The hypotenuse of a right triangle is 10 cm long. One of the triangle’s legs is 3
times the length of the other leg. Find the lengths of the two legs of the
triangle. Round to the nearest tenth if necessary

Answer: The width of the garden is 6 Meters

Step-by-step explanation:

3x + x = 24

The length is 3x and the width is x

24 / 4 = 6

x= 6

The width of the garden is 6 Meters

Answer:

x = 6

Step-by-step explanation:

3x + x = 24

24 / 4 = 6

x = 6

Answer:

A

Step-by-step explanation:

Given the equality y > -½, it means the values of y is greater than -½.

The values of y would range from 0 upwards. I.e. 0, ½, 1, 1½, 2. . .

Thus, when graphed on a number line, the circle that appears like "o" would start from -½, and the "o" would not be full or shaded to indicate that -½ is not included in the values of y, which are greater than -½. Since the values of y are greater than -½ the direction of the arrow that indicates values of y would point towards our far right, to indicate the values included as y.

Therefore, the graph that indicates the inequality y > ½ is A

Answer:

A

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

What must be applied to know if the result is true or reliable is a  test statistic, since due to it we can calculate how true or rather what is the probability that this data will occur. There are many types of  test statistic, use the one that best fits the data.

The veracity of the medium where the information comes from is also important, whether they took a representative sample or not, among other parameters.

Answer:

c) H0: µ = 7 hours (null hypothesis)

H1: µ < 7 hours (alternative hypothesis and original claim)

Step-by-step explanation:

The hypothesis test is performed in order to see if a sample outcome gives evidence to reject a null hypothesis and support the researchers claim.

In this case, the claim is that the mean amount of sleep for adults is less than 7 hours.

For this claim, the alternative hypothesis will state the researcher's claim: the mean amount of sleep for adults is significantly less than 7 hours.

The null hypothesis will state the opposite: the mean amount of sleep for adults is not significantly less than 7 hours. In this case, it is the same to claim that the mean amount is 7 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=7\\\\H_a:\mu< 7[/tex]

Answer:

Solution,

[tex] \frac{ab}{bc} = tan \: 40 \\ ab = bc \times tan \: 40 \\ ab = 10 \times 0.84 \\ ab = 8.4 \: inches \: [/tex]

[tex] \frac{bc}{ac} = cos \: 40 \\ \frac{bc}{cos \: 40} = ac \\ ac = \frac{10}{cos \: 40} \\ ac = 13.05 \: inches[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

[tex]\$45[/tex]

Step-by-step explanation:

[tex]20+(2.5*20)=45[/tex]

Marking up means that the new value is added onto the original value.

As we are increasing the original price by 250% of the price, we need to multiply it by 2.5, as that is equal to 250%

Answer:

20*2.5 = $50 Gross margin $70 Selling price

Step-by-step explanation:

Answer:

0.15 or 15%

Step-by-step explanation:

If the price of a stock rose 3/4 on a point, it means that 1x became 1,75x (x + 3/4x). X is the price of the stock here.

To calculate how much the price went up each day on average, we will create exponential equation.

x = price of the stock

y = average daily change

[tex]x*y^{4} =1.75x[/tex]  divide by x

[tex]y^{4} = 1.75[/tex]

We will calculate it using logarithms.

y = 1.15016, rounded to 1.15

We see that the stock goes up 0.15 points every day.If we multiply it by 100%, we get 15%

Answer:

ADB = Major Arc

arc measure = 310

Step-by-step explanation:

major arc measure = 360 - 50 = 310

Answer:

8 and 4/9 i think... i am sorry if i am wrong

Step-by-step explanation:

Answer:

9x^4

Step-by-step explanation:

(3x)^2 * x^2

9x^2 * x^2

Add the exponents

9x^(2+2)

9x^4

Answer:

Seventeen billion, eight hundred fifty-seven million and twelve.

Step-by-step explanation:

Answer:

17,857,000,012 = 17 billion 857 million 12

Step-by-step explanation:

Bye lad!

Answer:1.P(exactly 2 kids are girls)=3/8

2. P(at least 1 is boy)=7/8

Step-by-step explanation:

1.P(exactly 2 kids are girls)=N(outcomes with 2 girls) /Total number of outcomes.

