a salad dressing is made by mixing yoghurt and mayonnaise in the ratio 3 : 5
karolina makes 800 ml of the salad dressing
how much yoghurt does she use?
give your answer in mililetres (ml)

The interest when the classmate is calculating the amount in a savings account after 10 years is $2600.

From the information, the classmate is calculating the amount in a savings account after 10 years and the deposit is $13,000 and the annual simple interest rate is 2%.

It should be noted that interest is calculated as:

= (Principal × Rate × Time) / 100

= ($13000 × 2 × 10) / 100

= $2600

The simple interest is $2600.

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Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.

Given:

At the local dairy farm, kareem buys a 32-oz container of yogurt for $2. 56. Jonah buys a 6-oz container of yogurt for $0. 48.

y varies directly as x :

y = kx

k = constant of proportionality

y = 2.56 and x = 32

y = kx

k = y/x

= 2.56/32

k = 0.08

substitute k we get

y = 0.08x.

so x and y are directly proportional.

Therefore Yes, the cost y in dollars and the amount of yogurt x are proportional the equation is y = 0.08x.

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The equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)

The first point = (3, 5)

The second point = (8, 10)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (10-5) / (8-3)
= 5 /5

= 1

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope of the line

Consider the point (3, 5)

Substitute the values in the equation

y-5 = 1(x-3)

Hence, the equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)

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Answer:

x=32 degrees

Step-by-step explanation:

Since the triangle is equilateral, each angle is = 60 degrees. This means that 2x-4=60

=) 2x=64

=) x=32

The measure of each angle of the triangle are 35°, 35°, 110°.

What is an isosceles triangle?

Let's Base angle =x°

Vertex angle = 5° +3x°

The sum of measure of angles of triangle are supplementary.

i.e., Sum of triangle = 180°

So,

x° + x° + 5° + 3x° =180°

5x° + 5° = 180°

5x° = 175°

x° = 175° /5°

 x = 35°

Base angle = 35°

Vertex angle = 5°+ 3x°

                      = 5° + 3×35°

                      = 5° +105°

Vertex angle = 110°

Hence, the measure of each angle of the triangle are 35°, 35°, 110°.

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Amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

As given in the question,

Amount  invested by Nathan is principal 'P' = $3,500

Interest rate 'r' = 3.5% compounded quarterly

Number of compounding periods per year for given quarterly 'n'  = 4

Time period 't'= 19 years

Amount of money in the account after 19 years when no deposits or withdrawals are done.

Let 'A' be the amount.

Formula used:

 [tex]A = P \times ( 1+ \frac{r}{n} )^{nt}[/tex]

Substitute the value in the formula we get,

A = 3500 × [ 1 + (0.035/4) ]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1 + 0.00875]⁽⁴⁾⁽¹⁹⁾

   =  3500 × [ 1.00875]⁷⁶

   = 6,786.06 (approximately)

   = $6800 (nearest hundred dollars)

Therefore, amount of money in the account after 19 years when no deposits or withdrawals are done for the invested amount $3,500 with 3.5% interest rate compounded quarterly is equal to $6,800(nearest hundred dollars).

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The graph of the given table of data is attached below. And the best scale for this one is x axis 1 cm = 20 units and y axis 1 cm = 1 units. The value of A is 60 and the value of B is 140.

Graph:

Graph can be used to view the table of data in a visual manner for the easy understanding of the given range of data.

Given,

Here we have the table of data that contains the details about the length and their corresponding mass in kg.

Now, we have to plot this data on the graph and then we have to find the best scale suitable for this graph.

Finally, we have to find the value of A and B in the plotted graph.

In order to plot the graph for the given table, we have to input the values on the graphing calculator,

Then we get the graph like the following.

While we lookin into the graph we have identified then the best scale suitable for this graph is

x axis

1 cm = 20 units and

y axis

1 cm = 1 units.

Now, the value of A is 60 and the value of B is 140.

