A cake recipe asked for 4⁄6 of a cup of oil, but Brad accidentally poured 5⁄6 of a cup of oil into the batter. How much extra oil did Brad pour into the batter?

Answer:

Dad made 90 steps during that period.

Step-by-step explanation:

Let x,y,z be the steps made by dad,Anna and Todd.

Given that while dad made 3 steps, Anna made 5 steps.

That is [tex]\frac{x}{y}= \frac{3}{5}[/tex]

           [tex]y=\frac{5x}{3}[/tex]

And for every 3 steps Anna made, Todd made 5 steps.

That is [tex]\frac{y}{z}= \frac{3}{5}[/tex]

            [tex]z=\frac{5y}{3} =\frac{5(\frac{5x}{3}) }{3} =\frac{25x}{9}[/tex]

It is also given that total number of steps made by Anna and Todd is 400.

That is y+z=400

let us plugin y and z in terms of x.

       [tex]\frac{5x}{3} +\frac{25x}{9} =400[/tex]

        [tex]\frac{15x}{9} +\frac{25x}{9}=400[/tex]

       [tex]\frac{40x}{9}=400[/tex]

       [tex]x=400X\frac{9}{40} =90steps[/tex]

Hence Dad made 90 steps during that period.

note that 5π /4 is in the third quadrant where the cos is negative

the related acute angle to 5π /4 is π/4, thus

cos( 5π /4 ) = - cos (π/4 ) = - √2/2

We can also evaluate using the addition formula for cosine

• cos (x + y ) = cosxcosy - sinxsiny

note that 5π /4 = (π + π/4 )

cos(5π /4 ) = cos (π + π/4 )

= cos(π)cos(π/4) - sin(π)sin(π/4)

= - 1 √2/2 - 0 = - √2/2

the answer would be 103 students

... f(x) = 4^x

... x for f(x) = 64

Rewrite 64 as a power of 4, then equate exponents.

... 64 = 4^x

... 4^3 = 4^x

... 3 = x

The store sells 64 caps in month 3.

By rounding to the nearest whole numbers and estimating, it is confirmed that Ruben's answer of 96.52 ÷ 12.7 equals 7.6 is indeed reasonable.

To assess if Ruben's answer that 96.52 ÷ 12.7 equals 7.6 is reasonable, let's consider the magnitude of the numbers involved. Firstly, we can simplify our estimation by rounding the numbers to the nearest whole digits, which gives us approximately 97 ÷ 13. By using division, we see that 13 goes into 97 about 7 times with some remainder, since 13 x 7 is 91, which is close to 97.

Now, 7.6 is indeed close to our estimation, so we can determine that Ruben's answer is within a reasonable range. Thus, the correct response to whether Ruben's calculation is reasonable would be:

D. Yes, Ruben's answer is reasonable.

James will end up with his original t cars and half of (t+13) cars, so will have ...

... t + (t+13/2) = (3t +13)/2 . . . . cars James has after Paul's gift

To find out how many cars James will have after Paul gives him half of his cars, we need to determine the numbers of cars James and Paul have. We then calculate half of Paul's cars and add that to James' original number of cars.

To find out how many cars James will have after Paul gives him half of his cars, we need to first determine how many cars Paul has in total.

We know that Paul has 13 more cars than James, so we can set up an equation:

Paul's cars = James' cars + 13. Next, we need to find out how many cars Paul will give to James, which is half of Paul's cars.

We can set up another equation: cars Paul gives to James = Paul's cars ÷ 2.

Finally, to find out how many cars James will have after Paul gives him half of his cars, we simply add the number of cars Paul gives to James to James' original number of cars.

Let's say James has 5 toy cars. Paul has 13 more, so Paul has 5 + 13 = 18 toy cars.

Half of Paul's cars is 18 ÷ 2 = 9 toy cars. James will have 5 + 9 = 14 toy cars after Paul gives him half of his cars.

y=4/3x+4

are you in k12 i tookthat test already

y = [tex]\frac{4}{3}[/tex] x + 4

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4 ) and (x₂, y₂ ) = (-3, 0 ) ← 2 points on line

m = [tex]\frac{x0-4}{-3-0}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]

the line crosses the y-axis at (0, 4 ) → c = 4

y = [tex]\frac{4}{3}[/tex] x + 4 ← in slope-intercept form

3(x + 12) does not, and never will, equal 3(x + 5)

We can solve the equation to verify.

3(x + 12) = 3(x + 5)

Distributive property.

3x + 36 = 3x + 15

Subtract 15 from both sides.

3x + 21 = 3x

Cancel like terms.

21 = 0 × this is incorrect.

D

Substitute the coordinates of the given points into the inequalities and if both are true then the point is a solution to the system.

A(1, 1 ) : 4 + 2 = 6 and 1 - 1 = 0 not a solution

B(8, 4 ) : 32 + 8 = 40 and 8 - 4  = - 4 not a solution

C(3, 9 ) : 12 + 18 = 30 and 3 - 9 = - 6 not a solution

D(9, 1 ) : 36 + 2 = 38 and 9 - 1 = 8 is a solution

the point (9, 1 ) is the only point that makes both inequalities true

solution = (4, - 2 )

substitute x = 4 into - y = [tex]\frac{1}{2}[/tex] x

- y = [tex]\frac{1}{2}[/tex] × 4 = 2 ( multiply both sides by - 1 )

y = - 2

solution is ( 4, - 2 )

Answer:

I think it is (4,-2)

Answer:

Matlab capacity to ascertain the surface territory of an inflatable  

work surfaceArea = surfaceBalloon(Volume,M)  

Step-by-step explanation:

% Matlab capacity to ascertain the surface territory of an inflatable  

work surfaceArea = surfaceBalloon(Volume,M)  

% compute R  

cubeOfR = 3 * Volume * ones(1,length(M));  

cubeOfR = cubeOfR ./(pi * (M+2));  

R = power(cubeOfR,1/3);  

% compute surface zone  

power1 = power(M,2);  

power1 = 1+ power1;  

power1 = power(power1,1/2);  

power1 = 2 + power1;  

surfaceArea = pi .* power(R,2) .* power1;  

end  

% End of capacity  

% Matlab content to utilize work surfaceBalloon to locate the surface zone of  

% expand  

clc;  

V = 14000;  

M = (0:10);  

surfaceArea = surfaceBalloon(V,M);  

plot(M,surfaceArea);  

xlabel('M');  

ylabel('Surface Area m^2');  

ylim([2900 5000]);  

title('M v/s Surface Area of an inflatable');  

saveas(gcf,'surfaceAreaPlot','png'); % spare the chart  

% end of primary content

Answer:

radius = ((3*Volume) ./ ((2+M).*pi)).^(1/3);

surfaceArea = pi .* radius.^2 .* (2+sqrt(1+M.^2));

Step-by-step explanation:

The OP didn't include this part, but the original problem has the equations written for you in the header. Here they are again:

A = [tex]\pi R^{2}[/tex](2 + [tex]\sqrt{1+M^{2} }[/tex])

V = [tex]\pi R^{3} (2+M)/3[/tex]  where M = H/R

The problem is asking for the surface area of the balloon, but the only values that the user inputs are volume and M. We need to solve for the radius before we can complete the code. So, we can solve for R in one equation and plug it into the second equation.

Let's adapt the given equation V = [tex]\pi R^{3} (2+M)/3[/tex] and solve for R to get the equation for the radius.

V = [tex]\pi R^{3} (2+M)/3[/tex]

3*V = [tex]\pi R^{3} (2+M)[/tex]

[tex]\frac{3*V}{\pi (2+M)} = R^{3}[/tex]

R = [tex](\frac{3*V}{\pi (2+M)})^{1/3}[/tex]

Now, let's convert the equation for R to MATLAB code. Because we are using arrays, each operational symbol must be preceded by a "." unless it is a + or -.

R = [tex](\frac{3*V}{\pi (2+M)})^{1/3}[/tex]

radius = ((3*Volume) ./ ((2+M).*pi)).^(1/3);

Okay, so the hard part is done. The second line of code is easy: all you have to do is transform the given equation for surface area into MATLAB code while using the variable we named "radius" in the last step. Again, because we are performing operations with arrays, use "." in front of all operational symbols (except + and -).

A = [tex]\pi R^{2}[/tex](2 + [tex]\sqrt{1+M^{2} }[/tex])

surfaceArea = pi .* radius.^2 .* (2+sqrt(1+M.^2));

Putting it all together, your answer should be

radius = ((3*Volume) ./ ((2+M).*pi)).^(1/3);

surfaceArea = pi .* radius.^2 .* (2+sqrt(1+M.^2));

(c)

substitute x = 350 into the equation for y

y = [tex]\frac{104000}{350}[/tex] + 235 ≈ 532 000

Final answer:

To find the size of the oil tanker that can be built for $350 per ton, solve the equation 350 = 104,000/x + 235 for x, yielding approximately 904 thousand tons. None of the multiple-choice options match this result.

Explanation:

The student is asked to calculate the size of an oil tanker that can be built for $350 per ton using the given model for cost per ton, which is y = 104,000/x + 235, where y is the cost in dollars per ton, and x is the tons in thousands. To find x, set the equation equal to 350 and solve for x.

350 = 104,000/x + 235

Subtract 235 from both sides to get:

350 - 235 = 104,000/x

115 = 104,000/x

To solve for x, multiply both sides by x and then divide both sides by 115:

x = 104,000 / 115

x ≈ 904.35

Since x is in thousands of tons, the size of the oil tanker that can be built for $350 per ton is approximately 904 thousand tons. However, this answer does not match any of the options provided in the multiple choice (a. 62 thousand tons, b. 6 thousand tons, c. 532 thousand tons, d. 178 thousand tons), suggesting there might be an error in the question or the offered choices.

Saturn takes 17.6 more years than Jupiter, so 17.6 + 11.9 will get you how long Saturn will take to orbit the sun, which would give you 29.5 years.

The time it takes Saturn to orbit the sun can be calculated by adding Jupiter's orbit time to the additional time Saturn takes after Jupiter. Saturn takes approximately 29.5 years to complete one orbit around the sun.

To find out how long it takes Saturn to orbit the sun, we know that Jupiter takes 11.9 years and Saturn takes 17.6 more years than Jupiter. So, Saturn takes 11.9 + 17.6 = 29.5 years to orbit the sun.

Answer:

  d║e, c║f

Step-by-step explanation:

The acute angle of intersection of e with t is ...

  180° - 112° = 68°

This angle is the same as the acute angle at d, so d and e are parallel.

The acute angle of intersection of c with t is ...

  180° -114° = 66°

This angle is the same as the acute angle at f, so c and f are parallel.

  d║e, c║f

_____

Note that the acute angles at the intersections with t are all "corresponding". That is why their congruence means the associated lines are parallel.

Answer:

Option C. and D. are correct

Step-by-step explanation:

c//f

d//e

good luck:)

Try this option (note, this is not the shortest way!), the additional elements are shown by green colour.

Answers: ∠1=∠2=50°; ∠3=82°

since y varies directly with y then

y = kx ( k is the constant of variation )

to find k use y = 3 when x = 2

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{3}{2}[/tex]

equation is : y = [tex]\frac{3}{2}[/tex] x

When x = 1 then y = [tex]\frac{3}{2}[/tex] × 1 = [tex]\frac{3}{2}[/tex]

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that}~~ \begin{cases} y=3\\ x=2 \end{cases}\implies 3=k2\implies \cfrac{3}{2}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{3}{2}x} \\\\\\ \textit{when x = 1, what is \underline{y}?}\qquad y=\cfrac{3}{2}(1)\implies y=\cfrac{3}{2}[/tex]

For this case we have the following data:

Polynomial function of grade 5

Given roots: -2, 2,[tex]4 + i[/tex]

Having an imaginary root given by [tex]a + bi[/tex], the other root, in the same imaginary way, must be given by its complex conjugate, that is, [tex]a-bi[/tex].

In this way, the fourth root is given by:

[tex]4-i[/tex]

Since the polynomial function is grade 5, it must have 5 roots. Thus, the fifth root must be given by a real number.

Thus, the roots of the polynomial function are given by: three real roots and two imaginary roots.

Answer:

Option D

f(x) has 3 real roots x = -2, x = 2 and x = 4

complex roots occur in conjugate pairs

x = i is a root then x = - i is a root

there are therefore 2 imaginary roots

f(x) has 3 real roots and 2 imaginary roots

Hey there!

Beth has seven cents or $0.07

Hope this helps!

Always remember you are a Work Of Art!

-Nicole :) <3

There are 100 penny's  in a dollar. So 7/100 would mean the 7 is represented by penny's, therefor beth has 7 cents.

-Steel jelly

Mila reads at a rate of 2 paragraphs per minute. After reading for 3 minutes, she had read a total of 6 paragraphs.

This situation can be represented with a linear equation written in point-slope form,  

Let 'x' represents the number of minutes and,

y represents the number of paragraphs.  

In one minute Mila reads 2 paragraphs .

So, y=2x

Let x=1 then y=2

x=2 then y =4

Here slope of equation is 2

Let( x1, y1) and (x2,y2) be the two point the equation y=2x the ,

we can write, (y2 - y1) = m(x2 - x1)

or (y2 - y1) = 2(x2 - x1)

Answer:

(3,6)

Step-by-step explanation:

Given that Mila reads at a rate of 2 paragraphs per minute. After reading for 3 minutes, she had read a total of 6 paragraphs.

This situation can be represented with a linear equation written in slope-intercept form,  as

[tex]y=2x[/tex]

where 'x' represents the number of minutes and,

y represents the number of paragraphs.  

Since y intercept is 0 i.e. 0 paras in 0 minutes we have the equation as

[tex]y=2x[/tex]

Since no of minutes or paragraphs cannot take negative values this line is defined only in the I quadrant where both x and y are positive

Out of the points given as follows:

(3,6) (2,3) (-3,6) or (-2,6) ,

we can remove last two since they have negative x which is impossible.

Consider  (3,6) (2,3)

Out of these only I point  (3,6) satisfies  [tex]y=2x[/tex] and second point   (2,3) does not satisfy

[tex]y=2x[/tex]

Hence answer is (3,6)

Mo Says that, 0.23567 is not a Rational Number.

Mo is Incorrect.

⇒She is Incorrect, because Decimal expansion of rational number is either terminating or Non terminating Repeating decimal.

As , 0.23567 is terminating decimal .So, it is a Rational Number.

In a scatter plot with two sets of data, the independent variable is the variable that was controlled by the researchers and is represented on the x-axis.

In a scatter plot with two sets of data, the independent variable is the variable that was controlled by the researchers. The independent variable is typically represented on the x-axis of a scatter plot. It is the variable that is manipulated or changed to observe its effect on the dependent variable, which is plotted on the y-axis.

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The naming of similar triangles has corresponding vertices in the same order in the name. That means segment QS corresponds to segment AC. We note that QS = 6 cm is 1/10 the length of AC = 60 cm.

Side AB is given as 50 cm, so the corresponding side QR will be 1/10 that value.

... QR = 5 cm

The 2-point form of the equation of a line can be written as ...

... y = (y2-y1)/(x2-x1)·(x -x1) +y1

For your points, this is ...

... y = (1-5)/(3-6)·(x -6) +5

... y = (4/3)(x -6) +5

It can also be written as

... y -5 = (4/3)(x -6)

Answer: The required equation is y= 4x/3 - 3

Step-by-step explanation:

Given points (6,5) and (3,1)

Two point slope equation is  given as

[tex]y - y1 = \frac{y2-y1}{x2-x1}(x-x1)[/tex]

where (x1, y1) and (x2,y2) are the points respectively

∴ [tex]y-5 =\frac{1-5}{3-6}(x-6)[/tex]

[tex]y-5 =\frac{-4}{-3} (x- 6)[/tex]

[tex]y -5 =\frac{4}{3} (x-6)[/tex]

[tex]y - 5 =\frac{4}{3}x - 8[/tex]

[tex]y = 5 +\frac{4}{3} x - 8[/tex]

[tex]y = \frac{4}{3}x -3[/tex]

It can also be written as

[tex]y -5 =\frac{4}{3}(x -6)[/tex]

Points C and D are equidistant from points A and B, so Dominic's square could be ACBD. To draw that square, his next move should be ...

... Use a straightedge to join points C and A, C and B, D and A, and D and B

(5x - 2 - g(x))(x)

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

(5x - 2 - (2x + 1) : 3x - 3

= 3x - 3

The equipment elevator descends to 176 feet below the surface while the miners' elevator descends to 210 feet below the surface after 14 seconds. Therefore, the miners' elevator is deeper.

To solve this, we first need to determine the position relative to the surface of both elevators in the gold mine. As the equipment elevator begins to descend first and moves at a speed of 4 feet per second, it had already traveled 30 (seconds) * 4 (feet per second) = 120 feet downward before the miners' elevator begins to descend.

Then, an additional 14 seconds pass. In these 14 seconds, the equipment elevator will descend a further 14 * 4 = 56 feet. Therefore, the equipment elevator is 120 + 56 = 176 feet below the surface.

The miners' elevator descends at 15 feet per second, and it has been moving for 14 seconds. Therefore, it is 15 * 14 = 210 feet below the surface. At this point in time, the miners' elevator is deeper than the equipment elevator by 210 - 176 = 34 feet.

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The equipment elevator will be at a depth of 176 feet, while the miners' elevator will be deeper at a depth of 210 feet from the surface after the given time. The miners' elevator is deeper.

The position of each elevator relative to the surface after another 14 seconds can be found by first determining the distance each has traveled. The equipment elevator descends at 4 feet per second, and it had already been descending for 30 seconds before the miners' elevator started. Therefore, by the time the miners' elevator begins to descend, the equipment elevator will have descended 4 feet/second * 30 seconds = 120 feet.

From that point, after another 14 seconds, the equipment elevator descends an additional 4 feet/second * 14 seconds = 56 feet. Thus, its total descent is 120 feet + 56 feet = 176 feet from the surface.

On the other hand, once the miners' elevator starts, it descends at a rate of 15 feet per second. After 14 seconds, the miners' elevator will have descended 15 feet/second * 14 seconds = 210 feet.

Comparing both distances, the elevator for the miners is at 210 feet while the equipment elevator is at 176 feet from the surface. So, the miners' elevator is deeper.

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