Jack swam 8 taps. He swam 6 fewer laps than Lea.
How many laps did Lea swim?
pls quick

The value of A that makes the equation true for all values of x is A = \(2x^2\). Answer (E).

To begin, consider the following equation:

\(2^(x/12) = A/12x^2\)

We must determine the value of A that makes this equation true for all x values.

To begin, we can take the natural logarithm of both sides of the equation:

\(2(x/12) = 2(A/12x2)\)

We can simplify the left side of the equation by using the logarithm property that states log(ab) = b*log(a):

(x/12)

\(ln(2) = 2ln(x) - ln(A) (12)\)

Then, on one side of the equation, we can isolate ln(A):

ln(A) = (x/12)

\(2ln(x) + ln(2) + ln (12)\)

With base e, we can now exponentiate both sides of the equation:

A is equal to \(e((x/12)ln(2) + 2ln(x) + ln(12)).\)

To simplify even further, we can use exponent properties to combine the terms with ln:

\(A = 2^(x/12) * (x^2) * 12\)

Simplifying:

\(A = 2x^2\)

Therefore, the value of A that makes the equation true for all values of x is \(A = 2x^2\). Answer (E).

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Answer: 360

Step-by-step explanation:

done

Answer:

Answer:

B

Step-by-step explanation:

10*10*10 =1000

5*5 =25

2*2 =4

1000+25+4 =1029

the sample proportion under probability has a mean sampling distribution of 82.

The population percentage is the major variable in the sampling distribution of this proportion, which has a quarter-um normal distribution. Variants include population proportion times one and population proportion divided by sample size. Additionally, we are aware that the population proportion is under the null hypothesis. 200 is the sample soil. When we enter the value of P into this calculation without normalisation, we can obtain the standing ovation as the variance's root. 025 in excess. The probability that we got a sample result of 188/58 or less is then calculated. We simply need to determine this left tail probability after that.

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On solving the provided question, we can say that - => K not equal to 0 at x= 0 and so, center of curvature exists.

In geometry, a curve's center of curvature is located at a point that is offset from the curve by an amount equal to the radius of curvature that lies on the normal vector. zero-curvature point at infinity. The center of the curve serves as the osculating circle. The sphere holding the spherical mirror's center serves as its center of curvature. A "C" is used to symbolize this. the center of a circle with a radius equal to the radius of curvature of a particular point on the curve, whose center is on the concave side of the curve and which is normal to that point.

The curvature K at the point (x,y) is given by if C is a graph of the twice differentiable function y = f(x)y=f(x).

\(K = \frac{|y^{''}|}{[1 + (y')^2 ]^{3/2}}\)

Curvature of the given curve at x=0x=0 is

=> K not equal to 0 at x= 0

so,

center of curvature exists.

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The equation for g(x) that matches the graph is g(x) =| -x - 3| +3

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

If we know that the function crosses x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

We are given that function, g(x), is shown below. It is a shifted graph of y = |x|.

The vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged.

The equation for g(x)  is g(x) =| -x - 3| +3

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After considering the given data we conclude that the probability that both bulbs selected are rated 75 W, given that at least one of them is rated 75 W, is 1/7 or approximately 0.143.

To evaluate the probability that both bulbs selected from a box containing four 40 W bulbs, five 60 W bulbs, and six 75 W bulbs are rated 75 W, given that at least one of them is rated 75 W, we can apply conditional probability.
Let A be the event that the first bulb selected is rated 75 W, and B be the event that the second bulb selected is rated 75 W. We want to find P(B|A'), where A' is the complement of A, i.e., the event that the first bulb selected is not rated 75 W.
We can apply the formula for conditional probability:
\(P(B|A') = P(A' \cap B) / P(A')\)
We can evaluate the probabilities as follows:
\(P(A') = (4+5) / (4+5+6) = 9/15\)
(since there are 4+5 bulbs that are not rated 75 W out of a total of 4+5+6 bulbs)
\(P(A \cap B) = (6/15) * (5/14) = 3/35\)
(since there are 6 bulbs that are rated 75 W out of a total of 15 bulbs on the first draw, and 5 bulbs that are rated 75 W out of a total of 14 bulbs on the second draw, assuming that the first bulb selected is not rated 75 W)
\(P(B|A') = P(A' \cap B) / P(A') = (3/35) / (9/15) = 1/7\)
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The union (F U H) and intersection (F n H) of sets F and H, represented in interval notation, are as follows: F U H = (-∞, 5) and F n H = [3, 5).

In interval notation, (a, b) represents an open interval, meaning it includes all values between a and b, but excludes both endpoints. [a, b] represents a closed interval, including both endpoints. The set F is defined as {z: z ≥ 3}, which can be represented as [3, ∞) since it includes all values greater than or equal to 3. The set H is defined as {z: z < 5}, which can be represented as (-∞, 5) since it includes all values less than 5.

To find the union (F U H), we combine the intervals of F and H. Since the set F includes all values greater than or equal to 3 and the set H includes all values less than 5, the resulting union includes all values less than 5 as well as all values greater than or equal to 3. Therefore, the union (F U H) can be represented as (-∞, 5).

To find the intersection (F n H), we find the common values between F and H. In this case, the intersection includes all values that are both greater than or equal to 3 and less than 5. This results in the interval [3, 5), which includes 3 but excludes 5.

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7/10

Step-by-step explanation: Your welcome

L*W=A

L*4/7=2/5

Answer:

The answer is D, -2. brainliest pls! :D

Step-by-step explanation:

-2*3=-6

-6+4=-2

-2*1/2=-1

-1=1/2x

1/2*-2=-1

-1=-1

The value of x such that it will make the given expression  (1/2)(3x+4)=(1/2)x true is x = - 2 therefore, option (D) will be correct.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given expression,

(1/2)(3x+4)=(1/2)x

(3/2)x + 4/2 = x/2

3x/2 + 2 = x/2

3x/2 - x/2 = -2

(3x - x)/2 = -2

2x = -4

x = -2

Hence "The value of x such that it will make the given expression  (1/2)(3x+4)=(1/2)x true".

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The given statement "For a sample with a standard deviation of s = 8, a score of x = 42 corresponds to z = -0.25. The mean for the sample is m = 40." is False because the calculated z-score does not match the given value.

To calculate the z-score, we use the formula z = (x - m) / s, where x is the score, m is the mean, and s is the standard deviation. Substituting the given values, we have z = (42 - 40) / 8 = 0.25. However, the given statement states that the z-score is -0.25, which is incorrect. Therefore, the statement is false.

The correct z-score for x = 42 with a mean of m = 40 and standard deviation of s = 8 is 0.25, not -0.25.

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Answer:

410

Step-by-step explanation:

Revenue is given by the relation :

x . (4,920 - 6x)

F(x) = 4920x - 6x²

To obtain the price, x which maximizes revenue, we take the first derivative of the revenue function and equate to 0

F'(x) = 0

F'(x) = 4920 - 12x

4920 - 12x = 0

-12x = - 4920

x = 4920 / 12

x = 410

Price will be 410

Answer:

The first... .........

The position of the mass in the undamped spring-mass system can be represented by the equation u(t) = (A cos(ωt) + B sin(ωt)) / k. Therefore, position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

In this case, the external force acting on the system is 108 cos(4t) lb. To determine the position of the mass, we need to solve the differential equation that represents the motion of the system.

Using Newton's second law, F = ma, and considering that the mass m = 24 lb, the equation becomes:

24 * d^2u/dt^2 = 108 cos(4t)

Simplifying, we have:

d^2u/dt^2 = 4.5 cos(4t)

This is a second-order linear homogeneous differential equation with a constant coefficient. The solution to this equation will be a linear combination of the homogeneous and particular solutions.

The homogeneous solution, representing the free oscillation of the system, is u_h(t) = C1 cos(2t) + C2 sin(2t).

The particular solution, representing the forced motion caused by the external force, can be assumed in the form u_p(t) = A cos(4t) + B sin(4t).

By substituting u_p(t) into the differential equation, we can determine the values of A and B.

Solving the differential equation for the particular solution, we find:

A = 18 and B = 0

The complete solution for the position of the mass in feet is:

u(t) = (18 cos(4t)) / 4

Simplifying further, we get:

u(t) = 4.5 cos(4t)

Therefore, the position of the mass at any time t in feet is given by u(t) = 4.5 cos(4t).

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Answer:

oiie4546

Step-by-step explanation:

Using the Pythagorean theorem:

X^2 = 10^2 + 24^2

X^2 = 100 + 576

X^2 = 676

X = sqrt(676)

X = 26

answer: 26

Answer:

26 :)

Step-by-step explanation:

Pythagorean theorem: a^2 + b^2 = c^2

Lets solve!!

10^2 + 24^2 = c^2

100 + 576 = c^2

676 = c^2

Now lets find the square root!!

\(\sqrt{676}\) = 26

Have an amazing day!!!

Please rate and mark brainliest!!

Amy will earn $28.70 + $3.80 = $32.50.

Profit and loss:

A profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year. These records provide information about a company’s ability or inability to generate profit by increasing revenue, reducing costs, or both. P&L statements are often presented on a cash or accrual basis. Company managers and investors use P&L statements to analyze the financial health of a company.

Amy will earn $28.70 from selling 7 large necklaces (7 x $4.10 = $28.70) and $3.80 from selling 1 small necklace, so in total, she will earn $28.70 + $3.80 = $32.50.

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Answer:

B. 4.09 cm²

Step-by-step explanation:

Let point O be the center of the circle.

As the center of the circle is the midpoint of the diameter, place point O midway between P and R.

Therefore, line segments OP and OQ are the radii of the circle.

As the radius (r) of a circle is half its diameter, r = OP = OQ = 5 cm.

As OP = OQ, triangle POQ is an isosceles triangle, where its apex angle is the central angle θ.

To calculate the shaded area, we need to subtract the area of the isosceles triangle POQ from the area of the sector of the circle POQ.

To do this, we first need to find the measure of angle θ by using the chord length formula:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Chord length formula}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the central angle.\\\end{minipage}}\)

Given the radius is 5 cm and the chord length PQ is 6 cm.

\(\begin{aligned}\textsf{Chord length}&=2r\sin\left(\dfrac{\theta}{2}\right)\\\\\implies 6&=2(5)\sin \left(\dfrac{\theta}{2}\right)\\\\6&=10\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{3}{5}&=\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{\theta}{2}&=\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=2\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=73.73979529...^{\circ}\end{aligned}\)

Therefore, the measure of angle θ is 73.73979529...°.

Next, we need to find the area of the sector POQ.

To do this, use the formula for the area of a sector.

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Substitute θ = 73.73979529...° and r = 5 into the formula:

\(\begin{aligned}\textsf{Area of section $POQ$}&=\left(\dfrac{73.73979529...^{\circ}}{360^{\circ}}\right) \pi (5)^2\\\\&=0.20483... \cdot 25\pi\\\\&=16.0875277...\; \sf cm^2\end{aligned}\)

Therefore, the area of sector POQ is 16.0875277... cm².

Now we need to find the area of the isosceles triangle POQ.

To do this, we can use the area of an isosceles triangle formula.

\(\boxed{\begin{minipage}{6.7 cm}\underline{Area of an isosceles triangle}\\\\$A=\dfrac{1}{2}b\sqrt{a^2-\dfrac{b^2}{4}}$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the leg (congruent sides). \\ \phantom{ww}$\bullet$ $b$ is the base (side opposite the apex).\\\end{minipage}}\)

The base of triangle POQ is the chord, so b = 6 cm.

The legs are the radii of the circle, so a = 5 cm.

Substitute these values into the formula:

\(\begin{aligned}\textsf{Area of $\triangle POQ$}&=\dfrac{1}{2}(6)\sqrt{5^2-\dfrac{6^2}{4}}\\\\ &=3\sqrt{25-9}\\\\&=3\sqrt{16}\\\\&=3\cdot 4\\\\&=12\; \sf cm^2\end{aligned}\)

So the area of the isosceles triangle POQ is 12 cm².

Finally, to calculate the shaded area, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Area of sector $POQ$}-\textsf{Area of $\triangle POQ$}\\\\&=16.0875277...-12\\\\&=4.0875277...\\\\&=4.09\; \sf cm^2\end{aligned}\)

Therefore, the area of the shaded region is 4.09 cm².

Answer:

1. n=-6

2. x=-17

Step-by-step explanation:

4n is the soultioncAnswer:

Step-by-step explanation:

Answer:

1.6

Step-by-step explanation:

12.8/8 = 1.6

15.2/9.5 = 1.6

Scale factor = 1.6

Hey there!

Fun fact:

• MONOMIAL contains ONE term because MONO- means 1

• BINOMIAL contains TWO terms because BI- means 2

• TRINOMIAL contains THREE terms.. because TRI- means 3.

• POLYNOMINAL contains FOUR or MORE terms because POLY- means 4 or more

ANSWERING YOUR QUESTION

(3/5x + 3)^2

= (3/5x)(3/5x) + (3/5x)(3) + (3/5x)(3) + 3(3)

• 3/5x(3/5x) = 9/25x

• 3/5x(3) = 9/5x

• 3(3) = 9

= 9/25^2 + 9/5x + 9/5x + 9

• COMBINE the LIKE TERMS

= (9/25)x^2 + 18/5x + 9

Therefore, your answer is:

“9/25x^2 + 18/5x + 9”

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

What the heII happened? aight nvm It's function

Step-by-step explanation:

my old answer got deleted ;(

The equation x² + 4x + 9 = 0 are complex numbers: x = -2 + i√5 and x = -2 - i√5.

To find the solutions for the equation x² + 4x + 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this equation with the given equation x² + 4x + 9 = 0, we can see that a = 1, b = 4, and c = 9.

Plugging in these values into the quadratic formula, we have:

x = (-4 ± √(4² - 4(1)(9))) / (2(1))

x = (-4 ± √(16 - 36)) / 2

x = (-4 ± √(-20)) / 2

Since the value inside the square root is negative, we know that the solutions will involve complex numbers. Simplifying further, we have:

x = (-4 ± i√20) / 2

x = (-4 ± 2i√5) / 2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

x = -2 ± i√5

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Answer:

Yes

Step-by-step explanation:

Answer:

a=27%

Step-by-step explanation:

-lukelaws

tell me if it helped

Answer:

A

Step-by-step explanation:

Equals 27 percent

I took the test and go it right

using exponents, On simplifying the equation, we get =4m+8.

The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.

Work simplification is to develop better work processes that boost output while cutting waste and costs.

Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.

Given equation,

m-(8-3m)

=m-8+3m

=4m+8

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