Last month, a cafe had 3200 customers. 600 of them ordered gluten-free meals. What percentage of the customers ordered gluten-free meals?

Answer:

the answer will be 44 I think I hoped I helped if not sorry.

Step-by-step explanation:

Solution :

[tex]$x=f(y) = \frac{e^y + e^{-y}}{2} , \ \ \ \ \ 0 \leq y \leq \ln 2$[/tex]

[tex]$\frac{dx}{dy} = \frac{e^y + e^{-y}}{2}$[/tex]

[tex]$\left(\frac{dx}{dy}\right)^2 = \frac{e^{2y} - 2 + e^{-2y}}{4}$[/tex]

[tex]$1+\left(\frac{dx}{dy}\right)^2 = 1+\frac{e^{2y} - 2 + e^{-2y}}{4} = \frac{e^{2y} + 2 + e^{-2y}}{4}$[/tex]

                  [tex]$ = \left(\frac{e^y + e^{-y}}{2}\right)^2$[/tex]

[tex]$\sqrt{1+\left(\frac{dx}{dy}\right)^2} = \sqrt{\left(\frac{e^y + e^{-y}}{2}\right)^2}=\frac{e^y + e^{-y}}{2}$[/tex]

[tex]$S = \int_{y=a}^b 2 \pix \sqrt{1+\left(\frac{dx}{dy}\right)^2 } \ dy$[/tex]

  [tex]$=\int_{0}^{\ln2} 2 \pi \left(\frac{e^y+e^{-y}}{2}\right) \left(\frac{e^y+e^{-y}}{2}\right) \ dy$[/tex]

  [tex]$=\frac{\pi}{2}\int_{0}^{\ln 2}(e^y+e^{-y})^2 \ dy = \frac{\pi}{2}\int_{0}^{\ln 2}(e^{2y}+e^{-2y}+2) \ dy $[/tex]

  [tex]$=\frac{\pi}{2} \left[ \frac{e^{2y}}{2} + \frac{e^{-2y}}{-2} + 2y \right]_2^{\ln 2}$[/tex]

  [tex]$=\frac{\pi}{2} \left[ \left(\frac{e^{2 \ln 2}}{2} + \frac{e^{-2\ln2}}{-2} + 2 \ln2 \right) - \left( \frac{e^0}{2} + \frac{e^0}{-2}+0\right) \right]$[/tex]

  [tex]$=\frac{\pi}{2}\left[ \frac{e^{\ln4}}{2} - \frac{e^{\ln(1/4)}}{2} + \ln 4 - \left( \frac{1}{2} - \frac{1}{2} + 0 \right) \right]$[/tex]

  [tex]$=\frac{\pi}{2} \left[\frac{4}{2} -\frac{1/4}{2} + \ln 4 \right]$[/tex]

  [tex]$=\frac{\pi}{2} \left[ 2-\frac{1}{8} + \ln 4 \right]$[/tex]

  [tex]$=\left( \frac{15}{8} + \ln 4 \right) \frac{\pi}{2}$[/tex]

Therefore, [tex]$S = \frac{15}{16} \pi + \pi \ln 2$[/tex]

Answer:

ofc its p/q

Step-by-step explanation:

Answer:

[tex] = { \tt{ \frac{30}{120} + \frac{40}{120} }} \\ = \frac{7}{12} [/tex]

Step-by-step explanation:

sin x0= 7/9.4

sin x0= 0.745

x0 = sin^-1 0.745

x0= 48.2

Answer:

Step-by-step explanation:

In an ordered pair the term before the comma is the x variable and the term after the comma is the y variable.

1.

4x + 3y = 12 . . . . . .(0, _)

here were given the x variable

finding the other term

4× 0 + 3y = 12

3y = 12

y = 4

therefore the ordered pair is (0, 4)

2.

. . . . . . . (-1, _)

here were given the x variable

4 × -1 + 3y = 12

3y = 12 + 4

3y = 16

y = 16/ 3

ordered pair is (-1, 16/ 3)

3.

