JAMES NEEDS TO BUY ONE CAN OF ORNGE SODA FOR EVERY FIVE CANS OF COLA. IF JAMES BUYS 35 CANS OF COLA, HOW MANY CANS OF ORANGE SODA SHOULD HE BUY?

Answer:

about 3 1/2 hours long

Step-by-step explanation:

70 goes into 240 evenly 3 times, and 70×3 equals 210. that leaves 30 miles remaining. since he is moving at an average rate of 70mph, 3/7 would be the remaining time. to decimal that equals a total of about 3 hours and 25 minutes, which, rounded up, equals 3 and 1 half hours.

Answer:

150 people took the test.

Step-by-step explanation:

Given:

Number of people liked the new flavor = 69

Percentage of people liked the new flavor = 46%

We need to find the number of people who took the test.

Solution:

Let the number of people who took the test be 'x'.

So we can say that;

Percentage of people liked the new flavor multiplied by the number of people who took the test is equal to Number of people liked the new flavor.

framing in equation form we get;

[tex]46\%\times x =69\\\\\frac{46}{100}x=69\\\\0.46x =69[/tex]

Dividing both side by 0.46 we get;

[tex]\frac{0.46x}{0.46}=\frac{69}{0.46}\\\\x= 150[/tex]

Hence 150 people took the test.

Answer:

its C i think

Step-by-step explanation:

Answer:

This system have 9000 different numbers.

Step-by-step explanation:

We know that the internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0.

We have total 10 digits.

In the first place we have 9 possibilities, because from the conditions of the task in the first place there cannot be 0.

In second, third and fourth place we have 10 possibilities.

Therefore, we get

[tex]N=9\cdot 10\cdot10 \cdot 10=9000[/tex]

This system have 9000 different numbers.

In this phone system, there are 9,000 different internal telephone numbers that can be assigned.

The internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0. To find the number of different numbers that can be assigned in this system, we need to consider the possibilities for each digit position. Since the first digit cannot be 0, there are 9 choices (1 through 9) for the first digit. For the remaining three digits, each digit can be any number from 0 to 9, resulting in 10 choices for each of the three remaining digits. Therefore, the total number of different numbers that can be assigned in this system is

9 * 10 * 10 * 10 = 9,000.

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Answer:

33%

Step-by-step explanation:

Assuming the weight of the mixture to be 100g**, then the weight of ryegrass in the mixture would be 30g.

Also, assume the weight mixture X used in the mixture is Xg, then the weight of mixture Y used in the mixture would be (100-X)g.

So we can now equate the parts of the ryegrass in the mixture as:

0.4X + 0.25(100-X) = 30

<=> 0.4X + 25 - 0.25X = 30

<=> 0.15X = 5

<=> X = 5/0.15 = 500/15 = 100/3

So the weight of mixture X as a percentage of the weight of the mixture

= (weight of X/weight of mixture) * 100%

= (100/3)/100 * 100%

= 33%

Answer:

  50% of market value

Step-by-step explanation:

The actual tax rate on the Combs home is ...

  $8719.38/$361800 = 0.0241 = 24.1 mils

The rate of assessment is ...

  (24.1 mils)/(48.2 mils) = 0.50 = 50%

The Combs pay tax on 50% of their home's market value.

Answer:

The sampling method used is Convenience sampling.

Step-by-step explanation:

Convenience sampling is a non-probability sampling method that involves the selection of sample from the easiest source available. In this sampling method the samples are selected from the most convenient possible way.

Foe instance, samples taken from social media, nearest shopping mall, and so on.

In this case the students selected 10 friends to answer the survey.

This is an example of convenience sampling method because sampling your friend is the easiest sample anyone could collect.

Thus, the sampling method used is Convenience sampling.

The mean and standard deviation for the Standard normal distribution is 0 and 1 respectively. Option b is correct.

The standard normal distribution is a type of normal distribution that has a mean of 0 and a standard deviation of 1. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centered at zero.

