15. a blueprint of a house has a bathroom that measures 2 inches by 3 inches. if the actual dimensions of…

15. a blueprint of a house has a bathroom that measures 2 inches by 3 inches. if the actual dimensions of the room are 8 feet by 12 feet, what is the scale factor of the blueprint?\na $\frac{1}{48}$\nb $\frac{1}{24}$\nc $\frac{1}{12}$\nd $\frac{1}{4}$\n16. a circle has a diameter of 6.4 yards. what is the circumference?\na $3.2pi$ yd\nb $6.4pi$ yd\nc $8.6pi$ yd\nd $12.8pi$ yd\n17. claire deposits $1,100 into a savings account. the account pays 1.5% simple interest each year. she does not add or withdraw any money from the account. which of these could be the interest earned after the given amount of time? select all that apply.\na 9 months; $12.38$\nb 15 months; $20.63$\nc 1.5 years; $28.88$\nd 2 years; $41.25$\ne 3 years; $49.50$\n18. which expression is equivalent to $(-8u - 3)-(-8 - 6u)$?\na $-1-2(5 + 7u)$\nb $-2(6 - u)+1$\nc $5 + 2(1 - u)$\nd $2(2 - u)+1$\n19. what is the area of a circle with a diameter of 14 feet?\na $7pi$ ft²\nb $14pi$ ft²\nc $28pi$ ft²\nd $49pi$ ft²\n20. reggie has completed 16 items on his homework. there are 14 more items remaining. what decimal, rounded to the nearest hundredth, represents the number of items he has completed?

15. a blueprint of a house has a bathroom that measures 2 inches by 3 inches. if the actual dimensions of the room are 8 feet by 12 feet, what is the scale factor of the blueprint?\na $\frac{1}{48}$\nb $\frac{1}{24}$\nc $\frac{1}{12}$\nd $\frac{1}{4}$\n16. a circle has a diameter of 6.4 yards. what is the circumference?\na $3.2pi$ yd\nb $6.4pi$ yd\nc $8.6pi$ yd\nd $12.8pi$ yd\n17. claire deposits $1,100 into a savings account. the account pays 1.5% simple interest each year. she does not add or withdraw any money from the account. which of these could be the interest earned after the given amount of time? select all that apply.\na 9 months; $12.38$\nb 15 months; $20.63$\nc 1.5 years; $28.88$\nd 2 years; $41.25$\ne 3 years; $49.50$\n18. which expression is equivalent to $(-8u - 3)-(-8 - 6u)$?\na $-1-2(5 + 7u)$\nb $-2(6 - u)+1$\nc $5 + 2(1 - u)$\nd $2(2 - u)+1$\n19. what is the area of a circle with a diameter of 14 feet?\na $7pi$ ft²\nb $14pi$ ft²\nc $28pi$ ft²\nd $49pi$ ft²\n20. reggie has completed 16 items on his homework. there are 14 more items remaining. what decimal, rounded to the nearest hundredth, represents the number of items he has completed?

Answer

15.

Explanation:

Step1: Convert feet to inches

1 pie = 12 pulgadas, entonces 8 pies = 8×12 = 96 pulgadas y 12 pies = 12×12 = 144 pulgadas.

Step2: Calcular la proporción para una dimensión

Para la dimensión de 2 pulgadas en el plano y 96 pulgadas en realidad, la proporción es $\frac{2}{96}=\frac{1}{48}$.

Step3: Comprobar la otra dimensión

Para la dimensión de 3 pulgadas en el plano y 144 pulgadas en realidad, la proporción es $\frac{3}{144}=\frac{1}{48}$.

Answer:

A. $\frac{1}{48}$

16.

Explanation:

Step1: Usar la fórmula de la circunferencia

La fórmula de la circunferencia de un círculo es $C = \pi d$, donde $d$ es el diámetro. Dado que $d = 6.4$ yardas, entonces $C=6.4\pi$ yardas.

Answer:

B. $6.4\pi$ yd

17.

Explanation:

Step1: Usar la fórmula de interés simple

La fórmula de interés simple es $I=Prt$, donde $P = 1100$ (principal), $r=0.015$ (tasa de interés) y $t$ es el tiempo en años.

Step2: Calcular el interés para 9 meses

9 meses = $\frac{9}{12}=0.75$ años. Entonces $I = 1100\times0.015\times0.75=1100\times0.01125 = 12.375\approx12.38$.

Step3: Calcular el interés para 15 meses

15 meses=$\frac{15}{12}=1.25$ años. Entonces $I = 1100\times0.015\times1.25=1100\times0.01875 = 20.625\approx20.63$.

Step4: Calcular el interés para 1.5 años

$I = 1100\times0.015\times1.5=1100\times0.0225 = 24.75\neq28.88$.

Step5: Calcular el interés para 2 años

$I = 1100\times0.015\times2=1100\times0.03 = 33\neq41.25$.

Step6: Calcular el interés para 3 años

$I = 1100\times0.015\times3=1100\times0.045 = 49.50$.

Answer:

A. 9 meses; $12.38$ B. 15 meses; $20.63$ E. 3 años; $49.50$

18.

Explanation:

Step1: Simplificar la expresión dada

$(-8u - 3)-(-8 - 6u)=-8u - 3 + 8+6u=-2u + 5$.

Step2: Simplificar cada opción

A. $-1-2(5 + 7u)=-1-10 - 14u=-14u-11$. B. $-2(6 - u)+1=-12 + 2u+1=2u-11$. C. $5 + 2(1 - u)=5 + 2-2u=-2u + 7$. D. $2(2 - u)+1=4-2u + 1=-2u + 5$.

Answer:

D. $2(2 - u)+1$

19.

Explanation:

Step1: Encontrar el radio

El radio $r$ de un círculo es la mitad del diámetro. Dado que $d = 14$ pies, entonces $r=\frac{14}{2}=7$ pies.

Step2: Usar la fórmula de área

La fórmula de área de un círculo es $A=\pi r^{2}$. Sustituyendo $r = 7$ pies, tenemos $A=\pi\times7^{2}=49\pi$ pies².

Answer:

D. $49\pi$ ft²

20.

Explanation:

Step1: Calcular el total de ítems

El total de ítems es $16 + 14=30$.

Step2: Calcular la proporción de ítems completados

La proporción de ítems completados es $\frac{16}{30}=\frac{8}{15}\approx0.53$.

Answer:

0.53