Solve each system using substitution.
3x+2y=23
1/2x-4=y

Answers

Answer 1

Answer: $\left\{\begin{array}{ccc}3x+2y=23&(1)\ny=(1)/(2)x-4&(2)\end{array}\right\n\nsubtitute\ (2)\ to\ (1)\n\n3x+2((1)/(2)x-4)=23\n3x+x-8=23\n4x-8=23\ \ \ \ |add\ 8\ to\ both\ sides\n4x=31\ \ \ \ \ |divide\ both\ sides\ by\ 4\n\boxed{x=7.75}\n\nsubtitute\ the\ value\ of\$

Answer 2

Answer: 1: 3x+2y=23
2: 1/2x-4=y
We have that y=1/2x-4 in 2
So lets substitu y in 1
3x+2(1/2x-4)=23
3x+x-8=23
4x=23+8
4x=31
X = 7,75
Now lets replace x in 2:
1/2.7,75-4=y
3,875-4 + y
Y= - 0,125
So (x;y)=(7,75;-0.125)

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dentify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 50005000 households, and the data collected todaytoday will be used to determinenbsp the proportion of households tuned to a particular sportssports program.. Which type of observational study is described in the problem statement?

Answers

Answer:

- A cross-sectional study.

Step-by-step explanation:

A Cross-sectional study is demonstrated as the type of observational study in which the data or a representative subset of a population collected at a particular point in time is analyzed.

As per the given details, the observational study conducted by the research company would exemplify 'a cross-sectional study' as it aims to evaluate the data('viewing habits of about 50005000 households) collected at a specific point in time i.e. 'today' in order to 'determine the proportion of households tuning to a particular sports program.'

Situation: a 25 gram sample of a substance that’s used for drug research has a K-value of 0.1205N0(zero)= initial mass(at time t=0)
N= mass at time t
K= a positive constant that depends on the substance itself and on the units used to measure time
t= time, in days
Find the substances half-life, in days. Round your answer to the nearest tenths????

Answers

The decay model is given as

$N=N_0e^(-Kt)$

The substance's half-life is the time it takes for the substance to decay to half its original amount. In other words, it's the time $t$ such that $N=\frac{N_0}2$ . Substituting into the model, you have

$\frac12=e^(-Kt)$

You can solve for $t$ now.

$\frac12=e^(-Kt)$
$\implies\ln\frac12=\ln e^(-Kt)$
$\implies-\ln2=-Kt\ln e$
$\implies\frac{\ln2}K=t\approx5.7523\text{ days}$

in a recent survey, 336 out of 500 people chose reallygood cola as their favorite soft drink. If a similar survey was conducted out of 2,000 people, how many people would choose reallygood cola as their favorite soft drink? explain.

Answers

In the first survery $(336)/(500)$ considered cola.
Assuming we can extrapolate this ratio, all we have to do is get the same ratio, but out of 2000 people.
$(336)/(500) * (4)/(4) \n (1344)/(2000)$
The answer is 1344 people.

12. A cereal company decided to make an odd-shaped box for a promotion they are doing. The new design is a rectangular prism with length of 10 cm, width of 8 cm, and height of 4 cm. and attached to the rectangular prism is a cylinder with a radius of 2 cm. and a height of 10 cm. How much cereal (in L) will fit in the box?

Answers

This one odd cereal box. We are asked to find the volume of the "box". This can be answered in 2 parts. The total volume is the sum of the rectangular prism volume and the volume of the cylinder. The volume of the rectangular prism is 8x4x10 = 320 cm^3. Then the volume of the cylinder is $\pi r^(2) h = V$ . The volume of the cylinder is then 125.66. The total volume is then 445.66 ml (Note: ml = cm^3). Then V = 0.45L