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3 years ago

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Which statements are true about David's work? Check all that apply. The GCF of the coefficients is correct. The GCF of the varia

ble b should be b4 instead of b2. The variable c is not common to all terms, so a power of c should not have been factored out. The expression in step 5 is equivalent to the given polynomial. In step 6, David applied the distributive property.

1 answer:

Anon25 [30]3 years ago

6 0

Answer:

The GCF of the coefficients is correct.

The variable c is not common to all terms, so a power of c should not have been factored out.

In step 6, David applied the distributive property.

Step-by-step explanation:

Given the polynomial :

80b⁴ – 32b²c³ + 48b⁴c

The Greatest Common Factor (GCF) of the coefficients:

80, 32, 48

Factors of :

80 : 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80

32 : 1, 2, 4, 8, 16, and 32

48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

GCF = 16

b⁴, b², b⁴

b⁴ = b * b * b * b

b² = b * b

b⁴ = b * b * b * b

GCF = b*b = b²

GCF of c³ and c

c³ = c * c * c

c = c

GCF = c

We can see that David's GCF of the coefficients are all correct

From the polynomial ; 80b⁴ does not contain c ; so factoring out c is incorrect

In step 6 ; the distributive property was used to obtain ; 16b²c(5b² – 2c² + 3b²)

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A garden table and a bench cost $804 combined the garden table costs $46 less than the bench. What is the cost of the bench

dsp73

Answer:

The cost of the bench is <u>425 dollars</u>.

Step-by-step explanation:

<u>Let x represent the garden table.</u>

<u>Let y represent the bench.</u>

x + y = 804

x = y - 46

<u>Use the substitution method.</u>

y - 46 + y = 804

2y - 46 = 804

<u>Add 46 to both sides.</u>

2y = 850

<u>Divide both sides by 2.</u>

y = 425

Answer:

The cost of the bench is 425 dollars.

8 0

3 years ago

62% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 48 owned dogs are r

dedylja [7]

Answer:

a) 0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b) 0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c) 0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d) 0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

Step-by-step explanation:

To solve this question, we use the binomial probability distribution, and also it's approximation to the normal distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

62% of owned dogs in the United States are spayed or neutered.

This means that $p = 0.62$

48 owned dogs are randomly selected

This means that $n = 48$

Mean and standard deviation, for the approximation:

$\mu = E(x) = np = 48*0.62 = 29.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{48*0.62*0.38} = 3.36$

a. Exactly 30 of them are spayed or neutered.

This is P(X = 30), which is not necessary the use of the approximation.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 30) = C_{48,30}.(0.62)^{30}.(0.38)^{18} = 0.1180$

0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b. At most 33 of them are spayed or neutered.

Now we use the approximation. This is, using continuity correction, $P(X \leq 33 + 0.5) = P(X \leq 33.5)$ , which is the pvalue of Z when X = 33.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{33.5 - 29.76}{3.36}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c. At least 31 of them are spayed or neutered.

Using continuity correction, this is $P(X \geq 31 - 0.5) = P(X \geq 30.5)$ , which is 1 subtracted by the pvalue of Z when X = 30.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30.5 - 29.76}{3.36}$

$Z = 0.22$

$Z = 0.22$ has a pvalue of 0.5871

1 - 0.5871 = 0.4129

0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d. Between 24 and 30 (including 24 and 30) of them are spayed or neutered.

This is, using continuity correction, $P(24 - 0.5 \leq X \leq 30 + 0.5) = P(23.5 \leq X \leq 30.5)$ , which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 23.5.

X = 30.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30.5 - 29.76}{3.36}$

$Z = 0.22$

$Z = 0.22$ has a pvalue of 0.5871

X = 23.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{23.5 - 29.76}{3.36}$

$Z = -1.86$

$Z = -1.86$ has a pvalue of 0.0314

0.5871 - 0.0314 = 0.5557

0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

8 0

3 years ago

Solve 2x3 + x2 - 15x completely by factoring.

zhuklara [117]

Answer: [D]: " x = 0, -3, 5/2 " .

{Assuming: " 2x³ + x²  − 15x = 0 ".}.
__________________________________________
Explanation:
___________________________________
Given:
_________________________________
2x³ + x² − <span>15x ;
__________________________________
</span> → (2x³ + x²) − 15x ;

  →   2x³ + x² − 15x  =   x * (2x² + x − 15) ;

  → Factor the expression: "(2x² + x − 15)" ;

→ (2x² + x − 15) =

→ 2x² − 5x + 6x − 15 ;

→ Add the "first TWO (2) terms", and pull out the "like factors" ; → x*(2x − 5) ;

→ Add the "last TWO (2) terms, pulling out "common factors";
→ 3*(2x − 5) ;

→ Now, add up the previous FOUR (4) terms; to get:

→ (x + 3)(2x − 5) ;

→ Now, we have factored the:

"(2x² + x − 15)" of: " x*(2x² + x − 15) " ;

→ So we add the "x"; and write the entire factored expression:
______________________________________________________
→ x*(x + 3)(2x − 5) ;
_____________________________________
Now, assume the question is asking to solve for "x" by factoring;
when the expression is "equal to zero" ;
_______________________________________
That is, when:

→ x*(x + 3)(2x − 5) = 0 ;
____________________________________________
Since we have THREE (3) multiplicands; and anything times "0" equals "0" ;
this equation holds true when:
________________________________
1) x = 0 ;
_______________
2) (x + 3) = 0 ;

Subtract "3" from each side of the equation;

x + 3 − 3 = 0 − 3 ;

x = -3 ;
_______________________
3) 2x − 5 = 0 ;

Add "5" to each side of the equation;

2x − 5 + 5 = 0 + 5 ;

2x = 5 ; Now, divide EACH side of the equation by "2" ; to isolate "x" on one side of the equation; and to solve for "x" ;

2x/2 = 5/2 ;

x = 5/2; or, write as 2.5; or write as 2<span>½ .
</span>_____________________________________
Put simply, the equation is true when:
_________________________________________
x = 0, -3, 5/2 ; which is: Answer choice: [D].
_________________________________________

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3 years ago

Is there anyone here that knows how to solve quadratic equations using the quadratic formula?

Ann [662]

Answer:

Me, I just learned it, I can help

Step-by-step explanation:

Formula:

ax^2 + bx + c

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