It takes Abby 3 hours to drive from Ashdown to Bridgeton at an average speed of 60 mph.
She then drives 30 miles from Bridgeton to Carton at an average speed of 40 mph.
Assuming Abby doesn't stop, what is her average speed from Ashdown to Carton to 1 dp?

a) The mistake that mara made in step 3 is that; she didn't apply the basic rule of logarithm which should have given the expression log 3^x = x log 3

b) The mistake that mara made in step 4 is that; you must eradicate the log at the same time and as such it should be x log 3 = 3log 3

c) The mistake she made throughout is not applying the basic rule of logarithm.

She is trying to solve the exponential function 7 x 3^x = 189 with the following steps;

Step 1. 7 x 3^x = 189

Step; 2. 3^x = 27; This step is correct because she got it by using division property of equality to divide both sides by 7.

Step 3; log^3 (^3) = log^27; This step is incorrect because from basic rules of logarithm, we know that; log 3^x = x log 3

Step 4. xlog^33=9; This is incorrect because you cannot remove the log on one side of the equation without doing the same on the second side. Thus, what she she should have had here is;

x log 3 = 3log 3

Step 5. x * 1 = 9; This is wrong because dividing both sides by log 4 gives; x = 3

Step 6. x = 9; This is wrong because x = 3

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Complete question is;

Mara solved an exponential equation by using logarithms. This is her work.

1. 7 x 3^x = 189

2. 3^x = 27

3. log^3 (^3) = log^27

4. xlog^33=9

5. x * 1 = 9

6. x = 9

Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)

a. Be sure to explain what she did and why it was correct or incorrect for Step 3.

b. Be sure to explain what she did and why it was correct or incorrect for Step 4.

c. Provide Mara with feedback on what the mistake was and how to fix it.

How can you stay safe as you evacuate during a flood? Select the three correct answers:

A, C, & D

Moving furniture is not beneficial in a flood situation.

A, C and D

hope this helps!

The value of the the two numbers are 5/8and 1/6

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.

They are called simultaneous equations because the equations are solved at the same time.

if the first number is x and second number is y then

x+y= 19/24 equation 1

x-y= 11/24 equation 2

using elimination method, subtract equation 1 from 2

x-x+y-(-y)=19/24-11/24

2y= 8/24

2y=1/3

divide both side by 2

y= 1/3×1/2= 1/6

substitute 1/6 for y in equation 2

x+1/6=19/24

x= 19/24-1/6

x= 15/24

x= 5/8

Therefore the value of the two numbers is 5/8 and 1/6

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Answer:

4x4x4

Step-by-step explanation:

3x4x5= 60

4x4x4= 64

64 is a higher volume than 60

Answer:

In order to find out which box can hold more, we can find the respective volumes of the boxes.

Volume of first box

= 3 inches × 4 inches × 5 inches

= 60 inches³

Volume of second box

= 4 inches × 4 inches × 4 inches

= 64 inches³

∴Since the second box has a greater volume than the first box, the former can hence hold more than the latter.

The result of the fractional operation in this problem is given as follows:

-21/5 = -4.20.

A fraction is represented by the division of a term x by a term y, as follows:

Fraction = x/y.

The terms that represent x and y are given as follows:

The numerator in this fraction is given as follows:

5 - (8 - 6) + 3 x 4 + 6.

The parenthesis and the multiplication have precedence, hence:

5 - (8 - 6) + 3 x 4 + 6 = 5 - 2 + 12 + 6 = 21.

The denominator in this fraction is given as follows:

5(4 - 5) = 5(-1) = -5.

The result is the division of the numerator by the denominator, hence:

21/(-5) = -21/5 = -4.20.

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Answer:
3/2

Step-by-step explanation:

the answer is 3/2 because you take the slope by using the equation y/x. I did this problem by starting prop the point (0,-6). I then counted for how many points I went up, how many did I go to the right or left. If it went to the right it’s positive, to the left it is negative. In this case it went to the right 2 times every time it went up 3. Meaning 3/2

Answer: -4, -1, 1, 3, 3.9, 3.99, 3.999, 4

Step-by-step explanation:

That inequality symbol means less than or equal to. So that includes 4 and any number that precedes it on the number line.

The number of items that are missing from the order if She ordered 27 products from one company, but unfortunately, some items were back-ordered, so she received only 19 items is 8.

The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given:

The number of the ordered products, O = 27,

The number of the received order, R = 19,

If m stands for the number of missing items, then,

m = O - R,

m = 27 - 19

m = 8

Therefore, the number of items that are missing from the order if She ordered 27 products from one company, but unfortunately, some items were back-ordered, so she received only 19 items is 8.

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Answer: The correct mean weekly grocery expense for Taylor is $62.51

How to find mean of a discrete data?

Suppose the data values be .

Then, their mean is evaluated as:

where n = number of observations.

For the given condition, Taylor recorded the weekly expenses for 12 weeks. Therefore, we get n = 12

Let the real weekly expenses for Taylor be

Let  observation is misinterpreted as T

Then, the mean of that misinterpreted set of data would be

Since we're given that:

Therefore, we get the mean of original weekly expenses as:

Therefore, the correct mean weekly grocery expense for Taylor is $62.51

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Step-by-step explanation:

Answer:272

Step-by-step explanation:

In the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.

So, the values of C are:

Calculate as follows:

(A) When x = -2 and y = 15.

(B) When x = 0 and y = 10.

(C) When x = 2 and y = 5.

(D) When x = 4 and y = 0.

Therefore, in the given equation [12.5x + 5y = C] the constant C is always 50 with different given values of x and y.

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If the same force acts upon another object whose mass is 5 kg, the object's acceleration will be 1.667 m/s^2.

We were told that the constant force acts upon an object, and  the acceleration of the object varies inversely with its mass, which can be interpreted as :

A = k/M

where M is the mass of the object.

A = acceleration

the k= proportionality constant

then we were told that mass is 3 kg, the acceleration of the object is 25 m/s^2

then substitute into the equation as:

25 =k*3

k= 25/3

then we were told that when mass is 5 kg, then acceleration will be ?

A= (25/3 )/5 = 1.667m/s^2.

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The expression that equals semantics -1 D is - 2x² + x + 15.

One or more terms in an algebraic expression each include variables and constants. These expressions utilize separators like +, -, and that are symbols or operations. An algebraic statement with variables and constants is a quadratic trinomial. It is written as ax² + bx + c, where a, b, and c are real non-zero values and x is the variable. The leading coefficient "a," linear coefficient "b," and additive constant "c" all refer to the same constant.

The given trinomial is D = 2x² - x - 15

Multiply both sides by -1 to find -1D

-1D = -( 2x² - x - 15) = 0

-1 D = - 2x² + x + 15

So, this is the trinomial equal to the semantics -1D.

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Answer:B

Step-by-step explanation:

Becauee it already says the first night how many tickets were sold also on the second and the third night. And if someone read the equation they would have known that the play went in for three nights.

Answer:

[tex]x= -4[/tex] + [tex]2\sqrt{5}[/tex]   and   [tex]x= -4 -2\sqrt{5}[/tex]

Step-by-step explanation:

[tex]ax^{2}[/tex] + [tex]bx[/tex] - [tex]c = 0[/tex]

For this equation: [tex]a = 2, b = 16, c = -8[/tex]

[tex]2x^{2}[/tex] + [tex]16x[/tex] - [tex]8 = 0[/tex]

Step 1: Use quadratic formula with [tex]a=2, b=16, c=-8[/tex]

[tex]x=\frac{-b + - \sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]x=\frac{-(16) + - \sqrt{16^{2}-4(2)(-8) } }{2(-2)}[/tex]

[tex]x=\frac{-16+- \sqrt{320} }{4}[/tex]

[tex]x= -4[/tex] + [tex]2\sqrt{5}[/tex]  and   [tex]x= -4 -2\sqrt{5}[/tex]

Hope this helps! :)

Based on the data on the income statement, the amount of the tax equals to $27,000.

Generally, a taxes refers to those mandatory contributions levied on individuals or corporations by a government entity either from local, regional, or national government.

Given that: EBIT = $547,000 Interest expense = $94,000 Net income = $426,000

EBT = EBIT - Interest expense

EBT = $547,000 - $94,000

EBT = $453,000

The tax reported in Income statement:

= EBT - Net income

= $453,000 - $426,000

= $27,000

In conclusion, the 2021 taxes reported on the income statement equals to $27,000.

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The values of x and y are 2 and -7 respectively, this forms an ordered pair of (6,-7) and (2,1).

Given the equation and ordered pair the question;

To determine, the y-value, plug the x-value into the equation and solve for y.

y = -2x + 5

Plug in x = 6

y = -2( 6 ) + 5

y = -12 + 5

y = -7

Determine the x-value by plunging in the y-value into the equation and solve for x.

y = -2x + 5

Plug in y = 1

1 = -2x + 5

1 + 2x = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2.

Therefore, the ordered pair are (6,-7) and (2,1).

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Step-by-step explanation:

you need to give us also some context.

because that sequence can be anything.

but I suspect you mean

4 : 5 = x : 480

0.8 = x / 480

x = 480 × 0.8 = 384

Number lines are significant because they depict numbers as they appear in daily life.

What is number line?

A number line is a representation of a graduated straight line in elementary mathematics that serves as a visual representation of the real numbers. It is assumed that every point on a number line corresponds to a real number, and that vice versa.

Research has revealed that number lines are crucial because they foster sound mental number sense and arithmetic procedures.

They assist in providing a mental approach for addition and subtraction. Number lines are crucial, we can all agree on that.

Number lines are significant because they depict numbers as they appear in daily life.

Primarily because they make it possible for negative integers to be represented in a meaningful fashion.

The ability to display all real numbers, even enigmatic irrational numbers such π, -π, √2, -√ 2, etc., was a secondary but no less significant result.

Hence, number lines are significant because they depict numbers as they appear in daily life.

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The value of c for the expression, -0.65(c-7) = 1.95, is 4.

According to the question,

We have the following expression:

-0.65(c-7) = 1.95

Now, 0.65 is in multiplication on the left hand side. So, it will be in the division on the right hand side. Note that the negative sign can also be moved to the right hand side.

c-7 = -1.95/0.65

c-7 = -3

Moving 7 from the left hand side will result in the change of the sign from minus to plus:

c = -3+7

c = 4

Hence, the value of c is 4 for the given expression.

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Presley have 1 bracelets left  and the expression which shows the difference is (9x - 10) - (4x + 5) .

What is linear polynomial equation?

Any polynomial written as the equation p(x) = ax + b, with a and b being real numbers and a 0, is referred to as a linear polynomial. The largest exponent of the variable in a linear polynomial, or one, is known as the degree of the variable.

If n elements are given and x element is subtracted from the n elements, hence the remaining element is y,  then expression can be expressed by n- x = y.

We have,

             (9x - 10)

             (4x + 5)          

Initially Presley has (9x - 10) bracelets and she sells (4x + 5), hence we have to calculate the remaining bracelets.

Therefore,

                         (9x - 10) - (4x + 5)      

By simplifying the above equation we get,

= 9x - 10 - 4x + 5

= 5x -5

x = 5 / 5

∴ x = 1

Hence, the Presley have 1 bracelets left.

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The expression will be; part (a) (f o g)(-2) = 2 and part (b) (g o f)(-2) = -95

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the functions as;

f(x)=4x-2

g(x)=5-x^2

We need to find (f o g)(-2)

So, first, we will find the function (f o g)(x) as follows:

[tex]\begin{gathered} \mleft(f\circ g\mright)(x)=f\lbrack g(x)\rbrack=4(5-x^2)-2 \\ (f\circ g)(x)=20-4x^2-2 \\ (f\circ g)(x)=18-4x^2 \end{gathered}[/tex]

Now, substitute with x = -2 then we get;

[tex](f\circ g)(-2)=18-4\cdot(-2)^2=18-4\cdot4=18-16=2[/tex]

Thus, the answer to the part is (a) (f o g)(-2) = 2

b) (g o f)(-2)

We need to find (g o f)(x) as follows:

[tex](g\circ f)(x)=g\lbrack f(x)\rbrack=5-(4x-2)^2[/tex]

Now Substitute with x = -2, then we get;

[tex]\begin{gathered} (g\circ f)(-2)=5-(4\cdot-2-2)^2 \\ =5-(-8-2)^2 \\ =5-(-10)^2 \\ =5-100 \\ =-95 \end{gathered}[/tex]

Thus, the answer to the part (b) is (g o f)(-2) = -95

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A. The data modeling the relation is an exponential function.

B. The function is: y = 2^x.

C. The rate of change from x = 2 to x = 4 is of 4.

The definition of an exponential function is presented as follows:

[tex]y = ab^x[/tex]

In which the variables of the function are listed as follows:

From this data-set, when x increases by one, y is multiplied by 2, hence the rate of change is:

b = 2.

When x is increased by n, the rate of change is:

b^n = 2^n.

Hence, when x is increased by 2, from 2 to 4, in item c, the rate of change is:

2² = 4.

When x = 1, the output is the output at x = 0 multiplied by 2, hence the coefficient a of the function is given as follows:

a = 2/2 = 1.

Then the exponential function is:

[tex]y = 2^x[/tex].

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The probability of rolling a number that is less than 3 is P = 1/2.

A standard six-sided die has the following outcomes:

{1, 2, 3, 4, 5, 6}

The outcomes that are less than or equal to 3 are:

{1, 2, 3}

Assuming all the outcomes have the same probability, the probability of rolling a number less than or equal to 3 on a standard six-sided die will be equal to the quotient between the number of outcomes that meet the condition and the total number of outcomes.

It will give:

P = 3/6 = 1/2 = 0.5

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A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%" and PV factor used is 0.62026 .

Hence,

The amount desired at end of a period is $9400.

The length of time is 4 years .

The rate is 2%.

Compounded is monthly.

The period used is 48.

The rate used is 1%.

The PV factor used is 0.62026 .

The PV of the amount desired at the end of the period is $5830.45

What is the percentage?

A percentage is a number or ratio expressed as a fraction of . It is often denoted using the percent sign, "%".

Here from the question,

PV factor = (1 + i) ----(1)

where, i = 12/12 % , i =1

and

n = 4(12)

n = 48

Substituting the values in the equation , we get

PV factor = (1 + 0.01)^ -48

PV factor = 0.62026

Hence,

the amount desired at end of a period is $9400.

The length of time is 4 years.

The rate is %.

Compounded is monthly.

The period used is 48 .

The rate used is 1%.

The PV factor used is 0.62026.

The PV of the amount desired at the end of the period is $5830.45

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Answer:

4 craft sticks

Step-by-step explanation:

Assuming that none of the craft sticks can be split in order to equally share the whole package, then the most craft sticks each person could have would be 9 because 9*9=81. This means that there would be 4 craft sticks left over because 85-81=4

The actual weekly labor cost compared to the target is 240 hours

What are Time and Work?

According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.

The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.

Target costing is a system under which a company plans in advance for the price points, product costs, and margins that it wants to achieve for a new product.

Given

Regular Rate $15.00/hr

Overtime Rate $22.50/hr

Targeted Labour Cost $12,000/wk

Labour Hours Needed 800/wk

According to the question:

Overtime means each employee can work beyond the input of 40 hrs. Per week.

Labor requirement = 800 hrs.

14 men labor capacity = 14× 40 = 560 hrs.

So overtime hours required = 800-560=240 hrs

Hence,

The actual weekly labor cost compared to the target is 240

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The length of the square for the 2.25 inches King's height will be 0.75. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, a chessboard is made using the ratio of square length to the king's height, 1.5 inches to 4.5 inches. If a chessboard is made with a king's height of 2.25 inches.

The square length will be calculated as,

Square length / Kings Height = 1.5 / 4.5

Square length = (King's height x 1.5 ) / 4.5

Square length = ( 1.5 x 2.25 ) / 4.5

Square length = 0.75 inches

Therefore, the length of the square for the 2.25 inches King's height will be 0.75. The correct option is A.

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