Find the missing side round to the nearest tenth

Answer:

y-3 = 2(x-1)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-3 = 2(x-1)

Answer:

3=2x+1

Step-by-step explanation:

Use the equation y=mx+b

where y is the y component, x is the variable and b is the x intercept

Answer:

m=[tex]7\sqrt3[/tex]

n=7

Step-by-step explanation:

Hi there!

We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14

We need to find the lengths of m and n

Firstly, let's find the measure of the other acute angle

The acute angles in a right triangle are complementary, meaning they add up to 90 degrees

Let's make the measure of the unknown acute angle x

So x+60°=90°

Subtract 60 from both sides

x=30°

So the measure of the other acute angle is 30 degrees

This makes the right triangle a special kind of right triangle, a 30°-60°-90°  triangle

In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is [tex]\frac{a}{2}[/tex], and the leg opposite from the 60 degree angle is [tex]\frac{a\sqrt3}{2}[/tex]

In this case, a=14, n=[tex]\frac{a}{2}[/tex], and m=[tex]\frac{a\sqrt3}{2}[/tex]

Now substitute the value of a into the formulas to find n and m to find the lengths of those sides

So that means that n=[tex]\frac{14}{2}[/tex], which is equal to 7

And m=[tex]\frac{14\sqrt3}{2}[/tex], which simplified, is equal to [tex]7\sqrt3[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.

Thus, from the diagram

the length = 8 - 2x   the width = 10 - 2x  and the height = x

So, the volume V = L*w*h

Volume (V) = (8 - 2x) (10 - 2x) x

V = (80 - 16x - 20x +4x²)x

V = 80x -36x² + 4x³

By rearrangement:

V = 4x³ - 36x² + 80x

Answer:

Step-by-step explanation:multiple 5 times 108 and that gives you your answer..

Answer:

M of aftershock = 4.90

Step-by-step explanation:

5.6 = log(x/1)

[tex]10^{5.6} = 398107.1 \\[/tex]

1/5 * 398,107.1 = 79,621.4

[tex]10^{m} =[/tex] 79,621.4

m = log (79,621.4) = 4.90  

[tex]\\ \sf\longmapsto y=(6x-5)\sqrt{8x-3}[/tex]

[tex]\\ \sf\longmapsto y=6(-4)-5\sqrt{8(-4)-3}[/tex]

[tex]\\ \sf\longmapsto y=-24-5\sqrt{-32-3}[/tex]

[tex]\\ \sf\longmapsto y=-29\sqrt{-35}[/tex]

[tex]\\ \sf\longmapsto y=-29\times 35i[/tex]

[tex]\\ \sf\longmapsto y=-1015i[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

a) 1/4 of 28 = 28/4 = 7 coins are quarters.

  2/3 of (28 -7) = (2/3)(21) = 14 coins are dimes

The remaining 28 -7 -14 = 7 coins are nickels

__

b) The amount of money in coins is ...

  7×$0.25 +14×$0.10 +7×$0.05 = $3.50 . . . in coins

__

c) 2 packs of cards at $1.35 each will cost 2×$1.35 = $2.70. After the purchase, the remaining money would be ...

  $3.50 -2.70 = $0.80 . . . remaining

9514 1404 393

Answer:

  $11,680.58

Step-by-step explanation:

Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.

__

The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.

The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...

  0.205×21,465 = 4400.325 ≈ 4400.33

The the total tax due on $70,000 is ...

  $7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000

_____

Additional comments

The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.

__

Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.

  ≤ 48535 -- income × 0.15

  ≤ 97069 -- income × 0.205 -2669.425

  ≤ 150,473 -- income × 0.26 -8008.22

  ≤ 214,368 -- income × 0.29 -12,522.41

  > 214,368 -- income × 0.33 -21,097.13

In this case, the second row of this simpler table would give the tax on $70,000 as ...

  tax = 70,000 × 0.205 -2669.425

  tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above

Answer:  

STEP 1  

M_{4,2} is set of 4x2 matrices hence each matrix has 4*2=8 entries. Each entry can be filled independently.  

Hence its basis has 8 linearly independent vectors.  

STEP 2  

Dimension= cardinality of basis = 8.

Answer:

the correct answer is |x – 18| ≤ 4

just took the test

Step-by-step explanation:

Answer:

PW, BW,  GW, PY,  BY, GY

Step-by-step explanation:

We need to determine the sample space

pink(P), blue (B), and green (G) cards,   (W) and yellow (Y) envelopes

Each color card can match with each color envelope

Start with the white envelopes and each color card

and then the yellow envelopes with each color card

PW   BW  GW

PY  BY   GY

Answer:

40

Step-by-step explanation:

Based on the Proportional Transversal Theorem, the three parallel lines hat intersects the two transversals, divides the transversal lines proportionally.

Therefore, we would have the following ratio:

28/35 = ?/50

Cross multiply

35*? = 50*28

35*? = 1,400

Divide both sides by 35

? = 1400/35

? = 40

Answer:

a.) .0469

b.) .9961

c.) .9492

Rounded these check below for full answers

Step-by-step explanation:

a.)

[tex]{4\choose3}*.25^3*(1-.25)=.046875[/tex]

b.)

Porbability of at most 3 successes is equal to 1-p(4)

p(4)=

[tex]{4\choose4}*.25^4=.003690625[/tex]

1-.003690625=.99609375

c.)

two or more failures is equa lto

p(0)+p(1)+p(2)=

[tex]{4\choose0}*.25^0*(1-.25)^4+{4\choose1}*.25^1(1-.25)^3+{4\choose2}*.25^2*(1-.25)^2=.94921875[/tex]

Answer:

Im pretty sure its 1,000 miles (dont forget the unit)

Step-by-step explanation:

Determine if this problem is a inverse variation or direct variation problem! This means that:

equation would be:

1=40

25=x

cross multiply*

x=25*40

x=1,000 miles apart! (dont forget the unit)

If this doesnt work then try this equation!

1=40

25=x

Multiply 1*40 and 25 *x

40=25x......    

40/25= 1.6

x=1.6! (Extra step)

Cheers!

Answer: 100 Miles

Step-by-step explanation: took the miles and got it correct.

(Also it's 2.5 inches apart, not 25.)

Answer:

y=2x+1

Step-by-step explanation:

y is directly proportional to x if it increases as x increases

Answer:

1                  

-------------  

(x+2)(x-4)

Step-by-step explanation:

x+4                    x+3

-------------   * --------------

x^2+5x+6        x^2 -16

Factor

x+4                    x+3

-------------   * --------------

(x+3)(x+2)        (x+4)(x-4)

Cancel like terms

1                  1

-------------   * --------------

(1)(x+2)        (1)(x-4)

1                  

-------------    x cannot equal -3, -4, -2, 4  

(x+2)(x-4)

9514 1404 393

Answer:

  (f•g)(x) = -16x^3 +10x^2 -14x

Step-by-step explanation:

  (f•g)(x) = f(x)•g(x) = (-2x)(8x^2 -5x +7)

Use the distributive property:

  (f•g)(x) = -16x^3 +10x^2 -14x

Answer:

Imaginary roots

Step-by-step explanation:

The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].

Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:

[tex]7x^2-5x+1=0[/tex]

Now assign variables:

The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].

What does this tell us about the roots?

Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.

Answer:

July 4th, 1776.

Step-by-step explanation:

By issuing the Declaration of Independence, adopted by the Continental Congress on July 4, 1776, the 13 American colonies severed their political connections to Great Britain. The Declaration summarized the colonists' motivations for seeking independence.

Answer:

C) SQRT(65)

Step-by-step explanation:

the magnitude of 1-8i is given by the following:

sqrt(a^2+b^2)  

sqrt(1^2+8^2)

=sqrt(1+64)

=sqrt(65)

It is to be noted that the magnitude of   |1 − 8i| is √(65) (Option C)

To find the magnitude (or absolute value) of a complex number, we use the formula |a + bi| = √(a² + b²). In this case, the complex number is 1 - 8i.

Using the formula, we have  -

|1 - 8i| = √(1² + (-8)²)

= √(1 + 64)

= √65

Hence, the magnitude of 1 - 8i is √65.

So the correct answer is C) √65.

Learn more about magnitude  at:

https://brainly.com/question/30337362

#SPJ6

Step-by-step explanation:

f(x)=log(x)

     =d(log(x)/dx)

=>y=1/x

Answer:iiii

Step-by-step explanation:iiiii

Answer:

17.9

Step-by-step explanation:

Answer:

There would be [tex]120[/tex] of them.

Step-by-step explanation:

There are [tex]6[/tex] distinct letters in the word "[tex]\verb!theory![/tex]".

Hence, there would [tex]6[/tex] possible choices for the first letter that was selected.

