A wave has frequency of 10 Hz and a speed of 30 m/s. What is the wavelength of the
wave?​

An equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is \(7x > -22.\)

To find an equivalent inequality, we can start by simplifying the given inequality and then make adjustments to preserve its truth.

Let's simplify the given inequality step by step:

\(-4(x + 7) < 3(x - 2)\)

Expanding both sides:

\(-4x - 28 < 3x - 6\)

Grouping like terms:

\(-4x - 3x < -6 + 28\)

Simplifying:

\(-7x < 22\)

To maintain the direction of the inequality, we need to multiply both sides by -1.

However, when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality is reversed.

Therefore, we need to flip the inequality sign:

\(7x > -22\)

Hence, an equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is

\(7x > -22.\)

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The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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Answer:

1. 6(m + 4) = 6m + 24

2. 2 + (m + x) = (2 + m) + x

3. x + 3 = 3 + x

4. 3(2y - 6) = 6y - 18

5. m(y + 5) = my +5m

Step-by-step explanation:

1. Distributive property "distributes"/multiplies the 6 outside the parentheses to each term inside the parentheses.

2. Associative property deals with how terms and numbers are grouped into parentheses. The terms/numbers stay in the same order.

3. The commutative property means terms can change in order, and you will still get the same result.

4, 5. See #1 above. Distribute/multiply the number/term outside the parentheses to the numbers/terms inside.

Let me know if you have questions.

Since the line segment PQ is tantgent to the circle, then the angle mTherefore we know that the angle OQR has to be 30°. This is shown in the figure:

Now, we know that the sum of all the internal angles of a triangle must be 180°, then for the triangle RQP we have:

For the triangle OQR we have

and for the triangle OQP we have

Summing up we have the system

At first glance we see that this system hava more unknown variables than equations, but we have to notice that the angles alpha and gamma are supplementary, then

The population of the island with growth rate of 4.5% per year and the current population is 1500 is 1953 after 6 years.

Let y represent the population after x years.

Given that the growth rate is 4.5% per year and the current population is 1500.

Hence a = 1500, b = 100% + 4.5% = 104.5% = 1.045

y = 1500(1.045)ˣ

After 6 years:

y = 1500(1.045)⁶ = 1953

The population of the island with growth rate of 4.5% per year and the current population is 1500 is 1953 after 6 years.

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Answer:

Seriously?

U don't know the answer

Interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.

Compound interest is the term for interest that is earned on interest.

This may be shown using simple math: if you start with $100 and it earns 5% interest every year, you will have $105 at the end of the first year.

At the end of the second year, you will have $110.25.

So, we know that:
Principal amount = $25000

Interest rate = 4.7%

Time = 2 years

Compounded annually

Then, using the compounding calculator:

(Refer to the graph attached below)

The amount after 2 years will be $27,405.23.

Interest in this is:
$27,405.23 - $25,000

$2,405.23

Therefore, interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.

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Correct question:

Find the interest earned on a $25,000 deposit for 2 years at 4.7% interest, compounded annually.

Answer:

  $42

Step-by-step explanation:

You want the price with tax of a $35 pair of shoes subject to a 20% tax.

The tax is the cost of the shoes multiplied by the tax rate. The final price is the sum of the cost of the shoes and the tax:

  final price = price + price × tax rate

  final price = price × (1 + tax rate) = $35 × 1.20 = $42

The final price of the shoes is $42.

Answer:

42$

Step-by-step explanation:

tax increase will be

20% of 35$

= 20/100 × 35

= 7$

Final price = Old price + Tax

= 35 + 7

= 42$

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

The expression for the given word phrase is

46M + M² + 2 + 1/M²

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number = M

Reciprocal of M = 1/M

Now,

46 x (M + 1/M)²

Step 1:

46M + M² + 2 + 1/M²

Thus,

The expression is 46M + M² + 2 + 1/M²

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

6

See photo for explaination.

Answer:

true

Step-by-step explanation:

Answer:

a. Using the empirical rule, approximately 68% of healthy adults have body temperatures within 1 standard deviation of the mean, or between 97.52°F and 98.70°F.

b. Using the empirical rule, approximately 99.7% of healthy adults have body temperatures between 96.34°F and 99.88°F, which is within 3 standard deviations of the mean.

The volume of the rectangular prism is given as follows:

344 cubic yards.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

Each ft is composed by 1/3 yards, hence the dimensions in yards are given as follows:

Hence the volume of the prism, in cubic yards, is given as follows:

V = 8.33 x 10.33 x 4

V = 344 cubic yards.

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The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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\( \bf \large \implies{6.5}\)

As shown in the figure, in the 40 games,

\( \bf{(3 + 6 + 4) = 13 \: ahead}\)

\( \bf{p \: = \: \frac{13}{40} }\)

\( \bf{So \: N = 20 \times p \: = 20 \times \frac{13}{40} = 6.5}\)

In the 20 games, the team will be ahead in atleast one of the halves in 10.5 games.

We can see in the given data that the number of halves which ended in atleast one ahead is  3 + 6+ 4 + 5 + 3 = 21

Hence, the probability of getting ahead is 21/40.

We have to find the number of games in which the team will get ahead in atleast one of the halves in the next 20 halves according to the given data.

Hence, the number of games in which the team will get ahead in atleast one of the halves in the next 20 halves  is 20*(21/40) = 21/2 = 10.5 games.

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Answer:

A.

Step-by-step explanation:

I just typed it in the calculator graph and scrolled down past the errors

x^2-14x=-25

To complete the square

Take the coefficent of the x term

-14

Divide by 2

-14/2 = -7

and square it

(-7)^2 = 49

Add this to both sides

x^2 -14x +49 = -25+49

(x-7)^2 = 24

Answer:

Mean = 53.

Step-by-step explanation:

The median is the middle value so the 3 cards are

36, 46, x       where x is to be found.

The range is 41, so:

x - 36 = 41

x = 41 + 36

x = 77.

Therefore, the mean is

(36+46+77) / 3

= 159/3

= 53.

Answer:

-6u + 7

Step-by-step explanation:

(-u+8)-(5u+1)

(-u+8)-5u-1

-u+8-5u-1

-u+7-5u

-6u+7

Answer:

7-6u

Step-by-step explanation:

(8-u)-(5u+1)

Remove the brackets

=8-u-5u-1

Collect the same terms

=8-1-u-5u

=7-6u

I hope this is helpful

The confidence interval from Part (b) is narrower than the confidence interval from Part (a) because the proportion of Americans age 8 to 18 who own an MP3 music player is higher than the proportion of Americans age 8 to 18 who own a cell phone.

a. 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone:

(1321/2002) ± (1.645*sqrt( (1321/2002)*(1-(1321/2002)) / 2002)) = (0.6608 ± 0.0402)

Interpretation: We are 90% confident that the true proportion of all Americans age 8 to 18 who own a cell phone is between 0.6206 and 0.7010.

b. 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own an MP3 music player:

(1522/2002) ± (1.645*sqrt( (1522/2002)*(1-(1522/2002)) / 2002)) = (0.7610 ± 0.0346)

Interpretation: We are 90% confident that the true proportion of all Americans age 8 to 18 who own an MP3 music player is between 0.7264 and 0.7956.

c. The confidence interval from Part (b) is narrower than the confidence interval from Part (a) because the proportion of Americans age 8 to 18 who own an MP3 music player is higher than the proportion of Americans age 8 to 18 who own a cell phone. This means that the sample size is more likely to result in a more accurate estimation of the true population proportion for the MP3 music player than for the cell phone.

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Answer: 0.87 percent are brick houses

Step-by-step explanation:

Answer:

y+5 = 3/4(x+8)

Step-by-step explanation:

The point slope form of the equation of a line is

y - y1 = m(x-x1) where m is the slope and ( x1,y1) is a point on the line

The slope is 3/4 and the point is (-8,-5)

y - -5= 3/4( x - -8)

y+5 = 3/4(x+8)

Answer:

5 = $ 5.25.    10= $ 6.50.   20= $9.00

Step-by-step explanation:

if this is wrong you can completely write me a really rude email or message or something