In Major League Baseball, the American League (AL) allows a designated hitter (DH) to bat in place of the pitcher, but in the National League (NL), the pitcher has to bat. However, when an AL team is the visiting team for a game against an NL team, the AL team must abide by the home team’s rules, and thus, the pitcher must bat. A researcher is curious if an AL team would score more runs for games in which the DH was used. She samples 20 games for an AL team for which the DH was used, and 20 games for which there was no DH. The data are below. The population standard deviation for runs scored is known to be 2.54 for both groups. Assume the populations are normally distributed.
DH no DH
0 3
6 6
8 2
2 4
2 0
4 5
7 7
7 6
6 1
5 8
1 12
1 4
5 6
4 3
4 4
2 0
7 5
11 2
10 1
0 4
Is there evidence to suggest that more runs are scored in games for which the DH is used? Use α=0.10.
Enter the test statistic - round to 4 decimal places.
Enter the P-Value - round to 4 decimal places.
Can it be concluded that more runs are scored in games for which the DH is used?
Yes or No

Answer:

by referencing the source

after sentence 2

Step-by-step explanation:

edge2020

a. The graph represents a proportional relationship.

b. The graph does not represent a proportional relationship.

c. The graph does not represent a proportional relationship.

d. The graph represents a proportional relationship.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:

y = kx.

Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.

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There are six 1/6’s in an hour

Multiply 2/3 hours by 6

2/3 x 6 = 12/3 = 4

It will take 4 hours.

Answer:

s

Step-by-step explanation:

s

A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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Answer:

The width of a block of wood with rectangular cross section is x cm. its height is 2/3 its width and its length is 4times its height what is its volume in cm3

The triangle given is a scalene acute triangle

A triangle can be classified based on the measures of its angles and the lengths of its sides.

In this case, the angle measures of the triangle are 82, 75, and 23 degrees. Since the sum of the angles in a triangle is always 180 degrees, we can verify that these angles satisfy this condition: 82 + 75 + 23 = 180.

The triangle is not an equilateral triangle because all the sides are not of equal length.

The triangle also doesn't have one right angle so it can't be right triangle.

Now, as per the angle measures, none of the angles are right angles, but one angle is greater than 90 degree, so this triangle is not acute triangle.

So, this triangle is not an Obtuse triangle since it has no angle greater than 90 degrees.

As the triangle has no sides of equal length, it is also a Scalene triangle.

Therefore, the triangle would be classified as a Scalene acute triangle (c).

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Answer:

its A on edge 2021

Step-by-step explanation:

your welcome :)

To calculate K, we use the following:

If you move a units in y for every b units in x, K= a/b

Let's use this in the four graphs:

For graph 1, notice that if we move 1 unit in x, we move 1 unit in y

Thereby, K=1

For graph 2, notice that if we move 1 unit in x, we move 7 units in y

Thereby, K=7

For graph 3, notice that if we move 9 units in x, we move 4 units in y

Thereby, K=4/9

For graph 4, notice that if we move 2 units in x, we move 10 units in y

Thereby, K=5

The value the equation related to S and N is 25.

What is algebraic expression ?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. A good example of an algebraic expression is 3x2 + 2xy + c.

N will be the function of S since the number of cookies made is dependent on the amount of sugar

N = 25S,  S ≥ 0

This is the for the every cup of sugar we make 25 cookies. for the graph we can plot some points

S          N

_________

0           0

1           25

1.5         37.5

2           50

This will be a line with slope of 25

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Answer:

it is true

it's a quadralateral

The pot can hold 1 \(\frac{5}{6}\) quarts of water more. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, frequently referred to as "arithmetic operations," are believed to accurately explain all real numbers. Division, multiplication, addition, and subtraction are followed by the mathematical operations quotient, product, sum, and difference.

We are given that the capacity of the pot is 5 \(\frac{1}{2}\) which means that the capacity is \(\frac{11}{2}\).

The pot is filled \(\frac{2}{3}\) by water.

So, the capacity left to be filled is obtained by using subtraction operation which gives

1 -  \(\frac{2}{3}\) = \(\frac{1}{3}\)

So, now by using multiplication, we get

⇒ Quarts of water pot can hold =  \(\frac{11}{2}\) *  \(\frac{1}{3}\)

⇒ Quarts of water pot can hold =  \(\frac{11}{6}\)

⇒ Quarts of water pot can hold = 1 \(\frac{5}{6}\)

Hence, the pot can hold 1 \(\frac{5}{6}\) quarts of water more.

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The question has been attached below.

The value of x is given as follows:

x = 25.

As quadrilateral ABCD is a rectangle, we have that BD is a diagonal, while BE is the midpoint of the diagonal.

The midpoint of a segment divides the segment into two segments of equal length, hence the equation is given as follows:

BD = 2BE.

Replacing the equations, the value of x is obtained as follows:

4x - 40 = 2(x + 5)

4x - 40 = 2x + 10

2x = 50

x = 25.

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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The maximum height reached after the 13th bοunce is 6.14 cm.

The height οf bοunce is the height tο which an οbject rebοunds after cοIIiding with a surface, such as a baII bοuncing οn the grοund οr a diver bοuncing οff a diving bοard. The height οf the bοunce depends οn severaI factοrs, incIuding the initiaI height οf the οbject, the surface it cοIIides with, the eIasticity οf the οbject and the surface, and the angIe οf incidence.

Tο sοIve this prοbIem, we need tο use the fοrmuIa fοr the height οf each bοunce:

\(h = (3/4)^{{n}} \times H\)

where h is the height οf the nth bοunce, H is the initiaI height (in this case, 187.00 cm), and n is the number οf bοunces.

We want tο find the maximum height reached after the 13th bοunce, which means we need tο find the height οf the 13th bοunce and then muItipIy it by 3/4 tο get the maximum height.

Using the fοrmuIa abοve, we can find the height οf the 13th bοunce:

\(h = (3/4)^{{13}} \times 187.00\)

h ≈ 8.18 cm

Nοw we can find the maximum height:

maximum height = (3/4) × h

maximum height = (3/4) ×8.18

maximum height ≈ 6.14 cm

Therefοre, the maximum height reached after the 13th bοunce is apprοximateIy 6.14 cm.

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Answer:

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Step-by-step explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40.  This means, \(\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}\).

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

\(f(x)=2x+100\)

This can be checked by using the values given in the problem:

\(f(30)=2(30)+120=180\\f(50)=2(50)+120=220\)

The base rate of $120 and $2 per person satisfies the given equation and established values.

You therefore paid $21.26 to travel to the beach.

One mile is 5,280 feet long. To determine how many steps this should require walking a mile, simply split 5,280 feet by the length of your typical stride. For instance, if your typical stride is 2 feet, walking a mile will need 2,640 steps.

a) We must divide the total amount of miles travelled by the quantity of gas consumed in order to compute mpg (miles per gallon). If 141 miles are covered by 3/8 of a tank, we may calculate the tank's total capacity as follows:

18 gallons = 8/8 tank (full tank)

So, 3/8 tank = (3/8) x 18 = 6.75 gallons

Therefore, the mpg is:

mpg = distance traveled ÷ gas used

mpg = 141 miles ÷ 6.75 gallons

mpg = 20.89 miles per gallon (rounded to two decimal places)

b) The entire amount of gas consumed must be multiplied by the gallon price in order to get the cost of gas. Gas is expensive at:

Cost of gas = gas used x price per gallon

Cost of gas = 6.75 gallons x $3.15/gallon

Cost of gas = $21.26

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Answer:

72

Step-by-step explanation:

do 24/2=12x6=72

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

Step-by-step explanation:

The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool

Answer:

The investment will be worth $16898.67 after 17 years, compounded semiannually at 3.3% per year.

Step-by-step explanation:

The compound interest formula is:

A = P * (1 + (r/n))^(nt)

where

A is the amount of the investment after t years,

P is the principal amount (9070),

r is the annual interest rate (3.3%),

n is the number of times the interest is compounded per year (2),

t is the number of years (17).

Using the formula:

A = 9070 * (1 + (0.033/2))^(2 * 17)

A = 9070 * (1.0165)^34

A = 9070 * 1.882611

A = 16898.67 to the nearest cent.

So the investment will be worth $16898.67 after 17 years, compounded semiannually at 3.3% per year.

Answer: $3660.96 or $3661.0

Step-by-step explanation:

To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:

Total number of months = 8 years x 12 months/year = 96 months

Next, we can calculate the interest for half a month:

Interest = Principal x Rate x Time

Where:

- Principal = $90,900.00

- Rate = 8.25% (annual interest rate)

- Time = 0.5/12 years (half a month, expressed in years)

Rate needs to be converted to a monthly rate, so we divide it by 12:

Rate = 8.25% / 12 = 0.6875% (monthly interest rate)

Time needs to be expressed in years, so we divide it by 12:

Time = 0.5/12 years

Now we can calculate the interest:

Interest = $90,900.00 x 0.006875 x 0.0416667

Interest = $25.08 (rounded to the nearest cent)

Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.

Answer:

The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64

Step-by-step explanation:

Make a plan:

Draw the conclusion:

Hope this helps!

Answer:

4 years ago

Step-by-step explanation:

y= Ramesh

x= Suresh

y-8=x

y=2x

Plug into each other:

x+8=2x

x=8

y=16

Suresh was 8 years old 4 years ago

Ramesh was 16 years old 4 years ago

La tarjeta de crédito tiene una tasa efectiva de interés anual de 21,375 %.

En este problema tenemos que Merle obtiene una tarjeta de crédito bajo la siguientes condiciones: 0 % E.A. para los primeros 60 días, 23,19 % E.A. para los 365 restantes.

Debemos determinar la tasa de interés efectiva anual equivalente, esto es posiblemente mediante una aplicación consecutiva del concepto de interés, descrito abajo:

I = (1 + r / 36500)ⁿ

Donde:

La situación es descrita por la siguiente expresión matemática:

1 + R / 100 = (1 + 0 / 36500)⁶⁰ + (1 + 23,19 / 36500)³⁰⁵

Donde R es la tasa efectiva de interés anual.

Finalmente, despejamos la variable correspondiente:

R = 21,375

La tasa efectiva de interés anual a sufragar por Merle por el uso de tarjeta de crédito es 21,375 %.

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3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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Answer:

your answer will be A. 38.5°

Step-by-step explanation:

m<ZYW=1/2(77)

=38.5

hope it helps..

Answer:

1009479

Step-by-step explanation:

637,391 + 372,088 = 1009479

Answer:

the answers 1009479

Step-by-step explanation:

The polynomial whose roots are 3+i , 2 and -4 is -

x³ - x² - 14x + 24.

The general form of a complex number is -

z = a + ib

Given are the roots of the polynomial as -

3+i , 2 and -4.

The polynomial whose roots are 3+i , 2 and -4 is -

x³ - x² - 14x + 24

Therefore, the polynomial whose roots are 3+i , 2 and -4 is -

x³ - x² - 14x + 24.

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The percent of the front page taken up by the prom story is 20%

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

The front page

From the front page, we have

Area front page = 5 * 4

Area front page = 20

Also, we have

Prom = 2 * 2

Prom = 4

So, we have

Percentage = 4/20 * 100%

Evaluate

Percentage = 20%

Hence, the percent of the front page taken up by the prom story is 20%

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Answer:

x = -25 / 3

Step-by-step explanation:

10 / 3 = x / (-5/2)

10 / 3 * (-5 / 2) = x

x = -50 / 6

x = -25 / 3

Answer:

\(x=\frac{-25}{3}\)

Step-by-step explanation:

\(\frac{10}{3}=\frac{x}{\frac{-5}{2} } \\\\\frac{-5}{2}*\frac{10}{3}=\frac{x}{\frac{-5}{2} }*\frac{-5}{2} \\\\\frac{-25}{3} =x\\\\x=\frac{-25}{3}\)