One book has 84 pages. Another book has 210 pages. Which is the greatest common factor of the number of pages in the two books? CLEAR SUBMIT 14 21 42 84

Answer:

Step-by-step explanation:

x=3(y-b)

or x=3y-3b

3y=x+3b

[tex]y=\frac{x+3b}{3}[/tex]

There are a total of 8 letters in student, with 6 different letters ( there are 2 s's and 2 t's).

First find the number of arrangements that can be made using 8 letters.

This is 8! which is:

8 x 7 x 6 x 5 x 4 3 x 2 x 1 = 40,320

Now there are 2 s's and 2 t's find the number of arrangements of those:

S = 2! = 2 x 1 = 2

T = 2! = 2 x 1 = 2

Now divide the total combinations by the product of the s and t's:

40,320 / (2*2)

= 40320 / 4

= 10,080

The answer is A. 10,080

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$906.25\\ P=\textit{original amount deposited}\\ r=rate\to 6.25\%\to \frac{6.25}{100}\dotfill &0.0625\\ t=years\dotfill &1 \end{cases} \\\\\\ 906.25=P(0.0625)(1)\implies 906.25=0.0625P\implies \cfrac{906.25}{0.0625}=P \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 14500=P~\hfill[/tex]

Answer:

The answer to your question is: I agree with you, the first option

Step-by-step explanation:

• (0,1) U (1,infinity)  This is the right answer because there are 2 invervals in which the graph decreases, and these intervals are listed in this option.

•(-infinity,-1)U(-1,0)  This option is wrong because from (-∞ , -1) the graph grows up and also from (-1, 0).

•(-infinity,-1)  The graph grows up, this option is incorrect

. (1,infinity) The graph decreases but the option is incomplete.

The correct option is A which is the function decreasing over the interval (0,1) U(1, infinity).

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

Check all the options:-

Therefore, the correct option is A which is the function decreasing over the interval (0,1) U(1, infinity).

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Answer:

9.271 inches.

Step-by-step explanation:

Let AC be the length of original line segment and point B divides it into two segments such that AB is longer and BC is smaller segment.

[tex]AB+BC=AC=15[/tex]

We can describe the golden ratio as:  

[tex]\frac{AB}{BC}=\frac{AC}{AB}=1.618[/tex]

[tex]\frac{AC}{AB}=1.618[/tex]

[tex]\frac{15}{AB}=1.618[/tex]

[tex]\frac{15}{1.618}=AB[/tex]

[tex]9.270704=AB[/tex]

[tex]AB=9.271[/tex]

We can verify our answer as:

[tex]AB+BC=15[/tex]

[tex]9.271+BC=15[/tex]

[tex]9.271-9.271+BC=15-9.271[/tex]

[tex]BC=5.729[/tex]

[tex]\frac{AB}{BC}=1.618[/tex]

[tex]\frac{9.271}{5.729}=1.618[/tex]

[tex]1.618=1.618[/tex]

Hence proved.

Therefore, the length of the longer side would be 9.271 inches.

Answer:

  $1,220,200

Step-by-step explanation:

The total of Mary's payments is ...

  $3695.20/mo × 30 yr × 12 mo/yr = $1,330,200

The difference between this repayment amount and the value of her loan is the interest she pays:

  $1,330,200 -110,000 = $1,220,200 . . . total interest paid

_____

Mary's effective interest rate is about 40.31% per year--exorbitant by any standard.

Answer:

13,18meters

Step-by-step explanation:

If the temple is in a height of 24 meters and to get there there are 91 steps, each step is 24 m / 91 = 26,37cm

The 50th step then is 26, 37cm. 50=13.18meters

Answer:

Probability 50%

Odds 5:5

Step-by-step explanation:

Probability is calculated as favorable cases divided by total cases.

While odds are calculated as favorable cases divided by (total cases - favorable cases)

Favorable cases (green) : 5

Total cases(green, red and blue): 10

Probability= 5/10 * 100%=50%

Odds = 5:(10-5) = 5:5

Answer:

it is 50%

Step-by-step explanation:

Answer:

   12.94%

Step-by-step explanation:

r = 100(1/2)^(d/5) = 100((1/2)^(1/5))^d ≈ 100(.87055)^d

The daily decrease is 1 - 0.87055 = 0.12944 ≈ 12.94%

American Airlines used cluster sampling by selecting entire flights (clusters) and surveying every passenger on those flights.

