Please solve for x and explain your steps.

We are given vectors u = (i, 7 - i), v = (6 + i, 7 + f), and w = (81, 9). The operation to be performed is 3u, which means multiplying vector u by a scalar 3. The result will be a new vector obtained by multiplying each component of u by 3. 3u = (3i, 21 - 3i).


To perform the operation 3u, we multiply each component of vector u = (i, 7 - i) by 3.

Multiplying the first component, i, by 3 gives us 3i.

Multiplying the second component, 7 - i, by 3 gives us 21 - 3i.

Therefore, the result of the operation 3u is a new vector: 3u = (3i, 21 - 3i).

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Answer:

-11/20

Step-by-step explanation:

The solution to the equation x plus 16 all over 3 = 3x  is x = 2

The mathematical statement is given as:

x plus 16 all over 3 = 3x

Rewrite the equation as:

(x + 16)/3 = 3x

Multiply both sides of the equation by 3

x  + 16 = 9x

Subtract x from both sides of the equation

8x = 16

Divide both sides of the equation by 8

x = 2

Hence, the solution to the equation x plus 16 all over 3 = 3x  is x = 2

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Answer:

5=2x

Step-by-step explanation:

poopu

The expression for the given statement according to the Pythagoras theorem is  b=sqrt(l^2+l^2).

According to the statement

we have given that the length of the line that runs diagonally across one of the faces of the cube in terms the edge length.

And we have to find the expression for the given terms.

So, for this purpose, we know that

Pythagoras theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

So, we have given that the

the length of the line that runs diagonally across one of the faces of the cube in terms the edge length.

It means that the

The line that runs diagonally is called a hypotenuse.and the value of line is b, which is a given.

Then

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

And the value of edge length is I. Then

Substitute the values in it then

(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

(b)^2 = (I)^2 + (I)^2

Then solve it value for the b

then the value becomes

\(b=sqrt(l^2+l^2)\)

So, The expression for the given statement according to the Pythagoras theorem is b=sqrt(l^2+l^2).

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By definition, when two figures are similar, their corresponding angles are congruent (this means that they have equal measure) and the ratios of the lengths of their corresponding sides are the same.

In this case you know that the triangles shown in the picture are similar, therefore, you can set up the following proportion:

You can identify that:

Therefore, you can substitute values into the proportion:

Now you have to solve for ST:

The answer is:

The lawnmower will travel 1/4 km before they meet.

a. The two variables to be used are t (time) and d (distance). They represent the time it takes for the two to meet and the distance between them.

b. The equation for hill-billie bean is d = 5t, since the lawnmower is traveling at 5 km/hour.

c. The equation for biker bean is d = 1 - 15t, since the motor scooter is traveling at 15 km/h and getting closer to the house.

d. To find the time it takes for them to meet, we need to set the two equations equal to each other and solve for t.

5t = 1 - 15t

20t = 1

t = 1/20 hours

Therefore, it will take 1/20 hours for them to meet.

e. The lawnmower will travel 5 km in 1/20 hours. To calculate this, we can use the equation d = 5t, where t is 1/20.

d= 5(1/20)

d = 1/4 km

Therefore, the lawnmower will travel 1/4 km before they meet.

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Answer:

the answer is A, x=2

Step-by-step explanation:

Answer:

48 , 132

Step-by-step explanation:

Let smaller angle = x

Larger angle = 3x - 12

x & (3x - 12) are supplementary

So, x + 3x - 12 = 180°

          4x - 12 = 180

                  4x = 180 +12

                   4x = 192

                     x = 192/4

x = 48°

Larger angle = 3*48 - 12 = 144 - 12 = 132

Answer: The measure of the smaller angle is 48,and the larger angle is 132.

Step-by-step explanation:

The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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Since the researcher is merely observing and comparing existing groups without any manipulation or intervention, this study is classified as an observational study.

In an observational study, the researcher observes and collects data on existing groups or individuals without intervening or manipulating any variables. In this case, the researcher selected two groups of grocery shoppers (one group shopping at a health food supermarket and the other at a neighborhood grocery store) and observed their food costs over a month. The researcher did not control or manipulate any factors or assign participants to specific groups.

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The key to this problem is to write out the probabilities and determine which one is most likely and least likely (or impossible).

Drawing a black card from a standard deck of playing cards:

There are 52 cards in a playing deck, 26 are red and 26 are black.

\(\frac{26}{52}\) = \(\frac{1}{2}\)

A spinner has 5 equal sections numbered 1 through 5. You spin and land on a number less than or equal to 4.

This means that all the numbers (1, 2, 3, and 4) except 5.

\(\frac{4}{5}\)

You roll a standard number cube and get a number less than 2.

A standard cube is from 1 to 6, and 1 is the only number on the cube that is less than 2.

\(\frac{1}{6}\)

You roll two standard number cubes and the sum is 1.

The smallest number on a standard cube is 1, so you can't make the sum 1 with 2 dice.

0

If we put these in order, we get:

\(\frac{4}{5}\), \(\frac{1}{2}\), \(\frac{1}{6}\), 0

So, the order going from top to bottom in the picture is: 2, 1, 3, 4

Answer:

The number of pounds of apples she bought = 10 pounds

The number of pounds of tomatoes she bought = 10 pounds

The number of pounds of the farmers cheese she bought = 5 pounds

The number of pounds of peaches she bought = 6 pounds

Step-by-step explanation:

The given information are;

The amount that Samantha's mother spent in the market = $78

The number of pounds of apples she bought = The number of pounds of tomatoes she bought

The number of pounds of the farmers cheese she bought = 1/2 of the  number of pounds of apples she bought

The number of pounds of peaches she bought = 1 + 1/2 of the number of pounds of apples she bought

The price of the apples = $1.50

The price of the tomatoes = $2.50

The price of the farmers cheese = $4.00

The price of the peaches = $3.00

If we put the number of pounds of the apples she bought = X, we have

X×$1.50 + X×$2.50 + 1/2×X×$4.00 + (1 + 1/2×X)×$3.00 = $78.00

Which gives;

X×$1.50 + X×$2.50 + 1/2×X×$4.00 + $3.00+ 1/2×X×$3.00 = $78.00

\(\dfrac{X \times \$15.00 + \$ 6.00}{2} = \$ 78\)

X × $15.00 + $6.00 = $78 × 2 = $156.00

X × $15.00 + $6.00 = $156.00

X × $15.00 = $156.00 - $6.00 = $150.00

X = $150.00/($15.00) = 10 pounds

Therefore;

The number of pounds of the apples she bought = X = 10 pounds

The number of pounds of apples she bought = 10 pounds

The number of pounds of tomatoes she bought = The number of pounds of apples she bought = 10 pounds

The number of pounds of tomatoes she bought = 10 pounds

The number of pounds of the farmers cheese she bought = 1/2 of the  number of pounds of apples she bought = 1/2 of 10 = 1/2×10 = 5 pounds

The number of pounds of the farmers cheese she bought = 5 pounds

The number of pounds of peaches she bought = 1 +The number of pounds of the farmers cheese she bought = 1 pound + 5 pounds = 6 pounds

The number of pounds of peaches she bought = 6 pounds.

The solution is: Samantha´s mother bought:

As the question of the problem is" How many pounds of each product Samantha´s mother bought" it is convenient to call:

According to that:

Spent

She spent 78 $ buying

1.50× x + 2.50×x + 4× y + 3 × z = 78      (1)

Now y = x/2       and   z = y + 1

By substitution in equation (1) we get

3.50× x + 4×(x/2) + 3× [( x/2 ) + 1 ] = 78

Solving for x

5.50×x + (3/2)×x + 3 = 78

11×x + 3×x + 6 = 156

14×x = 150

x = 10.71 Lbs

y = 10.71/2         y  = 5.36 Lbs  

and    z  =  5.36  +  1  = 6.36 Lbs

z = 6.36 Lbs

The difference in the area of the square 'a' and 'b' as per given side-length is equal to 8 ( x + 1 ) square meters.

Side length of square 'a' = (2x + 1) meters

Side length of square 'b' = ( 2x + 1 + 2 ) meters

                                         = ( 2x + 3 ) meters

Area of a square 'a' = ( side length )²

                                = ( 2x + 1 )²

Area of a square 'b' = ( side length )²

                                = ( 2x +3 )²

Difference in the area of the squares = ( 2x +3 )² - ( 2x +1 )²

                                                             = ( 2x + 3 -2x -1 )( 2x + 3 + 2x + 1 )

                                                             = ( 2 ) ( 4x + 4 )

                                                             = 8 ( x + 1 )

Therefore, the difference in the area of the given squares is equal to    8 ( x + 1 ) square meters.

The side length of square 'a' is (2x + 1) meters. The side length of square 'b' is 2 meters longer than that of square a. find the difference in the area of the squares.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \pounds 550\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=months\dotfill &6 \end{cases} \\\\\\ A = 550[1+(0.02)(6)] \implies A = 616~\hfill \underset{ \textit{money leftover} }{\stackrel{ 616~~ - ~~\stackrel{ bike }{590} }{\text{\LARGE 26}}}\)

After 6 months of accruing simple interest on her savings account, and after buying a bike costing £590, Holly would be left with £26.

The subject of this question is Mathematics, and it pertains to simple interest. Holly initially deposited £550 into a savings account. With an interest rate of 2% per month, the total interest gathered in 6 months can be calculated using the formula for simple interest: I = PRT (I is Interest, P is Principal amount, R is Rate and T is Time). Here, P is £550, R is 2/100 = 0.02 and T is 6. So, I would be £550 x 0.02 x 6 = £66 pounds. This means Holly's total savings after 6 months would be £550 (initial deposit) + £66 (interest) = £616 pounds. After buying a bike for £590, she would have £616 - £590 = £26 left.

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Answer:

x=22

Step-by-step explanation:

(5x+4)+44+x = 180. reason [being co-interior angle)

48+6x = 180

6x = 132

x=22

Answer:

$1.73 per pint

Step-by-step explanation:

2 quarts is the equivalent of 4 pints. Therefore, in order to get the price per pint you must divide 6.92 by 4. This gives you $1.73 per pint.

By solving the given equation, d = -4

           To find d in the equation -14d + 12d + 11d + 18 = -18, we need to combine similar terms on the left side of the equation and isolate the variable.

Combining similar terms, we get:

(-14 + 12 + 11)d + 18 = -18

9d + 18 = -18

           We can then extract the variable by shifting the constant term to the other side of the equation:

9d = -18 - 18

9d = -36

Finally, we can find d by dividing both sides of the equation by 9:

d = -36/9

d = -4

Therefore, the solution of the equation is d = -4. When d equals -4, the equation is balanced and both sides of the equation are equal.

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Answer:

it's going to be

-8x^2+14x^2+4y+y-5-1=

6x^2+5y-6

Step-by-step explanation:

hope this is what u are looking for

have a nice day

Answer:

C

Step-by-step explanation:

I believe it is c if I counted right

Answer:

x=58 degrees

Step-by-step explanation:

The angle is a right angle (90 degrees)

90-32=58

Answer:

58 degrees.

Step-by-step explanation:

This is because a right angle is 90 degrees and there's already 32 degrees of it "taken up." 90 - 32 = 58.

Answer:

3.  

If a conditional statement is written in the form “If p then q”, how is the inverse of the conditional statement written?

If not q, then not p

If not p, then not q  

If not q then p

If not p then q

To write the inverse of a conditional statement, you use the "opposite" of the hypothesis and the conclusion in a conditional statement.

Step-by-step explanation:

Contrapositive statement of "if p then q" written as If not q, then not p which is correct option (C).

Contrapositive of the conditional statement is defined as interchange the hypothesis and the conclusion of the inverse statement.

Contrapositive statement of "if p then q" written as If not q, then not p

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The voltage across the current source is 352 volts. In the given statement, there are several numbers mentioned, such as 352, 3152, 30, 2, and 122.

However, the context is not clear, and it is challenging to understand the specific meaning of these numbers in relation to the problem. To determine the voltage across the current source, it is crucial to have additional information, such as the circuit diagram or relevant equations.

Generally, to calculate the voltage across a current source, one needs to apply Ohm's law or Kirchhoff's laws, depending on the circuit configuration. Ohm's law states that voltage (V) is equal to the product of current (I) and resistance (R), i.e., V = I * R. Kirchhoff's laws, on the other hand, are used to analyze complex circuits and determine voltages and currents. Without more specific information about the circuit and its components, it is not possible to provide a detailed calculation or explanation for finding the voltage across the current source in this particular scenario.

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The question is incomplete, this is a general answer

Based on the given data,the calculated Economic Order Quantity( EOQ) is approximately 360.50 units.

Based on the given data, we can calculate the Economic Order Quantity (EOQ) using the formula:

EOQ = sqrt((2 * demand * setup cost) / holding cost)

First, we need to determine the setup cost, which is given as $120 per order. The holding cost is $35 per unit.

Demand = 19012 units per quarter

Setup cost = $120 per order

Holding cost = $35 per unit

Substituting these values into the EOQ formula:

EOQ = sqrt((2 * 19012 * 120) / 35)

= sqrt(4562880 / 35)

≈ sqrt(130082.29)

≈ 360.50

Therefore, the calculated EOQ is approximately 360.50 units.

To check the EOQ figures, you would compare this result to their current order quantity. If their current order quantity is close to 360.50 units, then the EOQ figures are in line with their current practice. However, if the current order quantity significantly differs from 360.50 units, further analysis may be required to understand the factors influencing their ordering decisions.

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The coefficient of correlation (r) for the given data is approximately -0.786.

To determine the value of the coefficient of correlation (r) for the given data, we can use the formula:

r = (Σ((X - Xbar)(Y - Ybar))) / sqrt(Σ((X - xbar)²) * Σ((Y - Y bar)²))

where Σ represents the sum of the values, Xbar is the mean of X, and Ybar is the mean of Y.

First, we need to calculate the means of X and Y:

Xbar = (3 + 6 + 7 + 11 + 16 + 17 + 21) / 7 = 11.571

Ybar = (18 + 11 + 13 + 8 + 7 + 7 + 3) / 7 = 10.571

Next, we calculate the sums of the squares of the deviations from the means:

Σ((X - Xbar)²) = (3 - 11.571)² + (6 - 11.571)² + (7 - 11.571)² + (11 - 11.571)² + (16 - 11.571)² + (17 - 11.571)² + (21 - 11.571)² = 220.857

Σ((Y - Ybar)²) = (18 - 10.571)² + (11 - 10.571)² + (13 - 10.571)² + (8 - 10.571)² + (7 - 10.571)² + (7 - 10.571)² + (3 - 10.571)² = 204.857

Then, we calculate the sum of the products of the deviations from the means:

Σ((X - Xbar)(Y - Ybar)) = (3 - 11.571)(18 - 10.571) + (6 - 11.571)(11 - 10.571) + (7 - 11.571)(13 - 10.571) + (11 - 11.571)(8 - 10.571) + (16 - 11.571)(7 - 10.571) + (17 - 11.571)(7 - 10.571) + (21 - 11.571)(3 - 10.571) = -81.143

Now, we can calculate the coefficient of correlation (r):

r = -81.143 / sqrt(220.857 * 204.857) ≈ -0.786

Therefore, the coefficient of correlation (r) for the given data is approximately -0.786.

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Answer:

mean is 4.86

mean absolute deviation is 4.86

Step-by-step explanation:

========================================================

Explanation:

Consider an example like 3, 6, 12, 24, 48, ...

The ratio between consecutive terms is

Each time we divide any given term over its previous one, we get the same ratio 2. We call this the common ratio. In terms of notation, the variable r is used for the common ratio, so r = 2 in this case.

As another example, the geometric sequence 5, 50, 500, 5000, ... has r = 10 as the common ratio because we multiply each term by 10 to get the next one. Moving forward has us multiply by r, moving backward and we divide by r. The value of r cannot be zero, but it can be negative.

An example with r being negative would be something like

1, -1, 1, -1, 1, -1, ....

we just bounce back and forth between those two values. In this case, r = -1.

To calculate the optimal profit, we need to find the value of D when the total cost is \($30,500\) and then substitute it into the given equation.

To find D, we can rearrange the equation to solve for D: Given:\(p = 180 - 0.2D\) and total cost =\($30,500\) Now, substitute the total cost ($30,500) into the equation to find D:

Since D cannot be negative in this context, it means that the given equation is not applicable for a total cost of \($30,500\). it is not possible to calculate the optimal profit using the given equation and the total cost of \($30,500\).

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The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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