when x=6 and y=3, which of the expressions below will be greater than 100?

Answer:

because -12 is smaller than x

Step-by-step explanation:

for example some one got 14$ and lost 12$ it mean this -12 and the remaining keep it as 12$ no plus sign

Explanation:

First, we need to find what is the total number of values in the data. So, taking into account the height of the bars, we can calculate the size of the data as follows:

6 + 2 + 3 + 5 + 4 + 4 = 24

Where each number in the sum is the height of each bar.

Then, the position of the median can be calculated using the following equation:

Where n is the size of the data.

Finally, the value in position 12.5 is in the interval 90 - 119

Because, there are 6 values in 0- 29, there are

Answer:105

Step-by-step explanation:

becasue you can mutiply 35 3 times and 21 5 times and you get the same number as 105

The remainder of the polynomial division \(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\) is 2y²

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

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\)

When the numerator is expanded, we have

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1) + 2y^2}{y^3 + 1}\)

Split the expanded expression

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1)}{y^3 + 1} + \frac{2y^2}{y^3 + 1}\)

Evaluate

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = y - 1 + \frac{2y^2}{y^3 + 1}\)

From the above, we have

Quotient = y - 1

Remainder = 2y²

Hence, the remainder of the polynomial division is 2y²

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Answer:

the answer is 3

Step-by-step explanation:

that is the answer

Answer:

12 1 / 12

Step-by-step explanation:

because 11 is one and 24× 2 = 48

The value of cos 75° = [ √2(√3-1) / 4 ]  

A branch of mathematics in geometry that deals with the sides and angles of a right-angled triangle are called Trigonometry

The six trigonometric ratios are sin, cos, tan, cot, cosec, and sec.

The formulas for the sum and difference of the two angles are given below

cos (x + y) = cos x cos y – sin x sin y

cos (x – y) = cos x cos y + sin x sin y

sin (x – y) = sin x cos y – cos x sin y

sin (x + y) = sin x cos y + cos x sin y

Here we have

cos 75°

As we know 75 = (30 + 45)

=> cos 75° = cos (30 + 45)°

From given problems

cos(x + y) = cosx cos y - sin x sin y

cos (30 + 45)° = cos 30° cos 45° - sin 30° sin 45°  

From the Trigonometric table

cos 30° = √3/2 and cos 45° = 1/√2

sin 30° = 1/2 and sin 45° = 1/√2    

cos (30 + 45)° = \(\frac{\sqrt{3}}{2} (\frac{1}{\sqrt{2}} ) - \frac{1 }{2} (\frac{1}{\sqrt{2} } )\)  

=  \(\frac{\sqrt{3}}{2} (\frac{\sqrt{2} }{2} ) - \frac{1 }{2} (\frac{\sqrt{2}}{2} )\)

=  \((\frac{\sqrt{6} }{4} - \frac{\sqrt{2} }{4} )\)

=  \(\frac{\sqrt{2} (\sqrt{3} - 1) }{4}\)  

Therefore,

The value of cos 75° = [ √2(√3-1) / 4 ]  

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The equation of logarithm are solved and

a) A = 2 + 3 log x + 4 log b

b) B = ( 36 + x + y ) ( log 6 )

c) C = ( 1/2 )x log 5

d) D = ln ( x⁴ / y² )

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

A = 2 log 10 + 3 log x + 4 log b

The base of the logarithm is 10 , so

A = 2 + 3 log x + 4 log b

b)

B = log 6³⁶ + log 6ˣ - log 6^ ( y )

From the properties of logarithm , we get

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

B = 36 log 6 + x log 6 + y log 6

On taking the common term , we get

B = ( 36 + x + y ) ( log 6 )

c)

C = ( 1/2 )log 5ˣ

From the properties of logarithm , we get

C = ( 1/2 )x log 5

d)

D = 4 ln x - 2 ln y

From the properties of logarithm , we get

D = ln x⁴ - ln y²

On further simplification , we get

D = ln ( x⁴ / y² )