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The equation that describing how x and y are related is y = 2x + 7

From the given table we have to choose two points

The first point = (1, 9)

The second point = (2, 11)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (11-9) / 2 - 1

= 2 / 1

= 2

From the table

At x = 0 the value of y = 7

Therefore the y intercept = 7

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Then,

y = 2x + 7

Hence, the equation that describing how x and y are related is y = 2x + 7

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Answer:

B) [tex]8(2)^{x}[/tex]

Step-by-step explanation:

Using the Product Property of Exponents, we know that two exponents with the same base can have their exponents added together.

Step 1 - Convert 8 to an exponent with a base of 2:

[tex]8 = 2^{3}[/tex]

Step 2 - Use the Product Property of Exponents:

[tex]2^{3} *2^{x}[/tex]

[tex]2^{x+3}[/tex]

Hope this helps and have a great day! :)

Answer:

y=3x-13

Step-by-step explanation:

Since the parallel equations have equal slope.

The equation of line parallel to y=3x+7 will be y=3x+k.

(4,-1) lies in the line so it satisfies the equation amd we get the value of k as -13 and finally we substitute the value of k in the eqn and we finally get the equation as 3x-y-13=0 or you can also write it as y=3x-13

See attached

Triangle DGF is plotted, blue figure.

Find the coordinates of the image using the rule:

The points added to same plot, red figure.

Answer:

D' = (-3, 0)

G' = (0, 3)

F' = (3, -3)

Step-by-step explanation:

Given vertices of the polygon:

To dilate a figure by a given scale factor, multiply the coordinates of the vertices of the figure by the scale factor:

Therefore, the vertices of the image after dilation are:

the factors of 28 are : 1, 2, 4, 7, 14, and 28.

the prime factors of 28 are : 2, 2, and 7.

The measure of all the angles is given below :

angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°

Given, ΔWXY is an equilateral triangle and ΔWZY is an isosceles triangle.

We have to find the measure of all the angles,

As, ΔWXY is an equilateral triangle

so, ∠WXY = ∠XYW = ∠YWX = 60°

Now, let ∠WZY = ∠WYZ = x and ∠ZWY = y

so, on applying angle sum property, we get

2x + y =180°

so, y = 60°

and 2x = 120°

x = 60°

Hence, angle 1 = angle 2 = angle 3 = angle 4 = angle 5 = 60°

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Answer:

g = 204 - 120

Step-by-step explanation:

T - CC = amount of gingersnaps

204 - 120 = 84

Warren and Dirk baked 84 gingersnaps

5x+4 is the simplified form of expression 1/2(13x+5x-6-8x+14)

An expression is combination of variables, numbers and operators.

The given expression is

1/2(13x+5x-6-8x+14)

one by two times of thirteen x plus five times of x minus six minus eight times of x plus fourteen.

In the equation x is the variable

plus, minus and multiply are the operators

1/2(13x+5x-6-8x+14)

1/2(10x+8)

Now apply distributive property

1/2(10x)+1/2(8)

5x+4

Hence 5x+4 is the simplified form of expression 1/2(13x+5x-6-8x+14)

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The value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.

According to the question,

We have the following expression:

(2x − 12) + (1/2xy-10)

Now, the values of x and y are given to be 8 and 2 respectively.

So, we will put these values of x and y in the given expression:

(2*8-12)+(1/2*8*2-10)

First, we will use multiplication:

(16-12)+(8-10)

4+(-2)

(Note that when two integers are of different signs then the integers are subtracted but the sign in the result is of the larger integer.)

4-2

2

Hence, the value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.

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Answer: 14

Explanation:

(3, -20)    (5, 8)

x1   y1       x2   y2

[tex]\frac{y2 - y1}{x2 -x1}[/tex]

[tex]\frac{8 - -20}{5-3}[/tex]  = [tex]\frac{8+20}{5-3} = \frac{28}{2} = 14[/tex]

The simplified expression is x² + 2x - 15.

We are given a mathematical expression. The expression has two terms. The first term is (x + 5) and the second  term is (x - 3). The terms are multiplied by each other to obtain the final expression. Let the resulting expression be represented by the variable "E". The expression has been solved below.

E = (x + 5)(x - 3)

We will use the distributive property.

E = x*(x - 3) + 5*(x - 3)

E = x*x - x*3 + 5*x - 5*3

E = x² - 3x + 5x - 15

E = x² + 2x - 15

Hence, the expanded and simplified form of the given expression is x² + 2x - 15.

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Answer:

D

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

3x - 4 > 5

3x > 9

x > 3

-8x - 19 > 21

-8x > 40

x < -5

This means that we can eliminate the first option, since it includes all real numbers. We can also eliminate the last option since it doesn't include any real numbers.

The middle option is the only graph that includes numbers from -∞ to -5, and 3 to ∞

Answer:

  domain: [0, (6+√39)/4] ≈ [0, 3.06125]

Step-by-step explanation:

You want the realistic domain of a height function h = -16t² +48t + 3.

The given polynomial is defined for all values of t. Since it represents height above the ground, and after the ball is thrown, only function values in the first quadrant are of interest: h ≥ 0, t ≥ 0.

The height becomes zero at t = (6+√39)/4 ≈ 3.061 seconds after the ball is hit. Hence the realistic domain is [0, (6+√39)/4], the interval in which the ball is above ground.

__

Additional comment

We can solve this using the "completing the square" method.

  t^2 -3t = 3/16 . . . . . . divide by -16, add 3/16

  (t -3/2)^2 = 3/16 +9/4 . . . . . add 9/4 to complete the square

  t = 3/2 ± √(39/16) = (6 ± √39)/4 . . . . . . take the square root, add 3/2

Only the positive value of the solution is applicable to this problem. That value is ...

  h = 0 at t = (6 +√39)/4 ≈ 3.061249

unable to see the graph

Answer: 45x + 75y < 2000

Step-by-step explanation:

x = # of desks

45 = cost/desk

y = # of tables

75 = cost/table

2000 = maximum dollar amount that can be spent

inequality:

45x + 75y < 2000

8 hours the driver worked and 240 miles the truck drove.

Assume that the truck traveled y miles per hour. and that the driver worked x hours per day.

The equations describing the provided issue will be

19x + 1.50 y = 512

y = 30x

y = 19 x + 1.50 y = 30 x + 1.50 y

When we enter the second equation into the first one, we get,

19 x + 1.50 (30 x) = 512

19x+ 45x = 512

64x = 512

x = 8

y = 240

The vehicle traveled 240 miles, and the driver put in eight hours' worth of work.

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Answer:

21g-8

Step-by-step explanation:

The product of Goran's score and 21 = 21g, then subtract 8 from that.

Answer:

lo siento no se mucho de este ap

The amount of cell taxes on finn’s purchase is $5.94.

Since Finn wants to buy a sweater for $29.50 and jeans for $42.50, the total cost will be:

= $29.50 + $42.50

= $72

If the sales tax rate is 8.25%, the amount on tax will be:

= Tax rate × Total cost

= 8.25% × $72

= $5.94

The tax is $5.94.

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For the given expression √3, its index form is written as ( 3 )¹/² .

As given in the question,

Given expression is equal to :

√3

Standard form of writing expression in index form is given by:

√  ( square root ) will express the value in index form as 1 / 2 in the exponent.

√x = ( x ) ¹/²

Here x = 3 substitute the value of x in the standard way of index form we have:

Index form of the given expression is written as :

√3

= ( 3 )¹/²

Therefore, for the given expression √3, its index  form is written as ( 3 )¹/² .

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A painter can paint 60 square feet every 1 hour.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A painter can paint 15 square feet every 1/4 hour.

Now,

Since, A painter can paint 15 square feet every 1/4 hour.

Let painter can paint in every 1 hour = x square feet

So, By definition of proportional as;

⇒ 15 / (1/4) = x / 1

Solve for x as;

⇒ 15 × 4 = x

⇒ x = 60 square feet

Thus, A painter can paint 60 square feet every 1 hour.

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