Question 1-5

Val needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 50m by 50m square. Find the

Area enclosed by the figure. Use 3. 14

50

50 m

square meters

The following intervals of the quadratic equation are listed below:

Herein we find a representation of a quadratic equation with a vertical axis and on a Cartesian plane, of which we must look for every positive and negative interval. Quadratic equation has the feature of having an absolute extreme, either a minimum or a maximum.

The strategy to determine to determine whether the interval is positive and negative is summarized below:

Then, the quadratic equation has two positive intervals on x ∈ (- ∞, - 5) and x ∈ (1, + ∞) and a negative interval: x ∈ (- 5, 1).

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The expression that is equivalent to the given question is option D. (7^5)/ (3^4)

Indices is a topic in mathematics which has its applications in performing  arithmetic operations on numbers with powers. This process requires some laws; which are referred to as the law of indices. These laws have their various applications as required.

By applying the appropriate law of indices to the given question, the equivalent expression can be determined as;

From the numerator;

(7^2)(7^6)(3^2) = (7^8)(3^2)

So that;

(7^8)(3^2)/ (7^3)(3^6) = (7^(8-3)) (3^(2-6))

                                  = (7^5)(3^-4)

The equivalent expression is;

(7^5)(3^-4) = (7^5)/ (3^4)

The equivalent expression is (7^5)/ (3^4). Thus option D.

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Answer:225 m^2

Step-by-step explanation:

Answer:

A = 225 m²

Step-by-step explanation:

the sides of a square are congruent

the perimeter is the sum of the 4 congruent sides (s) , then

s = 60 ÷ 4 = 15 m

the area (A) of a square is calculated as

A = s² , then

A = 15² = 225 m²

Answer:

The solution to the system of equations g(x) = x - 1 and f(x) = x^2 - 5 is the point where the two functions intersect, which is the point (1,0).

To confirm this, we can substitute x = 1 into each equation and see that they both equal 0:

g(1) = 1 - 1 = 0

f(1) = 1^2 - 5 = -4 + 1 = -3 = 0

So (1,0) is the solution to the system of equations.

So, the equation to determine the number of months is 200 + 10x = 0 + 60x.

Let x be the number of months you can belong to each gym for it to cost the same at both places.

The equation to determine the number of months is:

200 + 10x = 0 + 60x

To solve for x, we can subtract 200 from both sides of the equation:

10x = -200

And finally, we divide both sides by 10:

x = -20

Therefore, you can belong to each gym for -20 months for it to cost the same at both places. But since month are positive numbers, x=-20 is not a solution. Therefore, the statement is not true, the cost will never be the same for both gyms.

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Answer:

$32

$22

Step-by-step explanation:

We know

Membership cost per month = $20

Price of a slice of pizza for members = $2

How much would Alang have to pay the pizza shop if he bought 17 slices of pizza this month?

The total cost of Alang on 17 slices of pizza = membership cost per month + prices of 17 discounted pizza

$20 + $2(6) = $32

What would be the monthly cost for a slice of pizza

The monthly cost of Alang a slice of pizza = membership cost per month + price of 1 discounted pizza

$20 + 2 = $22

So,

Alang would have to pay $32 if he bought 17 slices of pizza this month.

The cost of a slice of pizza is $22

A:  y = 2x³, is a non-linear function.

B: y = x + 5, is a linear function.

C: y = x² − 3, is a non-linear function.

D: 5x + 5y = 25 and y = x² / 2, is a linear and non-linear function.

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

If the degree of the function is one. Then the function will be a linear function.

If the degree of the function is not one. Then the function will be a non-linear function.

Hence,

A:  y = 2x³, is a non-linear function.

B: y = x + 5, is a linear function.

C: y = x² − 3, is a non-linear function.

D: 5x + 5y = 25 and y = x² / 2, is a linear and non-linear function.

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A:  y = 2x³, is a non-linear function.

B: y = x + 5, is a linear function.

C: y = x² − 3, is a non-linear function.

D: 5x + 5y = 25 and y = x² / 2, is a linear and non-linear function.

A statement, idea, or rule that creates a link between two variables is known as a function. Mathematics has functions, which are necessary for the creation of meaningful connections.

if the function has a degree of one. The function will thereafter be linear in nature.

if the function's degree is not one. The function will then be non-linear in that case.

