the area of a right triangle is 77 m^2. the hypotenuse has a length of √317 m. what is the length of the legs?​

Answer:

{$3.60; $3.68}

Step-by-step explanation:

The confidence interval for a sample of size 'n', with mean price 'X' and standard deviation 's' is determined by:

[tex]X\pm z*\frac{s}{\sqrt n}[/tex]

The z-score for a 95% confidence interval is 1.96.

Applying the given data, the lower and upper bounds of the confidence interval are:

[tex]3.64\pm 1.96*\frac{0.0835}{\sqrt 20} \\L=\$3.60\\U=\$3.68[/tex]

The confidence interval for the mean price received by farmers for corn sold in January is:

CI : {$3.60; $3.68}

Answer:

  x = 17.349

Step-by-step explanation:

The right-most x-intercept is 17.349, where the curve continues upward to the right.

Answer:

[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]

Step-by-step explanation:

In parallelogram ABCD, BC=AD

Given:

BC=(6-x) units

AD =(x+2) units

Therefore:

6-x=x+2

x+x=6-2

2x=4

x=2

BC=(6-x) units

=(6-2) units

BC=4 units

The opposite angles of a parallelogram are equal. Therefore:

[tex]m\angle BCD=m\angle BAD\\12^\circ+y^\circ=100^\circ-y^\circ\\y^\circ+y^\circ=100^\circ-12^\circ\\2y^\circ=88^\circ\\y=44^\circ[/tex]

[tex]m\angle DAB=100^\circ-y^\circ\\=100^\circ-44^\circ\\m\angle DAB=56^\circ[/tex]

Therefore, the match is:

[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]

Answer:

Step-by-step explanation:

plato i guess

Answer:

(D)Jaleel's method is correct because 2(x-2)=2x-4.

Step-by-step explanation:

Jaleel and Lisa are simplifying the expression 2(x-2)+2 as shown.

[tex]J$aleel's Method: \left\{\begin{array}{ccc}2 (x -2) + 2 \\= 2 x - 4 + 2 \\= 2 x - 2\end{array}\right[/tex]

[tex]L$isa's Method: \left\{\begin{array}{ccc}2 (x-2) + 2 \\= 2 x -2 + 2 \\= 2 x\end{array}\right[/tex]

We can see that Jaleel's method is correct because:

2(x-2)=2x-4.

When you expand, you must multiply the term outside by all the terms inside the bracket.

The correct option is D.

Answer:

Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.

D is correct

Step-by-step explanation:

i just took the quiz.

Answer:

(B)24 Units

Step-by-step explanation:

Triangle MNO is an equilateral triangle with sides  measuring [tex]16\sqrt{3}[/tex] units.

The height divides the base into two equal parts of lengths [tex]8\sqrt{3}[/tex] units.

As seen in the diagram, we have a right triangle where the:

Using Pythagoras Theorem

[tex](16\sqrt{3})^2=(8\sqrt{3})^2+h^2\\16^2*3-8^2*3=h^2\\h^2=576\\h=\sqrt{576}\\ h=24$ units[/tex]

The height of the triangle is 24 Units.

The height of the given equilateral triangle is gotten as;

B: 24 units

Equilateral Triangles

The height of an equilateral triangle starts from the mid - point of the base to the ap ex.

Now, if the sides of the equilateral triangle are 16√3 units, then it means we can use pythagorean theorem to find the height h.

Half of the base will be; ¹/₂ * 16√3 = 8√3

Thus, the height h can be calculated from;

h²= ((16√3)² - (8√3)²)

h² = 3(256 - 64)

h² = 576

h = √576

h = 24 units

Read more about equilateral triangles at; https://brainly.com/question/4293152

Answer:

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Step-by-step explanation:

Step(i):-

Given mean of the Population  'μ'= 25c.m

Given standard deviation of the Population 'σ' = 8c.m

Given sample size 'n' = 256

Let X₁ = 24

[tex]Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2[/tex]

Let X₂ = 25

[tex]Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0[/tex]

Step(ii):-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)

                     = P( Z≤0) - P(Z≤-2)

                     = 0.5 + A(0) - (0.5- A(-2))

                     = A(0) + A(2)        ( ∵A(-2) =A(2)

                     = 0.000+ 0.4772

                     = 0.4772

Final answer:-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Answer:

No of rooms in Hotel G = 280

No of rooms in Hotel H = 145

Step-by-step explanation:

I solved the question using Elimination Method.

Answer:

Step-by-step explanation:

The angle next to 90 degrees is also 90 degrees and it's supplementary

the angle next to 133 degrees is 47 degrees and it's also supplementary

p + 90 + 47 = 180

p + 137 = 180

p = 43 degrees

the solution is d

Answer:

the slope equation is y2 - y1 divided by x2 - x1

Step-by-step explanation:

so the answer would be 3 over 2 because of this method

Answer:

3/2

Step-by-step explanation:

Use the easy rise over run method.

start at the point (50,20) then go up 3 units and 2 units to the right to get the next point.

3/2 should be the slope.

Hope I helped you!

Answer:

d

Step-by-step explanation:

Answer:

x = 74.3

Step-by-step explanation:

Using the trigonometric ratio formula, the missing side, x, of the right angled triangle, can be found as follows:

Ѳ = 22°,

adjacent side length = x

Opposite side length = 30

Thus, we would apply the formula:

tan Ѳ = opposite length/adjacent length

[tex] tan 22 = \frac{30}{x} [/tex]

Multiply both sides by x

[tex] tan 22*x = \frac{30}{x}*x [/tex]

[tex] tan 22*x = 30 [/tex]

[tex] 0.4040*x = 30 [/tex]

Divide both sides by 0.4040 to make x the subject of the formula

[tex] \frac{0.4040*x}{0.4040} = \frac{30}{0.4040} [/tex]

[tex] x = \frac{30}{0.4040} [/tex]

[tex] x = 74.26 [/tex]

x ≈ 74.3 (to the nearest tenth)

Answer:

-2/5

Step-by-step explanation:

The slope of two parallel lines will be the same.

Here, our equation is 5y + 2x = 12. Let's find the slope by isolating y:

5y + 2x = 12

5y = -2x + 12

y = (-2/5)x + 12/5

So, the slope is -2/5.

Thus, the slope of the line parallel to the given one will be -2/5.

~ an aesthetics lover

Answer:

-2/5

Step-by-step explanation:

5y+2x=12

Solve for y

Subtract 2x

5y = -2x+12

Divide by 5

5y/5 = -2/5 x +12/5

y = -2/5x +12/5

The slope is -2/5

Parallel lines have the same slope

Answer:

a) 135 seconds

b) 3.71 standard deviations below the mean

c) Z = -3.71

d) Unusual

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 245, \sigma = 36.4[/tex]

a. What is the difference between a duration time of 110 sec and the mean?

Duration of 110 seconds.

Mean of 245

245 - 110 = 135 seconds

b. How many standard deviations is that (the difference found in part (a))?

This is |Z|

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{110 - 245}{36.4}[/tex]

[tex]Z = -3.71[/tex]

[tex]|Z| = 3.71[/tex]

3.71 standard deviations below the mean

c. Convert the duration time of 110 sec to a z score

From b, Z = -3.71

d. If we consider "usual" duration times to be those that convert to z scores between -2 and 2, is a duration time of 110 sec usual or unusual?

Z is not in the interval of -2 and 2, so a duration time of 110 sec is unusual

Answer:

42 m

Step-by-step explanation:

First, find <S

<S = 180 - (41+113) [ sum of angles in a triangle)

<S = 180 - 154 = 26°

Next is to find length of ST, using the law of sines: a/sin A = b/sinc B = c/sin C

Let a = RT = 28m

A = <S = 26°

b = ST

B = <R = 41°

Thus, we have:

28/sin(26°) = b/sin(41°)

Cross multiply

28*sin(41°) = b*sin(26°)

28*0.6561 = b*0.4384

18.3708 = b*0.4384

Divide both sides by 0.4384 to make b the subject of formula

18.3708/0.4384 = b

41.9041971 = b

b ≈ 42m (rounded to nearest meter)

Length of ST to nearest meter = 42 meters

Answer:

8, 8, 13

Step-by-step explanation:

The three numbers 8, 8, 13 have a range of 5.

13 - 8 = 5

The mode is 8, the repeated number.

Answer:

need pls

Step-by-step explanation:

i think it is ur required ans..

Answer:

With 99% confidence the proportion of all smart phones that break before the warranty expires is between 0.041 and 0.069.

Step-by-step explanation:

We have to calculate a 99% confidence interval for the proportion.

The sample proportion is p=0.055.

[tex]p=X/n=97/1750=0.055[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.055*0.945}{1750}}\\\\\\ \sigma_p=\sqrt{0.00003}=0.005[/tex]

The critical z-value for a 99% confidence interval is z=2.576.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.005=0.014[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.055-0.014=0.041\\\\UL=p+z \cdot \sigma_p = 0.055+0.014=0.069[/tex]

The 99% confidence interval for the population proportion is (0.041, 0.069).

Answer:

357 mi²

Step-by-step explanation:

The shape is made of a triangle and a half-square

we will calculate the area of each one

let A1 be the area of the half-circle:

A1= (10²*π)/2 = 50π mi²

Let A2 be the area of the triangle:

A2= 10*20=200 mi²

let At be the total area:

At =A1+A2= 200+50π =357.07≈ 357 mi²

Answer:

The correct answer would be C

Step-by-step explanation:

please mark brainliest

The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.

From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.

Read more on cylinders;

https://brainly.com/question/9554871

#SPJ2

Answer:

m = 0.5

Step-by-step explanation:

m = (y2 - y1) / (x2 - x1)

= (0.25 - 0) / (0.5 - 0)

= 0.25/0.5

= 0.5

Answer:

The radioactive decay constant or  k = ln (.5) / Half-Life

Half-Life =  -.693147 / .00012

Half-Life = -5,776.225  years

We'll call beginning amount as 100%

Ending Amount = Beginning Amount / 2^n (where n = # of half-lives)

n = 4,050 / 5,776.225 = 0.7011499725

Ending Amount = 100% / 2^0.7011499725

Ending Amount = 100% / 1.625800202

Ending Amount = 61.5081729452%

Ending Amount = 61.5 % (rounded)

Step-by-step explanation:

Answer:

don't know

Step-by-step explanation:

sorry buddy

Answer:

y = -2x +4

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = -2x +4

I'm pretty sure that ' HL ' stands for "hypotenuse and leg". That's the one.

-- We see the little boxes in the lower left corners, so we know that these are right triangles, and we can use the rules we know about for right triangles.

-- The hypotenuses of both triangles are marked with the same length.

-- The base legs of both triangles are marked with the same length.

-- So we have (the hypotenuse and one leg of one right triangle) equal to (the hypotenuse and corresponding leg of another right triangle). That's exactly the description of the HL conguence theorem, so we know that these two triangles are congruent.

Answer:

a. The 95% confidence interval for the mean is (33.52, 35.48).

b. The 95% confidence interval for the mean is (34.02, 34.98).  

c. n=49 ⇒ Width = 1.95

n=196 ⇒ Width = 0.96

Note: it should be a factor of 2 between the widths, but the different degrees of freedom affects the critical value for each interval, as the sample size is different. It the population standard deviation had been used, the factor would have been exactly 2.

d. 5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.

Step-by-step explanation:

a. We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=34.5.

The sample size is N=49.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{49}}=\dfrac{3.4}{7}=0.486[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=49-1=48[/tex]

The t-value for a 95% confidence interval and 48 degrees of freedom is t=2.011.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.011 \cdot 0.486=0.98[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 34.5-0.98=33.52\\\\UL=M+t \cdot s_M = 34.5+0.98=35.48[/tex]

The 95% confidence interval for the mean is (33.52, 35.48).

b. We have to calculate a 95% confidence interval for the mean.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{196}}=\dfrac{3.4}{14}=0.243[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=196-1=195[/tex]

The t-value for a 95% confidence interval and 195 degrees of freedom is t=1.972.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.972 \cdot 0.243=0.48[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 34.5-0.48=34.02\\\\UL=M+t \cdot s_M = 34.5+0.48=34.98[/tex]

The 95% confidence interval for the mean is (34.02, 34.98).

c. The width of the intervals is:

[tex]n=49\rightarrow UL-LL=33.52-35.48=1.95\\\\n=196\rightarrow UL-LL=34.02-34.98=0.96[/tex]

d. The width of the intervals is decreased by a factor of √4=2 when the sample size is quadrupled, while the others factors are fixed.

Answer: m=0.5 or m=1/2

Step-by-step explanation:

To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Since we are given the coordinate points, we can directly plug them in.

[tex]m=\frac{0.25-0}{0.5-0} =\frac{0.25}{0.5} =0.5[/tex]

Answer: x=5 and 1/2

Step-by-step explanation:

You have to go to a graph and put it simply it, makes it a lot easier, hope this helps!

Steps to solve:

2x^2 + 5 = 11x

~Subtract 11x to both sides

2x^2 - 11x + 5 = 0

~Factor

(2x - 1)(x - 5) = 0

~Solve each factor

2x - 1 = 0

2x = 1

x = 1/2

x - 5 = 0

x = 5

Best of Luck!

Answer:

Decreases by 2 degrees

Step-by-step explanation:

The expression that describes temperature as a function of latitude is:

[tex]T=110-2(Latitude)[/tex]

This equation represents a linear relationship between latitude and temperature in a way that an increase in latitude causes a decrease in temperature. The magnitude of this decrease is quantified by the slope of the linear equation, which is -2. Therefore, the estimated temperature decreases by 2 degrees when latitude is increased by one.

Answer:

7/ (3a-1)

Step-by-step explanation:

3a^2 -13a +4        28+7a

------------------ * --------------------

9a^2 -6a+1         a^2 -16

Factor

(3a-1)(a-4)           7(4+a)

------------------ * --------------------

(3a-1) (3a-1)        (a-4)(a+4)

Cancel like terms

1                    7

------------------ * --------------------

(3a-1)                  1

Leaving

7/ (3a-1)