The width of a rectangle is fixed at 7 cm. Determine (in terms of an inequality) those lengths for which the area will be
less than 175 cm²

Using Euler's formula, the expressions can be rewritten as Im = sin(e^j) - sinh(1), exp(e^j) = e^(cos(1) + j*sin(1)) and e^[(1/2)√(2)e^(j(π/4+2π*n))] respectively

1.

Cos(e^j) can be expressed using Euler's formula as:

Cos(e^j) = (e^(je^j) + e^(-je^j)) / 2

= (cos(e^j) + cosh(1)) + j(sin(e^j) - sinh(1))

Re = cos(e^j) + cosh(1)

Im = sin(e^j) - sinh(1)

2.

exp(e^j) can also be expressed using Euler's formula as:

exp(e^j) = e^(cos(1) + j*sin(1))

3.

(sqrt(j))^sqrt(j) can be written as:

(sqrt(j))^sqrt(j) = e^[(1/2)√(2)e^(j(π/4+2π*n))]

where n is an integer. This is because the logarithm of a complex number has infinitely many possible values due to the periodicity of the exponential function.

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Answer:

RJ and his 2 brothers are given a weekly allowance of PHP 2,000. They have allocated 60% for food, 8% for fare, 15% for school needs, and 17% for savings.

For food, the allocation would be: PHP 2,000 x 60% = PHP 1,200.

For fare, the allocation would be: PHP 2,000 x 8% = PHP 160.

For school needs, the allocation would be: PHP 2,000 x 15% = PHP 300.

For savings, the allocation would be: PHP 2,000 x 17% = PHP 340.

So, for food, the allocation is PHP 1,200, for fare, it's PHP 160, for school needs, it's PHP 300, and for savings, it's PHP 340

The value of x is 9 by using the concept of corresponding angles.

Corresponding angles are the angles formed when two parallel lines are crossed by any other line. It may also be generated in matching edges(corners) or corresponding corners with the transversal.

From the information given:

(8x + 9) is corresponding to the opposite side of the transversal with an angle of 99 degrees.

Using the sum of angles on a straight line.

Step 1: (8x + 9)° + 99 = 180°

Step 2: 8x + 108 = 180

Step 3: 8x = 72

Step 4: x = 9

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Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

What is meant by budget?

Let's assume that Hannah needs to use x gallons of soda and y gallons of fruit drink to make 168 gallons of punch.

We know that the cost of soda is $1.57 per gallon and the cost of fruit drink is $2.41 per gallon, and Hannah's budget requires that the punch cost $1.66 per gallon.

So we can set up the following system of equations:

x + y = 168 (total amount of punch)

1.57x + 2.41y = 1.66(168) (total cost of punch)

Simplifying the second equation:

1.57x + 2.41y = 278.88

Now we can use substitution or elimination method to solve for x and y.

Using substitution:

x = 168 - y

1.57(168 - y) + 2.41y = 278.88

264.36 - 1.57y + 2.41y = 278.88

0.84y = 14.52

y = 17.29

So Hannah needs 17.29 gallons of fruit drink.

Using x + y = 168, we can find that she needs 150.71 gallons of soda.

Therefore, Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

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The average daily balance for Pete's credit card last month was a dollars. The finance charge was f dollars. APR algebraically is: 12f/a.

Finance charge = Monthly interest rate · Average daily balance

Monthly interest rate = APR/12

Where:

Finance charge = f

Average daily balance = a

f= Monthly interest rate · a

f = APR/12 · a

f/a  = APR/12

12.f/a = APR

Therefore APR algebraically is: 12f/a.

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Answer:

The height of the triangle is 14 m,

Step-by-step explanation:

Let the base be x, then the height is:

The area is half the product of base and height.

Set up equation and solve for x:

The first root is discarded as negative. The second root is the answer.

The base is 3 m, so the height is:

Answer:

The height of the triangle is 14 m.

Step-by-step explanation:

The area of a triangle can be found by using the following formula:

[tex]\boxed{A=\dfrac{1}{2}bh}[/tex]

where:

If the height of a triangle is 8 m more than twice the length of the base, then an expression for h in terms of b is:

[tex]h = 2b + 8[/tex]

Rewrite this equation to make b the subject:

[tex]\implies 2b=h-8[/tex]

[tex]\implies b=\dfrac{1}{2}h-4[/tex]

Given the area of the triangle is 21 m², substitute this value along with the found expression for b into the formula for area of a triangle:

[tex]\implies \dfrac{1}{2}\left(\dfrac{1}{2}h-4\right)h=21[/tex]

To find the height of the triangle, solve the equation for h.

[tex]\implies \dfrac{1}{4}h^2-2h=21[/tex]

[tex]\implies h^2-8h=84[/tex]

[tex]\implies h^2-8h-84=0[/tex]

[tex]\implies h^2-14h+6h-84=0[/tex]

[tex]\implies h(h-14)+6(h-14)=0[/tex]

[tex]\implies (h+6)(h-14)=0[/tex]

Apply the zero-product property:

[tex]h+6=0 \implies h=-6[/tex]

[tex]h-14=0 \implies h=14[/tex]

As length cannot be negative, the height of the triangle is 14 m.

The y-intercept b of the equation of the line is 30.

The graph represent a linear relationship between the temperature in degree farad and time in minutes.

Therefore, let's find the y-intercept b of the equation.

Hence, using slope intercept form,

y = mx + b

where

Therefore,

y = 20x + b

where

Using (6, 150) let's find b as follows:

y = 20x + b

150 = 20(6) + b

150 - 120 = b

Therefore,

b = 30

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Answer: the weight of the wheat still in the truck is 5000 pounds.

Step-by-step explanation:

Here are the steps to calculate the weight of the wheat still in the truck:

Convert the weight of the unloaded wheat to tons. To convert from pounds to tons, divide by 2,000:

1000 lbs / 2000 lbs/ton = 0.5 tons

Subtract the weight of the unloaded wheat from the original weight:

3 tons - 0.5 tons = 2.5 tons

Convert the answer back to pounds:

2.5 tons * 2000 lbs/ton = 5000 lbs

Therefore, the weight of the wheat still in the truck is 5000 pounds.

Answer:

3 inches is approximately equal to 76.2 millimeters.

Step-by-step explanation:

Answer:

3 inches = 76.2 millimeters

Step-by-step explanation:

The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

The test statistic for this hypothesis test can be calculated as follows:

t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)

Plugging in the values, we get:

t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36

Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator.

Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.

Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

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Answer:

This system of equations can be solved using substitution or elimination methods.

Using substitution, we can solve for one of the variables in one of the equations and substitute that expression into the other equation.

Solving for x in the second equation:

x + 3y = 1

x = 1 - 3y

Substituting this expression for x into the first equation:

-4(1 - 3y) - 15y = -10

Expanding and solving for y:

-4 + 12y - 15y = -10

12y - 4 = -10

12y = -6

y = -1/2

Now that we know y = -1/2, we can substitute this value back into the expression for x:

x = 1 - 3(-1/2) = 1 + 3/2 = 7/2

So the solution to the system of equations is (7/2, -1/2).

Checking the solution in both equations:

-4(7/2) - 15(-1/2) = -4(7/2) + 15/

Step-by-step explanation:

Answer:

  77.5°

Step-by-step explanation:

You want the measures of the angles formed when ray OX bisects the 155° angle AOB.

The angle bisector creates two equal angles, each of which is half the measure of the original angle. The measures of the angles formed are ...

  155°/2 = 77.5°

On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:

weight

x = 15bags X 28/1 X 0.453

x = 258.21 kg

volume

x = 15 X 4/27 = 2.222 yd

15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

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On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:

weight

x = 15bags X 28/1 X 0.453

x = 258.21 kg

volume

x = 15 X 4/27 = 2.222 yd

15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

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12 hours

If it takes 6 people 8 hours to finish a job, then 24 would take 2 hours, and then 4 would take 12 hours

Answer:

5.333 hours.

Step-by-step explanation:

Put this on a chart:

6 people = 8 hours

4 people = ? hours

To find ? Use crisscross multiplication and solve:

? = (4 * 8) / 6

? = 32 / 6

? = 5.333

Therefore, if it takes 6 people 8 hours to finish a job then it will take 5.333 hours for 4 people to finish a job.

The probability that the hiker will reach his destination is, 1/2

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Since the hiker chooses one of the four trails with equal probability by rolling a fair 4-sided die,

the probability of taking any one trail is 1/4.

Once the hiker is on a trail, there are two sub-trails, and the hiker chooses one of them by flipping a fair coin.

The probability of taking the correct sub-trail is 1/2.

P(reaching destination) = P(trail 1) x P(correct sub-trail on trail 1) + P(trail 2) x P(correct sub-trail on trail 2) + P(trail 3) x P(correct sub-trail on trail 3) + P(trail 4) x P(correct sub-trail on trail 4)

P(reaching destination) = (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2)

P(reaching destination) = 4/8

P(reaching destination) = 1/2

Therefore, the probability that the hiker will reach his destination is 1/2, or 50%.

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Answer:

the answer to this question is 936

Answer:

Step-by-step explanation:

Here's a step by step explanation for writing a function to approximate the number of annual visitors to the overlook x years after the nature center is built:

Start by defining the initial number of visitors as the baseline. We'll call this y0 and set it equal to 3,500 tourists:

y0 = 3,500

Define the rate of growth as a percentage increase. We're told that the number of visitors is expected to increase by 5% each year, so we'll call this rate "r" and set it equal to 0.05:

r = 0.05

Write the equation for exponential growth. The formula for exponential growth is given by:

y = y0 × (1 + r)^x

where x is the number of years after the nature center is built.

So, the equation for the function in this case would be:

f(x) = 3,500 × (1 + 0.05)^x

This function models the expected number of annual visitors to the overlook x years after the nature center is built. The function is exponential because the number of visitors is multiplied by a constant factor (1 + 0.05) raised to a power (x) at each time step.

Answer:

89392i + 788

Step-by-step explanation:

The divide by 5 and the multiply by 5 cancel out, and we cannot simplify 89392i + 788 any further, since we don't know what i is. Therefore the answer is 89392i + 788.

Hope that helps!

Answer:

1: 9 polar bears and 38 penguins

2: 47 snowglobes

3: 130 snowballs

4: 97 penguins

Step-by-step explanation:

i did the math

The below area rate can also be further answered as 14, since the supplied border rate can be further answered as 12. Their areas are compared 4/16.

What's meant by rate?

Areas If the scale factor of the sides of two analogous polygons is m/ n

 also the rate of the areas is (m/n)^2.

Area of analogous Polygons Theorem). Because area is a two- dimensional volume, you square the rate.

It's given that, the rate of peripheries of two analogous quadrilateral is 2 4

 now,  

to find the rate of area, we can take two quadrilaterals, say square.

Square ABCD of side 2 units and Square PQRS of side 4 units.

now rate of areas,

[tex]=\frac{area \ of\ square\ ABCD }{area \ of\ square\ PQRS }[/tex]

[tex]=\frac{2 \times 2}{4 \times 4}[/tex]

