Solve the inequality. Using a verbal statement, in simplest terms, describe the solution of the inequality. Be sure to include the terms, “greater than”, “greater than or equal to”, “less than”, or “less than or equal to”.

-2x + 3 > 3(2x - 1)

Answer:

678

Step-by-step explanation:

Answer:

(-1, 11) is a max value; parabola is upside down

Step-by-step explanation:

We can answer this question backwards, just from what we know about parabolas.  This is a negative x^2 parabola, so that means it opens upside down.  Because of this, that means that there is a max value.  

The vertex of a parabola reflects either the max or the min value.  In order to find the vertex, we put the equation into vertex form, which has the standard form:

[tex]y=a(x-h)^2+k[/tex]

where h and k are the coordinates of the vertex.

To put a quadratic into vertex form, you need to complete the square.  That process is as follows. First, set the quadratic equal to 0.  Then make sure that the leading coefficient is a positive 1.  Ours is a -5 so we will have to factor it out.  Then, move the constant to the other side of the equals sign.  Finally, take half the linear term, square it, and add it to both sides.  We will get that far, and then pick up with the rest of the process as we come to it.

[tex]-5x^2-10x+6=y[/tex]

Set it to equal zero:

[tex]-5x^2-10x+6=0[/tex]

Now move the 6 to the other side:

[tex]-5x^2-10x=-6[/tex]

Factor out the -5:

[tex]-5(x^2+2x)=-6[/tex]

Take half the linear term, square it, and add it to both sides.  Our linear term is 2x.  Half of 2 is 1, and 1 squared is 1, so add it to both sides.  Keep it mind that we have the =5 out front of those parenthesis that will not be forgotten.  So we are not adding in a +1, we are adding in a (+1)(-5) which is -5:

[tex]-5(x^2+2x+1)=-6-5[/tex]

In completing the square, we have created a perfect square binomial on the left.  Stating that binomial along with simplifying on the right gives us:

[tex]-5(x+1)^2=-11[/tex]

Now, bring the -11 over to the other side and set it back to equal y and you're ready to state the vertex:

[tex]-5(x+1)^2+11=y[/tex]

The vertex is at (-1, 11)

Answer:

She used inductive reasoning. (False)

She used the law of detachment.  (True)

Her conclusion is valid.  (True)

The statements can be represented as "if p, then q and if q, then r."  (False)

Her conclusion is true. (True)

Step-by-step explanation:

p = Two lines are perpendicular

q = They intersect at Right angles.

Given: A and B are perpendicular

Conclusion: A and B intersect at right angle.

According to the law of detachment, There are two premises (statements that are accepted as true) and a conclusion. They must follow the pattern as shown below.

Statement 1: If p, then q.

Statement 2: p

Conclusion: q

In our case the pattern is followed. The truth of the premises logically guarantees the truth of the conclusion. So her conclusion is true and valid.

Answer:

it's b, c, e

Step-by-step explanation:

Answer:

89

Step-by-step explanation:

So the line segment CD is 12.7 and half that is 6.35.  I wanted this 6.35 so I can look at the right triangle there and find the angle there near the center.  This will only be half the answer.  So I will need to double that to find the measure of arc CD.  

Anyways looking at angle near center in the right triangle we have the opposite measurement, 6.35, given and the hypotenuse measurement, 9.06, given. So we will use sine.

sin(u)=6.35/9.06

u=arcsin(6.35/9.06)

u=44.5 degrees

u represented the angle inside that right triangle near the center.  

So to get angle COD we have to double that which is 89 degrees.  

So the arc measure of CD is 89.  

Answer:

After how many years is the fish population 100?

x=3.97 years

Step-by-step explanation:

The fish population increases by a factor of 1.5 each year. We have the equation that represents this situation

[tex]f (x) = 20 (1.5) ^ x[/tex]

Where x represents the number of years elapsed f(x) represents the amount of fish.

Given this situation, the following question could be posed

After how many years is the fish population 100?

So we do [tex]f (x) = 100[/tex] and solve for the variable x

[tex]100 = 20 (1.5) ^ x\\\\\frac{100}{20} = (1.5)^x\\\\ 5= (1.5)^x\\\\log_{1.5}(5) = log_{1.5}(1.5)^x\\\\log_{1.5}(5) = x\\\\x =log_{1.5}(5)\\\\x=3.97\ years[/tex]

Observe the solution in the attached graph

Dave and Ellen could annually save $27 by installing dead-bolts and $9 by installing smoke detectors. This amounts to a significant discount on their homeowner's insurance premium.

Dave and Ellen's annual homeowner's insurance premium is $450. If they install dead-bolts on all the exterior doors, they would receive a 6 percent discount, while smoke detector installations would fetch them a 2 percent discount. Let's calculate these discounts:

A. Dead-bolts discount: 6 percent of $450 translates to $(450*(6/100)) which equals $27.

B. Smoke detectors discount: 2 percent of $450would be $(450*(2/100)) that equals $9.

To summarize, the couple could annualy save $27 by installing dead-bolts and $9 by installing smoke detectors, which is a substantial reduction on the insurance premium.

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Dave and Ellen can save $27 annually by installing dead-bolt locks and $9 annually by installing smoke detectors. Total savings from both installations would be $36 annually.

Let's break down the problem step by step to calculate the discounts that Dave and Ellen will receive if they install dead-bolt locks and smoke detectors.

Part (a): Discount for Dead-Bolt Locks

1. Annual premium: $450

2. Discount for dead-bolt locks: 6%

The discount amount is calculated as follows:

[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]

So, for the dead-bolt locks:

Discount amount for dead-bolt locks = 450 × [tex]\frac{6}{100} \][/tex]

Discount amount for dead-bolt locks = 450 × 0.06

Discount amount for dead-bolt locks = 27

Thus, Dave and Ellen will receive an annual discount of $27 if they install dead-bolt locks on all exterior doors.

Part (b): Discount for Smoke Detectors

1. Annual premium: $450

2. Discount for smoke detectors: 2%

The discount amount is calculated as follows:

[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]

So, for the smoke detectors:

Discount amount for smoke detectors} = 450 × [tex]\frac{2}{100}[/tex]

Discount amount for smoke detectors} = 450 × 0.02

Discount amount for smoke detectors} = 9

Thus, Dave and Ellen will receive an annual discount of $9 if they install smoke detectors on each floor of their house.

Answer:

  $1516.69 per month less

Step-by-step explanation:

The formula for the monthly payment A on a loan of principal P, annual rate r, for t years is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

For the 18.5% loan, the monthly payment is ...

  A = 150000(.185/12)/(1 -(1 +.185/12)^(-12·30)) ≈ 2321.92

For the 5% loan, the monthly payment is ...

  A = 150000(.05/12)/(1 -(1 +.05/12)^-360) ≈ 805.23

The mortgage at 5% would be $1516.69 less per month.

Final answer:

To determine how much less per month a $150,000 30-year mortgage would be at a 5% interest rate compared to an 18.5% rate, calculate monthly payments for both scenarios and subtract the lower payment from the higher one.

Explanation:

The question asks to compare monthly mortgage payments in two different interest rate scenarios for a 30-year, $150,000 mortgage: first at an 18.5% interest rate which was the average in the 1980s, and second at the current rate of 5%. To find out how much less the monthly payment would be at 5% compared to 18.5%, we can use the formula for calculating monthly mortgage payments:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

where:

M is your monthly payment.

P is the principal loan amount, $150,000 in this case.

i is your monthly interest rate. The annual rate needs to be divided by 12.

n is the number of payments (the number of months you will be paying the loan).

Calculating the monthly payment for an 18.5% interest rate over 30 years:

P = $150,000

i = 18.5% annual interest rate / 12 months = 1.5417% monthly interest rate

n = 30 years * 12 months/year = 360 payments

Doing the same calculation at a 5% interest rate:

P = $150,000

i = 5% annual interest rate / 12 months = 0.4167% monthly interest rate

n = 30 years * 12 months/year = 360 payments

After computing the monthly payments for both interest rates, we then subtract the monthly payment at 5% from the monthly payment at 18.5% to determine how much less it would be. As this is a high school-level mathematics problem, we use algebraic operations and functions to answer the question.

Answer:

Part 1) Option A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft.

Part 2) Option  A. 16 cm; 21 cm; 32 cm

Step-by-step explanation:

Part 1)

we have

[tex]h(t)=-16t^{2}+150[/tex]

where

t ----> is the time in seconds after the ball is dropped

h(t) ----> he height in feet of a ball dropped from a 150 ft

Find h(2)

That means ----> Is the height of the ball  2 seconds after the ball is dropped

Substitute the value of t=2 sec in the equation

[tex]h(2)=-16(2)^{2}+150=86\ ft[/tex]

therefore

After 2 seconds, the height of the ball is 86.00 ft.

Part 2) The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the lengths of the sides

Let

x----> the measure of the shortest side

y ----> the measure of the  middle side

z-----> the measure of the longest side

we know that

The perimeter of the triangle is equal to

P=x+y+z

P=69 cm

so

69=x+y+z -----> equation A

x=y-5 ----> equation B

z=(x+y)-5 ----> equation C

substitute equation B in equation C

z=(y-5+y)-5

z=2y-10 -----> equation D

substitute equation B and equation D in equation A and solve for y

69=(y-5)+y+2y-10

69=4y-15

4y=69+15

4y=84

y=21 cm

Find the value of x

x=21-5=16 cm

Find the value of z

z=2(21)-10=32 cm

The lengths of the sides are 16 cm, 21 cm and 32 cm

yeah it does because $68,000 is a numerical description of a sample of annual salaries. so it is only a PARAMETER

--mark brainliest please! thank you and i hope this helps

Answer:

8,000-24x

Step-by-step explanation:

Let

y ----> depreciated value of the car

x---> rate of depreciation

t ----> the time in months

we know that

The linear equation that represent this situation is

y=8,000-xt

For

t=2 years=2*12=24 months

substitute

y=8,,000-x(24)

y=8,000-24x

Answer:

the answer is 90

Step-by-step explanation:

296-96=90

Final answer:

To find the probability of the mean weight of 25 randomly selected ice cream cartons being greater than 20.06 ounces, we can use the Central Limit Theorem. By calculating the standard error, finding the z-score, and using a z-table or calculator, we can determine the probability.

Explanation:

To find the probability that the mean weight of 25 randomly selected ice cream cartons is greater than 20.06 ounces, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means from a population with any distribution will be approximately normal, as long as the sample size is large enough.

First, we need to find the standard error of the mean (SE). The formula for SE is SE = standard deviation / √(sample size). In this case, the standard deviation is 0.3 ounces and the sample size is 25. So, SE = 0.3 / √25 = 0.06 ounces.

Next, we calculate the z-score, which measures how many standard deviations the mean is from the population mean. The formula for z-score is z = (sample mean - population mean) / standard error. In this case, the sample mean is 20.06 ounces, the population mean is 20.1 ounces, and the standard error is 0.06 ounces. So, z = (20.06 - 20.1) / 0.06 = -0.67.

We can use a z-table or a calculator to find the probability associated with the z-score. From the table or calculator, we find that the probability of getting a z-score greater than -0.67 is approximately 0.748. Therefore, the probability that the mean weight of the 25 ice cream cartons is greater than 20.06 ounces is approximately 0.748.

Answer:

  9t^3 +t^2

Step-by-step explanation:

The perimeter of the figure is the sum of the lengths of the sides. The side lengths are represented by the polynomials shown, so the perimeter (P) is their sum:

  P = (4t^3 -5) + (4t^3 -5) + (t^2 +9) + (t^3 -t^2 -11) + (t^2 +12)

Rearranging to group like terms:

  P = (4t^3 +4t^3 +t^3) + (t^2 -t^2 +t^2) + (-5 -5 +9 -11 +12)

  P = 9t^3 +t^2

The perimeter of the figure is represented by the polynomial 9t^3 +t^2.

Answer:

[tex]9t^3+t^2[/tex]

Step-by-step explanation:

We are given a figure of a polygon with mentioned side lengths and we are to find the perimeter of it.

For that, we will simply add the given side lengths and simplify them.

