Emily is entering a bicycle race for charity. Her mother pledges $0.40 for every 0.75 mile she bikes. If Emily bikes 24 miles, how much will her mother donate?

On solving the provide question, we can say that Area of the triangle, [tex]A = \sqrt{s( s - a )( s - b )( s - c )} \\[/tex] =  34.98 sq units

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

in this triangle

[tex]A = \sqrt{s( s - a )( s - b )( s - c )} \\[/tex]

and here

s = a+b+c/3

a = 10

b = 7

c =12

s = 10+7+12 / 3

s = 14.5

A = 34.98 sq units

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Using half angle formula,

Half angle formulas are equations that contain the half angles of the trigonometric ratios.

Given that tanα = -1/2 and π/2 < α < π

To find sin(α/2), we use the half angle formula

sin(α/2) = √[(1 - cosα)/2]

Also, tan²α + 1 = sec²α = 1/cos²α

⇒ cosα = ±1/√(1 + tan²α)

Since π/2 < α < π

cosα = -1/√(1 + tan²α)

Substituing this into the equation for sin(α/2), we have

sin(α/2) = √[(1 - cosα)/2]

sin(α/2) = √[(1 - (-1/√(1 + tan²α)))/2]

Substituting  tanα = -1/2 into the equation, we have

sin(α/2) = √[(1 + 1/√(1 + tan²α))/2]

sin(α/2) = √[(1 + 1/√(1 + (-1/2)²))/2]

sin(α/2) = √[(1 + 1/√(1 + 1/4))/2]

sin(α/2) = √[(1 + 1/√(5/4))/2]

sin(α/2) = √[(1 + 1/√5/2)/2]

sin(α/2) = √[(1 + 2/√5)/2]

sin(α/2) = √[(√5 + 2)/√5)/2]

sin(α/2) = √[(√5 + 2)/2√5

sin(α/2) = √[(√5 + 2)/2√5 × √5/√5

sin(α/2) = √[5(√5 + 2)]/2 × 5

sin(α/2) = √[5(√5 + 2)]/10

So, sin(α/2) = √[5(√5 + 2)]/10

Using the half angle formula,  

tan(α/2) = sinα/(1 + cosα)

Using the trigonometric identity cosα = ±1/√(1 + tan²α)

cosα = ±1/√(1 + (-1/2)²)

cosα = ±1/√(1 + 1/4)

cosα = ±1/√(5/4)

cosα = ±1/√5/2

cosα = ±2/√5

Since π/2 < α < π

cosα = -2/√5

Also, since the trigonometric identity sinα = ±√(1 - cos²α)

So, sinα = ±√(1 - (-2/√5)²)

sinα = ±√(1 - 4/5)

sinα = ±1/√5

Since π/2 < α < π

sinα = +1/√5

Substituting cosα = -2/√5 and sinα = +1/√5 into the equation for tan(α/2), we have

tan(α/2) = sinα/(1 + cosα)

tan(α/2) = +1/√5/(1 + (-2/√5))

tan(α/2) = +1/√5/(1 - 2/√5)

tan(α/2) = +1/√5/(√5 - 2)/√5)

tan(α/2) = 1/(√5 - 2)

So, tan(α/2) = 1/(√5 - 2)

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The equation x(2x+3) = x² + 1 is the quadratic equation and the remaining equation (x²)² + 1 = 2x³, (x +  1) + 8 = (x²)(x²), and (x²)³ = (x³)⁴ are not in quadratic equation.

The term quadratic equation in math is defined as an equation containing one term in which the unknown is squared and no term in which it is raised to a power higher than 2.

Here we have to find the equation that was not in the form of the quadratic equation.

As per the definition, we have know that the quadratic equation must be in the form of

=> ax² + bx + c = 0

So, here we have to look into the given expression, then w e have identified that only the equation x(2x+3) = x² + 1 is in the quadratic form.

Because the quadratic equation only have the highest power value of 2.

And the remaining are not the quadratic equation.

Therefore, option (a), (b) and (d) are the resulting options.

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The number of doors in one-story building are 8 and the number of doors in two-story building are 12.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, an employee at a construction company is ordering interior doors for some new houses that are being built.

Let the number of doors in one-story houses be x and the number of doors in two-story houses be y.

There are 6 one-story houses and 2 two-story houses on the west side of the street which require a total of 72 doors.

Here, 6x+2y=72 -------(I)

On the east side there are 5 one-story houses and 7 two-story houses which require a total of 124 doors.

