working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. if it takes 40 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?​

Answer:

70

Step-by-step explanation:

110+70 is 180. angle is suppelmarly(cant spell) so it equals 180.

olution

2a.

The graph of as described is given below (showing at least five points)

The (clear) graph that has the dashed line of asymptotes

The table will be

Bb.

o write the equation

We start from

Translate the graph up by 3 units

Translate the graph 4 units to the left

2c.

o get the equation of asymptotes

Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:

p(x) = (x + 1) q(x)

for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:

p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0

So,

0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c

= -5 + 7 - 2 + 3 + c

= c = 3

So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.

Answer:

x > -5, so the correct answer is C.

The situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively

The given parameters are

Initial Fee = $2.80

Rate = $3.50 per mile

Let the number of miles be x and the total fee be y

So, we have

Total fee = Initial Fee + Rate * Number of miles

This gives

y = 2.8 + 3.5x

This means that the situation is a function, & the independent and dependent variables are the number of miles and total fee, respectively

Here, we have

Maximum number of miles = 20

This means that the domain is 0 <= x <= 20

Substitute 20 for x in y = 2.8 + 3.5x

y = 2.8 + 3.5 x 20

Evaluate

y = 72.8

This means that the range is 0 <= x <= 72.8

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This triangle(Fig. 9.120) is a right angled triangle.

So, the three angles in this triangle are :

▪︎angle 90°, angle 63° and angle y.

Sum of all angles in a triangle = 180°

Which means :

\( = \tt90 + 63 + y = 180\)

\( = \tt153+ y= 180\)

\( = \tt \: y = 180 - 153\)

\( \hookrightarrow \color{plum}\tt angle \: y = 27°\)

Since the sum of all angles equals 180°[90+63+27=180] we can conclude that we have found out the correct measure of angle y.

▪︎Therefore, the measure of angle y = 27°

The triangle in Fig. 9. 121 is a right angled triangle.

So, the angles in this triangle are :

▪︎angle 90°, angle 28.3° and angle z.

Sum of all angles in a triangle = 180°

Which means :

\( = \tt 90 + 28.3 + z = 180\)

\( = \tt118.3 + z = 180\)

\( = \tt z = 180 - 118.3\)

\( \hookrightarrow \color{plum} \tt \: angle \: z = 61.7°\)

Since the sum of all angles equals 180°[90+28.3+61.7=180°] we can conclude that we have found out the correct measure of angle z.

▪︎Therefore, the measure of angle z = 61.7°

The triangle in Fig. 9. 122 is a right angled triangle.

So, the angles in this triangle are :

▪︎angle 90°, angle 45.8° and angle x.

Sum of all angles in triangle = 180°

Which means :

\( = \tt90 + 45.8 + x = 180\)

\( = \tt135.8 + x = 180\)

\( = \tt x = 180 - 135.8\)

\( \hookrightarrow \: \color{plum}\tt \: angle \: x = 44.2°\)

Since the sum of all angles equals 180°[90+45.8+44.2=180°] we can conclude that we have found out the correct measure of angle x.

▪︎Therefore, the measure of angle x = 44.2°

The triangle in Fig. 9.123 is a right angled triangle.

So, the angles in this triangle are :

▪︎angle 90°, angle 35.7° and angle y.

Sum of all angles in a triangle = 180°

Which means :

\( = \tt90 + 35.7 + y = 180\)

\( = \tt 125.7 + y = 180\)

\( = \tt y = 180 - 125.7\)

\( \hookrightarrow \color{plum}\tt angle \: y = 54.3°\)

Since the sum of all angles equals 180°[90+35.7+54.3=180°] we can conclude that we have found out the correct measure of angle y.

▪︎Therefore, the measure of angle y = 54.3°

No, angle x is not twice of angle y. As we know the value of angle x in fig. 9.122 is equal to 44.2°. And the value of angle y in fig. 9.123 is equal to 54.3°. Since the measure of angle x is lesser than angle y it cannot be twice as much as angle y.

Therefore, angle x is not twice as much as angle y since angle x < angle y.

Answer: In particular, let’s focus our attention on the behavior of each graph at and around . 2 and x= -1 for x < 2. There are open circles at both endpoints (2, 1) and (-2, 1). The third is h (x) = 1 / (x-2)^2, in which the function curves asymptotically towards y=0 and x=2 in quadrants one and two."

Step-by-step explanation: I think this is the problem ur on

The given relation → If a = b and b = c, then a = c is called transitive law and it holds true for all real numbers.

An equation is a statement that the depicts the values of two mathematical expressions as equal using an (=) sign. Example -

2x = 5

An expression is written using individual terms (either constant or variable) separated by mathematical operations. Example -

3x + 5y + 3

We have -

If a = b and b = c, then a = c.

The given relation holds true for all real numbers. This law is called transitive law. So, if A=5 for example, then B and C must both also be 5 by the transitive property

Therefore, the given relation → If a = b and b = c, then a = c is called transitive law and it holds true for all real numbers.

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Answer:

Can you please post the picture of the question, then I can help.

Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Answer:

43.6 has 3 significant figures.

Answer:

A. Using the lens equation, 1/p + 1/q = 1/f, and substituting f = 5 cm and q = 7 cm, we can solve for p:

1/p + 1/7 = 1/5

Multiplying both sides by 35p, we get:

35 + 5p = 7p

Simplifying and rearranging, we get:

2p = 35

Therefore, the distance from the lens to the object, p, is:

p = 35/2 cm

B. Solving the lens equation, 1/p + 1/q = 1/f, for q, we get:

1/q = 1/f - 1/p

Substituting f = 5 cm, we get:

1/q = 1/5 - 1/p

Multiplying both sides by 5qp, we get:

5p = qp - 5q

Simplifying and rearranging, we get:

q = 5p / (p - 5)

Therefore, the expression that gives q as a function of p is:

q = 5p / (p - 5)

C. Here is a sketch of the graph of q(p):

The graph is a hyperbola with vertical asymptote at p = 5 and horizontal asymptote at q = 5. The image distance q is positive for object distances p greater than 5, which corresponds to a real image. The image distance q is negative for object distances p less than 5, which corresponds to a virtual image.

D. Taking the limit of q as p approaches infinity, we get:

lim q(p) = 5

This represents the horizontal asymptote of the graph. As the object distance becomes very large, the image distance approaches the focal length of the lens, which is 5 cm.

Taking the limit of q as p approaches 5 from the positive side, we get:

lim q(p) = -infinity

This represents the vertical asymptote of the graph. As the object distance approaches the focal length of the lens, the image distance becomes infinitely large, indicating that the lens is no longer able to form a real image.

In order for the lens to form a real image, the object distance p must be greater than the focal length f. When the object distance is less than the focal length, the lens forms a virtual image.

The scale factor is: 1.8

because of :

\(\frac{36}{20}=1.8\\ \\\\\frac{25.2}{14}=1.8\)

Answer:

If a class has 2/3 girls.

Lets ask ourselves, what does this mean?

It means that 2/3 of the class are girls and therefore 1/3 of the class are boys. I.e. for every 2 girls in the class there is 1 boy in the class.

Therefore the ratio of girls to boys is

2 : 1

Answer:

A.

Step-by-step explanation:

The mean is less than the median so it is skewed to the left or negatively skewed.

The students in 8th class who choose music are 16 in number,

The students in 7th class who choose music are 32 in number

The total who choose world language is 270

The totals who are in 7th grade be 194

The number of students who choose world language in 7th class are 162

Let x be the students in 8th class who choose music

x+108=124

x=124-108

x=16 students

Now  y be the students in 7th class who choose music

16+y=48

y=48-16

y=32

Let z be the total who choose world language

48+z=318

z=318-48

z=270

Now the totals who are in 7th grade be A

124+A=318

A=318-124

A=194

B be the number of students who choose world language in 7th class

Now 32+B=194

B=194-32

B=162

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Answer:

Step-by-step explanation:

The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.

Answer y == 3

+7

Step-by-step explanation:

The graph of a linear relationship contains the points (1, 10) and (3, 16).

Write the equation of the line in slope-intercept fo

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

b is the y-intercept - the y value when x = 0.

for the slope we see

x changes by +2 (from 1 to 3)

y changes by +6 (from 10 to 16)

so, the slope a is +6/+2 = 3

and the semi-ready equation is

y = 3x + b.

now we use one of the points in the equation to solve for b. I picked (1, 10) :

10 = 3×1 + b = 3 + b

b = 7

so, the full equation is

y = 3x + 7

The distance between the points (−3, −5) and (−3, −7) is 2 units.

The distance formula gives the shortest distance between two points in a two-dimensional plane.

The distance formula is a useful tool for calculating the distance between two points.

Therefore,

d = √(x₂ - x₁)²+(y₂ - y₁)²

Let's find the distance between the points (−3, −5) and (−3, −7).

Hence,

x₁ = -3

x₂ = -3

y₁ = -5

y₂ = -7

d = √(-3 + 3)² + (-7 + 5)²

d = √(-2)²

d = √4

d = 2

Therefore, the distance between the point is 2 units.

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Linear equations are two-variable equations that graph as a straight line.

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Two-variable equations that graph as a straight line are said to be linear equations. The slope and y-intercept of a linear equation allow it to be graphed. Y = mx + b, where m is the slope and b is the y-intercept, is the formula used to represent a line. A graph's straight line can be represented by a linear equation.

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The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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Answer:

1/12

Step-by-step explanation:

first we have to find all the possibilities of getting a sum of 3 or less: 1+1 or 1+2 and we count the second combination 2 times because the numbers can be on either of the dices so we have a total of 3 possibilities. all the possible pairimg of dice are 6*6=36 because each dice has 6 sides and we can get either of them. so the probability would be the chance of getting a sum of 3 or less divided by all the diff combination which equals 3/36 or 1/12 which is roughly around 8.3%

The acceleration of the rocket is 11.1 m/s^2.

We know that the acceleration can be obtained from the net force that is  acting on the rocket. Given that force is a vector quantity the direction of the forces that are acting is very important in the problem.

We know that;

Net force = Thrust force - Frictional force

If the net force is given by ma then;

2100a = 2.4×10^4 - 650

a = 2.4×10^4 - 650 /2100

a = 11.1 m/s^2

Thus, we can see that the magnitude of the acceleration is 11.1 m/s^2.

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Answer:

$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

Simple Interest Formula

I = Prt

where:

Given:

Create two equations from the given information:

\(\textsf{Equation 1}: \quad \sf P_1+P_2=7000\)

\(\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500\)

Rewrite Equation 1 to make P₁ the subject:

\(\implies \sf P_1=7000-P_2\)

Substitute this into Equation 2 and solve for P₂:

\(\implies \sf 0.05(7000-P_2)+0.08P_2=500\)

\(\implies \sf 350-0.05P_2+0.08P_2=500\)

\(\implies \sf 0.03P_2=150\)

\(\implies \sf P_2=\dfrac{150}{0.03}\)

\(\implies \sf P_2=5000\)

Substitute the found value of P₂ into Equation 1 and solve for P₁:

\(\implies \sf P_1+5000=7000\)

\(\implies \sf P_1=7000-5000\)

\(\implies \sf P_1 = 2000\)

$2000 was invested at 5% and $5000 was invested at 8%.

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The probability that all three number cubes will land on an odd number is 1/8

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

Number of cubes = 3

Sections on each cube = 6

Odd sections on each cube = 3

This means that

P(Odd) = Odd sections/Total sections

So, we have the following representation

P(Odd) = 3/6

Simplify

P(Odd) = 1/2

For the three cubes, we have

P(All odd) = P(Odd)^Number of cubes

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

P(All odd) = (1/2)³

Evaluate

P(All odd) = 1/8

Hence, the probability is 1/8

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Answer: 1/8

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                        .

      /.         ;      

      .

Step-by-step explanation:

Hi have a great day!! This is our answer. If it is wrong, apologies from our side.

Answer:

\(7\sqrt{2}\)

Step-by-step explanation:

We know that the missing angle is 45 degrees and the hypotenuse is 14.

If both side angles equal to 45, according to base angle theorem, this triangle is isosceles.

Since this triangle is isosceles, the two legs must be equal. Let x be the legs.

According to the 45 45 90 triangle theorem, the hypotenuse is equal to \(\sqrt2\)*x

If 14 = \(\sqrt{2}*x\)

\(\frac{14}{\sqrt{2} }\) = x

Rationalize denominator

\(x = \frac{14}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{14\sqrt{2} }{2} = 7\sqrt{2}\)

The answer is \(7\sqrt{2}\)

Hope this helps :)

Wdym by definition Answer:

Step-by-step explanation:

Step-by-step explanation:

This is of the form

(x-h)^2 + ( y-k)^2 = r^2        so r^2 = 16  means r = 4   units

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

well area is the space inside of a shape. so you would multiply 2 by 4 because there are 4 sides.

Step-by-step explanation:

Answer:  area is 10

Step-by-step explanation:

add top and bottom base

8+2=10

then divide by 2

10/2 = 5

then times 5 by 2

5*2=10

8+2/2 * 2 = 10

10 = area