Hence , the logarithmic equations are solved

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Answer:

\(\begin{bmatrix}y>2+x\\ y>\frac{2-x}{2}\end{bmatrix}\)

Step-by-step explanation:

Step 1: Solve the system of equations

\(\begin{bmatrix}-x+y>2\\ x+2y>2\end{bmatrix}\)

Isolate \(y\) for \(-x+y>2\)

\(\mathrm{Add\:}x\mathrm{\:to\:both\:sides}\)

\(-x+y+x>2+x\)

\(y>2+x\)

Isolate \(y\) for \(x+2y>2\)

\(\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}\)

\(2y>2-x\)

\(\mathrm{Divide\:both\:sides\:by\:}2\)

\(\frac{2y}{2}>\frac{2}{2}-\frac{x}{2}\)

\(y>\frac{2-x}{2}\)

\(\bold{=\begin{bmatrix}y>2+x\\ y>\frac{2-x}{2}\end{bmatrix}}\)

Step 2: Graph

Instructions for graphing:

\(\mathrm{1.\:Graph\:each\:inequality\:separately.}\)

\(\mathrm{2.\:Choose\:a\:test\:point\:to\:determine\:which\:side\:of\:the\:line\:needs\:to\:be\:shaded.}\)

\(3. \mathrm{The\:solution\:to\:the\:system\:will\:be\:the\:area\:where\:the\:shadings\:}\\\mathrm{from\:each\:inequality\:overlap\:one\:another.}\)

When done, it should look like this:

The probability that more than 2 students will attend is 0.9179.

Part (a) List the values that X may take on.

X may take on the values 0, 1, 2, 3, ..., 13.

Part (b) Give the distribution of X.

The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23

Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)

We can expect 3 students to attend the festivities.

Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)

The probability that at most 3 students will attend is 0.6923.

Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

The probability that more than 2 students will attend is 0.9179.

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Answer:

1.x=12

6/12 divided by 3 for both denominator and numerator

2. x=5

2/10 divided by 3 for both denominator and numerator

5. x=60

60/100 divided by 20 for both denominator and numerator

Find out #3 for yourself

Step-by-step explanation:

Answer:

y=-7x+9

Step-by-step explanation:

Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

<95141404393>

Answer:

\( x \leqslant \sqrt{5}\) ​

Step-by-step explanation:

Hope this helped!

Answer:

x= -71/20

Step-by-step explanation:

- 4 3/4 = x-1 1/5

-19/4 = x-6/5

-x= -6/5 + 19/4

-x=71/20

hope this helped u!

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Recall that the projection of a vector \(u\) onto \(v\) is \(\displaystyle proj_vu=\biggr(\frac{u\cdot v}{||v||^2}\biggr)v\).

Identify the vectors:

\(u=\langle-10,-7\rangle\)

\(v=\langle-8,4\rangle\)

Compute the dot product:

\(u\cdot v=(-10*-8)+(-7*4)=80+(-28)=52\)

Find the square of the magnitude of vector v:

\(||v||^2=\sqrt{(-8)^2+(4)^2}^2=64+16=80\)

Find the projection of vector u onto v:

\(\displaystyle proj_vu=\biggr(\frac{u\cdot v}{||v||^2}\biggr)v\\\\proj_vu=\biggr(\frac{52}{80}\biggr)\langle-8,4\rangle\\\\proj_vu=\biggr\langle\frac{-416}{80} ,\frac{208}{80}\biggr\rangle\\\\proj_vu=\biggr\langle\frac{-26}{5} ,\frac{13}{5}\biggr\rangle\\\\proj_vu=\langle-5.2,2.6\rangle\)

Thus, B is the correct answer

Problem 2

Treat the football and wind as vectors:

Football: \(u=\langle42\cos172^\circ,42\sin172^\circ\rangle\)

Wind: \(v=\langle13\cos345^\circ,13\sin345^\circ\rangle\)

Add the vectors: \(u+v=\langle42\cos172^\circ+13\cos345^\circ,42\sin172^\circ+13\sin345^\circ\rangle\approx\langle-29.034,2.481\rangle\)

Find the magnitude of the resultant vector:

\(||u+v||=\sqrt{(-29.034)^2+(2.481)^2}\approx29.14\)

Find the direction of the resultant vector:

\(\displaystyle \theta=tan^{-1}\biggr(\frac{2.841}{-29.034}\biggr)\approx -5^\circ\)

Because our resultant vector is in Quadrant II, the true direction angle is 6° clockwise from the negative axis. This means that our true direction angle is \(180^\circ-5^\circ=175^\circ\)

Thus, C is the correct answer

Problem 3

We identify the initial point to be \(R(-2,12)\) and the terminal point to be \(S(-7,6)\). The vector in component form can be found by subtracting the initial point from the terminal point:

\(v=\langle-7-(-2),6-12\rangle=\langle-7+2,-6\rangle=\langle-5,-6\rangle\)

Next, we find the magnitude of the vector:

\(||v||=\sqrt{(-5)^2+(-6)^2}=\sqrt{25+36}=\sqrt{61}\approx7.81\)

And finally, we find the direction of the vector:

\(\displaystyle \theta=tan^{-1}\biggr(\frac{6}{5}\biggr)\approx50.194^\circ\)

Keep in mind that since our vector is in Quadrant III, our direction angle also needs to be in Quadrant III, so the true direction angle is \(180^\circ+50.194^\circ=230.194^\circ\).

Thus, A is the correct answer

Problem 4

Add the vectors:

\(v_1+v_2=\langle-60,3\rangle+\langle4,14\rangle=\langle-60+4,3+14\rangle=\langle-56,17\rangle\)

Determine the magnitude of the vector:

\(||v_1+v_2||=\sqrt{(-56)^2+(17)^2}=\sqrt{3136+289}=\sqrt{3425}\approx58.524\)

Find the direction of the vector:

\(\displaystyle\theta=tan^{-1}\biggr(\frac{17}{-56} \biggr)\approx-17^\circ\)

Because our vector is in Quadrant II, then the direction angle we found is a reference angle, telling us the true direction angle is 17° clockwise from the negative x-axis, so the true direction angle is \(180^\circ-17^\circ=163^\circ\)

Thus, A is the correct answer

Problem 5

A vector in trigonometric form is represented as \(w=||w||(\cos\theta i+\sin\theta i)\) where \(||w||\) is the magnitude of vector \(w\) and \(\theta\) is the direction of vector \(w\).

Magnitude: \(||w||=\sqrt{(-16)^2+(-63)^2}=\sqrt{256+3969}=\sqrt{4225}=65\)

Direction: \(\displaystyle \theta=tan^{-1}\biggr(\frac{-63}{-16}\biggr)\approx75.75^\circ\)

As our vector is in Quadrant III, our true direction angle will be 75.75° counterclockwise from the negative x-axis, so our true direction angle will be \(180^\circ+75.75^\circ=255.75^\circ\).

This means that our vector in trigonometric form is \(w=65(\cos255.75^\circ i+\sin255.75^\circ j)\)

Thus, C is the correct answer

Problem 6

Write the vectors in trigonometric form:

\(u=\langle40\cos30^\circ,40\sin30^\circ\rangle\\v=\langle50\cos140^\circ,50\sin140^\circ\rangle\)

Add the vectors:

\(u+v=\langle40\cos30^\circ+50\cos140^\circ,40\sin30^\circ+50\sin140^\circ\rangle\approx\langle-3.661,52.139\rangle\)

Find the magnitude of the resultant vector:

\(||u+v||=\sqrt{3.661^2+52.139^2}\approx52.268\)

Find the direction of the resultant vector:

\(\displaystyle\theta=tan^{-1}\biggr(\frac{52.139}{-3.661} \biggr)\approx-86^\circ\)

Because our resultant vector is in Quadrant II, then our true direction angle will be 86° clockwise from the negative x-axis. So, our true direction angle is \(180^\circ-86^\circ=94^\circ\).

Thus, B is the correct answer

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Answer:

30 1/2

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

3rd and 5th square numbers means 3² and

5² .

so we know 3² is another word of saying 3×3

3×3=9

5×5=25

9+25=34

By finding all the four slopes, we can see that the word is ECHA.

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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Answer:

Step-by-step explanation:

first: x+(1/4)

second: (-1/3 )x +1/4

third: (3/4)x +1/3

The percent increase of the profit is 15%

In this question, the figures are given as

Profit in March = £2750

Profit in April = £3162.50

The percentage of the increase of the profit is then calculated using the following equation

Increase percentage = (Profit in April - Profit in March)/Profit in March * 100%

Substitute the known values in the above equation, so, we have the following representation

Increase percentage = (3162.50 - 2750)/2750 * 100%

Evaluate

Increase percentage = 15%

Hence, the increase in percentage is 15%

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Answer:

0

Step-by-step explanation:

slope= (y2-y1)/(x2-x1)

= [-2-(-2)]/[9-3]

=[-2+2]/6

=0/6

=0

Hope it helps:)

Answer:

d) 189.3 in²

Step-by-step explanation:

Area of rectangle is,

→ w × l

→ 10 × 15

→ 150 in²

Area of semi circle is,

→ (1/2)πr²

→ (1/2) × 3.14 × (5)²

→ 1.57 × 25

→ 39.3 in²

Now the total area will be,

→ 150 + 39

→ 189.3 in²

Thus, total area is 189.3 in².

Answer: B. a = b .

First of all, let's think that a is equal to b.

Then, let's link up these two triangles.

Now, we have a parallelogram.

x+y = a+60

and 75 = b . So, a = b. Then, a is also = 75.

Now apply the basic triangle rule.

75+75+x=180 .. x = 30 degree.

and for the other triangle....

y+75+60=180 .. y= 45 degree...

Now, let's consider that we want to write a as b.

So, x+b+75=180 ...x+b=105

and..

y+b+60=180...y+b = 120..

Then, let's exit the b from these two equations.

-1/  x+b=105

    y+b=120

Finally, we found this: y-x =15

and we have already found y and x values.

y was 45 and x was 30 degree.

So when we put these two numbers into that equation y-x=15

we found the value of 15.

So, our answer is a=b.

Answer:

\(\huge \boxed{\mathrm{B.} \ a=b}\)

Step-by-step explanation:

The two triangles form a parallelogram.

A parallelogram has opposite angles equal.

75 = b

Adjacent angles in a parallelogram are supplementary to one another.

They add up to 180 degrees.

a + 60 + 75 = 180

a + 135 = 180

Subtract 135 from both sides.

a = 75

Therefore, a = b.

Both representations are equivalent and describe the same function.the function rule for this table is:   f(x) = -1/2 x 2

The slope or gradient of a line is a number that describes both the direction and the steepness of the line. A slope of a line is the change in y coordinate with respect to the change in x coordinate.

To write a function rule for a given array, we need to determine how the values ​​in the output column (y) relate to the values ​​in the input column (x).

Looking at the given data, we notice that the output values ​​decrease by 1 every time the input value increases by 2. This suggests that the function is linear and that we can use the slope-intercept form of a linear equation to represent it. .

The slope-intercept form of a linear equation is y = mx b, where m is the slope and b is the y-intercept. In this case, the slope m is -1/2 because the output values ​​decrease by 1 every time the input values ​​increase by 2. The y-intercept b is 2 because the output value is 2 when the input value is 0.

Therefore, the function rule for this table is:

f(x) = -1/2 x 2

where x is the input value and f(x) is the output value.

Alternatively, we can also represent the function in table entries, for example:

f(0) = 2

f(2) = 1

f(4) = 0

f(6) = -1

Both representations are equivalent and describe the same function.

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