A boat is heading towards a lighthouse, whose beacon-light is 130 feet above the water. From point.� A, the boat’s crew measures the angle of elevation to the beacon, 6∘∘, before they draw closer. They measure the angle of elevation a second time from point � B at some later time to be 11∘∘ . Find the distance from point �A to point �B. Round your answer to the nearest foot if necessary.

Assume that the actual ratio is 0.07. If 310 people are sampled, there is a 0.0716 percent chance that the sample percentage and population proportion will deviate by more than 0.04.

The sample proportion, denoted by p', is an estimate of the population proportion p. The formula for the standard error of p' is:

SE = [tex]\sqrt{[p(1-p)/n]}[/tex]

where n denotes sample size and p denotes population proportion.

In this case, p = 0.07 and n = 310. Therefore, the standard error of p' is:

SE = [tex]\sqrt{[0.07(1-0.07)/310]}[/tex] = 0.019

To find the probability that the sample proportion will differ from the population proportion by more than 0.04, we need to find the probability that |p' - p| > 0.04. We can use the normal distribution to approximate this probability since the sample size is large (n = 310).

The z-score for a difference of 0.04 is:

z = 0.04 / 0.019 = 2.1053 (rounded to four decimal places)

Using a standard normal distribution table, the probability of a z-score being greater than 2.1053 or less than -2.1053 is approximately 0.0358. where n denotes sample size and p denotes population proportion.

P(|p' - p| > 0.04) = 2(0.0358) = 0.0716

Rounding to four decimal places, the probability is 0.0716.

The complete question is;-

A direct mail company wishes to estimate the proportion of people on a large mailing list that will purchase a product. Suppose the true proportion is 0.07. If 310 are sampled, what is the probability that the sample proportion will differ from the population proportion by more than 0.04? Round your answer to four decimal places.

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The vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).

The vertex of a parabola in the form of y = a[tex]x^{2}[/tex] + bx + c can be found using the formula x = -b/2a for the x-coordinate of the vertex and then substituting this value into the equation to find the y-coordinate.

For the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7, we can see that a = 3 and b = -12. We can use the formula to find the x-coordinate of the vertex:

x = -b/2a = -(-12)/(2*3) = 2

So the x-coordinate of the vertex is 2. To find the y-coordinate, we can substitute x = 2 into the equation:

g(2) = 3 [tex](2)^{2}[/tex]- 12(2) + 7 = -5

Therefore, the vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).

So the correct answer is (c) (2, −5).

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Step-by-step explanation:

A dilation is a transformation that enlarges or reduces an object by a certain scale factor, and it is centered at a fixed point. In this case, we want to dilate the point (-3, 0) by a scale factor of 2, and the center of dilation is at the origin (0, 0).

To perform the dilation, we first need to find the distance between the point (-3, 0) and the center of dilation (0, 0), which is simply the magnitude of the vector (-3, 0), or 3.

Next, we need to multiply this distance by the scale factor of 2 to get the new distance after dilation, which is 6.

Finally, we need to find the point that is 6 units away from the origin along the same line that passes through the origin and the original point (-3, 0). This can be done by multiplying the direction vector of this line by the distance of 6 and adding the result to the center of dilation (0, 0). The direction vector is (-3, 0), normalized to have unit length, which is (-1, 0).

So the image of (-3, 0) after dilation by a scale factor of 2 centered at the origin is:

(-1 * 6, 0 * 6) + (0, 0) = (-6, 0)

Therefore, the image point is (-6, 0).

Angle in a semi-circle is a right angle then, angle x is 90°, Z is 100° and y is 53° (refer below figure)

The six trigonometric functions of an angle in a right-angled triangle are connected by a set of fundamental identities known as the "Circle identities" in trigonometry.

In a semicircle AGE, angle at the circumference is 90 degree.

then, angle x = 90°

and arc Z° from the center of circle is a triangle AOB, see below figure,

40° + Z° + 40° = 180°

Then, Z° = 100°

Similarly, arc 74° from center of circle is a triangle EOG;

74°+ y° + y° = 180°

Then, y° = 53°

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Answer:

45 minutes

Step-by-step explanation:

We Know

Kristiana went to a yoga class at 12:30.

She went to lunch with her friends for 1hr and 35 minutes

She finished lunch at 2:50

How long was her yoga class?

We take

12:30 + 1:35 = 2:05

Then we take

2:50 - 2:05 = 45 minutes

So, her yoga class was 45 minutes.

The it is used to understand the likelihood of getting a particular outcome or event from a population.It is important to note that the probabilities for parametric probability distribution models are expressed as cumulative probabilities. Cumulative probabilities are used to evaluate the probability of a particular event or outcome.

