How much of a 60% orange juice drink must be mixed with 3 gallons of a 10% orange juice drink to obtain a mixture that is 50% orange juice

The 95% confidence interval for the population mean is (16.426, 26.574

To find the 95% confidence interval, we can use the formula:

Confidence interval = sample mean ± (z-score)*(population standard deviation/√n)

where the z-score for a 95% confidence level is 1.96.

Plugging in the values given in the question, we get:

Confidence interval = 21.5 ± (1.96)*(19.4/√49)

Simplifying this expression, we get:

Confidence interval = 21.5 ± 5.074

Therefore, the 95% confidence interval for the population mean is (16.426, 26.574) as an open-interval.

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Answer:

it's C. :)) u wanna explanation??

Applying multiplication of functions, the total number of seats in the auditorium is given by:

h(x) = 80x² + 560x.

They are multiplied applying the distributive property, that is, all the terms are multiplied and then the common terms are added.

In this problem, the functions are given as follows:

Then the multiplication is:

h(x) = f(x)g(x) = 80x(x + 7) = 80x² + 560x.

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Answer:

The answer is b

Step-by-step explanation:

:)

Answer:

The answer is 3 7/12 Hope this helps :)

Step-by-step explanation:

Step-by-step explanation:

y = kx, where k is a real constant.

When x = 12, y = 60.

=> (60) = (12)k, k = 5.

Therefore when x = 20,

y = kx = (5)(20) = 100.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

Simplify the expression.

2x-47

=6

Step-by-step explanation:

Answer:

x= -8.5

Step-by-step explanation:

1/3x - 47/6 =5

2. Get x onone side

1/3x = -17/6

3. Multiply for x

x= -8.5

Answer:

y=1/2x + 6

Step-by-step explanation:

Use point slope form

y-y1=m(x-x1)

y-5= 1/2 (x+2)

y-5= 1/2x + 1

y= 1/2x + 6

The correct option (a) 2000, is the miles are driven on each tire.

For the stated question-

Miles are driven on each tire = Total distance/number of tires.

Miles are driven on each tire = 10000/5

Miles are driven on each tire = 2000

Thus, the number of miles are driven on each tire is 2000 miles.

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Answer:

vsbnnsmelr bc ycmjsddm

The answer is c. Chi-square test. A Chi-square test is an inferential statistical technique used to analyze the relationship between two categorical variables organized in a bivariate table.

In a chi-square test, the data is organized into a contingency table, also known as a cross tabulation or bivariate tabulation. This table displays the frequency distribution of two categorical variables, showing how they are related or associated with each other.

The chi-square test evaluates whether there is a significant relationship or association between the variables. It calculates a test statistic based on the observed frequencies in the contingency table and compares it to the expected frequencies under the assumption of independence between the variables. If the test statistic is sufficiently large, it indicates that there is a significant relationship between the variables, rejecting the null hypothesis of independence.

The chi-square test is widely used in various fields, including social sciences, market research, and epidemiology, to determine if there is a significant association between categorical variables. It provides valuable insights into the relationship between variables and helps researchers make informed conclusions based on their data.

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Answer:

They will bump heads at 3.2 minutes

Step-by-step explanation:

Here, we want to calculate the time taken for them to meet at a point.

Let the distance traveled by the first swimmer be x, it means the second swimmer will meet the first swimmer at the point (480 - x)

The time taken for the first swimmer will be;

distance/ speed

= x/70

For the second swimmer, his time will be ;

(480-x)/80

Since we know the time they meet will be equal;

Then we equate both times;

x/70 = (480-x)/80

Cross multiply

80x = 70(480-x)

80x = 33600 - 70x

80x + 70x = 33,600

150x = 33,600

x = 33600/150

x = 224

So the time will be;

224/70 or (480-224)/80

= 3.2 minutes

Answer:

If x is the size of the child's head, 5 times that would be 5x and "plus 4/5" is + 4/5 so the equation is y = 5x + 4/5.

Answer:

(a) 5 mayflies

(b) 15 mayflies

(c) 84 flying flies

Step-by-step explanation:

Represent Mayflies with M and the total flying insects with F

The ratio can be represented as:

\(M : F = 5 : 14\)

Solving (a):

\(F = 14\)

Find M

Substitute 14 for F in \(M : F = 5 : 14\)

\(M : 14 = 5 : 14\)

Convert to fraction

\(\frac{M}{14} = \frac{5}{14}\)

Multiply through by 14

\(14 * \frac{M}{14} = \frac{5}{14} * 14\)

\(M = 5\)

Solving (b):

\(F = 42\)

Find M

Substitute 42 for F in \(M : F = 5 : 14\)

\(M : 42 = 5 : 14\)

Convert to fraction

\(\frac{M}{42} = \frac{5}{14}\)

Multiply through by 42

\(42 * \frac{M}{42} = \frac{5}{14} * 42\)

\(M = \frac{5}{14} * 42\)

\(M=5*3\)

\(M= 15\)

Solving (c):

\(M = 30\)

Find F

Substitute 30 for M in \(M : F = 5 : 14\)

\(30 : F = 5 : 14\)

Convert to fraction

\(\frac{F}{30} = \frac{14}{5}\)

Multiply through by 30

\(30 * \frac{F}{30} = \frac{14}{5} * 30\)

\(F = \frac{14}{5} * 30\)

\(F = 14*6\)

\(F = 84\)

Answer:

x     y

3     19

5     35

-2   -21

1      3

4      27

Step-by-step explanation:

I went through and mutliplied each x value by 8 and then subtracted 5. You were almost there!

Answer:

Right square pyramid

Step-by-step explanation:

A=a2+2aa2

4+h2

The probability that Rosa's mom chooses sausage and onion is: 1/8C₂.

Probability refers to the chance of an event occurring. It is given by the formula: number of favorable outcomes/number of total outcomes. The total number of groups from which Rosa's mom can make her choice is 1 and this is the number of favorable outcomes.

But, the total number of outcomes that Rosa can hope to expect are 2 two toppings(sausage or onions) out of 8. So, the selected answer is the representation of the probability.

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Answer:

Standard Deviation (σ) = √(n * p * q)

Step-by-step explanation:

To find the standard deviation of a binomial distribution, you can use the following formula:

Standard Deviation (σ) = √(n * p * q)

Where:

n is the number of trials or observations

p is the probability of success in a single trial

q is the probability of failure in a single trial (q = 1 - p)

Here are the steps to find the standard deviation of a binomial distribution:

Determine the values of n (number of trials) and p (probability of success).

Calculate the value of q (probability of failure) by subtracting p from 1 (q = 1 - p).

Multiply n, p, and q together.

Take the square root of the result obtained in step 3.

The final result will be the standard deviation (σ) of the binomial distribution.

Note: The formula assumes that the trials or observations in the binomial distribution are independent and have the same probability of success (p) for each trial.

After 30 years of 8.8% interest compounded monthly, an account has $4,000,000,he original deposit amount was $288,208.04

Compound Interest :

                          Compound interest is a form of interest calculated using the principal amount of a deposit  plus previously accrued interest.

  general formula for compound interest is

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

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

According to question,

Given final amount is (A) =  $4,000,000

time (t) = 30 years

Rate of interest (r) = 8.8%

                                = 8.8/100

                                = 0.088  , Compounded monthly

Let P be the principal amount

    using the formula for compound interest compounded monthly,

         A = P (1 + r/12)^12*t

or,

         P = A/(1 + r/12)^12*t

             Substituting all values we get,

            P =   $4,000,000/ (1 + 0.088/12)^12 x 30

                = $4,000,000/13.8788

                = $288,209.35

                ≈ $288,208.04

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Answer:

1) See below for table.

2) Domain: \(\{1, 2, 3, 4\}\)

Range: \(\{160, 160, 205, 250\}\)

Yes, this is a function.

Step-by-step explanation:

We know that the electrician charges a base fee of $70 plus $45 for each hour of work.

We also know that the minimum the electrician charges is $160.

Let's write an equation. Let x denote the number of hours worked and y denote the total price. There's also a base fee of $70. So, we can write the following equation:

\(y=45x+75\)

Part 1)

Let's create our table for 1, 2, 3, and 4 hours. To do so, we simply need to substitute each value for x in our equation.

1 Hour:

We have:

\(y_1=45(1)+70\)

Multiply and add:

\(y_1=45+70=\$115\)

However, notice that the minimum the electrician charges is $160. Therefore, for one hour of work, the electrician will still charge $160. So:

\(y_1=\$160\)

2 Hours:

Substitute 2 for x:

\(y_2=45(2)+70=90+70=\$160\\\)

So:

\(y_2=\$160\)

3 Hours:

Substitute 3 for x:

\(y_3=45(3)+70=135+70=\$205\)

So:

\(y_3=\$205\)

4 Hours:

Substitute 4 for x:

\(y_4=45(4)+70=180+70=\$250\)

So:

\(y_4=\$ 250\)

Therefore, for 1, 2, 3, and 4 hours of work, the prices will be $160, $160, $205, and $250, respectively.

We can create the following table (please scroll down to see the table. Also, y is measured in dollars).

Part 2)

The domain of a relation are the input values.

In this context, our input values are the amount of hours worked, and we calculated for 1, 2, 3, and 4 hours of work.

Therefore, our domain in this context is:

\(\{1, 2, 3, 4\}\)

The range of a relation are the output values.

In this context, the output values are the price for x hours of work.

Therefore, our range in this context is:

\(\{160, 160, 205, 250\}\)

This relation does represent a function. Remember that a function cannot have repeating input values. In other words, no one input can be equal to two or more different outputs. However, one output can be mapped to two or more different inputs.

For our table, none of the inputs are repeating. So, our relation is a function.

And we're done!

Using the concept of integer it can be concluded that Awad's claim is false.

Integer, a positive, negative, or 0 with a complete value. The counting numbers 1, 2, 3, and so forth are used to create the integers, together with the subtraction process. A counting number can be divided by itself and the result is always zero; for instance, 4 divided by 4 equals 0. The result of subtracting a larger number from a smaller one is a negative whole number; for instance, 2 - 3 = 1. By deriving each integer in this way from the counting numbers, a set of numbers that can be closed with the subtraction operation is produced.

You can have positive or negative numbers. Negative numbers are frequently surrounded by brackets to make them simpler to read, for example (-2). Positive numbers typically don't have the + before the number. 3 is actually +3. Positive and negative number combinations can be confusing to add and multiply, thus caution is advised.

Subtraction and Addition

Two "pluses" equal a "plus," and two "minuses" equal a "plus." A negative is made up of a plus and a minus.

Whenever you subtract a negative number, you always end up adding because two negatives make a positive. For example,

n = 4

m = -3

then,

4-(-3) is going to turn into 4+3 = 7.

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Answer:

well just add 128 and 0.4 miles and that's your answer

Answer:

The result of decimal expansion of  \(8/15\) is \(0.533\).

Step-by-step explanation:

Hence the decimal expansion by simple division of \(8/15\) is \(0.533\).

Each length should be dragged to the correct location on the triangle as follows;

In Mathematics and Geometry, a 30-60-90 triangle is a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 4√3

Hypotenuse = 2 × 4√3

Hypotenuse = 8√3.

Opposite side = √3 × 4√3

Opposite side = 12

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: Mustafa is incorrect. He made a mistake in step 2.

Step-by-step explanation: Mustafa was certainly correct in step 1 that x(9x+3) + 3(x+3) is 9x^2 + 6x + 9. However when he was factoring, he made a mistake.

(3x + 3)^2 is NOT equal to 9x^2 + 6x + 9. Rather, (3x + 3)^2 is equal to 9x^2 + 18x + 9. If you want to double check this, use FOIL.

The correct factoring of 9x^2 + 6x + 9 is actually 3(3x^2 + 2x + 3). So, Mustafa made a mistake in step 2.

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Answer:

\(\huge\boxed{x \approx 5.4}\)

Step-by-step explanation:

We can break down this problem by first realizing different parts of the circle.

With this, we can find out if we find the radius of the circle, we have our answer.

We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.

What we need is a way to find the radius of the circle. This will get us x. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.

If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).

We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:

Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!

Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.

The line X does just that. Therefore, the value of x is also 5.4.

Hope this helped!

The potato will take approximately 3.1 minutes to reach a temperature of 90 degrees Celsius to the nearest tenth of a minute.

According to Newton's equation, we need to find time taken for the potato to reach 90 degrees Celsius to the nearest tenth of a minute.

Newton's law of cooling equation is used.

Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature.

The law of cooling is given as

\(T(t) = T_m + (T_0 - T_m)e^{-kt}\)

whereT(t) is the temperature of the object at time t.

\(T_0\) is the temperature of the object initially.

\(T_m\) is the temperature of the medium in which the object is kept.

k is a positive constant.

The formula is used to solve for the time it will take the baked potato to reach 90 degrees Celsius.

This is given as:

\(T(t) = T_m + (T_0 - T_m)e^{-kt}\)

\(90 = 20 + (37 - 20)e^{-kt}\)

Let's start by solving for k.

\(37 = 20 + (37 - 20)e^{-k(10)}\)

\(17 = 17e^{-10k}\)

\(ln(1) = -10k\)

\(k = 0\)

Substituting k = 0 in the equation,

we have

\(90 = 20 + (37 - 20)e^{0(t)}\)

\(\frac{70}{17} = e^{(0(t))}\)

Taking the natural log of both sides,

\(ln\frac{70}{17}  = lne^{0(t)}\)

\(t= 3.0748 minutes\)

Therefore, it will take approximately 3.1 minutes for the potato to reach 90 degrees Celsius to the nearest tenth of a minute.

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Answer:

79

Step-by-step explanation:

We need to calculate the height after 23 months.

so m= 23

Plug in m=23

we have H(m) = 56 + 23 = 79

Answer is 79cm

Answer:

Rational

Step-by-step explanation:

Its rational because it has the same numbers/pattern

You can find the answer in the image above.