NameEstimate Lengths in FeetFind each object.Estimate how many 12-inch rulers willbe about the same length as the object.I. door

Given that

3cot =-√3

3cot /3=-√3/3...( take note the the 3's cancels each other)

∴cot = -√3/3

Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

The value of ∂x/∂s is  4s^2 * t^6.

To find ∂x/∂s, we need to differentiate x with respect to s while treating t as a constant. Let's begin by substituting the given expressions for x, y, and z into the function f(x, y, z):

f(x, y, z) = (x^2)(y^3) + z^3

Substituting x, y, and z:

f(s, t) = ((s^2)(t^3))^2 * (s*t)^3 + ((s^2)*t)^3

Expanding the expression:

f(s, t) = (s^4 * t^6) * (s^3 * t^3) + (s^6 * t^3)

Now, let's differentiate x with respect to s:

∂x/∂s = ∂/∂s [(s^2)(t^3)]^2

Using the chain rule, we can differentiate each term separately:

∂x/∂s = 2 * (s^2 * t^3)^1 * ∂/∂s [(s^2)(t^3)]

Differentiating (s^2)(t^3) with respect to s:

∂/∂s [(s^2)(t^3)] = 2s * t^3

Substituting back into the expression for ∂x/∂s:

∂x/∂s = 2 * (s^2 * t^3)^1 * 2s * t^3

Simplifying:

∂x/∂s = 4s^2 * t^6

Therefore, ∂x/∂s = 4s^2 * t^6.

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a. In the integrand ∫[x/(6x² + 5)²]dx, we make the substitution u =  (6x² + 5)

b. Writing the integrand ∫[x/(6x² + 5)²]dx in the form ∫f(u)du, f(u) = u²/12

Integration is the reverse of differentiation

a. Since we want to find the substitution in order to evaluate the following integrand ∫[x/(6x² + 5)²]dx, we proceed as follows

In the integrand ∫[x/(6x² + 5)²]dx, we see that the other function is the polynomial in the denominator which is (6x² + 5). So, we make the substitution u =  (6x² + 5)

b. To rewrite the integrand in terms of u so that ∫[x/(6x² + 5)²]dx is int he form ∫f(u)du, we proceed as  follows

Since  integrand ∫[x/(6x² + 5)²]dx and u = 6x² + 5. Differentiation u with respect to x, we have that

du/dx = d(6x² + 5)/dx

= d(6x²)/dx + d5/dx

= 12x + 0

= 12x

So, du/dx = 12x

xdx = du/12

So, substituting this into the integrand, we have that

∫[x/(6x² + 5)²]dx = ∫[x/u²]dx

= ∫[xdx/u²]

= ∫[du/12/u²]

=  ∫[du/12u²]  

So, comparing  ∫[f(u)du]  = ∫[du/12u²]  

So, f(u) = u²/12

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Answer:

\(f(u)=\dfrac{1}{12u^5}\)

Step-by-step explanation:

Integration by substitution is a technique used to simplify the integration of complex functions. It involves writing part of the function in terms of a new variable u, where u is some function of x.

Given integral:

\(\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x\)

Substitute u for 6x² + 5.

Differentiate u with respect to x and rearrange the equation to isolate dx:

\(\dfrac{\text{d}u}{\text{d}x}=12x \implies \text{d}x=\dfrac{1}{12x}\; \text{d}u\)

Substitute the expressions for u and dx into the original expression to rewrite the original integral in terms of u and du:

\(\begin{aligned}\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x &= \int \dfrac{x}{u^5} \cdot \dfrac{1}{12x}\; \text{d}u\\\\&= \int \dfrac{1}{12u^5}\; \text{d}u\\\\\end{aligned}\)

Therefore:

\(f(u)=\dfrac{1}{12u^5}\)

We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

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The first step to determine the function is assigning a variable to represent the height of the hellicopter, the problem suggests us to use H, so this will be the output of the function, while M will be the input. At the start of the movement, when M is 0, the helicopter should be at an altitude of 1450 feet. So we have:

We know that for every minute that passes the altitude will decrease by 75 feet, so the function must be:

Because everytime M increases the altitude decreases by 75.

If the number of boys on the honor roll increased by 19% and the number of girls on the honor roll increased by 20%, the total number of students on the honor roll increased by approximately 19.3% this year.

To solve this problem, we first need to calculate the new number of boys and girls on the honor roll this year. We know that the number of boys on the honor roll increased by 19%, which means that there are now:

100 + (19/100)*100 = 119 boys on the honor roll this year

Similarly, the number of girls on the honor roll increased by 20%, which means that there are now:

50 + (20/100)*50 = 60 girls on the honor roll this year

Therefore, the total number of students on the honor roll this year is:

119 + 60 = 179

To find the percentage increase in the total number of students on the honor roll, we need to compare this number to the total number of students on the honor roll last year:

100 + 50 = 150

The percentage increase is given by the formula:

( new value - old value ) / old value x 100

Substituting the values we have calculated, we get:

( 179 - 150 ) / 150 x 100 = 19.3%

We round this to the nearest tenth, which gives us an answer of 19.3%.

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Answer:

"Descartes' rule of sign is used to determine the number of real zeros of a polynomial function. It tells us that the number of positive real zeroes in a polynomial function f(x) is the same or less than by an even numbers as the number of changes in the sign of the coefficients."

Explanation:

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\(\dfrac{7!4!}{5!3!}=6\cdot7\cdot4=168\)

The function is the third choice

The x value of the functions should only correspond to one y value

The value of f(x) when x is 3 is 15

A Function in mathematics is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

For example, if f(x) = x² +2x +5 , the value of f(x) when x is 2 is calculated as;

f(x) = 2² + 2(2) + 5

f(x) = 4 +4+5

= 13

This done by substituting the given value of x into the expression.

Similarly , if f(x) = 5x, the value of f(x) when x is 3 is calculated as;

f(x) = 5(3)

f(x) = 15

therefore the value of f(x) when x is 3 is 15

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When investigating whether there is an association between cell phone brand and age-group, the appropriate test is a chi-square test of homogeneity.

When investigating whether there is an association between cell phone brand and age-group, the appropriate test is a chi-square test of homogeneity.

Chi-square test: The chi-square test is a statistical hypothesis test in which the sampling distribution of the test statistic is a chi-square distribution when the null hypothesis is valid.

A chi-square test may be used to see if there is an association between two variables.

The chi-square test of homogeneity is a statistical hypothesis test that is used to evaluate whether two or more populations have the same distribution of frequencies.

It's used to see if there's a significant difference between the proportions of categorical data in two or more independent groups.

In the same way, a chi-square test can be used to compare the frequency distributions of categorical variables in one or more populations.

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Answer:

q=2.6

P=3

Step-by-step explanation:

A^2 +b^2 =c^2

.

Answer:

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Suppose 54% of the registered voters in a country are Democrats. Sample of 770.

This means that:

\(p = 0.54, s = \sqrt{\frac{0.54*0.46}{770}} = 0.01796\)

What is the probability that the sample proportion of Democrats will be greater than 52%?

This is 1 subtracted by the p-value of Z when X = 0.52. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.52 - 0.54}{0.01796}\)

\(Z = -1.11\)

\(Z = -1.11\) has a p-value of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample proportion of Democrats will be greater than 52%.

The volume of the cuboid is 58 cubic units.

A cuboid is a 3 dimensional figure that has six rectangular faces. So that the volume of a cuboid can be determined by;

volume of cuboid = length x width x height

From the given question, we have;

the volume of a cuboid that is 2.9 x 5 x 4 can be determined as follows;

volume of cuboid = length x width x height

                             = 2.9 x 5 x 4

                             = 58

The volume of the cuboid with the given dimension is 58 cubic units.

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The equation of the parallel line will be y = (2/3)x - 8/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y - 4 = 2/3 (x - 3)

The equation of the line that is parallel to the given line will be written as,

y = (2/3)x + c

The equation of the line that passes through (1, -2), then we have

- 2= (2/3)(1) + c

- 2 = 2 /3 + c

c = - 8 / 3

Then the equation of the parallel line will be y = (2/3)x - 8/3.

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According to the information we can infer that the scale drawing of the football field will have dimensions of 2.5cm by 4.5cm.

To create the scale drawing, we need to convert the real-life dimensions of the football field into centimeters and then apply the scale of 1:2000.

Real-life dimensions:

Converting to centimeters:

Applying the scale of 1:2000:

According to the above, the scale drawing of the football field will have dimensions of 2.5cm by 4.5cm.

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Answer:

The answer is A

Step-by-step explanation:

Answer:

A would be correct

Step-by-step explanation:

the answer is A.

Therefore, the longest length of pencil that John can hide in the pencil holder is approximately 127.32 cm (rounded to two decimal places).

Given that John has a 100 cm³ pencil holder, the longest length of pencil he can hide in the pencil holder can be found by using the formula for the volume of a cylinder which is given by: V = πr²h where r is the radius of the cylinder and h is the height of the cylinder.The volume of a cylinder can also be expressed as V = lwh where l is the length of the cylinder, w is the width of the cylinder and h is the height of the cylinder.

If we assume that the pencil is cylindrical in shape, then its volume can be given by V = πr²l where r is the radius of the pencil and l is the length of the pencil.Since the volume of the pencil holder is given to be 100 cm³, then we have:100 = πr²h (Equation 1)

Now, we need to find the value of l that can fit inside the pencil holder. We can use the formula for the volume of the pencil to do this as follows:

V = πr²lLet V = 100 cm³ and

r = 0.5 cm

(since the pencil holder is cylindrical in shape, we can assume that it has a radius of 0.5 cm)Then, we have:100 = π(0.5)²lSolving for l, we get:

l = 100 / (π(0.5)²)

l = 100 / (0.7854)l ≈ 127.32 cm

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Answer:

B) 4,700

Step-by-step explanation:

6000 - 4000 = 2000

2000 in 15 year, find how much for each year

2000/ 15 = 133.3333333

133.3333333 estimated = 133

133 approximately for each year

1975 to 1980 is five years

133 x 5 = 665

4000 + 665 = 4665

4665 rounded the the nearest hundred

4700

Answer:

x = 19

Step-by-step explanation:

the question tells you that the angle CBD is 90°.

so, that means that angle DBE and angle CBE add up to 90.

using this, you can make the following equation:

2x - 1 + 5x - 42 = 90

2x + 5x + -43 = 90

7x - 43 = 90

add 43 to both sides

7x = 90 + 43

7x = 133

x = 133/7

x = 19

Answer:

144 inches

Step-by-step explanation:

If they are moving at the same speed and start at the same time, they have to go the same distance

That means they will meet in the middle

If they are 72 inches from the right side that means the middle is 72 inches from the right side

The road is 2 times 72 inches

2*72 = 144

144 inches

Step-by-step explanation:coordinates of first person in the line.

Answer:

x-9.

the expression that shows how many presents benjamin wrapped would be x-9

Answer:\(a^2-b^2=3\)

Step-by-step explanation:

We need to find the value of the below expression i.e.

\(a^2-b^2\) when a = 2 and b = 1.

So,

Put a = 2 and b = 1 in the above expression. So,

\(a^2-b^2=(2)^2-1^2\\\\=4-1\\\\=3\)

Hence, the value of the expression is equal to 3.

Step-by-step explanation:

False,

Vertical angles isn't always complementary l

Answer:

true

Step-by-step explanation:

If two angles are congruent, their measures are equal.

Answer:

0,1,4,9,16,25,36,49,64,81,121,144,169,196,225,256,289,324,361,400