Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can
be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the
constraints on the values of x and y?
O y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
O y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to
5.5.
O y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5.
O y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to
5.5.

The system of three equations and three unknowns to write the equation are: 5t²+80t+6990.

Given:

Elevation              Travel time

6990 feet                    0 hours

8290 feet                    10 hours

10875 feet                   21 hours

Using this formula

y(t)=at²+bt+c

Where:

At:

t=0; y=6990

6990=a(0)²+b(0)+c

c=6990 Equation 1

At:

t=10; y=8290

8290=a(10)²+b(10)+6990

1300=100a+10b Equation 2

At:
t=21; y=10,875

10875=a(21)²+b(21)+6990

3885=441a+21b Equation 3

Using equation 2 and 3 to solve for a and bc

1300=100a+10b

1300-10b/100=a

13-0.1b=a

Plug into equation 3

3885=441(13-0.1b)+21b

3885=5733-14.1b+21b

b=80

a=13-0.1(80)

a=13-8

a=5

Hence:

Write the Equation by plugging a,b and c

y(t)=5t²+80t+6990

Therefore the system of three equations and three unknowns to write the equation are: 5t²+80t+6990.

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Answer:

i think it is D but I am not for shore

Answer:

26π cm

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = πd ( d is the diameter )

   = π × 26

   = 26π cm

▶︎◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◇◆◀︎

[tex]Hello[/tex] [tex]There![/tex]

 We are looking for the circumference of the circle.

It's not hard, I promise! I will take you through a few steps, and we'll find the answer.

Are you ready? Then let's begin...:)

[tex]Procedure:[/tex]

First, we need a formula for the circumference. We can't find the circumference without a formula!

· Luckily, there is a formula for the circumference:

⇒ [tex]C=\pi d}[/tex]

Whoa. What's that?!

No worries, I'll clarify everything in a moment. :)

We are looking for the circumference.

In this formula, what stands for the circumference?

That's right, [tex]C[/tex].

Now, what is this: [tex]\pi[/tex]?

This letter stands for pi - a constant in maths that comes in handy when we're searching for the circumference of a circle (or area).

It has an infinite number of digits after the decimal point, and these digits never repeat!

You might be thinking, "Oh no! Are we really going to use that infinite number?!"

The answer is "No". Mostly, we use 3.14 for [tex]\pi[/tex], because these are the first three digits of pi, but since we aren't asked to use 3.14 for pi, we just press the [tex]\boxed{\pi }[/tex] button on our calculator.

Whew!

And then last but not least, we see "d". This isn't a constant, this is the diameter.

Checking our provided information, we see that the diameter is 26 cm.

Now, we substitute 26 for d:

[tex]\bold{C=\pi (26)}[/tex]

[tex]\bold{C=\pi *26}[/tex]

And now all we have to do is type these numbers into our calculator, and find the answer:

[tex]\bold{C\approx81.7\:cm}[/tex]

Hooray! We've found the circumference!

But wait - why isn't 81.7 an option?

Because what we need to do is write it in terms of pi, which is even easier, because we just substitute 26 for d:

[tex]\bold{C=\pi *26}[/tex]  

➢ Rearrange the order of the terms:

[tex]\bold{C=26\pi \:cm}[/tex]

▲ Circumference

Now there's another thing - why are all four options with units squared?

Circumference isn't measured in units squared, the area is!

▶︎ Incase you need the area, here it is:

[tex]\bold{A=\pi r^{2}}[/tex]

A=Area (what we're looking for)

[tex]\pi[/tex] = pi

Here we have a new variable - it's r, which is the radius.

Do you see that [tex]^2[/tex] next to r? It means that r is squared, or multiplied by itself.

You might be thinking, "But we don't have the radius!"

