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Question 14
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Use this situation to answer the problem
A river in one part of the Rocky Mountains has a flow rate of 250 cubic meters of
water per second. The flow of the water can be modeled mathematically with the
function, w(t) = 250t, where w(t) represents the volume of the water in cubic
meters, at time t, in seconds.
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Find the number of cubic feet of water that have flowed down the river in 5 minutes
58°F Clear

1. Numbers going up in value - Ascending order

2. The number being divided - Dividend

3. Numbers going down in value - Descending order

4. An approximate value close to the actual value - Estimation

5. The number divided by - Divisor

When the value of numbers is increasing then it's said to be in ascending order. Similarly, when the value of numbers is decreasing then it's said to be in descending order.

The number which is getting divided is called a dividend and the number through which we divide the dividend is called the divisor.

Estimation is said to be the approximate value or the value which is close to the actual value.

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The complete question is -

Match the following-

1. numbers going up in value

2. the number being divided  

3. numbers going down in value  

4. an approximate value close to the actual value

5. the number divided by

Options - descending order, dividend, estimation, divisor, ascending order.

Answer:

B) Corresponding angles are congruent, therefore 2x + 42 = 76.

Step-by-step explanation:

Yes, corresponding angles are congruent, however, the given angles do not fit the definition of a corresponding angle.

Instead, they form a straight line, which is 180° in total. If you were to solve using option B), the answer would look instead as:

(2x + 42)° + (76)° = 180°

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The equation of the circle on the y-axis is x² +(y-3)² = 36.

Here we have to find the equation of the circle

Data provided:

diameter(d) = 12 units

so radius(r) = 6 units

The center lies on the y-axis

The general equation of the circle:

(x-x1)² + (y - y1)² = r²

where (x1, y1) is the point on the circle.

So by putting x1 = 0 and y1 = 3 and r = 6 as the center lies of y-axis

x² + ( y - 3)² = 6²

x² + (y-3)² = 36

Therefore we get the equation as x² + (y-3)² = 36

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Using the implicit differentiation, it is found that the water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.

The volume of the cone of radius r and height h is given as follows:

V = π r² h / 3

Applying implicit differentiation to find the rate of change of the volume as function of time is given as follows:

[tex]\frac{dV}{dt}[/tex] = 2 π  [tex]\frac{rh}{3}[/tex][tex]\frac{dr}{dt}[/tex]  + [tex]\frac{π r² }{3}[/tex] [tex]\frac{dh}{dt}[/tex]

As the radius is constant, hence:

.[tex]\frac{dr}{dt}[/tex]  = 0

Considering that the radius is half of the diameter, the other parameters are:

r = 3 and [tex]\frac{dV}{dt}[/tex] = 2

Hence:

2 = [tex]\frac{π * 3^{2} }{3}[/tex] [tex]\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}[/tex] = 6 / 9 π

dh/dt = 0.21.

The water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.

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By using division, it can be calculated that

Coach Walker needs 15 boxes to fill the uniforms and 3 uniforms will be left over.

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

This is a problem sum on division

Total number of uniforms = 153

Number of uniforms in one box = 10

Number of boxes he can fill = 153 [tex]\div[/tex] 10

The quotient in this case is 15 and the remainder is 3

Coach Walker needs 15 boxes to fill the uniforms and 3 uniforms will be left over.

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Answer:

Step-by-step explanation:

The regular price is 275.82, according to given question.

What do you mean by regular price?

Regular price is the cost at which a provider continuously and actively sells goods or services to the general public over an extended period of time.

According to data in the given question,

We have the given information:

Sale discount 33% and the sale price 184.80.

Now, we will calculate the regular price:

Let Regular Price = x

33% Discount of x = 33/100 * x

33% Discount of x = 33x/100

Regular price - 33% Discount = Sale price

x-33x/100=184.80

(100x-33x)/100=184.80

67x/100=184.80

67x=18480

x=18480/67

x=275.82

Therefore, the regular price is 275.82.

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The linear function y = 3x is used to calculate the cost of 23 balloons as $69

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,

y = 3x

x = number of balloons

The cost of 1 balloon = $3

the cost of 23 balloon = x

x = 23 * 3

x = 69

The cost of 23 balloon is $69

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Answer: 0.83 laps per minute.

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.83 is the answer

Answer:

3%

Step-by-step explanation:

Apply distributive property as shown on all products-

All equations need to be distributed equally

x=3%

As shown, this should be what you do...

It's fine if you don't, but a little birdie said you should, just sayin'...

1300x+1200(x+0.02)=99

Rearrange

2500x+24=99

2500=75

[tex]75/100\\Properties[/tex]

[tex]3/100\\Prioritized(mathematically)[/tex]

The point  (6, -2) lie on the given line segment y= 1/2x-5.

A point denotes exact location on any surface,

and the collection of points in the definite pattern is called line.

So, every line itself have infinite points.

Given point = (6, -2)

Hence, the given line = y= 1/2x-5

So, to find whether any point is on the line or not,

we have to put the point on line.

If it satisfies it will lie on line segment.

