Write this number in standard notation.
4.702 x 10

Answer:

The first step to solve the expression is to solve () i.e. (10-7) will be solved first.

Step-by-step explanation:

Any algebraic expression is solved as per BODMAS rule i.e. in the following sequential order (one after the other).

B - Bracket i.e. ()

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

So, as per BODMAS rule, the bracket  i.e. () expression will be solved at first.

Solving the expression:

15 + 20 ÷ (10 – 7) + 12

[tex]\Rightarrow[/tex] 15 + 20 ÷ 3 + 12

[tex]\Rightarrow[/tex] 15 + 6.67 + 12

[tex]\Rightarrow[/tex] 21.67 + 12

[tex]\Rightarrow[/tex] 33.67

Hence, (10-7) will be evaluated first.

Answer:

10-7 will be done first.

Step-by-step explanation:

Answer:

0.982 mile

Step-by-step explanation:

1 mile = 5280 ft

h = (5183ft) *(1 mile/5280ft) = 0.982 miles

The height of Denver, Colorado above sea level rounded to three decimal places is 0.982miles.

Measurement is simply the process of associating numbers with physical quantities and events.

Converting measurements in foot to miles as;

1foot = (1/5280)miles

Given that;

Since 1foot = (1/5280)miles

5183ft = ( 5183 / 5280 )miles

5183ft = 0.982miles

Therefore, the height of Denver, Colorado above sea level rounded to three decimal places is 0.982miles.

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Answer:

B,D

Step-by-step explanation:

The true statements are given below.

The land the Pentagon become first planned to head on become bordered on 5 aspects through roads, so the architects designed a five-sided building.

A pentagon is a geometrical form, which has 5 facets and five angles. here, “Penta” denotes five, and “gon” denotes attitude. The pentagon is one of the forms of polygons. The sum of all the indoor angles for a normal pentagon is 540 ranges.

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Answer:

11x-2

Step-by-step explanation:

(3x2 - 4x + 6) + (7x - 2) This is the breakdown. (6 4x + 6)= 4x. + (7x-2) = 11x-2

Answer:

  a) Megan's total so far is 3 km more than necessary for an average of 15 km

  b) 22 km

Step-by-step explanation:

a) The total of differences from 15 is ...

  -1 + 8 + (-2) +(-2) = 3

Since this is more than 0, Megan's average is more than 15.

__

b) The total of differences from 17 is ...

  -3 +6 -4 -4 = -5

To increase her average to 17 km, Megan must walk 17+5 = 22 km on Friday.

_____

Comment on the approach

In general, I find it easier mentally to deal with small numbers than with larger ones. So adding small differences can be easier than computing larger sums.

a) By computing the difference from the supposed average, we have effectively found the difference of the sum of values from the total necessary to give the required average. That is, Megan's average would be 15 if her total distance were 4·15 = 60. Her total distance is (4·15 +3) = 63, so her average is more than 15.

b) By finding out how much the total is below that necessary for the desired average, we determine the amount above that average the final number needs to be.

  (14 -17) +(23 -17) +(13 -17) +(13 -17) +(Friday -17) = 0 . . . . the Friday value to make an average of 17

  14 +23 +13 +13 +Friday = 5·17 . . . . . . . add 5·17

  (14 +23 +13 +13 +Friday)/5 = 17 . . . . . . shows the Friday amount gives the required average

  Friday = 17 -((14 -17) +(23 -17) +(13 -17) +(13 -17)) . . . . first equation rearranged to show how we computed Friday

  Friday = 17 -(-5) = 17 +5 = 22

Answer:

Please read the complete procedure below:

Step-by-step explanation:

You have the following initial value problem:

[tex]y'+2y=4t\\\\y(0)=8[/tex]

a) The algebraic equation obtain by using the Laplace transform is:

[tex]L[y']+2L[y]=4L[t]\\\\L[y']=sY(s)-y(0)\ \ \ \ (1)\\\\L[t]=\frac{1}{s^2}\ \ \ \ \ (2)\\\\[/tex]

next, you replace (1) and (2):

[tex]sY(s)-y(0)+2Y(s)=\frac{4}{s^2}\\\\sY(s)+2Y(s)-8=\frac{4}{s^2}[/tex]  (this is the algebraic equation)

b)

[tex]sY(s)+2Y(s)-8=\frac{4}{s^2}\\\\Y(s)[s+2]=\frac{4}{s^2}+8\\\\Y(s)=\frac{4+8s^2}{s^2(s+2)}[/tex] (this is the solution for Y(s))

c)

[tex]y(t)=L^{-1}Y(s)=L^{-1}[\frac{4}{s^2(s+2)}+\frac{8}{s+2}]\\\\=L^{-1}[\frac{4}{s^2(s+2)}]+L^{-1}[\frac{8}{s+2}]\\\\=L^{-1}[\frac{4}{s^2(s+2)}]+8e^{-2t}[/tex]

