An architect is designing a house. He wants the bedroom to have the dimensions of 9 ft by 5 ft by 7 ft. The architect doubles one dimension to create the den. Does that mean the den will have double the volume of the bedroom?

The volume of water in the trough when it is 7 inches deep is 12 x (1/12 x 7) = 7 ft3.The rate of increase in water level is equal to the rate of water flow divided by the volume of water in the trough.Rate of increase in water level = 13 ft3/min / 7 ft3 = 1.86 ft/min

The trough is 12 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. We need to calculate how fast the water level is rising when the water is 7 inches deep. First, we need to calculate the volume of water in the trough when it is 7 inches deep. The volume of water in the trough is 12 x (1/12 x 7) = 7 ft3.Now, we can calculate the rate of increase in water level. The rate of increase in water level is equal to the rate of water flow divided by the volume of water in the trough.

(12 ft)(7 in/12 ft)(1 ft)

= 7/12 ft3

(13 ft3/min) / (7/12 ft3)

= (13/7) (12/1) ft/min

The rate of water level rising when the water is 7 inches deep is (13/7) (12/1) ft/min.

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The ability to order items in a sequence, such as longest to shortest, is known as Seriation.

Seriation is a cognitive skill that involves arranging objects, events, or ideas in a particular order or sequence. It is a crucial aspect of cognitive development and is typically acquired during early childhood. Seriation is the ability to mentally order objects along a quantitative dimension, such as size, weight, or length.

Seriation involves comparing and ordering items based on specific criteria. For example, if given a group of objects of different lengths, a child who has developed seriation skills will be able to arrange the objects in order from shortest to longest. Similarly, if given a group of numbers, a child who has developed seriation skills will be able to arrange them in order from smallest to largest.

Seriation is an important cognitive skill that is used in various areas of life, including academic, professional, and personal domains. It allows individuals to organize information and ideas in a logical and meaningful way, which can facilitate more efficient processing and understanding of complex concepts.

Overall, seriation is a fundamental cognitive skill that plays a crucial role in various aspects of life, including problem-solving, decision-making, and organization. It is an essential skill that supports the development of higher-order thinking skills, such as analysis, evaluation, and synthesis.

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Answer:

The answer is 12                                

Step-by-step explanation:

2 x 12 + 1 = 25

P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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Answer:

17/6

Step-by-step explanation:

El único problema aquí es conocer las operaciones con el surd por favor note que;

√a * √a = a Así;

√3 * √3 = 3

Entonces, la otra cosa a tener en cuenta es el orden de las ecuaciones.

Resolvemos los corchetes antes de proceder con cualquier otra cosa.

1 / 3√3 * 5 / 4√3 = 5/12 (3) = 5/36

Es esto lo que agregamos a 7/4

5/36 + 7/4 = (5 + 63) / 36 = 68/36 = 17/6

Answer: $500=$1.50x+$3.00y

Step-by-step explanation:

i’m p sure that bc the x and ya represent the amount of ppl buying it and it adds to a total of 500

Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the solutions to various problems involving ratios, proportions, and scale factors.

The ratio of 15 apples ot 25 oranges can be written several ways, with and without units:

  15 apples to 25 oranges, or 15 to 25.

  Reduced to 3 apples to 25 oranges, or 3 to 5

  15 apples : 25 oranges, or 15 : 25

  Reduced to 3 apples : 5 oranges, or 3 : 5

  15 apples / 25 oranges, or 15/25

  Reduced to 3 apples / (5 oranges), or 3/5

You can solve the proportion ...

  x/9 = 10/12

by multiplying both sides by 9:

  x = 9·10/12 = 90/12

  x = 15/2 = 7.5

If each inch represents 12 ft, then 8 inches represents 8·12 ft = 96 ft.

The actual length of the back wall is 96 feet.

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Answer:

m=-2

b=1

Step-by-step explanation:

y=mx+b

b=y-intercept

y intercept is at (0,1) so b is 1

m=slope

taking 2 points (0,1) and (-1, 3) and using the slope formula:

(1-3)/(0-(-1))=2/-1=-2

m=-2

Things to take away:

y-intercept form of a linear function is y=mx+b

where m is the slope

and b is the y value of the y-intercept

the slope formula is \(m=(y_{1} -y_{2})/(x_{1}-x_{2})\\\)

given points \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\)

Answer:

B

Step-by-step explanation:

edge 2021

Answer:

b

Step-by-step explanation:

Answer:

38 kids on each team about.

I am Not 100% sure but I hope this Helps!

So D.

The value of G, correct to three significant figures and in standard form, is\(4.59 \times 10^-^1\).

To work out the value of G using the given formula G = √(m/t^2), we need to substitute the given values for m and t.

Given:

m = 5.4 x 10^-5

t = 1.6 x 10^-2

Substituting the values into the formula:

\(G = \sqrt(5.4 \times10^-^5 / (1.6 \times10^-^2)^2)\)

First, we need to square the value of t:

\(t^2 = (1.6 \times10^-2)^2 = 2.56 \times 10^-^4\)

Next, we divide m by t^2:

m / t^2 = 5.4 x 10^-5 / 2.56 x 10^-4 = 0.2109375

Finally, we take the square root to find G:

G = √0.2109375 = 0.459

Rounding the answer to three significant figures, the value of G is approximately 0.459.

In standard form, this is 4.59 x 10^-1.

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Answer:

\( \dfrac{-7600}{3} \)

Step-by-step explanation:

The plane is descending, so the change in height is a negative change.

rate of descent = (change in height)/time

rate of descent = (new height - old height)/time

rate of descent = (7400 ft - 15000 ft)/(3 min)

rate of descent = (-7600 ft)/(3 min)

Answer: \( \dfrac{-7600}{3} \)

Answer:

8/2 or 4/1

Step-by-step explanation:

To find the slope, you simply count how high up one point is from another (0,0 to 2,8) and then how far over. Since 2,8 is 8 points up from 0,0 the numerator of our slope would be 8; and since 8,2 is two over from 0,0 the denominator is 2. Simplify this to 4/1.

Answer:

B is a true statement.

\( - 8 < - 3\)

Hope this image helps you :)

Answer:

the answer to question 1 is 24 and the answer to number 2 is 1

Answer:

frist one is 24. second is 1

Step-by-step explanation:

The graph of the function y = sec(x + π/3) is a periodic function with vertical asymptotes and a repeating pattern of peaks and valleys. It has a phase shift of -π/3 and the amplitude of the peaks and valleys is determined by the reciprocal of the cosine function.

The function y = sec(x + π/3) represents the secant of the quantity (x + π/3). The secant function is the reciprocal of the cosine function, so its values are determined by the values of the cosine function.

The cosine function has a period of 2π, meaning it repeats its values every 2π units.

The graph of y = sec(x + π/3) will have vertical asymptotes where the cosine function equals zero, which occur at x = -π/3 + kπ, where k is an integer.

These vertical asymptotes divide the graph into intervals.

Within each interval, the secant function has a repeating pattern of peaks and valleys. The amplitude of these peaks and valleys is determined by the reciprocal of the cosine function.

When the cosine function approaches zero, the secant function approaches positive or negative infinity.

To graph the function, start by identifying the vertical asymptotes and plotting points within each interval to represent the pattern of peaks and valleys.

Connect these points smoothly to create the graph of y = sec(x + π/3). Remember to label the vertical asymptotes and indicate the periodic nature of the function.

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The amount of milk the first and second container originally has is 174/43 gallons and 87/43 gallons, respectively.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let "x" = amount of milk the second container has

If the first container has twice as much milk as the second, then the amount of milk the first container has is "2x".

If 2 gallons of milk was used from the second container and 3 gallons of milk was used from the first container, and the first container has 45 times as much milk as the second, then

x - 2 = amount of second container

2x - 3 = amount of first container

2x - 3 = 45(x - 2)

Simplify and solve for x.

2x - 3 = 45(x - 2)

2x - 3 = 45x - 90

43x = 87

x = 87/43

2x = 2(87/43) = 174/43

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Answer:

C

Step-by-step explanation:

C is the only graph that passes the vertical line test.

Answer:

c

Step-by-step explanation:

The line doesn't cross eachother

The largest angle the swimmers must turn between the buoys is 82.8°. Therefore, option B is the correct answer.

Given the following data:

Side AB = c = 400 meters.

Side BC = a = 500 meters.

Side CA = b = 600 meters.

In order to determine the largest angle at which the swimmers must turn between the buoys, we would apply the law of cosine.

Form the law of cosine, for angle C we have:

cos C= (a²+b²-c²)/2ab

=(500²+600²-400²)/2×500×600

=450000/600000

cos C=0.75

⇒C=41.4°

For angle B we have:

cos B= (a²+c²-b²)/2ac

=(500²+400²-600²)/2×500×400

=1/8

cos B=0.125

⇒B=82.8°

For angle A, we have:

cos A= (b²+c²-a²)/2ac

=(600²+400²-500²)/2×600×400

=9/16

cos A=0.5625

⇒A=55.8°.

The largest angle the swimmers must turn between the buoys is 82.8°. Therefore, option B is the correct answer.

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Step-by-step explanation:

v = u + at

v-u = at

a = (v -u)/t

When t = 4, u=10, v=50

a = (50-10)/4

a= 40/4

a = 10

The 16th term of the arithmetic sequence is -60.

To find the 16th term of an arithmetic sequence with a first term of 0 and a common difference of -4

we can use the formula for the nth term of an arithmetic sequence:

nth term = a + (n - 1)d

where:

a = first term

d = common difference

n = term number

Substituting the given values, we have:

16th term = 0 + (16 - 1) × (-4)

= 0 + 15(-4)

= 0 - 60

= -60

Therefore, the 16th term of the arithmetic sequence is -60.

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Answer:

y = -3x - 4

Step-by-step explanation:

Find the slope.

y2-y1/x2-x1

-9/3 = -3

-3 is the slope. You know the y-intercept is -4 since (0, -4) is a point. The y-intercept is the value of y where x = 0.

So if you know the slope is -3 and the y-intercept is -4, plug it into slope-intercept form.

y = mx+b

y = -3x - 4

Answer:

A

Step-by-step explanation:

for the number to be greater than 11 x cannot be negative so we can rule out C and D. 0 does not work as x so we can rule out B. we are left with A as the answer.

When four and a half is divided by three-fifth is equal to seven and a half.

The division means the separation of something into different parts, sharing of something among different people, places, etc.

The expressions are given below.

Four and a half is divided by three-fifth.

Then we have

\(\rightarrow \dfrac{4 + \frac{1}{2}}{\frac{3}{5}}\\\\\\\rightarrow \dfrac{\frac{9}{2}}{\frac{3}{5}}\\\\\\\rightarrow \dfrac{9 \times 5}{2 \times 3}\\\\\\\rightarrow \dfrac{15}{2} \\\\\\\rightarrow 7 + \dfrac{1}{2}\)

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Answer:

(a)= 224

(b)=352

Step-by-step explanation:

(a) in a calculator type 35%x640 and it will have your answer, 224

(b) do the same thins as question a but just add the 2 numbers together

When k is o doesn't satisfy the equation.

Value of \($\mathrm{k}=(?)$\), equation \($\mathrm{kx}(\mathrm{x}-2)+6=0$\) has equal roots.

\(& \Rightarrow \mathrm{kx}(\mathrm{x}-2)+6=0 \\\)

\(& \mathrm{kx} x^2-2 \mathrm{kx}+6=0 \\\)

two roots of quadratic equation

\(& \alpha, \beta= \frac{-\mathrm{b} \pm \sqrt{\mathrm{b}^2-4 \mathrm{ac}}}{2 \mathrm{a}} \\\)

\(& \alpha, \beta= \frac{+2 \mathrm{k} \pm \sqrt{(-2 \mathrm{k})^2-4 \times 6 \times \mathrm{k}}}{2 \times \mathrm{k}} \\\)

\(& \alpha, \beta=2 \mathrm{k} \frac{\pm \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\\)

\(\alpha=\beta \\\) The roots are qual

\(& \Rightarrow \frac{2 \mathrm{k}+\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}}=\frac{2 \mathrm{k}-\sqrt{4 \mathrm{k}^2-24 \mathrm{k}}}{2 \mathrm{k}} \\\)

\(& \Rightarrow 2 \sqrt{4 \mathrm{k}^2-24 \mathrm{k}}=0 \\\)

\(& \Rightarrow 4 \mathrm{k}^2-24 \mathrm{k}=0 \\\)

\(& \Rightarrow 4 \mathrm{k}(\mathrm{k}-6)=0 \\\)

\(& \Rightarrow \mathrm{k}=0 \text { or } \mathrm{k}=6\)

\($\Rightarrow \mathrm{k}=6[\because \mathrm{k} \equiv 0]$\) as\($\mathrm{k}=0$\)  doesn't satisfy the equation.

The complete question is,

For what value of \($\mathrm{k}$\), are the roots of the quadratic equation, \($\mathrm{kx}(\mathrm{x}-2)+6=0$\) equal?

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Answer:

Step-by-step explanation:

milk: 3 *\(\frac{14}{15} = \frac{14}{5}\) ;

flavors: 3*\(\frac{1}{15} = \frac{1}{5}\);

The amount of milk is (14/5) and the quantity of flavours will be 1 / 5 litre.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the vanilla milkshake is made by mixing milk and flavours in a ratio of 14:1 . The quantity required to make 3 litres of the milkshake will be calculated as,

Ratio = 14: 1

Let the constant term between the ratio is x. From the equation,

14x + x = 3

15x = 3

x = 1 / 5

The quantity of milk = 14x = 14 x (1/ 5 ) = 14 / 5 liters

The quantity of flavors = x = 1 / 5 liters

Therefore, the amount of milk is (14/5) and the quantity of flavours will be 1 / 5 litre.

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