Kelly is a waitress and her average tip rate is 18%. After taking a sample of her tips from a week, she thinks her tip rate is actually higher. The data below is the tip rate for 15 randomly chosen checks (the numbers represent percentage). Assume that tip rates are normally distributed.
18.5 18.2 20 21.3 17.9 17.9 18.1 17.5 20 18
a) Express the null and alternative hypotheses in symbolic form for this claim.
H0 : Select an answer
Ha: Select an answer
b) What is the test statistic. Round to 2 decimals.
c) What is the p-value. Round to 4 decimals p-value =

Answer:

1) 4a + 8

2) 12a² - 8a

3) 2a² + 8a

4) 4 - 6a

Step-by-step explanation:

The GCF of two numbers is the greatest common number each of the original two numbers can be divided by to get a whole number.

Hope it helps <3

Answer:

4     4a+8

4a   [tex]12a^{2}[/tex]+8a

2a   [tex]2a^{2} +8a[/tex]

2     4-6a

Step-by-step explanation:

Okay basicly you wand to find the biggest number that can go into both numbers

like the greatest common fact for 4a+8 would be 4 since only one of the numbers have an a you would just leave that out

Since you can take a 4 and an a out of [tex]12a^{2} \\[/tex] and out of 8a the greatest common factor would be 4a

Since you are able to take a 2 and an a out of [tex]2a^{2} +8a[/tex] your greatest common factor would be a

Since the largest number that can go into 4 and 6 is 2 your answer would be 2

Hope this helps you understand!

Answer:

A, B, A

Step-by-step explanation:

(3)

Given

- 2x² + 10x + 12 ← factor out - 2 from each term

= - 2(x² - 5x - 6) ← factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 6 and + 1, since

- 6 × 1 = - 6 and - 6 + 1 = - 5, thus

x² - 5x - 6 = (x - 6)(x + 1) and

- 2x² + 10x + 12 = - 2(x - 6)(x + 1) → A

(4)

[tex]x^{4}[/tex] - 81 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), thus

[tex]x^{4}[/tex] - 81

= (x² )² - 9²

=(x² - 9)(x² + 9) ← note that x² - 9 is also a difference of squares

= (x - 3)(x + 3)(x² + 9) ← in factored form

x² - 3 is not a factor → B

(5)

Given

5[tex]x^{4}[/tex] - 320 ← factor out 5 from each term

= 5([tex]x^{4}[/tex] - 64) ← difference of squares

= 5(x² - 8)(x² + 8) → A

Answer:

a) $26.4

b) $324

Step-by-step explanation:

Hire purchase is the purchase of an item which can be paid instalmentally.

The bicycle costs $300 for an instant purchase.

For a hire purchase, a $60 deposit must be made and the rest paid instalmentally over 10 months. An interest of 10% is included in the outstanding balance

The outstanding balance after paying deposit= $300 - $60 = $240

Hence, 10% of 240 = 10/100 × 240 = 24

An interest of $24 is added.

Therefore, a total of $240 + $24 = $264 will be paid for the next 10 months.

a) Hence, the amount to be paid in instalment each month is $264/10 = $26.4

b) the total cost of buying the bicycle by hire purchase= deposit amount + instalment price

= $60 + $264

= $324

Hence, a total of $324 will be paid for the bicycle by hire purchase.

N.B: $300 is the sale price + $24 interest

Answer:

Remember to round!

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{5-\sqrt{3}}{2} \ \ }[/tex]

Step-by-step explanation:

Hello,

[tex]\dfrac{1+2\sqrt{3}}{1+\sqrt{3}}=\dfrac{(1+2\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\ \text{... to eliminate the root in the denominator ...} \\\\=\dfrac{1-\sqrt{3}+2\sqrt{3}-2*3}{(1-3)}\\\\=-\dfrac{1+\sqrt{3}-6}{2}\\\\=-\dfrac{\sqrt{3}-5}{2}\\\\=\dfrac{5-\sqrt{3}}{2}\\[/tex]

Do not hesitate if you have any question

Answer:

3x^2 -4

Step-by-step explanation:

f(x) = 2x^2 +3

g(x) = x^2 -7

(f+g) (x) =  2x^2 +3 +  x^2 -7

 Combine like terms

            = 3x^2 -4

Answer:

[tex]\boxed{3x^2-4}[/tex]

Step-by-step explanation:

[tex](f+g)(x)[/tex]

Rewrite.

[tex]f(x)+g(x)[/tex]

[tex](2x^2 +3)+(x^2-7)[/tex]

Combine like terms and simplify.

[tex](2x^2 +x^2 )+(3-7)[/tex]

[tex](3x^2 )+(-4)[/tex]

[tex]3x^2 +-4[/tex]

Answer:

C

Step-by-step explanation:

Given

2x² + x - 1 = 2 ( subtract 2 from both sides )

2x² + x - 3 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 3 = - 6 and sum = + 1

The factors are - 2 and + 3

Use these factors to split the x- term

2x² - 2x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(2x + 3) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]

Answer:

4(2x^3+ x^2-2x-1)

Step-by-step explanation:

the explanation is given above in the picture

pls do mark me the brainliest.

Answer:

4(2x^3+x^2-2x-1)

Step-by-step explanation:

Mulitply each term:

8x^3+4x^2-8x-4

Now simplify: 4(2x^3+x^2-2x-1)

Please mark me brainliest!!

Answer:

Step-by-step explanation:

Thank you for providing the details of the question.

Unfortunately none of the results you have to choose from will give you 44%

The problem resembles the first probability question you were likely asked. "What is the probability of getting a heads on every throw of a fair coin?" The answer is 1/2 no matter how many times you throw the coin or what has happened before any point in the throws.

The answer should be 6/50.  If this turns out not to be the answer and you have an instructor your safest course of action is to ask how 44% was obtained. Tell me in a comment.

Answer:

fraction 6 over 50

Step-by-step explanation:

In the question it says she pulls a tile out of the bag and records the color 50 times which means she pulled out 50 tiles.

Now the table says that she recorded 6 purple tiles.

Probability is equal to [tex]\frac{number of favorable outcomes}{number of possible outcomes}[/tex]

Number of favorable outcomes here is the number of purple tiles she pulled out (6) since we want to find the probability of choosing a purple tile and the number of possible outcomes is the total number of tiles she pulled out (50)

So the probability = [tex]\frac{6}{50}[/tex]

Answer:

31x² - 2

Step-by-step explanation:

5(2x²-1)+3(7x²+1) = 5*2x² - 5*1 + 3*7x² + 3 = 10x² - 5 + 21x² + 3 = 31x² - 2

Answer: m∠PNO =16.25°  , m∠ONM=57.5°

Step-by-step explanation:

Given: Circle k(O), m NM =65° ∠PNO≅∠PMO

To find: m∠PNO, m∠ONM.

Since, central angle is equal to the measure of minor arc.

⇒∠MON = m NM =65°

In Δ MON , ON = OM [Radii of circle]

⇒ ∠ONM = ∠NMO   (i)   [Angle apposite to equal side of triangle are equal]

In Δ MON , ∠ONM + ∠NMO+∠MON =180°

⇒ ∠ONM + ∠ONM+65°=180°  [from (i)]

⇒ 2∠ONM=115°

⇒ ∠ONM=57.5°

⇒ ∠ONM = ∠NMO =57.5°

Also, an inscribed angle is half of a central angle that subtends the same arc.

⇒∠MPN =half of∠MON

=  [tex]\dfrac{65^{\circ}}{2}=32.5^{\circ}[/tex]

Also, ∠PNO≅∠PMO  [Given]

⇒∠PNO =∠PMO

⇒ ∠PNO +∠ONM =∠PMO+∠NMO   [∵∠ONM = ∠NMO]

⇒∠PNM=∠PMN

In ΔNPM

⇒ ∠MPN +∠PNM+∠PMN = 180°

⇒ 32.5° +∠PNM + ∠PNM= 180°

⇒ 2(∠PNM)= 147.5°

⇒ ∠PNM = 73.75°

Also,  ∠PNM = ∠PNO+∠ONM

⇒73.75°= ∠PNO+57.5°

⇒ ∠PNO =16.25°

Hence, m∠PNO =16.25°  , m∠ONM=57.5°

Answer:

Answer: m∠PNO =16.25°  , m∠ONM=57.5°

Step-by-step explanation:

Given: Circle k(O), m NM =65° ∠PNO≅∠PMO

To find: m∠PNO, m∠ONM.

Since, central angle is equal to the measure of minor arc.

⇒∠MON = m NM =65°

In Δ MON , ON = OM [Radii of circle]

⇒ ∠ONM = ∠NMO   (i)   [Angle apposite to equal side of triangle are equal]

In Δ MON , ∠ONM + ∠NMO+∠MON =180°

⇒ ∠ONM + ∠ONM+65°=180°  [from (i)]

⇒ 2∠ONM=115°

⇒ ∠ONM=57.5°

⇒ ∠ONM = ∠NMO =57.5°

Also, an inscribed angle is half of a central angle that subtends the same arc.

⇒∠MPN =half of∠MON

=  

Also, ∠PNO≅∠PMO  [Given]

⇒∠PNO =∠PMO

⇒ ∠PNO +∠ONM =∠PMO+∠NMO   [∵∠ONM = ∠NMO]

⇒∠PNM=∠PMN

In ΔNPM

⇒ ∠MPN +∠PNM+∠PMN = 180°

⇒ 32.5° +∠PNM + ∠PNM= 180°

⇒ 2(∠PNM)= 147.5°

⇒ ∠PNM = 73.75°

Also,  ∠PNM = ∠PNO+∠ONM

⇒73.75°= ∠PNO+57.5°

⇒ ∠PNO =16.25°

Hence, m∠PNO =16.25°  , m∠ONM=57.5°

Step-by-step explanation:

Answer:

This graph represents the function above.

Answer:

11.7

Step-by-step explanation:

Let H be the heipotenys of the big triangle:

H= 28.04

Let's calculate the third side using the pythagorian theorem:

H²= 26²+ d²(the third side)

d² = 28.04²-26²= 110.24

d= 10.49

let's calculate x now

x= 11.65 ≈ 11.7

Answer:

10

Step-by-step explanation:

It's the $10 that is to be added to the cost for each produced item.

Answer:  60.1

Step-by-step explanation:  If you did 13/15 and then took  sin-1  and got 60.07356513, you did everything right.

But sometimes they want the answer rounded to one decimal point.

So try 60.1

Answer:

x = 2, x = -10

Step-by-step explanation:

(x+4)^2 = 36

(x+4) = 6, -6

x = 2, x = -10

Answer:

[tex]x + 0.05x = 15[/tex], solution is $14.29

Step-by-step explanation:

We can create an equation for this scenario to try and solve it.

Assuming the cost of the CD is x, it’s sale tax will be 0.05x (as that is 5% of x, 0.05.)

We can write the equation in two ways:

[tex]x + 0.05x = 15[/tex] or [tex]1.05x = 15[/tex].

Assuming we take the second one (easier to work with), we can divide both sides by 1.05. The equation simplifies to x = 14.289... which rounds to x = 14.29.

Therefore, the equation is [tex]x + 0.05x = 15[/tex] and the solution is $14.29.

Hope this helped!

Answer:

x + 0.05x = 15; x = $14.29

Step-by-step explanation:

Step-by-step explanation:

[tex]6x - 30 = 5(x - 4)[/tex]

[tex]6x - 30 = 5x - 20[/tex]

[tex]6x - 30 - 5x = - 20[/tex]

[tex]x - 30 = - 20[/tex]

[tex]x = - 20 + 30[/tex]

[tex]x = 10[/tex]

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

x=5,y=-1

Step-by-step explanation:

5x– 2y = 27

-3x +2y=-17

Add the two equations together to eliminate y

5x– 2y = 27

-3x +2y=-17

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

2x  = 10

Divide by 2

2x/2 = 10/2

x = 5

Now find y

-3x +2y = -17

-3(5)+2y = -17

-15+2y =-17

Add 15 to each side

-15+15 +2y = -17+15

2y = -2

Divide by 2

2y/2 = -2/2

y =-1

Answer:

{ 1,2}

Step-by-step explanation:

The ∩ means intersection, or what is in common for the two sets

The intersection of A and B is what is in the overlapping circles

The intersection of A and B is { 1,2}

Answer:

it is 3.375

Step-by-step explanation:

The volume inside the giant sugar cube is of 3.375m³.

To solve this question, we first find the side of the cube, given it's surface area, and with the side, we find the volume.

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

Finding the side:

Considering it took 13.5 m² of material to build the cube, we have that it's surface area is of 13.5m².

The surface area of a cube of side s is:

[tex]S_A = 6s^2[/tex]

In this question:

[tex]6s^2 = 13.5[/tex]

[tex]s^2 = \frac{13.5}{6}[/tex]

[tex]s = \sqrt{\frac{13.5}{6}}[/tex]

[tex]s = 1.5[/tex]

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

Volume:

The volume of a cube of side s is:

[tex]V = s^3[/tex]

In this question, [tex]s = 1.5[/tex], so:

[tex]V = 1.5^3 = 3.375[/tex]

The volume inside the giant sugar cube is of 3.375m³.

A similar question is found at https://brainly.com/question/11862932

Answer:

[tex]c =\sqrt{a^{2}+b^{2} }[/tex]

Step-by-step explanation:

You clear c, wich is the hypotenuse

[tex]c =\sqrt{a^{2}+b^{2} }[/tex]

Answer:

28

Step-by-step explanation:

We divide the shape covenientely, like this, and area 1 is 4*4=16

area 2=4*4/2=8

area 3= 2*4/2=4

Area total = Area 1 + Area 2 + Area 3=16+8+4=28

Answer:

Part A: check B, E and F.

Part B: check E and G.

Step-by-step explanation:

The equation [tex]y = a(x - b)^2 + c[/tex] is the equation of a parabola written in the vertex form, where the vertex will be (b, c).

So, if the vertex is (2, -1), we have that b = 2 and c = -1

To find the c value, we use the information that the y-intercept is 3, so we have the point (0, 3). Using x = 0 and y = 3, we have:

[tex]3 = a(0 - 2)^2 - 1[/tex]

[tex]3 = 4a - 1[/tex]

[tex]4a = 4[/tex]

[tex]a = 1[/tex]

So we have a = 1, b = 2 and c = -1.

Part A: check B, E and F.

To find the x-intercepts, we need to find the values of x where y = 0:

[tex]0 = (x - 2)^2 - 1[/tex]

[tex]x^2 - 4x + 4 - 1 = 0[/tex]

[tex]x^2 - 4x + 3 = 0[/tex]

Solving using Bhaskara's formula (a = 1, b = -4 and c = 3), we have:

[tex]\Delta = b^2 - 4ac = 16 - 12 = 4[/tex]

[tex]x_1 = (-b + \sqrt{\Delta})/2a = (4 + 2)/2 = 3[/tex]

[tex]x_2 = (-b - \sqrt{\Delta})/2a = (4 - 2)/2 = 1[/tex]

So the x-intercepts are 1 and 3

Part B: check E and G.

Answer: $(d-3c)

Step-by-step explanation:

Total amount Tina had = $d

Cost of cupcakes = $c

Number of cupcakes purchased = 3

Therefore,

Total cost of cupcakes = cost per cupcake × number of cupcakes

Total cost of cupcakes = $c × 3 = $3c

Amount left after cupcake purchase:

Total amount Tina had - total cost of cupcakes :

$d - $3c

Answer:

x-intercept → (-5, 0)

Step-by-step explanation:

Let the equation of the line having pairs given in the table is,

y - y' = m(x - x')

m = slope of the line

(x', y') is a point lying on the line.

From the given table,

Two points (33, -22) and (52, -33) lie on the line.

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

                        m = [tex]\frac{-33+22}{52-33}[/tex]

                        m = [tex]-\frac{11}{19}[/tex]

Equation of the line passing through (33, -22) and slope = [tex]-\frac{11}{19}[/tex] will be,

y + 22 = [tex]-\frac{11}{19}(x - 33)[/tex]

For x-intercept y = 0,

0 + 22 = [tex]-\frac{11}{19}(x-33)[/tex]

-38 = x - 33

x = -38 + 33

x = -5

Therefore, x-intercept of the line is (-5, 0).

Answer:

-5,0

Step-by-step explanation:

khan academy

Answer:

184 cm²

Step-by-step explanation:

Surface area of the rectangular box is expressed as S = 2(LW+LH+WH)

L is the length of the box = 90 cm

W is the width of the box = 50 cm

H is the height of the box= 90 cm

If there are error of at most 0.2 cm in each measurement, then the total surface area using differential estimate will be expressed as shown;

S = 2{(LdW+WdL) + (LdH+HdL) + (WdH+HdW)

Note that dL = dW = dH = 0.2 cm

Substituting the given values into the formula to estimate the maximum error in calculating the surface area of the box

S = 2{(90(0.2)+50(0.2)) + (90(0.2)+90(0.2)) + (50(0.2)+90(0.2))

S = 2{18+10+18+18+10+18}

S = 2(92)

S = 184 cm²

Hence, the maximum error in calculating the surface area of the box is 184cm²

Answer:

The answer is below

Step-by-step explanation:

The z score is a measure used in statistic to determine the number of standard deviations by which the raw score is above or below the mean. . The z score is given by:

[tex]z=\frac{x-\mu}{\sigma}\\ where\ \mu \ is \ the\ mean, \sigma\ is\ the\ standard\ deviation\ and\ x \ is\ the\ raw\ score[/tex]

(a) Z = -0.12 and Z = 0.12

From the normal distribution table, Area between z equal -0.12 and z equal 0.12  = P(-0.12 < z < 0.12) = P(z < 0.12) - P(z < -0.12) = 0.5478 - 0.4522 = 0.0956 = 9.56%

b) The area that lies between Z = - 0.35 and Z=0

From the normal distribution table, Area between z equal -0.35 and z equal 0  = P(-0.35 < z < 0) = P(z < 0) - P(z < -0.35) = 0.5 - 0.3594 = 0.1406 = 14.06%

c) The area that lies between Z = 0.02 and Z = 0.82

From the normal distribution table, Area between z equal 0.02 and z equal 0.82  = P(0.02 < z < 0.82) = P(z < 0.82) - P(z < 0.02) = 0.7939 - 0.5080 = 0.2859 = 28.59%

Answer:

[tex]\boxed{\sf \frac{15}{22} }[/tex]

Step-by-step explanation:

The radius of the circle is 7 cm.

The two legs of the triangles are 7cm as well.

Area of a trinagle is ( base × height )/2.

[tex]\frac{7 \times 7}{2} =24.5[/tex]

Multiply the value by 2 since there are two triangles.

[tex]24.5 \times 2 = 49[/tex]

Calculate the area of the circle.

[tex]\pi r^2[/tex]

The radius is given.

[tex]\pi (7)^2[/tex]

Take [tex]\pi[/tex] as [tex]\frac{22}{7}[/tex]

[tex]49(\frac{22}{7} )[/tex]

[tex]=154[/tex]

Subtract the area of the two triangles from the area of the whole circle.

[tex]154-49=105[/tex]

The area of the shaded part is 105 cm². The total area of the shape is 154cm².

[tex]\frac{105}{154} =\frac{15}{22}[/tex]