Cortney had 5 pieces of candy Cortney ate 1 piece how many pieces does Cortney have left?

The larger of to numbers is 12 more than the smaller. Their sum is 84. What are the two numbers?

Nataly_w [17]

36 and 48

a = b+12
a+b = 84

(b+12) + b =84
2b +12 = 84
2b = 72
b= 36

a = b + 12
a = 36 + 12
a = 48

3 0

4 years ago

5. The superintendent of the local school district claims that the children in her district are brighter, on average, than the g

anygoal [31]

Answer:

We conclude that children in district are brighter, on average, than the general population.

Step-by-step explanation:

We are given the following data set:

105, 109, 115, 112, 124, 115, 103, 110, 125, 99

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

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

$Mean =\displaystyle\frac{1117}{10} = 111.7$

Sum of squares of differences = 642.1

$S.D = \sqrt{\frac{642.1}{49}} = 8.44$

We are given the following in the question:

Population mean, μ = 106

Sample mean, $\bar{x}$ = 111.7

Sample size, n = 10

Alpha, α = 0.05

Sample standard deviation, s = 8.44

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 106\\H_A: \mu > 106$

We use one-tailed(right) t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{111.7 - 106}{\frac{8.44}{\sqrt{10}} } = 2.135$

Now,

$t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = 1.833$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

We conclude that children in district are brighter, on average, than the general population.

4 0

3 years ago

There are 82 trees at a park. Half of the trees are pecan trees and the

Marrrta [24]

Answer:

41 oak tree

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

Four ingredients costing $320 per kg $240 per kg $160 per kg and $85 kg are mixed so that air masses are in the ratio 4:1:3:2. c

Hoochie [10]

Answer:

2160

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. He puts twice as muc

Masteriza [31]

Let x represent amount invested in the higher-yielding account.

We have been given that a man puts twice as much in the lower-yielding account because it is less risky. So amount invested in the lower-yielding account would be $2x$ .

We are also told that his annual interest is $6600 dollars. We know that annual interest for one year will be principal amount times interest rate.

$I=Prt$ , where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

We are told that interest rates are 6% and 10%.

$6\%=\frac{6}{100}=0.06$

$10\%=\frac{10}{100}=0.10$

Amount of interest earned from lower-yielding account: $2x(0.06)=0.12x$ .

Amount of interest earned from higher-yielding account: $x(0.10)=0.10x$ .

$0.12x+0.10x=6600$

Let us solve for x.

$0.22x=6600$

$\frac{0.22x}{0.22}=\frac{6600}{0.22}$

$x=30,000$

Therefore, the man invested $30,000 at 10%.

Amount invested in the lower-yielding account would be $2x\Rightarrow 2(30,000)=60,000$ .

Therefore, the man invested $60,000 at 6%.

8 0

3 years ago