Two of the sides of a right triangle are 4 and 5. What is the length of the third side? Find all possible answers.

Solution

Rotation means the shape turns as it moves around a fixed point.

In this case, the correct option is

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

We accept null hypothesis

Step-by-step explanation:

We assume a normal distribution

The population mean  μ₀ = 65 mph      

Sample mean     μ  = 63,2  mph ( calculated from data )

Sample standard deviation  σ  =  7,309

Sample size    n  = 8

Degree of freedom  is   n - 1         8 - 1   = 7

As n < 30  we have to use the t-student test

We will do our test with a confidence interval of  95 % that means            α = 5  %

or α = 0,05 and as we are going through a two-tail test α/2  = 0,025

Test Hypothesis:

Null Hypothesis:                                  H₀              μ  =   μ₀

Alternate Hypothesis                          Hₐ              μ  ≠   μ₀

From  t-student table for the degree of freedom 7,  α/2  = 0,025 two-tail test we find tc

tc = 2,365

And  calculate ts   as

ts = ( μ - μ₀ ) / σ /√n

ts = ( 63,2 - 65 ) / 7,309/ √8

ts = - 1,8 *2,828/ 7,309

ts = - 5,091 /7,309

ts = - 06965

Now we compare   ts and tc

tc = 2,365      or  tc = - 2,365    ( by simmetry)   tc = -2,37

and  ts = -0,06965      ts = - 0,07

As |ts| < |tc|

ts is in the acceptance zone so we accept null hypothesis

Answer:

-0.70

Step-by-step explanation:

For the tabulated value the mean is calculated as:

Mean = (60.5 + 63.2 + 54.7 + 51.6 + 72.3 + 70.7 + 67.2 + 65.4)/8

= 505.6/8

Mean \bar{x}= 63.2

and population mean as assumption u= 65

and given that the sample standard deviation is: s= 7.309

The test statistic is calculated as:

Ζ = Τ –μ 63.2 - 65 = -0.696 -0.70 S

Hence the T statistic would be -0.70

Answer:

3+x

Step-by-step explanation:

sum= addition

a number= a number

Answer:

3+x  

eplanation                                  

Answer:

\(\displaystyle A=\frac{20}{3}\)

Step-by-step explanation:

\(\displaystyle A=\int^2_{-2}(|x|-(x^2-2))\,dx\\\\A=2\int^2_0(x-(x^2-2))\,dx\\\\A=2\int^2_0(-x^2+x+2)\,dx\\\\A=2\biggr(-\frac{x^3}{3}+\frac{x^2}{2}+2x\biggr)\biggr|^2_0\\\\A=2\biggr(-\frac{2^3}{3}+\frac{2^2}{2}+2(2)\biggr)\\\\A=2\biggr(-\frac{8}{3}+2+4\biggr)\\\\A=2\biggr(-\frac{8}{3}+6\biggr)\\\\A=2\biggr(\frac{10}{3}\biggr)\\\\A=\frac{20}{3}\)

Bounds depend on whether you use -x or +x instead of |x|, but you double regardless. See the attached graph for a visual.

Answer:

1. 2 + 12i

2. -3 - 4i

3. 7 - 11i

4. -9i

Step-by-step explanation:

just add and subtract like 'i' is a variable and make sure the answer is in the form a+bi

Answer:

Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

Step-by-step explanation:

The correlation​ matrix provided is:

Variables    Paper     Glass

  Paper           1         0.1853

 Glass        0.1853         1

Te hypothesis for the test is:

H₀: ρ = 0 vs. H₀: ρ ≠ 0

The test statistic is:

r = 0.1853 ≈ 0.185

As the alternate hypothesis does not specifies the direction of the test, the test is two tailed.

The critical value for the two-tailed test is:

\(r_{\alpha/2, (n-2)}=r_{0.05/2, (62-2)}=r_{0.05/2, 60}=0.250\)

The conclusion is:

Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

Using the compound interest formula, if the account compounds at 4.8% monthly and he withdraws $500 monthly, it will take Steve 33 years, 7 months (403 months) to reduce $100,000 to a balance (future value) of $0.

The future value is the compounded present value, while the present value is the discounted future value.

However, with periodic withdrawals, a present value that compounds at an interest rate into the future can become $0 (future value) after some periods.

The time (period) Steve reduces his inheritance to $0 can be computed using an online finance calculator as follows:

I/Y (Interest per year) = 4.8%

PV (Present Value) = $100,000

PMT (Periodic Payment) = $-500

FV (Future Value) = $0

Results:

N (# of periods) = 403.164

Sum of all periodic payments = $-201,581.83

Total Interest $101,581.83

Thus, after 403 monthly withdrawals, Steve's inheritance will be reduced to a $0 future value.

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Step-by-step explanation:

yes, the step is correct.

a² = cx | multiply by c

ca² = c²x

I am just not sure how that simplified the equation.

what do you want to achieve ? what's the goal here ?

to solve the equation for x it would be to divide both sides by c, which gives

a²/c = x

Answer: 750

Step-by-step explanation:

multiply 75 x 100 you will get 7500 than divide by 10

Answer: 1,599,960

Step-by-step explanation:

Since the population of crawfish in a section of the Louisiana bayou increased from 900,000 to 1.2 million between 2010 and 2011. The percentage increase in population will be:

= (1.2 million - 900000) / 900000 × 100

= 300000/900000 × 100

= 33.33%

Since the population increases by the same percentage between 2011 and 2012, then the population in 2012 will be:

= (100% + 33.33%) × 1.2 million

= 133.33% × 1.2 million

= 1.3333 × 1.2 million

= 1,599,960

The population in 2012 is 1,599,960

Answer:

1/6

Step-by-step explanation:

A (6,1)

B (12,2)

slope = (2-1)/(12-6)

1/6

Answer:

(-2, -3)

Explanation:

To find the center o the circle that can be circumscribed about the triangle, we need to draw the perpendicular bisector of two sides of the triangle. The perpendicular bisector is a line that divides the side into two equal parts and forms an angle of 90 degrees, so in this case, the perpendicular bisector are

The intersection of these lines is the center of the circle. Therefore, the center is (-2, -3)

The volume contained in a cup of oil is a fraction of the volume

contained in a pint of oil.

Correct response:

The measure of the volume of oil the car holds = Pints of oil

The measurement the man has for use = Cups of oil

Required:

The number of cups equal to three pints.

Solution;

1 pint of oil = 2 cups of oil

Therefore;

3 pints of oil = 3 × 2 cups of oil = 6 cups of oil

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Answer: The required sample size = 97

Step-by-step explanation:

If prior population standard deviation is known, then the minimum sample size can be computed as:

\(n=(\frac{z^*\times\sigma}{E})^2\)

,where z* = critical z-value

\(\sigma\) = population standard deviation

E = Margin of error

As per given,

\(\sigma=20,\ E= 4\)

Critical value for 95% confidence = 1.96

\(n=(\frac{1.96\times20}{4})^2\\= (1.96\times 5)^2\\= (9.8)^2\\=96.04\approx97\)

Hence, the required sample size = 97

Answer:

k=40

Step-by-step explanation:

subtract 12 from k we would get 28

The maximum temperature during summer in that year was 34°C.

It's not possible for the maximum temperature in Gulmarg, Kashmir to rise by 44°C during the summer.

A temperature rise of that magnitude would be extremely unusual and potentially dangerous.

However, assuming that the question meant to ask about the difference between the minimum temperature in January and the maximum temperature in summer, we can proceed with the calculation.

The minimum temperature in January was -10°C, and if we add 44°C to it, we get:

-10°C + 44°C = 34°C

Therefore, the maximum temperature during summer in that year was 34°C.

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Answer:

x = 45

Step-by-step explanation:

Because these are two congruent triangles inside of each other we can set up an equivalency ratio.

25/35 = x/65

Multiply both sides by 65 to get x alone

65 * 25/35 = x/65 * 65

(65 * 25)/35 = x1

1576/35 = x

x = 45

Hope this helps,

We are not given the radius of the circle or any other relevant data, so I assumed the radius of the circle r=5

Answer:

The y-coordinate of Q is 3

Step-by-step explanation:

Circles and Lines

The figure below shows a circle of radius r=5 and a segment that goes from the center of the circle to a point of the circumference, where x=4.

We can find the y-coordinate of that point by using Pithagora's theorem:

\(r^2=x^2+y^2\)

Solving for y:

\(y^2=r^2-x^2\)

\(y^2=5^2-4^2\)

\(y^2=25-16=9\)

\(y=\sqrt{9}=3\)

The y-coordinate of Q is 3

Answer:

Actual height of church = 512 feet

Step-by-step explanation:

Given:

Scale model;

1 inch = 256 feet

Height of church (Scale model) = 2 inches

Find:

Actual height of church

Computation:

Actual height of church = Height of church (Scale model) x scale length

Actual height of church = 2 inches x 256 feet/inches

Actual height of church = 2 x 256 feet

Actual height of church = 512 feet

Noah picked 3kg of cherries

if Mia picked half as many cherries as noah, this means Mia picked 1/2 of the cherries Noah picked = 1/2 x 3 =1.5kg

Together the both picked 3 + 1.5 = 4.5 kg of cherries

Answer:

Step-by-step explanation:

Answer:

8.25

Step-by-step explanation:

first substitution

x=4 and y=7

square root(i dont have it) 4(x)7 + 9(x)4 =

square root 28+36 =

square root 64 =

8.246211251

round to 3 significant figure = 8.25

Answer:

\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)

Step-by-step explanation:

Given trigonometric equation:

\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:

\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)

Therefore:

              \(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)

\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)

  \(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)

\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)

\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)

Simplify the numerator:

\(\dfrac{1-2\cos x}{\sin x}=0\)

Multiply both sides of the equation by sin x:

\(1-2 \cos x=0\)

Add 2 cos x to both sides of the equation:

\(1=2\cos x\)

Divide both sides of the equation by 2:

\(\cos x=\dfrac{1}{2}\)

Now solve for x.

From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:

\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)

Therefore, the values of x in the given interval [0, 2π), are:

\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)

Answer:

-$3

Step-by-step explanation:

Answer:

16 Times Greater

Step-by-step explanation:

Smaller cylinder:

radius = 6 inches

height = 8 inches

area = (pi)r^2h

area = (3.14)6^2(8)

radius = 24 inches

height = 8 inches

area = (pi)r^2h

area = (3.14)24^2(8)

.

[(3.14)6^2(8)] / [(3.14)24^2(8)]

[6^2(8)] / [24^2(8)]

[6^2] / [24^2]

[36] / [576]

16 times greater

Answer:

Step-by-step explanation:

Smaller cylinder:

h = 6 ft

r = 6 ft

Volume of smaller cylinder = πr²h

                                             = π * 6 * 6 * 6 cubic ft

Bigger cylinder:

r = 6 * 2 = 12 ft

h = 6 ft

Volume of bigger cylinder = π * 12 * 12 * 6 cubic ft

Volume of bigger cylinder = π * 12 * 12 * 6

Volume of smaller cylinder    π * 6 * 6 * 6

                                           = \(\frac{2 * 2}{1*1}\\\)

                                           = 4 : 1

The volume of greater cylinder is 4 times than the smaller cylinder.

Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.

The probability about an occurrence in an experiment is the likelihood that the event will occur. Any event's probability is a number between (including all) "0" and "1".

If an event's probability is represented by P(E), then we get

Given data:

Total pennies = 50

number of 1977 dated pennies = 12

probability = favourable outcome / total outcome

probability(1977 dated pennies) = number of 1977 dated pennies/ Total pennies

probability(1977 dated pennies) = 12/50

Divide numerator and denominator by 2.

probability(1977 dated pennies) = 6/25

Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.

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from,

m = y - y1

x - x1

m = 2 - 5

4 - 1

m = -3 = -1

3

then,

y - y1 = m(x - x1)

using coordinates (1, 5)

y - 5 = -1(x - 1)

y = -x + 1 + 5

y = -x + 6.