If we have the diameter, finding the radius is a piece of cake, because we divide the diameter by 2:

[tex]\bold{26\div2}[/tex]

[tex]\bold{13}[/tex]

Now we substitute 13 for r and evaluate:

⇒ [tex]\bold{A=\pi (13)^{2}}[/tex]

13 times itself is 169:

⇒ [tex]\bold{A=169\pi \:cm^{2}}[/tex]

Whew! We're finally done!

[tex]Greetings![/tex]

--

Answer:

D : 66

Step-by-step explanation:

separate the composite figure into 3 different shapes then multiple then find the area of them all. after this just add them and you're good to go

also to get the area of a triangle you gotta add both sides then divide by 2.

Answer:

0.7 miles

1.4 miles

Step-by-step explanation:

Distance of the first bench from the path = 1/3 x 2.1 miles = 0.7 miles

Distance of the second bench from the path = 2/3 x 2.1 miles = 1.4 miles

Step-by-step explanation:

if you could solve 3a and 3b, you can also solve 3c. it is the same principle.

x-intercepts means y = 0.

remember, a square root has always 2 results : a positive and a negative one.

3c

0 = -(x - 3)² + 25

(x - 3)² = 25

x - 3 = ±5

x1 = +5 + 3 = 8

x2 = -5 + 3 = -2

3a

0 = (x + 1)² - 4

4 = (x + 1)²

±2 = x + 1

x1 = +2 - 1 = 1

x2 = -2 - 1 = -3

3b

0 = (x + 2)² - 9

9 = (x + 2)²

±3 = x + 2

x1 = +3 - 2 = 1

x2 = -3 - 2 = -5

The ratio of the sides of the triangles ΔABC and ΔDEF are constant that is 1/2. Then the triangles ΔABC and ΔDEF are similar triangles.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The triangles are given below.

The ratio of the sides of the triangles ΔABC and ΔDEF will be

AB / DE = BC / EF = CA / FD

2 / 4 = 3 / 6 = 3.5 / 7

1 / 2 = 1 / 2 = 1 / 2

The ratio of the sides of the triangles ΔABC and ΔDEF are constant that is 1/2. Then the triangles ΔABC and ΔDEF are similar triangles.

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Answer: attached a picture

The fourth clock shows the time 25 minutes after 4:00.

The correct option is IV.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

There are four clocks.

To watch the time on the clock:

The small arrow line shows the time in hours.

And the large arrow shows the time in minutes.

At the first clock;

The time is 11:20.

At the second clock;

The time is 11:40.

At the third clock;

The time is 12:20.

At the fourth clock;

The time is 4:25.

25 minutes after 4:00 means the large arrow will be pointing towards 5.

Because 25 = 5 x 5.

Therefore, all the times on the clocks are given above.

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The complete question;

From the given choices,

which clock shows 25 minutes after 4:00?

The options are given in the attached image.

Answer:

16

Step-by-step explanation:

The two co-captians can be chosen in 21 different ways.

If the two co-capitans are equivalent, then we need to find combinations.

So we want to find how many combinations of 2 elements we can make out of a set of 7 elements.

This is given by:

[tex]C(7, 2) = \frac{7!}{(7 - 2)!*2!} = \frac{7*6}{2} = 21[/tex]

So the two co-captians can be chosen in 21 different ways.

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Answer:

D is not true.

Step-by-step explanation:

[tex] |4.5| = 4.5[/tex]

[tex] | - 45| = 45[/tex]

[tex]4.5 \leqslant 45[/tex]

Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2

(h, k) = center of the circle

r = radius of the circle

Center = (2, 0)

Radius = 7

Equation: (x - 2)^2 + (y - 0)^2 = 49

Answer: (x - 2)^2 + y^2 = 49

Hope this helps!

The total pounds of science books that sanya carried is; 6⁷/₈ pounds

From the attached Line Plot, we can see the book weights.

Now, we are told that Sanya carried all the books weighing 2¹/₄ pounds and 2³/₈ pounds.

