100 points! Please help If you don't know it don't answer it.
There are approximately 7.48 liquid gallons in a cubic foot. If a cylindrical water tank holds 1,200 liquid gallons and has a radius of 2.4 feet, what is the approximate height of the water tank? Approximate using π = 3.14 and round to the nearest tenth.

(A) 2.2 feet
(B)8.9 feet
(C)27.9 feet
(D) 124.1 feet

Answer:

Null hypothesis (H0): Children with antisocial tendencies have the same difficulty recognizing the emotion of surprise as children without antisocial tendencies. Symbolically: μ = 11.80

Alternative hypothesis (H1): Children with antisocial tendencies have a harder time recognizing the emotion of surprise compared to children without antisocial tendencies. Symbolically: μ > 11.80

The critical region for α = 0.05 with the t distribution would be in the upper tail of the distribution, as this is a one-tailed test (since the alternative hypothesis is directional). The degrees of freedom (df) would need to be determined based on the sample size and specific statistical test being used, but the given information does not provide the value of df.

The estimated standard error would need to be calculated using the given sample size, sample mean, and sample standard deviation. The t statistic would then be calculated as the difference between the sample mean and the hypothesized mean (11.80), divided by the estimated standard error.

Once the t statistic is calculated, it would need to be compared to the critical value of t for the appropriate degrees of freedom and α level (0.05) to determine if it falls in the critical region, and therefore whether the null hypothesis is rejected or not. Based on the given information, the t statistic is not provided, so it is not possible to determine if the null hypothesis should be rejected or not.

Step-by-step explanation:

Answer:

The answer would be (x+10)(x-7)

Step-by-step explanation:

The way I learned it was the numbers would multiply to get 70, but add to get 3. Multiples of 70 are 1, 2, 5, 7, 10, 14, 35, 70. Out of these the only one that works is 10 and 7. Using foil, we get x^2-7x+10x-70 which becomes x^2+3x-70

Answer: 6

Solution:

Suppose that the bag contains 2 red tokens, 4 yellow tokens, and x blue

tokens.

Then the likelihood of drawing a blue token is 2-4 ty, and the possibility of drawing a token that is not blue is 2+4+8

If the two likelihoods is equal, we can make the equation below.

X

2+4

2+4+*=2+4+*

Solve for x, = * = 6.

so, there must be 6 blue tokens in the bag.

Therefore, the equation of the line that is perpendicular to the given line and passes through the point (−3,4) is [tex]y=(-2/3)x+6[/tex].

Parallel lines are two lines in a plane that never intersect, no matter how far they are extended. In other words, they are always at the same distance from each other and never converge or diverge. Parallel lines have the same slope and are always equidistant. In geometry, parallel lines are denoted by a double vertical line symbol (||) placed between them. They are an important concept in geometry and have many real-world applications, such as in architecture, engineering, and computer graphics.

Find the equation of the line that is perpendicular to this line and passes through the point  3, 4.

The given line is −6x + 4y = 5. To find the equation of a line that is parallel to this line and passes through the point (−3,4), we can use the fact that parallel lines have the same slope. The slope of the given line can be found by rearranging it to the slope-intercept form: y = (3/2)x + (5/4), which has a slope of 3/2.

Therefore, the slope of any line parallel to the given line will also be 3/2. We can use this slope and the point-slope form of a line to find the equation of the line we're looking for:

[tex]y - y_1 = m(x - x1)[/tex], where (x1, y1) = (-3, 4) and m = 3/2

[tex]y - 4 = (3/2)(x + 3)[/tex]

[tex]y - 4 = (3/2)x + 9/2\\[/tex]

[tex]y = (3/2)x + 9/2 + 4[/tex]

[tex]y = (3/2)x + 17/2[/tex]

Therefore, the equation of the line that is parallel to the given line and passes through the point (−3,4) is y = (3/2)x + 17/2.

To find the equation of a line that is perpendicular to the given line and passes through the point (−3,4), we can use the fact that perpendicular lines have negative reciprocal slopes. The slope of the given line is 3/2, so the slope of any line perpendicular to it will be -2/3.

Using this slope and the point-slope form of a line, we can find the equation of the line we're looking for:

[tex]y - y_1 = m(x - x1)[/tex], where (x1, y1) = (-3, 4) and m = -2/3

[tex]y - 4 = (-2/3)(x + 3)[/tex]

[tex]y - 4 = (-2/3)x - 2[/tex]

[tex]y = (-2/3)x + 2 + 4[/tex]

[tex]y = (-2/3)x + 6[/tex]

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The area of Triangle A is 12 square units, the area of Rectangle B is 30 square units, and the area of the whole figure is 42 square units.

