Simplify the expression: 355 – (3+4. 2)2

Answer:

2.97 with the line

Step-by-step explanation:

the line tells you that the 97 will repeat

2.9797 is more than 2.9782

HOPE IT HELPS BUD

\(

Total \: number \: of \: letters \:  M \: = \: 2 \\

\\ Total \: number \: of \: letters \: or \: outcomes \:  = \: 11 \\

Probability \: of \: getting \: M \: = \: 112

\)

Answer:

A letter is chosen at random from the word 'MATHEMATICS, the probability of getting the letter M is 2/m.

total no of cards = 40

p(blue) = 8 out of 40

p(orange) = 8 out of 40

p(blue or orange ) = 16 out of 40

16÷40 = 2/5.

7 raised to the power of 4 equals 2,401, and the exponent we were looking for is 4.

What is meant by power?

Power is a function that represents the number of times a base number is multiplied by itself. It is the rate at which work is done or energy is transferred, measured in watts.

What is meant by exponent?

An exponent is a mathematical notation used to indicate the number of times a quantity is multiplied by itself. It is written as a superscript and represents the power to which a number or expression is raised.

According to the given information

To find the value of the exponent that satisfies the equation 7ˣ = 2,401, we can take the logarithm of both sides of the equation with respect to base 7. This gives us:

log7(7ˣ) = log7(2,401)

x = log7(2,401)

Using a calculator, we can find that log7(2,401) is approximately 3. Therefore, the value of x that satisfies the equation 7ˣ = 2,401 is 3.

Alternatively, we could also use the fact that 2,401 is equal to 7⁴ - 2, which can be written as:

7⁴ - 2 = (7²)² - 2

= 49² - 2

= 2,401

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Answer:

The probability of 213 or fewer cases of such cancer in a group of 479,908 people is 0.2776.

Step-by-step explanation:

We are given that assuming that cell phones have no​ effect, there is a 0.000462 probability of a person developing cancer of the brain or nervous system. We, therefore, expect about 222 cases of such cancer in a group of 479,908 people.

Let \(\hat p\) = sample probability of a person developing cancer of the brain or nervous system.

The z-score probability distribution for the sample proportion is given by;

                            Z  =  \(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\)  ~ N(0,1)

where, p = population probability of a person developing cancer of the brain or nervous system = 0.000462

            n = sample of cell phone​ users = 479,908

Now, the probability of 213 or fewer cases of such cancer in a group of 479,908 people is given by = P(\(\hat p\) \(\leq\) \(\frac{213}{479,908}\) )

     P(\(\hat p\) \(\leq\) 0.000444) = P(\(\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }\) \(\leq\) \(\frac{0.000444-0.000462}{\sqrt{\frac{0.000444(1-0.000444)}{479,908} } }\) ) = P(Z \(\leq\) -0.59)

                                 = 1 - P(Z < 0.59) = 1 - 0.7224 = 0.2776

The above probability is calculated by looking at the value of x = 0.59 in the z table which has an area of 0.7224.

These results suggest about media reports that cell phones cause cancer of the brain or nervous​ system that there is around 28% chance that 213 or fewer cases of such cancer in a group of 479,908 people can take place.

The angle between the two planes is 118.47 degrees.

A) To find the equation of the plane containing the points (0,0,1), (1,2,3), (2,4,5), and (4,8,11), we can use the point-normal form of the equation of a plane. This form is given by:

ax + by + cz + d = 0

where (a,b,c) is the normal vector to the plane, and d is the distance from the origin to the plane.

To find the normal vector, we can take the cross product of two nonparallel vectors in the plane. For example, we can take the cross product of the vectors (1,2,3) - (0,0,1) and (2,4,5) - (0,0,1). This gives us the normal vector:

(1,2,3) - (0,0,1) = (1,2,2)

(2,4,5) - (0,0,1) = (2,4,4)

(1,2,2) x (2,4,4) = (-8, -4, 4)

Now that we have the normal vector, we need to find the distance from the origin to the plane. We can do this by plugging the coordinates of any of the points in the plane and the normal vector into the point-normal form of the equation of the plane. For example, using the point (0,0,1):

(-8) * 0 + (-4) * 0 + 4 * 1 + d = 0

d = -4

So, the equation of the plane is:

-8x - 4y + 4z - 4 = 0

B) To find the equation of the tangent plane to the surface z = x^2 + xy - 3y at the point (2,3,1), we need to find the partial derivatives of z with respect to x and y at that point. The partial derivatives are given by:

\(z_x = 2x + y\\z_y = x - 3\)

Evaluating these partial derivatives at (2,3,1) gives us:

\(z_x = 2 * 2 + 3 = 7\\z_y = 2 - 3 = -1\)

So, the equation of the tangent plane is given by:

z - 1 = 7(x - 2) - 1(y - 3)

z - 1 = 7x - 14 - y + 3

z - 7x + y + 11 = 0

To find the angle of intersection between the plane from part (B) and the plane from part (A), we can use the dot product of their normal vectors. The normal vector to the plane from part (B) is (1, -1, 1). The dot product of these two normal vectors is:

(-8) * 1 + (-4) * (-1) + 4 * 1 = -4 - 4 + 4 = -4

The angle between the two planes is given by the inverse cosine of the dot product of their normal vectors divided by the product of their magnitudes. The magnitudes of the normal vectors are:

\($|(-8, -4, 4)| = \sqrt{((-8)^2 + (-4)^2 + 4^2) }= \sqrt{(64 + 16 + 16)}= \sqrt96 = 8$\\$|(1, -1, 1)| = \sqrt{(1^2 + (-1)^2 + 1^2)} = \sqrt{(1 + 1 + 1)} = \sqrt3$\)

So, the angle between the two planes is given by:

\(angle =cos\frac{-4}{8 \ * \sqrt3}\\= cos(\frac{-1}3)\\= cos(-0.33)\\= 118.47 \ degrees\\\)

Note that this angle is the acute angle between the planes, which is the angle between the planes when the planes intersect and the angle between the planes is less than 90 degrees. If the angle between the planes was greater than 90 degrees, the angle returned by the arccos function would be the obtuse angle between the planes, which is the complement of the acute angle (i.e., 180 degrees - the acute angle).

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1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

Answer:

QS ≅ TR

Step-by-step explanation:

QS and TR are diagonals.

Diagonals are equal in both rectangle as well as parallelogram.

Answer:

15 3/4 ÷13/4

/1. 1+3×4= 36/2

Answer:

Step-by-step explanation:

The percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

A division by 100 results in a percentage, often known as a percent. A percentage denotes a component of a total sum and indicates "per 100". For example, 45% represents 45 out of 100. Calculating a percentage is the process of determining a whole's proportion in terms of 100.

Given:

The total no cupcakes = 52,

The no of sprinkled cupcakes = 39,

Percentage of sprinkled cupcakes = The no of sprinkled cupcakes / The total no cupcakes × 100

Percentage of sprinkled cupcakes = 39 / 52 × 100

Percentage of sprinkled cupcakes = 75%

Therefore, the percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

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The larger number is 16 and the smaller number is -15.

The numbers are obtained by a system of equations, for which the variables are given as follows:

x and y.

The sum of two numbers is 1, hence:

x + y = 1.

y = 1 - x.

Three times the larger number plus two times the smaller number is 18, hence:

3x + 2y = 18.

Replacing the first equation into the second, the value of x is obtained as follows:

3x + 2(1 - x) = 18

3x + 2 - 2x = 18

x = 16.

Then the value of y is of:

y = 1 - x

y = 1 - 16

y = -15.

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Answer:r=2 cos^4(theta)

Step-by-step explanation:To find the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta), we need to find where the derivative of r with respect to theta is equal to zero, since the maximum r-values occur at these points.

First, we can simplify the equation by using the identity cos(2theta) = 2cos^2(theta) - 1 and substituting cos^2(theta) = (1 + cos(2theta))/2. This gives:

r = 2 cos^4(theta) = 2(1/2 + 1/2 cos(2theta))^2 = 1 + cos(2theta) + cos^2(2theta)/2.

Next, we can take the derivative of r with respect to theta, using the chain rule:

dr/dtheta = -sin(2theta) - 2cos(2theta)sin(2theta).

Setting this equal to zero and factoring out sin(2theta), we get:

sin(2theta)(-1 - 2cos(2theta)) = 0.

This equation is satisfied when sin(2theta) = 0 or cos(2theta) = -1/2.

When sin(2theta) = 0, we have 2theta = k*pi for some integer k. Therefore, theta = k*pi/2.

When cos(2theta) = -1/2, we have 2theta = 2*pi/3 + 2*k*pi or 2theta = 4*pi/3 + 2*k*pi for some integer k. Therefore, theta = pi/3 + k*pi or theta = 2*pi/3 + k*pi.

These are the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta).

According to the given picture the tables that represents a function would be the following:

A

B

E

This tables represents a function because what a define a function is that for every value of x corresponds only one value of y

Therefore in A B and E for the values of x corresponds only one value of y, hence those are the correct options

Answer:

Speed in km/hr Time in Minutes

90                       60

45                         120

30                         180

15                      360

10                      540

time Decrease when speed increase

Number of times the speed is increased the number of times time taken is reduced  so it is not possible to take no time at all

as we can see from the graph that it is exponential  , reduction in time keep reducing with increase in speed

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

I think the answer is 4/8 ✨

Given:

The length of the sides is a=18.3 cm,

The base of the triangle is b =3 cm.

Required:

We need to find the hypotenuse.

Explanation:

Use the Pythagorean theorem.

Substitute a =18.3 and b=3 in the equation.

Take square root on both sides.

Length is always positive.

Final answer:

The hypotenuse is 18.54cm.

The number of different committees that can be formed is 495

From the question, we have the following parameters that can be used in our computation:

People = 12

Committee = 4

These can be represented as

n = 12 and r = 4

The number of different committees that can be formed is

Number = nCr

So, we have

Number = 12C4

Evaluate

Number = 495

Hence, the committee are 495

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Answer:

The probability model is

= P(A or B)

Step-by-step explanation:

a) Data and Calculations:

Estimated revenue if the day is sunny = $3,000

Estimated loss if the day is rainy = $600

The probability of rain = 30%

Therefore, the probability of sunshine = 70% (100 - 30)

The probability model is based on the probability of rain or sunshine

= P(A or B)

= A*70% - B*30%

The outcome from either rain or sunshine

= ($3,000 * 70%)  -($600 * 30%)

= $2,100 - $180

= $1,920

Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

We have a multiplication problem within a whole number and a fraction.

When multiplying fractions with whole numbers, you always multiply the whole number with the numerator of the fraction.

\(\frac{numerator}{denominator}\)

\(\frac{4}{8} *4\)

\(\frac{4*4}{8}\)

\(\frac{16}{8}\)

Divide 16 by 8 :

\(2\)

The solution is:

a) 22-t mph; is the rate of the boat when it travels upstream.

b) 22+t mph. is the rate of the boat when it travels downstream.

Here, we have,

a) When the boat travels​ upstream, the current hinders the boat (the speed of the boat decreases). Thus, the speed of the boat upstream becomes

22-t mph.

b) When the boat travels​ downstream, the current helps the boat (the speed of the boat increases). Thus, the speed of the boat downstream becomes

22+t mph.

Hence, The solution is:

a) 22-t mph; is the rate of the boat when it travels upstream.

b) 22+t mph. is the rate of the boat when it travels downstream.

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Answer:

Solve for p by simplifying both sides of the equation, then isolating the variable.

p = − 300

Step-by-step explanation:

have a nice day

I think p=300???

Sorry if thiz is wrong. i dont really know that much

Answer:

5x^2 + x + 7.

Step-by-step explanation:

6x^2 + 7 + x - x^2

= (6x^2 - x^2) + (x + 7) // Rearranging the terms

= 5x^2 + x + 7

So, 6x^2 + 7 + x - x^2 simplifies to 5x^2 + x + 7.

Answer:

0.1105263157894737

Other:

Brainliest? Thanks!

Answer:

y+2=3(x-6)

or

y=3x-20

Step-by-step explanation:

formula for point slope form is

y-y1=m(x-x1)

plug it in

y+2=3(x-6)

because two is negative, you add the -2, not subtract it.

y+2=3x-18

we distributed the 3 to x-6

y=3x-20

we subtracted the two, to put it in slope-intercept form

Completing the table using the rounded values showing the relative frequencies is as follows:

Column Relative Frequency Table

                            Men         Women        Total

January - June    25%            25%             25%

July - December 75%             75%             75%

Total                   100%           100%           100%

Relative frequency shows the quotient between the number of events and the total number of possible events occurring.

The quotient of relative frequency is expressed over 100 to show the result in percentage terms.

Frequency Table

                            Men   Women    Total

January - June      21           19         40

July - December  62          58        120

Total                     83          77         160

Column Relative Frequency Table

                            Men                Women           Total

January - June    25% (21/83)     25% (19/77)        25% (40/160 x 100)

July - December 75% (62/83)     75% (58/77)       75% (120/160 x 100)

Total                   100%                100%                  100% (160/160 x 100)

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The expression which is the simplest form of; - (4x³ + x²) + 2 (x³ − 3x²) is; -2x³ -7x².

The expression given in the task content whose simplest form is to be determined is;

- (4x³ + x²) + 2 (x³ − 3x²)

Hence, upon opening up the parentheses, it follows that;

-4x³ - x² +2x³ -6x²

Upon collection and summing up of like terms; -2x³ -7x².

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Answer:

about 21 kids out of 170 are expected to be nearsighted (20:170)

Step-by-step explanation:

we find 12% out of 70 by muliplying 170 x 0.12 which equals 20.4

However it has to round up because we cant have half a child so 21 children.