Write the equation of the line.

The 90% confidence interval is (0.544, 0.612).

a) Find the best point estimate of the population proportion p.Point estimate of the population proportion p is given by the formula: $$\hat p = \frac{x}{n}$$Where n = 979 and x = 566$$\hat p = \frac{x}{n}$$$$\hat p = \frac{566}{979}$$$$\hat p = 0.578$$Therefore, the best point estimate of the population proportion p is 0.578. b) Identify the value of the margin of error E. Margin of error E can be calculated using the following formula: $$E=z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$Given that the confidence level is 90%, the corresponding z-score can be calculated from the table of z-scores.$$z^*=1.65$$Where n = 979, $\hat p = 0.578$.$$E=z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$Substituting the values,$$E=1.65*\sqrt{\frac{0.578(1-0.578)}{979}}$$$$E=0.034$$Therefore, the value of the margin of error E is 0.034. c) Construct the confidence interval.

Confidence interval for a population proportion p can be calculated as follows:$$\left(\hat p - E,\; \hat p + E\right)$$Substituting the values,$$\left(0.578 - 0.034,\; 0.578 + 0.034\right)$$$$\left(0.544,\; 0.612\right)$$Therefore, the 90% confidence interval is (0.544, 0.612).

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The symbolic forms for the given statements are: (b) p ∨ r, (c) p ∧ q, (d) q ~ r, and (e) p ∨ q. Statement (a) cannot be expressed symbolically.

(a) x ≥ 5: This statement represents a numerical inequality, and it cannot be expressed symbolically.

(b) p ∨ r: The symbolic form for the statement "p ∨ r" is a logical disjunction, meaning it represents the logical "OR" operation between the propositions p and r.

(c) p ∧ q: The symbolic form for the statement "p ∧ q" is a logical conjunction, indicating the logical "AND" operation between the propositions p and q.

(d) q ~ r: The symbolic form for the statement "q ~ r" is a negation, where the proposition r is negated, represented by the symbol "~".

(e) p ∨ q: The symbolic form for the statement "p ∨ q" is a logical disjunction, indicating the logical "OR" operation between the propositions p and q.

In logic, different symbols are used to represent various logical operations and relationships between propositions. The statements provided have different symbolic forms based on the logical operations they represent.

The "∨" symbol represents logical disjunction (OR), "∧" symbol represents logical conjunction (AND), and "~" symbol represents negation. It is important to understand the symbolic forms to accurately represent and analyze logical statements.

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Answer:

$365.93

$368.26

Step-by-step explanation:

The true balance :

Statement balance - outstanding cheques

Statement balance = 414.25

Outstanding cheques = 26.54 and 21.76

414.25−26.54−21.78 = 365.93

Adjusted Chequebook balance

Chequebioknvakance will en adjyat d for service charge :

Chequebook balance - service charge

$374.16 - $5.90 = $368.26

The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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The radius will be equal to 7.55 centimeters.

The arc length is the curved length on the circumference of a circle suspended by a small angle.

The radius will be calculated as follows:-

r = \(\dfrac{Arc}{Angle}\)

r = \(\dfrac{\dfrac{26\pi}{9}}{\dfrac{69\times \pi}{180}}\)

r = \(\dfrac{9.07}{1.20}\)

r = 7.55 centimeters

Therefore the radius will be equal to 7.55 centimeters.

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The answer choice which is incorrect about the "rating of perceived exertion (RPE)" is; The rating applies to the feeling of your whole body.

Rate of perceived exertion (RPE) is simply a measure of the level of exertion a person feels during physical activity. This measure is a useful tool that helps people manage the intensity of their physical exercise.

The Borg Rating of Perceived Exertion Scale is used when reporting RPE.

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Answer:

f^-1 (x)=sqrt(x/3), -sqrt(x/3).

Step-by-step explanation:

f(x)=3x^2

y=3x^2

x=3y^2

y^2=x/3

y=sqrt(x/3), -sqrt(x/3).

Answer:

\(y=3x^2\)

\(y=3x^2\)

Step-by-step explanation:

There is no step-by-step explanation because it's a graph. Well, it's how I did it. Therefore, the graph in the picture that I'm about to post will be your answer.

