Flying with the wind, a plane can travel 840 miles in 4 hours. Against the wind, the plane requires 5 hours to fly the same distance. Find the speed of the plane in calm air and the speed of the wind, both in miles per hour.

Answer:

152 cm^2

Step-by-step explanation:

To calculate the surface area of this figure, we just need to calculate the surface area of each side and add the total.

Surface area of rectangle = length times width

4 * 8 = 32

Now, we need to multiply 32 by 4 because there are 4 of these rectangles. This yields a value of 128, and we can now find the surface area of the other rectangles:

Surface area of rectangle = length times width

4 * 3 = 12

Now, we need to multiply 12 by 2 because there are 2 of these rectangles. This yields a value of 24 and we can add 24 to 128 to get the total surface area of the prism. This means that the surface area of the prism is 152 cm^2

Answer:

∠E = tan

∠D = tan

Step-by-step explanation:

Common sense, only perpendicular and base is present.

Answer:

Red Delicious: $1.30/lb

Honeycrisp: $2.55/lb

Red delicious is the better deal.

Step-by-step explanation:

Red Delicious:

($0.65)/(1/2 lb) = $1.30/lb

Honeycrisp:

($1.70)/(2/3 lb) = $2.55/lb

Red delicious is the better deal.

Answer:

Step-by-step explanation:

please count the multiplecation then you would look at the problem measure it into small bits

Answer:

1 out of 9

Step-by-step explanation:

I did this on khan academy a minute ago

Probability that both marbles are teal is 0.0571

Probability is a field of mathematics concerned with numerical representations of the likelihood of an event occurring or a statement being true.

Number of yellow marbles = 27

Number of teal marbles  = 9

Probability that both marbles are teal

\(=\frac{9}{36}\times \frac{8}{35} \\=0.0571\)

Hence the probability that both marbles are teal is 0.0571.

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Answer:

sinθ = -5/√61

secθ = √61/6

tanθ = -5/6

Step-by-step explanation:

From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Let us get the value of the radius 'r' first before calculating the trigonometry identities.

Using the Pythagoras theorem;

\(r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}\)

Using SOH, CAH, TOA to get the trigonometry identities;

Given x = 6, y =5 and r = √61

\(sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\\)

Since sin θ, is negative in the fourth quadrant, \(sin \theta = -5/\sqrt{61} \\\)

\(cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\\)

\(sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}\)

For tanθ:

\(tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\\)

Since tan θ, is negative in the fourth quadrant, \(tan \theta = -5/6\)

 \(SIN\Theta=\frac{-5}{\sqrt{61} }\),

\(SEC\Theta=\frac{\sqrt{61} }{6}\)  

\(TAN\Theta=\frac{-5}{6}\).

Given coordinate of point be (6, -5).

So the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Since (6, -5) is on the terminal side that puts us in the fourth quadrant. If we plot that point and draw a diagonal to it from the origin, we will be able to draw a right triangle with that diagonal as the hypotenuse.That means the adjacent side is 6 and opposite side it -5.

By Pythagorean theorem, we find that the hypotenuse

\(H=\sqrt{6^{2} +(-5)^{2} }\)

\(H=\sqrt{61}\)

We know from trigonometric ratios,

\(SIN\Theta=\frac{Perpendicular}{hypotenuse} \\\)

\(SIN\Theta=\frac{5}{\sqrt{61} }\)

Since \(SIN\Theta\) is negative in 4th quadrant,

so,

\(SIN\Theta=\frac{-5}{\sqrt{61} }\)

Similarly,

\(SEC\Theta=\frac{hypotenuse}{base}\)

\(SEC\Theta=\frac{\sqrt{61} }{6}\)

And,

\(TAN\Theta=\frac{perpendicular}{base}\)

\(TAN\Theta=\frac{-5}{6}\)

Hence,  \(SIN\Theta=\frac{-5}{\sqrt{61} }\), \(SEC\Theta=\frac{\sqrt{61} }{6}\)  and \(TAN\Theta=\frac{-5}{6}\).

