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Answer:

\(\boxed{\text{2. 4.7 units}}\)

Step-by-step explanation:

Assume your triangle has the dimensions shown below.

Before we can use the Law of Sines, we must find ∠C.

1. Calculate ∠C

\(\begin{array}{rcl}A + B + C & = & 180^{\circ}\\66^{\circ} + 76^{\circ} + C & = & 180^{\circ}\\142^{\circ} + C & = & 180^{\circ}\\C & = & 38\, ^{\circ}\\\end{array}\)

2. Calculate b

Use the Law of Sines

\(\begin{array}{rcl}\dfrac{b}{\sin B } & = & \dfrac{c}{\sin C}\\\\\dfrac{b}{\sin 76^{\circ}} & = & \dfrac{3}{\sin 38^{\circ}}\\\\\dfrac{b}{0.9703} & = & \dfrac{3}{0.6157}\\\\ & = & 4.873\\b & = & 0.9703\times 4.873\\& = & \boxed{\mathbf{4.7}}\\\end{array}\)

If you press the reduction button 7 times, the length of the copy of the poster will be approximately 0.45 feet.

Each time the reduction button is pressed, the poster reduces by 25%. After the first press, the length of the poster becomes 75% of the original length, which is 20 * 0.75 = 15 feet. Following the second press, it reduces to 75% of 15 feet, which is 15 * 0.75 = 11.25 feet. This process continues for the next five presses: 11.25 * 0.75 * 0.75 * 0.75 * 0.75 * 0.75 * 0.75 ≈ 0.45 feet. Rounded to the nearest whole number, the length of the copy of the poster is 0 feet.

The reduction of 25% after each press leads to an exponential decrease in the length of the poster. To calculate the length after 7 presses, we multiply the original length (20 feet) by 0.75 seven times. This can be expressed as (20 * 0.75^7). The value of 0.75 represents the reduction factor of 25%. Evaluating this expression gives us approximately 0.445 feet. Rounding this to the nearest whole number, the length of the copy of the poster is 0 feet. This means that after pressing the reduction button seven times, the poster is reduced to a negligible length.

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Answer:

y = -x + 3

Step-by-step explanation:

Slope intercept form is the form y = mx+b where m is the slope and b is the y intercept

Plugging in the values we get y=-x+3

Answer:

y = - x + 3

Step-by-step explanation:

y = mx + b

Slope m = -1.

y = - x + b

Point (0,3).

3 = 0 + b

b = 3

y = - x + 3

Answer:

Direct labor cost= $1,500,000

Step-by-step explanation:

Giving the following information:

Production:

September 50,000

Each sneaker requires 2 hours of direct labor time.

Direct labor wages average $15 per hour.

First, we need to calculate the number of direct labor hours required:

Direct labor hours= 50,000*2= 100,000 hours

Now, the direct labor cost:

Direct labor cost= 100,000*15= $1,500,000

the solutions to the equation\(sec^2x + 3tan^2x\) = 1 over the interval [0, 2π) are x = 0 and x = π.

To solve the equation \(sec^2x + 3tan^2x\)= 1 over the interval [0, 2π), we'll start by manipulating the equation using trigonometric identities.

First, we know that \(sec^2x\) is the reciprocal of cos^2x, and tan^2x is the same as \(sin^2x/cos^2x\). Substituting these identities into the equation, we get:

\(1/cos^2x + 3(sin^2x/cos^2x) = 1\)

Next, we can combine the fractions on the left-hand side:

\((1 + 3sin^2x) / cos^2x = 1\)

To simplify further, we'll multiply both sides of the equation by cos^2x:

\(1 + 3sin^2x = cos^2x\)

Now, let's manipulate the equation to isolate sin^2x:

\(3sin^2x = cos^2x - 1\)

Using the Pythagorean identity \(sin^2x + cos^2x = 1\), we can substitute it into the equation:

\(3sin^2x = 1 - 1\)

\(3sin^2x = 0\)

Dividing both sides by 3:

\(sin^2x = 0\)

Now, we need to find the solutions for \(sin^2x = 0\) over the interval [0, 2π). Since \(sin^2x = 0\) means sinx = 0, the solutions will be x-values where the sine function equals zero.

In the interval [0, 2π), the solutions for sinx = 0 are x = 0 and x = π.

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Step-by-step explanation:

4+2×3+2+3

By the concept of BODMAS,

4+6+2+3

15

The probability of selecting a penny is 4/15

The probability of selecting a nickel is 1/3

The probability of selecting a dime is 7/30

The probability of selecting a dime or a quarter is 2/5

From the formula for probability,

\(P(A) = \frac{Number\ of\ favourable\ outcomes\ to\ A}{Total\ number\ of\ possible\ outcomes}\)

Total number of possible outcomes = 30

\(P(penny) = \frac{8}{30}\)

\(P(penny) = \frac{4}{15}\)

The probability of selecting a penny is 4/15

\(P(nickel) = \frac{10}{30}\)

\(P(nickel) = \frac{1}{3}\)

The probability of selecting a nickel is 1/3

\(P(dime) = \frac{7}{30}\)

The probability of selecting a dime is 7/30

First, we will calculate the probability of selecting a quarter

\(P(quarter) = \frac{5}{30}\)

\(P(quarter) = \frac{1}{6}\)

Then, the probability of selecting a dime or a quarter is

\(P(dime \ or \ quarter) = \frac{7}{30}+ \frac{1}{6}\)

\(P(dime \ or \ quarter) = \frac{7+5}{30}\)

\(P(dime \ or \ quarter) = \frac{12}{30}\)

\(P(dime \ or \ quarter) = \frac{2}{5}\)

The probability of selecting a dime or a quarter is 2/5

Hence,

The probability of selecting a penny is 4/15

The probability of selecting a nickel is 1/3

The probability of selecting a dime is 7/30

The probability of selecting a dime or a quarter is 2/5

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If the student who dra'nk the most number of be'ers (9 beers) actually had a BAC of 0.15 grams/deciliter, the strength of the association change stronger than the strength of the association shown in the above scatter plot. So the option C is correct.

A linear model of the scatterplot's BAC-to-beer-cans connection shows this link. A greater BAC for a specific number of be'ers relative to the trend displayed in the scatterplot would be indicated if the highest number of be'ers dru'nk (9 be'ers) resulted in a BAC of 0.15 grams/deciliter.

A more significant correlation would suggest a more obvious connection between the quantity of be'ers consumed and the consequent BAC. This would imply that the impact of alcohol on blood alcohol co'ntent (BAC) is more pronounced, leading to greater BAC readings for the same number of be'ers consumed. So the option C is correct.

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The complete question is:

Sixteen student volunteers at Ohio State University dra'nk a randomly assigned number of cans of be'ers.

Thirty minutes later, a police officer measured their blood alcohol con'tent (BAC) in grams of alcohol per deciliter of blood.

Given is a scatterplot displaying the relationship between BAC and number of cans of beer as well as the linear model for predicting BAC.

If the student who dra'nk the most number of be'ers (9 be'ers) actually had a BAC of 0.15 grams/deciliter, how would the strength of the association change?

A. Roughly the same as the strength of the association shown in the above scatter plot

B. Weaker than the strength of the association shown in the above scatter plot

C. Stronger than the strength of the association shown in the above scatter plot

D. It is impossible to tell

The probability that the disc is either blue or white is 11/59

Given that

number of blue discs : number of white discs = 6:5

number of blue discs : number of green discs = 1:8

So, we have

Blue : White = 6 : 5

Blue : Green = 1 : 8

This can be expressed as

Blue : Green = 6 : 48

So, we have

Blue : White : Green = 6 : 5 : 48

So, we have

Blue or White : Green = 11 : 48

So, the probability is

P = 11/(48 + 11)

Evaluate

P = 11/59

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Answer:

x=12/5

Step-by-step explanation:

2(2.5x+8)=26

5x+14=26

5x=12

x=12/5

Answer:

The value of \(x\):

\(x = 2\)

Step-by-step explanation:

Solve for \(x\):

\(2(2.5x + 8) = 26\)

-Divide both sides by \(2\):

\(2(2.5x + 8) = 26\)

\(2.5x + 8 = \frac{26}{2}\)

-Divide \(26\) by \(2\):

\(2.5x + 8 = \frac{26}{2}\)

\(2.5x + 8 = 13\)

-Subtract both sides by \(8\):

\(2.5x + 8 - 8 = 13 - 8\)

\(2.5x = 5\)

-Divide both sides by \(2.5\):

\(\frac{2.5x}{2.5} = \frac{5}{2.5}\)

Expand to the form \(\frac{5}{2.5} = 2\) by multiplying both the numerator and the denominator by \(10\):

\(\frac{5}{2.5} = 2\)

\(x = \frac{50}{25}\)

Then, you divide \(50\) by \(25\):

\(x = \frac{50}{25}\)

\(x = 2\)

So, the final answer would be \(x = 2\) .

Answer:

is. there. a. picture

Step-by-step explanation:

The probability of choosing a man in section I is given as follows:

17/55.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, out of 55 people, 17 are man in section I, hence the probability is given as follows:

17/55.

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if the function is divided and we get the remainder of  zero then  it is said to be a factor of a function

According to the Remainder Theorem, by a factor x − an of that polynomial, then you will get a zero remainder. The point of the Factor Theorem is the turnaround of the Remainder Theorem: On the off chance that you synthetic-divide a polynomial by x = a and get a zero remainder, at that point not as it were is x = a, a zero of the polynomial(for the remainder theorem ) but x − a is additionally a factor of the polynomial according to of the Factor Theorem.

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Answer:

They are similar

Step-by-step explanation:

They are similar because angle MW connects and LV does to.

y=4x+1

y=x+2

Step-by-step explanation:

very simple you just put the numbers in the correct spot when doing slope intercept form

Answer:

About 73.93 books. Round that to 73 books, because you can't place 93% of a book.

Step-by-step explanation:

You first calculate to dimensions of the bookcase, then you calculate the dimensions of the books. As a result, divide the calculation of the bookshelf by the calculation of the books, and you should have your answer.

\(2 + 2 \times 2 = 8\)

The length of the hypotenuse is approximately 30.8 units.

The angle at vertex X is approximately 36.9 degrees.

The angle at vertex Y is approximately 35.2 degrees.

In your problem, we have a right triangle XYZ, where the angle at vertex Y is the right angle. The length of leg YZ is given as 18 units, and the length of leg XZ is given as 25 units.

In this particular problem, we can use the sine ratio to solve for the length of leg XY. Specifically, we have:

sin(XYZ) = XY / XZ

Since we know that XYZ is a right angle (i.e., 90 degrees), we can substitute in the appropriate values to get:

sin(90) = XY / 25

Since the sine of 90 degrees is 1, we can simplify this to:

1 = XY / 25

Multiplying both sides by 25 gives us:

XY = 25

So the length of leg XY is 25 units.

To find the other angles in the triangle, we can use the inverse trigonometric functions (such as arcsine or arccosine). For example, we can use the cosine ratio to solve for the angle at vertex X:

cos(XYZ) = XZ / hypotenuse

cos(90) = 25 / hypotenuse

0 = 25 / hypotenuse

Since the cosine of 90 degrees is 0, we know that hypotenuse = 25 / 0 is undefined. However, we can use the Pythagorean theorem to find the length of the hypotenuse:

hypotenuse² = XY² + XZ²

hypotenuse² = 25² + 18²

hypotenuse² = 625 + 324

hypotenuse² = 949

Taking the square root of both sides gives us:

hypotenuse = √(949) ≈ 30.8

Now that we know the lengths of all three sides of the triangle, we can use the sine and cosine ratios to solve for the other angles. For example, to find the angle at vertex X, we can use the cosine ratio:

cos(X) = XZ / hypotenuse

cos(X) = 25 / 30.8

cos(X) ≈ 0.811

Taking the inverse cosine (or arccosine) of both sides gives us:

X ≈ 36.9 degrees

Similarly, we can use the sine ratio to find the angle at vertex Y:

sin(Y) = YZ / hypotenuse

sin(Y) = 18 / 30.8

sin(Y) ≈ 0.584

Taking the inverse sine (or arcsine) of both sides gives us:

Y ≈ 35.2 degrees

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Power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x=1.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.

Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

The given equation: \(\left(x^2-2 x+26\right) y^{\prime \prime}+x y^{\prime}-4 y=0\)

It is necessary to determine the power series solutions' minimal radius of convergence R around the typical points x = 0 and x = 1.

The separation between the ordinary point and the differential equation's singularity is now the minimal radius of convergence.

The polynomial's root, which is connected to the second derivative, is the singularity point.

The singularity points will be determined as follows:

\(\begin{aligned}& x^2-2 x+26=0 \\& x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\& x=\frac{2 \pm \sqrt{(-2)^2-4 \times 1 \times 26}}{2} \\& x=1 \pm \sqrt{-100} \\& x=1 \pm 10 i\end{aligned}\)

In this case, x1 = 1+10i and x2 = 1-10i are the singularity sites.

The ordinary points at this time are z1 = 0+01 and z2 = 1+0i.

One can compute the minimum radius of convergence using the formula:

\(\begin{aligned}& r_1=\left|z_1-x_1\right| \\& =|0+0 i-1-10 i| \\& =\sqrt{101} \\& =10.0498 \\& r_2=\left|z_2-x_1\right| \\& =\sqrt{100} \\& =10\end{aligned}\)

Therefore, power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x = 1.

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Answer:

8x + 22

Step-by-step explanation:

The area left to be tiled on Wednesday is 1/6

Let the total area to tile be 60 sq feet

We have taken 60 sq feet as the LCM of 2 and 3 is 6. So taking up 60 makes our calculation part easy.

Area tiled on Monday = 1/3*60 = 20 sq feet

Area tiled on Tuesday = 1/2*60 = 30 sq feet

Area remaining to be tiled = 10 sq feet

So, a fraction of the area left to be tiled = Area left to be tiled/Total area to be tiled

= 10/60 = 1/6

Hence, 1/6 of the area is left to be tiled

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Answer:1/6

Step-by-step explanation:

Using the central limit theorem to find the mean is 5.4 and standard error of the mean of the indicated sampling distribution is 0.6.

In the given question, we have to use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution.

From the given question,

The company are normally distributed with a mean of μ = 5.4 years.

A standard deviation of σ = 2.1 years.

Random samples of size n = 12 are drawn from the population and the mean of each sample is determined.

Using the central limit theorem the mean is

μ(x) = μ = 5.4

Standard error of the mean of the indicated sampling distribution is:

σ(x) = σ/√n

σ(x) = 2.1/√12

σ(x) = 2.1/3.5

σ(x) = 0.6

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Answer:  x = 2

=============================================================

Explanation:

Refer to the diagram below.

I've added points D,E,F,G. This helps with labeling the segments and angles, and identifying the proper triangles (to see which are congruent pairs).

Triangle GEA is congruent to triangle GFA. We can prove this using the AAS congruence theorem. We have AG = AG as the pair of congruent sides, and the congruent pairs of angles are marked in the diagram (specifically the blue pairs of angles and the gray right angle markers)

Since triangle GEA is congruent to triangle GFA, this means the corresponding pieces segment GF and GE are the same length.

The diagram shows GF = 3x-4, so this means GE = 3x-4 as well.

----------------------

Through similar steps, we can show that triangle GEC is congruent to triangle GDC. We also use AAS here as well.

The congruent triangles lead to GD = GE. So GD = 3x-4. The diagram shows that GD = 6x-10

Since GD is equal to both 3x-4 and 6x-10, this must mean the two expressions are equal.

----------------------

Now let's solve for x

6x-10 = 3x-4

6x-3x = -4+10

3x = 6

x = 6/3

x = 2

Answer:

945

Step-by-step explanation:

This is how I got the answer:

First I transformed all of the measurements into feet( there are 3 feet in each yard)

6 feet

6 feet

9 feet

12 feet

Then I added 6 and  12, and 6 and 9= 18x15= 270

And then u multiply 270 by 3.50

which gets u 945

Therefore, his company will charge $945

Answer:

d=4-0.004m

Step-by-step explanation:

i did it on khan academy

Answer:

After Multiplying them.

we get 0 as an answer.