Shaq was climbing a cliff. He stopped for a snack. After that, he slipped 20 feet to an earlier foothold and then slipped 4 feet to another foothold. Model the distance Shaq traveled on the cliff after his snack as a sum.

Answer:

Step-by-step explanation:

At the beginning of the day, the temperature was of x.

It dropped 21 degrees to -9C. So

x - 21 = -9

x =

we have

then find c

therefore the distance is:

answer: 21.5 ft

Given,

The area of the regular octagon is 49 square metre.

The area of the another regular octagon is 100 square metre.

Here, the scaling factor of the regualar octagon is 7:10

Hence, the scaling factor is 7:10.

82.26%

The ratio of baskets made by Lebron James = 255/310

To find the percentage equivalent of the ratio, multiply it by 100%

Percentage of the baskets made by Lebron James = 255/310 x 100%

Percentage of the baskets made by Lebron James = 82.26%

Answer:

b)  26%

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

[tex]\large\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]

Given:

[tex]\textsf{Mean}\;\mu=3550[/tex]

[tex]\textsf{Standard deviation}\:\sigma=870[/tex]

Therefore, if the weights of the cars passing over the bridge are normally distributed:

[tex]\boxed{X \sim\text{N}(3550,870^2)}[/tex]

where X is the weight of the car.

To find the approximate probability that the weight of a randomly-selected car passing over the bridge is less than 3000 pounds, find[tex]\text{P}(X < 3000)[/tex].

Calculator input for "normal cumulative distribution function (cdf)":

[tex]\implies \text{P}=0.2636333503[/tex]

[tex]\implies \text{P}=26\%[/tex]

Therefore, the approximate probability that the weight of a randomly-selected car passing over the bridge is less than 3000 pounds is 26%.

Answer:

8 cubic meters

Explanation:

The length of one side of the cube = x

For any cube of side length, x:

Therefore, the volume of the cube with a side length of 2 meters is:

Answer: 104

Step-by-step explanation:

[tex]f(-8)[/tex] represents [tex]f(x)[/tex] evaluated at [tex]x=-8[/tex].

[tex]f(-8)=3(-8)^2 +9(-8)-16\\\\=192-72-16\\\\=120-16\\\\=104[/tex]

The rate of increase in water pressure in atm/km = 992 atm/km

Pressure can be defined as the external or internal force that acts on an area of an object which can be measured in atmosphere per meter.

The rate at which Mustafa dives = 0.992atm/meter.

That is,

0.992 atm = 1 meter

X atm = 1 km

But 1000m = 1 km

make X atm the subject of formula;

x atm = 0.992 × 1000

X atm = 992 atm/km

Therefore, the rate in atm/ km would be = 992 atm/km

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Answer:

There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.

Step-by-step explanation:

Ok, so

Here we have the function:

Now we want to find the tripling-time for this population of deer.

If we make t=0, we will find the initial population of deer. This is:

Now, we want to find the time "t" such that this population is the triple.

This is:

We got this exponential equation:

As the base is the same, we could equal the exponents:

Therefore, tripling-time for this population of deer are 3 years.

When two rays are with a common endpoint, an angle is formed and the common endpoint is called the vertex of the angle

 Polynomial equations are those created using exponents, coefficients, and variables. It may have several exponents, with the higher one being referred to as the equation's degree.

Polynomial equation illustration

     Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.

6h²(5 + 9h)(5 - 9h)

6h²(9h + 5)(5 - 9h)

6h²(9h + 5)(-9h + 5)

6h²(9h + 5)(-9h + 5)

54(-9h +5)h³ + 30(-9h + 5)h²

(-486h)4 + 270h³+30(-9h+5)h²

(-486h)4 + 270h³-270h³+150h²

(-486h)4 + 150h²

(-486h)4 + 150h²

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The equations given are

The graph of the equations will be shown below

Hence, the solution to the equations is the point where the two equations intersect.

Therefore, the solution is

Since angles ACB and ECD are vertical angles, they are congruent, so we have

Calculating the sum of internal angles in triangle ABC, we have:

Since triangles ACB and DCE are congruent, we have [tex]\begin{gathered} DEC=ABC \\ 5x=65 \\ x=13 \end{gathered}[/tex]

A triangle is a shape that has a total angle of 180°.

It's important to note that a triangle is a shape that has three sides and the total sum is equal to 180°.

In this case, we have 2x + 6 and 42°. The other angle isn't given and this can't be solved further

The sides will have been illustrated as:

= a + b + c = 180

The expression given will then be allocated for each side to solve it further.

Note that an overview was given as the information is incomplete.

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Step-by-step explanation:

area of a sector is theta ÷360 ×πr²

Step 1

Given;

Required; To find the value of y that makes the equation true

Step 2

Find the value of y

Hence, the value of y that makes the equation true is 16/3

Sue's total pay for the year given the salary, bonus and share of profit is  £38,110.

Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.

Salary for the year = monthly salary x number of months in a year

£1410 x 12 = £16,920

The next step is to determine the profit last year

Profit = total revenue - total cost

£549,000 - £473,500 = £75,500

Now determine the share of profit that Sue would earn.

Share of profit = 26% x  £75,500

0.26 x  £75,500 = £19,630

Now determine the total bonus she would earn : 4 x £390 = £1560

Total salary = £1560 +  £19,630 +  £16,920 = £38,110

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Given:

Each part costs $7 to produce and distribute.

The total number of parts on selling is 300 to make the profit P.

To write the function expression in terms of sale price C and profit P:

As we know,

So, if we produce 1 part and sell that part, then the profit is

For 300 parts, the profit is

Hence, the function is expressed in terms of P and C is,

Solution:

Given;

IF G and R denote the grade and the radian measure of an angle, i.e.

Where

we are asked to determine the area of a circle with a diameter of 6 cm. To do that we will use the following formula for the area of a circle:

Replacing the value of the radius:

Replacing the value of pi:

Solving the operations:

Answer: 1/4 is the absolute

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Absolute value just means the distance from zero.

The z-score is given by the following formula:

Where x is the data point, μ is the mean, and σ is the standard deviation.

First

We have a right triangle XYZ.

The length of the hypotenuse is YZ=85.

We also know that the tangent of Z is 4.

We have to find the length of XY.

We can start by drawing the triangle and writing the data:

The tangent of an angle can be related with the sides by the following trigonometric ratio:

We can not find the value of the legs from the trigonometric ratio, but we have a proportion between them. We can write the previous result as:

Now we can relate XY with the hypotenuse YZ using the Pythagorean theorem:

Answer: the length of the leg XY is 51 inches.

For statement one:

We need to add up to complex numbers and their sum must give us equal to 10.

Also, we need to use the complex numbers:

5+i√15 and 5-i√15.

Then, we can use:

(5+i√15)+( 5-i√15) =

5+i√15+5-i√15 =

5+5+ i√15-i√15 =

= 10 + 0

= 10

For the second statement:

We need to show the product of complex numbers:

Then, we use:

(5+i√15)(5-i√15))=

5*5 - 5*i√15) +5*i√15) +√15*√15=

25 + 0 + 15=

40

If both triangles are congruent by the HL theorem, then their hypotenuses are equal and at least one of the corresponding legs is equal too.

Hypothenuses:

From this expression, you can calculate the value of m

Legs:

Replace the expression with the calculated value of m

Now pass the n-related term to the left side of the equation and the numbers to the right side:

And divide both sides of the expression by 3

So, for m=3 and n=6 the triangles are congruent by HL

Answer:

Jenny scored 644th place.

Step-by-step explanation:

To find out what place she finished, you need to write it out first like this:

77% of 837.

Now, to make the equation possible to solve, we can take the 77 and make it a decimal: 0.77.

The term "of" means multiplication.

So, in turn, we have the equation:

0.77 x 837 = 644.49

And, if you round it, your answer would be:

Jenny scored 644th place.

Answer:

See below

Step-by-step explanation:

77th percentile means she scored better than 77 per cent of the test takers...

  So Jenny's place was    .23  *  837 = ~ 193 rd   Out of 837 people

A current of 5.5 amps produce across an identical resistor will produce 110Volts across an identical resistor

From above,

Current 1 (I₁) = 14 amps

P.d (V₁) = 280 V

By Ohm's law which states that that for a linear circuit the current flowing through it is proportional to the potential difference across it so the greater the potential difference across any two points the bigger will be the current flowing through it.

V₁ = I₁R

= 280 = 14R

= 20Ω = R

Current 2 (I₂) = 3.5 A

Resistance (R) = 20 Ω

Assuming the resistance stays the same,

Using Ohm's law,

V₂ = I₂R

= 5.5*20

= 110 Volts

110Volts would be produced across an identical resistor

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Answer: We have to find three unknown asked quantities, before we could do that we must find the g(x) from the coordinate points:

The answers are as follows:

The last answer is:

We know that the rod from which we made the triangle is 13 in long, this means that the perimeter of the triangle. from the diagram given we notice that the perimeter is:

equating this to 13 and solving for x we have:

Hence, the value of x=5 which means that the longest side measure 5 inches. To determine the length of the other sides we notice that they are given by x-1, which means that their length is 5-1=4 inches,

Therefore, the length of the longest side is 5 inches. The other two sides will each be 4 inches in length.