In the last basketball game, Elena scored 2 more than one fourth of herteam's total points.

Part A: Let n represent the number of points Elena's team scored.
Write an expression for the number of points Elena scored.

Part B: The team scored 40 points. How many points did Elena
score?

Step-by-step explanation:

We can also solve the equation x² + 4x + 4 = 8 by rearranging the terms and using the quadratic formula:

x² + 4x + 4 - 8 = 0

x² + 4x - 4 = 0

Applying the quadratic formula, we have:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 4, and c = -4. Substituting these values, we get:

x = (-4 ± √(4² - 4(1)(-4))) / 2(1)

x = (-4 ± √32) / 2

Simplifying the square root of 32, we get:

x = (-4 ± 4√2) / 2

x = -2 ± 2√2

Therefore, the solutions to the equation x² + 4x + 4 = 8 are x = -2 + 2√2 and x = -2 - 2√2.

The greatest possible integer value of the radius of the circle is 7 inches.

The area of a circle is given by the equation[tex]$A = \pi r^2$[/tex]. We know that the area is less than [tex]$60\pi$[/tex] square inches, so the equation can be written as [tex]$60\pi > \pi r^2$[/tex]. We can solve for the radius by dividing both sides by [tex]$\pi$[/tex], which gives us [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex], which is approximately 7.74 inches. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.

To explain this further, we can start with the equation for the area of a circle, which is[tex]$A = \pi r^2$[/tex]. Since the area is less than [tex]$60\pi$[/tex]square inches, this equation can be rewritten as[tex]$60\pi > \pi r^2$[/tex]. We can then divide both sides by [tex]$\pi$[/tex] to get [tex]$60 > r^2$[/tex]. Taking the square root of both sides gives us [tex]$r < \sqrt{60}$[/tex]. This result can then be rounded down to the nearest integer, which is 7. Therefore, the greatest possible integer value of the radius of the circle is 7 inches.

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The probability that the person is actually innocent given that they have failed the test is 0.4615... or approximately 0.462.

The question asks us to calculate the probability that the person is actually innocent given that they have failed the test. The probability that the person is actually innocent is given by the formula: P(innocent | fails test) = P(innocent and fails test) / P(fails test).

Now we need to calculate the values of the probabilities on the right-hand side of this equation. P(fails test) is equal to the sum of the probabilities that a guilty person fails the test and that an innocent person fails the test. Hence, P(fails test) = P(guilty and fails test) + P(innocent and fails test). P(guilty and fails test) = 0.2 × 0.7 = 0.14P(innocent and fails test) = 0.8 × 0.15 = 0.12. Therefore, P(fails test) = 0.14 + 0.12 = 0.26.

Finally, we can calculate the probability that the person is actually innocent given that they have failed the test: P(innocent | fails test) = P(innocent and fails test) / P(fails test)= 0.12 / 0.26= 0.4615 (rounded to four decimal places).

Therefore, the probability that the person is actually innocent given that they have failed the test is 0.4615... or approximately 0.462.

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In conclusion, the power series converges absolutely over an interval given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex]is a natural number.

The interval over which the power series converges absolutely is given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex] is a natural number.

In other words, for any given N, the series will converge absolutely over the interval \left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n>N.

This means that the series will converge absolutely over a larger interval as N increases, since the terms \frac{\left|a_n+1\right|}{\left|a_n\right|} get closer to 1 for larger values of n.

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Answer:

a) a is 13

b is 14

c is 5

b) a is 5

b is 13

c is-10

c) a is 1

b is 0

c is -4

d) a is -9

b is 0

c is 0

Step-by-step explanation:

hope this will be helpful:)

You have a 4/12 probability.

The heights of the tips of the propeller blades at π/6, 5π/6, and 3π/2 radians are 15.5 feet, 11.5 feet, and 10 feet, respectively.

What is the equation of a circle in parametric form?

The equation of a circle in parametric form is given by x=acosθ,y=asinθ.

We can use the equation for a circle in standard form:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

In this case, the center of the propeller is (0, 13) and the radius is 3. So the equation of the circle is:

x² + (y - 13)² = 9

We can use this equation to find the x and y coordinates of the tip of each propeller.

For the blade at π/6 radians, we can use the parametric equations for a circle:

x = r cos(t) + h

y = r sin(t) + k

where t is the angle in radians.

Substituting r = 3, h = 0, k = 13, and t = π/6, we get:

x = 3 cos(π/6) + 0 = 3√3/2

y = 3 sin(π/6) + 13 = 13 + 3/2 = 15.5

So the height of the tip of the propeller blade at π/6 radians is 15.5 feet.

Using the same method for the blades at 5π/6 and 3π/2 radians, we get:

Blade at 5π/6 radians:

x = 3 cos(5π/6) + 0 = -3√3/2

y = 3 sin(5π/6) + 13 = 13 - 3/2 = 11.5

Height of tip: 11.5 feet

Blade at 3π/2 radians:

x = 3 cos(3π/2) + 0 = 0

y = 3 sin(3π/2) + 13 = 10

Height of tip: 10 feet

Therefore, the heights of the tips of the propeller blades at π/6, 5π/6, and 3π/2 radians are 15.5 feet, 11.5 feet, and 10 feet, respectively.

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Tom will pay a total of $13,424.20 in interest over the term of the loan.

The formula to calculate the monthly payment for an amortized loan is given by:  `P = r(PV) / [1 - (1 + r)^(-n)]`Where P is the monthly payment, r is the interest rate per month, PV is the present value of the loan, and n is the number of payments or the total number of months.

Substituting the given values, we get:P = 0.0052083333 × 44,000 / [1 - (1 + 0.0052083333)^(-7×12)]P = 632.32Therefore, Tom's monthly payment is $632.32 (rounded to the nearest cent).b. Since Tom pays the monthly payment each month for the full term, his total amount to repay the loan is equal to the present value of the loan.

Therefore, the total amount to repay the loan is $44,000 (rounded to the nearest cent).c. The total amount of interest paid over the term of the loan can be calculated as the difference between the total amount repaid and the principal amount of the loan.

Therefore, the total interest paid is: Total interest paid = Total amount repaid - Principal amount of the loan Total interest paid = $57,424.20 - $44,000Total interest paid = $13,424.20

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The Polynomials that are listed in the question are the options labelled;

B, C, E

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents.

The variables represent unknown values, while the coefficients are constants that multiply the variables or their exponents. The exponents indicate the power to which the variables are raised.

Polynomials can be added, subtracted, multiplied, and divided to create more complex expressions, and they are used in a wide range of mathematical applications, including algebra, calculus, and geometry.

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Hence, x has a value of 49 as to find x, we add 9 to both sides and divide the result by 3.

The distance between two intersecting lines or planes is measured in terms of angles. The amount of rotation required to align one of the lines or planes with the other is usually expressed in terms of degrees. The range of an angle is 0 degrees (i.e., no rotation) to 360 degrees (corresponding to a complete rotation).

given

As angles 5 and 7 are a pair of linear angles, their sum must be 180 degrees. Angle 7 therefore has a measure of 180 - 42 = 138 degrees.

We can use the fact that angles 6 and 7 are vertical angles and have the same measure to find the value of x. As a result, we can set the following phrase to indicate that the measure of angle 6 is equal to angle 7:

3x - 9 = 138

In order to find x, we add 9 to both sides and divide the result by 3:

3x = 147

x = 49

Hence, x has a value of 49 as to find x, we add 9 to both sides and divide the result by 3.

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Answer:

The z-Table gives the area under the standard normal curve to the left of z. What does the t-Table give? The t-Table gives the area under the t-curve with n degrees of freedom to the left of it

HOPE THIS HELPSSS!

The height of the BD for the house using Pythagorean theorem is obtained as: 4.23 m.

According to the Pythagorean Theorem, for any triangle which is a right triangle, the squares of the legs added together equal the square of the hypotenuse.

In the given triangle ABC.

