Sarah bought a drink for $4 and bought 8 candy bars. She spent a total of 44 dollars. How much did each candy bar cost?

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the remainder of a number when divided by 3 if (1) the sum of digits is 5, and (2) the remainder from division by 9 is 5.

The sum of digits of a 2-digit number will be 5 if that number is one of ...

  {14, 23, 32, 41, 50}

In every case, the remainder when divided by 3 is 2. Effectively, it is the remainder of 5 when that is divided by 2.

In addition to the numbers listed above, 2-digit numbers with a sum of digits of 14 will also have a remainder of 5 when divided by 9. This adds five more numbers to the list:

  {59, 68, 77, 86, 95} . . . . have remainders of 5 when divided by 9

The remainders when divided by 3 are all 2 for these numbers as well.

__

Additional comment

The process of (recursively) summing the digits of a positive integer is called "casting out 9s". It effectively finds the modulo 9 value of the number, with the exception that a sum of 9 corresponds to a modulo 9 value of 0.

Since 9 is divisible by 3, the modulo 3 value of a number will be the modulo 3 value of the modulo 9 value. In other words, if the sum of digits is 5, or the remainder from division by 9 is 5, then the mod 3 value is 5 mod 3 = 2.

The probability that the distance between the two randomly selected points on a line of length 18, which are on opposite sides of the midpoint, is greater than 7 is 1/3.

Let the midpoint of the line be M. Since x is uniformly distributed over [0,9) and y is uniformly distributed over (9,18], the probability of selecting any point in [0,9) is 1/2 and the probability of selecting any point in (9,18] is also 1/2.

Let A be the event that the distance between x and M is less than or equal to 7, and let B be the event that the distance between y and M is less than or equal to 7.

Therefore, the probability of A is the ratio of the length of [0,9) and the length of the entire line, which is 9/18 or 1/2. Similarly, the probability of B is also 1/2.

Now, the probability that the distance between the two points is greater than 7 is the complement of the probability that either A or B occurs, which is 1 - P(A or B).

Using the formula for the probability of the union of two events, we have P(A or B) = P(A) + P(B) - P(A and B).

Since A and B are independent events, P(A and B) = P(A) * P(B) = 1/4.

Therefore, P(A or B) = 1/2 + 1/2 - 1/4 = 3/4.

Finally, the probability that the distance between the two points is greater than 7 is 1 - 3/4 = 1/4 or 0.25, which is equivalent to 1/3 when expressed as a fraction in the simplified form.

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The football will take approximately 1.03125 seconds to reach its highest point, and it will reach a maximum height of 16.769 feet.

To find the time it takes for the football to reach its highest point, we can use the formula:

t = (Vf - Vi) / g

Where:
t = time
Vf = final velocity (0 m/s at the highest point)
Vi = initial velocity (33 ft/s)
g = acceleration due to gravity (32 ft/s^2)

Plugging in the values:
t = (0 - 33) / (-32) = 1.03125 seconds

Next, to find the maximum height reached by the football, we can use the formula:

h = Vi * t + (1/2) * g * t^2

Where:
h = maximum height
Vi = initial velocity (33 ft/s)
t = time (1.03125 seconds)
g = acceleration due to gravity (32 ft/s^2)

Plugging in the values:
h = 33 * 1.03125 + (1/2) * (-32) * (1.03125^2) = 16.769 ft

Therefore, the football will take approximately 1.03125 seconds to reach its highest point, and it will reach a maximum height of 16.769 feet.

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Answer:  \(h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6\)

Work Shown:

\(h(\text{x}) = f(\text{x}) - g(\text{x})\\\\h(\text{x}) = ( 8\text{x}^2 - 2\text{x} + 3) - ( 12\text{x}^2 + 4\text{x} - 3 )\\\\h(\text{x}) = 8\text{x}^2 - 2\text{x} + 3 - 12\text{x}^2 - 4\text{x} + 3 \\\\h(\text{x}) = (8\text{x}^2-12\text{x}^2) + (- 2\text{x} - 4\text{x}) + (3 + 3) \\\\h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6 \\\\\)

To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.

Therefore, we have:

P(z ≥ c) = 0.55

P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45

Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.

So, c = -0.126.

Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.

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7 inches

[25]^2-(24)^2=49

Г49=7

The cosine for the other acute angle will be 7 / 25.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The hypotenuse of a right triangle is 25 inches. The sine of one of the acute angles is 24/25.

sin θ = 24 / 25

We know that the sum of square of the sine and cosine of the angle will be equal to one. That is given as,

sin² θ + cos² θ = 1

Then the cosine for the other acute angle will be given as,

sin² θ + cos² θ = 1

(24 / 25)² + cos² θ = 1

576 / 625 + cos² θ = 1

cos² θ = 1 - 576 / 625

cos² θ = 49 / 625

cos² θ = (7 / 25)²

cos θ = 7 / 25

The cosine for the other acute angle will be 7 / 25.

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7(k+1) gives the equivalent expression

Linear expressions are expressions that has a leading degree of 1. For instance y = mx + b is a linear equation.

Given the expression below
-k-(-8k+7)

Expand to have:

-k-(-8k+7) = -k + 8k - 7

-k-(-8k+7) = 7k + 7

Factor out the value of 7 from the expression

7k + 7 = 7(k+1)

Hence the factored form of the expression is 7(k+1)

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"The revenue is always more than the cost," is the incorrect statement in relation to the profit business model. It is untrue that the revenue is always greater than the cost since the cost of manufacturing and providing the service must be considered as well.

The profit business model is a business plan that helps a company establish how much income they expect to generate from sales after all expenses are taken into account. It outlines the strategy for acquiring customers, establishing customer retention, developing the sales process, and setting prices that enable the business to make a profit.

It is important to consider that the company will only make a profit if the total revenue from sales is greater than the expenses. The cost of manufacturing and providing the service must be considered as well. The revenue from selling goods is reduced by the cost of producing those goods.

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The simplified expression is  [1 + √15]/2

From the question, we have the following parameters that can be used in our computation:

2 + √60]/4

So, we have

2 + 2√15]/4

Divide

1 + √15]/2

Hence, the expression is [1 + √15]/2

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The monthly interest rate on Jada's student loans is 0.308%.

To find the monthly interest rate, we convert the annual interest rate of 3.73% to a monthly rate using the formula (1 + Annual Interest Rate)^(1/12) - 1.

Plugging in the values, we get (1 + 0.0373)^(1/12) - 1, which simplifies to approximately 0.003083, or 0.3083% when rounded to the nearest thousandth of a percent.

To calculate the monthly interest rate on Jada's student loans, we first need to convert the annual interest rate to a monthly rate.

The formula to convert an annual interest rate to a monthly rate is:

Monthly Interest Rate = (1 + Annual Interest Rate)^(1/12) - 1

In this case, the annual interest rate is 3.73%. Let's calculate the monthly interest rate:

Monthly Interest Rate = (1 + 0.0373)^(1/12) - 1

Using a calculator, we can find that the monthly interest rate is approximately 0.003083, or 0.3083%.

Rounding to the nearest thousandth of a percent, the monthly interest rate on Jada's student loans is 0.308%.

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The factorization  of the polynomial is:

(x - 4)*(x + i)*(x - i)

If (x - x₁) is a factor of a polynomial, then x₁ is a zero of the polynomial.

Now we can evaluate the polynomial in the values of the options and see which ones are zeros.

if x = 4

p(4) = 4³ - 4*4² + 4 - 4 = 0

So (x-  4) is a factor.

if x  = i

p(i)= i³ - 4*i² + i - 4

     = -i + 4 + i - 4  = 0

(x - i) is not a factor.

if x = -i

p(-i) = (-i)³ - 4*(-i)² - i - 4

        = i + 4 - i - 4 = 0

Then the factorization is:

(x - 4)*(x + i)*(x - i)

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Equation

The answer would be d = 46.41

Answer:13 to 14

Step-by-step explanation:

The volume of the ellipsoid obtained by rotating the given ellipse depends on the axis of rotation and the method used for calculation.

To find the volume of the ellipsoid obtained by rotating the ellipse 16x² + 9y² = 1 about the x-axis, we can use the Disk Method. By considering infinitesimally thin disks perpendicular to the x-axis, the volume of each disk can be calculated as πr²h, where r is the radius of the disk at a given x-coordinate, and h is the infinitesimal thickness of the disk.

Integrating the volumes of all these disks from the appropriate limits of x, we can obtain the volume of the solid.

To find the volume of the ellipsoid obtained by rotating the ellipse 16x² + 9y² = 1 about the y-axis, we can use the Shell Method. In this case, we consider cylindrical shells with infinitesimal thickness and infinitesimal height along the y-axis. The volume of each shell can be calculated as 2πrh, where r is the distance from the y-axis to the shell at a given y-coordinate, and h is the infinitesimal height of the shell.

Integrating the volumes of all these shells from the appropriate limits of y, we can determine the volume of the solid.

For the region bounded by the curves x = 4y² and y = 4x², rotating it about the y-axis, we can use the Disk Method. Similar to the first case, we consider infinitesimally thin disks perpendicular to the y-axis. The radius of each disk is determined by the y-coordinate, and the infinitesimal thickness is along the x-axis.

Integrating the volumes of these disks from the appropriate limits of y, we can find the volume of the solid.

Finally, to find the volume of the solid obtained by rotating the region bounded by the curves y = 4x - x² and y = 8x - 2x² about the line x = -2, we can use the Shell Method. By considering cylindrical shells with infinitesimal thickness and infinitesimal height along the x-axis, we can calculate the volume of each shell as 2πrh.

Here, r is the distance from the line x = -2 to the shell at a given x-coordinate, and h is the infinitesimal height of the shell. Integrating the volumes of all these shells from the appropriate limits of x, we can determine the volume of the solid.

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Answer:

5

Step-by-step explanation:

slopes of the parallel lines are always same this line has slope five

because equation in y intercept form is y=mx+b

where m is the slope.

so the slope of the new line will be five

Answer:

The True answer is -2>-3

The fraction of the occupied apartments is 9/10.

In mathematics, a fraction is a symbol for a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

Given that,

Total apartments in the building = 200.

Also,

The number of apartments leased by realtor = 180

The fraction of the apartments which is occupied by realtor

= number of apartments leased /Total apartments

= 180 / 200

= 18 / 20

= 9 / 10

The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.

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Consequently, the answer to the above fraction problem comes out to be 1/2 .

An element of a fraction or ratio is a piece of a whole. The number of equally sized pieces into which the whole has been divided is represented by the denominator b, and the number of parts that are included is represented by the numerator a. The LCM of two fractions' denominators is the least common multiple (LCD) of those denominators.

Here,

Given here is: (4√(2) - √(2)) × √(2) /  (2) (2) × √(18) (18)

The radical is then simplified in order to determine its value.

=> 3√(2) × √(2) / 2√(2) × 3√(2)

=> 3(2) / 6(2)

=> 3/6

=> 1/2 or 0.5

so,

after simplification, the answer is 1/2.

Consequently, the answer to the above fractional problem comes out to be 1/2 .

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The value of the integral is 3π. To evaluate the integral, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the cylinder x^2 + y^2 = 1 becomes r^2 = 1, and the limits of integration for z are -6 and 0.

The integral to be evaluated is:

∫∫∫E x^2 + y^2 dv

We can express x^2 + y^2 as r^2, and dv in cylindrical coordinates is given by r dz dr dθ. Therefore, the integral becomes:

∫θ=0 to 2π ∫r=0 to 1 ∫z=-6 to 0 r^3 dz dr dθ

Integrating with respect to z first gives:

∫θ=0 to 2π ∫r=0 to 1 (r^3)(0 - (-6)) dr dθ

Simplifying this, we get:

∫θ=0 to 2π ∫r=0 to 1 6r^3 dr dθ

Integrating with respect to r gives:

∫θ=0 to 2π [(3/2)r^4] from r=0 to r=1 dθ

Simplifying this further, we get:

∫θ=0 to 2π (3/2) dθ

Integrating with respect to θ gives:

(3/2)(θ) from θ=0 to θ=2π

Substituting the limits of integration gives us:

(3/2)(2π) - (3/2)(0)

Simplifying, we get:

3π

Therefore, the value of the integral is 3π.

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Answer:

  -2

Step-by-step explanation:

The floor function returns the largest integer not greater than the function's argument. The largest integer less than or equal to -1.1 is -2.

Answer:

\(f(x)=\displaystyle \frac{6}{x}=\sum^\infty_{n=0}6(-1)^n(x-1)^n\)

Step-by-step explanation:

Recall the formula for Taylor Series:

\(\displaystyle f(x)=f(c)+f'(c)(x-c)+\frac{f''(c)(x-c)^2}{2!}+\frac{f'''(c)(x-c)^3}{3!}+...+\frac{f^n(c)(x-c)^n}{n!}=\sum^\infty_{n=0}\frac{f^n(c)}{n!}(x-c)^n\)

Determine the derivative function fⁿ(c):

\(\displaystyle f(c)=\frac{6}{c}=\frac{6}{1}=6\\ \\f'(c)=-\frac{6}{c^2}=-\frac{6}{1^2}=-6\\ \\f''(c)=\frac{12}{c^3}=\frac{12}{1^3}=12\\\\f'''(c)=-\frac{36}{x^4}=-\frac{36}{1^4}=-36\\\\....\\\\f^n(c)=6(-1)^{n}n!\)

Therefore, the infinite series can be written as:

\(\displaystyle f(x)=\frac{6}{x}=\sum^\infty_{n=0}\frac{6(-1)^nn!}{n!}(x-1)^n=\sum^\infty_{n=0}6(-1)^n(x-1)^n\)

Answer:

324 cubic cm

Step-by-step explanation:

triangular prism

base*width*height/2

9x6x12/2

=9x6x6

=54x6

=324

Answer:

V = 324 cm³

Step-by-step explanation:

V = lwh/2

V = (6 · 12 · 9)/2

V = 648/2

V = 324 cm³

Hope this helps and God bless!

Based on the given algorithm, we can analyze the recurrence relation for the running time of the algorithm on inputs of arrays of n elements.

Let's denote the running time of the algorithm for an input of size n as t(n).

For n = 1, the algorithm computes f(g) for a single entry in the array, which costs a constant time, let's say C1. Therefore, we have:

t (1) = C1

For larger values of n, the algorithm splits the array into two subarrays of size 2n/3 each and runs recursively on each subarray. This step incurs a running time of t(2n/3) for each subarray.

Additionally, the algorithm performs the computation g(x, y) on the resulting ordered set of two integers, which costs a constant time, let's say C2.

Considering these factors, we can write the recurrence relation for the running time as:

t(n) = 2t(2n/3) + C2

Therefore, the correct option among the given recurrence relations that seems to fit the running time of the algorithm is:

c. t(1) = C, and t(n) = 2t(2n/3) + C2, for some positive constants C, C2

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Answer:

3600

Step-by-step explanation:

3x(y+4) 3 x ( y + 4 ); x = 2 and y = 6

Evaluate the value

3(2)[(6) + 4] 3(2)[(6) + 4 ]

6 × 10 × 6 × 10

3600

-TheUnknownScientist

Answer:

She would have to work 5 hours to make $105.

Step-by-step explanation:

First Step: Find Unit Rate

189/9 = 21

9/9 = 1

Every 1 hour she gets paid $21.

Step 2: Find how much she needs to work to get paid $105

105/21 = 5

The symbols d and sd represent:

The differences in the mean of the paired data entries in the dependent samples.

What is the standard deviation?

A measure of a set of values' variance or dispersion is called the standard deviation.

Here,

d: the difference between paired data in the dependent samples.

sd:  standard deviation.

The dependent samples' dependent samples' standard deviation for the variance between the means of the paired data items.

Hence, the differences in the mean of the paired data entries in the dependent samples.

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Answer:

∠1 ≅ ∠2 ⇒ proved down

Step-by-step explanation:

#11

In the given figure

∵ BA // CF

∵ BC is a transversal

∵ ∠1 and ∠BCF are interior alternate angles

∵ The interior alternate angles are equal in measures

∴ m∠1 = m∠BCF

∴ ∠1 ≅ ∠BCF ⇒ (1)

∵ BC // ED

∵ CF is a transversal

∵ ∠BCF and ∠2 are corresponding angles

∵ The corresponding angles are equal in measures

∴ m∠BCF = m∠2

∴ ∠BCF ≅ ∠2 ⇒ (2)

→ From (1) and (2)

∵ ∠1 and ∠2 are congruent to ∠BCF

∴ ∠1 and ∠2 are congruent

∴ ∠1 ≅ ∠2 ⇒ proved

The Confidence Interval for the hypothesis test at the 5% level to determine if 68% represents California is 0.65, 0.90.

First, we need to find H₀ and Hₐ. In this case, we want to check whether California community colleges take 68% of the online classes thought by full-time faculties, or not.

H₀ : p = 0.68; Hₐ : p ≠ 0.68

Second, we need to determine the distribution needed. State what our random variable P’ represents.

Normal: N

Test Statistic : z = 0.1873

Third, we have to calculate he p-value using the normal distribution for proportions.

p-value = 0.1873

If the null hypothesis is true (the proportion is 0.68), thus there is a 0.1873 probability which the estimated proportion is 0.773 or more.

Fourth, we need to compare \(\alpha\) and the p-value, then indicate the correct decision (reject or do not reject the null hypothesis).

\(\alpha\) = 0.05

Decision : Do not reject the null hypothesis

Reason for decision : p-value > 0.05

At the 5% level, the data do not provide statistically significant evidence that the true proportion of online courses taught by full-time faculty is not 68%.

Last, define the confidence interval. The confidence interval is (0.6275, 0.8725) = (0.65, 0.90).

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