Answer:

all you need to do is to put the fraction into simplest form

Step-by-step explanation:

6/9=2/3

8/14=4/7

2/3=2/3

8/21=8/21

Answer:

-3

Step-by-step explanation:

So just like the picture provides, the slope can be defined as: \(\frac{\text{change in y}}{\text{change in x}}\). So this means we can take any two points and find the change in x and y to define the slope, since the slope is constant throughout the entire line, since it's a linear line, meaning it's straight.

So you can use the points (0, 15) and (2, 9). So let's look at the x-values, and you want to make sure, you maintain the order at which you look at the  "change in x", for example I can define the change in x through the two points as 0 to 2, or 2 to 0, one case is 2, and the other is -2, but if I look at the change from 0 to 2, then I looked at the first point first then the second, this means when looking at the y-values I have to find the change from 15 to 9, and not 9 to 15, since I did 0 to 2 in the first case. I could look at the change from 9 to 15, but only if I looked at the changed from 2 to 0.

Anyways let's find the change from 0 to 2, it's 2. Now let's look at the change from 15 to 9, it's -6 (since the value went down). So this gives us equation: -6 / 2 = -3

The slope is -3

Answer: 0.2743

Step-by-step explanation:

Let X be a random variable that represents the weight of bags of grasecks chocolate candoes.

X that follows normal distribution with, Mean = 4.3 ounces, Standard devaition = 0.05 ounces

The probability that a bag of these chocolate candies weighs less than 4.27 ounces :\(P(X<4.27) =P(\dfrac{x-\mu}{\sigma}<\dfrac{4.27-4.3}{0.05})\)

\(=P(z<-0.6)\ \ \ z=\dfrac{x-\mu}{\sigma}]\\\\=1-P(Z<0.6)\\\\=1-0.7257\ [\text{ By p-value table}]\\\\=0.2743\)

Hence, the required probability = 0.2743

The probability that a bag of these chocolate candies weighs less than 4.27 ounces is 0.2743

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Let X be a random variable that represents the weight of bags of grasses chocolate candies.

X that follows normal distribution with, Mean = 4.3 ounces, Standard devaition = 0.05 ounces

The probability that a bag of these chocolate candies weighs less than 4.27 ounces :

\(P(x < 4.27)=P[\dfrac{x-\mu}{\sigma} < \dfrac{4.27-4.3}{0.05}\)

P ( x < 4.27 )   =   P (  z < -0.6  )

P (  x < 4.27  )  =  1  -  P (  z < -0.6 )

P ( x < 4.27 )   =   1  -  0.7257

P ( x < 4.27 )   =  0.2743

Hence,the probability that a bag of these chocolate candies weighs less than 4.27 ounces is 0.2743

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The Possible Energy Collected in kJ is 30,999 kJ.

The first step in solving this problem is to determine the area of the oven. To do this, we need to multiply the length (53.2 cm) by the width (44.5 cm). This gives a result of 2359.4 cm².

Next, we can calculate the energy collected in kJ. To do this, we need to multiply the power (1120.3 W/m²) by the area of the oven (2359.4 cm²) and then by the time (71.9 min) and then divide by 1000 to convert into kilojoules (kJ). This gives the following equation:

Energy collected (kJ) = (1120.3 W/m² × 2359.4 cm² × 71.9 min) / 1000

Substituting in the values, this gives a result of 30,999 kJ of energy collected.

Therefore, the Possible Energy Collected in kJ is 30,999 kJ.

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Answer:

1.) 27a^11 + 18a^9 -72a^7

2.) 6p^4q^3 - 10p^3q + 4p^2q3

Step-by-step explanation:

1.) Distribute and do the math

-9a^5 x (-3a^6) - 9a^5 X (-2a^4) - 9a^5 x 8a^2

27a^11 + 18a^9 -72a^7

2.)  Distribute and do the math

2pq^2q x 3p^2q^2 - sp^2q x 5p + 2p^2q x 2q^2

6p^4q^3 - 10p^3q + 4p^2q3

The percent markup of a department, if they sell 300 shirts at a cost of $9 each is 50%

According to the question, we learn that a department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. This means :

The selling price of 300 shirts = 300 × $9

The selling price of 300 shirts = $2700

Selling price > cost price i.e., 2700 > 1800

when selling price is greater than cost price it means department store made a profit.

Profit = selling price - cost price

Profit = 2700 - 1800 = $900

Profit percentage = profit/ cost price × 100

Profit % =\(\frac{900}{1800} \times 100\)

Profit % = 50%

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Answer:

It should be something like that :

Answer:

So we need to know the entire pans size, 1/3 goes in 3 times, so if he cuts 1/3 into 3 he gets 1/9 per slice of lasagna, so he will eat 1/9 of the pan each night

plz mark brainliest!

Step-by-step explanation:

h (-2) = (-2)^2 + 1 = 5

f (-2) = 2(-2) - 1 = -5

5 - (-5) = 10.

Step-by-step explanation:

now, let's turn the triangle, so that the angle (60°) is at the bottom left vertex, and the 90° angle is at the bottom right vertex.

now we see the trigonometric triangle again that we have to imagine to be inscribed into a circle, with the 60° angle being at the center of that circle.

8×sqrt(6) is then the radius of that circle.

x is sin(60)×radius

y is cos(60)×radius

sin(60) = sqrt(3)/2

cos(60) = 1/2 = 0.5

x = 8×sqrt(6)×sqrt(3)/2 = 4×sqrt(6)×sqrt(3) = 4×sqrt(18)

y = 8×sqrt(6)/2 = 4×sqrt(6)

In the below diagram, X represents the position of the University, H represents the Hospital, and S represents the Stadium. The line connecting H and S is the baseline for the bearings.

First, draw a map with the Stadium and the Hospital marked, and draw a line connecting them.

Then, from the Stadium, draw a line at a bearing of 070°. From the Hospital, draw a line at a bearing of 280°.

The University is located at the intersection of these two lines, which is where we should place the cross.

Bearings are usually measured in degrees clockwise from North, so 070° is almost due East, while 280° is slightly North of West. We can use a protractor or a compass to measure and draw these angles accurately.

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Answer:kepler's 3rd law

Step-by-step explanation:

Answer:

V = 28 m³

Step-by-step explanation:

V = (1/3)Bh

V = (1/3)(4 m²)(21 m)

V = 28 m³

You can use the power rule for derivatives for each problem (though you could also use the product rule for the fourth curve).

y = x ² + 6x - 1   ==>   dy/dx = 2x + 6

y = x ² - 5x + 1   ==>   dy/dx = 2x - 5

y = 2 - 4x - x ²   ==>   dy/dx = -4 - 2x

y = (1 + x) (7 - x) = 7 + 6x - x ²   ==>   dy/dx = 6 - 2x

--

or, using the product rule,

dy/dx = (1 + x) (-1) + 1 (7 - x) = -1 - x + 7 - x = 6 - 2x

--

Now, stationary points occur where the derivative is zero. We have

2x + 6 = 0   ==>   x = -3

2x - 5 = 0   ==>   x = 5/2

-4 - 2x = 0   ==>   x = -2

6 - 2x = 0   ==>   x = 3

Answer:

Step-by-step explanation:

Cost = Area Cylinder body* cost * 0.03 cm^3 + Area of 2 lids*cost 0.06 of cm^3

Volume = 300 cm^3

Volume = Base *h  

Volume = pi * r^2 * h = 300

h = 300/(pi * r^2 )

Area material =  2*pi * r * h * 0.03 + 2 pi r^2 * 0.06

Area material = 0.06*pi * r * 300/(pi* r^2) + 0.12 * pi * r^2

dmaterial/dr = (-1)18 r^-2 + 0.12 pi * 2*r

dmaterial/dr = -18 r^-2 + 0.24 pi * r

The minimum occurs when the right side = 0

18/r^2 = 0.24 *pi r

18 = 0.24*pi * r^3

18/(0.24 * pi) = r^3

23.89 = r^3

cube root (23.89) = cuberoot(r^3)

r = 2.88 cm

h = 300/pi * r^2

h = 300/(3.14 * 2.88^2)

h = 11.52

This isn't much of a check but we can try it.

Volume = 3.14 * 2.88^2 * 11.52

Volume = 302.01 which considering all the rounding is pretty close.

Here's a graph that confirms my answer.

