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2 years ago

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

Mathematics

1 answer:

Papessa [141]2 years ago

7 0

Answer:

The first solution is (-6, 29), and the second is (4, -11).

Step-by-step explanation:

Rewrite the 2nd equation as y = -4x + 5. Then the first equation becomes:

= -4x + 5 = x^2 - 2x - 19.

This equation has only one variable: x. Rewriting this equation in the standard form of a quadratic, we get:

0 = x^2 + 2x - 24

and this quadratic can be factored into 0 = (x - 4)(x + 6), whose roots are

{-6, 4}. This agrees with one of the two points mentioned in the problem:

(-6, 29) is a solution. What's the other one?

We have just found that the 2 roots are {-6, 4}. Then the missing root is 4, and the y-value there is found from y + 4x = 5:

y = -4x + 5, which here is y = -4(4) + 5, or y = -16 + 5, or y = -11.

The first solution is (-6, 29), and the second is (4, -11).

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The average American man consumes 9.8 grams of sodium each day. Suppose that the sodium consumption of American men is normally

Alex Ar [27]

Answer:

(a) The distribution of X is N (9.8, 0.8²).

(b) The probability that an American consumes between 8.8 and 9.9 grams of sodium per day is 0.4461.

Step-by-step explanation:

The random variable X is defined as the amount of sodium consumed.

The random variable X has an average value of, μ = 9.8 grams.

The standard deviation of X is, σ = 0.8 grams.

(a)

It is provided that the sodium consumption of American men is normally distributed.

The random variable X follows a normal distribution with parameters μ = 9.8 grams and σ = 0.8 grams.

Thus, the distribution of X is N (9.8, 0.8²).

(b)

If X ~ N (µ, σ²), then $Z=\frac{X-\mu}{\sigma}$ , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z ~ N (0, 1).

To compute the probability of Normal distribution it is better to first convert the raw score (X) to z-scores.

Compute the probability that an American consumes between 8.8 and 9.9 grams of sodium per day as follows:

$P(8.8$

$=P(-1.25$

Thus, the probability that an American consumes between 8.8 and 9.9 grams of sodium per day is 0.4461.

(c)

The probability representing the middle 30% of American men consuming sodium between two weights is:

$P(x_{1}$

Compute the value of z as follows:

$P(-z$

The value of z for P (Z < z) = 0.65 is 0.39.

Compute the value of x₁ and x₂ as follows:

$-z=\frac{x_{1}-\mu}{\sigma}\\-0.39=\frac{x_{1}-9.8}{0.8}\\x_{1}=9.8-(0.39\times 0.8)\\x_{1}=9.488\\x_{1}\approx9.5$ $z=\frac{x_{2}-\mu}{\sigma}\\0.39=\frac{x_{1}-9.8}{0.8}\\x_{1}=9.8+(0.39\times 0.8)\\x_{1}=10.112\\x_{1}\approx10.1$

Thus, the middle 30% of American men consume between 9.5 grams to 10.1 grams of sodium.

4 0

2 years ago

The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

Lemur [1.5K]

Answer:

Cardiac output: $F=0.055 L\s$

Step-by-step explanation:

Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.

To Find : Find the cardiac output.

Solution:

Formula of cardiac output: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

A = 3 mg

$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

Do, integration by parts

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Substitute the value in 1

Cardiac output: $F=\frac{3}{54.49}$

Cardiac output: $F=0.055 L\s$

Hence Cardiac output: $F=0.055 L\s$

4 0

2 years ago

How can Ari simplify the following expression? StartFraction 5 Over a minus 3 EndFraction minus 4 divided by 2 + StartFraction 1

Zielflug [23.3K]

Answer:

$-\frac{8}{3}$

Step-by-step explanation:

Given

$\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}$

Required

Simpify

The very first step is to take LCM of the given expression

$\frac{-10 -4 - 2}{6}$

Perform arithmetic operations o the numerator

$-\frac{16}{6}$

Divide the numerator and denominator by 2

$-\frac{16/2}{6/2}$

$-\frac{8}{3}$

The expression can't be further simplified;

Hence, $\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}$ = $-\frac{8}{3}$

8 0

2 years ago

Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.

steposvetlana [31]

4(2 - x) > -2x - 3(4x + 1)
8 - 4x > -2x - 12x - 3
-4x + 2x + 12x > -3 - 8
10x > -11
x > -11/10
x > -1.1

Therefore, x = 0 and x = 10 zre solutions to the inequality.

4 0

2 years ago

Read 2 more answers

After watching the video below, explain what is happening in your own words. What percent of the original dollar size will the 4

RSB [31]

Answer:

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6 0

2 years ago