which of the following are true statements? (check all that apply)

The side lengths of the given squares are 11 cm and 14 cm

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

Given that, the sides of two squares differ by 3cm and the sum of their areas is 317cm², we need to find the length of the sides of the two squares.

Let the sides of the squares be x and y, we know that the area of a square is their side's square.

Therefore, establishing the system of equations,

x-y = 3

x = y+3.......(i)

x²+y² = 317....(ii)

Put eq(i) in eq(ii)

(y+3)²+y² = 317

y²+9+6y+y² = 317

2y²+6y-308 = 0

On factorizing, we get,

y = 11 and y = -14

Since, the length can not be negative so, ignore -14

Put y = 11 in eq(i)

x = 11+3

x = 14

Therefore, the side lengths of the given squares are 11 cm and 14 cm

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The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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The car could drive approximately 293.04 miles on a full tank of gas. Drag and drop the number "293.04" into the response area to complete the statement.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent mathematical relationships and can be used to solve equations and perform calculations.

We can use the given information to find the car's fuel efficiency in miles per gallon (mpg) as follows:

mpg = miles driven / gallons of gas used

mpg = 249.48 miles / 12.6 gallons

mpg ≈ 19.8

This means that the car can travel approximately 19.8 miles on one gallon of gas. To find out how far the car could drive on a full tank of 14.8 gallons of gas, we can multiply the tank capacity by the car's fuel efficiency:

miles on full tank = mpg * gallons in full tank

miles on full tank = 19.8 mpg * 14.8 gallons

miles on full tank ≈ 293.04 miles

Therefore, the car could drive approximately 293.04 miles on a full tank of gas. Drag and drop the number "293.04" into the response area to complete the statement.

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(a) Bar A: A, Bar B: O, Bar C: F

(b) One interesting feature of the graphical display is the clear difference in the percentage of individuals who are considered unfit between adolescents and adults.

(a) Bar A: Adolescents

Bar B: Overall (both adolescents and adults)

Bar C: Adult Males vs. Adult Females

(b) The percentage of unfit individuals is much higher in adolescents (33.9%) than in adults (14%). Additionally, within the adult group, the percentage of unfit individuals is higher in females (16.2%) than in males (11.2%). Another interesting feature is that there is no significant difference in the percentage of unfit individuals between male and female adolescents.

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Answer:

I can lead you with this equation: 1.41x + 29 = Cost

I think it will be easy from here on for you.

Step-by-step explanation:

A and B are not independent since the result of one toss affects the second toss. Specifically, if the first toss result is a head (A), then the second toss will be more likely to result in a head (B).

A and B are conditionally independent given C since the probability of getting head(A) for the first toss does not depend on the type of coin selected (C).

P(A|C) = 1/2, P(B|C) = 1/2, P(A∩B|C) = 1/4, P(A) = 1/2, P(B) = 3/4, and P(A∩B) = 1/4. Therefore, given the information that a regular coin has been selected (C), the probability of A and B occurring independently is 1/4. This suggests that A and B are conditionally independent given C.

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Answer:

20%

Step-by-step explanation:

You can solve this by using the addition and multiplication properties of equality

the original equation is:

a divided by 6 - 11 = 25

then you can add 11 to both sides to get rid of it (addition property of equality)

a divided by 6 = 36

then you use the multiplication property of equality

a = 216

The statement that every diagonal of a trapezoid divides it into two congruent triangles is false.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

A trapezoid is a quadrilateral which has at least one pair of parallel sides.

The sides may or may not be equal.

Consider an isosceles trapezium, ABCD, given below which has two parallel opposite sides and the other pair of sides are equal.

If we draw a diagonal, AC, we have two triangles ABC and ADC.

AC = AC (common side)

AD = BC (given)

But AB ≠ CD

Hence the triangles cannot be congruent.

Hence the given statement is false.

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The number of units manufactured at the cost of $8200 will be 95.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the cost, C(x), for manufacturing x units of a certain product is

C(x) = x² - 9x + 30.

The number of units will be calculated as:-

C(x) = x² - 9x + 30

8200 = x² - 9x + 30

x² - 9x - 8170 = 0

Solve the equation as below,

x² - 9x - 8170 = 0

x² - 95x + 86x - 8170 = 0

x ( x - 95 ) + 86 ( x - 95 ) = 0

( x - 95 ) ( x + 86 ) = 0

x = 95 units

Therefore, the number of units manufactured at the cost of $8200 will be 95.

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The final volume of a system with initially of 2 liters if the pressure is tripled and the temperature is tripled, is 11.57 liters.

The combined gas law equation relates the initial and final conditions of a system of gas by considering the effect of changes in pressure, volume, and temperature:

P1 * V1 / T1 = P2 * V2 / T2

Given the initial conditions of the system:

V1 = 2 liters

P1 = 1 atm

T1 = 273 K (room temperature)

And the changes in pressure and temperature:

P2 = 3 * P1 = 3 atm

T2 = 3 * T1 = 819 K

We can calculate the final volume of the system:

V2 = (P1 * V1 / T1) * (T2 / P2) = (1 atm * 2 liters / 273 K) * (819 K / 3 atm) = approximately 11.57 liters

So the final volume of the system would be approximately 11.57 liters if the pressure is tripled and the temperature is tripled from the initial conditions.

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Answer:

Step-by-step explanation:

-3 1/3 goes to between -3 and -4

9/2=4 1/2 between 4 and 5

[tex]\sqrt{15}[/tex] between 3 and 4

16/5=3 1/5 between 3 and 4

\sqrt{15} between 2 and 3

The depreciated price of the car in the year 2022 is $148.47

Depreciation in economics is a measure of the amount of value an asset loses from influential factors affecting its market value.

Given that, in 1960 the average price of a new car was $2752. Between 1960 and 2022 car prices have decreased by an average of 4.6% per year.

We need to calculate the average price of a new car in 2022​

The question is depreciated price of the car,

Depreciated price =

A = P(1-r)ⁿ

A = final amount

P = initial amount

r = 4.6%

n = time

Here, the time = 2022 - 1960 = 62 years

Therefore,

A = 2752(1-0.046)⁶²

A = 2752(0.954)⁶²

A = 148.47

Hence, the depreciated price of the car in the year 2022 is $148.47

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The solution of the inequality is x > -2 and x < 7.

Inequality Notation: -2 < x < 7.

The graph is attached.

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4.

-5x - 7 < 3

-5x < 3 + 7

-5x < 10

x > 10/(-5)

x > -2

-5x - 7 > -42

-5x > -42 + 7

-5x > -35

x < -35/(-5)

x < 7

We have x > -2 and x < 7.

x > -2 can be written as -2 < x.

Inequality Notation: -2 < x < 7

This implies that x is in the range of -2 and 7. The graph is attached.

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(a) p ∨ r: "x≥7 or 12>x.", (b) r ∧ p: "12>x and x>7." and (c) r ∧ (q ∨ p) : "12>x and (x=7 or x>7),

" which simplifies to "12>x." The second part, (p ∨ q) ∧ r ∨ (p ∼ q) ∧ r ∨ (p ∧ q) ∧ r ∼ (p ∨ q), is always true when r is true, so it is equivalent to r. Thus, the entire statement is equivalent to "12>x and (x=7 or x>7)."

(a) p ∨ r: This statement is a logical disjunction, also known as an "or" statement. It is true if either the left side (p) is true or the right side (r) is true, or both. The statement "x>7" is equivalent to "x≥7 or x=7", so the statement p ∨ r can be read as "x≥7 or 12>x."

(b) r ∧ p: This statement is a logical conjunction, also known as an "and" statement. It is true only if both the left side (r) and the right side (p) are true. The statement "12>x" is equivalent to "x<12", so the statement r can be read as "x<12." Combining this with the statement p (x>7) gives "12>x>7."

(c) r ∧ (q ∨ p): This statement is a conjunction of r and a logical disjunction (q ∨ p). As we saw in part (a), p is equivalent to "x≥7 or x=7", so the statement (q ∨ p) can be read as "x=7 or x≥7". Combining this with the statement r (12>x) gives "12>x and (x=7 or x>7)", which can be simplified to "12>x."

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The system of linear equations x = 4 and y = -x -1 has a unique solution.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

Given is a graph of lines,

We need to find the number of solutions do the lines x = 4 and y = -x-1 have,

In the graph of the lines x = 4 and y = -x -1, intersecting at a point, we know that the lines which intersects at a single point will have only one solution.

Also,

The system of equation has the solution at the point where the line intersects,  

By observing the graph it can be concluded that the graph of x = 4 and y = - x - 1 intersect only at one point i.e (4, -5).

Therefore, the solution of the given system of equations is (4, -5)

Hence, the system of linear equations x = 4 and y = -x -1 has a unique solution.

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Length of the sides is 54 and 54 inches.

Length is defined as the measurement of distance of an object from one end to the other.

A headboard for a bed is shaped like an isosceles trapezoid.

Since it is a isosceles trapezoid the length are equal in number.

The we have to equate the given lengths,

i.e., 6x+18 = 8x+6

Rearranging the terms we get,

6x-8x = 6-18

-2x = -12

Divide by -2 on both sides we get,

x = 6

Sub x in the given lengths we get,

6x + 18 ⇒ 6 * 6 +18 = 54

8x + 6 ⇒8 *6 +6 = 54

So, length of the sides is 54 inches.

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To solve this problem, we can use the formula for calculating the quarterly payment of a loan with compound interest:

Payment = (r * P) / (1 - (1 + r)^(-n))

where:

r = quarterly interest rate (12% / 4 = 0.03)

P = principal amount (remaining debt after down payment) = $150,000

n = total number of quarterly payments (10 years * 4 quarters per year = 40)

(1) Calculation of Quarterly Payment:

Payment = (0.03 * 150,000) / (1 - (1 + 0.03)^(-40)) = $2,365.87 (rounded to the nearest cent)

Therefore, the quarterly payment is $2,365.87.

(2) Calculation of Total Amount of Payment:

Total amount of payment = (number of payments) * (quarterly payment)

number of payments = 10 years * 4 quarters per year = 40

Total amount of payment = 40 * 2,365.87 = $94,634.80

Therefore, the total amount of payment is $94,634.80.

(3) Calculation of Total Amount of Interest Paid:

Total amount of interest paid = total amount of payment - principal amount

Total amount of interest paid = $94,634.80 - $150,000 = -$55,365.20

Note that the result is negative because the down payment ($50,000) exceeds the total amount of interest paid over the life of the loan. Therefore, in this case, the total amount of interest paid is $0, and the man ends up paying a total of $100,000 ($50,000 down payment + $50,000 in quarterly payments).

The first line that should be removed is the print statement. The code should not display the result right away, as this will prevent it from counting the number of prime numbers in the list.

The second line of code that should be removed is the second statement, which checks to see if the index is equal to 0. This line of code is unnecessary, as the prime numbers are already tested in the if statement before it.

In order for the program to work as intended, the code should only include the if statement that checks to see if the number is a prime number, the for loop that iterates through the list and increments the counter for each prime number found, and the print statement that displays the result at the end. This will ensure that the program counts the number of prime numbers in the list and displays the result correctly.

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Answer: look at the images for the answer ( the first image is for #1 and the second image is for #2 )

Step-by-step explanation:

a) We cannot determine the probability

b) The mean of x - 55 is $28 - $55 = -$27, and the standard deviation of x - 55 is $0.45.

c) By the central limit theorem, the sampling distribution of x^-x will be approximately normal if the sample size is large enough.

d)  The probability that the average fee paid by the sample of households exceeds $55 is very close to 0.

a. We cannot determine the probability that the amount a randomly selected household pays for access to the internet exceeds $55 because we don't have information about the distribution of individual payments, only the mean and standard deviation of the population.

b. The mean of the sampling distribution of x is equal to the population mean, which is $28. The standard deviation of the sampling distribution of x is equal to the population standard deviation divided by the square root of the sample size, which is $10/sqrt(500) ≈ $0.45. Therefore, the mean of x - 55 is $28 - $55 = -$27, and the standard deviation of x - 55 is $0.45.

