What is the midpoint M of that line segment?

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

Answer:

[tex]v(x)=32+8(x-1)[/tex]

Step-by-step explanation:

We have been given that the number of visitors to a park is expected to follow the function [tex]v(x)=8(x-1)[/tex], where x is the number of days since opening. On the first day, there will be a ceremony with 32 people in attendance.

The total number of visitors including the ceremony would be number of people on ceremony plus people at x number of days since opening that is:

[tex]v(x)=32+8(x-1)[/tex]

Therefore, the function [tex]v(x)=32+8(x-1)[/tex] total visitors, including the ceremony.

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:

(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:

4

Step-by-step explanation:

Recall that for a function f(x) and for a constant k

f(x+k) represents a horizontal translation for the function f(x) by k units in the negative-x direction.

Hence f(x+k) is simply the graph of f(x) that has been moved left (negative x direction) by k units.

From the graph, we can see that g(x) = f(x+k) is simply the graph of f(x) that has been moved 4 units in the negative x-direction.

hence K is simply 4 units.

Answer:

Step-by-step explanation:

Yes I'd have to agree with @previousbrainliestperson

I'd go with solid 4

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:

What is it asking?

Step-by-step explanation:

Answer:

.

Step-by-step explanation:

Answer:

Option c. $284.85

Step-by-step explanation:

we know that

The amount of money Diego now has is equal to the amount of money he originally had plus deposits minus withdrawals.

so

[tex]272.79+(26.32+91.03+17.64)-(31.08+29.66+62.19)\\272.79+134.99-122.93\\\$284.85[/tex]

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:

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:

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:

$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%.

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:

A. Kelley uses 2 parts blue for every 3 parts yellow.

Step-by-step explanation:

Given equation that shows the amount of blue food coloring,

[tex]b=\frac{2}{3}y[/tex]

Where,

y = amount of yellow food coloring,

If y = 2,

[tex]b=\frac{2}{3}\times 2=\frac{4}{3}[/tex]

i.e. [tex]\frac{4}{3}[/tex] parts of blue for every 2 parts yellow.

If y = 3,

[tex]b=\frac{2}{3}\times 3=2[/tex]

i.e. 2 parts of blue for every 3 parts yellow.

If y = 5,

[tex]b=\frac{2}{3}\times 5=\frac{10}{3}[/tex]

i.e. [tex]\frac{10}{3}[/tex] parts of blue for every 5 parts yellow.

Hence, OPTION A is correct.

Answer:

3.5 seconds

Step-by-step explanation:

h(t) is a quadratic function, it indicate that the object start with initial height (56).

If you want to know when the object hit the ground (h=0) you have to use the quadratic formula [tex](-b +- \sqrt{b^{2}-4ac } )/2a[/tex] and take the positive root (the negative shows a negative time, so we have to discard it).

In this case: a=-6, b=5 and c=56, then the solve is 7/2=3.5

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:

128 posibilities

Step-by-step explanation:

We have 7 colleges (A,B,C,...,H) which form a set with seven elements.

What you are asking is the number of elements (or cardinality) of the set that contains all possible sets formed by those 7 elements (or the "power set").

It is known that if n is the number of elements of a given set X, then the cardinality of the power set is [tex]2^n[/tex].

Therefore, there are [tex]2^7[/tex] or 128 possibilities (or elements) for the set of colleges that he applies to.

Final answer:

The number of possible combinations of colleges that Jose can apply to from 7 options is 128. This includes the possibility of not applying to any college as well.

Explanation:

The question asks how many different combinations of colleges Jose may apply to given 7 different options.

This is a problem related to the field of combinatorics in mathematics, specifically the concept of the power set, where each college can either be chosen or not, resulting in 2⁷ possible combinations.

Since he can like none, some, or all colleges, we include the possibility of an empty set, leading to a total of 2⁷ = 128 possibilities.

In each case, Jose has two options for every college - to apply (like) or not to apply (dislike).

Therefore, the number of combinations is calculated by raising 2 (the number of options for each item) to the power of 7 (the number of items).

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

Answer:

8

Step-by-step explanation:

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:

The given statement is true.

Step-by-step explanation:

Yes this is true.

GAAP is a collection of certain standard accounting rules for financial reporting.

Few general principles of GAAP guidelines are :

1. Principle of Regularity.

2.  Principle of Sincerity.

3. Principle of Consistency.

4. Principle of Non-Compensation.

5. Principle of Continuity.

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%

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:

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:

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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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:

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:D

THE POPULATION OF SPECIES A IS DECREASING. AND IT HAD THE SMALLER INITIAL POPULATION

The statement that correctly compares the given functions is - 'The population of species A is decreasing, and it had the smaller initial population.'

The correct answer is an option (D)

"A function of the form [tex]f(x)=b^x[/tex] where b is constant."

" [tex]f(x) = a (1 + r)^x[/tex]

where a is the initial value

r is the growth rate

x is time"

For given question,

We have been given a exponential function [tex]f(x) = 1400(0.70)^x[/tex]

This function represents the population of species A, x years from today.

The population of species B is modeled by function g, which has an initial value of 1,600 and increases by 20% per year.

a = 1600

r = 20%

 = 0.2  

Using the exponential growth formula the exponential function that represents the population of species B would be,

[tex]g(x) = 1600 (1 + 0.2)^x\\\\g(x)=1600(1.02)^x[/tex]

We know that, if the factor b ([tex]f(x)=a\bold{b}^x[/tex]) is greater than 1 then the exponential function represents the growth and if b < 1 then the exponential function represents the decay of population.

From functions f(x) and g(x) we can observe that, the population of species A is decreasing, and it had the smaller initial population.

So, the correct answer is an option (D)

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