write each expression without the absolute value symbol

The distance BC from Tower 2 to the plane is equal to 18,674 feet.

The height of the plane from the ground is equal to 7,595 feet.

In order to determine the distance from Tower 2 to the plane (BC), we would apply the law of sine (sine law) because we have two angles and one side length.

In Mathematics and Geometry, the law of sine is modeled or represented by this mathematical equation:

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

[tex]\frac{sin8}{7600} =\frac{sin20}{BC}[/tex]

BCsin8 = 7600sin20

BC = 2599.35/0.1392

Distance, BC = 18,673.50 ≈ 18,674 feet.

Next, we would determine the height of the plane from the ground (CD);

sin24 = CD/18,674

CD = 18,674sin24

Height, CD = 7,595.40 ≈ 7,595 feet.

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Answer:

a)  The length of BC is 15,052 ft to the nearest foot.

b)  The length of CD is 6,122 ft to the nearest foot.

Step-by-step explanation:

Angles on a straight line sum to 180°. Therefore:

[tex]\implies m \angle ABC +24^{\circ}=180^{\circ}[/tex]

[tex]\implies m \angle ABC =156^{\circ}[/tex]

Interior angles of a triangle sum to 180°. Therefore:

[tex]\implies m \angle BCA+16^{\circ}+156^{\circ}=180^{\circ}[/tex]

[tex]\implies m \angle BCA=8^{\circ}[/tex]

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]

Use the Sine Rule to find the length of BC.

[tex]\implies \dfrac{AB}{\sin BCA}=\dfrac{BC}{\sin CAB}=\dfrac{AC}{\sin ABC}[/tex]

[tex]\implies \dfrac{7600}{\sin 8^{\circ}}=\dfrac{BC}{\sin 16^{\circ}}[/tex]

[tex]\implies BC=\dfrac{7600\sin 16^{\circ}}{\sin 8^{\circ}}[/tex]

[tex]\implies BC=15052.0746...[/tex]

[tex]\implies BC=15052\; \sf ft\;(nearest\;foot)[/tex]

Therefore, the length of BC is 15,052 ft to the nearest foot.

Interior angles of a triangle sum to 180°. Therefore:

[tex]\implies m \angle BCD+24^{\circ}+90^{\circ}=180^{\circ}[/tex]

[tex]\implies m \angle BCD=66^{\circ}[/tex]

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

To find the length of CD, use the sine trigonometric ratio.

[tex]\implies \sin 24^{\circ}=\dfrac{CD}{BC}[/tex]

[tex]\implies CD=BC\sin 24^{\circ}[/tex]

Substitute the found value of BC into the equation:

[tex]\implies CD=\left(\dfrac{7600\sin 16^{\circ}}{\sin 8^{\circ}}\right)\sin 24^{\circ}[/tex]

[tex]\implies CD=6122.23031...[/tex]

[tex]\implies CD=6122\; \sf ft\;(nearest\;foot)[/tex]

Therefore, the length of CD is 6,122 ft to the nearest foot.

The correct numerical expression for the given statement "multiply the sum of 7 and 6 by the sum of 4 and 5" is (7 + 6) x (4 + 5).

Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables. A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

The given statement, "multiply the sum of 7 and 6 by the sum of 4 and 5", can be represented as:

sum of 7 and 6 = (7 + 6)

sum of 4 and 5 = (4 + 5)

multiply: (7 + 6) x (4 + 5)

Hence, the correct numerical expression for the given statement is (7 + 6) x (4 + 5).

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Answer:

(7 + 6) x (4 + 5).

Step-by-step explanation:

hope this helps!

the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.

The statements that are true about the reflectional  symmetryof a regular heptagon are:

It has only one line of reflectional symmetry.

The line of reflectional symmetry passes through the center of the heptagon.

A regular heptagon is a polygon with seven equal sides and angles. Each vertex of the heptagon is equidistant from the center of the heptagon, and the lines connecting the center to the vertices divide the heptagon into seven congruent triangles.

To understand the reflectional symmetry of the regular heptagon, we need to define what it means. Reflectional symmetry is a type of symmetry where a figure is symmetric with respect to a line. In other words, if we fold the figure along this line, one half will coincide with the other half.

In the case of the regular heptagon, we can observe that if we draw a line passing through the center of the heptagon and perpendicular to any of its sides, we obtain a line of reflectional symmetry. This line divides the heptagon into two congruent halves. However, if we draw any other line of reflectional symmetry, it will not coincide with the sides of the heptagon, and therefore, it will not divide the heptagon into congruent halves.