As a result, the function A: y = 2x3 is not linear.

B: The linear function y = x + 5 is given.

C: The non-linear function y = x2 3 is.

D: The equation 5x + 5y = 25 has a linear and nonlinear component, y = x2 / 2.

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Therefore , the solution of the given problem of median comes out to be  the typical grade received by pupils is 80.

The median value of an arranged dataset is the precise value that makes up its mean. The ratio between the minimum and maximum 50% of the data is what is known as a likelihood measure, or an average. Based if there is an odd or perhaps an even number of points, multiple formulas are used to calculate the median and mode.

Here,

The range and scatter of statistical data are represented visually by this analysis (continuous data).

It establishes four quartile groups.

Min - 25th Percentile, Quartile Group 1 (Q1)

Group 2 of the Quartile: 25th Percentile (Q1) to 50th Percentile (Q2, Median)

50th percentile (Q2) and 75th percentile make up Quartile Group 3. (Q3)

75th percentile (Q3) for Quartile Group 4: Maximum

Q3-Q1 is the interquartile range in this (IQR)

the 40-point cutoff

a maximum score of 110

25% of the class received a score between 40 and 63.

50% of the pupils got scores under 81, and 50% got scores over 81.

75% of pupils had scores between 40 and 95. additionally, 25% of students achieved 95 or higher.

The typical grade received by pupils is 80.

Therefore , the solution of the given problem of median comes out to be  the typical grade received by pupils is 80.

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The complete question is " Professor A. has 40 students in her class. After giving a first quiz, she calculated 5 measures of relative standing: min =3, Q1 = 12, Median = 14, Q3 = 16, Max = 20. Draw a box plot for quiz scores of her class. What are the highest and the lowest quiz score? What is the score that separates the bottom 75% from the top 25%? How many students scored more than the median? How many students scored more than 14 points? What percent of her students received less than 12 points? Would the score of 4 be an outlier? (use the IQR method to explain)"

The number of gallons that are in the water cooler when it is completely full is; 183.49 gallons

The formula for the volume of a cylinder is;

V = πr²h

Where;

V is volume

r is radius

h is height

We are given;

Radius(r) = diameter/2 = 2.5/2 = 1.25 ft

Height(h) = 5 ft

Thus;

V = π * 1.25² * 5

V = 24.53125 ft³

There are approximately 7.48 gallons of water in a cubic foot, therefore;

Number of gallons in 24.53125ft³ = (24.53125 * 7.48)/1

Number of gallons = 183.49 gallons

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Answer: 183.49 gallons (D)

Step-by-step explanation:

Okay you are trying to find how many gallons of water the water cooler can hold.

So start by using the formula for the volume of a cylinder.

V = πr^2h

First find the radius, which is half the diameter.

The diameter is 2.5 so divide that by 2 to find the radius.

2.5/2 = 1.25

Now that you know the radius, times it by itself:

1.25 x 1.25 = 1.5625

Now multiply 1.5625 by the height, which is 5.

1.5625 x 5 = 7.8125

Now multiply 7.8125 by 3.14

7.8125 x 3.14 = 24.53125

And finally, multiply 24.53125 by 7.48

24.53125 x 7.48 = 183.49375 gallons

Now round to the nearest hundredth:

183.49 gallons

I did the same test and got it right and I have picture proof that it is correct.

If the value of  an antique vase decreases at a rate of 7% a year , and the price of vase a years ago was $1200 , then the current value of vase is $1116   .

The value of the antique vase a years ago was = $1200 ;

the percent decrease in the value of the antique vase is = 7% ,

So , let the present value of the vase be =  $x  ;

the present value of the vase ca be calculated as = [tex]1200-7\% \; of 1200[/tex] ;

= [tex]1200-0.07\times 1200[/tex] ;

Simplifying further ,

we get ;

= [tex]1200-84[/tex] ;

= 1116 .

Therefore , the current value of the antique vase is $1116 .

The given question is incomplete , the complete question is

The value of an antique vase decreases at a rate of 7% a year. If the vase was valued at $1200 years ago, what would its current value be?

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The rate of change is -1/2

Initial point is (-2,-1)

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Consider any two pairs of points:

(-2,-1)  and (0,-2)

The slope is the same as the rate of change

Rate of change = change in y values/change in x values

                         = (-2 - (-1) ) / (0-(-2))

                         = ( -2 + 1) / (+2)  

Rate of change  = (-1/2)

The rate of change is -1/2

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The indicated probability P(x >43) of the random variable x normally distributed is 0.8414.

Abraham de Moivre, a Frenchman, was the first to recognize the normal distribution (1667-1754). The curve was later developed further and its equation was developed by Carl Friedrich Gauss (1777–1855); for this reason, it is also more generally referred to as the "Gauss bell" or "Gaussian distribution."

Any point (x) from a normal distribution can be converted to the standard normal distribution using the formula z = (x-mean) / standard deviation (z).

Given:

Mean u = 50

Standard Deviation o = 7

To find the probability P(x>43),

= [tex]P(\frac{x - 50}{7} > \frac{43 - 50}{7} )[/tex]

= [tex]P(z > -1) = 0.8414[/tex]

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A perpendicular force is applied to a beam. The maximum force is 12 kN. The resulted shear function is S(x) = - 2x²

When a perpendicular force is applied to static material (in this case, a beam), shearing forces occur.

Shearing force is calculated as the algebraic sum of all transverse forces acting on either side of a beam or frame section.

First, look at the ratio between forces (in y-direction) and x.

y/x = 12/3

y = 4x

Let S(x) = shear function.

Applying Newton's first law on y-axis:

∑Fy = 0

S + x · 4x · 1/2 = 0

S + 2x² = 0

S = - 2x²

Therefore, the shear function is S(x) = - 2x²

The figure in your question is missing. Most likely it was like on the attached picture.

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I think the question should be tan theta = 1/√3, but I have given the solutions of both.

Hope it helps.

If you have any query, feel free to ask.

Yes, it is possible that both Emilio and Jim solved the problem correctly using addition and subtraction, respectively.

For example, let us consider the problem to find the solution for

(4/5) + (3/5)

Here (4/5) and (3/5) are rational numbers.

Emilio would use addition and get the solution of

(4/5) + (3/5)

= ( 4 + 3)/ 5

= 7/5

Jim could have used subtraction and found the solution of

(4/5) + (3/5)

= (4/5) - (-3/5)

= (4 - (-3))/5

= 7/5

In this example, both Emilio and Jim would have arrived at the correct solution of 7/5 though one person uses addition and other person uses subtraction.

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The following question can be solved using concepts of mathematical reasoning.

Mathematical reasoning is the process of using logical and systematic thinking to arrive at conclusions and make connections between mathematical concepts. It involves making logical deductions and inferences based on mathematical statements, definitions, postulates, and theorems.

Let p, q, and r be the propositions

p: Grizzly bears have been seen in the area.

q: Hiking is safe on the trail.

r: Berries are ripe along the trail.

a) Berries are ripe along the trail, but grizzly bears have not been seen in the area.

Solution:

r ∧ ~p

b) Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail.

Solution:

~p∧q∧r

c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area

Solution:

r → (q ↔ ~p)

d) It is not safe to hike on the trail, but grizzly bears have not been seen in the area and the berries along the trail are ripe.

Solution:

~q ∧ ~p ∧ r

e) For hiking on the trail to be safe, it is necessary but not sufficient that berries were not ripe along the trail and for grizzly bears not to have been seen in the area.

Solution:

q → (~r ∧ ~p)

f) Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are ripe along the trail.

Solution:

(f) (p ∧ r) → ~q

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The Scale On A Map Is 1 Inch = 60 Miles. If Two Cities Are 2 3/4 Inches Apart On The Map,  the number of miles they are apart is, 165  Miles

So, Option B is correct.

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

For example, Two spheres look similar but could have different radii.

Given that,

The Scale On A Map Is 1 Inch = 60 Miles

Two Cities Are 2 3/4 Inches Apart On The Map

The number of miles they are apart =?

1 Inch = 60 Miles

11/4 Inch = 60 × 11/4 Miles

              = 165  Miles

So, The actual distance is 165  Miles

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Answer:

The amount of phones that were not defective is 98% or 49/50 as a fraction in simplest form

Step-by-step explanation:

Steps to solve "what percent is 100 of 5000?"