To determine customer opinion of their check-in service, American Airlines employs a specific type of sampling method by randomly selecting 70 flights during a certain week and surveying all passengers on those flights. This is an example of cluster sampling, which is one of the probability sampling techniques.

In cluster sampling, the population is divided into clusters (e.g., flights in this case) and then entire clusters are randomly selected. All individuals within the chosen clusters are included in the sample. The key element here is that entire clusters are selected, and every member of those clusters is surveyed.

Answer: Just add then you have to multiply the main number i cant give you the anwser but i can help you∈∈∈

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

Step-by-step explanation:

We notice that the multiplier of the squared term in f(x) is 0.5; in g(x), it is -2, so is a factor of -4 times that in f(x).

If we scale f(x) by a factor of -4, we get ...

  -4f(x) = -2(x -2)² -12

In order for the squared quantity to be x+3, we have to add 5 to the value that is squared in f(x). That is, x -2 must become x +3. We have to replace x with (x+5) to do that, so ...

  (x+5) -2 = x +3

The replacement of x with x+5 amounts to a translation of 5 units to the left.

We note that the added constant after our scaling changes from +3 to -12. Instead, we want it to be -1, so we must add 11 to the scaled function. That translates it upward by 11 units.

The attached graph shows the scaled and translated function g(x):

  g(x) = -4f(x +5) +11

Answer:

.

Step-by-step explanation:

The maximum volume of such a box is determined by forming an equation that represents the condition about the width of the box and the perimeter of one of its nonsquare sides, then finding the maximum value of the volume function obtained by differentiating the function and setting it equal to zero.

The subject of this question is mathematics related to box dimensions, more specifically the geometry dealing with volume of a box. The box in question has a square base, which means the length and width are the same, let's call this x. Because the box is wider than it is tall, we know it's height, let's call it h, is less than x.

According to the question, the width of the box and the perimeter of one of the nonsquare sides of the box sum to no more than 117 inches. The perimeter of a nonsquare side (a rectangle) is given by 2(x+h), and if we add x (the width of the box) to this, we get x + 2(x+h) which must be less than or equal to 117. Simplifying gives 3x + 2h <= 117

We are interested in the volume of the box which can be determined by multiplying the length, width, and height (V = x*x*h). This can be simplified to V = x^2 * h. To get the maximum volume, we should make h as large as possible. Substituting 3x into the original inequality for h (since 3x <= 117), we get h <= 117 - 3x. Thus, the volume V becomes V = x^2 * (117 - 3x).

To find the maximum volume, we take the derivative of the volume function (V = x^2 * (117 - 3x)) with respect to x and set it equal to zero. This will give us the value of x for which the volume is maximum. Once we have the value of x, we substitute it back into the volume function to get the maximum volume.

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The maximum volume for such a box is 152,882.5 cubic inches

We have a box with a square base, where the width w is greater than the height h. The constraint given is that the width of the box plus the perimeter of one of the non-square sides cannot exceed 117 inches.

The perimeter of one of the non-square sides is 2h + 2d, where d is the depth. Therefore, the constraint equation becomes:

[tex]\[ w + 2h + 2d \leq 117 \][/tex]

Since the base is square, w = h. Let's denote this common value as s. So, the constraint equation simplifies to:

[tex]\[ 2s + 2d \leq 117 \][/tex]

Now, we need to express the volume of the box in terms of s and d:

[tex]\[ V = s^2d \][/tex]

We want to maximize V subject to the constraint [tex]\(2s + 2d \leq 117\).[/tex]

To proceed, let's solve the constraint equation for d:

[tex]\[ d \leq \frac{117 - 2s}{2} \][/tex]

Since d must be greater than zero, we have:

[tex]\[ 0 < d \leq \frac{117 - 2s}{2} \][/tex]

Now, we substitute [tex]\(d = \frac{117 - 2s}{2}\)[/tex] into the volume equation:

[tex]\[ V(s) = s^2 \left( \frac{117 - 2s}{2} \right) \]\[ V(s) = \frac{1}{2}s^2(117 - 2s) \][/tex]

To find the maximum volume, we'll take the derivative of V(s) with respect to s, set it equal to zero to find critical points, and then check for maximum points.

[tex]\[ V'(s) = \frac{1}{2}(234s - 6s^2) \]\\Setting \(V'(s)\) equal to zero:\[ \frac{1}{2}(234s - 6s^2) = 0 \]\[ 234s - 6s^2 = 0 \]\[ 6s(39 - s) = 0 \][/tex]

This gives us two critical points: s = 0 and s = 39. Since s represents the width of the box, we discard s = 0 as it doesn't make physical sense.

Now, we need to test s = 39 to see if it corresponds to a maximum or minimum. Since the second derivative is negative, s = 39 corresponds to a maximum.

So, the maximum volume occurs when s = 39 inches.

Substitute s = 39 into the constraint equation to find d:

[tex]\[ 2(39) + 2d = 117 \]\[ 78 + 2d = 117 \]\[ 2d = 117 - 78 \]\[ 2d = 39 \]\[ d = \frac{39}{2} \]\[ d = 19.5 \][/tex]

Therefore, the maximum volume of the box is achieved when the width and height are both 39 inches, and the depth is 19.5 inches. Let's calculate the maximum volume:

[tex]\[ V_{\text{max}} = (39)^2 \times 19.5 \]\[ V_{\text{max}} = 152,882.5 \, \text{cubic inches} \][/tex]

So, the maximum volume for such a box is 152,882.5 cubic inches.

Answer:

c. {(1, a), (0, a), (2, c), (3, b)}

Step-by-step explanation:

Answer:  0.1010052

Step-by-step explanation:

Given : Significance level : [tex]\alpha=0.01[/tex]

Alternative hypothesis : [tex]H_1:\ p\neq\dfrac{3}{4}[/tex]

The test statistic value : [tex]z=-1.64[/tex]

Since , the alternative hypothesis is two-tailed, so the test is a two-tailed test.

Using standard normal distribution table for z, we have

The P-value of two-tailed test will be :-

[tex]2P(z>|-1.64|)=2P(z>1.64)\\\\=2(1-P(z\leq1.64))\\\\=2(1-0.9494974)\\\\=0.1010052[/tex]

Hence, the P-value = 0.1010052

Answer:

Step-by-step explanation:

The distance formula is d=[tex]\sqrt{(x2-x1)^{2} +[tex]\sqrt{(0-0)^{2} + (12-3)^{2}}[/tex][tex]\sqrt{0 + (9)^{2}}[/tex]

[tex]\sqrt{(9)^{2}}[/tex]

[tex]\sqrt{(y2-y1)^{2} }[/tex]

[tex]\sqrt{81}[/tex] = 9

Answer:

The answer to your question is: height = 99.41 feet.

Step-by-step explanation:

Data

distance = 96 feet away from a building

angle = 46

height = ?

Process

Here, we have a right triangle, we know the angle and the adjacent leg, so let's use the tangent to find the height.

tan Ф = opposite leg / adjacent leg

opposite leg = height = adjacent leg x tan Ф

height = 96 x tan 46

height = 96 x 1.035

height = 99.41 feet.

The height of the building is approximately 77.55 feet.

To find the height of the building, we can use trigonometry, specifically the tangent function, which relates the angle of elevation to the opposite side (the height of the building) and the adjacent side (the distance from the point of observation to the base of the building).

Given:

- The distance from the point of observation to the base of the building is 96 feet.

- The angle of elevation to the top of the building is 46 degrees.

Using the tangent function:

[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]

[tex]\[ \tan(46^\circ) = \frac{h}{96} \][/tex]

To find the height [tex]\( h \)[/tex], we solve for[tex]\( h \)[/tex]:

[tex]\[ h = 96 \times \tan(46^\circ) \][/tex]

Using a calculator to find the tangent of 46 degrees and multiplying by 96, we get:

[tex]\[ h \approx 96 \times \tan(46^\circ) \approx 96 \times 0.9919 \approx 77.55 \text{ feet} \][/tex]

Answer:

Se below.

Step-by-step explanation:

The Chord Intersection Theorem:

If 2 chords of a circle are AB and CD and they intersect at E, then

AE * EB = CE * ED.

Problem.

Two Chords AB and CD intersect  at E.  If AE =  2cm , EB = 4 and CE = 2.5 cm, find the length of ED.

