Which shows the image of ΔRST after the rotation (x, y) → (y, –x)? On a coordinate plane, a triangle has points R (negative 2, 1

Answer:

Using integer tiles, you would either add five sets of negative two tiles or take away two sets of five positive tiles. On the number line, you would jump 5 spaces to the left

Step-by-step explanation:

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The adjusted equation , indicating that the graph has been altered 4 units leftward and 6 units downward.

Clarification:

The parent equation is .

The transformed equation is .

Applying the function transformation rules, it's clear that the parent function has been modified into the function .

According to the function transformation rules,

indicates shifting the function b units to the left.

Thus, the transformed function reflects a shift 4 units to the left.

Additionally, from the function transformation rules, we understand that,

indicates shifting the function b units downward.

Consequently, the transformed function mirrors a shift of 6 units downward.

In summary, the adjusted equation , shows the graph shifted 4 units to the left and 6 units downward.

B refers to the base of the triangle,
and a signifies the length of the two identical sides.

The measurement labeled as 'a' is larger than 'b' since those equal sides are longer than the base. Given "one of the longer sides measures 6.3 cm," we assign a = 6.3.

Substitute 6.3 for each 'a' in the equation and solve for b:
2a + b = 15.7
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 15.7 - 12.6 (applying subtraction property of equality)
b = 3.1

Respuesta:

0.0143 = 1.43% de probabilidad de que los primeros 4 dígitos del código sean números pares.

Explicación paso a paso:

Arreglos de elementos n:

El número de arreglos posibles de n elementos se determina por:

Probabilidad:

La probabilidad se calcula dividiendo el número de resultados deseados por el número total de resultados.

En esta pregunta:

Resultados deseados:

Los primeros cuatro dígitos son pares (2, 4, 6 y 8 son pares, así que se consideran 4 elementos).

Los últimos cuatro dígitos son impares (1, 3, 5 y 7 son impares, por lo que los últimos cuatro elementos son también arreglos de 4 elementos). Entonces

Resultados totales:

Arreglos de 8 dígitos. Así que

Probabilidad:

0.0143 = 1.43% de probabilidad de que los primeros 4 dígitos del código sean números pares.

Answer:

a) Null and alternative hypothesis

b) Point estimate d = -$78

c) Test statistic t = -2.438

P-value = 0.0113

Reject H0. This indicates that the average automobile premium in Pennsylvania is lower than in the nation.

Step-by-step breakdown:

This is a statistical test for the average population mean.

The hypothesis posits that car insurance in Pennsylvania is notably less expensive compared to the national average.

Accordingly, the null and alternative hypotheses are:

The significance level is set at 0.05.

The sample size is n=25.

The sample mean equates to M=1425.

A point estimate of the difference between the Pennsylvania mean premium and the national average can be computed using the sample mean:

Given that the standard deviation of the population is unknown, we approximate it using the sample standard deviation, which is s=160.

Then, we can calculate the t-statistic as:

The degrees of freedom for this sample size stand at:

This constitutes a left-tailed test, with 24 degrees of freedom and t=-2.438, rendering the P-value as (per a t-table):

As the P-value (0.0113) falls below the significance level (0.05), the results prove significant.

Thus, the null hypothesis obtains dismissal.

At a 0.05 significance level, there's sufficient evidence to assert that car insurance in Pennsylvania costs notably less than the national average.