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A fruit stand at the checkout line has 5 bananas, 3 apples, and 4 oranges. Find the probability that if you randomly chose 3 fruits:

A) Two oranges and one banana are chosen


B) One of each fruit is chosen


C) All three are bananas

Answer:

0

Step-by-step explanation:

\( {x3 \: - 4 {x \: }^{2} + 3x \: = 0}^{} \)

solve for x

\(x 1 = 0 \\ x2 \: = 1 \\ x3 \: = 3\)

Answer:

(5-x)feet.

Step-by-step explanation:

Let the other feet be y.Then,

x+y=5

y=5-x

Answer:

Have you ever wondered how a tiny little insect like a bee could ever fill a jar of honey? If it were just down to one bee it would be a mighty task but the work is shared by many thousands of bees and is a great example of what can be achieved by a co-ordinated effort. Think of it in terms of humans creating something like a pyramid.

A jar of honey weighs 454 grammes and a bee can carry about 0.04 grammes of nectar. But nectar is only about 40% sugar and honey needs to be about 80% sugar so the bee actually only carries about 0.02 grammes of honey on each trip.

Step-by-step explanation:

Answer:

the answer is 45 because there are four marbles so it would be a 50/50

Write each vector in component form and add the components separately. This new vector will represent the sum of the two original vectors. This is the most straightforward way to add two vectors.

1. Write each vector in component form. This means breaking down each vector into its x- and y-components.

2. Add the x-components of each vector together and the y-components of each vector together.

3. The result will be a single vector with both x- and y-components.

To add two vectors, I should write each vector in component form, breaking them down into their x and y components. Then, I should add the components together, resulting in a new vector with components that are the sum of the two original vectors' components. This new vector will represent the sum of the two original vectors. This is the most way to add two vectors.

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Answer: 9.61

Step-by-step explanation: The formula for radius to area is: A = πr2.

Answer:

Jackson needs 30 more widgets 2 hours

Step-by-step explanation:

Using the given zero . The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

If 1 + i is a zero of the polynomial function P(x), then its conjugate, 1 - i, must also be a zero of the polynomial, since complex zeros of polynomial functions with real coefficients always come in conjugate pairs.

To find the remaining zero, we can use polynomial division or synthetic division to divide P(x) by (x - 1 - i)(x - 1 + i), which is the quadratic factor corresponding to the two known zeros:

      2x^2 - 3x + 2

P(x) = --------------

       (x - 1 - i)(x - 1 + i)

Now we need to solve for the roots of the quadratic factor 2x^2 - 3x + 2. We can use the quadratic formula:

x = [3 ± sqrt(9 - 4*2*2)] / (2*2)

 = [3 ± sqrt(1)] / 4

 = 1/2 or 2

Therefore, the remaining zeros of P(x) are 1/2 and 2. The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.

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Answer:

Step-by-step explanation:

Identical bags should have both blue and yellow marbles inside.

Also each color should be divisible by the number of bags.

It becomes a question of finding the greatest common factor of 54 and 99.

Prime factors of both numbers:

Find the GCF:

The greatest number of bags is 9.

Answer: D) 54 inches = 1 1/2 yards

explanation: 1 1/2 yards = 54 inches.

Answer:

These x-values are known as the “roots” or “zeros” of the quadratic. To find these roots, we simply set the quadratic equal to zero and solve for x

Step-by-step explanation:

Answer:

  29.54 m

Step-by-step explanation:

You want the side opposite the 33.6° angle in a triangle that is 36 m between its 33.6° angle and its 104° angle.

In order to use the law of sines to find an unknown side opposite a given angle, we must have a known angle opposite a known side. The known side is opposite the third angle of the triangle, whose measure is ...

  180° -104° -33.6° = 42.4°

Now, we can use the law of sines:

  pole height/sin(33.6°) = (36 m)/sin(42.4°)

  pole height = (36 m)·sin(33.6°)/sin(42.4°) ≈ 29.54475 m

  pole height ≈ 29.54 m

We may infer from the number line that A and B are separated by 8 units (AB).

Let AB stand for the separation between points A and B, and let AC stand for the separation between points A and C. Let B stand for the separation between points B and C. Hence:

Point B being halfway between A and C, we can infer:

AB + BC Equals AC (Postulated segment addition)

As a result, since the distance between points A and B is equal to 1/3 of AC:

AC/3 = AB = 1/3(AC)

But as shown in the accompanying image:

AC equals 16 – (–8) to 24 units.

Therefore:

AB = 1/24 = 8 unit

A and B are separated by 8 units.

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On the number line, Point B is between points A and C. The distance between points A and B is 1/3 of AC. What is AB?​

Answer:

(0, 2)

Step-by-step explanation:

Answer:

He will have 2 cups :)

Answer:

he would have 2 cups in it cause 1 pint = 2 cups

Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

Part 1

∠FBA = 42° (alternate interior angles)

Part 2

∠FDC = 23° (linear pair)

∠BAD = 23° (alternate interior angles)

Part 3

∠AFBA = 115° (sum of angles in a triangle)

Answer:

a = 3

Step-by-step explanation:

mean is calculated as

mean = \(\frac{sum}{count}\)

Here mean = 15, sum = 342 + a and count = 20 + a , then

\(\frac{342+a}{20+a}\) = 15 ( multiply both sides by 20 + a )

342 + a = 15(20 + a) ← distribute

342 + a = 300 + 15a ( subtract a from both sides )

342 = 300 + 14a ( subtract 300 from both sides )

42 = 14a ( divide both sides by 14 )

3 = a

The accumulated amount in the account after 3 years, if $7000 was invested  is $7892.43.

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.

To calculate the the accumulated amount in the account at the end of the 3 years, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the accumulated amount in the account is $7892.43.

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Answer:

A. f(x)=5cos(x+pi/4)

F. f(x)=5sin(x+3pi/4)

Step-by-step explanation:

Answer: 1. A, F

2. B. C , F

3.A,C

Step-by-step explanation:I just finished the practice

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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On solving the provided questions, we can say that Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

he diameter of the ball bearings varies according to a distribution that is approximately Normal

mean 11.5 mm and standard deviation 0.05 mm

the probability that the difference in the diameters of the two ball bearings is less than 0.06 mm

Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

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Answer:

900 W

Step-by-step explanation:

Answer:320000

Step-by-step explanation:

Answer:

g(2)= -8

Step-by-step explanation:

g(2)= -4(2)

g(2)= -8

The first thing is to calculate the value of the root.

therefore, is between -12 and -13

decimal estimate: 0.24