Algebra ll Unit 12020-21
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5. The graph of the absolute value function y = 2 (x + 3)- 2 is given. What
is the solution for 2 when y = -2?

Answer:9

Step-by-step explanation:87-24=63 and 63 divided by 7 equals 9

The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

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Answer:

Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.

Step-by-step explanation:

The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.

The equation from the fourth column is:

0.35x + 0.10(1300 - x) = 0.25(1300)

Solving for x, we get:

x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600

Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.

We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000

At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.

For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals

1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000

For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2

For the seventh payment (end of year 7), the present value is:

7,000 x [(1 - (1 + r)-7) / r]

which equals

7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7

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If the possible values of x are given by x + 8 ≤ 6, then the greatest possible value of 7x is -14

The given inequality is

x + 8 ≤ 6

The inequality is the mathematical statement that show the relationship between one expression and another expression with inequality signs. The inequality signs are less than, less than or equal, greater than, greater than or equal. The equal sign will not be a part of inequality

The inequality is

x + 8 ≤ 6

Substract both side of the equation by 8

x + 8 - 8 ≤ 6 - 8

x ≤ -2

The greatest possible value of

x = -2

Then the greatest possible value of 7x is

7x = 7 × -2

= -14

Hence, if the possible values of x are given by x + 8 ≤ 6, then the greatest possible value of 7x is -14

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Therefore, the probability that the first number divided by the second number is greater than zero is 1/3.

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.

Here,

Since we are returning the first tile to the bag before selecting the second one, the two selections are independent of each other.

There are two cases to consider:

Case 1: We select a positive number on the first draw.

The probability of selecting a positive number on the first draw is 2/3, since there are two positive numbers (-12 and 1) out of a total of three tiles.

Regardless of what number we select on the first draw, there is only one negative number (-2) in the bag, so the probability of selecting a negative number on the second draw is 1/3.

Therefore, the probability of selecting a positive number on the first draw and a negative number on the second draw (which results in a quotient greater than zero) is:

(2/3) x (1/3) = 2/9

Case 2: We select the negative number (-2) on the first draw.

The probability of selecting the negative number (-2) on the first draw is 1/3.

In this case, we must select the positive number on the second draw in order for the quotient to be greater than zero. There is only one positive number (1) in the bag, so the probability of selecting it on the second draw is 1/3.

Therefore, the probability of selecting the negative number (-2) on the first draw and the positive number on the second draw (which results in a quotient greater than zero) is:

(1/3) x (1/3) = 1/9

Since these are the only two cases that satisfy the condition, the overall probability is the sum of the probabilities of these two cases:

2/9 + 1/9 = 3/9 = 1/3

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The final cost of the bicycle with VAT included was Rs 6,356.25. Since the VAT was 13% the price before taxes is:

The costumer got a 10% discount to reach that value, therefore the price marked up by the seller before the discount can be found by applying a rule of three as shown below:

We now know the price at which the seller marked up the bicycle and we want to find which percentage it represents compared to the cost price. To do that we will find the absolute difference in value and apply a rule of three.

Applying the rule of three:

The price was marked up 25% above the cost of the bicycle.

Answer: 3

Step-by-step explanation:

7x=21 21/7=3

Answer:

6x-

7y

=

-11

6x-7y=-11

Answer:

7)  Domain:  (-∞, ∞)

    Range:  [-1, ∞)

8)  Domain:  (-∞, ∞)

    Range:  (-∞, ∞)

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

Domain & Range

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

From inspection of the graph, the minimum y-value is y = -1.  

The end behavior of the relation is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the range of the relation is restricted:  [-1, ∞)

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

The end behavior of the function is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

Answer:

The change of the person landing on each side is 1/8

Step-by-step explanation:

Answer:

a. At the 0.05 level of significance,  there is evidence that the mean life is different from 6,500 hours.

b. The p value= ≈ 0.00480 for z- test which is less than 0.05 and H0 is rejected .

The p value= 0.006913 for t- test which is less than 0.05 and H0 is rejected for 49 degrees of freedom.

c. CI [6583.336 ,6816.336]

d.  The range of CI [6583.336 ,6816.336] tells that the cfls having a different mean life lie in this range.

Step-by-step explanation:

Population mean = u= 6500 hours.

Population standard deviation = σ=500 hours.

Sample size =n= 50

Sample mean =x`=  6,700 hours

Sample standard deviation=s=  600 hours.

Critical values, where P(Z > Z) =∝ and P(t >) =∝

Z(0.10)=1.282  

Z(0.05)=1.645  

Z(0.025)=1.960  

t(0.01)(49)= 1.299

t(0.05)= 1.677  

t(0.025,49)=2.010

Let the null and alternate hypotheses be

H0: u = 6500 against the claim Ha: u ≠ 6500

Applying Z test

Z= x`- u/ s/√n

z= 6700-6500/500/√50

Z= 200/70.7113

z= 2.82=2.82

Applying  t test

t= x`- u /s/√n

t= 6700-6500/600/√50

t= 2.82

a. At the 0.05 level of significance,  there is evidence that the mean life is different from 6,500 hours.

Yes we reject H0  for z- test as it falls in the critical region,at the 0.05 level of significance, z=2.82 > z∝=1.645

For t test  we reject H0   as it falls in the critical region,at the 0.05 level of significance, t=2.82 > t∝=1.677 with n-1 = 50-1 = 49 degrees of freedom.

b. The p value= ≈ 0.00480 for z- test which is less than 0.05 and H0 is rejected .

The p value= 0.006913 for t- test which is less than 0.05 and H0 is rejected for 49 degrees of freedom.

c. The 95 % confidence interval of the population mean life is estimated by

x` ±  z∝/2  (σ/√n )

6700± 1.645 (500/√50)

6700±116.336

6583.336 ,6816.336

d. The range of CI [6583.336 ,6816.336] tells that the cfls having a different mean life lie in this range.

The HCF of 560 and 729 is 1.

To find the HCF of 560 and 729, we use the Euclidean algorithm as follows;HCF of 560 and 729:Step 1: Divide the larger number by the smaller number, then find the remainder.729 ÷ 560 = 169 remainder 169Step 2: Divide the smaller number (i.e., 560) by the remainder (i.e., 169).560 ÷ 169 = 3 remainder 53.

Step 3: Divide the remainder from step 1 (i.e., 169) by the remainder from step 2 (i.e., 53).169 ÷ 53 = 3 remainder 10Step 4: Divide the remainder from step 2 (i.e., 53) by the remainder from step 3 (i.e., 10).53 ÷ 10 = 5 remainder 3Step 5: Divide the remainder from step 3 (i.e., 10) by the remainder from step 4 (i.e., 3).10 ÷ 3 = 3 remainder 1.

Step 6: Divide the remainder from step 4 (i.e., 3) by the remainder from step 5 (i.e., 1).3 ÷ 1 = 3 remainder 0The HCF of 560 and 729 is the last non-zero remainder, which is 1.

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Answer:

X=32, Y=148

Step-by-step explanation:

X is 32 degrees because it is parallel to that 32 between f and b.

Y is 148 degrees because x and y together make a straight line and a straight line is 180 degrees therefore, 180-32 = 148.

Answer:

P(0) = 4C0 * 0.75⁰ * 0.25⁴ = 0.00390625 . = 0.004

P(1) = 4C1 * 0.75¹ * 0.25³ = 0.046875 . . . = 0.047

P(2) = 4C2 * 0.75² * 0.25² = 0.2109375 . . = 0.211

P(3) = 4C3 * 0.75³ * 0.25¹ = 0.421875 . . . = 0.422

P(4) = 4C4 * 0.75⁴ * 0.25⁰ = 0.31640625 . = 0.316

Check:

P(0) + P(1) + P(2) + P(3) + P(4) = 1 . . . ok

Step-by-step explanation:

This is False in light of the stated statement. due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.

Y = mX + b, where X is the predictive (independent) factor, m is really the approx slope, and b is the expected intercept, is the methodology for simple linear regression.

Regress, from whence the word "regression" is derived, means "to go back" in Latin (to something). Regression is the method that enables "going back" from muddled, challenging data to a clearer and more significant model in this manner.

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Answer:

40,000,000 or 40 million

Step-by-step explanation:

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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Answer:

A=40.8 B=8

Step-by-step explanation:

A Explanation

£7.20*3=£21.6

£9.60*2=£19.2

19.2+21.6=40.8

B Explanation

£9.60*3=£28.8

86.40-28.8=57.6

57.6/7.20=8

The value of the missing side length x in the right triangle is 15 inches.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

( hypotenuse )² = ( leg 1 )² + ( leg 2 )²

The image in the diagram is a right triangle:

Hypotenuse = 17 inches

Leg 1 = 8 inches

Leg 2 = x

To solve for x, we use the pythagorean theorem.

( hypotenuse )² = ( leg 1 )² + ( leg 2 )²

( leg 2 )² = ( hypotenuse )² - ( leg 1 )²

( leg 2 )² = ( 17 )² - ( 8 )²

( leg 2 )² = 289 - 64

( leg 2 )² = 225

Take the square roots

Leg 2 = √225

Leg 2 = 15 inches.

Therefore, the value of x is 15 inches.

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Answer: 31

Step-by-step explanation: just took the test

Answer:

0.03593

Step-by-step explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 17,340

μ is the population mean = 15,000

σ is the population standard deviation = 1300

z score:

z = 17340 - 15000/1300

z =1.8

Probability value from Z-Table:

P(x<17340) = 0.96407

P(x >17340) = 1 - P(x<17340)

= 1 - 0.96407

= 0.03593

The probability that the life span of the monitor will be more than 17,340 hours is 0.03593

Using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Simply put, probability is the likelihood that something will occur.

When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.

So, we have the chart:

Penny = 2/5 = 0.4

Nickel = 1/5 = 0.2

Dime = 1/4 = 0.25

Then, the probability of getting a value of at least $0.10

P(E) = 3/3

P(E) = 1

Therefore, using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

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Using the graphical method for limits, it is found that:

\(\lim_{x \rightarrow 3} f(x) = 1\)

\(\lim_{x \rightarrow a} f(x) = \lim_{x \rightarrow a^+} f(x) = \lim_{x \rightarrow a^-} f(x)\)

In this problem, the definition as x goes to 3 is the same, hence:

\(\lim_{x \rightarrow 3} f(x) = \lim_{x \rightarrow 3^+} f(x) = \lim_{x \rightarrow 3^-} f(x) = 1\)

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The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer:

s = 20

Step-by-step explanation: