Solve.
x^2-9x+3=0
x=
or
x=

Answer:

4

Step-by-step explanation:

The given data is :

8, 10, 12,14,16,18,20

We need to find the standard deviation. Here,

Count = 7

Sum, Σx: 98

Mean, μ: 14

The standard deviation is given by :

[tex]\sigma=\sqrt{\dfrac{1}{N}\Sigma(x_i-\mu)^2}[/tex]

or

[tex]\sigma^2=\dfrac{1}{N}\Sigma(x_i-\mu)^2\\\\=\dfrac{(8-14)^2+...+(20-14)^2}{7}\\\\=\dfrac{112}{7}\\\\\sigma^2=16\\\\\sigma=4[/tex]

So, the standard deviation of the given data is 4.

Answer:

Step-by-step explanation:

Answer: (3a + 1) (a + 3)

Step-by-step explanation:

Concept:

Here, we need to know the idea of factorization.

It is like "splitting" an expression into a multiplication of simpler expressions. Factoring is also the opposite of Expanding.

Solve:

Given = 3a² + 10a + 3

STEP ONE: separate 3a² into two terms

3a

a

STEP TWO: separate 3 into two terms

3

1

STEP THREE: match the four terms in ways that when doing cross-multiplication, the result will give us 10a.

3a     1

a       3

When cross multiply, 3a × 3 + 1 × a = 10a

STEP FOUR: combine the expression horizontally to get the final factorized expression.

3a  ⇒   1

a   ⇒    3

(3a + 1) (a + 3)

Hope this helps!! :)

Please let me know if you have any questions

Answer: [tex]9a+14[/tex]

Step-by-step explanation:

Simplify: [tex]4(a+1)+5(a+2)[/tex]

Step 1. Distribute 4 into a and 1. By distributing you would get 4a and 4.

[tex]4*a=4a. \\4*1=4[/tex]

Step 2. Plug 4a+4 back into the remaining equation, which can be viewed below:

[tex]4a+4+5(a+2)[/tex]

Step 3. Distribute, [tex]5(a+2)[/tex] again. Same principle as what you did previously. You should get 5a and 10.

[tex]5*a=5a.\\5*2=10.[/tex]

Step 4. Plug 5a+10 back into the leftover equation, which is as follows.

[tex]4a+4+5a+10[/tex]

Step 5. Combine like terms. Which is broken down below,

[tex]4a+5a=9a.\\4+10=14.[/tex]

Once you're done combining like terms, you'll get the simplified answer which is: [tex]9a+14[/tex]

Answer:

9a +14

Step-by-step explanation:

4(a + 1) + 5(a + 2)

Distribute

4a+4  +5a+10

Combine like terms

4a+5a  +4+10

9a +14

Answer:

Option C, angle bisector

Answered by GAUTHMATH

Answer:

1/625 = 0.0016

Step-by-step explanation:

update, oh sorry, this is about 4 picks and not 5.

so, it is 1/5⁴ = 1/625 = 0.0016

1 in 5 own their own car.

that is 20% or a chance of 1/5 = 0.2 of picking a student owning a car.

let's assume that the total number of students is large enough that each pick does not change the individual probabilities.

each event (picking a student and checking the ownership of a car) is independent and non-overlapping.

so, the probability that all 5 own a car is the chance of picking the 5th student owning a car AND all 4 previous student picks owning a car.

the probability that all 4 previous picks own a car is the chance of picking the fourth student owning a car AND all 3 previous student picks owning a car.

the probability that all 3 previous picks own a car is the chance of picking the third student owning a car AND all 2 previous student picks owning a car.

the probability that all 2 previous picks own a car is the chance of picking the second student owning a car AND the previous student pick owning a car.

the probability that the first student pick owns a car is 1/5 or 0.2

so, we have a clean

1/5×1/5×1/5×1/5×1/5 = 1/5⁵ probability = 1/3125 = 0.00032

Answer:

H0 : μ = 60000

H1 : μ ≠ 60000

Test statistic = 3.464

Step-by-step explanation:

Given :

Sample mean salary, xbar = 80000

Sample standard deviation, s = 10000

Population mean salary , μ = 60000

Sample size, n = 3

Hypothesis :

H0 : μ = 60000

H1 : μ ≠ 60000

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (80000 - 60000) ÷ (10000/√(3))

T = 20000 / 5773.5026

T = 3.464

The Decison region :

If Tstatistic >Tcritical

Tcritical at 10%, df = 2 ; two - tailed = 2.9199

Tstatistic > Tcritical ; He

Answer:

17.3

Step-by-step explanation:

14.4 x 1.2

= 17.28

= 17.3 ( approximately )

Answer:

2666.01%

Step-by-step explanation:

Intrest=(PA)*I*T

1377.53=51.67*I*1

I=26.6601=2666.01%

Answer:

The function with blue line (see attachment) represents the graph of [tex]f(x) = -4\cdot |x|[/tex] after it is translated 3 units down.

Step-by-step explanation:

Mathematically speaking, a translation in the y-direction is defined by the following expression:

[tex]g(x) = f(x) + k[/tex] (1)

Where:

[tex]g(x)[/tex] - Resulting function.

[tex]f(x)[/tex] - Original function.

[tex]k[/tex] - Translation factor ([tex]k > 0[/tex] - Translation in the +y direction/[tex]k< 0[/tex] - Translation in the -y direction).

If we know that original function is translated 3 units down and [tex]f(x) = -4\cdot |x|[/tex], then the resulting function is:

[tex]g(x) = -4\cdot |x|-3[/tex]

Lastly, we graph both original and resulting functions with the help of a graphing tool, whose outcome is presented in the image attached below:

Please notice that the red line represents the original function, whereas the blue line represents the resulting function.

Step-by-step explanation:

hi

what is your question?

Step-by-step explanation:

please tell full questions

Answer:

Maaf saya tidak paham

jadikan jawaban tercerdas, terimakasih

Answer:

nợ tk 1381: 2 triệu / có tk 152: 2 triệu

Answer:

Step-by-step explanation:

Answer: B, Positive Correlation

Step-by-step explanation:

Every point after the first point increases. Therefore, we have a positive correlation. If it was a negative correlation, every point after the first would be decreasing.

Answer:

(0,2) and (8,10)

Step-by-step explanation:

Let the smaller integer be 2n. The larger will be 2x+2.

ATQ. 2n(2n+2)+10=5(4n+2). Solving it, we get 2n=0 or 2n=8. The pairs are (0,2) and (8,10)

Answer:

17 days

Step-by-step explanation:

as you see, 4=2^2

and 8=2^3

so we have a number sequence:

2+2^2+2^3+...+2^n=260000 (1)

multiply (1) by 2 we have:

2^2+2^4 +...+2^(n+1)=520000 (2)

(2) minus (1) we have:

2^(n+1)-2=260000

2^n*2=260002

2^n=130001

and we have 2^17=131072 >130001

so it will take her at least 17 days to buy the car

It will take her about 17 days to buy the car worth 260000 cents

If a student decides she wants to save money to buy a used car that cost $2600 (260,000 cents)

If she saves 2 cents the first day and doubles the amount thereafter, the sequence of savings will be:

2, 4, 8...

This sequence is geometric in nature

In order to determine how long it will take her to save 260,000, we will use the sum of a GP formula expressed as:

[tex]S_n = \frac{a(r^n-1)}{r-1}[/tex]

Given the folowing

a = 2

r = 4/2 = 8/4 = 2

Sn = 260,000

Substitute into the formula the given parameters

[tex]260000= \frac{2(2^n-1)}{2-1}\\260000/2=2^n-1\\130000 = 2^n - 1\\2^n = 130000 + 1\\2^n = 130001\\nlog 2=log130001\\n = \frac{log130001}{log2} \\n \approx 17[/tex]

This shows that it will take her about 17 days to buy the car worth 260000 cents

Learn more here: https://brainly.com/question/20548958

Answer:

1,-3,-5

Step-by-step explanation:

Given:

f(x)=x^3+7x^2+7x-15

Finding all the possible rational zeros of f(x)

p= ±1,±3,±5,±15 (factors of coefficient of last term)

q=±1(factors of coefficient of leading term)

p/q=±1,±3,±5,±15

Now finding the rational zeros using rational root theorem

f(p/q)

f(1)=1+7+7-15

  =0

f(-1)= -1 +7-7-15

    = -16

f(3)=27+7(9)+21-15

   =96

f(-3)= (-3)^3+7(-3)^2+7(-3)-15

    = 0

f(5)=5^3+7(5)^2+7(5)-15

   =320

f(-5)=(-5)^3+7(-5)^2+7(-5)-15

     =0    

f(15)=(15)^3+7(15)^2+7(15)-15

    =5040

f(-15)=(-15)^3+7(-15)^2+7(-15)-15

     =-1920

Hence the rational roots are 1,-3,-5 !

9514 1404 393

Answer:

  PQ = 46

Step-by-step explanation:

Midsegment ST is half the length of base segment PQ.

  2×ST = PQ

  2×(5x -22) = 3x +19

  10x -44 = 3x +19 . . . . . . . eliminate parentheses

  7x = 63 . . . . . . . . . . . . add 44-3x

  x = 9 . . . . . . . . . . . . divide by 7

PQ = 3x +19 = 3×9 +19

PQ = 46

Answer:

B

Step-by-step explanation:

-2/3x<31/3

x>-31/2

x>-15 1/2

Answer:

x > - 15 1/2

Step-by-step explanation:

-2/3 x -10 < 1/3

Multiply each side by 3

3(-2/3 x -10 < 1/3)

-2x -30 < 1

Add 30 to each side

-2x-30+30 <1+30

-2x < 31

Divide by -2 remembering to flip the inequality

-2x/-2 > 31/-2

x > -31/2

x > - 15 1/2

Answer:

Simpler equations and inequalities as such could be typed into an online graphing calculator such as Desmos! Remember this because you'll need it for future harder math classes :)

Step-by-step explanation:

Answer:

Option d (7.84 or less) is the right alternative.

Step-by-step explanation:

Given:

[tex]\sigma^2=1936[/tex]

[tex]\sigma = \sqrt{1936}[/tex]

   [tex]=44[/tex]

Random sample,

[tex]n = 121[/tex]

The level of significance,

= 0.95

or,

[tex](1-\alpha) = 0.95[/tex]

        [tex]\alpha = 1-0.95[/tex]

[tex]Z_{\frac{\alpha}{2} } = 1.96[/tex]

hence,

The margin of error will be:

⇒ [tex]E = Z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )[/tex]

By putting the values, we get

        [tex]=1.96(\frac{44}{\sqrt{121} } )[/tex]

        [tex]=1.96(\frac{44}{11} )[/tex]

        [tex]=1.96\times 4[/tex]

        [tex]=7.84[/tex]    

Answer:

If you multiply a decimal by 10, the decimal point will move one place to the right. If you divide a decimal by 10, the decimal point will move one place to the left.

Step-by-step explanation:

Multiplying a decimal by 10 increases the value of each digit by 10. Multiplying a decimal by a power of 10 increases the value of each digit by a number of times that is equivalent to that power of 10. When a digit's value is changed, that digit is moved to the appropriate place.

Answer: B

Step-by-step explanation:

A) [tex]a^\frac{3}{4}[/tex]÷[tex]a^\frac{1}{2}[/tex] cannot be the answer. When a to the power of x is divided by a to the power of y it is a to the power of x-y. Ex: [tex]a^x[/tex]÷[tex]a^y=a^x^-^y[/tex]

So 3/4-1/2 is 1/4 giving us [tex]a^{\frac{1}{4} }[/tex]

B is the answer because taking the square root of a is the same as [tex]a^\frac{1}{2}[/tex] which isn't the same as [tex]a^\frac{1}{4}[/tex]

C is not the answer because when a to the power of x is multiplied by a to the power of y it is a to the power of x+y. Ex:  [tex]a^x[/tex]·[tex]a^y[/tex]=[tex]a^{x+y}[/tex]

1/8+1/8=1/4 so it is [tex]a^\frac{1}{4}[/tex]

D can't be the answer. [tex]a^\frac{1}{8}[/tex] squared is the same as [tex]a^\frac{1}{8}[/tex]·[tex]a^\frac{1}{8}[/tex] so the same explanation of c applies to d

Answer:

Hello,

Answer B

Step-by-step explanation:

Since A=15*20+B and B<15

The max for B is 14

==> 300+14=314

9514 1404 393

Answer:

  x = 6√2

Step-by-step explanation:

The side ratios in an isosceles right triangle are ...

  1 : 1 : √2

These will be the same as ...

  x : x : 12

so, ...

  x = 12/√2

  x = 6√2

9514 1404 393

Answer:

  x = 1.35 (12.22)

Step-by-step explanation:

The selling price x is ...

  x = cost + markup

  x = cost + 0.35 × cost = cost(1 +0.35)

  x = 1.35(12.22)