A tank holds 3,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.

Answer:

The greatest common factor (GCF) of the numerator (4) and the denominator (16) is 4

GCF(4,16) = 4

4/16 = 4 ÷ 4/16 ÷ 4

= 1/4

hope it helps you

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

The total number of pennies you have at the end are 2^26 pennies

Imagine, at the first day  have only one penny. Then tomorrow  have 2 pennies, next day have 4 (2x2), next day have 8 (4x2), next day have 16 (8x2) and so forth.

Geometric Sequence

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio

It looks like geometric sequence  (the ratio between the number of pennies that  from the 2nd day and the 1st day is 2)

So, by using geometric sequence theorem  can total those pennies until day 27

S (total pennies at day-27) = (1)(2^27-1) / 2-1 = 2^26 pennies

So, have 2^26 pennies.. a big number of pennies=))

The formula is: S = a( r^n-1) / r-1

a= the number of pennies that have got at the 1st day

n= number of days  spent to collect those pennies)

r= the ratio of the number of pennies

2^26 pennies

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Answer:

The unit of measure used in the study is "inches"

Queremos ver cuantos miembros hay en la familia, veremos que son 10 en total.

Primero conocemos al señor y la señora Mostaza, es decir, tenemos dos personas.

Luego se nos dice que tienen 6 hijos, entonces ahora tenemos:

6 + 2 = 8 personas en total.

Finalmente, sabemos que tanto el señor Mostaza como la señora Mostaza tienen un hermano, es decir, sumamos otras 2 personas para obtener:

8 + 2 = 10 personas en total.

Así podemos concluir que hay 10 personas en la familia.

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Answer:

116°

Step-by-step explanation:

(Angle sum property of a triangle = 180°)

angle A + angle C + angle ABC = 180°

66° + 50° + angle BAC = 180°

116° + angle ABC = 180°

angle ABC = 180° - 116°

angle ABC = 64°

angle ABD + angle ABC = 180°

angle ABD + 64° = 180°

angle ABD = 180° - 64°

angle ABD = 116°

So, the measure of the unknown angle is 116°

Answer:7/8

Step-by-step explanation:

Answer:

The diagonals are perpendicular.

The diagonals are congruent to each other.

The diagonals bisect the vertex angles.

The statements that are true of squares include:

It should be noted that a square simply means a shape that has four sides equal. The angles are also 360° since they're 90° each.

In squares, the diagonals are perpendicular and the diagonals are congruent to each other.

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Answer:

The width is 64.3 inches

Step-by-step explanation:

Given

\(d = 90\) --- diagonal

\(h = 63\) --- height

Required

Determine the width (w) of the TV

To do this, we make use of Pythagoras theorem which is illustrated as:

\(d^2 = h^2 + w^2\)

So, we have:

\(90^2 = 63^2 + w^2\)

Evaluate all squares

\(8100 = 3969 + w^2\)

Collect like terms

\(w^2 = 8100 - 3969\)

\(w^2 = 4131\)

Take positive square roots of both sides

\(w = \sqrt{4131\)

\(w = 64.3\) -- approximated

Answer and Explanation: The answer and explanation is in the image.

Yes, you would distribute the exponent to both the denominator and numerator. For example, if you had an expression like (2/3)^4, you would distribute the exponent to end up with (2^4)/(3^4).

For example, if you have an expression like (2/3)^4, the exponent of 4 should be distributed to both the numerator and denominator, resulting in (2^4)/(3^4). This is equivalent to multiplying the numerator and denominator by the same amount, 4 times. This is the same as writing (2*2*2*2)/(3*3*3*3), or simply

16/81.

1. Start with the expression

(2/3)^4

2. Distribute the exponent of 4 to the numerator and denominator, resulting in

(2^4)/(3^4)

3. This is equivalent to multiplying the numerator and denominator by 4, so (2^4)/(3^4)

= (2*2*2*2)/(3*3*3*3)

4. Simplify the expression to 16/81

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Answer:

6.53

Step-by-step explanation:

cos(theta)= adjacent/hypotenuse

cos(40)= 5/h

H= 5/cos(40)

=6.527

Rounded to the nearest hundredth will be 6.53

Answer:

its b

Step-by-step explanation:

Answer:

4.2

Step-by-step explanation:

Constant of proportionality = y/x = 8.4 / 2 = 4.2

To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

Answer:

Solution given:

f(x) = x +1 and g(x) = x²,

now

(gºf)(x) =g(fx)=g(x+1)=(x+1)²

B) (gºf)(x) = (x + 1)^2

Answer:

Percentage Calculator: 100. is what percent of 500.? = 20.

Step-by-step explanation:

1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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Answer: 7

and maybe 5.83

Step-by-step explanation:

If she worked 5 days a week, and worked the same hours of those days, then the answer is 7. You simply divide 35/5 which gives you that answer. And they’ve already given you the answer for Saturday, so yeah.

But you did say she only worked 5 days a week—in 35 hours. And you also said “how many hours did she work on the other days”. If Saturday’s hours was already stated, then are you implying she worked for 6 days instead of 5? Because there’s 7 days a week and if Saturday is unaccounted for, then she worked 6 days. In that case, your answer would be 5.83.

We can identify the lower extreme (min), upper extreme (max), first quartile (Q1), second quartile (Q2) and third-quartile (Q3) in the box-plot as:

The box-plot always represent this values in the same way (with different numeric values for each case).

Answer:

1, 15, 6.5, 8 [Second option]

Answer:

be adding more money

Step-by-step explanation:

deposit means to add withdraw means to take out

Answer:

increase

Step-by-step explanation:

Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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Answer:

25/9

Step-by-step explanation:

I took the test (:

plz mark me brainliest <3

Answer:

C!!!!!!! MARK ME BRAINLIEST PLS!!!

Step-by-step explanation:

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

-147

Step-by-step explanation:

We can solve this by plugging in p = 5 and q=−2 and then evaluating using PEMDAS which tells us the order we do the math in by operation

Remember,

PEMDAS means

Parenthesis

Exponents

Multiplication and Division ( perform going left to right )

Addition and Subtraction ( perform going left to right )

-3(p-q)²

==> plug in p = 5 and q = -2

-3(5-(-2))²

==> remove parenthesis on -2

-3(5 + 2)²

==> do the operations inside of the parenthesis

-3(7)²

==> do the exponents

-3(49)

==> multiply -3 and 49

=-147

Answer:

See step by step.

Step-by-step explanation:

lets define the events:
A: cuban festival        C: tropical Garden
B: street art show      D: african festival

a) theoretically the probability is

\(P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\\)
This is 25% (for each one, equally)

b) The experimental probability is given by:

\(P(A)= \frac{32}{150} =0.2133\)

\(P(B)= \frac{38}{150} =0.2533\)

\(P(C)= \frac{35}{150} =0.2333\)
\(P(D)= \frac{45}{150} =0.3000\)

c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.