By the above theorem : 2 * 4 = 2.5 * ED

ED = (2 * 4) / 2.5

The measure of ∠XYZ is 35°.

Secants theorem states that the angle formed by the two secants which intersect inside the circle is half the sum of the intercepted arcs.

Here is the problem of chords that we would use the secants theorem

Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 110° degrees and arc W Z is 180° degrees. In the diagram of circle A, what is the measure of ∠XYZ?

We want to determine the angle ∠XYZ in the image attached.

To solve that, we will use the formula in the theorem for angles formed by secants or tangents. Thus;

According to Secants theorem,

∠XYZ = ½(arc WZ - arc XZ)

Given, arc WZ = 180° and arc XZ = 110°

Thus;

∠XYZ = ½(180 - 110)

∠XYZ = ½(70)

∠XYZ = 35°

Hence, the measure of ∠XYZ is 35°.

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Answer:

What is it asking?

Step-by-step explanation:

Answer: a) critical value = 0.0853, b) we reject the null hypothesis.

Step-by-step explanation:

Since we have given that

z = -1.37

And the hypothesis are given below:

[tex]H_0:p=\dfrac{1}{4}=0.25\\\\H_1:p\neq 0.25[/tex]

Since α = 0.01

since critical value = 0.0853

As we can see that 0.853 < 0.25.

so, we reject the null hypothesis.

Hence, a) critical value = 0.0853, b) we reject the null hypothesis.

Answer:

The answer to your question is EF = 12

Step-by-step explanation:

Data

DE = 6x

EF = 4x

DF = 30

Process

                DE    +    EF      = DF

               6x     +    4x       = 30

                           10x = 30

                            x = 30 / 10

                            x = 3

             6(3)    + 4 (3)     = 30

             18   +     12      = 30

                         30 = 30

DE = 6(3) = 18

EF = 4(3)  = 12

P = distance all around

P = 2x + 3(x)

15 = 2x + 3x

15 = 5x

15/5 = x

3 = x

The distance of one of the shorter sides is 3 inches.

The length of one of the shorter sides is 3 inches.

A trapezium is a quadrilateral with four sides where two sides are parallel to each other.

We have,

Trapezium has four sides and two parallel sides.

Now,

Let three sides be equal.

i.e x

The longer sides of the parallel sides.

= 2x

The shorter sides of the parallel sides.

= x

Now,

Perimeter of the trapezium = 15 inches

2x + x + x + x = 15

2x + 3x = 5x

5x = 15

x =3

Thus,

The length of the shorter side is 3 inches.

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The volume of a cylinder is changing at a rate of 256π cm³/min when the height of the cylinder is 12 cm, the radius is 4 cm, the circumference of the cylinder is increasing at a rate of π4 cm/min, and the height of the cylinder is increasing four times faster than the radius.

The primary equation you need for this problem is the volume of a cylinder, which is V = πr²h. Given the height h of the cylinder is increasing four times faster than the radius r, if we use dh/dt for the rate of change of the height and dr/dt for the rate of change of the radius, we have dh/dt = 4dr/dt.

Also, the rate at which the circumference of the cylinder is increasing is d(2πr)/dt=2πdr/dt = π4 cm/min. Hence we can set up an equation as 2πdr/dt = π4. Solving for dr/dt, we get dr/dt = 2 cm/min.

Substituting this into the previous equation, we find that dh/dt = 8 cm/min. Now, if we take the derivative of the volume equation with respect to time, we get dV/dt = πr²dh/dt + 2πrh*dr/dt.

With the values r = 4cm, h = 12cm, dr/dt = 2 cm/min, and dh/dt = 8 cm/min, replacing in the equation above gives us: dV/dt = π*4²*8 + 2π*4*12*2 = 256π cm³/min. So, the volume of the cylinder is changing at a rate of 256π cm³/min.

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Answer:

Step-by-step explanation:

The cost of the area of the deck is fixed, because the area is fixed. It will be ...

  ($12/ft²)×(100 ft²) = $1200

__

The cost of the railing is proportional to its length, so it will be minimized by minimizing the length of the railing. If the length of it is x feet parallel to the house, then the length of it perpendicular to the house (for a deck area of 100 ft²) is 100/x.

The total length of the railing is ...

  r = 2(100/x) + x

We can minimize this by setting its derivative with respect to x equal to zero:

  dr/dx = -200/x² +1 = 0

Multiplying by x² and adding 200, we get ...

  x² = 200

  x = √200 ≈ 14.142

So, the minimum railing cost will be had when the deck is 14.142 ft by 7.071 ft. That railing cost is about ...

  $9 × (200/√200 +√200) ≈ $254.56

__

We might imagine that dimensions near these values would have almost the same cost. Here are some other possibilities:

__

Then the total cost for a couple of possible deck sizes will be $1200 plus the railing cost, or ...

_____

Note on the solution process

It can be helpful to use a spreadsheet or graphing calculator to do the repetitive computation involved in finding suitable dimensions for the deck.

Answer:

$7,000 at a rate of 7% and $21,000 at a rate of 14%.

Step-by-step explanation:

Let x be amount invested at 7% and y be amount invested at 14%.

We have been given that a women's professional organization made two small-business loans totaling $28,000. We can represent this information in an equation as:

[tex]x+y=28,000...(1)[/tex]

The interest earned at 7% in one year would be [tex]0.07x[/tex] and interest earned at 14% in one year would be [tex]0.14x[/tex].

We are also told that the organization received from these loans was $3,430. We can represent this information in an equation as:

[tex]0.07x+0.14y=3,430...(2)[/tex]

Form equation (1), we will get:

[tex]x=28,000-y[/tex]

Upon substituting this value in equation (2), we will get:

[tex]0.07(28,000-y)+0.14y=3,430[/tex]

[tex]1960-0.07y+0.14y=3,430[/tex]

[tex]1960+0.07y=3,430[/tex]

[tex]1960-1960+0.07y=3,430-1960[/tex]

[tex]0.07y=1470[/tex]

[tex]\frac{0.07y}{0.07}=\frac{1470}{0.07}[/tex]

[tex]y=21,000[/tex]

Therefore, an amount of $21,000 was invested at a rate of 14%.

[tex]x=28,000-y[/tex]

[tex]x=28,000-21,000[/tex]

[tex]x=7,000[/tex]

Therefore, an amount of $7,000 was invested at a rate of 14%.

Answer:

(a) 120 choices

(b) 110 choices

Step-by-step explanation:

The number of ways in which we can select k element from a group n elements is given by:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

So, the number of ways in which a student can select the 7 questions from the 10 questions is calculated as:

[tex]10C7=\frac{10!}{7!(10-7)!}=120[/tex]

Then each student have 120 possible choices.

On the other hand, if a student must answer at least 3 of the first 5 questions, we have the following cases:

1. A student select 3 questions from the first 5 questions and 4 questions from the last 5 questions. It means that the number of choices is given by:

[tex](5C3)(5C4)=\frac{5!}{3!(5-3)!}*\frac{5!}{4!(5-4)!}=50[/tex]

2. A student select 4 questions from the first 5 questions and 3 questions from the last 5 questions. It means that the number of choices is given by:

[tex](5C4)(5C3)=\frac{5!}{4!(5-4)!}*\frac{5!}{3!(5-3)!}=50[/tex]

3. A student select 5 questions from the first 5 questions and 2 questions from the last 5 questions. It means that the number of choices is given by:

[tex](5C5)(5C2)=\frac{5!}{5!(5-5)!}*\frac{5!}{2!(5-2)!}=10[/tex]

So, if a student must answer at least 3 of the first 5 questions, he/she have 110 choices. It is calculated as:

50 + 50 + 10 = 110

Answer:

Given the equation 8 + 3y = 2·(x+5)

slope=2/3

y- intercept= (0, 2/3) or y= 2/3.

x-intercept=  (-1, 0) or x = -1.

Step-by-step explanation:

Given 8 + 3y = 2·(x+5) ⇒ 8 + 3y = 2x + 10 ⇒ 3y = 2x + 10 -8 ⇒ 3y = 2x + 2

⇒ y = (2/3)x + 2/3.

Here slope = 2/3 and y-intercept = 2/3.

To find x-intercept, we have to calculate the value of "x" when y =0.

⇒ 0 = (2/3)x + 2/3 ⇒ 0 - 2/3 = (2/3)x ⇒ -2/3 = (2/3)x ⇒ (-2/3)/(2/3)= x

⇒ x =-1.

Answer:here's ur answer

Step-by-step explanation: