The sum of three numbers is 56. The second number is 2 times the third. The first number is 8 less than the third. What are the numbers?

Answer:

Step-by-step explanation:

a:5

b:8

d:20

E:20

To solve this problem, we can use the principle of inclusion-exclusion and the given information to calculate the probabilities.

Let's define the events:

S = Student smokes

D = Student drinks alcoholic beverages

E = Student eats between meals

(a) Probability that the student smokes but does not drink alcoholic beverages:

P(S and not D) = P(S) - P(S and D)

P(S and not D) = 186/500 - 103/500

P(S and not D) = 83/500

(b) Probability that the student eats between meals and drinks alcoholic beverages but does not smoke:

P(E and D and not S) = P(E and D) - P(E and D and S)

P(E and D and not S) = 57/500 - 30/500

P(E and D and not S) = 27/500

(c) Probability that the student neither smokes nor eats between meals:

P(not S and not E) = 1 - P(S or E)

P(not S and not E) = 1 - [P(S) + P(E) - P(S and E)]

P(not S and not E) = 1 - [186/500 + 181/500 - 73/500]

P(not S and not E) = 1 - 294/500

P(not S and not E) = 206/500

Therefore, the probabilities are:

(a) P(S and not D) = 83/500

(b) P(E and D and not S) = 27/500

(c) P(not S and not E) = 206/500

To learn more about probabilities visit:

brainly.com/question/32004014

#SPJ11

Answer:

See below.

Step-by-step explanation:

The x-intercept occurs when k(x) = 0.

3x - 6 = k(x) = 0

3x - 6 = 0

3x = 6

x = 2

The x-intercept occurs (2, 0).

The y-intercept occurs when x = 0.

k(x) = 3x - 6

k(x) = 3(0) - 6

k(x) = -6

The y-intercept occurs at (0, -6).

A line graph is best suited for showing changes in statistics over time or space.

Line graphs are commonly used to visualize trends, patterns, and fluctuations in data over a continuous or discrete period. The x-axis represents time or space, while the y-axis represents the corresponding statistic being measured. The line graph connects the data points, allowing for a clear representation of how the statistic changes over the given time or space interval.

To know more about line graphs, visit:

https://brainly.com/question/31942903

#SPJ11

The variables, quantitative or qualitative, whose effect on a response variable is of interest are called explanatory variables or predictor variables.

In a study or experiment, the response variable, also known as the dependent variable, is the main outcome being measured or observed. The explanatory variables, on the other hand, are the factors that may influence or explain changes in the response variable.

Explanatory variables can be of two types: quantitative, which represent numerical data, or qualitative, which represent categorical data. The relationship between the explanatory variables and the response variable can be studied using statistical methods, such as regression analysis or analysis of variance (ANOVA). By understanding the relationship between these variables, researchers can make informed decisions and predictions about the behavior of the response variable in various conditions.

In conclusion, explanatory variables play a vital role in helping to analyze and interpret data in studies and experiments, as they help determine the potential causes or influences on the response variable of interest.

Learn more about Explanatory variables here: https://brainly.com/question/30372204

#SPJ11

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766). The margin of error is approximately 0.0140.

To construct a confidence interval for the proportion of Americans who drink tea daily, we can use the formula:

Where,

p = the sample proportion

Z = the critical value corresponding to the desired confidence level

n = the sample size

Given:

Now, let's calculate the confidence interval and margin of error:

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766), with a margin of error of approximately 0.0140.

Learn more about confidence interval in: https://brainly.com/question/32278466
#SPJ4

The solution for the inequality in this problem is problem is given as follows:

v ≤ 81.

The four inequality symbols, along with their meaning, are presented as follows:

The inequality is given as follows:

5v/9 ≤ 45.

v ≤ 45 x 9/5

v ≤ 9 x 9

v ≤ 81.

Hence the solution is composed by the numbers to the left of 81, with a closed interval at x = 81.

More can be learned about inequalities at brainly.com/question/25275758

#SPJ1

2 - 300 calories

3 - 1260 calories

6 - 20g

7 - 70mg

The polar coordinates of the point for the given conditions are:(a) (r,θ) where r > 0 and -π/2 ≤ θ ≤ 3π/2.(b) (r,θ) where r = 7 and θ = 0.(c) (r,θ) where r > 0 and π/6 ≤ θ ≤ π/4. The polar coordinates of the point (1,0) are given by (r,θ) = (1, 0).

We are given polar coordinates (2, 55) and we have to find other polar coordinates (1,0). We are also supposed to graph the point (2,57).

Solution: For point (2,55), we have:

r = 2θ = 55°

Converting 55° into radians, we get

θ = 55° × π/180°

= 0.96 radians

So, the polar coordinates of the point (2,55) are given by (r,θ) = (2, 0.96)

The graph of the point (2,57) is shown below:

From the above graph, we can see that r > 0 when the angle is between 0 and 90 degrees, and r < 0 when the angle is between 90 and 180 degrees.

(a) For the given condition, r > 0 and -2x ≤ 0, the angle θ lies between 90° and 270°.

So, the polar coordinates of the point can be written as (r,θ) where r > 0 and -π/2 ≤ θ ≤ 3π/2.

(b) For the given condition, r = 7, and 0 = 0 < 2π, the polar coordinates of the point can be written as (r,θ) where r = 7 and θ = 0.

(c) For the given condition, r > 0 and 2 ≤ 0 < 45, the polar coordinates of the point can be written as (r,θ) where r > 0 and π/6 ≤ θ ≤ π/4.

Now, we have to find the polar coordinates of the point (1,0).

The point (1,0) is located on the x-axis, so the angle θ = 0.

So, the polar coordinates of the point (1,0) are given by (r,θ) = (1, 0).

Therefore, the polar coordinates of the point for the given conditions are:(a) (r,θ) where r > 0 and -π/2 ≤ θ ≤ 3π/2.

(b) (r,θ) where r = 7 and θ = 0.

(c) (r,θ) where r > 0 and π/6 ≤ θ ≤ π/4.

The polar coordinates of the point (1,0) are given by (r,θ) = (1, 0).

To learn more about coordinates visit;

https://brainly.com/question/22261383

#SPJ11

Answer:

See below.

Step-by-step explanation:

40 + 15x = 30 + 19x

15x - 19x = 30 - 40

-4x = -10

x = 2.5

Two and a half hours.

The first plumber and the second plumber charge the same total amount for 2.5 hours of work.

Two or more expressions with an Equal sign is called as Equation.

The number of hours worked by both plumbers is "h". Then the total amount charged by the first plumber is:

Total cost for the first plumber = 40 + 15h

And, the total amount charged by the second plumber is:

Total cost for the second plumber = 30 + 19h

To find the number of hours for which both plumbers charge the same total amount, we need to solve the equation:

40 + 15h = 30 + 19h

4h = 10

h = 2.5

Therefore, the first plumber and the second plumber charge the same total amount for 2.5 hours of work.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

The answers are :

a. The cost of 5 kg rice if you buy 5 box of 1 kg will be equal to £ 7.

b. You need to buy 2 - 2kg rice box and 1 - 1kg box , and the cost will be £6.70.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

It is given that a shop has three different sized boxes of rice which are 1 kg box , 1.5 kg box and 2 kg box.

a.

As per the question , you want to buy 5kg of rice. And for that you could buy five boxes of size 1 kg.

We know that , cost of 1 kg rice box = £ 1.40

So  , the cost of 5 kg rice will be :

= 5 × 1.40

= £ 7

b.

It is given that you could buy 5 kg of rice in different ways.

Let's check when the cost to buy 5 kg of rice in cheapest way will be possible.

Cost of 2kg rice is £2.65.

So , if we buy 2 - 2kg rice box then it will cost :

= 2 × £2.65 = £5.30

Now 1 kg more is needed . So, if you buy 2 - 2kg rice box and 1 - 1kg rice box then total cost will be :

= £5.30 +  £1.40

=  £6.70

This is the cheapest way possible.

Therefore , the answers are :

a. The cost of 5 kg rice if you buy 5 box of 1 kg will be equal to £ 7.

b. You need to buy 2 - 2kg rice box and 1 - 1kg box , and the cost will be £6.70.

Learn more about algebra here :

https://brainly.com/question/12377332

#SPJ1

Answer:

Step-by-step explanation:

take b, divide it by 2 and then square it

(6/2)²=9 so add then subtract 9

(x²+6x+9)+3-9

x²+6x+9=(x+3)²

3-9= -6

(x+3)²-6

The vertex is a minimum and the coordinates are (-3,-6)

Answer:

6x2 + 16x = 672

Reorder the terms:

16x + 16x2 = 672

Solving

16x + 16x2 = 672

Solving for variable 'x'.

Reorder the terms:

-672 + 16x + 16x2 = 672 + -672

Combine like terms: 672 + -672 = 0

-672 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.

16(-42 + x + x2) = 0

Factor a trinomial.

16((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

Solution

x = {-7, 6}

Step-by-step explanation:

The given quadratic function models the projectile of the object as it is

launched off the top of the building.

The interpretation of the function values are;

The appropriate domain is 0 ≤ x ≤ 7

Reasons:

The given function for the height of the object is f(x) = -16·x² + 16·x + 672

The domain is given by the values of x for which the value of y ≥ 0

Therefore, when -16·x² + 16·x + 672 = 0, we get;

-16·x² + 16·x + 672 = 0

16·(-x² + x + 42) = 0

-x² + x + 42 = 0

x² - x - 42 = 0

(x - 7)·(x + 6) = 0

x = 7, or x = -6

The minimum value of time, x is 0, which is the x-value at the top of the

building, and when x = 7, the object is on the ground.

Therefore;

The maximum value of f(x) = a·x² + b·x + c, is given at \(x = -\dfrac{b}{2 \cdot a}\)

Therefore;

We have;

\(x = -\dfrac{16}{2 \times (-16)} = \dfrac{1}{2}\)

Which gives;

\(f \left(\frac{1}{2} \right) = -16 \times \left(\dfrac{1}{2} \right)^2 + 16 \times \left(\dfrac{1}{2} \right)+ 672 = 676\)

The height of the building is given when the time, x = 0, as follows;

Height of building, f(0) = -16 × 0² + 16 × 0 + 672 = 672

Learn more here;

https://brainly.com/question/10837575

Answer:

7 cats are black

Step-by-step explanation:

Since 33 out of 100 cats are black then that means that 33% of the cats are black.

Since he walked by 21 cats 33% of them are most likely black.

So you do .33 x 21= 6.93 which can be rounded up to 7 cats

Answer:

A. By the Side-Side-Side (SSS) Congruence Theorem, ΔABC ≅ ΔDEF.

B. \( \overline{AB} \cong \overline{DE} \)

\( \overline{BC} \cong \overline{EF} \)

\( \overline{AC} \cong \overline{DF} \)

Step-by-step explanation:

a. From the diagram given, it shows that all three sides of ∆ABC are congruent to all the three corresponding sides of ∆DEF.

Therefore, by the Side-Side-Side (SSS) Congruence Theorem, ΔABC ≅ ΔDEF.

b. The sides that are congruent in the ∆s given that applies to the SSS Congruence Theorem are:

\( \overline{AB} \cong \overline{DE} \)

\( \overline{BC} \cong \overline{EF} \)

\( \overline{AC} \cong \overline{DF} \)

Answer:

mine too

Step-by-step explanation:

Answer:

  38

Step-by-step explanation:

Sequential pairs will be ...

  38 - 87

  79 - 96

  17 - 74 or 79

  43 - 38

  74 - 43

  96 - (none)

  87 - 74 or 79

We notice that 17 has no preceding number. It must be first in the list. 79 cannot be second, because that skips a bunch of numbers. The sequence appears to be ...

  17 - 74 - 43 - 38 - 87 - 79 - 96

The 4th number in the list is 38.

Answer:

1/8 times x + 20=30; in this equation x equals 80. let's take it step by step

Step-by-step explanation:

First off its good to write the equation out so it's easier to read but here are the steps:

First off we know that a number increased by 20 will give us 30. THe only number that can be increased by 20 to give 30, is 10. So now we know that 1/8 of a number will give us 10. To find the number all we need to do is divide 1/8 by 10. 1/8 / 10= 8/1 x 10/1 = 80

now we can test our answer:

1/8 of 80 is 10 and 10 increased by 20 is 30.

Therefore your answer is 80.

Answer: I think that the answers are

a = 1

b = 10

the value of k that makes the piecewise function f(x) continuous at x = k is k = -16.80.

For the piecewise function f(x) to be continuous at x = k, the left-hand limit and the right-hand limit of f(x) at x = k must be equal.

