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2 years ago

11

Huong had $23 to spend on six notebooks. After buying them she had $11. How much did each notebook cost?

2 answers:

Nataly [62]2 years ago

8 0

23-11=12
She spent $12 on notebooks, and she bought six notebooks.
12/6=2

Each notebook costed $2.

Marianna [84]2 years ago

5 0

23-11=12
12 divided by 6 = 2
So each notebook cost $2

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Peter wants to fence the park in front of his home on three sides which measure 152m 40cm, 205m 10cm, 310m 39cm. What is the tot

Tpy6a [65]

One centimenter is 0.01 meters. So, you can write the measures as

$152.40\text{m},\quad 205.10\text{m},\quad 310.39\text{m}$

Once this rewriting is done, getting the total length $T$ is quite trivial, since all measurements are in the same unit, and we can simply sum everything:

$T = 152.40+205.10+310.39 = 667.89$

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2 years ago

4. Hydrocarbons in the cab of an automobile were measured during trips on the New Jersey Turnpike and trips through the Lincoln

pochemuha

Answer:

No these these result do not differ at 95% confidence level

Step-by-step explanation:

From the question we are told that

The first concentrations is $c _1= 30.0 \ g/m^3$

The second concentrations is $c _2 = 52.9 \ g/m^3$

The first sample size is $n_1 = 32$

The second sample size is $n_2 = 32$

The first standard deviation is $\sigma_1 = 30.0$

The first standard deviation is $\sigma_1 = 29.0$

The mean for Turnpike is $\= x _1 = \frac{c_1}{n} = \frac{31.4}{32} = 0.98125$

The mean for Tunnel is $\= x _2 = \frac{c_2}{n} = \frac{52.9}{32} = 1.6531$

The null hypothesis is $H_o : \mu _1 - \mu_2 = 0$

The alternative hypothesis is $H_a : \mu _1 - \mu_2 \ne 0$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \= x_2}{ \sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} }}$

$t = \frac{0.98125 - 1.6531}{ \sqrt{\frac{30^2}{32} +\frac{29^2}{32} }}$

$t = - 0.0899$

Generally the degree of freedom is mathematically represented as

$df = 32+ 32 - 2$

$df = 62$

The significance $\alpha$ is evaluated as

$\alpha = (C - 100 )\%$

=> $\alpha = (95 - 100 )\%$

=> $\alpha =0.05$

The critical value is evaluated as

$t_c = 2 * t_{0.05 , 62}$

From the student t- distribution table

$t_{0.05, 62} = 1.67$

So

$t_c = 2 * 1.67$

=> $t_c = 3.34$

given that

$t_c > t$ we fail to reject the null hypothesis so this mean that the result do not differ

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2 years ago

Alexeev081 [22]

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2 years ago

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the daily profit in dollars of a specialty cake shop is described by the function P(x)=-3x^2+168x-1920. Where x is the number of

forsale [732]

Answer:

28

Step-by-step explanation:

We have the following function:

$f(x)=-3x^{2} +168x-1920$

where a=-3, b=168 and c=-1920

In order to calculate the maxium profit for the company, and how many cakes should be prepared in order to reach it, we have to calculate where the parabola's vertex is ubicated. To do so, we use the following formula:

$Xv= \frac{-b}{2a}$

$Xv= \frac{-168}{2.(-3)}$

$Xv= \frac{-168}{2.(-3)}$

$Xv= 28$

So 28 cakes should be prepared per day in order to maximize profit.

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2 years ago

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Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly. What will his balance be after he has made exactly

damaskus [11]

Answer:

The balance be after he has made exactly half of his monthly payments is $56881.4.

Step-by-step explanation:

Given : Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly.

To find : What will his balance be after he has made exactly half of his monthly payments?

Solution :

Formula of monthly payment ,

$M=\frac{\text{Amount}}{\text{Discount factor}}$

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$

Where, Amount = $40,000

Rate r= 4% compounded monthly

$i=\frac{4}{100}=0.04$

Time = 10 years

$n=10\times12=120$

Now, put all the values we get,

$D=\frac{1-(1+i)^{-n}}{i}$

$D=\frac{1-(1+0.04)^{-120}}{0.04}$

$D=\frac{1-(1.04)^{-120}}{0.04}$

$D=\frac{1-0.00903}{0.04}$

$D=\frac{0.9909}{0.04}$

$D=24.7725$

$M=\frac{\text{Amount}}{\text{Discount factor}}$

$M=\frac{40000}{24.7725}$

$M=1614.69$

Half of the monthly payment is $807.345

Payment for 10 years is $807.345\times 120=96881.4$

The balance is $96881.4-$40000=$56881.4

Therefore, The balance be after he has made exactly half of his monthly payments is $56881.4.

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2 years ago

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