Goofy's fast food center wishes to estimate the proportion of people in its city that will purchase its products. Suppose the true proportion is 0.07. If 313 are sampled, what is the probability that the sample proportion will be less than 0.04

The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.

In this problem, the events are:

Event A: Puncture.

Event B: Smashed corner.

The "or" probability is given by:

[tex]P(AUB)=P(A)+P(B)-P(A[/tex]∩[tex]B)[/tex]

5% have a​ puncture, hence [tex]P(A)=0.05[/tex]

8% have a smashed​ corner, hence [tex]P(B)=0.08[/tex]

0.4% have both a puncture and a smashed corner, hence[tex]P(AUB)=0.004[/tex]

Then:

[tex]P(AUB)=0.05+0.08-0.004= 0.126[/tex]

Therefore, The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.

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Answer:

10

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

Answer:

67%

Step-by-step explanation:

268 ÷ 400 = 0.67 = 67%

[tex]\huge\boxed{67\%}[/tex]

This can be solved just with division.

[tex]\dfrac{268\ \text{cars on the wall}}{400\ \text{total cars}}=0.67[/tex]

Multiply the result by [tex]100[/tex] to get a percentage.

[tex]0.67=\boxed{67\%}[/tex]

Answer: C

Step-by-step explanation:

When doing an indirect proof, you begin by assuming the inverse of the statement you want to prove.

The logarithm of 10 to base 10 is 1

The given parameters are:

Base = 10

Number = 10

So, the expression is:

[tex]\log_{10}10[/tex]

As a general rule;

[tex]\log_{a}a = 1[/tex]

The above means that;

When the base and the number are the same, the logarithm is 1

So, we have:

[tex]\log_{10}10 = 1[/tex]

Hence, the logarithmic value is 1

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Answer:

If you didn't graduate from High school ,Then you are not in college

Step-by-step explanation:

statement :

if you are in college, then you graduated from high school

In the given statement we have :

The Hypothesis is : you are in college

The conclusion is : you graduated from high school

in order to get the contrapositive ,

• first we switch the hypothesis and the conclusion

( H ⇒ C becomes C ⇒ H )

• Second, we negate the hypothesis and the conclusion.

Then

• first ,if you graduated from high school , then you are in college

• second , If you didn't graduate from High school ,Then you are not in college

Answer:

Area of triangle = (base x height)/2

There are all together 4 triangles and 1 square.

Therefore, surface area = area of square + 4 x area of triangle

height = 5.8 in, base = 6 in. area of square = 6x6 = 36 in^2.

area of 1 triangle = (5.8x6)/2

area of 4 triangles = 2x5.8x6 = 69.6 in^2

surface area = 69.6 + 36 = 105.6 in^2

Step-by-step explanation:

The function g(x) = x³ - 2

The function h(x) = 2x³

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

parent function = x³

As, function is shifted vertically down by 2 units to obtain g(x).

So, g(x) = x³ - 2

function h(x) Horizontally by a factor of 2, to obtain, h(x).

So,  h(x) = 2x³

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Answer:

2120 mm

Step-by-step explanation:

→ Convert 2.12 metres into centimetres

2.12 × 100 = 212 cm

→ Multiply by 10 to get into mm

212 × 10 = 2120 mm

Answer:

a = 2

Step-by-step explanation:

Given:

To find:

Steps:

a = V^1/3 = 8^1/3 = 2

Answer: the mass of a neutron is approximately 2,000 times the mass of an electron

Step-by-step explanation:

- the easiest way to solve this (in my opinion) is to simply divide the mass of a neutron by the mass of an electron

- [tex]2 x10^{-24} / (9 x10^{-28} )[/tex]

=  [tex](2/9) x10^{-24--28}[/tex]

=  [tex](2/9)x10^{-24+28}[/tex]

≈  [tex]0.2222x10^{28-24}[/tex]

≈ [tex]0.2222x10^{4}[/tex]

≈ which is approximately 2222    

- so 2222 is approximately 2000 times

- therefore, the mass of a neutron is approximately 2,000 times the mass of an electron

hope this helps :)

Answer:

C. The mass of a neutron is approximately 2,000 times the mass of an electron.

Step-by-step explanation:

Divide the mass of the neutron by the mass of the electron:

[tex]\implies \sf \dfrac{mass\:of\:neutron}{mass \: of \: electron}=\dfrac{2 \times 10^{-24}}{9 \times 10^{-28}}[/tex]

Rewrite:

[tex]\implies \sf \dfrac{2}{9} \times \dfrac{10^{-24}}{10^{-28}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \sf \dfrac{2}{9} \times 10^{-24-(-28)}[/tex]

Simplify:

[tex]\implies \sf \dfrac{2}{9} \times 10^{4}[/tex]

[tex]\implies \sf 0.\.{2} \times 10^{4} \approx 2000[/tex]

Therefore, the mass of a neutron is approximately 2,000 times the mass of an electron.

Check

[tex]\begin{aligned}\textsf{mass of neutron} & = \sf \textsf{mass of electron} \times 2000\\\implies \textsf{mass of neutron} & =\sf 9 \times 10^{-28}\times 2000\\& =\sf 9 \times 10^{-28}\times 2 \times 10^3\\& =\sf 18 \times 10^{-28+3}\\& =\sf 18 \times 10^{-25}\\& = \sf 1.8 \times 10^{-24}\\& \approx \sf 2 \times 10^{-24}\end{aligned}[/tex]

Answer:

this is a cube so it has 6 faces

Hope This Helps!!!

Answer:

4x + y = 1

Step-by-step explanation:

Start with the familiar format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

With a slope of -4, we can write:

y = -4x + b

We need to find a value for b that forces the line through point (1,-3).  This is done by entering this point in the equation and solving for b:

y = -4x + b

-3 = -4*(1) + b

b = 1

The equation is y = -4x + 1,  This can be rewritten as:

4x + y = 1

Se attached graph.

Answer:

[tex]tan(\alpha)=-\frac{\sqrt{35}}{5}[/tex]

Step-by-step explanation:

Tan can be defined as: [tex]\frac{sin(\theta)}{cos(\theta)}[/tex] as it simplifies to opposite/adjacent. If you know a bit about the unit circle, you'll know that the x-coordinate is going to be cos(theta) and the y-coordinate is going to be sin(theta). Since the sin(theta) is defined as opposite/hypotenuse, and the hypotenuse = 1, so sin(theta) is defined as the opposite side, which is the y-axis. Same thing goes for cos(theta), except the adjacent side is the x-axis.

Using this we can define tan

[tex]sin(\alpha)=-\sqrt{7}\\cos(\alpha)=\sqrt{5}\\\\tan(\alpha)=-\frac{\sqrt{7}}{\sqrt{5}} * \frac{\sqrt{5}}{\sqrt{5}}\\tan(\alpha)=-\frac{\sqrt{7*5}}{5}\\tan(\alpha)=-\frac{\sqrt{35}}{5}\\[/tex]

Answer:

tan α = -√35/5

Step-by-step explanation:

tan α = y/x

tan α = -√7/√5

tan α = -√7/√5 × √5/√5

tan α = -√35/5

The number of blue marbles in the bag is 18.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of choosing a green marble = total number of green marbles / total number of marbles

0.55 = 22/x

x = 22 / 0.55

x = 40

Total number of blue marbles = 40 - 22 = 18

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Answer: 8.6

Step-by-step explanation:

[tex]19.6=2\pi r\left(\frac{130}{360} \right)\\\\r=\frac{19.6}{2\pi \left(\frac{130}{360} \right)}\\\\r \approx 8.6[/tex]

Considering the given information in the question, the value of x is [tex]12^{o}[/tex], and that of y is [tex]7.5^{o}[/tex].

A transversal is a line that cuts through two given parallel lines. Thus it intersects each parallel line at a point, forming four angles each.

From the given information in the question, it can be inferred that:

the given bottom right angle of the first intersection and the bottom right angle with the second intersection are congruent (corresponding angle property).

So that,

[tex](5x+4y)^{o}[/tex] = [tex](12y)^{o}[/tex]

[tex]5x^{o}[/tex] = [tex]12y^{o}[/tex] - [tex]4y^{o}[/tex]

[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]............ 1

Also given that the top right angle at the second intersection is a right angle, then;

    [tex]12y^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles on a straight line)

This implies that;

    [tex]12y^{o}[/tex] = [tex]180^{o}[/tex] -    [tex]90^{o}[/tex]

       [tex]12y^{o}[/tex]  =     [tex]90^{o}[/tex]

So that,

y = [tex]\frac{90}{12}[/tex]

y = [tex]7.5^{o}[/tex]

Thus substituting the value of y in equation 1, we have;

[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]........ 1

     = 8(7.5)

5x = 60

x = [tex]\frac{60}{5}[/tex]

x = [tex]12^{o}[/tex]

Therefore, x = [tex]12^{o}[/tex] and y = [tex]7.5^{o}[/tex]

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Kindly contact a 1-on-1 tutor if more explanations are needed.

Answer:

33in

Step-by-step explanation:

The probability of drawing two 10's is P = 1/221, so the correct option is D.

We know that in the deck of 52 cards, we have 4 10's.

Then, the probability of drawing the first 10 is:

p = 4/52.

At this point, we have 3 10's in the deck, and a total of 51 cards (because we already took one 10).

The probability of getting another is:

q = 3/51

The joint probability (of getting both 10's, one after the other) is given by the product of the individual probabilities:

P = p*q = (4/52)*(3/51) = (1/13)*(1/17) = 1/221

Then the correct option is D.