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Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

\( 6.7 -0.674 *1.1 =5.96\)

\( 6.7 +0.674 *1.1 =7.44\)

Step-by-step explanation:

Let X the random variable that represent the  head breadths of a population, and for this case we know the distribution for X is given by:

\(X \sim N(6.7,1.1)\)  

Where \(\mu=6.7\) and \(\sigma=1.1\)

We want the range of the middle 50% values on the distribution. Since the normal distribution is symmetrical we know that in the tails we need to have the other 50% and on each tail 25% by symmetry.

We can use the z score formula given by:

\(z=\frac{x-\mu}{\sigma}\)

The critical values that accumulates 0.25 of the area on each tail we got:

\( z_{crit}= \pm 0.674\)

And if we solve x from the z score we got:

\( x = \mu \pm z \sigma\)

And replacing we got:

\( 6.7 -0.674 *1.1 =5.96\)

\( 6.7 +0.674 *1.1 =7.44\)

The volume of the prism is 1323 feet³ (cubic feet).

Length= 21 feet.

Width= 9 feet.

Height= 7 feet.

The formula to calculate the volume of rectangular prisms is the following:

\(\sf V_{RP} =l*w*h\); where "l" is the length; "w" is the width, and "h" is the height of the prism.

Check the attached image to see where these values are measured from.

Substitute the variables in the formula by the values on step 1.

\(\sf V_{RP} =l*w*h=(21\ feet)*(9\ feet)*(7\ feet)=\boxed{\sf1323\ feet}.\)

The volume of the prism is 1323 feet³ (cubic feet).

-------------------------------------------------------------------------------------------------------

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Answer:

The volume of the rectangular prism is 1323 cubic feet.

Step-by-step explanation:

Step 1: Write down the formula for the volume of a rectangular prism:

\(\qquad\Large\boxed{\rm{\:\:\:V = l \times w \times h\:\:\:}}\)

Step 2: Substitute the given values for the length, width, and height:

\(\qquad\Large\rm{V = 21\: ft \times 9\: ft \times 7\: ft}\)

Step 3: Multiply the numbers together:

\(\qquad\Large\rm\implies{V = 1323\: ft^3}\)

Step 4: Write the final answer with the appropriate units:

The volume of the rectangular prism is 1323 cubic feet.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer: The answer is 18 bread pieces

Step-by-step explanation:

SECOND ONE he will need 9 loafs of bread because 108 divided by 12 equals 9 so he will ned 9 loafs

The union of sets A and B, indicated AUB, is the set of all components that have a place to set A or set B or both, inside the setting of the given all-inclusive set. 

In set hypothesis, the union of two sets A and B, indicated by A ∪ B, is the set of all components that have a place to either set A or set B or to both. The widespread set, signified by U, is the set that contains all the components beneath thought.

In this manner, to break down A ∪ B utilizing the widespread set, we ought to know what components have a place in the all-inclusive set, as well as which components have a place to set A and set B.

Let's say that U is the all-inclusive set, and A and B are subsets of U. At that point able to break down A ∪ B utilizing the taking after equation:

A ∪ B = {x | x ∈ A or x ∈ B}

In other words, A ∪ B is the set of all components x that have a place to A or B (or both).

Here are a few cases:

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}

A ∪ B = {x | x ∈ A or x ∈ B} = {1, 2, 3, 4, 5, 6}

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The true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

From the given options, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

Let's analyze each statement:

Its leading coefficient is positive:

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

From the graph, if the polynomial is going upwards on the right side, it indicates that the leading coefficient is positive.

It has an odd degree: The degree of a polynomial is the highest power of the variable in the polynomial expression.

If the graph has an odd number of "turns" or "bumps," it indicates that the polynomial has an odd degree.

None of the zeroes have even multiplicity:

The multiplicity of a zero refers to the number of times it appears as a factor in the polynomial.

In the given graph, if there are no repeated x-intercepts or no points where the graph touches and stays on the x-axis, it implies that none of the zeroes have even multiplicity.

The other statements (its leading coefficient is negative, it has an even degree, it has exactly two real zeroes, it has exactly three real zeroes, and none of the zeroes have odd multiplicity) cannot be determined based solely on the information given.

Therefore, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

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On solving the provided question, we got to know that - recursive function to model the geometric sequence is 0.25

In order to create a sequence of terms, a recursive function either repeats itself or uses a previous term to compute a new term. An arithmetic-geometric series with terms that differ from each other frequently is used to explain this function.

Given, geometric sequence

24, 6, 1.5

First term of this sequence = 6

a1 = 6

Recursive formula geometric sequence

\(a_{n} = a_{(n-1)}r\)

\(Here r = common. ratio .of .successive. and previous term\\From .the given .sequence\\\)

r = a2/a1

r = 6/24

r = 0.25

\(Recursive formula of the given sequence will be,\)

\(a_{n} = a_{(n-1)}(0.25)\)

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The true options regarding the triangle diagram are;

m∠5 + m∠6 = 180°

m∠2+ m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

We see the attached image showing ΔABC with Exterior angles as;

∠ 1 , ∠ 4 ,and ∠ 6

Now, the exterior angle property of triangles states that; An exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior ∠1 we have;

∠1 = ∠5 + ∠3 (Exterior angle Property of Triangle)

Similarly,

For Exterior ∠ 4 we have;

∠4 = ∠5 + ∠2   (Exterior angle Property of Triangle)

For Exterior ∠6 we have;

∠6 = ∠2 + ∠3   (Exterior angle Property of Triangle)

From Triangle Sum Property, we know that the sum of the measures of angles in a triangle is equal to 180°. Thus;

m∠2 + m∠3 + m∠5 = 180° (Triangle Sum Property)

Linear Pair of angles states that the measure of a straight angle is 180° and as such a linear pair of angles must add up to 180°. Thus;

m∠5 + m∠6 = 180°  (Linear Pair)

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Answer: 7 units

Step-by-step explanation:

Using the distance formula, the square root of (X2 - X1)^2 + (Y2 - Y1)^2 is equal to the distance between two points.

5-(-2) = 7 9^2 equals 49

-3-(-3) = 0

The square root of 49 plus 0 is 7, so the answer is 7 units.

Based on an equation, the amount that Isabel spent on bread was $2.42.

To solve the equation for the amount spent on bread, we determined the total amount Isabel spent by subtracting the change from the total bills she had.

An equation is a mathematical statement of the equality or equivalence of two or more mathematical expressions.

The amount Isabel spent on vegetables = $15.91

The amount she spent on fruits = $11.22

Let the amount she spent on bread = x

The total amount she went with = $30 (3 x $10)

The change she got after giving the cashier $30 = $0.45

The total amount Isabel spent for vegetables, fruits, and bread = $29.55 ($30.00 - $0.45)

x = $2.42 ($29.55 - $15.91 - $11.22)

Check:

Vegetables = $15.91

Fruits = $11.22

Bread = $2.42

Total expenses = $29.55

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Answer:

O a=0

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

6/12 students have taken fewer than 11 courses.

50% of students have taken fewer than 11 courses.

6/12=50/100

Answer:

The mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

Step-by-step explanation:

Let the random variable X be defined as the number of correct answers marked by a student.

It is provided that each question has 5 possible choices, 1 of the which is correct.

Then the probability of marking thee correct option is:

\(P(X)=\frac{1}{5}=0.20\)

There are a total of n = 20 questions to be answered.

As the students does not the answer to any question, they would be guessing for each question. This implies that for a random question, all the five options has the equal probability of being correct and each of the five options can be correct independently from the other.

All these information above indicates that the random variable X follows a Binomial distribution with parameters n = 20 and p = 0.20.

The mean and standard deviation of a Binomial distribution are:

\(\mu=np\\\\\sigma=\sqrt{np(1-p)}\)

Compute the mean and standard deviation of the random variable X as follows:

\(\mu=np=20\times 0.20=4\\\\\sigma=\sqrt{np(1-p)}=\sqrt{20\times 0.20\times(1-0.20)}=1.789\)

Thus, the mean and standard deviation of the number of questions that each student gets correct are 4 and 1.789 respectively.

According to the question,

The probability of making 3 correct options will be:

→ \(P(X) = \frac{1}{5}\)

            \(= 0.20\)

Total number of questions,

As we know,

The mean will be:

→ \(\mu = np\)

By substituting the values, we get

     \(= 20\times 0.20\)

     \(= 4\)

and,

The standard deviation will be:

→ \(\sigma = \sqrt{np(1-p)}\)

      \(= \sqrt{20\times 0.20\times (1-0.20)}\)

      \(= 1.789\)

Thus the responses above are correct.

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Answer:

i think it A i might be wrong

Step-by-step explanation:

The point (-4, 1) is in the top left or II quadrant.

9514 1404 393

Answer:

  the input that will cause function V to have an output of 80

Step-by-step explanation:

The interpretation of a function V(x) is ...

  the output of function V that corresponds to the input x

__

The corresponding interpretation of the inverse function V^-1(x) is ...

  the input to function V that will cause its output to be x

__

Then the meaning of V^-1(80) is ...

  the input to function V that will cause its output to be 80

Answer:

Maddy wrote a pattern for all the x coordinates starting at 3 and followed the rule "add 2.".

Step-by-step explanation:

Answer: Maddy wrote a pattern for all the x coordinates starting at 3 and followed the rule "add 2.".

Step-by-step explanation:

Given:

The coordinates of the figure ABC are,

A(-2,0)

B(-3,-4)

C(-1,-4)

To find the correct statement:

Let us find the coordinates after rotating the figure 90 degree clockwise direction.

As we know,

In a rotation of 90 degrees clockwise, every point (x,y) will be changed to (y, -x).

So, we get,

D(0,2)

E(-4, 3)

F(-4,1)

It perfectly matches with given graph.

So, Betty's statement is correct.

If we translate the figure two units up and two units right, the given point B (-3,-4) will be changed to (-1,-2) and its reflected point over the y-axis will be (1,-2).

But, this does not match with E(-4,3).

So, Veronica's statement is wrong.

Hence, Betty's statement alone is the correct one.

Answer:

I mean its 20% off that means you spend less money so you should wait for the deal next week if you want to save more money.

Step-by-step explanation:

The perimeter of the rectangle is Twenty and six-twentieths inches. Option D

The formula for calculating the perimeter of a rectangle is expressed as;

P = 2(l + w)

Where;

Now, we have that;

Length = 4 2/5

Length = 22/5

Width = 5 3/4

Width = 23/4

Substitute the values

Perimeter = 2(22/5 + 23/4)

multiply

Perimeter = 2(  88 + 115/20

expand the bracket

Perimeter = 2(203/20)

Perimeter = 20 3/20

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

It would take them approximately 6.24 hours (or 6 hours and 14 minutes) to complete the order if they work together.

To solve this problem, we can use the formula:

Time = Work ÷ Rate

Time is the time it takes to complete the job, Work is the amount of work to be done, and Rate is the rate of work.

Let's assume that the amount of work to be done is 1 (it doesn't matter what unit we use as long as we are consistent).

Then, Maria's rate of work is 1/12 (she can do 1 job in 12 hours) and the new clerk's rate of work is 1/13 (he can do 1 job in 13 hours).

If they work together, their combined rate of work is the sum of their individual rates:

Rate = Maria's rate + New clerk's rate

Rate = 1/12 + 1/13

Rate = (13 + 12) / (12 x 13)

Rate = 25 / 156

So, their combined rate of work is 25/156 jobs per hour.

Now, we can use the formula to find the time it takes for them to complete the job together:

Time = Work ÷ Rate

Time = 1 ÷ (25/156)

Time = 156/25

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Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.

To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.

The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).

Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.

However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).

Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.

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