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The answers are:

27. P(6) = 0.2 , 28. P(even number) = 0.6 , 29. P(6) = 1/10 , 30. P(even number) = 5/10 = 0.5

The experimental probability of getting a 6 is 0.2, because 2 out of 50 displays were 6s.

The experimental probability of getting an even number is 0.6, because 30 out of 50 displays were even numbers.

The theoretical probability of getting a 6 is 1/10, because there is 1 chance out of 10 that the calculator will display a 6.

The theoretical probability of getting an even number is 5/10, because there are 5 chances out of 10 that the calculator will display an even number.

As you can see, the experimental probabilities are close to the theoretical probabilities. This is because the calculator was programmed to randomly display a digit from 0 to 9, so the results should be evenly distributed. However, there is always some chance of variation, so the experimental probabilities may not be exactly equal to the theoretical probabilities.

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Answer:

56

Step-by-step explanation:

The angle on the top right is 90 degrees and the angle downwards is 34 degrees so subtract 90 and 34 to get 56.

The 10th term of the geometric sequence is given as follows:

\(a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}\)

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

Using the mth term as the reference, we have that:

\(a_n = a_mq^{n-m}\)

Hence:

\(a_5 = a_3q^2\)

\(q = \sqrt{\frac{a_5}{a_3}}\)

And then the 10th term is given as follows:

\(a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}\)

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There wouls be 18 geese in the pond

Hope this helps :)

Answer:

-49.518

This should suffice.

The Fraction of empty space in the container is 5/12. This means that 5/12 of the container is not filled with water or oil, and is instead empty.

The container is made up of two substances: water and oil. We know that the container has 1/4 water and 1/3 oil. This means that the remaining space in the container is made up of neither water nor oil, i.e., empty space.

To find the fraction of empty space, we need to add the fractions of water and oil together and subtract them from 1. This is because the sum of the fractions of water, oil, and empty space must equal 1, which represents the total volume of the container.

The fraction of water in the container is 1/4, and the fraction of oil is 1/3. Therefore, the fraction of the container that is not empty is:

1/4 + 1/3 = 3/12 + 4/12 = 7/12

To find the fraction of empty space, we subtract this fraction from 1:1 - 7/12 = 5/12

Therefore, the fraction of empty space in the container is 5/12. This means that 5/12 of the container is not filled with water or oil, and is instead empty.

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Answer:6/5 or 1.2

Step-by-step explanation:

4/5 divided by 2/3

=4/5 *3/2

=12/10

=6/5

=1.2

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Answer:

If you are solving for C,

C = -64

Answer:

Causas de la decadencia del Imperio Romano

Otros factores que contribuyeron a la decadencia de Roma incluyen: -Inestabilidad política debida al tamaño del imperio. -Los intereses propios de las dos mitades del imperio. -La invasión de las tribus bárbaras.

Step-by-step explanation:

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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Answer:

216

Step-by-step explanation:

hindi pa sure pero yan

Answer:

14 + 2x I think

Step-by-step explanation:

Wait for more responses if needed

Answer:

\( {6x}^{2} + 4x\)

Step-by-step explanation:

1) Collect like terms.

\((7 {x}^{2} - {x}^{2} ) + 4x\)

2) Simplify.

\( {6x}^{2} + 4x\)

Therefor, the answer is 6x² + 4x.

By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

Answer:

16 flowerpots

Step-by-step explanation:

12 divided by 3/4=16

Answer:

She drove 8 miles each day.

Step-by-step explanation:

Given that she drove equal number of miles in 5 days. So in order to find the number of miles in each days, you have to divide it by 5,

\(5days = 40miles\)

\(1day = 40 \div 5\)

\(1day = 8miles\)

Answer:

8.2

Step-by-step explanation:

Answer:

x= 5/12,y=− 5/4

​

Step-by-step explanation:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

6x−12y=24,4x+2y=8

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

6x−12y=24

Add 12y to both sides of the equation.

6x=12y+24

Divide both sides by 6.

x= 6/1 (12y+24)

Multiply  6

1 times 24+12y.

x=2y+4

Substitute 4+2y for x in the other equation, 4x+2y=8.

4(2y+4)+2y=8

Multiply 4 times 4+2y.

8y+16+2y=8

Add 8y to 2y.

10y+16=8

Subtract 16 from both sides of the equation.

10y=−8

Divide both sides by 10.

y=− 5/4

​Substitute − 5/4  for y in x=2y+4. Because the resulting equation contains only one variable, you can solve for x directly.

x=2(− 5/4 )+4

Multiply 2 times − 5/4 .

x=− 5/8 +4

Add 4 to − 5/8 .

x= 5/12

Answer:

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755
0.0755 * 100 = 7.55%

Step-by-step explanation:

To find the percentage of 1 - 3√(5/35), we need to first evaluate the expression.

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755

To convert this decimal to a percentage, we simply multiply by 100:

0.0755 * 100 = 7.55%

The tree is approximately 12 feet tall to the nearest tenth of a foot.

We have,

To find the height of the tree, we can set up a proportion using the measurements of the shadow.

Since we know that Tyler is 6 feet tall and his shadow is 10 ½ feet long, we can set up the following expression:

Tyler's height / Tyler's shadow length = Tree's height / Tree's shadow length

6 feet / 10.5 feet = Tree's height / 21 feet

To find the tree's height, we can cross-multiply and solve for it:

6 feet x 21 feet = 10.5 feet x Tree's height

126 feet = 10.5 feet x Tree's height

Dividing both sides of the expression by 10.5 feet:

126 feet / 10.5 feet = Tree's height

12 feet = Tree's height

Therefore,

The tree is approximately 12 feet tall to the nearest tenth of a foot.