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The correct rows in the inequalities are

The rows are given as:

-3x - 4 < x + 4  ⇒ -3x < x

2(x - 5) + 1 ≤ 5  ⇒ 2(x - 5) ≤ 4

-4x ≥ -24  ⇒ x ≤ 6

x = 2y and 2x + 2y > 60  ⇒ 6y > 60

y + 2 ≤ 4 - x and 4 - x ≤ 3y  ⇒ y + 2 ≤ 3y

To determine the correct rows, we simply solve each inequality.

This is done as follows:

-3x - 4 < x + 4

Collect like terms

-3x - x < 4 + 4

Evaluate the like terms

-4x < 8

Divide by -4

x > -2

This means that:

-3x - 4 < x + 4  ⇒ -3x < x is false.

2(x - 5) + 1 ≤ 5  

Subtract 1 from both sides

2(x - 5) ≤ 4

This means that:

2(x - 5) + 1 ≤ 5   ⇒ 2(x - 5) ≤ 4 is true.

-4x ≥ -24  

Divide through by -4

x ≤ 6

This means that:

-4x ≥ -24  ⇒ x ≤ 6 is true.

x = 2y and 2x + 2y > 60

Substitute 2y or x in 2x + 2y > 60

2(2y) + 2y > 60

Evaluate the product

4y + 2y > 60

Evaluate the like terms

6y > 60

This means that:

x = 2y and 2x + 2y > 60  ⇒ 6y > 60 is true.

y + 2 ≤ 4 - x and 4 - x ≤ 3y

We have:

y + 2 ≤ 4 - x and 4 - x ≤ 3y

This can be rewritten as:

y + 2 ≤ 3y

This means that:

y + 2 ≤ 4 - x and 4 - x ≤ 3y  ⇒ y + 2 ≤ 3y is true

Hence, the correct rows are 2, 3, 4 and 5

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Answer:

[tex]x \leqslant - 21[/tex]

Step-by-step explanation:

[tex]5(x + 27) \geqslant 6(x + 26)[/tex][tex]5x + 135 \geqslant 6x + 156[/tex]

[tex] - 21 \geqslant x[/tex]

[tex]x \leqslant - 21[/tex]

Answer:

332519000 in scientific notation is 3.32519 x 10^8

Step-by-step explanation:

Hope that helped

Answer:

The form is a * 10ᵇ where 0 < a < 10

The numbers of passengers that need to be booked to ensure the cruise line makes a profit, using a compound inequality is x ≥ 2,052 and x ≤ 2,462.

From the information given, we are told that the cruise ship needs to book at least 2,052 passengers to be profitable, but the most passengers the ship can accommodate is 2,462.

Learn x be the number of people that can be accommodated. Therefore, the model is x ≥ 2,052 and x ≤ 2,462.

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Chef should prepare 4 cakes and 5 batches of pastry in order to achieve maximum profits and his maximum profit or revenue by solving through inequality is $260.

Given Chef uses 5 cups of cake batter for 1 cake and 4 cups of batter for 1 batch of cupcakes. Chef wants to make at least 4 cakes. Profit on 1 cake is $35 and $30 for 1 batch of cupcake.

let the number of cakes be x and the number of batches of cupcakes be y such that

5x+4y<=40--------1

x>=4---------------2

Maximize Profit=35x+30y

Inequalities contains different signs so we have to change one inequality.

5x+4y<=40

-x<=-4

Now assume them equalities

5x+4y=40-------3

-x=-4

multiply second equations by 5

-5x=-20-----------4

now  add 3 and 4

5x+4y-5x=40-20

4y=20

y=5

now put the value of y in 5x+4y=40

5x+4*5=40

5x+20=40

5x=20

x=4.

Maximum Profit=35x+30y

=35*4+30*5

=$260

Hence chef should make 4 cakes and 5 batches of pastry and maximum profit of $260.

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The value of c is 3

The complete question is in the attached image

The function definition is given as:

g(x) = f(x) - c

From the graph of functions f(x) and g(x), we can see that:

f(x) is shifted down by 3 units to get to g(x)

This means that:

g(x) = f(x) - 3

By comparing g(x) = f(x) - 3 and g(x) = f(x) - c,

We have:

c = 3

Hence, the value of c is 3

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Answer:

12

Step-by-step explanation:

16/4=4

4+8=12

Answer:

Horizontal line with y-intercept at (0,0)

Step-by-step explanation:

y - 9 = -9

Adding 9 to both sides:

y = 0

So it is the x axis.

Answer: B. 150°

Step-by-step explanation:

The angle is obviously obtuse and is therefore greater than 90°.

This rules out A. and C.

Also, this angle is not 180° because then it would be flat.

This rules out D.

Leaving the correct answer to be B. 150°

Answer:

-8 ≤ x ≤ -1

Step-by-step explanation:

When working with inequalities, closed circles always represent greater than or equal to and less than or equal to signs.  

The x is placed between the -8 and the -1, as it represents all numbers greater than -8 and less than -1

Answer: -8 ≤ x ≤ -1

Step-by-step explanation: :p