Serena forms a random sample of 200 seventh graders from her school to learn which type of school lunch they most prefer. The results of her survey are shown below.

Food Type Chicken Nuggets Tacos Spaghetti
Number of students 87 86 27


Which is the best inference you can form based on the data? (3 points)



a
Chicken nuggets and tacos were almost liked the same amount

b
Tacos are twice as popular as spaghetti.

c
Chicken nuggets is twice as popular as spaghetti.

d
Tacos were the students' top choice

The option that applies to 2cos(x)+sqrt2=0 less than x less than 2pi is options C and D:

c.5pi/4

d.7pi/4

To solve this equation, we can start by isolating the cosine term on one side of the equation:

[tex]2cos(x) = -\sqrt{2[/tex]

[tex]cos(x) = \sqrt{\frac{2}{2} } }[/tex]

The cosine function has a range of [-1, 1], so the only possible value for cos(x) is -sqrt(2)/2. This means that the only solution to the equation is x = acos(-sqrt(2)/2).

The inverse cosine function, denoted as "arccos," gives us the angle whose cosine is a given value. In this case, we want to find the angle whose cosine is -sqrt(2)/2. The domain of the arccos function is [-1, 1], so the range of the function is [0, pi]. This means that the solution x must be an angle in the range [0, pi].

Since the problem specifies that the solution must be in the range [0, 2pi], we need to consider all possible angles in that range that satisfy the equation. This means that the possible solutions are:

[tex]x = acos(-\sqrt (2)/2) + 2\pi *k[/tex]

where k is an integer.

Substituting the values from the given choices into this equation, we find that the possible solutions are:

[tex]a. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 0 = \pi /4 + 0 = \pi /4\\b. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 1 = \pi /4 + 2\pi = 3\pi /4\\c. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 2 = \pi /4 + 4\pi = 5\pi /4\\d. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 3 = \pi /4 + 6\pi = 7\pi /4[/tex]

Therefore, the correct answer is c. and d.

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Answer:

b.3pi/4 

c.5pi/4 

Step-by-step explanation:

The mean is 1.2 ,variance is 0.96 and standard deviation of the given data is 96 square root.we can find all these data by using formula of probability.

Probability means possibility.It is a branch that deals with occurrence of random event.The value is given in the probability from 0 to 1.Probability is how likely something is to happen.It is  used in real life for analysis data.we can find probability to favorable outcomes divided by total outcomes.

Standard deviation measures how far apart numbers are in a data set.Variance gives us the actual value to how much the numbers in a data set vary from the mean.The variance is equal to the square standard deviation and standard deviation is the square root of the variance.

NOW we have data

Person(ill)=20% =0.20        n=6

For Exactly two  p(x) =2

now we get  24.58% by using binomial theorem and putting value in the formula.

NOW for at least one p(x)>1  By putting value we get 0.7379.

Now for less than three p(x<30) we get 0.9011

Now to find mean

Mean=person (ill) multiply n

Mean = 0.20 * 6

Mean= 1.2

Variance= 1.2*0.80

             =0.96

IN the last we find standard deviation.it will be 96 square root.

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According to question.

Given data,

The dilation of ABCD using centre D

And scale factor 1/3

Lebel the dilation IJKL.

With the help of figure,

The dilation of ABCD shown in the figure,

The centre of D shown in the figure,

when EFGH, IJKL are obtained from scaling factor ½,1/3 respectively,

then,

ABCD≈EFGH

and

ABCD≈IJKL

Therefore,

EFGH≈IJKL

(Quadrilaterals similar to the same quadrilateral)

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The day and time that Thereas should take her 7th dose, given that she should take the dose every 12 hours is 9 am on Thursday.

From the first day that Therease took the dose which was 9 am on Monday, the table to show the days and times she takes the other doses, based on her taking them every 12 hours is:

                                       Day                                 Time

First dose                    Monday                               9 am

Second dose              Monday                               9 pm

Third dose                  Tuesday                               9 am

Fourth dose                Tuesday                               9 pm

Fifth dose                   Wednesday                          9 am

Sixth dose                  Wednesday                          9 pm

Seventh dose               Thursday                            9 am

Therese will therefore take the seventh dose at 9 am on Thursday.

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The final score is of:

4-2 for the Blue team.

The number of ways that each score could have been obtained is of:

8.

These three bullet points are given:

The possible scores with six goals and the blue team winning are of:

If the team didn't score more than two goals in a row at any point of the game, the difference is of two, hence the score was 4 - 2.

The goals can be arranged as follows:

Then the total number is of ways that the goals could be obtained is of:

3! + 1 + 1 = 8.

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Answer:

32

Step-by-step explanation:

1536 divided by 48 is 32.

I'd say the answer is reasonable because the number is a positive number and also because each item/thing is equal to they are the same thing and nothing is too big or too small.

Alison has traveled six miles on her bike.

Distance is defined as the product of speed and time.

To find how far Alison has ridden her bike, we need to first convert 8 1/2 miles to miles as a mixed number.

We can do this by multiplying the fractional part of the mixed number by the denominator of the fraction:

8 1/2 miles = 8 miles + (1/2 x 2) miles = 8 miles + 1 mile = 9 miles

We can now multiply this distance by 2/3 to find how far Alison has ridden her bike:

9 miles x 2/3 = 6 miles

Therefore, she has ridden her bike 6 miles.

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Answer:

7.5 minutes

4/3 km

Step-by-step explanation:

Use a proportion.

2 km is to 3 min as 5 km is to x min

2/3 = 5/x

2x = 3 × 5

2x = 15

x = 7.5

Answer: 7.5 minutes

2 km is to 3 min as x km is to 2 min

2/3 = x/2

3x = 2 × 2

3x = 4

x = 4/3

Answer: 4/3 km

Therefore ,the answer of this integration problem comes out to be  4/9.

To describe notions like displacement, area, volume, and other results of the combination of incredibly small inputs, an integral in mathematics imparts numerical values to functions. Integration is a method used in the process of integral discovery.

Here,

Given :

=>  [tex]\int\limits^9_7 {\frac{14}{(x-8)^{2} } } \, dx[/tex]

=> substitute x- 8 =u

=>du/dt =d(x-8)/dx = 1

=>du/dt =1

=> [tex]\int\limits^9_7 14{\frac{1}{(x-8)^{2} } } \, dx[/tex]

Substituting x- 8 =u

=> [tex]\int\limits^9_7 14{\frac{1}{(u)^{2} } } \, dx[/tex]

=> 14 [ [tex]\left \{ {{9} \atop {7}} \right. (\frac{-1}{u} )[/tex]  ]

=> 14( -1/9) + 1/7)

=> 14   ( ( 9 -7 ) / 63 )

=> 14 (2/63)

=> 28/63

=>4/9

Therefore ,the answer of this integration problem comes out to be  4/9.

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Answer: see below

Step-by-step explanation:

x=0 -3(0)-6y=0 -6y=0 y=0

x=1 -3(1)-6y=0       -4-6y=0    -6y=4      y=4/6 or 2/3

x=2 -3(2)-6y=0      -6-6y=0      -6y=6    y=-1    

x=3 -3(3)-6y=0         -9-6y=0        -6y=9       y= -9/6   or -3/2

x=-1 -3(-1)-6y=0          3-6y=0           -6y=-3       y=1/2  

x              y

-1               1/2

0              0

1               -2/3

2              -1

3             -1 1/2

Answer:

B

Step-by-step explanation:

g(x) = 12x - 2

g(1/4) = 12(1/4) - 2  ==> plug in 1/4 for x

g(1/4) = 12 * 1/4 - 2

g(1/4) = 12/4 - 2

g(1/4) = 3 - 2

g(1/4) = 1 ==> B

Answer:

Step-by-step explanation:

To evaluate g(1) for the function g(x) = 12x - 2, you can substitute the value 1 for x in the function:

g(1) = 12(1) - 2

g(1) = 12 - 2

g(1) = 10

Therefore, g(1) = 10. B

The amount of money on the card decreases by $1.43 per week. The slope is a measure of the steepness of a line

The slope can be positive, negative, or zero. A positive slope means that the line slopes upward from left to right, which means that the value of the dependent variable (in this case, M) increases as the value of the independent variable (t) increases. A negative slope means that the line slopes downward from left to right, which means that the value of the dependent variable decreases as the value of the independent variable increases.

To find the linear equation that models the data, we need to find the slope of the line. The slope is calculated by using the formula:

slope =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]

Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points on the line. In this case, we can use week 0 and week 14 as our two points. Let's say that at week 0, M = $100 and at week 14, M = $80. Then the slope would be:

slope = ($80 - $100) / (14 - 0) = -$20 / 14 = -$1.43

So the linear equation that models the data is:

M = -$1.43 * t + $100

The missing part in the question is shown in the attachment.

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The specified number of New Year's resolutions Harry makes which is 5 more than the resolutions Tim makes, and the total number of resolutions of 13 indicates a word problem with a solution that Harry makes 9 New Year's resolutions.

A word problem is a mathematics or science question, presented using complete sentences, rather that mathematical expressions or science symbols.

A word problem consists of presenting a problem in terms of a real  situation such, with the solution being obtained easiest through the use of mathematical or science procedures.

Let x represent the number of resolutions Tim makes

The number of resolutions Harry makes = x + 5

The number of resolutions Harry and Tim made together = 13

Therefore, we get; x + x + 5 = 13

2·x + 5 = 13

2·x = 13 - 5 = 8

x = 8 ÷ 2 = 4

The number of resolutions Tim makes, x = 4

The number of resolutions Harry makes = x + 5

Therefore, the number of resolutions Harry makes = 4 + 5 = 9

Harry made 9 New Year's resolutions

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Answer:

The inequality has two prime solutions. To determine the number of prime solutions that the inequality has, we need to first solve the inequality to find its solutions. Since the inequality involves a polynomial, we can use the techniques of algebraic manipulation and factoring to solve it.

We begin by multiplying out the left-hand side of the inequality to obtain:

(n²-17)(n²-100)≤0

This expression can be further simplified by multiplying out the terms in the brackets, which gives us:

n⁴ - 117n² + 1700 ≤ 0

To solve this inequality, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting the expression equal to zero and then factoring it to obtain:

n⁴ - 117n² + 1700 = 0

n² (n² - 117) + 1700 = 0

(n² - 19)(n² - 90) + 1700 = 0

(n² - 19)(n² - 90) = -1700

To find the solutions of this equation, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting each factor equal to zero and solving for n:

n² - 19 = 0 or n² - 90 = 0

n² = 19 or n² = 90

n = ±√19 or n = ±√90

Since the problem states that n is a prime number, we need to consider only the solutions where n is a prime number. Of the solutions above, only n = ±√19 and n = ±√90 are prime numbers, so these are the only solutions that we need to consider. Since there are two such solutions, the inequality has two prime

The population of the island after 10 years will be approximately 2385.

The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0e^{(-kt)}[/tex].

Increases in a population's or a dispersed group's membership are referred to as population growth. The actual annual increase in the human population is about 83 million, or 1.1%.

Given,  an island's population grows exponentially and the continuous growth rate is 3% per year and the current population is 1,767.

∴ The population be 10 years from now will be,

[tex]y_{10} = y_0e^{(0.03)\times10}[/tex].

We have written 3% as a decimal and it is the correct way of putting it into the formula for exponential growth or decaying equations.

[tex]y_{10} = 1767e^{0.3}[/tex].

[tex]y_{10} = 1767\times1.35[/tex].

[tex]y_{10} = 2385[/tex].

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The average rate of change of g (x)=-2x³ +5x² from x=2 to x = 3 is

a(x)= -13

It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends. Following is the formula for the average rate of change:

a(x) = [f(b) - f(a)]/(b - a)

where,

a(x) = Average Rate of Change

f(a) = Function Value at a

f(b) = Function Value at b

Given,

g (x)=-2x³ +5x² from x=2 to x = 3

Average rate of change is a(x)

g (x)=-2x³ +5x²

Put x=2 in the above equation

g(2)= -2(2)³+5(2)²

= -16+20

=4

g(2)=4

Now, put x=3 in the above equation

g(3)= -2(3)³+5(3)²

= -57+45

= -9

We know that,

Average rate of change a(x)= (g(b)-g(a))/(b-a)

a(x)= g(3)-g(2)/(3-2)

a(x)= (-9-4)/1

a(x)= -13

Therefore, the average rate of change a(x)= -13

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When Haresh weighs 54 pounds on Earth, his weigh on the moon will be 9 pounds.

From the information, person's weight varies directly with gravity. If a person weighs 180 pounds on Earth, they will weigh only 30 pounds on the moon.

The constant of proportionality will be:

= 180 / 30.

= 6..

Therefore, Haresh weighs 54 pounds on Earth, his weigh on the moon will be:

= 54 / 6

= 9 pounds.

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Answer:

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Step-by-step explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40.  This means, [tex]\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}[/tex].

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

[tex]f(x)=2x+100[/tex]

This can be checked by using the values given in the problem:

[tex]f(30)=2(30)+120=180\\f(50)=2(50)+120=220[/tex]

The base rate of $120 and $2 per person satisfies the given equation and established values.

Step-by-step explanation:

correct interpretation of the mean?answer choicesA value randomly selected from the distribution of S is expected to be 4.66.In repeated sampling from the distribution of S, the average of the values will approach 4.66.For

The computation of the profitability ratios for Western Bookkeeping and Tax Service is as follows:

Profitability ratios are the financial ratios that evaluate an entity's ability to convert its earnings (revenue) into profit versus different criteria.

Some of the common profitability ratios include:

Stockholders' equity = $442,600

Total assets = $640,000

Net sales = $480,000

Net income = $36,000

Profit margin ratio = Net income/Net Sales x 100

= $36,000/$480,000 x 100

= 7.5%

= 8%

Return on equity ratio = Net income/Shareholders' Equity x 100

= $36,000/$442,600 x 100

= 8.13%

= 8%

Asset turnover ratio = Net Sales/Total Assets

= $480,000/$640,000

= 0.75

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Answer:

number is 4

Step-by-step explanation:

let n be the number then 4 times the number is 4n and

4n = n + 12 ( subtract n from both sides )

3n = 12 ( divide both sides by 3 )

n = 4

that is the number is 4

Answer:

Step-by-step explanation:

Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.

The point that divides a line segment into two equal halves is known as the midway in geometry. A point that divides a line segment into two equal halves is the midpoint of the segment. In other words, the line segment's midpoint is precisely in the middle. The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

Given,

VZ = s + 14

WY = s

VZ bisects WY

VZ = 2WY

s + 14 = 2(s)

s + 14 = 2s

2s - s = 14

s = 14

Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.

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Answer:

160 cm

Step-by-step explanation:

the question says twice this length

the length is 80 cm, therefore

[tex]80 \times 2 = 160[/tex]

This is because the question is dimply asking you to double the length of the shirt

Answer:

4x + 1.9 = 22.2

22.2 - 4x = 1.9

Step-by-step explanation:

Define the variable:

Given information:

First equation

The cost of 4 tire patches and the amount remaining on the gift card equals the total amount on the gift card:

⇒ 4x + $1.90 = $22.20

⇒ 4x + 1.9 = 22.2

Second equation

The total amount on the gift card less the cost of 4 tire patches equals the amount remaining:

⇒ $22.20 - 4x = $1.90

⇒ 22.2 - 4x = 1.9

Answer:

4x + 1.9 = 22.2

22.2 - 4x = 1.9

Step-by-step explanation:

The triangle ΔBHK and ΔBDE are congruent with each other. Then the side length ED is equal to the side length HK.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

Replace F with H.

The triangles ΔBHK and ΔBDE are shown.

In triangles ΔBHK and ΔBDE, then we have

BD ≅ BH (Given)

∠HBK = ∠DBE (Common angle)

∠BHK = ∠BDE = 90° (Right angle)

The triangle ΔBHK and ΔBDE are harmonious with one another. Then, at that point, the side length ED is equivalent to the side length HK.

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The results were as follows: a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.

Get a number that, when multiplied twice by itself, equals the original number in order to find the square root of any integer. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to get the cube root of any integer. equivalently for 4throots and so on.

We have

a)

[tex]x^{2}[/tex] = 36

so x= [tex]\sqrt{36}[/tex]

x = +6, -6

b)

[tex]x^{2}[/tex] = [tex]\sqrt{50}[/tex]

x = [tex]\sqrt[4]{50}[/tex]

x = +-2.6591

c)

[tex]x^{2}[/tex] = [tex]\sqrt{100}[/tex]

x = [tex]\sqrt[4]{100}[/tex]

x = +- 3.1622

d)

2[tex]x^{2}[/tex] = 50

[tex]x^{2}[/tex] = 50/2

[tex]x^{2}[/tex] = 25

x   =+-5

Thus a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.

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The interest earned over the 1103 day period is $840

Aaliyah will have $7840 in the account at the end of the 1103 day period.

Simple interest is defined as the amount of money that is paid to an individual following an investment that is made to an account.

The amount of money invested = $7,000.00

The rate of interest= 4%

The time of investment = 1103 = 3 years

Simple interest = P×T×R/100

= 7000×4×3/100

= 84000/100

= $840

The amount of money that is in the account at the end of the 1103 day period = 7000 + 840 = $7,840

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