Mai poured 2. 6 liters of water into a partially filled pitcher. The pitcher then contained 10. 4 liters. How much water did the pitcher contain before Mai added more water?

Answers

Answer 1

The amount of water that the pitcher contained before Mai added more water was 7.8 liters.

Let x be the amount of water the pitcher contained before Mai added more water.

When Mai poured 2.6 liters of water, the total amount of water in the pitcher became x + 2.6 liters.

According to the problem, the pitcher then contained 10.4 liters of water. Therefore, we can write:

x + 2.6 = 10.4

Subtracting 2.6 from both sides, we get:

x = 7.8

Therefore, the pitcher contained 7.8 liters of water before Mai added more water.

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Related Questions

The table shows four transactions (in dollars) for a bank account. Positive numbers represents deposits, and negative numbers represent withdrawals. The balance before the transactions is $75.50. What could the transaction for 11/7 be if the final balance in the bank account is $86.92? Date Amount 11/4 50.68 11/4 -22.16 11/7 11/11 56.65 End Balance 86.92

Answers

Answer:

11/7: +9.42

Step-by-step explanation:

FIND THE MISSING SIDES OF THE KITE

Picture for more info!

Thank you.

Answers

The required sides of kite are √61, √61, √221 and √221 units.

What is Pythagoras theorem?

According to the Pythagoras theorem, the square of the hypotenuse in a right-angled triangle equals the total of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two sides. Pythagoras theory triangles are another name for these triangles.

According to question:

In ΔAOD

AD = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units

In ΔAOB

AB = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units

In ΔBOC

BC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units

In ΔDOC

DC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units

Thus, required sides of kite are √61, √61, √221 and √221 units.

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1. if you repeated a hypothesis test 1000 times (i.e. 1000 different samples from the same population), how many times would you expect to commit a type i error, assuming the null hypothesis were true, if:

Answers

If we repeated a hypothesis test 1000 times, the number of times we would expect to commit a Type I error, assuming the null hypothesis were true, would depend on the significance level (α) of the test.

A Type I error occurs when we reject the null hypothesis when it is actually true. The significance level of a test (α) is the probability of making a Type I error when the null hypothesis is true. In other words, if we set a significance level of α = 0.05, we are saying that we are willing to tolerate a 5% chance of making a Type I error.

Assuming a significance level of α = 0.05, if we repeated the test 1000 times, we would expect to make a Type I error in approximately 50 tests (0.05 x 1000 = 50). This means that in 50 out of the 1000 tests, we would reject the null hypothesis even though it is actually true.

However, it is important to note that the actual number of Type I errors we make in practice may differ from our expectation, as it depends on the specific characteristics of the population being tested and the sample sizes used in each test.

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165. 1% of 384. 7. Round to the nearest thousandth

Answers

Rounding to the nearest thousandth means rewrite the number and deleting all digits to the right of the rounded number. The percentage value for 165.1% of 384.7 is equals to the 42.917%.

In mathematics, a percentage is a number that represents a fraction of hundred. We have to calculate the value of 165.1% of 384.7. Percentage solution with steps:

Step 1: We make the assumption that 384.7 is 100% since it is our output value.

Step 2: We next represent the value we need with x. From step 1, it follows that 100% = 384.7.

Step 3: In the same sense, x% = 165.1.

Step 5: Now, we have a pair of simple equations:

100% = 384.7 --(1).

x% = 165.1 ---(2).

Step 6: By simply dividing equation (1) by equation 2 and taking note of the fact that both the LHS (left hand side) of both equations have the same unit (%); we have 100% /x% = 384.7/165.1.

Step 7: Taking the inverse or reciprocal in both sides, x% / 100% = 165.1/384.7

=> x = ( 165.1/384.7) × 100

=> x = 42.91655835716 ~ 42.917 (round to the nearest thousandth). Therefore, 165.1 is 42.917% of 384.7.

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A bag has 11 blue cubes, 6 red cubes, and 8 green cubes. If you draw a cube and replace it in the bag 200 times, which of the following amounts would you expect to pull? Select all that apply.

A) Pull a blue cube 88 times
B) Pull more red cubes than blue cubes
C) Pull a green cube 64 times
D) Pull a blue cube 150 times
E) Pull a red cube 10 times

Answers

Option E is incorrect in light of the provided assertion, and only options A,B,C, and D are acceptable.

What fundamentals of probability are there?

Probability is simply the chance that something will happen. We can discuss the likelihood of various outcomes when we are unable to foresee how an incident will unfold.

The probability of drawing a blue cube is 11/25, the probability of drawing a red cube is 6/25, and the probability of drawing a green cube is 8/25. Since we are replacing the cube after each draw, each draw is independent and follows the same probability distribution.

To find the expected number of times we would pull a certain color cube, we can simply multiply the probability of drawing that color cube by the total number of draws:

Expected number of blue cube draws: (11/25) x 200 = 88 times. So option A is correct.

The probability of drawing more red cubes than blue cubes is a bit more complicated to calculate, but it can be done by summing the probabilities of drawing 0, 1, 2, 3, 4, 5, or 6 blue cubes and 6, 5, 4, 3, 2, 1, or 0 red cubes. However, it is easier to notice that the probability of drawing more red cubes than blue cubes is the same as the probability of drawing more blue cubes than red cubes, which is 1/2 since both events are equally likely. Therefore, option B is correct.

Expected number of green cube draws: (8/25) x 200 = 64 times. So option C is correct.

Expected number of blue cube draws: (11/25) x 200 = 88 times. So option D is correct.

Expected number of red cube draws: (6/25) x 200 = 48 times. So option E is not correct since it expects less than 48 red cube draws.

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An isosceles right triangle is removed from
each corner of a square piece of paper, as
shown, to create a rectangle. If AB = 12 units,
what is the combined area of the four removed
triangles, in square units?

Answers

The combined area of the four removed triangles is 48 sq.units. Answer: 48

We need to find out the combined area of the four removed triangles, in square units. Given: AB = 12 units.

Let's consider the given square, and let's draw an altitude BD and also draw perpendiculars to BD from the three vertices A, C and D.

Let AB = x cm. Area of square = x² sq.cm.

Now, we are cutting a triangle with base x and height x, which is a right-angled triangle. Hence, area of each removed triangle = (1/2) * x * x = (x²/2) sq.cm.

Now, BD = x/√2. Area of rectangle = AB * BD = 12 * 12/√2 = 72√2 sq.cm.

Now, area of 4 triangles = (x²/2) + (x²/2) + (x²/2) + (x²/2) = 2x² sq.cm.

We know that, Area of rectangle = Area of 4 triangles + Area of square => 72√2 = 2x² + x² => 72√2 = 3x² => x² = 24√2 cm² => x = √(24 * 2) cm = √(48) cm = 4√3 * √2 cm.

Area of 4 triangles = 2x² sq.cm = 2 * 24 cm² = 48 sq.cm.

Hence, the combined area of the four removed triangles is 48 sq.units. Answer: 48.

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in a certain large city, 45% of families earn less than $35,000 per year. assuming the distribution is binomial and you can use the exact binomial calculation, what's the probability that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year?

Answers

The probability of obtaining 10 or fewer families earning less than $35,000 per year in a simple random sample of 30 families from a large city with 45% of families in that income bracket is approximately 0.041 or 4.1%.

We can use the binomial distribution formula to calculate the probability of obtaining 10 or fewer families earning less than $35,000 per year in a simple random sample of 30 families from a large city where 45% of families earn less than $35,000 per year.

Let's denote the probability of a family earning less than $35,000 per year as "p", which is 0.45 in this case, and the number of trials or families sampled as "n", which is 30 in this case.

The probability of obtaining k families earning less than $35,000 per year in a simple random sample of 30 families can be calculated using the binomial distribution formula:

P(X ≤ 10) = Σ(i=0 to 10) [n choose i] * p^i * (1-p)^(n-i)

where n = 30, p = 0.45, and X is the random variable representing the number of families earning less than $35,000 per year in the sample.

Using a binomial calculator or software, we can calculate:

P(X ≤ 10) ≈ 0.041

Therefore, the probability that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year is approximately 0.041 or 4.1%.

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How do I solve this I don’t get it

Answers

Surface area , Lateral area and volume of triangular prism area 262.25 square in, 231 square in and 156.25 cubic in respectively.

The meaning of the triangular prism

With two triangular bases and three rectangular sides, a triangular prism is a kind of polyhedron. Alternatively, because it has five faces overall, it may be thought of as a pentahedron in which the bases' edges and vertices are connected by three rectangular sides.

Surface area of triangular prism:

Given, base (b) =5 in ,

the height of the triangle (h) = 6.25 in

length of a prism (l) = 12 in

and the hypotenuse of the right triangle = 8 in

The surface area of a right triangular prism = b×h + (S1 + S2 + h)L

On substituting the values, we get

SA = (5 × 6.25) + [(5 + 6.25 + 8) × 12]

⇒ SA = 60 + (30 × 11)

⇒ SA =262.25 square in

Therefore, the total surface area of a right triangular prism is 262.25 square in.

Lateral area of triangular prism:

Lateral  Area = ( S1 + S2 + S3 ) × l

On substituting the values, we get

LA=(5+6.25+8)×12

LA=(19.25)×12

LA=231 square in

Therefore, the lateral surface area of a right triangular prism is 231 square in.

Volume of triangular prism:

the base area = (1/2) × (b×h) = (1/2) × (5 ×6.25) =15.625 square in

The length of the prism is, L = 12 in

Using the volume of the triangular prism formula,

The volume of the given triangular prism = base area × length of the prism = 15.625 ×10=156.25 cubic in

Hence, The volume of the given triangular prism is 156.25 cubic in.

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Pls just say a b c or d

Answers

This answer is c in this question

Answer:

c

Step-by-step explanation:

Identify all expressions below that are polynomials.

Answers

Answer:

All the expressions except d are polynomials.

[y=-z+2
y=-2²+z+1
Which ordered pair is the solution of the system?
The graph shows the system
0 (0, 2)
O (1,2)
(1,1)
(0, 1)
+

Answers

Therefore , the solution of the given problem of ordered pair comes out to be the ordered pair (1, 1/2).

What exactly are ordered pairs?

"Ordered pairs" are two separate variables that are arranged in a way that suggests a specific sequence. The coordinates for x and y in an order pair are represented, respectively, by the main and second components. The sample following uses close parentheses to indicate the ordered combination.

Here, The formulae are as follows:

=>y = -z + 2      ...(1)

=> y = -2x² + z + 1  ...(2)

Equation (1) can be substituted for equation (2) to find the value of z:

=> Z = x² + 1/2 - z + 2 = -2x² + z + 1

=> 2z = 2x² + 1

We can now enter this value of z into equation (1) and find the value of y:

=> y = -z + 2

=> y = -(x² + 1/2) + 2

=> y = -x² + 3/2

As a result, the equation system can be expressed as:

=> z = x² + 1/2

=> y = -x² + 3/2

When x=0:

=> z = 0² + 1/2 = 1/2

=> y = -0² + 3/2 = 3/2

Therefore, there is no answer for the ordered pair (0, 3/2).

When x=1:

=> z = 1² + 1/2 = 3/2

=> y = -1² + 3/2 = 1/2

The answer is the ordered pair (1, 1/2).

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please help i will give brainliest along with 20 pnts. ONLY ANSWER IF YOU KNOW IT

Answers

Giovanna deposited $1600 into two accounts, half in First Oak and half in West United.

Interest earned in First Oak account after 5 years at 6% simple interest:

= 0.06 x $800 x 5

= $240

Interest earned in West United account after 5 years at 5% compounded annually:

= $800 x (1 + 0.05)^5 - $800

= $800 x 1.27628 - $800

= $221.02

Total interest earned in both accounts:

= $240 + $221.02

= $461.02

Therefore, Giovanna will have earned $461.02 in interest from both accounts at the end of 5 years.

The relation between hours studied and LSAT scores in a random sample of students is found to be S = 130 + 2.2h. How will a student’s score be affected if she studies for 10 hours?

Answers

Answer:

We can use the given equation to find the expected LSAT score (S) for a student who studies for 10 hours:

S = 130 + 2.2h

S = 130 + 2.2(10)

S = 130 + 22

S = 152

Therefore, if a student studies for 10 hours, we would expect her LSAT score to be 152.

If the function, g(x), has the ordered pairs (-4, 15), (-2, 3), and (0, -1), fill in the ordered pairs that know exist on the graph of g−1(x)

Answers

Answer:

(15, - 4 ) , (3, - 2 ) , (- 1, 0 )

Step-by-step explanation:

given a point (x, y ) on a function f(x) , then the corresponding point on the inverse function is (y, x )

given the points on g(x) , then the corresponding points on [tex]g^{-1}[/tex] (x) are

(- 4, 15 ) → (15, - 4 )

(- 2, 3 ) → (3, - 2 )

(0, - 1 ) → (- 1, 0 )

factorise x²-2xy-y²-z²

Answers

Answer:

(x^2−2xy+y^2)−z^2

⇒[x(x−y)−y(x−y)]−z^2

⇒(x−y)(x−y)−z^2

⇒(x−y)^2−z^2

⇒[(x−y)+z][(x−y)−z]

⇒(x−y+z)(x−y−z)

Sophie has a small cube-shaped box. Its volume is 64 cubic centimeters.
What is the area of one face of the box?

Answers

Answer:

The answer to your problem is, [tex]16cm^{2}[/tex]

Step-by-step explanation:

Sophie has a small cube shaped box.

Volume of the box is [tex]64cm^{3}[/tex]

We have to find the area of one face of the box.

Let one side of the box is x

Then volume = [tex]x^{3}[/tex] = 64

x³ = 4³

= 4

Now area of one face of the cube = x²

then area = 4² = 16 cm²

Thus the answer to your problem is, [tex]16cm^{2}[/tex]

six less than six times a number

Answers

Answer:

6n-6 or 6(n-1)

Step-by-step explanation:

six times a number, n, can be shown as 6n. "Six less" indicates -6. So combining the two parts leaves 6n-6. This can be simplified to 6(n-1)

what is the mean of the sample means? the mean of the sample means is equal to the population mean, divided by the square root of the sample size. the mean of the sample means is equal to the population mean,divided by the sample size. the mean of the sample means is equal to the population mean, divided by the population standard deviation. the mean of the sample means is equal to the population mean. the mean of the sample means is undefined because all possible sample means can never be found.

Answers

The mean of the sample means is equal to the population mean.

The mean of the sample means is the average of all sample means taken from the population. It is an estimate of the population mean. The sample mean is calculated by taking the sum of all values in the sample and dividing it by the sample size. The mean of the sample means is equal to the population mean, as all sample means come from the same population and therefore have the same mean. It is not affected by the sample size or the population standard deviation. Therefore, the mean of the sample means is equal to the population mean.

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y < 2x + 3

x+y≥ 3

x < 4

Write an ordered pair that is a solution to the systems.​

Answers

The solution to the system of equations is (2, 1). To find this solution, we must first solve the first equation, Y < 2x + 3, for x.

What is subtracting?

Subtracting involves taking the difference between two numbers. It is the opposite of addition and is represented by the '-' sign.

We can do this by subtracting 3 from both sides of the equation, which gives us Y - 3 < 2x.

We then divide both sides of the equation by 2, which gives us

Y - 3/2 < x.

Next, we must solve the second equation, x + y ≥ 3, for y. To do this, we subtract x from both sides of the equation, which gives us y ≥ 3 - x.

Finally, we must set both equations equal to each other,

Y - 3/2 = 3 - x.

We can then solve for x by adding 3/2 to both sides of the equation, which gives us

x = 2.5.

We can then plug this value for x into the second equation, which gives us y ≥ 3 - 2.5.

We then solve for y by subtracting 2.5 from both sides of the equation, which gives us y = 0.5.

Since the value for x must be less than 4, we must round down the value of x to 2. This means that the solution to the system of equations is (2, 1).

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Ousmane envoie une carte a Arnaud par pigeon voyageur. Le pigeon vole a une vitesse de 84km/h et met 1h45 à délivrer la lettre. A quelle distance Arnaud et Ousmane vivent-ils l'un de l'autre ?

Answers

On peut commencer par utiliser la formule suivante pour calculer la distance parcourue par le pigeon voyageur :

distance = vitesse x temps

où la vitesse est donnée en km/h, le temps en heures et la distance en km.

Dans ce cas-ci, la vitesse est de 84 km/h et le temps de voyage est de 1h45, soit 1.75 heures. On peut donc calculer la distance parcourue par le pigeon :

distance = 84 km/h x 1.75 h = 147 km

Donc, la distance entre Ousmane et Arnaud est de 147 km.

every morning, mr. cross bakes 80 strawberry frosted donuts unless there is a special order. each donut costs $3 to make, and is sold for $5; unsold donuts are given away to a charity at the end of the day, at a discounted price of $1.50.

Answers

Every morning, Mr. Cross bakes 80 strawberry frosted donuts unless there is a special order. Each donut costs $3 to make, and it is sold for $5. Unsold donuts are given away to a charity at the end of the day, at a discounted price of $1.50. What will be Mr. Cross’s total earnings if he sells all 80 donuts?

Total revenue if all 80 donuts are soldRevenue = Total units sold × Selling price per unitSince there are 80 donuts and each donut costs $5,Total revenue if all 80 donuts are sold = 80 × 5 = $400Total cost if all 80 donuts are soldTotal cost of making all 80 donuts = Cost of one donut × Total units madeSince each donut costs $3,Total cost of making all 80 donuts = 3 × 80 = $240Total profitTotal profit = Total revenue - Total cost

Since revenue is $400 and the total cost is $240,Total profit = 400 - 240 = $160At the end of the day, unsold donuts are given away to charity at a discounted price of $1.50 each. Therefore, Mr. Cross’s total earnings would be $160 if he sold all 80 donuts.

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Property taxes on homes decreased this year by an average of $75. 90 in Silvertown. There are 270 homes in Silvertown. Which describes the change in Silvertown’s revenue from last year to this year?

Answers

The change in Silvertown’s revenue from last year to this year can be described by c. 20,493.

Property taxes on homes decreased this year by an average = $75. 90

Total number of homes = 270

It is essential to compare the overall property tax revenue from this year to the total revenue from last year after the $75.90 per-home drop in order to ascertain the change in Silvertown's property tax revenue.

Calculating the total decrease in revenue -

= Average decrease x total number of homes

= 75.90 x 270

= 20,493

Complete Question:

Property taxes on homes decreased this year by an average of $75. 90 in Silvertown. There are 270 homes in Silvertown. Which describes the change in Silvertown’s revenue from last year to this year?

a. - 21,093

b. - 20, 493

c. 20,493

d. 21930

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WILL MARK BRAINLIEST!!!
PLEASE HELP!
Write Tan A and Tan B

Answers

Answer:

Hope this is what you were looking for :)

Step-by-step explanation:

tan = opposite/adjacent

IF YOU DONT NEED TO FIND THE VALUES OF THE SIDES:

tan A =  [tex]\frac{x}{11}[/tex]

tan B = [tex]\frac{11}{x}[/tex]

Replace the x for whatever the value of BC is or if it doesn't have a value, you can just leave it as x.

IF YOU DO NEED TO FIND THE VALUES OF THE SIDES:

tan 45 = 1

tan 45 =  [tex]\frac{BC}{11}[/tex]

(11) tan 45 = BC

BC = 11

tan 45 = [tex]\frac{11}{AC}[/tex]

AC = [tex]\frac{11}{tan 45}[/tex]

AC = 11

This can also be done without using tangent from taking a look at special right triangles.

In 45-45-90 triangles, the two legs are the same size while the hypotenuse is equal to one of the legs multiplied by [tex]\sqrt{2}[/tex]. In doing this, we can find that both legs are 11 and the hypotenuse is [tex]11\sqrt{2}[/tex].

If f(x) is a function and f(1) = 5, then which of the following could not be true?

Answers

If f(x) is a functiοn and f(1) = 5, then  f(1) = 1 cοuId nοt be true.

Thus οptiοn a is cοrrect.

Define functiοn.

A functiοn is a reIatiοn between twο sets, caIIed the dοmain and the range, such that fοr each eIement in the dοmain, there is exactIy οne eIement in the range. A functiοn maps each eIement in the dοmain tο a unique eIement in the range.

In οther wοrds, a functiοn is a ruIe οr a fοrmuIa that assοciates each input vaIue with a unique οutput vaIue. The input vaIues are the dοmain οf the functiοn, and the οutput vaIues are the range. Functiοns are οften denοted by a symbοI such as f(x), where x is an eIement in the dοmain and f(x) is the cοrrespοnding eIement in the range.

In mathematicaI anaIysis, the generaI cοncept οf functiοn, appIicatiοn οr mapping refers tο a ruIe that assigns tο each eIement οf a first set a singIe eIement οf a secοnd set.

Using this definitiοn, severaI eIements οf the dοmain can resuIt in the same eIement οf the range οf the functiοn.

But, the same eIement οf the dοmain, can nοt have different vaIues οf the range οf the functiοn.

Therefοre, the fοIIοwing expressiοn can nοt be true:

f (1) = 1

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Complete Question:

If f(x) is a function and f(1) = 5, then which of the following could not be true?

a. f(1) = 1

b. f(2) = 1

c. f(5) = 5

Examine the system of equations.

2x − 4y = 6,

x − 2y = 3

How many solutions does this system of equations have?

Answers

Answer:

Step-by-step explanation:

8

Can anybodyhelp me with these please? I need help please!​

Answers

1: The measure of arc JML is: arc JML = 176°

3: m∠WXY = 59°

5: The measure of the arc is: arc FE = 54°

7: The measure of the angles are: m∠A  = 79° and m∠B  = 112°

9: The value of x is: x = 9

How to find the angle or arc measure in a circle?

No. 1

The measure of inscribed angle is half the measure of its intercepted arc. That is:

∠ JKL = 1/2 * arc JML

88 = 1/2 * arc JML

arc JML = 2 * 88

arc JML = 176°

No. 3

arc WY =  360 - 86 - 156 = 118° (sum of angles in a circle)

m∠WXY = 1/2 * arc WY

m∠WXY = 1/2 * 118

m∠WXY = 59°

No. 5

An angle inscribed in a semicircle is a right angle. Thus, m∠DFE = 90°

m∠EDF = 180 - 90 - 63 = 27° (sum of angles in a triangle)

m∠EDF  = 1/2 * arc FE

27°  = 1/2 * arc FE

arc FE = 2 * 27

arc FE = 54°

No. 7

The opposite angle in a cyclic quadrilateral add up to 180°. That is:

m∠A + m∠C  = 180°

m∠A + 101 = 180

m∠A  = 180 - 101

m∠A  = 79°

m∠B + m∠D  = 180°

m∠B + 68 = 180

m∠B  = 180 - 68

m∠B  = 112°

No. 9

67 = 1/2 * (16x - 10)

67 * 2 = (16x - 10)

16x - 10 = 134

16x  = 134 + 10

16x = 144

x = 144/16

x = 9

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Which summary about The Secret Garden includes a personal opinion?

Responses
Mary Lennox is described as a sallow, sickly, unpleasant girl.
Mary Lennox is described as a sallow, sickly, unpleasant girl.

Mr. Craven, "a miserable hunchback," has been withdrawn and depressed for ten years.
Mr. Craven, "a miserable hunchback," has been withdrawn and depressed for ten years.

Dickon and Mary secretly begin bringing Colin out into the secret garden.
Dickon and Mary secretly begin bringing Colin out into the secret garden.

Mrs. Lennox is the worst mother imaginable, and everybody knows it.


PLS HELP FAST

Answers

Answer:

"Mrs. Lennox is the worst mother imaginable, and everybody knows it."

Step-by-step explanation:

The first one uses "described", therefore isn't a personal opinion.

The second uses quotations, so isn't a personal opinion.

The third doesn't have any sort of opinion or connotation.

Therefore it must be the last one.

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you are making cookies and missing a key ingredient eggs. you have most of the other ingredients, except you only have 1.33 cups of butter. the recipe calls for two cups of butter and three eggs to make six dozen cookies. how many eggs do you need use all of the butter?

Answers

By using equation in two variable we need to use 2 eggs to make all the cookies with 1.33 cups of butter.

To make six dozen cookies, the recipe calls for two cups of butter and three eggs. We can use proportionality to solve this question: If 2 cups of butter require 3 eggs to make 6 dozen cookies, then 1.33 cups of butter require x eggs to make all of the cookies.

x eggs = (1.33 cups of butter x 3 eggs)/(2 cups of butter). x = 1.99 eggs. Since we cannot use .99 eggs to make cookies, we would need to round up to the nearest whole number of eggs.

Therefore, we need to use 2 eggs to make all the cookies with 1.33 cups of butter.

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a coin is flipped 6 times. if more heads are flipped than tails, the probability that all 6 are heads is , what is the value of ?

Answers

The probability that all 6 flips result in heads is 1/64

The given coin is flipped 6 times. The number of heads and tails could vary from 0 to 6.Let H be the number of heads and T be the number of tails. Then the possible values of H and T are, H=0 and T=6 H=1 and T=5 H=2 and T=4 H=3 and T=3 H=4 and T=2 H=5 and T=1 H=6 and T=0

For the given question, it is given that more heads are flipped than tails.So the possible values of H are 4, 5 and 6.So the total number of possible outcomes with more heads than tails is the sum of the possible outcomes with 4, 5 and 6 heads which is, 1+6+15 = 22 (from the combinations formula)Now, the probability that all 6 flips result in heads, given more heads are flipped than tails is,

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T)P(H > T) = 22/64

P(all 6 are heads | H > T) = 1/21 (there is only one possibility where all 6 flips are heads)

P(all 6 are heads) = P(H > T) × P(all 6 are heads | H > T) = (22/64) × (1/21) = 1/64

Therefore, the probability that all 6 flips result in heads, given more heads are flipped than tails is 1/64.

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The prism-shaped roof has equilateral triangular bases. Use the model you created in question #1 to calculate the height of the roof, to the nearest tenth of a foot, if the side lengths each measure 25 feet. In your final answer, include all necessary calculations. You may include a sketch as part of your work

Answers

The height of the roof is approximately 21.6 feet, to the nearest tenth of a foot.

To calculate the height of the roof, we need to use the formula for the volume of a prism with a triangular base. This is given by V = 1/3 B h, where B is the area of the base and h is the height of the prism.
In this case, we know that the base is an equilateral triangle with side length 25 feet. The area of an equilateral triangle with side length s is given by A = √3/4 s². Therefore, the area of the base of the prism is:
B = √3/4 (25 ft)²
B = 25√3/4 ft²
Now, we need to use the model to determine the height of the prism. We can do this by measuring the height of one of the triangular faces. The model is not provided, so I cannot provide specific measurements. However, we can use the Pythagorean theorem to relate the height of the triangular face to the height of the prism:
h² = (25 ft)² - (1/2 s)²
h² = 625 ft² - (1/2 (25 ft))²
h² = 625 ft² - 156.25 ft²
h² = 468.75 ft²
h ≈ 21.6 ft
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