[tex] \sf{x {}^{2} + 6x + 7 = 0 }[/tex]
x² + 6x + 7 = 0
help please it's due today :(​

The number of ways committees of 2 men and 3 women can be formed is 60.

The method of arranging objects in order is called Permutation and the method of selecting things from a group of objects such that the order doesn't matter is called Combination.

Total Men = 6

Total Women = 4

Committee should consists of 2 men and 3 women

2 men from 6 men can be selected in [tex]\rm ^6 C _2[/tex] ways

3 women from 4 women can be selected in [tex]\rm ^4C_3[/tex] ways

The number of ways committees of 2 men and 3 women can be formed can be determined by Multiplication Principle

[tex]\rm ^6 C _2[/tex] *  [tex]\rm ^4C_3[/tex]

15 * 4

= 60 ways

Therefore the number of ways committees of 2 men and 3 women can be formed is 60.

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The probability for part (a) is 0.18, for part (b) is 0.08, and for part (c) is 0.26.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

a. Find the probability that a randomly selected student is from east of the school and in the math club:

P(east ∩ math club)  = 0.6×0.3 = 0.18

b. Given that a student is from west of the school, what is the probability that he or she is in the math club?

P(west ∩ math club)  = 0.4×0.2 = 0.08

c. Is participation in the math club independent of whether a student lives east or west of the school?

P(math club)  = P(east ∩ math club) + P(west ∩ math club)

= 0.18 + 0.08

= 0.26

Thus, the probability for part (a) is 0.18, for part (b) is 0.08, and for part (c) is 0.26.

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Answer:

(1/2)

Step-by-step explanation:

From one point, if you go up one and over 2 you will get exactly one block up than from your initial point. And since the graph is pointing down on left side, that means it's positive.

Answer: 30

Step-by-step explanation:

Since there are two angles that measure [tex]60^{\circ}[/tex], the triangle is equilateral. This means that the angle bisector of the third angle is an altitude, and thus we have two right triangles with acute angles [tex]60^{\circ}[/tex] and [tex]x[/tex]. It follows that x=30.

Answer:

Emily raised $37.50

Justin raised $57.50

Step-by-step explanation:

(Step 1)

Say "x" equals the amount of money Emily made and "y" equals the amount of money Justin made. You can set up an equation with both of these variables because we know that they made a combined $95.

x = Emily's earnings

y = Justin's earnings

Emily + Justin = 95

x + y = 95

(Step 2)

The fact that there are two variables makes it difficult to find how much each person made individually. However, we can eliminate the "y" variable when we remember that Justin made $20 more than Emily. Now, we can substitute "x + 20" in for "y".

x + 20 = y

x + y = 95

x + (x + 20) = 95

(Step 3)  

Finally, we can solve for the "x" variable.

x + (x + 20) = 95

2x + 20 = 95                                <------ Combine like terms

2x = 75                                         <------ Subtract 20 from both sides

x = 37.5                                        <------- Divide both sides by 2

(Step 4)

Since we know the value of "x", we can plug it into one of the equations to find the value of "y".

x + 20 = y

37.5 + 20 = y

y = 57.5

Answer:

Emily raised $37.5 and justin raised $57.5

There's nothing particularly tricky about the limits of integration. The upper limit is a telescoping series converging to 2,

[tex]\displaystyle \sum_{n=1}^\infty \frac4{4n^2-1} = 2 \sum_{n=1}^\infty \left(\frac1{2n-1} - \frac1{2n+1}\right) \\\\ ~~~~~~~~ = 2 \left(\left(1-\frac13\right)+\left(\frac13-\frac15\right) + \left(\frac15 - \frac17\right) + \cdots\right)[/tex]

The lower limit reduces to 0 using the Riemann-Liouville definition of the fractional derivative. For [tex]q\in\Bbb Q[/tex], let

[tex]\displaystyle \frac{d^q}{dx^q} f(x) = \frac1{\Gamma(\lceil q\rceil-q)} \frac{d^{\lceil q\rceil}}{dx^{\lceil q\rceil}} \int_a^x (x-t)^{\lceil q\rceil-q-1} f(t) \, dt[/tex]

With [tex]a=0[/tex], [tex]q=\frac12[/tex] and [tex]\lceil q\rceil=1[/tex], it follows that

