Simplify the fractions, show your work
35/90
3/36

Answer:

B

Step-by-step explanation:

5.21 x 10^19 + 3.149 x 10^17

10^17(5.21 x 10^2 + 3.149)

10^17(521 + 3.149)

10^17(524.149)

5.24149 x 10^17 x 10^2

5.24149 x 10^(17+2)

5.24149 x 10^19

Answer: b. 5.24149 × 1019

Step-by-step explanation: I took the test

Answer:

5832

Step-by-step explanation:

The correct option regarding whether the two functions are inverse functions is given as follows:

B. No, because the composition does not result in an answer of x.

Two functions are inverses of each other if the composition of these two function has a result of x.

From the image given at the end of the answer, the two functions in this problem are defined as follows:

Their composition is given as follows:

[tex](G \circ F)(x) = G(\sqrt{x} + 4)[/tex]

[tex](G \circ F)(x) = (\sqrt{x} + 4)^2 - 4[/tex]

[tex](G \circ F)(x) = x + 8\sqrt{x} + 16 - 4[/tex]

[tex](G \circ F)(x) = x + 8\sqrt{x} + 12[/tex]

The composition does not result in x, hence the two functions are not inverses and the correct statement is given by statement B.

The problem is given by the image shown at the end of the answer.

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Answer:

-2

Step-by-step explanation:

we use the y2-y1/x2-x1 fomrula to find slope

14-8/7-10

6/-3

-2 is the slope

hopes this helps

Answer:

A. -2, -5, -8, -11, -14, -17, ...

Step-by-step explanation:

The difference between consecutive terms is constant.

The correct inequality for the statement - highest temperature possible today is 95 °F

x ≤ 95 °F

The statement saying the highest temperature possible today is 95 °F is represented by

knowing that the temperature will never be greater than 95 °F, hence the temperature values is from 95 °F and downwards

assuming x represents the measles of the temperatures then

x is less than or equal to 95 °F means x can be any value but never greater than 95 °F

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Answer:

What is 213 divided? 2 I think

Also how do you break 23 into tens and ones? It would be 2 tens and then it would be 3 ones

We can arrange the group in 120960 different ways.

Given,

Number of adults = 7

Number of children = 4

We have to find the number of ways they can stand when no two children are allowed to stand together;

Here,

Arrange 7 adults in a row of 7 ; 7

Number of arrangements = 7! = 5040

Consider that there are four possible placements for a child, but only one youngster can be placed in each of them: on either side of the row of adults, or in between two adults.

Consequently, pick one place for each youngster from the possibilities below: 4 for the first adult, 3 for the second,... the final adult's two options are = 4 × 3 × 2 = 24 arrangements

Add the two groupings together =  5040 × 24 = 120960

Therefore,

There is 120960 ways to arrange the standing position of the group.

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Retain the null because 1.74 is greater than 1.645.

What is z - test statistic?

Any statistical test for which the test statistic's distribution under the null hypothesis can be roughly represented by a normal distribution is known as a Z-test.

Z-tests examine a distribution's mean.

Let X be the average time that prescholars spend on tablets.

X ~ N(μ, α^2)

To test H0: μ = 3 hours Vs H1: μ ≠ 3 hours.

The z - test statistic is obtained as 1.74.

Taking level of significance α = 0.05

Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex]

Since the observed z - statistic is 1.74 which is less than Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex],

so we retain the null hypothesis.

Hence, retain the null because 1.74 is greater than 1.645.

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Complete question:

Complete question is attached below.

The number of boxes of sugar that Alonso can buy are 4.5 boxes.

Given is that Alonso went to the market with $55 to buy eggs and sugar. He knows he needs a package of 12 eggs that costs $2.75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money.

The money remaining after buying 12 eggs : {r} = $(55 -2.75).

Cost of one box of sugar = $11.5

The number of boxes that he can buy are -

n = (55 - 2.75)/11.5

n = 4.5 boxes {approx.}

Therefore, the number of boxes of sugar that Alonso can buy are 4.5 boxes.

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Answer:

Below

Step-by-step explanation:

3x+15      <==== factor out '3'

3 * ( x+5)       done !

As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).

The cartesian plane is defined in mathematics as a two-dimensional coordinate plane formed by the intersection of the x- and y-axes. The origin is the point where the x- and y-axes intersect perpendicularly.

Quadrant one (QI) is the top right fourth of the coordinate plane, where all coordinates are positive. Quadrant two (QII) is the coordinate plane's top left fourth. Quadrant three (QIII) is the fourth from the bottom left. Quadrant four (QIV) is the fourth from the bottom right.

Given:

The direction of rotation = clockwise, (from the first quadrant to forth quadrant then third quadrant, and so on)

Angle of rotation = 90° about the origin

According to the question, let's take our start point as A(x, y)

So, A( x, y) will lie in the first quadrant.

After 90° rotation about the origin A' will lies in fourth quadrant.

As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).

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Answer:

[tex]A \approx 38 \, \textrm{cm}^2[/tex]

Step-by-step explanation:

The area of a triangle is defined as:

[tex]A_\triangle = \dfrac{1}{2}bh[/tex]

where [tex]b[/tex] is the length of its base and [tex]h[/tex] is its height.

So, we can plug the given values into this formula along with the inch to centimeter conversion to get the answer to this problem.

[tex]A=\dfrac{1}{2}\left(4.75\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)\left(2.5\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)[/tex]

And simplify.

[tex]A \approx 38 \, \textrm{cm}^2[/tex]

The value of x and z are [tex]4^\circ, 96^\circ[/tex].

Now from the picture I can say that, [tex]\angleAOB[/tex][tex]\angle AOB[/tex] and [tex]\angleCOD[/tex][tex]\angle COD[/tex] are opposite angles.

We know the measure of the triangle are equal in Pair.

So we have got the equation as -

[tex]10x+44=13x+32[/tex]

⇒[tex]13x-10x=44-32[/tex]

⇒3x=12

⇒x=4.

We have got that the measure of [tex]\angle AOB, \angle COD[/tex] are both [tex]84^\circ[/tex].

Now angles around a point add to [tex]360^\circ[/tex].

So, [tex]\angle AOD[/tex] and [tex]\angle BOC[/tex] are equal since they are pairwaite wisw.

Now, [tex]z+z= 360^\circ - (84^\circ+84^\circ)[/tex]

⇒[tex]2z=192^\circ[/tex]

⇒ [tex]z=96^\circ[/tex],

Hence we have got the value of x and z i.e. 4 and 96.

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Answer:

Step-by-step explanation:

g(x) = (-x)1/2

Slope of the line is .[tex]\frac{-4}{3}[/tex]

Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. As opposed to the net change in the x coordinate, the net change in the y coordinate is y.

y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

A line's slope is a measurement of how steep it is or the direction it is going in relation to a coordinate system.

where m is the slope and m = y/x

Take notice that tanФ = y/x.

This tanФ is often referred to as the line's slope.

The given equation is of the form [tex]ax+by=c[/tex]

On comparing we can say that a is -8 and b is -6

So using the slope formula [tex]\frac{-A}{B}[/tex] we get slope as [tex]\frac{4}{-3}[/tex]

The perpendicular line slope can be found out by equation [tex]m1.m2=-1[/tex]

Therefore substituting slope from the above as m1 we get m2 = [tex]\frac{3}{4}[/tex]

Slope of the line is .[tex]\frac{-4}{3}[/tex]

Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]

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Spanish is a Romance language of the Indo-European language family that emerged from the Iberian peninsula's colloquial Latin. It is now a worldwide language with around 500 million native speakers, primarily in the Americas and Spain. Twenty nations have Spanish as their official language.

These numbers in Spanish are:

1. 49: cuarenta y nueve

2. 97: noventa y siete

3. 113: ciento trece

4. 632: seiscientos treinta y dos

5. 1.781: mil setecientos ochenta y uno

6. 3.558: tres mil quinientos cincuenta y ocho

7. 1.006.015: un millon seis mil quince

8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta

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Answer:

49: cuarenta y nueve

2. 97: noventa y siete

3. 113: ciento trece

4. 632: seiscientos treinta y dos

5. 1.781: mil setecientos ochenta y uno

6. 3.558: tres mil quinientos cincuenta y ocho

7. 1.006.015: un millon seis mil quince

8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta

Step-by-step explanation:

The equation that gives the relationship between cost (c) and area (a) is c = 2a

A variation is a relation between a set of values of one variable and a set of values of other variables

Given that: the cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet

We can write:

c α a

c = ka

where k is the constant of proportionality

since c = $3,000 and a = 1500

c = ka

3000 = 1500k

k = 3000/1500

k = 2

Thus, the equation of the relationship is c = 2a

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The solution is

a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01

b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125

The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

a)

Let the principal be P = amount after first period =  $ 402

Now , the rate of interest r = 6 %

The compound interest is calculated by compounding monthly

Now , the interest for the second period = ( PRT / 100 x 12 )

Substituting the values in the equation , we get

The interest for the second period = ( 402 x 6 x 1 ) / 1200

The interest for the second period = $ 2.01

The amount after the second period = amount after first period +  interest for the second period

The amount after the second period = 402 + 2.01

The amount after the second period = $ 404.01

b)

Let the principal be P = $ 18260

The rate of interest r = 2.5 %

The compound interest is calculated by compounding quarterly

Now , the interest for the first period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the first period = ( 18260 x 2.5 ) / 400

The interest for the first period = 45650 / 400

The interest for the first period = $ 114.125

The amount for the first period = 18260 + 114.125

The amount for the first period = $ 18,374.125

Now , the principal for the second period = interest + amount of first period

The principal for the second period = $ 18,374.125

The rate of interest = 2.5 %

The interest for the second period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the second period = ( 18374.125 x 2.5 ) / 400

The interest for the second period = 45935.3125 / 400

The interest for the second period = $ 114.83828125

The amount for the second period = 18,374.125+ 114.84

The amount for the second period = $ 18,488.96

Hence , the amount and interest is calculated

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Answer:

Step-by-step explanation:

[tex]x^{2} +2x+16=0\\x^{2} +2x+1-1+16=0\\(x^{2} +2x+1)-1+16=0\\(x+1)^{2} +15=0\\(x+1)^{2}=-15[/tex]

The solution does not exist because all numbers squared are greater than zero.

Answer:

5/13

Step-by-step explanation:

[tex]CE=\sqrt{10^2 + 24^2}=26 \\ \\ \cos E=\frac{10}{26}=\frac{5}{13}[/tex]

The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes. Therefore, option D is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 5+0.75x.

In the given expression, 5 is constant term and 0.75x is another term.

In the term 0.75x, 0.75 is the coefficient of x

In the expression 5+0.75x, 5 is fixed price and 0.75 is price for second or minute or hour or year and x can be number seconds or minutes or hours or years.

Therefore, option D is the correct answer.

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The final answer is that the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order is 1.54.

This is calculated by probability of independent events.

We know that any die can get any of the six sides and all the throws are independent, so their intersection is given by the product.

So, P(A and B occurring together )= P(A)P(B) if A and B are independent.

And the probability of the throws i.e. the no. of ways every throw gets a unique number is (6/6) x (5/6) x (4/6) x (3/6) x (2/6) x (1/6)

This is because, being the probability of independent events , they are multiplied.

so, the total probability is 6.5.4.3.2.1/6^6 = 1.54

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Answer: x=3.2

Ste by Step

We have that for the Question "The figures are similar, and the ratio of the perimeters is 2 : 5. Find x." it can be said that  the perimeters of x is

x=3.2

From the question we are told

The figures are similar, and the ratio of the perimeters is 2 : 5. Find x.

Generally the equation for the the ratio is mathematically given as

2=x

and

5=8

Therefore

x=3.2

Therefore

the perimeters of x is

x=3.2

The volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.

What is a rectangular Prism ?

A polyhedron with two congruent and parallel bases is known as a rectangular prism. It's also known as a cuboid.

A rectangular prism has six faces, each of which is in the shape of a rectangle and has twelve edges. It's called a prism because of its cross-section along its length.

It is given that length of the rectangular prism has length of 2 cm more than  the width and 3 cm less than the depth

Let the depth be x cm

and width be y cm

Then the length will be y+2 cm and x-3 cm

y+2 = x- 3

x = y+5

A rectangular prism is a cuboid with six faces

Volume of a rectangular prism can be written as

length * width * depth

= (y+2) *x*y

= (y+2)* (y+5)*y

= (y²+2y)(y+5)

= y³ +5y²+2y²+10y

= y³ +7y² +10y cm³

Therefore the volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.

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The mark that is required to receive an A on the test is; 75.68

The formula for z-score here with the parameters given is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

p-value = 10% = 0.1

μ = 68

σ = 6

Now, from z-score tables, the z-score at a p-value of 0.1 is z = 1.28. Thus;

1.28 = (x' - 68)/6

x' = 68 + (1.28 * 6)

x' = 75.68

We conclude that this value is the mark required to receive an A on the test.

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Net payout will you be promised in a fair betting game in case your bet works out is $0 .

Given :

browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins .

P ( browns ) = 60 / 100 = 0.60

P ( steelers ) = 40 / 100 = 0.40

Net payout = Number of wins * 10 - Number of loses * 10

= 1 * 10 - 1 * 10

= 10  - 10

= $0.

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Answer:

Below

Step-by-step explanation:

To complete the square, the coefficient of x^2 must be 1  ( it is already)

   then take 1/2 of the x coefficient  .... 1/2.... square it and add it to both sides of the equation

   x^2 + x + 1/4   + 9   = 1/4

 then you can reduce this to

   ( x+ 1/2)^2  + 9 = 1/4   for further 'solving'

Answer:0.41

Step-by-step explanation: