Add:
[tex]4 { x }^{ 2 } y+-3x { y }^{ 2 } +-5x { y }^{ 2 } +5 { x }^{ 2 } y[/tex]

Answer:

The chance of the committee being all boys is 28.57% or 29%

Based on the amounts that Geraldo Saldana deposited in the month of May, the total simple interest comes to $18.98.

the simple interest earned can be found as:

= (3,600 x 3.5%/360 days x 30 days) + (3,000 x 3.5%/360 days x 20 days) x (5,000 x 3.5%/360 days x 6 days)

= 10.5 + 5.83 + 2.65

= $18.98

rest of the question is:

How much simple interest did his money earn?

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Ada is incorrect, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.

For Rectangle PQRS:-

By Pythagoras Theorem, in right triangle PQS,

SQ² = PQ² + PS²,

or, SQ² = 8² + 16² sq. inches,

or, SQ² = 64 + 256 sq. inches,

or, SQ = √320 sq. inches,

or, SQ = 8√5 inches.

Thus, the length of diagonal SQ, of rectangle PQRS is 8√5 inches.

For Square LMNO:-

By Pythagoras Theorem, in right triangle LMO,

OM² = LM² + LO²,

or, OM² = 8² + 8² sq. inches,

or, OM² = 64 + 64 sq. inches,

or, OM = √128 sq. inches,

or, OM = 8√2 inches.

Thus, the length of diagonal OM, of square LMNO is 8√2 inches.

We know that 2*OM ≠ SQ, as 2*8√2 ≈ 8√5.

Thus, Ada is incorrect, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.

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Rewrite the second expression as

[tex]\dfrac1{1+x^m + x^{-n}} = \dfrac{x^{\ell+n}}{x^{\ell+n} + x^{\ell+m+n}+x^\ell} = \dfrac{x^{-m}}{x^{-m} + 1 + x^\ell}[/tex]

and the third expression as

[tex]\dfrac1{1 + x^n + x^{-\ell}} = \dfrac{x^\ell}{x^\ell + x^{\ell+n} + 1} = \dfrac{x^\ell}{x^\ell + x^{-m} + 1}[/tex]

so the fractions all have the same denominator.

Then combining the fractions gives the desired result,

[tex]\dfrac1{1+x^\ell+x^{-m}} + \dfrac1{1+x^m+x^{-n}} + \dfrac1{1+x^n+x^{-\ell}} = \dfrac{1+ x^\ell + x^{-m}}{1+x^\ell+x^{-m}} = \boxed{1}[/tex]

Answer:

[tex]y = -x^{2} +4x-10[/tex]

Step-by-step explanation:

I used a graphing calculator to calculate the points so I'm not sure how to do it without, but I hope this helped!

Answer:

2 hours 46 minutes and 40 seconds

Step-by-step explanation:

First we divide by 60 to find how many minutes are in 10000 seconds :

10000÷60 = 166 minutes with remainder 40 seconds

If 166 minutes and 40 seconds is 100000 seconds then we change 166 minutes into hours and minutes :

We do this by dividing 166 by 60 :

166 ÷ 60 :

2 hours Remainder 46 minutes

So our final answer is :

2 hours 46 minutes and 40 seconds

Hope this helped and have a good day

Step-by-step explanation:

18z+10z+40z+5+1=360

68z+6=360

68z=360-6

68z=364

z≈5.353

The correct labels are matched to their appropriate locations on the graph as shown in the image attached below.

A graph refers to a type of chart that's used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

In this exercise, you're required to drag the correct labels to their appropriate locations on the graph as shown in the image attached below.

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Part A:

According to a life cycle analysis of the U.S. food system conducted by the University of Michigan, the U.S. consumes 13.9 quads of mostly fossil fuel energy to produce 1.75 quads of food energy annually. A quad is a unit of energy equal to 1 quadrillion (10¹⁵) British thermal units (BTUs). One quad is equal to the energy of 183 million barrels of petroleum.

For this, multiply 150 × .20 = 30

Therefore, 20% of 150 is 30.

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The function given can be classified as a function. That is option C.

Function can be defined as the expression that has both an x domain value and a y range value and it's being classified based on the quality of these values.

A function can be represented based on their roster forms.

Using the function equation given, f(X) = 10.2^2

Here, the first element is the domain or the x value and the second element is the range or the f(x) value of the function.

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The correct answer is (40, 35) because by plugging in,  40 +35 = 75 and

(40 x 5) + (35 x 3) > 300

Word problem can be solved by interpreting the problem into its best fit equation. The equation may be linear, quadratic or simultaneous equations.

Given that

5x + 3y > 300

x + y = 75

Let us first assume that 5x + 3y = 300. That is,

5x + 3y = 300

x + y = 75

Eliminate y by multiplying equation 2 by 3

5x + 3y = 300

3x + 3y = 225

2x = 75

x = 75/2

x = 37.5

Substitute x in equation 2

37.5 + y = 75

y = 75 - 37.5

y = 37.5

The correct answer is (40, 35) because 40 +35 = 75 and

(40 x 5) + (35 x 3) > 300

Therefore,  the solution to the system is (40, 35)

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Based on the information provided in the first table, we have the following angle and trigonometric function:

Based on the information provided in the first table, we have the following trigonometric function:

tanθ = √3

θ = tan⁻¹(√3)

θ = 60°.

In radians, we have:

θ = 60 × π/180

θ = 1.0472 radian.

sin60 = √3/2

cos60 = 1/2

csc60 = 2/√3

sec60 = 2

cot60 = 1/√3

Based on the information provided in the second table, we have the following trigonometric function:

θ = 30 × π/180

θ = 0.5236 radian.

sin30 = 1/2

cos30 = √3/2

tan30 = 1/√3

csc30 = 2

sec30 = 2/√3

cot30 = √3

Based on the information provided in the third table, we have the following trigonometric functions:

sinθ = √2/2                                   tanθ = 1

θ = sin⁻¹(√2/2)                               θ = tan⁻¹(1)

θ = 45°.                                          θ = 45°.

In radians, we have:

θ = 45 × π/180

θ = 0.7854 radian.

cos45 = √2/2

csc45 = √2

sec45 = √2

cot45 = 1

Based on the information provided in the fourth table, we have the following trigonometric function:

sinθ = 1                                

θ = sin⁻¹(1)                      

θ = 90°.

θ = 90 × π/180

θ = 1.5708 radian.

cos90 = 0

tan90 = not defined

csc90 = 1

sec90 = not defined

cot90 = 0

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Answer:

C

Step-by-step explanation:

cosecΘ = [tex]\frac{1}{sin0}[/tex] = [tex]\frac{2}{\sqrt{3} }[/tex] ( cross- multiply )

2sinΘ = [tex]\sqrt{3}[/tex] ( divide both sides by 2 )

sinΘ = [tex]\frac{\sqrt{3} }{2}[/tex] , then

Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{2}[/tex] ) = 60°

Answer:

C.  60°

Step-by-step explanation:

by definition,  cosec(θ) is the reciprocal of sin(θ)

In other words ,

[tex]\text{cosec} \left( \theta \right) =\frac{1}{\sin \theta }[/tex]

Then

[tex]\text{cosec} \left( \theta \right) =\frac{2}{\sqrt{3} }[/tex]

[tex]\Longleftrightarrow \frac{1}{sin \left( \theta \right) } =\frac{2}{\sqrt{3} }[/tex]

[tex]\Longleftrightarrow sin \left( \theta \right) =\frac{\sqrt{3} } {2}[/tex]

Then

θ = 60°

Answer:

The field is 1 and 4/10 mile long.

Step-by-step explanation:

If I understand the question:

(1/2) + (9/10) =

(5/10) + (9/10) = (14/10)

(14/10) is 1 and 4/10

The field is 1 and 4/10 mile long.

The length of the missing length in the triangle is 53.6 units

The given triangle is a right triangle.

Right triangles are triangles that have a measure of angle that is 90 degrees.

The missing side is x, and the value of x is calculated using the following sine rule

We have

sin(angle) = opposite/hypotenuse

This gives

sin(66) = 49/x

Divide both sides by sin(66)

1 = 49/x sin(66)

Multiply both sides by x

x = 49/sin(66)

Divide the expression

x = 53.6

Hence, the length of the missing length is 53.6 units

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Answer:

  (d)  1 unit

Step-by-step explanation:

The length of the dilated line segment is the product of the dilation factor and the length of the original line segment. It can also be computed as the length of the segment between the dilated coordinates.

The length of the original horizontal line segment BC is the difference of its x-coordinates:

  BC = 6 -4 = 2 . . . . units

(We know the segment is horizontal because the y-coordinates of the end points are the same.)

Multiplying the length of the original segment by the dilation factor, we find the length of B'C':

  B'C' = dilation factor × BC

  B'C' = 0.5×(2 units)

  B'C' = 1 unit

The dilation factor multiplies each coordinate value:

  B' = 0.5B = 0.5(4, 3) = (2, 1.5)

  C' = 0.5C = 0.5(6, 3) = (3, 1.5)

The length of B'C' is the difference of x-coordinates: 3 -2 = 1 unit.

Answer:

M = 4.5

N = 2.1

Step-by-step explanation:

angle p would be 25.  180 - 155 = 25

M = 5cos25 =4.5 rounded to the tenths place.

M = 5sin25 = 2.1 rounded.

The solution of the system of equation is x = 7 and y = 12.5.

2y + 4x = 18

2y - 3x = 4

2y = 4 + 3x

y = 2 + 3 / 2 x

Hence, let's substitute the value of y in equation(1)

2( 2 + 3 / 2 x) + 4x = 18

4 + 3x + 4x = 18

4 + 7x = 18

7x = 14

x = 14 / 2

x = 7

2y - 3(7) = 4

2y - 21 = 4

2y = 25

y = 25 / 2

y = 12.5

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Answer:

f(2) = 3

Step-by-step explanation:

Plug in 2 for x

Using Percentage, the eighth graders voted for Luke is of 72 percentage or 72%.

According to the question,

They are 450 eighth graders at Wilson Middle School. In the class president, 324 students voted for Luke, 81 students voted for Alice, and 45 students voted for Chris.

In order to find the percentage of eighth graders voted for Luke only if 252 divided by 350.

[tex]\frac{252}{350} = 0.72[/tex]

To convert decimal into Percentage multiply 0.72 into 100.

0.72*100 = 72%.

Hence, the percentage of the eighth graders voted for Luke is of 72 percentage or 72%.

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The proportional relationship that represents the market that sells their carrots at a lower rate per pound is: y = 1.6x.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

From the table, the rate is:

k = $8.8/4.4 = 2.

From the market, the rate is:

k = $4.8/3 = $1.6.

Hence the equation is y = 1.6x.

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Step-by-step explanation:

Therefore,the answer is [tex] \cfrac{3}{y} - x[/tex].

Answer:

58%

Step-by-step explanation:

47/81 x 100%

≈ 58%

Hope it helps : )

Answer:

I have wrote just answer.

Answer:

1.2

2.4√3÷3

3. x=45, y=15

Step-by-step explanation:

OK,

1. So the first part requires the Pythagoreanism formula which is: b²=a²+c²:

AC²=AB²+BC²====> AC²=(1)²+(√3)²===> AC²=4===> AC=2

2.The second part requires the formula of tan:

tan A=BC÷AB===> tan A=√3÷1===> tan A=√3

tan C=AB÷BC===> tan C=1÷√3===> tan C=√3/3

tan A+tan C=√3+√3/3===> 4√3÷3

3.And the last part requires the equation of angles:

A+B+C=180===>

x+y+x-y+90=180===> 2x=90===> x=45, y=15

If the graph of the line falls from left to right the slope is negative.

Slope = (y2 - y1)/(x2 - x1)

---> y = -2x + 3

As the value of x increases and the function of f(x) also increases since it is moving in the upward direction. The x-intercept is (-3,0)

A function is a set of input values into a program that produces the desired output. In mathematical terms, we can say a function is a set of x values that maps to a set of y values.

Functions can also be represented on the graph called graphical representation.

From the given graphical information, as the value of x increases, the function of f(x) also increases since it is moving in the upward direction.

The x-intercept is the value where the line cuts the horizontal x-axis when y is zero, therefore the x-intercept is (-3,0)

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Using the relation between velocity, distance and time, it is found that a reasonable estimation of the current is of 1 mph.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Upstream, against the current, he traveled 3 miles in t hours, hence the equation is:

[tex]2 - c = \frac{3}{t}[/tex]

[tex]c = 2 - \frac{3}{t}[/tex]

Downstream, with the current, he traveled 3 miles in 4 - t hours, hence the equation is:

[tex]2 + c = \frac{3}{4 - t}[/tex]

Hence:

[tex]c = \frac{3}{4 - t} - 2[/tex]

Then, taking the two equal equations:

[tex]2 - \frac{3}{t} = \frac{3}{4 - t} - 2[/tex]

[tex]\frac{3}{4 - t} + \frac{3}{t} = 4[/tex]

[tex]\frac{3t + 12 - 3t}{t(4 - t)} = 4[/tex]

12 = -4t² + 16t

4t² - 16t + 12 = 0

t² - 4t + 3 = 0

(t - 3)(t - 1) = 0.

The current is positive, hence:

[tex]c = 2 - \frac{3}{3}[/tex]

c = 2 - 1

c = 1 mph.

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The area under the curve between the two values is (d) 0.0750

From the table, we have:

P(z = -0.45) = 0.3264

P(z = -0.67) = 0.2514

The area under the curve is calculated as:

Area = P(z = -0.45) - P(z = -0.67)

So, we have:

Area = 0.3264 - 0.2514

Evaluate the difference

Area = 0.0750

Hence, the area under the curve between the two values is (d) 0.0750

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For a population where the distribution is unknown, the sampling distribution of the sample mean will be b which is approximately normal for all sample sizes.

Given options regarding sample sizes.

We have to choose the correct option which shows the sample mean characteristics when the distribution is unknown.

Based on the central limit theorem the sampling distribution of the sample mean for either skewed variable ir normally distributed variable can be approximated given the mean and standard deviation.

The central limit theorem is said to be  true when n greater than or equal to 30.

When n is greater than 30 ,z test is used, when n is less than 30 ,t test is used.

Hence for a population where the distribution is unknown ,the sampling distribution of the sample mean will be approximately normal for all sample sizes.

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Question is incomplete as it includes options in a right way:

1)exactly normal for large sample,

2) approximately normal for all sample sizes,

3) exactly normal for all sample sizes.