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Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost pounds less than times the pounds he lost the first week. The third week, he lost 1 pound more than of the pounds he lost the first week.


Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than times the pounds Luke lost the first week. The second week, he lost 4 pounds less than times the pounds Luke lost the first week. The third week, he lost pound more than times the pounds Luke lost the first week.


Assuming they both lost the same number of pounds over the three weeks, complete the following sentences. Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost 3/2 pounds less than 3/2 times the pounds he lost the first week. The third week, he lost 1 pound more than 3/4 of the pounds he lost the first week.


Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than 3/2 times the pounds Luke lost the first week. The second week, he lost 4 pounds less than 5/2 times the pounds Luke lost the first week. The third week, he lost 1/2 pound more than 5/4 times the pounds Luke lost the first week.


Assuming they both lost the same number of pounds over the three weeks, complete the following sentences.

Answer:

14

Step-by-step explanation:

We can find the number of five-dollar bills creating a system of equations, where F represents the number of five-dollar bills and T represents the number of ten-dollar bills.  

Thus, we have 5F + 10T = 170 and F + T = 24.

We can use substitution in the second equation first to find T then finally F.

[tex]5F + 10T = 170\\F + T = 24\\\\F = 24-T\\\\5(24-T)+10T = 170\\120-5T+10T=170\\120+5T=170\\5T=50\\T=10\\\\F+10=24\\F=14[/tex]

The linear function h(x) = 2x + 3, with the domain {-2, -1, 0, 1, 2}, has the range {-1, 1, 3, 5, 7}.

To find the range, we substitute each value of the domain for x, in the linear function h(x) = 2x + 3, as follows:

For the domain value, x = -2:

h(-2) = 2(-2) + 3,

or, h(-2) = -4 + 3,

or, h(-2) = -1.

Therefore, for the domain value, x = -2, the range value h(-2) is -1.

For the domain value, x = -1:

h(-1) = 2(-1) + 3,

or, h(-1) = -2 + 3,

or, h(-1) = 1.

Therefore, for the domain value, x = -1, the range value h(-1) is 1.

For the domain value, x = 0:

h(0) = 2(0) + 3,

or, h(0) = 0 + 3,

or, h(0) = 3.

Therefore, for the domain value, x = 0, the range value h(0) is 3.

For the domain value, x = 1:

h(1) = 2(1) + 3,

or, h(1) = 2 + 3,

or, h(1) = 5.

Therefore, for the domain value, x = 1, the range value h(1) is 5.

For the domain value, x = 2:

h(2) = 2(2) + 3,

or, h(2) = 4 + 3,

or, h(2) = 7.

Therefore, for the domain value, x = 2, the range value h(2) is 7.

Therefore, the linear function h(x) = 2x + 3, with the domain {-2, -1, 0, 1, 2}, has the range {-1, 1, 3, 5, 7}.

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Answer:

4:3

Step-by-step explanation:

If you divide both 12 and 9 by 3 (the smallest number they can both be divided by), you get 4 and 3. the ratio is for every 4 apples, 3 would be green. So 4:3

The length of the rectangular book is 5.8cm

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term oblong is occasionally used to refer to a non-square rectangle.

The perimeter of a rectangle is found by adding up the length of all four sides. The formula for the perimeter of a rectangle is,

P = length + breadth + length + breadth. Or, P = 2(length + breadth)

Given:

Perimeter = 16.84 cm.

length = 18/7 cm

substituting in the formula we get

16.84 = 2( 18/7 + width)

8.42 = 18/7 + width

5.8 cm = width

Thus the length of the rectangular book is 5.8cm.

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The value of x is  21√2/2

The correct option is (A)

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

In triangle having angle 60.

sin 60 = P/ 7√3

√3/2= P/7√3

2P= 21

P= 21/2

Now again

cos 45= 21/2/x

1/√2 = 10.5/x

x=  21√2/2

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Using long division, 189 divided by 7 is 27

The picture below represent how to use long division.

Firstly, we divided 1 by 7, it can't go. Therefore, it zero. we put zero at the quotient space.

Multiply zero by 7 and subtract from 189.

We use 18 to divide 7. It will give us 2 remainder 4. we put the 2 at the quotient side and multiply it by 7 to get 14.

Then we subtract 14 from 18. And so on. This is done till we get 0.

Therefore, using long division, 189 divided by 7 is 27

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Answer: [tex]52.6^{\circ}[/tex]

Step-by-step explanation:

Let the angle of depression be x.

[tex]\sin x=\frac{27}{34}\\\\x=\sin^{-1} \left(\frac{27}{34} \right) \approx 52.6^{\circ}[/tex]

Answer:

Answer: x ≤ q - 17/6.

Step-by-step explanation:

Divide both sides of the inequality by the coefficient of variable

Answer:

According to Dr. Davis' law of conversion, we are able to rewrite the equation in any order we need to so that we can solve it in multiple ways. For example, we may choose to add/subtract first, then multiply/divide. Dr. Davis discovered that when solving equations order of operations does not need to be followed.

Step-by-step explanation:

Let's suppose you're getting a new phone plan. The phone plan charges a flat fee of $5 and costs $9 a month. How can we represent this relationship?

Since $5 is a flat fee, it doesn't change based on how many months you've had the plan because it always remains $5, so this is our y-intercept.

Because the plan costs $9 a month, this represents our rate of change, or slope, showing that every month you have the plan, you multiply by $9.

So, we can show this as y=9x+5 where x is the number of months of the phone plan and y is the cost of the phone plan given x amount of months

Now, what if you wanted to know how much the phone plan would cost after 4 months?

Simple enough, we can just substitute x=4 into our equation and get y=9(4)+5=36+5=41. So, getting the phone plan for 4 months costs $41.

Let's take this the other way around. What if we wanted to figure out how many months of the phone plan are covered by $50?

We would then substitute y=50 into our equation and solve for x:

y=9x+5

50=9x+5

45=9x

5=x

This would mean $50 would cover 5 months of the phone plan.

All in all, these are real-life examples of algebra.

Using the z-distribution, the 90% confidence interval for the difference of proportions is given by: (-0.0534, 0.0434).

For each sample, the mean and the standard error are given as follows:

For the distribution of differences, they are given by:

The interval is given by:

[tex]\overline{p} \pm zs[/tex]

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

Hence the bounds of the interval are:

[tex]\overline{p} - zs = -0.005 - 1.645(0.0294) = -0.0534[/tex]

[tex]\overline{p} + zs = -0.005 + 1.645(0.0294) = 0.0434[/tex]

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The probability that kids will be able to write something about both the French and Spanish classes after he is finished with the interviews is 91/100.

Given 25 kids has enrolled in atleast one foreign language class. 18 kids are in French class and 21 kids are in Spanish class.

We have to find the probability that kids will be able to write something about both the French and Spanish classes after Michael is finished with the interviews.

Let F is a set showing students knowing French,

S be a set showing students knowing Spanish ,

FS= Showing students both enrolled in one languages.

FS=F+S-(F∪S)

=18+21-25

=14

F-18-14=4

S=21-14

=7

4 outcomes lead to Michael being able to write both the languages are (F,S),(FS,S)(FS,F)(FS,FS)

Required probability is the sum of all the probabilities of (F,)(FS,S)(FS,F)(FS,FS)

P(F,S)=[tex]4C_{1}*7C_{1}/25C_{2}[/tex]

=(4*7)/300

=28/300

P(FS,S)=[tex](14C_{1}*7C_{1} )/25C_{2}[/tex]

=14*7/300

=98/300

P(FS,F)=[tex](14C_{1}*4C_{1} )/25C_{2}[/tex]

=14*4/300

=56/300

P(FS,FS)=[tex]14C_{2}/25C_{2}[/tex]

=91/300

Required probability=28/300+98/300+56/300+91/300

=(28+98+56+91)/300

=273/300

=91/100

Hence the probability that kids will be able to write both the languages is 0.91.

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Answer:

B. 39.59

Step-by-step explanation:

So 43 degrees, you know the length of the opposite side (27) and the angle (43 degrees), the only unknown is the hypotenuse. So you're looking for a trigonometric ratio that uses the angle (all of them do, except technically the inverse don't), the opposite side, and the hypotenuse. Sine is defined as [tex]\frac{opposite}{hypotenuse}[/tex]. So let's plug in known values:

[tex]sin(43) = \frac{27}{x}[/tex]

Multiply both sides by x

[tex]sin(43) * x = 27[/tex]

divide both sides by sin(43)

[tex]x=\frac{27}{sin(43)}[/tex]

Normally I would use a calculator, but in this case I'll use the approximation given in the problem of 0.682

[tex]x=\frac{27}{0.682}[/tex]

simplify the fraction

[tex]x\approx39.59[/tex]

The correct option is 'The domain of both functions is all real numbers'.

According to statement

Here, functions are f(x) = 5x and g(x) =5x

Since the domain of f(x) is, D= { x : x belongs to all real numbers.}

Therefore, Domain of f(x) is all real numbers.

Since f(x) and g(x) have the same value,

Therefore, Domain of g(x) is also the set of real numbers.

Now, range of f(x) is , R=  { 5x : x belongs to all real numbers.}

Therefore, Range of f(x) is all real numbers.

Range of g(x) is also all real numbers.

So, we can say by the above explanation, only option (1) is correct.

DISCLAIMER: The question was incomplete. Please find the full content below.

QUESTION

Keshawn is asked to compare and contrast the domain and range for the two functions.

f(x) = 5x

g(x) = 5x

Which statements could he include in his explanation? Check all that apply.

1. The domain of both functions is all real numbers.

2. The domain of f(x) is x > 5.

3. The domain of g(x) is x > 5.

4. The range of both functions is y > 5.

5. The range of f(x) is y > 0.

6. The range of g(x) is y > 0.

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Answer:

[tex]\huge\boxed{\sf x\leq 2}[/tex]

Step-by-step explanation:

[tex]56-10x\geq 20+8x\\\\Subtract \ 20 \ from \ both \ sides\\\\56-20-10x\geq 8x\\\\36-10x\geq 8x\\\\Add \ 10x \ to \ both \ sides\\\\36\geq 8x+10x\\\\36\geq 18x\\\\Divide \ 18 \ to \ both \ sides\\\\2 \geq x\\\\OR\\\\x\leq 2\\\\\rule[225]{225}{2}[/tex]

[tex]\bf{56-10x\geq 20+8x }[/tex]

Subtract 8x on both sides.

[tex]\bf{56-10x-8x\geq 20 }[/tex]

Combine −10x and −8x to get −18x.

[tex]\bf{56-18x\geq 20 }[/tex]

Subtract 56 from both sides.

[tex]\bf{-18x\geq 20-56 }[/tex]

Subtract 56 from 20 to get −36.

[tex]\bf{-18x\geq -36 }[/tex]

Divide both sides by −18. Since −18 is <0, the inequality direction is changed.

[tex]\bf{x\leq \dfrac{-36}{-18} }[/tex]

Divide −36 by −18 to get 2.

[tex]\bf{x\leq 2 \ \ \to \ \ \ Answer}[/tex]

We conclude that the correct option is "C".

There are 80 different combinations of 3 cupcakes are there if order does not matter

The given parameters are:

Flavors = 10

Flavors to choose = 3

The number of combination is calculated using:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

This gives

[tex]^{10}C_3 = \frac{10!}{7!3!}[/tex]

Expand

[tex]^{10}C_3 = \frac{10 * 9 * 8 * 7!}{7!3 * 2 * 1}[/tex]

Evaluate quotient

[tex]^{10}C_3 = 80[/tex]

Hence, there are 80 different combinations of 3 cupcakes are there if order does not matter

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Answer:

at 5 mins Holly traveled 2 miles. At 10 mins Holly traveled 4 miles. from there on she stayed there for 10 mins then went on her way. At 30 mins she traveled 5 1/2 miles. when she hit 35 mins she hit her destination then went back home.

Step-by-step explanation:

pretty simple

Answer:

B. 8

Step-by-step explanation:

Triangle's weight is equal to the sphere's weight.

Total of 16 blocks. Since the triangle's weight is equal to the sphere's, the weight will be half of the blocks.

Divide 2 from 16.

16/2=8

The triangle's weight is equal to 8 blocks.

Hope this helps!

If not, I am sorry.

We'll prove first the triangles formed by diagonal are congruent then we'll prove the angles on either side of diagonal are congruent.

The steps are:

=============================================================

Answer:

5

Step-by-step explanation:

substitute in 2 for x

3(2) - 1 = 5

Answer:

x=55°

Step-by-step explanation:

x=180°-125°

x=55°

Answer:

see attached graphs

Step-by-step explanation:

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Parent function:  [tex]f(x) = x[/tex]

Each transformation is a transformation of the parent function only:

Translation of 4 units down

[tex]\implies f(x)-4=x-4[/tex]

[tex]\implies y=x-4[/tex]

A stretch by a factor of 3

[tex]\implies 3f(x)=3x[/tex]

[tex]\implies y=3x[/tex]

A reflection and a translation 1 unit up

[tex]\implies f(-x)+1=-x+1[/tex]

[tex]\implies y=-x+1[/tex]

Using a calculator for the chi-square distribution, the critical value is given by:

A) 20.090

For a chi-square critical value, three parameters are needed:

In this problem, we have a one-tailed test(as we are testing if the mean is greater than a value), with a significance level of 0.01 and 8 df, hence, using a calculator, the critical value is of 20.09, hence option A is correct.

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So, 40 Customers are waiting at 10 A.M.

According to statement

Number of customers arrives at coffee shop per hour = 100

Capacity of shop for per minute per customer = 0.8 minute

Capacity of shop for customers per hour = 80

Find number of customers are by

Queue growth rate = Demand - Capacity

Put the values in the formula and find the growth rate

So,

Queue growth rate= 100 - 80 = 20.

Length of queue at 10 a.m. = 2 × 20 = 40.

So, 40 Customers are waiting at 10 A.M.

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if stretched vertically by a factor of 2, the resulting function will be g(x) = 2|x| and a horizontal compression by a factor of 2, the resulting function will be 1/2|x|

Transformation is a technique used to change the position of an image on an xy-plane.

If the function f(x)is vertically stretched by "a" units, the resulting function will be f(x) = a|x|.

Hence if stretched vertically by a factor of 2, the resulting function will be g(x) = 2|x|

For a horizontal compression by a factor of 2, the resulting function will be 1/2|x|

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Answer:

6.708 miles

Step-by-step explanation:

She walked 3 miles to the right, and 6 miles up. The shortest route she could take back to her starting point is a diagonal, which we can solve for using the Pythagorean theorem, a^2 + b^2 = c^2. We're solving for c.

9 + 36 = c^2

c^2 = 45

c = 6.708

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Considering the given graph of the function, we have that:

To find the numeric value of the function, we get a value of x(horizontal axis), and then look at the corresponding value y(vertical axis), then y = f(x).

In the graph of this function, we have that when x = 1, y = -3, hence:

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