A garden hose can fill a swimming pool in 7 days, and a larger hose can fill the pool in 4 days. How long will it take to fill the pool if both hoses are used?

The provided rectangular box's surface area as a function of the base's side length is S(a) = a² + 8/a.

A solid object's surface area is a measurement of the overall space that the object's surface takes up.

In comparison to the definition of arc length for one-dimensional curves or the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, the mathematical definition of surface area in the presence of curved surfaces is significantly more complex:

Let a be the base's side length and h be the box's height. We are aware that the formula: can be used to calculate the volume of a rectangular box.

V = length * Width * Height

Since the base of this particular box is square,

l = a

w = a

h = h

Now, if we plug these values into the volume formula, we'll get:

2 = a*a*a

2  =a²h

h = 2/a²

Since the surface area up until this point will depend on only two variables, the objective was to minimize the number of variables.

We had to calculate h in terms of a because we wanted to make it a function of a.

We may now apply these to the box's surface area.

Given that this is an open rectangular box, one of the bases in the formula must be removed.

[tex]\begin{aligned}S & =2(b h+h l)+l b \\S & =2(a h+h(a))+a(a) \\S & =2(2 a h)+a^2 \\S & =a^2+4 a h \\S(a) & =a^2+4 a\left(\frac{2}{a^2}\right) \\S(a) & =a^2+\frac{8}{a}\end{aligned}[/tex]

Therefore, the provided rectangular box's surface area as a function of the base's side length is S(a) = a² + 8/a.

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Answer:

Step-by-step explanation: (Do not read this if it is a test)

Hello! 2 + 7x = 4x + 3 + 3x - 8.  How you first want to do this is to solve for x.  7x + 2 = 4x + 3 + 3x - 8.  Simplify the like terms.  7x + 2 = 4x + 3x + 3 - 8 is also equal to 7x + 2 = 7x - 5.  Subtract 2 from both sides.  7x = 7x - 7.  Divide both sides by 7.  7x/7 = 7x/7 - 7/7.  The answer is x = x - 1.  There is no solution because x cannot equal x minus 1.  An example of this is 3 cannot equal 3 - 1 or 2.  3 does not equal 2.  The answer is C.

Answer:The answer is C.

Step-by-step explanation:Hello! 2 + 7x = 4x + 3 + 3x - 8.  How you first want to do this is to solve for x.  7x + 2 = 4x + 3 + 3x - 8.  Simplify the like terms.  7x + 2 = 4x + 3x + 3 - 8 is also equal to 7x + 2 = 7x - 5.  Subtract 2 from both sides.  7x = 7x - 7.  Divide both sides by 7.  7x/7 = 7x/7 - 7/7.  The answer is x = x - 1.  There is no solution because x cannot equal x minus 1.  An example of this is 3 cannot equal 3 - 1 or 2.  3 does not equal 2.

The density of the unknown metal exists 8.9 g/mL.

The mass of an object divided by its volume is how dense it is. The gram per cubic centimeter (g/cm³) unit of density is frequently used. How much mass is present in a given area is referred to as density. Try to picture a drawer full of socks. Its density is particular. Consider that when you remove a sock, the drawer's density changes. This is due to the socks' shifting mass while the drawer's remaining constant volume.

The definition of density is the mass of a substance per unit volume. The degree to which matter is packed together is fundamentally measured by density. It is a specific physical quality of a specific object. Greek scientist Archimedes is credited with discovering the density principle.

The density (D) is equal to mass (m) divided by volume (V): D = m/V

To find the mass of the object:

m = 156 g - 105.5 g = 50.5 g

To find the volume of the volume:

V = 30.7 mL - 25 mL = 5.7 mL

The density is:

D = m/V = 50.5 g  / 5.7 mL = 8.9 g/mL

Therefore, the density exists 8.9 g/mL.

The complete question is:

A graduated cylinder was filled with water to the 25.0 mL mark and weighed. Its mass was 105.5g. An object made of an unknown metal was placed in the cylinder and completely submerged in the water. The water level rose to 30.7 mL. When reweighed, the cylinder, water and metal object had a total mass of 156.0g. Based on these measurement, what is the density of the unknown metal?

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Answer:

The amount invested at 8% is 64,500-32,000 = 32,500

Step-by-step explanation:

one investment: 3%, amount: x

the other: 8%, amount: 64,500-x because x is invested at 3%

0.03x+0.08(64,500-x) = 3,560

0.03x+5,160-0.08x = 3,560

-0.05x = -1,600 divide both sides by 0.05 and remember that -/- = +

x = 32,000 This is the amount invested at 3%

The amount invested at 8% is 64,500-32,000 = 32,500

An inequality for x considering the figure is written as

the value of x is 82.5

x cannot be right angle because it will be against the rule of angle in a point is 360 degrees

The inequality that represents the figure in terms of x is written using the knowledge that angles in a point is 360 degrees

x + 2x + x + 30 < 360

adding like terms

4x + 30 < 360

solving for x

4x < 360 - 30

4x < 330

x < 82.5

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Answer:

Why don't you use this app and take a picture and see if someone got the answer

The mode in data set of 12 students that gives the number of pets is 4, 3,0 as these number has frequently  many times .

The mode is the value that occurs the most frequently in a data set when it is unique. Like the median and mean, it can be used as a measure of central tendency. However, there may be multiple modes or none at all at times. When all observed values appear in a data set the same number of times, there is no mode.

The value that appears most frequently in a data set is the mode. One mode, multiple modes, or none at all can be present in a data set. The mean, or the set's average, and the median, or the set's middle value, are two other common measures of central tendency.

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The best name for quadrilateral QRST with coordinates Q(0, 0), R(2, 6), S(6, 6), and T(8, 0) include the following: C. Trapezoid.

In Geometry, there are different types of quadrilateral and these include the following:

Next, we would use an online graphing calculator to construct (plot) quadrilateral QRST on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral QRST on the x-coordinate and y-coordinate respectively as shown in the table.

By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a trapezoid.

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Answer:

To find the remainder when f(x) is divided by (x-a) , we substitute x = a in the polynomial f(x) and we get the remainder.

remainder = f(a)

In this case, we have f(x)=5x^6-2x^2-5, and x+2 is the divisor and we substitute x=-2

so, remainder = f(-2) = 5*(-2)^6-2*(-2)^2-5 = -643

So, the remainder when f(x) is divided by x+2 is -643

The slope-intercept form of the equation is y = (-5/3)x + 19

Her set-up time decrease by 5/3 hours/day

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system

(a) The slope-intercept form of  the equation of a line is y = mx+b,

where m is the slope (rate) and b is the y-intercept (starting point)

Let y be the set up time (hours) and x be the time (days)

m = (y₂-y₁)/(x₂-x₁)

where (x, y) are the coordinate of points on the line

From the graph: x₁ =3, y₁ = 14 and x₂ = 6, y₂ = 9

m = (9-14)/(6-3) = -5/3

y = mx + c

14 = (-5/3)×3 + c

14 = -5 + c

c = 14 + 5

c = 19

Thus, the equation is y = (-5/3)x + 19

(b) At day 0, x = 0:

y = (-5/3)x + 19

y = (-5/3)(0) + 19

y = 19 hours

The slope is decrease rate. Thus, her set-up time decrease by 5/3 hours/day

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Answer:



Step-by-step explanation:

sin 300° = sin (300° - 360°) = sin (-60°) = -sin 60° = -(1/2)

cos 945° = cos (945° - 360°) = cos (585°) = cos (-295°) = -cos 295°

tan (-675°) = -tan (675° - 360°) = -tan 315°

so

sin 300° − cos 945° + tan(−675°) = -(1/2) - (-cos 295°) + (-tan 315°)

It is not a trivial task to simplify the above equations without using a calculator.



= -(1/2) + cos 295° + tan 315°

As we know that cos(x) = cos(360°-x) = -cos(x) and tan(x) = -tan(360°-x) = -tan(x)

= -(1/2) - cos 295° - tan 315°

As we know that cos(295°) = cos(360°-65°) = cos(65°) and tan(315°) = tan(360°-45°) = tan(45°)

= -(1/2) - cos(65°) - tan(45°)

= -(1/2) - 0.4226 - 1

= -0.5 - 0.4226 - 1

= -1.4226

.

a. visits of the college students, b. herbal tea, d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.

Despite the name, herbal tea is not actually "tea" as these beverages typically do not contain the leaves or leaf buds of tea plants. Herbal teas are made from tisanes, which are blends or infusions of dried fruits, flowers, spices or herbs in water.

The lurking variable in this experiment is - a. visits of the college students.

The explanatory variable in this experiment is - b. herbal tea

Which of the following may be correctly concluded from this study - d. The results of the study are not convincing because the effect of herbal tea is confounded with several other factors.

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Answer:

I didn't understand the question

Step-by-step explanation:

I think u have written wrong question..

Answer: 1 3/4 = 3/4 + 3/4 + 1/4, or 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4

Step-by-step explanation:

To earn back the amount Helen spent on certification, she would need to earn $90. Since her base salary is $55 per month, she would need to teach an additional $90 - $55 = $35 in classes. Since she earns $5 per class, she would need to teach $35 / $5 = 7 classes.

So, Helen will need to teach 7 classes to earn back the amount she spent on certification.

Her total earning for teaching 7 classes would be $55 (base salary) + $5 (per class) * 7 (classes) = $110

Therefore Helen's expenses and earning would be $90 (certification cost) and $110 (earning) respectively.

Answer:

y=5/7

Step-by-step explanation:

-7y=-34+29

-7y=-5

y=-5/-7

y=5/7

Answer:

y = 9

Step-by-step explanation:

-x -7y = -34

if x = -29:

-(-29) -7y = -34

+29 - 7y = -34

-7y = -34 - 29

-7y = -63

y = -63/-7

y = 9

Check:

-(-29) - (7*9) = -34

29 - 63 = -34

Answer:4999 combos

Step-by-step explanation:

max:75999

min:71000

*zip codes are 5 digits long

75999-71000=4999

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

[tex]Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7[/tex]

The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.

f(x) 10 3 5 2 Let glx) be a twice differentiable function defined by another differentiable function f(x), such that 9 (2) = 21+ J' f (t) dt: Selected values of f(x) are given in the table above.

We can calculate g'(x) as follows:

g'(x) = 2f'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3

1. Start by taking the derivative of g(x) with respect to x. This is done using the chain rule, since g(x) is defined by another differentiable function f(x):

g'(x) = d/dx[21 + J' f(t) dt] = 2f'(x)

2. Now, substitute the function f(x) into the equation for g'(x):

g'(x) = 2(10 + 3x + 5x^2 + 2x^3) = 20 + 6x + 10x^2 + 4x^3

The derivative of the function g(x), which is defined by another differentiable function f(x), is g'(x) = 20 + 6x + 10x^2 + 4x^3.

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Answer:

the first expression i think is the line going downwards

and the second is the line going upwards

Step-by-step explanation:

i think sorry if it wrong

hope the annotating will help you! If this is not the thing you want let me know so that I can edit the way the question actually is...

The decimal number will be rounded to the nearest hundredth value as 1.93 to the nearest hundredth.

Look at the rightmost place value to see how to round a number to the closest hundredth (the thousandths this time). In the same way, simply eliminate all the digits to the right if the number is four or less. Remove all the digits to the right after adding 1 to the digit in the hundredths position if the number is five or above.

Take into account the hundredths place (9) to convert 1.299 to the nearest tenth, 1.3. To round to the nearest hundredth, consider the thousandths place (9) The tenth would be rounded up in this situation to the nearest whole number, 1.30, which is equal to 1.3.

   Cos θ= adj/hyp

   Cos 74° = x/7

         x = 1.93

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The value of the following venn expressions of sets is (A)=1 ,(B)=50,(C)=20 and (D)=130 respectively.

A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.

Symmetric difference between two sets A and B defined by,

AΔB=(A\B) ∪ (B\A)

AΔB=(A∩B') ∪(A'∩B).

we have n(A)=20 n(B)=50, n(A∩B)=0, n(U)=200

SO,

(A) Find n(A∩B)

n(A∩B) =0 (GIVEN)

(B) Find n(A∩B')

n(A∩B') =n(B)-n(A∩B)

          = 50-0

           =50

(C) Find n(A∩B')

n(A'∩B) =n(A)-n(A∩B)

          =20-0

          =20

(D) n(A'∩B') =n(U)-n(A'∩B)-n(A∩B)-n(A∩B')

             =200-20-0-50

            = 130.

thus, the above is the value of expression.

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Answer: 2/3

Step-by-step explanation: you are looking for the constant of proportionality. We find this with the following formula: K = Y/X

About 80 necklaces have more than 28 beads. Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.

P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)

P(x > 28) = P(x - 24 / 4 > 1)

P(x > 28) = 1 - ∅1

P(x > 28) = 1 - 0.8413

P(x > 28) = 0.1587

Multiply both sides by 500, then we have

500 P(x > 28) = 0.1587 × 500

500 P(x > 28) = 79.35

500 P(x > 28) ≈ 80

About 80 necklaces have more than 28 beads. Then the correct option is C.

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The missing options are given below.

A. About 24 devices have more than 28 beads.

B. About 48 necklaces have more than 28 beads.

C. About 80 necklaces have more than 28 beads.

D. About 96 necklaces have more than 28 beads.

A. The probability that a sample of taxpayers from this income group are:

n = 30: 0.8159

n = 50: 0.8796

n = 100: 0.9332

n = 400: 0.9984

B. Advantages of a larger sample size are:

it increases precision

reliability of estimate of the population mean

standard error of the mean decreases

Using the z-score below:

For a sample size of 30, the z-score is 1.28.

For a sample size of 50, the z-score is 1.64.

For a sample size of 100, the z-score is 2.33.

For a sample size of 400, the z-score is 3.29.

a. The probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $157 of the population mean for each of the following sample sizes:

n = 30: 0.8159

n = 50: 0.8796

n = 100: 0.9332

n = 400: 0.9984

b. The advantage of a larger sample size when attempting to estimate the population mean is that it increases the precision and accuracy of the estimate. As the sample size increases, the sample mean becomes a more reliable estimate of the population mean, and the standard error of the mean decreases.

In this case, as the sample size increases from 30 to 400, the probability of the sample mean being within 157 of the population mean increases from 0.8159 to 0.9984.

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0.708 more of the deck did connor take than ethan.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

connor takes 7/8 of the cards from a deck,

ethan took 1/6 of the cards from the same deck.

i.e. difference of them = 7/8 - 1/6

                                      =0.708

Hence, 0.708 more of the deck did connor take than ethan.

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The required solution of the given algebraic expression is x = 6.

The algebraic expression consists of constants and variables using mathematical operators. eg x + y + z, or y = x + z etc.

Here,
Given an algebraic expression,
x + 1 +1 +1 +1 +1 +1 +1  = 1 +1 +1 +1 +1 +1 +1 + 1 +1 +1 +1 +1 +1

Combining like terms on each side of the equation, we get,
According to the question

x + 7 = 13
x = 6

Thus, the required solution of the given algebraic expression is x = 6.

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Answer:

x + 7 = 13

Step-by-step explanation:

(in case you also need it) x = 6

Hey there!

Answer:

[tex]b=3,-\frac{8}{3}, -\frac{5}{2}[/tex]

Hope this helps!

The potential energy of the spring-mass system is equal to  1/2kx². Thus, figure I is a correct representation.

where x is the mass's deviation from the average location, or O.

Consequently, the graph would be symmetric about a vertical line that passes through O and would exhibit a quadratic variation with respect to x.

Thus, figure I is a correct representation.

The graph illustrates how the potential and kinetic energy of a block coupled to a spring that follows Hooke's law changes over time.

Due to the potential and kinetic energy's x2 variation, both graphs are parabolas.

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Answer: It's the top right

Step-by-step explanation:

Every time the line hits a point on a line where the x and y values are whole numbers, it rises 3 and goes over 2 to get to the next point.