. . . . . . . . (_, 10)

here were given the y variable

finding the other term

4x + 3 × 10 = 12

4x + 30 = 12

4x = 12 - 30

4x = -18

dividing both sides by 2

2x = -9

x = -9/ 2

ordered pair is (-9/ 2, 10)

Answer:

y = 5/2

Step-by-step explanation:

An inverse variation is of the form

xy = k where k is a constant

From the first pair of point

2*5 = k

10 = k

xy = 10

Using the second pair of points

4y = 10

Divide by 5

4y/4 = 10/4

y = 5/2

Answer:

4,3

Step-by-step explanation:

it went up two so i guess the other has to go down two?

Answer:

(-5, 3)

Step-by-step explanation:

Answer:

Cost of each football ticket=$41.56

Cost of each  basketball ticket=$43.56

Step-by-step explanation:

Let

Cost of each football ticket=x

Cost of each basket ball ticket=y

According to question

[tex]2x+y=126.77[/tex]...(1)

[tex]x+2y=128.86[/tex] ....(2)

We have to find  the cost of each ticket.

Equation (1) multiply by 2 then we get

[tex]4x+2y=253.54[/tex]  .....(3)

Now, subtract equation (2) from (3)

[tex]3x=124.68[/tex]

[tex]x=124.68/3[/tex]

[tex]x=41.56[/tex]

Now, using the value of x in equation (2)

[tex]41.56+2y=128.86[/tex]

[tex]2y=128.86-41.56[/tex]

[tex]2y=87.3[/tex]

[tex]y=87.3/2=43.65[/tex]

Hence, cost of each football ticket=$41.56

Cost of each  basketball ticket=$43.56

Answer: 11/18          

1. Convert 0.5 to a fraction

5/10

5/10 simplifies to 1/2

2. Add 1/2 and 1/9 by finding a common denominator

Common deniminator is 18 (2*9=18, 9*2=18)

1/2=9/18

1/9=2/18

3. Add

9/18+2/18=11/18

4. The answer is 11/18

[tex]\displaystyle\ \Large \boldsymbol 0,5+\frac{1}{9} =\frac{1^{/9}}{2} +\frac{1^{/2}}{9}=\frac{9+2}{18} =\boxed{\frac{11}{18} }[/tex]

Answer: 36

Step-by-step explanation= First let's calculate the area of the the inner rectangle so 6x4=24. Now let's add the area of the rectangle,(BY CUTTING IT INTO HALF) this part is hard but first lets add 3 cm then, 2 cm then lets add, 1 cm. So (3x2 is 6) now lets multiply that by 1, so you get 6. Multiply that by 4 it = 24 now let's add 24+24 which = 48. Hope it helps!!

Answer:

6/100 = x/40

Step-by-step explanation:

6% is represented by 6/100, x is the variable in the proportion, and 40 is the whole you are finding the percentage of

Answer:

3.5

Step-by-step explanation:

From the graph,

x1 = 0

x2 = 4

y1 = 0

y2 = 14

Formula : -

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

Slope

= ( 14 - 0 ) / ( 4 - 0 )

= 14 / 4

= 7 / 2

= 3.5

Answer:

7/2

Step-by-step explanation:

the slope of a line is the ratio of y/x.

it describes how many units y changes, when x changes a defined number of units.

an increase is indicated by "+", and a decrease by "-".

the point with full integer/natural numbers as coordinates is (4, 14).

that means that when coming from point 0 (0, 0) x increases by 4 units, and y increases by 14 units.

so, the slope of line is 14/4 = 7/2

Answer:

23

Step-by-step explanation:

The answer is 23 by the definition of angle bisector.

Answer:

The measure of angle B is 29°.

Answer:

(-infinity, -1/2] and [3, infinity]  Let e know if anything didn't make sense.  

Step-by-step explanation:

A good way to think about it is a graph is either at 0, greater than 0 or less than 0.  If you can find all of the zeroes  then you can test each zero by checking points before and after.  the graph will either cross and change signs, or stay the same.

So we want to find the zeroes.

Much like the factored form of a quadratic (x - a)(x - b) this inequality has two expressions  being multiplied together, so if you can find when they are 0 you will have all the zeros.  We shoudl also check when they do not exist just to be safe.

(x^2 - 3x) itself is a quadratic.  so lets find its zeroes.

x^2 - 3x

x(x - 3)

So the zeroes are 0 and 3.  lets find the zeroes of the other expression before checking signs.

sqrt(2x^2-3x-2) will be at 0 when the quadratic inside is at 0, and will not exist if the quadrati is negative, so let's look for both.  first the 0s.  I am going to complete the square

2x^2 - 3x - 2 = 0

2(x^2 - (3/2)x - 1) = 0

2[(x - 3/4)^2 - 25/16] = 0

2(x - 3/4)^2 - 25/8 = 0

2(x - 3/4)^2 = 25/8

(x - 3/4)^2 = 25/16

x - 3/4 = +/- 5/4

x = +/-5/4 + 3/4

x = -2/4 or 8/4

x = -1/2 or 2

Let me know if you couldn't follow that.  Anyway, using those zeroes we can tell 2x^2 - 3x - 2 is negative  between the two zeroes, since it is a parabola that opens upwards and crosses the x axis at those zeroes.  this means sqrt(2x^2 - 3x - 2) does not exist from x=-1/2 and x=2.  This means for the other zero above at x=0, the iequality will not exist.  So now we have 3 points to look at.

-1/2 for its first 0 and where it then stops existing up to 2, which is also a 0.  Finally 3 is the last 0.

at x=-1/2 all values before it are positive

x=2 has values immediately after it negative

x=3 then it switches so all values after that are positive since it is the last 0

Now we know that (x^2 - 3x) * sqrt(2x^2 - 3x - 2)is positive or equal to 0 along the intervals, (-infinity, -1/2] and [3, infinity]

Answer:

n = ±6 .

Step-by-step explanation:

A quadratic equation is given to us and we need to find out the solution of the given equation . The given equation is ,

[tex]\rm\implies -\dfrac{1}{2}n^2+18=0 [/tex]

Subtracting 18 both sides ,

[tex]\rm\implies -\dfrac{1}{2}n^2 = -18 [/tex]

Multiplying both sides by -2 ,

[tex]\rm\implies -2\times\dfrac{1}{2}n^2 = -2\times -18 [/tex]

On simplyfing , we get ,

[tex]\rm\implies n^2= 36 [/tex]

Putting squareroot both sides ,

[tex]\rm\implies n= \sqrt{36} [/tex]

This equals to ,

[tex]\rm\implies \boxed{\quad\blue{\rm n =\pm 6 }} [/tex]

Hence the value of n is ±6 .

Answer: f(t) = 1.5t + 5

Answer:

Josh's ERA had a z-score of -3.26.

Alice's ERA had a z-score of -1.11.

Due to the lower z-score(ERA is a stat that the lower the better), Josh had a better year relative to his peers.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Josh:

ERA of 2.89, mean of 5.083, standard deviation of 0.672. So

[tex]X = 2.89, \mu = 5.083, \sigma = 0.672[/tex], and the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.89 - 5.083}{0.672}[/tex]

[tex]Z =  -3.26[/tex]

Josh's ERA had a z-score of -3.26.

Alice:

ERA of 3.31, mean of 4.032, standard deviation of 0.649. So

[tex]X = 3.31, \mu = 4.032, \sigma = 0.649[/tex], and the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3.31 - 4.032}{0.649}[/tex]

[tex]Z =  -1.11[/tex]

Alice's ERA had a z-score of -1.11.

Which player had the better year relative to their​ peers, josh or alice ?

Due to the lower z-score(ERA is a stat that the lower the better), Josh had a better year relative to his peers.

Answer:

-5 <x<-1

Step-by-step explanation:

4|x+3|<8

Divide by 4

4|x+3| /4<8/4

|x+3|<2

There are two solutions one positive and one negative, remember to flip the inequality for the negative

x+3 <2    and x+3 >-2

Subtract 3 from each side

x+3-3 <2-3   and x+3-3 >-2-3

x<-1   and x>-5

-5 <x<-1

Answer:

Step-by-step explanation:

-5n^2-45=7--->-5n^2=52--->n^2=52÷(-5)= there is no answer for this question...I mean Paired power never has a negative answer.

Answer:

A) (0,-3)

Step-by-step explanation:

to get the y-intercept let x = 0, then

y = 0 + 0 -3

y = -3

Answer:

(0,-3)

Step-by-step explanation:

The y intercept is where x=0

ƒ(x) = –x^2 + 4x – 3?

f(0) = -0^2 +4(0)-3

f(0) = -3

(0,-3)

Answer:

the minimum distance each of them can cover equally is 8 m.

Step-by-step explanation:

Given;

different distance covered by Laiba, tauseef and Nadia = 24 m, 42 m and 52 m

for the 24 m, distance covered by each = 24 m/3 = 8 m

for the 42 m, distance covered by each, = 42 m/3 = 14 m

for the 52 m, distance covered by each, = 52 m/3 = 17.33 m

From the results above, the minimum distance each of them can cover equally is 8 m.

Answer:

-3/2

Step-by-step explanation:

the slope of a line is expressed as ratio y/x showing how many units y changes, when x changes a certain number of units.

so, going from A to B, x changes 4 units (from -3 to +1), and y changes 6 units (down, from +3 to -3). that makes the y change negative.

so, the slope is

-6/4 = -3/2

Answer:

81 cm ^3

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h where r is the radius and h is the height

We are given the diameter of 6 so the radius is 1/2 the diameter

r = 1/2 (6) = 3

V = 1/3 pi r^2 h

   = 1/3 ( 3) * (3) ^2 * 9

 = 81 cm ^3

Answer:

Step-by-step explanation:

The formula for arc length is

[tex]AL=\frac{\theta}{360}*\pi d[/tex] where theta is the central angle. We are given the central angle when we are told that the measure of arc EFG is 240 degrees. The diameter is given as 36, so filling in:

[tex]AL=\frac{240}{360}*\pi (36)[/tex] which can be simplified down a bit to

[tex]AL=\frac{2}{3}*\pi (36)[/tex] and a bit more to

[tex]AL=2\pi(12)[/tex] which gives us, finally,

[tex]AL=24\pi[/tex]

I can't tell which of your answers matches this one because they're much too small to read.

Answer:

[tex]\text{C. }a_n=-8+(n-1)5[/tex]

Step-by-step explanation:

The explicit formula for an arithmetic sequence is given by [tex]a_n=a_1+(n-1)d[/tex], where [tex]a_n[/tex] is the [tex]n[/tex]th, [tex]a_1[/tex] is the first them of the sequence, and [tex]d[/tex] is the common difference.

In the given sequence -8, -3, 2, 7, we can see that we're adding 5 to each term. Therefore, the common different is positive five (+5). We can also identify the first term is -8. Therefore, we have:

Thus, the explicit formula for this sequence is:

[tex]\boxed{a_n=-8+(n-1)5}[/tex]

In case of Nina:

slope of graph = speed = 48-32/6-4 = 16/2 =8

y-32 =8(x-4)

y-32=8x-32

y=8x

d=8t

at x= 0 i.e at t= 0

d= 0m

In case of Ryan:

slope =speed = 47.5-35=6-4 = 12.5/2 =6.25

y-35=6.25(x-4)

y-35=6.25x-25

y=6.25x+10

d=6.25t+10

at t = 0, d= 10m

RYAN had a head start of 10 m