Let A and B be two disjoint events such that P(A) = .30 and P(B) = .60. What is P(A and B)? 0.18 0.72 0.90 0 none of the above

Answer:

ghjdsawzGr

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

\(2\sqrt[3]{(1-3x)} =6-4=2\\\sqrt[3]{(1-3x)}=\frac{2}{2} =1\\\sqrt[3]{(1-3x)}^{3} =1^{3} \\(1-3x)=1\\-3x=0\\x=0\)

Step-by-step explanation:

so, what's the problem ?

it's all there, we only need to take the calculator (or simply our heads) and do the calculation :

2×5 - 5×2 = 10 - 10 = 0

you see ? that was all that was needed.

put the given values for the variables into the places of these variables, and then calculate !

that is what variables are for : placeholders for actual values.

Answer:

  3.48%

Step-by-step explanation:

Interest rate is the one variable in the amortization formula that cannot be solved for directly. An iterative or graphical approach is needed. There is no formula. Financial calculators, financial apps, and spreadsheets are all able to do this calculation.

__

In the attached, we have used a graphing calculator to find the value of interest rate (in %) that makes the loan payment be $200 for a loan of $11,000. It shows us the rate is 3.48%. (A financial calculator confirms this value.) The x-intercept in the graph is the interest rate that makes the difference between the payment and $200 be zero. In our formula for the payment, we have used t for years. 60 monthly payments is 5 years.

The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

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The data shows that the more sodas a person drinks, the poorer their health becomes.

The scatterplot shows a clear negative correlation between soda drinking and health. As the average number of sodas a person drinks increases, their healthy index decreases. This suggests that drinking soda is not conducive to good health, as it has a deteriorating effect on one's health. The doctor could explain this to his patients and emphasize that drinking soda regularly can negatively affect their health.

In general, the data shows that the more sodas a person drinks, the poorer their health becomes. The healthier people (with a healthy index score of 30) tend to drink fewer sodas, while people with lower health index scores (approaching -5) tend to drink more sodas. This indicates that drinking soda is linked to poorer health.

Therefore, the data shows that the more sodas a person drinks, the poorer their health becomes.

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Answer: An implicit function is a function, written in terms of both dependent and independent variables, like y-3x2+2x+5 = 0. Whereas an explicit function is a function which is represented in terms of an independent variable.

Step-by-step explanation: To find the implicit derivative,

Differentiate both sides of f(x, y) = 0 with respect to x.

Apply usual derivative formulas to differentiate the x terms.

Apply usual derivative formulas to differentiate the y terms along with multiplying the derivative by dy/dx.

Solve the resultant equation for dy/dx (by isolating dy/dx).

Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

The amount earned is $79,500, percentage of fans that will be able to park the colour is 20% and the types of meals offered are All-you-can-eat, Two-for-one, Value meals.

First part -

The amount earned in parking 10,600 vehicles = number of vehicles × charge of parking on one vehicle

Keep the values in formula to find the amount earned

The amount earned in parking 10,600 vehicles = 10,600 × 7.5

Performing multiplication

The amount earned in parking 10,600 vehicles = $79,500

Second part -

Number of cars = total number of fans ÷ number of fans in one car

Keeping the values

Number of cars = 70000 ÷ 2

Performing division

Number of cars = 35000

Percentage = number of accomodates vehicles ÷ total number of vehicles × 100

Keep the values

Percentage = 7000 ÷ 35000 × 100

Performing division and multiplication

Percentage = 100/5

Percentage= 20%

Third part -

The type of ticket offered at the ballpark is All-you-can-eat, Two-for-one, Value meals.

Hence, the answers are $79,500, 20% and All-you-can-eat, Two-for-one, Value meals.

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The correct question is -

if it costs $7.50 to park, how much will the stadium make from parking 10,600 vehicles?

A stadium's parking lot can accommodate 7,000 vehicles. What percentage of tonight's 70,000 fans will be able to park in the stadium lot if they arrive two fans per car?

Which is a type of ticket offered at the ballpark?

All-you-can-eat, Two-for-one, Value meals

Answer:

(29.14 ; 30.06)

Step-by-step explanation:

Given that'

Sample size (n) = 57

Mean (m) = 29.6

Population standard deviation (σ) = 2.7

Confidence interval = 80%

= (1 - 0.8) / 2 = 0.1

Mean ± z * σ/√n

Using the Z probability calculator : Z0. 1 = 1.28

Hence,

29.6 ± 1.28 * (2.7 / √57)

29.6 - (1.28 * 0.3576237) ; 29.6 + (1.28 * 0.3576237)

29.142241664 ; 30.057758336

(29.14 ; 30.06)

Answer: 21:9 and 42:18

Step-by-step explanation:

14:6 at its most basic form is 7:3, so find anything that could be equal to this if a number is multiplied on both sides.

21:9 is our simplified ratio multiplied by 3 on both sides.

42:18 is our simplified ratio multiplied by 6 on both sides.

But, the final ratio doesn't work, because 7 and 3 respectively cannot multiply to 13 and 8 with the same value.

The equation of the new function after shifting 6 units right and 4 units down is f(x) = (x + 6)² - 4.

If we are to apply the changes below to the quadratic parent function, F(x) = x², what is the equation of the new function, given that we are to shift 6 units to the right and 4 units down? We will approach this question by following the steps outlined below.

Step 1: Identify the parent function F(x) = x² and its transformations

Step 2: Write the equation of the new function

Step 3: Simplify the new equation of the function.Step 1: Identify the parent function F(x) = x² and its transformations

Here, we are given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down.

The general equation for the horizontal and vertical shifts of a quadratic function is given by:f(x) = a(x - h)² + k, where a, h, and k are constants.

The value of a determines the direction of opening of the parabola, while (h, k) represents the vertex of the parabola.

If a > 0, the parabola opens upwards, while a < 0, the parabola opens downwards. If the values of (h, k) are positive, the parabola is shifted right and up, respectively. On the other hand, if the values of (h, k) are negative, the parabola is shifted left and down, respectively.

Therefore, given the quadratic parent function F(x) = x² and two transformations: shift 6 units right and shift 4 units down, we can represent these changes by the following:

a = 1 (since the parabola opens upwards)h = -6 (since we are shifting the parabola 6 units to the right)k = -4 (since we are shifting the parabola 4 units down)

Step 2: Write the equation of the new function Now that we have identified the constants a, h, and k, we can write the equation of the new function as follows:f(x) = a(x - h)² + kf(x) = 1(x - (-6))² + (-4)Replacing the constants a, h, and k in the equation, we have:f(x) = (x + 6)² - 4

Step 3: Simplify the new equation of the function.f(x) = (x + 6)² - 4= (x + 6)(x + 6) - 4= x² + 12x + 36 - 4= x² + 12x + 32Therefore, the equation of the new function after shifting 6 units right and 4 units down is f(x) = x² + 12x + 32.

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Answer:

1. Equal. 2. 1500

Step-by-step explanation:

6 x 16 = 96 + 11= 117

3/4 x 2000 = 1500

Answer:

When dealing with radicals and exponents, one must realize that fractional exponents deals directly with radicals. In that sense, sqrt(x) = x^½. In a fractional exponent, the numerator represents the actual exponent of the number. So, for x^2/3, the x is being squared.For the denominator, that deals with the radical. The index, to be exact. The index describes what kind of radical (or root) is being taken: square, cube, fourth, fifth, and so on. So, for our example x^2/3, x is squared, and that quantity is under a cube root (or a radical with a 3).^^^Exponential fractions still follow the same rules of simplifying, so...

x^2/4 = x^1/2 = sqrt(x)

Step-by-step explanation:

When dealing with radicals and exponents, one must realize that fractional exponents deals directly with radicals. In that sense, sqrt(x) = x^1/2

Now, how to go about doing this:

In a fractional exponent, the numerator represents the actual exponent of the number. So, for x^2/3, the x is being squared.

For the denominator, that deals with the radical. The index, to be exact. The index describes what KIND of radical (or root) is being taken: square, cube, fourth, fifth, and so on. So, for our example x^2/3, x is squared, and that quantity is under a cube root (or a radical with a 3). Here are some more examples to help you understand a bit more:

x^6/5 = Fifth root of x^6

x^3/1 = x^3

^^^Exponential fractions still follow the same rules of simplifying, so...

x^2/4 = x^1/2 = sqrt(x)

Answer:

  x = 10

Step-by-step explanation:

You want the value of x in triangle RST with angle bisector UT dividing RS into parts RU=3x and US=x+2, while RT=40 and ST=16.

The angle bisector divides the sides of the triangle proportionally;

  3x/40 = (x +2)/16

  6x = 5x +10 . . . . . . . multiply by 80

  x = 10 . . . . . . . . . subtract 5x

The value of x is 10.

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The frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell to total frequency.

It is given that:

24 children were asked which is their favourite colour from a choice of red, blue

green or yellow

From the data given in the question.

Red : 6

Blue: 4

Green: 8

Yellow : 1 (half of 2)

Pink: 1 (half of 2)

Thus, the frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).

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Answer:

$56

Step-by-step explanation:

cost of 8 packages of clay = $ 32

cost of 1 package of clay = 32 / 8 = $4

cost of 14 packages = 14*4 = $ 56

Answer:

For x = -5: -16

For x = 9: √5

Explanation:

The function is given by

f(x) = √(x - 4) when x ≥ 4 and

f(x) = 2x - 6 when x < 4

Since -5 is lower than 4, we need to use f(x) = 2x - 6 to evaluate f(x) for x = -5. So, replacing x by -5, we get:

f(x) = 2x - 6

f(-5) = 2(-5) - 6

f(-5) = -10 - 6

f(-5) = -16

On the other hand, 9 is greater than 4, so we will use the function f(x) = √(x - 4). Then, replacing x = 9, we get

f(x) = √(x - 4)

f(9) = √(9 - 4)

f(9) = √5

Therefore, the answers are

For x = -5: -16

For x = 9: √5

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

The volume of the cylinder is the product of the height, pie, and square of the radius.

The volume of the cylinder = \(\pi* r^2 *h\)

Part A

The total length of the assembled rocket will be the length of the cone and the cylinder.

The total length of the assembled rocket  = 25 + 3 = 28cm

Part B

The volume of the rocket is the combined volume of the cone and cylinder.

=  4/3 × 3.14 × 16 × 28

= 1875.62 cubic cm

To convert cm into pounds

1875.62 cubic cm = 4.135 pound

Part C

If Cole’s rocket parts are made of aluminum weighing 0.006 pounds per cubic centimeter.

Then 1875.62 cubic cm × 0.006

= 11.253

For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.

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654 over 3 = divide the both 654 and 3 by 3.

It will give you 218 over 1.

So the answer is 218.

Answer:

x = 52 due to vertical angle theorem

Step-by-step explanation:

Vertical angles mean that the angles are congruent.

If we know that one angle is 52 the other one shall be 52 as well because vertical angles state that ones that are directly across are congruent known as equal.

Answer:

yes

Step-by-step explanation:

Answer:

a.\(y+1=0\)

b.\(2x+4y=1\)

Step-by-step explanation:

We are given that

\((x^2+y^2)^2=3x^2y-y^3\)

a.(0,-1)

Differentiate w.r.t x

\(2(x^2+y^2)(2x+2yy')=6xy+3x^2y'-3y^2y'\).....(1)

Substitute x=0 and y=-1 in equation (1)

\(2(0+1)(-2y')=-3y'\)

\(-4y'+3y'=0\)

\(-y'=0\)

\(y'=0\)

\(m=y'=0\)

Point-slope form:

\(y-y_0=m(x-x_0)\)

Using the formula

\(y+1=0\)

This is required equation of tangent line to the given curve at point (0,-1).

b.(-1/2,1/2)

Substitute the value in equation (1)

\(2(1/4+1/4)(-1+y')=6(-1/2)(1/2)+3(1/4)y'-3(1/4)y'\)

\(2(2/4)(-1+y')=-3/2+3/4y'-3/4y'\)

\(-1+y'=-3/2\)

\(y'=-3/2+1=\frac{-3+2}{2}=-\frac{1}{2}\)

\(m=y'=-1/2\)

Again using point-slope formula

\(y-1/2=-1/2(x+1/2)\)

\(\frac{2y-1}{2}=-\frac{1}{4}(2x+1)\)

\(2y-1=-\frac{1}{2}(2x+1)\)

\(4y-2=-2x-1\)

\(2x+4y=2-1\)

\(2x+4y=1\)

Answer:

115 adults and 156 children were admitted at the amusement park.

Step-by-step explanation:

Given that the admission fee at an amusement park is $ 2.25 for children and $ 5.40 for adults, and on a certain day 271 people enter the park and the admission fees collected a total of $ 972, to determine how many children and how many adults were admitted se you must perform the following calculation:

5.40 - 2.25 = 3.15

271 x 2.25 = 609.75

(972 - 609.75) / 3.15 = X

362.25 / 3.15 = X

115 = X

(115 x 5.40) + ((271-115) x 2.25) = X

621 + (156 x 2.25) = X

621 + 351 = X

972 = X

Thus, 115 adults and 156 children were admitted at the amusement park.

Answer:

克拉克夫人的植物高 4/3 4 英寸。它比吉米的植物高 1/7 8 英寸。何

For Puzzle #1: \(log_5 2*7\) produces an integer, \(log_3 8/7\) produces an irrational number, and \(log_6 4^5\) produces a rational number. For Puzzle #2: \(log 9^8 = log 7*6 = log 1/3\), \(log 5*2 = 1 = log8*0\), \(log 4/1 = log 3*9 = log 2^7\).

For Puzzle #1, we are given three requirements for the logs we need to fill in:

We need to fill in the blanks with digits 1 to 9, using each digit only once.

To fulfill the first requirement, we need to choose two digits that, when multiplied, produce an integer. The only two digits that can do this are 2 and 7 (2 x 7 = 14). We can then choose any base for the log function. In this case, we chose 5. So \(log_{5} 2*7\) produces an integer.

To fulfill the second requirement, we need to choose two digits that, when divided, produce an irrational number. There are many pairs of digits that can do this. For example, 8 and 7 (8/7 is irrational). Again, we can choose any base for the log function. In this case, we chose 3. So \(log_3 8/7\) produces an irrational number.

To fulfill the third requirement, we need to choose two digits that, when raised to a power, produce a rational number. Again, there are many pairs of digits that can do this. For example, 4 and 5 (\(4^5 = 1024\)). We can then choose any base for the log function. In this case, we chose 6. So \(log_6 4^5\) produces a rational number.

For Puzzle #2, we are given a chart with three columns and three rows. Each box in the chart represents a logarithmic expression, with the base being 10. We need to fill in the blanks with digits 0 to 9, using each digit only once in the blue boxes and once in the red boxes.

The goal is to make sure that the logarithmic expressions in each row and column satisfy the indicated conditions. We can do this by choosing appropriate digits to fill in each blank.

We can continue this process for each blank, making sure to use each digit only once in each blue and red box. Once we have filled in all the blanks, we can check that the logarithmic expressions in each row and column satisfy the indicated conditions.

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200 shirts x $30 = $6000

Total sales would be $6000

Profit = 6000 - 5400 = $600

Divide profit by cost:

600/5400 = 0.1111

Multiply by 100 for percentage:

0.111 x 100 = 11.1%

Rounding to nearest percent would be 11% markup

Answer:

is it 2.00?

Step-by-step explanation: