The Greatest Common Factor (GCF) of 4x3 - 2x2 + 8x is:
A. 2x
B. 2.
C. X
D.None of these choices are correct.

Answer:

see below

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

4x - 3y = 12

Solve for y

Subtract 4x from each side

4x-4x - 3y =-4x+ 12

-3y = -4x+12

Divide by -3

-3y/-3 = -4x/-3 + 12/-3

y = 4/3x -4

The slope is 4/3 and the y intercept is -4

The slope is Positive

Answer:

Ans) 42.7%

Step-by-step explanation:

For a continuous probability distribution, a curve known as probability density function contains information about these probabilities.

in the given range -

The probability that a continuous random variable = equal to the area under the probability density function curve

The probability that the value of a random variable is equal to 'something' is 1.

As per the diagram,

Weight of chocolate bar between 4 ounces and 7 ounces is highlighted in the blue part. That area is said to be 0.42739 and the total area under the curve is 1.

Hence required probability

=0.42739/1=0.42739

Ans) 42.7%

Round to nearest tenth of a percent

Answer:

2/3

Step-by-step explanation:

There are 2 numbers out of 3 that fit the rule, 1 and 3. There is a 2/3 chance picking one of them.

Answer:

Step-by-step explanation:

This is the answer because one number that is select is one. A number greater than 2 is 3. SO it is 2/3.

Answer:

g=22

Step-by-step explanation:

add 8 to both sides

g-8=14

g-8+8=14+8

g=14+8

g=22

The solution of expression g - 8 = 14 is,

⇒ g = 22

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ g - 8 = 14

Now, We can simplify as,

⇒ g - 8 = 14

Add 8 both side,

⇒ g - 8 + 8 = 14 + 8

⇒ g = 22

Thus, The solution of expression g - 8 = 14 is,

⇒ g = 22

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Answer:

[tex]153.86 \: {units}^{2} [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]

Answer:

153.86 [tex]units^{2}[/tex]

Step-by-step explanation:

Areaof a circle = πr^2

[tex]\pi = 3.14[/tex](in this case)

[tex]r^{2} =7[/tex]

A = πr^2

= 49(3.14)

= 153.86

Answer:

(190-5a)°

Step-by-step explanation:

Sum of internal angles of a triangle equals to 180°

If the third angle is x, then we have:

The third angle is: (190-5a)°

Answer:

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.05, n = 212, \mu = 0.05, s = \sqrt{\frac{0.05*0.95}{212}} = 0.015[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 0.03?

This is the pvalue of Z when X = 0.03 + 0.05 = 0.08 subtracted by the pvalue of Z when X = 0.05 - 0.03 = 0.02. So

X = 0.08

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.08 - 0.05}{0.015}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772

X = 0.02

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.02 - 0.05}{0.015}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Step-by-step explanation:

yeah,when 15-7=8

the number is 8

Answer:

a) 16xy³

Step-by-step explanation:

For a binomial expansion (a + b)ⁿ, the r+1 term is:

nCr aⁿ⁻ʳ bʳ

Here, a = 4x, b = y, and n = 4.

For the fourth term, r = 3.

₄C₃ (4x)⁴⁻³ (y)³

4 (4x) (y)³

16xy³

Answer:2/3

Step-by-step explanation:

Given that the length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. The domain of the function is (0, ∞).

The domain of a function is the set of all possible inputs for the function. In other words, domain is the set of all possible values of x. In this question, x is the width of the rectangle. Width of a rectangle existing in two dimensional space, cannot be negative or zero. Thus it is the set of all positive real numbers, or we say, (0, ∞).

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Answer:

1/7

Step-by-step explanation:

There are 7 cards, 1 of which is less than 2. Therefore, P (less then 2) = 1/7

Answer:

1/7

Step-by-step explanation:

The number from the list that is less than 2 is 1.

1 number out of a total of 7 numbers.

= 1/7

Answer:

  5 feet

Step-by-step explanation:

"Twice as tall" means "2 times as tall".

  2 × (2 1/2 ft) = (2 × 2 ft) +(2 × (1/2 ft)) = 4 ft + 1 ft = 5 ft

The child's mother is 5 feet tall.

Answer:

The mother is 5ft tall

Step-by-step explanation:

2 1/2 + 2 1/2 = 5ft

2ft+2ft = 4ft

1/2+1/2= 1ft

4ft+1ft = 5ft

Answer:

The sampled populations have equal variances

Step-by-step explanation:

ANOVA which is fully known as Analysis of variances can be defined as the collection of statistical models as well as their associated estimation procedures which enables easily and effectively analyzis of the differences among various group means in a sample reason been that ANOVA is a total variance in which the observed variance in a specific variable is been separated into components which are attributable to various sources of variation which is why ANOVA help to provides a statistical test to check whether two or more population means are equal.

Therefore the required condition for using an ANOVA procedure on data from several populations for mean comparison is that THE SAMPLED POPULATION HAVE EQUAL VARIANCE.

Answer:

a) Mean of X = 0.40

Variance of X = 0.24

b) Y is a Bernoulli's distribution. Check Explanation for reasons.

c) Mean of Y = 0.80 points

Variance of Y = 0.96

Step-by-step explanation:

a) The probability that play is successful is 0.40. Hence, the probability that play isn't successful is then 1 - 0.40 = 0.60.

Random variable X represents when play is successful or not, X = 1 when play is successful and X = 0 when play isn't successful.

The probability mass function of X is then

X | Probability of X

0 | 0.60

1 | 0.40

The mean is given in terms of the expected value, which is expressed as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

Mean = E(X) = (0 × 0.60) + (1 × 0.40) = 0.40

Variance = Var(X) = Σx²p − μ²

μ = mean = E(X) = 0.40

Σx²p = (0² × 0.60) + (1² × 0.40) = 0.40

Variance = Var(X) = 0.40 - 0.40² = 0.24

b) If the conversion is successful, the team scores 2 points; if not the team scores 0 points. If Y ia the number of points that team scores.Y can take on values of 2 and 0 only.

A Bernoulli distribution is a discrete distribution with only two possible outcomes in which success occurs with probability of p and failure occurs with probability of (1 - p).

Since the probability of a successful conversion and subsequent 2 points is 0.40 and the probability of failure and subsequent 0 point is 0.60, it is evident that Y is a Bernoulli's distribution.

The probability mass function for Y is then

Y | Probability of Y

0 | 0.60

2 | 0.40

c) Mean and Variance of Y

Mean = E(Y)

E(Y) = Σ yᵢpᵢ

yᵢ = each variable

pᵢ = probability of each variable

E(Y) = (0 × 0.60) + (2 × 0.40) = 0.80 points

Variance = Var(Y) = Σy²p − μ²

μ = mean = E(Y) = 0.80

Σy²p = (0² × 0.60) + (2² × 0.40) = 1.60

Variance = Var(Y) = 1.60 - 0.80² = 0.96

Hope this Helps!!!

Answer:

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

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

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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.

In this question, we have that:

[tex]\mu = 13, \sigma = 0.2[/tex]

What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster

We have to find the pvalue of Z when X = 13.36.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13.36 - 13}{0.2}[/tex]

[tex]Z = 1.8[/tex]

[tex]Z = 1.8[/tex] has a pvalue of 0.9641

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Answer:

Each table is $6 and each chair is $2.50

Step-by-step explanation:

Answer:

Solved below.

Step-by-step explanation:

The data is provided for the starting salary (in $1,000) at some company and years of prior working experience in the same field for randomly selected 10 employees.

(a)

The formula to compute the correlation coefficient is:

[tex]r=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\[/tex]

The required values are computed in the Excel sheet below.

[tex]\begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 10 \cdot 7252 - 97 \cdot 661 } {\sqrt{\left[ 10 \cdot 1335 - 97^2 \right] \cdot \left[ 10 \cdot 45537 - 661^2 \right] }} \approx 0.9855\end{aligned}[/tex]

Thus, the sample correlation coefficient r is 0.9855.

(b)

The slope of the regression line is:

[tex]b_{1} &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 10 \cdot 7252 - 97 \cdot 661 }{ 10 \cdot 1335 - \left( 97 \right)^2} \\\\\approx 2.132[/tex]

Thus, the slope of the regression line is 2.132.

(c)

The y-intercept of the line is:

[tex]b_{0} &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 661 \cdot 1335 - 97 \cdot 7252}{ 10 \cdot 1335 - 97^2} \\\\\approx 45.418[/tex]

Thus, the y-intercept of the line is 45.418.

(d)

The equation of the sample regression line is:

[tex]y=45.418+2.132x[/tex]

(e)

Compute the predicted starting salary for a person who spent 15 years working in the same field as follows:

[tex]y=45.418+2.132x\\\\=45.418+(2.132\times15)\\\\=45.418+31.98\\\\=77.398\\\\\approx 77.4[/tex]

Thus, the predicted starting salary for a person who spent 15 years working in the same field is $77.4 K.

Answer:

Yes correct

Step-by-step explanation:

I think this is correct becase: 2 50

5 55

7 62

etc

these are all correct

Answer:

The percentage of area is between Z =-2 and Z=2

P( -2 ≤Z ≤2) = 0.9544 or 95%

Step-by-step explanation:

Explanation:-

Given data Z = -2 and Z =2

The probability that

P( -2 ≤Z ≤2) = P( Z≤2) - P(Z≤-2)

                   = 0.5 + A(2) - ( 0.5 - A(-2))

                  = A (2) + A(-2)

                 = 2 × A(2)     (∵ A(-2) = A(2)

                = 2×0.4772

              = 0.9544

The percentage of area is between Z =-2 and Z=2

P( -2 ≤Z ≤2) = 0.9544 or 95%

Answer:

by using distance formula

d=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

by putting the values of coordinates

[tex]d=\sqrt{(2-(-0.5))^2+(5-(-5))^2}[/tex]

[tex]d=\sqrt{(2+0.5)^2+(5+5)^2}[/tex]

[tex]d=\sqrt{(2.5)^2+(10)^2}[/tex]

[tex]d=\sqrt{6.25+100}[/tex]

[tex]d=\sqrt{106.25}[/tex]

[tex]d=10.3[/tex]

Step-by-step explanation:

i hope this will help you :)

Answer:

x < 5 or x > 1

Step-by-step explanation:

2x - 6 < 4

2x < 4 + 6

2x < 10

x < 10/2

x < 5

2x - 6 > - 4

2x > - 4 + 6

2x > 2

x > 2/2

x > 1

Answer:

5! = 120

Step-by-step explanation:

5! is basically 5(4)(3)(2)(1).

Answer:

Do you have an image because I'm a bit confused with you just asking the measure of PSQ.

Step-by-step explanation:

Step-by-step explanation:

pnotgrt8rthan4 = 3 ÷ 7 × 100

= 42.8571428571 / 43%

Answers:

A ' = (-2, -3)

B ' = (0, -3)

C ' = (-1, 1)

=======================================================

Explanation:

To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.

Algebraically, the reflection rule used can be written as [tex](x,y) \to (x,-y)[/tex]

Applying this rule to the three given points will mean....

The diagram is provided below.

Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.

Answer:

(-2,-3)...(0,-3)...(-1,1)

Step-by-step explanation:

Answer:

CI: {0.4085; 0.6647}

Step-by-step explanation:

The confidence interval for a proportion (p) is given by:

[tex]p \pm z*\sqrt{\frac{(1-p)*p}{n} }[/tex]

Where n is the sample size, and z is the z-score for the desired confidence interval. The score for a 90% confidence interval is 1.645. The proportion of depositors who ask for cash back is:

[tex]p=\frac{22}{41}=0.536585[/tex]

Thus the confidence interval is:

[tex]0.536585 \pm 1.645*\sqrt{\frac{(1-0.536585)*0.536585}{41}}\\0.536585 \pm 0.128109\\L=0.4085\\U=0.6647[/tex]

The confidence interval for the proportion of all depositors who ask for cash back is CI: {0.4085; 0.6647}

Answer:

3/10ths of the money

Step-by-step explanation:

Add together the two numbers to get the total.

Josh gets 30 percent and Lucy gets 70 percent.

3/10

Answer:

3/10

Step-by-step explanation:

3+7=10  

Josh=3

Lucy=7

Answer:

She makes conclusion about a population that is not well represented by the sample.

Step-by-step explanation:

The conclusion she is making is about a population that is not well represented by her sample: the population is the homeowners in the nation, but the sample is made of homeowners or only her state.

The population about which she can make conclusions with this sample is the homeowners of her state, given that the sampling is done right.

Answer: The sample is biased

Answer:

D

Step-by-step explanation:

The numbers that are less than 0 are negative. Negative numbers have the "-" sign in front of them so the answer is D.

Answer:

d

Step-by-step explanation:

The other ones will always be positive four

Answer: a. 0.1031; fail to reject the null hypothesis

Step-by-step explanation:

Given: Significance level : [tex]\alpha=0.05[/tex]

The test statistic in a two-tailed test is z = -1.63.

The P-value for two-tailed test : [tex]2P(Z>|z|)=2P(Z>|-1.63|)=0.1031[/tex] [By p-value table]

Since, 0.1031 > 0.05

i.e. p-value > [tex]\alpha[/tex]

So, we fail to reject the null hypothesis. [When p<[tex]\alpha[/tex] then we reject null hypothesis  ]

So, the correct option is a. 0.1031; fail to reject the null hypothesis.