Jack has 1 3/5 cups of yogurt to make smoothies. Each smoothie uses 2/5 How many smoothies can Jack make with the yogurt?

Answer:

  y = (2/3)x -1

Step-by-step explanation:

The line crosses the y-axis at -1, so that is the y-intercept.

From that point. the next grid intersection is 3 units to the right and 2 units up, so the slope is ...

  m = rise/run = 2/3

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . where m is the slope (2/3) and b is the y-intercept (-1)

Your line has equation ...

  y = (2/3)x -1

x=-11

we know that

Points A,B,C,and D are collinear and positioned in that order

so

AD=AB+BC+CD -----> by addition segment postulate

we have

AB=2x+30

AD=x=32

substitute the given values and solve for x

x+32 = (2x+43)

Group terms that contain the same variable

2x-x=32-43

x=-11

Answer:

x = -1, y = 2

Step-by-step explanation:

6x + 5y = 4

6x - 7y = -20

We already have a similar leading coefficient (6 for X), so we just subtract equation 1 from equation 2 to get:

12y = 24

Now solve normally:

y = 2

Then substitute into the first equation (or second, it doesn't matter)

6x + 10 = 4

6x = -6

x = -1

Answer:

24.8 ft (1 dp)

Step-by-step explanation:

Arc length of semicircle = \(\pi r\)  (where r is the radius)

Given:

⇒ Arc length = 2 × 3.14 = 6.28 ft

Use Pythagoras' Theorem \(a^2+b^2=c^2\) to find the hypotenuse of the right triangle with legs 2 ft and 4 ft:

\(\implies 2^2+4^2=c^2\)

\(\implies c^2=20\)

\(\implies c=\sqrt{20}=2\sqrt{5}\:\sf ft\)

Therefore:

perimeter = 6 + 6.28 + 6 + 2 + 2√5

                = 24.75213596...

                = 24.8 ft (1 dp)

Perimeter of semicircle

#Rectangle

For triangle

Use Pythagorean theorem

Total Perimeter

Answer:

what do u need help with

Step-by-step explanation:

??

The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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Answer:

\( \huge{ \boxed{36 {x}^{3} - \frac{6 {x}^{2} }{ \sqrt{x} } - 12x \sqrt{x} + 2 \sqrt{x} }}\)

Step-by-step explanation:

To find the derivative of the function \((3 {x}^{2} - \sqrt{x} )^{2} \) , the chain rule can be applied.

According to the chain rule, the derivative of f(x) with respect to x is given by:

\( \dfrac{df}{dx} = \dfrac{df}{du} \times \: \dfrac{du}{dx} \)

where

\( \dfrac{df}{du} \) represents the derivative f(x) with respect to u.

\( \dfrac{df}{du} = 2u(x)\)

\( \frac{du}{dx} = \frac{d}{dx} ( {3x}^{2} ) - \frac{d}{dx} ( \sqrt{x} ) \\ \\ \frac{du}{dx} = {6x} - \frac{1}{2 \sqrt{x} } \)

\( \frac{df}{dx} = 2u(x) \times (6x - \frac{1}{2 \sqrt{x} } ) \\ \)

\( \frac{df}{dx} = 2(3 {x}^{2} - \sqrt{x} ) \times (6x - \frac{1}{2 \sqrt{x} } ) \\ = (6 {x}^{2} - 2 \sqrt{x} )( 6x - \frac{1}{2 \sqrt{x} } ) \\ = 36 {x}^{3} - \frac{6 {x}^{2} }{ \sqrt{x} } - 12x \sqrt{x} + 2 \sqrt{x} \)

We have the final answer as

\(36 {x}^{3} - \frac{6 {x}^{2} }{ \sqrt{x} } - 12x \sqrt{x} + 2 \sqrt{x} \)

Option B, The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times

Step-by-step explanation:

The distribution of apple candies can be represented as normal curve and hence the sample proportion for this is true and can be drawn.

The rest other cases do not represent a normal distribution and hence it will not be easy to plot curve for these samples.

hence, option B is correct

Answer:

41.93 degrees

Step-by-step explanation:

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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If for every amount of $d , $0.20d is tipped, then for amount of $56, $11.6 will be tipped to the waiter

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.

If for every $d , $0.20d is tipped, then this means that the total amount spent is $56 and the amount Anthony's family tip the waiter is calculated as:

0.2 × 56

= $11.6

Therefore the waiter was tipped $11.6

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Answer:

A dinner bill of d dollars calls for a tip of 0.20d dollars. You want to find how much the family tipped the waiter for a bill of d=$56.

Evaluate the expression 0.20d for d=56.

0.20d

=

0.20(56)

=

11.2

The family tipped the waiter $11.20.

Answer:

each ice coffee is $2.25

Step-by-step explanation:

13.50 - 9 = 4.50

4.50 / 2 = 2.25

Answer:

2w = -3 + 5

W = 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

24/300 = 0.08 = 8%

Answer:

14.24%

Step-by-step explanation:

We have found that the yield to call (YTC) formula is:

YTC = [C + (F-P) / N] / [(F + P) / 2]

Where:

C = Periodic coupon amount = 95

P = Current Price = 980

F = Redemption amount = 1150

N = time left to redemption = 3

We replace:

YTC = [95 + (1150-980) / 3] / [(1150 + 980) / 2]

YTC = 0.1424

In other words, the yield to call (YTC) is equal to 14.24%

a.) The area of the floor = 246.5ft²

b.) The amount that it will cost to put down the new floor would be = $2,711.5

C.) The new dimensions of the area rug would be= Length= 21ft, width = 18.5 ft.

d.) The area of the area rug would be = 388.5ft²

For question a.)

The floor has a rectangular shape. The area of a rectangle = length×width

area of the floor= 17×14.5

= 246.5ft²

For question b.)

For a square foot(1ft²) = $11

246.5ft² = 246.5×11 = $2,711.5

For question c.)

Since the rug will be extended by 2ft at each side, the new dimensions would be:

length = 2+2+17 = 21ft

width = 2+2+14.5 = 18.5ft

For question d.)

The area of the floor with the new dimensions = 21×18.5 = 388.5ft²

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Two-variable linear equations have a line as their graph, which is why they are referred to as linear equations. Plotting (x1,y1) and (x2,y2), then creating a line that connects the two.

\($\frac{d}{d x}\left(-(x-2)^2+1\right)$\)

Domain of \($-(x-2)^2+1:\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$\)

Range of \($-(x-2)^2+1:\left[\begin{array}{cc}\text { Solution: } & f(x) \leq 1 \\ \text { Interval Notation: } & (-\infty, 1]\end{array}\right]$\)

Interception zones on the axis \($-(x-2)^2+1: \quad X$\) Intercepts: \($(3,0),(1,0), Y$\)Intercepts: (0,-3) .

Vertex of \($-(x-2)^2+1: \quad$\) Maximum (2,1) .

The graph of the equation y=2x+1 shows a straight line, or it is a linear equation. When the value of x rises, eventually the value of y rises by twice the rise in x plus one. With a ruler and the specified amount as the starting point, draw a vertical line. From the line across to the -axis, create a horizontal line using a ruler. Look at the value on the -axis.

There are three fundamental ways to graph linear functions. The initial method involves charting points and then tracing a line through them. The second is by using the slope and y-intercept. The identity function f(x)=x is transformed as the third method.

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The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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Answer:

No

Step-by-step explanation:

10 is not less than 6, so 10 < r when r=6 is not true.

The value of the given expression in simplest form is  34/63.

Mixed fraction

It is a form of a fraction which is defined as the ones having a fraction and a whole number.

Example: 2(1/7), where 2 is a whole number and 1/7 is a fraction.

To convert 2(1/7) into improper fraction , we will multiply 7 and 2 and then add 1 to it to get the numerator part and 7 will be the denominator of the fraction that is 15/7.

Given expression:

4(6/7) ÷ 9

We have to find the value of the given expression in simplest form.

We can write the mixed fraction 4(6/7) as 34/7

(34/7)  ÷ 9

(34/7)*(1/9) = (34*1)/(7*9) = 34/63

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Answer:

\(-5x-5\)

Step-by-step explanation:

original functions:

\(f(x)=3x-8\\g(x)=8x-3\)

Subtract the polynomials:

\(f(x)-g(x) = (3x-8) - (8x-3)\)

Distribute the negative sign:

\(3x-8-8x+3\)

Combine like terms:

\((3x-8x)+(-8+3)\)

Add like terms:

\(-5x-5\)

Answer:

\(y =2x + 3\)

Step-by-step explanation:

Given

(-2,-1) and (3,9).

Required

Determine the line equation

First, we calculate slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where

\((x_1,y_1) = (-2,-1)\)

\((x_2,y_2) = (3,9)\)

So, we have:

\(m = \frac{9 - (-1)}{3- (-2)}\)

\(m = \frac{9+1}{3+2}\)

\(m = \frac{10}{5}\)

\(m = 2\)

The equation is then calculated using:

\(y - y_1 = m(x - x_1)\)

\(y - (-1) =2(x - (-2))\)

\(y - (-1) =2(x +2)\)

\(y +1 =2(x +2)\)

Open bracket

\(y +1 =2x + 4\)

Subtract 1 from both sides

\(y +1-1 =2x + 4-1\)

\(y =2x + 3\)

Answer:

slope = -5/2

Step-by-step explanation:

Ax + By = C

By = -Ax + C

y = (-Ax + C)/B

slope = -A/B = -5/2

Answer:

45 premium tickets were sold

Step-by-step explanation:

p = premium

d = deluxe

r = regular

p+d+r = 273

6p+4d + 2r = 836

118+d = r

Replace r with 118+d

p+d+118+d = 273

p +2d = 273-118

p+2d = 155

6p+4d + 2(118+d) = 836

6p+4d + 236+2d = 836

6p +6d = 836-236

6p + 6d = 600

Divide by 6

p+d = 100

d = 100-p

Replace d in p +2d= 155

p +2(100-p) = 155

p+200-2p = 155

-p = 155-200

-p =-45

p =45

45 premium tickets were sold

Answer:

Step-by-step explanation

We get three linear equations from the information given, where

p= number of premium tickets

d = number of deluxe tickets

r = number of regular tickets:

\(\left \{ {{p+d+r=273} \atop \\{6p+4d+2r=836} \right.\)

and the applying third r=118+d, we get

\(\left \{ {p+d+118+d=273} \atop {6p+4d+2d+236=836}} \right.\)

\(\left \{ {{p+2d=115} \atop {6p+6d=600}} \right.\)

Now we get from the upper one

p=115-2d

solving the another equation gives us

6*115-12d+6d=600,

hence d=15

and by replacing

p=115-2*15=85.

85 premium tickets were sold

Answer:

21

Step-by-step explanation:

3 times 7 equals 21 and you cant make 21 with 6

(please mark me brainliest if you get it correct)

The consumer surplus is approximately $145.83.

To find the consumer surplus, we first need to find the demand function's inverse, which gives us the willingness to pay for each unit of the product. The demand function is:

D(x) = √(739 - 3x)

Setting D(x) equal to the equilibrium price of $25, we get:

25 = √(739 - 3x)

Squaring both sides, we get:

625 = 739 - 3x

Solving for x, we get:

So at a price of $25 per unit, the consumer is willing to buy 38 units per month.

Now we can calculate the consumer's surplus.

The consumer\(x = (739 - 625) / 3 = 38\) surplus is the difference between the total amount that consumers are willing to pay for a certain quantity of a good and the total amount they actually pay. In this case, the consumer's surplus can be calculated as:

\(CS = \int_0^{38} [D(x) - 25] dx\)

where D(x) is the demand function, and the integral is taken over the range of 0 to 38, which represents the quantity demanded at a price of $25 per unit.

Evaluating this integral, we get:

\(CS = \int_0^{38} [\sqrt{(739 - 3x)} - 25] dx\\\\= [1/6 (739 - 3x)^{(3/2)} - 25x]_0^{38}\\\\= \$ 145.83\)

Therefore, the consumer surplus is approximately $145.83.

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The correct value of Jessica's new net salary will be $225.

To calculate Jessica's new net salary after a 5% raise, we need to first determine Sarah's gross salary. We know that Sarah's net salary is $212.50, and 15% of her gross salary is withheld each week.

Let's denote Sarah's gross salary as "G." We can set up the following equation:

G - 15% of G = $212.50

Simplifying the equation, we have:

G - 0.15G = $212.50

0.85G = $212.50

G = $212.50 / 0.85

G ≈ $250

Sarah's gross salary is approximately $250.

Now, to find Jessica's new net salary after a 5% raise, we can calculate 5% of Sarah's gross salary and subtract the withheld amount:

Jessica's net salary = Sarah's gross salary + 5% of Sarah's gross salary - 15% of Sarah's gross salary

Jessica's net salary = $250 + 0.05 * $250 - 0.15 * $250

Jessica's net salary = $250 + $12.50 - $37.50

Jessica's net salary = $225

Therefore, Jessica's new net salary will be $225.

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