The Royal Fruit Company produces two types of fruit drinks. The first type is 80 % pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 95% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 220 pints of a mixture that is 95% pure fruit juice?

Answer:

The dogs path is shorter to the water bowl

Step-by-step explanation:

Answer:

The problem statement suggests that the series of donations is arithmetic, as each student's donation increases by one as their number increases. Therefore, we can apply the formula for the sum of an arithmetic series to solve this problem.

In an arithmetic series, the sum S of n terms is given by:

S = n/2 * (a + l)

where:

- n is the number of terms (which represents the number of students in this case),

- a is the first term (in this case, the first student's number, which would be 1), and

- l is the last term (in this case, the last student's number, which we don't know yet).

Given that S = Rs. 13225, we have:

13225 = n/2 * (1 + l)

Since this is an arithmetic series starting from 1, the last term, l, is equal to n. Thus, we can substitute l with n:

13225 = n/2 * (1 + n)

Multiplying through by 2 to clear the fraction gives:

26450 = n * (1 + n)

Rearranging to a quadratic equation gives:

n^2 + n - 26450 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. To solve for n, we can use the quadratic formula, n = [-b ± sqrt(b^2 - 4ac)] / (2a). But since n cannot be negative in this context (as it represents the number of students), we will only consider the positive root.

Applying the quadratic formula, we find that the positive root is approximately 162.5. However, the number of students must be a whole number. Therefore, the number of students is 163, because the 163rd student did not donate fully as per their number, and that's why the total amount doesn't reach the full sum for 163 students.

So, there were 163 students who donated money to the fund.

The 99\(\%\) confidence interval for the difference between the mean yields for the two fertilizers is (32.11, 93.89).

A confidence interval is a range of values that provides an estimate of the unknown population parameter with a certain level of confidence.

Given that

Sample 1:

Sample mean, \(\bar{X_1}\) = 457,

Sample size, \(n_1\) = 18,

Standard deviation, \(s_1\) = 38.

Sample 2:

Sample mean, \(\bar{X_2}\) = 394,

Sample size, \(n_2\) = 18,

Standard deviation, \(s_2\) = 23.

Point estimate = \(\bar{X_1}\) - \(\bar{X_2}\)

                        = 457 - 394

                        = 63.

\(Standard Error=\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }\\\)

                          \(=\sqrt{\frac{38^2}{18}+\frac{23^2}{18} }\\=11.14924\).

Level of significance, α = 0.01 (given that 99\(\%\) confidence interval).

Degrees of freedom = \(\dfrac{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2})^2 }{\frac{(\frac{s_1^2}{n_1})^2}{n_1-1} + \frac{(\frac{s_2^2}{n_2})^2}{n_2-1} }\) = 28.

Critical values:

\(t_\frac{\alpha}{2} = \pm2.771\)

The confidence interval is

\((\bar{X_1}-\bar{X_2})\pm t_\frac{\alpha}{2}\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} }\)

\(= 63 \pm 2.771 \times 11.14924\\=63 \pm 30.89\\=(63-30.89,63+30.89)\\=(32.11,93.89)\)

Hence, the confidence interval is (32.11, 93.89).

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Answer:

I hope this helps!

Step-by-step explanation:

Please mark brainiest

Answer: its 1

Step-by-step explanation: -7 to -3 by two spaces, means +2 each space, so the middle one is -5 but thats irrelevant, going another two spaces to the right means +4 and -3+4 is 1

Answer:

7/10 = .70

3/5 = .60

9/11 = .81

1/2 = .50

9/11 is the most

The price of a pair of jeans was reduced from $20 to $15.

Difference between the price : New price-Olde price

Difference between the price : 20 -15 = $5

The precentage of reduce is:

So, the percentage was the price of the jeans reduced is 25%

Answer: 25%

Answer:

Equation: y = -4x + 1

Slope: -4

Y-intercept: y = 1

Step-by-step explanation:

To find the equation of the line you need the gradient and the y-intercept

To find the gradient we need to divide the change in y by the change in x:

As the graph has a negative correlation the gradient would have a minus which is why it would be -4!

To find the y-intercept we need to find the number on the y-axis that the line crosses which in this case would be y = 1!!

Hope this helps, have a great day!!

Answer:

equation:y=4x+1

y-intercept:1

slope:4/1 or 4

Step-by-step explanation

the equation has to be in slope intercept form which is \(y=mx+b\) where m is the slope and b is the y-intercept. the y-intercept is when x is 0 in this case when x is 0 y is 1 (0,1) so the y-intercept is 1. the slope is rise/run so pick two points that cross the grid perfectly and count the units rise and run. this line rises 4 and runs 1 so the slope is 4/1 so 4 hence the equation \(y=4x+1\)

Answer:

Option C

Step-by-step explanation:

have a great Day

Answer:

πr^2 h

π(11)^2 (15)

= 1815π or = 5701

Answer: 8.06 Inches

The area of the circle is 28.26 ft². 3. The diameter of the circle is 8.06 inches.

Answer:

volume is 36.25inches

145/4

Step-by-step explanation:

L= 3 5/8inches

W= 2 1/2inches

H= 4inches

VOLUME = L×W×H

3 5/8 × 2 1/2 × 4 =

29/8 × 5/2 × 4 = 36.25inches

36.25→145/4

The possible values of x are 51% < x < 59%.

When you are given various values, the range of those values is how big the difference is between the largest value and the smallest value. In other words, the range is what you get when you subtract the smallest value in the group from the largest value in the group.

Its possible values are 1, 2, 3, 4, 5, and 6; each of these possible values has a probability of 1/6. 4. The word “random” in the term “random variable” does not necessarily imply that the outcome is completely random in the sense that all values are equally likely.

Let K represent Kofi

1st paper = 45/100

2nd paper = x / 100

Mean score = ( 45 + x ) % / 2

The possible range of x = 48% < (45+X)/2 < 52%

Cross multiplying

96% < 45 + x < 104%

Subtract 45 from both sides

Range = 51% < x < 59%

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Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

Answer:

Exact Form:

x=15/8

Decimal Form:

x=1.875

Mixed Number Form:

x=1 7/8

Step-by-step explanation:

steeper, downward

1) Analyzing both functions, we have y=x+2 becoming under transformations y=3x+1

2) So we can write that the slope is steeper since the slope has become 3 times greater than the original slope, m=1.

And the line is shifted downward since that +1 is below +2.

3) Hence, the answer is steeper, downward

Answer:

80, 0.9, 8, 0.09

Step-by-step explanation:

Places are...

1 - ones

10 - tens

100 - hundreds

etc.

Decimal places are...

0.0 - tenths

0.00 - hundredths

0.000 - thousandths

etc.

(a) The digit in the ones place is 8. It is 1/10 of 80 because...

1/10 * x = 8

x/10 = 8

Multiply both sides by 10

x=80

(b) The digit in the hundredths place is 0.09. It is 1/10 of 9 because...

1/10 * x = 0.09

x/10 = 0.09

Multiply both sides by 10

x=0.9

(c) The digit in the tens place is 80. We can divide it by 10 to find that it is 10 times as much as 8.

(d) The digit in the tenths place is 0.9. We can divide it by 10 to find that it is 10 times as much as 0.09.

The scientific notation of the given number is 1.24×10⁻⁶.

The given number is 0.00000124.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

Here, 0.00000124=1.24×10⁻⁶.

Therefore, the Scientific notation of the given number is 1.24×10⁻⁶.

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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The equation, \( \frac{2 \cdot x + p}{q} = \frac{2 \cdot x + q}{p} \), gives;

When p = q, the number of solutions is infinite.

When p ≠ q, the equation has no solution

The given equation is presented as follows;

\( \frac{2 \cdot x + p}{q} = \frac{2 \cdot x + q}{p} \)

If p = q, we have;

\( \frac{2 \cdot x + q}{q} = \frac{2 \cdot x + q}{q} \)

\( \frac{2 \cdot x + p}{p} = \frac{2 \cdot x + p}{p} \)

Therefore, the equation has an infinite number of solutions when p = Q

If p ≠ q, and x = 3, we have;

\( \frac{2 \cdot x + p}{q} = \frac{2 \times 3 + p}{q} = \frac{6 + p}{q} \)

\( \frac{2 \cdot x + q}{p} = \frac{6 + q}{p} \)

\( \frac{6 + p}{q} \) = \frac{6 + q}{p} \)

6•p + p² = 6•q + q²

However;

p ≠ q

Therefore;

6•p ≠ 6•q

p² ≠ q²

6•p + p² ≠ 6•q + q²

Which gives;

\( \frac{6 + p}{q} \neq \frac{6 + q}{p} \)

The equation is not defined when p ≠ q

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A rule that represents the functions that we have here would be (x + 2)².

(1, 9) =

(1 + 2)² = 3² = 9

(2, 16)

= (2 + 2)²

4² = 16

(3, 25)

(3 + 2)²

= 5²

= 25

(4, 36)

= (4 + 2)²

= 6²

= 36

(5, 49)

= (5 + 2)²

= 7²

= 49

Hence we can see that the values in the second parts of the brackets can be gotten when we take the x value to be the first part of the equation, add it to 2 and then square the solution.

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\(3 {x}^{2} + 11x - 4\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\((3x - 1)(x + 4) \\ \\ = 3x(x + 4) - 1(x + 4) \\ \\ = 3 {x}^{2} + 12x - x - 4 \\ \\ = 3 {x}^{2} + 11x - 4\)

\(\bold{ \green{ \star{ \orange{Mystique35}}}}⋆\)

Question 958954: One number is five less than a second number. Five times the first is eight more than two times the second. Find the numbers.

hope this helps!

Answer:

70

Step-by-step explanation:

The prime factors of 350 are 2,5,7. Therefore, the product of prime factors = 2×5×7=70

Given:

Lines DE and AB intersect at point C.

To find:

The value of x.

Solution:

In the given figure it is clear that the angles  and  are lie on a straight line AB.

              [Linear pair]

Subtract 5 from both sides.

Divide both sides by 7.

Therefore, the correct option is B.