Since the standard normal distribution is a normal distribution curve in which the values of the mean is 0 and the value of The standard normal distribution is a normal distribution curve where the values of the mean and standard deviation is 1.

Thus, the correct option for the given question is Option B.

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In a standard normal distribution, the mean is 0 and the standard deviation is 1. This defines a distribution where data is symmetrically spread around the mean, and a z-score can be used to determine how many standard deviations a value is from the mean.

In a standard normal distribution, the correct answer to the student's question is that the mean is 0 and the standard deviation is 1. This is represented by option b. In a standard normal distribution, often denoted as Z ~ N(0, 1), the mean (μ) equals 0, which signifies that the distribution is centered on the zero point on a number line.

The standard deviation (σ) equals 1, indicating that the values within the distribution are spread out in such a way that one standard deviation away from the mean encompasses approximately 68% of the data in a symmetrical fashion on both sides of the mean.

The concept of z-scores in the context of the standard normal distribution allows for the comparison of different values within different populations. A z-score represents how many standard deviations away a value is from the population mean.

It is crucial to note that the standard deviation cannot be negative; it represents the dispersion of the dataset around the mean, and therefore can only be positive or zero.

Answer:

y = 2x^2 - 12x + 27

Step-by-step explanation:

Step 1:  Distribute the power

y = 2(x - 3)² + 9

y = 2(x^2 - 6x + 9) + 9

y = 2x^2 - 12x + 18 + 9

y = 2x^2 - 12x + 27

Answer: y = 2x^2 - 12x + 27

Answer: the balance is $5328.95

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = 3200

r = 8.5% = 8.5/100 = 0.085

t = 6 years

Therefore,

A = 3200 x 2.7183^(0.085 x 6)

A = 3200 x 2.7183^(0.51)

A = $5328.95 to the nearest hundredth

Answer:

FOR PLATO/EDMENTUM USER THE right answer is: 5328.93

Step-by-step explanation:

Answer:

Step-by-step explanation:

In a parallelogram, the opposite sides are equal and parallel.

Also, consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles is 180 degrees.

Angle 2m and angle n are supplementary angles. Therefore,

2m + n = 180 - - - - - - - - - - - -1

Also, the opposite angle in a parallelogram are equal. This means that

2m = 70

m = 70/2

m = 35 degrees

Substituting m = 35 into equation 1, it becomes

2 × 35 + n = 180

70 + n = 180

n = 180 - 70

n = 110 degrees

The value of m and n are 35 and 110 respectively.

We are given that one of the angles of the parallelogram is [tex]70^\circ[/tex].

Since opposite angles in a parallelogram are supplementary, the angle directly opposite the 70° angle must be [tex]180^\circ -70^\circ = 110^\circ[/tex].

We are also given that one of the non-consecutive interior angles has a measure of 2m°.

Since consecutive interior angles in a parallelogram add up to 180°, the angle next to the 2m° angle must have a measure of 180°- 2m°.

The opposite sides of a parallelogram are congruent.

This means that n° must be congruent to 110°. So, n = 110.

We can now solve for 'm'.

Since the angle next to the 2m° angle must have a measure of 180°−2m° and this angle is also congruent to 110°.

We have the equation: [tex]110^\circ = 180^\circ - 2m^\circ[/tex]

[tex]2m^\circ = 70^\circ[/tex]

[tex]m=35[/tex]

Answer:

30

Step-by-step explanation:

Look at the bottom line of the chart.

He sold 41 sides of French fries and 40 sides of onion rings.

41 + 40 = 81

Since he sold a total of 81 sides with bacon cheeseburgers, that means he sold a total of 81 bacon cheeseburgers.

We have a ratio:

81 bacon cheeseburgers to 40 sides of onion rings

Now he sold 120 bacon cheeseburgers, so we set up a proportion to find the number of sides of onion rings. Let the unknown number be x.

81 burgers is to 40 sides as 120 burgers is to x sides

81/40 = 120/x

We solve for x by cross multiplying.

