If m∠3=115°, find m∠6.

Distance of the keys on ground from the base of the tower = 7.38 ft

Given:

Height of tower = 94 ft

Tower is leaning and makes an angle of 85.5 degrees from the ground.

Keys are dropped from the top of the tower.

To find the distance of the keys on ground from the base of the tower.

From the data given to us we can construct a right triangle ABC.

For the Δ ABC

AB= 94 ft

∠A= 85.5°

We can apply trigonometric ratio to find side BC which is the distance of the keys on ground from the base of the tower.

Using cosine ratio: \(cos\theta = \frac{Adjacent \ side}{Hypotenuse}\)

In Δ ABC

\(cos85.5^{o} = \frac{AC}{AB}\)

Multiplying both sides by AB.

\(AB \times cos85.5^{o} = \frac{AC}{AB} \times AB\)

\(AB \ cos85.5^{o} = AC\)

\(AC = AB \ cos85.5^{o}\)

Substituting value of AB and cos 85.5°

\(AC = 94 \ cos85.5^{o}\)

AC = 7.38 ft

Distance of the keys on ground from the base of the tower = 7.38 ft

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Answer:

x = 4, x = 8

Step-by-step explanation:

(9)

Given 2 secants from an external point to the circle, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

x(x + 6) = 5(5 + 3)

x² + 6x = 5 × 8 = 40 ( subtract 40 from both sides )

x² + 6x - 40 = 0 ← in standard form

(x + 10)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 10 = 0 ⇒ x = - 10

x - 4 = 0 ⇒ x = 4

x > 0 then x = 4

(11)

Given a secant and a tangent from an external point to the circle, then

The square of the tangent is equal to the product of the external part and the whole of the secant, that is

x(x + 10) = 12²

x² + 10x = 144 ( subtract 144 from both sides )

x² + 10x - 144 = 0 ← in standard form

(x + 18)(x - 8) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 18 = 0 ⇒ x = - 18

x - 8 = 0 ⇒ x = 8

x > 0 then x = 8

Answer:

The answer wound be C. {-6, -5, -4, 4, 5, 6}.

Step-by-step explanation:

For g(x) = 1:

|x| - 3 = 1

|x| = 4

The equation |x| = 4 has two solutions: x = 4 and x = -4.

For g(x) = 2:

|x| - 3 = 2

|x| = 5

The equation |x| = 5 has two solutions: x = 5 and x = -5.

For g(x) = 3:

|x| - 3 = 3

|x| = 6

The equation |x| = 6 has two solutions: x = 6 and x = -6.

Now, we have six possible values for x: 4, -4, 5, -5, 6, and -6. Therefore, the domain of g(x) = |x| - 3, given that the range is {1, 2, 3}, is {-6, -5, -4, 4, 5, 6}.

The probability that none of the ten freshmen graduates from the local community college is approximately 0.006 or 0.6%.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Assuming that the probability of each freshman graduating is independent of the others, the probability that none of the ten freshmen graduates is -

\(P = (0.6)^{10}\)

= 0.0060466176

Here, we are using the fact that the probability of a freshman not graduating is 1 - 0.4 = 0.6.

So, the probability value is obtained as 0.006 or 0.6%.

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The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer:

4/5 or .8

Step-by-step explanation:

This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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The correct matches are:

N Σ i=1 cai is equal to C.

n Σ i=1 i is equal to B.

n Σ i=1 c is equal to C.

n Σ i=1 ai is equal to C.

n Σ i=1 i^3 is equal to D.

n Σ i=1 i^2 is equal to B.

A: n Σ i=1 cai represents the summation of the product of constant c and variable ai from i=1 to n. This matches the property of C, which states that the constant c can be factored out of the summation.

B: n Σ i=1 i represents the summation of the terms i from i=1 to n, which is a common arithmetic series. This matches the property of B, which is the formula to calculate the sum of an arithmetic series.

C: n Σ i=1 c represents the summation of the constant c from i=1 to n, resulting in a total of n * c. This matches the property of D, which states that the sum of a constant repeated n times is equal to n times that constant.

D: n Σ i=1 ai represents the summation of the terms ai from i=1 to n, which is a common series. This matches the property of A, which is the formula to calculate the sum of a series involving the terms ai.

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Correct question:

Enter the correct letter to match each summation expression with the property or formula. N Σ i=1 cai is equal to . A n(n + 1)(2n + 1) 6 n Σ i=1 i is equal to . B n(n + 1) 2 n Σ i=1 c is equal to . C c n Σ i=1 ai n Σ i=1 i3 is equal to . D cn n Σ i=1 i2 is equal to

Answer:

The graph is moved to the left three spaces and up four spaces.

Step-by-step explanation:

The reason is if the graph were moved to the right three spaces, then the x+3 should be a x-3. Since it has a +4 on the outside, that means the y values are moving up four.

The value of k for the medication is -0.0065.

The formula for the half-life of a medication is f(t) = Ced, where C is the initial amount of the medication, k is the continuous decay rate, and t is time in minutes.

Initially, there are 11 milligrams of a particular medication in a patient's system.

After 70 minutes, there are 7 milligrams. We are to find the value of k for the medication.

The formula for the half-life of a medication is:

                           f(t) = Cedwhere,C = initial amount of medication,

k = continuous decay rate,

t = time in minutes

We can rearrange the formula and solve for k to get:

                                  k = ln⁡(f(t)/C)/d

Given that there were 11 milligrams of medication initially (at time t = 0),

we have:C = 11and after 70 minutes (at time t = 70),

the amount of medication left in the patient's system is:

                                     f(70) = 7

Substituting these values in the formula for k:

                                              k = ln⁡(f(t)/C)/dk

                                                  = ln⁡(7/11)/70k

                                                   = -0.0065 (rounded to 4 decimal places)

Therefore, the value of k for the medication is -0.0065.Answer:  O-0.0065 (rounded to 4 decimal places).

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Answer:

The absolute error is the absolute value of the difference between the actual value and the estimated value:

Absolute error = |actual value - estimated value| = |9.5 kg - 9 kg| = 0.5 kg

The percent error is the absolute error expressed as a percentage of the actual value:

Percent error = (|actual value - estimated value| / actual value) x 100%

Plugging in the given values, we get:

Percent error = (0.5 kg / 9.5 kg) x 100% = 5.3%

Rounding to the nearest tenth, the absolute error is 0.5 kg and the percent error is 5.3%.

The most appropriate conclusion is: There is not enough evidence to conclude that the course improves SAT scores.

When conducting a hypothesis test, we start with a null hypothesis that assumes there is no difference or no effect between two groups or variables. In this case, the null hypothesis would be that the mean SAT score of students who took the course is not significantly different from the mean SAT score of students who did not take the course.

We then collect data and calculate a test statistic (such as a t-statistic) and a p-value. The test statistic measures the difference between the sample means and tells us how far apart they are in standard deviation units. The p-value measures the probability of observing the test statistic or a more extreme value if the null hypothesis is true.

If the p-value is smaller than the chosen level of significance (usually 0.05 or 0.01), we reject the null hypothesis and conclude that there is enough evidence to suggest that the two means are significantly different. If the p-value is larger than the chosen level of significance, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the two means are significantly different.

In this scenario, if the mean of the SAT scores of students who took the course is not significantly different from the mean of the SAT scores of students who did not take the course, it means that we failed to reject the null hypothesis. Therefore, we cannot conclude that the course has an effect on SAT scores. We can only say that there is not enough evidence to suggest that it does.

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Answer:

10

Step-by-step explanation:

We cannot use the Pythagorean Theorem here because we only have one side length. However, we can use the fact that \(\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}\)

I decided to make the corner with the 60° as ∠A, the corner with the 30° as ∠B, and the corner with the right angle as ∠C. While then making side a as the unmarked side, side b as the side with 5, and the hypotenuse p as side c.

Since we do not need to solve for a in this equation to solve for p, we can simply use the sides and numbers we are given.

Manipulating two of our equations, preferably the equations with the variables b and c, we can get \(\frac{b}{sin(B)}=\frac{c}{sin(C)}\) and solving for c, which is p in this case, will give us \(c=\frac{bsin(C)}{sin(B)}\)

Plugging in the numbers we have gives us \(c=\frac{5sin(90)}{sin(30)}\) = 10 mi

(136-160):160*100 =

(136:160-1)*100 =

85-100 = -15

Answer:

The probability of getting two of the same color is 61/121 or about 50.41%.

Step-by-step explanation:

The bag is filled with five blue marbles and six red marbles.

And we want to find the probability of getting two of the same color.

If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.

In other words, we can find the independent probability of each case and add the probabilities together*.

The probability of getting a red marble first is:

\(\displaystyle P\left(\text{Red}\right)=\frac{6}{11}\)

Since the marble is replaced, the probability of getting another red is: \(\displaystyle P\left(\text{Red, Red}\right)=\frac{6}{11}\cdot \frac{6}{11}=\frac{36}{121}\)

The probability of getting a blue marble first is:

\(\displaystyle P\left(\text{Blue}\right)=\frac{5}{11}\)

And the probability of getting another blue is:

\(\displaystyle P\left(\text{Blue, Blue}\right)=\frac{5}{11}\cdot \frac{5}{11}=\frac{25}{121}\)

So, the probability of getting two of the same color is:

\(\displaystyle P(\text{Same})=\frac{36}{121}+\frac{25}{121}=\frac{61}{121}\approx50.41\%\)

*Note:

We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.

Answer: It would be option D :)

Step-by-step explanation: the formula for volume in a cylinder is π r squared times height. You plug those in and that’s your answer!

Answer: r = 4

Step-by-step explanation:

See the image.

Answer:

.

Step-by-step explanation:

Step-by-step explanation:

the answer is

the Value of b to 2

Answer:

Number of the squares on chessboard = 64

Exponent form = \(8^{2}\)

Step-by-step explanation:

8 x 8 = 64

exponent form of  of the chessboard

= \(8^{2}\)

Answer: x = 3 and y = 5

Step-by-step explanation:

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

t = 10

Step-by-step explanation:

z^t ⋅ z^5 = z^15

We know that a^b*a^c = a^(b+c)

z^(t+5) = z^15

Since the bases are the same, the exponents are the same

t+5 = 15

t = 15-5

t = 10

Answer:

6^10

Step-by-step explanation:

6^0 is essentially just 1. So 6^10 x 1 is 6^10.

Answer:

6^10

Step-by-step explanation:

When multiplying exponents with the same base number, you simply add the exponents and keep the bases the same

a^m * a^n = a^m+n

6^10 * 6^0 = 6^10+0

You can also look at it this way:

Any non-zero number to the power of 0 will ALWAYS equal 1

a^0=1

6^10 * 6^0 = 6^10 * 1 = 6^10

The statement (b) the sum is a binomial with a degree of 3 is correct.

Expressions are defined as the combination of constants and variables with mathematical operators.

We have expressions:

6s²t – 2st²

4s²t – 3st²

Adding the above two expressions, we get;

= (6s²t – 2st²) + (4s²t – 3st²)

Combining like terms:

= 10s²t - 5st²

The above expression has degree 3(2+1)

Thus, statement (b) the sum is a binomial with a degree of 3 is correct.

Complete question:

What is true about the sum of the two polynomials?

6s2t – 2st2

4s2t – 3st2

a.) The sum is a binomial with a degree of 2.

b.) The sum is a binomial with a degree of 3.

c.) The sum is a trinomial with a degree of 2.

d.) The sum is a trinomial with a degree of 3.

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Answer:

The slope of the line passing through both points is 0

Step-by-step explanation:

Mathematically, we can calculate the slope as follows;

m = (y2-y1)/(x2-x1)

where (x1,y1) = (-6,-7)

(x2,y2) = (-24,-7)

Thus m = (-7 -(-7))/(-24 + 6) = 0/18 = 0

The slope of both is 0