Shown below are the steps of a proof by contraposition of the statement "If n is an integer and 5n + 3 is odd, then n is even." Match each step with its explanation.1. Assume n is not even, that is, it is odd. 2.Then n = 2k + 1 for some integer k. 3.5n + 3 = 5(2k + 1) + 3 = 10k + 8 = 2(5k + 4) 4. Hence, 5n + 3 is even. Negation of the conclusion Definition of an odd integer Definition of an even number Arithmetic

The answer is C. increasing on (0,2).

What is Strictly convex function?

A real-valued function is said to be convex if the line segment connecting any two points on its graph falls above the graph connecting the two points. A function is convex if and only if its epigraph is a convex set.

Since f"(x) > 0 for all x in (0,2), it follows that f is a strictly convex function on that interval, meaning that its second derivative is positive and its first derivative is increasing.

If f is a strictly convex function on [0,2], then f(2-x) is a strictly concave function on [0,2]. The sum of a strictly convex and a strictly concave function is also a strictly convex function.

Therefore, since f''(x) = f(x) + f(2-x), it follows that f''(x) is a strictly convex function on [0,2], which means that its first derivative is increasing.

Thus, The answer is C. increasing on (0,2).

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1. The formula to find the measure of each interior angle of a regular n-gon is (180 * (n-2))/n degrees.

2. The formula to find the measure of each individual exterior angle in any polygon is 360/n degrees.

3. The most precise name for the quadrilateral ABCD with the given vertices is a parallelogram.

The formula to find the measure of each interior angle of a regular n-gon is given by:

(180 * (n-2))/n degrees

In a regular n-gon, all interior angles are equal.

The sum of the interior angles of a polygon can be found using the formula:

(n-2) * 180 degrees, where n is the number of sides in the polygon.

Dividing the sum of the interior angles by the number of sides (n) gives us the measure of each interior angle:

(180 * (n-2))/n degrees.

2. The formula to find the measure of each individual exterior angle in any polygon is:

360/n degrees.

In any polygon, the sum of the exterior angles is equal to 360 degrees.

3. To find the measure of each individual exterior angle, we divide the sum of the exterior angles (360 degrees) by the number of sides (n) in the polygon:

360/n degrees.

The precise name for the quadrilateral ABCD is a parallelogram because:

It has opposite sides that are parallel to each other.

It has equal opposite sides.

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The equation can be given as y = 0.4x +22 and the monthly cost is $368.4

What is a linear equation?

A linear equation is an expression whose degree is one. The most general linear equation is y = mx + c. Where m is the slope and c is the y-intercept.

A) To find the equation in the form y = mx + b.

We are given two points (390, 178) and (940, 398).

Now we substitute these points into the standard equation y = mx + c

We get

y = mx + b

178 = m * 390 + b

398 = m * 940 + b

We subtract the two equation we get,

550m = 220

m =0.4

Now we substitute these values in the equation 1 we get

178 = 0.4 * 390 + b

178 = 156 + b

b = 22

So the equation is:

y = 0.4x + 22

B) We are asked to find the cost for 866 minutes we substitute x = 866 in the equation

y = 0.4x + 22

y = 0.4 * 866 + 22

y = 346.4 + 22

y = 368.4

So if 866 minutes are used, the total monthly cost will be $368.4.

The equation can be given as y = 0.4x +22 and the monthly cost is $368.4

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The 17-foot-long ladder pulled out 3 feet farther from the wall from a distance of 8 feet, indicates, using Pythagorean Theorem that the top of the ladder moves about 2.039 feet down the wall.

Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the length of the legs of the right trianglde.

Length of the ladder = 17 foot ladder

Distance of the bottom of the ladder from the wall = 8 feet

The extra distance to which the bottom of the ladder is pulled = 3 feet

The ladder resting on the wall forms a right triangle, with the length of the ladder being the hypotenuse side.

The initial vertical distance reached by the ladder on the wall, h, can be found using Pythagorean Theorem as follows;

h² = 17² - 8² = 225 = 15²

h² = 15²

The initial vertical distance up the wall the ladder reaches, h, is therefore;

h = √(15²) = 15

The ladder initially reaches 15 feet high on the wall

The ladder is then pulled 3 feet farther, from which we get;

New horizontal distance of the ladder from the wall = 8 feet + 3 feet = 11 feet

The square of the new height the ladder reaches up to on the wall, h'², can therefore be found as follows;

h'² = 17² - 11² = 168

√h'² = h' = √(168) = 2·√(42)

The new height the ladder reaches up to on the wall, h' ≈ 2·√(42) feet

The distance the ladder moves down the wall, Δh = h - h', therefore;

Δh = 15 - 2·√(42) ≈ 2.039

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(a) The probability that the vehicle is a crossover is 0.30.

