The Beta club is selling chocolate to raise money for Beta convention. Chocolate bars sell for $1.25 each and chocolate covered almonds sell for $2.00 each. The Beta club needs to raise more than $375 for all members to attend the convention. The students can sell up to 500 bars and covered almonds altogether.

1. Write a system of inequalities that can be used to represent this situation.



2. The club sells 100 chocolate bars. What is the least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention? Justify your answer.

To find the magnitude of a vector we use the following equation

This comes from taking the value of the hypotenuse by Pythagoras, graphically it can be seen in the following image:

In the case of your exercise, the values would be

Area of the cricket pitch is 660 square feet

Given

1 chain is equal to 10 feet

There are 3 feet in a yard

And 22 yards in a chain

Hence it is evident that

One chain is equal to 22 x 3

1 chain = 66 Feet

Area of a rectangle is Length x Width

Length = 66

Width =  10

Hence Area = 66 x 10

Area = 660 Square feet

Hence area of the cricket pitch is 660 square feet.

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Using the t-distribution, the 95% confidence interval estimate of the population mean rating for Miami is of:

(4.29, 7.71).

The bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the meaning of the parameters are:

Using a calculator from the 50 observations given in this problem, the values of the parameters are as follows:

[tex]\overline{x} = 6, s = 2.86, n = 50[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Hence the lower bound of the interval is given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6 - 2.0096\frac{6}{\sqrt{50}} = 4.29[/tex]

The upper bound of the interval is given by:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6 + 2.0096\frac{6}{\sqrt{50}} = 7.71[/tex]

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Answer:

$7,000

Explanation:

To find the simple interest on any principal, we use the formula:

From the given question:

• Principal = $50,000

• Rate= 7%

• Time = 2 years

Therefore:

The simple interest is $7,000.

The linear function that passes through the points (-3, 18) and (2, -7) is defined by the rule:

y = -5*x + 3

We can find a general linear function in the slope-intercept form as:

y = m*x + k

Where m is the slope and k is the intercept of the y-axis.

If we know that the line passes through the points (a, b) and (c, d) then the slope of the function is:

m = (d - b)/(c - a)

In this case the line passes through the points (-3, 18) and (2, -7), then the slope is:

m = (-7 - 18)/(2 + 3) = -5

So the line is something like:

y = -5*x + k

To find the value of k, we can use one of the two given points, I will use (2, -7), so we get:

-7 = -5*2 + k

-7 = -10 + k

-7 + 10 = k

3 = k

So the linear function is:

y = -5*x + 3

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Answer:

slope would be 4/1

Step-by-step explanation:

its rise over run, so up 4 and out 1

have a good day!

3750 is the planning value for the population standard deviation.

In the sampling, one should not recommend trying to obtain the $100 margin of error since the sample size is large.

Firstly, the planning value will be:

= (60000 - 45000) ÷ 4

= 3750

Then the number will be:

= 1.96 × (3750 ÷ 500)²

= 217

Also, for error 200, the desired margin will be:

= 1.96 × (3750 ÷ 100)²

= 5403.

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1) What we have in the polygon P is at first a

90º Rotation Clockwise because it is in the direction of the clock.

90º Rotation Clockwise

Tracing a line inside the polygon P, we can count approximately 10 units to the right in the translation.

T

Answer:

hmmph..

(32, 31)

(33,30)

(34, 29)

(35, 28)

(36,27)

(37, 26)

Step-by-step explanation:

That all I got....

The length of the diagonal of the napkin is 11 inches.

Here, we are given that a square napkin has a side of length 8 inches.

All the sides of a square are equal and the measure of angle formed by any two adjacent sides is also equal and 90°.

Thus, by using Pythagoras theorem, we can form the following equation-

[tex]side^{2} + side^{2} = diagonal^{2}[/tex]

Let the diagonal of the square be d. Then, we have-

[tex]8^{2} +8^{2} =d^{2}[/tex]

64 + 64 = [tex]d^{2}[/tex]

128 = [tex]d^{2}[/tex]

[tex]d^{2}[/tex] = 128

d = [tex]\sqrt{128}[/tex]

d = [tex]8\sqrt{2}[/tex]

the value of [tex]\sqrt{2}[/tex] is approximately 1.41. Thus,

d = 8 × 1.41

= 11.28

Thus, the length of the diagonal of the napkin to the nearest inch comes out to be 11.

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The space sample is the total quantity of possible results

for each toss there are 3 possible results

so the total results are 2x 3 = 6

The only option with 6 elements is B

so the answer is B.

Given:

To find:

The roots.

Explanation:

Here,

Using the quadratic formula,

On substitution we get,

Therefore, the solutions are,

Final answer:

The solutions are,

[tex]9y - 2y + 3 = 5y - 10 + 2 \\ 7y + 3 = 5y - 8 \\ 7y - 5y = - 8 - 3 \\ 2y = - 11 \\ \frac{2y}{2} = \frac{ - 11}{2} \\ y = \frac{ - 11}{2} [/tex]

ATTACHED IS THE SOLUTION OF Y

BE AWARE THERE IS A SOLUTION FOR THE PROBLEM.

To complete the square, we want a number such that:

because in this way we can writte the square as follows:

Hence the answer is the last option:

Answer: F

Step-by-step explanation:

[tex]\sin(x+y)=\sin x \cos y+\cos x \sin y[/tex]

[tex]\tan x=2 \implies \sin x=\frac{2}{\sqrt{5}}, \cos x=\frac{1}{\sqrt{5}}\\\\\sin y=\frac{8}{17} \implies \cos y=-\frac{15}{17}\\\\\sin (x+y)=\left(\frac{2}{\sqrt{5}} \right) \left(-\frac{15}{17} \right)+\left(\frac{1}{\sqrt{5}} \right) \left(\frac{8}{17} \right)\\\\=-\frac{30}{17\sqrt{5}}+\frac{8}{17\sqrt{5}}\\\\=-\frac{22}{17\sqrt{5}}\\\\=-\frac{22\sqrt{5}}{85}[/tex]

The maximum displacement of this cosine wave function is equal to 8 inches.

The frequency of this cosine wave function is equal to 1/8 Hertz.

The time (t) required for one cycle is equal to 8 seconds.

Mathematically, a cosine wave simply refers to an equation of simple harmonic motion (SHM) and it is modelled by this mathematical expression:

y = asinωt = asin2πft     ......equation 1.

Where:

From the information provided, the equation for this simple harmonic motion (SHM) is given by:

d = -8cos(π/4)t           ......equation 2.

By comparing equation 1 and equation 2, we have the following parameters:

Maximum displacement or amplitude, a = |-8|

Taking the absolute value of a, we have:

Maximum displacement or amplitude, a = 8

For the frequency, we have:

Angular velocity, ω = 2πf

Making frequency (f) the subject of formula, we have:

Frequency (f) = ω/2π

Frequency (f) = (π/4)/2π

Frequency (f) = π/8π

Frequency (f) = 1/8 Hertz.

Finally, we would calculate the amount of time (t) required for one cycle as follows:

Time (t) = 1/f

Time (t) = 1/(1/8)

Time (t) = 8 seconds.

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Complete Question:

An object moves in simple harmonic motion described by the equation d = -8cos(π/4)t, where t is measured in seconds and d in inches. Find the following:

maximum displacement

the frequency

the time required for one cycle.

Answer: When the Ice Cream Parlor sells 50 ice cream cones, they make $85 dollars in profit.

Step-by-step explanation:

x = cones

the function f tells us the profit for whatever x

we have that

Two times the sum of a number and 7 -----> 2(w+7)

Two times the sum of a number and 7 equals 6 ----> 2(w+7)=6

the answer is

ANSWER:

The value of x is 16

STEP-BY-STEP EXPLANATION:

With the information given, they tell us that TVQ can be expressed in two ways, but in the end the value must be the same because it is the same angle.

Thanks to this we can make the following equality:

Solving for x:

Answer:

16 is the answer

The system of inequalities is x + y ≤ 300, 11x + 15y ≥ 3630, x ≥ 0 and y ≥ 0 while the three points are (70, 200), (150, 140) and (140, 150)

From the question, we have the following parameters that can be used to determine system of inequalities

Represent the adult with y and the students with x

So, we have the following representations

x + y ≤ 300 ---- the ticket holders cannot exceed the capacity

11x + 15y ≥ 3630 --- the total sales cannot be less than $3630

x ≥ 0 -- the number of students cannot be negative

y ≥ 0 -- the number of students cannot be negative

Write out the inequalities

x + y ≤ 300

11x + 15y ≥ 3630

x ≥ 0

y ≥ 0

Next, we represent the inequalities on a graph

See attachment for the graph of the inequalities

To get the combination, we make use of the coordinate points that are in the shaded region of the graph

Using the above as a guide, we have

(70, 200), (150, 140) and (140, 150)

There are other points too

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We are given the following information

Slope of the line = m = -3

The line passes through the point (5, -7)

Recall that the equation of a line in the point-slope form is given by

Where m is the slope and (x₁, y₁) is a point on the line.

Let us substitute the given values into the above equation

Therefore, the equation of the line in slope-intercept form is

Answer:

x = 0 and 2pi/3

Explanation

Given the expression

cos(2x)=cos(x)

In trigonometry expression;

cos2x = 2xos^2x - 1

Substituting into the equation given;

cos(2x)=cos(x)

2xos^2x - 1 = cos x

Rearrange

2xos^2x - 1 - cosx - 1 = 0

Let P = cosx

2P^2 - P - 1 = 0

Factorize

2P^2 - 2P+P-1 = 0

2P(P-1)+1(P-1) = 0

2P+1 = 0 and P-1 = 0

P = -1/2 and 1

Recall that P = cosx

-1/2 = cosx

x = cos^-1(-1/2)

x = 120 degrees = 2pi/3

If P = 1

cosx = 1

x = cos^-1(1)

x = 0

Hence the value of x that satisfies the equation is 0 ad 2pi/3

Since ∠VST measures 90°, the measure of ∠RSV must also be 90° because the two angles are linear pair.

Since m∠RSU=51°, then the measure of ∠USV is as follows:

hello

to solve this question, we need to use the formula for volume of a sphere

from the image above, we can now find the radius of the sphere

from the calculations above, the volume of the sphere is equal to 3052.08cm^3

There will not be enough T-shirts for all the students

From the question, the given parameters are:

Number of T-shirt = 1437

From the question, we understand that the principal approximates the number of T-shirts to the nearest hundred

When the number of T-shirts is approximated to the nearest hundred, we have

Approximation = 1400

By comparison, 1400  is less than 1437

This means that the T-shirts will not be enough

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The complex expression (2+5) - (-6 +bi) in the form a + bi is 13 - bi

The expression is given as

(2+5) - (-6 +bi)

The above expression is a complex expression

So, we have the following expression

(2+5) - (-6 +bi)

Remove the brackets in the above expression

So, we have the following expression

(2+5) - (-6 +bi) = 2 + 5 + 6 - bi

Evaluate the like terms in the above equation

So, we have the following expression

(2+5) - (-6 +bi) = 13 - bi

Hence, the solution to the complex expression is 13 - bi

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95% of the people the doctor expects to have hip replacement surgery will be between the ages of 47 and 63.

The definition of average is that it is the mean value, which is the ratio of the sum of the values in a particular set to all the values in the set.

The amount of variance from the mean is shown by the standard deviation.

Given that the standard deviation is 8 years and the average age is 55.

x=x0, where x0 and are the mean age and standard deviation, respectively, defines the relationship.

The standard deviation is 8 years, while the mean age is 55 years.

The answer is that 55+8=63 and 55-8=47.

Consequently, the age range is 47 years to 63 years.

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the probability of getting a 2 tree times is