What is the fractional equivalent of the repeating decimal n = 0.1515... ?

Charlie has a piece of toast that has cream cheese on one side, and he dropped it once. One time, it landed with the cream chees

Anna11 [10]

There is a 1 in 6 chance of this happing

5 0

3 years ago

In a school, the ratio of teachers to girls is 1:7 while that of boys to girls is 3:4, If there are 280 girls in the school, wha

Nuetrik [128]

Answer:

The total number of pupils and their teachers = 530

Step-by-step explanation:

No. of girls in the school = 280

The ratio boys to girls is 3:4 and that of teachers to girls is 1:7

∴ The ratio boys to girls is 3x : 4x where, 4x = 280

and The ratio of teachers to girls is x : 7x where, 7x = 280

4x = 280

$\frac{280}{4\\}$ = x

70 = x

So, the no. of girls in the school = 4x = 4(70) = 280 and the no. of boys in the school = 3x = 3(70) = 210

7x = 280

$\frac{280}{7\\}$ = x

40 = x

So, the no. of girls in the school = 7x = 7(40) = 280 and the no. of teachers in the school = x = 40

∴ The total number of pupils and their teachers = 280 + 210 + 40

= 530

3 0

3 years ago

Help me with this please

Elenna [48]

Answer:

2,700 sq yds :)))) (d)

Step-by-step explanation:

2(30)=60

1.5(30) =45

60(45)= 2700

3 0

3 years ago

A random sample of n measurements was selected from a population with unknown mean mu and standard deviation sigmaequals50 for e

Andre45 [30]

Answer:

a) (26.50;57.50)

b) (117.34;128.66)

c) (12.13;27.87)

d) (-4.73;11.01)

e) No. Since the sample sizes are large (n ≥ 30), the central limit theorem guarantees that $\bar x$ is approximately normal, so the confidence intervals are valid

Step-by-step explanation:

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The confidence interval is given by this formula:

$\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$ (1)

And for a 95% of confidence the significance is given by $\alpha=1-0.95=0.05$ , and $\frac{\alpha}{2}=0.025$ . Since we know the population standard deviation we can calculate the critical value $z_{0.025}= \pm 1.96$

Part a

$n=40,\bar X=42,\sigma=50$

If we use the formula (1) and we replace the values we got:

$42 - 1.96 \frac{50}{\sqrt{40}}=26.50$

$42 + 1.96 \frac{50}{\sqrt{40}}=57.50$

The 95% confidence interval is given by (26.50;57.50)

Part b

$n=300,\bar X=123,\sigma=50$

If we use the formula (1) and we replace the values we got:

$123 - 1.96 \frac{50}{\sqrt{300}}=117.34$

$123 + 1.96 \frac{50}{\sqrt{300}}=128.66$

The 95% confidence interval is given by (117.34;128.66)

Part c

$n=155,\bar X=20,\sigma=50$

If we use the formula (1) and we replace the values we got:

$20 - 1.96 \frac{50}{\sqrt{155}}=12.13$

$20 + 1.96 \frac{50}{\sqrt{155}}=27.87$

The 95% confidence interval is given by (12.13;27.87)

Part d

$n=155,\bar X=3.14,\sigma=50$

If we use the formula (1) and we replace the values we got:

$3.14 - 1.96 \frac{50}{\sqrt{155}}=-4.73$

$3.14 + 1.96 \frac{50}{\sqrt{155}}=11.01$

The 95% confidence interval is given by (-4.73;11.01)

Part e

No. Since the sample sizes are large (n ≥ 30), the central limit theorem guarantees that $\bar x$ is approximately normal, so the confidence intervals are valid

8 0

3 years ago

6(x – 1) = 9(x + 2)<br> Solve

Tom [10]

Answer:

x=−8

Step-by-step explanation:

6(x−1)=9(x+2)

Step 1: Simplify both sides of the equation.

6(x−1)=9(x+2)

(6)(x)+(6)(−1)=(9)(x)+(9)(2)(Distribute)

6x+−6=9x+18

6x−6=9x+18

Step 2: Subtract 9x from both sides.

6x−6−9x=9x+18−9x

−3x−6=18

Step 3: Add 6 to both sides.

−3x−6+6=18+6

−3x=24

Step 4: Divide both sides by -3.

−3x/−3=24/−3

8 0

3 years ago