The table shows the amount of time four students practiced the trumpet one day.

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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The distance between  Georgetown and clayton on the scale model  is 2 inches.

In math, the term scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.

The distance between Georgetown and clayton on a map with a scale of 1 inches: 14 miles can be found as follows;

They are actually 28 miles.

Therefore,

14 miles = 1 inches

28 miles = ?

cross multiply

distance between Georgetown and clayton on the scale model = 28 / 14

distance between Georgetown and clayton on the scale model = 2 inches

Therefore, the distance on the scale model is 2 inches.

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Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

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Answer:

DO YOURE WORK!

Step-by-step explanation:

Please.

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

Answer:

40°

Step-by-step explanation:

56+84=140

180-140=40°

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Answer:

B . 10.50

Why ? Because 8.50+3.50=12 , Then 12 × 5 = 60 , 2.50×3=7.5 , 60-7.5= 52.5 . divide 52.5 by 5 = 10.50 . So each friend paid 10.50

The equation of the line passing through the given point that is

parallel to the given lines are;

16) y = ²/₃x + 6

17) y = ²/₇x - 1

18) y = ³/₄x - 11

19) y = -4x + 12

16) We are given the equation of a line as;

y = ²/₃x - 2

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

y = mx + c

where;

m is slope

c is y-intercept

Thus, equation passing through (-3, 4) is;

y - 4 = ²/₃(x - (-3))

y - 4 = ²/₃x + 2

y = ²/₃x + 6

17) We are given the equation of a line as;

-2x + 7y = 14

7y = 2x + 14

y = ²/₇x + 2

Thus, equation passing through (-7, -3) is;

y - (-3) = ²/₇(x - (-7))

y + 3 = ²/₇x + 2

y = ²/₇x - 1

18) We are given the equation of a line as;

3x - 4y = 16

4y = 3x - 16

y = ³/₄x - 4

Thus, equation passing through (8, -5) is;

y - (-5) = ³/₄(x - 8)

y + 5 = ³/₄x - 6

y = ³/₄x - 11

19) We are given the equation of a line as;

4x + y = 7

y = -4x + 7

Thus, equation passing through (2, 4) is;

y - 4 = -4(x - 2)

y - 4 = -4x  + 8

y = -4x + 12

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Answer:

Here

Step-by-step explanation:

Answer: 136  17/36

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

To solve the equation 2x - 7 + 3x = 4x + 2 for x, you can follow these steps:

Combine like terms on both sides of the equation. Add the x terms together and move the constant terms to one side of the equation:

2x + 3x - 4x = 2 + 7

Simplifying the left side: x = 9

Simplify the right side of the equation:

x = 9

Therefore, the solution to the equation is x = 9.

Answer:

3x + y = 9.5

Step-by-step explanation:

1) The equation of a line is in the form of y = mx + c, where m is the gradient and c is the y-intercept. Write the given values in that form.

y = -3x + c

2) Find the value of k by using the following formula: m = y2 - y1 / x2 - x1. We already know m.

-3 = 8 - k / k - 3

-3(k - 3) = 8 - k

-3k + 9 = 8 - k

-3k + k = 8 - 9

-2k = -1

k = -1/-2

k = 1/2

3) Therefore, a line with gradient of - 3 passes through the points (3, 1/2) and (1/2, 8). We can find the y-intercept (c). To do so, choose one of the coordinates and substitute.

y = -3x + c

1/2 = -3(3) + c

1/2 = -9 + c

1/2 + 9 = c

9.5 = c

Completed equation of the line: y = -3x + 9.5

4) Write it in the form of ax + by = c.

3x + y = 9.5

Answer:

42 liters= 42000 milliliters

Answer:

42000

Step-by-step explanation:

1 litre = 1000 ml

42 l = 42 × 1000 ml

42 li = 42000ml

Answer:

250 of 65% acid

100 gallons of 30% acid

Really sorry if this is incorrect, I had this question on my Lesson 16 test, and I don't know if it's correct or not...

Following are the calculation to the given question:

Assuming

x=The number of gallons of pure acid \((50\%)\)

y = The number of liters of pure acid at \((80\%)\) a concentration

\(\to x+y = 350\)

The total quantity of gallons of each of the two types of pure acids............(1)

\(\to 0.65x+0.30y = 0.55(x+y)\)

the mixture's acidity

\(\to 0.65x+0.30y = 0.55(350)\\\\\to 0.65x+0.30y = 192.5 ..........(2)\)

So we have two equations and two variables to work with.

\(\to x+y = 350\\\\\to 0.65x+0.30y = 192\)

multiply the first equation by \(0.30\)

\(\to 0.30x+0.30y = 105\\\\\to 0.65x+0.30y = 192\)

Subtract the second equation from the first

\(\to 0.35x = 87\\\\\to x = 248. 57 \approx 248 \ gallons\\\\ \to y = 350-248 = 102\ gallons\\\\\)

As a result, we'll need 248 gallons of 65% pure acid and 102 gallons of 30% pure acid.

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Answer:

12.0 units is the answer

Step-by-step explanation:

Pythagorean theorem can be written as,

\(d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\d=\sqrt{(6-(-2))^2 + (1-(-8))^2}\\\\d=\sqrt{(8\\)^2+(9)^2} \\\\d=\sqrt{64+81} \\\\d=\sqrt{145} \\\\d=12.041...\)

Rounding off,

d = 12.0 units

Answer:

6x2+12x+18

Hope that helps :)

Step-by-step explanation:

Answer:

hey what are you doing i think is 6x2+12x+18

Answer:

Answer:

1). Option (A)

2). Option (A)

Step-by-step explanation:

1). A worker bee has the mass = 0.00011 kg

  In scientific notation we can convert the mass of bee as,

  0.00011 =

                =

  Since 1.1 ≈ 1,

  Therefore, 1.1 × 10⁻⁴ ≈ 1 × 10⁻⁴ kg

  Option (A) is the answer.

2). An African elephant has a mass = 8139 kg

   In scientific notation,

   8139 = 8.139 × 10³

   Since, 8.139 ≈ 8

   Therefore, 8139 kg = 8.139 × 10³ kg

   Option (A) is the answer.

Hope this helps! ;)

Step-by-step explanation:

Answer:

Answer:

1). Option (A)

2). Option (A)

Step-by-step explanation:

1). A worker bee has the mass = 0.00011 kg

  In scientific notation we can convert the mass of bee as,

  0.00011 =

                =

  Since 1.1 ≈ 1,

  Therefore, 1.1 × 10⁻⁴ ≈ 1 × 10⁻⁴ kg

  Option (A) is the answer.

2). An African elephant has a mass = 8139 kg

   In scientific notation,

   8139 = 8.139 × 10³

   Since, 8.139 ≈ 8

   Therefore, 8139 kg = 8.139 × 10³ kg

   Option (A) is the answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

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Answer:

12 only

Step-by-step explanation:

It means x is zero, and the only point on x=0 is 12 :)

According to the graph the function  f(0) is  12 only .

The x-intercept is the point where a line crosses the x-axis or at y = 0, and the y-intercept is the point where a line crosses the y-axis or at x =0.

According to the question

The graph shows the function in which

f(0) is

i.e

x = 0  or y intercept

Now, according to the graph

at x = 0 , y = 12

Or

f(0) = 12

Hence, The function  f(0) is  12 only .

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The value of minimum usual value is, \(\mu-2\sigma=-119.2\)

The value of maximum usual value is, \(\mu+2\sigma=1311.2\)

Given the values of the parameters of Binomial Distribution are,

Total number of trials (n) = 1490

probability of success in one trial is (p) = 2/5

The probability of failure in on trial is given by,

\(q=1-p=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}\)

For Binomial distribution we know that,

Mean \((\mu)=np=1490\times\frac{2}{5}=596\)

and Standard Deviation \((\sigma)=\sqrt{npq}=\sqrt{1490\times\frac{2}{5}\times\frac{3}{5}}=357.6\)

Now, calculating the required measurement we get,

The minimum usual value is given by,

Mean -2 Standard Deviation \(=\mu-2\sigma=596-2\times357.6=-119.2\)

The maximum usual value is given by,

Mean + 2 Standard Deviation \(=\mu+2\sigma=596+2\times357.6=1311.2\)

Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.

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Answer:

C. 7

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = 7x + 3

Step 2: Break Function

Identify Parts

Slope m = 7

y-intercept b = 3

Answer:

a) 4

b) 2

Step-by-step explanation:

I use this sentence to remember quadrants:

All Students Take Coffe

- All trigs are positive in 1 Quadrant

- Sin and (cosine) is positive in 2 quadrant

-Tan and (Cotan) are positive in 3 quadrant

- Cos and (Sec) are positive in 4 quadrant

all other trigs other than those are negative.

a) cos is positive in 1 and 4 quadrant. Csc is reciprocal of Sin and is negative in 3 and 4 quadrant. 4th quadrant satisfies both conditions.

b) csc  is reciprocal of Sin and is positive in 1 and 2 quadrants. Sec is reciprocal of Cos and is negative in 2 and 3 quadrant. 2nd quadrant fulfills both conditions.