James has a 34-foot ladder leaning against the side of his house. If the bottom of the ladder is
16 feet away from his house, how many feet above the ground does the ladder touch the
house?

With a TI-84 Plus calculator, the shaded areas beneath the standard normal curve are (a) 0.705, (b) 0.976, (c) 0.01, and (d) 0.09.

We must determine the region beneath the normal distribution curve.

a) region of the standard normal curve outside of the range between z = − 1.98 and z = 0.61.

= P (-1.98 < z < 0.61)

= P (z < 0.61) - P ( z < - 1.98)

= 0.729 - 0.024

= 0.705

= 70.5 %

b) region to the left of the standard normal curve under z = 1.98

= P ( z < 1.98)

= 0.976

= 97.6%

c) region to the right of the standard normal curve under z = 2.34

P (z > 2.34)

= 1 - P (z < 2.34)

= 1 - 0.990

= 0.01

= 1 %

d) space between the standard normal curve's upper and lower bounds z = -0.94 and z = -0.63

= P ( -0.94 < z < -0.63)

= P (z < -0.63) - P (z < -0.94)

= 0.264 - 0.174

= 0.09

= 9%

The complete question is:

Using the TI-84 calculator, find the area under the standard normal curve. Round the answers to four decimal places.(a) Find the area under the standard normal curve that lies outside the interval between z= −1.98 and z=0.61.(b) Find the area under the standard normal curve to the left of z=1.98.(c) Find the area under the standard normal curve to the right of z= 2.34.(d) Find the area under the standard normal curve that lies between z= −0.94 and z= −0.63.

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Answer:

ans is 10

Step-by-step explanation:

by using pythagoras theorm

26^2=a^2+24^2

a^2=100

a=10

Hi there!

\(\large\boxed{k> 6.125}\)

We can use discriminants to determine the value of k for which the equation would have complex solutions. (Those involving i)

If b² - 4ac < 0, then the equation will have complex solutions. Therefore:

Plug in the given values of b and a to solve:

7² - 4(2)(k) < 0

Simplify:

49 - 8k < 0

Solve the inequality:

49 < 8k

6.125 < k

k > 6.125. Anything greater than 6.125 would result in complex solutions.

Answer:

See below

Step-by-step explanation:

One will be negative and one will be positive

6    -1

-6    1

3    -2

-3    2

The solution to the equation is ( 1 , -6 ) , ( -1 , 6 ) , ( 2 , -3 ) , ( -2 , 3 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is A = -6

Let the first number be a

Let the second number be b

Now , A = a x b

when a = 1 and b = -6

A = 1 x -6

The value of A = -6

when a = -1 and b = 6

A = -1 x 6

The value of A = -6

when a = 2 and b = -3

A = 2 x -3

The value of A = -6

when a = -2 and b = 3

A = -2 x 3

The value of A = -6

Therefore , the value of A is -6

Hence , ordered pair to the equation is ( 1 , -6 ) , ( -1 , 6 ) , ( 2 , -3 ) , ( -2 , 3 )

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Answer:

So it would take Yolanda 9 hours to drive 495 miles at the same rate.

Step-by-step explanation:

To solve this problem, we can use the formula: distance = rate x time.

We know that Yolanda's rate of driving is 605 miles in 11 hours, so we can find her average speed by dividing the distance by the time:

rate = distance / time

rate = 605 miles / 11 hours = 55 miles per hour

Now that we know Yolanda's average speed, we can use it to find the time it would take her to drive 495 miles at that rate:

time = distance / rate

time = 495 miles / 55 miles per hour = 9 hours

The correct value of inverse of the function f(x) = 8√x is f^(-1)(x) = x^2/64.

The inverse of the function f(x) = 8√x, we can follow these steps:

Replace f(x) with y: y = 8√x.

Swap the x and y variables: x = 8√y.

Solve the equation for y: Divide both sides by 8 to isolate the square root of y: x/8 = √y.

Square both sides to eliminate the square root: (x/8)^2 = (√y)^2.

Simplify: x^2/64 = y.

Replace y with f^(-1)(x): f^(-1)(x) = x^2/64.

Therefore, the inverse of the function f(x) = 8√x is f^(-1)(x) = x^2/64.Let's go through the steps again and provide more explanation:

Start with the original function: f(x) = 8√x.

Replace f(x) with y to obtain the equation: y = 8√x. This step is done to represent the function in terms of y.

Swap the x and y variables: Instead of y = 8√x, we now have x = 8√y. This step is done to isolate the variable y on one side of the equation.

Solve the equation for y: Divide both sides of the equation by 8 to isolate the square root of y. This gives us x/8 = √y.

Square both sides of the equation: By squaring both sides, we eliminate the square root and obtain (x/8)^2 = (√y)^2.

Simplify the equation: Simplify the right side of the equation to get x^2/64 = y. This step is done by squaring the square root, resulting in the elimination of the square root symbol.

Replace y with f^(-1)(x): The equation x^2/64 = y represents the inverse function of f(x). To denote this, we replace y with f^(-1)(x) to get f^(-1)(x) = x^2/64.

Therefore, the inverse of the function f(x) = 8√x is f^(-1)(x) = x^2/64. This means that for any given value of x, applying the inverse function will yield the corresponding value of y that satisfies the equation.

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Answer:

5

Step-by-step explanation:

2+2+1=5

The error interval for d is from 391.6 to 391.9 and 392.1 to 392.4.

We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, The depth 'd' of a lake is 392 m, rounded to the nearest integer.

Now a number rounded to the nearest integer to 392 is only possible when the number is less than 392.5 which is 392.4 and greater than 391.5.

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Answer:

X= -4

Step-by-step explanation:

Hello. For to solve that, you need to use the sustitution method:

1. You need clear X in the first equation and put in the second

X+Y = -10

X = -10-Y

2.  Y = X-2, then you replaced the X in this equation:

Y = (-10-Y) - 2

Y+2=-10-Y

2Y=-10-2

2Y= -12

Y= -12/2

Y=-6

3. Now you use the Y value for to solve X:

X=-10-Y, then

X =- 10-(-6)

X = -4

Ortiz would be paid $1056 for working 48 hours under the given pay rate of $22 per hour.

If Ortiz worked for 48 hours at a pay rate of $22 per hour, the calculation of his total earnings can be done by multiplying the number of hours worked by the hourly rate.

To calculate Ortiz's earnings for 48 hours, we multiply 48 by $22, which gives us a total of $1056.

Therefore, Ortiz would be paid $1056 for working 48 hours under the given pay rate of $22 per hour.

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It is found that Ortiz paid $1056 for working 48 hours under the given pay rate of $22 per hour.

We are given that Ortiz worked for 48 hours at a pay rate of $22 per hour

Then the calculation of his total earnings could be done by multiplying the number of hours worked by the hourly rate.

To determine Ortiz's earnings for 48 hours, we multiply 48 by $22, that will gives us a total of $1056.

48 x 22 = 1056

Therefore, Ortiz will be paid 1056 dollars for working 48 hours under the  pay rate of $22 per hour.

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The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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Answer:

Smaller factor/larger figure = 3/6 = ½

Step-by-step explanation:

Scale factor of similar figures is usually the ratio of one to the other.

In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.

Length of smaller figure = 3

Corresponding length of larger figure = 6

Scale factor = smaller figure/larger figure = 3/6

Simplify

Scale factor = ½

The unit rate of the car's speed is 70 miles per hour.

The equation given, d = 70t, represents the relationship between the distance traveled (d) and the time elapsed (t) for the car traveling at a constant speed. To determine the unit rate, we need to find the rate of change of distance with respect to time, which is the coefficient of t in the equation.

In this case, the coefficient is 70, indicating that for every hour (t), the car travels 70 miles (d). Therefore, the unit rate of the car's speed is 70 miles per hour, meaning it is covering a distance of 70 miles in one hour of travel.

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To find the average rate of change in revenue R(x) as x increases from 13 to 26 units, we need to calculate the difference in revenue divided by the difference in units.

First, let's find the revenue at x = 13 units:

R(13) = 46(13) - 0.01(13)²

= 598 - 1.69

= 596.31 dollars

Next, let's find the revenue at x = 26 units:

R(26) = 46(26) - 0.01(26)²

= 1196 - 0.676

= 1195.324 dollars

Now, we can calculate the average rate of change:

Average rate of change = (Change in revenue) / (Change in units)

= (1195.324 - 596.31) / (26 - 13)

= 599.014 / 13

≈ 46.08 dollars per unit

Therefore, the average rate of change in revenue as x increases from 13 to 26 units is approximately $46.08 per unit.

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The formula to use to write cos(17.6p) + cos(8.4p) as a product is: B. sum of cosines: \(2cos(\frac{x\;+\;y}{2} )cos(\frac{x\;-\;y}{2} )\).

The average of the original inputs is \(\frac{x\;+\;y}{2} =13p\)

Half the distance between the original inputs is \(\frac{x\;-\;y}{2} =4.6p\)

The sum as a product is: cos(17.6p) + cos(8.4p) = 2cos(13p)cos(4.6p).

In Mathematics and Geometry, the Bhaskaracharya sum and difference formulas that shows the relationship between sine and cosine values for trigonometric identities (two angles) can be modeled by the following mathematical equation;

cos(u + v) = cos(u)cos(v) - sin(u)sin(v)

cos(u - v) = cos(u)cos(v) + sin(u)sin(v)

cos(u + v) + cos(u - v) = 2cos(u)cos(v)

In this context, the formula to use in writing cos(17.6p) + cos(8.4p) as a product is given by:

sum of cosines: \(2cos(\frac{x\;+\;y}{2} )cos(\frac{x\;-\;y}{2} )\).

For the average of the original inputs, we have:

\(\frac{x\;+\;y}{2} =\frac{17.6\;+\;8.4}{2} \\\\\frac{x\;+\;y}{2} =13p\)

For half the distance between the original inputs, we have:

\(\frac{x\;-\;y}{2} =\frac{17.6\;-\;8.4}{2} \\\\\frac{x\;-\;y}{2} =4.6p\)

Therefore, the sum as a product can be written as follows:

cos(17.6p) + cos(8.4p) = 2cos(13p)cos(4.6p).

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The Laplace transformation is:

                 \(L [f(t)] = \frac{5 - 8e^{-7s} }{2}\)

Rewriting the f in terms of the unit step function:

\(\left \{ {{y=5} for 0\leq t\leq 7 \atop {x=-3}for t\geq 7} \right.\)

⇒ f(t) = 5[u(t) - u (t-7)] - 3u(t -7 )

         = 5u(t) - 8u (t-7)

Unit Step Function:

The unit step function, also known as the Heaviside function, is known in engineering applications as a function that can describe the switching process mathematically. We often encounter functions whose values ​​change rapidly over a certain time unit t.

where,

u(t) = \(\left \{ {{y=1 for t\geq 0} \atop {x=0 for t < 0}} \right.\)

Recall the time-shifting property of the Laplace transform:

    L{u(t - c) f( t - c)}

= \(e^{-es} L{f(t)}\)

Laplace Transformation:

In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace, is an integral transform that transforms a function of real variables (usually t in the time domain) into a function is. Complex variable (complex frequency domain, also called s-domain or s-plane). As transformations are tools for solving differential equations, they have many applications in science and engineering. In particular, it converts ordinary differential equations to algebraic equations and converts convolutions to multiplications.

and the Laplace transform of a constant function,

L[k] = k/s

So we have

L[f(t)] = L[5u(t) - 8u (t-7)]

        =  \(5[L_{1} ] - 8e^{-7s} L[1]\)

Therefore,

\(L [f(t)] = \frac{5 - 8e^{-7s} }{2}\)

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the value of the expression is 12.

To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.

The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.

It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.

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The error in the set of instructions can be resolved by rearranging the steps so they are in sequential order. The Option A is correct.

The most effective solution would be to rearrange the steps so they follow a logical order.

For example, the steps could be rearranged as follows:

Therefore, by doing this would make the instructions clearer and easier to follow. The Option A is correct.

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Answer:

PLz give brainliest

Step-by-step explanation:

Y=60

x=33

The height of the cone with a base radius of 8cm and a slant height of 17cm is 15cm.

Let the height of the cone be h.

Apply Pythagoras' theorem,

h² + r² = l² --------- (1)

where, h⇒ height of the cone

r ⇒ radius of the base of the cone

l ⇒ slant height

Now, as per the question:

The slant height, l = 17 cm

The radius of the base of the cone, r = 8 cm

Substitute the value into equation (1):

h² + 8² = 17²

evaluate the powers:

h² + 64 = 289

subtract 64 from both sides:

h² = 225

Take the square root on both sides:

h = 15

Thus, the height of the cone with a base radius of 8cm and a slant height of 17cm is 15cm.

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Since we have that y is directly proportional to x, then the relationship can be written like this:

Now, since y=12 when x=6, we have the following:

Therefore, the equation would be y = 2x.

Finally, if x=-30, then:

The side lengths of the triangle are:

Longer side= 36m, shorter side= 27m and hypotenuse=45m

Here, we have,

Let x be the longer leg of the triangle

According to the problem, the shorter leg of the triangle is 9 shorter than the longer leg, so the length of the shorter leg is x - 9

The hypotenuse is 9 longer than the longer leg, so the length of the hypotenuse is x + 9

We know that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we can use the Pythagorean theorem:

(x + 9)² = x² + (x - 9)²

Expanding and simplifying the equation:

x² + 18x + 81 = x² + x² - 18x + 81

x²-36x=0

x=0 or, x=36

Since, x=0 is not possible in this case, we consider x=36 as the solution.

Thus, x=36, x-9=27 and x+9=45.

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Answer:

Scenario 1 represents a greater speed

Step-by-step explanation:

scenario 1 - find equation of line on graph to compare

- use the points given to find the slope

rate = slope = (y2-y1)/(x2-x1) = (240-60)/(4-1) = 60

y intercept = 0

line equation -> y = 60x

for every mile, 60 miles are traveled

scenario 2 - interpret the equation

for every mile, 50 miles are traveled

Scenario 1 represents a greater speed

Answer:

2.-2y=x

Step-by-step explanation:-2y=x

y=kx  for constant k

Answer:

f^-1(x) = -4 / x - 2

Step-by-step explanation:

First swap the x and y values. This is done by setting f(x) to x, and x to y.

f(x) = (2x - 4) / x → x = (2y - 4) / y

*Then solve for y like you would for a normal equation*

x = (2y - 4) / y

×y ×y

(multiplication property of equality)

*This will isolate the extra y term*

__________________________

xy = 2y - 4

-2y -2y

(subtraction property of equality)

*This is done to group the like terms together, because they both share a y term now*

_____________________________

xy - 2y = -4

| |

v v

( x - 2 )

(GCF)

*In this case the GCF is y because it is the factor held in common, reverse distributive property*

________________________________

y(x-2) = -4

÷(x-2) ÷(x-2)

(Division property of equality)

*This is the last and final step to isolate the y term completely, so we can find the inverse*

y = -4/x-2

*This is the inverse*

Now just set it in function form as an inverse:

y = -4/x-2 → f^-1(x) = -4/x-2

Aloioi

Step-by-step explanation:

Answer:

C (-6, -1)

Step-by-step explanation:

The given statement is true, according to the question.

Exponents with the same base have a ratio that is equal to the difference between their exponents with the same base. The division rule of exponents with the same base is another name for the quotient law of exponents with the same base.

According to the question,

Division in mathematics involves two exponents with the same base, however unlike dividing numbers, it is not possible to divide one exponential expression by another. As a result, the indices with the same base must be divided using a particular quotient rule.

By subtracting any two exponents with the same base, you may apply the property for dividing powers with the same base to calculate the quotient of any two exponents with the same base.

f'(x) equals [u(x)/v(x)]. '= [v(x) u'(x) - v'(x) u(x)] /[v(x)] 2

where,

The function of the form u(x)/v(x) for which the derivative must be determined is denoted by f(x).

u(x) = A differentiable function that serves as the function f's numerator (x).

Function derivative u'(x) equals u (x).

v(x) = A differentiable function that creates the supplied function f's numerator (x).

V'(x) = The function's derivative v(x).

The quotient rule says that when you are dividing x^m by x^n, you can simply subtract the two exponents (m-n) and keep the same base.

Therefore, the statement is true.

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