Whitney works at an aquarium. She uses hoses of different sizes to fill the fish tanks. Hose A takes 16 min to fill a 160-gal tank. Hose B takes 30 min to fill a 240-gal tank.
Which hose fills at a faster rate?
Choose one option from each drop-down menu to answer the question.
Hose A fills at a rate of Choose... 0.1, 10, 144, 160 gal per min.
Hose B fills at a rate of Choose... 0.125, 8, 210, 240 gal per min.
Hose Choose... A or B fills at a faster rate.

Answer:

7

Step-by-step explanation:

we have 1008=2×2××2×3×3×3

The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.

Now 1008×7=2×2×2×2×3×3×7×7

7056=2×2×3×7

=84

Answer : 7

Answer:

1.   7

2.  square root is 84.

Step-by-step explanation:

First find the prime factors:

1008 =2*2*2*2*3*3*7

There's an even number of 2's and 3's but only one 7, so we multiply by 7

Smallest number = 7.

The square number is 1008 * 7

= 7056.

Its square root is  2*2*3*7 = 84.

Answer:

Step-by-step explanation:

This function will have a minimum point only if f(x) has one.

Examples:  

y = x + 5:  straight line with no minimum

y = x^2 + 5:  parabola that opens up and has vertex at (0, 5); thus, the minimum is (0, 5)

What f(x) did you have in mind?  Please share it.

Present value of the loan amount is $[tex]27[/tex] with a maturity value of $[tex]15000[/tex] for [tex]9[/tex] months at [tex]6[/tex]%

How to find the present value of loan amount ?

We know that

Maturity value of loan amount [tex]= 15000[/tex]

Time period is [tex]=9[/tex] months

Rate (r)[tex]=6[/tex] %

Present value of loan amount=?

So we can use the formula of maturity level

[tex]MV=PV*(1+r*t)[/tex]

Substitute the values

[tex]15000=PV *(1+6*9)\\15000=PV(55)\\\frac{15000}{55} =PV\\27.27=PV[/tex]

So present value of the loan amount is $[tex]27[/tex] in round figure.

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Using the normal distribution, the value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is:

z = -0.52.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is is the 30th percentile, which is Z with a p-value of -0.3, hence z = -0.52.

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Answer:

[tex]G(x) = x^{3} -1[/tex]

Step-by-step explanation:

The red graph is the blue graph translated 1 unit down, so the answer is A.

As a rule of thumb, when each component is selected independently from the same population, the sampling distribution of the sample percentage may be estimated by a regular probability distribution.

Therefore the main solution is- from the identical group, each component is individually chosen.

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The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).

According to the question,

The circle with center at (-1,-4) that passes through the point (-4,0).

To find the radius of the circle:

Radius r = √[(-4 - (-1))² + (0- (-4))²]

=√(-4+1)² + (4)²

=√9+16

=√25

=5.

In order to find the standard equation of the circle is

(x - (-4))² + (y - (0))² = (5)²

(x + 4)² + (y )² = 25

x² + 8x + 16 + y² = 25

x² + y² + 8x + 16 = 25

x² + y² + 8x = 25 - 16

x² + y² + 8x = 9

x² + y² + 8x - 9 = 0

Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.

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Answer: (-4,2)

Step-by-step explanation:

To find the midpoint of AB, we have to find the mean of the x coordinates for the x coordinate of the midpoint and the mean of the y coordinates for the y coordinate of the midpoint

So the midpoint is ((-9+1)/2,(-3+7)/2) = (-4,2)

To plot the line AB, just find the points A and B on the graph and draw a straight line from A to B

La ecuación de la recta que contiene el punto (x, y) = (0, 6)  y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.

En esta pregunta tenemos que derivar una ecuación de la recta a partir de una recta y un punto. Dos rectas bajo forma implícita son paralelas si y solo si comparten los mismos coeficientes dependientes, entonces tenemos que el coeficiente independiente de la recta es:

2 · 0 + 3 · 6 + k = 0

18 + k = 0

k = - 18

Por tanto, la ecuación de la recta que contiene el punto (x, y) = (0, 6)  y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.

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Answer:

y^2 + 5y = 0

y(y + 5) = 0

y = 0, -5

The answer is y = 0 and y = -5.

The given question :

Answer:

D

Step-by-step explanation:

a quintic polynomial is a polynomial of degree 5

A is a polynomial of degree 4 (- [tex]x^{4}[/tex] term )

B is a polynomial of degree 3 (x³ term )

C is a polynomial of degree 2 ( x² term )

D is a polynomial of degree 5 ( 3[tex]x^{5}[/tex] term )

Answer:

-5

Step-by-step explanation:

Slope is rise over run. The graph decreases by 5 units every 1 unit to the right, so the slope is -5.

He is  2√19 miles far way from starting point.

Suppose Billy starts at point A, turns at point B, and ends at point D, as shown below.

If Billy turns 60◦ northward and walks six miles, then we can draw a 30 − 60 − 90 triangle whose hypotenuse is 6 miles

It follows that Billy traveled 6/2 = 3 miles eastward during these 6 miles, and that he traveled 3√3 miles northward during these 6 miles. In total, Billy traveled 4 + 3 = 7 miles  eastward and 3√ 3 miles northward.

By the Pythagorean Theorem, the distance from his starting point is q:

(7)2 + (3√3)2

=√49 + 27

= √76

= 2√19 .

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Answer:

940

Step-by-step explanation:

Since there is a 5 in the ones spot we round the number is the tens spot up by 1: 935 --> 940

Answer:

20 + 4y

Step-by-step explanation:

The 4 multiplies the 5 and the y, i.e., it distributes over the terms of the expression in ( ).

Step-by-step explanation:

To prove that 3 + 2√5 is an irrational number, we will use the contradiction method.

Let us assume that 3 + 2√5 is a rational number with p and q as co-prime integers and q ≠ 0

⇒ 3 + 2√5 = p/ q

⇒ 2√5 = p/ q - 3

⇒ √5 = (p - 3q ) / 2q

⇒ (p - 3q ) / 2 q is a rational number.

However, √5 is an irrational number

This leads to a contradiction that 3 + 2√5 is a rational number.

3.60

t = r√n − 2/1 − √r2

= 0.6√25 − 2/√1 − 0.62

= 3.5969 t or about 3.60 rounded to two decimal places.

Hypothesis Testing:

Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H0.

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If the value of the sample standard deviation increases, the confidence interval becomes wider and is denoted as option A.

This term is used in statistics and refers to the probability that a population parameter will fall between two set values.

it has a direct relationship with standard deviation in which its increase will also lead to the set of values being wider thereby making it the most appropriate choice.

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The options are :

a. It becomes wider

b. It becomes more precise

c. It does not change

d. It narrows

Answer: 4

Step-by-step explanation:

yeh

Step-by-step explanation:

324+x²=729

x²=405===> x=√405===> 9√5

The pythagorean theorem (leg 1)2 + (leg 2)² = (hypotenuse)² the values is about 8.5, -8.5.

The Pythagorean theorem is used to find the length of the sides of a right triangle, not for solving equations like x² = 72.

To solve the equation x² = 72,  to take the square root of both sides to find the value of x:

√(x²) = √(72)

Since the square root of x² is x (the absolute value of x), the equation simplifies to:

x = √(72)

Now, let's find the approximate value of √(72):

√(72) ≈ 8.49

So, the equation becomes:

x≈ 8.49

Now, remember that the absolute value of x is a positive value, so the equation gives two possible solutions for x:

x= 8.49 → x = 8.49

x = -8.49 → x = -8.49

Rounded to the nearest tenth, the solutions are:

x ≈ 8.5 and x ≈ -8.5

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Answer:

C) as x –> ∞, q(x) –> –∞, and as x –> -∞, q(x) –> –∞

Step-by-step explanation:

use the end behavior chart to figure out the end directions of the graph. remember these

   E   O

+|↑↑|↓↑

–|↓↓|↑↓

all you need to do is look at the first number of the equation and ask yourself:

1. Is the first number even or odd?

2. is the first number positive or negative?

find where the answers to both meet on the chart.

so, in this question, the first number is even and negative. when using the chart we see that they meet at the ↓↓ which means that the end behavior on both sides is going towards negative infinity.