Since the chosen card won't be placed back in the pool, there would be only [tex](6 - 1) = 5[/tex] possible choices for the second letter.

Likewise, there would be [tex](6 - 2) = 4[/tex] choices for the third letter.

[tex]6 \times 5 \times 4 = 120[/tex]. In other words, there are [tex]120[/tex] possible ways to draw three cards out of [tex]6[/tex] one after another.

Since the question states that the order of the cards matters, it won't be necessary to eliminate repetitions such as "[tex]\verb!the![/tex]" and "[tex]\verb!het![/tex]" from the number of combinations.

The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.

Given:

Probability of student smoke,

P = 27.7%

  = 0.277

Number of students (n) = 632

[tex]q = 1-p[/tex]

  [tex]=1-0.277[/tex]

  [tex]=0.723[/tex]

(i)

Here,

Number of students (n) = 60

then,

⇒ [tex]n_P=60\times 0.277[/tex]

         [tex]=16.62[/tex]

⇒ [tex]n_q=60\times 0.723[/tex]

        [tex]=43.38[/tex]

We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.

Now,

[tex]\mu = n_P= 16.62[/tex]

[tex]\sigma = \sqrt{n_{Pq}}[/tex]

  [tex]= \sqrt{60\times 0.277\times 0.723}[/tex]

  [tex]=3.9664[/tex]

Now,

⇒ [tex]P(X<19) = P(X<18.5)[/tex]

                      [tex]=P(Z_{18.5})[/tex]

The Z-score is:

= [tex]\frac{18.5-16.62}{3.4664}[/tex]

= [tex]0.5423[/tex]

hence,

The probability will be:

⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]

or,

⇒ [tex]P(Z<19) = 0.7062[/tex]

(ii)

Here,

Number of students (n) = 75

[tex]\mu = n_P = 75\times 0.277[/tex]

            [tex]=20.775[/tex]

[tex]\sigma = \sqrt{n_{Pq}}[/tex]

   [tex]=\sqrt{75\times 0.277\times 0.723}[/tex]

   [tex]=3.8756[/tex]

Now,

⇒ [tex]P(X>17) = P(X> 17.5)[/tex]

                      [tex]=1-P(X \leq 17.5)[/tex]

                      [tex]=1-P(Z_{17.5})[/tex]

The Z-score is:

= [tex]\frac{17.5-20.775}{3.8756}[/tex]

= [tex]-0.9740[/tex]

then, [tex]P(Z_{17.5}) = 0.165[/tex]

hence,

The probability will be:

⇒ [tex]P(X>17) = 1-0.165[/tex]

                      [tex]=0.835[/tex]    

Learn more about Probability here:

https://brainly.com/question/9825651

Answer:

Following are the solution to the given points:

Step-by-step explanation:

As a result, Poisson for each driver seems to be the number of accidents.

Let X be the random vector indicating accident frequency.

Let, [tex]\lambda=[/tex]Expected accident frequency

[tex]P(X=0) = e^{-\lambda}[/tex]

For class 1:

[tex]P(X=0) = \frac{1}{(1-0.2)} \int_{0.2}^{1} e^{-\lambda} d\lambda \\\\P(X=0) = \frac{1}{0.8} \times [-e^{-1}-(-e^{-0.2})] = 0.56356[/tex]

For class 2:

[tex]P(X=0) = \frac{1}{(2-0.4)} \int_{0.4}^{2} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{1.6} \times [-e^{-2}-(-e^{-0.4})] = 0.33437[/tex]

For class 3:

[tex]P(X=0) = \frac{1}{(3-0.6)} \int_{0.6}^{3} e^{-\lambda} d\lambda\\\\P(X=0) = \frac{1}{2.4} \times [-e^{-3}-(-e^{-0.6})] = 0.20793[/tex]

The population is equally divided into three classes of drivers.

Hence, the Probability

[tex]\to P(X=0) = \frac{1}{3} \times 0.56356+\frac{1}{3} \times 0.33437+\frac{1}{3} \times 0.20793=0.36862[/tex]

Answer:

D

Step-by-step explanation:

(x^2+3)(x-5)

That's the answer

Answer:

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

Step-by-step explanation:

There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.

At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just

[tex]\frac{4}{52}[/tex]

After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is

[tex]\frac{4}{51}[/tex]

Now to get the total probability we need to multiply the two probabilities together

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

Answer:

one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.

The answer would then be D

Answer:

28 seconds ..............