If not it will not pass through given line segment.

y= 1/2x-5

Putting x= 6 and y= -2

-2 = 3- 5

Hence, -2 = -2

Hence the (6, -2) lie on the given line segment y= 1/2x-5

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The value of the required mean of the sampling distribution of sample means is approx. 21 ounces when this process is in control.

Sample mean: The arithmetic mean of the values of the variables in the sample. If the samples are drawn from probability distributions with a common expected value, the sample mean is an estimate of that expected value.

Sample means for all days using formula,

Monday = (23+22+23+24)/4 = 23

Tuesday = (23+21+19+21)/4 = 21

Wednesday = (20+19+20+21)/4 = 20

Thursday = (18+19+20+19)/4 = 19

Friday = (18+20+22+20)/4 = 20

We have to calculate the mean of sampling distribution of sample means.

Mean of the sampling distribution of sample means = Sum of sample means of all days / Number of days

= (23+21+20+19+20)/5

= 20.6 = 21 ounces

Hence, the required mean is approx. 21 ounces.

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Answer:

y= -2x-4

Step-by-step explanation:

parallel==> a line has the same slope ===> (m = -2)

y= -2x+b

and a line pass through the (-3,2) ===> x=-3, y=2

2= -2(-3)+b

2=6+b (subtract 6 from both sides )

-4=b

y= -2x-4



The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.

A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.

Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.

Sodium contains in a can of soup is 300mg

Sodium contains in a can of frozen dinners is 450mg

Let the number of cans of soup purchased be x

Then, the number of frozen dinners purchased=x+5

Total sodium purchased=6000mg

So, 300x+450(x+5)=6000mg

Therefore, the system is 300x+450(x+5)=6000mg

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Solving for x in the equation 7 2/5 = 2/3x −4 1/2 gives   17 17/20

In the given equation, we find the value of x by applying the following operations

7 2/5 = 2/3x −4 1/2

7 2/5 = 2x/3 −4 1/2

collecting like terms

7 2/5  + 4 1/2 =

2x/3 = 119/10

multiplying by 3

2x = 119/10 * 3

2x = 357/10

dividing by 2

x = 357 / 10 * 1/2

x = 357/20

x = 17 17/20

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Answer:

92*12=1104

Step-by-step explanation:

The vector (nu) x is an eigenvector of A and corresponds to each nonzero complex scalar (nu) (lambda).

Let x in Cn be an eigenvector of A that corresponds to an eigenvalue. Assume that A is a n x n matrix (lambda). Ax = (lambda)x follows.

Let (nu) now be a complex scalar that is nonzero. A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x)

As a result, (nu)x is an eigenvector of A that corresponds to (nu) (lambda).

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The transformation of the function g ( x ) = | x + 4 | - 2 is

Horizontal shift : Left by 4 units

Vertical shift : Down by 2 units

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs)

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching shift:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be f ( x )

The value of f ( x ) = | x |

Now , the transformation from the first function f ( x ) to g ( x ) is of the form

g ( x ) = | x + 4 | - 2

And , transformation is

y = a | x - h | + k

where the values of y , a , x , h and k are

The value of a = 1

The value of h = -4

The value of k = -2

Now , The Horizontal shift  is given by

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

So , h = -4 means left shift by 4 units

And , The Vertical shift is given by

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

So , k = -2 means down shift by 2 units

Hence , The transformation of the function g ( x ) = | x + 4 | - 2 is

Horizontal shift : Left by 4 units

Vertical shift : Down by 2 units

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The larger number is 15 and the smaller number is 9.

What is substitution method?

In order to solve a system of equations, the substitution method is typically used in mathematics. This approach involves first solving the equation for one variable, then changing the value of the variable in the second equation.

Suppose

'a' be the larger number and 'b' be the smaller number.

As the difference of two numbers is 6.

⇒ a - b = 6        ..(1)

As  two times the smaller is 3 more than the larger.

⇒ 2b = 3 + a        ..(2)

From equation (2),

a = 2b - 3

Substitute the value of 'a' in equation (1)

2b - 3 - b = 6

       b - 3 = 6

            b = 6 + 3

            b = 9

Substitute b = 9 in equation (1),

a - 9 = 6

    a = 6 + 9

    a = 15

Hence, the larger number is 15 and the smaller number is 9.

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Answer:

Original price was $56

Step-by-step explanation:

If $14 is 25% then to find 100% multiply $14 by 4

then you will get $56

Answer: 254400

Step-by-step explanation:

We notice that dividing by 0.001 is the same as multiplying by 1000.

So we take 254.4 timed 1000= 254400

Answer:

254,400

Step-by-step explanation:

1. Count how many zeros are in 0.001

0.001 = 3 zeros

2. Move the decimal point according to the zeros

(There are 3 zeros, so move the decimal point to the right 3 times):

254.4

2,544.

25,440.

254,400

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The given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.

Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable.

Independent, dependent, and controlled variables are typically present in an experiment.

The variable that is altered by the scientist is the independent variable.

A false correlation between two variables indicates that their correlation coefficient is almost zero.

When two variables have a strong correlation, altering the value of one will not affect the other.

Therefore, the given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.

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The probability that the mean height of the American women is between 63 and 64 is 0.6687

The probability of an event occurring is defined by probability. There are numerous instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

Mean = 63.8

S = 4

n = 100

P(63 <=X-bar<=64) = P(63.638/4/[tex]\sqrt{100}[/tex] < z < 64.638/4/[tex]\sqrt{100}[/tex])

=P(0.2 < z < 0.5)

=P(z<0.5) - P(z<-2)

0.6915 - 0.0228

0.6687

So, the probability is 0.6687

p-values from the z table

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This set is closed under scalar multiplications. Statement 1 is false.

This set is a subspace. This statement is also false because this set does not contain a zero vector so it is not a subspace.

This set is closed under vector addition. This is false. Because let v and w be two vectors such that v=(v1,v2); w=(w1,w2).

The set contains the zero vector. Statement 4 is false because the sum of two zero vectors cannot be equal to 1.

Since v and w are vectors satisfying the condition of space so v1+v2=1;w1+w2=1

Now we check whether v+w also belongs to the same space or not.

v+w=(v1,v2)+(w1,w2)=(v1+w1, v2+w2)

We shall check whether components of v+w also add up to 1.

v1+w1+v2+w2=v1+v2+w1+w2=1+1=2

So it means that this space is not closed under addition too.

Consider a vector v=(v1,v2) from the space.

Obviously v1+v2=1

Now let us take a constant 'c'  and consider the behavior of

cv=c(v1,v2)=(cv1,cv2)

Now we check whether components of this vector add up to 1.

cv1+cv2=c(v1+v2)=c\neq 1

which clearly indicates that vectors of this space are not closed under scalar multiplication.

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Using the equation y=x/4+16, it is possible to estimate how many minutes will pass after 4:00 pm when she reaches her destination.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Let x be the time of original flight before delay.

Let y be the new time of flight after delay.

She will to arrive 4 times faster that in original flight time,

y=x/4

The flight is delayed by 16 minutes,

y=x/4+16

The equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination will be y=x/4+16.

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Answer:b

Step-by-step explanation: did the test

Answer:

B because (16-4)/2=6

Step-by-step explanation:

Answer:  The correct answer is b=2a

Step-by-step explanation:

Solve for b

A = (a + b)/3

Flip the equation

1/3a + 1/3b = a

Add (-1)/3a to both sides.

1/3a + 1/3b + −1/3a = a + −1/3a

1/3b = 2/3a

Divide both sides by 1/3

(1/3b)/(1/3) = (2/3a)/(1/3)

b=2a

Answer:

[tex]b = 3A - a[/tex] (if A and a are two different variables).

[tex]b = 2a[/tex] (If the A and a denote the same variable.

Step-by-step explanation:

[tex]A = \frac{(a + b)}{3}[/tex]

Isolate the variable, b. Note the equal sign, what you do to the one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, multiply 3 to both sides of the equation:

[tex]A (*3) = \frac{(a + b)}{3} (* 3)\\A * 3 = (a + b)[/tex]

Next, subtract a from both sides of the equation:

[tex]A * 3 = a + b\\3A = a + b\\3A (-a) = a (-a) + b\\b = 3A - a[/tex]

[tex]b = 3A - a[/tex] is your answer.

IF, however, you meant to put both lower case variable a (or vice versa), then you can further simplify:

[tex]b = 3a - a\\b = 2a[/tex]

[tex]b = 2a[/tex] is your answer if the a are supposed to be the same variable.

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Answer:

29,028 ft.

Step-by-step:

Consider the following:

Mt. Everest - x

Equation:

We are given that Mt. McKinley is 20,321 ft in elevation, and that it is 8,707 ft. lower than Mt. Everest.

When writing this numerically:

20,321 = x - 8,707

Solve for x:

20,321 = x

+8,707     + 8,707

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

x = 29,028

Mt. Everest is 29,028 ft. in elevation.

The answer of a) Probability = 0.386 and of b) Probability = 0.017

Explain probability.

Estimating the likelihood that experiments will succeed or fail is one use of probability theory. The likelihood of flipping a coin and getting heads or tails, for example, or the likelihood of making a research error, can all be calculated using probabilities. In order to fully appreciate this area of mathematics, it is crucial to comprehend the formula for computing probabilities in equiprobable sample spaces, as well as the probabilities of the complementary event, etc., as well as the likelihood of two occurrences joining together.

no of seniors = 3

no of juniors = 15

a) probability that a group consist of a senior and two juniors =

[tex]\frac{^{3}C_{1} * ^{15}C_{2}}{^{18}C_{3}} \\= \frac{3*105}{316}=0.386\\[/tex]

b) if the name of a student given then there is only one way to select it

For example = we have to select 1 senior which name is already given means there is only one way to select it, and 2 junior in which one name is given then it can only selected by one way, but still one junior student has to be selected out of remaining 14 student which can be selected by ([tex]^{14}C_{1}=14[/tex]) different ways.

probability = [tex]\frac{1*1*^{14}C_{1} }{^{18}C_{3} }=\frac{14}{316}=0.017[/tex]

Hence the answer of a) is 0.386 and of b) is 0.017

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