Let's first find the left-hand limit as x approaches k. According to the given definition, for x less than or equal to k, f(x) = 80x + 59. Therefore, the left-hand limit is given by:

lim┬(x→k^-)⁡〖f(x) = lim┬(x→k^-)⁡(80x + 59) = 80k + 59〗

Next, let's find the right-hand limit as x approaches k. According to the given definition, for x greater than k, f(x) = 99x + 75. Therefore, the right-hand limit is given by:

lim┬(x→k^+)⁡〖f(x) = lim┬(x→k^+)⁡(99x + 75) = 99k + 75〗

For the piecewise function to be continuous at x = k, the left-hand limit and the right-hand limit must be equal. So, we have:

80k + 59 = 99k + 75

Solving this equation for k, we find:

19k = 16

k ≈ -16.80 (rounded to two decimal places)

Therefore, the value of k that makes the piecewise function f(x) continuous at x = k is k = -16.80.

Learn more about piecewise function here:

https://brainly.com/question/28225662

#SPJ11

Pam had 3/4 of the pizza left after her birthday party. She ate 3/4 of the remaining pizza for lunch. To find the fraction of the remaining pizza she ate, you need to multiply the two fractions:
3/4 (left after party) * 3/4 (eaten for lunch) = 9/16. Pam ate 9/16 of the remaining pizza for lunch.

To solve this problem, we first need to find out how much pizza Pam had left after her birthday party. We know that she had 3/4 of a pizza left, so we can represent this as a fraction:
3/4
Pam ate 3/4 of the remaining pizza for lunch. To figure out how much pizza she ate, we need to find out what fraction of the remaining pizza 3/4 represents.
To do this, we need to subtract 3/4 from 1 (since 1 represents the whole pizza). This will give us the fraction of the pizza that Pam did not eat for lunch.
1 - 3/4 = 1/4

Pam had 1/4 of the pizza left after eating her lunch. Now we can find out what fraction of the remaining pizza she ate by dividing the amount she ate (3/4) by the amount remaining (1/4):
3/4 ÷ 1/4 = 3
Pam ate three-fourths, or 3/4, of the remaining pizza.

To know more about fraction visit:-

https://brainly.com/question/10354322

#SPJ11

Answer:

37.5%

Step-by-step explanation:

40÷100=0.4

15÷0.4=37.5

Answer:

the answer is 37.5%

Step-by-step explanation:

because thats what

Complete question

The complete question is shown on the first uploaded image

Answer:

The  function is \(y = \frac{1}{18} (x -4 )^2 + 3.5\)

The  domain is  [1, 7]

Step-by-step explanation:

Generally from the Graph we can see that

   For the y-coordinate the point of symmetry is  \(y = g = 4\)

    For  the x-coordinate the point of symmetry is x  =  4

The general form of quadratic equation representing this type of curve is

      \(y = b(x-g)^2 + u\)

Now considering the coordinate (4, 3.5) along the axis of symmetry we have that

        \(3.5 = b(4-4)^2 + u\)

=>      \(u = 3.5\)

Now considering point B having the coordinates (7,4)

       \(4 = b(7-4)^2 + 3.5\)

     \(4 = 9b + 3.5\)

      \(b = \frac{1}{18}\)

Generally the function that define the given graph is

      \(y = \frac{1}{18} (x -4 )^2 + 3.5\)

From the graph the  first element for x  is 1 (i.e  [1 . 4] )and the last element for x is  7 (i.e [7,4])

So the domain of the function is [1, 7]

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

To solve more questions on inequalities, we get -

https://brainly.com/question/11897796

#SPJ1

The probability of having the sums that would exceed 100 has been calculated to be 0.5

We have the set or the sample space as:{1 , 5 , 10 , 100) It is said that two numbers would be able to be gotten from the set that we have. Given that the total numbers are 4, we would have ⁴C₂ = 6

The two numbers would be gotten from the set of 4 numbers in 6 different ways.

We are to find the numbers which when we add them up would be able to give us a sum that is greater than 100 these values are (100, 1), (100, 5), (100, 10)

Hence three pairs out of the given six that we already have would be able to give us values that are more than 10. We would have to divide through such that 3 / 6 = 1 / 2 = 0.5

Hence the probability that their values when summed would have to be greater than 100 is 0.5

Read more on probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

w=3

Step-by-step explanation:

5-2(2w-1)=-11+2w

PEMDAS

5-4w+2=-11+2w

Simplify the format

-4w+7=-11+2w

Combine like terms

-4w-2w=-11-7

-6w=-18

Divide by -6 to solve for w

w=3