The Heights Of 13 Men In Centimetres Are Given Below. 162, 160,163, 160 , 165,187,170, 167, 174, 176, (2024)

For this case we can see that the point A is on the negative side of the line and we can see that the answer would be

[tex]-3\frac{1}{3}=-\frac{10}{3}[/tex]

But the absolute value would be:

[tex]\left|-3\frac{1}{3}\right|=\left|3\frac{1}{3}\right|[/tex]

And the best answer would be:

[tex]3\frac{1}{3}[/tex]

To grap the given lineal inequality:

[tex]y

Find two points in the boundary line:

[tex]y=x[/tex]

As y=x the points have the same coordinate value for x and y

Points (5,5) and (-3,-3)

Put those points in the plane and link them with a dotted line (as the inequality sing is < the boundary line is a dotted line).

The shadow area is under the line (the inequality sing is < (less than), then the solution is the values that are less than the line (under the line).

As you can see above the quadrant that is completely shaded is IV.Solution is all the values in the shaded area.

Given

Price: $225

Discount: 75%

Procedure

Selling price sofa

[tex]225\cdot(1-0.75)=56.25[/tex]

The answer would be $56.25

Given

Statements

Find

Which of the following can be used to estimate the instantaneous rate of change at a point on a continuous function.

Explanation

as we know that the slope of the tangent line through a point on the graph of a function gives the function's instantaneous rate of change at that point.

so , option b is correct .

Final Answer

Hence , the slope of the tangent line drawn at the point gives the instantaneous rate of change at a point.

It is given that the expression for the distance an object falls in t seconds is:

[tex]16t^2[/tex]

It is required to find out if a rock that is 64 feet above water will hit the water in 2 seconds.

To do this, equate the distance above water to the expression given for distance:

[tex]16t^2=64[/tex]

Next, solve the equation for t:

[tex]\begin{gathered} 16t^2=64 \\ \text{Divide both sides by 16:} \\ \Rightarrow\frac{16t^2}{16}=\frac{64}{16} \\ \Rightarrow t^2=4 \\ \Rightarrow t=\sqrt[]{4}=2 \end{gathered}[/tex]

The time it will take for the object to fall a distance of 64 feet, is calculated to be 2 seconds.

This implies that if the rock is 64 feet from the water, it will hit the water in 2 seconds.

Yes, the rock will hit the water in 2 seconds.

The mean is determined by dividing the sum by the number of values. Let s be the sum, we can expressed it as

[tex]\frac{s}{5}=41[/tex]

Solve for s by multiplying both sides by 5

[tex]\begin{gathered} \frac{s}{5}\cdot5=41\cdot5 \\ \frac{s}{\cancel{5}}\cdot\cancel{5}=41\cdot5 \\ s=205 \end{gathered}[/tex]

Therefore, the sum of values is 205.

Solution

Draw a diagramatic representation of the question

Step 2

Add both heights to determine the height of the block including the tower antenna

[tex]\begin{gathered} \frac{1}{4}+4\frac{2}{3} \\ =\frac{1}{4}+\frac{14}{3} \\ =\frac{59}{12}\text{feet} \\ =4\frac{11}{12}\text{ f}eet \end{gathered}[/tex]

Hence the total height required = 59/12 feet or 4 11/12 feet approximately

Given:

13, 19, 25, 31, 37, ...

Required:

We need to find the expression to determine the nth term of the given pattern.

Explanation:

Consider the individual options.

1)

[tex]7+6n[/tex]

Substitute n=1 in the expression we get the first term.

[tex]7+6(1)=13[/tex]

Substitute n=2 in the expression we get the second term.

[tex]7+6(2)=7+12=19[/tex]

Substitute n=3 in the expression we get the third term.

[tex]7+6(3)=7+18=25[/tex]

Substitute n=4 in the expression we get the fourth term.

[tex]7+6(4)=7+24=31[/tex]

Substitute n=5 in the expression we get the fifth term.

[tex]7+6(5)=7+30=37[/tex]

All five terms of the given pattern satisfy the expression 7+6(n).

Hence the nth term of the given pattern is 7+6(n).

Final answer:

[tex]7+6(n)[/tex]

We have to calculate the increase in price and the price of the new model.

The next model will cost 6.2% more than the current model.

