2. Construct Arguments Explain why -7 has a
greater absolute value than the absolute value
of 6.
5.-9
7.1-5
9. --
11.-1

The least amount of money that was originally put in the savings account is $426.

The amount of money in the savings account is a function of the money that was originally in the account and the amount by which the account was increased by.

The inequality that represents the total amount of money in the savings account is:

amount originally in the account + amount deposited > 500

x + $75 > $500

x > $500 - $75

x > $425

The least amount would be $426 because this is the smallest number that is greater than $425 that would make the total amount more than $500.

To check:

$75 + $426 = $501

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Since matching angles are formed and the equal corners are congruent when a line joins two parallel lines, one of the choices isc=d.

Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.

Here,

Given :  vertical angles, A = d also represents a solution.

B+d=180 as a result of b+c=180 therefore

B+d=180 as a result of b+c=180 therefore Since a=d, c=d, and b+d=180, the answer is B,C,E.

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Answer:

Step-by-step explanation:

Answer:

increase amount = 32× 4.4%

= 32 × 4.4 ÷ 100

= 32 × 44 ÷ 1000

= 1.408

32 increased by 4.4% = 32 + 1.408 = 33.408

The  answer is distance from P to l. is equal to square root of 2

Line I contains points (0, -3) and (7,4). Point P has coordinates (4,3)

Find the slope of line l we have the points (0, -3) and (7,4)

m=(4+3)/(7-0) m=7/7 m=1

Find the equation of the line perpendicular to the line l that passes through the point P

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1, the slope of the perpendicular line is

m=-1 .Find the equation in point slope form

y-y1=m(x-x1)

(x1,y1)=P(4,3)

substitute

y-3=-1(x-4)

y-3=-x+4

y=-x+7

m=1 (see the step 1)

and we have the point (0,-3) -----> y-intercept

so the equation of the line l is

y=x-3

Find the intersection point line l and its perpendicular line

y=x-3 ------> equation A

y=-x+7 -----> equation B

solve the system of equations

Adds equation A and equation B

2y=-3+7

2y=4

y=2

substitute in equation A

2=x-3 x=2+3 x=5

the intersection point is (5,2)

Find the distance between point (5,2) and point P(4,3)

Remember that, this distance is the distance from P to l.

the formula to calculate the distance between two points is equal to

we have

(x1,y1)=(5,2)

(x2,y2)=(4,3)

substitute in the formula

therefore

The  answer is distance from P to l. is equal to square root of 2

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Therefore , the solution of the given problem of function comes out to be satisfies the given function is x=9 and y=21.

Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.

Here,

Given : A table of values of x and y

To find : the function is linear or not

Thus,

F(x) = y -3x =0

So,

Putting the values of x and y in given function

The value which satisfies the given function is x=9 and y=21.

Therefore , the solution of the given problem of function comes out to be

satisfies the given function is x=9 and y=21.

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If Christopher measured a line to be 12.2 inches long. If the actual length of the line is 12.1 inches, the percent error of the measurement, to the nearest tenth of a percent is: 0.83%.

Using this formula to find the percent error

Percent error = Measurement - Actual length / Actual length

Let plug in the formula

Percent error = 12.2 - 12.1 / 12.1

Percent error = 0.1 /12.1

Percent error = 0.0083 or 0.83%

Therefore we can conclude that the percent error is 0.83%.

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Answer:

It is a known fact that there are rectangular prisms with the same volume but different dimensions.

This is a simple cross multiplication problem! Any time you're given a ratio and then the actual quantity of something, you can use cross multiplication to figure out the quantity of the other thing!

We know that the ratio of toads to frogmen is 7 : 2. We also know there were 98 actual toads. Therefore we can set up our equations!

[tex]ratio_{toads}=ratio_{frogmen}\\actual_{toads}=actual_{frogmen}\\\\7=2\\98 = x\\\\7x=196\\x=28[/tex]

The first two equations above everything is how you would have everything set up! The second equations under them are the numbers plugged in, and the rest is just simplification.

So, your final answer should be 28 frogmen!

Answer:

Step-by-step explanation:

read the data numbers

Answer:

y = 10

Step-by-step explanation:

given DEFG = SPQR

QR = FG

=> 2x - 4 = 12

=> 2x = 16

=> x = 8

angle PQR = EFG

=> 6y + x = 68

=> 6y + 8 = 68

=> 6y = 60

=> y = 10

If

f

(

x

)

=

2

x

4

−

9999999kwwkqkkaosos

A line with a slope of three and the point three on the line have the equation y=3 z+1. The equation of a straight line can be found using the formula y = mx + b.

If a line has a slope of 3 and a y intercept of 1, you need to determine its equation. Remember the line's equation by first going back: when y=mz+b , M is the slope, and Y-intercept b is the value.

In order to solve for y in the equation y=m z+b, all you need to do is swap out m for 3, the slope you provided, and b for 1, the y-intercept. The line's equation is given by y=3 z+1, where z represents the line's y-intercept and slope. If you are aware of the slope of the line being studied and the provided point is also the y intercept, you can utilise the slope intercept formula, y=mx+b (0,b).

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If Ryan spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The  distance the plane traveled from point A to point B is: 13,027ft .

Constant altitude =6300 feet

Angle of elevation =15 to the plane at point A

An angle of elevation =31 to the plane at point B.

So,

Tan 15° = 6300/ON

ON =23,511.92

Tan 31° =6300/OB

OB = 10,484.96

So,

AB =23,511.92 - 10,484.06

AB = 13,026.96

AB = 13,027ft (Approximately)

Therefore the distance is 13,027ft.

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h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.

Here,

We can draw the graph as

h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)

h(x) = f(x) + 5

The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.

Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).

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Answer:

Step-by-step explanation:

[tex]N^{2} =49[/tex]

To solve take the square root of 49.

[tex]\sqrt{49}[/tex] = 7

Option c which is 7

Step-by-step explanation:

Let’s see … one division every 20 minutes? That would be like <grinding noise> three binary doublings per hour, right? Now for the tough part … three doublings per hour, for eight straight hours? <more grinding noises> … Is that even mathematically possible? After much thinking, I decide that the total number of binary doublings has to be in the neighborhood of no less than eight times three!

Would you believe that 224=16777216 ? While mathematically true, it is not the answer to the posted question… Since we started at 0 minutes, there are only 23 buddings inside eight hours … so the answer has to be 223=8388608 , right?

Wrong again, this time forgetting all about the newlybud bacteria generations, that all go on budding side by side of their ancestors …

Now that you’ve caught on to the basic idea, I leave it to you to figure out the real answer! Keep in mind that after 20 minutes, you have two budding bacteria to reckon with, for 440 minutes … after 40 minutes another two (for 420 minutes), and so on, down the line.

Hint: the answer still is not 16777216 …

Answer:

after 1 division,there is 3 cell

after 2 divisions,there is 9 cell.

after 3 divisions,there is 27 cell

The above data takes the form of Geometric sequence.

3,9,27......,last term

here,Common ratio(r)=9/3=27/9=3

and,first term(a)=3

Let, n be the no.of divisions.

then, n=8 hrs/20 min=480 min/20min=24

Now,from the G.S,

last term=ar^n-1

=3×3^24-1

=9²³

Hence,9²³ organisms will there be after 8 hours

It can be written as 8.86293812×10²¹ as well

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Answer:

-3,950

Step-by-step explanation:

First -5,000(1-0.21)

Then multiply -5,000 x 0.79 = -3,950

The area of the trapezoid is 1.5x² + 2x. If the height is increased by 4 feet, the new area would be 1.5x² + 8x

An equation is an expression that shows the relationship between two or more numbers.

Let x represent the height of the trapezoid.

a) One base of trapezoid measures five feet greater than its height. Hence:

First base = x + 5

The other base is one foot less than twice its height, hence:

Second base = 2x - 1

Area = (1/2)(sum of bases) * height = (1/2)(x + 5 + 2x - 1)(x) = 1.5x² + 2x

b) The height is increased by 4 feet. New height = x + 4

First base = (x + 4) + 5 = x + 9

Second base = 2(x + 4) - 1 = 2x + 7

Area = (1/2)(sum of bases) * height = (1/2)(x + 9 + 2x + 7)(x) = 1.5x² + 8x

The area of the trapezoid is 1.5x² + 2x.

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An area surrounding a measurement that indicates how accurate it is called a confidence interval.

Let X = The proportion of n randomly selected consumers who receive the discount. So, X = B(n, p), where p is the likelihood that a consumer will receive the discount.

Back-up Theory 100(1 - α) % Confidence Interval for the population proportion, p is:

p ± Zα/2[√{P(1 –p)/n}] ……(1)

where

Zα/2 is the upper (α/2)% point of N(0, 1),

pcap = sample proportion, and

n = sample size.

One can conclude with 100(1 - )% confidence that the population proportion, p, is p if a 100(1 - )% Confidence Interval for p holds a specific hypothesized value of p…………. (2)

Now to work out the solution,

The given confidence interval is: 0.12 ± 0.05 i.e., [0.07, 0.17] or [7%, 17%]……………………. (3)

for Part (a)

equation (2) and (3), [7%, 17%] holds 15%. Hence the statement is NOT valid.

for Part (b)

equation(2) and (3), [7%, 17%] holds 15%. Hence the statement is valid.

For Part (c)

Margin of error is: Zα/2[√{P(1 –P)/n}]

If the sample sizes under Part (c) and (a) are respectively, n2 and n1, the ratio of respective margin of errors would be

[Zα/2.√t{P(1 –P)/n2}]/[Zα/2√{P(1 –P)/n1}]

= √(n1/n2)

= 1/√6 [given the second sample size is 6 times the first sample size]

= 0.4082

= > the margin of error under Part (c) = the margin of error under Part (c) x 0.4082

= 0.05 x 0.4082

= 0.020.

Thus, the margin of error when the sample size if 6-fold is 0.020.

For Part (d)

The revised Confidence Interval from Part (c) is 0.12 ± 0.02 or [0.10, 0.14], which does not hold 0.15 as a result, according to (2), the program is NOT operating as anticipated.

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Answer:

the aswer is A  i did this

Step-by-step explanation

The remainder of the given division 5884/ 94 is 56 and hence the complete sentence is 5884/94 = 62 + 56/94.

The amount that remains after division is complete is known as a remnant. Simply divide the number by another number that is one of its multiples to obtain the remainder.

The division of any number can be written as follows:

a/n = q + r/n

where, a is the dividend, n is the divisor, r is the remainder and q is the quotient.

When we divide the number 5884 by 94 using the long division method the quotient is 62 and the remainder is 56.

Hence, the complete sentence is 5884/94 = 62 + 56/94.

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Answer:

19

Step-by-step explanation:

Karen and Kate have 50 CDs between them. Karen has 6 less than kate. How many each has?

25&25  

If Karen Has 6 Less Then Kate, Karen Would Have 19 CDS

Hope This Helps

Answer:

x = 14

Step-by-step explanation:

2(x + 4) = 3( -2 + x)  distribute the 2 and the 3.

2(x) + 2(4) = 3(-2) + 3(x)

2x + 8 = -6 + 3x  Subtract 2x from both sides

2x - 2x + 8 = -6 +3x -2x

8 = -6 +x  Add 6 to both sides

8 + 6 = 6 - 6 + x

14 = x

Answer:

d7-dx=(20x|x-3|+40)x  x-3 (|x-3+2)x| x-3|

Step-by-step explanation:

Hope this helps :D

In response to the above problem, we may state that the triangle's - 5/13 measurements correspond to sin and cos.

The first six essential trigonometric functions are used in trigonometry. These functions are trigonometric ratios. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six basic trigonometric functions. The side ratio of a right-angled triangle is equivalent to the identities and functions of trigonometry. Trigonometric formulas are applied to the perpendicular side, hypotenuse, and base of a right triangle in order to calculate the sine, cosine, tangent, secant, and cotangent values.

as base/hypotenuse = cos x

and sin x = hypotenuse/perpendicular

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Answer: To calculate the sample mean of a distribution, you add up all the values and divide by the number of values in the sample. The sample mean is also known as the average.

The formula for the sample mean is:

X-bar = (X1 + X2 + ... + Xn) / n

To calculate the sample variance of a distribution, you first need to calculate the sample mean. Then, for each value, you subtract the sample mean and square the result. You add up all these squared differences, and divide the sum by the number of values in the sample.

The formula for the sample variance is:

s^2 = ( (X1 - X-bar)^2 + (X2 - X-bar)^2 + ... + (Xn - X-bar)^2 ) / (n - 1)

It would be helpful to have the sample data, however I cannot complete this task without it.

Please provide me with the data.

Step-by-step explanation:

Therefore ,We can see that in equation 1 plunk yields the most lorgs at 30. So the plunk coin is the most valuable.

A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 5x - 5 = 25 is an equation. We can find that the variable x has a value of 6  by resolving this equation.

Here,

we need to convert everything to the same unit in order to establish a legitimate comparison when comparing units like inches, feet, and yards. Therefore, we would have to convert everything, for example, to inches. For these five coins, the same concept holds true. Either lorgs, sinds, plunks, harps, or dalts must be used for everything (pick one of those five).

It's equivalent to attempting to change a dollar amount into cents (for example, $1.37 becomes 137 cents). The alternative is to think about it as 1 dollar = 100 cents, 1 quarter = 25 cents, 1 dime = 10 cents, and so on.

The procedures in the various parts below are designed to convert all coinage to lorgs, which will serve as our base unit. Trial and error led me to the conclusion that the lorg coin had the lowest worth, thus I'm striving to obtain everything in lorgs.

The four equations provided are

4 lorgs to a sind

5 dalts x 2 plunks

2 harps from 5 sinds.

3 harps equal 1 plunk.

In that order, I'll refer to them as equations (1) through (4).

One sind equals four logs (1)

5 sinds = 20 lorgs; add 5 to both sides.

2 harps = 20 lorgs; in the equation, swap out "5 sinds" with "2 harps" (3)

1 harp = 10 lorgs; multiply both sides by 2, then write this as an equation (5)

Equation: 1 plunk = 30 lorgs (6)

Each of those equations enables us to determine the lorg value of the coins sind, dalt, harp, and plunk.

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The complete question is : " A nation has five types of coins: sinds, dalts, lorgs, harps, and plunks.1 sind = 4 lorgs ,2 plunks = 5 dalts ,5 sinds = 2 harps , 1 plunk = 3 harps Which coin is the most valuable? a) sindb) daltc) harpd) plunk"

Answer: 571.11111...(Fraction: 9/28)

Step-by-step explanation:

5,140÷9 = 571.11111...