A student correctly draws a square with side lengths of 4 centimeters. Which statement about the resulting figure is true?

A. The figure has three 45°
angles and exactly one pair of parallel sides.

B. The figure has three 90° angles and exactly one pair of parallel sides.

C. The figure has four 60°
angles and exactly two pairs of parallel sides.

D. The figure has four 90°
angles and exactly two pairs of parallel sides.

To solve this problem, we can use the Pythagorean theorem to find the height of the balloon. In particular, we can consider the right triangle formed by the stake, the top of the balloon, and the part of the string that is attached to the stake.

[asy]

unitsize(2 cm);

pair A, B, C, D, E;

A = (0,0);

B = (0,8);

C = extension(A,B,A+(1,0),B+(1,0));

D = extension(A,C,A+(0,1),C+(0,1));

E = extension(B,D,B+(0,-1),D+(0,-1));

draw(A--B--C--cycle);

draw(A--D--E--cycle);

draw(rightanglemark(A,D,C,2));

label("$A$", A, S);

label("$B$", B, N);

label("$C$", C, E);

label("$D$", D, E);

label("$E$", E, W);

[/asy]

Let $a$ be the distance from the stake to the top of the balloon, $b$ be the height of the balloon, and $c$ be the length of the string. We know that $a = 8$ feet and $c = 15$ feet, so we can use the Pythagorean theorem to find $b$:

$a^2 + b^2 = c^2$

$8^2 + b^2 = 15^2$

$64 + b^2 = 225$

$b^2 = 161$

$b = \sqrt{161} = \boxed{12.8}$ feet

Therefore, the height of the balloon is approximately 12.8 feet.

the edges of a cube increase at a rate of 5 centimeters per second. The surface area is changing at a rate of 150 cm²/sec.

To calculate the rate at which the surface area of a cube is changing when each edge is 10 cm long, we first need to calculate the surface area of the cube. The surface area of a cube can be calculated by multiplying the length of one edge cubed by 6. In this case, the length of one edge is 10 cm, so the surface area of the cube is 600 cm². Since the edges of the cube are increasing at a rate of 5 cm/sec, the rate at which the surface area of the cube is changing is equal to the surface area multiplied by the rate of increase, or 600 cm² * 5 cm/sec = 300 cm²/sec.

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The value of x in the triangle is 140 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Applying the exterior angle theorem,

40 + 100 = x

140 = x

x = 140 degrees.

Therefore, x is 140 degrees.

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Answer:

1/125

Step-by-step explanation:

Answer:

1\/125 and 1/5^3

Step-by-step explanation:

Answer:

  45 units

Step-by-step explanation:

Given that the perimeter and diagonal length of a polygon are proportional and that a polygon with a diagonal of 8 units has a perimeter of 36 units, you want the perimeter for a diagonal of 10 units.

The proportion of interest is ...

  P/d = p/10 = 36/8

Multiplying by 10 gives ...

  p = 10(36/8) = 45

The perimeter of the larger polygon is 45 units.

Ana should choose option (a) because she pays the least in interest.

To determine which option would be the most cost-effective for Ana, you need to consider the total amount of interest she would pay over the course of the loan.

Option (a) is monthly simple interest, which means that the interest is calculated on the principal balance of the loan at the end of each month, based on the annual interest rate. Option (b) is quarterly compound interest, which means that the interest is compounded and added to the principal balance of the loan at the end of each quarter. Option (c) is continuous compound interest, which means that the interest is compounded continuously, rather than at fixed intervals.

Using the formula for simple interest, the total amount of interest that Ana would pay over the course of the loan under option (a) is:

$166.25 = $5,000 * 3.99% * 10

Each color pencil in the first case costs $0.12. Each color pencil in the second case costs $0.11. The cheapest pencil is in the second case.

The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to achieve the required value.

Here,

Cost of 24 color pencil=$2.88

Cost of 1 color pencil=$2.88/24

=$0.12

Cost of 18 color pencil=$1.98

Cost of 1 color pencil=$1.98/18

=$0.11

The cost of each color pencil from first case is $0.12. The cost of each color pencil from second case is $0.11. The second case has cheapest pencil.

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Answer:

The answer is quad 1 and quad 2 are congruent because quad 2 can be created rotating and then translating quad 1

Step-by-step explanation:

Answer:

To find the value of r₂, we need to know how the dilations with scale factors r₁ and r₂ affect the coordinates of the point P.

