An equation and some of the steps used to solve the equation are shown below. One step is missing: 2(x-3) + 10x = 5(3 + x) ? 2x-5x + 10x = 15 + 6 7x = 21 x=3 Which set of statements is most likely the missing step and the property that justifies the step?

If she records the liquid volume using milliliter and deciliter, then the deciliter gives more precise measure

The total capacity = 3 gallon

Convert the gallon to milliliter

We know

1 gallon = 3.785 ml

The total capacity in milliliter = The total capacity × 3.785

Substitute the values in the equation

= 3 × 3.785

= 11.355 milliliter

Convert the gallon to deciliter

We know,
1 gallon = 37.854 deciliter

Total capacity in deciliter = The total capacity × 37.854

Substitute the values in the equation

= 3 × 37.854

= 113.562 deciliter

Here deciliter is much smaller than millimeter

Therefore, deciliter gives more precise measure

Learn more about liquid volume here

brainly.com/question/14535251

#SPJ4

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +5}{1 +5} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{1 }{ 3 }}(x-\stackrel{x_1}{(-5)}) \implies y +5 = \cfrac{1 }{ 3 } ( x +5)[/tex]

When the population of a protozoa develops with a constant relative growth rate of 0.6685 per member per day, and there are two members on the day zero, the population after will consist of 7 at the end of seven days period.

The total population of the protozoa at the end of the seven days can be computed using the calculations given below,

Total Population = Growth Rate x Number of Days + Day zero Population

Total Population = (0.6685 x 7) + 2

Total Population = 6.667, or ~ 7.

Therefore, there will be 7 protozoa at the end of seven days.

Learn more about growth rate here:

https://brainly.com/question/14263843

#SPJ4

Answer: When multiplying a whole number by a PROPER fraction (always less then 1), the product is always less than a whole number. So yes, i agree with jenny when using proper fractions.

The rate in the height of water changing for the given cylinder is equal to 0.318m/s.

As given in the question,

Change in volume represent the decrease in rate of change of water height in the cylinder in time t

dV/dt = 4m³/sec.

Decrease in volume represent the change in the height of the water

Let 'h' be the height

h = 10m

radius 'r' = 2m

V = πr²h

Rate of change of leaking water only change the height radius remain constant.

⇒V = (3.14)(2²) h

Differentiate both the side with respect to 't' to get the rate of change

dV/dt = (3.14)(4)dh/dt

⇒4 =(3.14)(4)dh/dt

⇒dh/dt = 4/ (3.14)(4)

⇒dh/dt = 0.318 m/s

Therefore, the rate of change of height is equal to 0.318m/s.

The complete question is:

A vertical cylinder is leaking water at a rate of 4m3/sec. If the cylinder has a height of 10m and a radius of 2m, at what rate is the height of the water changing when the height is 3m?

Learn more about height here

brainly.com/question/10726356

#SPJ4

So when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.

A confidence level of both the CI refers to the likelihood that its confidence interval contains the actual population mean value.

Thus, when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.

To know more about the confidence interval, here

https://brainly.com/question/14825274

#SPJ4

No, the mean time to spoil is not necessarily greater if the banana is hung from the ceiling.

This can only be determined by analyzing the data from the experiment with 15 bananas. If the sample mean is greater than 6.5 days, then the mean time to spoil is greater when the banana is hung from the ceiling. If the sample mean is less than or equal to 6.5 days, then the mean time to spoil is not necessarily greater when the banana is hung from the ceiling.

Learn more about mean here

https://brainly.com/question/15323584

#SPJ4

28.9641 ≤ x-bar(t) ≤ 39.0359.

Knowing that we have 10 different values of speed, the size of the sample is 10; n=10. Therefore, this sample is considered statistically small because n < 30.

Arithmetic mean= (Sum of all values) / (Amount of values)

x-bar= (340) / (10)

x-bar= 34.0000.

x-bar= arithmetic mean.

We're going to use the Microsoft Excel tool for the standard deviation for samples (check attached image 1).

Standard deviation for samples (s)= 7.0396.

Check attached image 2.

σ(x-bar)= 2.2261.

α is the error that the confidence interval will have. Given a 95% confidence level, we know that the error is 5%; Error= 1 - Confidence.

α/2= 5%/2= 0.05/2= 0.025.

You can either use the probability tables or the Microsoft Excel tools to find the inverse of a t-student distribution for this α/2 value (check attached image 3).

In this case we use the t-student distribution instead of the normal distribution because the sample size is small and the standard deviation of the population is unknown.

T-student value= -2.2622

Absolute t value= 2.2622.

Check attached image 4 to see the formulas.

Lower limit = (34) - (2.2622*2.2261) = 28.9641

Upper limit = (34) + (2.2622*2.2261) = 39.0359

28.9641 ≤ x-bar(t) ≤ 39.0359

This result means that the value of speed could be any value between 28.9641 and 39.0359, including, with a 95% confidence level. There's a 5% chance that a newly measured value of speed is outside this interval.

The number of songs that were originally on the player is 41.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, a DJ added 20 more songs to his MP3 player, making the total more than 61. The number of songs will be the subtraction of the value.

This will be:

= 61 - 20

= 41

The original songs are 41.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

At 0.01 significance level the hypothesis is rejected.

Null Hypothesis (H₀): The sample data occurs purely from chance.

Alternative Hypothesis (H₁): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .01), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.

Given that,

x = 28

s = 2.9

μ = 31

n = 8

α = 0.01

Then, the Null Hypothesis : H₀ = 31

          The Alternate Hypothesis : H₁ < 31

The average number of cigeratte smoker  per day is less than 31.

Test Statistics:

t = x -μ / s√n

   = 28 - 31/ 2.9√8

   = -3/ 8.41

   = -0.356

Since the p-value of 0.0046 is less than the significance level of 0.01, the auditor rejects the null hypothesis.

Learn more about Null hypothesis:

https://brainly.com/question/28920252

#SPJ4

The distance, in feet, on Main Street between First Avenue and Canal Street, using relations in a right triangle, is of:

319.25 ft.

The situation is represented by a right triangle, hence the three trigonometric measures are defined as follows:

From the image given at the end of the answer, the parameters are given as follows:

Hence the distance of the Main Street is found using the sine of the angle of 70º, as follows:

sin(70º) = 300/x

x = 300/sin(70º)

x = 319.25 ft.

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

More can be learned about the relations in a right triangle at https://brainly.com/question/16437014

#SPJ1

Answer:

can u see when i do this????

Step-by-step explanation:

The amount of the salmon left after Mr Jones used some part is

Total amount of salmon  bought is 6 and 2/7 lb = 6 2/7 lb

The amount used is 1/5 of the amount Mr Jones bought

= 1/5 * 6 2/7

= 44 / 35

= 1 9/35

= 1.257

The amount left is calculated by subtraction

= 6 2/7 - 1 9/35

= 176 / 35

= 5 1/35

Learn more about fractions:

https://brainly.com/question/29402981

#SPJ1

The number of cards in the deck are either a jack or a heart are 17.

What is card deck?

A playing card is a specially made piece of card stock, heavy paper, thin cardboard, paper coated with plastic, cotton-paper blend, or thin plastic that is imprinted with distinctive motifs. To make handling easier, each card frequently has a finish on the front and back.

Given:

A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.

We have to find the number of cards in the deck are either a jack or a heart.

Since, there are four Jack in a 52 card deck.

So, one jack can be chosen by 4C1 ways.

Also there are 13 cards of hearts in a 52 card deck.

So, one heart can be chosen by 13C1 ways.

The number of ways = 4C1 + 13C1 = 4 + 13 = 17.

Hence, the number of cards in the deck are either a jack or a heart are 17.

To know more about card deck, click on the link

https://brainly.com/question/10559888

#SPJ4

Answer:

0.2

Step-by-step explanation:

First part yields 0.008 if you take sqrt((1/25)^3).

Then the cuberoot of 0.008 is 0.2.

Answer:

Look at the attachment! :D

Hope this helps!

Step-by-step explanation:

Answer: x = 18

Step-by-step explanation:

1) 100% - 54.5% = 45.5%.

2) 45.5/100 = 0.455.

3) 0.455 * X = 8.19g.

4) x = 8.19/0.455.

5) x = 18.

The distance between two points (4, 0) and (2, -9) is √85 units in the simplest radical form.

The length of the line segment connecting two points in a plane is defined as the distance between them. The formula for calculating the distance between two points is commonly presented as √(x₂-x₁)²+(y₂-y₁)².

Distances in geometry are usually positive, unless when the points coincide. We consider two points A(a, b) and B to obtain the formula for the distance between two points in the plane (c, d).

The given two points are (4, 0), (2, -9).

Distance between two points is given by,

Distance=√(x₂-x₁)²+(y₂-y₁)²

Where x₁, x₂, y₁, y₂ are the points.

So, the distance between (4, 0) and (2, -9)

=√(2-4)²+(-9-0)²

=√4+81

=√85 units

Therefore, the distance between two points (4, 0) and (2, -9) is √85 units in the simplest radical form.

To know more about radical form, visit:

https://brainly.com/question/27272065

#SPJ1

The measure of the value of [x] is x = √5/2

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle as shown in the image.

We can write -

sin(30) = x/(√5)

x = √5 sin (30)

x = √5/2

Therefore, the measure of the value of [x] is x = √5/2.

To solve more questions on 2 -D figures, visit the link below-

brainly.com/question/25950519

#SPJ1

The confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,

±31.06.

On Subtracting 1 from your sample size, we get

330 – 1 = 229.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 229 and α = 0.025

from the table at df = 999 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

150 / √(330) = 1.37

Now, 2.262 × 1.37 = 31.06

So, the confidence interval be,

(150 - 31.06 , 150 + 31.06) = (138.94 , 181.06)

Hence, the confidence interval for the one-way analysis of variance experiment be, (138.94 , 181.06) and the margin of error of the poll be,

±31.06.

Learn more about Statistics here https://brainly.com/question/27165606

#SPJ4

A ball must be fast rolled is 185.2cm/sec, according to the question.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have the given information:

Table height = h = 70cm

Distance = s = 70cm

g = 9.8[tex]ms^{-1}[/tex]

Now, we have to find the time of falling,

[tex]t=\sqrt{\frac{2h}{g} }=0.378c[/tex]

Horizontal velocity,

[tex]v=\frac{s}{t}=\frac{70cm}{0.378s}=185.2cm/s[/tex]

Therefore, the required answer is 185.2cm/sec.

To learn more about distance, visit:

https://brainly.com/question/15256256?referrer=searchResults

#SPJ4

Answer:

x=3,x=4

Step-by-step explanation:

(x-3)(x-4)=0

x=3, 4

Answer:

x = 3

x = 4

Step-by-step explanation:

"find the roots" means to find the solutions to the equation.

Roots are solutions are zeros are x-intercepts.

You are being asked to solve the equation.

First, factor the quadratic.

x^2 -7x + 12 = 0

(x - 3)(x - 4) = 0

This works because -3 × -4 is 12 and

-3 + -4 is -7

You see the 12 in the equation is the constant and the -7 is the middle term, the x-term in the trinomial.

So we have

(x - 3)(x - 4) = 0

Separate the two factors into two separate tiny, one-step equations.

x - 3 = 0 , x - 4 = 0

Solve.

x = 3 , x = 4

These are the roots (solutions, zeros and x-intercepts)

A triangle is a plane figure that consists of three sides and three internal angles. Thus m&lt;FHG is [tex]122^{o}[/tex].

A triangle is a family of polygon which is bounded by three straight sides, thus forming three internal angles. The sum of the internal angles of a trigon is [tex]180^{o}[/tex]. While exterior angles are angles which are outside the edges of a triangle.

From the given question;&lt;IGH = &lt;BGD = 42°   (vertically opposite angles)&lt;HIG = 180 - &lt;CIH         = 180 - 100&lt;GIH = [tex]80^{o}[/tex]

Thus, we can conclude that;&lt;IGH + &lt;GIH + &lt;GHI =   [tex]180^{o}[/tex]42 + 80 + &lt;GHI =  [tex]180^{o}[/tex]&lt;GHI =  [tex]180^{o}[/tex] - 122         = 58&lt;GHI = [tex]58^{o}[/tex]So that;m&lt;FHG

=  [tex]180^{o}[/tex] - M&lt;GHI             =  [tex]180^{o}[/tex] - 58            

= [tex]122^{o}[/tex]m&lt;FHG

= [tex]122^{o}[/tex]

Learn more about the exterior angle of a triangle at https://brainly.com/question/21481521

#SPJ1

Gregory has 10 ways to choose 3 boxes of cereal.

What do you mean by purchase?

A corporation or organization uses the purchasing process to buy products or services in order to achieve its objectives. Although many organizations make an effort to establish standards for the purchasing process, procedures can differ significantly between organizations.

According to data in the given question,

We have :

The purchase of 3 boxes and the store has 5 different varieties of munchie brand cereal.

The order in which the boxes of cereal are chosen is not important as Gregory can randomly choose any 3 different varieties. So, this is a combination problem.

Use the combination formula:

[tex]_nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Putting n=5 (5 different varieties) and r=3 (3 different varieties). So, the number of ways Gregory choose 3 boxes of cereal is:

[tex]_{5}C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!2!}= \frac{5.4.3.2.1}{3.2.1.2.1} _{5}C_3=\dfrac{5\cdot 4}{2\cdot 1}=10[/tex]

Therefore, the required answer is 10 ways.

To learn more about purchasing, visit:

https://brainly.com/question/29484017?referrer=searchResults

#SPJ4

A car travels 500/3 meters in 2 seconds.

What is speed?

The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.

Here, we have

Speed of car  = 100 KM/ hour

1 km= 1000m

1 hour = 3600 seconds

Let's find the speed of the car in Meters/second

Speed of car in m/sec = 100*1000 m/3600 second

Here we have taken 1000 for km and 3600 for an hour

Speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second

Speed of car in m/sec = 250/9  m per sec

We know that

Distance = speed*time

Speed = 250/9  m per sec

Time = 2 second

Distance = 250/9 * 2 meters = 500/3 meters

Hence, a car travels 500/3 meters in 2 seconds.

To learn more about the speed from the given link

https://brainly.com/question/24739297

#SPJ4

Answer:

48

Step-by-step explanation:

the ratio of blue cards to yellow cards can be expressed with

4:3.

the total amount of blue and yellow cards can be interpreted as 4x+3x=7x

then you can find the value of x by dividing 84/7, which is 12

since the value of blue cards is 4x, 4(12) = 48

The value of f(0) is f(0) = 3 and the value of f(-4) is f(-4) = 1

From the question, we are to determine the value of the given functions

The functions are

f(0) and f(-4)

First, we will determine the value of f(0)

Since 0 ≥ -2, we will use the function

f(x) = x² + 2x + 3

Thus,

f(0) = (0)² + 2(0) + 3

f(0) = 0 + 0 + 3

f(0) = 3

Now, we will determine the value of f(-4)

Since -4 < -2, we will use the function

f(x) = x + 5

Thus,

f(-4) = -4 + 5

f(-4) = 1

Hence, f(0) = 3 and f(-4) = 1

Learn more on Determining the value of a function here: https://brainly.com/question/14379796

#SPJ1

Answer:

[tex]1\frac{1}{2}[/tex]

Step-by-step explanation:

we multiply the fractions

1/8 x 12/1

12/8

1 4/8

1 1/2

Hopes this helps please mark brainliest

For the square on the diagram, we can see that:

Remember that all the sides of a square have the same length.

Here we know that AC, the diagonal of the square, has a measure of 20 cm.

Then the length of DE, which is half of the diagonal of the square, is half of that, then:

20cm/2 = 10cm

DE = 10cm

DC is one of the sides of the square. Remember that for a square of sidelength S, the diagonal is:

D = √2*S

Then the sidelength is:

S = D/√2

Here we know that the diagonal measures 20 cm, then:

DC = S = 20cm/√2 = 14.14 cm

DC = 14.14cm

Finally, mADE refers to the measure located at the vertex D on the triangle on the angle ADE.

Remember that all the angles of a square measure 90°, and here the ray DE divides that angle in two halves, then mADE = 90°/2 = 45°

Learn more about squares:

https://brainly.com/question/24487155

#SPJ1

An equation to represent this situation is 16x - 5 = 14x + 1. The value of x is equal to 3.

The perimeters of the rectangle and triangle are equal to 43 units.

Mathematically, the perimeter of a rectangle can be calculated by using this equation;

P = 2(L + W)

Where:

An equation for the perimeter of this rectangle is given by:

P = 2[(5x - 2) + (3x - 0.5)]

P = 2(8x - 2.5)

P = 16x - 5.

Mathematically, the perimeter of a triangle can be calculated by using this equation:

P = a + b + c

Where:

P = (2x + 3) + (2x + 3) + (10x - 5)

P = 14x + 1

Since the perimeter of both geometric figures are the same, we can calculate the value of x as follows:

16x - 5 = 14x + 1

2x = 6

x = 3

For the perimeter of this rectangle, we have:

P = 16x - 5.

P = 16(3) - 5.

P = 43 units.

For the perimeter of this triangle, we have:

P = 14x + 1.

P = 14(3) + 1.

P = 43 units.

Read more on perimeter of a rectangle here: https://brainly.com/question/17360327

#SPJ1