1 pizza costs £3.20 more than a bottle of coke. The total cost of the items is £19.40 for 3 pizzas and 1 bottle of coke How much does a pizza cost? How do you work this out please?

Answer:

4. ± 3.012

Step-by-step explanation:

Hello!

Assuming that for both variables X₁ and X₂ n₁= n₂ = 16

You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.

The hypotheses are:

H₀: β₁= 0

H₁: β₁≠ 0

α: 0.01

[tex]t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}[/tex]

The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"

The rejection region for this test is two-tailed, the critical values are:

±[tex]t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012[/tex]

I hope this helps!

Answer:

  (f-g)(x) = -x² +4x +6

Step-by-step explanation:

We assume you want to find (f -g)(x).

 [tex](f-g)(x)=f(x)-g(x)=(4x+1)-(x^2-5)\\\\\boxed{(f-g)(x)=-x^2+4x+6}[/tex]

Answer:

Yeah, you got the answer right.

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

12 is divisible by: 1, 2, 3, 4, 6, 12

Because 3 is a factor of a, that means 3 multiplied by another number equals a. Additionally, a is a divisor of 12, meaning a multiplied by another number equals 12.

Out of the numbers, 12 is divisible by, only 3 are also divisible by 3: 3, 6, 12 This gives three possible values of a.

Answer:

  5

Step-by-step explanation:

Substitute the given values and do the arithmetic.

  [tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]

Explanation:

The identity we'll use is cos(-x) = cos(x) for any value of x.

So cos(-150) = cos(150).

Then locate the angle 150 on the unit circle. The terminal point is [tex]\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)[/tex]

The x coordinate of this terminal point is the value of cos(150).

Answer:

Cos(-150°)=-√3/2

Step-by-step explanation:

-150° is found at the third quadrant so the cost value at third quadrant is negative

Cos(-150°)= -cos(30)=-cos(210)

Cos(-150°)=- (√3/2)

Cos(-150°)=-√3/2

Hope it helps

Answer:

85.4

Step-by-step explanation:

first you have to find the radius before you find the area. so given the height, the radius is 11.3 meters. then, you need to find the area behind the arc, which is 85.4 meters/

Answer:

56.52 in

Step-by-step explanation:

Circumference Formula: C = 2πr

Since we are given radius r = 9, simply plug it into the formula:

C = 2π(9)

C = 18π

C = 56.5487

Answer:

56.5

Step-by-step explanation:

The circumference is the product of the diameter and PI

P = (9+9)*π = 18*3.14=56.52

Answer:

[tex]\boxed{\sf \ \ \ 11,464 \ \ \ }[/tex]

Step-by-step explanation:

hello

we need to compute the following

[tex]\sum\limits^9_{i=0} {1000(1.03)^i}=1000\dfrac{1.03^{10}-1}{1.03-1}=11463.879...[/tex]

hope this helps

Answer:

y=15; y=5

Step-by-step explanation:

y=x2+2x

plug in x as 3:

y=3 2+ 2*3

y=9+6

y=15

Next problem:

y=x3-3

plug in x as 2:

y=2 3-3

y=8-3

y=5

Answer:

[tex]-\frac{8}{3}[/tex]

Step-by-step explanation:

Given

[tex]\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}[/tex]

Required

Simpify

The very first step is to take LCM of the given expression

[tex]\frac{-10 -4 - 2}{6}[/tex]

Perform arithmetic operations o the numerator

[tex]-\frac{16}{6}[/tex]

Divide the numerator and denominator by 2

[tex]-\frac{16/2}{6/2}[/tex]

[tex]-\frac{8}{3}[/tex]

The expression can't be further simplified;

Hence, [tex]\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}[/tex] = [tex]-\frac{8}{3}[/tex]

Answer:

(A) 1199.168

(B) 1503.372

(C) 159.17728

Step-by-step explanation:

(A) To determine the 30th percentile for the number of chocolate chips in the bag, we find the z-score for the 30th percentile.

Found using a z-table or z-calculator, the z-score for the 30th percentile is -0.524

The formula for finding X (the number of items in a given percentile) is:

X = M + Z(S.D.)

Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.

So for the 30th percentile,

X = 1261 + (-0.524)(118)

X = 1261 - 61.832 = 1199.168

(B) The number of chocolate chips that make up the middle 98% of chips in the bag is

X = 1261 + (2.054)(118)

X = 1261 + 242.372 = 1503.372

(C) For normal distributions, Interquartile range is Q3 - Q1, that is; 3rd quartile minus 1st quartile.

This is within 1.34896 standard deviations of the mean.

IQR = (1.34896)(118)

IQR = 159.17728

Step-by-step explanation:

36 ÷ (4 x 3)

36 ÷ 12

= 3

54 - 48 - (16 ÷ 4)

54 - 48 - 4

= 2

So first one is greater

Answer:

B is a function of A

Step-by-step explanation:

If you do something to another thing, it is a function of that.

Answer:

3(7) + 2* |7 - 8| - 12 = 11

Step-by-step explanation:

3(7) + 2* |7 - 8| - 12

21 + 2* |-1| - 12

21 + 2* 1 - 12

21 + 2 - 12

23 - 12 = 11

Hope this helps! :)

Answer:

[tex]3{x}^{3} + 2x + 5[/tex]

Step-by-step explanation:

Sorry if my notes weren't very clear.

Answer:B

Step-by-step explanation: got it right

Answer:

36pi

Step-by-step explanation:

Answer:

36pi

Step-by-step explanation:

i got it right on my test

Answer:

Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]

Step-by-step explanation:

Ratio of the areas of the given circles are 1 : 4 : 16

Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]

                                                                             = 1 : 2 : 4

If the radius of the smallest circle = x units

Then the radius of the middle circle = 2x units

and the radius of the largest circle = 4x units

Area of the smallest circle = πx²

Area of the middle circle = π(2x)² = 4πx²

Area of the largest circle = π(4x)²= 16πx²

Area of the region which is not shaded in the middle circle = πx²(4 - 1)

                                                                                                  = 3πx²

Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded

= 16πx² - 3πx²

= 13πx²

Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]

= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]

= [tex]\frac{13}{16}[/tex]

Answer:

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 28.983051

Chi-square value = χ² = 2.154239

Degree of freedom = 1

Critical value = 3.841

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Step-by-step explanation:

He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.

So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Data collected by Dr. Pagels:

                                              meadow voles     common voles      Row Total

apple slices                                     26                          32                      58

peanut butter-oatmeal                   35                          25                     60

Column Total                                   61                          57                     118

Where 118 is the grand total.

The expected number is given by

Expected = (row total)×(column total)/grand total

Expected meadow vole/apple slices = 58×61/118

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 58×57/118

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 60×61/118

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 60×57/118

Expected common vole/peanut butter-oatmeal = 28.983051

The chi-square statistic value is given by

χ² = Σ(Observed - Expected)²/Expected

χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051

χ² = 2.154239

The degrees of freedom is given by

DoF = (row - 1)×(col - 1)

For the given case, we have 2 rows and 2 columns

DoF = (2 - 1)×(2 - 1)

DoF = 1

The given level of significance = 0.05

The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be

Critical value = 3.841

Conclusion:

Reject H₀ If χ² > Critical value

We reject the Null hypothesis If the calculated chi-square value is more than the critical value.

For the given case,

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Answer:

Step-by-step explanation:

hello

[tex]\dfrac{1}{9}-y^2=(\dfrac{1}{3})^2-y^2=(\dfrac{1}{3}-y)(\dfrac{1}{3}+y)=\dfrac{(1-3y)(1+3y)}{9}[/tex]

hope this helps

Answer: (1 and 22/45)

Step-by-step explanation:

I guess that we are working with mixed numbers here, and we have the equation:

(8÷2 2/9) − (2 11/15)

first we solve: 8÷2 = 4.

Now, we can write this as:

(4 + 2/9) - (2 + 11/15)

(4 - 2) + (2/9 - 11/15)

now, 9*5 = 45

        15*3 = 45

then we can write the right side as: 2/9 - 11/5 = 10/45 - 33/45 = -23/45

2 - 23/45

But in mixed numbers we also need to work with a positive rational, then we have:

2 - 23/45 = 1 + 1 -23/45 = 1 + 45/45 - 23/45 = 1 + 22/45

then the solution is:

(1 and 22/45)

Answer:

No

Step-by-step explanation:

If they were opposite, they would be equal.

But they are not, (on one of the spaces in between them is smaller and one is larger.)

Hope I have helped you, since it seems I haven't helped "other people" the last time :/

Answer:

No

Step-by-step explanation:

Answer:

A. BA + 2πrh

C. 2πr² + 2πrh

Step-by-step explanation:

height of cylinder = h

Radius of cylinder = r

=>Lateral area of cylinder = LA (THis is the area of the cylinder excluding the area of its circular bases)

L.A of a cylinder = 2πrh

=>Base area = BA (this is the area of both circular bases of the cylinder)

Area of circle = πr²

Area of the 2 circular bases of the cylinder (BA) = 2(πr²) = 2πr²

=>Surface area of a right cylinder = B.A + L.A

= 2πr² + 2πrh

The formulas that can be used to find surface area of a right cylinder from the given options are:

A. BA + 2πrh (note: BA = 2πr², LA = 2πrh)

C. 2πr² + 2πrh

Answer:

A.50-n=44, 6 shorts borrowed

Step-by-step explanation:

If her sister borrowed n shorts, that means Shelly now has n less shorts. Since her amount of shorts is 50, then 50-n must equal how many shorts she has now, meaning 50-n=44. Solving the equation we get n=6. This means that her sister borrowed 6 shorts.

Answer:

A

Step-by-step explanation:

50 minus the shorts Shawnie borrowed (n) equal to 44

Answer:

b)A cube with side lengths of 4 feet has a volume of 64cubic feet

Step-by-step explanation:

volume=length×width×height

=4×4×4

=64feet³

Answer:

d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle

Step-by-step explanation:

13 − 01 + 1 = 13

34 − 14 + 1 = 21

56 − 35 + 1 = 22

99 − 57 + 1 + 1 = 44

Answer:

AB = 3π

Step-by-step explanation:

See attachment for correct format of question.

Given

From the attachment, we have that

θ = 20°

Radius, r = 27

Required

Find length of AB

AB is an arc and it's length can be calculated using arc length formula.

[tex]Length = \frac{\theta}{360} * 2\pi r[/tex]

Substitute 20 for θ and 27 for r

[tex]Length = \frac{20}{360} * 2\pi *27[/tex]

[tex]Length = \frac{20 * 2\pi * 27}{360}[/tex]

[tex]Length = \frac{1080 \pi}{360}[/tex]

[tex]Length = 3\pi[/tex]

Hence, the length of arc AB is terms of π is 3π

Answer:

Step-by-step explanation:

There are 9 possible outcomes for (Bill, Ben)'s cards:

  (4, 4) total 8; (4, 5) total 9; (4, 6) total 10;

  (5, 4) total 9; (5, 5) total 10; (5, 6) total 11;

  (6, 4) total 10; (6, 5) total 11; (6, 6) total 12.

Of these 9 outcomes, 4 have an odd total; 6 are less than 11.

 P(odd) = 4/9

  P(sum < 11) = 2/3