If a dilation with scale factor r₁ maps a point P with coordinates (x, y) to another point P' with coordinates (x', y'), then the coordinates of P' are related to the coordinates of P by the equation:

x' = r₁x

y' = r₁y

Similarly, if a dilation with scale factor r₂ maps a point P' with coordinates (x', y') to another point P'' with coordinates (x'', y''), then the coordinates of P'' are related to the coordinates of P' by the equation:

x'' = r₂x'

y'' = r₂y'

Since we are given that the dilations map P to P and P' to P, we can set the coordinates of P and P'' equal to each other, and the coordinates of P' and P'' equal to each other. This gives us the following system of equations:

x'' = x

y'' = y

x'' = r₂x'

y'' = r₂y'

Substituting the second set of equations into the first set, we get:

x = r₂x'

y = r₂y'

Since we know that the dilation with scale factor r₁ maps P to P', we can substitute the equations for x' and y' into the above equations to get:

x = r₂*(r₁x)

y = r₂(r₁*y)

Solving for r₂, we find that:

r₂ = 1/r₁

Substituting the value of r₁ = 1/4, we find that:

r₂ = 1/(1/4) = 4

So the value of r₂ is 4.

Answer:

-3

Step-by-step explanation:

The formula for the rate of change (slope) between two points is:

[tex]\frac{y_2 - y_1}{x_2-x_1}[/tex]      
So, we plug in the two points:

[tex]\frac{-20-(-5)}{6-1} =\frac{-15}{5} =-3[/tex]
The rate of change is -3

probability that exactly 5  customers pay in cash  is 0.178863

Total number of customer = 20

probability of payment in cash = 0.3

probability of payments via other methods  = 1 - 0.3 =0.7

let probability of payment in cash be p

and probability of payments via other methods be q

To find the probability that exactly y customers pay in cash

p [ x = y ] =  [tex]n_c__x p^x q ^(n-x)[/tex]

here value of y= 5 and n=20 , p =0.3 , q= 0.7

putting the values in above equations we get:

p [ x =5 ] = [tex]20_c__5 * 0.3 ^5 * 0.7 ^15[/tex]

p [ x =5 ] = (15504) * (0.00243) * (0.0047475615)

p [ x =5 ] = 0.178863

so the probability that exactly 5  customers pay in cash  is 0.178863

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Answer:

Described below.

Step-by-step explanation:

To graph the solution to an inequality on the number line, we need to determine the values of the variable that satisfy the inequality and then plot those values on the number line. In the given inequality, 35z > 34, we can solve for z by dividing both sides of the inequality by 35 to get:

z > 34/35

This gives us the solution z > 0.96857. To graph this solution on the number line, we can plot a dot at the value 0.96857, which represents the smallest value of z that satisfies the inequality. We can then draw a line segment to the right of this point, indicating that all values of z greater than 0.96857 are also solutions of the inequality. This is shown in the following diagram:

[Insert diagram of number line with dot at 0.96857 and line segment to the right]

As the inequality is strict (i.e., it uses the ">" symbol rather than "≥"), the values of z that exactly equal 0.96857 are not considered to be solutions. Only values of z that are greater than 0.96857 are considered to be solutions of the inequality.

Answer:

2662

Step-by-step explanation:

it is really good to this 2.66÷2 X 100

Answer:

B

Step-by-step explanation:

On a coordinate plane, parallel lines have the same slope as geometric figures are true. Thus option B is correct.

Marks, splines, spheres, and curved are used to build enclosed geometric shapes. We can see these shapes all around us. Illustrations of geometric shapes include circles, rectangles, triangles, and others. Any configuration of points, columns, or angles is a geometry figure.

A point is the most fundamental algebraic concept because it has no boundaries. Simply put, a point upon that plane is a location. A dot is used to symbolize it. A plane can be identified by three non-straight-line points.

As two or much more vectors seldom cross each other and are located on the same dimension, these are said to be parallel. The slope of these lines is constant. Coplanar lines that seem to be parallel are the ones that don't cross. Therefore, option B is the correct option.

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The principal and coupon payment made on January 15, 2020 would be calculated based on the difference between the CPI on the date of issue and the CPI on due time January 15, 2020.

Using the values given, the principal and coupon payment would be equal to the original principal and coupon multiplied by the ratio of the two CPI values. Therefore, the principal and coupon payment would be equal to (CPI on date of issue/CPI on January 15, 2020) * (original principal + coupon).

1. Calculate the ratio of the two CPI values by dividing the CPI on the date of issue by the CPI on January 15, 2020 with time:

ratio = (CPI on date of issue / CPI on January 15, 2020)

2. Multiply the original principal and coupon by the ratio from step 1:

principal and coupon payment = (ratio) * (original principal + coupon)

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inverse of function

-

f (x) = 7(x - 5) + 1

y = 7x - 34

x = (y + 34) / 7

g (x) = (x + 34) / 7

____

Answer:

2

Step-by-step explanation:

4 green balls

5%

would equal 2

The correct description will be;

⇒ y = - 2x + 3

4x + 2y = 6

These are independent.

⇒ y = -2x + 3

4x + y = 9

These are consistent.

⇒ y = -2x+3

4x + 2y = 9

These are inconsistent.

