Aisha and Malik are making fruit salads for a picnic. Aisha mixes 4 cups of melon and 1 cup of apple and Malik mixes 13 cups of melon and 3 cups of apple. Use Aisha and Malik’s percent of melon to determine whose fruit salad will taste more melony.

Answer:

Step-by-step explanation:

Answer:

The probability that atleast one ticket labeled 2-6 is drawn is 0.94

Numbered ticket = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Number of draws = 4

Required picks = {2, 3, 4, 5, 6}

Recall :

Probability = required outcome / Total possible outcomes

Probability of choosing a required ticket :

5/10 = 1/2

Therefore, the probability that none of the required tickets is chosen :

(1/2 × 1/2 × 1/2 × 1/2) = 1/16

The probability that atleasr one ticket labeled 2-6 is drawn is :

1 - P(none is chosen) = 1 - 1/16 = 15/16 = 0.9375

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Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.

Mean absolute deviation (MAD) is a statistical measure that calculates the average distance between each data point in a dataset and the mean or median of that dataset. It measures the dispersion or variability of the data points in relation to the central tendency of the dataset.

To calculate the MAD, you first find the mean or median of the dataset, and then you calculate the absolute difference between each data point and the mean or median. The absolute differences are then averaged to give the mean absolute deviation.

MAD is expressed in the same units as the original data and is commonly used in finance, economics, and other fields to measure the variability of financial returns, economic indicators, or other datasets. MAD is a robust measure of dispersion that is less sensitive to extreme values or outliers compared to other measures of dispersion such as standard deviation.

Let's say the times taken by the four people are:

Diane: 2 minutes

Friend 1: 1.5 minutes

Friend 2: 2.5 minutes

Friend 3: 1.75 minutes

The mean of these times is:

Mean = (2 + 1.5 + 2.5 + 1.75) / 4 = 1.9375 minutes

Next, we need to find the absolute deviations of each time from the mean. To do this, we subtract the mean from each time and take the absolute value of the result:

|2 - 1.9375| = 0.0625

|1.5 - 1.9375| = 0.4375

|2.5 - 1.9375| = 0.5625

|1.75 - 1.9375| = 0.1875

Then, we find the mean of these absolute deviations:

MAD = (0.0625 + 0.4375 + 0.5625 + 0.1875) / 4 = 0.3125 minutes

Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.

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The median is the average that is most representative of the data.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

In this problem, we have that smaller values have a higher number of observations, meaning that the data-set is not symmetric.

As the data-set is not symmetric, it means that the median is the average that is most representative of the data.

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The statement that shows the quantity of gallons of gas that he can buy would be =g≤11.82. That is option A.

The total number of money he has to spend on his vehicle = $230

The amount of money he wishes to save = $160

The remaining amount he can spend = 230+160 = $70

The amount he wishes to spend on oil change = $24.95

The remaining amount = 70-24.95

= $40.05

The cost per gallon of gas = $3.81 per gallon.

The quantity of gallons of gas he can purchase = 40.05/3.81 = 10.51 gallons.

Therefore the quantity of gallons of gas he can purchase would be g≤11.82

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The Sum of interior angles of the given polygon is: 540°

The value of the angle x is: 85°

The interior angle-sum formula for an irregular polygon is the same as the sum of interior angle in a regular polygon.

Sum of interior angles in a n-sided polygon is:

Sum = (n - 2)180

where:

n is the number of sides of the irregular polygon.

This is a 5-sided irregular polygon

Thus:

Sum = (5 - 2)180

Sum = 540°

Thus:

x + 115 + 115 + 130 + 95 = 540

x + 455 = 540

x = 540 - 455

x = 85°

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a. K = E + (x + y). This implies that Kofi is (x + y) older than Esenam.

b. (i) Adoma = (5 + y) years

   (ii) Kofi = (5 + (x+y)) years

Word problem is a topic that requires the transformation of a mathematical statement into an equation, such that the variable is to be determined.

In the given question, we have;

Let the age of Kofi, Adoma, and Esenam be represented by K, A and E respectively. So that;

K = A + x ...... i

A = E + y........ ii

substitute i into ii

K = (E + y) + x

  = E + (x + y)

K = E + (x + y) ........ iii

Thus,

a. From equation iii, we can deduce that Kofi is (x + y) years older than Esenam.

b. The age of Adoma = 5 + y years

ii. The age of Kofi = 5 + (x + y) years

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Answer:

b but I'm not exactly sureb

the balance after 6 years is approximately $926.45.

What is Continuous compounding ?

Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.

We can use the formula for continuous compounding to find the balance after 6 years:

[tex]F = Pe^{(rt)}[/tex]

where F is the future value, P is the present value, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.

In this problem, P = $550, r = 8.5% = 0.085 (note that we need to use the decimal form of the interest rate), and t = 6 years.

[tex]F = 550e^{(0.085*6)}[/tex]

F ≈ $926.45

Therefore, the balance after 6 years is approximately $926.45.

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The values  of x and y that make the triangles congruent by HL are:

x = 3 and y = 1

From the question, we are to determine the values of x and y that make the triangles congruent by HL.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Thus,

For the triangles to be right congruent by HL

x = y + 2

and

x + 1 = 4y

Solve the equations simultaneously

Substitute x = y + 2 in the second equation

x + 1 = 4y

y + 2 + 1 = 4y

y + 3 = 4y

3 = 4y - y

3 = 3y

Divide both sides by 3

3/3 = 3y/3

1 = y

Therefore,

y = 1

Substitute the value of y into the first equation

x = y + 2

x = 1 + 2

x = 3

Hence,

The values are:

x = 3 and y = 1

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Answer:

I have my answer in the picture i will upload

please check the below pictures.

There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.

n C r = r! * (n-r)!

where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).

By replacing these values, we obtain:

20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140

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Answer:

------------------------------

We are given three sides and need to find one of angles.

Use the law of cosines:

  [tex]cos(A) = \cfrac{ b^2 + c^2 - a^2}{2bc}[/tex]

Here we are given:

Substitute above values into the given equation:

   [tex]cos(R) = \cfrac{ 52^2 + 41^2 - 59.7^2}{2*52*41} =0.1925[/tex]

Find m∠R:

Answer:

The y-intercept represents Adam's base salary

Step-by-step explanation:

Since it's y = 0.28x + 38,000, when x is 0, the salary is 38,000 without commission.

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In linear equation, The graph in option 3 models the length of the new rectangle.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

According to the problem,

width of the rectangle is  x units

Area of the rectangle is 10 square units

Length of the rectangle is given by f(x) = 10/x

Now if width becomes (x+1) units

∴ Length will be represented as 10/(x+1)

Now from the given options we need to find the exact graph of              f(x) = 10/(x +1)

Here if x = 4 , y =2

So the point (4 , 2) is satisfied which is only happening in the graph of option 3

Option 3 represents the correct graph.

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Answer:

To graph the equation y=-x^2+12x-35, we need to find the vertex and the roots of the equation.

The equation can be written in vertex form as y=-(x-6)^2+1, where the vertex is (6,1).

To find the roots, we need to set y=0 and solve for x:

0=-x^2+12x-35

x^2-12x+35=0

(x-5)(x-7)=0

x=5 or x=7

So the roots are (5,0) and (7,0).

The vertex is at (6,1) and the roots are at (5,0) and (7,0). The curve is a downward-facing parabola.

Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean so option A is correct.

In mathematics, the absolute value (also known as modulus) of a real number is its distance from zero on the number line. It is denoted by enclosing the number between two vertical bars, such as |x|.

For example, the absolute value of 5 is 5, because 5 units to the right of zero on the number line is at a distance of 5 units from zero. Similarly, the absolute value of -5 is also 5, because 5 units to the left of zero on the number line is at a distance of 5 units from zero.

To determine which Z-score represents the location closest to the mean, we need to know the sign of each Z-score, as well as the absolute value of each Z-score.

The sign of the Z-score indicates whether the location is above (+) or below (-) the mean. The absolute value of the Z-score indicates how far away the location is from the mean, measured in standard deviations.

Looking at the options provided, we see that:

A. Z=+0.5 is positive, indicating a location above the mean, and has an absolute value of 0.5.

B. Z=+1.0 is positive, indicating a location above the mean, and has an absolute value of 1.0.

C. Z=-1.5 is negative, indicating a location below the mean, and has an absolute value of 1.5.

D. Z=-0.3 is negative, indicating a location below the mean, and has an absolute value of 0.3.

Since we want to find the Z-score closest to the mean, we should look for the option with the smallest absolute value. Therefore, the answer is A. Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean.

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Applying the inscribed angle theorem, we have the missing measures as: 15. m<DEF = 127°         16. m(PL) = 62°

15. Angle DEF is an inscribed angle while arc FGD is the intercepted arc. Thus, according to the inscribed angle theorem, we have:

m<DEF = 1/2(m(FGD)

Plug in the values:

6x + 37 = 1/2(19x - 31)

2(6x + 37) = 19x - 31

12x + 74 = 19x - 31

12x - 19x = -74 - 31

-7x = -105

x = 15

m<DEF = 6x + 37 = 6(15) + 37 = 127°

16. m<LMP = m<LNP

Plug in the values:

5x - 19 = 2x + 11

5x - 2x = 19 + 11

3x = 30

x = 10

m(PL) = 2(LMP) [based on the inscribed angle theorem]

Plug in the values:

m(PL) = 2(5x - 19)

Plug in the value of x:

m(PL) = 2(5(10) - 19)

m(PL) = 62°

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Fro the one to one functions g and h defined, the value of :

g⁻¹(6) = 2

h⁻¹(x) = 7x + 8

(h⁻¹ o h)(1) = 1

Given one to one functions h and g.

We have that,

g(2) = 6

So, g⁻¹(6) = 2

We have,

y = (x - 8) / 7

Switch x and y.

x = (y - 8) / 7

7x = y - 8

y = 7x + 8

So, h⁻¹(x) = 7x + 8

(h⁻¹ o h) (x) = h⁻¹ (h(x))

                  = h⁻¹ ((x - 8) / 7)

                  = 7 ((x - 8) / 7)) + 8

                  = x - 8 + 8

                  = x

(h⁻¹ o h) (1) = 1

Hence the functions are found.

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In a case whereby Richard is saving money for a down payment on a car He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate  y-intercept of linear model represent B. The starting amount in his savings account.

It should be noted that in a  linear equation the y intercept  can be seen as one that is starting point  whereby x is zero, which implkies that starting balance he had is 1000 in the bank.

Therefore, from the  equation y = 200x + 500, the  y-intercept of linear model serves as the starting amount in his savings account.

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we know that,

[tex] \sf \dashrightarrow \: cos(a - b) = cos a \times cos b + sin a \times sin b[/tex]

Therefore,

[tex] \sf \leadsto \: cos \: 15 \degree[/tex]

[tex] \sf \leadsto \: cos \: (45 \degree - 30 \degree)[/tex]

[tex] \sf \leadsto \: cos \: 45 \degree . \: cos \: 30 \degree + \: sin \: 45 \degree . \: sin \: 30 \degree[/tex]

[tex] \sf \leadsto \: \frac{1}{ \sqrt{2} } \: . \: \frac{ \sqrt{3} }{2} + \: \frac{1}{ \sqrt{2} } \: . \: \: \frac{1}{2} \\ [/tex]

[tex] \sf \leadsto \: \frac{1. \: \sqrt{3} }{ \sqrt{2} \: . \: 2} \: + \: \frac{1 \: .\: 1}{ \sqrt{2} \: .\: 2} \\ [/tex]

[tex] \sf \leadsto \: \frac{ \: \sqrt{3} }{ 2\sqrt{2} \: } \: + \: \frac{1}{ 2\sqrt{2} \: } \\ [/tex]

[tex] \sf \leadsto \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: \\ [/tex]

Therefore Value of cos 15° is [tex] \sf \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: [/tex]

Answer:

A. 4.5 hours

Step-by-step explanation:

We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:

117 miles / x hours = 13 miles / 0.5 hours

We can cross-multiply to get:

117 miles * 0.5 hours = 13 miles * x hours

Simplifying:

58.5 = 13x

x = 58.5 / 13

x = 4.5 hours

Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.

Hope this helps!

Answer:

A. 4.5 hours

Step-by-step explanation:

We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:

117 miles / x hours = 13 miles / 0.5 hours

We can cross-multiply to get:

117 miles * 0.5 hours = 13 miles * x hours

Simplifying:

58.5 = 13x

x = 58.5 / 13

x = 4.5 hours

Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.

Hope this helps!

Answer:

If only 60% of the seeds planted by the class grow into plants, we can find the number of plants by multiplying the total number of seeds planted by the percentage of seeds that grow, expressed as a decimal.

To do this, we can start with the total number of seeds planted, which is 20, and multiply by 0.6:

20 x 0.6 = 12

Therefore, the class has 12 plants.

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Answer:

264π

Step-by-step explanation:

The midpoint of the line joining the endpoints (-1, 5) and (-8, -4) will be (-4.5, 0.5).

Given that:

Endpoints, (-1, 5) and (-8, -4)

The coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The midpoint is calculated as,
(x, y) = [(-1 - 8) / 2, (5 - 4) / 2]

(x, y) = (-9 / 2, 1 / 2)

(x, y) = (-4.5, 0.5)

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Answer:

Parameter= 98ft

Area=180ft^2

Step-by-step explanation:

Parameter= Length times 2 plus width times 2 or

L2+W2=P 4(2)+45(2)=8+90=98

Area= LxW=A^2

4x45=180^2

Please refer to the attachment