Probabilities for parametric probability distribution models are expressed as cumulative probabilities.Parametric probability distribution refers to a type of probability distribution in which the probability distribution is defined by the probability distribution's parameters. The parameters are usually numeric values that define the distribution's probability density function (PDF) or probability mass function (PMF).The probability distribution is usually used to model a population's characteristics.

It is used to help understand the probability of obtaining a particular set of results from a population.Cumulative probabilities Cumulative probability refers to the probability of obtaining a score equal to or lower than a particular value in a given distribution. It is a probability value that is used in statistical analysis, which is usually represented by the area under the probability distribution's curve.The cumulative probability can be expressed as follows:P(X ≤ x)Where;X: random variablex: score or valueCumulative probabilities are used to evaluate the probability of a particular event or outcome.

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The better buy for david is churro at the swap

To determine which is the better buy for David, we need to compare the cost per churro for each purchase.

For the farmers market purchase, David bought 3 churros for $2.1, so the cost per churro is:

Cost per churro at farmers market = 2.1/3 = 0.7

For the swap meet purchase, David bought 5 churros for $3.20, so the cost per churro is:

Cost per churro at swap meet = 3.2/5 = 0.64

Since the cost per churro at the swap meet is lower than the cost per churro at the farmers market, buying churros at the swap meet is the better buy for David.

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Answer:

Step-by-step explanation:

if an equation needs only one step to isolate the variable, it is 1-step. For example, 4x=16, which means x=4. Generally I’m not sure of a way other than that to know if an equation is one step or multi-step.

-4(x+5)-2=6x

So, use distributive property.

-4x-20-2=6x

Add 4x to both sides.

-20-2=10x

Solve -20-2.

-22=10x

Divide 10 from both sides.

x=-10/22

Simplify

x=-5/11

Answer: 12800 cm³

Step-by-step explanation:

Area of Rectangular Prism = [tex]lwh[/tex]

A = 32 x 25 x 16

A = 12800

Answer:

45x261

Step-by-step explanation:

261

x45

---------

11745

The function f with its inverse function [tex]f^{-1}[/tex] is equal to the identity function. The value of [tex]f^{-1}(4)f[/tex] is equal to 4.

To determine the value of [tex]f^{-1}[/tex](4)f−1(4)f, we would need to know the function f and its inverse function [tex]f^{-1}[/tex].

In this case, we are asked to find [tex]f^{-1}[/tex](4)f−1(4)f, start superscript minus 1, end superscript, left parenthesis 4, right parenthesis. This means we need to find [tex]f^{-1}(4)[/tex] and then plug that value into the original function f.

Now, [tex]f(f^{-1}(4))[/tex] can be simplified as follows:

[tex]f(f^{-1}(4)) = 4[/tex]

This is because [tex]f^{-1}(4)[/tex] is the input that produces an output of 4, and then f is applied to that input to produce the same output.

Multiplying [tex]f^{-1}(4)[/tex] by f is equivalent to evaluating the function f at the point [tex]f^{-1}(4)[/tex]. Thus, we have:

[tex]f(f^{-1}(4)) = 4[/tex]

This means that the composition of the function f with its inverse function [tex]f^{-1}[/tex] is equal to the identity function. Therefore, the value of [tex]f^{-1}(4)f[/tex] is equal to 4.

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Answer:

60°

Step-by-step explanation:

We know that a straight line would be 180 °.

we can see that  the line is split into 3 equal sides .

180° ÷ 3 = 60°

The object would weight 42 pounds on Earth.

In physics, weight is a measure of the force exerted on an object due to gravity. It is a vector quantity, which means that it has both magnitude (numerical value) and direction.

Let's denote the weight of the object on Earth as W and set up a proportion:

Weight on Earth / Weight on Moon = Gravitational force on Earth / Gravitational force on Moon

Using the given information, we can substitute the weights and simplify:

W / 7 = 180 / 30

W / 7 = 6

Multiplying both sides by 7, we get:

W = 7 ×6 = 42

Therefore, the object would weigh 42 pounds on Earth.

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Triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:

AB || DC, as required.

What is the congruent angle?

When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.

Corresponding Parts of Congruent Triangles are Equal

AD || BC, AD = CB

Given

1 = 4

From statements 1 and 5, we can conclude that:

ACD is congruent to CAB because they are corresponding angles of parallel lines AD and BC.

If Lines are Parallel, then Alternate Interior Angles are Equal.

