Solve for x assume that lines which appear to be diameters are actual diameters

The quantity of pasta is served to Olivia is 60 in³.

Olivia's mother packed her lunch in a lunch box which is in the shape of rectangular prism, with dimension = length= 5 in, width= 4 in, height= 3 in,

We need to find the quantity of the lunched packed in the box,

So, we will find the volume of the box = length × width × height

= 5 × 4 × 3

= 60 in³

Hence the quantity of pasta is served to Olivia is 60 in³.

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The conclusion is there is not a significant difference between the preference for the three food containers.

The appropriate statistic to use in this case is a chi-squared test. This test will help us determine if there is a significant difference between the preference of the three food containers.

The critical value for the chi-squared test with 2 degrees of freedom is 5.991.

The chi-squared statistic is calculated as follows:

(74-103)²/103 + (103-123)²/123 + (123-103)²/103

= 3.9/3.9

= 1.0

The chi-squared statistic (1.0) is less than the critical value (5.991). Therefore, there is not a significant difference between the preference for the three food containers.

The statistical results can be presented in the following form:

Chi-squared statistic = 1.0

Critical value = 5.991

Therefore, the conclusion is there is not a significant difference between the preference for the three food containers.

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The value of variable θ would be,

⇒  θ = 5π/3 and θ = 4π/3

We have to given that;

Expression is,

⇒ - 10sin θ - 8 = 5√3 - 8

Now, We can simplify as;

⇒ - 10sin θ - 8 = 5√3 - 8

⇒ - 10sin θ = 5√3

⇒ sin θ = - 5√3/10

⇒ sin θ = - √3/2

We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).

However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.

Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.

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Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

If the question is asking you to add the two fraction you would need to follow these steps:

Step 1: find a common denominator (both of the number 20 in common

Step 2: add the numerators ( 7/20 + 1/20 would = 8/20 )

Step 3 simply the fraction ( 8/20 will be simplyed to 2/5)

Answer:

33/20

Step-by-step explanation:

First find the Least common denominator

Then you check how many times each denominator goes into de Least common denominator

After multiply the number you got when you checked for the times the denominator will go into the LCM with the numerator then simplify

Answer:

x = - [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

consider the right triangle formed by the x- axis, the y- coordinate of the given point and the radius of the circle 1 , to the point from the centre.

using Pythagoras' identity

x² + ( [tex]\frac{4}{5}[/tex] )² = 1²

x² + [tex]\frac{16}{25}[/tex] = 1 ( subtract [tex]\frac{16}{25}[/tex] from both sides )

x² = 1 - [tex]\frac{16}{25}[/tex] = [tex]\frac{9}{25}[/tex] ( take square root of both sides )

x² = ± [tex]\sqrt{\frac{9}{25} }[/tex] = ± [tex]\frac{\sqrt{9} }{\sqrt{25} }[/tex] = ± [tex]\frac{3}{5}[/tex]

since the given point is in the second quadrant , then

x = - [tex]\frac{3}{5}[/tex]

Answer: G=36

Step-by-step explanation:

Step 1: Write out the equation
1/4g-3=6

Step 2: Add 3 to both sides
1/4g=9

Step 3: Divide both sides by 1/4, or 0.25
G=36

In this example of heart attack, it would be appropriate to calculate Conditional row percentages. Therefore, the correct option is option A.

When the blood supply for the heart is significantly impeded or blocked, a heart attack happens. The accumulation of fat, cholesterol, and other chemicals in the heart's (coronary) arteries is typically what causes the obstruction. Plaques are the name given to the fatty, cholesterol-containing deposits.

Atherosclerosis is the name for the phenomenon of plaque accumulation. A plaque may occasionally burst and generate a clot that restricts blood flow. A portion for the heart muscle can be harmed or destroyed by a shortage of blood flow. In this example, it would be appropriate to calculate Conditional row percentages.

Therefore, the correct option is option A.

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Your question is incomplete but most probably your full question was,

Answer:

The graph of the function appears to be a cosine function that has been shifted to the left by π/2 units, and has an amplitude of 4.

Option (a) is a cosine function that has been shifted to the left by π units, but does not have the amplitude of 4.

Option (b) is a cosine function that has a period of π/2, which is much shorter than the period of the graph.

Option (c) is a sine function that has been shifted to the right by π units, but does not have the amplitude of 4.

Option (d) is a cosine function that has been shifted to the left by π units and has the correct amplitude of 4.

Option (e) is not a cosine or sine function, so it cannot be the correct answer.

Therefore, the function represented by the graph is:

f(x) = -4 cos(x + π)

which is Option (d).

Step-by-step explanation:

In a case wherby new bicycle sells for $300 It is on sale for 1/4 off the regular price all the expressions that represent the sale price of the bicycle in dollars are

From the option B)300•3/4, we cam see that (300*3)/4 = 225

From the option C)300•(1-1/4),   (300*3)/4 = 225

From the E.)300 - 1/4•300, 300 - 75 = 225

Therefore, the correct options are the option BCE as listd below because they are seen as the one that gives the  regular price all the expressions hence they are correct.

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The pressure of 1000 Pa is equal to 0.145 pound per square inche(PSI)

Let the pressure be 1000 pascal

We have to convert it to pound per square inche

1 psi = 6896.6 Pa

Therefore, to convert 1000 Pa to psi, we can divide by this conversion factor:

1000 Pa ÷ 6896.6 Pa/psi

= 0.145 psi

Hence, the pressure of 1000 Pa is equal to 0.145 psi.

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The slope of the polar curve at θ = π/4 is 24. Therefore, option D is correct.

To find the slope of the polar curve r = 6cos(2θ) - 5 at θ = π/4, we need to find the derivative of r with respect to θ, and then substitute θ = π/4 into the resulting expression.

Using the chain rule of differentiation, we have:

dr/dθ = dr/d(cos(2θ)) * d(cos(2θ))/dθ

To find the first derivative, we can use the power rule of differentiation:

dr/d(cos(2θ)) = -12sin(2θ)

To find the second derivative, we can use the chain rule again:

d(cos(2θ))/dθ = -2sin(2θ)

Substituting these into the expression for dr/dθ, we get:

dr/dθ = -12sin(2θ) * (-2sin(2θ)) = 24sin^2(2θ)

Now, substituting θ = π/4, we get:

dr/dθ|θ=π/4 = 24sin^2(π/2) = 24

The slope of the polar curve at θ = π/4 is therefore 24.

None of the given options match this result.

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The probability of at least 8 homes would prefer brand B compare to compare A is given by 0.672.

Sample size 'n'= 25

Proportion of people prefer brand A = 0.4

This implies ,

Proportion of people prefer brand B 'p' = 1 - 0.4

                                                                  = 0.6

Using the binomial distribution.

Let X be the number of homes that prefer brand B out of the 25 homes surveyed.

Then X follows a binomial distribution with parameters n = 25 and p = 0.6

Probability that at least 8 homes would state a preference for brand B. expressed as,

P(X ≥ 8) = 1 - P(X < 8)

Using the binomial distribution, compute P(X < 8) as follows,

P(X < 8) = Σ [²⁵Cₓ] × 0.6ˣ × 0.4²⁵⁻ˣ, for x = 0, 1, 2, ..., 7

where ²⁵Cₓ is the binomial coefficient which represents the number of ways to choose k homes out of 25.

Use a binomial calculator ,

⇒P(X < 8) = [²⁵C₀] × 0.6⁰× 0.4²⁵⁻⁰ + [²⁵C₁] × 0.6¹× 0.4²⁵⁻¹ + [²⁵C₂] × 0.6²× 0.4²⁵⁻² + .......+ [²⁵C₇] × 0.6⁷× 0.4²⁵⁻⁷  

⇒P(X < 8) ≈ 0.328

This implies,

P(X ≥ 8) = 1 - P(X < 8)

             ≈ 1 - 0.328

             = 0.672

Therefore,  the probability that at least 8 homes would state a preference for brand B is approximately 0.672.

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The above question is incomplete , the complete question is:

A manufacturer of floor wax has developed two new brands, A and B.  which she wishes to subject to homeowners' evaluation to determine which of the two is superior. Both waxes are applied to the floor surfaces in each of a sample of 25 homes. It is known that the proportion of people that prefer A is 0.4 while the rest prefer brand B.

Find the probability that at least 8 homes would state a preference for brand B.

Answer:

V = π(19.1^2)(11.8) = 13,523.8 cubic mm

V = 3.14(1.91^2)(11.8) = 13,516.9 cubic mm

The value of length BD is 3.0 units

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

since AC is a radius that joins a tangent, the angle between them is 90°. Therefore ∆ABC is a right triangle and Pythagoras theorem can be applied.

therefore c² = a²+b²

c² = 4.5²+6²

c²= 20.25+36

c²= 56.25

c = √7.5

AC = CD(radii of a circle)

therefore BD = BC -CD

= 7.5-4.5

= 3.0units

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The given statement, "Signed numbers are also called directed numbers" is true.

Signed numbers are numbers that can be positive, negative, or zero, and they are sometimes referred to as directed numbers because they have a direction or orientation on the number line. Positive numbers are usually associated with movements to the right on the number line, while negative numbers are associated with movements to the left.

Therefore, the given statement, "Signed numbers are also called directed numbers" is true.

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The IQR of the data set is 4.

First, let's arrange the data set in order from smallest to largest:

1, 2, 3, 5, 6, 6, 6, 7, 9

Next, let's find the median (Q2) of the data set. Since there are an odd number of values in the data set, the median is the middle value:

Q2 = 6

Now, let's find the median (Q1) of the lower half of the data set. This includes the values from the minimum (1) up to (but not including) the median (6). There are four values in this lower half, so the median is the average of the two middle values:

Q1 = (2 + 3) / 2 = 2.5

Finally, let's find the median (Q3) of the upper half of the data set. This includes the values from the median (6) up to (and including) the maximum (9). There are also four values in this upper half, so the median is the average of the two middle values:

Q3 = (7 + 6) / 2 = 6.5

Now that we have Q1, Q2, and Q3, we can calculate the IQR as:

IQR = Q3 - Q1

IQR = 6.5 - 2.5

IQR = 4

Therefore, the IQR of the given data set is 5.5.

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The discriminant value is 120 and 2 is the  x - intercept will have the graph of f.

The intercept of a line is the point on a graph where the line crosses an axis. There can be both x and y intercepts on a graph. The x-axis is the horizontal line on the graph, therefore the x-intercept can also be referred to as the horizontal intercept. This is the point where the line crosses the x-axis. At this point, the value of y is zero. The y-axis is the vertical axis on a graph. The y-intercept is the point where the line crosses the y-axis and x has a value of zero.

The function, we have:

[tex]f(x) = -7x^2 + 8x + 2[/tex]

We have to find the value of the discriminant of f and how many x- intercepts of the graph?

Firstly, We have to find the value of discriminant is

[tex]b^2 -4ac[/tex]

[tex]where ,ax^2 +bx+c[/tex]

a= -7,  b = 8, c=2

The discriminant is:

= [tex]8^2 - 4(-7) (2)[/tex]

= 64 +56

= 120

This will have 2 real x intercepts because 120 > 0

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The calculated value of the prime fractorization of the number 130 is 2 * 3 * 5

From the question, we have the following parameters that can be used in our computation:

Number = 130

When the above number is expanded, we have

Number = 2 * 5 * 13

The above product of numbers cannot be further simplified

This means that 2 * 5 * 13 is the prime fractorization of the number 130

Hence, the prime fractorization of the number 130 is 2 * 3 * 5

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Answer:

Step-by-step explanation:

29 ft

7  in

The city with a population of 500,000 would produce 305,000 tons of pollutants.

We have,

Let's call the unknown amount of pollutants in the second city "x".

According to the problem,

The amount of pollution is directly proportional to the number of people. This means that we can set up a proportion:

Pollution/number of people

= pollution/number of people

Using the values we know:

= 21350/35000

= x/500000

Simplifying:

0.61 = x/500000

To solve for x, we can cross-multiply:

0.61 x 500000 = x

x = 305000

Therefore,

The city with a population of 500,000 would produce 305,000 tons of pollutants.

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Using the translation vector of 3 units up and 1 unit right resulted to image coordinate of

(3, 7)

(3, 5)

(2, 5)

The image is attached

The translation vector is of the rule 3 units up and 1 unit to the right

The coordinate of the preimage are

(2, 4)

(2, 2)

(1, 2)

The translation is done as below

(2 + 1, 4 + 3) = (3, 7)

(2 + 1, 2 + 3) = (3, 5)

(1 + 1, 2 + 3) = (2, 5)

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The length of the intercepted arc is 4π unit.

We have,

Angle = 2π/3 = 2(180)/ 3 = 120 degree

r = 6 unit

So, length of Arc

= θ /360 x 2πr

= 120/360 2 π(6)

= 1/3 (12)π

= 4π unit

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Answer:

(2,0)

Step-by-step explanation:

Using synthetic division, the value at w(-3) of the expression w(x)=11x³ -6x² +2 is -349

Synthetic substitution is a mathematical method that is used for evaluating the algebra polynomial in the simpler process.

To determine the value of the polynomial at w = -3, we need to carry out the synthetic division.

Then, the value of the remainder is taken as the value of the expression at the particular value

We have the expression as;

w(x)=11x³ -6x² +2/x-3

Let's carry out the synthetic division

Then, this is represented as;

-3)  11     -6      0      2

             -33    -117   -351

     11     -39    -117   -349

The value is -349

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Answer:174

Step-by-step explanation:

209-22=187

361-22=174

The relationships between the figures is a dilation of 3.5 from the small triangle to the big triangle

From the question, we have the following parameters that can be used in our computation:

The two triangles

From the figure, we can see that

These mean that the triangles are related by dilation

The constant of dilation is then calculated as

k = (7, 7)/(2, 2)

Evaluate

k = 3.5

Hence, the scale factor is 3.5

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Answer:

26,225.3 = 3.14(12^2)h + (2/3)(3.14)(12^3)

26,225.3 = 452.16h + 3,617.28

452.16h = 22608.02

h = 50 feet

26,225.3 = π(12^2)h + (2/3)π(12^3)

26,225.3 = 144πh + 1,152π

144πh = 26,225.3 - 1,152π

h = (26,225.3 - 1,152π)/(144π)

h = 49.97 feet = 50 feet

The surface area of the figure = 2733.3 sq. in.

First we fine the surface area of the top surface of the figure.

The top surface is an rectangle with length = 19 in. and width = 17 in

Using the formula for the area of rectangle, the area of top face would be,

A₁ = 19 × 17

A₁ = 323 sq. in.

The slant face of the figure is a rectangle with  length = 22 in. and width = 17 in

Using the formula for the area of rectangle, the area of slant surface of the figure would be,

A₂ = 22 × 17

A₂ = 374 sq. in.

There are two parallel trapezoidal surface of the figure with bases 35 in. and 19 in. respectively.

The height of the trapezoid = 20.3 in.

Using the formula for that area of trapezoid, the area of two trapezoidal surface of the figure would be,

A₃ = 2 × (sum of lengths two bases/2) × height

A₃ = 2 × (35 + 19/2) × 20.3

A₃ = 1096.2 sq. in.

The area of the bottom surface would be,

A₄ = 35 × 17

A₄ = 595 sq. in.

The area of right surface would be,

A₅ = 20.3 × 17

A₅ = 345.1 sq. in.

So, the total surface area would be,

A = A₁ + A₂ + A₃ + A₄ + A₅

A = 323 + 374 +  1096.2 +  595 + 345.1

A = 2733.3 sq. in.

Therefore, the surface area of the figure = 2733.3 sq. in.

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