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The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the compounding formula:

A = P * \(e^{rt}\)

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * \(e^{0.02 * 4}\)

Using a calculator, we can calculate:

A = $16,000 * \(e^{0.08}\)

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

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Answer:

10

Step-by-step explanation:

-7y + 35 + 8 = -27

collect like terms

-7y = -27 - 35 - 8

-7y = -70

y= -70/-7

y= 10

The final expression that represent the total owed is 3c  + 25

He owed 3 months cable at a price of c dollars for each month, plus a one-time equipment fee of $25,

Therefore, the situation can be expressed as follows:

For a single month he pays c dollars

Hence, 3 month will be 3 × c.

Recall he also needs to pay a one time fees of 25 dollar.

Therefore, the final expression that represent the total owed is as follows:

total owed  =  3c  + 25

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A.= \($\left( -4,\frac{5\pi}{4}\right)\,\, \left( 4,\frac{-7\pi}{4}\right)\),  B = \($\left( 4,\frac{3\pi}{4}\right)\,\, \left( -4,\frac{-\pi}{4}\right)\),

C=\($\left( -4,\frac{\pi}{4}\right)\,\, \left( 4,\frac{5\pi}{4}\right)\),  D = \($\left( -4,\frac{3\pi}{4}\right)\,\, \left( 4,\frac{7\pi}{4}\right)\)

\($\left( -4,\frac{5\pi}{4}\right) = \left( 4,\frac{5\pi}{4}+\pi = 2\pi + \pi/4\right )\,\,, \left( 4,\frac{-7\pi}{4}\right) =\left( 4,\frac{-7\pi}{4}+2\pi = \pi/4\right)\)

\($\left( 4,\frac{3\pi}{4}\right)\,\, , \,\left( -4,\frac{-\pi}{4}\right) = \left(4,\frac{-\pi}{4}+\pi = 3\pi/4\right)\)

\($\left( -4,\frac{\pi}{4}\right)=\left( 4,\frac{\pi}{4}+\pi = 5\pi/4\right)\,\, ,\,\left( 4,\frac{5\pi}{4}\right)\)

\($\left( -4,\frac{3\pi}{4}\right)=\left ( 4,\frac{3\pi}{4}+\pi = 7\pi/4 \right)\,,\, \left( 4,\frac{7\pi}{4}\right)\)

When \(r\geq 0\) and \(0\leq \theta < 2\pi\), we call the polar coordinates \((r,\theta)\) standard polar coordinates. To convert any given coordinates to standard coordinates 1. if r<0 then replace r with |r| and \(\theta\) with \(\theta + \pi\). 2. Now if \(\theta < 0 \textrm{ or }\theta\geq 2\pi\), we add a suitable multiple of \(2\pi \textrm{ to }\theta\) to bring it inside [0,\(2\pi\)) interval.

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Answer:

Yes, Dayson can completely cover the package with wrapping paper.

Step-by-step explanation:

Given: The rectangular prism is 50 centimeters by 20 centimeters by 18 centimeters.

Area of wrapping paper is 1 square meter.

To find: whether he can completely cover the package with wrapping paper

Solution:

Total surface area of the rectangular prism = 2(lb + bh +hl)

where l denotes length, b denotes breadth and h denotes height

Total surface area of the rectangular prism = \(2\left [ (50)(20)+(20)(18)+(18)(50) \right ]\)

\(=2\left ( 1000+360+900 \right )\\=2(2260)\\=4520\,\,cm^2\)

As \(1\,m^2=10000\,cm^2\),

Total surface area of the rectangular prism = \(4520\,cm^2=0.4520\,m^2\)

As Dayson has \(1\,m^2> 0.4520\,m^2\) of wrapping paper, he can completely cover the package with wrapping paper.

The significance of a is that it shows the expected GPA for a student with an SAT score of 0. The significance of b is that it shows how much the GPA is expected to change for each unit increase in the SAT score.

Determine the least-squares regression line for estimating freshman grade point average (GPA) based on total SAT score. Show all your work.

Let x represent the SAT score and y represent the freshman GPA.

 x          y

1150  3.60

1200 2.75

900  2.40

1120         3.20

1030 2.50

1340 3.80

950  2.30

1090 3.10

The least-squares regression line is given by:

ŷ = bx + a

where b is the slope and a is the y-intercept.

To calculate b, we use the formula:

b = [∑xy - (∑x)(∑y)/n] / [∑x2 - (∑x2/n)]

n = 8

∑x = 1150 + 1200 + 900 + 1120 + 1030 + 1340 + 950 + 1090 = 8160

∑y = 3.60 + 2.75 + 2.40 + 3.20 + 2.50 + 3.80 + 2.

is the slope of the regression line, which can be calculated by taking the sum of the product of the x and y values, minus the product of the sums of the x and y values divided by n, then dividing this by the sum of the squares of the x values minus the sum of x values squared divided by n. a is the y-intercept of the regression line, which can be calculated by taking the product of the sums of the x and y values divided by n, and subtracting this from the product of the slope and the sum of the x values divided by n.

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Find how much 20% is by setting up a proportion:

\( \frac{20}{100} = \frac{x}{19.5} \)

Cross multiply:

\(100x = 390\)

Divide both sides by 100 to isolate x:

\(x = 3.9\)

Now because it says the new packaging contains 20% more, you add 3.9 ounces to 19.5 ounces.

\(3.9 + 19.5 = 23.4\)

Your answer is 23.4 ounces.

Answer:

5/8 quart

Step-by-step explanation:

Answer:

5 hotdogs

Step-by-step explanation:

Deduct the price of French fries + drink from the total amount of money he has.

5.00 - 0.80 - 0.95 = 3.25

Divide the amount of money left with the amount of money each hotdog cost.

3.25 ÷ 0.65 = 5