(b) Given that the vehicle is not a passenger car, the probability that it is a pickup truck is 0.50.

(c) The probability that the vehicle is a pickup truck, SUV, or minivan is 0.90.

I determined the probabilities based on the information provided in the problem. The problem states that the probability distribution for the type of vehicle chosen is given and lists the probabilities for each type of vehicle (crossover, pickup truck, SUV, minivan, and passenger car). To find the requested probabilities, I simply used basic probability formulas and the given probabilities for each type of vehicle.

P(pickup truck | not passenger car) = P(not passenger car | pickup truck) * P(pickup truck) / P(not passenger car).

0.40 / (1 - 0.20) = 0.50.

The denominator P(not passenger car) is found by subtracting the probability of a passenger car (0.20) from 1, and the numerator P(not passenger car | pickup truck) is 1, since a vehicle can either be a pickup truck or not a pickup truck but not both. The requested probability is then equal to 0.50.

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The required container of fries costs $1.20, as er the given condition

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let's call the cost of a container of fries "x".

We know that 4 burgers cost 4 * $3.20 = $12.80.

So the total cost of burgers and fries is $12.80 + 3x = $16.40.

Subtracting the cost of the burgers from both sides:

3x = $16.40 - $12.80 = $3.60

Dividing both sides by 3:

x = $3.60 / 3 = $1.20

So each container of fries costs $1.20.

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the confidence intervals for the situation is 46%

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.

the particular week that they had 50 patients the table shows the record numbers of dogs use the given data to complete the sample proportion.

Let's calculate the percentage or proportion of patients that were dogs:

p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46

Hence the confidence intervals for the situation is 46%

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Answer:

He would be 15 years old.

Step-by-step explanation:

If the difference is 15, and sarah is double the age, whatever age the youngest brother is, that number if multiplied by 2 or added to 15 needs to be the same answer. You could make a equation by writing those two on either side of the equation and making the unknown sum “x”. This would look like “2x=x+15”. Then to get the final product you would subtract the x on the right side from both side, ending up to be “x=15” in this scenario, that would be the final answer.

You would need to walk 4 miles less if you walk along the diagonal rather than the two sides.

A key concept in mathematics is the Pythagorean Theorem, which describes the relationship between the sides of a right-angled triangle. Pythagorean triples are another name for the right triangle's sides. Here, examples are used to explain the theorem's formulation and proof.

The Pythagorean theorem is mostly used to determine a triangle's angle and the length of an ambiguous side. The base, perpendicular, and hypotenuse formulas can all be derived using this theorem.

Given that, park is in the shape of a rectangle 8 miles long and 6 miles wide.

The diagonal of the park is calculated using the Pythagoras theorem.

The Pythagoras theorem is given as:

c² = a² +b²

c² = 8² + 6²

c² = 64 + 36

c² = 100

c = 10

If you walk along the diagonal you need to walk 10 miles.

If you walk along the two sides the distance is:

d = 8 + 6 = 14 miles

Hence, the difference between the distance is:

14 - 10 = 4 miles.

Hence, you would need to walk 4 miles less if you walk along the diagonal rather than the two sides.

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Answer:

Zeroes & Multiplicity:

x = 0        :   Multiplicity = 2

x = -6/5   :   Multiplicity = 9

x = 8        :   Multiplicity = 2

Step-by-step explanation:

The equation provided is: [tex]f(x)=x^2(5x+6)^9(x-8)^2[/tex]

We're given the polynomial in factored form, which just means the polynomial is broken down into each of its factors. This is a really convenient form to have a polynomial in as we can easily find the zeroes of the polynomial.

This is due to the Zero Property of Multiplication, which essentially states zero times any number results in zero. So we just have to set each factor equal to zero, and solve, since if one of the factors is zero, then the entire thing becomes zero.

So this gives us the following equations:

[tex]x^2=0\implies x = 0\\\\(5x+6)^9=0\implies x = -\frac{6}{5}\\\\(x-8)^2=0\implies x = 8[/tex]

Now for the multiplicity, we just look at the exponent of the factor we set equal to zero. So x^2 gives us a zero of x = 0, and the exponent is 2, which is also the multiplicity of this zero.

The (5x + 6)^9 gives us a zero of x = -6/5, and the exponent is 9, which is also the multiplicity of the zero. Same thing applies for the zero at x = 8, which has a multiplicity of 2.

Answer:

Step-by-step explanation:

If Charlie buys 3 computer tables for $390, then he paid $390 / 3 = $130 for each table.

Answer: 130 dollars for each table

Step-by-step explanation: Because 3 tables is 390 dollars, we have to divide 390 and 3 to see how much 1 table costs.

390 / 3 = 130

Answer:

a. 1; b. 2; c. 1.

Step-by-step explanation:

1] if the given functions are:

[tex]1: \ h=-3.1d^2+4.8;\\2: \ h=-3.5d^2+1.9;\\3: \ h=-1.1d^2+1.6, \ then[/tex]

2] a. d=0, ⇒ max[h] is no.1 (h=-3.1d²+4.8);

b. h=0, ⇒ min[d] is no.2 (h=-3.5d²+1.9);

c. h=0, ⇒ max[d] is no.1 (h=-3.1d²+4.8).

Answer:

The son is 7 years old.

The father is 35 years old.

Step by step explantation:

Father's age-[tex]5x[/tex]

Son's age-[tex]x[/tex]

[tex]5x+x=42[/tex]

[tex]6x=42[/tex]

[tex]42[/tex]÷[tex]6=7[/tex]

[tex]7[/tex]×[tex]5[/tex][tex]=35[/tex]

Please mark it the brainliest.

First find the actual difference:

   82 - 67 = 15

Now divide that difference by the starting value (82 in this case):

    15 / 82 ≈ 0.182927

Convert that to a percent:

   0.182927 = 18.2927%

That's the percent change, a decrease of about 18.2927%

Answer:

c = 4

Step-by-step explanation:

if (x - a) is a factor , that is divisible by, of f(x) then f(a) = 0

then for p(x) to be divisible by (x - 1) , p(1) = 0

then

2[tex](1)^{4}[/tex] - 5(1)² + c(1) - 1 = 0

2 - 5 + c - 1 = 0

- 4 + c = 0 ( add 4 to both sides )

c = 4

Answers:

1.             The graph is in the shape of a parabola, there is a vertex point at (20, 400), and the zeros (x-intercepts) of the graph are at the origin of the coordinate plane (0, 0) and (40, 0).

2.            The greatest area possible for a rectangle with a perimeter of 80 meters is 400 [tex]m^2[/tex], and the dimensions of this rectangle will be 20 meters in length and 20 meters in width.

3.             The area of the rectangle whose length is 10 meters and the area of the rectangle whose length is 30 meters are the same, both being 300 [tex]m^2[/tex]. This is because the perimeter is set as 80 meters total, and as they are both rectangles, the opposite sides must be the same length.

               For the rectangle with a length of 10 meters, 2 of the 4 sides will use 20 meters of material, so there will be 60 meters of material left for the remaining 2 sides, or 30 meters per side. So the dimensions of that rectangle would be 10 meters in length and 30 meters in width.

               For the rectangle with a length of 30 meters, it's the same thing, except the length is 30 meters, and the width is 10 meters. And for both rectangles, their areas are 30 meters multiplied by 10 meters, which equals 300 [tex]m^{2}[/tex], so the way these two rectangles are related is that they have the same area.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

1.  See below.

2.  400 m²

    20 m x 20 m

3.  300 m²

Step-by-step explanation:

The graph is a parabola that opens downwards.

Its vertex is (20, 400) and its axis of symmetry is x = 20.

From inspection of the given graph, the greatest possible area (y-value) is 400 m².  This is when the length of the rectangle is 20 m.

The largest possible area of a rectangle is when the length equals the width. Therefore, the dimensions of the rectangle with the greatest area possible are:

From inspection of the graph, when the length of the rectangle is 10 m, its area is 300 m².

Similarly, when the length of the rectangle is 30 m, its area is also 300 m².

A rectangle has two pairs of parallel sides of equal length.

Therefore, as both rectangles have the same area, this means that the one pair of parallel sides is 10 m in length and the other pair of parallel sides is 30 m in length.  The dimensions of both rectangles are the same: 10 m x 30 m, where the width and length are interchangeable.

The measurements arranged from smallest to largest are 0.15 cm, 2.5 mm, 0.000035 m, and 4.5 km.

A. 1.5 cm

B. 2.5 x 10^3 mm

C. 3.5 x 10-5 m

D. 4.5 km

Convert all units to the same unit type.

A. 1.5 cm = 15 mm

B. 2.5 x 10^3 mm

C. 3.5 x 10-5 m = 0.000035 m

D. 4.5 km = 4500 m

Arrange the measurements from smallest to largest.

A. 15 mm

B. 2.5 x 10^3 mm

C. 0.000035 m

D. 4500 m

Convert the measurements back to their original units.

A. 15 mm = 0.15 cm

B. 2.5 x 10^3 mm

C. 0.000035 m = 3.5 x 10-5 m

D. 4500 m = 4.5 km

Rearrange the measurements from smallest to largest.

A. 0.15 cm

B. 2.5 x 10^3 mm

C. 3.5 x 10-5 m

D. 4.5 km

Simplify the units to the same unit type.

A. 0.15 cm

B. 2.5 mm

C. 0.000035 m

D. 4.5 km

Rearrange the measurements from smallest to largest.

A. 0.15 cm

B. 2.5 mm

C. 0.000035 m

D. 4.5 km

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The measurements arranged from smallest to largest are:

C. 3.5 x 10^-5 m

A. 1.5 cm

B. 2.5 x 10^3 mm

D. 4.5 km

To arrange the measurements from smallest to largest, it is necessary to convert all the units to the same type. The units in the measurements A, C, and D are different, so they need to be converted.

Measurement A is 1.5 cm, which can be converted to millimeters by multiplying by 10: 1.5 cm x 10 mm/cm = 15 mm.

Measurement C is 3.5 x 10^-5 m, which can be converted to millimeters by multiplying by 1000: 3.5 x 10^-5 m x 1000 mm/m = 3.5 mm.

Measurement D is 4.5 km, which can be converted to millimeters by multiplying by 10^6: 4.5 km x 10^6 mm/km = 4.5 x 10^6 mm.

Now that all the units are in millimeters, the measurements can be arranged from smallest to largest:

Measurement C (3.5 mm) is smallest, followed by Measurement A (15 mm), Measurement B (2.5 x 10^3 mm), and finally Measurement D (4.5 x 10^6 mm) is largest.

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The value of the probability is 0.167

From the question, we have the following parameters that can be used in our computation:

6   7   8

The probability of picking a 8 on the first draw and then picking a number above 7 on the second draw is:

P(6 and then >7) = P(6) x P(>7 | 6)

Given that the cards are not replaced, we have

P(6 and then >7) = 1/3 * 1/2

Evaluate

P(6 and then >7) = 0.167

Hence, the probability is 1/6

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The value of x is 65°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:
Angle PQR is a right angle.

The measure of angle SQR is 25 degrees.

The measure of PQS is x degrees.

The angle addition postulates:

∠PQR = ∠SQR  + ∠PQS

90° = 25° + x

x = 90° - 25°

x = 65°

Hence, ∠PQS = 65°.

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Answer:

D because angle U is equal to angle W because it is diverting angle

The mean of the probability distribution is 3.188, the sampling distribution is 2.25 and x is an unbiased estimator.

a. To find the mean (u) of a probability distribution, we calculate the expected value as follows:

u = ∑x * p(x) = (0.5 * 0.0625) + (2.5 * 0.125) + (0.25 * 0.25) + (0.25 * 0.25) + (0.25 * 0.25) = 2.25

To find the variance (o^2) of the distribution, we calculate it as follows:

o^2 = ∑(x - u)^2 * p(x) = (0.5 - 2.25)^2 * 0.0625 + (2.5 - 2.25)^2 * 0.125 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 = 0.5625

So, o = √0.5625 = 3.188

b. The sampling distribution of the sample mean x for a random sample of n=2 measurements from this distribution is given by:

x = (x1 + x2) / n = (2.25 + 2.25) / 2 = 2.25

As n approaches infinity, the sample mean x approaches the population mean u, and the distribution of x becomes more and more concentrated around u.

c. Yes, x is an unbiased estimator of u because its expected value is equal to the population mean: E(x) = u.

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Required value of (1513÷3) is 504R1.

What is division?

Division is the opposite of multiplication. If 3 groups of four are multiplied by 12, 12 divided into three equal groups gives 4 in each group.

The main purpose of distribution is to see how many equal groups are formed or how many are in each group in a fair distribution.

In the above example, to divide the 12 donuts into 3 similar groups, you need to put 4 donuts in each group. So, 12 divided by 3 is 4.

Here given two digits are 1513 and 3.

We want to find value of 1513 ÷ 3.

Now,

[tex]1513 ÷ 3 = \frac{1513}{3} = 504 R1[/tex]

Therefore, the quotient is 504 and the remainder is 1.

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The total surface area of the composite shape is 488.7 in².

What is a composite shape?

A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently. Every day, composite shapes are around us.

The given composite shape can be divided into multiple shapes, to find the area easily.

For the given question, we can see that the lower portion of the shape is a cuboid and the upper portion is half of the cylinder cut vertically.

We find the areas of the figures separately.

Area of cuboid

Length l = 6 in.

Breadth b = 10 in.

Height h = 8 in.

Area = Area of each faces =  2(lb) + 2(bh) +2(lh)

                                             = 2(6*10) + 2(10*8) + 2(6*8)

                                               = 2*60 +2* 80 + 2* 48

                                                 = 376 in²

Area of cylinder

Radius of semicircles r = 5 in.

Height of cylinder h = 6 in.

Area =  Area of semicircles + Area of half of the curved surface

        =  2 *1/2 * πr² + 1/2 * 2πrh =  πr² + πrh = 3.14 * 5² + 3.14 * 5 * 6

                                                                 = 172.7 in²

The total surface area of the composite shape = Area of cylinder + Area               of cuboid - Area of the common surface(rectangle)

                = 172.7  + 376 - (l *b) = 548.7 - ( 10*6) = 488.7 in²

Hence the total surface area of the composite shape is 488.7 in².

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Answer:

y=1.25x+10

Step-by-step explanation:

you can put this into the formula “y=mx+b”. y is the final amount, x is how many times joana gets food or goes on a ride. You can plug into the equation the two parts we know. We know that no matter what, if she goes into the fair, she is going to spend $10 on the admission, even if she does not go on any rides or gets any food. So we put 10 where the “b” is. Then each time she gets food or goes on a ride, she pays another $1.25. Therefore, you can plug 1.25 into where the m is. That leaves you with “y=1.25x+10”.

Method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.

A relation is a function if it has only One y-value for each x-value.

One method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.

To do this, you can start by selecting a set of corresponding terms from each sequence and attempt to express the relationship between them using mathematical operations.

It's important to note that finding a mathematical relationship between two sequences can sometimes be difficult, and in some cases may not be possible.

In such cases, it may be helpful to analyze the sequences using other methods, such as graphical representation or statistical analysis, to gain insight into their behavior.

Hence, method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.

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Answer:

The area of the top of the crate can be found by multiplying the length by the width.

        3/4 yard = 9/12 yards

        2/4 yard = 6/12 yards

    2. Now we can find the area by multiplying the length by the width:

     Area = 9/12 yards * 6/12 yards = (9/12) * (6/12) = 3/4 * 1/2 = 3/8                         yards^2

So, the area of the top of the crate is 3/8 yards^2.

Answer:

$40

Step-by-step explanation:

We know

Her father gave her $20 for every $50 she saved

$50 + $20 = $70

$50 + 20 + 50 + 20 = $140

$182 - $140 = $42

It is not $50 yet, so her father only give her 2 times

So, her father gives her $40

Answer:

182÷50 = 3.64, 3.64x20=72.8$

her dad gave her 72.8$

Answer:

The vertex of the parabola is at x = 3, and a point on the parabola can be (4, 0). Here is a Brainly link that can provide you with more information about graphing the function f(x) = (x+2) (x-4): https://brainly.com/question/31009433.

The triangles are not similar because the dimensions of GDM are larger than those of PQR.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

Even though triangles GDM and PQR have the same angle measure, the triangles are not congruent / similar because they are not the same size. Triangle GDM is larger than PQR and so is not congruent to it.

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