100 of 5000 can be written as:

100/5000

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

100

5000

×

100

100

= (

100 × 100

5000

) ×

1

100

=

2

100

Therefore, the answer is 2%

If you are using a calculator, simply enter 100÷5000×100 which will give you 2 as the answer. That lets you know how many were defective

If only 2% were defective, then 98% were not

The supplied differential equation by variable separation is y(x) = sin(x²/2+c), as stated in the statement.

Any equation containing one or more terms and first or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f (x) In this case, the variables "x" and "y" are isolated and dependent, respectively. For illustration, dy/dx = 5x. Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.

With respect to that differential equation [tex]\frac{d y}{d x}=x \sqrt{1-y^2}[/tex]

[tex]\frac{d y}{\sqrt{1-y^2}}=x d x[/tex]

By implementing integration across both sides,

[tex]\begin{aligned}& \int \frac{d y}{\sqrt{1-y^2}}=\int x d x \\& \sin ^{-1}(y)=\frac{x^2}{2}+c \quad\left[\int \frac{d y}{\sqrt{a^2-y^2}}=\sin ^{-1}\left(\frac{y}{a}\right)\right]\end{aligned}[/tex]

[tex]y(x)=\sin \left[\frac{x^2}{2}+c\right][/tex]

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Cannot be answered because of incomplete data.

It is not possible to determine the number of cubes that can be shipped in this box for $7.95 without more information about the size and weight of the cubes. The weight constraint of ten pounds and the size constraint of 18 cm x 18 cm x 18 cm box only applies to the overall package and not to the individual cubes. The weight and volume of the individual cubes would need to be taken into account in order to determine how many could fit within the package while still adhering to the weight and size constraints.

The correct question should be:

if weshipit offers a flat rate of $7.95 to ship a parcel up to ten pounds (as long as it fits within a 18 cm x 18 cm x 18 cm box), how many cubes can be shipped in this box for $7.95? be sure to check both the size and the weight constraints. ignore the weight of the box. Consider the weight of the cube as 2 grams.

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Answer: (a^2 - 4)/(x^2 - 9) + (a^2 - 2a + (2-y))/(xy + 3y) - (x-3)

Step-by-step explanation: First, you need to simplify the fraction in the first term:

(a^2 - 4)/(x^2 - 9)

Next, you simplify the fraction in the second term:

(a^2 - 2a + (2-y))/(xy + 3y)

Then you subtract (x-3) from the fractions obtained in step 1 and 2:

(a^2 - 4)/(x^2 - 9) + (a^2 - 2a + (2-y))/(xy + 3y) - (x-3)

This is the final result of the operation.

It is important to note that the answer is a simplified fraction and only valid if x does not equal 3. If x=3, the denominator x-3 would be equal to zero, which is not allowed in mathematics.

The volume of the spherical glass bulb is approximately 14.1 cubic cm.

To find the volume of a spherical glass bulb, we can use the formula for the volume of a sphere:

[tex]V = 4/3 * pi * r^3[/tex]

Where V is the volume, pi is a mathematical constant (approximately equal to 3.14), and r is the radius of the sphere.

We know the diameter of the bulb is 31.5mm and to find the radius of the sphere, we divide the diameter by 2.

So, radius (r) = 31.5mm / 2 = 15.75mm

Now we can substitute this value into the formula for the volume of a sphere:

[tex]V = 4/3 * pi * (15.75mm)^3[/tex]

We can convert the value of radius from mm to cm by multiplying it by 10^-3

[tex]V = 4/3 * pi * (15.75 * 10^{-3})^3[/tex]

Now we can calculate the value of V

V ≈ 14.1 cubic cm

Therefore, the volume of the spherical glass bulb is approximately 14.1 cubic cm.

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The value of upper quartile is, 300.

The value of 7th decile is, 250.2.

The value of 35th percentile is, 100.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The donations are as follows,

⇒ 50, 50, 50, 100, 100, 100, 150, 150, 200, 250, 250, 300, 300, 400, 500.

Now, We find the values as;

a) The upper quartile is,

⇒ Qₐ = a/4 (n + 1)

Here, n = 15

So, We get;

⇒ Q₃ = 3/4 (15 + 1)

        = 3/4 × 16

        = 12

So, Q₃ is in 12th position.

So, The value of Q₃ = 300

The value of 7th decile is,

⇒ D₇ = 7/10 (15 + 1)

        = 7/10 × 16

        = 11.2

Here, 11.2 is between the position 11th and 12th position which are 250 and 300 respectively.

Then, We get;

⇒ 300 - 250 = 50

Hence, The value of D₇ = 250 + 0.2

                                     = 250.2

Now, The value of 35th percentile is,

⇒ Pₐ = a/100 (n + 1)

⇒ P₃₅ = 35/100 (15 + 1)

         = 35/100 × 16

         = 5.6

Here, 5.6 is between the 5th and 6th position which are 100 and 200 respectively.

Hence,  P₃₅ = 100

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the expression StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot is equivalent to 25x9y3 / 64x6y11.

StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot

= 25x9y3 / 64x6y11

StartRoot is the beginning of the root expression and StartFraction is the beginning of the fraction within the root expression. 25x9y3 is the numerator of the fraction and 64x6y11 is the denominator of the fraction. Superscript is used to raise the numbers to the power indicated. Baseline is the number which the Superscript is raised to. EndFraction indicates the end of the fraction and EndRoot indicates the end of the root expression.

Therefore, the expression StartRoot StartFraction 25 x Superscript 9 Baseline y Superscript 3 Baseline Over 64 x Superscript 6 Baseline y Superscript 11 Baseline EndFraction EndRoot is equivalent to 25x9y3 / 64x6y11.

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Answer:

25 and 9

Step-by-step explanation:

to find ( u ￮ w )(8)

evaluate w(8) then substitute the value obtained into u(x)

w(8) = [tex]\sqrt{8+8}[/tex] = [tex]\sqrt{16}[/tex] = 4 , then

u(4) = 4² + 9 = 16 + 9 = 25

------------------------------------------------------------

to find (w ￮ u )(8)

evaluate u(8) then substitute the value obtained into w(x)

u(8) = 8² + 9 = 64 + 9 = 73 , then

w(73) = [tex]\sqrt{73+8}[/tex] = [tex]\sqrt{81}[/tex] = 9

The slope m of the tangent to the curve will be m = -3/a^2.

Calculating the slope of the tangent line to the curve y = 3/x at a point where x = a > 0 is an important mathematical concept. To do this, we will first need to find the derivative of the curve y = 3/x.

Let's start by taking a look at the equation for the slope of a line: m = (y2-y1) / (x2-x1). We'll use this equation to find the slope of the tangent line at the point (a, 3/a).

To do this, we'll need to calculate the derivative of the given equation, which is y' = -3/x^2.

At the point (a, 3/a), the derivative is equal to -3/a^2. Therefore, the slope of the tangent line at the point (a, 3/a) is m = -3/a^2.

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This is a condition known as ankylosis, and it describes a situation in which two bones lose their contact with each other.

Ankylosis can result from a variety of causes, including trauma, infection, or degenerative joint diseases. In cases of trauma, the articulating surfaces of the bones can be damaged, leading to a complete absence of contact between the two bones. Similarly, if an infection is present, the cartilage and ligaments of the joint can be destroyed, leading to ankylosis.

Finally, in cases of degenerative joint diseases, such as arthritis, the joint's articulating surfaces can be damaged, leading to a complete loss of contact between the two bones.

The symptoms of ankylosis vary depending on the severity of the condition. In mild cases, the patient may experience stiffness, pain, and reduced range of motion in the joint. In more severe cases, the joint may become completely immobile, and the patient may have difficulty walking or performing other activities.

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Answer:

X = 1.7

Step-by-step explanation:

To solve for x, you can subtract 8.7 from both sides of the equation.

8.7 + X = 7

-8.7 -8.7

X = -1.7

So X = -1.7

[tex]8.7+x=7[/tex]

Rearrange:

[tex]x+8.7=7[/tex]

Subtract 8.7 from both sides:

[tex]x+8.7-8.7=7-8.7[/tex]

[tex]\fbox{x = -1.7}[/tex]

Answer: Simon can use the function P(z) = -125z^2 + 25000 to determine the total profit he will make at different retail prices for his board game. The function shows that his profit will be maximum at 25000 dollars and it will decrease as the price increases or decreases from that point. Simon can use this function to determine the optimal price to sell his game at in order to maximize his profit.

Step-by-step explanation:

Answer:

r=-7

See explanation below

Step-by-step explanation:

slope= y2-y1/x2-x1

1-r/5-1=2

1-r/4=2. (simplify)

1-r=8 (cross multiply)

-r=7

r=-7