Determine each lengths in right triangle ABC.
BD———>
AB———>

88% of the students in the school are enrolled in health.

We have,

Students enrolled in health = 440

Students not enrolled = 60

Total students = 500

So, x% of 500 = 440

x/100 (500) = 440

5x = 440

x = 88%

Thus, 88% of the students in the school are enrolled in health.

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We can see here that the measure of variability using the range will be: 1.

A statistical metric known as a measure of variability tells us how widely spaced or dispersed a group of data points are. Measures of variability are used to quantify how significantly different a dataset's individual data points are from one another.

The measure of variability using range will:

Mean (Peak season) - Mean (Off Peak Season) = 6 - 5 = 1.

We see here that the mean of the peak season population is increased compared to that of the off-peak season. The mean of the off-peak season is seen to be lower.

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Answer: A

Step-by-step explanation: -87

Answer:

V = (4/3)π(6^3) = 288π square inches

= 904.78 square inches

Using 3.14 for π, V = 904.32 square inches.

Answer:

Since the triangles are similar, their corresponding sides are in proportion. The ratio of sides AB to DE is 9:13.5, which simplifies to 2:3. Therefore, the ratio of their areas is the square of the ratio of their sides, which is 4:9.

If the area of triangle ABC is 34 cm, then the area of triangle DEF is:

Area of DEF = (Area of ABC) x (DE^2/AB^2) = 34 x (13.5^2/9^2) = 34 x 1.5^2 = 34 x 2.25 = 76.5 cm^2

Therefore, the area of triangle DEF is 76.5 cm^2.

Step-by-step explanation:

Answer:

  (b)  10; 150°

Step-by-step explanation:

You want the polar coordinate equivalent of (-5√3, -5).

The polar form of (a, b) is ...

  (a, b) = (r; θ)

where ...

  r = √(a² +b²)

  θ = arctan(b/a) . . . . . with attention paid to quadrant

For the given values, the polar form is ...

  r = √((-5√3)² +5²) = √(75 +25) = 10

  θ = arctan(5/(-5√3)) = arctan(-1/√3) = 150°

The angle is a quadrant II angle with a reference angle of 30°.

The polar form is (10; 150°).

__

Additional comment

Some calculators will do the coordinate conversion based on a vector or ordered pair. Others require the coordinates of the point to be expressed as a complex number, as in the attachment. (Note the calculator mode is set to DEGrees.)

Differentiating y = x^3 ln 2x/e^x Sin x is: y' = x^2 [(3 ln 2x/e^x Sin x + 3/x) - 2 ln 2x/e^x Sin x cos x + cos x].

Differentiate y can be find using the product and chain rule.

Using the chain rule

v'(x) = [1/(2x/e^x)] * (2e^x - e^x*2x) / (2x/e^x)^2

v'(x) = [e^x(2-e^x)] / (2x)^2

Using the product rule

y' = 3x^2 ln(2x/e^x) sin(x) + x^3 [e^x(2-e^x)] / (2x)^2 sin(x) + x^3 ln(2x/e^x) cos(x)

Simplifying

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

So,

derivative of y is:

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

Therefore the differentiate of y is 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x).

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Answer:16x-4-2x+8=14x+4

Step-by-step explanation:

In order to solve this question you first want to multiply everything inside the bracket by the number outside.

4(4x-1)

so 4 times 4x which is 16x and 4 times -1 which is -4 so the first bracket is

(16x-4)

then do the same for the second bracket

-2(x-4)

so -2 times x would be -2x and -2 times -4 would be 8

for the final step collect the like terms and solve

so your answer would be

16x-2x which would be 14x and -4+8 which would be 4

so in conclusion the answer is

14x+4

Answer: Given the following equations, determine the x value(s) that result in an equal output for both functions. f(x) = 3* g(x)=4x+1. C0 and 2.

Step-by-step explanation:

Given the following equations, determine the x value(s) that result in an equal output for both functions. f(x) = 3* g(x)=4x+1. C0 and 2.

Answer: 7

Step-by-step explanation: he spends 7 hours a day take 3 away from 10.

The probability that the sum of the numbers is even is,

⇒ P = 0.47

Since, We know that;

To have this kind of event you can have the following events, where

(d₁ ,d₂),  d1 is the number that appears uppermost on die 1 and d2 is the number that appears uppermost on dice 2:

(1, 1), (1, 3) , (1, 5), (2, 2), (2, 4) (2, 6) (3, 1) (3, 3) (4, 2) (4, 4) (4, 6), (5, 1) (5, 3), (5, 5) (6, 2) (6, 4) (6, 6)

And,  the total number of events is 36 since every dice have 6 numbers.

The probability is:

P(Event)=P(sum is even)/Total number of events

P = 17/36

P = 0.47

Thus, The probability that the sum of the numbers is even is,

⇒ P = 0.47

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Answer:

The three numbers are -4, 0, and 1.

Step-by-step explanation:

mark brainliest

The required two pairs of polar coordinates for the point (0, -10) are:

(10, π/2) and (10, -π/2)

To convert from Cartesian coordinates (x, y) to polar coordinates (r, θ), we can use the following formulas:

[tex]r = \sqrt{(x^2 + y^2)}\\\theta = \tan^{-1}(y/x)[/tex]

Since the x-coordinate of the point (0, -10) is 0, we can directly say that the angle θ is either π/2 or -π/2, depending on whether y is positive or negative.

For y = -10, we get:

[tex]r = \sqrt{(0^2 + (-10)^2)} = 10[/tex]

Therefore, two pairs of polar coordinates for the point (0, -10) are:

(10, π/2) and (10, -π/2)

Both of these pairs have the same distance from the origin (r = 10) but different angles (π/2 and -π/2).

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There are 27.558 meters of wire does she have remaining after the first day.

We have to given that;

An electrician has 42.3 meters of wire to use on a job.

And, On the first day, she uses 14.742 meters of the wire.

Hence, We get;

The remaining wire does she have remaining after the first day is,

⇒ 42.3 - 14.742

⇒ 27.558 meters

Thus, There are 27.558 meters of wire does she have remaining after the first day.

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The order will be $50.4 with the price increase

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

Order = $45

Percentage increase = 12%

Using the above as a guide, we have the following:

New order = Order * (1 + Percentage increase)

Substitute the known values in the above equation, so, we have the following representation

New order = 45* (1 + 12%)

Evaluate

New order = 50.4

Hence, the new order is $50.4

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Answer:

A) Kevin has been saving money for 19 weeks.

B) Kevin still needs $515.

Step-by-step explanation:

A) 277=600-17x /-600

-17=-323 /÷(-17)

x=19

B) x=600-17×5

x=600-85

x= 515

Solution: 11/5 as a mixed number is 2 1/5.

Answer:translation, 12^2+35^2, squre root the answer, thgen add it to 12

Step-by-step explanation:

Answer: z = 8

Step-by-step explanation:

The diagram shows us that 8z + 3z + 2 = 90

so we can say that: 11z = 88

therefore z = 8.

Note: diagrams can be misleading! this diagram technically shows us that 64 < 26!

The equation of proportion will be x/4 = 36/x. Then the value of 'x' will be 12 units.

According to the hypotenuse-leg (HL) principle, a right triangle is harmonious if each of its third side and legs are congruent with its equivalent hypotenuse and legs in another right triangle. The HL theorem proves that these triangles are identical.

The equation is given as,

x/4 = 36/x

Simplify the equation, then we have

x/4 = 36/x

x² = 2² × 6²

x = 2 × 6

x = 12

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The angle measures for the triangles are given as follows:

Similar triangles are triangles that share these two features listed as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle Z is given as follows:

m < Z + 20 + 105 = 180

m < Z + 125 = 180

m < Z = 55º.

Hence the measures are given as follows:

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Answer:No, X=-3, yly =-4,0,4

Step-by-step explanation:

Answer:twelve million, three hundred and four thousand, six hundred and fifty two

Step-by-step explanation:

Answer:

n = -5

Step-by-step explanation:

We know that when two lines are perpendicular, the slopes of the two lines are negative reciprocals as

[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the line we're usually not given, and m1 is the slope of the line we're given

Thus, we know that m2 must equal -1/2 from the formula since m1 is 2:

[tex]m_{2}=-\frac{1}{2}[/tex]

Of course, -1/2 is already simplified so m2 is the slope of the line passing through (8, n) and (2, -2)

To find n, we must use our knowledge of the slope formula that gives us the slope, m:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point on the line and x2 and y2 are another point on the line:

If we allow (8, n) to be our x1 and y1 point and allow (2, -2) to be our x1 and y2 point and -1/2 to be our m, we can now solve for m by plugging everything into the slope formula and solving for n (aka y1 in the formula:

[tex]-1/2=\frac{-2-n}{2-8}\\ \\-1/2=\frac{-2-n}{-6}\\ \\3=-2-n\\\\5=-n\\\\-5=n[/tex]

We can even check that we get -1/2 when we plug in -5 into the slope formula:

[tex]-1/2=(-2-(-5))/(2-8)\\-1/2=(-2+5)/(-6)\\-1/2=3/-6\\-1/2=-1/2[/tex]

Answer:

Point B is 4 units to the right and 2 units down

Step-by-step explanation:

Since our x is positive, we are going to the right of the x-axis (where positive values lay).

Since our y is negative, we are going down in the y-axis (where negative values lay).

[tex]\cfrac{10}{x}=\cfrac{x}{7}\implies 70=x^2\implies \sqrt{70}=x[/tex]

Answer:

To find the mean of the data, we add up all the heights and then divide by the number of players:

Mean = (58 + 60 + 61 + 59 + 63) / 5

Mean = 301 / 5

Mean = 60.2 inches

Therefore, the mean height of the players on the Tracy basketball team is 60.2 inches.

The answer is 60.2in.

Step-by-step explanation:

Answer:

E. 108 in.²

Step-by-step explanation:

The piece of wood has the shape of a triangular prism.

SA = lateral area + area of the bases

SA = perimeter × height + 2 × bh/2

SA = (5 + 3 + 4) in. × 8 in. + 3 in. × 4 in.

SA = 108 in.²

The factor form of the given expression is [tex]x^2 - 14 - 4x = (x - 4)(x - 14).[/tex]

To factor the expression x^2 - 14 - 4x, we can use the technique of grouping.

First, we can rearrange the terms as:

x^2 - 4x - 14

Next, we can factor out a common factor of x from the first two terms:

x(x - 4) - 14

Then, we can factor out a negative 1 from the last two terms:

x(x - 4) - 1(14)

Finally, we can write the expression as the product of two binomials:

(x - 4)(x - 14)

Therefore, the factored form of x^2 - 14 - 4x is (x - 4)(x - 14).

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11.2% of the mass of a water molecule is hydrogen

As water is composed of two parts hydrogen and one part oxygen, the total mass of a single molecule may be determined by ascertaining the following:

The Total Mass of Water = (2 x Mass of Hydrogen) + (1 x Mass of Oxygen)

Total Mass of Water = (2 x 1.01u) + (1 x 16.00u)

Total Mass of Water = 18.02u

Consequently, the overall mass of one molecule of water is determined to be 18.02 atomic mass units (u).

% mass of hydrogen = (mass of hydrogen / total mass of water) × 100

% mass of hydrogen = (2.02u / 18.02u) × 100

% mass of hydrogen = 11.2%

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