The wavelength for radio waves with frequency 3 × 10⁹ Hz is 0.1 m.

Wavelength of the radio wave= 3×10⁸/3×10⁹ = 0.1 m

Thus, we can conclude that the wavelength of the radio wave with frequency of 3 × 10⁹ Hz is 0.1 m.

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The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72

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The best point estimate for the proportion of all the residents opposed to the photo cop use is 60%  which is the fourth option.

Given that in a survey of 456 residents , 279 were opposed to the use of the photo cop for issuing traffic tickets.

We have to find the best point estimate for the proportion of all residents opposed to the photo cop use.

Total residents=456

Residents who opposed to the use of the photo cop for issuing traffic tickets=279

Proportion=number of residents who opposed/ total residents

=279/456

=0.611

=61.1%

The nearest option is fourth which is 60%.

Hence the best point estimate for the proportion for the proportion of all the residents opposed to the photo cop use is 60% which is option 4.

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Question is incomplete as it should include options which are :

1) 500

2)50%

3)300

4)60%

5)40%

The value for x and y are 140° and 70° respectively.

There are two ways to solve polygon question. Formula for the sum of interior angle and sum of the  exterior angle of regular polygon.

Sum of the interior = (n - 2)180

Sum of the exterior = 360/n

Where n = number of sides of a polygon.

The regular polygon in which x is one of its angle is called decagon

Sum of the interior = (n - 2)180

n = 10

Substitute n into the formula

Sum of the interior angle = (10 - 2)180

Sum of the interior angle  = (8)180

Sum of the interior angle = 1440

Each angle = 1400/10

x = 140°

For y, the three angles are similar.

sum of angle in a triangle = 180

Since the each triangle is an isoceles triangle, angle at each base will be y

40 + y + y = 180

2y = 180 - 40

2y = 140

y = 70°

Therefore, the value for x and y are 140° and 70° respectively.

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The domain of the function f(x) is:

11 ≥ x

Here we have the function:

[tex]f(x) = \sqrt{11 - x}[/tex]

Now, remember that the argument of a square root can only be a number equal to or larger than zero, so the domain of our function is defined by:

11 - x ≥ 0

Then, solving this for x, we get:

11 ≥ x

Concluding, the domain of the function f(x) is:

11 ≥ x

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The length of the rectangle = 2 - (1/3n) +(3/n²).

The formula for the area (taking this exists as a rectangle)

Area = length ⋅ width

where A exists the area of the rectangle

l exists the length of the rectangle and w exists the width of the rectangle.

If Area of the rectangle = length ⋅ width

then length of the rectangle = area/ width

Area = 6n² − n +9​

width = 3n²

Area = length [tex]*[/tex] width

length = area/ width

= (6n²  − n +9)/3n²

= 2 - (1/3n) +(3/n²).

The length of the rectangle = 2 - (1/3n) +(3/n²).

Therefore, the correct answer is option A. 2 - (1/3n) +(3/n²).

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Two ways to measure the relationship between the returns of two securities are correlation and covariance. That is options C and D.

Correlation can be defined as the measure of the difference between two variables in a statistical analysis.

Covariance can be defined as the measure of the relationship between two variables in statistical analysis.

Therefore, Two ways to measure the relationship between the returns of two securities are correlation and covariance.

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Answer:

25,132.74 miles

Step-by-step explanation:

Hello!

We are basically asked to find the circumference of the Earth's cross-section.

Circumference: [tex]C = 2\pi r[/tex]

We can replace 2r with the diameter, because the diameter is 2 times the radius.

Multiply the Diameter by pi:

It is around 25,132.74 miles around.