the number of words tom types varies directly with the amount of time he sepnds typing. if tom types 100 words in 2.5 minutes, how many words does he type in 15 minutes

The average rate of change of the function f(x) over the interval 5 ≤ x ≤ 8 is 81.

The average rate of change of a function f(x) over an interval [a, b] is given by:

average rate of change = (f(b) - f(a)) / (b - a)

In this case, we want to find the average rate of change of the function f(x) = 5x^2 + 7x + 9 over the interval 5 ≤ x ≤ 8.

So, we need to evaluate f(8) and f(5) and then plug the values into the formula:

f(8) = 5(8)² + 7(8) + 9 = 389

f(5) = 5(5)² + 7(5) + 9 = 144

Now we can plug these values into the formula for the average rate of change:

average rate of change = (f(8) - f(5)) / (8 - 5)

= (389 - 144) / 3

= 81

Therefore, the average rate of change of the function f(x) over the interval 5 ≤ x ≤ 8 is 81.

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The distance from home plate is approximately 188 ft. The key concept involved in solving this question is to find the horizontal distance traveled by the ball.

How far from home plate is the ball, approximately? Initial velocity of the baseball is given as 103 feet per second at an angle of 28° with respect to horizontal. Initial height is given as 4 feet. We can break the initial velocity vector into two components, horizontal and vertical components.

The horizontal component remains constant throughout the time of flight. We can find it by using the following formula;Initial velocity = horizontal component + vertical componentHorizontal component = initial velocity × cos 28°H = 103 × cos 28°H = 92.15 feetThe horizontal component tells us the ball traveled 92.15 feet before hitting the ground. Now we have to find the time of flight of the baseball, after which it hits the ground.We can use the vertical component of the initial velocity to find the time of flight of the baseball. The vertical component tells us how high the baseball will go before hitting the ground. We can use the following formula to find the time of flight;Vertical component = initial velocity × sin 28°v = 103 × sin 28°v = 49.67 feetThe time of flight can be found by using the following formula; v = u + at49.67 = 0 + 16t (acceleration due to gravity, g = 32 feet per second squared)t = 3.104 seconds.Now we can find the horizontal distance traveled by the baseball; Horizontal distance traveled = H × time of flight Horizontal distance traveled = 92.15 × 3.104Horizontal distance traveled = 286.17 feet≈ 188 ftHence, option C (188 ft.) is correct.

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Answer:

12

Step-by-step explanation:

You have to divide the total by the number per day to solve this problem.

1.08/0.09=12

Answer:

3/5

Step-by-step explanation:

Hi! i see your having trouble the answer is 3/5

answer: 3/5 as a decimal its 0.6

Answer:

Hey there the best answer would be A.=

Step-by-step explanation:

The average monthly temperature for July is $90 degrees Fahrenheit.

To calculate the average monthly temperature for July, we need to determine the value of y when t corresponds to July.

In the given equation, y = 70.5 + $19.5sin[(π/6)(t - 4)], t represents the number of months, with t = 1 representing January.

Since July is the seventh month of the year, we can substitute t = 7 into the equation to find the average monthly temperature for July:

y = 70.5 + $19.5sin[(π/6)(7 - 4)]

= 70.5 + $19.5sin[(π/6)(3)]

= 70.5 + $19.5sin[π/2]

= 70.5 + $19.5(1)

= 70.5 + $19.5

= 90

Hence the temperature in july is 90 degree farenheit.

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Answer:

PQ is 17

Step-by-step explanation:

2x+1=3x-7

+7 -2x          +7-2x

1+7=3x-2x

8=x

3•8=24

24-7=17

Answer:

4-5x

5x-4

Step-by-step explanation:

For a square with coordinates points ( -1,4) and (2,-3) of adjacent vertices, the area of square is equals to the fifty-eight square units.

A square is one of a two-dimensional closed shape includes 4 equal sides and 4 vertices. The area of a square is equal to multiplcation of side of square with itself, i.e., (side) × (side) square units. We have coordinates for an adjacent vertices of a square. That are ( -1,4) and (2,-3). We have to determine the area of square. First we have to determine the length side of square from coordinates. Distance formula,\(d = \sqrt{(x_2- x_1)²+(y_2 - y_1)²}\), where

Using the distance formula, distance between the two points, i.e., ( -1,4) and (2,-3), \(d = \sqrt{ (2-(-1))² + (-3 -4)²}\)

\(= \sqrt{ 9 + 49}\)

\(= \sqrt{ 58}\)

Since these points are the endpoints of one side of the square, so side of square, s = \(\sqrt{ 58}\) units

Using the formula of area of square, the required area = \(s² = ( \sqrt{ 58})²\)

= 58 square units

Hence, required value is 58 square units.

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The congruent segments, \( SC \cong HR \) and \( HR \cong AB\), according to the substitution property of equality, gives; \( SC \cong AB \)

The given parameters are;

Required;

To prove;

\( SC \cong AB\)

Solution;

From the given parameters, and the definition of congruency, we have;

According to the symmetric property of equality, we have;

SC = HR

Therefore;

According to the substitution property of equality, we have;

If a = b and a = c, therefore;

b = c

Which gives;

HR = SC

HR = AB

Therefore;

SC = AB

Which gives;

\( SC \cong AB \) (Inverse of the definition of congruency)

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Hello~

4+1=5

5+2=12

6+3=21

8+11 =

The First one is correct!

Ary~

The minimum score required for the scholarship is 646.765.

Standard deviation is a measure of the distribution of statistical data, whereas variance is a measure of how data points differ from the mean. The main distinction between the two is that whereas variance is expressed in squared units, standard deviation is expressed in the same units as the data's mean.

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = \(\frac{X - mean}{s.d.}\)

In this problem, we have that:

mean  = 488 , s.d. = 113

What is the minimum score required for the scholarship?

Top 8%, which means that the minimum score is the 100-8 = 92th percentile, which is X when Z has a pvalue of 0.92. So it is X when Z = 1.405.

Z =  (X - mean) / s.d.

1.405 = (X - 488) / 113

X = (1.405 x 113) + 488

X =   646.765

the minimum score required for the scholarship is 646.765.

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the probability that no two people of the same sex sit next to each other is 2/7.

One way to solve this problem is to use the principle of inclusion-exclusion. Let A be the event that the boys sit next to each other, and let B be the event that the girls sit next to each other. Then, we want to find the probability of the complement of (A or B), which is the probability that neither A nor B occurs.

The probability of A occurring is the same as the probability of the 5 boys sitting in a row, which is 5! (since each order is equally likely). Similarly, the probability of B occurring is 5!. However, we need to subtract the probability of A and B occurring simultaneously. This can be seen as follows: once the boys are seated in a row, there are 6 spaces (between or on the ends) where the girls can be seated. Thus, the probability of A and B occurring is 2*5!*6.

Therefore, the probability of neither A nor B occurring (i.e., the probability that no two people of the same sex sit next to each other) is:

P(neither A nor B) = 1 - P(A or B) = 1 - [P(A) + P(B) - P(A and B)]

= 1 - [(25!) / 10! - (25!6) / 10!]

= 1 - [25!*(1 - 6/9!)]

= 2/7

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The equation is y = 2.5x+38 using slope form.

So, we know that formula two find the slope of the line joining two points which is:

So y = MX +c.

m is the slope and c is the constant intersect.

Therefore, the equation is y = 2.5x+38 using slope form.

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Answer:

12.56

Step-by-step explanation:

find the circumference of the circle : 2πr

C=2(12)(3.14)

C=75.36

the length of the arc is: arc length will be (60/360) one 1/6 of the total circumference.

(60/360)(75.36)= 12.56

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

\(--------------------------------------------\)

\(\frac{1}{3}\cdot\frac{1}{4}+\frac{5}{12}\) = \(?\)

\(\frac{1}{12}+\frac{5}{12}\) = \(?\)

\(\frac{6}{12}\) = \(\frac{3}{6}\) = \(?\)

\(\frac{1}{2}\)

\(--------------------------------------------\)

Hope this helps! <3

\(--------------------------------------------\)

Answer:

I think it's y = 3/2x - 5

Step-by-step explanation:

when we multiply the slopes of perpendicular lines, we get -1

Answer:

7/8,5/6

Step-by-step explanation:

Two fractions are equivalent when their division is equal to one.

When we are dividing fractions, we multiply the numerator by the inverse of the denominator.

1/9,2/18

7/8,5/6

The division is not 1, so this par of fractions is not equivalent.

3/16, 9/48

6/15, 4/10​

Using degree of freedom,

Two degrees of freedom would we report when we report the results of our study is (2,24).

Degree of freedom:

The statistical degrees of freedom (DF) indicate the number of independent values that can be changed in the analysis without violating the constraints.

degrees of freedom is the number of independent values that can be estimated in a statistical analysis. It can also be thought of as the number of values that are free to vary when estimating the parameters

DF = N – P

Where:

N = sample size

P = the number of relationships

We given that,

Number of groups , k = 3

Number of total participants, n = 27

Degrees of freedom for F-test is F(k-1,n-k)

= F(3-1 , 27-3)

= F(2,24)

Hence, (2,24,) are required two degrees of freedom.

