Consider the steps to solve the equation. 2 5 ( 1 2 y + 20 ) − 4 5 = 9 20 (2y − 1)
Distribute: 1 5 y + 8 − 4 5 = 9 10 y − 9 20
What is the next step after using the distributive property?

*Use the multiplication property of equality to isolate the variable term on one side of the equation.

*Use the multiplication property of equality to isolate the constant on one side of the equation.

*Combine the like terms on the right side of the equation.

*Combine the like terms on the left side of the equation.

Answer: 4.0 * 10^0 kg = 4.0 kg essentially

Step-by-step explanation:

No need to convert these to numbers...

Weight of 1 bee: 1 * 10^-4 = (0.0001 kg)

Number of bees: 4 * 10^4 = (40000 bees)

(1 * 10^-4) * (4 * 10^4) =

(1 * 4) * (10^-4 * 10^4) =

(10^0 because when multiply exponential numbers, you add the exponents)

4 * 10^0 =

4 * 1 = 4 kg

Answer:

6

Step-by-step explanation:

The growth factor is the same as the base of the exponential factor.

The value of the function [tex]$f(x)=(1/3)(6)^x[/tex] growth factor exists 6.

function [tex]$f(x)=(1/3)(6)^x[/tex]?

Given: [tex]$f(x)=(1/3)(6)^x[/tex]

For any equation [tex]$ f(x)=ab^x[/tex]

Let, 'a' exists the initial value

b exists the growth or decay factor.

When the value of b exists greater than 1 then its growth factor

when the value of b exists between 0 and 1 then it exists a decay factor

Let x exists the number of years

Given function, [tex]$ f(x)=(1/3)(6)^x[/tex]

The value of b exists 6.

So the growth factor exists 6.

Therefore, the correct answer is option c. 6.

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1/2 value can be used as the common ratio in an explicit formula that represents the sequence.

Definition of sequence -

A sequence that progresses geometrically has the first term as 12.

Each number is the previous number divided by 2.

so the sequence will be 12, 6, 3, 1.5...........

Explicit formula of a geometric sequence is given by

[tex]T_{n} = ar^{n-1}[/tex]

Where [tex]T_{n}[/tex]  = nth term of the sequence

a = first term

r = common ratio

and n = number of term

In this sequence common ratio = [tex]\frac{Successive term }{previous term}[/tex]

            = 6/12

            =  1/2

Therefore, common ratio will be 1/2.

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Angelique takes 8 hours to drive from a to b.

How quickly something or someone is moving is indicated by their speed. If you know how far something travels and how long it takes, you can calculate their average speed. Speed equals distance  x times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

let us assume distance from a to b be x units.

let us assume speed of vehicle be y units/hour.

For Satia, speed=y units time=4 hours we know the formula of distance is:

     distance=speed × time distance=(y× 4) units               -------------------(1)

        Angelique :speed=y / 2 units time=?

We know the formula of distance is:

Distance=speed × time distance=(y/2)× time            -------------------(2)

We can see that distance in both cases is equal,

So compare case (1) ad (2) ,

We get  (y× 4)=(y/2)× time

On rearranging ,

Time= (4×2) hours=8 hours

hence,

Angelique takes 8 hours to cover the distance from a to b.

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Answer:

22.05

Step-by-step explanation:

First, convert 63% into a decimal.

To do this, divide it by 100.

[tex] \frac{63}{100} = 0.63[/tex]

Multiply 0.63 by 35.

[tex]35 \times (0.63) = 22.05[/tex]

Answer:

Step-by-step explanation:

.63(35)= 22.05

Multiply .63(35)

Answer:

Step-by-step explanation:

The relevant relations here are ...

The given arc CD is part of the semicircular arc CDA. The remaining arc, DA, is the supplement of CD:

  arc DA = 180° -CD = 180° -125° = 55°

Central angle AOD has the same measure, 55°. That is one of the acute angles in right triangle AOB, so the other one is the complement of 55°.

 ∠ABO = 90° -∠AOB = 90° -55°

  ∠ABO = 35°

In right triangle ABC, angle ABC is given as 55°. The other acute angle, ACB, will be the complement of this.

  ∠ACB = 90° -∠ABC = 90° -55°

  ∠ACB = 35°

In the figure, angles ABO and ACB have measures of 35°.

Answer:

2280 minutes.

Step-by-step explanation:

Time spent each week in lessons = (Lessons per week)(Time per lesson)

= (6)(38)

= 228 minutes/week

Time spent in a 10-week period:

10 weeks * 228 minutes/week

= 2280 minutes

Use conversion factors to determine the time in the desired units (i.e. Hours, seconds, etc.).

Hope this helps!

well, let's notice the denominators, hmmm so we can use as the LCD say the expression of "rpq", so, let's multiply both sides by the LCD of "rpq" to do away with the denominators.

[tex]\cfrac{2}{r}+\cfrac{1}{p}=\cfrac{1}{q}\implies \stackrel{\textit{multiplying both sides by } ~~ \stackrel{LCD}{rpq}}{rpq\left( \cfrac{2}{r}+\cfrac{1}{p} \right)=rpq\left( \cfrac{1}{q} \right)}\implies 2pq+1rq=1rp \\\\\\ 2pq+rq=rp\implies rq=rp-2pq\implies rq=\stackrel{\textit{common factoring}}{p(r-2q)}\implies \cfrac{rq}{r-2q}=p[/tex]

is there a picture included in this problem? if so please comment it so i can answer this problem.

Step-by-step explanation:

1 meter = 100 centimeter = 1000 millimeter

therefore, 1 cm = 10 mm

4.6 m = 4.6 × 1000 = 4600 mm

88 cm = 880 mm

and so, they cut off

880 mm + 1630 mm = 2510 mm

that means

4600 - 2510 = 2090 mm = 2.09 m

are left.

[tex]\Large\texttt{Answer}[/tex]

[tex]equation=[/tex][tex]\bold{y=5x-33}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\Large\texttt{Process}[/tex]

⇨ Use the formula below

[tex]\bf{y-\hfill\stackrel{y \:co-ordinate}{y1}=\hfill\stackrel{slope}{m}(x-\hfill\stackrel{x\:co-ordinate}{x1)}}[/tex]

⇨ Substitute the parameters:

[tex]\bold{y-(-8)=5(x-5)}[/tex]

[tex]\bold{y+8=5x-25}[/tex]

[tex]\bold{y=5x-33}[/tex]

Hope that helped

No, we can only suppose that the observed distribution deviates from the expected distribution when we reject the null hypothesis.

The null hypothesis exists as a specific mathematical theory that claims that there exists no statistical relationship and significance between two sets of observed data and estimated phenomena for each set of selected, single observable variables. The null hypothesis can be estimated to define whether or not there exists a relationship between two measured phenomena, which creates it useful. It can let the user comprehend if the outcomes exist as the product of random events or intentional manipulation of a phenomenon.

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Answer:

A = 0; B = -9/2

Step-by-step explanation:

To have no solutions, you need parallel lines with equal slopes and different y-intercepts.

3x + 4y = A      Eq. 1

Bx - 6y = 15     Eq. 2

In Eq. 1, notice that the coefficient of x is 3/4 of the coefficient of y.

We must have the same ratio for the coefficients in Eq. 2.

B/(-6) = 3/4

4B = -6(3)

4B = -18

B = -9/2

Now we have

3x + 4y = A      Eq. 1

-9/2 x - 6y = 15     Eq. 2

How do we change the left side of the second equation into the left side of the first equation? -6/4 = -3/2 and also -9/2 ÷ 3 = -3/2

To change the left side of the second equation into the left side of the first equation, divide the left side by -3/2.

If we divide 15 by -3/2 we get -10.

The equation -9/2 x - 6y = -10 is the same as Eq. 1, so that would create a system of equations with only one equation and an infinite number of answers.

To have no equations, the y-intercepts must be different, so A can be any number other that -10.

Answer: A = 0; B = -9/2

The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)

In this question we have a kind of recursive function known as Fibonacci's function, where a value of the series is generated from at least immediately previous elements. In this case, we need to find the first three elements from the fifth and fourth elements of the series:

[tex]a_{n-2} = a_{n-1} - a_{n} + 4[/tex]

a₄ = a₅ - a₆ + 4

a₄ = - 2 - 0 + 4

a₄ = 2

a₃ = a₄ - a₅ + 4

a₃ = 2 - (- 2) + 4

a₃ = 8

a₂ = a₃ - a₄ + 4

a₂ = 8 - 2 + 4

a₂ = 10

a₁ = a₂ - a₃ + 4

a₁ = 10 - 8 + 4

a₁ = 6

The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)

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Answer:

Step-by-step explanation:

3 units

Answer:

3 units.

Step-by-step explanation:

Opposite sides of a parallelogram are equal in length,

So side OD = side WS.

We see from the diagram that OD is 3 units long so

WS = 3 also.

The 125 feet long line and the angles 65°10', and 60°10' obtained from the surveying equipment gives the length of the bridge as approximately 1234.2 feet.

Given;

Location of the tree = The other side of the river from the surveyor

Length of the line measured along the river, L = 125 feet

Angle to the tree from the start of the line = 65°10'

1° = 60'

10' = ((1/60)×10)° = (1/6)°

65°10' = (65 + 10/60)° = (65 + 1/6)°

Angle measured at the end of the line, E = 60°10'

Similarly;

E = 60°10' = (60 + 1/6)°

The interior angle, S, of the triangle formed by the tree and the line, at the start of the line is therefore;

Angle S = 180° - (65 + 1/6)° = (114+5/6)° (linear pair angles)

S = (114+5/6)°

From the angle sum property of a triangle, angle formed at the tree, T, is therefore;

T = 180° - ((114+5/6)° + (60 + 1/6)°) = 5°

According to the rule of sines, we have;

l/(sin T) = b/(sin E)

Where;

b = The length of the bridge

Which gives;

124/(sin 5°) = b/(sin (60 + 1/6)°)

b = (sin (60 + 1/6)°) × (124/(sin 5°)) ≈ 1234.2

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Use hit and trial method

Answer is (-1,4)

Verification

Put x and. y

Option A

The 95% confidence interval for the population standard deviation will be,

[tex]$\sqrt{\frac{(n-1) s^{2}}{\chi^{2}} \frac{\alpha}{2}} & < \sigma < \sqrt{\frac{(n-1) s^{2}}{\chi^{2}}} \\[/tex]

simplifying the equation, we get

[tex]$\sqrt{\frac{2551.5}{26.1}} & < \sigma < \sqrt{\frac{2551.5}{5.63}} \\9.887 & < \sigma < 21.288[/tex]

The 95% confidence interval exists (9.887, 21.288).

A random sample of 15 men exists selected. The mean weight exists at $165.2 pounds and the standard deviation exists at $13.5 pounds. The population exists normally distributed.

So, [tex]$n=15, \bar{X}=165.2, s=13.5$[/tex]

where n exists the sample size, [tex]$\bar{X}$[/tex] exists the sample size

s exists the sample standard deviation.

The degrees of freedom will be n - 1 i.e.15 - 1 = 14.

For a 95% confidence interval, the level of significance will be [tex]$\alpha=0.05$[/tex].

The 95% confidence interval for the population standard deviation will be,

[tex]$\sqrt{\frac{(n-1) s^{2}}{\chi^{2}} \frac{\alpha}{2}} & < \sigma < \sqrt{\frac{(n-1) s^{2}}{\chi^{2}}} \\[/tex]

substitute the values in the above equation, we get

[tex]$\sqrt{\frac{(15-1)(13.5)^{2}}{\chi^{2}} 0.05} & < \sigma < \sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0}^{2}}} \\[/tex]

[tex]$\sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0.975}^{2}}} & < \sigma < \sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0.025}^{2}}} \\[/tex]

simplifying the above equation, we get

[tex]$\sqrt{\frac{2551.5}{26.1}} & < \sigma < \sqrt{\frac{2551.5}{5.63}} \\9.887 & < \sigma < 21.288[/tex]

The 95% confidence interval exists (9.887, 21.288).

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Answer:

1/311875200.

There is exactly 1 way to have all 5 of these cards.  For the first card, there are 52 total cards to be had; for the second, 51; for the third, 50; for the fourth, 49; and for the fifth, 48:

(1/52)(1/51)(1/50)(1/49)(1/48) = 1/311875200.

Step-by-step explanation:

A graph for the data (time and distance) shown in the given table is plotted in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, the data of a linear graph are directly proportional and as such as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.

In this exercise, you're required to plot a graph for the data (time and distance) that are recorded for an object that is starting from rest.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

y = 67.814x

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Answer:

x=0, x= -9

Step-by-step explanation:

First we simplify the equation into the form

ax^{2}+bx+c=0

By adding 4x+3 on both sides, we form the equation

x^{2}+9x=0

Now, we factor out the common factor: x.

x(x+9)=0

The only values that allow x(x+9) to be equal to 0 are:

x=0  or

x+9=0

The solutions are x=0 or x= -9

Answer:

[tex]y=\frac{-x}{78} -\frac{220}{78}[/tex]

Step-by-step explanation:

Remember to create a line perpendicular to one another the slope has to be the reverse reciprocal of the first line.

Given the current slope is [tex]\frac{-78}{1}[/tex] the new slope would be [tex]\frac{1}{78}[/tex].

To find the line that passes through a point with a given slope we must use point slope form, remember the default equation of point slope form:

[tex]y-y1=m(x-x1)[/tex]

Where y1 is the y value of the point, m is the slope, and x1 is the x value of the point.

Lets substitute in our values

[tex]y-(-3)=\frac{-1}{78} (x-14)[/tex]

Simplify the equation

[tex]y+3=-\frac{1}{78}\left(x-14\right)\\y+3=\frac{-x}{78}+\frac{14}{78}\\y=\frac{-x}{78}-\frac{220}{78}\\[/tex]

The perimeter of the rhombus FGHJ is 20 units

The coordinates are given as:

F = (-2, -2)

G = (-2, 3)

H = (2, 6)

From the question, we understand that vertex J is directly below vertex H.

This means that vertices H and J have the same x coordinate.

So, we have

J = (2, y)

The distance between F and G is 5 units,

So, we have

J = (2, y - 5)

Where

y = 6 i.e. the y coordinate of H

This gives

J = (2, 6 - 5)

Evaluate

J = (2, 1)

See attachment for the graph of the rhombus

In (a), we have:

The distance between F and G is 5 units,

This means that

FG = 5

The side lengths of a rhombus are equal.

So, the perimeter is

P = 4 * FG

This gives

P =4 * 5

Evaluate

P = 20

Hence, the perimeter of the rhombus is 20 units

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The summary of the given data is are as follows :-

Minimum: 11

Lower quartile:11

Median:24

Upper quartile:34

Maximum:45

Interquartile range:23

Given :- 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45

Minimum = The smallest number of data

Thus Minimum = 11

Maximum = The largest number of data

Thus Maximum = 45

Median = The middle number of the data if data consists of odd number of elements

Thus Median = 45

Lower quartile = The median of the lower half of data

Thus Lower quartile = 11

Upper quartile = The median of the upper half of data

Thus Upper Quartile = 34

Interquartile range = The difference of upper and lower quartiles,

Thus Interquartile range = 34 -11 = 23

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The width on the blueprint is 4 inches.

The blueprint is a scale drawing of the building. A scale drawing is a reduced form in terms of dimensions of an original image / building / object

The scale of a drawing is usually written in this format - length in the drawing, a colon (:), then the matching length on the original image. An example of a scale is 1 inch 12 feet. This scale means that 1 inch of the blueprint represents 12 feet of the building.

Width of the building on the blueprint = 48 / 12 = 4 inches

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Answer:

-2

Step-by-step explanation:

<________|____|___-2___|___0___|____|____|____4________>

                                    E                                                    D

The Point E is located at -2.

Given that Point D is located at 4. Point E is 6 less than Point D.

We need to find the location of the point E.

Based on the information provided, Point D is located at 4. Now, we know that Point E is 6 less than Point D.

When we say, "less than," it means we need to subtract the given value from Point D to find the location of Point E.

If Point D is located at 4, and Point E is 6 less than Point D, then the location of Point E can be calculated as follows:

E = D - 6

Since D is 4, we can substitute that value into the equation:

E = 4 - 6

E = -2

So, Point E is located at -2.

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Answer:

1441.503 square inches

Step-by-step explanation:

155×60cm=9300square centimeter

9300 divide 6.452 to change to square inches.

Ans=1441.503

Answer:

64.58 sq.in

Step-by-step explanation:

The mode of the set of 10 observations is 2.

What is the mode?

Mode refers to a value that appears most frequently in a data set. Mode is a measure of central tendency of a data set. Other measures of central tendency are mean and median.

According to the information in the question, 6 appears twice in the data set and all other values are different. Thus, 6 has the frequency of 2 which is the highest. 6 is the mode.

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Answer:

Y-intercept = 22

Step-by-step explanation:

The equation of a line in slope-intercept format is given by the equation y=mx+c

where m is the slope and c the y-intercept.

(The y-intercept is the value of y when x = 0)

Slope given as -4

And we know it passes through the point(4,6) ie at x=4, y =6

Substitute in above equation to get value of c, the y-intercept

6 = -4(4) + c

6 = -16 + c

c = 22

And this is the y-intercept

The equation of the line is y = -4x + 22

See attached figure for graph