Let y= [2 3] and u=[4 −7] . write y as the sum of two orthogonal vectors, one in span {u} and one orthogonal to u.

Answer:

M= 7/3 hope that helps ya out

The value of x in the given image is 19.4.

The image shown is of two intersecting lines, which create eight angles. Two of these angles are marked as 4x - 5 and 5x + 10. We are required to identify the relationship between these two angles and then find the value of x for these angles

.Let's start with identifying the relationship between these two angles. When two lines intersect, they create eight angles. Of these eight angles, four are adjacent angles that form linear pairs, four are opposite angles that form vertical angles, and four are non-adjacent angles that form supplementary angles.

Let's check which relationship applies to angles 4x - 5 and 5x + 10.To form a linear pair, two adjacent angles should add up to 180 degrees. The angles 4x - 5 and 5x + 10 are not adjacent angles, so they can't form a linear pair.To form a vertical angle, two non-adjacent angles should be formed by intersecting lines.

Since the angles 4x - 5 and 5x + 10 are not opposite to each other, they can't form vertical angles.To form supplementary angles, two non-adjacent angles should add up to 180 degrees. The angles 4x - 5 and 5x + 10 are non-adjacent and add up to 180 degrees.

Therefore, they form supplementary angles.Now, we can set up an equation:4x - 5 + 5x + 10 = 180Combining like terms, we get:9x + 5 = 180Subtracting 5 from both sides, we get:9x = 175 Dividing by 9 on both sides, we get:x = 19.4

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Answer:

x=8

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

4x+6−6=38−6

4x=32

Step 2: Divide both sides by 4.

Answer:

x=8

Step-by-step explanation:

Answer:

Step-by-step explanation:

A = P(1-r)^n

A = 35098(1-2.33%)^13

   = $25 833.18

"15 + r" is the expression that represents the total number of rows knitted by Christine. Thus, option B is correct.

To find the total number of rows Christine has knit, we need to add the number of rows she knit over the weekend (represented by the variable "r") to the number of rows she had already knit (15).

This can be done by using the expression:

This expression states that the total number of rows is equal to the initial number of rows (15) plus the additional rows knit over the weekend (represented by the variable "r"). The value of "r" could be any number, so the expression "15 + r" could represent any total number of rows.

For example, if Christine knit 5 more rows over the weekend, the expression "15 + 5" would equal 20, so Christine has knit a total of 20 rows.

This question should be provided as:

Christine had already knit 15 rows of a scarf. She knitted r more row over the weekend. Choose the expression that shows the number of rows Christine has knitted in all.

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Answer:

40%

Step-by-step explanation:

24/60 = .4

Answer:

40%

Step-by-step explanation:

Divide the total by the amount possible.

An expected 479,512 duplicates of the book have been offered to date. The principal month of delivery is 38,900 and addresses 8.1% of the absolute number of duplicates offered to date.

On the off chance that the quantity of duplicates sold in the main month of delivery is 38,900 and addresses 8.1% of the absolute number of duplicates offered to date, then, at that point, we can utilize this data to appraise the all out number of duplicates offered to date. To do as such, we partition the quantity of duplicates sold in the primary month by the rate portrayal:

38,900 ÷ 0.081 = 479,512

A book has sold 38,900 duplicates in its most memorable month of delivery. This is viewed as 8.1% of the absolute number of duplicates offered to date. To decide the absolute number of duplicates offered, we can utilize this data to appraise the quantity of duplicates offered to date. To do this, we take the quantity of duplicates sold in the main month and gap it by the rate portrayal of the primary month deals comparable to add up to deals. Partitioning 38,900 by 0.081 provides us with an expected absolute of 479,512 duplicates offered to date. This assessment expects that the pace of deals in the principal month is illustrative of the general deals pattern. In any case, minus any additional data about deals in ensuing months, this assessment ought to be taken with alert.

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The exact value of A in the general solution is 87/2 and B is 0

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

y = Ax² + Bx + C

The differential equation is given as

y' = 87x

When y = Ax² + Bx + C is differentiated, we have

y' = 2Ax + B

So, we have

87x = 2Ax + B

By comparing both sides of the equation, we have

2Ax = 87x

B = 0

So, we have

2A = 87

B = 0

Divide both sides of 2A = 87 by 2

A = 87/2

B = 0

Hence, the value of A in the general solution is 87/2 and B is 0

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Answer: 7

Step-by-step explanation:

i wish i knew why

To find the length of QR in triangle PQR, we can use the trigonometric ratio known as the sine function.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Given that angle P = 26° and the length of PQ = 8.5 feet, we can use the sine function to find the length of QR.

sin(P) = Opposite / Hypotenuse

sin(26°) = QR / 8.5

To solve for QR, we can rearrange the equation:

QR = sin(26°) * 8.5

Using a calculator, we find:

QR ≈ 3.6761 * 8.5

QR ≈ 31.2449

Rounding to the nearest tenth, the length of QR is approximately 31.2 feet.

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Answer:

c. $13. 43

Step-by-step explanation:

Here's the simple interest formula: Interest = P x R x N. P = Principal amount (the beginning balance). R = Interest rate (usually per year, expressed as a decimal). N = Number of time periods (generally one-year time periods).

Using sine rule formula to resolve the value for angle D

The sine rule formula is,

Given:

Therefore,

Simplify

Hence, the answer is

Answer:

Obliviousness: Being unaware of something.

Step-by-step explanation:

so, clearly, the triangles BCF and DCF are congruent.

that makes the line CF a bisector of the kite figure.

and so, both angles are identical halves of the total angle at C.

therefore,

3x + 13 = 13x - 7

13 = 10x - 7

20 = 10x

x = 20/10 = 2

Answer:

3/50

Step-by-step explanation:

The experimental probability that a person selected at random is going to City B is 19/50.

Experimental probability is a probability that is determined on the basis of a series of experiments.

The table shows the results of a survey of 100 people selected at random at an airport.

The total number of responses is;

= 24 + 38 + 14 +22 +2

= 100

The experimental probability that a person selected at random is going to City B is given by;

\(\rm Probability =\dfrac{Responses \ from \ city \ B}{Total \ responses}\\\\ Probability =\dfrac{38}{100}\\\\ Probability =\dfrac{19}{50}\)

Hence, the experimental probability that a person selected at random is going to City B is 19/50.

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We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be      \(\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx\)  .

The definition of the average value of a continuous function f(x) can be expanded to include the infinitely long interval [a,∞] as follows:

\(\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx\)

Let's assume that f(x) is any continuous function. Assume that the integral \(\int\limits^i_0 {f(x)} \, dx\)   is divergent and that f(x)≥0 in the range [a,∞].

Show that, if this limit exists, \(f_{ave} = \lim_{x \to \infty} f(x)\) .

Hence, We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be      \(\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx\)  .

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Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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Answer:

1,400 children attend the school

Step-by-step explanation:

If 20% is 280, we can set up a proportion to solve for how many attend the school. I will put the percentages on top and the number of children on the bottom:

-> Please note that a percentage divided by 100 becomes a decimial

\(\frac{20}{280}=\frac{100}{x}\)

Cross multiply:

.2 * x = 280 * 1

.2x = 280

Divide both sides of the equation by .2:

1,400 children attend the school

We can check our work by multiplying 1,400 by 0.2:

1,400 * 0.2 = 280 ✓

Answer:

34%

Step-by-step explanation:

Answer

33.3%

Step-by-step explanation

Answer:

sqrt66

Step-by-step explanation:

Area of a square is

A = s^2

Here, the area is 66.

66 = s^2

Squareroot both sides to solve.

sqrt66 = s

The side of the square is sqrt66 ft.

This number, sqrt66 is not a rational number because 66 is not a perfect square. Sqrt64 is 8, sqrt81 is 9. But sqrt66 is 8.1240384046 (continuing, neverending, never repeating decimal)

That is not rational.

To calculate the number of four-card hands chosen from a standard 52-card deck that contain two cards of one suit and two cards of another suit, we need to consider the following:

1. Selecting the suits: There are 4 suits in a deck (hearts, diamonds, clubs, and spades). We need to choose two suits out of these four.

2. Selecting the two cards of one suit: Once we have chosen the two suits, we need to select two cards from one of the chosen suits. There are 13 cards in each suit, so we can choose 2 cards from the 13 available.

3. Selecting the two cards of another suit: After selecting the first suit, we need to choose two cards from the remaining suit. Again, there are 13 cards to choose from.

To calculate the total number of four-card hands satisfying these conditions, we multiply the number of choices at each step. Therefore, the total number of such hands is:

4C2 * 13C2 * 13C2 = (4! / (2! * 2!)) * (13! / (2! * 11!)) * (13! / (2! * 11!))

= 6 * (13 * 12 / (2 * 1)) * (13 * 12 / (2 * 1))

= 6 * 78 * 78

= 36,432.

Therefore, there are 36,432 four-card hands chosen from a standard 52-card deck that contain two cards of one suit and two cards of another suit.

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The expression for the number of games Holly now has in standard form is D: -9 - 5x - x^2 + 3x^3 + 7x^4.

To determine the expression for the number of games Holly now has, we analyze the given information step by step. Holly starts with 3x^3 games and buys another 7x^4, resulting in a total of 3x^3 + 7x^4 games.

She then gives away x^2, which reduces the total to 3x^3 + 7x^4 - x^2. Next, she sells 5x games, leading to 3x^3 + 7x^4 - x^2 - 5x.

Finally, she donates another 9 games, resulting in a final expression of 3x^3 + 7x^4 - x^2 - 5x - 9. Simplifying further, we get the expression in standard form: -9 - 5x - x^2 + 3x^3 + 7x^4.

Therefore, the correct expression is D.


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Answer: 13

Step-by-step explanation:

Firstly, you would plug in the values that you were given for x and y into the equation.

((4 * (3) * (2)) + (2))/2 = 13

Answer:

13

Step-by-step explanation:

(4xy+y) ÷ 2

= (4x3x2+2) ÷ 2

= 26 ÷ 2

= 13

Answer:

Step-by-step explanation:

1_|   1     -2     -5    6

               1      -1   -6

       1     -1      -6   0

Q(x)= x^2 - x - 6

R: 0

Based on the information provided, we can conclude that the average starting salary of recent graduates at the institution is likely not significantly different from the overall NACE average of $48,127.

This is because the 95% confidence interval obtained from the institution's SRS includes the NACE average.

However, it is important to note that this conclusion is limited to the specific sample size and methodology used by the institution for their survey.

The National Association of Colleges and Employers (NACE) Spring Salary Survey indicates an average starting-salary offer of $48,127 for recent college graduates.

In comparison, your institution conducted a survey using a Simple Random Sample (SRS) of 300 graduates and calculated a 95% confidence interval of ($46,382, $48,008) for their average starting salary.

In summary, the confidence interval suggests that the average starting salary of recent graduates at your institution is likely to fall between $46,382 and $48,008.

Since the NACE average of $48,127 is not within this interval, it can be concluded that there is a difference between the average starting salary at your institution and the overall NACE average, with your institution's average being slightly lower.

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Answer:

14

Step-by-step explanation:

If he has a total of 24

and he just purchased 10

24-10= 14

Answer:

3x(2x - 3)

Step-by-step explanation:

Given

y = 6x² - 9x ← factor out 3x from each term

  = 3x(2x - 3)

The quadratic function of the jump is y = -0.22x^2 +0.89x + 6.11 if the jump changes so that the axis of symmetry becomes X=2 , the height stays the same 7 and also passes through the point (5,5)

Quadratic function involving vertex is given by

y = a(x-h)^2 + k

Where (h,k) is the vertex which is given as (2,7)

y = a(x-2)^2 + 7

y = a(x-2)(x-2)  + 7

y = a(x^2 -4x +4) + 7

Recall that

h = -b/2a

k = -(b^2 -4ac)/4a

2 = -b/2a

-b = 4a

b = -4a

Put b = -4a

k = -(b^2 -4ac)/4a

7= -(b^2 -4ac)/4a

7 = -((-4a)^2 -4ac)/4a

7 = -(16a^2 - 4ac)/4a

7 =  (-16a^2 + 4ac)/4a

7 = -4a + c

c = 7 + 4a

The path of the jump also passes through (5,5)

y = ax^2 + bx + c

5 = a5^2 + b5 + c

5= 25a +5b + c

Put b = -4a in above

5= 25a +5(-4a) + c

5= 25a -20a+ c

5 = 5a + c

Put c = 7 + 4a

5 = 5a + 7 +4a

Collect like terms

5-7 = 5a + 4a

-2 = 9a

a = -2/9

Put a in

y = a(x^2 -4x +4) + 7

y = -2/9(x^2 -4x +4) + 7

y = (-2x^2 +8x -8)/9 +7

Multiple through by 9

9y = -2x^2 +8x -8 + 63

9y = -2x^2 +8x + 55

Dividing through by 9

y = -0.22x^2 +0.89x + 6.11

Therefore the equation of the jump is

y = -0.22x^2 +0.89x + 6.11.

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Answer:

( - ∞ , ∞ )

Step-by-step explanation:

The probability of randomly selecting or fewer adults having excellent health is:P(X≤) = P(X=0) + P(X=1) + P(X=2) + … + P(X=) + P(X=)= (nC0) p0(1−p) n−0+ (nC1) p1(1−p) n−1+ (nC2) p2(1−p) n−2+ …+ (nC) p(1−p) n−= ∑ P(X≤) , where x=≤nCalculate the value of P(X≤)

The given data says that of adults questioned reported that their health was excellent and a researcher wishes to study the health of people living close to a nuclear power plant. Among adults randomly selected from this area, only reported that their health was excellent.The total adults who participated in the study are not given, so we cannot calculate the probability of randomly selecting adults from the given area. But, we can find the probability of adults who have excellent health from this area that is less than or equal to .To find the probability, we can use binomial distribution theory.

A binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent trials with a given probability of success in each trial.Mathematically, a binomial distribution is represented by:P(x) = (nCx) px(1−p) n−xHere, n is the number of trials, p is the probability of success, and x is the number of successes.Using the above formula, we can find the probability of randomly selecting x adults having excellent health from n adults who participated in the study.

The probability of randomly selecting or fewer adults having excellent health is given by the sum of probabilities of randomly selecting 0, 1, 2, … , , , adult(s) having excellent health.P(X≤x)= P(X=0) + P(X=1) + P(X=2) + … + P(X=) + P(X=)Therefore, the probability of randomly selecting or fewer adults having excellent health is:P(X≤) = P(X=0) + P(X=1) + P(X=2) + … + P(X=) + P(X=)= (nC0) p0(1−p) n−0+ (nC1) p1(1−p) n−1+ (nC2) p2(1−p) n−2+ …+ (nC) p(1−p) n−= ∑ P(X≤) , where x=≤nCalculate the value of P(X≤) using the given information.

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