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Answer:

30/72 is 0,4166666666666

or

15/36

5/12

Answer:

30/72 in simplest form is 5/12

Step-by-step explanation:

Find the prime factors of the numerator of given fraction 30/72.

Prime factors of 30 = 2 x 3 x 5

Do the same thing for the denominator

Prime factors of 72 = 2 x 2 x 2 x 3 x 3

Rewrite the fraction 30/72 in the form of prime factors

\(\frac{30}{72}= \frac{(2 x 3 x 5)}{(2 x 2 x 2 x 3 x 3)}\)

The x in the equation stands for multiply

Check and cancel the factors of 30 and 72 if any factors in the numerator and denominator can be canceled each other in the above fraction of prime factors

\(\frac{(2 x 3 x 5)}{(2 x 2 x 2 x 3 x 3)} \\\frac{( 5)}{( 2 x 2 x 3)}\)

Simplify and rewrite the fraction and you will get 5/12

Hope this helps

Answer:

382.5 Inches

Step-by-step explanation:

Hope this helped

Answer:

382.5

Step-by-step explanation:

1 1/5 × 5,+ 5× 3

hope you got that lol

Answer:

12.8

Step-by-step explanation:

1) Through any two points, there is exactly one line (postulate)

2) A line segment is a part of a line and is bounded by two endpoint. - (Definition)

3) If two lines intersect, then each pair of opposite angles are congruent. - (Theorem)

Postulates are statements that are assumed to be true without proof."

Definition; "It is used to give a precise meaning to a new term."

Theorem is a statement that can be proved to be true by accepted mathematical operations and arguments.

We need to classify the three statements as theorem, postulate and definition.

The first statement is; 'Through any two points, there is exactly one line.'

Here We know that this is the fundamental postulate use in Geometry.

The second statement is; 'A line segment is a part of a line and is bounded by two endpoint.'

This statement is the definition of line segment.

And The last statement is 'If two lines intersect, then each pair of opposite angles are congruent.'

We can prove above statement by using Euclid's axiom.

So, This statement is a theorem.

Therefore, 1) Through any two points, there is exactly one line.' - postulate.

2) A line segment is a part of a line and is bounded by two endpoint. - Definition.

3) If two lines intersect, then each pair of opposite angles are congruent. - Theorem.

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Answer:

a.  rate to empty the tank = - 2/3 gal/min

b,  7.5 min to empty the tank

c.  4.5 min.

Step-by-step explanation:

I use the formula that the work done = rate of work times the time working = W = rt

The work in this problem is emptying the tank.  

a.  The rate to empty the tank is -2 gal/3 min or - 2/3 gal/min

b.   5/(2/3) = 15/2 = 7.5 min to empty the tank

c.    Since 3 gal. had already drained, 3/(2/3) = 9/2 = 4.5 min.

The number \(-14 - 5i\) is located in the third quadrant.

The complex plane is a coordinate system in which complex numbers are represented by points, with the real part of the number corresponding to the horizontal axis and the imaginary part corresponding to the vertical axis. Quadrants in the complex plane are similar to those in the Cartesian coordinate system, with the first quadrant consisting of positive real and imaginary parts, the second quadrant having negative real parts and positive imaginary parts, the third quadrant having negative real and imaginary parts, and the fourth quadrant having positive real parts and negative imaginary parts.
The number \(-14 - 5i\) has a negative real part (\(-14\)) and a negative imaginary part (\(-5i\)). According to the properties of quadrants in the complex plane, this number is located in the third quadrant, where both the real and imaginary parts are negative. Therefore, the correct answer is c) Third quadrant.

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To factor the expression, we should first apply difference of squares method. This method is suitable because expression can be written as the difference of two perfect squares, namely (7x^3)^2 - (5y)^2.

The expression 49x^7 - 25y^2 can be rewritten as (7x^3)^2 - (5y)^2, which represents the difference of two perfect squares. The difference of squares method states that for any two perfect squares, say a^2 - b^2, it can be factored as (a + b)(a - b).

In this case, a = 7x^3 and b = 5y. Applying the difference of squares formula, we can factor the expression as follows:

49x^7 - 25y^2 = (7x^3 + 5y)(7x^3 - 5y).

Thus, the first method of factoring to be used for the given expression is the difference of squares method.

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Answer:

D should be right

Step-by-step explanation:

5

The slope-intercept form is  y = m x + b y = m x + b , where  m m  is the slope and  b b  is the y-intercept. y = m x + b y = m x + b

Rewrite in slope-intercept form.

Subtract  3 x 3 x  from both sides of the equation. − 8 y = 5- 3 x - 8 y = 5-3 x

Divide each term by  −8 -8  and simplify. y = 3 x 8 − 58 y = 3 x 8 - 58

Rewrite in slope-intercept form. y = 38 x − 58 .