a line segment is drawn between (4,8) and (8,5). find it’s gradient.

Answer: I remember this question very well. I believe that the correct answer is 99.7%

68% of data falls between 15 and 25.

95% of data falls between 10 and 30.

99.7% of data falls between 5 and 35.

The result of sin (A - B) is 21/221.

To evaluate sin (A - B), we can use the formula:

sin (A - B) = sin A * cos B - cos A * sin B.

We are given that sin A = 12/13 and cos B = 8/17. We need to find cos A and sin B to use the formula.

Since A is in Quadrant II, cos A is negative. We can use the Pythagorean identity, sin²A + cos²A = 1, to find cos A:

cos²A = 1 - sin²A
cos²A = 1 - (12/13)²
cos²A = 1 - 144/169
cos²A = 25/169
cosA = -5/13

Similarly, since B is in Quadrant IV, sin B is negative. We can use the Pythagorean identity to find sin B:

sin²B = 1 - cos²B
sin²B = 1 - (8/17)²
sin²B = 1 - 64/289
sin²B = 225/289
sinB = -15/17

Now we can plug in the values into the formula:

sin (A-B) = (12/13)*(8/17) - (-5/13)*(-15/17)
sin (A-B) = 96/221 - 75/221
sin (A-B) = 21/221

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To find (f ∘ g)(x), we need to substitute g(x) into f(x) wherever we see x in the expression for f(x).

So we have:

f(g(x)) = f(3x + 1) = (3x + 1)^2 - 8 = 9x^2 + 6x - 7

Therefore, the correct answer is: 9x^2 + 6x - 7.

The solution to the inequality is x <= 50. This means that any value of x less than or equal to 50 will satisfy the inequality.

To solve the inequality 100 - 3x >= -50, we want to find the values of x that satisfy this inequality.

Makayla solved the equation 100 - 3x = -50 and got x = 50. This equation is not the same as the inequality we want to solve, but we can check whether Makayla's solution is a valid solution to the inequality.

Substituting x = 50 into the inequality, we get:

100 - 3x >= -50

100 - 3(50) >= -50

100 - 150 >= -50

-50 >= -50

This is a true statement, so x = 50 is a valid solution to the inequality.

However, we also need to check whether there are any other values of x that satisfy the inequality. We can do this by rearranging the inequality to isolate x:

100 - 3x >= -50

100 + 50 >= 3x

150 >= 3x

50 >= x

Therefore, the solution to the inequality is calculated to x <= 50.

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You would receive $13.50 if you cashed in 135 dimes. That's the equivalent of 1,350 pennies.
If you cashed in 135 dimes, you would receive 1,350 pennies.

This is because each dime is worth 0.1 dollars, or 10 pennies. So, to find the total number of pennies you would receive, you can simply multiply the number of dimes by the number of pennies in each dime:
135 dimes * 10 pennies/dime = 1,350 pennies
So, you would receive 1,350 pennies if you cashed in 135 dimes.

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Answer:

attached is the answer

Step-by-step explanation:

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Answer:

Let's start by defining some variables to represent the given information:

T0 = 48°F (the current temperature)

deltaT = -1.5°F/hour (the rate of change in temperature)

T = 36°F (the target temperature)

We want to find how many hours it will take for the temperature to drop from 48°F to 36°F, so let's call that time h. We can use the formula for the linear relationship between temperature and time:

T = T0 + deltaT * h

We want to solve for h when T = 36°F, so we can substitute the given values and solve for h:

36 = 48 + (-1.5) * h

-12 = -1.5h

h = 8

Therefore, it will take 8 hours for the temperature to drop from 48°F to 36°F, assuming the temperature continues to decrease at a rate of 1.5°F per hour.

The total number of campers at the camp is calculted to be 100 campers.

To find the total number of campers at the camp, we need to use the given information about the percentage of campers that went on the hike and the number of campers that went on the hike.

35% = 35 campers / Total number of campers

Cross-multiplying and simplifying gives us:

35% * Total number of campers = 35 campers

Dividing both sides by 35% gives us:

Total number of campers = 35 campers / 35%

Converting 35% to a decimal gives us:

Total number of campers = 35 campers / 0.35

Solving for the total number of campers gives us:

Total number of campers = 100 campers

So the total number of campers at the camp that went on for hike is 100 campers.

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The transformation is (a) Graph opens down, it moves 2 units left and 5 units down.

From the question, we have the following parameters that can be used in our computation:

y = -|x + 2| - 5

Where the parent function is

y = |x|

When we modify the equation to y = -|x + 2| - 5, we are applying several transformations to the parent graph:

So the resulting graph (a)

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x1 = -2, x2 = 1, and x3 = 5.5

This system of equations can be solved by first combining the equations and then isolating one of the variables. To combine the equations, subtract the first equation from the second equation:

4x1 + 5x2 + 5x3 = 9

- (x1 + x2 + 3x3 = -4)

3x1 + 4x2 + 2x3 = 13

Next, isolate one of the variables. In this case, let's isolate x3:

3x1 + 4x2 + 2x3 = 13

- (2x3) - (-2x3) = 0

3x1 + 4x2 = 13

x3 = \frac{13 - (3x1 + 4x2)}{2}

Now that x3 has been isolated, substitute it into one of the original equations and solve for the remaining two variables:

x3 = \frac{13 - (3x1 + 4x2)}{2}

x1 + x2 + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x2:

x2 = \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4}

Substitute this expression for x2 into one of the original equations and solve for x1:

x1 + \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4} + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x1 and then plug this value back into the expression for x2 to find x2:

x1 = -2

x2 = 1

x3 = \frac{13 - (-2 + 4x2)}{2}

x3 = \frac{13 - (-2 + 4 \cdot 1)}{2}

x3 = \frac{13 - 2}{2}

x3 = 5.5

Therefore, the solution to the system of equations is x1 = -2, x2 = 1, and x3 = 5.5.

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The value of the variable 'x' using the external angle theorem will be 84°.

The polygonal form of a triangle has a number of flanks and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is practically always equivalent to the accumulation of the interior and opposing interior angles. The term "external angle property" refers to this segment.

The graph is completed and given below.

By the external angle theorem, the equation is given as,

x + 180° - 154° + 180° - 110° = 180°

x + 26° + 70° = 180°

x + 96° = 180°

x = 84°

The value of the variable 'x' using the external angle theorem will be 84°.

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Answer:

8

Step-by-step explanation:

Let's call the unknown side [tex]c[/tex].

The Pythagorean Theorem states that in any right triangle, [tex]a^{2} + b^2 = c^2[/tex]

Now plug in the known values.

[tex]6^2 + (2\sqrt 7)^2 = c^2\\36 + 4(7) = c^2\\36 + 28 = c^2\\64 = c^2\\c = \sqrt{64} = 8[/tex]

The individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.

What is the Present Value of an Annuity?

With a specific rate of return, or discount rate, the present value of an annuity is the current value of the future payments from an annuity. The present value of the annuity decreases as the discount rate increases.

To determine the amount needed for retirement, we can use the formula for the present value of an annuity:

  [tex]PV= PMT* \frac{1-\frac{1}{(1+r)^{n} } }{r}[/tex]

where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $15,265, r = 4.5%/2 = 0.0225 (since the interest is compounded semi-annually), and n = 35 x 2 = 70 (since there are 70 semiannual periods in 35 years).

Plugging in these values, we get:

[tex]PV = (15,265\times(1 - (1 + 0.0225)^{(-70))) / 0.0225[/tex]

PV = $405,840.13

Therefore, the individual would need $405,840.13 at the start of retirement to make semiannual withdrawals of $15,265 for 35 years from an account paying 4.5% compounded semiannually.

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The area of the shaded segment of the circle is 5.79 square metre.

The area of a segment is equal to the area of a sector less the triangle-shaped portion.

A=[tex]\frac{1}{2}[/tex](∅-Sin∅)×[tex]r^{2}[/tex]

Every point in the plane of a circle, which is a closed, two-dimensional object, is evenly separated from the centre. All lines that cross the circle join together to produce the line of reflection symmetry. Moreover, every angle has rotational symmetry around the centre.

r=8m

∅=60°

Applying the formula's values, we obtain

A=[tex]\frac{1}{2}[/tex](∅-Sin∅)×[tex]r^{2}[/tex]

A=[tex]\frac{1}{2}[/tex]([tex]\frac{π}{3}[/tex]-Sin60°)×[tex]8^{2}[/tex]

A=5.79

Hence,  the area of the shaded segment of the circle is 5.79 square metre.

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Therefore , the solution of the given problem of equation comes out to be julian must  sell at least 28 wallets in order to make even.

Mathematical formulas frequently use the same variable letter to try to impose unity between two assertions. Many academic numbers are shown to be equal using mathematical fraction equations, also known as assertions. Using y + 6 as an illustration, the normalise does not divide 12 into two parts, but instead b + 6. It is possible to determine the connection between each sign part and the number of lines. The significance of a symbol usually contradicts itself.

Here,

For Julian to break even, his revenue must match his expenses. Therefore, we can equalise the two equations and find x:

=> 18x - 140 = 7x + 160

7x is subtracted from both lines to yield:

=> 11x - 140 = 160

140 added to both ends results in:

=> 11x = 300

When we multiply both parts by 11, we get:

=> x = 27.27 (rounded to two integer places) (rounded to two decimal places)

We can round up to the nearest whole amount because Julian cannot sell a fraction of a wallet. Julian must therefore sell at least 28 wallets in order to make even.

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The guy wire's length should be approximately 120.5 feet.

To find out, we can use trigonometry. The guy wire, the tower, and the ground form a right triangle, with the guy wire as the hypotenuse. We know the angle between the guy wire and the ground (20°), and we know the height of the tower (578 feet). We want to find the length of the guy wire. Using the trigonometric function tangent, we can set up the following equation:

tan(20°) = 578 / (guy wire length - 6)

Solving for the guy wire length, we get:

guy wire length = 578 / tan(20°) + 6

guy wire length ≈ 120.5 feet

Therefore, the guy wire should be approximately 120.5 feet long.

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The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).

To express the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form, we need to multiply the two expressions together and then simplify. Here are the steps:

1. Distribute the first term of the first expression to the second expression: (4/3)x * (5/6)x + (4/3)x * (5/3) = (20/18)x^2 + (20/9)x
2. Distribute the second term of the first expression to the second expression: -6 * (5/6)x + -6 * (5/3) = (-30/6)x + (-30/3)
3. Combine the like terms: (20/18)x^2 + (20/9)x + (-30/6)x + (-30/3) = (20/18)x^2 + (-10/9)x + (-30/3)
4. Simplify the fractions: (10/9)x^2 + (-10/9)x + (-10)

So the product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).

The product of ((4)/(3)x-6) and ((5)/(6)x+(5)/(3)) as a trinomial in simplest form is (10/9)x^2 + (-10/9)x + (-10).

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Answer:

[tex]27\pi[/tex]

Step-by-step explanation:

The area of a circle is given by the formula [tex]A = \pi r^2[/tex].

We are given the radius of this circle, so we can plug in.

[tex]A = \pi r^2\\A=6^2\pi \\A=36\pi[/tex]

Seeing that there is [tex]\frac{3}{4}[/tex] of the circle left, multiply [tex]36\pi[/tex] by [tex]\frac{3}{4}[/tex].

[tex]36\pi(\frac{3}{4})\\ 9\pi (3)\\27\pi[/tex]

a) P (20 < or = X) =  0.8617: This is the probability that 20 or more of the 30 patients will be helped by the medicine.

b) P (18 < or = X < 25) = 0.8557: This is the probability that between 18 and 25 of the 30 patients will be helped by the medicine.

c) P ( X < 16) = 0.0266: This is the probability that less than 16 of the 30 patients will be helped by the medicine.

The given situation can be modeled using a binomial distribution, where the number of trials is 30, and the probability of success is 0.75. We can use the binomial probability formula to find the probabilities for each of the given conditions. The binomial probability formula is:

P(X = x) = (n choose x) * p^x * (1-p)^(n-x)
where n is the number of trials, x is the number of successes, p is the probability of success, and (n choose x) is the binomial coefficient.

a) P (20 < or = X) = 1 - P (X < or = 19) = 1 - sum_{x=0}^{19} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8617

b) P (18 < or = X < 25) = P (X < or = 24) - P (X < or = 17) = sum_{x=18}^{24} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.8557

c) P ( X < 16) = sum_{x=0}^{15} (30 choose x) * (0.75)^x * (0.25)^(30-x) = 0.0266

Therefore, the probabilities are 0.8617, 0.8557, and 0.0266 for the conditions a), b), and c) respectively.

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Julia will finish the upcoming 6.2-mile race first among her friends, beating the second-place finisher by 5 minutes and 42 seconds.  

Distance is the measure of how far apart two objects or points are. It is expressed in terms of length, area, volume, or time. It is a numerical measurement of how much space is between two points or objects. Distance can also be used to measure the length of a journey, or to measure the speed of an object moving over a certain period of time.

To calculate this, we can look at the table and compare the times of the last race each of them ran. Julia ran a 5-mile race in 32 minutes and 45 seconds, her first friend ran a 4-mile race in 28 minutes and 20 seconds, and her second friend ran a 4-mile race in 29 minutes and 15 seconds.

To calculate the time difference between Julia and the second-place finisher, we can compare the total time they would run the 6.2-mile race. Julia would run the 6.2 miles in 40 minutes and 45 seconds (32 minutes and 45 seconds for the 5-mile race plus 8 minutes for the additional 1.2 miles) and the second-place finisher would run the 6.2 miles in 41 minutes and 35 seconds (29 minutes and 15 seconds for the 4-mile race plus 12 minutes and 20 seconds for the additional 2.2 miles). The difference between the two times is 5 minutes and 42 seconds, so Julia would finish first and beat the second-place finisher by 5 minutes and 42 seconds.

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Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

First, let's calculate the total amount he will need to finance:

Total amount to finance = R160,000 + 0.15 x R160,000 (VAT at 15%) = R184,000

Next, let's calculate the total interest he will need to pay over the 60 months:

Total interest = (principal x rate x time) / 100

where

Total interest = (R184,000 x 10% x 5) / 100 = R92,000

Therefore, the total amount Michael will need to pay over the 60 months is the sum of the total amount financed and the total interest:

Total amount to pay = Total amount to finance + Total interest = R184,000 + R92,000 = R276,000

So, Michael will need to pay a total of R276,000 over the 60 months for the Mex tractor.

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The greatest common factor (GCF) of the polynomial ab+8a+2b+16 is 2.

To factor the given polynomial ab + 8a + 2b + 16 by grouping, follow these steps:

1. Group the terms in pairs: (ab + 8a) + (2b + 16).

2. Factor out the Greatest Common Factor (GCF) from each group. - For the first group (ab + 8a), the GCF is "a". So, factor out "a" from the group: a(b + 8).

-For the second group (2b + 16), the GCF is "2". So, factor out "2" from the group: 2(b + 8).

3. Notice that both groups have a common factor of (b + 8). So, factor out (b + 8) from the entire expression: (b + 8)(a + 2).

Thus, the factored form of the polynomial ab + 8a + 2b + 16 by grouping is (b + 8)(a + 2).

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Therefore , the solution of the given problem of unitary method comes out to be in a group of 15, we would anticipate that 5 pupils would choose a candy.

To finish a job using the unitary method, divide the lengths of just this minute subsection by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait. There are changes and unanswered issues (mathematics, algebra).

Here,

There are a total of 12 sweets in the bag: 5 + 1 + 2 + 4 candies. Given that there are 4 gold-wrapped candies out of a total of 12, the chance of choosing one during any given draw is 4/12 = 1/3.

. Therefore, regardless of how many draws have been conducted before, the chance of choosing a gold-wrapped treat is always 1/3.

In a class of 15 pupils, the predicted proportion of students who would choose a gold-wrapped treat would be:

Expected number of gold-wrapped candies = (1/3) * (number of draws) * (probability of choosing gold-wrapped candy on one draw) = 5

Therefore, in a group of 15, we would anticipate that 5 pupils would choose a candy that was wrapped in gold.

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[tex] \: [/tex]

_________

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[tex] \: [/tex]

[tex] \: [/tex]

[tex] \small{\star \boxed{ \tt \color{blue} volume \: of \: cone \: = \frac{1}{3}h\pi {r}^{2} }}[/tex]

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hope it helps! :)

The two polygons are similar using the SAS criteria.

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end. A polygon's line segments are therefore referred to as its sides or edges. The vertex or corners made by two line segments are where an angle is created. A triangle with three sides is an illustration of a polygon. A circle is a planar figure as well, but since it is curved and lacks sides and angles, it is not regarded as a polygon. Hence, we may argue that while all two-dimensional forms are polygons, not all two-dimensional figures are polygons.

For the given polygons we find the scale factor to determine whether the two figures are similar.

The scale factor is given as:

SF = length of original/ length of new image

SF = 4 / 6

SF = 2/3

For the second segment:

SF = 6/9

SF = 2/3

The ratios of the segment are same. Also the angle between the corresponding segments is 86 degrees.

Hence, the two polygons are similar using the SAS criteria.

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Answer:

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

Vertical compression of a function by a factor of a is:

Vertical compression of a function by a factor of 5 is:

Shifting up by b units is:

If we apply both transformations we get:

Option C is correct.

The polynomial p(x) in the form p(x) = (x+1)q(x), where q(x) is a polynomial of degree n-1.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

x2+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x2, x, and -12.

Since we know that p(-1)=0, we can use this information to substitute -1 into p(x), giving us:

p(-1) = 0

We can then rearrange this equation to get:

0 = p(-1) = (x+1)q(x)  

This gives us the form of p(x) that we are looking for:

p(x) = (x+1)q(x)

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Using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.

What is Graph ?

A graph is a visual representation of data that displays the relationship between variables or sets of data. Graphs are commonly used in various fields such as mathematics, statistics, economics, and science to help people understand and analyze data.

IQR, because it is a measure of variability that is resistant to outliers and is appropriate for both symmetric and skewed distributions. It measures the spread of the middle 50% of the data, which gives a good indication of how consistent the temperatures are around the median.

Therefore, using IQR would be the appropriate measure of variability to compare the consistency of temperatures between Desert Landing and Flower Town.

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2x^2 + 7x + 3 factors into (2x + 1)(x + 3).

What is factoring?

The factoring approach can be used if the quadratic polynomial can be divided into two linear factors:

Look for two numbers that add up to b and multiply to c.

With these numbers, rewrite the quadratic polynomial as the sum of two terms.

Choose the term that has the most in common with each group of terms.

Remove the common binomial factor between the two groups.

Take the quadratic polynomial 2x2 + 7x + 3, for instance. We must choose two values that sum up to seven and multiply by three in order to factor this polynomial. These are the numbers 3 and 1. The quadratic can then be rewritten as follows:

2x² + 3x + 4x + 3

Then, for each collection of terms, we factor out the term with the highest common factor:

x(2x + 3) + 1(4x + 3)

Lastly, we remove the common binomial factor between the two groups:

(2x + 1)(x + 3)

As a result, 2x2 + 7x + 3 equals (2x + 1)(x + 3).

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