Question 1:Lauren wants to buy 3 shirts at $15.00 each. At home, she calculates the total cost as $46.20, using the sales tax of 8%. At the store, Lisa (the cashier) tells Lauren the total cost is $48.60. Which person is wrong, Lauren or Lisa


Question 2:What’s the cost of the shirts before tax


Question 3:How much is the sales tax for all shirts


Question 4:What is the total cost of the shirts, including tax?

Answer:

A and C

Step-by-step explanation:

3 - 4 - 5

6 - 8 - 10

7 - 24 - 25

5 - 12 - 13

are some basic right triangle

(about more, look picture)

Just use hypotenuse formula :

3 x 3 = 9

4 x 3 = 12

5 x 3 = 15

Option C is correct

[tex] {5}^{2} + { \sqrt{6} }^{2} = { \sqrt{31} }^{2} [/tex]

Option A is correct

[tex] {5}^{2} + {5}^{2} = { \sqrt{50} }^{2} [/tex]

But B isn't correct

Hope this helps ^-^

Answer:

Oioj[

Step-by-step explanation:

Step-by-step explanation:

Write the equation to solve it in order to know the exact value of X.

Answer:

[tex]x=-8[/tex]

Step-by-step explanation:

[tex]6\left(x-1\right)=9\left(x+2\right)\\\mathrm{Expand\:}6\left(x-1\right):\quad 6x-6\\6\left(x-1\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=6,\:b=x,\:c=1\\=6x-6\cdot \:1\\\mathrm{Expand\:}9\left(x+2\right):\quad 9x+18\\9\left(x+2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=9,\:b=x,\:c=2\\=9x+9\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18\\=9x+18\\6x-6=9x+18\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}[/tex]

[tex]6x-6+6=9x+18+6\\Simplify\\6x=9x+24\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\6x-9x=9x+24-9x\\Simplify\\-3x=24\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{24}{-3}\\Simplify\\\frac{-3x}{-3}=\frac{24}{-3}\\\mathrm{Simplify\:}\frac{-3x}{-3}:\quad x\\\frac{-3x}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3x}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1\\=x\\\mathrm{Simplify\:}\frac{24}{-3}:\quad -8\\\frac{24}{-3}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{3}=8\\=-8\\[/tex]

Answer:

x=-8

Step-by-step explanation:

6(x-1)= 9(x+2)

6x-6= 9x+18

6x-9x= 18+6

-3x= 24

-3x÷-3= 24÷-3

x=-8

Answer:

2.52

Step-by-step explanation:

4.2 × 0.6

Multiply the terms.

= 2.52

Answer:

2.52

hope it helps

Step-by-step explanation:

4.2 x 0.6

To solve this first, you simply multiply 42*06

(Exclude the decimal point)

42 x 6

= 252

Now since there are two numbers after the point (one is 4.2 and one is 0.6)

Move 252 two decimal places to left

= 2.52

Answer:

Option (B).

Step-by-step explanation:

Percentage change between two numbers a and b can be calculated by the formula,

% change = [tex]\frac{|b-a|}{a}\times 100[/tex]

Where, (b - a) = Change in values

a = Initial value

If a = 16 and b = 20

Percentage change between 16 and 20 will be,

= [tex](\frac{20-16}{16})\times 100[/tex]

= [tex]\frac{4}{16}\times 100[/tex]

= 25%

If a = 20 and b = 16,

Percentage change = [tex]\frac{|16-20|}{20}\times 100[/tex]

                                 = 20%

Therefore, %change between 16 and 24 may be 16% or 20%.

Option (A),

[tex]\frac{20-16}{16}\times 100[/tex] = 25%

Option (B),

[tex]\frac{20}{16}-1\times 100[/tex] = 1.25 - 1 × 100

                   = 1.25 - 100

                   = -98.75%

Option (C),

[tex]100\times \frac{1}{4}[/tex] = 25%

Option (D),

[tex]\frac{(20-16)}{20}\times 100[/tex] = 20%

Therefore, we can not use the calculation used in Option (B).

Area = 0.785

Area=0.79

I hope it helps

Answer:

A, C, D

Step-by-step explanation:

Answer: A , C , D

Step-by-step explanation: edge2022

Answer:

Joanna bought 21 items that come out to a total of $33.33. She bought 9 notebooks and 12 pencils.

Step-by-step explanation:

Notebooks (N) = $1.85 Pencils (P) = $1.39

9N+12P= $33.33

9*1.85=16.65

12*1.39=16.68

16.65+16.68=33.33

Answer:

x= 60°, y = 80°, z = 40°

Step-by-step explanation:

Look at the line substending 40° and Z°; you would see that both lines are parallel and so their angles are they the same.

Hence z= 40° { corresponding angles of parallel lines}

Similarly;

Look at the line substending 60° and x°; you would see that both lines are parallel and so their angles are they the same.

60° = x° { corresponding angles of parallel lines}

Now looking at the angle between x and y; let's call the angle between them r

And you would observe closely that r = z° = 40°{ vertically opposite angles are equal}

Note that x + r + y = 180°{ angle on a straight line}

y = 180° - ( x + r)

y = 180 - (60+40)

y = 180° - 100°

= 80°

Answer: A. The average midterm score for those who listen to classical music while studying is higher than the average midterm score for those who don't listen to music while studying.

Step-by-step explanation:

An Alternative Hypothesis is one that disproves the Null Hypothesis in that it believes that indeed there is a change in the dependent variable due to a change in the independent variable.

The Alternative Hypothesis essentially aims to prove the assertion of the Researcher that there is an effect as a result of the introduction of a variable.

Null Hypothesis on the other hand believes that no significant difference exists between a change in a dependant Variable as a result of a change in an independent one.

The correct answer above therefore is that indeed music while studying inspires people to do better in exams than those who do not listen to music while studying. This is the alternative hypothesis because it believes that there was a change in the exam results due to reading while studying.

Answer:

D

Step-by-step explanation:

2(x+b) = ax+c

2x+2b = ax+c

c = 2b

Answer:

252

Step-by-step explanation:

Answer:

68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 250, \sigma = 8, n = 64, s = \frac{8}{\sqrt{64}} = 1[/tex]

What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean?

This is the pvalue of Z when X = 64 + 1 = 65 subtracted by the pvalue of Z when X = 64 - 1 = 63. So

X = 65

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

By the Central Limit Theorem

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

[tex]Z = \frac{65 - 64}{1}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413.

X = 63

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

[tex]Z = \frac{63 - 64}{1}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.

Answer:

[tex]10\dfrac{5}{8}[/tex]

Step-by-step explanation:

The perimeter of a shape is the sum of the lengths of the sides.

[tex]2\dfrac{1}{8}+3\dfrac{3}{16}+2\dfrac{1}{8}+3\dfrac{3}{16}=10\dfrac{5}{8}[/tex] yards

Hope this helps!

Answer:

10 5/8

Step-by-step explanation:

The perimeter is the sum of all sides

2 1/8 + 3 3/16 + 2 1/8 + 3 3/16

Add the whole numbers

2 + 3 + 2 + 3 = 10

Add the fractions

1/8+ 1/8 + 3 3/16 + 3 3/16

2/8 + 6/16

1/4 + 3/8

2/8+3/8 = 5/8

Put them back together

10 5/8

Answer:

The truncated cube has 6 more faces than the truncated tetrahedron.

Step-by-step explanation:

==>Given:

truncated cube=>

edges (E) = 36

vertices (V) = 24

faces (F) = ? (unknown)

According to Euler's polyhedron formula, Vertices (V) - Edges (E) + Faces (F) = 2, let's find how many faces the truncated cube has

=> 24 - 36 + F = 2

- 12 + F = 2

F = 2 + 12

F = 14

truncated tetrahedron=>

edges (E) = 18

vertices (V) = 12

faces (F) = ? (unknown)

Using V - E + F = 2, find F

=>12 - 18 + F = 2

- 6 + F = 2

F = 2 + 6

F = 8

Comparing the faces of the truncated cube (14) and the truncated tetrahedron (8), the truncated cube has 6 more faces than the truncated tetrahedron (14 - 8 = 6)

Answer:

Answer A:The truncated cube has 6 more faces than the truncated tetrahedron.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of 8.35 hours per household. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household.

(a.) what is the probability that a household views television between 6 and 8 hours a day (to 4 decimals)?

(b.) How many hours of television viewing must a household have in order to be in the top 5% of all television viewing households (to 2 decimals)?

(c.) What is the probability that a household views television more than 5 hours a day (to 4 decimals)?

Solution:

Let x be the random variable representing the television viewing times per household. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 8.35

σ = 2.5

a) the probability that a household views television between 6 and 8 hours a day is expressed as

P(6 ≤ x ≤ 8)

For x = 6,

z = (6 - 8.35)/2.5 = - 0.94

Looking at the normal distribution table, the probability corresponding to the z score is 0.1736

For x = 8

z = (8 - 8.35)/2.5 = - 0.14

Looking at the normal distribution table, the probability corresponding to the z score is 0.4443

Therefore,

P(6 ≤ x ≤ 8) = 0.4443 - 0.1736 = 0.2707

b) the top 5% means greater than 95%. It means that the sample mean is greater than the population mean and the z score is positive. The corresponding z score from the normal distribution table is 1.645. Therefore,

(x - 8.35)/2.5 = 1.645

Cross multiplying, it becomes

x - 8.35 = 2.5 × 1.645 = 4.11

x = 4.11 + 8.35 = 12.46

c) the probability that a household views television more than 5 hours a day is expressed as

P(x > 5) = 1 - P(x ≤ 5)

For x = 5

z = (5 - 8.35)/2.5 = - 1.34

Looking at the normal distribution table, the probability corresponding to the z score is 0.0901

Therefore,

P(x > 5) = 1 - 0.0901 = 0.9099

Answer:

The company must sell 60 or 70 items to obtain a weekly profit of 200.

Step-by-step explanation:

The profit is the difference between the revenue and the cost of a given task, therefore:

[tex]\text{profit} = R - C\\\text{profit} = 66*x - 0.2*x^2 - (40*x + 640)\\\text{profit} = 66*x - 0.2*x^2 - 40*x - 640\\\text{profit} = - 0.2*x^2 + 26*x - 640[/tex]

To have a profit of 200, we need to sell:

[tex]-0.2*x^2 + 26*x - 640 = 200\\-0.2*x^2 + 26*x -840 = 0\text{ } *\frac{-1}{0.2}\\x^2 -130 + -4200 = 0\\x_{1,2} = \frac{-(-130) \pm \sqrt{(-130)^2 - 4*1*(-4200)}}{2*1}\\x_{1,2} = \frac{130 \pm \sqrt{16900 + 16800}}{2}\\x_{1,2} = \frac{130 \pm \sqrt{100}}{2}\\x_{1,2} = \frac{130 \pm 10}{2}\\x_{1} = \frac{130 + 10}{2} = \frac{140}{2} = 70\\ x_{2} = \frac{130 - 10}{2} = \frac{120}{2} = 60[/tex]

The company must sell 60 or 70 items to obtain a weekly profit of 200.

Answer:

Step-by-step explanation:

morning mean: 14 mins

afternoon: 14 mins

both morning and afternoon have the same mean time

Answer:

GCF: 1

Step-by-step explanation:

Factors are numbers that can be evenly divided into another number. The greatest common factor of a set of numbers is the biggest number than can evenly divide into all the the numbers.

Let's list the factors of 60, 45 and 82

Factors of 60:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Factors of 45:

1, 3, 5, 9, 15, 45

Factors of 82:

1, 2, 41, 82

The greatest factor that all 3 numbers share is 1.

The right answer is 1.

Please see the attached picture for full solution

Hope it helps

Good luck on your assignment..

