Matt and Wei are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small boxes of fruit and large boxes of fruit. Matt sold 18 small boxes of fruit and 25 large boxes of fruit for a total of $529.50. Wei sold 18 small boxes of fruit and 10 large boxes of fruit for a total of $282.00. Find the cost of one small box of fruit and the cost of one large box of fruit.

The account would be worth more after 6 years if calculating interest compounded daily versus calculating simple interest by $62.46

Compound interest:

A = P(1 + r/n)^nt

= 2,000(1 + 0.04/365)^(365×6)

= 2,000.00(1 + 0.000109589041095)^(2190)

= 2000(1.0.000109589041095)^2190

= 2000 (0.00010958904109589)

= $2,542.46 to the nearest cent

Simple interest:

S.I = principal × rate × time

= 2,000 × 0.04 × 6

= $480

Total = Principal + simple interest

= $2,000 + $480

= $2,480

To find the amount more would the account would be worth after 6 years by calculating interest compounded daily versus calculating simple interest

= Compound interest - Simple interest

= $2,542.46 - $2,480

= $62.46

In conclusion, the account would be worth $62.46 more if compounded daily than simple interest.

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By using the equation of the line and properties of perpendicular lines, we find that the equation of the line is equal to y = - 2 · x - 6.

Herein we need to find a line that passes through point (- 5, 4) and is perpendicular to a given line in implicit form: x - 2 · y = - 4. The complete procedure is shown below. First, rewrite the equation of the perpendicular line into explicit form:

x - 2 · y = - 4

2 · y = x + 4

y = (1 / 2) · x + 2

Second, determine the slope of the new line:

m · m' = - 1

(1 / 2) · m' = - 1

m' = - 2

Third, calculate the intercept of the new line:

b = y - m · x

b = 4 - (- 2) · (- 5)

b = 4 - 10

b = - 6

Fourth, complete the new equation of the line:

y = - 2 · x - 6

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we have that

the distance city B to city C is equal to

405+401=806 miles4

therefore

the answer is

Answer:

Answer is - 4  1/15

Step-by-step explanation:

-6 2/5 = -32/5

-32/5   + 7/3       to add fractions they must have the same denominator

- 96/15   + 35/15   =  ( -96 + 35) / 15 = - 61/15  = - 4  1/15

Answer: 6 blue, 6 yellow, 6 red

Step-by-step explanation:

A fair stack of cards is an equal amount of cards.

3 colors, 18 total

18 / 3 = 6

Therefore 6 of each

Answer:

y = -3/2x +11

Step-by-step explanation:

First you have to change the equation from standard form to slope form.

y = mx + b

2x-3y=7 --> subtract 2x from both sides

-3y = -2x + 7 --> now divide both sides by -3 to get y by itself

y = 2/3x - 7/3  --> the reason 2/3x is positive is because when there are two negatives it turns to a positive.

now you have to use point slope form y - y1 = m (x - x1)

x1 and y1 would be your point. 2 is x1 and 8 is y1

y - 8 = -3/2 (x - 2) --> the reason that m is -3/2 is because a perpendicular equation is the opposite reciprocal of the original slope

next distribute the -3/2

y-8 = -3/2x + 3 --> and now add 8 to 3 to get why by it self

now you have y = -3/2x + 11

The zeros of the quadratic are (1 and 3), the vertex is (2, -1). Draw the parabola with a "solid" line. Shade the "interior" of the parabola.

For the given question;

The inequality of the function is given as;

= x² - 4x + 3

Find the factors;

(x - 3)(x - 1) = 0

x = 1 and x = 3 are the zeros of the equation.

Now, to graph the equation find the point;

Put x = 0; y = 3

Put x = 1; y = 0

Put x = 2, y = -1

Plot the points on the graph and join the points with solid line.

The vertex of the parabola is found at (2, -1).

Thus, the graph of the parabola is plotted.

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Answer:

1 hour, 28 minutes, 15 seconds

Step-by-step explanation:

1) To find the scale factor for these triangles, we need to write a pair of ratios and then solve for x:

Now, we can plug x=8 into those:

2.5% of 8 = .2

5/8 + .2/8 = 5.2/8

5.2/8 = .65 x 100 = 65%

65% of games cost 1 or 2 dollars

100% - 65% = 35%

!! after doing it i did realize I could've just converted 5/8 into a percent than added it.

or

5/8 = .625 + .025 = .65 x 100 = 65%; 100% - 65% = 35%

When you're reading a study that reports selecting a random sample of hospitals and estimating admission delay times, it's an example of C. probability sampling.

Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection. In general, probability sampling is more difficult, time-consuming, and expensive than non-probability sampling.

Using a method based on probability theory, probability sampling is a strategy in which the researcher selects samples from a larger population.

Researchers can produce a sample that accurately represents the relevant real-world population by using probability sampling.

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You are reading a study that reports selecting a random sample of hospitals and estimating admission delay times. You know this is an example of:

a. Quota sampling

b. Convenience Sampling

c. Probability sampling

d. Sampling bias

The ball reaches a maximum height of 96 feet and it spent 0 seconds in the air

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

h(t) = -16t^2 + 96

Differentiate the equation of the function

So, we have

h'(t) = -32t

Set the differentiated function to 0

So, we have

-32t = 0

Divide both sides by -32

So, we have

t = 0

Substitute t = 0 in the equation h(t) = -16t^2 + 96

So, we have

h(0) = -16(0)^2 + 96

Evaluate

h(0) = 96

This means that the maximum height of the ball is 96 feet

Recall that the quadratic equation is given as

h(t) = -16t^2 + 96

Next, we differentiate the equation of the function

So, we have

h'(t) = -32t

Set the differentiated function to 0

So, we have

-32t = 0

Divide both sides by -32

So, we have

t = 0

Hence, the ball spent a total of 0 seconds in the air

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======================================================

Explanation:

x = width

2x = length, since it is twice as long as it is wide

area = length*width = 2x*x = 2x^2

Set this equal to the area of 450 sq ft and solve for x

2x^2 = 450

x^2 = 450/2

x^2 = 225

x = sqrt(225)

x = 15 feet is the width

2x = 2*15 = 30 feet is the length

Check:

area = length*width = 30*15 = 450

The answers are confirmed.

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.

Numerous different coordinate systems can be used to describe geometrical figures.

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For profit with the revenue of R=113.95x and cost of C=93x + 750 the value of x is 36units.

As given in the question,

Revenue for selling x units of a product is R = 113.95 x

Cost of producing x units is C = 93 x + 750

For profit, the revenue must be greater than the cost.

R > C

113.95x > 93x +750

Subtract 93x from both the sides

113.95x -93x >93x-93x +750

⇒20.95x > 750

Divide by 20.95

⇒x > 750/20.95

⇒x>35.7995

Nearest whole number is 36.

Value of x to produce a profit is 36units

Therefore, to make a profit with the revenue of R=113.95x and cost of

C =93x + 750 the value of x is 36units.

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i think 16? 1/2+1/2=1 so 8*2=16

64 ^ (-2/3)

Rewrite 64 as 4^3

(4^3) ^ (-2/3)

Using the power rule a^b^c = a^(b*c)

4 ^(3*-2/3)

4^ -2

We know that a^ -b = 1/ a^b

1 / 4^2

1/16

Answer:

n=2.4

Step-by-step explanation:

The value of n is ∛14.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=).

To solve the equation −8 + n³= 6

Add 8 to both sides of the equation to isolate the term with n:

−8 + n³ + 8 = 6 + 8.

Simplifying the equation gives: n³ = 14.

Take the cube root of both sides to solve for n.

Taking the cube root of n³ = 14

∛(n^3) = ∛14.

Therefore, n = ∛14.

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Answer:

168.28

Step-by-step explanation:

Answer:

She will have 23.1 gallons left after 3 days.

Step-by-step explanation:

We know Margaret uses an average of 1.3 gallons of gas every day and her car holds 27 gallons total. In three days, she would use 3 times her daily average, or 3 * 1.3 = 3.9 gallons consumed in 3 days. To find how many gallons are left in her tank after 3 days, we would subtract 3.9 gallons from 27 gallons. This equals exactly 23.1 gallons of gas.

The fraction of counters Lesley get if Adam gives 10 counters out of 18 counters is 5/9.

The fraction of counters Adam have now is 4/9.

This is an expression which consists of a numerator and a denominator

A numerator is the upper of top value of a fraction

A denominator is the lower or bottom value of a fraction

Number of counters Adam has left = Number of counters Adam has - Number of counters Adam gave to Lesley

= 18 - 10

= 8

Fraction of the 18 counters Lesley get = Number of counters Adam gave to Lesley / Number of counters Adam has

= 10/18

= 5/9

Fraction of the 18 counters Adam have now = Number of counters Adam has left / Number of counters Adam has

= 8 / 18

= 4/9

In conclusion, the fraction of counters Adam have now after giving out 10 counters to Lesley is 4/9

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The logarithms in terms of a and b are:

a) log 72 = 3a + 2b

b) log √27 =  [tex]\frac{3}{2} b[/tex]

c) log 360 = 3a + 2b + log 5

         nˣ = a ⇔ logₙ a = x , log stands for logarithm here.

       Where,

         Two positive real numbers are a and n. x is a real number.

Given:

log 2 = a

log 3 = b

a) log 72

= log (2³ × 3²)

= log 2³ + log 3²   [ By product rule of logarithms, log mn = log m + log n]

= 3log 2 + 2log 3   [By power rule of logarithms, log mⁿ = nlog m]

Replacing with the values of log 2 and log 3.

= 3a + 2b

b) log √27

= [tex]\frac{1}{2}[/tex] log 27    [By power rule of logarithms, log mⁿ = nlog m]

=  [tex]\frac{1}{2}[/tex] log 3³

= [tex]\frac{1}{2} *3 log3[/tex]

= [tex]\frac{3}{2} log 3[/tex]

= [tex]\frac{3}{2} b[/tex]

c) log 360

= log (2³ × 3² × 5)  

= log 2³ + log 3² + log 5 [By product rule of logarithms,log mn = log m +  log n]

= 3log 2 + 2log 3 + log 5  [By power rule of logarithms, log mⁿ = nlog m]

= 3a + 2b + log 5

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The inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

From the graph:

The vertex is:

(25, 200)

The vertex form of the parabola:

y = a(x - h)² + k

y = a(x - 25)² + 200

Plug x = 30 and y = 150

a = --2

y = -2(x - 25)² + 200

The inequality will be:

y < -2(x - 25)² + 200

Thus, the inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.

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The powers can be used in the following manner using multiplicative identity.

Powers are mathematical expressions of the kind where x is the base and n is the exponent. In powers, the exponent specifies how many times to multiply the base by itself whereas the base is the integer or variable that is continuously multiplied.

The quotient rule states that exponents should be subtracted when dividing powers by the same base. For instance, h(6-2) Equals h when h(6) is divided by h(2) (4). Subtracting the exponents is a quick and easy way to simplify the issue.

When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. The trick is to eliminate only exponents with compatible bases.

Since the multiplicative identity, or one, is the simple outcome of no numbers at all, it follows that every integer raised to the power of zero equals one.

Thus, we came to the logical conclusions.

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It should be noted that the z-score for the sample mean that's given is 0.5.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

The following can be seen from the information illustrated:

Mean ( u ) =55

Standard Deviation ( sd )=12

Number ( n ) = 4

Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)

Z = (58-55)/12/ Sqrt ( 4 )

Z = 3/6= 0.5

Therefore, the z score is 0.5.

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Answer:

A

Step-by-step explanation:

The centroid cuts the median in a 2:1 ratio from vertex to side.

Answer:

[tex]y = \frac{3}{5} x + \frac{13}{5} [/tex]

Step-by-step explanation:

The equation of a line can be written in the slope-intercept form y= mx +c, where m is the slope and c is the y-intercept.

Let's rewrite the given equation into the slope-intercept form, so that we can identify its slope.

5x +3y= 15

3y= -5x +15

Divide both sides by 3:

[tex]y = - \frac{ 5}{3} x + 5[/tex]

Thus, the slope of the given line is [tex] - \frac{5}{3} [/tex]

The slope of a perpendicular line is the negative reciprocal of the given line. In simpler terms, the slope of the perpendicular line can be found by flipping the denominator and numerator, and by multiplying -1 afterwards.

Slope of perpendicular line= [tex] \frac{3}{5} [/tex]

Substitute the value of the slope into the equation:

[tex]y = \frac{3}{5} x + c[/tex]

To find the value of c, substitute a pair of coordinates the line passes through.

When x= -1, y= 2,

[tex]2 = \frac{3}{5} ( - 1) + c[/tex]

Solve for c:

[tex]c = 2 + \frac{3}{5} [/tex]

[tex]c = \frac{13}{5} [/tex]

Thus, the equation of the line described is [tex]y = \frac{3}{5} x + \frac{13}{5} [/tex].

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