How many gallons of pure water should be added to 10 gallons of a solution containing 15% juice so that
the remaining solution contains 5% juice?
Fill in the table:
What is the amount of juice in the original solution? a =
What is the original amount of solution in gallons? b =
How much juice is added? c =
How much total solution is added? d =
Original
Added
New
Amount of juico
a
Total solution

Answer: E

Step-by-step explanation:

The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.

The Distance that Ellie ran each evening is 16.5 miles for a entirety week.

We can use the following equation to find how many miles, x, Ellie ran each afternoon:

x + 2.5(3) = 24

Here, x represents the number of miles Ellie ran each afternoon, 2.5 represents the number of miles she ran each morning, and 3 represents the number of days she trained. The total number of miles she ran, 24, is on the right side of the equation.

To solve for x, we can start by simplifying the left side of the equation:

x + 7.5 = 24

Then, we can subtract 7.5 from both sides:

x = 16.5

So, Ellie ran 16.5 miles each afternoon.

To know more on equation at:

brainly.com/question/2972832

#SPJ4

Answer:

He would need 3/4 a gallon to paint the wall

Step-by-step explanation:

Answer:

my answer is A

Step-by-step explanation:

if you work out the equation where you know that at the x intercept y=0 you will find A to be true

Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

Answer:

  2.6 km

Step-by-step explanation:

You want the total distance from Tracey's house to John's house to school, and back again, when the distance from Tracey's to John's is 0.5 km, and the distance from John's to school is 0.8 km.

The total distance will be the sum of the parts:

Total distance = (0.5 +0.8 +0.8 +0.5) km = 2(0.5 +0.8) km = 2(1.3 km)

  = 2.6 km

Tracey rode 2.6 km altogether.

Answer:

42

Step-by-step explanation:

since x is parallel to y m 26 remains constant

Answer:

power = work/ time

2hrs = 60×2 seconds = 120s

power = 1987/120

= 16.5 watt

LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.

To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:

LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))

where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).

First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01

1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.

2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39

First Scenario Result:
LCL = 158.61
UCL = 161.39

Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05

1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.

2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35

Second Scenario Result:
LCL = 69.65
UCL = 70.35

Learn more about LCL and UCL here: brainly.com/question/29048041

#SPJ11

There are 8 feet³ of these sheets will Jill need to cover the floor.

We have to given that;

Plywood is sold in 1/4 inch thick sheets that have a length of 8 feet and a width of 4 feet.

Hence, The volume of for sheets are,

⇒ 1/4 × 8 × 4

⇒ 8 feet³

Therefore, There are 8 feet³ of these sheets will Jill need to cover the floor.

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ1

The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

Given that,

Because watching TV via digital streaming is becoming more and more common, tv advertising companies are having a harder time connecting with viewers. 53% of the 2343 American adults surveyed by the Harris Poll on November 13, 2012, claimed they had viewed digitally streamed television content on at least one device.

We have to find what is the sample proportion? firstly, the z-critical value is ? What is the confidence interval at 99%?

We know that,

n = 2343

Point estimate = sample proportion = \(\hat p\) = 0.530

1 - \(\hat p\) = 1 -0.530 = 0.470

At 99% confidence level

α = 1-0.99% =1-0.99 =0.01

α /2 =0.01/ 2= 0.005

Z(α /2) = Z0.005 = 2.576

Z (α/2) = 2.576 = 2.58

Margin of error = E = Z (α/2) × √((\(\hat p\) × (1 - \(\hat p\) )) / n)

=2.576 × (√(0.530×(0.470) /2343 )

= 0.027

A 99% confidence interval for population proportion p is ,

\(\hat p\)- E < p < \(\hat p\) + E

0.530 -0.027 < p < 0.530 +0.027

0.503 < p < 0.556

( 0.503, 0.556 )

Therefore, The sample proportion is 0.530 and the z-critical value is 2.58 and the confidence interval at 99% is ( 0.503, 0.556 ).

To learn more about interval visit: https://brainly.com/question/15050000

#SPJ4

Answer: A. -1

Step-by-step explanation:

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

2x-4 + 5x -10= -6

Combine like terms

7x-14=-6

Add 14 to both sides

7x=8

Divide

X= 8/7 or 1.14 (rounded)

1.14 - 2= -0.86 which can be rounded to -1

Answer:

to show the changes in private school enrollment

1. We can conclude that T(n) = 1 + 5(n-1).

2. This recurrence relation can be solve as  T(n) = O(n²).

(1) T(n) = {1, T(n-1) + 5} for n = 1, and for n ≥ 2

To solve this recurrence relation, we can use the substitution method.

We'll start by finding the pattern for a few values of n:

T(1) = 1

T(2) = T(1) + 5 = 1 + 5 = 6

T(3) = T(2) + 5 = 6 + 5 = 11

T(4) = T(3) + 5 = 11 + 5 = 16

From the pattern, we can observe that T(n) = T(n-1) + 5 = T(n-2) + 5 + 5 = T(n-3) + 5 + 5 + 5 = ... = T(1) + 5(n-1).

Therefore, we can conclude that T(n) = 1 + 5(n-1).

(2) T(n) = {1, 3T(n/2) + n^2} for n = 1, and for n ≥ 2

To solve this recurrence relation, we can use the recursion tree method.

First, let's build the recursion tree:

                       T(n)

                 /                 \

             T(n/2)          T(n/2)

              /   \                /   \

          T(n/4) T(n/4) T(n/4) T(n/4)

           /   \     /   \     /   \     /   \

        ...      ...  ...     ...    ...  ... ...

The height of the recursion tree is log₂n, and at each level, the work done is n². Therefore, the total work done can be calculated by multiplying the work done at each level by the number of nodes at that level.

Total work = n² + 2(n/2)² + 4(n/4)² + ... + 2ᵏ(n/2ᵏ)²

The recursion tree terminates when n/2ᵏ = 1, which implies k = log₂n.

Using the formula for the sum of geometric series, we can simplify the total work:

Total work = n²(1 + 1/2² + 1/4² + ... + 1/(2^(log₂n))²)

= n²(1 + 1/4 + 1/16 + ... + 1/n²)

= n²(1 - 1/(4^log₂n))/(1 - 1/4)

= n²(1 - 1/n²)/(3/4)

= 4/3 n² - 4/3

Therefore, T(n) = O(n²).

Learn more about recurrence at https://brainly.com/question/32660587

#SPJ11

Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

For more such questions on inches, click on:

https://brainly.com/question/876758

#SPJ8

Both of the given equations have no solution.

1. sec x-tanx sinx = 1/sec x

The left-hand side of the equation can be simplified by using the identity that sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x). So,

sec x - tan x sin x = 1/cos x - sin x/cos x sin x = 1/cos x - sin^2 x/cos x = 1/cos x - (1-cos^2 x)/cos x = 1/cos x - (1/cos x) = 1/cos x - 1/cos x = 0.

On the right-hand side, sec x = 1/cos x, so 1/sec x = cos x. Hence,

0 = cos x

This equation has no solution, which means that the original equation sec x - tan x sin x = 1/sec x has no solution.

2. 1 +cosx/sinx = csc x Cot x

We can simplify the left-hand side of the equation by using the identity that csc(x) = 1/sin(x) and cot(x) = cos(x)/sin(x). So,

1 + cos x/sin x = 1/sin x * cos x/sin x = cot x.

Hence,

1 + cot x = cot x

This equation has no solution, which means that the original equation 1 +cosx/sinx = csc x Cot x has no solution.

To learn more about trigonometry

Visit; brainly.com/question/29140174

#SPJ4

Answer:

2

Step-by-step explanation:

The function θ : p(z) → p(z) defined as θ(x) = x is injective and surjective, therefore bijective.

The function θ(x) = x takes an element x from the set p(z) and returns the same element x. This means that for any input x in p(z), the function simply returns x as the output.

To determine whether θ is injective, we need to check if distinct inputs produce distinct outputs. In this case, since the function θ simply returns the input element x, it is evident that if two different elements are provided as input, they will always produce different outputs. Thus, θ is injective.

To assess the surjectivity of θ, we need to determine if every element in the codomain p(z) has a corresponding preimage in the domain p(z). In this scenario, since the function θ returns the same element x that is provided as input, it covers all elements in p(z). Therefore, for any given element in the codomain, there exists a preimage in the domain. Hence, θ is surjective.

Since the function θ is both injective and surjective, it is bijective. This means that for every input element x, there is a unique output element x, and every element in the codomain p(z) has a corresponding preimage in the domain p(z).

Learn more about Concepts of injective

brainly.com/question/17255939

#SPJ11

The value of t when the ball hits the ground is 5 seconds. When the ball hits the ground, its velocity is 80 ft/sec. What is the time (value of t) at which the ball hits the ground? To determine the time (value of t) at which the ball hits the ground, the quadratic equation should be set to zero since the height of the ball when it strikes the ground is zero.s(t) = 0 ==> 160 + 48t - 16t^2 = 0.

A quadratic equation in standard form is: ax² + bx + c = 0where a = -16, b = 48, and c = 160Therefore, the quadratic equation is: -16t² + 48t + 160 = 0Divide each term by -16 to obtain the quadratic equation in the form: t² - 3t - 10 = 0Then solve the quadratic equation, using the quadratic formula:$$t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$Substitute the values of a, b and c in the quadratic formula.$$t = \frac{-48 \pm \sqrt{48^2 - 4(-16)(160)}}{2(-16)}$$Simplify the expression.$$t = \frac{-48 \pm \sqrt{2304 + 10240}}{-32}$$.$$t = \frac{-48 \pm \sqrt{12544}}{-32}$$.$$t = \frac{-48 \pm 112}{-32}$$t = -2 or t = 5The time when the ball hits the ground is t = 5 sec.

What is the velocity of the ball at the moment it hit the ground? To determine the velocity of the ball when it hits the ground, differentiate the height function s(t) with respect to time. It is given that s(t) = 160 + 48t - 16t²ds/dt = 48 - 32tWhen the ball hits the ground, the value of t is 5 seconds, and its velocity is given by:v = ds/dt at t = 5s.v = ds/dt at t = 5 = 48 - 32(5) = -32 ft/secTherefore, the velocity of the ball when it hits the ground is 80 ft/sec (downward direction).

Learn more about velocity at https://brainly.com/question/33412867

#SPJ11

Answer:

890238  is the answer

Step-by-step explanation:

Slope of the median-median line is option A. m = 0.5469.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given are 7 data coordinates.

In order to find the median-median line, arrange the data in ascending order of x.

x : 6   10   11   20   30   34   46

y : 2    1    22  35   41    14    24

There are 7 coordinates.

Make this into three equal groups.

Group 1 : (6, 2), (10, 1)

Group 2 : (11, 22), (20, 35), (30, 41)

Group 3 : (34, 14), (46, 24)

Median is the middle element in the data set.

Median of group 1  = ([6+10]/2, [2+1]/2) = (8, 1.5)

Median of group 2 = (20, 35)

Median of group 3 = ([34+46]/2, [14+24]/2) = (40, 19)

Slope of the line can be found using the points (8, 1.5) and (40, 19).

Slope = (19 - 1.5) / (40 - 8) = 17.5 / 32 = 0.546875 ≈ 0.5469

Hence the slope of the line is m = 0.5469.

Learn more about Median-Median Line here :

https://brainly.com/question/23566556

#SPJ3

Answer:

1.12 pounds

Step-by-step explanation:

3.5 - 2.38 = 1.12

Answer:

1.12 pounds of ground beef.

Step-by-step explanation:

3.50-2.38

1.12

After calculation, we know that the time taken by the lorry is 3 hours and 20 minutes.

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Military time starts with 0000, also known as "zero hundred hours" or just "zero hundred," at the stroke of midnight.

Then, multiply each hour by one hundred, such that 1 a.m. is equal to 0100 (zero one hundred) hours, 2 a.m. is equal to 0200 (zero two hundred) hours, and so on.

So, we need to calculate the time as follows:

Leaving time = 14:55

Arriving time = 18:15

Then,

14:55 to 15:15 = 20 minutes

Then, 15:15 to 18:15 = 3 hours

Then, the total time taken would be:

3 hours and 20 minutes

Therefore, after calculation, we know that the time taken by the lorry is 3 hours and 20 minutes.

Know more about time here:

https://brainly.com/question/26046491

#SPJ1

Complete question:

On the return journey, the lorry leaves at 14 55 and arrives at the factory at 18 15. Calculate the time taken.

Based on the sequence formula, the number of cubes in the 5th pattern is 9

From the question, we have the following parameters that can be used in our computation:

Number of cubes in the nth pattern = 2n - 1

Also from the question, we have the pattern to be the 5th pattern

This means that n = 5

Substitute the known values in the above equation, so, we have the following representation

Number of cubes in the 5th pattern = 2 * 5 - 1

Evaluate the product

Number of cubes in the 5th pattern = 10 - 1

Evaluate the difference

Number of cubes in the 5th pattern = 9

Hence, the number of cubes is 9

Read more about sequence at

https://brainly.com/question/6561461

#SPJ1

Complete question

a pattern using cubes is shown to the right. the number of cubes at a particular place in the pattern can be calculated using the expression. 2n-1 the variable n represents the place in the pattern

How many cubes are in the 5th pattern

(a) There are 81 possible answer sequences for the four questions.

(b) The probability of getting all four answers correct when guessing is approximately 0.01235 when rounded to five decimal places.

(c) The probability of answering at least one question correctly when guessing is approximately 0.51775 when rounded to five decimal places.

(a) Since there are three possible answers for each of the four questions, there are a total of 3^4 = 81 possible answer sequences for the four questions.

(b) If you are guessing on each question, the probability of getting one question correct is 1/3. Since there are four questions, the probability of getting all four correct is (1/3)^4 = 1/81, which is approximately 0.01235 when rounded to five decimal places.

(c) The probability of not getting any question correct is (2/3)^4, since there are two incorrect answers for each question and we are guessing on all four questions. Therefore, the probability of getting at least one question correct is 1 - (2/3)^4, which is approximately 0.51775 when rounded to five decimal places.

Learn more about probability here

brainly.com/question/11234923

#SPJ4

If f is continous on [a,b], then f attains an absolute maximum value f(c) and absolute minimum value f(d) at some numbers c and d in [a,b] then it is a true statement

What is an absolute maximum?

An absolute maximum point is a point where the function obtains its greatest possible value. Similarly, an absolute minimum point is a point where the function obtains its least possible value.

learn more about of absolute max here

https://brainly.com/question/7128867

#SPJ4

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

Learn more about tangent here:

https://brainly.com/question/10053881

#SPJ11