Digital genius manufactures a cell phone charging pad that can fully charge any cell phone that is placed on it in 15 minutes. the analytics department determined that at a price of $103.00 each, the demand would be 6 thousand pads, and at $53.00 each, the demand would be 16 thousand pads. based on the assumption that a linear relationship exists between price and demand, the price-demand equation is given by where x is the number of thousands of pads in demand. at what price point should they sell the pads to have a demand of 14 thousand pads?

Answer:[tex]x = 18[/tex]

* also think you meant x instead of c*

Step-by-step explanation:

[tex]\frac{x}{6} - 7 = -4[/tex] --> +7 on both sides

[tex]\frac{x}{6} - 7 + 7 = -4 + 7[/tex]

[tex]\frac{x}{6} = 3[/tex] --> multiple by 6 by both sides

[tex]6 * \frac{x}{6} = 3 * 6[/tex] --> the 6 and the [tex]\frac{x}{6}[/tex] cancel out

[tex]x = 18[/tex]

The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.

What is algebraic equation ?

An algebraic equation is a mathematical expression containing one or more variables and an equal sign, where the goal is to find the value(s) of the variable(s) that make the equation true. The equation is formed by combining numbers, variables.

PART A:

Let x be the number of hours of cleaning that Premier Housekeeping provides, and let y be the number of hours of cleaning that Best House Care provides. The system of equations representing the housekeeping services is:

Premier Housekeeping: 25 + 65x = cost in dollars

Best House Care: 75y = cost in dollars

PART B:

The solution of this system of equations represents the point (x,y) in the coordinate plane, where x represents the number of hours of cleaning that Premier Housekeeping provides and y represents the number of hours of cleaning that Best House Care provides. The cost in dollars of each service will be given by the corresponding equation: the cost of Premier Housekeeping will be 25 + 65x, while the cost of Best House Care will be 75y.

The solution represents the number of hours of cleaning and cost of two housekeeping services, Premier and Best House Care.

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Answer: Midpoint

Step-by-step explanation:

maybe try not

Step-by-step explanation:

Answer:

it would be 6 miles a day

Step-by-step explanation:

do to 41.2 miles in 1 week and a 4 mile start plus six more days it would be 6x6=36+4=40

These identities are not true and cannot be derived from the first identity.

What is trignomentry ?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of angles and circles, and to solve problems involving geometric shapes and measurements. Trigonometry is used in many fields such as physics, engineering, and navigation.

The statement "sin 0 + cos 0 = 1" is a correct foundational trigonometric identity. However, it is not possible to derive the identities "1+cot^2(0) = csc^2(0)" or "tan^2(0)+1 = sec^2(0)" by dividing through by cot^2(0) or by tan^2(0) respectively. These identities are not true, and are not a direct consequence of the first identity.

These identities are not true and cannot be derived from the first identity.

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All of the rectangles together measure 1250 meters in length.

A textile square with a 25 square meter surface area. We are aware that the area of a square is determined by multiplying one side's length by itself. The square root of 25 square meters, or 5 meters, is the length of one side of the square in this instance.

Secondly, we are aware that the fabric is being cut into 50 cm-wide rectangles. We can use the following formula to determine each rectangle's length:

(Rectangle width) x (Square cloth length) / (Width of square cloth)

The equation in this instance is (50 cm) x (25 m) / (5 m) = 2500 cm or 25 meters.

Therefore, each rectangle is 25 meters long.

We divide the square cloth's length by each rectangle's width to get the total number of rectangles.

25m / 0.5m (50cm) = 50 rectangles.

Finally, we multiply the quantity of rectangles by the average length of each rectangle to determine the total length of all the rectangles:

50 m x 25 m = 1250 m

Therefore, a square piece of fabric that is 25 square meters in size and has been divided into 50 rectangles, each measuring 50 cm wide and 25 meters long.

Therefore the rectangles together measure 1250 meters in length.

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The amounts of each type that should be produced to maximize profit is given as follows:

Hence the maximum profit is of:

birr 710.

A system of inequalities is used to model the situation, for which the variables are given as follows:

The number of products is a countable amount, meaning that it cannot assume negative values, hence the first two constraints are given as follows:

For table A, the constraint is of at most 108 hours, hence:

6x + 4y ≤ 108.

For table B, the constraint is of at most 24 hours, hence:

x + y ≤ 24.

Hence the four constraints are combined to form a system of inequalities, which is solved graphically.

The profit function is given as follows:

P(x,y) = 40x + 30y.

As products of type A contribute more to profit, we must find the vertex on the solution which has the highest value of x, which is of:

(17,1).

Meaning that 17 items of type A are made and one item of type B, and the profit is given as follows:

P(17,1) = 40 x 17 + 30 = birr 710.

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1. The  triangles, which are similar to ΔAED  are ΔAFE, ΔEFD, ΔECD, ΔABE

2.  The length of segment FA is, 32/3 units

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

A rectangle ABCD having triangles in it,

1.  ΔAED is a right angle triangle,

all the triangle which are right angle triangle will be similar to  ΔAED

So,  ΔAFE, ΔEFD, ΔECD, ΔABE are similar triangles

2. Now, consider ΔEFD

EF = 8 unit

ED = 10 unit

∠CEB = 53°

∠CEF = 90°

∠DEF = 37°

∠AED = 90°

∠AEF = 53°

tan53° = FA/FE

4/3 = FA/8

FA = 32/3

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Answer: n = -16

Step-by-step explanation:

1) Distribute

—2(3n +6) = 3(-n + 12)

—6n - 12 =3(-n + 12)

2) Distribute

—6n - 12 = 3(-n + 12)

—6n — 12 = —3n +36

3) Add 12 to both sides

—6n — 12 = -3n +36

-6n = 12+ 12 = - 3n + 36 + 12

4) Simplify

----Add the numbers

—6n = -3n +48

5) Add 3n to both sides

—6n = -3n +48

—6n + 3n = —3n + 48 + 3n

6) Simplify

- Combine like terms

—3n = 48

7) Divide both sides by the same factor

—3n = 48

-3n ÷ -3 = 48 ÷ -3

8) Simplify

- Cancel terms that are in both the numerator and denominator

- Divide the numbers

n = —16

Please give brainliest

The 205th term of the given geometric sequence is given by 6

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Given here: The first term of a given geometric sequence as 6 and second term -6.

Thus clearly we can deduce that the common ratio of the sequence is given by -1

Therefore the geometric sequence has two elements that are alternating sequence of the form 6,-6,6,-6,6.........

Therefore the 205th term of the sequence will be given by

T₂₀₅=6×-1²⁰⁵⁻¹

       =6×1

        =6

Hence, The 205th term of the given geometric sequence is given by 6

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Answer:

DB = 15

Step-by-step explanation:

∠ C and ∠ D are the base angles of Δ BCD

since they are congruent , that is ∠ D = ∠ C

Then the triangle is isosceles with the legs being congruent, so

DB = BC = 15

Answer:

5 4/9

Step-by-step explanation:

7/9 of 7

= 7/9 × 7

= 7/9 × 7/1

Multiply top×top and bottom×bottom

= 49/9

means 49÷9

9 goes into 49, 5 times. And 9 × 5 is 45. 49 - 45 is 4. So

49÷9 is 5 and 4 leftover.

49 ÷ 9

= 5 4/9

Monetary conversion is essentially the price measure of one currency against another.

A conversion rate is the ratio between two currencies, most commonly used in foreign exchange markets, which designates how much of one currency is needed to exchange for the equivalent value of another currency. Conversion rates fluctuate regularly for all currencies traded in forex markets.

Given here: monetary conversion

Customers exchange their native currency for the currency of the country they are visiting. On the other hand, currency conversions are the process of converting prices to match the customer's native currency.

For example: Suppose you have 40 cents, how many cents would you need to make one dollar!

You can understand this through the following conversion. Since, $1 = 100¢, therefore, we subtract 40 cents from 100 cents. That is 100 cents – 40 cents = 60 cents. Since you already have 40¢, you would need 60¢ more to make it a dollar. This is how we can express 60 cents with different coins.

Hence, Monetary conversion is essentially the price measure of one currency against another.

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Answer:

Impossible: Pigs can fly. It will rain in the Sahara Desert for a week.

Probability is the likelihood that an event will happen.

Unlikely: It will snow today. Dying in a shark attack.

Likely: If you are underwater for more than 2 minutes, you drown. A cat chases a mouse.

Certain: The year is 2023.

On solving the provide question, we can say that by plotting data they can own 8 to 10 video games.

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

Here,

We can therefore deduce from the provided number that the cluster owns between 8 to 10 video games.

How do we know the range is 8 to 10 then? In the example figure, the dots are referred to as the cluster.

Based on this, we may deduce that our range is between 8 and 10, the amount of games that are owned as a minimum and maximum, respectively.

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The complete question is " A group of children, 6 to 10 years old, were asked how many video games they owned. The scatter plot shows the results.

What is the range of video games owned for the cluster?"

