If Ying Zyiyu covers the first 200 miles of a trip going 50mph. and the last hundred going 40mph, what was his average speed for the entire trip?

Final answer:

The smallest possible dimension for the null space of a 13 by 91 matrix is 78. This is determined using the Rank-Nullity Theorem, taking into account that the rank of a matrix cannot exceed the number of its rows.

Explanation:

The question pertains to the dimension of the null space (also known as the nullity) of a matrix 'a.' The dimensions of matrix 'a' are 13 by 91, which means it has 13 rows and 91 columns. The null space of a matrix 'a' is the set of all vectors that, when multiplied by 'a,' give the zero vector. The dimension of the null space is referred to as the nullity of 'a.'

To find the smallest possible dimension of the null space, we consider the Rank-Nullity Theorem, which states that for any matrix 'A' of size m by n, the rank of 'A' plus the nullity of 'A' is equal to n, the number of columns in 'A.' The maximum rank a matrix can have is limited by the smaller of the number of rows or columns, so for matrix 'a' with dimensions 13 by 91, the maximum rank is 13 since there are only 13 rows.

Using the Rank-Nullity Theorem, we can say:

Therefore, the smallest possible dimension for the null space of matrix 'a' is 78.

Answer:

65

Step-by-step explanation:

divide them

17.16/0.624 = 27.5

27.5 is the answer

double check by multiplying 27.5 by 62.4%

27.5*.624 = 17.16

To solve this problem, let us assume linear motion so that we can use the equation:

t = d / v

where t is time, d is distance and v is velocity

First let us assign some variables, let us say that the velocity upstream is Vu while Velocity downstream is Vd, so that:

35 / Vu + 55 / Vd = 12                     ---> 1

30 / Vu + 44 / Vd = 10                     ---> 2

We rewrite equation 1 in terms of Vu:

(35 / Vu + 55 / Vd = 12) Vu

35 + 55 Vu / Vd = 12 Vu

12 Vu – 55 Vu / Vd = 35

Vu (12 – 55 / Vd) = 35

Vu = 35 / (12 – 55 / Vd)                  ---> 3

Also rewriting equation 2 to in terms of Vu:

Vu = 30 / (10 – 44 / Vd)                  ---> 4

Equating 3 and 4:

35 / (12 – 55 / Vd) = 30 / (10 – 44 / Vd)   

35 (10 – 44 / Vd) = 30 (12 – 55 / Vd)

Multiply both sides by Vd:

350 Vd – 1540 = 360 Vd – 1650

10 Vd = 110

Vd = 11 km / h

Using equation 3 to solve for Vu:

Vu = 35 / (12 – 55 / 11)

Vu = 5 km / h

Answers:

Vu = 5 km / h = velocity upstream

Vd = 11 km / h = velocity downstream

The solutions to the equation 15 tan^3 x=5 tan x in the interval [0, 2π) are approximately x = 0.6155, x = 3.757, x =2.527, x = 5.669.

The trigonometric equation provided in the question is 15 tan3 x=5 tan x. We can start solving this equation by dividing both sides by tan x, which gives 15 tan2 x = 5. Dividing again by 5, we get tan2 x = 1/3. The solutions to tan2 x = 1/3 are values of x in the interval [0, 2π) where the square of the tangent of x equals 1/3. However, these values cannot be easily computed, thus we use a calculator to approximate the results. We find the solutions to the equation by considering all angles whose tangent is either sqrt(1/3) or -sqrt(1/3). Therefore, the solutions for x in the interval [0, 2π) are approximately x = 0.6155, x = 3.757, x = 2.527, x = 5.669.

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#include< stdio.h;
// #include< math.h;
int main() {
int I = 0;
double value[8];
for(I = 0; I < ;8; i++){
printf(“Enter value at index %d: “; (i +1 ));

Please note, always use %lf and not %f when reading double data from the user. double is %lf, while float is %f. That is the difference.

In this problem, we use two headers, stdio.h and math.h. The math.h defines a lot of mathematical functions. It returns double as a result since all functions in this library takes double as an argument.

The stdio.h header defines 3 variable types, namely size_t, FILE, and fpos_t.

Answer:

Step-by-step explanation:

The easiest way is to divide the number by 100, 10 and 1 in that order so:

15638/100=156.38 <- From this number you take only the integer (or the number without decimals), and that would be your hundreds, for this case 156 is the integer part, so 156 hundreds.

Next we take take the 38 we had left from the above division, and we divide it by 10.

38/10=3.8   <- we apply exactly the same steps as before but with the tens, working only with the integer, meaning 3, so you end up with 3 tens.

Last but not least, the rest, that is 8, will be your ones. In this case, just 8 ones.

Now, the combinations are infinite, if you take one from the hundreds it becomes 10 tens or 100 ones, and if you take 1 from the tens you get 10 ones. So you could have

155 hundreds (155-1), 12 tens (3+10-1), and 18 ones. Or any permutation you prefer.

For quick studies, it is easier to round down to the nearest 5 or 0, so another way to see this would be:

155 hundreds, 10 tens, and 38 ones.

The probability that the card chosen is not a heart is 0.75

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

Sample space ={13 H + 13 D + 13 S + 13 C}

= 52 cards

The total number of cards in a deck is 52

Number of cards with hearts = 13

Therefore, P(getting one heart) = 13/52 = 1/4

P( getting NO heart) = 1-1/4 = 3/4 = 0.75

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The question asks for the required contact area between a suction cup and a ceiling to support an 80.0 kg person. Using principles of physics pressure calculations, a suction cup with a minimum contact area of 7.74 cm² would be needed.

The subject of your question is physics given it requires an understanding of pressure, force, and area relationships. To keep the suction cup adhered, the pressure difference between the lower (inside) of the suction cup and the outside (room pressure) must be large enough to support the weight of the person. This principle makes use of a simple physics equation: Pressure = Force/Area.

To support an 80.0-kg person, the force exerted due to weight would be mass multiplied by gravity or 80.0 kg * 9.8 m/s² = 784 N. The atmospheric pressure is about 101,325 Pascal (Pa) or N/m². Rearranging the equation for Pressure will give us the needed area: Area = Force/Pressure. So, the necessary contact area would be 784 N / 101325 Pa ≈ 0.00774 m² or 7.74 cm².

This means, that in ideal conditions and neglecting factors such as surface roughness, a suction cup with a contact area of at least 7.74 cm² would be needed to support an 80.0-kg person.

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The expression 3(8 + 7) is equivalent to 45. The calculation follows the distributive property rule in mathematics, whereby we first simplify the expression inside the parentheses before multiplication.

The mathematical expression of 3(8 + 7) is based on the principle of distribution in mathematics. This principle can be interpreted as 'spread' or 'distribute' and applies when you multiply a number by addends within parentheses.

For the given expression 3(8 + 7), do the operation inside the parentheses first. So 8 + 7 equals 15. Now the expression becomes 3(15).

To find the solution, just multiply 3 by 15, which equals 45. So, 3(8 + 7) is equivalent to 45.

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to calculate circumference you can either use

 2 x PI x r

 or

pi x d

Answer:

PI X D

Step-by-step explanation:

Have a nice day :)

Step 1

Find the value of s

we know that

In a Rhombus all sides are congruent

so

[tex]AB=BC=CD=DA[/tex]

[tex]AB=9s+29\\CD=10s-16[/tex]

equate AB and CD

[tex]9s+29=10s-16\\[/tex]

Combine like term

[tex]10s-9s=29+16\\[/tex]

[tex]s=45\ units[/tex]

The answer Part a) is

the value of s is [tex]45\ units[/tex]

Step 2

Find the value of side AB

[tex]AB=9s+29[/tex]

substitute the value of s

[tex]AB=9*45+29=434\ units[/tex]

Remember that the sides are congruent

[tex]AB=BC=CD=DA[/tex]

therefore

the answer Part b) is

The length of the side BC is [tex]434\ units[/tex]

The value of s is 45 and the length of side BC is; 434.

A rhombus is a plane shape of the form given I'm the attached image with all its sides equal.

Hence,

To determine the value of s;

The length of side BC = CD = 10(45) - 16 = 450 - 16

The length of side BC = 450 -16 = 434

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Answer:

A

Step-by-step explanation:

The best location for the satellite coordinates is

(Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3).

We have,

From the figure given,

Assume that the coordinates of the three families are:

Sanchez = (a, b)

Perez = (c, d)

Reyes = (e, f)

The point equidistant from all three families' coordinates can be calculated using the formula.

Midpoint = ((m + o) / 2, (n + p) / 2)

Where (m, n) and (o, p) are the coordinates.

Midpoint between Sanchez and Perez:

Midpoint(SP) = A = ((a + c) / 2, (b + d) / 2)

Midpoint between Perez and Reyes:

Midpoint(PR) = B = = ((c + e) / 2, (d + f) / 2)

Midpoint between Sanchez and Reyes:

Midpoint(SR) = C = ((a + e) / 2, (b + f) / 2)

Equidistant Point

= (Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3)

Where "Ax" represents the x-coordinate of the midpoint between Sanchez and Perez, Bx" represents the x-coordinate of the midpoint between Perez and Reyes, and Cx" represents the x-coordinate of the midpoint between Sanchez and Reyes. Similarly, Ay, By, and Cy" represent the y-coordinates of the respective midpoints.

Thus,

The best location for the satellite coordinates is

(Ax + Bx + Cx) / 3, (Ay + By + Cy) / 3).

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To calculate the number of different ways 30 qualifiers can be selected from 50 competitors in a ski jumping event, use the combination formula C(n, k) = n! / (k!(n - k)!), where in this case n=50 and k=30.

The question here is focused on finding the number of different combinations in which the qualifying round can be selected from a group of competitors in a sport event, specifically men’s ski jumping. This falls under the category known as combinatorics, which is a part of mathematics that deals with counting, both in a concrete and abstract way, as well as finding certain properties of finite structures.

The total number of different ways 30 competitors can be chosen from a group of 50 can be found using the combination formula, which is expressed as C(n, k) = n! / (k!(n - k)!), where "n" is the total number of competitors, "k" is the number of competitors to choose, "n!" signifies the factorial of "n", and "(n - k)!" is the factorial of the difference between "n" and "k".

In this situation, to find the number of different ways to select the 30 qualifiers from 50 competitors, we plug the values into the formula to calculate C(50, 30).

Final answer:

To find the number of different ways the qualifying round can be selected, you need to use combinations. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of competitors and r is the number of competitors moving on to the qualifying round.

Explanation:

To find the number of different ways the qualifying round can be selected, we need to use combinations. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of competitors and r is the number of competitors moving on to the qualifying round.

In this case, n = 50 and r = 30. Plugging these values into the formula, we get C(50, 30) = 50! / (30!(50-30)!). Simplifying this expression, we find that C(50, 30) = 211915132760.

Therefore, there are 211,915,132,760 different ways the qualifying round can be selected.

To solve this problem, we make use of the z statistic. We are to look for the bottom 8% who has the shortest lifespan, this is equivalent to a proportion of P = 0.08. Using the standard distribution tables for z, the value of z corresponding to this P value is:

z = -1.4

Now given the z and standard deviation s and the mean u, we can calculate for the number of years of the shortest lifespan:

x = z s + u

x = -1.4 (0.7) + 2.4

x = -0.98 + 2.4

x = 1.42 years

Therefore the life span is less than about 1.42 years

Answer:

The number of identical containers are 27

Step-by-step explanation:

The picture below shows a container that Sue uses to freeze water.

We need to make 2000 cm³ of ice using small identical container.

Volume of cylinder [tex]=\pi r^2 h[/tex]

Where,

r = radius of cylinder (r=2 cm)

h = height of cylinder ( h=6 cm)

Volume of small cylinder [tex]=\pi (2)^2\cdot 6 = 75.39\text{ cm}^3[/tex]

We need to find number of small cylinder.

[tex]\text{Number pf small cylinder }=\dfrac{\text{Volume of ice}}{\text{Volume of each cylinder}}[/tex]

[tex]\text{Number pf small cylinder }=\dfrac{2000}{75.39}\approx 27[/tex]

Hence, The number of identical containers are 27

Answer:

The company pays $60 a day for food and lodging and $0.65 for each mile traveled.

David drove 600 miles and was reimbursed $3,390.

Part A:

Let the number of days of trip be = x

Equation forms:

[tex]600(0.65)+60x=3390[/tex]

=> [tex]390+60x=3390[/tex]      .......(1)

Part B:

Solving (1) for x.

[tex]390+60x=3390[/tex]     (given)

Applying subtraction property of equality;

[tex]60x+390-390=3390-390[/tex]

Now simplifying this we get;

[tex]60x=3000[/tex]

Applying division property by dividing 60 on both sides, we get

x = 50

Part C:

We get x = 50, so David spent 50 days on the trip.

Since there is no angle restriction in this case, therefore the one rule that is applicable to this is that in forming a triangle, the sum of the lengths of the two smaller sides (A + B) should be larger than the length of the biggest side (C):

Triangle length rule: Side A + Side B > Side C

We can see that no matter how we combine the rods, the only combination of rods that satisfies this rule is:

 Triangle formed by rods 3 meters, 5 meters, and 7 meters

Therefore, there is only 1 triangle that can be formed from these four rods.