ACD = CAB

From statement 4, we know that angles ACD and CAB are equal because AD is parallel to BC. Therefore:

ACD = CAB

Reflexive Property of Equality

AC = AC

From statement 2, we know that segment AC is equal to itself because of the reflexive property of equality. Therefore:

AC = AC

If Alternate Interior Angles are Congruent, then Lines are Parallel.

2 = 3

From statement 3, we know that if alternate interior angles are congruent, then the lines are parallel. Therefore, since ACD = CAB (statement 4) and AC = AC (statement 2), we can apply the SAS (Side-Angle-Side) congruence theorem to triangles ACD and CAB to conclude that they are congruent.

SAS (Side-Angle-Side)

AB || DC

Hence, As a result, since triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:

AB || DC, as required.

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Answer:

12

Step-by-step explanation:

Green beads

=60/100x20

=12

Answer:An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Step-by-step explanation:basically its more than 90 degrees

Answer:

An obtuse triangle is a triangle where one of the interior angles measures more than 90°

Answer:

Step-by-step explanation:

We can use algebra to determine how many years it has been since the cost of a box of pencils was $0.00, and therefore calculate how many years the price has been increasing by $1.10 per year.

Let's say that x is the number of years since the cost of a box of pencils was $0.00.

If the price of a box of pencils is increasing by $1.10 per year, then the cost of a box of pencils x years after it cost $0.00 would be:

$0.00 + ($1.10 * x)

We know that the current cost of a box of pencils is $2.19. Setting this equal to the expression above, we can solve for x:

$0.00 + ($1.10 * x) = $2.19

$1.10 * x = $2.19

x = $2.19 / $1.10

x = 1.99

So, it has been approximately 1.99 years (or just under 2 years) since the cost of a box of pencils was $0.00, and the price of a box of pencils has been steadily increasing by $1.10 per year during that time.

Mikey needs to save for at least 9 weeks to buy the bike.

What is inequality?

An inequality is a mathematical statement that compares two values, indicating that they are not equal. It uses symbols such as <, >, ≤ (less than or equal to), or ≥ (greater than or equal to) to express the relationship between the two values.

Let's call the number of weeks that Mikey needs to save "w". We can set up an equation using the given information:

$25 x w > $200

Simplifying this inequality, we get:

w > 8

This means that Mikey needs to save for more than 8 weeks to have more than $200. Since the number of weeks has to be a whole number, Mikey needs at least 9 weeks to save enough money to buy the bike.

Therefore, Mikey needs to save for at least 9 weeks to buy the bike.

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To calculate the mean, we first need to find the midpoint of each class interval. We can do this by adding the lower and upper limits of each interval and dividing by 2. We can then multiply each midpoint by its corresponding frequency and add up the products. Finally, we divide by the total frequency to get the mean:

Class interval   Midpoint    Frequency   Midpoint x Frequency

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

1-5                3          2             6

6-10               8          5            40

11-15              13          8           104

16-20              18         10           180

21-25              23         14           322

26-36              31          6           186

21-35              28          4           112

36-40              38          1            38

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

Total frequency:   50

Mean = (6 + 40 + 104 + 180 + 322 + 186 + 112 + 38) / 50 = 921 / 50 = 18.42

Class interval   Midpoint   Mean   Midpoint - Mean   (Midpoint - Mean)^2   Frequency   (Midpoint - Mean)^2 x Frequency

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

1-5                3       18.42     -15.42            238.1764           2              476.3528

6-10               8       18.42     -10.42            108.5764           5              542.8820

11-15              13       18.42      -5.42             29.3764           8              235.0112

16-20              18       18.42      -0.42              0.1764          10                1.7640

21-25              23       18.42       4.58             20.9764          14              293.6704

26-36              31       18.42      12.58            158.4964           6              950.9784

21-35              28       18.42       9.58             91.9364           4              367.7456

36-40              38       18.42      19.58            383.4464           1              383.4464

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

Total frequency:   50                                                                                   3251.8512

To calculate the standard deviation, we first need to find the variance, which is the sum of the squared deviations divided by the total frequency:

Variance = (476.3528 + 542.8820 + 235.0112 + 1.7640 + 293.6704 + 950.9784 + 367.7456 + 383.4464) / 50

= 65.0378

Then, we take the square root of the variance to get the standard deviation:

Standard deviation = sqrt(65.0378) = 8.06

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Answer:

i think the right answer is 9/21

Step-by-step explanation:

hope it will help you!!

Answer: Well look at it closely so it will help you understand more of it.

Step-by-step explanation: I read it over and over and over again and I think this will help.

A total of 336 tubs of cookie dough were sold in all.

A ratio or figure stated as a fraction of 100 is called a percentage. The sign "%" is frequently used to indicate it as a percentage or a component of a total.

So, the number of tubs sold in each week can be represented by the following sequence:

Week 1: 100

Week 2: 0.8(100) = 80

Week 3: 0.8(80) = 64

Week 4: 0.8(64) = 51.2 ≈51

Week 5: 0.8(51) = 40.8≈41

To find the total number of tubs sold in all 5 weeks, we can add up the number of tubs sold in each week:

Total = 100 + 80 + 64 + 51 + 41

Total = 336

Therefore, a total of 336 tubs of cookie dough were sold in all.

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if you invest $2,500 at a weekly compounding rate of 4.5% for 4 years, you will have approximately $3,157.22 to use as a down payment on your Can-Am Spyder.

How to solve investment?

If you invest $2,500 at a 4.5% weekly compounding rate, it will grow to a considerable amount in 4 years. To calculate this, we need to use the compound interest formula:

A = P(1 + r/n)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate

n = the number of times the interest is compounded per year

t = the number of years

In this case, we have:

P = $2,500

r = 4.5% = 0.045

n = 52 (since compounding is weekly)

t = 4 years

Plugging in these values, we get:

A = $2,500(1 + 0.045/52) in power (52*4) = $3,157.22

So, if you invest $2,500 at a weekly compounding rate of 4.5% for 4 years, you will have approximately $3,157.22 to use as a down payment on your Can-Am Spyder.

It's important to note that this calculation assumes that the investment vehicle will have a steady and reliable return rate for the entire 4 years. There is always some level of risk involved with investing, so it's important to do your research and make informed decisions about where to put your money.

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The mathematical equations of each problem is 24 = 2x - 2, y + 16 = 85, 56 = (1/2)x - 6, x = 1/3 * 12600 and 120 + 50x = 270 and their solution are Sister is 13 years old, Arvin sold 69 cakes yesterday, You have 124 stamps, Chiz earned P4,200 this month and The horse ride lasted for 60 minutes, with 30 minutes being the initial ride and 30 minutes for the additional ride, respectively.

The translation of each problem into a mathematical equation then solution is.

Let x be the age of the sister.

Then, we have the equation:

24 = 2x - 2

Adding 2 to both sides gives:

26 = 2x

Dividing both sides by 2 gives:

x = 13

Therefore, the sister is 13 years old.

Let y be the number of cakes Arvin sold yesterday.

Then, we have the equation:

y + 16 = 85

Subtracting 16 from both sides gives:

y = 69

Therefore, Arvin sold 69 cakes yesterday.

Let x be the number of stamps you have.

Then, we have the equation:

56 = (1/2)x - 6

Adding 6 to both sides gives:

62 = (1/2)x

Multiplying both sides by 2 gives:

x = 124

Therefore, you have 124 stamps.

Let x be the amount Chiz earned this month.

Then, we have the equation:

x = 1/3 * 12600

Simplifying gives:

x = 4200

Therefore, Chiz earned P4,200 this month.

Let x be the number of 10-minute blocks for the additional horse ride time.

Then, we have the equation:

120 + 50x = 270

Subtracting 120 from both sides gives:

50x = 150

Dividing both sides by 50 gives:

x = 3

Therefore, the additional horse ride time was 3 blocks of 10 minutes, or 30 minutes in total. Adding this to the initial 30 minutes gives a total ride time of 60 minutes.

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_____The given question is incomplete, the complete question is given below:

Learning Task 3: Translate each problem into a mathematical equation then

solve:

1. i am 24 years old. My age is 2 less than twice my sister's age.

2. Arvin has a bake shop. He sold 85 cakes today. That is 16 cakes

fewer than yesterday. How many cakes did he sell yesterday?

3. Ann has 56 stamps that is 6 less than one-half of my stamps. How

many stamps do I have

4. This month Chiz eamed only of his earnings last month. If his

eaming last month is P12,600. How much did he earn this month?

5. In Baguio City a horse ride costs P120.00 per person for the first 30

minutes and P50.00 for every additional 10 minutes. If you spent

P270.00 for a horse ride, for how long did you ride?​

The greatest number of gift bags Ms. Bryant can make with 72 pencils and 54 pens is 18, with 4 pencils and 3 pens in each bag.

To find the greatest number of gift bags that Ms. Bryant can make, we need to find the greatest common factor (GCF) of the numbers of pencils and pens she has.

We can start by listing the factors of each number:

Factors of 72: [tex]1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72[/tex]

Factors of 54: [tex]1, 2, 3, 6, 9, 18, 27, 54[/tex]

To find the GCF, we look for the largest factor that is common to both lists. In this case, the largest common factor is 18.