The quadratic equation written in the vertex form is:

y = 2*(x - 3)^2 - 1

We know that for a leading coefficient a, and a vertex (h, k), we can write the quadratic equation as:

f(x) = a*(x - h)^2 + k

Here we know that the leading coefficient is 2, and the vertex of our quadratic equation is (3, -1)

Then the values that we have are:

a = 2

h = 3

k = -1

Then we can write the quadratic equation in the vertex form as:

y = 2*(x - 3)^2 - 1

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Answer:

12 students earned B Honor Roll

Step-by-step explanation:

Let A be the number of students who earned A Honor Roll and B the number who earned B.

We are told that A = 24,

and that A = 3B-12  [ . . .were twelve less than three times the number of students who earned B Honor Roll]

Since we know the value of A (24) use the second equation to find B:

A = 3B-12

24 = 3B-12

3B = 36

B = 12

CHECK:

Is 24 12 less than three times B(12)?

 24 = 3*12 - 12?

 24 = 36 - 12?

  24 = 24

 YES

The first statement is correct. The 99% confidence interval is (0.3162, 0.5238). We are 99% confident the true proportion of students attending the Winter Formal is between 31.62% and 52.38%. However, the rest of the statements are incorrect.

"There is a 99% chance that a randomly selected student who will attend the Winter Formal lies between 31.62% and 52.38%." is incorrect, this statement is about a probability of a single student, but the confidence interval is about a probability of the whole population.

"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.3162, 0.5238)." is correct, this statement is true, but it doesn't add any additional information.

"The 99% confidence interval is (0.4762, 0.6838)." is incorrect, this value is not the correct confidence interval.

"We are 99% confident that the true proportion of students attending the Winter Formal is between 47.62% and 68.38%." is incorrect, this statement is not true, as the confidence interval is not (0.4762, 0.6838) but (0.3162, 0.5238)

"Ninety-nine percent of all samples of this size will yield a confidence interval of (0.4762, 0.6838)." is incorrect, as this is not the correct confidence interval.

In conclusion, the faculty members at McAdenville High School can be 99% confident that the true proportion of students who will attend the Winter Formal is between 31.62% and 52.38%.

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function f(x) is said to be discontinuous at a point ‘a’ of its domain D if it is not continuous there. The point ‘a’ is then called a point of discontinuity of the function.

he function of the graph which is not connected with each other is known as a discontinuous function.

A function f(x) is said to have a discontinuity of the first kind at x = a,

if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.

f(x) is said to have a discontinuity of the first kind from the left at x = a,

if the left hand of the function exists but not equal to f(a)

There are three types of discontinuity.

Jump Discontinuity

Infinite Discontinuity

Removable Discontinuity

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Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.

What is compound interest?

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is different from simple interest, which is calculated only on the initial principal.

To find out how much Caleb needs to invest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal or initial investment

r = the annual interest rate (expressed as a decimal)

n = the number of times per year that interest is compounded

t = the number of years the investment will be held

We know that Caleb wants the future value of the investment to be $1,900 in 5 years and interest is compounded daily with an annual rate of 6%. So we can set up the equation as:

A = P(1 + r/n)^(nt)

1900 = P(1 + 0.06/365)^(365*5)

To solve for P, we can use a calculator to get the result:

P = $1,764.69

Hence, Caleb would need to invest $1,764.69 to the nearest cent, for the value of the account to reach $1,900 in 5 years with an interest rate of 6% compounded daily.

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The required altitude of the trapezoid ABCD is 2.5 cm.

The Greek roots of the term trapezoid are trapeza, which means "table," and -oeides, which means "formed." A trapezoid is shaped like a table. It has two parallel sides, which are often referred to as the figure's bases. Take the average of the bases and multiply it by the height to determine the area of a trapezoid.

Here, we must utilise the area of a trapezoid formula, which is

where h is the height or altitude and b1 and b2 are the two bases.

[tex]Area =\frac{ (b_{1}+b_{2})h}{2}[/tex]

Given are the values of Area = 7.5, b1 = 1, b2 = 5, and h is unknown.

Then,

7.5 = (1+5)h/2

7.5 = 3h

h = 2.5cm

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When two line segments are of equal length then both the line segments are congruent to each other.

As given in the question,

Therefore, the two line segments with equal lengths they both are congruent to each other.

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Answer:

1.3 * c + 1.5

Step-by-step explanation:

(5.2c-7) + (-3.9c + 8.5)

5.2 * c - 7 - 3.9 * c + 8.5

1. add constants ( - 7 and 8.5)

5.2 * c - 3.9 * c + 1.5

2. add both of the coefficients of c

when a variable is multiplied by a coefficient, we can add another coefficient * variable combination if the variable is the same. for example, 1 * x + 2 * x = 3 * x by adding the 1 and 2 together

similarly, 5.2 * c - 3.9 * c = (5.2 - 3.9) * c = 1.3 * c

1.3 * c + 1.5

The number of places you put the lens to form a well-focused image of the candle flame on the wall is either we have to move the screen towards the lens or the lens towards the screen.

