find y when x=17 if y varies directly as x, and y=43 when x=11

Juan wants to buy a video game for $63  He saves  every Friday $12.

An equation to represent Juan’s total savings, , in dollars, after  Fridays y is  

Part A is

y =12x

Fridays will it take for Juan to save up enough money for the video game is .

Part B

y >  63

12 x > [tex]5\frac{1}{4}[/tex]

x  =  6

so

That means 6 fridays

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The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.

In the given question,

The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;

C(x) = 3x^2-1500x+199,000

(a) In the given question we have to find the number of bicyles that must be  manufactured to minimize the cost.

The given function is

C(x) = 3x^2-1500x+199,000

To find the maximum or minimum value we firstly find the value of f'(x).

C'(x) = 6x-1500

Now put f'(x)=0

6x-1500=0

Add 1500 on both side, we get

6x=1500

Divide by 6 on both side we get

x=250

Hence, the number of bicycles that must be manufactured to minimize the cost of 250.

(b) Now finding the value of function at x=250

C(250) = 3(250)^2-1500*250+199,000

C(250) = 3*62,500-375,000+199,000

C(250) = 187,500-375,000+199,000

C(250) = 11,500

The minimum cost is $11,500.

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Answer:

Step-by-step explanation:

to find area of a rectangle we use (L)(W) so we do that here for both of these rectangles first find the area of the black top

5x(3x)

15x^2 is the area of the blacktop

The “!ield” area is next

12x(7x)

84x^2 is the area now we just subtract the two numbers by subtracting coefficients but keeping the rest the same

84x^2-15x^2

69x^2 is the area of the rectangle that is not black top

B- the foundtain we find with the area of circle formula r squared times pi

3x(3x)pi

9x^2pi

Now we just subtract this from the area of the rectangle

69x^2 -9x^2pi is the area

Hopes this helps please mark brainliest

It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.

Given that;

Finding the hourly cost of stamping parts for each machine is one way to approach this issue.

In 4 hours, the outdated equipment can stamp 1000 pieces. That means that it produces 250 parts per hour (1000 divided by 4). The new machine produces 1000 parts in two hours, which translates to 500 components every hour of stamping (1000 divided by 2).

If t is the amount of time that both machines are simultaneously stamping, then to determine the output, which must be 1000 parts, we simply multiply the rates of the two machines by t.

By multiplying the unknown time, t, by each of the two machines' rates and setting the result equal to 1000, it is possible to determine the precise amount of time required. Equation form of this is;

250t + 500t = 1000

750t = 1000

t = 1000/750

t = 1.333

It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.

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Greek mathematicians, who were first influenced by the Egyptians, would go on to produce innovations like Pythagoras' theory of right-angled triangles and, by concentrating on the abstract, bring accuracy and clarity to venerable mathematical conundrums.

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The speed of the tip of her shadow would be 5.714 ft/sec.  ft/sec.

let H, be the height of the pole = 20 ft.

h, be the height of the woman = 6 ft.

x, be the length of the woman's shadow,

and s, be the distance from the pole to the woman = 15

by using the equation of similar triangles,

[tex]\frac{H}{h} = \frac{(s+x)}{x}[/tex] or Hx = h(x+s)

differentiating, [tex]H\frac{dx}{dt} = h (\frac{ds}{dt} + \frac{dx}{dt} )[/tex]

[tex]20\frac{dx}{dt} = 6(4 + \frac{dx}{dt} ) = 24 + 6 \frac{dx}{dt}[/tex]

[tex]14\frac{dx}{dt} = 24[/tex],

[tex]\frac{dx}{dt} = \frac{24}{14}[/tex] ≈ 1.714 ft/sec, is how fast her shadow is lengthening.

the speed of the tip of her shadow would be the speed of shadow lengthening + speed of her traveling = 1.714 + 4 = 5.714 ft/sec.

thus, a street light is at the top of a 20 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. the speed of the tip of her shadow would be 5.714 ft/sec.