Therefore, we conclude that the regular heptagon has only one line of reflectional symmetry, and it passes through the center of the heptagon. This property is common to all regular polygons, and it is related to their rotational symmetry.

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Example of samples of 100 people for two-sided p-value of less than 0.001 represents that the new drug is indeed effective.

Example of a scenario that could lead to a two-sided p-value of less than 0.001 is ,

To investigate whether a new drug reduces blood pressure in patients.

Randomly select 100 patients with hypertension and divide them into two groups.

One group receives the new drug, while the other group receives a placebo.

After a month of treatment, you measure the blood pressure of each patient .

And compute the difference between the pre- and post-treatment measurements.

Assuming that the blood pressure measurements are normally distributed.

Perform a two-sample t-test to compare the mean difference in blood pressure between the two groups.

If the difference is statistically significant at the 0.001 level.

It means that the probability of obtaining such a large difference by chance is less than 0.001.

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Answer: A

y < 2x + 1

y > 1/2x + 2

Mason would save $7,618.32 in interest by paying off $8,500 immediately.

In other terms, compound interest is interest on principle + interest and refers to the addition of interest to the principal amount of a loan or deposit. Reinvesting interest, or adding it to the lent capital rather than paying it out or requesting payment from the borrower, results in interest being generated on the principle amount plus previously accrued interest in the next month. In economics and finance, compound interest is common.

Comparing compound interest to simple interest, which has no effect on previously accrued interest

Given that, Mason has a credit card debt of $15,600.

Using his original payment plan of 60 months we have:

[tex]I = P * (1 + r/n)^{(n*t)} - P[/tex]

Substitute the values we have:

[tex]I = 15,600 * (1 + 0.18/12)^(12*5) - 15,600\\I = 9,316.84[/tex]

For the new plan:

New balance = $15,600 - $8,500 = $7,100

[tex]I = 7,100 * (1 + 0.18/12)^(12*2) - 7,100\\I = $1,698.52[/tex]

Hence, over the course of 24 months, Mason would pay approximately $1,698.52 in interest.

The difference in interest paid between the two scenarios is:

$9,316.84 - $1,698.52 = $7,618.32

Therefore, Mason would save approximately $7,618.32 in interest by paying off $8,500 immediately.

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Answer:b

Step-by-step explanation:

The diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

A common example of a random experiment is rolling a regular six-sided die. For this action, all possible outcomes/sample space can be specified, but the actual result on any given experimental trial cannot be determined with certainty.

Martin features a spinner with four compartments marked A, B, C, and D.

To get the correct result of the filling, first take the value of the horizontal bar and write the value from the corresponding vertical bar where both column are meeting.

Thus, the diagram included shows the letter pairs that should go into each box to appropriately finish the table and display the sample area of Martin's experiment.

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Answer:

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

Find the prime factors of 1352:

We need another factor of 2 as a minimum added in order to have even number of same factors:

Hence we need to multiply the given number by 2.

True. The p-value is a probability value that measures the power of evidence in against to the null hypothesis in a statistical test.

Mainly, it represents the possibility of staring at a test statistic as a minimum as extreme as the one computed, assuming that the null hypothesis is genuine.

If the p-value is small, commonly less than a chosen significance stage (e.g., 0.05), it shows that the determined data is unlikely to have took place by danger alone and provides proof against the null hypothesis. alternatively, a large p-value suggests that the determined information is consistent with the null speculation, and the evidence isn't sturdy enough to reject it.

Consequently, the p-value is an critical tool in statistical inference, permitting researchers to draw conclusions about the population based totally on pattern information and degree the extent of uncertainty in their outcomes.

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To find the slope of a line that passes through two points, you can use the slope formula. The slope formula is:

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

Using the points given in your question, the slope formula to find the slope of the line is:

Slope = (2 - 8) / (4 - (-4))

Using the order of operations, the calculation of the slope formula is as follows:

Slope = -6 / 8

Therefore, the slope of the line passing through (-4, 8) and (4, 2) is -3/4.

Answer:

Unfortunately, the provided statement does not contain sufficient information to determine the loan term of the truck.

Step-by-step explanation:

The loan term refers to the length of time over which the loan for the truck is scheduled to be repaid. It is typically determined at the time of purchase and specified in the loan agreement.

To determine the loan term of the truck, we would need to know additional information such as the date of purchase, the loan agreement terms, the payment schedule, and any other relevant details about the loan.

This means that in order for the profits in 2022 to match those in 2020, the profits in 2021 would also need to match those in 2020.

 [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.

Profits for mesne. According to Section 2(12) C.P.C., the term “mesne profit” refers to any earnings that the person who is in wrongful possession of a piece of property has actually received or may obtain in the future. High Court of Telangana.

The earnings in 2022 must match the profits in 2020, hence we must choose the value of r such that:

[tex]P \times(1-r/100)^² = P[/tex]

By simplifying and dividing both sides by P, we obtain:

[tex](1-r/100)^² = 1[/tex]

Taking the square root of both sides, we get:

1-r/100 = ±1

Each time we solve for r, we obtain:

[tex]1-r/100 = 1[/tex] , which implies [tex]r = 0[/tex]

and

 [tex]1-r/100 = -1,[/tex] which implies [tex]r = 200[/tex]

We reject the [tex]r = 200[/tex] Option because a percentage drop cannot be larger than 100%.

Therefore,  [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.

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Answer: 325

Step-by-step explanation:

65% is more than half of the 500 people. Half of the number of people is 250. 325 is the only answer over 250

Answer:

C) 60º, 60º, 120º, 120º

Step-by-step explanation:

We know the sum of all the angles in a rectangle is 360 degrees, whether it's irregular or not.

Given: x + 2x + 2x + x = 360

Calculate the linear equation, to find x.

x + 2x + 2x + x = 360

3x + 3x = 360

6x = 360  (Divide both sides by 6)

x = 60 degrees.

Then you can calculate the polygons.

x + 2x + 2x + x

For the first x, = 60.

Then for 2x, 60 * 2 = 120.

Then for 2x again, = 120.

Finally for the last x, = 60.

Therefore, the answer is C) 60º, 60º, 120º, 120º.

This circumstance may happen if one of the RHS coefficients is 0. The objective value and solution remain the same in this situation, but there are still variables. Degeneracy describes this condition.

The energy levels in a three-dimensional box are provided by the formula E = (h2/8m) [(n x2/a2) + (n y2/b2) + (n z2/c2)].

where n x, n y, and n z are the quantum numbers for the x, y, and z dimensions, respectively, and h is Planck's constant, m is the particle'smass, a, b, and c are the dimensions of the box.

The amount of various quantum number combinations that result in the same energy is the degeneracy of an energy level.

The degeneracies of the first four energy levels for a three-dimensional box with a=b=1.5c are as follows:

1 degeneracy at first energy level (n=1)

Third degeneracy at second energy level (n=2)

6 degeneracies at third energy level (n=3)

10 degeneracies at energy level four (n = 4)

Hence, This circumstance may happen if one of the RHS coefficients is 0. The objective value and solution remain the same in this situation, but there are still variables. Degeneracy describes this condition.

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Therefore , the solution of the given problem of standard deviation comes out to be option C with n = 1,000 and p near to 1/2 is the right response.

Statistics uses variance as a way to quantify difference. The image of the result is used to compute the average deviation between the collected data and the mean. Contrary to many other valid measures of variability, it includes those pieces of data on their own by comparing each number to the mean. Variations may be caused by willful mistakes, irrational expectations, or shifting economic or business conditions.

Here,

The following algorithm determines the standard deviation of the sampling distribution of a sample proportion p:

=> √((p*(1-p))/n)

where n is the sample size, and p is the population percentage.

For the sampling distribution of a sample proportion p,

the pair of sample number n and population proportion p that would result in the highest standard deviation is:

=>n =1,000, and p is almost half.

Because p=1/2

yields the highest possible value of the expression (p*(1-p)), a bigger sample size will result in a smaller standard deviation.

The standard deviations will be lower for the other choices, which have smaller sample sizes or extreme values of p.

Therefore, (C) with n = 1,000 and p near to 1/2 is the right response.

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Using the discriminant of the quadratic equation, the temperature will part after 50 minutes

The temperature of the machine part is given by the equation:

T = -0.005x^2 + 0.45x + 125

We need to find out if the temperature will ever reach or exceed 135°F, which means we need to check if there exists a value of x for which T = 135.

Substituting T = 135 in the above equation, we get:

135 = -0.005x^2 + 0.45x + 125

Simplifying the equation, we get:

0.005x^2 - 0.45x + 10 = 0

This is a quadratic equation of the form ax^2 + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.