81x = 40 * 120

81x = 4800

x = 4800/81 = 59.3

That means he serves 59 sides of onion rings.

Each serving of onion rings is half pound.

59 * 0.5 = 29.5

For 120 bacon cheeseburgers, he serves approximately 29.5 lb of onion rings.

Answer: 30

Answer:

30 pounds

Bacon cheeseburger with onion rings:

40

(41 + 40)

=

40

81

= 0.4938

then,

120 x 0.4938 = 59.256

then,

59.256 x .50 = 29.628

Answer:

Option B) 31.348  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 49

Sample standard deviation, s = 2.6 minutes

Population  standard deviation, [tex]\sigma[/tex] =  2.9 minutes

Significance level, [tex]\alpha[/tex] = 0.05

We have o find the test statistic.

Formula:

[tex]\chi^2 = \dfrac{(n-1)s^2}{\sigma^2}\\\\\chi^2 =\displaystyle\frac{(40-1)(2.6)^2}{(2.9)^2}\\\\\chi^2=31.348[/tex]

Thus, the test statistic is

Option B) 31.348

Answer:

c= 1/26

Step-by-step explanation:

The joint probability mass function for X and Y must comply that:

[tex]\[\sum\]\sum\] c(x +y) = 1[/tex]   for  x∈{1,2,4} and  y∈{1,3}

thus, all the possible values for the pairs (x,y) are:

(1,1)  (1,3) (2,1) (2,3) (4,1) (4,3)

and then

c [(1+1)+(1+3)+(2+1)+(2+3)+(4+1)+(4+3)] = 1

c[26] = 1

c= 1/26

The domain is the X value ( input).

The line starts at (0,2) so 0 is the first part of the domain. The horizontal line has an arrow on it pointing to the right which means the line can continue to infinity.

The answer is the second choice, 0 to infinity

Answer:

-√(3/10)

Step-by-step explanation:

cos(x) = 2[cos(x/2)]² - 1

-2/5 = 2[cos(x/2)]² - 1

3/5 = 2[cos(x/2)]²

3/10 = [cos(x/2)]²

cos(x/2) = +/- sqrt(3/10)

Since x is in the 3rd quadrant, x/2 would be in the second quadrant.. so cos(x/2) is negative

[tex]x[/tex] is in quadrant III, so [tex]\pi<x<\frac{3\pi}2[/tex].

This makes [tex]\frac\pi2<\frac x2<\frac{3\pi}4[/tex], which means [tex]\frac x2[/tex] lies in quadrant II, for which we expect [tex]\cos\frac x2<0[/tex].

Recall the double-angle identity:

[tex]\cos^2\dfrac x2=\dfrac{1+\cos x}2[/tex]

[tex]\implies\cos\dfrac x2=-\sqrt{\dfrac{1-\frac25}2}=-\sqrt{\dfrac3{10}}[/tex]

Yo sup??

by Pythagoras theorem we can say

38²=34²+b²

b²=1444-1156

=288

b=17

Hope this helps

Answer:

D = 17

Step-by-step explanation:

Hope this helps

Answer:

The 90% confidence interval is (0.383,0.497)    

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 200

Number of children that would attend  Valentine's Day Forma, x = 88

[tex]\hat{p} = \dfrac{x}{n} = \dfrac{88}{200} = 0.44[/tex]

90% Confidence interval:

[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]z_{critical}\text{ at}~\alpha_{0.10} = \pm 1.64[/tex]

Putting the values, we get:

[tex]0.44\pm 1.64(\sqrt{\dfrac{0.44(1-0.44)}{200}}) = 0.44\pm 0.057\\\\=(0.383,0.497)[/tex]

Interpretation:

The 90% confidence interval is (0.383,0.497). We are 90% confident that the proportion of children attending Valentine's Day Formal is between 38.3% and 49.7%

Answer:

180 degrees rotation

Step-by-step explanation:

Solution:

- The congruency statements are as follows:

  Angles:      L   ≅   X

                     M   ≅   Y

                     N   ≅   Z

  Sides:        LM   ≅   XY

                    MN   ≅   YZ

                     LN    ≅   XZ  

   Transformation:

                    L ( -4 , 1 )  ------- > X ( 4 , - 1 )

                        ( x , y ) -----------> ( -x , -y )

                         180 degrees rotation

The congruence can be expressed as ∆LMN ≅ ∆XYZ. To map LMN onto XYZ, a transformation like translation, rotation, reflection, or a combination thereof can be used.

If triangles LMN and XYZ are congruent to each other, the corresponding parts must be equal in both measure and shape. The congruence statement for these triangles would be ∆LMN ≅ ∆XYZ, which implies that angle L is congruent to angle X, angle M to angle Y, and angle N to angle Z. Additionally, side LM is congruent to side XY, side MN to side YZ, and side NL to side XZ.

Regarding the transformation that maps triangle LMN onto XYZ, if they are congruent, any of the following rigid motions (also known as isometries) could be used: a translation, a rotation, a reflection, or a combination of these. Since these transformations preserve distance and angle measures, the size and shape of triangle LMN will remain unchanged, and it will match exactly onto triangle XYZ.

Answer:

Bobby around 131 minutes and Billy around 111 minutes

Step-by-step explanation:

To solve the problem it is important to raise equations regarding what happens.

 They tell us that Billy (Bi) and Bobby (Bo) can mow the lawn in 60 minutes. That is to say that what they prune in a minute is giving as follows:

1 / Bo + 1 / Bi = 1/60 (1)

They say Billy could mow the lawn only in 20 minutes less than it would take Bobby, therefore

1 / Bi = 1 / (Bo-20) (2)

Replacing (2) in (1) we have:

1 / Bo + 1 / (Bo-20) = 1/60

Resolving

(Bo - 20 + B0) / (Bo * (Bo-20) = 1/60

120 * Bo - 1200 = Bo ^ 2 - 20Bo

Rearranging:

Bo ^ 2 - 140Bo -1200 = 0

Now applying the general equation

Bo = 130.82 or Bo = 9.17, this last value cannot be because Billy took 20 minutes less and neither can he prune faster than the two together, therefore Bobby only takes around 131 minutes and Billy around 111 minutes

Checking with equation 1:

1/131 +1/111 = ~ 1/60

Final answer:

Bobby would take 120 minutes to mow the lawn by himself.

Explanation:

The question asks us to calculate how long it will take Bobby to mow the lawn by himself if it takes his twin brother Billy 20 minutes less to do the job on his own, and they can mow the lawn together in 60 minutes. To solve this, we can use the concept of work rate and the idea that the combined work rate of Billy and Bobby equals the reciprocal of the time they take to work together.

Let's assume Bobby takes x minutes to mow the lawn by himself. Thus, Billy would take x - 20 minutes. We can express their work rates as:

The combined work rate when they mow together is the sum of their individual work rates, which is equal to 1/60 since they take 60 minutes together. So, we have:

1/x + 1/(x - 20) = 1/60

By solving this equation for x, we find the time it takes Bobby to mow the lawn by himself.

Hence, Bobby will take 120 minutes to mow the lawn by himself.

To determine the amount of candy per sack, divide the total one fourth pound of rock candy by four, resulting in 1/16 pound of candy in each sack.

Demont has made one fourth pound of rock candy and needs to divide this equally into four sacks. To find the amount of candy in each sack, we divide the total amount of rock candy by the number of sacks.

Here's the calculation:

Total rock candy = 1/4 pound

Number of sacks = 4

Amount of candy per sack = 1/4 pound ÷ 4 = 1/16 pound per sack

Therefore, each sack will contain 1/16 pound of rock candy.

Answer:

Boi

Step-by-step ex:

Answer:

Option 4

Step-by-step explanation:

x - 4 is negative for x < 4

Mod makes it positive,

-(x - 4) = 4 - x

4 - x for x < 4,

x - 4 for other x values (which are greater than/equal to 4)

Answer:

  -540

Step-by-step explanation:

The coefficient of the k-th term of (a+b)^n is nCk. (k = 0, 1, 2, ..., n)

Here, we want the coefficient of a^3b^3 for n=6, so k=3 and the coefficient is ...

  6C3 = 6!/(3!(6-3)!) = 5·4 = 20

So for a=3x and b=-y, we want ...

  20a^3b^3 = 20(3x)^3(-y)^3 = -540x^3y^2

The coefficient you're looking for is -540.

Answer:

Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain one tick mark. Sides B D, U W, V S, and R A each contain two tick marks. Sides A S and W D each contain three tick marks. The angles represented by vertex letters U, B, R, and V each contain two tick marks. The angles represented by vertex letters D, W, S, and A each contain one tick mark.

Answer:

b m d j and k z y a

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

Answer:

I) There are [tex]8.760\times 10^3[/tex] hours in 1 year.

II) The exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.

Step-by-step explanation:

Given : 1 hour=3600 seconds

1 year = 31556952 seconds.

To find :

I)  Use scientific notation to estimate the number of hours in one year.

1 day = 24 hours

1 year = 365 days

So, number of hours in one year is given by,

[tex]n=24\times 365[/tex]

[tex]n=8760[/tex]

In scientific notation,

[tex]8760=8.760\times 10^3[/tex]

So, there are [tex]8.760\times 10^3[/tex] hours in 1 year.

II) 1 year = 31556952 seconds.

1 hour = 3600 seconds

In one year the number of hour is given by,

[tex]n=\frac{31556952}{3600}[/tex]

[tex]n=8765.82[/tex]

In scientific notation,

[tex]8765.82=8.76582\times 10^3[/tex]

So, the exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.

III) In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences.

Answer:

Total amount of books in the bookcase =  225 books

Step-by-step explanation:

Each shelf is to have 15 books

Therefore total amount of books in the bookcase = {9×15} + {6×15} = 225 books

Step-by-step explanation:

Below is an attachment containing the solution.

Final answer:

The dimensions are 24cm x 15cm x 20cm.

Explanation:

To find two possible sets of lengths and widths for the rectangular prism with a height of 20cm and a surface area of 2400cm2, we need to understand the formula for the surface area of a rectangular prism: SA = 2(lw + lh + wh). Here, l = length, w = width, and h = height.

Since we know the height (h = 20cm) and the surface area (SA = 2400cm2), we can set up the equation:

2(lw + 20l + 20w) = 2400

We will consider two cases: one where the length and width are equal (since that is a specific request), and another where they are not.

Case 1: Length and width are equal (l = w). We simplify the equation to:

2(l2 + 40l) = 2400

Solving for l gives us l = w = 20cm. Therefore, the dimensions are 20cm x 20cm x 20cm.

Case 2: Length and width are not equal. To find a possible set, we can assume a width and solve for the length:

Let's assume w = 15cm. Plugging this into the equation gives us:

2(l15 + 20l + 20 x 15) = 2400

Solving for l gives us l = 24cm.

Therefore, the dimensions are 24cm x 15cm x 20cm.

Answer:

$0.36 per share

Step-by-step explanation:

The data provided in the question are as follows

Common stock outstanding = 50,000 shares

Preferred stock outstanding = 4,000 shares

Par value of common stock = $4

Interest rate and par value of preferred stock = 9% and $100

Total dividend payment declared = $54,000

So, the amount of dividend for each share of common stock is

= (Total dividend payment declared - Preferred stock outstanding × interest rate × par value) ÷ (common stock outstanding)

= ($54,000 - 4,000 × $100 × 9%) ÷ (50,000 shares)

= ($54,000 - $36,000) ÷ (50,000 shares)

= $18,000 ÷ 50,000 shares

= $0.36 per share