The length of a marathon is 138,435 ft. Each stride, or step, by a particular runner is 3 ft long. Does the number of strides the runner takes fit evenly into the length of the race? Explain.

Answer:

$45.5

Step-by-step explanation:

12 guests and himself : 13×3.50=45.5

Answer:

2.73 meters away from the building.

Step-by-step explanation:

To find the distance from the building to the flagpole, we can use the tangent function. Let's call the distance from the building to the flagpole "d".

The tangent of the angle of elevation is equal to the height of the flagpole (h) divided by the distance from the building to the flagpole (d):

tan 48° = h / d

The tangent of the angle of depression is equal to the distance from the building to the flagpole (d) divided by the height of the observer (3.5 m):

tan 35° = d / 3.5

We can use these two equations to find the value of d. Solving the first equation for h:

h = tan 48° * d

And substituting that into the second equation:

tan 35° = d / (tan 48° * d / 3.5)

Solving for d:

d = 3.5 * tan 35° / tan 48°

Using a calculator, we can find that:

d = 3.5 * tan 35° / tan 48° = 3.5 * 1.3602668 / 1.7415198 = 2.73 m

So the flagpole is 2.73 meters away from the building.

Answer:

lol

Step-by-step explanation:

that sucks

The coordinates of the endpoints of rs are r(1,11) and s(6,1). point t is on rs and divides it such that rt:st is 4:1.

the coordinates of the point t are (5, 3)

We may utilise the notion of section formula to get the coordinates of point T, which states that if we have two points A(x1, y1) and B(x2, y2) and a point P splitting the line segment AB in the ratio m:n, then the coordinates of point P can be calculated using the following formula:

P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))

In this situation, we have the coordinates of points R and S, as well as the ratio of T divided by RS. So, let's enter the following values into the formula to determine T's coordinates:

Let the coordinates of point T be (x, y), and the ratio of T to RS be 4:1, implying that RT:ST = 4:1. This means that RT = 4/5 (RS length) and ST = 1/5. (length of RS).

RS length =[tex]sqrt((6-1)^2 + (1-11)^2)[/tex] = [tex]sqrt (146)[/tex]

RT=[tex](4/5) * sqrt(146)[/tex] = [tex](4/5) * 12.083[/tex] = 9.666

ST =[tex]1/5* sqrt(146)[/tex] = [tex]1/5* 12.083[/tex] = 2.4166

We get the following using the section formula:

x = (4×6 + 1×1)/(4+1) = 5

y = (4×1 + 1×11)/(4+1) = 3

T = (5, 3)

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15 liquids that can be found in a kitchen include:

15 solids in a kitchen are:

When it comes to solids in the kitchen, we can mostly find either food ingredients, such as salt, flour, and spices, or actual food that can be prepared such as meat, vegetables, and bread.

As for liquids, these can be anything from drinks such as juice, water and wine, to liquids used for cooking such as oil, soy sauce and vinegar.

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Answer:

3/8

Step-by-step explanation:

If 5/8 of the staff are male, then the remaining staff must be female, which is 1 - 5/8 = 3/8 of the staff.

So, the fraction of the staff that is female is 3/8.

ALLEN

Answer:

{y l y > 9}

Step-by-step explanation:

Given function:

[tex]f(x)=3^x+9[/tex]

The given function is an exponential function.

The parent function is the basic equation before the function has undergone any transformation(s).  Therefore, the parent function of the given function is:

The range of the parent function is restricted to positive real numbers as it never takes a negative value.  Furthermore, it never reaches zero (although it approaches y = 0 as x → -∞).  Therefore, the range of the parent function is {y | y > 0}.

As the given function has been translated up 9 units (by the addition of "+ 9"), the range of the given function is translated 9 units up.  So as x approaches negative infinity, y approaches (but never reaches) 9. Therefore, the range of the given function is:

The probability of a defect (weights less than -0.36 ounces or greater than 0.36 ounces) is approximately 0.0521 × 2 = 0.1042 or 10.42% to four decimal places.

To find the probability of a defect, we need to determine the range of weights that would be considered as defects. The process control limit is set at plus or minus 2.4 standard deviations, which means that any weight outside the range of mean ± 2.4× standard deviation would be considered a defect. Let's calculate the mean weight (μ): μ = 0

And the control limit (LCL and UCL):

LCL = μ - (2.4 × standard deviation)

= 0 - (2.4 × 0.15) = -0.36 UCL

= μ + (2.4 × standard deviation)

= 0 + (2.4 × 0.15) = 0.36.

Since the standard deviation is 0.15 ounces and the normal distribution is symmetrical, the probability of a weight being less than -0.36 ounces or greater than 0.36 ounces is equal. To calculate the probability, we can use the cumulative distribution function (CDF) of a standard normal distribution. Using a standard normal table or a calculator with statistical functions, we can find that the probability of a standard normal distribution being less than -0.36 or greater than 0.36 is about 0.0521 or 5.21%. So, the probability of a defect (weights less than -0.36 ounces or greater than 0.36 ounces) is approximately 0.0521 × 2 = 0.1042 or 10.42% to four decimal places.

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The probability of selecting a person who is either a Democrat or a woman is 0.8, or 80%.

Probability is a branch of mathematics that deals with the study of random events. It is used to predict the likelihood of an event occurring.

Let's start by finding the probability of selecting a Democrat. We are given that there are 60 Democrats in the group of 100 people. Therefore, the probability of selecting a Democrat at random is:

P(Democrat) = 60/100 = 0.6

Next, let's find the probability of selecting a woman. We are given that there are 60 women in the group of 100 people. Therefore, the probability of selecting a woman at random is:

P(Woman) = 60/100 = 0.6

Now, we need to find the probability of selecting both a Democrat and a woman. We are given that 40 of the Democrats are women. Therefore, the probability of selecting a woman who is also a Democrat is:

P(Democrat and Woman) = 40/100 = 0.4

To find the probability of selecting a person who is either a Democrat or a woman, we add the probabilities of selecting a Democrat and selecting a woman, and then subtract the probability of selecting both a Democrat and a woman. Therefore, the probability of selecting a person who is either a Democrat or a woman is:

P(Democrat or Woman) = P(Democrat) + P(Woman) - P(Democrat and Woman)

= 0.6 + 0.6 - 0.4

= 0.8

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Using the concept of rates, the machine will complete 9 9/64 inches in 8.67 minutes

To determine how long it will take to turn a particular length of iron, we can calculate the rate at which it works and it must be in a definite proportion.

If the lathe moves 3/128 in one revolution.

And the machine completes 45 revolutions in 1 minutes, we can determine how many inches in moves in that minute.

3/128 in = 1 rev

x in = 45

45 * (3/128) = 45 revolutions = 1 minute

1.054 inches in 1 minute.

We can further use this to determine the time it takes to move 9 9/64 inches

1.054 inches = 1 minute

9 9/64 inches = x minute

cross multiply both sides and solve

x = 8.67 minutes

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Answer: The tip is $2.90

Step-by-step explanation: 20% of 14.50 is 2.9

Answer: To convert a Senary (base 6) number to decimal, we can use the following formula:

Decimal = (5 * 6^4) + (4 * 6^3) + (7 * 6^2) + (2 * 6^1) + (5 * 6^0)

= (5 * 1296) + (4 * 216) + (7 * 36) + (2 * 6) + (5 * 1)

= 6480 + 864 + 252 + 12 + 5

= 7603

So the Senary (base 6) number 54724 is equivalent to the decimal number 7603.

Step-by-step explanation:

The plane's true bearing is $27.9°N of W, and its estimated ground speed is 473.3 mph.

Math is made more fascinating and enjoyable using Speed Maths (Vedic Maths). by assisting the child in quickly performing some improbable computations. By combining the correct amount of enjoyment, memory, skills, memory recall, and formula application, your child will become a superstar performer.

Let's start with the airplane's speed.

A bearing of N25°W corresponds to a anticlockwise angle of 65° when measured from the westward direction (W).

As a result, the airplane's velocity vector can be divided into its north-south and east-west components as shown below:

V_A,north = 480 cos(65°) ≈ 200.5 mph (northward)

V_A,west = 480 sin(65°) ≈ 447.3 mph (westward)

V_W,north = 45 sin(75°) ≈ 43.5 mph (northward)

V_W,west = 45 cos(75°) ≈ 11.3 mph (westward)

To find the net velocity of the airplane, we can add the north-south and east-west components of the airplane velocity and wind velocity separately:

V_net,north = V_A,north + V_W,north ≈ 200.5 + 43.5 ≈ 244.0 mph (northward)

V_net,west = V_A,west + V_W,west ≈ 447.3 + 11.3 ≈ 458.6 mph (westward)

Now we can use the Pythagorean theorem to find the magnitude of the net velocity:

|V_net| = sqrt(V_net,north² + V_net,west²) ≈ 473.3 mph

To find the actual bearing of the airplane, we can use the inverse tangent function:

tan⁻¹(V_net,north / V_net,west) ≈ 27.9°

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Answer:

The possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

Step-by-step explanation:

The coefficient of x² in the expansion of (2 - x)(3 + bx)³ can be found by expanding the brackets.  

Expand the cubed part by using the (a + b)³ formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Therefore:

[tex]\begin{aligned}(3 + bx)^3 &= (3)^3 + 3(3)^2(bx) + 3(3)(bx)^2 + (bx)^3\\&= 27 + 27bx + 9b^2x^2 + b^3x^3\end{aligned}[/tex]

So:

[tex](2-x)(3 + bx)^3 = (2-x)(27 + 27bx + 9b^2x^2 + b^3x^3)[/tex]

To find the coefficient of the term in x², multiply the constant in the first parentheses by the coefficient of the term in x² in the second parentheses and add this to the product of the coefficient of the term in x in the first parentheses and the coefficient of the term in x in the second parentheses:

[tex](\bold{2}-x)(27 + 27bx + \bold{9b^2}x^2 + b^3x^3)\\\phantom{.}\underbrace{\uparrow \qquad \qquad\qquad\qquad\;\uparrow}\\ \phantom{wlwww}\text{multiply}[/tex]

[tex](2-x)(27 + \bold{27b}x + 9b^2x^2 + b^3x^3)\\\phantom{bbb..}\underbrace{\uparrow \qquad \quad\;\uparrow}\\ \phantom{ww.w}\text{multiply}[/tex]

Therefore, the expression for the coefficient of x² is:

[tex]2 \cdot 9b^2 + (-1) \cdot 27b[/tex]

Since the coefficient of x² in the expansion is 45, set the expression to 45 and solve for b:

[tex]\begin{aligned}2 \cdot 9b^2+(-1) \cdot 27b&=45\\18b^2-27b&=45\\18b^2-27b-45&=0\\9(2b^2-3b-5)&=0\\2b^2-3b-5&=0\\2b^2-5b+2b-5&=0\\b(2b-5)+1(2b-5)&=0\\(b+1)(2b-5)&=0\\\\ \implies b+1&=0 \implies b=-1\\ \implies 2b-5&=0 \implies b=\dfrac{5}{2}\end{aligned}[/tex]

Therefore the possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

To check if a curve represents a function, draw vertical lines all over the graph intersecting the curve at different regions.

Now, check how many times a line cuts the curve, if all the vertical lines cuts the curve at a single point then it represents a function, and if the vertical line cuts the curve at more than one point, then its not a function.

By keeping the above instructions in mind, conclusion can be made that :

Functions : (i), (ii), (iii), (iv) and (vi)

Non function : (v) and (vii)

A large tank hold 1. 9 time 10 to the 7th power gallons of oil. The amount of oil that can be stored in 9 tanks is 1.71 x 10^8 gallons in scientific notation.

To find the amount of oil that can be stored in 9 tanks that each hold 1.9 x 10^7 gallons of oil, we can use the following steps:

Write down the number of gallons that one tank can hold: 1.9 x 10^7 gallons. Multiply this value by the number of tanks: 1.9 x 10^7 gallons/tank x 9 tanks.

To multiply the two numbers, we can simply multiply the coefficients (1.9 and 9) and add the exponents (7 in this case): (1.9 x 9) x 10^(7+0) gallons.

Simplifying the coefficient gives us 17.1, so the amount of oil that can be stored in 9 tanks is 17.1 x 10^7 gallons.

Finally, we can express this result in scientific notation by writing it as 1.71 x 10^8 gallons, since 17.1 is equivalent to 1.71 x 10.

Therefore, the amount of oil that can be stored in 9 tanks is 1.71 x 10^8 gallons in scientific notation.

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Answer:

Number is -10

Step-by-step explanation:

Let Number be x

so, 5x= 30+8x

Take 30 other side and 5x other side

so, 8x-5x=-30

3x=-30

x=-10

HOPE THIS HELPS... THANK YOU

The Mean Value Theorem is satisfied for c = 3 on the closed interval [0,3]. This can be expressed as:

The Mean Value Theorem (MVT) of differential calculus states that for any differentiable function f(x) on the closed interval [a,b], there exists a point c between a and b such that the slope of the tangent at c is equal to the average rate of change of f(x) over [a,b]. Mathematically, this can be expressed as:

f'(c) = [f(b) - f(a)] / (b - a)

In the given function f(x) = x^3 - 3x^2, we need to find all values of c that satisfy the conclusion of the MVT on the closed interval [0,3].

First, we need to find the derivative of f(x):

f'(x) = 3x^2 - 6x

Then, we need to evaluate the average rate of change of f(x) over [0,3]:

[f(3) - f(0)] / (3 - 0) = (27 - 0) / 3 = 9

Therefore, we need to find all values of c between 0 and 3 such that f'(c) = 9.

Setting f'(c) = 9, we get:

3c^2 - 6c = 9

c^2 - 2c - 3 = 0

(c - 3)(c + 1) = 0

Thus, the two possible values of c that satisfy the conclusion of the MVT are c = 3 and c = -1. However, we need to check if these values actually lie in the closed interval [0,3]. Since -1 is not in [0,3], the only value of c that satisfies the conclusion of the MVT on [0,3] is c = 3.

Therefore, the conclusion of the Mean Value Theorem is satisfied for c = 3 on the closed interval [0,3]. This means that there exists a point c between 0 and 3 where the slope of the tangent to the graph of f(x) is equal to the average rate of change of f(x) over [0,3].

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The rounded number to the nearest thousands place is 9,910,000

To change a number into an approximation having fewer significant digits is called rounding a number.

Given that, a number 9,909,937 we are asked to round it,

9,909,937 in words =

nine million nine hundred nine thousand nine hundred thirty-seven

Therefore, to round to the nearest thousand;

You rounded to the nearest thousands place. The 9 in the thousands place rounds up to 10 because the digit to the right in the hundreds place is 9.

Because the thousands place was rounded up from 9 to 10, the thousands place becomes 0 and the ten thousands place is increased by 1. When a 9 is rounded up to 10, that place value becomes 0, and we add 1 to the previous place value.

9,910,000

When the digit to the right is 5 or greater we round away from 0. 9909937 was rounded up and away from zero to 9,910,000

Hence, the rounded number to the nearest thousands place is 9,910,000

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No, you cannot stop at the step 3x = 126 degrees. The measure of angle JML is approximately 56.67 degrees

What is the measure of angle θ?

A radian is the length of an arc formed by an angle that, when shown as a central angle, equals the length of the circle's radius.

No, you cannot stop at the step 3x = 126 degrees.

To find the measure of angle JML, we need to solve for x and then use that value to find the measure of the angle.

We can start by using the fact that the angles in triangle JLM must add up to 180 degrees. We have:

m∠JLM + m∠JML + m∠LMJ = 180

Substituting the given values, we get:

4x + (2x + 18) + (3x - 12) = 180

Simplifying and combining like terms, we get:

9x + 6 = 180

Subtracting 6 from both sides, we get:

9x = 174

Dividing both sides by 9, we get:

x = 19.33...

Now that we have the value of x, we can use it to find the measure of angle JML. We have:

m∠JML = 2x + 18

Substituting x = 19.33..., we get:

m∠JML = 2(19.33...) + 18 = 56.67...

Therefore, the measure of ∠JML is approximately 56.67 degrees

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The algebraic expression that represents the amount that they still need to raise is given as follows:

A. 2x² - 9xy - 1.

The total amount that the three friends want to raise is defined as follows:

7x² - 4xy + 8.

The total amount raised is obtained adding the amounts raised by each of the friends, as follows:

5xy + 16 + x² + 4x² - 7 = 5x² + 5xy + 9.

Then the remaining amount to be raised is obtained by the subtraction of the total amount by the amount raised, as follows:

7x² - 4xy + 8 - (5x² + 5xy + 9) = 7x² - 5x² - 4xy - 5xy + 8 - 9

7x² - 4xy + 8 - (5x² + 5xy + 9) = 2x² - 9xy - 1.

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As per the ratio, the number of men on the sight-seeing tour is 4.

In the given sight-seeing tour, we are told that there were 14 people in total. We are also given the ratio of women to children, which is 5 to 2. This means that for every 5 women on the tour, there were 2 children.

To find the number of men on the tour, we need to first find the number of women and children. We can do this by dividing the total number of people by the ratio of women to children.

Let's use a variable to represent the number of sets of 5 women and 2 children. We'll call this variable "x".

So, the number of women on the tour is 5x and the number of children is 2x.

Now, we can set up an equation to find the value of x:

5x + 2x = 14

This equation represents the total number of women and children on the tour, which is equal to 14.

Simplifying the equation, we get:

7x = 14

Dividing both sides by 7, we get:

x = 2

This means that there were 2 sets of 5 women and 2 children on the tour. So, the number of women is:

5x = 5(2) = 10

The number of children is:

2x = 2(2) = 4

Now, we can find the number of men by subtracting the number of women and children from the total number of people:

14 - 10 = 4

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Inequality for the number of weeks lily will need to save to have at least $300 is 40 + 65*x >= 300  and  4 week needed to buy the cellphone.

The phenomenon of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is referred to as inequality. To different people and in various contexts, the word "inequality" may mean different things. Additionally, inequality has distinct yet overlapping social, economic, and geographic dimensions. The conflict between the normative concept of "deservingness" and the moral ethics of equity and social justice, on the one hand, and on the other, further complicates discussions about inequality. Inequalities that can be seen both within and between social groups have come to the forefront of public consciousness in recent years. The growing realization that inequality is systemic and ingrained in various socioeconomic and political structures is the result of this awareness. The contributions of geographers to the subject.

she needs to save at least $300 before she is able to buy the phone and

her grandfather gives her $40  so she need 300 - 40

and she earns $65 tutoring after school each week so until she will not have 260 she not able to buy.

40 + 65*x >= 300

65x >= 260

x >= 260/65

x >= 4

4 week needed.

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Total 21 teams completed the escape room this week.

An employee records the number of minutes it takes each team to complete the escape room this week the dot plot shows the data.

To determine how many teams completed the escape room this week we use the dot plot.

From the dot plot we can see that at 41 min have one found one employee escape from room.

At 44 min have one found 3 employee escape from room.

At 45 min have one found 2 employee escape from room.

At 46 min have one found 4 employee escape from room.

At 47 min have one found 5 employee escape from room.

At 48 min have one found 3 employee escape from room.

At 49 min have one found 2 employee escape from room.

At 50 min have one found one employee escape from room.

Team completed the escape room this week = 1 + 3 + 2 + 4 + 5 + 3 + 2 + 1

Team completed the escape room this week = 21

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Answer:21 i got it correct

Step-by-step explanation:

Answer: x=92x=−7

Step-by-step explanation:x=−b±b2−4ac2a=−±2−4√2Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

Answer:it’s 3

Step-by-step explanation:

so what u do is multiply

Answer:

433 1/8ft

Step-by-step explanation:

this is my answer

Answer:

You are correct it is 12.

Step-by-step explanation:

Answer: Square root of 288, or estimated 16.97

Step-by-step explanation:

Conveniently, the points form a diagonal line as you show, so we can use the Pythagorean Theorem to find the distance.

The x-component of this is the distance between -6 and 6, which is 12, and the y-component is again the distance between -6 and 6, which is also 12.

Therefore, the distance is the square root of 12^2 + 12^2, or the squareroot of 288.