11. Determine the values of \( r \) for which \( v=\left[\begin{array}{c}2 \\ r \\ -1\end{array}\right] \) is in the span of \( \mathcal{S}=\left\{\left[\begin{array}{c}1 \\ 0 \\ -1\end{array}\right],

Answer:

88

Step-by-step explanation:

METHOD 1:

Find 68% of 275:

275 * 0.68 = 187

Subtract 187 from the total:

275 - 187 = 88 coins

METHOD 2:

100% - 68% = 32%

Find 32% of total:

275 *0.32 = 88 coins

Answer:

40

Step-by-step explanation:

The geometric mean will equal the square root of the product of the two numbers.

√64 * √25

   8  *     5  = 40

Answer: D, 912

Step-by-step explanation:

g(21) = 24 (21 + 17)

g(21) = 24 x 38

g(21) = 912 (Use your calculator for this part)

The volume of 9/5x2/3x is 2/15.

Volume is the amount of space an object or substance occupies or contains. It is measured in three-dimensional space and is often given in cubic units such as cubic centimeters, cubic meters, and cubic millimeters. Volume is an important concept in physics, chemistry, and other sciences, and is used to describe the size of all kinds of substances, from solids, liquids, and gases to particles and energy fields. Volume is also used to compare the relative sizes of different objects, and to measure the capacity of containers.

To calculate this, we first need to multiply 9/5 and 2/3 together. This gives us 18/15. Then, we multiply this by x. This gives us 2/15x. Therefore, the volume of 9/5x2/3x is 2/15.

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The required with the help of trig ratios we have,
1. x = 30.69
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
1.

Apply the sine rule,
Sin21 = perpendicular/hypotenus
sin21 = 11 / x
x = 11/sin21
x = 30.69

Similarly,
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°

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Answer:16.67%.

Step-by-step explanation:

The ratio of raisins to almonds is 2:10, which can be simplified to 1:5.

This means that for every 6 parts of the mix, 1 part is raisins.

To find the percentage of raisins in the mix, we need to divide the amount of raisins by the total amount of mix, and then multiply by 100 to convert to a percentage.

So if we let x be the total amount of mix (in any unit of measurement), then the amount of raisins is (1/6)x.

The percentage of raisins in the mix is:

[(1/6)x / x] x 100% = 16.67%

Therefore, the percent of the raisins in the mix is 16.67%.

The guy wire's length should be approximately 120.5 feet.

To find out, we can use trigonometry. The guy wire, the tower, and the ground form a right triangle, with the guy wire as the hypotenuse. We know the angle between the guy wire and the ground (20°), and we know the height of the tower (578 feet). We want to find the length of the guy wire. Using the trigonometric function tangent, we can set up the following equation:

tan(20°) = 578 / (guy wire length - 6)

Solving for the guy wire length, we get:

guy wire length = 578 / tan(20°) + 6

guy wire length ≈ 120.5 feet

Therefore, the guy wire should be approximately 120.5 feet long.

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Given vectors ū = (u1, u2) and ✓ = (v1, v2), we can find vector w = 4ữ - 5✓ by using the formula:
w = (4u1 - 5v1, 4u2 - 5v2)
To find the magnitude of vector w, we can use the formula:
|w| = √((4u1 - 5v1)² + (4u2 - 5v2)²)

Since we do not have the exact values of u1, u2, v1, and v2, we cannot compute the exact values of w and |w|.
w = (4u1 - 5v1, 4u2 - 5v2), |w| = √((4u1 - 5v1)² + (4u2 - 5v2)²)

Problem 4:
Given the point P(-15, 8) on the terminal side of angle O in standard position, we can find the values of the six trigonometric functions of O using the following formulas:
sin O = y/r
cos O = x/r
tan O = y/x
csc O = r/y
sec O = r/x
cot O = x/y
Where x = -15, y = 8, and r = √(x² + y²) = √((-15)² + 8²) = √(225 + 64) = √289 = 17

Therefore, the exact values of the six trigonometric functions of O are:
sin O = 8/17
cos O = -15/17
tan O = -8/15
csc O = 17/8
sec O = -17/15
cot O = -15/8

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The rectangular coordinates of the polar coordinates are as follows:-

a) x = 0 and  y = ( -2 )

b) x = ( -√3/2 ) and y = 1

To convert these polar coordinates to rectangular coordinates, we calculate the following,

a) ( 2, 3π/2 ) :

r=2 ; θ = 3π/2

x = r * cosθ

x = 2 * cos( 3π/2 )

x = 2 * 0

Therefore, x = 0

y = r * sinθ

y = 2 * sin( 3π/2 )

y = 2 * ( -1 )

Therefore, y = ( -2 )

b) ( 1, 5π/6 ) :

r = 1 ; θ = 5π/6

x = r * cosθ

x = 1 * cos( 5π/6 )

x = 1 * ( -√3/2 )

Therefore, x = ( -√3/2 )

y = r * sinθ

y = 2 * sin( 5π/6 )

y = 2 * ( 1/2 )

Therefore, y = 1

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The correct answer is Option c. The test statistic has the value 3.361 and hence the correlation is significant. Since the test statistic (2.824) is lower than the critical value (2.824), the correlation is not significant.

The sample correlation coefficient, r, estimates the population correlation coefficient, ρ. It indicates how closely a scattergram of x,y points cluster about a 45° straight line.

The test statistic has the value 2.824 and hence the correlation is not significant. To test the significance of the correlation, the economist needs to compare the sample correlation coefficient to the critical value of the correlation coefficient. In this case, the critical value of 0.4165 with a sample size of 40 and a 5% level of significance is 2.824.

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Answer:

x= -4
y=1

Step-by-step explanation:

-7x + 6y = 34

7x+ 4y =-24
You would add them up together

-7 +7x cancels out. 6y+4y = 10y
34+ (-)24 = 34 - 24 = 10
y= 1
substitute y
7x + 4 = -24
7x= -28
x=-4

Step-by-step explanation:

what is the question ?

to solve this system of 2 equating in 2 variables ?

if so, we start by adding both equations :

-7x + 6y = 34

7x + 4y = -24

----------------------

0 + 10y = 10

y = 1

with that we go into one of the original equations (it did not matter which one, I like the second better) :

7x + 4×1 = -24

7x + 4 = -24

7x = -28

x = -4

Therefore , the solution of the given problem of expressions comes out to be x = 1.0730 is roughly the answer to the equation 10*e(³ˣ) = 250.

When variables are shifting, estimates should be created that mix joining, disabling, and instead of randomly  dividing. They could answer a puzzle collectively, offer some information, and instead software. Formulas, elements, and mathematical operations like addition, subtraction, grouping, and combination are all found in a statement of truth. Words and sentences can both be evaluated and analysed.

Here,

In order to find x in the equation 10*e(3x) = 250, we can start by dividing both parts by 10 to isolate the exponential term:

=> e³ˣ = 25

The exponential can then be removed by taking the natural logarithm (ln) of both sides:

=> ln(e(³ˣ) = ln(25)

We can simplify the left half by using the fact that ln(ey) = y:

=> 3x = ln(25)

By multiplying both parts by 3, we can finally find the value of x:

=>x = (1/3) * ln(25)

We can use a computer to determine that the value of ln(25) is roughly 3.2189. Therefore:

=> x ≈ (1/3) * 3.2189

=> x ≈ 1.0730

So x = 1.0730 is roughly the answer to the equation 10*e(³ˣ) = 250.

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To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.

The partial fraction decomposition for the given fraction is:

(4x-3)/(x^(2)(x+3)(x^(2)+2x+9)(x^(2)+1)^(3)) = A/x + B/x^(2) + C/(x+3) + D/(x^(2)+2x+9) + E/(x^(2)+1) + F/(x^(2)+1)^(2) + G/(x^(2)+1)^(3)

Where A, B, C, D, E, F, and G are constants that need to be determined.

To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.

However, since the question only asks to set up the partial fraction decomposition, we do not need to solve for the constants at this time.

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The ramp rises about 10.4 inches off the ground to the nearest inch.

A ramp is an inclined plane that connects two different levels, allowing people or objects to move between them with less force than if they had to be lifted vertically.

We can use trigonometry to solve this problem. Let's call the height of the ramp "h". Then we have:

tan(3.2°) = h/15

To solve for h, we can multiply both sides by 15:

h = 15 tan(3.2°)

Using a calculator, we get:

h ≈ 0.87 feet

To convert this to inches, we can multiply by 12:

h ≈ 10.4 inches

So, the ramp rises about 10.4 inches off the ground to the nearest inch.

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Answer:

Step-by-step explanation:

We can rewrite the situation using cost equations for the two companies

If c1 and c2 represent the total costs for companies 1 and 2 respectively and w the weight of sugar transported

For the first company we have
c1 = 2804 + 100.50w

For the second company
c2 = 275.75w

Costs are the same when c1 = c2

or

2804 + 100.50w = 275.75w

To Solve:

At 16 tons of sugar, the costs will be the same for both companies

At this tonnage, the cost is
275.75 x 16 = $4412

Christine will pay $6.30 for shipping and handling for the lawn mower.

To find the amount of shipping and handling Christine will pay, we can use the formula:

Shipping and Handling = Price x 10%

Substituting the given values into the formula, we get:

Shipping and Handling = $63 x 10%

Simplifying the equation, we get:

Shipping and Handling = $6.30

Therefore, Christine will pay $6.30 for shipping and handling for the lawn mower.

The percentage represents a certain amount, expressed as a fraction of 100 equal parts.

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The equation has two solutions:[tex]x=5[/tex] and [tex]x=-4[/tex].

To solve an absolute value equation, we need to consider both the positive and negative solutions. We can do this by setting up two separate equations and solving each one individually.

The first equation is:
[tex]2x-1 = 9[/tex]

We can solve for x by isolating the variable on one side of the equation:
[tex]2x = 10[/tex]
[tex]x = 5[/tex]

The second equation is:
[tex]2x-1 = -9[/tex]

We can also solve for [tex]x[/tex] in this equation:
[tex]2x = -8[/tex]
[tex]x = -4[/tex]

Therefore, the solution to the absolute value equation[tex]|2x-1|=9[/tex] is [tex]x=5[/tex] or [tex]x=-4[/tex].

In conclusion, the equation has two solutions: [tex]x=5[/tex] and [tex]x=-4[/tex].

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To find a linear function h(x) given two points, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
Where m is the slope, (x1, y1) and (x2, y2) are the two points.

In this case, the two points are (-3, -4) and (-9, -5). Plugging in the values into the formula, we get:
m = (-5 - (-4)) / (-9 - (-3))
m = (-1) / (-6)
m = 1/6
Now that we have the slope, we can use the point-slope form of a linear equation to find the function h(x):
y - y1 = m(x - x1)
Plugging in the slope and one of the points, we get:
y - (-4) = (1/6)(x - (-3))
y + 4 = (1/6)(x + 3)
y = (1/6)x + 3/6 - 4
y = (1/6)x - 21/6

Simplifying the equation, we get:
y = (1/6)x - 7/2

Therefore, the linear function h(x) is:
h(x) = (1/6)x - 7/2

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The number of residents in a city is a discrete variable with ratio level of measurement. Therefore, the correct option is option 3. When a pair of dice are rolled, the pair of mutually exclusive events are getting an odd number on the first die; getting a 4 on the second die. Therefore, the correct option is option 2.

The number of residents in a city is a discrete variable because it can only take on whole number values. The level of measurement for this variable is ratio level because there is a true zero point (a city with zero residents) and the differences between values are meaningful. Therefore, the correct answer is discrete, ratio level which is the third option.

Mutually exclusive events are events that cannot occur at the same time. In the case of rolling a pair of dice, the pair of mutually exclusive events is "Getting an odd number on the first die; getting a 4 on the second die." This is because if the first die is an odd number, the second die cannot be a 4 at the same time.

The other options are not mutually exclusive because they can occur at the same time. For example, it is possible to get an even number on the first die and a double 5 at the same time. Therefore, the correct answer is "Getting an odd number on the first die; getting a 4 on the second die" which is the second option.

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The ratio of pages to minutes is 3:4. If he read 16 minutes, then the number of pages is 12 pages. And Tyler has to read 24 pages for homework. Then the number of minutes is 32 minutes.

The utilization of two or more additional numbers that compares is known as the ratio.

Tyler reads 3/4 pages per minute. Then the ratio of pages to minutes is given as,

Ratio = (3/4) / 1

Ratio = 3: 4

If he read 16 minutes, then the number of pages is calculated as,

⇒ (3/4) x 16

⇒ 3 x 4

⇒ 12 pages

Tyler has to read 24 pages for homework. Then the number of minutes is given as,

⇒ 24 / (3/4)

⇒ 24 x (4/3)

⇒ 8 x 4

⇒ 32 minutes

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Answer:

Height = 8

Volume = 48

Step-by-step explanation:

(4x4)x3 = 48

According to the question the solution to the inequality is x < 6.

Inequality is the unequal distribution of resources, rights, and opportunities among individuals or groups in a society. It is a form of systemic injustice that can take on many forms, such as economic, social, and political. Economic inequality is when people have unequal access to resources such as wealth, income, and education; social inequality is when people have unequal access to social opportunities and resources such as political power, public services, and health care; and political inequality is when people have unequal access to the political process and decision-making, such as voting rights and other forms of representation.

To solve this inequality, we need to isolate the variable on one side. First, let's subtract 8 from both sides:
-4x + 8 > -16
-4x > -24
Now, divide both sides by -4:
-4x/-4 > -24/-4
x < 6
Therefore, the solution to the inequality is x < 6.

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Answer:

This

Step-by-step explanation:

( x y z) = (-1,7,4) explanation is big

The probability of winning on the first try is 0.000003426 .

P(MUF) = P(M) + P(F) - P(M and F) = 73/293 + 79/293 - 14/293 = 138/293

P(B) = 80/293

P(E/S) = P(E and S)/P(S) = 20/293 / 78/293 = 20/78 = 10/39

P(ENS) = P(E and S and N) = 0 (since there is no N category in the table)

P(MUJUH) = P(M and J and H) = 0 (since there is no intersection of all three categories in the table)

P(SEUM) = P(SE and M) = 10/293

P(F/B) = P(F and B)/P(B)

=> 16/293 / 80/293

=> 16/80

=> 1/5

P(AUB) = P(A) + P(B) - P(A and B)

=> .4 + .35 - (.4 * .35)

=> .595
If order matters, the probability is

(5/30) * (4/29) * (3/28) * (2/27) * (1/26) * 5!

=> 0.00002056

The probability of winning on the first try is

(5/30) * (4/29) * (3/28) * (2/27) * (1/26)

=> 0.000003426

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By answering the above question, we may infer that The rocket will thus equation touch down 2.5 seconds after it was fired (to the nearest tenth of a second).

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Hence, we may solve for t by setting the equation for h equal to 0:

[tex]-16t^2 + 120t + 200 = 0\\2t^2 - 15t - 25 = 0\\(-b \sqrt(b2 - 4ac)) / 2a[/tex]

where a=2, b=15, and c=25

[tex]t = (15 \sqrt(625)) / 2(2) (-(-15) \sqrt((-15)2 - 4(2)(-25))) / 4\st = (15 + 25) / 4[/tex]

T thus equals 10/2 or -5/2. Time cannot be negative, thus we may ignore the negative number.

The rocket will thus touch down 2.5 seconds after it was fired (to the nearest tenth of a second).

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Anne and Maya drive for 2 1/2 hours.

A mixed fraction is a combination of a whole number and a proper fraction. For example, 2 1/3 is a mixed fraction, where the whole number is 2 and the proper fraction is 1/3.

To convert an improper fraction into a mixed fraction, Divide the numerator by the denominator and write down the whole number result as the whole number part of the mixed fraction.

Write down the remainder as the numerator of the fractional part of the mixed fraction.

Here we have

Anne and Maya each drive the same amount of time to complete the 5-hour trip.  

Let both of them be derived for 'x' hours

=> x + x = 5 hours

=> 2x = 5 hours

=> x = 5/2

Hence, Anne and Maya drive for 5/2 hours

Here 5/2 can be converted as 2 1/2  

Therefore,

Anne and Maya drive for 2 1/2 hours.  

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Answer:

Distributive property

Step-by-step explanation:

In this problem, you are distributing the 5 to both the [tex]\sqrt{3}[/tex] and the 2. Therefore, the answer is the distributive property

Answer: Distributive property.

Step-by-step explanation: The initial terms are being multiplied by 5 into both terms and they are equivalent by the distributive properly.  

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Therefore , the solution of the given problem of equation comes out to be every term in this sequence will be a whole number greater than 7.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization produces a + 7 as opposed to a different algorithm that splits 12 into two parts and can evaluate data received from x + 7.

Here,

The given equation can be used to create a table of values for this sequence, beginning with a1 = 7:

n an

1 7

2 19

3 31

4 43

5 55

6 67

7 79

8 91

9 103

10 115

... ...

We multiply the first term of the sequence by a factor of 1 and add 12 to determine each succeeding term.

=> a2 = a1 + 12 = 7 + 12 = 19

Similarly, we enter n = 3 and a2 = 19 to determine a3:

=> a3 = a2 + 12 = 19 + 12 = 31

so forth.

Because a1 is a whole number greater than 7 and each term in the sequence is obtained by adding 12 to the preceding term,

it should be noted that every term in this sequence will be a whole number greater than 7.

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Answer:

The difference in elevation between the bottom of the canyon and the bird's nest is the sum of the depths, which is:

72 1/2 + 719 2/5

To add these two mixed numbers, we first convert them to improper fractions:

72 1/2 = 145/2

719 2/5 = (3595/5) + (2/5) = 3597/5

Now we can add them:

145/2 + 3597/5

To add fractions with different denominators, we need to find a common denominator. The smallest common multiple of 2 and 5 is 10, so we can rewrite the fractions with a denominator of 10:

145/2 × 5/5 = 725/10

3597/5 × 2/2 = 7194/10

Now we can add the fractions:

725/10 + 7194/10 = 7929/10

Finally, we can simplify the fraction and convert it back to a mixed number:

7929/10 = 792 9/10

Therefore, the difference in elevation between the bottom of the canyon and the bird's nest is 792 9/10 feet.