Emily’s pet snake is 5 feet long. Kristen’s snake is 50 inches long. Kristen says her snake is much longer because 50 is so much bigger than 5. Is Kristen right? Why or why not?

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.

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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.

Answer:

ROI = 150

Step-by-step explanation:

ROI = (25,000-10,000)/10,000 ×100=150

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

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.

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.

Answer:

Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4 . Add the resulting equations together.

Step-by-step explanation:

Given the simultaneous equation below:

4x+3y=−1 ...(1) × 3

3x−5y=4 ...(2) × -4

Using elimination method to solve the problem,

Before we can eliminate x, the coefficient of x in both equation must have similar whole number as coefficient.

To make the coefficient equal, we will multiply equation 1 by 3 and equation 2 by -4 as shown above

The equations will then become

12x+9y = -3

-12x+20y = -16

Then we will add the resulting simultaneous equations.

The steps that would allow her to eliminate the x terms in the system of equations is to "Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4 . Add the resulting equations together"

To determine the total cost including sales tax, first calculate the subtotal of the items, then apply the 7% tax rate to this subtotal. After adding the sales tax to the subtotal, the final cost comes to $90.23.

To calculate the total cost of your purchase including sales tax, first figure out the total cost of the items before tax. You bought one skirt at $18.27, two shirts at $15.78 each, and a pair of shoes at $34.50. The cost of the shirts needs to be doubled since you bought two. Then, apply the 7% sales tax to the subtotal to find the overall total.

Subtotal before tax: $18.27 + $31.56 + $34.50 = $84.33

To calculate the sales tax, convert the tax rate to a decimal (7% = 0.07) and multiply by the subtotal: $84.33 × 0.07 = $5.90 (rounded to the nearest cent).

Add the sales tax to the subtotal for the total cost: $84.33 + $5.90 = $90.23.

Therefore, the total cost of your purchase after including the 7% sales tax is $90.23.

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.

Answer:

1 1/2 hours

Step-by-step explanation:

Time spent by Antonio in driving = 3 1/4 = 13/4

Time spent in gardening = 1 3/4 = 7/4

In order to find how much he spend driving than gardening, we can subtract 13/4 and 7/4.

[tex]\frac{13}{4}-\frac{7}{4}[/tex]

Te denominator is same. So, we can directly subtract the numerators.

[tex]\frac{13-7}{4}\\\\=\frac{6}{4}\\\\=\frac{3}{2}=1\frac{1}{2}[/tex]

Therefore, Antonio spent 1 1/2 hours more in driving than gardening.

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.

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.