Tabitha defines a sphere as the set of all points equidistant from a single point. Is Tabitha's definition valid?

Answer:

ROI = 150

Step-by-step explanation:

ROI = (25,000-10,000)/10,000 ×100=150

To solve this problem, you have to determine the value of the number 3 in both numbers:

6,300 – the number 3 is in the hundreds place so its value is 300

530 – the number 3 is in the tens place so its value is 30

To answer the question, the value of 3 in 6,300 is 10 times the value of 3 in 530.

Let xbe a positive integer number. Then x, x+1 and x+2 are three positive consecutive integers (the first one is x, the second is x+1 and the third is x+2).

The product of the second integer and the third integer is (x+1)·(x+2) and is equal to 72. So you have the equation

[tex](x+1)\cdot (x+2)=72.[/tex]

Solve it:

[tex]x^2+2x+x+2=72,\\ \\x^2+3x+2-72=0,\\ \\x^2+3x-70=0,\\ \\D=3^2-4\cdot (-70)=9+280=289,\\ \\\sqrt{D}17,\\ \\x_1=\dfrac{-3-17}{2}=-10,\ x_2=\dfrac{-3+17}{2}=7.[/tex]

Solution [tex]x_1=-10[/tex] is extra because [tex]x_1[/tex] is negative.

Answer: three positive consecutive integers are 7, 8 and 9.

Final answer:

The value of n, or the number of trials in a binomial experiment, affects the shape of the binomial probability histogram. As n increases, the histogram becomes more symmetric and bell-shaped, reflecting the Central Limit Theorem. The correct answer is (c): as n increases, the binomial distribution becomes more bell-shaped.

Explanation:

The shape of the binomial probability histogram is indeed influenced by the value of n, which stands for the number of trials in a binomial experiment. As the value of n increases, the distribution becomes more symmetrical and tends to resemble a normal distribution. Specifically, the correct statement regarding the effect of n on the shape of the histogram is: as n increases, the binomial distribution becomes more bell-shaped. Therefore, the correct answer to the student's question is (c).

When the sample size n is small, the histogram may appear skewed left or right, depending on the probability of success p. However, as n becomes larger (especially when both np and n(1-p) are greater than 5), the distribution's shape becomes more symmetric due to the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases.

To find the length marked x, establish the ratio 0.5 inch/20 miles = 8 inches/x miles, cross-multiply, and solve for x to get x = 320 miles, making sure to round only after the final calculation step.

To solve for the length labeled x, you would first need to set up the correct ratio. Given that the scale length is 8 inches and the corresponding actual length is unknown, the initial ratio would be 0.5 inch/20 miles = 8 inches/x miles. You can solve this proportion by cross-multiplication.

Following these steps:

Therefore, the unknown length x is 320 miles. Remember to always perform rounding off at the final step of your calculation to ensure accuracy.

The length of side [tex]\( x \)[/tex] is approximately 13.9 units when rounded to the nearest tenth.

To find the length of side [tex]\( x \)[/tex], we utilize the tangent function because it relates the opposite side to the adjacent side in a right-angled triangle. The tangent of [tex]\( 41^\circ \)[/tex] equals the ratio of side [tex]\( x \)[/tex] (the side opposite to [tex]\( 41^\circ \))[/tex] to 16 (the side adjacent to [tex]\( 41^\circ \))[/tex]:

[tex]\[ \tan(41^\circ) = \frac{x}{16} \][/tex]

To solve for [tex]\( x \)[/tex], we multiply both sides by 16:

[tex]\[ x = 16 \times \tan(41^\circ) \][/tex]

[tex]x=13.9[/tex]

The length of side [tex]\( x \)[/tex] is approximately 13.9 units when rounded to the nearest tenth.

The recursive formula for a geometric sequence is a₁=-4 and [tex]a_n}=6.a_{n-1}[/tex]. Therefore, option D is the correct answer.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

The given geometric sequence is -4, -24, -144, -864.

A recursive formula for a geometric sequence with common ratio r is given by [tex]a_n}=ra_{n-1}[/tex] for n≥2.

Here, a=-4 and r=-24/(-4) =6

So, recursive formula is [tex]a_n}=6.a_{n-1}[/tex]

Therefore, option D is the correct answer.

To learn more about the geometric sequence visit:

https://brainly.com/question/11266123.

#SPJ7

Final answer:

To determine the diameter of a circle with a circumference of 12.56 feet using π as 3.14, divide the circumference by π resulting in a diameter of 4 feet.

Explanation:

The student has asked to find the length of the diameter of a circle if the circumference is 12.56 ft using 3.14 for π (Pi). The formula for the circumference C of a circle is C = π * d, where d is the diameter of the circle. To find the diameter, we rearrange the formula to d = C / π. Substituting the given values, we get:

d = 12.56 ft / 3.14

After dividing the circumference by pi, we find that:

d = 4 ft

Therefore, the length of the diameter is 4 feet.

Answer:

15cm

Step-by-step explanation:

i had the same question but difrent if you know what i mean. in mine you solved it for me in your picture of 6.

Look at changes of signs to find this has 1 positive zero, 1 or 3 negative zeros and 0 or 2 non-Real Complex zeros.

Then do some sums...

f(x)=−3x4−5x3−x2−8x+4

Since there is one change of sign, f(x) has one positive zero.

f(−x)=−3x4+5x3−x2+8x+4

Since there are three changes of sign f(x) has between 1 and 3 negative zeros.

Since f(x) has Real coefficients, any non-Real Complex zeros will occur in conjugate pairs, so f(x) has exactly 1 or 3 negative zeros counting multiplicity, and 0 or 2 non-Real Complex zeros.

f'(x)=−12x3−15x2−2x−8

Newton's method can be used to find approximate solutions.

Pick an initial approximation a0 .

Iterate using the formula:

ai+1=ai−f(ai)f'(ai)

Putting this into a spreadsheet and starting with a0=1 and a0=−2 , we find the following approximations within a few steps:

We can then divide f(x) by (x−0.42) and (x+2.195) to get an approximate quadratic −3x2+0.325x−4.343 as follows:

Notice the remainder 0.013 of the second division. This indicates that the approximation is not too bad, but it is definitely an approximation.

Check the discriminant of the approximate quotient polynomial:

Since this is negative, this quadratic has no Real zeros and we can be confident that our original quartic has exactly 2 non-Real Complex zeros, 1 positive zero and 1 negative one.

Answer:

Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0

The correct solution of the quadratic equation 3x^2 - x = 10 is found using the quadratic formula, giving two solutions x = -5/3 and x = 2.

The equation given is 3x2 − x = 10, which is a quadratic equation that needs to be rearranged to the standard form ax2 + bx + c = 0.

First, we subtract 10 from both sides of the equation, resulting in 3x2 − x − 10 = 0. Now, we can use the quadratic formula:

x = −b ± √(b2 - 4ac) / (2a)

Substituting the values a = 3, b = −1, and c = −10 into the formula yields:

x = −(−1) ± √((−1)2 - 4 × 3 × (−10)) / (2 × 3)

This simplifies to:

x = 1 ± √(1 + 120) / 6

Which further simplifies to:

x = 1 ± √121 / 6

And results in:

x = 1 ± 11 / 6

Therefore, the two solutions are:

x = 2 (1 + 11 / 6)

x = − five over three (1 − 11 / 6)

Hence, the correct answer is x = − five over three and x = 2.

The quadratic equation 3x^2 - x = 10 is solved via the quadratic formula, resulting in two solutions: x = 2 and x = -5/3 (or -1.67 when expressed as a decimal).

To solve the quadratic equation 3x2 − x = 10, we first need to set it to zero by subtracting 10 from both sides, yielding 3x2 − x − 10 = 0. This is a standard form quadratic equation, ax2 + bx + c = 0, where a = 3, b = -1, and c = -10. We can solve for x by using the quadratic formula, x = ∛ ( b2 - 4ac ) / (2a).

Plugging in our values, we get:

x = (-(-1) ± √ ( (-1)2 - 4(3)(-10) ) ) / (2(3))
x = (1 ± √ ( 1 + 120) ) / 6
x = (1 ± √ (121) ) / 6
x = (1 ± 11) / 6

Thus:

Therefore, the solutions are x = 2 and x = -5/3.