The perimeter of a quarter circle is 3.57
yards. What is the quarter circle's radius?
P = 3.57 yd

The length of the bridge is 12.12 feet.

The length the dog swam is 32.36 feet.

The situation forms a right angle triangle.

A right angle triangle has one of its angles as 90 degrees. Therefore, the sides and angle can be found using trigonometric ratios.

The length of the bridge is the opposite side of the triangle and the length the dog swim is the hypotenuse side of the triangle.

Therefore,

Let's find the length of the bridge as follows:

tan 68° = opposite / adjacent

tan 68° = 30 / l

cross multiply

l = 30 / tan 68

l = 12.1212121212

length of the bridge = 12.12 ft

The length the dog swim is as follows:

sin 68°= opposite / hypotenuse

sin 68° = 30 / h

h = 30 / sin 68

h = 32.3561767942

The distance the dog swimmed = 32.36 ft

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Answer:

4

3

Step-by-step explanation:

Answer:

3.92

Step-by-step explanation:

From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is 3.92.

The margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result would reflect the result of a census of the entire population. The margin of error will be positive whenever a population is incompletely sampled and the outcome measure has positive variance, which is to say, the measure varies.

Margin of error at alpha level of significance =

Z score at alpha level of significance * sqrt(variance/ sample size)

Z score at 5% level of significance = 1.96

Variance = 900

Sample size = 225

Margin of error = [tex]1.96 *\sqrt{\frac{900}{225} } = 1.96*\frac{30}{15} = 3.92[/tex]

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To change a decimal to a percentage, all that we have to do is multiply the decimal by 100 (or move the decimal point to the right two places).

1.276 x 100 = 127.6

Percentage: 127.6%

Hope this helps!

Answer:

Step-by-step explanation:

Complementary angles are angles that add up to 90°.

We have C and D as complementary.

Their sum is:

Substitute values and solve for x:

Answer:

x = 7

Step-by-step explanation:

Complementary angles are two angles that sum up to 90°. In this case, we are given that ∠C and ∠D are complementary. This means that the sum of ∠C and ∠D is equivalent to 90°.

⇒ ∠C + ∠D = 90°

⇒ 8x + 5x - 1 = 90°                                                          [∠C = 8x; ∠D = 5x - 1]

⇒ 13x - 1 = 90°

⇒ 13x = 90 + 1

⇒ 13x = 91

⇒ 13x/13 = 91/13

⇒ x = 91/13 = 7

Answer:

50+80 = 130

Step-by-step explanation:

Answer:

50+80=130

Step-by-step explanation:

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Parallelogram is a quadrilateral with equal diagonals. The statement BO = 7.8 cm is the only false statement

From the given diagram, the opposite sides and angle of the figure are the same but the diagonals are not equal. This shows that:

m<B = m<D

m<A = m<C

Since the diagonals are not equal that is BD is not equal to AC, hence:

OB ≠ OC

Hence the statement BO = 7.8 cm is the only false statement

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Answer:BO = 7.8 cm

Step-by-step explanation: just did the quiz

Answer:

80092

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given equation:

Step-By-Step:

Step 1

Subtract the numbers:

Step 2

Multiply the numbers:

Step 3

Add the numbers:

Answer is 80092.

Answer:

B  12

Step-by-step explanation:

4 x 6 = 24 divided by 2 = 12

Answer:

2.35619

Step-by-step explanation:

Answer:

2.35619

Step-by-step explanation:

Deg to Rad = ° x pi / 180

Answer:

$9.50

Step-by-step explanation:

Divide 237.50 by 25

My answer:

My Explanation:

The reason why this is my answer, is because you can see in the picture, I have this coordinate grid, and on that, I drew out these points, and hence, I got this picture.

Refer to the picture below!

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Answer:

The answer i 9

Step-by-step explanation:

If the ball bounces 2/3 of the height of 9, and a 1/3 of 9 is 3, then 6 is the answer.

Answer:

Its 452.16

Step-by-step explanation:

Because the formal is  [tex]\pi[/tex]r2

Which is 3.14*12*12=452.16

Answer:

6

Step-by-step explanation:

2 x 3

Hey there!

Answer: [tex] \Rightarrow \sf{\frac{x+3}{x -2}}[/tex]

[tex] \rightarrow \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } }[/tex]

[tex] \rightarrow{ \rm{factorise} \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } } = \frac{(x + 2)(x + 3)}{ {x}^{2} - 4} = \frac{(x + 2)(x + 3)}{(x + 2)(x - 2)} = \Rightarrow \sf{\frac{x+3}{x -2}}}[/tex]

Answer:

7.21 units

Step-by-step explanation:

hope this helps!

equation of line will be

y+1=1/2(x+2)

Hello!

Let's write the equation of the line in both Point-Slope Form and Slope-Intercept Form.

First, point-slope form:

y-y1=m(x-x1)

y-(-1)=1/2(x-(-2) (Point-Slope Form)

Now, convert into Slope-Intercept form:

y+1=1/2(x+2)

y+1=1/2x+1

y=1/2x+1-1

y=1/2x

Hence, the equation of the line is

[tex]\boxed{\boxed{\bold{y=\frac{1}{2}}} }[/tex] (Slope-Intercept Form)

Hope everything is clear.

Let me know if you have any questions!

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:-)

Answer:

In ∆ABC, ∆CBA, ∆ACB

^B = 90°

Answer: C

Step-by-step explanation:

The answer is: Yes, all conditions for inference are met.

