A floodlight is on the ground 45 meters from a building. A thief 2 meters tall runs from the floodlight directly towards the building at 6 meters per second. How rapidly is the length of his shadow on the building changing when he is 15 meters from the building

A z-score of -2.5 means that a score is located 2.5 standard deviations to the left of the mean.

A z-score is a measure of how many standard deviations a data point is away from the mean of a distribution. It helps in understanding the relative position of a particular value within a dataset. When a z-score is negative, it indicates that the data point is located to the left of the mean.

In the case of a z-score of -2.5, it means that the score is located 2.5 standard deviations to the left of the mean. This implies that the value is significantly lower than the mean. Since the z-score is negative, it indicates that the data point falls below the mean value in the distribution.

In a standard normal distribution, where the mean is 0 and the standard deviation is 1, a z-score of -2.5 indicates that the data point is located 2.5 standard deviations below the mean. This implies that the score is relatively low compared to the average value in the distribution. The negative sign signifies that the data point is to the left, or below, the mean.

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The answer will be .25 and .25 for both set of question. using probablity.

What is Probability ?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities.

Total number of students =1-juniors+chemistry+neither+both

(a) For both a junior and chemistry major =1/4 =. 25

(b) probability that she is also a chemistry major will be 1/4 =. 25

Hence The answer for the above two set of qustion will be .25 and .25.

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The probability of getting:

a) 2 apples is 5/33

b) 1 apple and 1 orange 35/132 .

Here, we have,

given that,

A fruit basket contains 5 apples and 7 oranges.

Paul picks a fruit at random from the basket and eats it.

He then picks another fruit at random to eat.

so, we get,

total number of fruits = 12

now, we have,

a) P( pick 1 apple) = 5/12

then, P( pick another 1 apple) = 4/11

so, we get,

P( picking 2 apples) = 5/12 * 4/11 = 20/132 = 5/33

b) P( pick 1 apple) = 5/12

then, P( pick 1 orange) = 7/11

so, we get,

P( picking 1 apple and 1 orange) = 5/12 *  7/11 = 35/132

Hence, The probability of getting:

a) 2 apples is 5/33

b) 1 apple and 1 orange 35/132 .

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1/4π is area of a circle when the radius is 6 cm.

What is the circumference of a circle?

 A = πr²

differentiate both sides with respect to 't'

dA/dt = πr² dr/dt

dA/dt = 2πr dr/dt

dA/dt = 3  ,     r = 6

3 = 2π * 6dr/dt

dr/dt = 1/4π

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Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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The equation represents the relationship between c, the total cost of napkins, and n is 750c = 300n.

Since, equation is an expression that shows the relationship between two or more numbers and variables.

Given that manager of a restaurant ordered 300 linen napkins from a supplier for $750.

Thus, the equation represents the relationship between c, the total cost of napkins, and n, the number of napkins purchased.

750c = 300n

Hence, the equation represents the relationship between c, the total cost of napkins, and n is 750c = 300n.

The answer is A.

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The inequalities that represent the line in the graph will be y < x - 3 and y = -(2/3)x. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, the blue line has a slope of 1 and the y-intercept is at (0, -3), then the inequality is calculated as,

y < x - 3

The red line is passing through the origin and (3, -2), then the equation is given as,

y - 0 = [(-2 - 0) / (3 - 0)](x - 0)

y = -(2/3)x

The disparities that address the line in the chart will be y < x - 3 and y = - (2/3)x. Then the right choice is B.

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Answer:

13

Step-by-step explanation:

y^2 = 169

y = \(\sqrt{169}\)

y = 13

The weight of the Avery's lunch box using given weights is equal to 0.92 pounds (rounded to two decimal places).

Total weight of the backpack= 2 2/3 pounds

                                                = 8/3 pounds

The weight of the each book =7/8 pounds.

Let x be the weight of the lunch box in pounds.

An equation that represents the total weight in Avery's backpack,

2(7/8) + x = 8/3

To solve for x, simplify and solve for x,

⇒14/8 + x = 8/3

Multiplying both sides by 24 the least common multiple of 8 and 3 to clear the fractions,

⇒42 + 24x = 64

Subtracting 42 from both sides,

⇒24x = 22

Dividing both sides by 24,

⇒x = 22/24

Simplifying the fraction,

⇒x = 11/12

     =  0.92 pounds (rounded to two decimal places).

Therefore, the  weight of the lunch box is equal to 0.92 pounds (rounded to two decimal places).

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The required function h(x) is  h (x) = 2 cosine (x + StartFraction 11 pi Over 8 EndFraction) minus 3. Option d is correct.

Function g(x) =  2cos (x + π/2) - 2

What are trigonometric equations?

Equation which includes trigonometric operators eg sin, cos.. etc.. In algebraic processes.

Here, the phase of the curve is increase by 7π/8.

So the phase = π/2 + 7π/8

                      = 11 π/8

And Shift of curve along y axis is by -1.

So, the total shift = -2-1

                             = -3

⇒ h(x) = 2cos (x + 11π/8) - 3

Thus, the function h(x) results when g(x) is translated.h (x) = 2 cosine (x + StartFraction 11 pi Over 8 EndFraction) minus

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Answer:kara Had $17-$12. Pizza cost =leave u with $5 x.50=10topping

Step-by-step explanation:

The probability that a student earned a score of at least 3 is, 0.610.

Therefore, the correct option is option e. 0.610

To find the probability that a student earned a score of at least 3, we need to sum the probabilities of scoring a 3, 4, or 5.

Probability of scoring at least 3 = Probability(3) + Probability(4) + Probability(5)

Probability of scoring at least 3 = 0.249 + 0.217 + ?

We know that the sum of all probabilities must equal 1, so we can solve for the missing probability:

0.235 + 0.155 + 0.249 + 0.217 + ? = 1

? = 0.144

Now we can complete the calculation:

Probability of scoring at least 3 = 0.249 + 0.217 + 0.144 = 0.61

Therefore, the answer is e. 0.610.

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Answer:

the answer is A

Step-by-step explanation:

Answer:

A. 4xy \(\sqrt[4]{3y}\)

Step-by-step explanation:

4√768x⁸y⁵

---> factor 768 --> 4x4x4x4x3

---> x⁸ = x⁴⁺⁴ = x⁴ . x⁴

---> y⁵ = y⁴⁺¹ = y⁴ . y¹

4√4⁴x3 x⁴ . x⁴ . y⁴ .y  

since is 4th root, all the numbers with power to 4 comes out of the root

4x.x.y\(\sqrt[4]{3y}\)

4x²y\(\sqrt[4]{3y}\)

Step-by-step explanation: x =9

Answer: 3(x-3)/4-1/2=2/3  

Step-by-step explanation:

The least common denominator will be the least common multiple of 4,2,3 which is the product of the highest occurring primes of the numbers prime factorization...

4=2*2, 2=2, 3=3, so the least common denominator is 2*2*3=12

Answer:

12

Step-by-step explanation:

got it right on my quiz

Answer:

A = 8, B = 1/8, C = 13/5, D = 13/50

Step-by-step explanation:

4a = 32

divide both sides by 4

4a/4 32/4 =8

Basically repeat this process on every equation, and remember to divide both sides by the number on the left.

There are 150 calories per sandwich in a box of ice cream sandwiches.

To find the number of calories per sandwich in a box of ice cream sandwiches, you need to divide the total number of calories by the number of sandwiches in the box.

The unit rate for this situation is the number of calories per sandwich.

Here's how to find it: Unit rate = Total number of calories ÷ Number of sandwiches= 1,800 ÷ 12= 150 calories per sandwich

Therefore, there are 150 calories per sandwich in a box of ice cream sandwiches.

Similar to a teaspoon or an inch, a calorie is a unit of measurement. The amount of energy released by your body when it digests and absorbs food is called a calorie. Your body can use more energy from a food if it has more calories.

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The hazard-free POS expressions for the given functions are:

To obtain the hazard-free product of sums (POS) expression for the given functions, we need to follow these steps:

Let's go through each function and apply these steps:

1. Function FEW,X,Y,Z(1,3,4,6,7,11-13):

The given function has the following minterms: 1, 3, 4, 6, 7, 11, 12, and 13.

Writing it in SOP form:

F = WXY'Z' + W'XYZ' + W'XY'Z' + W'XYZ + W'X'Y'Z' + WXY'Z + X'Y'Z' + X'Y'Z

Identifying the essential prime implicants:

Determining the hazard-free prime implicants:

All prime implicants in this case are hazard-free since there are no adjacent minterms.

The hazard-free POS expression is:

F = WXY'Z' + W'XY'Z' + W'X'Y'Z'

2. Function F=EA,B,C,D,E(0,4-7,9,14-17,23) + d(12,29-31):

The given function has the following minterms: 0, 4, 5, 6, 7, 9, 14, 15, 16, 17, and 23.

It also has the don't-care conditions: 12, 29, 30, and 31.

Writing it in SOP form:

F = ABCD'E' + AB'C'D'E + AB'CD'E' + ABC'DE' + ABCDE' + A'BC'D'E' + A'BC'DE' + A'B'C'D'E + A'B'CD'E' + A'B'C'DE' + A'B'CDE'

Identifying the essential prime implicants:

Determining the hazard-free prime implicants:

The hazard-free POS expression is:

F = ABCD'E' + ABCDE' + A'BC'DE' + A'B'CD'E'

So, the hazard-free POS expressions for the given functions are:

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Answer:

hey so you know they the fractions arent there

zeros of function  f⁡(x)=-(x+1)⁢(x−3)⁢(x+2) are -1, 3, and -2 and it is located at ( 0, -1) , ( 0, 3) and ( 0, -2)

The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0.

according to the question

f⁡(x)=-(x+1)⁢(x−3)⁢(x+2) are -1, 3, and -2

and it is located at

( 0, -1)

( 0, 3)

and ( 0, -2)

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Answer:

Step-by-step explanation: If 2¹² = 1 K, then we know that 1 K is equal to 2¹², or:

1 K = 2¹²

To find out what 0.5 K is equal to, we can divide 1 K by 2, since 0.5 is half of 1. Therefore:

0.5 K = (1 K) / 2

Substituting 1 K with 2¹², we get:

0.5 K = (2¹²) / 2

Simplifying the expression on the right-hand side, we get:

0.5 K = 2¹¹

Therefore, 0.5 K is equal to 2¹¹.

Answer:  0.5 K is equal to 512.

Step-by-step explanation:

Since 2¹² = 1 K, we know that 1 K = 2¹². To find the value of 0.5 K, we can divide 1 K by 2:    1 K / 2 = 2¹¹

Therefore, 0.5 K = 2¹¹. Using the property of exponents, we can simplify this to:

0.5 K = 2¹² / 2 = 2¹¹

Hence, 0.5 K is equal to 512.

The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

Answer:

99 in³

Step-by-step explanation:

Let the radius and height of each be r and h in. respectively.

Write an equation for the volume of cone.

Volume of cone= ⅓πr²h

⅓πr²h= 33

Multiply both sides by 3:

πr²h= 99

Volume of cylinder= πr²h

We have found the value of πr²h previously, which is 99.

Thus, the volume of the cylinder is 99 in³.

Answer:

7 tonnes

Step-by-step explanation:

the vehicle is x

the load is 5/2 tonnes ( i simplify this)

the load is 5/9 the vehicle

we got the equation: 5/9x = 5/2

therefore x = 4.5 so the total mass of the vehicle is 4.5 + 5/2 = 7

Answer:

-2 x 3/8 x 5/-7 =15/28

Step-by-step explanation:

-2 x 3/8 =  -3/4 x 5/-7=  15/28

Answer:

15/28 or 0.53571428

Step-by-step explanation: