A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.
A. True
B. False

The probability of getting 3 tails, when tossing a coin 4 times is 25%

To find the probability of getting 3 tails when tossing a coin 4 times, we can use the binomial probability formula:

[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]

Where:

- P(X = k) is the probability of getting exactly k successes (in this case, 3 tails).

- n is the number of trials (coin tosses).

- k is the number of successes we are interested in (in this case, 3 tails).

- p is the probability of success on each trial (in this case, the probability of getting tails).

- [tex]\( (1 - p) \)[/tex] is the probability of failure on each trial (in this case, the probability of getting heads).

Since the coin is fair, the probability of getting tails p is [tex]\( \frac{1}{2} \)[/tex], and the probability of getting heads [tex](\( 1 - p \))[/tex] is also [tex]\( \frac{1}{2} \)[/tex].

Substituting these values into the formula:

[tex]\[ P(X = 3) = \binom{4}{3} \times \left(\frac{1}{2}\right)^3 \times \left(1 - \frac{1}{2}\right)^{4 - 3} \][/tex]

[tex]\[ P(X = 3) = \binom{4}{3} \times \left(\frac{1}{2}\right)^3 \times \left(\frac{1}{2}\right)^1 \][/tex]

[tex]\[ P(X = 3) = 4 \times \left(\frac{1}{8}\right) \times \left(\frac{1}{2}\right) \][/tex]

[tex]\[ P(X = 3) = \frac{4}{16} \][/tex]

[tex]\[ P(X = 3) = \frac{1}{4} \][/tex]

To express the probability as a percentage, we multiply by 100:

[tex]\[ P(X = 3) = \frac{1}{4} \times 100\% = 25\% \][/tex]

Therefore, the probability of getting 3 tails when tossing a coin 4 times is 25%.

Given that the preference for red and blue pens is equal and that there are 48 workers, Clark should order 24 blue pens for the office.

The student is interested in figuring out how many blue pens to order for 48 workers in an office knowing that the preferences for red and blue pens are equal. This means that for every 6 people who prefer red, the same number of people will prefer blue.

To determine the number of blue pens needed, we can use a simple proportion. Since 6 people prefer red and the same number prefer blue, we have a 1:1 ratio of red to blue preferences.

Therefore, the total number of blue pens needed would be half of the total number of workers:

The equation of the tangent line to the curve y = 2sinx at the point (pi/6,1) is y = sqrt(3)x + (1 - sqrt(3)(pi/6)).

To find the equation of the tangent line to the curve y = 2sinx at the point (pi/6, 1), we need to find the slope of the curve at that point. The slope of a curve at a point is equal to the derivative of the function at that point.

Taking the derivative of y = 2sinx, we have dy/dx = 2cosx. Evaluating this derivative at x = pi/6, we get dy/dx = 2cos(pi/6) = sqrt(3). Therefore, the slope of the tangent line is sqrt(3).

Now we have the slope and a point on the line, (pi/6, 1). We can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Plugging in the values, we have y - 1 = sqrt(3)(x - pi/6).

Simplifying this equation, we get y = sqrt(3)x - sqrt(3)(pi/6) + 1. Finally, we can rewrite the equation in the form y = mx + b by simplifying the y-intercept, giving us y = sqrt(3)x + (1 - sqrt(3)(pi/6)).

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The value of the given trigonometric ratio tan 39° is approximately 0.8098.

Use the concept of trigonometric ratio defined as:

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate to a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

The given trigonometric ratio is: tan 39°

Since,

[tex]\text{tan }\theta = \dfrac{\text{sin }\theta}{\text{cos }\theta}[/tex]

The value of the sine of 39° is approximately 0.6293.

The value of the cosine of 39° is approximately 0.7771.

Therefore,

tan 39° = 0.6293 / 0.7771

tan 39°≈ 0.8098     (After rounding to four decimal places).

Hence,

The required value tan 39° is approximately 0.8098.

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Answer:

[tex]f(x)=\dfrac{1}{4}x+25[/tex]

Step-by-step explanation:

Clearly from the graph we could see that it passes through two points (0,25) and (20,30) and also as the graph is linear so with the help of these two points we can find the relation between f(x) and x.

We know that the equation of a line passing through two points (a,b) and (c,d) is given by:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

Here we have:

y=f(x) , (a,b)=(0,25) and (c,d)=(20,30).

Hence the equation of this graph is given as:

[tex]f(x)-25=\dfrac{30-25}{20-0}\times (x-0)\\\\f(x)-25=\dfrac{5}{20}\times x\\\\f(x)-25=\dfrac{1}{4}\times x\\\\f(x)=\dfrac{1}{4}x+25[/tex]

Hence,

[tex]f(x)=\dfrac{1}{4}x+25[/tex]

Answer:

He bought 375 paper clips.

Step-by-step explanation:

Given,

The initial number of packs of paper clips = 7,

Also, the additional number of packs of paper clips = 8,

So, the total number of packs of paper clips = 7 + 8 = 15,

Now, the number of paper clips in each pack = 25,

Hence, the total number of paper clips = number of paper clips in each pack × total packs

= 25 × 15

= 375

This is an exponential growth problem. Let's write the equation for exponential growth.

[tex]P=P_{0} (1+r)^{n}[/tex]

Where,

From the problem, we know initial number of views, [tex]P_{0}[/tex], is 25. Rate of increase, r, is 0.18. Time, n, is 4 weeks. Plugging in these values in the equation and solving for P will give us the number of views expected in four weeks time.

[tex]P=(25)(1+0.18)^{4}\\=(25)(1.18)^{4}\\=48.47[/tex]

Rounding to nearest whole number, it is 48.

ANSWER: 48

In algebra, terms are separated by addition (+), subtraction (-), multiplication (x), and division (÷) symbols. The equals (=) sign is used to show equality, not to separate terms.

In the realm of mathematics, particularly in algebra, algebraic terms are separated by addition (+), subtraction (-), multiplication (x), and division (÷) symbols. These operations are the main components that allow us to manipulate and solve algebraic expressions and equations. For example, in the expression 3x - 2y + 5z, the terms (3x, 2y, 5z) are separated by subtraction (-) and addition (+) symbols. Please note that the equals (=) sign does not separate terms; rather, it is used to show the equality between two mathematical expressions.

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Final answer:

Algebraic terms are separated by plus (+) and minus (-) signs, which denote addition or subtraction between terms in an expression.

Explanation:

Algebraic terms are separated by plus (+) and minus (-) signs.

These signs denote addition or subtraction between terms in an algebraic expression.

While the multiplication sign (x) and division sign (÷) indicate operations between terms, they do not separate independent terms within an expression.

For instance, in the expression 2x + 3y - 5z, the plus and minus signs separate the terms 2x, 3y, and 5z.

Answer:

Option b is correct

5b; when b = 3.4 miles , the distance Sandra rode is 17 miles

Step-by-step explanation:

Here, b represents the distance Barbara rode.

As per the statement:

Sandra rode her bike 5 times as many miles as Barbara.

⇒[tex]\text{Distance Sandra rode} = 5b[/tex] miles           ....[1]

It is also given that:

the distance Barbara rode, equals 3.4 miles

⇒[tex]b = 3.4[/tex] miles

Substitute in [1] we have;

[tex]\text{Distance Sandra rode} = 5(3.4)=17[/tex] miles

Therefore, the correct expression and distance Sandra rode is

5b ; when b = 3.4 miles , the distance Sandra rode is 17 miles

To reduce the fraction 28/98 to lowest terms, we prime factorize each number, cancel out the common factors, and simplify. The fraction 28/98 simplifies to 1/7.

The correct prime factorization of 28 is 2×2×7 (or 2²×7), and for 98 it's 2×7×7 (or 2×7²). To reduce the fraction 28/98 to lowest terms, we can remove the common factors in the numerator and the denominator.

Since both numerator and denominator have a 2 and a 7, we can replace them with '1'. After simplifying, the remaining factors in the numerator are 1 and the remaining factors in the denominator are 7. Therefore, 28/98 reduced to lowest terms is 1/7.

Answer:

its (c) 3 1/2

Step-by-step explanation:

Answer:

Answer would be 15.

Step-by-step explanation:

We have to complete the expression given as

[tex]z^{2}+9z-90=(z-6)(z+?))[/tex]

We will try to factorize the expression given in the left side.

[tex]z^{2}+9z-90=z^{2}+15z-6z-90[/tex]

                      = z(z+15)-6(z-15)

                      =[tex](z-6)(z-15)[/tex]

Now we will compare this factorized form with the right side of the expression.

(z-6) (z-15) (= (z-6) (z+?)

We find question mark is 15.

Therefore, the answer is 15.

Celeste is making fruit baskets for her service club, and she is not following the specific ratio but using a similar ratio of apples to oranges in her baskets.

Celeste is making fruit baskets for her service club, and the directions say to fill the boxes using 5 apples for every 6 oranges. However, Celeste is filling her baskets with 2 apples for every 3 oranges. To determine if Celeste is following the directions, we can compare the ratio of apples to oranges in her baskets with the ratio specified in the directions.

In the directions, the ratio of apples to oranges is 5 apples: 6 oranges, which can be simplified to 5/6. In Celeste's baskets, the ratio of apples to oranges is 2 apples : 3 oranges, or 2/3.

To compare these ratios, we can find the least common multiple (LCM) of the denominators (6 and 3), which is 6. Then, we can convert both ratios to have the same denominator using equivalent fractions:

5/6 * 1/1 = 5/6 and 2/3 * 2/2 = 4/6.

Since 4/6 is less than 5/6, Celeste is not following the directions exactly. However, she is still using a similar ratio of apples to oranges in her baskets.

Answer:

It is a variable

Step-by-step explanation:

A variable is a characteristic, number, or quantity that increases or decreases over time or takes different values in different situations. Hope this helps.

Answer:

r and s are parellel

Step-by-step explanation:

The correct answer is that lines 4 and 5 are parallel if  [tex]\( m_4 = m_5 \).[/tex]

The area of the square as a product is a multiplication of the two sides.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.

The square is a quadrilateral having all the sides to be equal and all the angles at 90 degrees. The area of the square will be calculated as,

Area = side x side

Therefore, the area of the square as a product is a multiplication of the two sides.

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