(Multiplying and Dividing with Scientific Notation MC)
How many times larger is 7 x 105 than 2 x 10³?

Answer: f(x) = x³ + 7x² -8x

Step-by-step explanation:

Zeros means that at that x-value, the graph crosses the x-axis and y = 0. Hence, to meet those criteria, the function would be:

[tex]f(x)=x(x+8)(x-1)[/tex]

At those three x-values, the corresponding y-values would equal 0.

Multiply them out to find the polynomial function:

[tex]f(x)=x(x+8)(x-1)=x(x^{2} -x+8x-8)=x^{3} +7x^{2} -8x[/tex]

The magnitude of the second earthquake, using an logarithmic function, is of:

5.77.

The magnitude of an earthquake is given by the logarithmic rule presented as follows:

[tex]M = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]

The first earthquake had a magnitude of 3.9, hence it's energy is obtained as follows:

[tex]3.9 = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]

[tex]\log{\left(\frac{E}{E_0}\right)} = \frac{3.9 \times 3}{2}[/tex]

[tex]\log{\left(\frac{E}{E_0}\right)} = 5.85[/tex]

The logarithm and the base 10 are inverse functions, hence the base 10 is applied to both sides to isolate the energy variable as vollows:

[tex]\frac{E}{E_0} = 10^{5.85}[/tex]

[tex]E = 707945.784E_0[/tex]

For the second earthquake, it's energy was 650 times greater, hence:

[tex]E = 707945.784 \times 650E_0 = 460164760E_0[/tex]

Hence it's magnitude is obtained as follows:

[tex]M = \frac{2}{3}\log{\left(\frac{460164760E_0}{E_0}\right)}[/tex]

M = 5.77.

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The equation of the line that goes through the point (3, 1) and is perpendicular to the line 2x + 4y = 5 can be written in the form y = mx + b where m= 2 and b= -5.

According to the question,

We have the following information:

Points = (3,1)

Equation of the line: 2x+4y = 5

Now, converting this line into y = mx+b form:

4y = -2x+5

y = -2y/4+5/4

y = -y/2+5/4

Now, the slope of this line is -1/2.

Slope of the line perpendicular to this line will be 2 (-1/m).

Now, the equation of the line will be:

(y-y') = m(x-x')

x' = 3 and y' = 1

y-1 = 2(x-3)

y-1 = 2x-6

y = 2x-6+1

y = 2x-5

The value of m is 2 and b is -5.

Hence, the equation of the line that goes through the point (3, 1) and is perpendicular to the line 2x + 4y = 5 can be written in the form y = mx + b where m= 2 and b= -5.

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Answer: 190

Step-by-step explanation:

first you add 29 + 29 and you get 58.  Next, you add 66 + 66 which is 132 then you add the 2 sums together and get 190.  :)

The number of cars that Tim has in all is 215.

The boxcars that Tim has is written in standard form. While the boxcars that Tim's grandfather gave him is written in scientific form. The first step is to convert the scientific form to standard form.

Number of boxcars that Tim's grandfather gave him: 1.62 x 10²

= 1.62 x 100

= 162

The next step is to add the boxcars that Tim's grandfather gave him to the number of boxcars that Tim has.

Total boxcars that Tim has = 162 + 53 = 215 box cars

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The previous population for the city is 23460.

Given that the population of a city has increased by 15% since it was last measured, the previous population will be:

= 1 - 15%

= 85%

Therefore, the previous population will be:

= Percentage × New population

= 85% × 27600

= 0.85 × 27600

= 23460

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Answer:

1.914 %

Step-by-step explanation:

Compounded quarterly means 4 periods per year  = n

   interest in decimal form per period    i = .019/4 = .00475

   Formula    

       annual yield =  ( 1+ i)^n  -1

                   (1+ .00475)^4  -1  = .01914  = ~ 1.914%

The probability is 0.5881.

From the question, we have

n = 20

P(X[tex]\geq[/tex]10) = 1-P(X<10)

P(X[tex]\geq[/tex]10) = 1-P(X[tex]\leq[/tex]9)

P(X[tex]\leq[/tex]9) = P(X=0)+P(X=1)+..................+P(X=9)

=0.4119

P(X[tex]\geq[/tex]10) = 1-P(X[tex]\leq[/tex]9)

=1-0.4119

=0.5881

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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The number of calories in each serving is 125.14 calories.

The bad of popcorn has 438 calories. Also, it was stated that it can serve 3.5 people.

The number of calories for each serving will be the division of the calories given.

This will be:

Number of calories = Total calories / Number of people

= 438 / 3.5

= 125.14 calories

Each serving has 125.14 calories.

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Answer:

a)  Line r

b)  Line q

c)  Line s

d)  Line q

e)  Line p

Step-by-step explanation:

A transversal is a line that crosses two other lines in the same plane at two distinct points.

a) The transversal connecting ∠1 and ∠5 is line r.

b) The transversal connecting ∠7 and ∠14 is line q.

c) The transversal connecting ∠8 and ∠11 is line s.

d) The transversal connecting ∠6 and ∠15 is line q.

e) The transversal connecting ∠3 and ∠9 is line p.

Answer: not a function

Step-by-step explanation: one input has more than one output and to be a function it must have one output for every input.

I hope it’s right, best of luck :)

According to the given APR, the monthly interest charge is $47.46

APR

Basically, APR refers the refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors.

Given,

Maxine's credit card has an APR of 21.99%.

Here we have to find the monthly interest charge if her current monthly balance, before interest, is $2,586.50.

While we looking into the given question, we have identified the following,

APR = 21.99%

For one month the APR is calculated as,

APR = 21.99 / 12

APR = 1.8325%

When we convert this into decimal form then we get,

=> APR = 1.8325/100

=> APR = 0.01835

And the current monthly balance is $2,586.50,

So, the interest change for the month is

=>2,586.50 x 0.01835

=> 47.46

Therefore, the monthly interest charge is $47.46.

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The exact interval notation of given equation is  x > - 8.

What is interval notation for compound inequalities?

The numbers that bound a continuous set of real numbers can be used to express the continuous set in interval notation. Intervals have many characteristics in common with ordered pairs when written.

We have,

            3x+1 > 2x-3 > x-11

Apply the rule that if m > v > n, then m > v and v > n to the given compound inequality to find the solution.

∴ m = 3x + 1,

   v = 2x - 3,

   n = x - 11.

Hence, by applying the rule of compound inequality we get,

          3x + 1 > 2x - 3 and 2x - 3 > x - 11

3x + 1 > 2x - 3

3x + 1 - 1 > 2x - 3 -1

3x > 2x - 4

3x - 2x > 2x - 4 - 2x

x > - 4

2x - 3 > x - 11

2x - 3 + 3 > x - 11 + 3

2x  > x - 8

2x  - x > x - 8 - x

x > - 8

The two computations above indicate that the acquired intervals, x > - 4 and x > - 8, will be combined to yield the answer to the given inequality.

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Answer:

1

Step-by-step explanation:

Answer:17

Step-by-step explanation:

its just the order of operations aka PEMDAS If you want to know more about the order of operations just look it up. :)

Step-by-step explanation:

your intercepts are:

y-intercept:

y = - 7/2x + 2

y = - 7/20 + 2

y = 2

( 0 , 2 )

x-intercept:

y = - 7/2x + 2

0 = - 7/2x + 2

-2 = - 7/2x

-7/2x = -2

2x = 2/7

x = 4/7

( 4/7 , 0 )

The area of triangle XYZ in the given graph with points X(-6,-5), Z(-4,-2) and Y(-2,-6) is 4 units square.

If the triangle's three vertices are specified on the coordinate plane, the area of a triangle in coordinate geometry may be determined. In coordinate geometry, a triangle's area is the area or space it occupies in the 2-D coordinate plane. The formula for finding the area of a triangle with three coordinates [tex](x_1,y_1), (x_2,y_2),[/tex] and [tex](x_3,y_3)[/tex]  is as follows:

Area of triangle [tex]=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

Now, finding the area of trianlge with points X(-6,-5), Z(-4,-2) and Y(-2,-6).

Area of triangle [tex]=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

[tex]=\frac{1}{2}|-6(-2+5)-4(-6+5)+-2(-5+2)|\\=\frac{1}{2}\times|-18+4+6|\\ =4[/tex]

Therefore, the area of triangle XYZ in the given graph is 4 units square.

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Answer:

y = -2/3 x + 8

Step-by-step explanation:

here is the answer in the image above

Answer: 12,000pd=6 tons

Step-by-step explanation:

Answer:

36.147580645161

Step-by-step explanation:

Hope it helps you

Area of the given figure is 27.852 in².

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

In the given figure there is a square.

First let us find the area of square, which has length of side 3 in

Area of square=3²=9

Now there are two semicircles with diameter 3 in.

Radius of semicircle = 3/2=1.5 in

Area of semicircle=2πr

=2×3.142×1.5

=9.426

As there are two semicircles

2×9.426

18.852

Area of figure is 9+18.852

27.852 in²

Hence, area of the given figure is 27.852 in².

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Answer:

3

Step-by-step explanation:

[tex]27^{\frac{1}{3}}[/tex]

1 ) Factor the number [tex]27=3^{3}[/tex]

[tex]=\left(3^3\right)^{\frac{1}{3}}[/tex]

2 ) Simplify...

3

Hope this helps! :)

By applying the distributive property of multiplication, this mathematical expression can be rewritten as -3(-4x + 5) = 12x - 15.

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Mathematically, the distributive property of multiplication can be represented by this mathematical expression:

a(b + c) = ab + ac.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

-3(-4x + 5) = -3(-4x) + [-3(5)]

-3(-4x + 5) = 12x - 15.

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Answer: function

Step-by-step explanation: for ever input the is one output, even though -10,5 showed up multiple times it had the same input and output. So it’s a function …if I remember correctly.

If the 5 is negative on just one, it’s not a function.

so sorry if it’s wrong, best of luck :)

The probabilities are given as follows:

a) P(both marbles are red) = 0.167 = 16.7%.

b) P(red then green) = 0.111 = 11.1%.

c) P(green then blue) =  0.083 = 8.3%.

d) P(blue and red, any order) = 0.333 = 33.3%.

The probability of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

In this problem, the are nine marbles, of which four are red, hence the probability of both red is:

p = 4/9 x 3/8 = 0.167 = 16.7%.

(the marble is not replaced, hence for the second marble there will be eight possible marbles, of which 3 are red).

For red then green, the probability is:

p = 4/9 x 2/8 = 0.111 = 11.1%.

For green then blue, the probability is:

p = 2/9 x 3/8 = 0.083 = 8.3%.

For blue or red, there are two possible outcomes, blue then red or red then blue, hence:

p = 3/9 x 4/8 + 4/9 x 3/8 = 0.333 = 33.3%.

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Answer:

87 [tex]ft^{2}[/tex]

Step-by-step explanation:

11x9=99

99 ft is the area of the rectangle

Now we need the area of the triangle

4x6=24

24/2=12

12 ft is the area of the triangle so we subtract this from the area of the rectangle

99-12=87

Hopes this helps please mark brainliest

1. The journal entries to record the transactions for Kohler Corporation are as follows:

January 2 Debit Treasury Stock $90,0000

Credit Paid-in capital in excess $30,000 Cash $120,000

January 5 Debit Dividend $88,000

Credit Dividend Payable $88,000

January 5 Debit Retained Earnings $88,000

Credit Dividend $88,000

February 28 Debit Dividend Payable $88,000

Credit Cash $88,000

July 6 Debit Cash $72,000

Credit Treasury Stock $45,000

Credit Paid-inn Capital in excess $27,000

August 22 Debit Cash $48,000

Credit Treasury Stock $45,000

Credit Paid-inn Capital in excess $3,000

September 5 Debit Dividend $100,000

Credit Dividend Payable $100,000

September 5 Debit Retained Earnings $100,000

Credit Dividend $100,000

October 28 Debit Dividend Payable $100,000

Credit Cash $100,000

December 31 Debit Income Summary $428,000

Credit Retained Earnings $428,000

2. The preparation of the statement of retained earnings for the current year ended December 31 is as follows:

Kohler Corporation

For the current year ended December 31

Beginning balance     $400,000

Dividends                       (88,000)

Dividends                     (100,000)

Income Summary          428,000

Ending balance          $640,000

The preparation of the stockholder's equity section of the balance sheet as of December 31 of the current year is as follows:

Kohler Corporation

As of December 31 of the current year

Common stock—$15 par value, 100,000 shares authorized

50,000 shares issued and outstanding                   $ 750,000

Paid-in capital in excess of par value, common stock 70,000

Retained earnings                                                        640,000

Total stockholders' equity                                       $1,460,000

January 2 Treasury Stock $90,0000 Paid-in capital in excess $30,000 Cash $120,000

January 5 Dividend $88,000 Dividend Payable $88,000 (50,000 - 6,000 x $2)

January 5 Retained Earnings $88,000 Dividend $88,000

February 28 Dividend Payable $88,000 Cash $88,000

July 6 Cash $72,000 Treasury Stock $45,000 Paid-inn Capital in excess $27,000 (3,000 x $24)

August 22 Cash $48,000 Treasury Stock $45,000 Paid-inn Capital in excess $3,000 (3,000 x $16)

September 5 Dividend $100,000 Dividend Payable $100,000 (50,000 x $2)

September 5 Retained Earnings $100,000 Dividend $100,000

October 28 Dividend Payable $100,000 Cash $100,000

December 31 Income Summary $428,000 Retained Earnings $428,000

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The sales tax percent when Ava went shopping for a new pair of pants is 3%.

From the information, Ava went shopping for a new pair of pants the listed price of the pair of pants was $21 but the price with tax came out to $21.63.

The sales tax will be:

= $21.63 - $21

= $0.63

The percentage of sales tax will be:

= Sales tax / Original price × 100

= 0.63 / 21 × 100

= 3%

The sales tax is 3%.

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We have an odd degree polynomial wit a positive leading coefficient, then the end behavior is:

as x → ∞, f(x) → ∞

as x → -∞, f(x) → -∞

Here we have the function:

f(x) = -10 + 6x^5 + 4x^3

Notice that this is a polynomial of degree 5 (odd degree).

When we have a odd degree polynomial, we know that:

If the leading coefficient is positive, then the end behavior is:

as x → ∞, f(x) → ∞

as x → -∞, f(x) → -∞

If instead, the leading coefficient is negative, then:

as x → -∞, f(x) → ∞

as x → ∞, f(x) → -∞

For the case of:

f(x) = −10+6x^5+4x^3

The leading coefficient is 6, so it is positive, then the end behavior of our function is:

as x → ∞, f(x) → ∞

as x → -∞, f(x) → -∞

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