Here we have given that the lens to form a well-focused image of the candle flame on the wall.

As we all know that if the candle is further from the wall than the focal length of the lens, then there are two places which will result in an image. Here we have know that one of them is just beyond the focal length from the wall.

Here we have given the other is that same distance from the candle.

Then the position near the wall will yield a small image.

Here the position near the candle will produce a large image.

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The length of the rope must be, at least, 5.9 meters.

The rope will allow the sheep to move in an almost perfect circle (except for the part where the shed is) so we will have 3/4 of a circle.

So here we just need to find the length L of the rope such that:

10 yd² = (3/4)*pi*L^2

Where (3/4)*pi*L² is the area of 3/4 of a circle of radius L.

and pi = 3.14

Solving for L we will get:

L = √( 10 yd²*(4/3*3.14)) = 6.4 yd

Writting this in meters, we will get:

1 yd = 0.9144 m

then:

L = 6.4* 0.9144 m = 5.9m

The rope must be at least 5.9 meters long.

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Factors of polynomial x²+5x+6 are -2,-3.

Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. For polynomial expressions, addition, subtraction, multiplication, and positive integer exponents are all possible; however, division by variable is not. x2+x-12 is an illustration of a single-variable polynomial. Three terms are involved in this example: x2, x, and -12.

The expression is categorised as monomial based on how many terms are included in it:

An expression with just one term is referred to as a monomial. A monomial expression must have a single term that is not zero in order to qualify. A Monomial examples include 5x and 3.

Binomial:-

An expression of a polynomial with exactly two terms is called a binomial.  Examples of binomials are:

– 5x+3, 6a^4 + 17x.

Trinomial:-A trinomial is an expression which is composed of exactly three terms. A Examples of trinomial expressions are:

– 8a^4+2x+7, 4x^2 + 9x + 7.

Now Given polynomial is x^2+5x+6

To find factors put it equal to zero

x^2+3x+2x+6=0

x(x+3)+2(x+3)=0

x+3=0, x+2=0

x=-2,-3

Hence, The factors of the given polynomial are -2,-3.

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The greatest integer that does not exceed S/10 is 2.

1000 can be factored as 1000 = 2^3 * 5^3. The positive divisors of 1000 are the numbers of form 2^i * 5^j, where i and j are non-negative integers and i <= 3, j <= 3.

The sum of all numbers of the form a/b, where a and b are relatively prime positive divisors of 1000, is the sum of all numbers of the form 2^i * 5^j / (2^k * 5^l), where i, j, k, and l are non-negative integers and i, j, k, l are non-negative integers and i <= 3, j <= 3 and (i,j) is not equal to (k,l).

There are total 24 such terms in the sum.

We can evaluate the sum as:

(1/1 + 1/2 + 1/4 + 1/5 + 1/8 + 1/10 + 1/20 + 1/25 + 1/40 + 1/50 + 1/80 + 1/100 + 1/125 + 1/200 + 1/250 + 1/400 + 1/500 + 1/625 + 1/1000 + 2/5 + 4/25 + 8/125 + 16/625)

S = (1 + 0.5 + 0.25 + 0.2 + 0.125 + 0.1 + 0.05 + 0.04 + 0.025 + 0.02 + 0.0125 + 0.01 + 0.008 + 0.005 + 0.004 + 0.0025 + 0.002 + 0.0016 + 0.001 + 0.0004 + 0.0008 + 0.00016 + 0.000064)

S = (2.93120)

Therefore, the greatest integer that does not exceed S/10 is 2.

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It is not possible to construct a triangle with 6cm, 9cm, and 17cm.

The sides measure 6 cm, 9 cm, and 17 cm in length.

Only when the third side is greater than the sum of any two sides can a triangle be drawn. This the condition.

Let's verify the rule now.

6 + 9 > 17        Not true

6 + 17 > 9        True

9 + 17 > 6        True

As 6 + 9 > 17 does not satisfy the condition.

Hence, it is not possible to construct a triangle having 6cm, 9cm, and 17cm in length.

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Check the picture below.

Answer:

True

Step-by-step explanation:

(3,2) is a solution to the equationExplanation:If (3 ,2) is a solution then it must 'satisfy' the equation. That is make it True.To determine this, substitute x = 3 and y = 2 into the left side of the equation and if the result is 12 then it is a solution.⇒(2×3)+(3×2)=6+6=12LHS = RHS hence (3,2) is a solution