Answer the questions
(1) 150 cola cans and 260 fruit juice cans need to be stacked in a school canteen. If each stack is
to be of the same height and is to contain cans of the same type, what would be the greatest
number of cans each stack can have?

Step-by-step explanation:

that is the same as calculating the perimeter of the rectangle (the way 1 time around the rectangle).

the perimeter of a rectangle is

2×length + 2×width

in our case that is

2×11 + 2×4 = 22 + 8 = 30 ft

the stripping costs $5 per foot, and we have 30 ft.

so, the total costs are

5 × 30 = $150

The inequality to represent the number of tickets Bianca can buy without over drawing on her debit card is 14.50 + 6.50x ≤ 50  .

In the question ,

it is given that

amount of money present in Bianca's Debit card = $50

amount of money spend on lunch = $14.50

cost of 1 movie ticket = $6.50

le the number of ticket = "x"

according to the question ,

the inequality is

14.50 + 6.50x ≤ 50

6.50x ≤ 50 - 14.50

6.50x ≤ 35.5

x ≤ 35.5/6.50

x ≤ 5.46

≈ 5

Therefore , The inequality to represent the situation is 14.50 + 6.50x ≤ 50  

, and the number of tickets she can buy is 5 .

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The two expressions to be evaluated are

The problem asks for two expressions with positive and negative numbers

the positive numbers in the expressions are 2x and 4x

the negative numbers in the expressions are -5 and -3

At x = 5.

evaluating the first expression gives

y = 2x - 5

y = 2 * 5 - 5

y = 10 - 5

y = 5

evaluating the second expression gives

y = 4x - 3

y = 4 * 5 - 3

y = 4 * 2

y = 8

One of the expressions evaluated has error and on is error free

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Answer:

65c

Step-by-step explanation:

Answer:

The height of the flagpole is about 25.6 feet.

Step-by-step explanation:

The figure is omitted--please sketch it.

Put your calculator in degree mode.

Let h be the height of the flagpole.

[tex] \tan(52) = \frac{h}{20} [/tex]

[tex]h = 20 \tan(52) = 25.6[/tex]

In the given graph the correct statements are:

q ⊥ n

m ║ n

p ⊥ m

Parallel lines are two straight lines that never intersect and are located in the same plane. They are equidistant lines that are always at the same distance from one another. Parallel lines are denoted by the apostrophe ||. AB || CD, for instance, denotes that line AB and line CD are parallel. Perpendicular lines, on the other hand, are when two lines cross at an angle of 90 degrees. The symbol stands for perpendicular lines. Line PQ is perpendicular to line RS, for instance, if PQ RS. Examine the following illustration and the characteristics of parallel and perpendicular lines to recognize and distinguish between them.

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84.78 mm² is area of circle .

What is a circle ?

radius of the circle = 27 mm

area of the circle = πr²

                          =  3.14 * 27

                         =  84.78 mm²

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Answer:

$69.98

Step-by-step explanation:

8.5% of 64.50 is around 5.48 or to be exact, 5.4825 which there are no more dollar denominations beyond the hundredth place so it would be 5.48. 64.50+5.48 is $69.98.

Answer:

$69.98

Step-by-step explanation:

It is percent increase.

So, 100% + 8.5% = 108.5% which is 1.085.

64.50 × 1.085 = 69.9825

we need to round to 2 decimal places

$69.98

The logarithmic expression given as logₙ(1/63) has its value to be -4.143

From the question, the given parameters are

logₙ(7) = 1.946

logₙ(9) = 2.197

logₙ(16) = 2.773

The logarithmic expression to calculate is given as

logₙ(1/63)

Express 1/63 as 1/7 * 1/9

So, we have the following representation

logₙ(1/63) = logₙ(1/7 * 1/9)

Apply the product of logarithm

This gives

logₙ(1/63) = logₙ(1/7) + logₙ(1/9)

Apply the exponent of logarithm

This gives

logₙ(1/63) = -logₙ(7) - logₙ(9)

Substitute logₙ(7) = 1.946 and logₙ(9) = 2.197 in logₙ(1/63) = -logₙ(7) - logₙ(9)

logₙ(1/63) = -1.946 - 2.197

Evaluate

logₙ(1/63) = -4.143

Hence, the value of the logarithmic expression is -4.143

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The probability that the Yankees will win when they score fewer than 5 runs is; 0.567

We are given;

Event A which is when Yankees win has a probability of; P(A) = -.45

Thus, Event that the Yankees don't win which is when they lose is;

P(A') = 1 - 0.45 = 0.55

Event B which is the event that the Yankees score 5 or more runs has a probability of; P(B) = 0.6

Event that the Yankees score 4 or less run is given by the probability;

P(B') = 1 - 0.6 = 0.4

The probability that the Yankees win and score 5 or more runs is;

P(A' ∩ B') = 0.34

Thus, the probability that the Yankees will win when they score fewer than 5 runs wanted is given by the chain rule in conditional probability of the formula;

P(A' | B') = P(A' ∩ B')/P(B') = 0.34/0.6

P(A' | B') = 0.567

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Answer:

(10, -1)

Step-by-step explanation:

x + 2x = 3x

-y + y = 0

11 + 19 = 30

3x = 30

3/3 x = 30/3

x = 10

10 - y = 11

y = -11 + 10

y = -1

Answer:

(-2/5,0)

Step-by-step explanation:

if y=0,

5/12 x + 1/6 = 0

5x + 2 = 0

x = -2/5

or, multiply by 6 to get the intercept form:

6y = 5/2 x + 1

-5/2 x + 6y = 1

x/(-2/5) + y/(1/6) = 1

Answer: $402

Step-by-step explanation: I believe this answer is correct i did all the math

Answer:

12*(1/4+1/3)(1/4+1/3)+2/3= 12*(1/16+1/12+1/12+1/9)+2/3=12*(9/144+12/144+12/144+16/144)+2/3= 12*(49/144)+2/3=12*49/144+2/3= 49/12+2/3=49/12+8/12=57/12= 4*9/12=4* 3/4

Step-by-step explanation:

Answer:cap

Step-by-step explanation:C A P

Answer:

B (x = 3 + √5)

Explanation:

x² + 9 = 5

Take square root of both sides

x + 3 = ± √5

Add 3 to both sides

x = 3 + √5 or x = 3 - √5

solution

3x+18/18

ans4

Answer:

(10 + 8) - (7 * 2) = x, 4 pounds of birdseed left

Step-by-step explanation:

      For the first part of our equation, we will find the total amount of pounds of seeds among the bags (addition).

      For the next part, we will find out how much of the bird seed is used (subtraction).

      Then, it will equal whatever is left.

(10 + 8) - (7 * 2) = x, x = pounds of bird seed left

      Now, we will solve.

(10 + 8) - (7 * 2) = x

(18) - (14) = x

x = 4 pounds of birdseed left

The ball was in the air for 1.5 seconds. The answer is true.

The equation of the form ax² + bx +c is known as a quadratic equation.

The given equation is h(t) = -16t² + 20t + 6.

To find the time for which the ball was in the air, substitute h(t) =0.

0 = -16t² + 20t + 6

Use the quadratic formula to solve the equation:

[tex]t= \frac{- 20 \pm\sqrt{20^2 - 4(-16)(6)}}{2(-16)}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{784}}{-32}\\\\t= \frac{- 20 \pm28}{-32}[/tex]

t = (-20 + 28)/(-32) or t = (-20-28)/(-32)

t = -0.25 or t = 1.5

Since time cannot be negative, discard the negative value.

Hence, the ball was in the air for 1.5 seconds. The answer is true.

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Step-by-step explanation:

6x-4+60=14x-8

6x+56=14x-8

8x=64

x=8

Answer: 17:4

Step-by-step explanation:

21 washing machines

4 broken

21 - 4 = 17

17:4

The equation of the line  in slope-intercept form is y = -x/12 + 23/4

Given that: the line is perpendicular to the line y= 12x−2 and it contains the (−3,6).

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The slope-intercept form of a straight line is:

y = mx + c,

where m is the slope and c is the y-intercept

When the two lines are perpendicular, the product of their slope is -1 i.e.

m₁ x m₂ = -1

where m₁ and m₂ represent the slope of the lines

Let the slope of the given line be m₁ and the slope of the unknown line be m₂

Line1(given):

y = 12x−2   and m₁ x m₂ = 12

m₁ x m₂ = -1

12 x m₂ = -1

m₂= -1/12

Line 2(unknown) with the point (−3,6):

y = mx + c

6 = -1/12 (-3) + c

6 = 1/4 + c

c = 6 -1/4 = 23/4

y = -x/12 + 23/4

Therefore, the slope-intercept form of the equation of the line is y = -x/12 + 23/4

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1:3

= 15:45

= 15/45

= 15/45 {can be divided by 15}

= 15/15 = 1 ; 45/15 = 3

Therefore, 15/45 is 1/3

                  15:45 is 1:3

The equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.

According to the question,

We have the following information:

The line is parallel to y = -4/3x + 11 and passes through the point (–6, 2).

Now, we know that the following formula is used to find the equation of the line:

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

In this case, m is the slope of the line.

m = -4/3

We have the following values:

x' = -6 and y' = 2

Now, we have the following expression:

(y-2) = -4/3(x+6)

y-2 = -4x/3-8

Adding 2 to both sides of the equation:

y = -4x/3-8+2

y = -4x/3-6

Hence, the equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.

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Answer: (1/3)x - 8

Step-by-step explanation:

one - third means 1/3

one - third of a number means (1/3)x

       ( x being the number )

Eight less means -8

Eight less than 1/3 of an number is (1/3)x - 8

The linear function of the table is a) g(x)=x-7

What is linear function?

 If the largest power of the variables in a function is 1, then that function is linear. A line across these two points with a straightedge is needed to complete the graph because two points determine a line. When m and b are real numbers, the slope of a linear function has the form f(x)=mx+b. To find the x-intercept, set f(x)=0 and solve for x. Because y=f(x), we can use y and f(x) interchangeably.

Here let us take g(x) as y values. In given table take any two points ,

[tex](x_1,y_1)=(0,-7)\\(x_2,y_2)=(2,-5)[/tex]

Now using slope formula ,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = 2/2 = 1

Now using equation formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y+7=1(x-0)

=> y+7=x

=> y =x-7

Then y=g(x)

=> g(x) = x-7

Therefore the linear function of the given table is g(x)=x-7 .

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There are 9 numbers from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4

The difference can be represented as

Largest - Smallest = 4

Also, we have two instances to be

15 and 51

And the range is given as

Range = 10 to 99

In a range of 10, there is only one number whose difference between the digits is 4

There are 9 ranges of 10 from 10 to 99

So, the count of the range is

Count = 9 range * one number

Rewrite as

Count = 9 * 1

Evaluate

Count = 9

Hence, there are 9 of such numbers from 10 to 99

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Answer:   $11.50

==================================================

Explanation:

x = cost of one burger

y = cost of one hot dog

3 burgers = 3x dollars

2 hot dogs = 2y dollars

3 burgers + 2 hot dogs = 3x+2y = 8 dollars

The first equation to set up is 3x+2y = 8 which is based on the info of what Ricky purchased.

Through similar logic, the other equation is x+2y = 6 based on what Betty ordered.

This is the system of equations

[tex]\begin{cases}3x+2y = 8\\x+2y = 6\end{cases}[/tex]

There are a few approaches we could take. I'll use substitution.

Let's isolate x in the 2nd equation.

x+2y = 6

x = -2y+6

Then plug this into the 1st equation. Solve for x.

3x + 2y = 8

3(-2y+6) + 2y = 8

-6y+18+2y = 8

-4y+18 = 8

-4y = 8-18

-4y = -10

y = -10/(-4)

y = 2.50 dollars is the cost of one hot dog

Then,

x = -2y+6

x = -2*2.50+6

x = -5+6

x = 1 dollar is the cost of one burger

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

Check:

The x and y values are confirmed correct.

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

The last thing to find out is how much is spent if Billy bought 4 burgers and 3 hot dogs

4x+3y = 4*1 + 3*2.50 = 4 + 7.50 = 11.50 dollars is the final answer

This assumes that Billy is paying for himself and the other people pay for themselves as well. If Billy is paying for everyone, then the total comes to 11.50+8+6 = 25.50 dollars.

Answer:

b

Step-by-step explanation:

because you solve it and you get B

The null and alternative hypothesis regarding the test on whether the mean error is of zero is given by the following option:

D. H0: μ = 0 minutes, H1: μ ≠ 0 minutes.

The first step in identifying the hypothesis is to identify the claim tested, given as follows:

The mean prediction error is equals to zero.

At the null hypothesis, it is tested if there is not enough evidence to go against the claim, hence we suppose that the mean is of zero minutes, as follows:

H0: μ = 0 minutes.

At the alternative hypothesis, it is tested if there is enough evidence to reject the null hypothesis, that is, if there is enough evidence to conclude that the mean prediction error is different of zero minutes, hence it is given as follows:

H1: μ ≠ 0 minutes.

Thus option D gives the correct null and alternative hypothesis in the context of this problem.

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