From the line plot we see that;

Number of books weighing 2¹/₄ pounds are 2 books

Number of books weighing 2³/₈ pounds is 1 book

Thus;

Total weight of books carried by Sanya = 2(2¹/₄) + 1(2³/₈)

Total weight = 4¹/₂ + 2³/₈

Total Weight = 6⁷/₈ pounds

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Take two points

Slope

Parallel lines so slopes are equal

Only y intercept will vary

So both lines have y intercept at -3 and -1 respectively

The equations

Put (0,0) on first one

On second one

So as lines are dashed symbols remain >

The inequalities are

Answer:

the answer is 12

Step-by-step explanation:

[tex] \frac{756}{63} \\ = 12[/tex]

The quotient of 874 and 23 determined using an area model is 38.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have:

= 874 ÷ 23

= (800 + 74 + 4) ÷ 23

We can get the answer by using the area model:

If divide 874 with 23 we get 184 as a remainder and 030 as a quotient

Further, if  we divide 184 with 23 we get 0 as a remainder and 008

874 ÷ 23 = 030 + 008 = 38

Thus, the quotient of 874 and 23 determined using an area model is 38.

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Answer:

88km

Step-by-step explanation:

If a car travels 40 km in 1 hour, then that same car would travel 40*2.2 km in 2.2 hours.

So, the car travelled 88km in 2.2 hours

Remember that speed is a rate!

Answer:

speed=distance/travel time

distance=2*40+60*3=80+180=260 km

travel time=2+3=5 hrs

Average speed during entire journey=260/5=52 km/h

The two-way table that shows the joint and the marginal relative frequencies is:

            Aerobic          Anaerobic     Total

Male       0.48              0.63               0.55

Female   0.52             0.37               0.45

Total         1                    1                      1

The table is given as:

            Aerobic     Anaerobic

Male       88               104

Female  96                62

The column total are:

Aerobic = 88 + 96 = 184

Anaerobic = 104+ 62 = 166

So, we have:

            Aerobic                        Anaerobic

Male       88/184 = 0.48              104/166 = 0.63

Female  96/184 =  0.52             62/166 = 0.37

The total count of the table is

Total = 184 + 166 = 350

So, we have:

            Aerobic          Anaerobic     Total

Male       0.48              0.63              (88 + 104)/350 = 0.55

Female   0.52             0.37               (96 + 62)/350 = 0.45

Hence, the two-way table that shows the joint and the marginal relative frequencies is:

            Aerobic          Anaerobic     Total

Male       0.48              0.63               0.55

Female   0.52             0.37               0.45

Total         1                    1                      1

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Based on the number of males and females doing aerobic and anaerobic respiration, the relative and marginal frequencies can be shown as:

                           Aerobic                     Anaerobic                        Total

Male                     47.8%                          62.7%                            54.9%

Female                 52.2%                          37.3%                            45.1%

                            100%                             100%                             100%

The frequencies for males are:

Aerobic = 88 / (88 + 96)                                    Anaerobic = 104 / (104 + 62)

= 47.8%                                                                                 = 62.7%

For females:                      

Aerobic = 100% - 47.8%                                    Anaerobic = 100 - 62.7%

= 52.2%                                                                                 = 37.3%

Total males frequency:                                Total females
= (88 + 104) / (88 + 104 + 96 + 62)               = 100% - 54.9%

= 54.9%                                                          = 45.1%

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Answer:

Jenny has worked out the area of the whole circle using the formula π × r² where r is the radius length. She has assumed π is 3.14 which leads to her working of 3.14 × 10² = 314 units². She has to divide the total area by 4 to calculate the sector area.

Let's check

Area of sector

             - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

         Find the slope of the line that passes through (6, 9) and (9, 5).

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond[/tex]

[tex]\boxed{\\\begin{minipage}{3cm}\xrightarrow {slope\:formula\:below} \\ $\displaystyle\frac{y_2-y_1}{x_2-x_1}$ \\ \end{minipage}}}[/tex]

Substitute 5 for y₂, 9 for y₁, 9 for x₂ and 6 for x₁:-

[tex]\boxed{\frac{5-9}{9-6}}[/tex]

On simplification,

↬ [tex]\boxed{\frac{-4}{3}}[/tex]

   ►So we conclude that the slope of the line is

 ►[tex]\boxed{-\frac{4}{3}}[/tex] ◀︎

              - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]12\sqrt{23 x^{13}}+14\sqrt{23 x^{13}}\\\\=(12+14)\left(\sqrt{23 x^{13}}\right)\\\\=26\left(\sqrt{23 x^{13} }\right)\\\\=26\sqrt{23} \sqrt{x^{13}}\\\\=26\cdot 23^{\tfrac 12} \cdot x^{\tfrac {13}2}[/tex]

Answer:

3

Step-by-step explanation:

Answer:

12% decrease

Step-by-step explanation:

given:

In 2017, a chocolate bar had a mass of 250g.

In 2018, the mass of the chocolate bar was reduced to 220g.

The difference in mass is 250 - 220 = 30g

30 / 250 = 0.12 which is how much out of the 250g

0.12 x 100 = 12

12% decrease in the mass of chocolate bars from 2017 to 2018.

A percentage is a number or ratio expressed as a fraction of 100.

According to the question, it is given that

The mass chocolate bar had a mass of 250g in 2017

The mass of the chocolate bar was reduced to 220g in 2018

We have to find the percentage decrease in the mass of chocolate bars from 2017 to 2018.

Percentage decrease in the mass of chocolate bars from 2017 to 2018

=(250-220)/250×100

Percentage decrease in the mass of chocolate bars from 2017 to 2018

=30/250×100

=0.12×100

=12%

Therefore 12% decrease in the mass of chocolate bars from 2017 to 2018.

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Step-by-step explanation:

5x - 3y + 4 = 0

we rearrange it to look like this:

y = mx + c

3y = -4 - 5x

we can also write it like this so it rhymes with the formula

3y = -5x - 4

y = -5x - 4 / 3 (the division sign is dividing all the numbers and not only 4 ).

Soo..

y = -5x/3 -4/3

y = mx. + c

so

m = -5/3

c = -4/3.

Hope this helps.

Good luck ✅.

[tex]\rule{200}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

        Work out m and c for the line 5x-3y+4=0.

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

We can't determine the slope (m) and the y-intercept (c) yet, so we need

to convert this equation into slope-intercept form [tex]\bold{y=mx+c}[/tex].

[tex]\dagger[/tex] First, subtract 5x and 4 on both sides:-

[tex]\dagger[/tex] Next, divide by -3 on both sides:-

[tex]\bigstar[/tex] A negative divided by a negative is a positive.

[tex]\dagger\dagger[/tex] Now finding the slope is a piece of cake; it's just the number next to x:-

And the y-intercept is:-

[tex]\rule{300}{1}[/tex]

Answer:

302cm³

Step-by-step explanation:

The formula for the volume of a hemisphere is [tex]\frac{\frac{4}{3} \pi r^{3}} {2}[/tex] (volume of a sphere over 2)

Plugging in 4 for r we get the answer of [tex]\frac{256}{6}\pi[/tex]

Next we have to find the height of cone. We can get this by subtracting the radius of the hemisphere from the height of the solid. (14-4=10)

We can now find the volume of the cone using the formula [tex]\frac{1}{3} \pi r^{2} h[/tex]

Plugging in 4 for r and 10 for h we get the answer [tex]53 \frac{1}{3} \pi[/tex]

Now we can add our 2 volumes to get the volume of the solid which is 302 in decimal form (3 significant figures)

That is the answer

- Kan Academy Advance

Answer:

13r+10

Step-by-step explanation:

1. Combine Like Terms

(2r+11r)+(7+3)

13r+10

Answer:

13r+10

Step-by-step explanation:

2r+7+11r+3

collect like terms

2r+11r+7+3

13r+10