AB = BC = 6 cm

So, ∠A = ∠C  (by isosceles triangle)

Then, AD = DC = 8.5/2

So, in right angles triangle ABD, applying Pythagorean theorem:

AB² = AD² + BD²

6² = (8.5/2)² + BD²

36 - 18.0625 = BD²

BD = √17.9375

BD =  4.23

Thus, the height of the BD for the house using Pythagorean theorem is obtained as: 4.23 m.

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Answer:

Step-by-step explanation:

If there are five knights and they need to divide the guard duty equally for the 24 hours in a day, each knight would spend 24/5 = 4.8 hours on guard duty in one day.

However, since it's not possible to guard for a fraction of an hour, they would need to round that number to the nearest whole number. In this case, each knight would spend 5 hours per day on guard duty.

Answer:

The formula for the area of a circle is A = πr^2, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14159.

If the radius of the circle is 11 inches, then we can substitute this value into the formula:

A = πr^2

A = π(11)^2

A = π(121)

So the area of the circle is 121π square inches, which is approximately 380.1327 square inches when rounded to four decimal places.

Answer:

The correct table of values that could be used to graph g(x), a reflection of f(x) across the x-axis, is:

x f(x) g(x)

-2 1/108 12

-1 1/18 2

0 1/3 1/3

1 2 1/18

2 12 1/108

To reflect a function across the x-axis, we need to change the sign of the y-coordinate for every point on the function. Therefore, to find g(x), we take the negation of f(x) for every value of x. The second column in the third option is the negation of f(x), so it is the correct table of values for g(x).

Answer:

Its A.

Step-by-step explanation:

Other one was not clear enough lol ^

The present value that must be invested to get $2500 after 6 years at a simple interest rate of 11.0% is $1509.64.

In this case, we know the final amount that we want to have after 6 years, which is $2500. We also know the interest rate, which is 11.0%. What we need to find is the principal amount, which is the present value that we must invest now to achieve the desired future value.

Using the formula for simple interest, we can rearrange it to solve for the principal:

Principal = Simple Interest / (Rate x Time)

We know that the simple interest is the difference between the final amount and the principal amount. Therefore, we can substitute the values into the formula:

$2500 - Principal = (Principal x 0.11 x 6)

Simplifying the equation, we get:

$2500 = Principal + (0.66 x Principal)

$2500 = 1.66 x Principal

Dividing both sides by 1.66, we get:

Principal = $1509.64

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The vertices of the image of QRTW for a dilation with center (0, 0) and a scale factor of 1/4 include the following:

Q' (-0.5, 0.75).

R' (-0.75, 0.25).

T' (0.5, -0.25).

W' (0.25, 1).

In Mathematics and Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin (0, 0) as follows:

Ordered pair Q (-2, 3) → Ordered pair Q' (-2 × 1/4, 3 × 1/4) = (-0.5, 0.75).

Ordered pair R (-3, 1) → Ordered pair R' (-3 × 1/4, 1 × 1/4) = (-0.75, 0.25).

Ordered pair T (2, -1) → Ordered pair T' (2 × 1/4, -1 × 1/4) = (0.5, -0.25).

Ordered pair W (2, 4) → Ordered pair W' (2 × 1/4, 4 × 1/4) = (0.25, 1).

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Answer:

The answer to your question would be true.

The given statement 'full-time high school students spend more time per week on their courses than full-time college students' is true because full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class.

Full-time high school students spend more time per week on their courses than full-time college students. It is because full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class.

College courses usually last for one hour per day, whereas high school students attend classes for 5-6 hours per day. Hence, college students spend around 15-18 hours per week attending classes, while high school students spend around 30 hours per week in the classroom.

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If at a school of 550 children 80% walk to school, the 110 children come to school by other means.

If 80% of the children walk to school, then the remaining 20% of children must arrive at school by other means (such as being driven by a parent, taking public transportation, etc.).

To find out how many children come to school by other means, we can use the following formula:

Number of children who come to school by other means = Total number of children x Percentage who don't walk to school

In this case, we have:

Number of children who come to school by other means = 550 x 20% = 110

Therefore, 110 children come to school by other means.

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The given question is incomplete, the complete question is:

At a school of 550 children 80% walk to school, how many comes in other way ?

Answer:

d=-3

Step-by-step explanation:

d^3=-27

d=[tex]\sqrt[3]{-27} \\[/tex]

d=-3

Answer:

d=-3

Step-by-step explanation:

You must that 3rd root of -27, which is -3

The given statement "the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size" is True as it is proved by the central limit theorem.

The central limit theorem (CLT) states that for large enough sample sizes, the distribution of the sample means approximates a normal distribution regardless of the shape of the initial population distribution.

It is a statistical theory that clarifies how the mean of a random sample of independent observations drawn from a non-normal population converges in distribution to a normal population.

According to this theory, the sample size should be at least 30 for the sample mean to have an approximately normal distribution. The following are the fundamental assumptions of the central limit theorem:

Therefore, we can say that the sampling distribution becomes approximately normal, for all statistics, if there is a large enough sample size. The statement is true.

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Answer:

[tex]y=3cos(3\pi x)+4[/tex]

Step-by-step explanation:

[tex]f(x)=cos(x)\\[/tex]

[tex]A(f(Bx+C)+D)[/tex]

The outside constants, A & D stretch and shift vertically. The inside constants, B & C stretch and shift horizontally. B & C work oppositely, basically multiplying by B stretches by a factor of 1/B and similarly adding C shifts f(x) horizontally to the left.

[tex]f(x)=cos(x) \text{ The function which we are transforming}\\\text{It currently has a amplitude of 1, time period of $2\pi$ and mid line at $y=0$}[/tex]

[tex]A=3 \text{ As we want to stretch it by 3 units vertically.}\\\text {To find B:}\\T' = T*(1/B)\\\text{Where $T'$ is new time period and T is existing time period}\\2/3=2\pi*(1/B)\\B=3\pi\\\text{C is not needed}\\D=4 \text{ To shift function by 4 units up}[/tex]

I hope this helps

The circumference of a circle with a radius of 15 inches is 30π inches, or 94.25 inches

The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.

In this case, the radius is 15 inches. Substituting this value into the formula, we get:

C = 2π(15) = 30π

So the circumference of a circle with a radius of 15 inches is 30π inches, or approximately 94.2478 inches.

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The value of the given lengths are as follows:

a.) KL = 11.1ft

LO = 5.7ft

b.) m<OMN = 45°

For Side LO ;

7/11 = 7√2/7√2+LO

7(7√2+LO) = 11×7√3

69.3+7LO = 108.9

7LO = 108.9-69.3

LO = 39.6/7

LO = 5.7 ft

For KL ;

This can be solved using the Pythagorean theorem;

c²= b²+a²

C = 5.7+7√2 = 15.6

b = 11

a²= 15.6²-11²

= 243.36 - 121

= 122.36

a= √122.36

a= 11.1ft

For angle OMN;

This can be solved using SOHCAHTOA.

Sin∅ = opposite/hypotenuse

opposite = 7

hypotenuse = 7√2

sin∅ = 7/7√2

sin∅ = 0.707106781

∅= sin-1 0.707106781

∅ = 45°

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Therefore, it would take about 3322 years for the Gregorian and tropical years to be out of step by exactly one day.

Length is a physical quantity that describes how long or how far apart two points or objects are from each other in space. It is typically measured in units such as meters, feet, or inches, and is one of the basic dimensions used to describe the size and position of objects in the physical world.

given by the question.

The difference between the length of the Gregorian year and the tropical year is:

365.242500 - 365.242199 = 0.000301

This means that every year, the Gregorian calendar gains 0.000301 days on the tropical year. To be out of step by exactly one day, the Gregorian calendar needs to gain one full day on the tropical year, which would take:

1 / 0.000301 = 3322.26 years.

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Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day

What is linear function ?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:

y = mx + b

where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.

According to the question:
If Daisy calls in sick, then Lisa will be the only stylist at the salon, and all customers will go to her. Let's use x to represent the number of Lisa's customers. Then the income generated by Lisa's customers can be represented by the equation:

18x = projected income

We can solve for x by dividing both sides of the equation by 18:

x = projected income / 18

Substituting the given projected income of $216, we get:

x = 216 / 18 = 12

Therefore, Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day.

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Answer:

0.15 expressed as a fraction in its simplest form is 3/20.

Step-by-step explanation:

To express a terminating decimal as a fraction:

Write the decimal as a fraction by dividing it by 1:

[tex]\boxed{\dfrac{0.15}{1}}[/tex]

Multiply the numerator and denominator by 10 for every number after the decimal point.

As there are two numbers after the decimal point, multiply the numerator and denominator by 100:

[tex]\boxed{\dfrac{0.15 \times 100}{1 \times 100}=\dfrac{15}{100}}[/tex]

Find the highest common factor (HCF) of the numerator and denominator.

Therefore, the HCF of 15 and 100 is 5.

Divide the numerator and denominator by the HCF to reduce the fraction to its simplest form:

[tex]\boxed{\dfrac{15 \div 5}{100 \div 5}=\dfrac{3}{20}}[/tex]

0.15 expressed as a fraction in its simplest form is 3/20.

Answer:

See below, please.

Step-by-step explanation:

The length of altitude CD is 133/25 units.

What is the length if altitude?

To find the length of altitude CD, we need to find the length of the line segment CD, which is perpendicular to AB and passes through the point C.

First, let's find the equation of the line AB. We can use the two-point form:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the points on the line. Using points A and B, we get:

m = (0 - 6)/(8 - 0) = -3/4

y - 6 = (-3/4)(x - 0)

y = (-3/4)x + 6

Next, let's find the slope of the line CD, which is the negative reciprocal of the slope of AB. This is because perpendicular lines have slopes that are negative reciprocals of each other. Therefore:

m_CD = 4/3

Now we can use the point-slope form to find the equation of line CD. We know that the line passes through point C (5, 8), so:

y - 8 = (4/3)(x - 5)

Simplifying, we get:

y = (4/3)x - 4/3 + 8

y = (4/3)x + 20/3

Now we need to find the intersection of line CD with line AB. We can solve the system of equations:

y = (-3/4)x + 6

y = (4/3)x + 20/3

Setting the two expressions for y equal to each other, we get:

(-3/4)x + 6 = (4/3)x + 20/3

Multiplying both sides by 12, we get:

-9x + 72 = 16x + 80

25x = -8

x = -8/25

Substituting this value of x into either equation, we get:

y = (-3/4)(-8/25) + 6 = 57/25

Therefore, the point of intersection is (-8/25, 57/25).

Finally, we can use the distance formula to find the length of CD, which is the distance between C and the point of intersection:

d = √[(5 - (-8/25))² + (8 - 57/25)²]

d = √[(125/25 + 8/25)² + (200/25 - 57/25)²]

d = √[(133/25)² + (143/25)²]

d = √(17689/625)

d = 133/25

Therefore, the length of altitude CD is 133/25 units.

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Three strategies that implement to encourage the use of BEVs are incentives, Infrastructure and Regulations. The cost of gasoline per mile for an ICE vehicle is $0.016 per mile.

Incentives: The federal government could offer financial incentives such as tax credits, rebates, or grants to consumers who purchase BEVs. This would make BEVs more affordable and help to offset the higher upfront cost of these vehicles.

Infrastructure development: The federal government could invest in the development of charging infrastructure for BEVs, such as public charging stations. This would help to alleviate range anxiety and make BEVs more convenient and practical for consumers.

Regulations: The federal government could implement regulations that incentivize or require automakers to produce more BEVs. This could include emissions standards that are more favorable to BEVs, or mandates for automakers to produce a certain percentage of their vehicles as electric.

To calculate the cost of gasoline per mile for an ICE vehicle with fuel efficiency of 235 miles per gallon and gasoline cost of $3.75 per gallon, we divide the cost of gasoline by the fuel efficiency:

Cost per mile = $3.75 / 235 miles per gallon

Cost per mile = $0.016 per mile

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In Linear equation, 260.2 would they each earn if they divided their earnings equally.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                                         Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

three friends earned $359 in August, $522 in July, and $420 in September

                = $359 + $522 $ 420  

                = 1301/5 = 260.2

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