[tex]\displaystyle \frac{d^{1/2}}{dx^{1/2}} 1 = \frac1{\Gamma\left(\frac12\right)} \frac d{dx} \int_0^x (x-t)^{-1/2} \, dt = \frac1{\sqrt{\pi x}}[/tex]

Let

[tex]\displaystyle I = \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right)}{x^2-4x-1} \, dx[/tex]

Observe that

[tex]f(x) = \dfrac{2-x}{1+2x} = f^{-1}(x)[/tex]

is its own inverse, so by substituting [tex]\frac{2-x}{1+2x}\mapsto x[/tex], we get the equivalent integral

[tex]\displaystyle \int_0^2 \frac{\tan^{-1}(x)}{x^2-4x-1} \, dx[/tex]

We have the identity

[tex]\tan^{-1}(x) + \tan^{-1}\left(\dfrac{2-x}{1+2x}\right) = \tan^{-1}(2)[/tex]

so that

[tex]\displaystyle I + I = \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right) + \tan^{-1}(x)}{x^2-4x-1} \, dx[/tex]

[tex]\implies \displaystyle I = \frac{\tan^{-1}(2)}2 \int_0^2 \frac{dx}{(x-2)^2-5}[/tex]

The remaining integral is trivial,

[tex]\displaystyle \int_0^2 \frac{dx}{(x-2)^2-5} = \int_{-2}^0 \frac{dx}{x^2-5} \\\\ ~~~~~~~~ = \frac1{2\sqrt5} \int_{-2}^0 \left(\frac1{x-\sqrt5} - \frac1{x+\sqrt5}\right) \, dx \\\\ ~~~~~~~~= -\frac{\ln(2+\sqrt5)}{2\sqrt5} \\\\ ~~~~~~~~ = -\frac1{\sqrt5} \tanh^{-1}\left(\dfrac2{\sqrt5}\right)[/tex]

Then the integral we want is

[tex]I = \displaystyle \int_0^2 \frac{\tan^{-1}\left(\frac{2-x}{1+2x}\right)}{x^2-4x-1} \, dx = \boxed{-\frac1{2\sqrt5} \tan^{-1}(2) \, \tanh^{-1}\left(\dfrac2{\sqrt5}\right)} \approx -0.357395[/tex]

The ratio of blue paint to yellow paint is 2 : 3.

The total number of blue paint he used on the first and second day is 10.

The number of yellow paint he used on the first and second day is 15.

On the third day, the highest number of can of blue paint he can use is 2

On the third day, the highest number of can of yellow paint he can use is 3.

The ratio of blue paint to yellow paint can be determined by determining the simplest form of the paints used: 4 : 6 = 2: 3

Total blue paint cans used on the first and second day = 4 + 6 = 10

Blue paint cans remaining = 14 - 10 = 4

Total yellow paint cans used on the first and second day = 6 + 9 = 15 cans

Yellow paint cans remaining = 20 - 15 = 5 cans

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Total area of the circle is 1.12π square inches.

The Area of circle is π times the square of the radius.

i.e., A = πr²

Given:

Area of one circle = 0.56π

As the second circle is also identical then the area will be same.

So, the total area of circle is

=2* 0.56π

=1.12π square inches.

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Answer:

best ans is { f(x)| –∞ < f(x) ≤ 4}

Step-by-step explanation:

usually to find the range of a fn, u need to see what the value can be. the graph show only a small range of x values. but u can see f(x) is definitely <  4. so the ans is { f(x)| –∞ < f(x) ≤ 4}

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Answer:

Step-by-step explanation:

Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.

Las utilidades (U') se obtienen de sustraer los costes de producción (Cp) a las utilidades netas (U). Los costes de producción (Cp) son la suma de costes variables (C') y costes fijos (C). y la utilidades netas proceden de la venta de botellas. En consecuencia, tenemos la siguiente expresión:

U' = U - Cp

U' = U - C' - C

A continuación, desarrollamos y resolvemos la ecuación resultante:

30000 = 4.50 · x - 2.50 · x - 18500

1.50 · x = 11500

x = 7667

Por la ecuación de utilidad, necesitamos una producción de 7,667 botellas de un litro de capacidad para obtener un total de utilidades de S/ 30.000.

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Answer: [tex]y=26^{\circ}[/tex]

Step-by-step explanation:

Using linear pairs, we can determine the two angles in the picture attached.

