Johnathan is using a hose to fill his pool with water. The pool already had 2,000 gallons of water in it before he started, and the hose puts water into the pool at a rate of 360 gallons per hour. Let g represent the number of gallons that the hose has put into the pool after a given number of hours. Let h represent the number of hours that the hose has put water into the pool. Let w represent the total number of gallons of water in the pool. Complete the equations so that: Equation 1 shows the relationship between g and h. Equation 2 shows the relationship between g and w.

Answer:

Step-by-step explanation:

a) (x-1)(2x-5)

b) x=-1 x=-2.5      x+1=0 x=-1        2x-5=0      2x=5     x=2.5

c) The degree is even so the ends of the graph will point in the same direction, the leading coefficient is positive so both ends will point up

d) First plot the x intercepts, then plug f(0) into the equation to get the y intercept. Plot the y intercept and then connect the points

e)

The probability that the sample mean will be greater than M = 10 pounds is 0.9525.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating the event is impossible and 1 indicating it is certain. Probability is used in many fields, including mathematics, statistics, science, and finance.

To solve this problem, we need to use the central limit theorem (CLT), which states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough.

Since the sample size is small (n = 4), we need to use the t-distribution instead of the normal distribution. However, since the population standard deviation is known, we can use the standard normal distribution with a z-score.

First, we need to calculate the standard error of the mean:

SE = σ / sqrt(n) = 6 / sqrt(4) = 3

Next, we can calculate the z-score:

z = (M - µ) / SE = (10 - 15) / 3 = -1.67

Finally, we can use a standard normal distribution table or calculator to find the probability of a z-score greater than -1.67:

p(M > 10) = P(z > -1.67) = 0.9525 (rounded to four decimals)

Therefore, the probability that the sample mean will be greater than M = 10 pounds is 0.9525.

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Answer:

r=9

Step-by-step explanation:

the radius is half of the circumference because the equation for circumference is 2 X radius, so dividing the circumference by 2 will undo the problem.

(18/2 = 9 )

Answer:      132 hours

Step-by-step explanation:

First you divide 11/2 which equals 5.5 then you multiply it with 24, which is equal to 132

Answer:

EF = 3.16

Step-by-step explanation:

Assume the triangles are similar.

BC/EF = BA/ED

7.9/EF = 11/4.4

11(EF) = 4.4 × 7.9

EF = 0.4 × 7.9

EF = 3.16

The signs of the coordinates of ΔS'T'U' the x-coordinate is positive and the y-coordinate is negative.

Coordinates are a set of numbers or values that define the position of a point or object in space or on a surface. They are used to locate a point or object in a specific location relative to a reference point, axis, or plane.

The coordinate system is divided into four quadrants, numbered from I to IV, which are separated by the x- and y-axes. The origin is located at the intersection of the x- and y-axes, and has coordinates (0, 0)

The ΔSTU lies in Q3 if it reflected then ΔS'T'U' lies in Q4, it means that the point is located in the fourth quadrant of the Cartesian coordinate system. In this quadrant, the x-coordinates are positive and the y-coordinates are negative.

More specifically, if we assume that the point ΔS'T'U' is represented by the coordinates (x, y), then we have:

x > 0 (because it lies to the right of the y-axis)

y < 0 (because it lies below the x-axis)

For example, if the point ΔS'T'U' has coordinates (3, -2), then it lies in Q4, since the x-coordinate is positive and the y-coordinate is negative.

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Answer:

0.4 seconds or

0.00667 minutes

Step-by-step explanation:

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pi times radius times 2 = circumference

pi times 10 inches times 2 = 62.83 inches = circumference

In one revolution, the wheel covers a distance equal to its circumference. So, at a speed of 22 revolutions per minute, the wheel covers a distance of:

22 x 62.83 inches inches per minute

1382.26 revolutions per minute

The wheel travels 1383.8 ft. in 60 seconds.

The wheel travels 1 ft. in (60 /  1383.8) seconds.

The wheel travels 10 ft. in (60 /  1383.8) * 10 seconds = 0.4 seconds

= 0.4 seconds divided by 60 = 0.00667 minutes

By answering the presented question, we may conclude that Therefore, triangle the measure of BCD is 120°.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles.

Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides.

Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees).

The region of a triangle may be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

Since triangle ABC is isosceles with AB = BC, angles A and C are also equal to each other. Let x be the measure of angles A and C. Then we have:

angle A + angle B + angle C = 180° (sum of angles in a triangle)

x + 60° + x = 180°

2x + 60° = 180°

2x = 120°

x = 60°

So angles A and C each measure 60°, making triangle ABC an equilateral triangle.

Now, angle BCD is an exterior angle of triangle ABC. By the Exterior Angle Theorem, the measure of angle BCD is equal to the sum of angles A and C:

angle BCD = angle A + angle C = 60° + 60° = 120°

Therefore, the measure of BCD is 120 degrees.

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The answer is 27 units of potassium. To determine the amount of potassium in the soil sample, we first need to use the given ratio of nitrogen to potassium to find the ratio between their respective quantities in the soil.

The ratio of nitrogen to potassium is 12:9, which can be simplified to 4:3 by dividing both sides by 3. This means that for every 4 units of nitrogen, there are 3 units of potassium in the soil sample. Since we know that the soil sample contains 36 units of nitrogen, we can use the ratio we just found to calculate the amount of potassium. To do this, we can set up a proportion: 4 units of nitrogen : 3 units of potassium = 36 units of nitrogen : x units of potassium

Solving for x, we cross-multiply and simplify:

4x = 3 * 36

4x = 108

x = 27

Therefore, the soil sample contains 27 units of potassium.

In summary, we used the given ratio of nitrogen to potassium to find the ratio between their respective quantities in the soil, and then set up a proportion using the known quantity of nitrogen to solve for the unknown quantity of potassium. The answer is 27 units of potassium.

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Answer:

Step-by-step explanation:

Let S be the number of specimens and W be the number of weeks.

We know that initially Joe starts with 83 specimens, and every week the number of specimens doubles. Therefore, the equation that represents the scenario is:

S = 83 * 2^(W-1)

Here, (W-1) is used to account for the initial number of specimens already given in the problem.

This equation gives the number of specimens S after W weeks, taking into account the doubling of specimens every week.

Answer:

14.0°

Step-by-step explanation:

[tex]\frac{sin(35)}{19} = \frac{sin(B)}{8}[/tex]

There is a B next to sin, but it represents m∠B. Note that both angles are in degrees.

Cross multiply the above equation.

8sin(35) = 19sin(B)

m∠B = [tex]sin^-1(\frac{8sin(35)}{19} )[/tex]

m∠B = 0.24391 rad

        ≅ 14.0°

NO IDEA i'm only in 5th grade sorry.

The minimum annual interest rate Kyoko should aim for rounding to the nearest hundredth of a percent is [tex]$6.76%$.[/tex]

What is meant by interest rate?

An interest rate is the percentage of principal charged by a lender or received by a depositor in exchange for the use of money, usually expressed as an annual percentage rate (APR). It is the amount of interest charged on a loan or earned on an investment.

Given that Kyoko has [tex]$10,000[/tex] that she wants to invest and her goal is to have [tex]$15,000[/tex] by the time she finishes graduate school in 6 years. Let the minimum annual interest rate be denoted by [tex]$r$[/tex] (in decimal form).

Using the compound interest formula, we have:

[tex]$A = P(1 + \frac{r}{n})^{nt}$[/tex]

where

A is the future value of the investment (which is [tex]$15,000$[/tex] in this case)

P is the present value of the investment (which is [tex]$10,000$[/tex] in this case)

r is the annual interest rate (what we need to find)

n is the number of times the interest is compounded per year (which is 365 since the interest is compounded daily)

t is the time (in years)

Plugging in the given values, we get:

[tex]$15000 = 10000(1 + \frac{r}{365})^{365\times 6}$[/tex]

Taking natural logarithm on both sides, we get:

[tex]$\ln(1.5) = \ln(1 + \frac{r}{365})^{365\times 6}$[/tex]

Using the property of logarithms, we can write the exponent on the right-hand side as:

[tex]$6\cdot 365\cdot \ln(1 + \frac{r}{365})$[/tex]

Dividing both sides by [tex]$6\cdot 365$[/tex] and simplifying, we get:

[tex]$\ln(1.5) = \ln(1 + \frac{r}{365})$[/tex]

[tex]$1.5 = 1 + \frac{r}{365}$[/tex]

[tex]$r = 365\times (1.5-1) = 365\times 0.5 = 182.5$[/tex]

Therefore, the minimum annual interest rate Kyoko should aim for is [tex]$r=182.5%$.[/tex] Rounding to the nearest hundredth of a percent, we get [tex]$6.76%$.[/tex]

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The area of the rectangle is the product of its length and width, while the area of the triangle is half the product of its base and height. The total area of the polygon is 96 [tex]in^{2}[/tex] + 30 [tex]in^{2}[/tex] = 126 [tex]in^{2}[/tex].

A polygon that has sides of varying lengths and unequal angles is said to have irregular sides. A regular polygon, on the other hand, has equal-length sides and angles.

An irregular polygon can have any number of sides, any number of angles, and any shape for its sides. The area and perimeter of irregular polygons must be determined using particular formulae that take into consideration the unique characteristics of each individual polygon since irregular polygons can have a wide range of varied sizes and forms.

To find the area of an irregular polygon, we can divide it into smaller shapes such as triangles and rectangles, find the area of each shape, and add them together.

In this case, we can divide the polygon into a rectangle and a right triangle, as shown in the diagram below:

The area of the rectangle is the product of its length and width:

Area of rectangle = 8 in x 12 in = 96 [tex]in^{2}[/tex]

The area of the triangle is half the product of its base and height:

Area of triangle = 1/2 x 6 in x 10 in = 30 [tex]in^{2}[/tex]

Therefore, the total area of the irregular polygon is:

Area = Area of rectangle + Area of triangle

= 96 [tex]in^{2}[/tex] + 30 [tex]in^{2}[/tex]

= 126 [tex]in^2[/tex]

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Answer:

c

Step-by-step explanation:

the open circle means less than or equal too so it cant be B or D

and its pointing to the right so the mouth will eat the bigger number and the bigger number is X

173 units2 is the area of the figure.

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

Hence, 173 units2 is the area of the figure.

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Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1

The comparison of the connection here between variable and its value is a compound inequality. In a compound inequality, a variable is compared across two ranges which may provide the variable's range by satisfying either one or both of the limitations .

The given absolute value inequalities :

|(x+1)/2 - x/2| < 1/2

Removing the modulus sign will for 2 equations:

(x+1)/2 - x/2 < 1/2  and  (x+1)/2 - x/2 < - 1/2

Simplifying each:

(x+1)/2 - x/2 < 1/2  

x/2 + 1/2 - x/2 < 1/2

Both values will get cancelled:

0 < 0

But 0 = 0

and  (x+1)/2 - x/2 > - 1/2

x/2 + 1/2 - x/2 > -1/2

0 > -1 (correct)

here also the terms are getting completely cancelled to

Thus, the solution set of the given absolute value inequalities is found as: 0 ≥ x ≥ -1

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Complete question:

Find the set of the solutions of the following absolute value inequalities.

|(x+1)/2 - x/2| < 1/2

Assessment for Learning is a type of assessment that is used to evaluate students' progress and understanding throughout the learning process.

An evaluation that is brief and specifically focused on supporting planning and decision-making is known as a micro-assessment. A micro-assessment can be utilized to quickly and easily acquire data that is required for making decisions, establishing objectives or directions, or carrying out elevated or early planning.

Assessment for Learning:

Assessment for Learning is a type of assessment that is used to evaluate students' progress and understanding throughout the learning process. It is designed to provide teachers with feedback on how well their students are learning and to identify areas where students may need additional support. Assessment for Learning involves ongoing, interactive assessments that focus on identifying students' strengths and weaknesses.

Importance of Assessment for Learning:

It assists teachers in determining the areas in which students are having difficulty and in modifying their pedagogical approaches accordingly.

Implementation of Assessment for Learning in my Learning Area:

Provide regular feedback to students on their work, highlighting areas of strength and areas that need improvement.

Assessment Used for Learning (Formative):

Formative assessment is a type of assessment that is used to evaluate students' progress and understanding throughout the learning process. It is designed to provide teachers with feedback on how well their students are learning and to identify areas where students may need additional support. Formative assessment involves ongoing, interactive assessments that focus on identifying students' strengths and weaknesses.

Importance of Formative Assessment:

Teachers might then modify their pedagogical approaches in light of the areas in which their students are having difficulty.

Implementation of Formative Assessment in my Learning Area:

Provide regular feedback to students on their work, highlighting areas of strength and areas that need improvement.

Assessment Used for Promotional Purposes (Summative):

Summative assessment is a type of assessment that is used to evaluate students' learning at the end of a unit or course. It is designed to provide a summary of what students have learned and to determine whether they have met the expected learning outcomes.

Importance of Summative Assessment:

It provides a summary of what students have learned and helps to determine whether they have met the expected learning outcomes.

Implementation of Summative Assessment in my Learning Area:

Provide students with clear expectations and learning outcomes at the beginning of a unit or course.

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Answer:

We can use the formula for compound interest:

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

where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period in years

In this case, we have:

P = £1430

r = 0.005 (0.5% per month)

n = 12 (compounded monthly)

t = 9/12 = 0.75 (9 months is three-quarters of a year)

So we can plug in these values to find the final amount:

A = £1430(1 + 0.005/12)^(12*0.75)

A ≈ £1481.18

Therefore, the amount of money in the account after 9 months will be approximately £1481.18.

0.006678 rounded to 3 decimal places is 0.0067.

We have,

To round 0.006678 to 3 decimal places, we need to look at the fourth decimal place (the digit 7).

Since 7 is greater than or equal to 5, we round up the last digit (8) by adding 1 to it.

Now,

The rounded number is 0.0067

So 0.006678 rounded to 3 decimal places is 0.0067.

Thus,

0.006678 rounded to 3 decimal places is 0.0067.

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Option D (132 square centimeters)

Here is how I got my answer (Look at picture below):

• First, I did the rectangle outlined in red, 4×10=40

• Second, I did triangles outlined in yellow, [(4×3)÷2]×2=12

• Third, I did the rectangle outlined in blue, 10×5=50

• Fourth, I did the rectangle outlined in purple, 3×10=30

Lastly, I added up the sum which was 40+12+50+30=132

—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

Thus, the total area of the figure made by square grids paper in three-dimensional figure is found as: 48 in².

Three-dimensional (3D) shapes have three dimensions, like length, breadth, and height. Prisms and spheres are two examples of 3D shapes. Multidimensional and physically holdable 3D forms.

The three - dimensional dimensions comprising width, height, and depth are referred to as three dimensions, or 3D. The physical world is three dimensional, as is everything that can be seen there.

For the given net of 3-D figure.

Each  square of grip represents 1 in².

Total area = rectangle area + 2*triangle area

Total area = length*breadth + 2*(1/2*base*height)

Total area = 12*3 + 3*4

Total area =  48 in².

Thus, the total area of the figure made by square grids paper in three-dimensional figure is found as: 48 in².

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Answer:

first box, first box, second box

Step-by-step explanation:

Answer:

69 mph

Step-by-step explanation

Let the speed of boat be x hence speed downstream is x+3 but speed upstream will be x-3

Speed is distance per unit time and time is same hence

24(x-3)=22(x+3)

24x-72=22x+66

2x=138

X=138/2=69

Therefore, the speed of boat is 69 miles per hour or

The boat in the problem travels different distances at different rates, but in the same amount of time for each trip. Distance is rate times time, d=r⋅t, which, solving for t, becomes

t=dr.

The trip against the current has rate r=s−3, so the time it takes to complete the trip is

t=20s−3.

The time it takes to complete the trip with the current is

t=22s+3.

The time to complete each trip is the same, so set the fractions equal to each other.

20s−3=22s+3

Multiply each side by (s−3)(s+3).

20(s−3)(s+3)(s−3)=22(s−3)(s+3)(s+3)

Simplify.

20(s+3)=22(s−3)

Distribute coefficients.

20s+60=22s−66

Combine like terms.

2s=126

Divide each side by 2 to find the solution,

s=69 mph.

Sorry if im wrong

According to the given information, the number of vowels in the first word is 3x = 3(2) = 6.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, a left-hand side and a right-hand side, separated by an equal sign. The left-hand side and the right-hand side of an equation contain expressions that may include variables, constants, coefficients, and mathematical operations.

Let the number of vowels in the first word be 3x (since the ratio of vowels in the first word to the second word is 3:5)

Then, the number of vowels in the second word is 5x (since the ratio of vowels in the first word to the second word is 3:5)

Given that the second word contains 10 vowels. So, 5x = 10

Hence, x = 2

Therefore, according to the given information, the number of vowels in the first word is 3x = 3(2) = 6.

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Answer:top one

Step-by-step explanation:

im doing it

Answer:

51

Step-by-step explanation:

To find the value of the expression, you need to simplify it following PEMDAS (Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction) If you try and simplify the problem without following the order of operations, you won't always get the right answer.

You want to start by simplifying what is inside the parenthesis.

[tex](10+5)+6*8-12\\15+6*8-12[/tex]

Next you want to do the multiplication:

[tex]15+6*8-12\\15+48-12[/tex]

Now we can just combine the rest of the terms

[tex]15+48-12\\51[/tex]

Answer:

V = 27

Step-by-step explanation:

62 = −19 + 3v

Swap sides so that all variable terms are on the left-hand side.

−19 + 3v = 62

Add 19 to both sides.

3v = 62 + 19

Add 62 and 19 to get 81.

3v = 81

Divide both sides by 3.

v = 81/3

​Divide 81 by 3 to get 27.

v = 27

I hope this will help you! :)