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Answer: 13

Step-by-step explanation: 5, 12, and 13 is a Pythagorean Triple so if 12 were replaced with 13 in the word problem the answer would be 12 because all these numbers "travel" together.

Tony would require 13 meters of garland to reach from one corner to the opposite corner of the rectangular ceiling.

The ceiling of the ballroom is rectangular in structure.

The dimensions of the rectangle are 12 by 5 meters.

So we have to find the length of the diagonal of the ceiling which is the length from one corner to the other.

We will use Pythagoras theorem to calculate the length of the diagonal.

12² +5 ² = D²

or, D² = 144 + 25

or, D =√169

or, D = 13

Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares on the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.

The hypotenuse in this case is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides are squared to produce a Pythagorean triple equation.

Hence Tony will need 13 meters of garland.

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Question 1

[tex]\frac{a-0}{a-0}=1[/tex]

Question 2

[tex](1)(-1)=-1[/tex]

The rule in expressed in function notation and slope-intercept form of a line is f(x) = 3x -2

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The equation of a line in slope-intercept form is y = mx + c.

Where m is the slope and c is the intercept

In order to obtain the equation of the line, we are going to pick any two convenient values of x and y from the table. Let's pick the first and last point. Thus:

point1: x₁ = 1, y₁  = 1

point2: x₂ = 4, y₂ = 10

Using the equation for 2 points:

y-y₁ / y₂-y₁ =  x-x₁ / x₂-x₁

y-1 / 10-1 = x-1 / 4-1

y-1 / 9 = x-1 /3

3(y-1) = 9(x-1)

y-1 = 3(x-1)

y-1 = 3x -3

y = 3x -3+1

y = 3x - 2

Thus, f(x) = 3x -2

Therefore, the rule in function notation, using the slope-intercept form of a line is f(x) = 3x -2

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Answer:f(x)=10e^4x

Step-by-step explanation:

f(x)=C*e^4x

f(0)=c*e^4.0

10=C*e^4.0

10=C

f(x)=C*e^kx

f(x)=C*e^4x

Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

A discount store sells 5.5 - ounce jars of fish in bundles of 5. A bundle of 5 jars costs $10.45. Then the unit rate is given as,

⇒ ($10.45 x 5) / (5.5 x 5 x 5)

⇒ $0.38 per ounce

The store likewise sells 4.5-ounce jars of similar fish in bundles of 8. A bundle of 8 jars costs $12.96. Then the unit rate is given as,

⇒ ($12.96 x 8) / (4.5 x 8 x 8)

⇒ $0.36 per ounce

The store sells 3.5 - ounce jars in bundles of 4 jars for $4.76. Then the unit rate is given as,

⇒ ($4.76) / (3.5 x 4)

⇒ $0.34 per ounce

Best buy is the last one. And the smallest unit rate will be $0.34 per ounce.

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Answer:

A town's population grows at a rate of 5.3% every year.

If we graph the angel's ppc then the slope of angel's ppc will be -1.

Given, Tim and Angel are working on promoting an event for a club they are in on campus.

In one afternoon, Tim can make 4 flyers or 5 posters, and Angel can make 3 flyers or 6 posters.

we have to find the slope of the angel's ppc if we graph the angel's ppc.

As, the graph of the angel's ppc will pass through the point (3 , 6).

so, the slope = (6 - 5)/(3 - 4)

slope = 1/-1

slope = -1

Hence, if we graph the angel's ppc then the slope of angel's ppc will be -1.

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This measure of effect is influenced by the relative risk of the disease in exposed individuals versus unexposed individuals and also the prevalence of exposure in the population.

As stated, population etiology fraction is a measure of the disease rate in a population attributable to the exposure of interest. This is a measure that can be influenced only by the exposure caused due to a particular disease. Hence it can be influenced by the relative risk of the disease in exposed individuals versus unexposed individuals and also with the prevalent of the exposure in the population.

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Answer:

40 cm²

Step-by-step explanation:

Let,

length ( l ) = 4 cm

Height ( h ) = Width ( w ) = 2 cm

To find : Surface are of cuboid : -

Formula : -

Surface are of cuboid = 2 [ lh + hw + wl ]

Surface are of cuboid

= 2 [ ( 4 )( 2 ) + ( 2 )( 2 ) + ( ( 2 )( 4 ) ]

=  2 [ 8 + 4 + 8 ]

= 2 [ 20 ]

= 2 x 20

= 40 cm²

The sample is a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion .

A sample is a collection of people, things, or things used in research that is taken for analysis from a larger population. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.

We must utilize inferential statistics to discover a population's characteristics by directly observing only a subset (or sample of the population) in order to derive conclusions about populations from samples.

Since it is frequently impractical and hardly ever possible, we acquire a sample of the population.

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The length of rectangle is 1170 ft and width is 770 ft.

The perimeter of a form is the space surrounding its edge. A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. We must sum up the lengths of the rectangle's four sides in order to get its perimeter. Since there are two of each side length, it is easy to accomplish this by simply adding the length and width and multiplying the result by two. The perimeter formula is defined as perimeter=(length + width)2.

Given,

The perimeter of the flag is 2,280 ft .

Length = 400 ft

Let l represent the size of the flag.

and

The width is w.

then in line with the preceding statement

l = w+400

Sphere size is 2280 feet.

The perimeter formula is provided by:

Perimeter = 2(Length + Width)

2280 = 2( w + w+ 400)

2280/2 = 2w - 400

1140 + 400 = 2w

1540 = 2w

width = 770

Length = 770 + 400

Length = 1170

The length of rectangle is 1170 ft and width is 770 ft.

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The probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days is 0.3969.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. By dividing the number of positive outcomes by the entire number of possible outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.

Given,

Mean = 4 minutes

= 1/4

= 0.25

The probability that someone will be attended to in less than three minutes on any given day is:

P( X ≤3)

= 1- e⁻⁰²⁵⁽³⁾

= 0.5267

The probability is:

P( X ≥ 4)

= P( X = 4) +P( X = 5 ) + ( X = 6)

= 0.2594 + 0.1159 + 0.216

= 0.3969

The probability that a person gets there in less than 3 minutes on at least 4 of the next 6 days is 0.3969.

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Given that the signal gets larger than 210 microvolts, there is a 2.335 % chance that it is also larger than 240 microvolts.

As, per the given question.

Gaussian random variable n (200, 256)

Part a: Probability that signal will exceed 240 micro volts.

P(x > 240) = 1 - P(x ≤ 240)

P(x > 240) = 1 - P(240 - 200)/16

P(x > 240) = 1 - P(2.5)

See p value for z = 2.5

P(x > 240) = 0.00621

Thus, Probability that signal will exceed 240 micro volts is 0.00621.

Part b:  larger than 210 micro volts.

P(x ≥ 240) | x ≥ 210) = P(x ≥ 240) / P(x ≥ 210)

P(x ≥ 240) | x ≥ 210) = 1 - P(240 - 200)/16 /  1 - P(210 - 200)/16

P(x ≥ 240) | x ≥ 210) = 0.00621 / 0.26599

P(x ≥ 240) | x ≥ 210) = 0.02335

Thus, for the signal gets larger than 210 microvolts, there is a 0.02335 percent chance that it is also larger than 240 microvolts.

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An inequality correctly compares One-half, Three-fourths, and Two-thirds is: One-half < Two-thirds < Three-fourths.

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values (numbers) and variables in an algebraic equation, especially based on any of the following inequality symbols:

Translating the numbers in word to numerical values, we have:

One-half = 1/2 or 0.5

Three-fourths = 3/4 or 0.75

Two-thirds = 2/3 or 0.67

Next, we would compare the above numerical values by using the less than (<) inequality symbol as follows:

0.5 < 0.67 < 0.75

One-half < Two-thirds < Three-fourths.

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The diagonals of a square are equal to each other

Let ABCD be a square.

We need to prove that the diagonals are equal to each other

AC=BD and AC and BD bisect each other at right angles

(i) Considering the ΔABC and ΔBAD,

AB=AB ( common line)

BC=AD ( opppsite sides of a square)

∠ABC=∠BAD ( = 90° )

ΔABC≅ΔBAD( By SideAngleSide property)

AC=BD ( by CPCT).

(ii) Now in triangles ΔOAD and ΔOCB,

AD=CB ( opposite sides of a square)

∠OAD=∠OCB ( transversal AC )

∠ODA=∠OBC ( transversal BD )

ΔOAD≅ΔOCB (ASA property)

OA=OC ---------(i)

Similarly OB=OD ----------(ii)

From (i) and (ii)  we can conclude that AC and BD bisect each other.

Now in a ΔOBA and ΔODA,

OB=OD ( from (ii) )

BA=DA

OA=OA  ( common line )

ΔAOB=ΔAOD----(iii) ( by CPCT

∠AOB+∠AOD=180°  (linear pair)

2∠AOB=180°

∠AOB=∠AOD=90°

Therefore, it is proved that AC and BD bisect each other at right angles.

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The 12 months past and the fruit turned into sonic the hedge hog #PERIODAHHPERIODUHH

The sum of the digits of n is 3 if n is the second smallest positive integer that is divisible by every positive integer less than 7

What is least common multiple?

The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.

It can be calculated for two or more numbers as well.

For example, LCM of 10, 2 and 7 is 70.

According to the given question:

Now n must be divisible by every positive integer less than 7, or

1, 2, 3, 4, 5, and 6.

Each number that is divisible by each of these is a multiple of their least common multiple.

LCM (1,2,3,4,5,6) = 60

So each number divisible by these is a multiple of 60.

The smallest multiple of 60 is clearly 60, so the second smallest multiple of 60 is 2 x 60 = 120.

Therefore, the sum of the digits of n is 1+2+0 = 3

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The equation in terms of x, which represents the amount of money left on the gift card of Aaliyah upon buying a cup of coffee is; A = 30 - 2x  dollars.

The original value of the gift card was $30.

Coffee costs $2 per cup.

Let 'x' be the number of cup of coffee purchased by Aaliyah.

Total cost be 'A' be paid by her.

Thus, the equation in terms of x, which represents the amount of money left on the gift card upon buying a cup of coffee is;

A = 30 - 2x  dollars.

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Answer:

(2x + 1) and (x - 5)

Step-by-step explanation:

(2x + 1)(x - 5) = 2x^2 - 9x - 5

Answer:

Adult is 10$ and Child is 7$.

Unfortunately for the family, they do not have enough to go to the theater. They do not have that extra dollar.

Hope this helps!

Step-by-step explanation:

2x + 4y = 48

5x + 2y = 64

2x + 4y = 48

10x + 4y = 128

( 10x - 2x ) + ( 4y - 4y ) = ( 128 - 48 )

8x = 80

x = 10

2 ( 10 ) + 4y = 48

20 + 4y = 48

4y = 48 - 20

4y = 28

y = 7

The missing base for the expression x² = 100 is given by:

± x = 10.

The expression in this problem is given as follows:

x² = 100.

The missing base is represented by the variable x, hence we have to solve the above expression x² = 100 for the variable x.

To solve for x, we need to isolate the variable x, applying the inverse operation to the second power, which is the square root, hence the variable x is isolated as follows:

x = plus/minus square root of 100.

The plus/minus sign is necessary because the x-squared function is even, then the missing base is obtained as follows:

x = ± 10.

Plus/minus 10 because both of these statements are true:

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Answer:

1111

Step-by-step explanation: