Tristan has some dimes and some quarters. He has at least 20 coins worth at most $4.25 combined. If Tristan has 10 dimes, determ

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the tea

Svet_ta [12734]

Answer:

a) 1.92

b) 3.25

c) 1.5

d) -5.23

Step-by-step explanation:

We are provided with the following in the question:

4, 7, -1, 1, 0, 5, -2, 2, -1, 6, 5, -3

a) mean change score

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{23}{12} = 1.92$

b) standard deviation for the population

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$

where $x_i$ represents data points, $\bar{x}$ is the average, and n denotes the count of observations.

Sum of squared deviations = 126.92

$\sigma = \sqrt{\frac{126.92}{12}} = 3.25$

c) median change score

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Arranged data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

Median equal to

$\dfrac{6^{th} + 7^{th}}{2} = \dfrac{1+2}{2} = 1.5$

d) change score that is 2.2 standard deviations lower than the mean.

$x = \mu - 2.2(\sigma)\\x = 1.92-2.2(3.25)\\x = -5.23$

4 0

2 months ago

Caleb’s school is five blocks due north of his home, and the library is two blocks due west of his home. If each city block is a

tester [12383]

Response:

The direct straight-line distance between Caleb's school and the library amounts to:

1480.92 feet

Step-by-step explanation:

Picture a triangle where one side measures five blocks and another side measures two blocks; to calculate the most direct straight-line distance from Caleb's school to the library, you can apply the Pythagorean theorem, with the hypotenuse being the straight-line distance:

$perpendicular^{2} +base^{2} =hypotenuse^{2}$

Solving for the hypotenuse results in:

$\sqrt{perpendicular^{2}+base^{2}}= hypotenuse$

To figure out the distance in each case, consider the following:

Five blocks = 275 feet * 5 = 1375 feet.

Two blocks = 275 feet * 2 = 550 feet.

Finally, you need to substitute the determined distances into the cleared equation:

$\sqrt{1375 feet^{2}+550 feet^{2}}= hypotenuse$

The hypotenuse, or the closest straight-line distance, equals 1480.92 feet.

Thus, we can conclude that the direct distance from Caleb's school to the library is 1480.92 feet.

4 0

1 month ago

Workers have packed 1,400 glasses in 7 boxes. If they pack 3 more boxes, how many glasses will they have packed in all?

Svet_ta [12734]

2000

1 caja = 1400/7 = 200
200×3=600
1400+600=2000

Explicación paso a paso:
Dado: Los trabajadores han empaquetado 1,400 vasos en 7 cajas.
A buscar: Si empacan 3 cajas más, ¿cuántos vasos habrán empaquetado en total?
Solución:
Vasos empaquetados en 7 cajas = 1400
Vasos en 1 caja =
Vasos en 3 cajas =
Por lo tanto, al inicio empacaron 1400 vasos.
Si empacan 3 cajas más, agregarán 600 vasos adicionales.
Por lo tanto, el número total de vasos empaquetados por los trabajadores = 1400+600 = 2000
Así que han empaquetado 2000 vasos en total.

5 0

2 months ago

There were 2.605 people at the basketball game. A reporter rounded this number to the nearest hundred from a newspaper article.

Svet_ta [12734]

Rounded to the nearest hundred, 2605 becomes 2600. If it had been 2650 or more, it would have rounded to 2700.

7 0

1 month ago