Students and teachers at a school were asked if they preferred blue, green, red, or yellow. The table shows the results of the survey. Blue Green Red Yellow Total Students 5 10 20 15 50 Teachers 15 10 5 20 50 Total 20 20 25 35 100 Choose three statements that can be inferred from the data in the table. A. 20% of all people surveyed chose blue. B. 20% of the students surveyed chose red. C. 20% of the students surveyed chose blue. D. 20% of the teachers surveyed chose green. E. 20% of those who chose red were teachers. F. 20% of those who chose yellow were teachers.​

Answer:

This prism has: 5 Faces. 6 Vertices (corner points) 9 Edges.

Step-by-step explanation:

Answer:

Contrapositive

Step-by-step explanation:

Original Statement: if p then q

Negation: not p

Contrapositive: if not q then not p

Inverse: if q then p

Converse: if not p then not q

Hey there! I'm happy to help!

These are corresponding angles since they both connect a parallel line and the transversal. This means they are congruent and have the same value. So, we can set up the following equation.

8x-8=5x+25

Subtract 5x from both sides.

3x-8=25

Add 8 to both sides.

3x=33

Divide both sides by 3.

x=11.

Have a wonderful day! :D

Answer:

x = 11

∠B = 80

Step-by-step explanation:

∠A = ∠B

where

∠A = 8x - 8°

∠B = 5x + 25°

8x - 8° = 5x + 25°

8x - 5x = 25 + 8

3x = 33

x = 33/3

x = 11

plugin x into ∠B = 5x + 25°

∠B = 5x + 25°

∠B = 5(11) + 25°

∠B = 80

Step-by-step explanation:

16 - 10 × 1/5 + 13

16 - 5 + 13

11 + 13

24

Step-by-step explanation:

10/5=2

16-2+13=27.

d. 27

Answer:

a)9/14

b)5/14

Step-by-step explanation:

For the past two weeks, Benita has been recording the number of people at Eastside Park at lunchtime

Answer:

Given that,

Akeelah’s storage box has a volume of 315 cubic centimeters.

It has a width of 9 cm and a length of 7 cm.

To find the height.

Explanation:

Length (l) = 7 cm

width (w) = 9 cm

Let hight be h,

we know that,

Volume is given by,

Substitute the values we get,

Required height is 5 cm

Answer is: 5 cm

The value of u is 2 in the given right-angled triangle.

The given figure is a right-angled triangle with hypotenuse 'u' and the other two sides as \(\sqrt{2}\) and v.

We have to find the value of 'u' using Pythagoras theorem or trigonometric identities.

It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In a right-angled triangle ABC, if

BC = hypotenuse

AC and AB are the other two sides then,

\(BC^2 = AC^2 + AB^2\).

For this problem, we can find the value of u by using trigonometric identities.

From the figure, we have an angle of 45°.

Consider Cos 45°.

Cos Ф = base / hypotenuse

Cos 45° = \(\sqrt{2}\) / u ...........(1)

From trigonometric identities of cosine.

We have,

Cos 45° = 1 / \(\sqrt{2}\)............(2)

From (1) and (2)

We get,

1 / \(\sqrt{2}\) = \(\sqrt{2}\) / u

u = 2.

Thus the value of u is 2 in the given right-angled triangle.

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The Interpretatiom of the equation is that;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

The algebra word problem can be solved by using variables to denote certain parameters I'm the question.

The general form of equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

We are given the equation:

$25w + $65

This equation represents the amount of money Kelly will have saved after some amount of weeks.

Thus;

w represents number of weeks she will have saved for the remaining items

$25 represents the amount she saves per week

$65 represents the amount she has already saved

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Answer:

A

Step-by-step explanation:

\(\frac{5}{6}\cdot \frac{1}{2}=\frac{5}{12}\)

Multiply top and bottom, on the top we get 5*1 which is 5 and on the bottom we get 6*2 which is 12.

The domain restrictions for (f/g)(x) are (c) x = 0, 6

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

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

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

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Answer:

Celsius and Fahrenheit are two important temperature scales that are commonly misspelled as Celcius and Farenheit. The formula to find a Celsius temperature from Fahrenheit is: °F = (°C × 9/5) + 32 The formula to find a Fahrenheit temperature from Celsius is: °F = (°C × 9/5) + 32 The two temperature scales are equal at -40°.

Step-by-step explanation:

PA BRAINLIEST

The length of the longer wire is 82 feet.

Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.

We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.

In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:

cos(θ) = adjacent/hypotenuse = 16/L

Given that cos(θ) = 8/41, we can substitute this value into the equation:

8/41 = 16/L

To solve for L, we can cross-multiply and solve for L:

8L = 41 * 16

L = (41 * 16)/8

L = 82

Therefore, the length of the longer wire is 82 feet.

In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.

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Answer:

\( {x}^{4} = 2880\)

Step-by-step explanation:

\( {y}^{2} = 20 \: (eq . \: 1)\)

\( {x}^{2} = {(2 \sqrt{3y)} }^{2} = 12y \)

Putting value of eq. 1 in the following:

\( {x}^{4 } = {(12y)}^{2} = 144{y}^{2} = 144 \times 20 = 2880\)

Answer:

hope it helped have a nice day

Answer:

• As x approaches -∞, g(x) approaches -∞; and as x approaches ∞, g(x) approaches ∞.

Step-by-step explanation:

\({ \tt{g(x) = \frac{ {x}^{2} + 5x}{3x} }} \\ \)

If x approaches -∞;

\({ \tt{g( {}^{ - } \infin}) = \frac{ {( {}^{ - } \infin)}^{2} + {}^{ - } \infin}{ {}^{ - } \infin} } \\ \\ { \boxed{ \tt{g( {}^{ - } \infin) = {}^{ - } \infin }}}\)

If x approaches +∞;

\({ \tt{g( {}^{ + } \infin) = \frac{ {( \infin)}^{2} + \infin}{ \infin} }} \\ \\ { \boxed{ \tt{ g( {}^{ + } \infin) = {}^{ + } \infin }}}\)

Note: I'm taking my infinite value to be 1,000

Answer: diameter

Step-by-step explanation:

Answer:

diameter

Step-by-step explanation:

The diameter connects two points on the edge of a circle through it's centre.

The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

Answer:

21. 2x + 28

22. 18a - 17b

23. He flipped the numerator and denominator, 6.4 with 7.2 and he added the exponents instead of subtracting.

24. 8.8888888888889 × 10^{0}

Step-by-step explanation:

Answer:

240%

Step-by-step explanation:

100 x (425 - 125) / 125

Answer:

The answer to your problem is, 0.275 0.273 0.400 and 0.300

Step-by-step explanation:

My calculation ( May not be correct )

P ( low iron or LI )  \(\frac{165}{600}\) = 0.275

P ( low pH | LI ) = \(\frac{45}{165}\) = 0.273

P ( low pH ) = \(\frac{150}{600}\) = 0.400

P ( LI | Low pH ) = \(\frac{45}{150}\) = 0.300

Thus by making these calculations the answer to your problem is, 0.275 0.273 0.400 and 0.300

Answer: (√2)(2) = 2√2

Step-by-step explanation:

To simplify the expression 3√2 - √2, you can factor out the common term √2:

3√2 - √2 = (√2)(3 - 1)

Now, subtract the numbers in parentheses:

(3 - 1) = 2

(√2)(2) = 2√2

Answer:

To the nearest hundredth, the value is

x = 1091.63

Step-by-step explanation:

Solving,

\(7 = ln(x+5)\\exponentiating,\\e^7 = e^{ln(x+5)}\\e^7 = x+5\\x = e^7-5\\x = 1091.63\)

Answer:

You will need four runners.

Step-by-step explanation:

If you multiply 1/16 by four you will get 4/16, which is simplified to 1/4

Answer:

A. \(h(x)=\sqrt{x-3}\)

Step-by-step explanation:

The parent function of \(\sqrt{x}\) is translated to the left when \(h\) is positive in the transformation \(\sqrt{x+h}\).

If \(h\) is negative, the graph translates towards the left with the distance equal to the value of \(h\).

Here the graph moved 3 units towards the right. This means that \(h\) is negative and has the value of 3.