Answer: #4

Step-by-step explanation:

I haven't done anything like this in years but I think it is the 4th answer :)

Sorry if I'm wrong. I am a year ahead in math and in an honors class so i would think I'm pretty smart

The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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Answer:

x = (y + 26)/5

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

y + 6 = 5(x - 4)

Step 2: Distribute

y + 6 = 5x - 20

Step 3: Isolate x

y + 26 = 5x

Step 4: Isolate variable x

(y + 26)/5 = x

Step 5: Rewrite

x = (y + 26)/5

Answer:

y = 5x - 26

Step-by-step explanation:

Since x is the independent variable, you have to solve for y.

y + 6 = 5(x-4)

Now distribute:

y + 6 = 5x - 20

subtract the 6 from both sides

y + 6 - 6 = 5x - 20 - 6

y = 5x - 26

a) The probability that the Bulls will sweep the initial best-of-7 playoff series is 0.6561 or 65.61%.

b) The probability that the Bulls will win the initial best-of-7 playoff series is 0.738 or 73.8%.

a) In order to use Table A.1 to find the probability of the Bulls sweeping the initial best-of-7 playoff series, we need to make an assumption that the probability of winning each game is the same.

Therefore, the probability of winning one game is 90% or 0.9. The probability of winning all four games in a row is the product of the probability of winning each game.

P(Win 4 games in a row) = 0.9⁴ = 0.6561

So, the probability that the Bulls will sweep the initial best-of-7 playoff series is 0.6561 or 65.61%.

b) Now, to find the probability that the Bulls will win the initial best-of-7 playoff series, we need to consider all possible outcomes. The Bulls can win the series in four, five, six or seven games. We already calculated the probability of them winning in four games, so we just need to calculate the probabilities for the other scenarios and add them up.

P(Win in 5 games) = P(Win first 3 games) P(Lose 4th game) P(Win 5th game) = (0.9³) (0.1) (0.9)

          = 0.0729

P(Win in 6 games) = P(Win first 3 games) P(Lose 4th game) P(Lose 5th game) * P(Win 6th game) = (0.9³) (0.1) (0.1)(0.9)

                                          = 0.0081

P(Win in 7 games) = P(Win first 3 games) P(Lose 4th game) P(Lose 5th game) P(Lose 6th game) P(Win 7th game) = (0.9³) (0.1) (0.1) (0.1) (0.9)

                                                                     = 0.0009

Finally, we add up all the probabilities to get the total probability of winning the series:

P(Win series) = P(Win in 4 games) + P(Win in 5 games) + P(Win in 6 games) + P(Win in 7 games) = 0.6561 + 0.0729 + 0.0081 + 0.0009

                                              = 0.738

So, the probability that the Bulls will win the initial best-of-7 playoff series is 0.738 or 73.8%.

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Answer:

Your answer is 8.75 or 8 ¾

Step-by-step explanation:

3 ½ × 2 ½ = 8 ¾

Have a nice day! :)

Answer:

13

Step-by-step explanation:

Given statement solution is :- a) The scale factor from shape A to shape B is 7/5.

b)The  Similar shapes: Scale factor value of t is 20/7 cm or approximately 2.857 cm.

To calculate the scale factor from shape A to shape B, we can use the corresponding side lengths.

In shape A, the corresponding side lengths are 5 cm and 15 cm.

In shape B, the corresponding side lengths are 7 cm and 12 cm.

The scale factor can be determined by dividing the corresponding side lengths from shape B by the corresponding side lengths from shape A:

Scale factor = (corresponding side length in shape B) / (corresponding side length in shape A)

Scale factor = (7 cm) / (5 cm)

Simplifying this fraction, we get:

Scale factor = 7/5

Therefore, the scale factor from shape A to shape B is 7/5.

b) To find the value of t, we can use the scale factor.

In shape A, the side length is 4 cm.

In shape B, the corresponding side length is t cm.

Since the scale factor is 7/5, we can set up the following proportion:

4 cm / 7/5 = t cm / 12 cm

To solve for t, we can cross-multiply and then divide:

4 cm * 12 cm = 7/5 * t cm

48 \(cm^2\) = 84/5 * t cm

To isolate t, we divide both sides by 84/5:

t cm =\((48 cm^2)\) / (84/5)

Simplifying this fraction, we get:

t cm = \((48 cm^2)\) * (5/84)

t cm = 4 cm * (5/7)

t cm = 20/7 cm

Therefore, the Similar shapes: Scale factor value of t is 20/7 cm or approximately 2.857 cm.

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Answer:I believe the answer is b (62.8 cubic units)

Step-by-step explanation:

Answer:

62.8

Step-by-step explanation: