John saves $15 every pay check. He gets paid
$225 every paycheck. What percent of his
paycheck does he save?

28%

20%

7%

Logical form:

P: Oleg is a math major

Q: Oleg is an economics major

R: Oleg is required to take Math 362

Argument:

1. P ∨ Q

2. P → R

Therefore, Q ∨ ¬R

In the logical form of the argument, we assign propositions to each statement. P represents the statement "Oleg is a math major," Q represents "Oleg is an economics major," and R represents "Oleg is required to take Math 362."

To test the validity of the argument, we construct a truth table that includes columns for the premises (P ∨ Q and P → R) and the conclusion (Q ∨ ¬R). The truth table will account for all possible truth values of P, Q, and R and determine whether the conclusion is always true whenever the premises are true.

Truth table:

| P | Q | R | P ∨ Q | P → R | Q ∨ ¬R |

|---|---|---|-------|-------|--------|

| T | T | T |   T   |   T   |   T    |

| T | T | F |   T   |   F   |   T    |

| T | F | T |   T   |   T   |   T    |

| T | F | F |   T   |   F   |   T    |

| F | T | T |   T   |   T   |   T    |

| F | T | F |   T   |   T   |   T    |

| F | F | T |   F   |   T   |   F    |

| F | F | F |   F   |   T   |   T    |

In the truth table, we evaluate each row to determine the truth value of the premises and the conclusion. The conclusion is considered valid if and only if it is true in every row where all the premises are true.

From the truth table, we can see that in all rows where the premises (P ∨ Q and P → R) are true, the conclusion (Q ∨ ¬R) is also true. Therefore, the argument is valid.

Validity means that if the premises of an argument are true, then the conclusion must also be true. In this case, the truth table confirms that whenever both premises (P ∨ Q and P → R) are true, the conclusion (Q ∨ ¬R) is also true. Thus, the argument is valid because the conclusion follows logically from the given premises.

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Answer:

0

Step-by-step explanation:

The y-coordinate of the point where the function's graph intersects the y-axis, also known as the y-intercept, is the beginning value of a linear function. The y-intercept of the given linear function y = 5x is the value of y when x equals 0.

When we enter x = 0 into the provided function, we get:

y = 5(0) = 0

As a result, the linear function y = 5x has an initial value of 0.

The cost of materials for the least expensive such container is 245.31 dollars .

Suppose the width of container is x (m),

length of the base of container is 2x (m)

the base area of container is (length × width)sq. m i.e 2x² meter².

Since the volume of container is 10 m³.

the height of container = area of container/ volume of container

height of container= 10/2x² m = 5/x² m

The cost of making such container is cost of base = 2x²*10 = 20x².

cost of sides of container = (2×2x × 5/x² + 2× x × 5/x²)×6 = 180/x

The overall cost is hence the sum of the base and the sides: f(x) = 20x² + 180/x

The get the minimum,

df(x)/dx = 20×(2x - 9/x²) = 0

so 2x = 9/x^2 => 2x = 2.0800 ==> x = 1.651 m

f(x) = 245.31 dollars

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Answer:

Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 + x – 1

Step-by-step explanation:

The answer is A because the axis of symmetry is in between 0 and 1, the vertex lies on 0.5 and -0.75, and the parabola opens down so the coefficient of a is -1, and the y-int or the value of c is -1

The vertex of the function is  axis of symmetry is  and the formula for the function is  Option (a) is correct.

Further Explanation:

Given:

Calculation:

The standard form of the parabola is shown below.

Here, the parabola has vertex at  and has the symmetry parallel to x-axis and it opens left.

The general form of the parabola can be expressed as follows,

The graph is a downward parabola.

From the graph it has been observed that the vertex of the parabola is

Symmetry of the graph is  

The -intercepts of the graph is  Therefore, the value of is  

The value of  is -1 as the graph is a downward parabola.

The vertex of the function is  axis of symmetry is  and the formula for the function is  Option (a) is correct.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Conic sections

Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola.

A fragment of code that assigns the least of these three variables to another variable named min. is given,

The error in the code is due to the incorrect syntax used in the if statement. The colon : is used to indicate the beginning of a block of code that should be executed if the condition in the if statement is true. In this case, the colon should come after the condition, not before. Here is the corrected code:

python

min = x

if y < min:

   min = y

if z < min:

   min = z

In this code, the if statements check whether y or z is less than the current value of min, and if so, update the value of min to be y or z. The corrected code should compile without errors and correctly assign the least of the three variables to the variable min.

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____The given question is incomplete, the complete question is given below:

Assume the variables

x,y

, and

z

have each been assigned an integer value. Write a fragment of code that assigns the least of these three variables to another variable named min.

1min=x

2 if: y<min:min=y

3 if: z<min:min=z

​

Code Analysis: Compiler Error(s) Compiler error messages SyntaxError: invalid syntax (CTest.py, line 3) 3 if:

y<min:min=y

Answer:

Step-by-step explanation:

Given triangle LNK

Interior angles sum to 180°

To solve this problem, we can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where:
- P(X=k) is the probability of getting k nonconforming washing machines in the sample
- n is the sample size, which is 10 in this case
- p is the probability of getting a nonconforming washing machine, which is 0.08
- (n choose k) is the binomial coefficient, which is the number of ways to choose k items from n without replacement, and is calculated as n! / (k! * (n-k)!)

So, to find the probability of getting 1 nonconforming washing machine in the sample, we plug in k=1:

P(X=1) = (10 choose 1) * 0.08^1 * (1-0.08)^(10-1)
P(X=1) = 10 * 0.08 * 0.9227
P(X=1) = 0.0738

Therefore, the probability of getting 1 nonconforming washing machine in the sample is approximately 0.0738, or 7.38%.

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Answer:
Each pound of jelly beans costs $2.50 and each pound of almonds costs $1.25.

I really struggled while trying to solve this, good luck. (┬┬﹏┬┬)<3

Step-by-step explanation:

2.50*3 = 7.50
1.25*2 = 2.50

7.50 + 2.50 = 10.00

-------------------------------

2.50*8 = 20.00
1.25*4 = 5

20 + 5 = 25

There are 87 possible outcomes that contain at least three heads when a coin is flipped 9 times.

When a coin is flipped nine times, there are 512 possible outcomes, or 29. Using the equation:

P (At least one head) = 1 - 0.5n,

where n is the total number of flips, we can determine the number of outcomes that contain at least three heads.

Therefore, P (At least three heads) = 1 - P (No heads) - P (One head) - P (Two heads)

= 1 - (0.5)⁹ - 9(0.5)⁹ + 36(0.5)⁹

= 0.1718751.

The formula used to calculate the number of possible outcomes that contain at least three heads is C(9,3) + C(9,4) + C(9,5) + C(9,6) + C(9,7) + C(9,8) + C(9,9),

where C(n,r) denotes the variety of options for selecting item(s) r from a set of item(s) n.

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The correct order for constructing a perpendicular bisector is as follows:

1. Draw a baseline AB

2. Draw arcs above and below the line

3. Open the compass over half the distance of the baseline at point A

4. Draw an arc from point B using the same compass setting

5. Identify the points of intersection

6. Connect the points of intersection with a straight edge

7. Draw a small square at the point of intersection to indicate a 90° angle.

To construct a perpendicular bisector, the steps should be followed in the following order:

Draw a baseline and label it AB.

Draw an arc above and below your line.

Open your compass over half the distance of your baseline and place your compass on point A.

Keeping your compass at the same setting, draw an arc from point B.

Your arc should intersect the other arc at two points.

Locate the points of intersection and connect them using a straight edge.

Draw a small square to indicate a 90° angle.

Step 1 is the starting point, where we establish the baseline AB. This line will be bisected perpendicularly.

In Step 2, we draw arcs above and below the baseline to create points of intersection.

Step 3 involves opening the compass over half the distance of the baseline and placing the compass on point A. This allows us to create arcs that will intersect with the arcs from Step 2.

Next, in Step 4, we use the same compass setting to draw an arc from point B. This arc will also intersect with the arcs created in Step 2.

Step 5 indicates that the arcs from Step 3 and Step 4 should intersect at two points. These points are the locations where the perpendicular bisector will pass through the baseline.

In Step 6, we connect the points of intersection using a straight edge. This line will be the perpendicular bisector of the baseline AB.

Finally, in Step 7, we draw a small square at the point of intersection between the baseline and the perpendicular bisector to indicate a 90° angle.

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Answer:

C

Step-by-step explanation:

They are the same without rotation and translation

The chi-square test for independence in a 2x2 contingency table is equivalent to comparing two proportions to determine if they are significantly different.

For a 2x2 contingency table, testing for independence with the chi-square test is the same as conducting a test comparing two proportions, specifically the two proportions of one variable (column) against the proportions of another variable (row).

1. Start with a 2x2 contingency table, which is a table that displays the counts or frequencies of two categorical variables. The table has two rows and two columns.

2. Calculate the marginal totals, which are the row and column totals. These represent the totals for each category of the variables.

3. Compute the expected frequencies under the assumption of independence. To do this, multiply the row total for each cell by the column total for the same cell, and divide by the total sample size.

4. Use the chi-square test statistic formula to calculate the chi-square value. This formula involves subtracting the expected frequency from the observed frequency for each cell, squaring the difference, dividing by the expected frequency, and summing up these values for all cells.

5. Determine the degrees of freedom for the chi-square test. In this case, it is (number of rows - 1) multiplied by (number of columns - 1), which is (2-1) x (2-1) = 1.

6. Compare the calculated chi-square value to the critical chi-square value from the chi-square distribution table at the desired significance level (e.g., 0.05).

7. If the calculated chi-square value is greater than the critical chi-square value, then the proportions of the two variables are significantly different, indicating dependence. If the calculated chi-square value is not greater, then the proportions are not significantly different, suggesting independence.

In summary, testing for independence with the chi-square test for a 2x2 contingency table is equivalent to conducting a test comparing two proportions, where the proportions represent the distribution of one variable against another.

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Answer:

4%

Step-by-step explanation:

12/300

hope this helps

The limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

To use the ratio test, we take the limit of the absolute value of the ratio of the (k+1)th term to the kth term:

lim as k approaches infinity of |(6(k+1)^4)/(6k^4)|

Simplifying this expression, we get:

lim as k approaches infinity of |(k+1)^4/k^4|

Using L'Hopital's rule, we can evaluate this limit:

lim as k approaches infinity of |4(k+1)^3/4k^3|

lim as k approaches infinity of |(k+1)/k|^3

Since the limit is less than 1, by the ratio test, the series converges absolutely.

Alternatively, we can use the root test, which involves taking the kth root of the absolute value of the kth term:

lim as k approaches infinity of |(6k^4 k)^(1/k)|

Simplifying this expression, we get:

lim as k approaches infinity of |6^(1/k) * k^(4+1/k)|

The exponent 4+1/k approaches 4 as k approaches infinity, so we can ignore the 1/k term. Taking the limit of just the k^(4) term, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k)

Using the fact that lim as k approaches infinity of 6^(1/k) = 1 and lim as k approaches infinity of k^(4/k) = 1, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k) = 1

Since the limit is less than 1, by the root test, the series converges absolutely.
To determine if the given series converges absolutely or diverges, we can use the Ratio Test. The series is given as:

Σ(6k^4 * k) for k = 1 to ∞

First, let's simplify the series:

Σ(6k^5) for k = 1 to ∞

For the Ratio Test, we need to compute the limit as k goes to infinity of the ratio of consecutive terms:

lim (k → ∞) (|a_(k+1)| / |a_k|)

For our series, a_k = 6(k+1)^5 and a_(k+1) = 6k^5. So we have:

lim (k → ∞) (|6(k+1)^5| / |6k^5|)

We can simplify by canceling the common factor of 6:

lim (k → ∞) ((k+1)^5 / k^5)

Now, let's take the limit:

lim (k → ∞) (1 + 1/k)^5 / 1 = 1^5 / 1 = 1

For the Ratio Test, if the limit is less than 1, the series converges absolutely; if it is equal to 1, the test is inconclusive; if it is greater than 1, the series diverges.

In this case, the limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

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Answer:

(x + 7)(x - 4) = x2 - 4x + 7x - 28 = x2 + 3x - 28

Answer:

  a) $12609.04

  b) $12879.28

  c) interest is compounded more often

Step-by-step explanation:

You want to know the future value of an annuity if $1200 per year is contributed for 7 years and interest is 12%. The first annuity has payments made and interest compounded 2 times per year. The second annuity has payments made and interest compounded 4 times per year.

You also want to know why the second annuity earns more than the first.

The future value of these annuities can be found using the annuity formula, or using a financial calculator. The formula is ...

  FV = P(n/r)((1 +r/n)^(nt) -1)

For a payment of 600 twice a year for 7 years at an interest rate of 12%, this is ...

  FV = 600(2/0.12)((1 +0.12/2)^(2·7) -1) = 600(21.01506593) ≈ 12,609.04

For a payment of 300 four times per year, the same calculation gives ...

  FV = 300(4/0.12)((1 +0.12/4)^(4·7) -1) = 300(42.93092252) ≈ 12,879.28

The future value of annuity A is equivalent to about 10.508 payments of $1200. That is, the interest effectively added 3.508 annual payments to the value paid in.

The future value of annuity B is equivalent to about 10.733 payments of $1200. The interest effectively added 3.733 annual payments to the value paid in.

The additional value comes from compounding interest more frequently.

For annuity B, the interest paid after 6 months is computed on both the account value and the interest that was paid after 3 months. The interest computation for annuity A is based only on the account value, so is a little less. That difference adds up over time.

A race car with wheels with diameter 66 cm must turn 1,088,000 times to cover a 300 km race. This is because the circumference of a wheel is equal to its diameter multiplied by pi, which is approximately 3.14.

So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.

The circumference of a circle is equal to its diameter multiplied by pi, which is approximately 3.14. So, the circumference of a 66 cm wheel is 66 * 3.14 = 208.2 cm. To travel 300 km, the car must turn its wheels 300,000 / 208.2 = 1,445 times.

In other words, the car must turn its wheels 1,445 times to cover the race distance. This is a lot of turns, but it is possible for a Formula 1 car to do this. The cars are designed to be very efficient and to have very low rolling resistance, which means that they can turn their wheels very quickly without losing too much energy.

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Answer:

y = (1/2)x

Step-by-step explanation:

Lets look for an equation of the form y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = zero).  We can find the slope by calculating the Rise/Run between the two given points:

Going from (0,0) to (8,4):

Rise = (4-0) = 4

Run = (8-0) = 8

Slope = Rise/Run   (4/8) or (1/2)

The equation becomes y = (1/2)x + b

We need a value of b that forces the line through both points.  The point (0,0) actually tells us that b is 0, since b is the value of y when x=0.  If we weren't ask lucky to get a point where x is zero, we could cacalute b by putting either point in the above equation and solving for b:

y = (1/2)x + b

4 = (1/2)*(8) + b  for (8,4)

b = 0

The equation is y = (1/2)x

See the attached graph.

The predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.

In this question,

The equation for least regression line to this data set is

y' = 76.82x + 88.56 ------- (1)

Number of years, x = 7

The general form of equation for least regression line is

y' = a + bx

where y is the dependent variable, x is the independent variable, a is the intercept of regression line and b is the slope of regression line.

The predicted value (in dollars) for maintenance expenses when a truck is 7 years old can be calculated as

y' = 76.82x + 88.56

Substitute the value of x in the above equation, we get

y' = 76.82(7) + 88.56

y' = 537.74 + 88.56

y' = 626.3

Hence we can conclude that the predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.

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Answer:

To write a decimal in word form, follow these steps: Write the whole number part. Write "and" for the decimal point. Write the decimal part the same way you would write a whole number.

Step-by-step explanation:

Please mark me brainliest

Answer:

for the fist one is 44 and the last one is 8

Step-by-step explanation:you just divide the last answer incase you dont understand here is a better explanation you divide 24 by 6 and you get 4 not 11 times 4 equals 44 and for the second one you do the same thing 96 divided by 12 equals 8 so 64 divided by 8 equals 8

If x ≡ 7 (mod 20), then

x ≡ 7 ≡ 27 ≡ 47 ≡ 67 ≡ 87 ≡ … (mod 20)

or equivalently, x = 7 + 20k for some integer k.

Taken mod 4, we have

x ≡ 7 + 20k ≡ 3 (mod 4)

and mod 5,

x ≡ 7 + 20k ≡ 2 (mod 5)

so that a = 3 and b = 2.

To find the equivalent ratios, we must simplify the fractions when it is possible:

Therefore, the equivalent ratios are 4:7, 16:28 and 20:35

\(\\ \ast\bull\rm\longmapsto 56thousandths-23thousandthas\)

\(\\ \ast\bull\rm\longmapsto (56-23)thousandths\)

\(\\ \ast\bull\rm\longmapsto 33thousandths\)

\(\\ \ast\bull\rm\longmapsto 33000\)

AB = BC

Area of shaded part = Area of the square - the area of the circle

Area of shaded part = 37.68- 12 =25.68 square inche

Answer:

Step-by-step explanation: