Five swimmers race in the ocean. Amy is ahead of Max, but behind Louie. Dan is between Cindy and Max. Louie is ahead of Max. Cindy is behind Dan. Who is in the lead?

Answer:

  see below

Step-by-step explanation:

It works well to think about what these compound inequalities mean. One way to do that is to graph them, or to imagine what the graph of them looks like.

Since the result is a single inequality (x < 2), the compound will be "and" with x < 2 being more restrictive, or will be "or" with x < 2 being the least restrictive of completely overlapping inequalities.

Of the choices offered, C is the one of interest.

_____

Comment on other choices

A has all real numbers as solutions except in the range 2 ≤ x ≤ 3.

B has no solutions

C simplifies to x < 2 . . . . the one we want

D simplifies to x < 4

Answer:

13

Step-by-step explanation:

To solve this, lets first find the number of footballs he still needs:

75-24 = 51

Now to find the number of packages, divide by 4, since there are 4 balls per package:

51/4 = 12 Remainder 3

Since there is a remainder, and the Coach MUST have at least 75, then we need to add a package to include the remainder:

12 + 1 = 13 Packages

Answer:

you need to give the question

Step-by-step explanation:

there is no question

The height, ab, is 6 cm

The volume of the pyramid is 100 cm3.

we know that

ABC is a right triangle and we know that

∠ACB=45°

AC=hypotenuse------ 6√2 cm

sin 45=AB/AC----- AB=AC*sin 45----> AB=6√2*√2/2----> AB=6 cm

AB=6 cm

we already know that the formula for getting the volume of a pyramid

volume of the pyramid=(1/3)*Area of the base*height

We will now Substitute all the values in the formula;

area of the base=50 cm²

height=6 cm

so

volume of the pyramid=(1/3)*50*6---->

1/3*300

300/3

1=00 cm³

volume=100 cm³

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Answer:

6, 100

Step-by-step explanation:

right on edge

Both the square root of 15 and the number π are irrational numbers.

The numbers for this problem are given as follows:

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The equation of a line passing through the point (5,-3) and parallel to 6x+3y=-12 is y =-2x+7.

Parallel lines are those that never intersect. As a result, two parallel lines must have the same slope but different intercepts (if they had the same intercepts, they would be identical lines).

The equation of the line is 6x+3y=-12.

6x+3y=-12​

3y =-12-6x

y = -2x-4    

The slope of this line is -2.

Because parallel lines have the same slope, the new line will also have a slope of -2.

You now have a point (5,-3) and a slope; thus, use the Point-Slope form to solve the equation of a line.

y-y₁= m(x-x₁)

y+3 = -2(x -5)

y+3 = -2x+10

y =-2x+7

The equation of a line passing through the point (5,-3) and parallel to 6x+3y=-12 is y =-2x+7.

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\(a-(-3.75)=6.11\\a+3.75=6.11\\a=6.11-3.75\\a=2.36\)

ANSWER: a = 2.36

ok done. Thank to me:>

Answer:

2.36

Step-by-step explanation:

It is subtraction between integers. For subtraction within positive and negative integers, you have to add the opposite.

To add the opposite, the first digit, a, (which happens to be a variable), remains the same. The second digit, - will be changed to +. The last digit, a number, which is -3.75, will be rewritten as 3.75, its integral opposite.

This is fairly similar to the keep-change-flip method used in fractions.

Now, let's put the problem together.

Our equation is now displayed as:

a - 3.75 = 6.11

The question is pretty straightforward from now on- To find out the variable a, we need to subtract 3.75 from 6.11, thus resulting in the answer of 2.36.

Hope this helped!

Answer:

I have attached a picture of the completed graph.

The equation is k = r + 7

Kyle will be 59 when Ryan is 52.

Explanation:

Kyle's age is always seven years higher than Ryan's age.

Therefore, k (Kyle's age) = r (Ryan's age) + 7 (Number of years different)

The power rule for logarithms states that logb(M^p) = p * logb(M). The logarithm of a number with an exponent is the product of the exponent and the logarithm of that number.

The power rule states that logb(M^p) = p * logb(M), where M, b, and p are positive real numbers.

To understand this rule, let's consider an example. Suppose we have log2(8^2). According to the power rule, this is equivalent to 2 * log2(8).

In this case, M is 8, b is 2, and p is 2. The power rule tells us that we can bring the exponent (p) down and multiply it with the logarithm of the base (b) raised to the number (M).

So, log2(8^2) can be simplified as 2 * log2(8), which is 2 * 3 = 6.

In general, the power rule allows us to simplify logarithmic expressions by bringing the exponent down and multiplying it with the logarithm of the base.

This rule is particularly useful when dealing with complex logarithmic expressions and simplifying them to a more manageable form.

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Answer:

-7°F

Step-by-step explanation:

At first, you might think that the answer is -9 because 9 > 7, right? Actually, the "rules" for numbers are switched when you are dealing with negative numbers. Therefore, -7 > -9 so -7°F is the correct answer.

Answer:  x < 4 and x > -4

===================================================

Work Shown:

-2 | x | > -8

| x | < -8/(-2)

| x | < 4

-4 < x < 4

-4 < x and x < 4

x < 4 and x < -4

x < 4 and x > -4

Side note: the inequality sign flips in the 2nd step because we divided both sides by a negative number. Also, I used the rule that \(| x | < k\) leads to\(-k < x < k\) only when k is positive.

The total number of possible 7-place license plates are 67600000.

Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible

Let's solve the given problem:

The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.

Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled

= 676 × 100000

= 67600000 ways

Hence the total number of possible 7-place license plates are 67600000.

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Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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The pounds of the Earl Grey tea and Orange Pekoe tea are required from selling the new blend versus selling the other types is 225 pounds and 75 pounds.

Let x = amount of Earl Grey tea to mix

so, 300-x = amount of Orange Pekoe tea to mix

After putting the equations together,

6x+4(300-x)=5.5*300

6x+1200-4x=1650

2x=450

x=225

So amount of Earl Grey tea to mix is 225 pounds

amount of Orange Pekoe tea to mix = 300-x

300-225 = 75

So the amount of Orange Pekoe tea to mix is 75 pounds.

Amount of Earl Grey tea to mix=225 pounds

Amount of Orange Pekoe tea to mix=75 pounds

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Answer:

distance TS ≈ 19 m (nearest meter)

Step-by-step explanation:

The point T is on the horizontal ground and the angle of elevation of the top R of a tower is 63° and the height of the tower is 38 m high. The illustration forms  a right angle triangle. The height RS of the tower is the opposite side of the triangle formed. The hypotenuse side of the triangle is the point from the ground T to the top of the tower R.  The adjacent side of the triangle is the side TS.

using tangential ratio

tan 63° = opposite/adjacent

tan 63° = 38/adjacent

cross multiply

adjacent tan 63° = 38

divide both sides by tan 63°

adjacent side = 38/tan 63°

adjacent side = 38/1.96261050551

adjacent side = 19.3619670807

distance TS ≈ 19 m (nearest meter)

Answer:

Area = 34 cm squared

Step-by-step explanation:

First,

Top = 5

Bottom = 5

Left side = 2

Right side = 2

Front = 10

Bottom = 10

Total = 34

Hope this helps!

Answer: D

Step-by-step explanation:

To determine the maximum number of stories that can be constructed before friction losses prevent proper valve operation, we need to calculate the pressure loss due to friction as the water flows through the piping to each floor.

Using the Hazen-Williams formula, which is commonly used for sizing water supply systems:

P = (4.52Q1.85L10.67/C1.85)d4.87

where:

P = pressure loss due to friction (psi)

Q = flow rate (gpm)

L = length of pipe (feet)

C = Hazen-Williams coefficient (dimensionless)

d = inside diameter of pipe (inches)

Assuming the flow rate is 10 gpm, the length of pipe from floor to floor is the height of the building divided by the number of stories, and the inside diameter of the pipe is 4 inches (since 4 type-L copper corresponds to a 4-inch nominal diameter), the pressure loss for each story can be calculated using a Hazen-Williams coefficient of 130 for copper piping:

P = (4.52 x 10^1.85 x (1 story height/number of stories)10.67/1301.85)4.87

P = 3.3 x (1/number of stories)^1.85

For example, for a 2-story building, the pressure loss would be:

P = 3.3 x (1/2)^1.85

P = 1.6 psi

To ensure that the minimum working pressure of 25 psi is maintained at each flush valve, the pressure loss for each story cannot exceed 25 - 50 = -25 psi (since lower pressures can cause valve malfunctions).

Solving for the maximum number of stories:

3.3 x (1/number of stories)^1.85 <= -25

(1/number of stories)^1.85 <= -25/3.3

1/number of stories <= (-25/3.3)^0.54

number of stories >= 1/(-25/3.3)^0.54

number of stories >= 6.7

Therefore, the maximum number of stories that can be constructed before friction losses prevent proper valve operation is D. This floor only.

Part A - The cycle has a total distance travelled of 130 meters.

Part B - The cycle has an acceleration of 0 meters per square second at t = 8 seconds.

In this question we find the case of a graph between time (t), in seconds, and velocity (v), in meters per second, from which we need to determine the total distance travelled (s), in meters, on the cycle and the acceleration (a), in meters per square second, at a given time.

Part A - The total distance travelled is the area below the curve, defined as the sum of the areas of two triangles and rectangle, thus:

s = 0.5 · (6 s) · (10 m / s) + (6 s) · (10 m / s) + 0.5 · (8 s) · (10 m / s)

s = 30 m + 60 m + 40 m

s = 130 m

The total distance traveled by the cycle is 130 meters.

Part B - The acceleration at a given time t is the slope of the curve at point (t, v). In this case, we find that slope can be found by secant line formula:

a = [v(12) - v(6)] / (12 - 6)

a = (0 - 0) / (12 - 6)

a = 0 m / s²

The acceleration of the cycle at t = 8 seconds is equal to 0 meters per square second.

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We would need a sample size of at least 1073 children under age 6 in Washington to estimate the true proportion of children living in poverty with 95% confidence and a margin of error of 2%.

To estimate the true proportion of children under age 6 living in poverty in Washington with 95% confidence and a margin of error of 2%, we can use the formula:

n = (Z² * p * q) / E²

where:

Z = the Z-score corresponding to the desired confidence level (1.96 for 95% confidence)

p = the estimated proportion (0.17 based on the federal report)

q = 1 - p

E = the desired margin of error (0.02)

Plugging in these values, we get:

n = (1.96² * 0.17 * 0.83) / 0.02²

n = 1072.45

Rounding up to the next whole number, we would need a sample size of at least 1073 children under age 6 in Washington to estimate the true proportion of children living in poverty with 95% confidence and a margin of error of 2%.

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Using the difference, the difference between the number of heads and half the number of tosses is 1.

In the given question,

The proportion of heads is 0.49 in 100 tosses.

We have to find the difference between the number of heads and half the number of tosses.

The proportion of heads=0.49

Total tosses =100

So the total number of heads

=0.49*100

=49

Since we have to find the difference between the total number of head and half the number of tosses.

So the half on the number of tosses=Total number of tosses/2

The half on the number of tosses=100/2

The half on the number of tosses=50

So, The difference=The half on the number of tosses−Total number of heads

The difference=50−49

The difference=1

Hence, the difference between the number of heads and half the number of tosses is 1.

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Answer:

should be 10, then 15, then 20. please tell me if I'm wrong

Step-by-step explanation:

well 7 × 5 is 35 so I decided 2 × 5 is 10 and 3 × 5 is 15 and then 4 × 5 is 20 tell me if I'm wrong ty.

Answer:

10,15,20

Step-by-step explanation:

The speed of a particle is the magnitude of its velocity. The velocity of a particle is the derivative of its position. In this case, the position of the particle is given by r(t) = (3 cos t, 3 sin 1, 12). The derivative of r(t) is v(t) = (-3 sin t, 3 cos t, 2). The magnitude of v(t) is 2, so the speed of the particle is 2.

The speed of a particle is given by the following formula:

speed = |velocity|

The velocity of a particle is given by the following formula:

velocity = d/dt(position)

In this case, the position of the particle is given by r(t) = (3 cos t, 3 sin 1, 12). The derivative of r(t) is v(t) = (-3 sin t, 3 cos t, 2). The magnitude of v(t) is 2, so the speed of the particle is 2.

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Answer:

9 and 40

21 and 40

Step-by-step explanation:

I just did the test on edg. 2020

Factors of 9:

1,3,9

Factors of 15:

1,3,5,15

Factors of 21:

1,3,7,21

Factors of 40:

1,2,4,5,8,10,20,40

We have to find the pairs of numbers which are relatively prime.

Relatively prime number: The numbers in which gcd 1 are called relative prime numbers.

a.9 and 15

GCD(9,15)=3

9 and 15 are not relatively prime.

b.9 and 40

GCD(9,40)=1

Hence, 9 and 40 are relatively prime.

c.9 and 21

GCD(9,21)=3

9 and 21 are not relatively prime.

d.15 and 21

GCD(15,21)=3

15 and 21  are not relatively prime.

e.21 and 40

GCD(21,40)=1

21 and 40 are relatively prime.

While solving the proof, Sammy made a mistake as option b), he assumed secθ = 1/sinθ but secθ = 1/cosθ

Here we see that in the first line, Sammy writes

cos²θ . tan²θ = cos²θ(sec²θ -1)

This is definitely correct as 1 + tan²θ = sec²θ

Now, in the next line, he expanded the expression by solving the brackets to get

cos²θ . tan²θ = cos²θ . sec²θ - cos²θ

Now, he changes the sec²θ expression. We know that,

secθ = 1/cosθ

Hence, sec²θ = 1/cos²θ

But, Sammy wrote, 1/sin²θ, hence he was wrong here.

Therefore, the correct proof will be

cos²θ . tan²θ = cos²θ/cos²θ - cos²θ

or, cos²θ . tan²θ = 1 - cos²θ

= sin²θ

Hence Sammy assumed secθ = 1/sinθ but secθ = 1/cosθ and made a mistake

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Answer:

Answer is in the attachment

Answer:4.5 hours, 4 hours and 30 minutes, 4 and a half hours

Step-by-step explanation: you are averaging, so you add all of the numbers together and divide that by the number of numbers.

3+6=9, 9 divided by 2=4.5

Answer:

2hours

Step-by-step explanation:

let windows = x

Mrs. Saunders can clean one-third of the windows in an hour = x/3

daughter can clean one-sixth of the windows in an hour = x/6

so,

x/3+x/6 = 1

thus, x = 2

mother and daughter together can clean the windows in 2 hours

Answer:

50*（1-30%） =35

Step-by-step explanation:

Answer:

50*（1-30%） =35

Step-by-step explanation:

Answer:

multiply each coordinate by 2

Step-by-step explanation:

your welcome