Thus, as angles in a triangle add to [tex]180^{\circ}[/tex], [tex]y=26^{\circ}[/tex]

The best option is C. Provide multiple worksheets with pictures of the basic shapes for children to colour.

The process of learning has often been described to include all but not limited to the following:

Children according to experts learn faster and easily remember what they see. Hence, providing multiple worksheets with pictures of the basic shapes for children to colour is the most cost-efficient strategy to support children in learning about shapes.

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Answer:

volume= [tex]912.9ft^{3}[/tex] (not sure how you want to round the answer. it could be rounded to 913 or left as 912.9)

Step-by-step explanation:

volume of cone: to find the height of the cone, subtract the cylinder height from the total height (H-h= cone height)

[tex]V=\pi r^2\frac{h}{3} \\V=\pi (5.6)^2(\frac{6.8}{3} )\\V=\pi (31.36)(2.2666...)\\V=71.08057\pi \\V=223.3062[/tex]

volume of cylinder:

[tex]V=\pi r^2h\\V=\pi (5.6)^2(7)\\V=\pi (31.36)(7)\\V=219.52\pi \\V=689.6424[/tex]

add them together:

[tex]V=223.3062+689.6424\\V=912.9486[/tex]

It is important to use the correct units of measurement when working with conversions because errors may occur. 5 feet = 60 inches.

Conversion means to convert the same thing into different units.

It is important to use the correct units of measurement when working with conversions because errors may occur.

1 foot = 12 inches

Then we have

5 feet = 60 inches

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The amount and compound interest are Rs22169.11 and Rs6169.11 respectively

The formula for calculating the compound interest is expressed as:

P(t) = P0(1+r)^t

Substitute the given parameters

P(7/3) = 16000(1+0.15)^7/3

P(7/3) = 16000(1.15)^7/3

P(7/3) = 22169.11

For the interest

Interest = 22169.11 - 16000

Interest = 6169.11

Hence the amount and compound interest are Rs22169.11 and Rs6169.11 respectively

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Answer:

x=2 , y=6

Given: the interval (-5, 2) The graph are given that;

•°• g(x) = [ [ x +4 ] ]

g(-5) = [[ -5+4]]

= -1 (imposible)

g(2) = [[2+4]] = 6

x = 2

Let g(x) = y

= [[ x+4]]

y = 6

g(x) = 6 ✔

•°• x + 4 = 6

x = 2

g(y) = [[ y+4]] = 10

y + 4 = 10

y = 6

x = 2 , y = 6 ✔✔✔✔

Using the Fundamental Counting Theorem, it is found that 80 different scores are possible if everyone gets at least one point.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

There are 4 darts, and for each dart 3 possible scores, hence:

[tex]n_1 = n_2 = n_3 = n_4 = 3[/tex]

Hence the number of possible scores, removing the one score with zero points on all four rounds, is:

N = 3 x 3 x 3 x 3 - 1 = 80.

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Step-by-step explanation:

0 <= income <= 31000 : 10.8%

31000 < income <= 31000+36000 = 67000 : 12.75%

67000 < income < anything above 67000 : 17.4%

the total income is

$85,000

the taxes paid are

10.8% of 31000 = $3348

12.75% of 67000 - 31000 = 12.75% of 36000 = $4590

17.4% of 85000 - 67000 = 17.4% of 18000 = $3132

so, out of $85000 you paid

3348

4590

3132

----------

$11,070

taxes

100% = 85000

1% = 100%/100 = 85000/100 = 850

how many % are 11070 ?

well, as many as how often 1% fits into that amount :

11070 / 850 = 13.02352941...% ≈ 13.02%

To find the length of the missing side x, use Tan trigonometric formula

Tan: [tex]\frac{opposite}{Adjacent}[/tex]

Tan 21 = [tex]\frac{10.5}{x}[/tex]

Tan 21 × [tex]\frac{1}{10.5}[/tex] = [tex]\frac{10.5}{x}[/tex]×[tex]\frac{1}{10.5}[/tex]

[tex]\frac{10.5}{Tan 21}=x[/tex]

x=27.4

X= 27.4 ft

Hope it helps!

Answer:

x = 27.4 ft

Step-by-step explanation:

Here given:

So, use tan rule:

[tex]\sf tan(\theta) = \dfrac{opposite}{adjacent}[/tex]

insert values

[tex]\sf tan(21) = \dfrac{10.5}{x}[/tex]

make 'x' subject

[tex]\sf x= \dfrac{10.5}{tan(21) }[/tex]

calculate value

[tex]\sf x = 27.35343...[/tex]

rounded to nearest tenth

[tex]\sf x = 27.4 \ ft[/tex]

The probability of rolling an even number first and an odd number second is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of rolling an even number first and an odd number second = (numbers that have the even number first and odd number second / total sample space)

9/36 = 1/4

Here is the complete question:

The table below shows all of the possible outcomes for rolling two six-sided number cubes. What is the probability of rolling an even number first and an odd number second?

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Answer:

Step-by-step explanation:

Hello

   If a line's equation has the form [tex]\boldsymbol{\rm{y-y1=m(x-x1)}}[/tex], then it's considered to be in point-slope form.

In that formula,

Now you know why this equation is called point-slope form!

Now that we're familiar with the equation, let's plug in the information that's given to us...

[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x-(-1)}}[/tex] | simplify

[tex]\boldsymbol{\rm{y-2=\displaystyle\frac{3}{2}(x+1)}}[/tex]

[tex]\pmb{\tt{done~!!}}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

The strategy when figuring out the IQR and the 5-number summary for the data include arrangement from lowest to highest.

This is used to summarize distribution of data obtained or given in a sample and they include:

Proper arrangement of the data ensures accuracy in the results/values thereby making the most appropriate choice.

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The amount of interest that the principal in each account had earned is as follows:

Raul Avila = $167.12

Samuel Griffin = $364.91

The compound interests can be calculated using the compound interest formula:

A = P(1 + \frac{r}{n})^{nt}

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

It can also be computed using an online finance calculator as follows:

N (# of periods) = 110 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $10,000

PMT (Periodic Payment) = $0

Results:

FV = $10,167.12

Total Interest = $167.12

N (# of periods) = 120 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $20,000

PMT (Periodic Payment) = $0

Results:

FV = $20,364.91

Total Interest = $364.91

Thus, using the online finance calculator, the compound interest for each principal has been computed as $167.12 and $364.91, respectively.

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The rate is 1.2%.

Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account.

Given:

P = 5000

T =6 month= 1/2 year

SI= 300

We know,

SI= P*R*T/100

300= 500* R * 1 /200

60000= 500R

R= 60000/500

R= 120

R= 1.2%

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Answer:

in fraction form it is : 5 11/16

Decimal form it is : 5.6875

Step-by-step explanation:

convert the mixed number into improper fractions: 11 3/8 = 91/8

= 91/8 / 8/2

Apollyon the fraction rule: a/b / c = a / b * c

= 91/8 * 2

Multiply the numbers: 8 * 2 = 16

= 91/15

convert the improper fractions into mixed numbers: 91/16 = 5 11/16

Final answer of:
= 5 11/16

Answer:

y = -5x - 11

Step-by-step explanation:

We are given that a line passes through the point (-3,4) and also has a slope of -5.

We want to write an equation of this line.

The equation of the line can be written in 3 different ways:

Since the question did not specify, any of these 3 options will be valid, however, the most common way to write the equation of the line is in slope-intercept form, so let's do it that way.

Because we are already given the value of the slope, we can immediately plug that into the equation.

Replace m with -5.

y = -5x + b

Now we need to find b.

As the equation passes through the point (-3, 4), we can use its values to help solve for b.

Substitute -3 as x and 4 as y.

4 = -5(-3) + b

Multiply

4 = 15 + b

Subtract 15 from both sides.

-11 = b

Substitute -11 as b in the equation.

y = -5x - 11

Topic: finding the equation of the line

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Two bikers meet at a park at A

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles.

By following of the above statement the triangle is formed shown in  the image attached below.

Thus, without using cosine formula, by drawing the triangle according to
the statement. At point A both the bikers were meet

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Based on the triangle sum theorem, exterior angle theorem, the true statements are:

m∠5 + m∠6 = 180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

According to the triangle sum theorem, m∠2 + m∠3 + m∠5 = 180°.

Also, based on the exterior angle theorem, m∠2 + m∠3 = m∠6.

∠5 and ∠6 are a pair of linear angles, therefore: m∠5 + m∠6 = 180°.

In summary, the true statements about the diagram given are:

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