Each of 16 students measured the circumference of a tennis ball by four different methods, which were: A: Estimate the circumference by eye B: Measure the diameter with a ruler, then compute the circumference C: Measure the circumference with ruler and string D: Measure the circumference by rolling the ball along a ruler

[tex]\color{plum}m∠ABC = 71° [/tex]

Which means :

m∠ABC = ∠ADC (opposite angles of a parallelogram)

m∠ABC :

= 37° + 34°

= 71°

Thus, the measure of ∠ABC = 71°

Let us find the measures of the other angles as well :

m∠BCD + m∠ADC = 180°

m∠BCD + 71 = 180°

m∠BCD = 180 - 71

m∠BCD = 109°

Thus, the measure of∠BCD = 109°

m∠BCD = ∠BAD (opposite angles of a parallelogram)

m∠BAD = 109°

Thus, the measure of ∠BAD = 109°

Therefore, m∠ABC = 71°

Answer:

Step-by-step explanation:

Given isosceles trapezoid AB = CD

Angles B and C are congruent and angles A and D are congruent.

A and B, as well as C and D sum to 180 as supplementary angles, therefore:

Answer:

x=−4 or x=6

Step-by-step explanation:

Answer:

YES:  direct variation

Step-by-step explanation:

2x = 3y is equivalent to y = (2/3)x, which has the form of a proportional relationship (direct variation) y = kx.  YES

Answer:

-43 degrees

Step-by-step explanation:

Start: -28 degrees

-28 degrees - 15 (dropped means subtract)

-28 - 15 = -43

Answer:

-43

Step-by-step explanation:

Answer:

The observed value of the chi-square statistic is 34.71

Step-by-step explanation:

Given the data in the question';

Calculate the observed value of the chi-square statistic

The chi-square statistic will be;

∑[tex]_{i}[/tex][ ( O[tex]_{i}[/tex] - E[tex]_{i}[/tex])² / E[tex]_{i}[/tex] ]

here O[tex]_{i}[/tex] is observed frequency of [tex]_{i}[/tex]th class

E[tex]_{i}[/tex] is expected frequency of [tex]_{i}[/tex]th class

[tex]_{i}[/tex]  = 1, 2 which denote the class of food experts who guess correctly and who didn't guess correctly

so  

∈[tex]_{i}[/tex] = n × probability of not guessing correctly = 168 × 2/3 = 112

∈1 = n × probability of guessing correctly 168 × 1/3  = 56

so

∑[tex]_{i}[/tex][ ( O[tex]_{i}[/tex] - E[tex]_{i}[/tex])² / E[tex]_{i}[/tex] ] = [ ( 92 - 56)² / 56 ] + [ ( 76 - 112)² / 112 ]

= 1296/56 + 1296/112

= 23.14 + 11.57

= 34.71

Therefore, the observed value of the chi-square statistic is 34.71

Answer:

15.6%

Step-by-step explanation:

Since each day there is a 6% chance that Lisa smiles at him then that means that each day there is a 94% chance that Lisa does not smile at him. To find the probability of Milhouse going longer than a month (30 days) without a smile from Lisa we need to multiply this percentage in decimal form for every day of the month. This can be solved easily by putting 94% to the 30th power which would be the same, but first, we need to turn it into a decimal...

94% / 100 = 0.94

[tex]0.94^{30}[/tex] = 0.156

Now we can turn this decimal into a percentage by multiplying by 100

0.156 * 100 = 15.6%

Finally, we can see that the probability that Milhouse goes longer than a month without a smile from Lisa is 15.6%

Using the binomial distribution, it is found that there is a 0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.

For each day, there are only two possible outcomes, either Lisa smiles at him, or she does not. The probability that she smiles at him on day is independent of any other day, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that Milhouse goes longer than a month without a smile from Lisa is the probability of no smiles during 30 days, that is, P(X = 0), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{30,0}.(0.06)^{0}.(0.94)^{30} = 0.1563[/tex]

0.1563 = 15.63% probability that Milhouse goes longer than a month without a smile from Lisa.

To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377

Answer:

54 inches

Step-by-step explanation:

let 4x = the bigger piece

let x = the smaller one

4x + x = 270

5x = 270

x = 54

Answer:

54 inches

Step-by-step explanation:

x + 4x = 270

5x = 270

x = 54 (shorter piece)

4x = 216 (longer piece)

Answer:

Step-by-step explanation:

66

Explanation

-1.25+2.5=1.25

Answer:

1.25 is the answer .......

Step-by-step explanation:

hello will u be friend with me

Answer: c

Step-by-step explanation: because 7 squared is 49 and 8 squared is 64

nvm i read the question wrong

Step-by-step explanation:

the person above is correct

Answer/Step-by-step explanation:

1. Sin A = opp/hyp

Opp = 3

Hyp = 5

[tex] sin(A) = \frac{3}{5} [/tex] (substitution)

[tex] sin(A) = 0.6 [/tex]

2. Sin B = opp/hyp

Opp = 4

Hyp = 5

[tex] sin(B) = \frac{4}{5} [/tex] (substitution)

[tex] sin(B) = 0.8 [/tex]

3. Cos Q = adjacent/hypotenuse

Adjacent = 12

Hypotenuse = 13

[tex] cos(Q) = \frac{12}{13} [/tex] (substitution)

[tex] cos(Q) = 0.9231 [/tex] (4 decimal places)

4. Cos S = adjacent/hypotenuse

Adjacent = 5

Hypotenuse = 13

[tex] cos(S) = \frac{5}{13} [/tex] (substitution)

[tex] cos(S) = 0.3846 [/tex] (4 decimal places)

Answer:

Simplifying

27 + y = 10

Solving

27 + y = 10

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-27' to each side of the equation.

27 + -27 + y = 10 + -27

Combine like terms: 27 + -27 = 0

0 + y = 10 + -27

y = 10 + -27

Combine like terms: 10 + -27 = -17

y = -17

Simplifying

y = -17

Step-by-step explanation:

Answer:

[tex]\sqrt{72a^8b^5} = 6a^4b^2 \sqrt{2b}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{72a^8b^5[/tex]

Required

Simplify

Express 72 as 36 * 2

[tex]\sqrt{72a^8b^5} = \sqrt{36 * 2*a^8b^5}[/tex]

Express [tex]b^5[/tex] as [tex]b^4*b[/tex]

[tex]\sqrt{72a^8b^5} = \sqrt{36 * 2*a^8*b^4*b}[/tex]

Reorder

[tex]\sqrt{72a^8b^5} = \sqrt{36 *a^8*b^4* 2*b}[/tex]

Split:

[tex]\sqrt{72a^8b^5} = \sqrt{36} *\sqrt{a^8} *\sqrt{b^4} * \sqrt{2*b}[/tex]

Simplify each term

[tex]\sqrt{72a^8b^5} = 6 * a^{\frac{8}{2}} * b^{\frac{4}{2}} * \sqrt{2*b}[/tex]

[tex]\sqrt{72a^8b^5} = 6 * a^4 * b^2 * \sqrt{2*b}[/tex]

[tex]\sqrt{72a^8b^5} = 6a^4b^2 * \sqrt{2*b}[/tex]

[tex]\sqrt{72a^8b^5} = 6a^4b^2 \sqrt{2b}[/tex]

Answer:

The answer is 15.00+0.80x

Step-by-step explanation:

I know because I just did this question Lol-

Answer:

Function A is non-linear and Function B is linear.

Step-by-step explanation:

Linear function:

Has the following format:

y = mx + b

In which m is the slope and b is the y-intercept.

In a linear function, when x changes by 1, y will always changes by the same amount.

Function A:

When x changes by 1, y can change by various amounts. So function A is non-linear.

Function B:

y = -x + 5

In the format of a linear function, so linear

Answer:

y + 1 = 8 (x + 7)

Step-by-step explanation:

point slope form is

y - y1 = m (x - x1)

So replace the y1 with the y point, and the x1 with the x point

y - (-1) = m (x - (-7) )

then replace the m with the slope

y - (-1) = 8 (x - (-7) )

now solve

y + 1 = 8 (x + 7)

Answer:

75.8 is your answer

Step-by-step explanation:

119:157*100 =

(119*100):157 =

11900:157 = 75.8

Answer:

187.301 is 157% of 119.3

Step-by-step explanation:

Answer:

The answer is "[tex]\bold{\frac{6}{10}}[/tex]"

Step-by-step explanation:

[tex]\to p(\frac{\text{Market is falling}}{\text{The expected demand is fall Don}}) =1\\\\\to p(\frac{\text{Market is falling}}{\text{The expected demand is rising Don}}) =0.6[/tex]

That's why the answer is [tex]\to \frac{6}{10}[/tex]

Answer:

The triangle formed is Equilateral triangle.

I have taken Perpendicular = P ( you can say M)

√400 - x²  = OP (OM)

√3 x = AP (AM)

The length of the string of each person = 20√3 m

Step-by-step explanation:

As given , circular park with radius 20m

Let , Ankur sit on boundary point A

       Syed sit on boundary point S

       David sit on boundary point D

As given,

Ankur, Syed and David are sitting at equal distance on its boundary

⇒AS = AD = SD

Let AS = AD = SD = 2x

As the sides are equal

⇒ The triangle formed is Equilateral triangle.

Now,

Draw a perpendicular on the side SD

Let OP be the perpendicular

⇒SP = PD = [tex]\frac{1}{2}[/tex]SD = [tex]\frac{1}{2}. 2x = x[/tex]

So, we get

SP = x , PD = x

Now, Draw the line OS and OA

AS , we can see that ,

ΔOPS and ΔAPS are right angle triangle ,

So , apply Pythagoras theorem to ΔOPS and ΔAPS

In ΔOPS

OS² = OP² + PS²

⇒20² = OP² + x²

⇒400 - x² = OP²

⇒√400 - x²  = OP

Now,

In ΔAPS

AS² = AP² + PS²

⇒(2x)² = AP² + x²

⇒4x² - x² = AP²

⇒√3x²  = AP

⇒√3 x = AP

Now,

We can see that,

AP = AO + OP

⇒√3 x  = 20 + √400 - x²

⇒√3 x  - 20 + = √400 - x²

Squaring both side

⇒(√3 x  - 20 )²= (√400 - x²)²

⇒3x² + 400 - 40√3 x = 400 - x²

⇒3x² + x² =  40√3 x

⇒4x² = 40√3 x

⇒x = 10√3

∴ we get

AS = SD = AD = 2(10√3) = 20√3 m

⇒The length of the string of each person = 20√3 m

Given:

Purchasing price = 6.1 lakh

Amount spent of repair = 30000

Selling price = 8 lakh

To find:

The gain percentage.

Solution:

We have,

Purchasing price = 6.1 lakh

Amount spent of repair = 30000 = 0.3 lakh

So, total cost price is

[tex]C.P.=6.1+0.3[/tex]

[tex]C.P.=6.4[/tex]

The total cost price is 6.4.

Selling price(S.P.) = 8 lakh

Now,

[tex]Gain\%=\dfrac{S.P.-C.P.}{C.P.}\times 100[/tex]

[tex]Gain\%=\dfrac{8.0-6.4}{6.4}\times 100[/tex]

[tex]Gain\%=\dfrac{1.6}{6.4}\times 100[/tex]

[tex]Gain\%=\dfrac{1}{4}\times 100[/tex]

[tex]Gain\%=25\%[/tex]

Therefore, the gain percent is 25%.

Answer:

12 meters

Step-by-step explanation:

30 times 40 = 1200

100 cm in a meter

1200/100= 12

Answer:

False

Hope my answer helps you pls mark me as brainiest :)

Step-by-step explanation:

16$ per seat

*5 seats                16 * 5 = 80

80$ for 5 seats

160$ - $80 = 80$

The remaining money is 80 dollars which need to be spent on snacks:

4$ per snack

80$ / by 4$ = 20 snacks

Work ✔:

20 snacks = 80$

5 seats = 80$                                  Charity Goal = 160$

80$ + 80$ = 160$  

Final answer:

The charity must sell 20 snacks to every five seats to reach the charity goal of 160$

Hope this Helps! :D

Answer:

y = 4x + 3

Step-by-step explanation:

To do this, put the new line into the form y = mx + b where m is the slope and b is the y-intercept.

When two lines are parallel, they have the same slope. Since, the slope of the first line is 4, that means the slope of the second line is also 4.

So far, the equation is y = 4x + b.

Then, since you know (-2, -5) is a solution, x = -2, y = -5 is a solution so you can plug this into the equation.

This would be:

-5 = 4 * -2 + b

-5 = -8 + b

3 = b

This means the equation is y = 4x + 3.

Answer:

..   ..

..   ..

Step-by-step explanation:

8/2=4