The score which is assigned from 1 to 4 by the teacher to each student for the project and is most likely to be is 3 with 0.48 probability.

Probability distribution is the statistical model which represent all the achievable and similar values of a random variable that it can possess in a specified range.

A teacher assigns a score from 1 to 4 to each student project. the table below shows the probability distribution of the scores for a randomly selected student.

In the above data, the height probability of selection is 0.48. This probability belongs to the score 3.    

Thus, the score which is assigned from 1 to 4 by the teacher to each student for the project and is most likely to be is 3 with 0.48 probability.  

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Answer:

C on edge

Step-by-step explanation:

3

Answer:

4:8 in simplified form would be 1/2

Step-by-step explanation:

Think of 4:8 as a fraction, so 4/8. Now, you can reduce it to the lowest form, which is 1/2. How? 4 is the numerator, and 8 is our denominator. Now, we divide 4 by 8. 4 divided by 8 equals 0.5, where 0.5 is converted into 1/2!

Answer:

4x

Step-by-step explanation:

X is incremented by 1

Answer:

Step-by-step explanation:

There is a 1 in front of the x. 1 is never written, but really the question looks like

1x +1x +1x +1x which when summed gives 4 x

b = 4

An equation is formed of two equal expressions. The equation x²+6x+5 into the form a(x − h)²+k is written as (x+3)²-4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The transformation of the equation from x²+6x+5 into the form a(x − h)²+k can be done in the following steps as shown below,

1. Taking +5 on the right-hand side of the equation,

[tex]x^2+6x+5 = 0\\\\x^2+6x = -5[/tex]

2. Now if we add +9 on both sides of the equation, we will get,

[tex]x^2+6x = -5\\\\x^2+6x+9 = -5+9[/tex]

3. Now we look at the left side of the equation as the square of the binomial expression (x+3).

[tex]x^2+6x+9 = -5+9\\\\(x+3)^2 =4[/tex]

4. Taking +4 from the right side of the equation to the left side of the equation,

[tex](x+3)^2 =4\\\\(x+3)^2 -4=0[/tex]

Thus, the equation is in the form of a(x − h)²+k, where the value of a is 1, h is -3 and the value of k is -4.

Hence, the equation x²+6x+5 into the form a(x − h)²+k is written as (x+3)²-4.

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Answer:

if u make the square half by its midpoint then we can find its area by using the area of rectangle.

if u make the square half from the diagonal we can find its area by using area of triangle.

Answer:

44/7x

Step-by-step explanation:

circumference of circle= 2πr

=2×22/7×x

=44/7x

The number of distinct subset of the set is an illustration of combination

There are 34 distinct subset of the set that have three digit sums

The set is given as:

S = {1,8,9,39,52,91}

Group the elements

S = {(1,8),9,39,52,91}

So, we have:

S ={s1,s2,s3,s4,s5}

To have a three-digit sum, the sum of the selected elements must be 100 or above.

The number of ways the above set can be selected is:

[tex]n_1 = 4 * [^3C_1 + ^3C_2 + ^3C_3] + 1[/tex]

Evaluate

[tex]n_1 = 4 * [3 + 3 + 1] + 1[/tex]

[tex]n_1 = 29[/tex]

The set can be further rearranged as:

S = {(52,39),9,(8,1)}

i.e.

S = {b1,b2,b3}.

The number of ways the above set can be selected such that the sum is 100 or above is:

[tex]n_2 = 2 * [^2C_1] + 1[/tex]

Evaluate

[tex]n_2 = 2 * 2 + 1[/tex]

[tex]n_2 = 5[/tex]

So, the total number of ways is:

[tex]n = n_1 +n_2[/tex]

This gives

[tex]n = 29 +5[/tex]

[tex]n = 34[/tex]

Hence, there are 34 distinct subset of the see that have three digit sums

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There are 34 distinct subsets of the see that have three-digit sums.

When we know that S is a subset of T, we place the circle representing S inside the circle representing T.

The set is given as:

S = {1,8,9,39,52,91}

Group the elements

S = {(1,8),9,39,52,91}

S ={s1,s2,s3,s4,s5}

To have a three-digit sum, the sum of the selected elements must be 100 or above.

The number of ways the above set can be selected is:

[tex]\rm n_1=4\times (^3C_1+^3C_2+^3C_3)+1\\\\n_1=4(3+3+1)+1\\\\n_1=4 \times 7+1\\\\n_1=28+1\\\\n_1=29[/tex]

The set can be further rearranged as:

S = {(52,39),9,(8,1)}

S = {b1,b2,b3}.

The number of ways the above set can be selected such that the sum is 100 or above is:

[tex]\rm n_2=2\times ^2C_1+1\\\\n_2= 2\times 2+1\\\\n_2=4+1\\\\n_2=5[/tex]

The distinct subsets of the set are;

[tex]\rm n_1+n_2=29+5 =34[/tex]

Hence, there are 34 distinct subsets of the see that have three-digit sums.

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Answer: 9 meters

Step-by-step explanation:

Let's list what we know

The garden is in the shape of a triangle

The perimeter of the garden is 27 meters

Each side is the same length

The perimeter of something is the sum of all the side lengths added together. We know that the garden is a triangle and triangles have 3 sides

Since all the sides are the same length we can divide 27 by 3 to find the length of each side

27/3=9