Answer:

53.33mph

Step-by-step explanation:

Let's calculated the total time spent on the journey first;

For the first 300miles the time spent is ;

From Distance = speed× time

time = Distance/ speed

= 300/60 = 5 hours

Similarly for the last 100mile the time taken is ;

100/40 = 2.5 hours

Total time spent = 5 +2.5 = 7.5 hours

Total distance covered 400miles

Therefore average speed = 400/7.5 =53.33mph

Answer:

53.33 mph

Step-by-step explanation:

I just wanted to say that the other guy's answer is correct, I checked :)

Answer: There can be 2 gold 1 silver, 2 silver one gold, 3 silver, or 3 gold.

I'm not really sure if this is correct but I hope this helps:)

Answer:

A. 38.3

Step-by-step explanation:

[tex]circumference \\ \: \: \: \: \: = 2 \times radius \times \pi \\ or =diameter \times \pi \\ thus \: the \: answer \: is \\ 12.2 \times 3.14 = 38.3 \\ ( \: a \: ) [/tex]

Answer:

x=106 degrees

Step-by-step explanation:

The two opposite angles in a parallelogram are always the same and we know 360 degrees in a parallelogram.

x+x+74+74=360.

2x+148=360

2x=212

x=106 degrees

Answer:

D

Step-by-step explanation:

Find out if they match in all of them

Hope this helps

Answer:

-10 sqrt(10)

Step-by-step explanation:

-2 sqrt(250)

We know that sqrt(ab) = sqrt(a) sqrt(b)

-2 sqrt(25*10)

-2 sqrt(25)*sqrt(10)

-2 *5*sqrt(10)

-10 sqrt(10)

Answer:

3 and 8 are the extremes of the given proportion (first listed answer option)

Step-by-step explanation:

In a proportion of the type:

[tex]\frac{A}{B} =\frac{C}{D}[/tex]

the values "A" and "D" are called "extremes of the proportion, while "B" and "C" are called the "means" of the proportion.

This comes from writing it as:   A : B = C : D

where we observe that A and D are the more "extreme" values being further away from the equal sign than the quantities B and C which are more towards the middle (center of the proportion).

So in your case, the numbers 3 and 8 are the extremes

Answer:

3 and 8

Step-by-step explanation:

Answer:

a

The average cost is [tex]E(C) = 66[/tex]

b

The standard deviation of  cost is  [tex]\sigma = 9.798[/tex]

Step-by-step explanation:

From the question we are told that

          [tex]E(X) = 4[/tex]

          [tex]E(Y) = 2[/tex]

          [tex]E(X^2) = 24[/tex]

           [tex]E(Y^2) = 8[/tex]

The cost of replacing the two component is  C =  50 + 2 X + 4 Y

The variance   of X is mathematically represented as

           V(X) =  [tex]E(X^2) - [E(X)]^2[/tex]

Substituting values  

              [tex]V[X] = 24 - 4^2[/tex]

               [tex]V[X] =8[/tex]

The variance  of Y is mathematically represented as

           V(Y) =  [tex]E(Y^2) - [E(Y)]^2[/tex]

Substituting values  

              [tex]V[Y] = 8 - 2^2[/tex]

               [tex]V[X] =4[/tex]

The average of  replacing the two component is  

        [tex]E(C) = 2 * E(X) + 4* E(Y)[/tex]

substituting value

         [tex]E(C) = 50 + 2 * (4) + 4* (2)[/tex]

         [tex]E(C) = 66[/tex]

The variance  of replacing the two component is  

        [tex]V(C) = V(50 + 2X +4Y)[/tex]      Note: The variance of constant is zero

                                                                  and X and  Y are independent  

=>      [tex]V(C) = 2^2 * V(X) + 4^2 * V(Y)[/tex]

substituting values

=>       [tex]V(C) = 4 * 8 + 16 * 4[/tex]        

=>         [tex]V(C) = 32 + 64[/tex]

=>         [tex]V(C) = 96[/tex]

The standard deviation is

         [tex]\sigma = \sqrt{V(C)}[/tex]  

substituting values

           [tex]\sigma = \sqrt{96}[/tex]

           [tex]\sigma = 9.798[/tex]

Answer:

It would be 4.v5