Perimeter of polygon = [tex] ( 4 t ^ 3 - 5 ) + ( 4 t ^ 3 - 5 ) + ( t ^ 2 + 9 ) + ( t ^ 2 + 1 2 ) + ( t ^ 3 - t ^ 2 - 1 1 ) [/tex]

= [tex] 4 t ^ 3 + 4 t ^ 3 + t ^ 3 + t ^ 2 - t ^ 2 + t ^ 2 - 5 - 5 + 9 - 1 1 + 1 2 [/tex]

Perimeter of polygon = [tex]9t^3+t^2[/tex]

Answer:

The product is:

[tex]-28x^4y^6[/tex]

Step-by-step explanation:

We need to find product of the terms:

-4x3y2(7xy4)

For multiplication we multiply constants with constants and power of same variables are added

[tex]-4x^3y^2(7xy^4)\\=(-4*7)(x^3*x)(y^2*y^4)\\=(-28)(x^{3+1})(y^{2+4})\\=(-28)(x^4)(y^6)\\=-28x^4y^6[/tex]

So, the product is:

[tex]-28x^4y^6[/tex]

Answer:

a) The volume in cubic inches is 36000

b) The volume in cubic feet is 125/6

c) The volume in cubic yard is 125/162

Step-by-step explanation:

* Lets study the information of the problem to solve it

- The dimensions of the piece of cardboard are 90 inches by 70 inches

- The side of the cutting square is 15 inches

- The squares are cutting from each corner

∴ Each dimension of the cardboard will decrease by 2 × 15 inches

∴ The new dimensions of the piece of cardboard are;

90 - (15 × 2) = 90 - 30 = 60 inches

70 - (2 × 15) = 70 - 30 = 40 inches

- The dimensions of the box will be:

# Length = 60 inches

# width = 40 inches

# height = 15 inches

- The volume of any box with three different dimensions is

V = Length × width × height

∵ The length = 60 inches

∵ The width = 40 inches

∵ The height = 15 inches

∴ V = 60 × 40 × 15 = 36000 inches³

a) The volume in cubic inches is 36000

* Now lets revise how to change from inch to feet

- 1 foot = 12 inches

∵ 1 foot = 12 inches

∴ 1 foot³ = (12)³ inches³

∴ 1 foot³ = 1728 inches³

∵ The volume of the box is 36000 inches³

∴ The volume of the box in cubic feet = 36000 ÷ 1728 = 125/6  

b) The volume in cubic feet is 125/6

* Now lets revise how to change from feet to yard

- 1 yard = 3 feet

∵ 1 yard = 3 feet

∴ 1 yard³ = (3)³ feet³

∴ 1 yard³ = 27 feet³

∵ The volume of the box is 125/6 feet³

∴ The volume of the box in cubic yard = 125/6 ÷ 27 = 125/162  

c) The volume in cubic yard is 125/162

Answer:

3600 cubic inches , 2.08 cubic feet , 0.0771 cubic yards

Step-by-step explanation:

Here we are given that the open box has been constructed from a card board with length 90 inches and width 70 inches by

1. cutting  a square card board

2. of each side 15 inches

Hence when we are done with folding it for our cuboid , we find our new

1. Length = 90-15-15 = 60 inches

2. width = 70-15-15 = 40 inches

3. Height = 15 inches

Now we know the volume of any cuboid is given as

V= Length * width * height

 = 60*40*15

 = 3600 cubic inches

Part 2 . Now let us convert them into  cubic feet

1 cubic inch = 0.000578704 cubic feet

Hence 3600 cubic inches = 3600 * 0.000578704  cubic feet

                                           =2.083 cubic feet

Part 3. Now let us convert them into  cubic yards

1 cubic inch = 0.0000214335 cubic yards

Hence 3600 cubic inches = 3600 * 0.0000214335 cubic yards

                                           = 0.0771 cubic yards

For this case we have the following expression:

[tex](\frac {-27x ^ 0 * y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

By definition we have to:

[tex]a^0= 1[/tex]

So:

[tex](\frac {-27y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

Simplifying:

[tex](\frac {-y ^ {- 2}} {2x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So, rewriting the expression we have:

[tex]\frac {-y ^ {- 2 * -2}} {4x ^ {- 5 * -2} * y ^ {- 4 * -2}} =\\\frac {-y ^ {4}} {4x ^ {10} * y ^ {8}} =[/tex]

SImplifying:

[tex]\frac {-y ^ {4-8}} {4x ^ {10}} =\\\frac {-y ^ {- 4}} {4x ^ {10}} =\\- \frac {1} {4x ^ {10} y^ {4}}[/tex]

Answer:

[tex]- \frac {1} {4x ^ {10} y ^ {4}}[/tex]

Answer:

  8.   D. Constant

  6.   A. No

  16.   A. No solution

Step-by-step explanation:

8. There is no "x" on the right side of the equal sign in the function definition. There is only the constant 13/6. The function shown is constant.

__

6. The equation will graph as a parabola that opens to the right. Solving for y, you get ...

  y = ±√(x+3)

This is double-valued. A relation that gives two values for the same value of x is not a function.

__

16. In standard form, the two equations are ...

These equations are "inconsistent". There are no values of x and y that can make them both be true. Thus, there is no solution.

Answer:

The area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.

Step-by-step explanation:

We need to find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28.

The standard normal table represents the area under the curve.

[tex]P(z<-2.94)\cup P(z>-2.28)=P(z<-2.94)+P(z>-2.28)[/tex]          .....(1)

According to the standard normal table, we get

[tex]P(z<-2.94)=0.0016[/tex]

[tex]P(z>-2.28)=1-P(z<-2.28)=1-0.0113=0.9887[/tex]

Substitute these values in equation (1).

[tex]P(z<-2.94)\cup P(z>-2.28)=0.0016+0.98807=0.9903[/tex]

Therefore the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.

The area under the standard normal curve to the left of z  = −2.94 and to the right of z = −2.28 is 0.9903 square units.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 will be

The standard normal table represents the area under the curve.

[tex]\rm P(z < -2.94) \cap P(z > -2.28) = P(z < -2.94) + P(z > -2.28)[/tex] ...1

According to the standard normal table, we have

[tex]\rm P(z < -2.94) = 0.0016\\\\P(z > -2.94) = 1- P(z < -2.94) = 1-0.0113 = 0.9887[/tex]

Substitute these values in equation 1, we have

[tex]\rm P(z < -2.94) \cap P(z > -2.28) = 0.0016 + 0.9887 = 0.9903[/tex]

More about the normal distribution link is given below.

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Answer: 0.14

Step-by-step explanation:

Given: Mean : [tex]\lambda=15\text{ per seconds}[/tex]

In minutes , Mean : [tex]\lambda=4\text{ per minute}[/tex]

The exponential distribution function with parameter [tex]\lambda[/tex]  is given by :-

[tex]f(t)=\lambda e^{-\lambda t}, \text{ for }x\geq0[/tex]

The probability of waiting more than 30 seconds i.e. 0.5 minutes is given by the exponential function :-

[tex]P(X\geq0.5)=1-P(X\leq0.5)\\\\=1-\int^{0.5}_{0}4e^{-4t}dt\\\\=1-[-e^{-4t}]^{0.5}_{0}\\\\=1-(1-e^{-2})=1-0.86=0.14[/tex]

Hence, the probability of waiting more than 30 seconds = 0.14

The probability of waiting more than 30 seconds for a job, when jobs arrive every 15 seconds on average, can be calculated using the Poisson distribution model. The probability is approximately 13.5%.

This problem involves the concept of Poisson distribution, which is a mathematical concept used to model events such as the arrival of customers in a given time interval. Since the question states that jobs arrive every 15 seconds on average, we can use this information to calculate the probability of waiting more than 30 seconds.

In a Poisson distribution, the average rate of arrival (λ) is 1 job every 15 seconds. This rate can be converted to a rate per 30 seconds by multiplying by 2, giving us λ=2. The probability that no jobs arrive in a 30-second interval in a Poisson distribution is given by the formula:

P(X=0) = λ^0 * e^-λ / 0! = e^-2 ≈ 0.135

This means that the probability of waiting more than 30 seconds is approximately 0.135, or 13.5%.

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let's recall that on the IV Quadrant the sine/y is negative and the cosine/x is positive, whilst the hypotenuse is never negative since it's just a distance unit.

[tex]\bf \stackrel{\textit{on the IV Quadrant}}{cot(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{opposite}{-7}}}\qquad \impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{6^2+(-7)^2}\implies c=\sqrt{36+49}\implies c=\sqrt{85} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{adjacent}{6}}\qquad \qquad sec(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{adjacent}{6}}\qquad \qquad csc(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{opposite}{-7}}[/tex]

[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{\cfrac{-7}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies -\cfrac{7\sqrt{85}}{85}} \\\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{\cfrac{6}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies \cfrac{6\sqrt{85}}{85}}[/tex]

Answer:

These are the five remaining trigonometric functions:

Explanation:

Quadrant IV corresponds to angle interval 270° < θ < 360.

In this quadrant the signs of the six trigonometric functions are:

The expected values of the five remaining trigonometric functions of θ are:

1) Tangent:

2) Secant

       sec θ = ± (√85)/ 6

       Choose positive, because secant is positive in Quadrant IV.

       sec θ = (√85) / 6

3) Cosine

4) Sine

       sin²θ = 1 - 36×85/(85)² = 1- 36/85 = 49/85

       sinθ = ± 7 / (√85) = ± 7(√85)/85

       Choose negative sign, because it is Quadrant IV.

       sinθ = - 7 (√85) / 85

5) Cosecant

Answer:

Height of cables = 23.75 meters

Step-by-step explanation:

We are given that the road is suspended from twin towers whose cables are parabolic in shape.

For this situation, imagine a graph where the x-axis represent the road surface and the point (0,0) represents the point that is on the road surface midway between the two towers.

Then draw a parabola having vertex at (0,0) and curving upwards on either side of the vertex at a distance of [tex]x = 600[/tex] or [tex]x = -600[/tex], and y at 95.

We know that the equation of a parabola is in the form [tex]y=ax^2[/tex] and here it passes through the point [tex](600, 95)[/tex].

[tex]y=ax^2[/tex]

[tex]95=a \times 600^2[/tex]

[tex]a=\frac{95}{360000}[/tex]

[tex]a=\frac{19}{72000}[/tex]

So new equation for parabola would be [tex]y=\frac{19x^2}{72000}[/tex].

Now we have to find the height [tex](y)[/tex]of the cable when [tex]x= 300[/tex].

[tex]y=\frac{19 (300)^2}{72000}[/tex]

y = 23.75 meters

Answer: 23.75 meters

Step-by-step explanation:

If we assume that the origin of the coordinate axis is in the vertex of the parabola. Then the function will have the following form:

[tex]y = a (x-0) ^ 2 + 0\\\\y = ax ^ 2[/tex]

We know that when the height of the cables is equal to 95 then the horizontal distance is 600 or -600.

Thus:

[tex]95 = a (600) ^ 2[/tex]

[tex]a = \frac{95} {600 ^ 2}\\\\a = \frac {19} {72000}[/tex]

Then the equation is:

[tex]y = \frac{19}{72000} x ^ 2[/tex]

Finally the height of the cables at a point 300 meters from the center is:

[tex]y = \frac{19}{72000}(300) ^ 2[/tex]

[tex]y =23.75\ meters[/tex]

Answer:

11

Step-by-step explanation:

-2×pi is approximately-6.28

3×sqrt(2) is approximately 4.24

Now if you really need... just list out the integers between those two numbers and then count like so: -6,-5,-4,-3,-2,-1,0,1,2 3,4

That is 11 integers

The question is about finding the number of integers between -2π and 3√2. This involves understanding the definition of the function a*b, and then applying this to the given values. The correct answer is 11.

The function a*b defined in this problem represents the number of integers greater than a and less than b.

When we substitute a with -2π and b with 3√2, we are basically finding the number of integers between -2π and 3√2.

Knowing that -2π is approximately -6.28, and 3√2 which is approximately 4.24, we count the integers that fall between these two numbers.

Our list of integers will be: -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4. Hence, the answer is 11 (option c).

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Answer:

[tex]4a^{2}[/tex]

Step-by-step explanation:

We need to simplify the following expression:

[tex]y=\frac{32a^{3}b^{2}}{8ab^{2}}[/tex]

We know that: [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]. Applying this rule, we have that:

[tex]y = \frac{32a^{3}b^{2}}{8ab^{2}} = 4a^{3-1}b^{2-2} = 4a^{2}[/tex]

Then, the solution is: [tex]4a^{2}[/tex]

Answer: The ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]

Step-by-step explanation:

Since we have given that

Radius of first sphere = 5 inches

Radius of second sphere = 10 inches

We need to find the ratio of volume of first sphere to volume of second sphere:

As we know the formula for "Volume of sphere ":

[tex]Volume=\dfrac{4}{3}\pi r^3[/tex]

So, it becomes,

Ratio of first volume to second volume is given by

[tex]\dfrac{4}{3}\pi (5)^3:\dfrac{4}{3}\pi (10)^3\\\\=5^3:10^3\\\\=125:1000\\\\=1:8[/tex]

Hence, the ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]

The ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches is 1/8.

To find the ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches, we can use the formula for the volume of a sphere, which is V = (4/3)πr³. Let's calculate the volumes of the two spheres:

For the sphere with a radius of 5 inches:

V1 = (4/3)π(5)³ = (4/3)π(125) = 500π inches³

For the sphere with a radius of 10 inches:

V2 = (4/3)π(10)³ = (4/3)π(1000) = 4000π inches³

Therefore, the ratio of the two volumes is:

R = V1/V2 = (500π)/(4000π) = 1/8

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Answer:

  (-9, 6)

Step-by-step explanation:

It's all about pattern matching.

A circle centered at (h, k) with radius r has the equation ...

  (x -h)^2 + (y -k)^2 = r^2

Comparing this pattern to the equation you have, you can see that ...

Then the center is (h, k) = (-9, 6).

Answer:

 (-9, 6)

Step-by-step explanation:

i took the test

Answer: Our required probability is 47.3%.

Step-by-step explanation:

Since we have given that

Probability of schools or district in a country use digital content = 86% = 0.86

Probability of schools or district uses digital content as a part of their curriculum out of 86% = [tex]\dfrac{11}{20}[/tex]

So, Probability that a selected school or district uses digital content and uses it as a part of their curriculum is given by

[tex]\dfrac{86}{100}\times \dfrac{11}{20}\\\\=0.86\times 0.55\\\\=0.473\\\\=47.3\%[/tex]

Hence, our required probability is 47.3%.

The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3% and this can be determined by using the given data.

Given :

The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is given by:

[tex]=\dfrac{11}{20}\times \dfrac{86}{100}[/tex]

Now, multiply 11 by 86 and also multiply 20 by 100 in the above expression.

[tex]=\dfrac{11\times 86}{20\times 100}[/tex]

SImplify the above expression.

[tex]=\dfrac{946}{2000}[/tex]

= 0.473

So, the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3%.

For more information, refer to the link given below:

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Answer: 0.42

Step-by-step explanation:

Given: Mean : [tex]\mu=954\text{ dollars}[/tex]

Standard deviation : [tex]234\text{ dollars}[/tex]

Sample size : [tex]n=61[/tex]

The formula to calculate z score is given by :-

[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For X=960

[tex]z=\dfrac{960 -954}{\dfrac{234}{\sqrt{61}}}=0.200262812203\approx0.2[/tex]

The p-value =[tex]P(X\geq960)=1-P(X<960)=1-P(z<0.2)=1-0.5792597=0.4207403\approx0.42[/tex]

Hence,  the probability that a single randomly selected value is at least 960 dollars = 0.42

Answer:9

Step-by-step explanation:

1st triangle is similar to the second one as the angles of both of the triangles are the same..

So we know the ratio of the similar lines will be constant.it means,

XY/PQ=XZ/PR=YZ/QR

So,Xy/PQ=XZ/PR

21/7=27/x

X=(27×7)/21

X=9

Thats the value of pr..

Answer:

[tex]y^{2}=-16x[/tex]

Step-by-step explanation:

we know that

The standard equation of a horizontal parabola is equal to  

[tex](y-k)^{2}=4p(x-h)[/tex]

where

(h,k) is the vertex

(h+p,k) is the focus

In this problem we have

(h,k)=(0,0) ----> vertex at origin

(h+p,k)=(-4,0)

so

h+p=-4

p=-4

substitute the values

[tex](y-0)^{2}=4(-4)(x-0)[/tex]

[tex]y^{2}=-16x[/tex]