To find the inverse Laplace transform of the first term you use partial fractions:

[tex]\frac{4}{s^2(s+2)}=\frac{-s+2}{s^2}+\frac{1}{s+2}\\\\=(\frac{-1}{s}+\frac{2}{s^2})+\frac{1}{s+2}[/tex]

Thus, you have:

[tex]y(t)=L^{-1}[\frac{4}{s^2(s+2)}]+8e^{-2t}\\\\y(t)=L^{-1}[\frac{-1}{s}+\frac{2}{s^2}]+L^{-1}[\frac{1}{s+2}]+8e^{-2t}\\\\y(t)=-1+2t+e^{-2t}+8e^{-2t}=-1+2t+9e^{-2t}[/tex]  

(this is the solution to the differential equation)

Answer:

Step-by-step explanation:

The amplitude is the multiplier of the sine function: 3.

The period is 2π divided by the coefficient of x: 2π/2 = π.

The equation of the axis is any added constant: y = 0.

The range is the axis value ± the amplitude value: from -3 to +3.

Answer:

  3.33×10⁴

Step-by-step explanation:

You can use the hint, or you can use a common exponent. Here is the latter case.

  (3.9×10⁴) -(5.7×10³) = (3.9×10⁴) -(0.57×10⁴) = (3.9 -0.57)×10⁴

  = 3.33×10⁴

_____

With a little practice, you can see the effect on exponents of moving the decimal point. Here, we have ...

  5.7×10³ = (0.57×10)×10³ = 0.57×(10×10³) = 0.57×10⁴

__

When adding or subtracting in scientific notation, all that is required is that the exponents of all the numbers be the same. The hint says make all the exponents be 0. Above, we have chosen to make them all be 4. You could also use 3:

  (3.9×10⁴) -(5.7×10³) = (39×10³) -(5.7×10³) = (39 -5.7)×10³

  = 33.3×10³ = 3.33×10⁴

Answer:

The experimental probability of tossing heads is

[tex]\frac{8}{20}=\frac{(8 \div 4)}{(20 \div4)} = \boxed{\frac{2}{5} } ✓ \\ [/tex]

Answer:

[tex]f(x) -g(x) =(5x^3) +(-4x^2- 3x^2) + (0+2x) +(10-7)[/tex]

And if we simplify we got:

[tex]f(x) -g(x) =5x^3 -7x^2 +2x+ 3[/tex]

And the best option for this case is:

A) 5x3-7x2+2x+3

Step-by-step explanation:

For this case we have this function given:

[tex] f(x) = 5x^3 -4x^2 +10[/tex]

And we want to subracr from the last function this one:

[tex] g(x) =3x^2 -2x+7[/tex]

So we want to find [tex] f(x)-g(x)[/tex] and replacing we got:

[tex]f(x) -g(x) =(5x^3 -4x^2 +10) -(3x^2 -2x +7)[/tex]

And if we aggrupate the terms we got:

[tex]f(x) -g(x) =(5x^3) +(-4x^2- 3x^2) + (0+2x) +(10-7)[/tex]

And if we simplify we got:

[tex]f(x) -g(x) =5x^3 -7x^2 +2x+ 3[/tex]

And the best option for this case is:

A) 5x3-7x2+2x+3

Answer:

  5.6

Step-by-step explanation:

We assume that 7 is the measure of the portion of the secant that is inside the circle between the circle and the intersection with the other chord.

The product of segment lengths on the same chord is a constant for chords that intersect at the same point. That is, ...

  10x = 8·7

  x = 56/10

  x = 5.6

_____

Comment on the geometry

If you draw the figure to scale, you find the geometry shown is impossible. The arc measures and chord lengths are incompatible.

Answer:

  see below

Step-by-step explanation:

Corresponding letters (vertices) are in the same order in the similarity statement. That is, if L is the first letter in ∆LMN, then it corresponds to the first letter (R) in ∆RST. That is the meaning of ∆LMN ~ ∆RST.

3. Everywhere you see L, replace it with R.

  Everywhere you see M, replace it with S.

  Everywhere you see N, replace it with T.

This goes for both segments and angles.

__

4. Everywhere you see A, replace it with H.

  Everywhere you see B, replace it with G.

  Everywhere you see C, replace it with F.

  Everywhere you see D, replace it with E.

This goes for both segments and angles.

Answer:

(6x)*(4x^7) = (6*4)*(x*x^7) = 24*x^8

(6x)*(4x^7) = 24*x^7 is wrong in calculation of x

Hope this helps!

:)

Answer:

Nothing is wrong with it

x= 1

Step-by-step explanation:

It has a solution; here is the solution.

(6x)(4x^7) = 24 x^ 7

x * 24x^7= 24x^7

x = 24x^7 / 24x^7

x = 1

Answer:

26.00 + 2x = y           14.00 + 4x = y

Step-by-step explanation:

depending on the amount of people in the car determines numbers of the equation so variables had to be placed instead.

Answer:

408cm

Step-by-step explanation:

U got this

The total surface area of the triangular prism is 14 cm². Then the correct option is B.

A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangular surface.

The total surface area of the triangular prism will be

[tex]\rm Total\ area = 3(area \ of\ rectangle) + 2(area\ of \ triangle)[/tex]

The area of the triangle will be

[tex]\rm area\ of \ triangle = \dfrac{1}{2} * 2 * 4\\\\area\ of \ triangle = 4[/tex]

The area of the rectangle will be

[tex]\rm area\ of \ rectangle = 2 *1\\\\area\ of \ rectangle = 2[/tex]

Then the total area will be

[tex]\rm Total\ area = 2*4 + 3*2\\\\Total\ area = 8 + 6 \\\\Total\ area = 14[/tex]

The total surface area of the triangular prism is 14 cm². Then the correct option is B.

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Answer:

Odd.

Step-by-step explanation:

You don't need the point, its pretty much useless.

If its even, when you plug -x into the equation, it will stay the same

If its odd, when you plug -x into the equation, the signs will change

g(x) = [tex]x^{3}[/tex]    

Lets plug in -x.

g(x) = (-x)³

g(x) = -x³

The equation is different! That means the equation is odd!

Answer:

  the selected list is correct

Step-by-step explanation:

Negative numbers with larger magnitudes are smaller in value, so -2 is less than -1.5.

A fraction is smaller in value if it has a smaller numerator and the same denominator. It is also smaller in value if it has the same numerator and a larger denominator.

2/5 is smaller than 3/4 because it has both a smaller numerator and a larger denominator. So the ordering of the positive numbers is 2/5, 3/4.

The ordering you want is the one checked.

Answer: 0 represents he stays in the same place

jdjejejeeeeeeeeeeeStep-by-step explanation:

Answer: Circumference of cake board is 35π cm.

Step-by-step explanation:Since we have given that

Diameter of a round cake = 30 cm

Diameter of a cake board is 5 cm longer than the diameter of a round cake.

So, Diameter of a cake board = 30+5=35 cm

So, radius of a cake board will be

As we know the formula for " Circumference of Circle ":

So, According to question, we get,

Hence, Circumference of cake board is 35π cm.

Answer: 35π cm

Step-by-step explanation:

[tex] - 2 = \dfrac{3x}{5} + 1 | \times 5 \\ - 10 = 3x + 5 \\ - 3x = 15 | \div ( - 3) \\ x = - 5[/tex]

Answer:

Check the explanation

Step-by-step explanation:

a. there are two categorical variables here:

region with two level : China and US

and cooperation with two level : Defect and cooperate.

b. Chi-square test for association can be used here since the variables are categorical in nature.

Chi-Square Test for Association: C6, Worksheet columns

Rows: C6 Columns: Worksheet columns

defect cooperate All

China 31 36 67

39.54 27.46

US 41 14 55

32.46 22.54

All 72 50 122

Cell Contents: Count

Expected count

Pearson Chi-Square = 9.985, DF = 1, P-Value = 0.002

Likelihood Ratio Chi-Square = 10.231, DF = 1, P-Value = 0.001

Answer:

(a) The probability distribution of the random variable X is Binomial.

(b) The mean and standard deviation of the 25-question test are 5 and 2 respectively.

(c) The value of x is 0.34.

Step-by-step explanation:

The random variable X is defined as the number of correct answers given by a person who is guessing each answer on a 25-question exam.

There are five possible answer for every question.

This implies that the probability of getting a correct answer is:

P (X) = 0.20.

There are a total of n = 25 questions.

Every answer is independent of the others.

(a)

The random variable X has  finite number of independent trials (i.e. 25 questions). There are only two outcomes for each trial, i.e. Success = correct answer and Failure = wrong answer. Each trial has the same probability of success (, i.e. P (X) = 0.25).

Thus, the probability distribution of the random variable X is Binomial with parameters n = 25 and p = 0.20.

(b)

Compute the mean of the random variable X as follows:

[tex]E(X)=np\\=25\times 0.20\\=5[/tex]

Compute the standard deviation of the random variable X as follows:

[tex]SD(X)=\sqrt{np(1-p)}\\=\sqrt{25\times 0.20\times (1-0.20)}\\=2[/tex]

Thus, the mean and standard deviation of the 25-question test are 5 and 2 respectively.