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

Given that;

The expressions are,

1. y = -2x+3

4x + 2y = 6

2. y = -2x+3

4x+y=9

3. y = -2x+3

4x + 2y = 9

Now,

From (1);

1. y = -2x+3

4x + 2y = 6

⇒ 2x + y = 3

4x + 2y = 6

⇒ 2x + y = 3

So We get;

⇒ 2/2 = 1/1 = 3/3

⇒ 1/1 = 1/1 = 1/1

These are independent.

From (2);

1. y = -2x+3

4x + y = 9

⇒ 2x + y = 3

4x + y = 9

So We get;

⇒ 2/4 ≠ 1/1

⇒ 1/2 ≠ 1/1

These are consistent.

From (3);

1. y = -2x+3

4x + 2y = 9

⇒ 2x + y = 3

4x + 2y = 9

So We get;

⇒ 2/4 = 1/2 = 3/9

⇒ 1/2 = 1/2 ≠ 1/3

These are inconsistent.

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The ratio of boy to girl who play kickball at race is 6 to 2. There are 18 girl on the team. the number of boys who play kickball at race is 12 boys.

The ratio of boy to girl who play kickball at race is 6 to 2

6 boys: 2 girls

Multiply the number of girls by the ratio:

18 girls x (6 boys / 2 girls) = 18 x 3 = 54

Subtract the number of girls from the total to get the number of boys:

54 - 18 = 36

Therefore, there are 12 boys who play kickball at race.

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Answer:

20

Step-by-step explanation:

When you have two minuses, it will result in a plus.

Answer:

it's 20

Step-by-step explanation:

i just hv to know the sign

A type II error is when you fail to reject a false null hypothesis. This means that you conclude that the null hypothesis is true, even though it is actually false. This error occurs when you do not have sufficient evidence to reject the null hypothesis, and you end up accepting it as true.

Here are the possible options for type II errors:

1.Failing to reject a false null hypothesis (correct answer).

2.Accepting a false alternate hypothesis.

3.Rejecting a false null hypothesis.

4.Rejecting a false alternate hypothesis.

A hypothesis is a tested assertion about the relationship between two or more variables or a theory put up to explain an observed occurrence in a scientific environment.

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The accuracy of the given test for meningitis is; 95%

The accuracy of a test is gotten by dividing the number of correct results  by the number of tests.

In this problem, there were 80 volunteers who took the tests, of which the number that had correct results is;

80 - 2 - 2 = 76

Thus, the accuracy is given by:

A = 76/80 = 0.95 = 95%.

That gives us the accuracy of the meningitis test.

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Step-by-step explanation:

S=6a^2

294=6a^2

294/6=a^2

a^2=49

a=

[tex] \sqrt{49} [/tex]

a=7

V=a^3

V=7^3

V=343cm3

The statement about the polynomial is an example of deductive reasoning. This is shown by the Option labelled A

We know that the term deductive reasoning has to do with the kind of knowledge that we arrive at by the consideration of the facts of the problem that has been set before us.

In effect, we can be able to define deductive reasoning as a kind of reasoning that moves from the general to the particular. We are looking at the fact that the result that we have in the given instant is obtained after the consideration of a more general proposition.

In this case, we have been told that the remainder would be zero based on the kind of polynomial that we have and this has been induced by looking at the polynomial.

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Answer:

2.8mm

Step-by-step explanation:

using the sine rule.

so, she has three boards, 36, 39 and 42 inches, hmmm but she wants the length or longer side to be 3.25 ft, hmmm 36 ÷ 12 is just 3, so that won't do, 42 ÷ 12 is 3.5 ft, nope not that one, 39 ÷ 12 is 3.25, well, that's our board.

so the width has to be smaller than the length, and it has to be a full board, so since we used the 39 incher already, smaller than 39 is 36, so we'll use the 36 incher for the width, that is, the 3 feet one.

From the 3rd board, Mia is going to have to make it match with the 36 incher, that means she needs to saw it off by 6 inches, 42 - 6 = 36, and 6 inches is just 6 ÷ 12 = 0.5 feet.

Check the picture below.

64grams of bismuth-214 must be prepared if the shipping time is 120minutes.

What is half cycle?

Time required for a quantity to reduce to half of its initial value is termed as half life. It can help us to know how quickly unstable atoms undergo radioactive decay. This is used generally to characterize any type of exponential decay. It occurs when unstable atomic particles lose energy. Twenty-nine elements are capable of this process.

Rutherford applied the principle of a radioactive element's half-life in the age determination of rocks by calculating the decay period of radium to lead-206.

Given half life of 20min of 1g of Bismuth-214

If the shipping time is 120minutes, then

10min/20min/half life

=6 half life

=1/2^6=1/64

Grams of bismuth-214 that can be prepared in 120 min,

=1gm*64

=64grams.

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