Soda is often sold in 20 ounce bottles. A pack of sugar (the kind they have at restaurants for your coffee or tea) typically contains 4 grams of sugar. If an 8 ounce bottle of cream soda has 30 grams of sugar, then drinking a 20 ounce bottle of cream soda would be equivalent to eating how many packets of sugar?

The false statement from the stem-and-leaf plot is given as follows:

b. The data for Paul’s group has two modes.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The mode of a data-set is the data-set that appears the most times in a data-set.

Hence, for Paul's group, the mode is given as follows:

44.

As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.

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Step-by-step explanation:

A 12 cubic centimeters I think

Answer:

700 + 50x ≥ 1200

where x represents the number of weeks needed to save.

Step-by-step explanation:

Check the picture below.

whatever those savings are on week "x", they have to be at least $1200

Step-by-step explanation:

Since we have three sides and trying to find an angle, use Law of Cosines

\(c = \sqrt{ {a}^{2} + {b}^{2} - 2ab \times \cos(d) } \)

where c is

Solving for the angle d.

\( \cos {}^{ -1 } (( \frac{ {c}^{2} - {b}^{2} - {a}^{2} }{ - 2ab} ) = d\)

where d is in degrees

The angle d is the opposite of the side c.

It does not matter what a and b is(they can be either 4 or 5)

let

c=7

a=4

b=5

\( \cos {}^{ - 1} ( \frac{ - 1}{5} ) = d\)

This angle must be within 0 and 180

We get

\(d = 101.54\)

If ABCD is dilated by a scale factor of 3, the coordinate of B' would be (-6, 6).

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

This ultimately implies that, the size of the geometric shape would be increased (stretched or enlarged) or decreased (compressed or reduced) based on the scale factor applied.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 3 centered at the origin as follows:

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3, 2 × 3) = Ordered pair B' (-6, 6).

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Answer: n= 0

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

8n−6(−5n−3)=18+7n

8n+(−6)(−5n)+(−6)(−3)=18+7n(Distribute)

8n+30n+18=18+7n

(8n+30n)+(18)=7n+18(Combine Like Terms)

38n+18=7n+18

38n+18=7n+18

Step 2: Subtract 7n from both sides.

38n+18−7n=7n+18−7n

31n+18=18

Step 3: Subtract 18 from both sides.

31n+18−18=18−18

31n=0

Step 4: Divide both sides by 31.

31n /31  = 0 /31

n=0

Answer:

n=0

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Answer: The formula for the area of a rectangle is: A = L * W where L is the length and W is the width. where S is the length of one side.

Step-by-step explanation:

Hope This helps, Brainlees, please

The number 2/5 is both a ratio and a fraction.

The number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.

The expression is also a ratio because it indicates the quantitative relationship between the figures.

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Answer: 34,650 permutations

For the given triangles:

(1) x = 5.4

(2)  x  =  √23

(3) θ = 25.84 degree

(4)   x = 9.5

(5) n = 41

(1) In the given triangle,

One angle = 16 degree

Perpendicular = x

Hypotenuse    = 20

Since we know that

Sinθ = opposite side of θ/hypotenuse

Therefore,

⇒ sin 16 = x/20

⇒   0.27 = x/20

⇒         x = 5.4

(2)  In the given triangle,

Hypotenuse = 12 km

Base = 11 km

perpendicular = x

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (12)²= (x)² + (11)²

⇒ 144 = (x)² + 121

⇒   x² =  23

Taking square root both sides we get,

Hence,

⇒   x  =  √23

(3) In the given,

Base = 20

Perpendicular = 42

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² =  (42)² + (20)²

⇒ (Hypotenuse)² =  2164

Taking square root both sides,

⇒ (Hypotenuse)  = 46.51

⇒ cosθ = Adjacent/hypotenuse

             = 42/46.51

             = 0.90

Taking inverse of cosθ,

⇒ θ = 25.84 degree

(4) In the given triangle,

One angle = 30 degree

Base = x

Hypotenuse    = 11

Since we know that

cosθ = Adjacent/hypotenuse

Therefore,

⇒ cos 30  = x/11

⇒   √3/2 = x/11

⇒         x = 9.5

(4) In the given triangle,

Base = 40

Perpendicular = 9

Hypotenuse = n

We know that the Pythagoras theorem for a right angled triangle:

⇒  (Hypotenuse)²= (Perpendicular)² + (Base)²

⇒  n² = 9² + 40²

⇒  n² = 81 + 1600

⇒  n² = 1681

⇒  n = 41

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Answer:

\(8 - x\)

Step-by-step explanation:

additive inverse means multiplying by -1

therefore :

\( - 1 \times (x - 8) \\ = - x + 8 \\ = 8 - x\)

240 soldiers were transferred to the other camp. Let's assume the number of soldiers transferred to the other camp is "x." we can solve for the unknown variable representing the number of soldiers transferred.

Initially, the food provision was planned for 800 soldiers for 35 days. This means that the total food supply is equal to 800 soldiers multiplied by 35 days, which gives us a total of 28,000 soldier-days of food.

After some soldiers were transferred, the remaining soldiers had enough food to last for 50 days. So the food supply for the remaining soldiers can be calculated as the product of the number of remaining soldiers and the number of days, which gives us (800 - x) * 50 soldier-days of food.

Since the amount of food remains the same, we can set up the following equation:

\(28,000 = (800 - x) * 50\)

Now, let's solve this equation to find the value of x, representing the number of soldiers transferred to the other camp:

\(28,000 = 50 * 800 - 50x28,000 = 40,000 - 50x50x = 40,000 - 28,00050x = 12,000x = 12,000 / 50x = 240\)

By setting up the equation based on the total food supply for the initial and remaining soldiers, we can solve for the unknown variable representing the number of soldiers transferred. In this case, 240 soldiers were transferred to the other camp.

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Answer:

36 yards x 144 yards

Step-by-step explanation:

Let the width of the rectangle field be x and the length be 4x.

The perimeter is 2(4x + x). So:

2(4x + x) = 360

10x = 360

x = 36

Then the width is 36 yards and the length is 144 yards.

Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

10 ÷ 8 = 1.25

Step-by-step explanation:

To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:

9^2 + 3(9) - 5 = 81 + 27 - 5 = 103

Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.

rate my answer, please.

Answer:

1106

Step-by-step explanation:

PEMDAS [the order of operations]

M[ultiplication] comes before S[ubtraction], so we should multiply first:

26 × 43 = 1118

Now, we can subtract:

1118 - 12 = 1106

you can write this equation as:

(26 × 43) - 12

if that makes more sense to you

hope this helps!! :)

It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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The Expression x^2 - 6x + 9 when x = 2 + i   is -2i

To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:

(2 + i)^2 - 6(2 + i) + 9

Simplifying the first term, we get:

(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2

Since i^2 = -1, we can substitute that in and simplify further:

(2 + i)^2 = 4 + 4i - 1 = 3 + 4i

Now we substitute this into the original expression:

(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9

Simplifying further, we get:

= 3 + 4i - 12 - 6i + 9

= 0 - 2i

= -2i

Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.

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To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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The lowest carrier frequency at which each modulated wave S(t) component may be uniquely defined by m(t) is

Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz

-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz

"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.

Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz

-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz

This is further explained below.

For a modulated wave with frequency components, the equation looks like this:

Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz

-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz

"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.

b)

In conclusion, we may state that the modulated wave has frequency components as well.

Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz

-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz

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I think (i said think) the answer is E

Answer:

Step-by-step explanation:

Since we are given two points in the graph, we can use the slope equation shown below:

(y2-y1)/(x2-x1)

reading the graph left from right (1,11) will be the first point and (3,1) the second. plug in and solve!

(1-11)/(3-1) = -10/2 = -5

The slope is -5

a negative slope makes sense since the graph is leaving the first quadrant.

hope this helps!

Answer: A) -5. Graph slope.

Step-by-step explanation:

The formula to calculate the slope of the line is:

\(\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff m=\dfrac{x_2-x_1}{y_2-y_1} }}\)

We have that the points are:

We substitute these points in the previous formula and solve:

     \(\boldsymbol{\sf{m=\dfrac{x_2-x_1}{y_2-y_1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{1-11 }{3-1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{-10}{5} }}\\ \\ \\ \boxed{\boldsymbol{\sf{m=-5}}}\)

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Tamisha needs 5 lengths of the 8-foot border to put around her bedroom.

To calculate the number of lengths of the border Tamisha needs for her bedroom, we can determine the perimeter of the room and divide it by the length of each border available.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the length of the room is 11 feet and the width is 9 feet.

Perimeter = 2(length + width)

Perimeter = 2(11 + 9)

Perimeter = 2(20)

Perimeter = 40 feet

Now, we divide the perimeter by the length of each border available, which is 8 feet.

Number of lengths needed = Perimeter / Length of each border

Number of lengths needed = 40 feet / 8 feet

Number of lengths needed = 5 lengths

To calculate the number of lengths of the border Tamisha needs for her bedroom, we can determine the perimeter of the room and divide it by the length of each border available.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the length of the room is 11 feet and the width is 9 feet

Perimeter = 2(length + width)

Perimeter = 2(11 + 9)

Perimeter = 2(20)

Perimeter = 40 feet

Now, we divide the perimeter by the length of each border available, which is 8 feet.

Number of lengths needed = Perimeter / Length of each border

Number of lengths needed = 40 feet / 8 feet

Number of lengths needed = 5 lengths

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Comparing the three in their simplest form we have the smallest ratio as 3 to 4.

A mathematical phrase that compares two values is called a ratio. It is written as the product of the division of two different quantities. As in 2:1 or 2/1, ratios are frequently expressed as a fraction or with a colon.

Mathematicians employ ratios in many different contexts, such as arithmetic, algebra, and geometry. They are used to compare amounts, identify equivalent values, and resolve proportional and rate-of-change issues.

Convert the ratios in their simplest form:

3 to 4 can be simplified by dividing both terms by their greatest common factor, which is 1. Therefore, 3 to 4 is already in its simplest form.

10 to 12 can be simplified by dividing both terms by their greatest common factor, which is 2. So, 10 to 12 simplifies to 5 to 6.

2 to 1 is already in its simplest form.

Thus, comparing the three we have the smallest ratio as 3 to 4.

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