= 4/16

= 1/4

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In this question you're given that a coin is flipped 12 times. Now I'll make some assumption here. The first assumption is that the coin is fair. That means the probability of getting ahead in a trial in the toss is the same as probability of getting a deal in the toss and that would be half And second. The all the 12 flips or tosses are independent of each other. And thirdly that the probability of getting ahead, it's the same in each toss and you can see that in each talks there's only two outcomes ahead or not ahead which is a so this is considered a success and this is a failure. It just happened to be the probability of the success and the probability of failure is the same at heart. So this actually follows a binomial distribution model. But in the event that you have not learned by normal distribution we can just go by simple probability multiplication rule. So in probability and it's times or is plus. But the assumption of independent trials and the coin is fair is still the same whether you're using binomial distribution or just simple probability multiplication rule, no Probability of obtaining 12 heads in a row when flipping a coin would be the first pulse, you get a hit. And the second course you also get ahead. And the third toss you get ahead. So on so forth. Up to the last toss, which is the 12th toss, you also get a hit. So it's hit for every toss. So what this means is that probability of first courses ahead is half so that's half now. N and in probability means multiple execution. So just times and second hand is second thoughts is also ahead. So there's a half and so N. S. A. Terms enter is ahead, so that's another half, so so on, so forth. All the way to the last end here. Mr toms And the 12 is also a hit. So this times, how so what we have here is half to the power of 12 since half is multiplying itself 12 times. And so the answer is 1/4 oh 96 Or 0.0002, 44 six, decimal places. Now, if you are using binomial distribution to solve this problem, you will be after this part here. You will be letting X be the number of heads. Oh 12 courses. Right, So X follows the binomial distribution Number of trials is 12, 12 horses. And probability of success in this case is probability of getting ahead in a in a toss is half, so probability of X equals two. R. Where r is the number of heads in 12 courses will be 12, choose our half to the power of our and one minus half is also half To the power of 12 minus are so probability of obtaining 12 heads in a role. So we will be looking at probability of X equals 2, 12. So just suck 12 into the arm. So is this and you will get the same answer of 0.000244

Solving the provided question, we can say that equatiοn of slope intercept will me as y -y1 = m(x-x1) => 3x - y = -1

In mathematics, the intersectiοn point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crοsses on a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equation fοr the straight line to show this.

The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept fοrm. When an equatiοn has the intercept form (y=mx+b), the slοpe is m and the y-intercept is b. Sοme equations can also be rewritten such that they seem to be slοpe intercepts. If y=x is rewritten as y=1x+0, fοr instance, the slοpe and y-intercept are bοth changed to 1.

Here,

coordinates are

M(2,5) and P(a,-2)

equation of slope intercept will me as

y -y1 = m(x-x1)

y - 5 = 3x-4

3x - y = -1

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Liters of 10% solution = 1 liters

Liters of 70% solution = 5 liters

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x +3 = 8 is an equation.

We have,

10% solution = x

70% solution = y

Now,

A 10% antifreeze solution is to be mixed with a 70% antifreeze solution to get 6 liters of a 20% solution.

This means,

We can make two equations.

0.10x + 0.70y = 6 x 0.20

0.10x + 0.70y = 1.2 ______(1)

x + y = 6 ______(2)

Solve for x and y.

From (2),

x = 6 - y

Substituting in (1) we get,

0.10x + 0.70y = 1.2

0.10 (6 - y) + 0.70y = 1.2

0.6 - 0.10y + 0.70y = 1.2

0.6 + 0.60y = 1.2

0.60y = 1.2 - 0.6

0.60y = 0.6

y = 1

And,

x = 6 - y

x = 6 - 1

x = 5

Thus,

10% solution = 1 liter

70% solution = 5 liters

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Answer:

2,19/3 this is answer this is correct

The angle of the base and the ladder is 69. 34 degrees

Note that the six trigonometric identities are;

From the information given, we have that;

Hypotenuse = 17 meters

Adjacent = 6 meters

The identity to use is the cosine

cos θ = adjacent/hypotenuse

Substitute the  values

cos θ = 6/17

cos θ =,0. 3529

Take inverse of cos

θ = 69. 34 degrees

Hence, the value is 69. 34 degrees

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