(c)

The sample is large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 5

2. n(1 - p) ≥ 5

Check the conditions as follows:

[tex]np=25\times 0.20=5=5\\\\n(1-p)=25\times (1-0.20)=20>5[/tex]

Thus, a Normal approximation to binomial can be applied.

So,  [tex]X\sim N(5, 2^{2})[/tex]

It is provided that the minimum passing score foe the test is such that only 1% of students who are guessing will pass the test.

That is P (X < x) = 0.01.

⇒ P (Z < z) = 0.01

The value of z is -2.33.

Compute the value of x as follows:

[tex]z=\frac{x-\mu}{\sigma}\\\\-2.33=\frac{x-5}{2}\\\\x=5-(2.33\times 2)\\\\x=0.34[/tex]

Thus, the value of x is 0.34.

Answer:2

Step-by-step explanation:

So they are both equal right. They gave us what a is which was 2 so that means b must be 2 as well.

Hope I helped

Answer:

2

Step-by-step explanation:

The slope of line b is also 2 as they are parallel to eachother and parallel lines have equal slopes.

Answer:

a) The null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

b) Yes.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of all NYC residents that can name a player on the Knicks differs from the proportion of all Toronto residents who can name a player on the Raptors.

As the claim is that the proportions differs, the difference to reject the null hypothesis can be positive or negative. Then, this is a two-tailed test.

The null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]

The conditions to met for this test are:

- The sampling method for each population is simple random sampling.

- The samples are independent.

- Each sample includes at least 10 successes and 10 failures.

[tex]\text{Failures (NY):} \, F=200*0.45=90\\\\\text{Failures (T):} \, F=120*0.3=36\\\\\text{Note: we use failures as they have the lower proportions.}[/tex]

- Each population is at least 20 times as big as its sample.

This conditions are met, so all criteria for the hypothesis test is satisfied.

Answer:

  t ≈ 0.0664731

Step-by-step explanation:

Use the inverse sine function.

  sin(12t) = 141/197

  12t = arcsin(141/197)

  t = arcsin(141/197)/12

  t ≈ 0.0664731 . . . . . . . radians

__

This is the principal value. There are other solutions at values of t that have integer multiples of π/6 added to this. There are also solutions where any of those values is subtracted from π.

_____

In general, angles in math are assumed to be in radians, unless specified otherwise. This angle corresponds to about 3.81°. (In geometry, the usual assumption is that angles are measured in degrees.)

There are six space shuttles with 8 people inside. Meaning, for every space shuttle, there are 8 people so multiply that by six to get the overall people who visited your planet (48)

Answer: the slope is -3

Step-by-step explanation:

(Pls see pic for the work)

Answer:

I graphed all of the equations on the graph below.

Step-by-step explanation:

At the point (6,4), the equation [tex]x+y\ge10[/tex] uses 6 + 4 ≥ 10. Also, the equation [tex]2x+3y\le24[/tex] uses 2(6) + 3(4) ≤ 24.

If this answer is correct, please make me Brainliest!

Answer:

its A !!

Step-by-step explanation:

Answer:

Blank 1) 150

Blank 2) (3)²

3) (4)²

4) (x+3)²

5) (y-3)²

6) (x+3)²+(y-3)² = 100

Relax this isn't really that hard. We're given a triangle with coordinates

X(4,4), Y(12,12), Z(4,12)

and we're told to dilate it around the origin by scale factor 1/4.   The origin part makes it easy; this just means we multiply all the coordinates by 1/4.

So our new triangle is

X'(1,1), Y'(3,3), Z'(1,3)

which we plot in red.

Is that third page asking for the lengths?  We have

X'Y' is the hypotenuse of a right triangle with legs 2 and 2, so

|X'Y'| = 2√2

|Y'Z'| is 3-1 = 2

|Z'X'| = 2

The rule is

(x,y) → (x/4, y/4)

Scale factors are used to enlarge or reduce the size of a shape

The coordinates of the dilated triangle are (1,1), (3,3) and (1,3)

The coordinates of the triangle are given as:

[tex]X = (4,4)[/tex]

[tex]Y = (12,12)[/tex]

[tex] Z = (4,12)[/tex]

The scale factor of dilation is given as:

[tex]k=\frac 14[/tex]

The coordinates of the new triangle after dilation are calculated as follows:

[tex]X' = (4,4) \times \frac 14[/tex]

[tex]X' = (1,1)[/tex]

[tex]Y' = (12,12) \times \frac 14[/tex]

[tex]Y' = (3,3)[/tex]

[tex]Z' = (4,12) \times \frac 14[/tex]

[tex]Z' = (1,3)[/tex]

So, the dilation rule is:

[tex](x,y) \to \frac 14(x,y)[/tex]

Hence, the coordinates of the dilated triangle are (1,1), (3,3) and (1,3)

See attachment for the image of the triangle

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