Solve logarithm Equation: 3 log5 x-log5 4= log5 16 

Final answer:

To round 0.9998 to three decimal places, consider the fourth decimal digit (8). Since it's 5 or higher, the third decimal digit (9) rounds up, resulting in 1.000 after taking the carry-over into account.

Explanation:

To round the number 0.9998 to three decimal places, you need to look at the fourth decimal place to decide whether to round up the third decimal place. The fourth decimal place is 8, which is 5 or more, so we round up the third decimal place from 9 to 10. However, since the third place is already at the maximum digit (9), this causes a carry-over, changing the number to 1.000. But, rounding to three decimal places means you want three digits after the decimal point, so the rounded number is 1.000. Rounding introduces a small amount of imprecision, determined by the digits you're eliminating or adjusting. However, in this situation, it's clear that the number essentially rounds up to one.

The product is 3x² - 7x - 6 after combining like terms.

The student asked to multiply the binomials (3x+2) and (x-3). To do this, we use the FOIL method, which stands for First, Outside, Inside, Last. This refers to the elements in each binomial we need to multiply together.

First, we multiply the first terms in each binomial: (3x) and (x), which gives 3x².

Next, we multiply the outside terms: (3x) and (-3), which gives -9x.

Then we multiply the inside terms: (2) and (x), which produces +2x.

Last, we multiply the last terms of each binomial: (2) and (-3), yielding -6.

Finally, we combine the like terms to get the expanded product - 3x² - 7x - 6.

Ans

Step-by-step explanation:

The probability of choosing one red bulb and then one yellow bulb from 27 bulbs (11 red, 9 yellow, and 7 purple) is calculated by multiplying the chance of picking a red bulb first and a yellow bulb second. This results in approximately 1 in 7.1, or roughly 0.14.

The question you are asking is about finding the probability that one bulb is red and one is yellow out of a total of 27 bulbs, with a distribution of 11 red, 9 yellow, and 7 purple bulbs. To calculate this probability, we use the following steps:

Using the multiplication rule of probability, we get:

P(Red then Yellow) = (11/27) × (9/26)  = 99/702 = 1/7.1 (approximately).

So the probability that one bulb is red and one is yellow is about 1 in 7.1, or approximately 0.14.

0.0703 written in scientific notation is 7.03 × [tex]10^{-2[/tex], representing the original number more compactly with the mantissa (7.03) and exponent (-2).

To express 0.0703 in scientific notation, we first need to move the decimal point to the right until only one digit is to its left. Count the number of places you moved the decimal point, which gives us the exponent of 10. In this case, we move the decimal point three places to the right to obtain 7.03. Thus, we have 7.03 × [tex]10^{-2[/tex]. Since we moved the decimal point three places to the right, the exponent of 10 is -3.

Therefore, 0.0703 in scientific notation is 7.03 × [tex]10^{-2[/tex]. This notation represents the original number in a more compact form, where the mantissa (7.03) indicates the significant digits and the exponent (-2) denotes the power of 10 by which the mantissa is multiplied.

To solve for V in the equation C = Q/V, you need to multiply both sides of the equation by V and then divide both sides by C.

To solve the equation C = Q/V for V, we need to isolate V on one side of the equation. We can do this by multiplying both sides of the equation by V. This gives us CV = Q. To solve for V, we divide both sides of the equation by C. Therefore, V = Q/C.

Answer:

The correct option is C.

Step-by-step explanation:

The given expression is

[tex]21x-18x+28xy[/tex]

The factors of each term are

[tex]21x=3\times 7\times x[/tex]

[tex]18x=3\times 6\times x[/tex]

[tex]28xy=2\times 2\times 7\times x\times y[/tex]

The common factor is x.

[tex]G.C.F.=x[/tex]

Therefore correct option is C.

Answer:

The probability that 3 red balls are chosen is: 2.2%

Step-by-step explanation:

A bag contains 4 black, 5 red, and 6 pink balls.

Total balls in the bag= 4+5+6= 15 balls in the bag

We need to know what is the probability that 3 red balls are chosen without replacement?

[tex]P_r=\frac{R_b}{T_b}*\frac{R_b-1}{T_b-1}*\frac{R_b-2}{T_b-2}[/tex]

Where:

[tex]P_r:[/tex] Probability that 3 red balls are chosen

[tex]R_b:[/tex] Number of red balls

[tex]T_b:[/tex] Number of total balls

[tex]P_r=\frac{5}{15}*\frac{5-1}{15-1}*\frac{5-2}{15-2}\\P_r=\frac{5}{15}*\frac{4}{14}*\frac{3}{13}\\P_r=\frac{1}{3}*\frac{4}{14}*\frac{3}{13}\\P_r=\frac{2}{91}\\P_r=0.022[/tex]

[tex]P_r=0.022=2.2[/tex]%

The probability that 3 red balls are chosen is: 2.2%

Answer:45

Step-by-step explanation:

Final answer:

The equation of the circle x² + y² - 2y - 15 = 0 is rewritten in vertex form by completing the square for the y terms, resulting in x² + (y - 1)² = 4², indicating a center at (0, 1) and a radius of 4.

Explanation:

To rewrite the equation of the circle in vertex form, you want to complete the square for both the x and y terms. The equation given is x² + y² - 2y - 15 = 0. First, we need to isolate the x and y terms:

Since there's no x-term to complete the square with, we can leave the x² term as it is. For the y-terms, add and subtract (1/2 * coefficient of y)2, which is (1/2 * -2)² = 1:

Now the equation inside the parentheses is a perfect square trinomial and can be factored as (y - 1)². After adjustment, we get:

So the circle in vertex form is x² + (y - 1)² = 4², with the center at (0, 1) and a radius of 4 units.

Answer:

HFKHP[;U7P

Step-by-step explanation:

Answer: 360,000

See for yourself

The equation ax = bx + 1 is the same as x = 1/(a  - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b. This is the answer from the sample response.

Answer:

The equation ax = bx + 1 is the same as x = 1/(a  - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b. This is the answer from the sample response.

Step-by-step explanation: