Please solve the following. 12 divided by 3 . 5 - 4 to the power of 2

The 90% confidence interval for the class is [73.49, 76.51].

Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.

CI = μ ± z x SD/√n

where CI = confidence interval

μ = sample mean = 75

z = found by using a z-score table

SD = sample standard deviation = 5

n = sample size = 30

At 90% confidence level, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.

(100 - 90) / 2 = 5

100 - 5 = 95

Find 0.95 in the z-table to get the value of z.

At p = 0.95, z = 1.65

Plug in the values to the formula for confidence interval, CI.

CI = μ ± z x SD/√n

CI = 75 ± 1.65 x 5/√30

CI = 75 ± 1.51

CI = [73.49, 76.51]

Hence, for every 100 samples, at 90% confidence level, the mean will be between 73.49 and 76.51.

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we have the vector

u=-8i+5j

see the attached figure to better understand the problem

tan(x)=5/8

x=tan^-1(5/8)

x=32 degrees

Find out the angle theta

148 degrees

the answer is 148 degrees

Hello!

Let's solve:

               [tex]\hookrightarrow \text{In other words: } x + 59+ 84 + x + 51=180[/tex]

              [tex]x + 59 + 84 + x + 51= 180\\2x + 194=180\\2x = -14\\x = -7[/tex]

              m∠A = x + 51 = -7 + 51 = 44

Answer: 44

Hope that helps!

The amount that must be deposited to get a final amount of
$ 125,000 is $ 26.34 .

What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/n))^t

Given, the amount that will be developed after interest is laid
= A = $125,00
Also, number of years for which amount is loaned = n = 16 years
Annual Percentage Rate of the loan availed = R = 7.3
Frequency with which interest is paid out per year = 1
Following the formula established in the literature, we have:
125000 = P(1 + 7.3)⁴ ⇒ P = 125000/(1 + 7.3)⁴ ⇒ P = 125000/8.3⁴ = 26.34
Therefore, the amount that must be deposited to get a final amount of
$ 125,000 is $ 26.34 .

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The phrase of the expression x - 6 is 6 less than a number.

Expression:

The expression refer the sentence with a minimum of two  numbers/variables and at least one math operation in it.

Given,

Here we have the expression x -6.

And we need to convert this expression in order to get the phrase form.

In order to get the phrase form, we have to translate the given expression into word.

While we looking into the given expression we have identified the following three terms.

They are, x , (-) and 6.

Here x represents the unknown number.

(-) represents that we have to less the unknown number by the given number.

And 6 is the given number.

So, the phrase for this situation is 6 less than a number.

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Answer:

(2,-3)

Step-by-step explanation:

[tex]\frac{\left(y+3\right)^2}{9}-\frac{\left(x-2\right)^2}{2}=1\\\frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}=1\:\mathrm{\:is\:the\:standard\:equation\:for\:an\:up-down\:facing\:hyperbola}\\\frac{\left(y-\left(-3\right)\right)^2}{3^2}-\frac{\left(x-2\right)^2}{\left(\sqrt{2}\right)^2} =1\\(2,-3)[/tex]

Answer:

I do!

Decimal Form: f=−0.¯6,5

Step-by-step explanation:

If any individual factor on the left side of the equation is equal to 0 the entire expression will be equal to

0.3f+2=0f−5=0

Set

3f+2 equal to 0 and solve for f.

more steps...

f=−23

Set

f−5 equal to 0 and solve for f.

more steps...

f=5

The final solution is all the values that make

(3f+2)(f−5)=0

true.

f=−23,5

The result can be shown in multiple forms.

Exact Form :f=−23,5

HOPE IT HELPS :)

If the two equations are x - y = 11 and -x + y = -11 then the system has  infinitely many solutions.

Let the two equations be

x - y = 11 ..................(1)

-x + y = -11  ..................(2)

Express the first equation in the term of x and substitute it into the second equation:

From (1) and (2), we get

-(y + 11) + y = -11

simplifying the above equation, we get

-y - 11 + y = -11

-y + y = 11 - 11

0 = 0

So, the system has infinitely many solutions.

Therefore, the correct answer is option c. infinitely many solutions.

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Explanation

By observation, we can see that the transformation from the original to the image, is a rotation of 90 degrees counterclockwise about the origin.

Answer: Option D

Answer:

[tex]\frac{109}{20}[/tex]

Step-by-step explanation:

.45 mean [tex]\frac{45}{100}[/tex] so  5.45 means 5 [tex]\frac{45}{100}[/tex]  = [tex]\frac{9}{20}[/tex]  If I divide the top and bottom of [tex]\frac{45}{100}[/tex] by 9

5 [tex]\frac{9}{20}[/tex] is a mixed number.  I can make this an improper fraction by changing 5 to 1+1+1+1+1  Another name for 1 is any number over itself as a fraction.

I am going to write 1 as [tex]\frac{20}{20}[/tex]

5 can be written

[tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] + [tex]\frac{20}{20}[/tex] = [tex]\frac{100}{20}[/tex]

5 [tex]\frac{9}{20}[/tex]  Can be written

[tex]\frac{100}{20}[/tex] + [tex]\frac{9}{20}[/tex] = [tex]\frac{109}{20}[/tex]

Answer:

(109/20) Is the answer.

Answer:

what is the question?

Step-by-step explanation:

The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite.

If the side of DF = 7.7 cm then DE = 3.7 cm.

The right angle, or 90°, is always one angle. The hypotenuse is the side with the 90° angle opposite. The longest side is always the hypotenuse. The other two inner angles add up to 90 degrees.

A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a rectangled triangle. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

Given: DF = 7.7 cm and ∠ E = 29°

Let the equation be

sin θ = P/h = DF / DE

substitute the values in the above equation, we get

⇒ sin 29° = 7.7 / DE

⇒ DE = 7.7 / 0.48 = 3.696 = 3.7 cm

Therefore, the correct answer is option a) 3.7 cm.

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In the graph you can see two variables: Cost and Number of rooms to clean in house.

You can find the cost when both cleaning companies clean the same number of rooms as the point when the value in the varibles (y-axis and x- axis) are the same in the lines of both companies (the point where the lines cross each other)

Answer:equal

Step-by-step explanation: no number but equal as it is tossed 4 times

Answer:

16

Step-by-step explanation:

The number of possible outcomes at each coin toss = 2.

The total number of possible outcomes after 4 times = 2⁴ = 16.

Using ratios and assuming the given values, the rate of the total cost for items in the United Kingdom to that of the total cost of items in Australia is 2/3.

Assume that the costs are:

The ratio would be:

So, we have:

Simplify:

Express as rate

Therefore, using ratios and assuming the given values, the rate of the total cost for items in the United Kingdom to that of the total cost of items in Australia is 2/3.

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Answer: the area of triangle PQR is 7.5 square units

Step-by-step explanation:

[tex]\displaystyle\\A_{PQR}=\frac{PR*QS}{2} \\\\1.\ (3,-3)\ \ \ \ \ (5,-2)\\\\PR=\sqrt{(5-3)^2+(-2-(-3))^2}\\\\PR=\sqrt{2^2+(-2+3)^2} \\\\PR=\sqrt{4+1^2} \\\\PR=\sqrt{4+1}\\\\ PR=\sqrt{5} \ units[/tex]

[tex]\diplaystyle\\2.\ (8,7)\ \ \ \ \ (11,1)\\\\QS=\sqrt{(11-8)^2+(1-7)^2} \\\\QS=\sqrt{3^2+(-6)^2} \\\\QS=\sqrt{9+36} \\\\QS=\sqrt{45}\\\\QS=\sqrt{9*5} \\\\QS=\sqrt{3^2*5} \\\\QS=3\sqrt{5}[/tex]

[tex]\displaystyle\\Hence,\\A_{PQR}=\frac{\sqrt{5}*3\sqrt{5} }{2} \\\\A_{PQR}=\frac{(\sqrt{5}*\sqrt{5}) *3 }{2} \\\\A_{PQR}= \frac{5*3}{2}\\\\A_{PQR}=\frac{15}{2}\\\\A_{PQR}=7.5 \ units^2[/tex]

Answer:

1

Step-by-step explanation:

(5−5)^2+(−5−(−4))^2

0^2+-1^2

1

Answer:

B

Step-by-step explanation:

9 - 3 = 6

6 ÷ -2

= -3

I think it's b

Using the formula for the area of a rectangle is, A = l×w where l represents the length of the rectangle and w represents its width, the area of a rectangle with the length of 3.5 centimeters and a width of 2.2 centimeters will be  7.7 cm^2.

The area of the rectangle can be calculated using the formula,

(A = l×w )

and the  l = the length of the rectangle

w = represents the width of the rectangle

Then to calculate the area of the rectangle, we can substitute the values that is been given as :

(A = l×w )

A = (2.2 * 3.5) = 7.7 cm^2

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Answer:

7.7

Step-by-step explanation:

The answer was already in the question... He must've edited it or somethin'

The probability that a randomly selected car gets more than 40 mpg is equal to 0.771.

Let us assume that the miles-per-gallon rating of passenger cars be represented by random variable X. According to the question we know that X ≈ N (μ = 33.8 mpg and σ² = 3.5² mpg). Now, to compute the probability that a randomly selected passenger will gets less than 40 mpg will be given as

P(X < 40) = P(X - μ/σ  >  40 - 33.8/3.5)

= P(Z < 1)

= P(Z > 1) - 1

= 1.771 - 1

= 0.771 which is the required probability.

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The remaining amount of the substance with the half life of 64.9 days after 100 days is 2.749.

To calculate the amount that remains  after 100 days, this formular can be used

amount remaining = [tex]a (0.50)^{\frac{t}{h} }[/tex]

where t is the time that was required for the process to take place, where t is 100 days.

h is the halftime, which is been given as 64.9 days

where a is given as the initial amount that is present which is 8.

Then the values can be substituted to have

[tex]=a (0.50)^{\frac{100}{64.9} }[/tex]

= 2.749

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Answer:

x = [tex]\frac{16}{5} = 3\frac{1}{5} = 3.2[/tex]

Step-by-step explanation:

25.6 = 8x

Divide both sides by 8.

[tex]\frac{25.6}{8} = x\\[/tex]

Expand [tex]\frac{25.6}{8}[/tex] by multiplying both numerator and the denominator by 10.

[tex]\frac{256}{80} = x[/tex]

Reduce the fraction  [tex]\frac{256}{80\\}[/tex]  to lowest terms by extracting and canceling out 16.

[tex]\frac{16}{5} = x[/tex]

Swap sides so that all variable terms are on the left-hand side.

[tex]x = \frac{16}{5}[/tex]

If you answer is meant to be a fraction, then your correct answer is [tex]3\frac{1}{5}[/tex] and if you answer is meant to be a decimal then you correct answer is 3.2.

Hope I helped and have a good day. ~sunshine~ =D

Answer:

It will be

.. y = -4/3x +c . . . . . for some value of c

_____

The slope of the perpendicular line will be the negative reciprocal of the slope of the given line, which is 3/4.

Solution

Solution

The final answer

253.75 gallons remain in the tank when the depth of oil is 3.5 ft

Using the segment addition postulate, the lengths of the sides are given as follows:

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the smaller segments.

In this problem, the line AM is divided into two segments by point R, as follows:

The total length of the line is given by:

AM = -5x + 3.

Hence the solution for x is given as follows:

AR + RM = AM

9x + 2 + 2x + 6 = -5x + 3

11x + 8 = -5x + 3

16x = -5.

x = -5/16

x = -0.3125.

Hence the lengths are:

There is a typo in the signals as we have a negative length, which is not possible, but the procedure is as shown in this problem.

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The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.

Given that, Juanita has a part-time job that pays $12/hour and works about 50 hours every month.

Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.

Now, total money earned in a month

= 12 × 50 = 600

Now

6.2% of 600 = $37.2

= 600 - 37.2 = $562.8

1.45% of 562.8 = $8.1606

= 562.8 - 8.1606 = $554.6394

10% of 554.6394 = $55.46394

= 554.6394 - 55.46394 = $499.17546

Total deductions = $499.17546

So, net pay = grass pay - deductions

= 600 - 105.9

= $499.17546

The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.

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Answer:

• (a)The length of the side opposite 31.0° is 1.96 meters.

• (b)The length of the side adjacent 31.0° is 3.26 meters.

Explanation:

In the right triangle:

• The length of the hypotenuse = 3.80 m

• Let the side ,opposite ,angle 31.0° = x

• Let the side ,adjacent ,angle 31.0° = y

(a)

From trigonometric ratios:

Cross multiply:

The length of the side opposite 31.0° is 1.96 meters.

(b)From trigonometric ratios:

Cross multiply:

The length of the side adjacent 31.0° is 3.26 meters.

Part A: The multiplication expression is  L×w

Part B: The expression is written as N= r+ g + w + b

The final product = 200 boxes

It is crucial to note that the formula for determining the area of a rectangle is expressed as;

Area = lw

Given that;

The area can be calculated by multiplying the length and the width and also by then adding the number of boxes.

We have the expression as;

10( 4 + 5 + 4 + 7)

Also,

L × w =  r + g + w + b

Hence,  we have that L×w is a multiplication expression.

Total number of boxes for the length = 20

Total number of boxes for the width = 10

Total area = L×w = 20×10=200

We have;

N= r+ g + w + b

but r = g = b

Also,

L×B =  3r + w

Hence, a multiplication expression is an expression that has its variables or numbers being multiplied.

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Opposite Q is length PR

Adjacent is 7

Hypotenuse is 19

We got AH - which is CAH or cos

Cos-1( 7/19) = 68.38....

It's 68.4 degrees

The closest answer to this is B. So, choose that because it maybe due to a typing error.

Hope this helps!