 5 because its ends with a 5.

Answer:

2.635 × 10⁻⁵

Step-by-step explanation:

(3.1 × 10⁻⁴) × (8.5 × 10⁻²)

2.635 × 10⁻⁵

-TheUnknownScientist

Answer:20/24

Step-by-step explanation:

To find the fraction of members that voted yes, we need to divide the number of members that voted yes by the total number of members.
Given:
- Total number of members (two dozen): 1 dozen is 12 members, so two dozen is 2 x 12 = 24 members.
- Number of members that voted 'yes': 20 members.
Now, to find the required fraction, we perform the following division:
Fraction of members that voted yes = (Number of members that voted 'yes') / (Total number of members)
                                   = 20 / 24
This fraction can be simplified to its lowest terms by dividing both the numerator (20) and the denominator (24) by their greatest common divisor (GCD), which is 4:
Simplified fraction = (20 ÷ 4) / (24 ÷ 4)
                    = 5 / 6
Therefore, the fraction of members that voted yes is 5/6.

Answer:

2 cows and 5 chickens.

Step-by-step explanation:

NOTE: This will be solved using simultaneous equations.

Let x = cows and y = chickens

1. form two equations

4x + 2y = 18 ... (1)

x + y = 7 .... (2)

2. make y (or x) the subject of one equation

x + y = 7

y = 7 - x ... (3)

3. Substitute (3) into (1)

4x + 2( 7 - x) = 18

4. solve for x

4x + 14 - 2x = 18

2x = 4

x = 2

5. Now substitute x value into equation (2)

x + y = 7

2 + y = 7

y = 5

∴ cows (x) = 2

chickens (y) = 5

The number of cows is 2 and that of chickens are 5

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, There are 7 animals in a farmer's field. ​Some are cows and some are chickens. ​The farmer counts 18 legs in all.

This will be solved using system of equations.

Let x = cows and y = chickens

4x + 2y = 18 ... (1)

x + y = 7 .... (2)

x + y = 7

y = 7 - x ... (3)

4x + 2(7 - x) = 18

4x + 14 - 2x = 18

2x = 4

x = 2

2 + y = 7

y = 5

Hence, the number of cows are 2 and that of chickens are 5

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Answer:

x = 20

Step-by-step explanation:

When two lines intersect they form two pairs of opposite angles which are also known as vertical angles.  Vertical angles are always congruent which means that they are equal.

Angle TRS = Angle VRW

x + 40 = 3x

x - x + 40 = 3x - x

40 = 2x

40/2 = 2x/2

20 = x

(20 + 40) = 3(20)

60 = 60

Answer:

x = 20

Step-by-step explanation:

The given angles are vertical and congruent, so

3x = x + 40 ( subtract x from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

Answer:

84%.

Step-by-step explanation:

Let X be the time in minutes for a student chosen at random to finish the test.  [tex]X\sim N(40, 8^{2})[/tex].

The probability that a student chosen at random finishes the test in less than 48 minutes will represented as

[tex]P(X< 48)[/tex].

Evaluate the cumulative normal probability on a calculator, where

[tex]P(X < 48) = 0.8413[/tex].

[tex]x = 48[/tex].

[tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{48 - 40}{8} = 1[/tex].

Look up the entry that corresponds to [tex]z = 1.000[/tex] on a z-score table: 0.8413.

In other words,

[tex]P(X < 48) = P(Z < 1) = 0.8413[/tex].

The Z-score for 48 minutes is 1, corresponding to a cumulative probability of approximately 84%.

Calculating Probability for Normally Distributed Data

The time required to finish a test is normally distributed with a mean of 40 minutes and a standard deviation of 8 minutes. We need to find the probability that a student chosen at random will finish the test in less than 48 minutes.

        Z = (X - μ) / σ

where X is the value of interest (48 minutes), μ is the mean (40 minutes), and σ is the standard deviation (8 minutes). This gives us:

      Z = (48 - 40) ÷ 8 = 1

    2. Next, use the Z-score to find the probability from the standard normal distribution table. A Z-score of 1 corresponds to a probability of approximately 0.8413 or 84.13%.

Therefore, the probability that a student chosen at random will finish the test in less than 48 minutes is 84%.

Answer:

  D. The constant 250 represents the average collection when no seniors ride.

Step-by-step explanation:

A -- the entire expression represents the driver's pay, not just the constant 250.

B -- collections continue to increase as x goes up, so 250 is the minimum, not the maximum.

C -- x is the number of seniors; 250 is in units of collections (dollars?), not numbers of seniors.

D -- indeed, 250 is the "y-intercept" of the expression, hence the collection when no seniors ride.

Answer:

They would be normally distributed.

Step-by-step explanation:

Because there are more than 30 samples, the distribution would closely resemble the normal distribution.

40 ticketholders are winning the contest. 40 ≥ 30. This is enough to make the distribution approximately normal.

Based on the information given regarding the sampling distribution, the approximation would be normally distributed.

It should be noted that sampling distribution simply means a probability distribution of a statistic obtained from a larger number of samples that are drawn.

In this case, since there are more than 30 samples, the distribution would closely resemble the normal distribution. Therefore, this makes the distribution approximately normal.

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Answer:

A

Step-by-step explanation:

40ml/kg

Kg are 80 so i multiply 40×80 and I get 3200Ml, that is the amount of watet the rottwailer needs in 12 hours. But, because i need to find the amount in 1 hour i do 3200/12 and i get 266,666666 that i approximate to 267.

The flow rate per hour of the 80 Kg Rottweiler is Option(A) 267 mL/hr.

It is given that the 80 kg Rottweiler needs 40 mL/kg over 12 hours.

Therefore, the flow rate per hour can be found out just by comparing the units and dimensions of the given sample with the required sample to found out.

The flow rate per hour is -

= ( 80 kg ) * (40 mL/kg) * (1/12 hours)

= (80 * 40) / 12  mL/Hours

= 266.6667 mL/hr

≈ 267 mL/hr .

Thus, the flow rate per hour of the 80 Kg Rottweiler is Option(A) 267 mL/hr.

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50 miles per hour

80.5 km per hour

80,467 meters per hour

4,828,032 meters per minute

Hope this helps!! :)

What they said ^^^^^^^^^^^^^^^