5x+7y=124 -------(II)

Multiply equation (I) by 7, we get

42x+14y=504  -------(III)

Multiply equation (II) by 2, we get

10x+14y=248 -------(IV)

Subtract equation (IV) from (III), we get

32x=256

x=8

Substitute x=8 in equation (I), we get

48+2y=72

2y=24

y=12

Therefore, the number of doors in one-story building are 8 and the number of doors in two-story building are 12.

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Number Zero is neither positive nor negative.

A whole number, an integer can be positive, negative, or zero but cannot be a fraction or a decimal because it is a whole number. The natural numbers (1, 2, 3,...), their opposites (-1, -2, -3,...), and zero are all considered to be integers. Numerous branches of mathematics use integers, but number theory and algebra place a special emphasis on them.

Zero is not an integer that may be either positive or negative. It is regarded as a non-negative or neutral number. The absolute value of zero is also zero in terms of magnitude. |0| = 0. In the set of integers, zero is also regarded as the identity element of addition and the absorbing element of multiplication.

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At point, the parametric curves cross (4, 1, 32).

t functions expressed as x = f(y) = y = f(x) = (some function of the variable x) (some function of the variable y).

It is frequently more easier to view functions of two or more variables (although we'll keep it at two here) as parametric functions, particularly in physical science.

The introduction of the idea of time makes parametric functions the most simple to understand.

Imagine tracing a parabola-like function from left to right as time passes.

Then, it is simple to begin considering how the x-coordinate and the y-coordinate change as a function of time: x = f(t), y = g. (t). In this sense, time is actually referred to as the parameter.

We will investigate functions for which a point exists in this section.

Hence, At point, the parametric curves cross (4, 1, 32).

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Answer: Rotation around the origin

Step-by-step explanation:

If you rotate ABCDE around the point (0,0), you will see that it maps onto A'B'C'D'E'.

Answer:that doesn’t seem possible to figure out

Step-by-step explanation:

?

Perimeter of rectangular hexagon = 6 × length of side, length of side of given hexagon = 30/6   =5 cm and perimeter of new figure = Number of outer sides × length of each side  =10×5=50 cm

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Perimeter of rectangular hexagon = 6 × length of side

length of side of given hexagon = 30/6   =5 cm

perimeter of new figure = Number of outer sides × length of each side

=10×5=50 cm

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As per the given frequency distribution, the value of variance is 9.8 and the value of standard deviation is 3.126

The term frequency distribution is defined as the distribution of a variable is the pattern of frequencies, meaning the set of all possible values and the frequencies associated with these values

Here we have the following frequency distribution with average number of pupils per teacher in some states of the United States.

While we looking into the table we have identified the value of variance as,

But in order to calculate the variance we must need the value of mean, it can be calculated as follows:

= >Mean (x) = ∑(f(x)) / ∑f

Apply the values on it, then we get

=> 660/42 = 15.71

Now, the value of variance is calculated as

=> Variance = ∑(f(x)²) / ∑f - (Mean²)

Apply the values on it, then we get,

=>  [10782/42] - [15.71] = 9.8

Then through the variance the value of standard deviation is calculated as,

=> standard deviation = √9.8 = 3.126

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0.1 is probability  in distribution table.

What are examples and probability?

The quantity of success-producing options. the total number of outcomes that could occur.

                             For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.

Here X is a random variable. P(X) is its probabilities corresponding to the different values of X.

now according to the properties of probability theory we know that sum of probabilities is 1.

so here to find the value of the probability of X coresponding to the value 53 we should use the following steps:

sum of given probabilities =(0.2+0.4+0.3) = 0.9

required probability = 1 - sum of given probabilities = 1 - 0.9 = 0.1

hence the complete probability table is

X P(X)

20 0.2

49 0.4

53 0.1

80 0.3

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The inequality describing how much she can withdraw is x < 3550

An equation is a expression that shows the relationship between numbers and variables.

Inequalities are used in expression for non equal comparison of variables.

Let x represent the amount of money that can be withdrawn.

Tabitha’s account balance is $3,800. Of this, $750 is for rent. Hence:

Money remaining = 3800 - 750 = 3050

Tabitha wants to keep a balance greater than $500. Hence:

3050 - x > 500

x < 3550

The inequality is x < 3550

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The TQ is a chord, PR is a secant line and WU is a tangent line.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

A chord of a circle is the line segment joining two points on the circle.

Line segments TQ and QV are chords.

TV is also a chord, which is the diameter.

A secant line is a line which intersects the circle at two different points.

Line PR is a secant line which intersects the circle at T and Q.

A tangent line is a line which intersects the circle at exactly one point.

Line WU is a tangent line which intersects the circle at V.

Hence the chords in the given figure are TQ and QV, secant line is PR and tangent line is WU.

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Significant figures are in this measurement 1.090

In a number, to determine the number of significant figures following three rules are used:  

The digits which are non-zero are always significant.

Any zeros between two digits which are non-zero are significant.

In the decimal portion, trailing zeros are significant.  

Significant figures = Numbers that carry meaning in the measurements of a number.

The number is 1.090, it has two non-zero digits, 1 zero in between two non-zero digit and one trailing zero thus, all of them are significant figures.

Therefore, it has 4 significant figures : 1.090

Significant figures are in this measurement 1.090

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Answer:

To solve this problem, we will use the following steps:

Step 1: Convert the minutes to hours by dividing the minutes by 60: 45 minutes / 60 = 0.75 hours

Step 2: Add the hours and minutes together to find the total time: 3 hours + 0.75 hours = 3.75 hours

Step 3: Multiply the total time by the average speed to find the distance: 3.75 hours * 80 km/hour = 300 km

Final Answer: Tim drives 300 km.

The plot of 2 1/3, −5/6, and −3 1/2 on the number line is attached below

Generally, The uneven distribution of resources, opportunities, and advantages among different persons or groups in a society is what we mean when we talk about inequality.

This may manifest itself in a variety of ways, such as economic inequality (differences in income or wealth), social inequality (differences in status or access to resources), or political inequality (differences in power or influence) (differences in power or representation).

inequality, A statement in mathematics that establishes an order connection between two numbers or algebraic expressions, such as "greater than," "greater than or equal to," "less than," or "less than or equal to."

The mathematical symbol for "equals" has been substituted by an arrowhead in the statement "5x - 4 > 2x + 3," which gives it the appearance of an equation. It is an illustration of the concept of inequality. This indicates that the section on the left, which reads 5x minus 4, is more significant than the section on the right, which reads 2x plus 3.

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Answer:

4 and 7

Step-by-step explanation:

7-4=3

4x7=28

Answer:

  3√7 ≈ 7.937 units²

Step-by-step explanation:

You want to know the area of the isosceles triangle with congruent sides 4 units and base 6 units.

The perimeter of the triangle is ...

  P = 4 + 4 + 6 = 14

so the semiperimeter is ...

  s = P/2 = 14/2 = 7

By Heron's formula, the area of the triangle is ...

  A = √(s(s -a)(s -b)(s -c))

  A = √(7(7 -4)(7 -4)(7 -6)) = 3√7

The area of the triangle is 3√7 ≈ 7.937 square units.

__

Additional comment

You can also compute the area after finding the altitude (the length of the dashed line) using the Pythagorean theorem. The figure consists of two right triangles, each with leg 3 and hypotenuse 4. The missing leg (the triangle height) is then ...

  h = √(4² -3²) = √7

The area is ...

  A = 1/2bh = 1/2(6)(√7) = 3√7 . . . . square units

Answer:

A- x+3

Step-by-step explanation:

each number is growing by 3

The pair of equations y = 0 and y = -7 have no solutions.

The pair of equations y = 0 and y = -7 have no solutions because the equations are not equal. The left side of the equation is y = 0, while the right side of the equation is y = -7. Since the two sides of the equation do not have the same value, there is no solution that can satisfy both equations.

The pair of equations y = 0 and y = -7 have no solutions because the two equations are not equal. The left side of the equation is y = 0, while the right side of the equation is y = -7. Since the two sides of the equation do not have the same value, there is no solution that can satisfy both equations simultaneously. This can be confirmed by substituting the value of y on the left side into the equation on the right side. Since the value of y would be 0 on the left side and -7 on the right side, they cannot be equal and thus there is no solution. Therefore, the pair of equations y = 0 and y = -7 have no solutions.

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Answer:

y = 21/4 or 5[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

step 1:  multiply -8 and 0.5y to get -4y

step 2:  multiply -8 and -3 to get 24

now you have distributed -8 and have removed parentheses to get:

-4y + 24 = 3

subtract 24 from each side to get:

-4y = -21

divide each side by -4 to get:

y = 21/4 or 5[tex]\frac{1}{4}[/tex]

The monthly payment is $130.50. Therefore, option C is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$2700, rate of interest =8% and time =2 years

Here, SI=(2700×8×2)/100

= 43200/100

= $432

Amount =Principal+Interest

= 2700+432

= $3132

We know that 2 years =24 months

Now, the monthly payment = 3132/24

= $130.50

Therefore, option C is the correct answer.

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Profit made by each girl Sarah, Lilly and Paula respectivly are R 200 , R 400 and R 600

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. Indicators of proportions include "::" and "=".

The amount of investment done by each girl Sarah, Lily and Paula respectivly is x, 2x and 3x

So, the profit will be

x + 2x + 3x = 1200

⇒6x  =1200

⇒ x = 200

Profit made by each girl respectivly are x = R 200 , 2x = R 400 and 3x = R 600.

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Answer: 127

Step-by-step explanation:

the image has steps

Answer:

the answer is 127 cm^2 ig

The required rate of change of the surface area of the cube is 66 sq,feet/second.

The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time. R = (D2 - D1)/T is a general formula for calculating the rate of change.

[tex]\frac{V}{dt}[/tex] = 1327 cubic feet per second

volume(V) = 528528 cubic feet

We know that

V = a^3

528528 = a^3

a = 80.85

Differentiate w, r, t

[tex]\frac{V}{dt}[/tex] = 3a^2[tex]\frac{da}{dt}[/tex]

1327 = 3(80.85)^2da/dt

da/dt = 0.068

Now,

Surface area(S) = 6a^2

Differentiate w, r, t

dS/dt = 12a(da/dt)

dS/dt = 12(80.85)(0.068)

dS/dt = 66 Sq.feet/second

Thus, required rate of change of the surface area of the cube is 66.

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Using the linear function, the monthly cost for 6 HCF is $36.72.

If the monthly water bill is a linear function with a slope of 1.65, it means that for every additional HCF used, the cost increases by $1.65.

Let's denote the monthly cost as C(HCF) and the number of HCF used as HCF. We know that C(12) = $46.62.

Now, to find the monthly cost for 6 HCF (C(6)), we can use the slope information:

C(12) = $46.62

C(12) - C(6) = $46.62 - C(6) = (12 HCF - 6 HCF) * 1.65

C(6) = $46.62 - (6 HCF * 1.65)

Now, let's calculate:

C(6) = $46.62 - (6 * 1.65)

C(6) = $46.62 - 9.90

C(6) = $36.72

So, the monthly cost for 6 HCF is $36.72.

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(a)- The study was experimental.

(b)- No, the researchers would not be justified in doing so.

(c)- Such a method leads to an incorrect conclusions for justifiable reasons.

This problem involves minute statistical knowledge and assesses the student's ability to differentiate between an experiment and an observation and also his/her potential to make justifiable logics as to draw conclusions for a scientific research. The explainations are-

Part - (a)

The study was not an observation, it was an experiment because the treatments involving D-Cycloserine or placebo were imposed by the researchers on the people with acrophobia.

Part (b) -No, the experiment was designed to compare the D-Cycloserine group with a control group that received a placebo . The researchers can conclude that the D-Cycloserine and two therapy sessions show significantly more improvement than a placebo and two therapy sessions. However, there is no basis for comparison with the other group of people with acrophobia who received eight therapy sessions and no pill.

Part (c)-

We can cite an example that if the therapists were allowed to choose who received a placebo and who received D-Cycloserine, they might assign the people with more severe acrophobia with the other group. Thus, the improvement after only two therapy sessions can be related to the initial severity of the acrophobia rather than to the effects of D-Cycloserine.

Therefore, the answers are -

(a)- The study was experimental.

(b)- No, the researchers would not be justified in doing so.

(c)- Such a method leads to an incorrect conclusions for justifiable reasons.

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Answer:

a^n(a+1)

This is just to reach the minimum character limit.

113875.44746 is principal and interest will he have already paid when his balloon payment is due.

What exactly does "interest rate" mean?

An interest rate informs you of how much borrowing will cost you and how much saving will pay off. The amount you pay for borrowing money, expressed as a percentage of the entire loan amount, is what you will pay in interest if you are a borrower.

                        The financial fee for borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR). Lenders may charge interest for the use of their money, or borrowers may charge interest for the use of those funds.

=PMT(5.25%/12,12*30,-245500)*12*7

= 113875.44746

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The probability that the selected pool has a pH level that is not considered safe pool is 0.1336.

The given parameters are:

a =7.5

b= 4

Start by calculating the probability that a pool is safe.

This is represented as: P (7.2 <x<7.8)

Calculate the z-scores for x=7.2 and 7.8 using:

So, we have:

P(7.2<x<78) P (-1.5 <x<1.5)

This gives.

P(7.2<x<7.8) = P(<1.5)-P(z<-1.5)

Using z table of probabilities, we have:

P(7.2<x<7.8) = 0.9332-0.0668

P(7.2<x<7.8) = 0.8664

The probability that the pool is not safe is calculated using the following complement formula.

P (Not Safe) = 1-P(Safe)

So, we have:

P (Not Safe) = 1-0.8664

P (Not Safe) = 0.1336

So, the probability that the pool is not safe is 0.1336.

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