This means that Ms. Bryant can make 18 gift bags, each containing 4 pencils and 3 pens, with no pencils or pens left over.

Therefore, the greatest number of gift bags Ms. Bryant can make with the given number of pencils and pens is 18.

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Answer:

The circumference of a circle is calculated using the formula `C = 2πr`, where `r` is the radius of the circle. Since you have given the radius as 4 and asked to use 3.14 for π, we can calculate the circumference as `C = 2 x 3.14 x 4 = 25.12`.

The area of a circle is calculated using the formula `A = πr^2`, where `r` is the radius of the circle. Using the same values for π and r as before, we can calculate the area as `A = 3.14 x (4)^2 = 50.24`.

So, for a circle with a diameter of 8 and a radius of 4 (using 3.14 for π), its circumference is approximately **25.12** and its area is approximately **50.24**.

Answer/Step-By-Step Explanation:

Part A:

To determine the measure of angle A (m/A), we can use the Law of Cosines, which states that:

c^2 = a^2 + b^2 - 2ab*cos(A)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

Substituting the given values, we have:

(32)^2 = (16)^2 + (16√5)^2 - 2(16)(16√5)*cos(A)

Simplifying:

1024 = 256 + 1280 - 512√5*cos(A)

512√5*cos(A) = 512

cos(A) = 1/√5

Using a calculator, we find:

A ≈ 63.43 degrees

Therefore, m/A ≈ 63.43 degrees.

Part B:

To use the unit circle to find tan A, we first draw a unit circle with its center at the origin of a coordinate plane. We then draw a ray from the origin through the point (1,0) on the circle, which corresponds to the angle of 0 degrees.

Next, we draw another ray from the origin through the point on the circle that corresponds to angle A. This ray intersects the circle at a point (x,y), where x = cos(A) and y = sin(A).

Since cos(A) = 1/√5, we have:

x = cos(A) = 1/√5

To find y, we use the Pythagorean theorem:

x^2 + y^2 = 1

Substituting x = 1/√5, we get:

(1/√5)^2 + y^2 = 1

y^2 = 4/5

y = ± 2/√5

Since angle A is in the first quadrant, we take y = 2/√5.

Therefore, tan(A) = y/x = (2/√5)/(1/√5) = 2.

Part C:

To calculate the area of triangle AABC, we can use Heron's formula, which states that:

Area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by:

s = (a+b+c)/2

Substituting the given values, we have:

s = (16+16√5+32)/2 = 24+8√5

Using this value of s, we can calculate the area:

Area = √[(24+8√5)(8√5-8)(8√5)(24-8√5)]

Simplifying:

Area = √[4096] = 64

Therefore, the area of triangle AABC is 64 square inches.

In this problem, we use the tangent function to solve for angle A, understand that the unit circle cannot be directly used to find the tangent of A, and finally find the area of the triangle using the formula 1/2*base*height.

Part A: Assuming triangle AABC is a right triangle, we can determine m∠A by using the tangent function (tan ∠A = opposite side / adjacent side). Here, the opposite side is 'b' and the adjacent side is 'a'. So, m∠A = tan⁻¹ (b/a) = tan⁻¹ (16 5/16). To get the correct result, we then use a calculator with the inverse tangent or arctan function.

Part B: The unit circle is a fundamental tool in trigonometry. But in this case, having calculated m∠A in Part A, we cannot directly use the unit circle to find tan A as tan A is not represented on the unit circle.

Part C: The area of a triangle can be calculated using the formula 1/2*base*height. In a right triangle, this can be represented as 1/2*a*b: 1/2*16*16 5 = 130 square inches.

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Answer:

Your friend's error is that having two equal discriminants doesn't necessarily mean that the two quadratic equations will have the same roots. The discriminant of a quadratic equation determines whether the roots are real, complex, or equal. If two quadratic equations have the same discriminant, then they have the same nature of roots, but that does not mean that their roots are equal.

As an example, consider the following two quadratic equations:

1. x^2 + 4x + 4 = 0

2. x^2 + 6x + 9 = 0

Both equations have the same discriminant: (b^2 - 4ac) = 16 - 16 = 0, but their roots are different. The first equation has one real root: x = -2, while the second equation has only one root, which is repeated twice: x = -3.

Therefore, it is incorrect to conclude that two quadratic equations have the same roots just because they have the same discriminants.

Answer: x < -35

Step-by-step explanation:

Answer:

a) discrete ; only from a particular building that stays the same

b) continuous ; the population of a country fluctuates and therefore shows trends

c) discrete ; information of a particular place

d) continuous ; there are trends of apple masses because there are different types of apples

Step-by-step explanation: