All categories

2 years ago

If f(x) and g(x) are quadratic functions but (f+g)(x) produces true graph below, hutch statement must be true ?

Mathematics

1 answer:

alexgriva [62]2 years ago

3 0

Answer:

A. the leading coefficients of f (x) and g (x) are opposites

Step-by-step explanation:

A. the leading coefficients of f (x) and g (x) are opposites

A quadratic function in its generic form is:

f (x) = ax2 + bx + c

g (x) = dx2 + ex + f

The sum of the functions is:

(f + g) (x) = (a + d) x2 + (b + e) x + (c + f)

For the function to be linear necessarily:

a = -d

You might be interested in

Below are boxplots that summarize the weights (in pounds) of large samples from two breeds of dog: the Anatolian Shepherd and th

koban [17]

Answer:

(a) The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of both plots is also same that is 75 pounds.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively

(b) Any data point which is greater than 155 or smaller than 80 will be considered an outlier.

Step-by-step explanation:

A box plot is a graph which shows five statistical characteristics of a data set.

1. Maximum value

2. Minimum value

3. Median

4. Upper Interquartile

5. Lower interquartile

(a) Compare the distributions of weights for the two dog breeds

Please refer to the attached diagram of the question.

The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of Anatolian Shepherd is,

Range = Maximum value - Minimum value

Range = 175 - 100 = 75 pounds

The range of Black Russian Terrier is,

Range = Maximum value - Minimum value

Range = 155 - 80 = 75 pounds

Therefore, the range of both plots is also same that is 75 pounds.

A box-plot is considered to be normally distributed when the median is at the center of upper quartile and lower quartile.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively distributed.

(b) What weights would a Black Russian Terrier have to be to be considered an outlier?

An outlier is a data point in the data set that is very different from the other data points.

In this case, the maximum and minimum values in the Black Russian Terrier box-plot are

Maximum = 155

Minimum = 80

Therefore, any data point which is greater than 155 or smaller than 80 will be considered an outlier.

5 0

2 years ago

Suppose that in one region of the country the mean amount of credit card debt perhousehold in households having credit card debt

kvv77 [185]

Answer:

The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 15250, \sigma = 7125, n = 1600, s = \frac{7125}{\sqrt{1600}} = 178.125$

The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly

This probability is the pvalue of Z when X = 1600 + 300 = 1900 subtracted by the pvalue of Z when X = 1600 - 300 = 1300. So

X = 1900

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

By the Central Limit Theorem

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

$Z = \frac{1900 - 1600}{178.125}$

$Z = 1.68$

$Z = 1.68$ has a pvalue of 0.9535.

X = 1300

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

$Z = \frac{1300 - 1600}{178.125}$

$Z = -1.68$

$Z = -1.68$ has a pvalue of 0.0465.

0.9535 - 0.0465 = 0.907.

The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.

7 0

2 years ago

Loretta’s income last year was $81,300. She made $56,800 at her salaried job and had additional passive income. If Loretta earne

aalyn [17]

Answer:

Option a. $2,040

Step-by-step explanation:

step 1

To find out the amount of the additional passive income last year, subtract the amount earned at her salaried job from Loretta’s income last year

$\$81,300-\$56,800=\$24,500$

step 2

Divide the additional passive income last year by 12 (number of months in a year)

$\$24,500/12=\$2,041.67$

therefore

approximately $2,400 per month

5 0

2 years ago

Read 2 more answers

Monogram Masters advertises on its website that 92% of customer orders are received within five working days. They performed an

quester [9]

Answer:

a yes

0.0094

Step-by-step explanation:

Part a

p = 0.92, n = 200

np = 184 > 10

n(1 − p) = 16 > 10

Therefore, normal approximation can be used.

μ = p = 0.92

σ = √(p (1 − p) / n)

σ = √(0.92 × 0.08 / 200)

σ = 0.0192

x = 175/200 = 0.875

z = (x − μ) / σ

z = (0.875 − 0.92) / 0.0192

z = -2.34

P(z < -2.34) = 0.0096

Part b

It is 99% that the proportion is not 0.92

Therefore, there is enough evidence at the 0.01 level, that monogram master ships less tha 92% of its order on time

4 0

2 years ago

A cyclist completes a journey of 500 meters in 22seconds part of the way at 10 meter per seconds and the remainder at 50 meter p

lorasvet [3.4K]

Answer:

plz like and mark for me brainlist plz

Step-by-step explanation:

A cyclist completes a journey of 500m in 22 seconds, part of the of the way at 10m/s and the remainder at 50m/s. how far does she travel at each speed? ... Let x = distance traveled at 10m/s and y = distance traveled at 50m/s. ... x+y=500. 50x+10y=11000. 50x+50y=25000. 50x+10y=11000. 40y=14000.

3 0

2 years ago