c. By the central limit theorem, the sampling distribution of x^-x will be approximately normal if the sample size is large enough. In this case, since the sample size is 500 and greater than 30, we can assume that the sampling distribution is approximately normal.

d. To find the probability that the average fee paid by the sample of households exceeds $55, we need to standardize the value of x using the sampling distribution of x^-x and then find the probability of a z-score greater than or equal to:

z = (55 - 28)/0.45 ≈ 60. The probability of a z-score greater than or equal to 60 is extremely small, as the normal distribution tails off quickly. Therefore, the probability that the average fee paid by the sample of households exceeds $55 is very close to 0.

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To prove that ΔAED ≅ ΔCFD, we will use the two given angle equalities and the fact that D is the midpoint of AC:

Given: D is the midpoint of AC, ∠AED ≅ ∠CFD, and ∠EDA ≅ ∠FDC

To prove: ΔAED ≅ ΔCFD

Proof:

Thus, we have proved that ΔAED ≅ ΔCFD.

The measure of angle 2 from the diagram is equivalent to 111 degrees

An angle is defined as the point where two lines meet. From the diagram shown the measure of <1 and <2 lies on the same straight line.

Since the sum of angles on a straight line is 180 degrees, hence;

<1 + < 2 = 180

Substitute the given angle

69 + <2 = 180

<2 = 180 - 69

<2 = 111 degrees

Hence the measure of <2 from the given diagram is 111 degrees.

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According to the given information the answer is JK thus has a 10-unit length.

The measurement or size of a thing end to end is referred to as its length. In other words, it is the larger of an object's elevated two or three geometric dimensions. For instance, a rectangle's dimensions are determined by its length and width.

We must determine the separation among points J and K in order to get the length of JK. The distance formula is as follows:

d = √((x2 - x1)² + (y2 - y1)²)

Where (x1, y1) = (-5, 6) is the coordinate of J and (x2, y2) = (5, 6) is the coordinate of K.

Plugging in the values, we get:

d = √(5 - (-5))² + (6 - 6)²)

= √(10² + 0²)

= √100

= 10

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Answer:

A) Yes, Rolle's Theorem can be applied!

Step-by-step explanation:

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

Here, for our continuous function [tex]f(x)=-x^2+2x[/tex] over the closed interval [tex][0,2][/tex], we can tell that the function is clearly differentiable over the interval [tex](0,2)[/tex] as [tex]f'(x)=-2x+2[/tex], so we'll need to check if [tex]f(0)=f(2)[/tex]:

[tex]f(0)=-0^2+2(0)=0\\f(2)=-(2)^2+2(2)=-4+4=0[/tex]

Next, we'll need to check if f'(x) = 0 for some x within the closed interval:

[tex]f'(x)=-2x+2=0\\-2x+2=0\\-2x=-2\\x=1[/tex]

As x=1 is contained in [0,2] and the previous conditions were met, Rolle's Theorem can be applied!

If Cecily purchases a box of 100 paper clips. She puts 37 /100 of the paper clips in a jar on her desk and puts another 6 /10 in her drawer at home. The number  of the paper clips that are in Cecily's jar  is: 43.

Here is a grid to show the number of paper clips that Cecily has in her jar and drawer:

JAR | DRAWER

|

37 | 60

|

100 | 100

The fraction that the grid represents is :

37/100 + 6/100 = 43/100.

Therefore, Cecily has 43 out of 100 paper clips in her jar and drawer.

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The value of the expression (1/2)^3 include the following: D. 1/8.

In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;

bⁿ

Where:

the variables b and n represent numerical values or an algebraic expression.

From the information provided, we can logically deduce the following as the only true statement:

Expression = (1/2)^3

Expression = 1/2 × 1/2 × 1/2

Expression = 1/8

In conclusion, the numerical value 3 represents the power of the given expression.

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Complete Question:

What is the value of the expression (1/2)^3?

Responses

19

1/9

18

1/8

16

1/6

32