Julia found the equation of the line perpendicular toy = -2x + 2 that passes through (5.-1).Analyze Julia's work. Is she correct? If not, what washer mistake?1 y25= 1/2 (-2) + 6Yes, she is correct,No, she did not use the opposite reciprocal for theslope of the perpendicular line.No, she did not substitute the correct x and yvaluesNo she did not apply inverse operations to solve forthe y-intercept.3+5b=555y=x5.5

As, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively. So,  if a commutes with d, then it must be block diagonal.

Let's suppose that d is a diagonal matrix with repeated diagonal entries grouped contiguously, i.e.,

d = \(\begin{pmatrix} D_1 & 0 & 0 & \cdots & 0 \ 0 & D_1 & 0 & \cdots & 0 \ 0 & 0 & D_2 & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & D_k \end{pmatrix}\),

where \(D_1, D_2, \dots, D_k\) are scalars and appear with frequencies \(m_1, m_2, \dots, m_k\), respectively, so that \(m_1 + m_2 + \dots + m_k = n\), the size of the matrix.

Suppose that \(a\) is a matrix that commutes with d, i.e., ad = da.

Then, for any \(i \in {1, 2, \dots, k}\), we have

\(ad_{ii} = da_{ii}\)

Here, \(d_{ii}\) denotes the \(i$th\) diagonal entry of d, i.e., \(d_{ii} = D_i\) for \(i = 1, 2, \dots, k\). Since d is diagonal, \(d_{ij} = 0\) for \(i \neq j\), and

hence

\(ad_{ij} = da_{ij} = 0\)

for all \(i \neq j\).

Therefore, a is also diagonal, with diagonal entries \(a_{ii}\), and we have

\(a = \begin{pmatrix} a_{11} & 0 & 0 & \cdots & 0 \ 0 & a_{11} & 0 & \cdots & 0 \ 0 & 0 & a_{22} & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & a_{kk} \end{pmatrix}\)

Thus, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively.

Therefore, if a commutes with d, then it must be block diagonal.

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Answer:

the answer to the first question is the first one and the second answer might be the second one

The first condition is that there must be at least 3 hamburgers or 3 bratwursts for each of the 30 participants. This means that the sum of hamburgers and bratwurst must be at least 90. This can be expressed as:

The second condition says that the maximum amount to pay is $120, this means that the total cost of hamburgers and bratwurst must be less than $120. This can be expressed as:

Therefore, the system that represents the situation is:

Nope, it sure isn't, because both pairs of its opposite sides are not parallel.

Trapezoid IS NOT a parallelogram. A parallelogram is a given shape with BOTH pairs of its opposite sides are parallel.

Answer:

Area = 81ft^2

Step-by-step explanation:

           _______________________________

          |                                                                    |

          |             ___________________             |

          |             |                  14ft                 |             |

          |             | 10ft                                  |             |

          |     3ft    |                                        |             |

          |             | __________________|             |

          |                                                                    |

          |_______________________________|

To find the area, first do the Area of the entire pool (10ft x 14ft) then do the area of the tiled section ( (10ft+3ft) x (14ft+3ft) ) then subtract them

10ft x 14ft = 140ft^2 for the pool

13ft x 17ft = 221ft^2 for both tile and pool

221ft^2 - 140ft^2 = 81ft^2 for the tile

Answer:

54

Step-by-step explanation:

If we know that Josh edits at a rate of 1/6 of a page in three minutes... then using the Unit rule... we can determine that he edits 1 whole page 6 times longer than that. By doing that... we find that Josh edits 1 page in 18 minutes. From there... we multiply the time at which it takes him to edit one page (18 minutes) by 3 (pages) to get our answer.

18 x 3 = 54

Answer:

False

Step-by-step explanation:

The sum of angles of a parallelogram is equal to 180°. So,

8x+3y+2x+(7x+18)=180

or

17x+3y = 180-18

17x+3y = 162

Put x = 44 and y = 18 in the above expression.

So,

17(44)+3(18) = 748+54

= 802

≠ 162

Hence, the given statement is false.

Answer:

The original price is 180$

Answer:

Step-by-step explanation:

If there is a 10 percent discount, that means that this is 90 percent of the total.

So, let us find 10 percent is made up of how many dollars.

$162/9=$18 (do note that the slash sign means divide! When you write down the equation on a paper, please write the actual divide sign. Sorry for the inconvenience)

Since the original price is 100 percent, and we have 10 percent, that means we can just multiply the 10 percent by 10, to get 100 percent, as 10 times 10 is hundred.

$18x10=$180

Hope this helped! If you need another method, along with a different explanation, or separate, do comment below, so I can know. Any part you do not understand, please don't be afraid to tell me. If you think I can improve my answer, or change any parts to perhaps make it clearer, i'm open to suggestions!

Considering the vertex of the quadratic equation, it is found that the value of b is of b = 3.

A quadratic equation is modeled by:

y = ax^2 + bx + c

The vertex is given by:

\((x_v, y_v)\)

In which:

The axis of symmetry is of \(x = x_v\). In this problem, we have that a = 0.25 and x_v = 6, hence:

b/2a = 6.

b/0.5 = 6

b = 6 x 0.5

b = 3.

The value of b is of b = 3.

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The question that can be best modeled as a division expression is how many 3/8's are in 48.

Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The other mathematical operations are addition, multiplication and division.

In order to determine the 3/8's in 48, divide 48 by 3/8.

In order to determine 3/8 of 48, multiply 48 by 3/8.

In order to determine the total of 3/8 and 48, add the numbers together.

In order to determine how much more than 3/8 is 48, subtract 3/8 from 48.

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Answer:  its  correct

Step-by-step explanation:

Answer:

11 1/4

Step-by-step explanation:

Add all whole numbers first

4+4+2= 10

Then add the numerators since the denominator is the same

1/4 + 3/4 + 1/4= 5/4  

5/4= 4/4 and 1/4    4/4 is a whole number = 1

10+1 = 11

11 1/4

Answer:

11 1/4

Step-by-step explanation:

4 + 4 + 2 = 10

1/4 + 3/4 + 1/4 = 5/4

5 divided by 4 = 1.25

0.25 as a fraction is 1/4

1.25 as a fraction is 1 1/4

So u add the 1 to 10 which is 11

Now u put the answer together which is 11 1/4

Step-by-step explanation:

The probability that Becky's proportion of poses held for over a minute is greater than Carla's is 0.741.

This can be determined by using the z-table, which shows the probability that a random variable is in the range that is a certain distance away from the mean.

In this case, we are looking at the probability that a random variable is greater than C, so we use the z-value for 0.741.

Answer:

Adding +6 in turn

Step-by-step explanation:

-13+6=(-7)

(-7)+6=(-1)

(-1)+6=5

5+6=11

11+6=17

17+6=23

23+6=29

29+6=35

........... And so on

Answer:

Hello,

Step-by-step explanation:

1) boys

\(\overline{x}=\dfrac{\displaystyle \sum_{i=1}^n\ x_i}{n}\\\\\Longrightarrow\ \displaystyle \sum_{i=1}^n\ x_i=n*\overline{x}=15*74=1110\\\\\\var=\sigma^2=\dfrac{\displaystyle \sum_{i=1}^n\ x_i^2}{n}-\overline{x}^2\\\\\Longrightarrow\ \displaystyle \sum_{i=1}^n\ x_i^2=n*(var+\overline{x}^2)=15*(1046.25+74^2)=97833,75\\\)

2) females

\(\displaystyle \sum_{i=1}^n\ x_i=n*\overline{x}=12*77=924\\\\\displaystyle \sum_{i=1}^n\ x_i^2=n*(var+\overline{x}^2)=12*(948.64+77^2)=82531,68\\\)

3)exam test

\(n=15+12=27\\\displaystyle \sum_{i=1}^n\ x_i=1110+924=2034\\\\\displaystyle \sum_{i=1}^n\ x_i^2=97833,75+82531,68=180365,43\\\\\)

\(var=m_2-m_1^2=180365.43/27-75,33333333^2=1005,09\)

Answer:

bye

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

Simply, multiply 75x0.18 = 13.5

0.18 (being the percentage)

if the percentage tipped was 8% then you would multiply 75 by 0.08

Answer:

A.  4

Step-by-step explanation:

Given inequality:

\(x+9 < 4x\)

Rearrange the inequality to isolate x.

Subtract x from both sides of the inequality:

\(\begin{aligned}x+9-x & < 4x-x\\9& < 3x\end{aligned}\)

Divide both sides of the inequality by 3:

\(\begin{aligned}\dfrac{9}{3}& < \dfrac{3x}{3}\\\\3& < x\\\\x& > 3\end{aligned}\)

So the values of x that make the inequality true are:

Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.

To check this, substitute x = 4 into the inequality:

\(\begin{aligned}x+9& < 4x\\x=4\implies 4+9& < 4(4)\\13& < 16\end{aligned}\)

As 13 is less than 16, the inequality is true when x = 4.

Answer:

independent variable is the shape of the paper

dependent variable is the time it takes to fall

Answer:

x = -0.55

Step-by-step explanation:

When we use the quadratic formula, we should get the roots -14.45 and -0.55 for this quadratic.

Answer:

\(8*10^3\)

Step-by-step explanation:

\(\frac{6.4*10^6}{8*10^2} \\=\frac{64*10^{-1}*10^6}{8*10^2}\\=\frac{64*10^5}{8*10^2}\\=8*10^{(5-2)}\\=8*10^3\)

2. The transformations are given as follows:

3. The transformations are given as follows:

For item 2, the transformations in this problem are given as follows:

For item 3, the transformations are given as follows:

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Mathematical induction is a method used to prove statements for all positive integers.

To prove the formula 1 + 2 + 3 + ... + (n-1) + n = n(n+1)/2 using induction,

we first show it holds for the base case n = 1.

When n = 1, the formula becomes 1 = 1(1+1)/2, which is true.

Then, we assume the formula holds for some integer k, and prove it holds for k+1.

Inductive step: Assume that the formula holds for some integer k, i.e., 1 + 2 + ... + (k-1) + k = k(k+1)/2. We need to prove that the formula also holds for k+1.

So, 1 + 2 + ... + (k-1) + k + (k+1) = k(k+1)/2 + (k+1) = (k+1)(k+2)/2, which shows that the formula holds for k+1 as well.

By repeating this process, we conclude the formula holds for all positive integers.

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Answer: \(2\sqrt{13}-\sqrt{697}\)

Step-by-step explanation:

Since ABD is a right triangle, 14^2 = 12^2 + BD^2

196 = 144 + BD^2

52 = BD^2

BD = \(\sqrt{52} = 2\sqrt{13}\)

ADC is also a right triangle, so 29^2 = 12^2 + DC^2

841 = 144 + DC^2

DC^2 = 697

DC = \(\sqrt{697}\)

Since x = BD + DC,

x = \(2\sqrt{13} +\sqrt{697}\) :>

a.  the probability of getting exactly 3 cards from the heart suit is approximately 0.0585. b.  the probability of getting 4 or fewer cards from the heart suit is approximately 0.7681. c. the probability that every card in the hand is from a different suit is approximately 0.395. d. the probability that every card in the hand is red or every card in the hand is black is approximately 0.00198.

(a) To calculate the probability of getting exactly 3 cards from the heart suit, we can use the combination formula:

number of ways to choose 3 hearts out of 13 hearts * number of ways to choose 2 non-hearts out of 39 non-hearts / number of ways to choose 5 cards out of 52 cards

= (13 choose 3) * (39 choose 2) / (52 choose 5)

= 0.0585 (rounded to 4 decimal places)

Therefore, the probability of getting exactly 3 cards from the heart suit is approximately 0.0585.

(b) To calculate the probability of getting 4 or fewer cards from the heart suit, we can use the complement rule:

1 - (number of ways to choose 5 non-hearts out of 39 non-hearts / number of ways to choose 5 cards out of 52 cards)

= 1 - (39 choose 5) / (52 choose 5)

= 0.7681 (rounded to 4 decimal places)

Therefore, the probability of getting 4 or fewer cards from the heart suit is approximately 0.7681.

(c) To calculate the probability that every card in the hand is from a different suit, we can use the multiplication principle:

number of ways to choose 1 card of each suit / number of ways to choose 5 cards out of 52 cards

= (13 choose 1) * (13 choose 1) * (13 choose 1) * (13 choose 1) / (52 choose 5)

= 0.395 (rounded to 3 decimal places)

Therefore, the probability that every card in the hand is from a different suit is approximately 0.395.

(d) To calculate the probability that every card in the hand is red or every card in the hand is black, we can use the addition rule:

probability of all red cards + probability of all black cards

= (26 choose 5) / (52 choose 5) + (26 choose 5) / (52 choose 5)

= 0.00198 (rounded to 5 decimal places)

Therefore, the probability that every card in the hand is red or every card in the hand is black is approximately 0.00198.

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Answer:

\(x=\frac{In(0.5)-1}{2}\)

Step-by-step explanation:

Just took the test - this is correct

Answer:

x = 55

Step-by-step explanation:

A triangle has angles that add up to 180, so lets make an equation

25 + 100 + x = 180

125 + x         = 180

-125                -125

         x         = 55

Tell me in the comments of this answer if you have any questions! If you could mark this answer as the brainliest, I would greatly appreciate it!

If a package of 5 pairs of insulated gloves costs $28.955,then the unit price of the pairs of gloves is $5.791

A package of 5 pairs of insulated gloves costs ​$28.955

The price of 5  pairs of insulated gloves = $28.955

Here we have to use the unitary method

The price of 1 pair of insulated gloves = The price of 5  pairs of insulated gloves / 5

Substitute the values in the equation and divide it

The price of 1 pair of insulated gloves = 28.955/5

= $5.791

Hence, if a package of 5 pairs of insulated gloves costs $28.955,then the unit price of the pairs of gloves is $5.791

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The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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