Expand and simplify (t-9) (t-16)

Answer:

1960

Step-by-step explanation:

ateral area: (21+29+20) x 22= 70 x 22 = 1540

both bases: 20 x 21 = 420

total: 1540+420=1960

If researchers report that the results from their study were significant, p < .05, this means that we would expect the results to occur by chance less than 5 times out of 100.

When researchers report that the results from their study were significant, p < .05, it means that we would expect the results to occur by chance less than 5 times out of 100. This threshold is commonly used in statistical hypothesis testing.

In statistical hypothesis testing, the p-value represents the probability of obtaining results as extreme as the observed results, assuming that the null hypothesis is true. If the p-value is less than the predetermined significance level of .05 (or 5%), it is considered statistically significant. This means that the observed results are unlikely to have occurred by chance alone, and there is evidence to support the alternative hypothesis.

Therefore, option D, "We would expect the results to occur by chance less than 5 times out of 100," is the correct interpretation of reporting significant results with p < .05.

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Answer: The answer is $2009.04

Step-by-step explanation:

I hope this helps.

Answer:

The adult has 32 teeth

Step-by-step explanation:

20*.1.60=32

Answer:

32

Step-by-step explanation:

100% - 20   60% (20x0.60) 12 20+12 32

401(k) investment has over other types of investments is the employer match and contribution.

The graphic shows that for the sample 401(k) investment, there is an annual contribution of $5,000 from the individual. Additionally, there is an employer match of 5% and an employer contribution of $2,500, bringing the total contribution to $7,500.

The advantage of this 401(k) investment is that the employer is providing additional funds towards the individual's retirement savings. The employer match means that for every dollar the individual contributes, the employer contributes an additional 5 cents. This is essentially free money added to the investment, which can significantly boost the overall savings over time.

Furthermore, the employer contribution of $2,500 further enhances the advantage of this 401(k) investment. This contribution is made by the employer without any additional cost to the individual, increasing the overall investment amount.

Compared to other types of investments, such as individual retirement accounts (IRAs) or taxable investment accounts, the employer match and contribution in a 401(k) provide an immediate boost to the individual's retirement savings.

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Answer: 2.25 x 10^18

Step-by-step explanation:

When dividing with exponents you subtract

56-38= 18

10 cancels out

(9 x 10^18) / 4

= 2.25 x 10^18

The three attempts, the valid solution is x = 2 and y = 2, which means there are 2 small tables and 2 large tables.

To find three possible solutions in the context of the problem, we need to substitute different values for x and y that satisfy the equation 4x + 8y = 24.

Let's start by substituting x = 1 and solving for y:

4(1) + 8y = 24

4 + 8y = 24

8y = 24 - 4

8y = 20

y = 20/8

y = 2.5

Since the number of tables cannot be in fractions, this solution is not valid.

Let's try another combination. Substituting x = 2:

4(2) + 8y = 24

8 + 8y = 24

8y = 24 - 8

8y = 16

y = 16/8

y = 2

This gives us a valid solution with x = 2 and y = 2, meaning there are 2 small tables and 2 large tables.

Now, let's try one more combination. Substituting x = 3:

4(3) + 8y = 24

12 + 8y = 24

8y = 24 - 12

8y = 12

y = 12/8

y = 1.5

Similar to the first attempt, this solution is not valid as it results in a fraction for the number of tables.

Therefore, among the three attempts, the valid solution is x = 2 and y = 2, which means there are 2 small tables and 2 large tables.

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There are two terms in the given expression 5xy²+ 35xy².

What is meant by term?

Terms comprise expressions. A term may be a constant, a variable, or a combination of variables and constants.

What is an example of a term?

It could be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase. Single-word examples: A single phrase is 3x.

There are two terms in the equation 5xyA ^2 + 35xyA^2 that is separated by an arithmetic operator +.

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Answer:

To find out how many giant parade balloons could be filled with 6.2 billion cubic feet of helium, we can divide the total volume of helium by the volume of one balloon:

Number of balloons = Total volume of helium / Volume of one balloon

First, we need to convert 6.2 billion cubic feet to cubic feet:

6.2 billion = 6,200,000,000

Now we can calculate the number of balloons:

Number of balloons = 6,200,000,000 / 700,000

Number of balloons = 8,857.14

So, approximately 8,857 giant parade balloons could be filled with 6.2 billion cubic feet of helium.

Answer:

AROC = - \(\frac{2}{3}\)

Step-by-step explanation:

the average rate of change of g(x) in the closed interval [ a, b ] is

\(\frac{g(b)-g(a)}{b-a}\)

here [ a, b ] = [ - 4, 5 ] , then

g(b) = g(5) = - 1 ← point (5, 1 ) on graph

g(a) = g(- 4) = 5 ← point (- 4, 5 ) on graph

average rate of change = \(\frac{-1-5}{5-(-4)}\) = \(\frac{-6}{5+4}\) = \(\frac{-6}{9}\) = - \(\frac{2}{3}\)

\( \bf \implies{\angle{JND} = 57 \degree}\)

\( \bf \longrightarrow{\angle{BNL} = 33 \degree}\)

\( \bf \longrightarrow{\angle{JND} = \: ?}\)

\( \bf \longrightarrow \: \: \: \angle{BNL} = \angle{DNS} \: \\ \: \: \: \bf [Verically \: Opposite \: Angle]\)

\( \bf \therefore\angle{DNS } = 33 \degree\)

\( \bf \longrightarrow \angle{JND} + \angle{ DNS} = 90 \degree \\ \bf \: \: \: \: \: \: \: \: \: [form \: a \: right \: angle]\)

\( \bf \longrightarrow \angle{JND} +33 \degree= 90 \degree\)

\( \bf \longrightarrow \angle{JND}= 90 \degree - 33 \degree\)

\( \bf \longrightarrow \angle{JND}= 57 \degree \)

Answer:

$2,400

Step-by-step explanation:

Note: The correct years is 4 not 44

The Principal  = $10,000

Time period = 4 years

Rate = 6 % p.a.

Simple Interest = Principal * Rate * Time

Simple Interest = $10,000 * 6% * 44

Simple Interest = $2,400

So, the amount of interest Diego earned after four years is $2,400

Answer:

4√3 (about 6.9) cm.

Step-by-step explanation:

In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

Here, the length of the longer leg is 4√3, or about 6.9, cm.

This is simply what I wrote for my assignment, sorry I am a bit late.

It was confusing when she took out the negative and postive pairs, but then I soon knew that the negative tiles are like subtracting positive tiles. Then once she got the total I was amazed with how easy it was to find out the value of x.

hope this helps! <3

Answer:

the distance is five units up!

Step-by-step explanation:

Answer:

10:7

Step-by-step explanation:

take 10 as it is and it becomes 10

then,10-3 it is because when 3 don't grow it subtracts and becomes 7

Answer:

60/100 times by 95 so 57

Step-by-step explanation:

Answer:

6b+18

Step-by-step explanation:

4×b= 4b

4×3=12

2×b=2b

2×3=6

(combine like terms)

4b+2b=6b

12+6=18

Hope this helped!

The equivalent value of the expression is A = 2b + 10

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 4 + 2 ( b + 3 )

On simplifying the equation , we get

A = 4 + 2b + 6

A = 2b + 10

Hence , the expression is A = 2b + 10

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The given statement " if a random variable is discrete, it means that the random variable can only take non-negative integers as possible values." is False because it can also take negative integers.

A discrete random variable is a random variable that can only take on a countable number of distinct values, which may or may not be integers. These values can be positive, negative, or zero, and they do not have to be restricted to non-negative integers.

For example, the number of cars that pass through a certain intersection in an hour is a discrete random variable, which can take on any non-negative integer value. However, the number of children in a family is also a discrete random variable, which can take on any non-negative integer value, but it doesn't have to be an integer.

Conversely, a continuous random variable is a random variable that can take on any value in a specified range or interval, typically representing measurements such as time, distance, or weight. Examples of continuous random variables include the height of a person, the temperature of a room, and the amount of rainfall in a given area.

Therefore, whether a random variable is discrete or continuous does not necessarily imply anything about the range of values that it can take.

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The given statement is True.

What are parallel lines?

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

True. Two lines either intersect or are parallel.

This means that there are only two possibilities for the relationship between two lines: they either meet at a single point, in which case they are said to intersect, or they never meet, in which case they are said to be parallel.

If two lines are intersecting, then they are not parallel, and if two lines are parallel, then they do not intersect.

Hence, The given statement is True.

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Answer:

225.1°

155mph

if a+bi is a root of a polynomial equation with real coefficients and b ≠ 0, then its conjugate a-bi is also a root of the equation.

If a+bi is a root of a polynomial equation with real coefficients, where b ≠ 0, then its conjugate a-bi is also a root of the equation. This property is known as the Complex Conjugate Root Theorem.

To understand why this is the case, let's consider a polynomial equation with real coefficients:

P(x) = (x - (a + bi))(x - (a - bi)) * Q(x)

In this equation, Q(x) represents the other factors of the polynomial. By the fundamental theorem of algebra, every complex root has its conjugate as a root as well.

Expanding the equation further, we have:

P(x) = (x - a - bi)(x - a + bi) * Q(x)

= (x - a)^2 - (bi)^2 * Q(x)

= (x - a)^2 + b^2 * Q(x)

Since the coefficients of the polynomial are real, the imaginary terms (bi)^2 simplify to -b^2. Therefore, we have:

P(x) = (x - a)^2 - b^2 * Q(x)

From this equation, we can see that if (a + bi) is a root of the polynomial equation, then its conjugate (a - bi) will also be a root. This is because substituting (a + bi) into the equation will make the term (x - a)^2 zero, resulting in P(x) = -b^2 * Q(x), which is satisfied when (a - bi) is substituted.

This property is a consequence of the complex conjugate root theorem, which states that complex roots always occur in conjugate pairs when the coefficients of the polynomial equation are real.

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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The relationship between the heights of two right circular cylinders with the same volume. The radius of the second cylinder increases, its height must decrease to maintain the same volume as the first cylinder.

In order to find the volume of a cylinder, we use the formula V = πr²h, where V represents the volume, r is the radius, and h is the height of the cylinder.

Given that both cylinders have the same volume, let's denote their volumes as V1 and V2, their radii as r1 and r2, and their heights as h1 and h2. The given information states that r2 > r1. We can now write the equations for the volumes of the two cylinders:

V1 = π(r1)²h1
V2 = π(r2)²h2

Since V1 = V2, we can set the two equations equal to each other:

π(r1)²h1 = π(r2)²h2

We can now solve for the relationship between the heights of the two cylinders:

h1/h2 = (r2/r1)²

This equation shows that the ratio of the heights of the two cylinders is equal to the square of the ratio of their radii. As the radius of the second cylinder is greater than the radius of the first (r2 > r1), the height of the second cylinder will be less than the height of the first (h2 < h1). In other words, as the radius of the second cylinder increases, its height must decrease to maintain the same volume as the first cylinder.

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False. Cronbach's alpha is a measure of internal consistency reliability, not a measure of the correlation between scale items.

It assesses the extent to which the items in a scale or questionnaire are measuring the same underlying construct.

Cronbach's alpha is calculated based on the inter-item correlations among the items in a scale. It provides a measure of the average correlation between all possible pairs of items in the scale. The range of Cronbach's alpha is between 0 and 1, with higher values indicating greater internal consistency or reliability.

Essentially, Cronbach's alpha quantifies the extent to which the items in a scale are consistently measuring the same construct or concept. It assesses how well the items "hang together" as a reliable measurement tool.

While correlation between scale items is related to internal consistency, Cronbach's alpha specifically measures the degree to which the items are interrelated and provides a single coefficient that reflects the overall reliability of the scale. It does not directly indicate the extent of item-item correlations or the strength of individual item contributions to the scale.

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a. The mass remaining after t years, 130 is the initial mass, and 30 is the half-life of cesium-137.

b.  About 19.35 mg of the sample will remain after 100 years.

c.  After about 330 years, only 1 mg of the sample will remain

(a) The mass remaining after t years can be found using the formula:

\(y(t) = 130 * 2^(-t/30)\)

where y(t) represents the mass remaining after t years, 130 is the initial mass, and 30 is the half-life of cesium-137.

(b) To find how much of the sample remains after 100 years, we can substitute t = 100 into the formula:

\(y(100) = 130 * 2^(-100/30) = 19.35 mg\)

Therefore, about 19.35 mg of the sample will remain after 100 years.

(c) We need to solve the equation y(t) = 1 for t. Substituting y(t) and solving for t, we get:

\(1 = 130 * 2^(-t/30)\)

\(2^(-t/30) = 1/130\)

\(-t/30 = log2(1/130)\)

\(t = -30 * log2(1/130) = 330 years\)

Therefore, after about 330 years, only 1 mg of the sample will remain.

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a) The decay of cesium-137 can be modeled by the function \(y(t) = 130 * 2^{(-t/30)\)

b) after 100 years, only about 31.57 mg of the sample remains.

c) after about 207.1 years, only 1 mg of the sample will remain.

(a) The decay of cesium-137 can be modeled by the function \(y(t) = 130 * 2^{(-t/30)\), where t is the time in years and y(t) is the remaining mass of the sample in milligrams.

To find the mass that remains after t years, we simply plug in the value of t into the function:

\(y(t) = 130 * 2^{(-t/30)\)

(b) To find the amount of the sample that remains after 100 years, we plug in t = 100:

\(y(100) = 130 * 2^{(-100/30)\) ≈ 31.57 mg

So after 100 years, only about 31.57 mg of the sample remains.

(c) To find the time it takes for only 1 mg to remain, we set y(t) = 1 and solve for t:

\(1 = 130 * 2^{(-t/30)}\\\\2^{(-t/30)} = 1/130\)

Taking the natural logarithm of both sides, we get:

\(ln(2^{(-t/30)}) = ln(1/130)\)

Using the logarithmic identity \(ln(a^b) = b * ln(a)\), we can simplify the left side:

(-t/30) * ln(2) = ln(1/130)

Solving for t, we get:

t = -30 * ln(1/130) / ln(2) ≈ 207.1 years

So after about 207.1 years, only 1 mg of the sample will remain.

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The equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.

In accordance with the statement, car travels in a straight line at constant speed. The distance traveled (d), in miles, is equal to the product of the speed (v), in miles per hour, and time (t), in hours:

d(t) = v · t     (1)

If we know that v = 60 mi/h, then the equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.

The statement is incomplete and complete form cannot be found. Then, we decided to complete the statement by asking for the equation that describes the distance of the car.

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