A recipe for Kool-Aid calls for 1/4 cup of sugar for every 3 cups of liquid. How many cups of sugar would be needed for 18 cups of liquid?​

The numbers that Austin could choose from are: 80, 100 which have 4, 5, and 10 as their multiples

The numbers between 61 and 107 are:

62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106

we will observe that only 70, 80, 90 and 100 have 10 and 5 as their multiple, amongst which, only 80 and 100 have 4 as their multiple.

Therefore, Austin must choose only the two numbers 80 and 100 which have 4, 5, and 10 as their multiples.

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Answer: Gabriella's distance from the stadium is modeled by the function G(t) = 550 - 25t.

Ian's distance from the stadium is modeled by the function I(t) = 950 - 50t.

To find the number of hours after noon when Gabriella and Ian are the same distance from the stadium, we need to set the two equations equal to each other and solve for t:

G(t) = 550 - 25t = I(t) = 950 - 50t

Combining like terms we get:

25t = 400

t = 16

So, 16 hours after noon, Gabriella and Ian will be the same distance away from the stadium.

To graph the functions, we can substitute different values of t into the equations to find the corresponding values of G(t) and I(t). Then we can plot the points on a coordinate plane and connect them to form the graph of the two functions.

It is important to note that we are assuming that both Gabriella and Ian don't make any stops, so the speed is constant through the whole trip and no time is wasted.

Step-by-step explanation:

Step-by-step explanation:      

         length of the pole : 15 m

        angle inclined by the wire to the  pole from ground :60 deg

        let the length of wire : x

        therefore

                       sin (angle)  = opposite/hypothesis

                       sin 60 = 15/x

                        √3/2 = 15/x

                         x= 2*15/√3

                         x = 30/√3

                         x = 17.320

the length of the wire is :17 m.

Answer: ∠1= 53°

∠3, ∠6, ∠7 are all 127°

∠4,∠5,∠8 are all 53°

Step-by-step explanation: 127° and ∠1 are supplementary angles meaning they add up to 180° You subtract 127° from 180° to get 53°.

∠3 and 127°are vertical which makes them equal and both 127°.

∠4 is vertical to ∠1 which makes them equal and both 53°.

∠5 is corresponding to ∠1 so they are equal and both 53°.

∠6 is corresponding to 127° so they are equal and both 127°.

∠7 is vertical to ∠6 so they are equal and both 127°.

∠8 is vertical to ∠5 so they are equal and both 53°.

a) Angular acceleration is 0.53 rad/s^2

b) Tangential acceleration is 2.56 m/s^2

c) Centripetal acceleration is 2.56  rad/s^2

We know that the angular acceleration can be obtained from the equations of circular motion. We know that we have the equation for the circular motion as;

α = ω2 -  ω1/t

α =  angular acceleration

ω2 = final angular velocity

ω1 = initial angular velocity

α = 0.8 - 0/1.5

= 0.53 rad/s^2

b) The tangential acceleration = v^2/r

But V = ωr

V = 0.8 * 4

V = 3.2 m/s

Then;

(3.2)^2/4

= 2.56 m/s^2

c) Centripetal acceleration = ω^2 r

= (0.8)^2 * 4

= 2.56 rad/s^2

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The correct option is Option 1 - 3520.

A farmer owns 3520 acres in which three full sections, four half-sections, and two quarter-sections are there.

Three of a farmer's sections were full. Let's say a full section is 640, which is

=3 x 640,

= 1,920.

He had four half portions as well. Divide 640 by two to get 320 (640/2), which is

= 4 X 320

= 1,280.

He had three quarter portions as well. Divide 640 by 4 to create a quarter piece (640/4 = 160)

= 2 X 160

= 320.

Now we have to add all these,

Three full sections       = 1920

Four half-sections        = 1280

Two quarter-sections  = 320

= 1,920 + 1,280 + 320

= 3,520.

Therefore the acres a farmer had is 3520.

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The following question may be like this:

A farmer owns three full sections, four half-sections, and two quarter-sections. How many acres is this?

Answer:

First one is 3^16

Second one is 3^10

Third one is 3^2 * 8^2

Forth one is 3^2/8^2

fifth one is 3^8/3^2

Step-by-step explanation:

The quantity is a variable is the lowest overnight temperature

In math the term variable is defined as variable is an alphabet which is used to represent the unknown number and this one represents the value.

Here we have know that it rained 0. 5 inches on Tuesday and 0. 2 inches on Wednesday.

And the climate was warmer on Thursday than it was on Friday.

Where the humidity was 15% for 3 days of the week and thus the lowest temperature overnight was 68∘F.

Here we have identified that the temperature is continually falling and it will lead the lowest temperature overnight.

Then the correct option is (c).

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The Standard form of y= 4/9x - 3 is 4x - 9y = 27.

What is standard form of an equation?

The general form of a linear equation, commonly referred to as the standard form, is written as Ax + By = C.

Given equation : y= 4/9x - 3

Taking LCM on both sides

we get, 9y = 4x - 27

Since the standard form of a linear equation is Ax + By = C.

So, we can write it as 4x - 9y = 27

        where A= 4, B = -9 and C= 27.

Hence, the standard form of y= 4/9x - 3 is 4x - 9y = 27.

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The total number of 18,181 bottles should be sold to break the business even based on the investment.

Firstly calculating the profit earned on each soft drink. Based on this, the formula for profit to be used is -

Profit = Selling price - cost price

Keep the values in formula

Profit = 1.20 - 0.65

Performing subtraction on Right Hand Side of the equation

Profit = $0.55

For the business to break even, the total profit earned by company must be equal to the investment. So, let the number of bottles required to break even the business be x.

0.55 × x = 10,000

Performing multiplication on Left Hand Side of the equation

0.55x = 10000

x = 10,000/0.55

Performing division on Right Hand Side of the equation

x = 18181.8

Rounding off = 18181.

Thus, 18,181 bottles need to be sold.

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The water depths can be modeled by a sinusoidal function. So the value of period is 18 hours, amplitude is 14.5, maximum is 24, equation of the midline is 10, and minimum is -4.

The tide at an Eastern seaport is at its maximum at 3 a.m.

High tide is 24 ft deep.

Low tide occurs at 9 a.m. with a depth of 4 ft.

We have to determine the period.

Period = time between two consecutive high tides

Period = 2 × Time between high and low tide

Time between 3 a.m. and 9 a.m. is 6 hours.

Period = 2 × 6

Period = 18 hours

We have to determine the Amplitude.

Amplitude = (High - Low)/2

Amplitude = (24 - (-5))/2

Amplitude = (24 + 5)/2

Amplitude = 29/2

Amplitude = 14.5

We have to determine the Maximum.

The maximum tide is 24.

We have to determine the Equation of the midline.

Equation of the midline = (max + min)/2

Equation of the midline = {24 + (-4)}/2

Equation of the midline = (24 - 4)/2

Equation of the midline = 20/2

Equation of the midline = 10

We have to determine the minimum.

The minimum tide is -4.

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The complete question is:

The tide at an Eastern seaport is at its maximum at 3 a.m. High tide is 24 ft deep. Low tide occurs at 9 a.m. with a depth of 4 ft. The water depths can be modeled by a sinusoidal function. Allow x=0 to represent midnight

Find the following and make sure to show work for the midline and amplitude:

period=

Amplitude=

Maximum=

Equation of the midline:

minimum:

The cost of wrapping both boxes is $0.92.

In three-dimensional space, a prism is a polyhedron where two ends are similar.

Given:

Two boxes need to be wrapped in paper (with no overlap).

Both boxes are in the shape of right rectangular prisms.

Box A measures 1.2 feet high, 0.8 feet long, and 1 foot wide.

The surface area of the rectangular prism A,

= 2(1.2 × 0.8 + 1 × 0.8 + 1 × 1.2)

= 5.92 square feet.

Box B measures 1.6 feet high, 0.5 feet long and 0.8 feet wide.

The surface area of the rectangular prism A,

= 2(1.6 × 0.5 + 0.5 × 0.8 + 0.8 × 1.6)

= 4.96 square feet.

The wrapping paper costs $6.79 per 80 square feet.

That means,

unit rate = 6.79 / 80 = $0.08 per square feet.

The cost of wrapping both boxes,

= 5.92 x 0.08 + 4.96 x 0.08

= $0.92

Therefore, the cost is $0.92.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 1.75\%\to \frac{1.75}{100}\dotfill &0.0175\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (5000)(0.0175)(6) \implies I = 525[/tex]

By finding the intercept between the graphs of the equations, we can see that the solution is (-1, 3)

Here we have a system of linear equations:

3x - y = -6

y = x + 4

To solve the system of equations graphically, w ejust need to graph both equations on the same coordinate axis and find the point where the lines do intercept.

The graph of the system of equations can be seen on the image at the end.

There you can see that the lines intercept at the point (-1, 3), so that is the solution of the system of equations.

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If the new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams , then the equation best models the situation here is (b) 4(x+9) = 76 .

the number of sensor in the boxes is = 4 ;

let the weight of each of sensors be = x ;

So , in new design the weight of each sensor is increased by 9 grams ,

the new weight of sensor becomes = x + 9  ;

the new weight of 4 sensors will be = 4(x + 9) ;

the total weight of new package is = 76 grams ;

So , the equation representing the situation is (b) 4(x+9) = 76  .

The given question is incomplete , the complete question is

A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams how much did each sensor weigh originally ?

Which equation best models the situation here ?

(a) 4x + 9 = 76

(b) 4(x+9) = 76

(c) 4(9x) = 76

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Answer:

  (c)  (-∞, -2) ∪ (-2, 1) ∪ (1, ∞)

Step-by-step explanation:

You want the domain of the given piecewise-defined function.

For x < 2, the function is ...

  [tex]g(x)=\dfrac{x^2+2x}{x^2+x-2}-\dfrac{x(x+2)}{(x-1)(x+2)}=\dfrac{x}{x-1}\quad x\ne\{-2,1\}[/tex]

Both of these exclusions are in the region x < 2, so both must be excluded from the domain.

The log function is defined for all values x > -2, so there are no exclusions in this region.

The domain is (-∞, -2) ∪ (-2, 1) ∪ (1, ∞).

The coordinates of the vertices of quadrilateral A’B’C’D’ after a translation along vector <2, -3> is: A. A' (-2, 5), B' (1, 7), C' (2, 5), D' (1, 3).

In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.

Note: We would move in the opposite direction of the given vector <2, -3>.

By applying a translation to the pre-image of quadrilateral ABCD vertically up by 3 units and horizontally left by 2 unit, the coordinates of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 2, y + 3)

Coordinate A = (0, 2)   →    Coordinate A' (0 - 2, 2 + 3) = (-2, 5)

Coordinate B = (3, 4)   →    Coordinate B' = (3 - 2, 4 + 3) = (1, 7)

Coordinate C = (4, 2)   →   Coordinate C' = (4 - 2, 2 + 3) = (2, 5)

Coordinate D = (3, 0)   →    Coordinate D' = (3 - 2, 0 + 3) = (1, 3)

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urrrrrrrrrrrrrrrf mooookoommm

Answer: B) 2x²-3y=9

Step-by-step explanation:

This is not a linear function because the equation for a linear function is mx+b=y this means that x cannot have an exponent which in B it does.

A line passing between the points (1, 6) and (1, 31) has an undefined slope.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

The slope of a line can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where m is the slope of the line, (x1, y1) and (x2, y2) are two points on the line.

In this case, we have (x1, y1) = (1, 6) and (x2, y2) = (1, 31). Plugging these values into the formula:

m = (31 - 6) / (1 - 1)

Hence, the denominator is zero, the slope is undefined. This means that the line is a vertical line and has no slope.

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The dimensions of the base would be: base: 12 cm ; height : 8 cm

The correct answer is an option (D)

We know that the formula for the volume of a pyramid is:

V = 1/3 × B × h

where B is the base area of the pyramid

h is the height of the pyramid

The shape of the box is a triangular pyramid.

Each box contains 240 cubic centimeters of confetti.

this means, the volume of the box is V = 240 cubic centimeters

Using above formula of the volume of a pyramid,

V = 1/3 × B × h

here V = 240 cubic centimeters and h = 15 centimeters

240 = 1/3 × B × 15

240 = B × 5

B = 240/5

B = 48 square centimeters

The dimensions of the base must be such that the area of the base would be  48 square centimeters.

Here, a pyramid has triangular base.

Using the formula for the area of triangle,

B = 1/2 × base of triangle × height of triangle

48 = 1/2 × base of triangle × height of triangle

base of triangle × height of triangle = 96

for the dimensions Base, 12 cm; height, 8 cm

12 × 8 = 96

Thus, the dimension of the base: base of triangle = 12 cm and the height of triangle = 8 cm

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At store B, they charge $0.09 more for pineapple juice than store A.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, Brody was comparing the price of pineapple juice at two stores.

Equation to represent the cost of pineapple juice at store A is

y=0.7x

Equation to represent the cost of pineapple juice at store B is

From the table, we have (9, 7.11) and (13, 10.27)

Now, slope m= (10.27-7.11)/(13-9)

= 3.16/4

= 0.79

Substitute m=0.79 and (x, y)=(9, 7.11) in y=mx+c, we get

7.11=0.79(9)+c

7.11=7.11+c

c=0

So, the equation is y=0.79x

Cost of 1 bottle juice at store A is $0.7 and Cost of 1 bottle juice at store B is $0.79

Difference in cost =0.79-0.7=$0.09

Therefore, at store B, they charge $0.09 more for pineapple juice than store A.

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Refer to the image attached.

The answer for the given senary expressions is 35₆.

What are senary numbers?

A senary numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3). As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to senary.

Now,

To find 2434₆/42₆

2434\(_6\) to base 10

2 \(\times\) 6\(^3\) + 4 \(\times\) 6\(^2\) + 3 \(\times\) 6\(^1\) + 4 \(\times\) 6\(^0\)

2 \(\times\) 216 + 4 \(\times\) 36 + 3 \(\times\) 6 + 4 \(\times\) 1

432 + 144 + 18 + 4 = 598

And: 42\(_6\) to base 10

4 \(\times\) 6\(^1\) + 2 \(\times\) 6\(^0\)

4 \(\times\) 6 + 2 \(\times\) 1

24 + 2 = 26

Then divide 598 by 26

= 23

Then convert 23\(_{10}\) to base 6

i.e. 35₆

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The final cost for the tile was $208 − $52 = $156.

208/8 = x/2

8x = 416

x = 416/8

x = 52

The price for the two unopened cases was $52.

Thus, The final cost for the tile was $208 − $52 = $156.

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The graph of equations y - 1 = - 3(x - 2) and y = - 3x + 7 is illustrated below with the attached image.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, An equation of a line y - 1 = - 3(x - 2) in point-slope form.

y - 1 = - 3x + 6.

y = - 3x + 7.

The next equation is 3y = x - 9.

y = (1/3)x - 3.

Now, The graph of these two equations can be sketched by assuming two or more arbitrary values of 'x' that correspond to different values of 'y'.

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It's worth noting that this form is known as the standard form of a linear equation, where the variables x and y appear only in the first degree and the constant term is on the right side of the equation.

What is the Quadratic Equation?

A quadratic equation is a type of polynomial equation that has the general form of ax^2 + bx + c = 0, where x is the variable, a, b, and c are constants, and a is not equal to zero. The degree of the equation is two, hence the name "quadratic".

x+1/6-y can be rewritten in terms of a,b, and c by using the following equation:

ax + by + c = 0

To get x+1/6-y in the values of a,b, and c we can rewrite the equation as follow:

a = 1, b = -1, c = -1/6

So, x+1/6-y can be written as:

1x - 1y - 1/6 = 0

or

ax + by + c = 0 where a=1, b=-1 and c=-1/6

It's worth noting that this form is known as the standard form of a linear equation, where the variables x and y appear only in the first degree and the constant term is on the right side of the equation.

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