We can calculate the increase in price by multiplying the price of the current model by the increase proportion (0.062, which is the decimal expression for 6.2%):

[tex]I=\frac{6.2}{100}\cdot39000=0.062\cdot39000=2418[/tex]

With the increase, we can calculate the price of the next model as:

[tex]N=P+I=39000+2418=41418[/tex]

Answer:

Increase in price: $2,418

Price of next model: $41,418

SOLUTION:

We want to draw graphs showing the following:

A, All values to the right of z = 2.86

This is the plot, the area is marked in red;

The numerical value for this area is;

[tex]P\left(z>2.86\right)=0.0021182[/tex]

B. All values Not between -1.09 and 0.16 standard deviations from the mean.

The numerical value for this area which is the sum of the blue and red areas is;

[tex]P\left(z<-1.09\text{ }or\text{ }z>0.16\right)=0.5743[/tex]

Irrational numbers are all the real numbers which cannot be expressed as the ratio of two integers:

In this case, the elipsis (...) means that this number does not stop, so there is no repeating pattern of digits. Since the number does not stop and does not repeat, it is irrational.

ANSWER: 0.231124...

Explanation:

We have to divide the length of the ribbon by 6:

[tex]\frac{3}{6}=\frac{1}{2}[/tex]

Answer:

Each ribbon has a length of 1/2yd (option A)

In order to predict the number of cats at that shelter with 30 dogs, we can use the given equation

c = 2.1d - 26

and make d = 30:

c = 2.1 * 30 - 26

Now, we need to develop the calculations to find c (we first solve the multiplication, and then the subtraction):

c = 2.1 * 30 - 26

= 63 - 26

= 37

Therefore, the predicted number of cats at that shelter is 37.

Since these are parallel lines, the angles formed are congruent ( equal).

So, Angle B=A =60°

Correct option: A-60 °

Answer:

The length of the line segment is;

[tex]7.62\text{ units}[/tex]

Explanation:

Given the line segment in the attached image.

Drawing a right angled triangle to get the length of the line segment;

We can then use pythagoras theorem to calculate length of the line segment;

[tex]c=\sqrt[]{a^2+b^2}[/tex]

From the attached image;

[tex]\begin{gathered} a=3 \\ b=7 \end{gathered}[/tex]

substituting the given values;

[tex]\begin{gathered} c=\sqrt[]{3^2+7^2} \\ c=\sqrt[]{9+49} \\ c=\sqrt[]{58} \\ c=7.62\text{ units} \end{gathered}[/tex]

Therefore, the length of the line segment is;

[tex]7.62\text{ units}[/tex]

1)

The expression to factor,

[tex]x^4-81[/tex]

We can use the formula shown below to simplify the expression.

Addition Distributive Law

[tex]a^2-b^2=(a+b)(a-b)[/tex]

In order to use this law to simplify, let's re-arrange our expression given,

[tex]\begin{gathered} x^4-81 \\ \text{This can be written as:} \\ (x^2)^2-(9)^2 \end{gathered}[/tex]

This form of the expression is perfect to use the addition distributive law upon.

Using the rule, we can write the expression as,

[tex]\begin{gathered} (x^2)^2-(9)^2 \\ =(x^2+9)(x^2-9) \end{gathered}[/tex]

This is not the fully factored form. Because we can use the same rule to further simplify the term (x^2 - 9).

Let's write it in the form:

[tex]\begin{gathered} (x^2-9) \\ \text{This can be written as:} \\ (x)^2-(3)^2 \end{gathered}[/tex]

The image below clarifies this,

So, this can be written as:

[tex]\begin{gathered} x^4-81 \\ =(x^2)^2-(9)^2 \\ =(x^2+9)(x^2-9) \\ =(x^2+9)((x)^2-(3)^2) \\ =(x^2+9)(x+3)(x-3) \end{gathered}[/tex]

This is the fully factored form.

ANSWER:

28 feet

STEP-BY-STEP EXPLANATION:

We can determine the actual size of the house, since we know the ratio between centimeters and feet, just like this:

[tex]12\text{ cm}\cdot\frac{7\text{ ft}}{3\text{ cm}}=28\text{ ft}[/tex]

The house is 28 feet in real life.

Step 1

Given;

[tex]2\text{ cups of cranberry juice - 3 gallons of punch}[/tex]

Required; To find the amount of cranberry juice required for 1 gallon of punch juice.

Step 2

So basically, you can set this up in proportion.

For every gallon of punch, 2 cups of cranberry juice is needed. What you need to find is the amount of cranberry juice is needed for one gallon. So then you would have to set up your proportion like this:

[tex]\begin{gathered} \frac{2\text{ cups of cranberry juice}}{\text{3 gallons of punch}}=\frac{x\text{ cups of cranberry juice}}{1\text{ gallon of punch}} \\ or \\ \frac{2}{3}=\frac{x}{1} \end{gathered}[/tex]

We will now find the value of x by cross multiplying

[tex]\begin{gathered} 2\times1=3\times x \\ 2=3x \\ \frac{3x}{3}=\frac{2}{3} \\ x=\frac{2}{3} \end{gathered}[/tex]

So you will need 2/3 cups of cranberry juice for 1 gallon of punch

Answer;

[tex]\frac{2}{3}\text{ cups of cranberry juice}[/tex]

Step 3

2) The elevator rises 480ft in 30 seconds

One minute=60 seconds.

Therefore, we will have;

[tex]\begin{gathered} \frac{480ft}{\text{xft}}=\frac{30\sec onds}{1\text{ minute}} \\ 1\text{ minute=60 seconds} \\ \frac{480ft}{\text{xft}}=\frac{30\sec onds}{60\text{ seconds}} \\ or \\ \frac{480}{x}=\frac{30}{60} \\ \frac{480}{x}=\frac{1}{2} \\ \end{gathered}[/tex][tex]\begin{gathered} x=480\times2 \\ x=960ft\text{ per second} \end{gathered}[/tex]

First, we have to find the derivative

[tex]\begin{gathered} h^(\theta)=3cos(\frac{\theta}{2}) \\ \\ h^{\prime}(\theta)=3\frac{d}{d\theta}(cos(\frac{\theta}{2})) \\ h^{\prime}(\theta)=3\text{ \lparen - }\sin(\frac{\theta}{2})\frac{d}{d\theta}(\frac{\theta}{2})) \\ \\ h^{\prime}(\theta)=3(\text{ -}sin(\frac{\theta}{2})(\frac{1}{2}) \\ \\ h^{\prime}(\theta)=\text{ -}\frac{3}{2}sin(\frac{\theta}{2}) \end{gathered}[/tex][tex]\begin{gathered} \text{ - }\frac{3}{2}sin(\frac{\theta}{2})=0 \\ sin(\frac{\theta}{2})=0 \\ \sin^{-1}(0( \\ sin0º=0 \\ andsin180º=0 \\ \\ \\ \end{gathered}[/tex]

now he solve for h(theta)

[tex]\begin{gathered} h(\theta)=3cos(\frac{\theta}{2}) \\ \\ h(\text{ -}2\pi)=3cos(\text{ -}\frac{2\pi}{2})=3cos(\text{ -}\pi)=3(\text{ -1\rparen= -3} \\ h(0)=3cos(\frac{0}{2})=3cos0=3(1)=3 \end{gathered}[/tex]

Answer:

∠CGE is a right angle and has a measure of 90.

∠BGD is an obtuse angle and has a measure of 93.

∠CGB is an acute angle and has a measure of 50.

Acute angles are angles that measure less than 90.

Right angles are angles that measure exactly 90.

Obtuse angles are angles that measure greater than 90.

∠CGE

As we can see, ray C is at 70, while ray E is at 160.

160 - 70 = 90, since it measures 90, it is a right angle.

∠BGD

Ray B is at 20 while Ray D is at 113

113 - 20 = 93, since it measures greater than 90, it is an obtuse angle.

∠CGB

Ray C is at 70, Ray B is at 20

70 - 20 = 50, since it measures less than 90, it is an acute angle.

Since $51 was 3/5 of her money, then if we multiply 3/5 by the amount of money she had, x, we should obtain 51.

[tex]\frac{3}{5}x=51[/tex]

We can then solve the above equation for x.

[tex]\begin{gathered} 3\cdot x=51\cdot5 \\ 3\cdot x=255 \\ x=\frac{255}{3} \\ x=85 \end{gathered}[/tex]

She had $85.

We have the expression:

[tex]f(t)=13000\cdot(1.024)^t[/tex]

We can find how much the annual tuition increases each year by calculating:

[tex]\begin{gathered} \Delta=\frac{f(t+1)-f(t)}{f(t)}=\frac{f(t+1)}{f(t)}-1=\frac{13000\cdot(1.024)^{t+1}}{13000\cdot(1.024)^t}-1 \\ \Delta=1.024^{\mleft\{t+1-t\mright\}}-1=1.024-1=0.024\cdot100\%=2.4\% \end{gathered}[/tex]

Answer: b. 2.4%

Solution

Since we already given

[tex]\begin{gathered} m=0 \\ b=-6 \end{gathered}[/tex]

Note: The equation for a line in slope-intercept is given as

[tex]y=mx+b[/tex]

Putting m and b

[tex]\begin{gathered} y=mx+b \\ y=0(x)-6 \\ y=-6 \end{gathered}[/tex]

Therefore,

[tex]y=-6[/tex]

In this problem we have a linear equatiion of the form

f(x)=mx+b

where

m=2 -----> slope or unit rate

b=3 -----> initial value or y-intercept

substitute

f(x)=2x+3

therefore

The answer is

Option C

Answer:

x-intercept=-1/3

y-intercept=-4

Step-by-step explanation:

Find the x-intercept by setting y to zero:

-12x+0=4

-12x=4

x= 4/(-12)

x= -1/3

Find the y-intercept by setting x to 0

-12(0) + y=-4

y=-4

Draw a line through the intercepts

Given:

[tex]f(x)=2x^3[/tex]

To write:

The function when f(x) is stretched vertically by a factor of 5 and shifted 3 units left.

Explanation:

In general, a vertical stretch by a factor b and shift a units left is given by the equation

[tex]y=bf\left(x+a\right)[/tex]

So, the new function becomes,

[tex]\begin{gathered} y=5f(x+3) \\ y=g(x)=5\times2(x+3)^3 \\ g(x)=10(x+3)^3 \end{gathered}[/tex]

Final answer:

The new function is,

[tex]g(x)=10(x+3)^{3}[/tex]

The amount earned painting 24 rooms is 243.5 dollars.

How to find the amount he earns painting?

Sam has a summer job at a new office building. Sam can paint 34 of a room in 23 of an hour. He gets paid $15 per hour.

The amount of money he will earn painting 24 rooms can be calculated as follows:

Therefore,

34 rooms = 23 hours

24 rooms = ?

cross multiply

number of hours he will paint = 23 × 24 / 34

number of hours he will paint = 552 / 34

number of hours he will paint = 16.2352941176

He earns 15 dollars per hour.

Therefore,

amount earn painting 24 rooms = 16.2352941176 × 15

amount earned painting 24 rooms = 243.529411765

Therefore,

amount earned painting 24 rooms = 243.5 dollars

learn more on earnings here:https://brainly.com/question/13821000

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The length of the room is

[tex]=k+5[/tex]

The width of the room is

[tex]=k[/tex]

The image below illustrates the question

The side of the room should have a 1-meter border, this means that on both sides of the room,the length and breadth of the room will be reduced by 2 meter

Hence,

The length of the carpet will be

[tex]\begin{gathered} =\text{length of the room - 2} \\ =k+5-2 \\ =k+3 \end{gathered}[/tex]

The width of the carpet will be

[tex]\begin{gathered} =\text{width of the room}-2 \\ =k-2 \end{gathered}[/tex]

The area of the uncovered part will be

[tex]=\text{area of the room - area of the carpet}[/tex]

The area of the room is

[tex]\begin{gathered} =\text{length of room}\times\text{width of room} \\ =k(k+5) \end{gathered}[/tex]

The area of the carpet will be

[tex]\begin{gathered} =\text{length of carpet}\times width\text{ of carper} \\ =(k+3)(k-2) \end{gathered}[/tex]

Hence,

the area of the uncovered part will be

[tex]=k(k+5)-(k+3)(k-2)[/tex]

Therefore,

k+3 represents the length of the carpet

The final answer is OPTION B

Complementary angles add up to 90°.

So:

Za+Zb=90°

Replacing with the value of Za = 37°

37°+Zb =90°

Solving for Zb:

Zb = 90°-37°

Zb= 53°

Ok, so

Here we have an inequality, so, we're going to solve it.

-5x<2. If we solve this inequality, we obtain x > (-2/5).

(Remember that sign change because of division by a negative number).

So, the interval of solution will be (-2/5, infinity).

Then, two values that make -5x<2 true would be:

- 1 and 2. for example.

And, two values that make -5x<2 false would be:

- -3 and -4, for example.