What is rectangle?

A rectangle is a four-sided two-dimensional geometric shape in which all angles are right angles (90 degrees) and opposite sides are parallel and equal in length. This means that a rectangle has two pairs of congruent sides and its opposite sides are parallel.

To find the area of each part of the figure and the whole figure, we need to use the formulas for the area of a triangle and the area of a rectangle.

First, we can find the area of the triangle:

Area of Triangle A = (1/2) x base x height = (1/2) x 4 x 6 = 12 square units.

Next, we can find the area of the rectangle:

Area of Rectangle B = length x width = 5 x 6 = 30 square units.

To find the area of the whole figure, we can add the area of Triangle A and Rectangle B:

Area of Whole Figure = Area of Triangle A + Area of Rectangle B

= 12 + 30

= 42 square units.

Therefore, the area of Triangle A is 12 square units, the area of Rectangle B is 30 square units, and the area of the whole figure is 42 square units.

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Answer:

The answer to your problem is, ∞

Step-by-step explanation:

Well there can be multiple ways to make 2/3 equivalent to another here’s how.

We know that 4/6 is equivalent to 2/3 but how exactly?

Well put it into a fraction like this:

[tex]\frac{2*2}{3*2}[/tex] Note: The denominator and the numerator needs to be multiplied by the same number in order for the fraction to be equiavalent.

= 4/6

Thus the answer to your problem is, ∞

The limit of f(x) as x approaches 0 is 0.

As x approaches 0, we can see that both the numerator and denominator of the expression in the given inequality approach 0. Thus, we can use L'Hopital's rule to evaluate the limit.

Taking the derivative of the numerator and denominator separately, we get:

lim x→0 [(2x - 4x^3) / 2x] = lim x→0 [1 - 2x^2] = 1

lim x→0 [x^3 / 4] = 0

Since 0 ≤ f(x) ≤ 1/4x^3, we can conclude that as x approaches 0, f(x) approaches 0 (by the squeeze theorem).

Therefore, the limit of f(x) as x approaches 0 is 0.

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The value of angle x as represented can be determined to 1 decimal place as required to be; 57.8°.

It follows from the task content that the given triangle can be solved for variable x using the sine rule.

Therefore;

11 / sin x = 8 / sin (38)

sin x = 11 sin (38) / 8

x = 57.8°.

Ultimately, the value of angle x as required in the task content is; 57.8°.

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Answer:

arc ADB = 10π m

A (shaded) = 30π m^2

Step-by-step explanation:

Given:

∠AOB = 60° (it is a central angle, which is equal to the arc on which it rests on)

r (radius) = 6 m

Find: arc ADB - ? A (shaded) - ?

If arc AB is 60°, then arc ADB is (remember, that a full circle forms an angle of 360°):

[tex] \alpha = 360° - 60° = 300°[/tex]

Now, we can find the length of the arc ADB:

[tex]l = \frac{2\pi \times r \times \alpha }{360°} = \frac{2\pi \times 6 \times 300°}{360°} = \frac{3600\pi}{360°} = 10\pi \: m[/tex]

The shaded region is a cutout of a circle

We can find its area by using this formula:

[tex]a(shaded) = \frac{\pi {r}^{2} \times \alpha }{360°} = \frac{\pi \times {6}^{2} \times 300°}{360°} = \frac{10800\pi}{360°} = 30\pi \: {m}^{2} [/tex]

the probability of getting a hand with exactly 2 face cards is about 2.41%, or roughly 1 in 41 hands.

How to solve the probability?

A standard deck of 52 cards contains 12 face cards (4 Kings, 4 Queens, and 4 Jacks) and 40 non-face cards (10s, 9s, 8s, 7s, 6s, 5s, 4s, 3s, 2s, and Aces). To find the probability that a 5-card poker hand contains exactly 2 face cards, we need to count the number of possible hands that satisfy this condition and divide by the total number of possible 5-card hands.

To count the number of hands with exactly 2 face cards, we can use the following steps:

Choose 2 face cards from the 12 available: 12 choose 2 = 66 ways.

Choose 3 non-face cards from the 40 available: 40 choose 3 = 91,390 ways.

Multiply the results of steps 1 and 2 to get the total number of possible hands with exactly 2 face cards: 66 x 91,390 = 6,270,540.

To count the total number of possible 5-card hands, we can use the formula for combinations: 52 choose 5 = 2,598,960.

Therefore, the probability of getting a hand with exactly 2 face cards is:

6,270,540 / 2,598,960 = 0.0241, or approximately 2.41%.

So the probability of getting a hand with exactly 2 face cards is about 2.41%, or roughly 1 in 41 hands.

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The area of the circle with a circumference of 8 cm is 16/π square cm.

What are the area and circumference of a circle?

The relationship between the area of a circle and its circumference can be described using the formula:

A = (π/4) x D²

where A is the area of the circle, D is the diameter of the circle, and π is the mathematical constant pi, approximately equal to 3.14159.

Similarly, the circumference of a circle can be calculated using the formula:

C = π x D

If the circumference of a circle is 8 cm, we can use the formula for circumference to find the radius:

C = 2πr

8 cm = 2πr

r = 4/π cm

Now that we know the radius, we can find the area using the formula:

A = πr²

A = π(4/π)²

A = 16/π square cm

So the area of the circle with a circumference of 8 cm is 16/π square cm (or approximately 5.09 square cm if we use 3.14 as an approximation for π).

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Volume of the water that has flowed through the pipe in 3 minutes is 36489.6

The flow of water through a pipe is determined by several factors, including the pressure difference between the two ends of the pipe, the diameter and length of the pipe, the viscosity and density of the water, and any obstructions or bends in the pipe.

The rate of flow, or the volume of water that passes through the pipe per unit of time, can be calculated using the formula:

Q = A × V

where Q is the flow rate, A is the cross-sectional area of the pipe, and V is the velocity of the water.

now area = angle / 360πr²

A= 70 / 360(3.14)(4.8)²

14.06

Now Length = Speed x time

L = 14 x 3 x 60 = 2520 cm

Now Volume = area x length

2520 x 14.06 = 36489.6

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As a result ,By using Pythagoras  each leg is the equivalent of **10 feet** and **16 feet**.

A fundamental relationship between a right triangle's three sides in Euclidean geometry is known as the Pythagorean theorem. The hypotenuse is the side that forms the right angle, and the rule says that the square of its length is equal to the sum of the squares of the lengths of the other two sides

``` a² + b² = c² ```

where the lengths of the right triangle's two legs (a and b) and the hypotenuse (c) are indicated.

Let's designate the triangle's two legs as "a" and "b," respectively. We are aware that: The length of the hypotenuse is 55 feet.

One leg of the triangle is 22 feet shorter than the other leg, which is 22 feet longer.

To find the values of "a" and "b," we can utilize the Pythagorean theorem. According to the Pythagorean theorem, the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the legs. We thus have:

``` a² + b² = 55² ```

We also are aware of:

``` a = 2b - 22 ```

When we add this to our initial equation, we obtain:

''' (2b - 22)²+ b² = 55²

b² - 22b + 96 = 0

4b² - 88b + 384 = 0

(b - 16)(b - 6) = 0

4b² - 88b + 384 = 0

Therefore, "b" can be either "16" or "6." A = 2(16) - 22 = 10 if b = 16, otherwise b = 16.

In the event that b = 6, a = 2(6) - 22 = -10. We can disregard the negative solution because we are working with lengths.

As a result, each leg is the equivalent of **10 feet** and **16 feet**.

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The option that has the same variation or mean absolute deviation would be option c

Mean absolute deviation (MAD) is a statistical measure that calculates the average distance between each data point in a dataset and the mean of that dataset.

It is a measure of how spread out the data is around the mean, and it is calculated by finding the absolute difference between each data point and the mean, adding up all of these absolute differences, and then dividing by the total number of data points.

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The quadratic equations are classified as follows:

If the discriminant of the quadratic equation is positive, then the equation has two real solutions.

If the discriminant is zero, then the equation has one real solution.

If the discriminant is negative, then the equation has no real solutions (but may have complex solutions).

Let's classify the given quadratic equations based on the number of solutions:

20² +5 = 9 is not a quadratic equation because it does not have a variable with a degree of two. Instead, it is just a number that evaluates to a false statement.

Therefore, it has no solution.

2x² + 3x = 5 is a quadratic equation with a = 2, b = 3, and c = -5. The discriminant is 3² - 4(2)(-5) = 49, which is positive.

Therefore, the equation has two real solutions.

3x² + 2x = 22 is a quadratic equation with a = 3, b = 2, and c = -22. The discriminant is 2² - 4(3)(-22) = 100, which is positive.

Therefore, the equation has two real solutions.

4x² + 12x = 19 is a quadratic equation with a = 4, b = 12, and c = -19. The discriminant is 12² - 4(4)(-19) = 400, which is positive.

Therefore, the equation has two real solutions.

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Drag each equation to the correct location on the table.

Classify the quadratic equations based on the number of solutions.

20² +5 = 9

2x² + 3x = 5

3x² + 2x = 22

4x² + 12x = 19

One Solution

Two Solutions

No Solution

Answer:

The new coordinates of point C after reflection and translation are (-2, -2).

Step-by-step explanation:

I hope it helps:)

All other expressions are equivalent to [tex]y^6 - 16y^2[/tex]  except [tex]y^4 - 16[/tex].

An expression is a group of terms joined together with the operations

+, -, x, . An equation is a claim that two expressions have values that

are equivalent, as in 4 + 2 = 6, and is denoted by an equals sign.

[tex](y^2 + 4) (y + 2) (y - 2)[/tex]

All other expressions are equivalent to [tex]y^2 (y^4 - 16).[/tex]

For example:

[tex](y^3 + 4y)(y^3 - 4y)[/tex](This is equivalent to [tex]y^6 - 16y^2[/tex] ) because ( it is the difference of two squares.)

[tex]16y^2 - y^6[/tex] (This is equivalent to [tex]-1(y^6 - 16y^2)[/tex] .

Therefore, the expression that is not equivalent to [tex]y^6 - 16y^2[/tex] is:

[tex]y^4 - 16[/tex] (This is equivalent to [tex](y^2 + 4) (y^2 - 4)[/tex]), which simplifies to

[tex](y^2 + 4) (y + 2) (y - 2)[/tex].

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Answer: 595

Step-by-step explanation:

Answer:

[tex] \frac{11\pi}{2 } \: ft[/tex]

Step-by-step explanation:

Given:

∠AOB = 30° (it is a central angle, which is equal to the arc on which it rests on)

r (radius) = 3 ft

Find: arc ACB - ?

If arc AB is 30°, then arc ACB is (remember, that a full circle forms an angle of 360°)

[tex]360° - 30° = 330°[/tex]

Now, we can find the length of the arc ACB:

[tex]l = \frac{2\pi \times r \times \alpha }{360°} = \frac{2\pi \times 3 \times 330°}{360°} = \frac{11\pi}{2} \: ft[/tex]

Answer: The value of x is 9.

Step-by-step explanation: n a regular hexagon, all interior angles have the same measure.

Since a hexagon has six sides, the sum of its interior angles is given by the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

Since all interior angles of a regular hexagon have the same measure, we can find the measure of each angle by dividing the sum by the number of angles:

Measure of each angle = Sum of interior angles / Number of angles = 720° / 6 = 120°

We are given that one of the angles in the hexagon is (11x + 21)°. Setting this equal to 120° and solving for x, we get:

11x + 21 = 120

11x = 99

x = 9

Therefore, the value of x is 9.

Consequently, y = -2x + 1 is the equation of the slope-intercept form of the line passing.

A line can be represented using the slope-intercept form of a straight line. Typically, a linear equation in the form y=mx+c is used to represent it. It places emphasis on the slope and y-intercept of a particular line1.

m is the line's slope and c is the y-intercept in this equation. The slope of a line is the ratio of the change in y to the change in x between any two distinct places on the line. The y-intercept is the point at which the line intersects the y-axis.

x - 2y = 8 defines the given line. This equation can be expressed in slope-intercept form as follows:

y = (1/2)x - 4

This line has a slope of 1/2. A line that is perpendicular to this line will have a slope that is the negative reciprocal of 1/2, or -2.

We are aware that the line traverses the given point. (2,-3). The equation of the line can be written as follows using the point-slope form:

y - y₁= m(x - x₁)

where (x₁,y₁) is the line's passing point and m is the slope of the line.

replacing the specified values:

y - (-3) = -2(x - 2)

Simplifying:

y + 3 = -2x + 4

y = -2x + 1

So , y = -2x + 1 is the equation of the slope-intercept form of the line passing through the point (2,-3) and perpendicular to the line described by x - 2y = 8.

The work given below :

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A graph shows the solution to the system of linear inequalities include the following: B. graph B.

In order to graph the solution for the given system of linear inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of linear inequalities and then check the point of intersection;

x + 5y ≥ 5          .....equation 1.

y ≤ 2x + 4         .....equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of linear inequalities is the shaded region above the solid lines, and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (6, 2).

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Answer:

B

Explanation:

By placing the given value in equation , we get u + v - 4u = (-20, 13)

A physical quantity that has both directions and magnitude is referred to as a vector quantity.

A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.

To evaluate u + v - 4u, we first need to find the vector 4u, which is obtained by multiplying the vector u by the scalar 4:

4u = 4(5,-2) = (20,-8)

Now, we can add u and v, and subtract 4u from the result:

u + v - 4u = (5,-2) + (-5,7) - (20,-8)

= (5 - 5 - 20, -2 + 7 + 8)

= (-20, 13)

Therefore, u + v - 4u = (-20, 13).

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Answer:

Step-by-step explanation:

The probability of getting exactly 25 heads in 50 coin flips would be higher than flipping a coin 6 times and getting exactly 3 heads.

To understand why, we can use the formula for calculating the probability of getting a specific number of heads in a given number of coin flips, which is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where P(X=k) is the probability of getting exactly k heads, n is the total number of coin flips, p is the probability of getting heads on a single coin flip, and (n choose k) is the binomial coefficient.

For the first scenario of flipping a coin 50 times and getting exactly 25 heads, we can plug in the values and get:

P(X=25) = (50 choose 25) * 0.5^25 * 0.5^25 = 0.112

For the second scenario of flipping a coin 6 times and getting exactly 3 heads, we can similarly plug in the values and get:

P(X=3) = (6 choose 3) * 0.5^3 * 0.5^3 = 0.3125

As we can see, the probability of getting exactly 25 heads in 50 coin flips is much higher than the probability of flipping a coin 6 times and getting exactly 3 heads. This is because the probability of getting a single head on a coin flip is 0.5, and as the number of coin flips increases, the probabilities of different outcomes converge towards a bell-shaped distribution centered around 0.5. This means that the probability of getting a specific number of heads in a large number of coin flips becomes more likely as the number of coin flips increases.

Answer:

1 / 20 or 0.05

Step-by-step explanation:

1/5 ÷ 4

= 1/5 × 1/4

= 1 / 20

1.) Over half of the iguanas measure 14 centimeters or more in length.

The assertion that is most supported by the data is, "More than half of the iguanas measure 14 centimeters or more in length." According to this claim, more than 50% of the iguanas are 14 cm or longer in length. The other two claims describe precise iguana lengths (12 centimeters and 11 centimeters or less, respectively), but they do not mention how common such lengths are in comparison to other lengths. Therefore, out of the available probability, the first statement is the one that is most illuminating and best substantiated.

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Complete question is :

At the zoo, the length of each iguana is measured. Which statement is best supported by the information below?

The first monthly payment is equal to $4,375.00 and its principal amount for the first payment is equal to $612.50.

Mortgage loan amount = $750,000

Rate of interest = 7%

Monthly payment amount = $4,987.50

First monthly payment is for interest

= Monthly interest rate and the portion of the payment that goes towards the principal.

Monthly interest rate = Divide annual interest rate by 12.

Substitute the value we have,

⇒ Monthly interest rate = 7% / 12

                                       = 0.583%

Principal portion of first payment

= Total payment - Interest portion

= $4,987.50 - ($750,000 x 0.583%)

= $4,987.50 - $4,375.00

= $612.50

Therefore, $4,375.00 of the first monthly payment of $4,987.50 is for interest, and $612.50 is for the principal.

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Therefore, the length of the third side of the right-angled triangle is 2√55.

Using the Pythagorean theorem to solve for the length of the third side of the right-angled triangle:

So, if we let the third side be x, we have:

6^2 + x^2 = 16^2

Simplifying this equation:

36 + x^2 = 256

Subtracting 36 from both sides:

x^2 = 220

Taking the square root of both sides:

x = √220

Simplifying the square root:

x = 2√55

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The value of the quadratic equation when x = 3 is 67.

What is a quadratic equation?

Any algebraic equation that can be expressed in standard form as where x represents an unknown number and where a, b, and c represent known values, with a ≠ 0, is a quadratic equation.

We are given a quadratic equation as 3[tex]x^{2}[/tex] + 5x + 25.

Now, when x = 3, we get

⇒ 3* [tex]3^{2}[/tex] + 5 (3) + 25

⇒ 3 (9) + 5 (3) + 25

⇒ 27 + 15 + 25

⇒ 67

Hence, the value of the quadratic equation when x = 3 is 67.

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Question: Evaluate : 3x² + 5x + 25 when x = 3.