So, plugging that into the parent function for translation, the function becomes:

\(h(x)=\sqrt{x-3}\)

Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts

Step-by-step explanation:

Answer:

3) Equation of line is: 5x-8y+34=0

4) Equation of line is: 5x+y+5=0

Step-by-step explanation:

3) Equation of line parallel to \(5x-8y+12=0\) and through point (-2,3)

When two lines are parallel they have same slope.

Converting the given equation \(5x-8y+12=0\) to Slope intercept form i.e \(y=mx+b\)

\(5x-8y+12=0\\-8y=-5x-12\\y=-\frac{5x}{-8}-\frac{12}{-8}\\y= \frac{5x}{8}+\frac{3}{2}\)

Now comparing with \(y=mx+b\) we get value of m i.e 5/8 which is slope of line.

Now, finding y-intercept using point (-2,3) and slope 5/8

\(y=mx+b\\3=\frac{5}{8}(-2)+b\\3=-\frac{5}{4}+b\\b=3+\frac{5}{4}\\b=\frac{3*4+5}{4}\\b=\frac{12+5}{4}\\b=\frac{17}{4}\)

So, y-intercept is b= 17/4

The required equation is:

\(y=mx+b\\y=\frac{5x}{8}+\frac{17}{4}\)

Writing in Standard form

\(y=\frac{5x}{8}+\frac{17}{4}\\y=\frac{5x+17*2}{8} \\y=\frac{5x+34}{8} \\8y=5x+34\\5x-8y+34=0\)

So, Equation of line is: 5x-8y+34=0

4) Equation of line perpendicular to \(x-5y+2=0\) and through point (-2,5)

When two lines are perpendicular they have opposite slope i.e m=-1/m.

Converting the given equation \(x-5y+2=0\)  to Slope intercept form i.e \(y=mx+b\)

\(x-5y+2=0\\-5y=-x-2\\y=-\frac{x}{-5}-\frac{2}{-5}\\y= \frac{x}{5}+\frac{2}{5}\)

Now comparing with \(y=mx+b\) we get value of m i.e 1/5 which is slope of given line.

Slope of required line will be: m=-1/m = -5

Now, finding y-intercept using point (-2,5) and slope -5

\(y=mx+b\\5=-5(-2)+b\\5=10+b\\b=5-10\\b=-5\)

So, y-intercept is b= -5

The required equation is:

\(y=mx+b\\y=-5x-5\)

Writing in Standard form

\(y=-5x-5\\5x+y+5=0\)

So, Equation of line is: 5x+y+5=0

The equation of the line that passes through the point (-3, 7) and has a slope of -5/3 is y - 7 = (-5/3)(x + 3).

We are given the point (-3, 7) and the slope of the line as -5/3.The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.

To obtain the equation of the line, we need to substitute the values of slope and point in the slope-intercept form and solve for b.(7) = (-5/3)(-3) + b 21/3 = b.

Now we have the value of b, and we can substitute the values of m and b in the slope-intercept form.y = (-5/3)x + 21/3 is the equation of the line in slope-intercept form.

To obtain the equation in the standard form Ax + By = C, we multiply each term by 3.3y = -5x + 7Add 5x to both sides5x + 3y = 7.

This is the equation of the line in standard form.

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(a) Given the position function

x(t) = (B m/s²) t² + 5 m

it's clear that the object accelerates at B m/s² (differentiate x(t) twice with respect to t), so that the force exerted on the object is

F(t) = (2 kg) (B m/s²) = 2B N

(b) Recall the work-energy theorem: the total work performed on an object is equal to the change in the object's kinetic energy. The object is displaced by

∆x = x(5 s) - x(0 s)

∆x = ((B m/s²) (5 s)² + 5 m) - ((B m/s²) (0 s)² + 5 m)

∆x = 25B m

Then the work W performed by F (provided there are no other forces acting in the direction of the object's motion) is

W = (2B N) (25B m) = 50B² J = 200 J

Solve for B :

50B² = 200

B² = 4

B = ± √4 = ± 2

Since the change in kinetic energy and hence work performed by F is positive, the sign of B must also be positive, so B = 2 and the object accelerates at 2 m/s².

(c) We found in part (b) that the object is displaced 25B m, and with B = 2 that comes out to ∆x = 50 m.