How would I solve this?

The rate of increase of the depth of the water (W(t)) is constant.

What is rate ?

In mathematics and physics, the rate is a measure of change of a certain quantity with respect to another quantity. The rate can be a number, a ratio or a derivative. It is often represented by the symbol "d" or "dx/dt" or "dy/dt" and it measures how fast a quantity is changing.

Water is poured into the top half of a spherical tank at a constant rate, this means that the rate of increase of the depth of the water (W(t)) is constant.

In this case, W(t) is constant.

It is important to keep in mind that the rate of change of the function doesn't indicate the shape of the function, it just tells us the change of the dependent variable with respect to the independent variable. The shape of the function can be visualized by creating a graph of the function.

So , The rate of increase of the depth of the water (W(t)) is constant.

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Answer:

Grouping of like terms.

Step-by-step explanation:

(x² - 2x - 4) - (x² + 3x + 5)

= x² - 2x - 4 - x² + 3x + 5

Grouping of like terms

= x² - x² - 2x + 3x- 4 + 5

= x + 1.

As per the question, 33 boys tried the track and 87 boys didn't, whereas 12 girls tried the track and 68 girls didn't.

Total number of boys = 120

Total number of girls = 80

Students who tried out for track = 45

Students that were girls = 45

If 12 were girls, therefore,

Total number of boys -

= 45 - 12

= 33

This means that 33 boys tried the track

Now, since 12 girls tried the track

Boys who did not try the track -

= 120 - 33

= 87

Girls who did not try the track -

= 80 - 12

= 68

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The given hypotheses of the thing will be 9.7cm.

What is Pythagoras theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

b²=h²-p²

given b=5.2cm

p=8.2cm

h²=l²+b²

h²=8.2²+5.2² = 94.28

h = 9.7 cm

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Using trigonometric ratio and the angle of depression, the altitude of the plane is 98m

The angle of depression is an angle formed by a horizontal line and a line of sight from a point above that line to an object below that line. It is used in trigonometry to calculate the distance between the observer and the object of interest.

Using trigonometric ratio, we can calculate the height or altitude which the plane is flying.

Data;

Using tangent of the angle;

tan θ = opposite / adjacent

tan 27 = x / 193

x = 193 * tan27

x = 98m

The altitude is 98m

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Answer:

123.2

Step-by-step explanation:

First find area of the square ABCD, then the triangle AMN.

Find CD:

sin30 = CD/20

CD = 20(sin30) = 10

CD = AD = 10

Find MD:

cos30 = MD/20

MD = 20(cos30) = 17.32

AM = MD - AD = 17.32 - 10 = 7.32

Area of ABCD = (10)(10) = 100

Find height of triangle AMN:  AN

cos30 = AN/7.32

AN = cos30(7.32) = 6.34

Area of triangle ANM = 1/2(7.32(6.34) = 23.2

Total Area of the shape = 100 + 23.2 = 123.2

Answer:

The answer would be 70

Step-by-step explanation:All you have to do is divide 840 by 12 and you get 70 Hope this helps and have a great week:)

Answer:

70

Step-by-step explanation:

This is because 840/12=70

Hope it helps you

PLS RATE AS BRAINLIEST ANSWER

Answer: If 7 men can paint 42 square feet in a day, then we can say that each man paints 42/7 = 6 square feet per day.

If 20 men paint, then they would paint 20 * 6 = 120 square feet per day.

Step-by-step explanation:

The rate of change of the surface area of the sphere is 1903784*pi cubic inches^2 per minute.

The volume of a sphere can be found using the equation V = 4/3 * pi * r^3, where V is the volume and r is the radius of the sphere.

The surface area of a sphere can be found using the equation A = 4 * pi * r^2, where A is the surface area.

To find the rate of change of the surface area, we can use the chain rule of calculus:

dA/dt = dA/dr * dr/dt

We know that dr/dt = 2409 cubic inches per minute (from the problem statement). To find dA/dr, we can take the derivative of the surface area equation with respect to r:

dA/dr = 8 * pi * r

Now we can substitute these values into the chain rule equation:

dA/dt = 8 * pi * r * dr/dt

When the radius of the sphere is 99 inches, we can substitute this value into the equation:

dA/dt = 8 * pi * 99 * 2409 cubic inches^2 per minute

So, the rate of change of the surface area of the sphere is 1903784*pi cubic inches^2 per minute.

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Answer: 2x + 3y + 1

Step-by-step explanation:

That is your answer

Please give brainliest

Answer: -4.2

Step-by-step explanation:

=1-6+0.8

=-4.2

The probability is g / (b + g).

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

Let Gi be the event that the person in the ith position is a girl.

let the simple space S is all the ways to order (b + g) people, where b for boys and g for girls.

then, P(Gi) = [tex]\frac{|Gi|}{|s|}[/tex]

|s| = (b + g)! / b! g!

for the purpose of this problems, individuals of the same sex are indistinguishable.

since, if we put a girl in the ith position, the other (b + g - 1) positions can be filled in randomly.

|Gi| = (b + g - 1)! / (g - 1)! b!

then, P(Gi) = [tex]\frac{|Gi|}{|s|}[/tex]

P(Gi) = [ (b + g - 1)! / (g-1)! b! ] / [ (b + g)! / b! g! ]

P(Gi) = g / (b + g)

Therefore, the probability is g / (b + g).

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The answer reads "40," is the correct response to the earlier question.

What is median ?

The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.

There are data of 9 students and we need to arrange them in ascending order to find our answer.

So, the arrangement looks like the following:

⇒ 25, 35, 45, 50, 60, 80, 90, 95, 100

We are aware that

In all cases, the middle value is the median.

Therefore, it is safe to say that the Median of the aforementioned arrangement is 60.

Hence, Median of the numbers on the left of the median is 60=35+45/2 = 40

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The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.

The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.

So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

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Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.

Here,

Given :

A discrete random variable's anticipated value

So, in order to determine the expected value of a discrete random variable,

we may infer from the provided data that it is calculated as a weighting factor of the potential outcomes of that variable,

where weights are the probability of that outcome.

Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.

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If the factor (x - a)^n shows up in the complete factorization of a polynomial, then the multiplicity of a is: A. n.

In Mathematics, a polynomial function can be defined as a type of mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

This ultimately implies that, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

In this context, we can logically deduce that the graph of a polynomial function would touch the x-axis (x-coordinate) and turns around at r when the value of r is a zero of even multiplicity.

In conclusion, the multiplicity of a must be n since the factored form in the complete factorization of this polynomial function is (x - a)^n.

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Answer:

34

Step-by-step explanation:

They gave us -3+5i.

The conjugate of -3+5i is

-3 - 5i

You use the same numbers -3 and 5i, but with a minus sign instead of a plus.

Then multiply them together.

(-3 + 5i)(-3 - 5i)

-3•-3 + 15i - 15i - 25i^2

= 9 - 25i^2

Remember i^2 is -1.

= 9 - 25(-1)

= 9 + 25

= 34

Shortcut version:

When you multiply a complex number and its conjugate, square both numbers and add them together.

3^2 + 5^2

= 9 + 25

= 34

The amount of money that John Xina wants would be = $47,899.8

Percentage is defined as the part of the value that can be expressed as per 100 of the whole given value. This can be represented with a symbol such as %.

The amount of money Uzi has = $69,420

The percentage of money John wants from uzi = 69%

The amount of money that is 69% of Uzi's money;

= 69/100×69,420

= 4789980/100

= $47,899.8.

Therefore, the amount of money that John wants from Uzi would be = $47,899.8.

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Answer:

Bicycle workout, Andrea, and Wendy

Step-by-step explanation:

In the bicycle workout it is a multiplicative relationship because there is a constant increase of 15 / hour

Andrea's is multiplicative because the constant increase of $20 / month

Wendy's is as well because of the constant increase of 2 miles / day

Answer:

1/2

Step-by-step explanation:

i hope it helps you all

Answer:

y = x + 9 ==> x + (-y) = -9

y = -6x - 5 ==> 6x + y = -5

y = 2/3x + 1​ ==> 2x/3 + (-y) = -1

Step-by-step explanation:

y = x + 9  ==> isolate the constant 9

**Don't subtract x on both sides as x has to be positive**

y - 9 = x ==> keep x positive by subtracting 9 on both sides

-9 = x - y  ==> subtract y on both sides to isolate the constant

x + (-y) = -9  ==> make the equation in the form of ax + by = c

y = -6x - 5  ==> isolate the constant -5

y + 6x = -5  ==> isolate -5 by adding 6x on both sides, making x positive

6x + y = -5  ==> make the equation in the form of ax + by = c

y = 2x/3 + 1​  ==> isolate the constant 9

**Don't subtract 2x/3 on both sides as x has to be positive**

y - 1 = 2x/3 ==> keep x positive by subtracting 1 on both sides

-1 = 2x/3 - y  ==> subtract y on both sides to isolate the constant

2x/3 + (-y) = -1  ==> make the equation in the form of ax + by = c

The distance from the initial point to the corner pocket is 164 cm.

The angle between the path as the ball approaches the rail and the path after it strikes the rail is 45 degrees.

We know that the ball traveled 100cm before ricocheting off the rail and another 120cm into the corner pocket.

We can use the Pythagorean Theorem to find the distance from where the cue initially struck the ball to the corner pocket.

Let x be the distance from the initial point to the corner pocket.

x^2 = 100^2 + 120^2 - 2100120*cos(45^{\circ})

x = \sqrt{28000} = \sqrt{700*40} = \sqrt{28000} = 164.856

Rounded to the nearest centimeter, the distance from the initial point to the corner pocket is 164 cm.

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The inequality which represents the number and each type of clothing you can buy is 10.25x + 17y ≤ 50

This inequality represents the maximum amount of money you can spend at the store, given the cost of shirts and pants, and the number of each type of clothing you buy.

The x represents the number of shirts, and the y represents the number of pants. The inequality states that the total cost of the shirts (10.25x) plus the total cost of the pants (17y) must be less than or equal to $50.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality.

Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

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Answer: x=5

Step-by-step explanation:

[tex]\displaystyle(\frac{125}{27} )*(\frac{125}{27} )^x=(\frac{5}{3})^{18} \\\\(\frac{5^3}{3^3})*(\frac{5^3}{3^3})^x=(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*((\frac{5}{3})^3)^x =(\frac{5}{3})^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3*x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3} )^3*(\frac{5}{3})^{3x}= (\frac{5}{3} )^{18}\\\\(\frac{5}{3})^{3x+3}= (\frac{5}{3} )^{18}\\\\Hence,\ \\\\3x+3=18\\\\3x+3-3=18-3\\\\3x=15\\\\[/tex]

Divide both parts of the equation by 3:

[tex]x=5[/tex]

The translation in y = (x + 3)² is of 3 units to the left. The correct option is the last one.

For a general function y = f(x), we define a horizontal translation of N units as:

g(x) = f(x + N)

Here the original function is y = x² and the translated one is:

y = (x + 3)²

So we just added 3 on the argument, so this is a shift of 3 units to the left, the correct option is the last one.

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ok yx goes opposite side do cross multiplication

Answer:

The answer is Inconsistent.

Step-by-step explanation:

There is no solution.

The length of the median of the trapezoid is 12.

The area of a trapezoid is given by the formula (1/2)h(b1+b2), where h is the height and b1 and b2 are the lengths of the bases. We know that the area is 60, the height is 5 and b1 = b2 + 4.

So, we can write the equation as follows:

(1/2) * 5 * (b1 + b2) = 60

To find the length of the median of a trapezoid, we need to find the length of the mid-segment. The mid-segment of a trapezoid connects the midpoints of the non-parallel sides. The length of the midsegment is the average of the lengths of the bases.

So, the length of the median is (b1 + b2) / 2.

We can substitute the value of the area to find the lengths of the bases and then use that to find the length of the median.

(1/2) * 5 * (b1 + b2) = 60

(1/2) * 5 * (b1 + b2) = 60

b1 + b2 = 24

b1 = b2 + 4

b2 = 24 - b1

b1 = (24 - b1) + 4

b1 = 24 - b1 + 4

b1 = 28 - b1

b1 = 28 - (24 - b1)

b1 = 4 + b1

b1 = b2 + 4

b1 = b1

So, the lengths of the bases are equal to 14 and 10.

Length of median = (14 + 10) / 2 = 12.

Therefore, The length of the median of the trapezoid is 12.

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12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.

Given here: Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.

Thus the ratio of the number of cups of water to scoops of powdered fruit mix is equal to 3:3/2=2:1

∴ With 6 scoops of fruit mix we will be required to mix 12 cups of water.

Again unit rate ( scoops of fruit mix / cup of water)= 1.5/3

                                                                                   =0.5 scoops/cup of water

The unit rate means the number of scoops that are required to be mixed with  a cup of water.

Hence, 12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup

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Answer:

1. 10

2. 12

Step-by-step explanation:

1. 8² + 6² = y² (Taking the unknown side as y)

64 + 36 = 100

y² = 100

y = 10

2. 5² + x² = 13² (Taking the unknown side as x)

x² = 13² - 5²

= 169 - 25

= 144

x² = 144

x = 12

In the rectangle given, the values of x and m<VUT are;

i. x = 6

ii. m<VUT = 64^o

A rectangle is a plane figure which is a family of quadrilateral since it has four straight sides. It has some properties which are:

i. the diagonals are equal and divides it into two equal parts

ii. the opposite sides are equal in length

iii. the measure its internal angles are right angle

These properties can be used to determine the values required in the given question.

i. RT = SU = 5x + 16

But,

2RV = RT

2(3x + 5) = 5x + 16

6x + 10 = 5x + 16

collect like terms

6x - 5x = -10 + 16

x = 6

ii. m<RUV + m<VUT = 90^o

But,

m<RUV = m<VRU = 26^o

So that,

m<RUV + m<VUT = 90^o

26^o + m<VUT = 90^o

m<VUT = 90^o - 26^o

            = 64^o

m<VUT = 64^o

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