The discriminant of this quadratic equation is given by:

D = b^2 - 4ac

= (-0.45)^2 - 4(0.005)(10)

= 0.2025 - 0.2

= 0.0025

Since the discriminant is positive, the quadratic equation has two real roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.

We can also find the roots of the quadratic equation using the formula:

[tex]x = (-b \± \sqrt(D)) / 2a[/tex]

Substituting the values of a, b, and D, we get:

[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]

Taking the positive value, we get:

x = 50

Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.

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The area of the triangle with the given base and height where a = 4 and c = 2 is: 608 cm²

Area = 1/2(base)(height).

Given the parameters:

If a = 4 and c = 2, then:

Area = 1/2(base)(height) = 1/2(2ac²)(2ac² + 6)

Area = 1/2(2 × 4 × 2²)(2 × 4 × 2² + 6)

Area = 1/2(32)(38)

Area = 608 cm²

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The height of the tree is closest to 8.66 meters (option B).

Angle of elevation is the angle between a horizontal line of sight and an object above the line of sight, as measured from the observer's eye.

In other words, it is the angle formed between the observer's line of sight and the line drawn from the observer's eye to the object being observed, when the object is above the observer's eye level.

To solve this problem, we can use the property of similar triangles, which states that the ratios of corresponding sides of similar triangles are equal.

For the boy and his shadow, we have:

height of boy / length of boy's shadow = height of tree / length of tree's shadow

Substituting the values given, we get:

56 / 48 = height of tree / x, where x is the length of the tree's shadow

Solving for the height of the tree, we get:

height of tree = (56 / 48) * x

We are not given the length of the tree's shadow, but we can use the information given in the second part of the problem to find it.

For the tree and its shadow, we have:

height of tree / length of tree's shadow = tan(30)

Substituting the value of the length of the tree's shadow as 15 meters and solving for the height of the tree, we get:

height of tree = 15 * tan(30)

height of tree ≈ 8.66 meters

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Using synthetic division for the given dividend and divisor the required quotient is given by option a. x^3 + 2x - 5.

Dividend is equal to,

x^4-2x^3+2x^2-9x +10

Divisor is equal to,

( x - 2 )

Using synthetic division we have,

Use double equals to method to simplify the dividend we have,

x^4-2x^3+2x^2-9x +10

= x^4 - 2x^3 + 2x^2 - 4x -5x + 10

= x^3 (x -2) +  2x ( x -2 ) - 5 ( x - 2 )

= ( x - 2 ) ( x^3 + 2x - 5 )

Now ,

Simplify by dividing it,

( x^4-2x^3+2x^2-9x +10 ) ÷ ( x - 2 )

= ( x - 2 ) ( x^3 + 2x - 5 ) ÷ ( x -2 )

= ( x^3 + 2x - 5 )

Therefore, the quotient of the synthetic division for the given dividend is equal to option a . ( x^3 + 2x - 5 ).

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Answer:

14

Step-by-step explanation:

When we round 61.604 to the nearest whole number, we get 62, and when we round 48.44 to the nearest whole number, we get 48.

Therefore, we can estimate 61.604 - 48.44 by subtracting 48 from 62:

62 - 48 = 14

So, the estimated answer is 14.

The equation that represents the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

Explanation:

To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).

Therefore, the equation for the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

This can also be written as:

Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)

Therefore, the value of the collection after 5 years is $246.90.

Answer: 254.26

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

That is what Slope is.

Answer:

Step-by-step explanation:

Slope :( 1,1)

You start on the y-axis point which is (0,1) as you can see it is going up so I used the “up left” strategy. You go up 1 to the left 1 since the line intersects at point (1,2)

Answer:

Step-by-step explanation:

The probability of x successes in n independent trials of the experiment is given by the Binomial probability formula, where n is the total number of trials and p is the probability of success in each trial.

Since n = 9 and p = 0.4, we can calculate the probability of x ≤ 3 successes as follows:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (9C0)(0.4)^0(0.6)^9 + (9C1)(0.4)^1(0.6)^8 + (9C2)(0.4)^2(0.6)^7 + (9C3)(0.4)^3(0.6)^6

= 0.17496 + 0.41472 + 0.36608 + 0.04320

= 0.99976

Therefore, the probability of x ≤ 3 successes is 0.99976.

Answer:

a straight line that connects two points on the circumference of a circle

Step-by-step explanation:

Answer: I really don't know I'm just trying to get a quest done sorry