All possible outcomes are ggb,gbg, bgg, gbb, bgb, bbg, ggg, bbb - total 8

Outcomes where are exactly 2 girls are:

ggb,gbg, bgg - total 3 outcomes

So P(exactly 2 are girls)=3/8

2. P(at least 1 is boy)=Number of outcomes , where are at least 1 boy (1,2 or all 3 kids are boys)/ Total number of outcomes

All possible outcomes are ggb,gbg, bgg, gbb, bgb, bbg, ggg, bbb - total 8

Outcomes, where at least 1 kid is boy: ggb,gbg, bgg, gbb, bgb, bbg, bbb - total  7

P(at least 1 is boy)=7/8

Answer:

k = -10/9 and k = 10/9

Step-by-step explanation:

given y = cos(kt) and the differential equation 81y'' = -100y

y' = -ksin(kt)

y'' = -k²cos(kt)

Substituting the value of y and y'' in the differential equation we have;

81 (-k²cos(kt))= -100 (cos(kt))

-81k²cos(kt)) = -100cos(kt))

-81k² = -100

k² = 100/81

k = ±[tex]\sqrt{\frac{100}{81} }[/tex]

k = ±10/9

k = -10/9 and k = 10/9

Answer:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Step-by-step explanation:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Answer:

C. Approaches 35

Step-by-step explanation:

If we graph the expression, we see that we have an asymptote at y = 35.

What is your question?

Answer:

yeah what's your question?

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints.  If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

Answer:

A ∪ B = {1,3,6,9,12,15,18,24}

Step-by-step explanation:

Let A = {3,6,9,12,15}

B = {1,6,12,18,24}

So,

A ∪ B = {3,6,9,12,15} ∪ {1,6,12,18,24}

A ∪ B = {1,3,6,9,12,15,18,24}

Answer:

{1,3,6,9,12,15,18,24}

Step-by-step explanation:

The union is joining of the elements of the sets

{3, 6, 9, 12, 15}U {1, 6, 12, 18, 24}

= {1,3,6,9,12,15,18,24}

Answer:D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the sequence [tex]a_n = \frac{9+14n^{2} }{n+15n^{2} }[/tex]

To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;

[tex]\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\[/tex]

As [tex]n[/tex] tends to [tex]\infty[/tex], [tex]\frac{a}{n}[/tex] tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;

[tex]= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\[/tex]

Therefore [tex]\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15[/tex]

Since the limit of the sequence gave a finite number , the sequence converges.

Note that the only case when the sequence diverges id when the limit of the sequence is infinite

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

All outcoms of the dices:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

36 in all

Total outcomes:

In this question, we want all with no repetition.

There are 6 repetitions, they are (1,1), (2,2), ..., (6,6). So 36 = 6 = 30 outcomes.

Desired outcomes:

One landing on six:

(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).

10 desired outcomes.

Probability:

10/30 = 0.3333

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Answer:

a. [tex]N(1)=2600[/tex]

b. [tex]N'(a) = 470/a[/tex]

c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)

d. lim a→[infinity] N′(a) = 0

Step-by-step explanation:

a.

the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:

[tex]N(1)=2600 + 470ln(1)[/tex]

[tex]N(1)=2600 + 470*0[/tex]

[tex]N(1)=2600[/tex]

b.

To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:

[tex]N'(a) = 2600' + (470ln(a))'[/tex]

[tex]N'(a) = 0 + 470*(1/a)[/tex]

[tex]N'(a) = 470/a[/tex]

c.

The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).

The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.

d.

When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.

Answer:

B.

Step-by-step explanation:

According to SohCahToa, when using Sin to find a side value, you must use opposite over hypotenuse.

So in this case to find x, you would do the Sin(L)=x/y

Answer:

B.  Sin(L)=x/y  indeed!

Step-by-step explanation:

Answer:

Length=29.8 inches

Width=11.8 inches

Height=4.6 inches

Volume=1,617.54 cubic inches

Step-by-step explanation:

Let the side of congruent square cut =x inches

So the length of the rectangular box=(39-2x)

width = (21-2x)

height = x

The volume V=Length*Width*Height

= (39-2x)*(21-2x)*x

dV/dx= (39-2x)(21-4x)-2x(17-2x)=0

Simplify the equation above

819-156x-42x+8x^2-34x+4x^2=0

We have,

12x^2 -232 +819=0

Solve the quadratic equation using formula

a=12

b= -232

c=819

x= -b +or- √b^2-4ac/2a

= -(-232) +- √(-232)^2 - (4)(12)(819) / (2)(12)

= 232 +or- √53824 - 39312 / 24

= 232 +or- √14512 / 24

= 232 +or- 4√907 / 24

x= 232 / 24 + 4√907 / 24

=14.6861

Or

x=232 / 24 - 4√907 / 24

=4.64726

x=4.6 inches

Length=(39-2x)

={39-2(4.6)}

= 29.8 inches

Width=(21-2x)

={21-2(4.6)}

= 11.8 inches

Height=x= 4.6 inches

Volume=(39-2x)*(21-2x)*x

={39-2(4.6)}*{21-2(4.6)*4.6

=(39-9.2)*(21-9.2)*4.6

=29.8*11.8*4.6

=1,617.544

Approximately 1,617.54

Volume=1,617.54 cubic inches

Answer:

The range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Step-by-step explanation:

The complete question is:

The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Solution:

As the sample size is large, i.e. n = 47 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean by the normal distribution.

So,[tex]\bar X\sim N(\mu,\ \frac{\sigma^{2}}{{n}})[/tex]

The range of the middle 98% of most averages for the lengths of pregnancies in the sample is the 98% confidence interval.

The critical value of z for 98% confidence level is,

z = 2.33

Compute the 98% confidence interval as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=267\pm 2.33\cdot\frac{17}{\sqrt{47}}\\\\=267\pm5.78\\\\=(261.22, 272.78)\\\\\approx (261, 273)[/tex]

Thus, the range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Answer:

0.015 radians per second.

Step-by-step explanation:

They tell us that at the moment the speed would be 6 ft / s, that is, dx / dt = 6 and those who ask us is dθ / dt.

Which we can calculate in the following way:

θ = arc sin 100/200 = pi / 6

Then we have the following equation of the attached image:

x / 100 = cot θ

we derive and we are left:

(1/100) * dx / dt = - (csc ^ 2) * θ * dθ / dt

dθ / dt = 0.01 * dx / dt / (- csc ^ 2 θ)

dθ / dt = 0.01 * 6 / (- csc ^ 2 pi / 6)

dθ / dt = 0.06 / (-2) ^ 2

dθ / dt = -0.015

So there is a decreasing at 0.015 radians per second.

The horizontal distance and the height of the kite are illustration of rates.

The angle is decreasing at a rate of 0.24 radian per second

The given parameters are:

[tex]\mathbf{Height =y= 100ft}[/tex]

[tex]\mathbf{Speed =\frac{dx}{dt}= 6fts^{-1}}[/tex]

[tex]\mathbf{Length = 200}[/tex]

See attachment for illustration

Calculate the angle using the following sine ratio

[tex]\mathbf{sin(\theta) = \frac{100}{200}}[/tex]

[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]

The horizontal displacement (x) is calculated using the following tangent ratio:

[tex]\mathbf{tan(\theta) = \frac{100}{x}}[/tex]

Take inverse of both sides

[tex]\mathbf{cot(\theta) = \frac{x}{100}}[/tex]

[tex]\mathbf{cot(\theta) = \frac{1}{100}x}[/tex]

Differentiate both sides with respect to time (t)

[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dx}{dt}}[/tex]

Substitute known values

[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 6}[/tex]

[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]

Recall that:

[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]

Take inverse of both sides

[tex]\mathbf{csc(\theta) = 2}[/tex]

Square both sides

[tex]\mathbf{csc^2(\theta) = 4}[/tex]

Substitute [tex]\mathbf{csc^2(\theta) = 4}[/tex] in [tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]

[tex]\mathbf{-4 \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]

Divide both sides by -4

[tex]\mathbf{\frac{d\theta}{dt} = -\frac{24}{100}}[/tex]

[tex]\mathbf{\frac{d\theta}{dt} = -0.24}[/tex]

Hence, the angle is decreasing at a rate of 0.24 radian per second

Read more about rates at:

https://brainly.com/question/6672465

Answer: 95 degrees.

Step-by-step explanation:

A quadrilateral has a total combined angle measure of 360 degrees. If you do 360-(80+110+75) it would equal 95.

Answer:

Option C is the correct option

Solution,

The sum of the angles in the quadrilateral is 360°

Let the forth angle be X

X + 80° + 110° + 75° = 360°

Calculate the sum:

X + 265° = 360°

Subtract 265° on both sides

X + 265° - 265° = 360° - 265°

Calculate the difference

X = 95°

Hope this helps...

Good luck on your assignment...

Answer:

sin(B) = cos(90 – B)

Step-by-step explanation:

Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.

sin(B) = sin(A)

sin(B) = cos(90 – B)

cos(B) = sin(180 – B)

cos(B) = cos(A)

Assuming the angles are in degrees, the second relation is always true.

By definition of sine,

sin(B) = AC/AB

cos(90-B) = cos (A) = AC/AB

therefore the second relation is true, for arbitrary values of B.

Answer:

sin(B) = cos(90 – B)

Step-by-step explanation:

Which relationship in the triangle must be true?

Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.

Answer:

8 is in the hundreds place as well as in the tens place.

Step-by-step explanation:

We use the base 10 system. 880 would represent eight hundred and eighty. So our 0 would be the ones place, 8 in the tens place, and 8 also in the hundreds place.