hello! can anyone explain to me how to solve this problem step by step?

Answer:

Step-by-step explanation:

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i hope this helps

If guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent (E), above average (AA), average (A), below average (BA), or poor (P). The frequency is : 1, 8, 6, 3, 2.

Analysis

E = E =1

AA= AA +AA + AA + AA + AA+ AA + AA +AA = 8

A= A + A+ A+ A+ A+ A = 6

BA = BA + BA + BA =3

P = P + P =2

Hence,

Class     frequency

E                     1

AA                  8

A                     6

BA                   3

P                      2

Total               20

Therefore  1, 8, 6, 3, 2 is the frequency .

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Answer:

a) The sample space for this experiment includes

(Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (diamonds, tail), (hearts, head), (hearts, tail)

b) The two events are not mutually exclusive or disjoint as both events can occur at the same time and the set of A intersect B is not an empty set and P(A n B) ≠ 0.

c) P(A u B) = (3/4) = 0.75

d) P(A n B') = (1/4) = 0.25

Step-by-step explanation:

Let A be the event a club or spade is picked from a regular 52-card deck.

Let B the event a heads appears when the coin is tossed.

a) A sample space consists of all the possible outcomes of the whole process of picking a random suit and then tossing the coin for heads or tails.

There are 4 suits in a 52 deck card namely, clubs, spades, diamonds and hearts.

And in a toss of a coin, there are only 2 possible outcomes, a head or a tail.

The possible outcomes for the random pick of cards include

{clubs, spades, diamonds, hearts}

And for the second event

{Head, tail}

Combined, the sample space is

(Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (diamonds, tail), (hearts, head), (hearts, tail)

Noting that P(A) = probability of a club or a spade being picked = (26/52) = (1/2)

P(A') = Probability that a club or spade will not be picked, that is, a diamond or a heart will be picked = (26/52) = (1/2)

P(B) = Probability of a head turning up from the coin toss = (1/2)

P(B') = Probability of a head not turning up, that is, a tail turning up = (1/2)

b) Disjoint events are events that are mutually exclusive and cannot both occur at the same time. The set of the intersection of the two mutually exclusive/disjoint events is a null set.

Mathematically, mutually exclusive/disjoint events are proven through the relation that P(A n B) = 0.

But from the sample spaces obtained in (a) above, the event

(A n B) = (Clubs, head), (spades, head)

And it isn't a null set.

Since the probability of an event is the number of elements in the event divided by the total number of elements in the sample space.

n(A n B) = 2

n(total sample space) = 8

P(A n B) = (2/8) = (1/4) ≠ 0

Hence, the two events aren't disjoint.

c) P(A u B)

This represents the probability of obtaining a club or spade from the deck of card or getting head from the coin toss.

From the Total sample space, the set (A u B) includes (Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (hearts, head)

n(A u B) = 6

n(total sample space) = 8

P(A u B) = (6/8) = (3/4) = 0.75

d) P(A n B')

This represents the probability of obtaining a club or spade from the deck of card and NOT getting a head from the coin toss.

The set (A n B') includes (Clubs, tail), (spades, tail)

n(A n B') = 2

n(total sample space) = 8

P(A n B') = (2/8) = (1/4) = 0.25

Hope this Helps!!!

Considering the definition of exponential function, the value of the car is 11,287.25 dollars.

An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

f(x)= aˣ

Being a a positive real, a > 0, and different from 1, a ≠ 1.

When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.

In this case, the value of that car depreciates based on the function f(t)=12,000×\(0.96^{t}\) where t is measured in years after purchase.

After 3/2 years, the value of the car is calculated as:

f(3/2)=12,000×\(0.96^{3/2}\)

Solving:

f(3/2)= 11,287.25

Finally, the value of the car is 11,287.25 dollars.

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Answer:

b

Step-by-step explanation:

when an reflected across the y axis only the x value changes and it changes negatively

Answer:

Objective Function: P = 2x + 3y + z

Subject to Constraints:

3x + 2y ≤ 5

2x + y – z ≤ 13

z ≤ 4

x,y,z≥0

Step-by-step explanation:

The x intercept means the moment when the computer completely loses its value and becomes obsolete

x intercept is given by y = -300x + 3000 = 0, which implies x = 3000/300 = 10 years

For y = -300x + 3000 = 1500, we have x = 1500/300 = 5 years

Therefore, it takes 5 years for the computer value to drop a half and more 5 years to the computer became completely obsolete

Answer:

Around 16.92

(I think, have a nice day!)

Step-by-step explanation:

Use the distance formula and add them all together.

The distance formula is

\(d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}\)

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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Answer:

8 ft

Step-by-step explanation:

i forgot what law it was called srry

The answer is 48. Becuase you need to multipluy and also didived the numbers by the quatum number of X.

Answer:

Step-by-step explanation:

The system of equation we get are x+y=14 and 7x+14y=140 and the x and y values we get as 8 and 6.

Given that,

Angel is earning $7 per hour washing cars and earning $14 per hour clearing tables while working two summer jobs. He can only work a maximum of 14 hours each week and must make at least $140. He must also put in at least three hours washing automobiles.

We have to write down a system of inequalities, solve it graphically, and identify one potential solution if x represents the number of hours spent washing cars and y represents the number of hours spent cleaning tables.

We know that,

x+y=14  ------->equation(1)

7x+14y=140  ------->equation(2)

Take the equation(1)

x+y=14

x=14-y

Substitute x=14-y in equation(2)

7(14-y)+14y=140

98-7y+14y=140

7y=140-98

7y=42

y=42/7

y=6

Substitute y=6 in equation(1)

x+y=14

x+6=14

x=14-6

x=8

Therefore, The system of equation we get are x+y=14 and 7x+14y=140 and the x and y values we get as 8 and 6.

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The total surface area of the solid shape made from the cube and cylinder is approximately 583.31 cm².

The side length of the cube is 8.7 cm, so the surface area of one face is A = 8.7²

= 75.69 cm²

Since there are six faces, the total surface area of the cube is 6 * 75.69 = 454.14 cm²

Since there are two circular bases, the total surface area of the bases is 2 * 22.91 = 45.82 cm².

In this case, the radius of the cylinder is 2.7 cm and the height is 4.9 cm, so the curved surface area is A_curved = 2 * π * 2.7 * 4.9 ≈ 83.35 cm².

Total surface area = surface area of the cube + surface area of the cylinder

Total surface area = 454.14 cm² + 45.82 cm² + 83.35 cm²

Total surface area ≈ 583.31 cm²

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Using percentage, the true proportion of registered voters who are Democrats is = 64.

What do you mean by percentage?

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%.

It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage.

In the question,

Sample size, n = 140.

Now 46% of the registered voters are Democrats.

Now the no. of registered voters =

46% of 140

= 46/100 × 140

= 6440/100

= 64.4

≈ 64

Therefore, 64 is the true proportion of registered voters who are Democrats.

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Answer:

B. Tangent

Step-by-step explanation:

Tangent always makes 90 degree angle with the radius. Now in triangle let's see if it's right angled triangle or not.

To confirm if it's a right angled triangle it should follow Pythagoras Theorem.

Which states square of hypotenuse = sum of squares of other two legs

\(12 {}^{2} + 16 {}^{2} = 20 { }^{2} \\ 144 + 256 = 400 \\ 400 = 400\)

it proves that it's a right angled triangle. Hence AB is a tangent to circle.

Yes, line AB is tangent to the circle.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Since, Tangent always makes 90 degree angle with the radius.

Hence, in triangle we can see if it's right angled triangle or not.

Now, To confirm if it's a right angled triangle it should follow Pythagoras Theorem as;

12² + 16² = 20²

144 + 256 = 400

400 = 400

Which states square of hypotenuse = sum of squares of other two legs

it proves that it's a right angled triangle. Hence AB is a tangent to circle.

Hence, We can say that;

⇒ line AB is tangent to the circle.

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Answer:

-12 and 12

Step-by-step explanation:

-12 squared is also 144 bcoz two negatives multiplied make a positive.

12 is the sqrt of 144

Step-by-step explanation:

The square root of 144 is 12, because by multiplying the same number twice as a result we will get 144. 12 * 12 = 144

Answer:

800:1200 or  2:3

Step-by-step explanation:

400 payed

1200 in total

1200-400=800

800:1200 or 2:3

To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:

Monthly basic salary: Rs 48,000

Social security tax rate: 1%

Income tax rate on income up to Rs 5,00,000: 0% (no tax)

Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%

Dashain allowance: 1 month's salary

Deposit in Citizen Investment Trust (CIT): 10%

Rebate on income tax: 10%

(i) Annual Income:

Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:

Annual Basic Salary = Monthly Basic Salary x 12

= Rs 48,000 x 12

= Rs 5,76,000

Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:

Annual Income = Annual Basic Salary + Dashain Allowance

= Rs 5,76,000 + Rs 48,000

= Rs 6,24,000

Swornima's annual income is Rs 6,24,000.

(ii) Tax Rebate:

Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.

(iii) Annual Income Tax:

First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.

Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000

= Rs 1,24,000

Income Tax in this range = Taxable Income x Tax Rate

= Rs 1,24,000 x 0.1

= Rs 12,400

Now, let's calculate the total annual income tax:

Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000

= Rs 12,400

Next, we calculate the rebate on income tax:

Tax Rebate = Total Annual Income Tax x Rebate Rate

= Rs 12,400 x 0.1

= Rs 1,240

Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.

To summarize:

(i) Swornima's annual income is Rs 6,24,000.

(ii) Swornima's tax rebate is Rs 1,240.

(iii) Swornima should pay an annual income tax of R

By using the data in the given table, the missing coefficients should be filled as followed;

y = x + 6.128.

In this scenario, the x-values would be plotted on the x-axis (x-coordinate) of the scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the line of best fit is given by

y = x + 6.128

In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates a linear relationship between the x-values and y-values.

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Answer:

68°

Step-by-step explanation:

Total angle in a quadrant = 90°

x + 22° = 90°

x = 90 - 22

x = 68°

a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.

b) An equation representing the situation is x = (125 - 80)/5.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

The mathematical operations provide solutions to mathematical problems using operands.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

The total number of balloons that Andre has = 125

The number of balloons remaining after hanging some for the school party = 80

The difference (number of balloons used) = 45 (125 - 80)

The number of friends who hang the balloons = 5

The number of balloons hung by each friend of Andre = 9 (45/5)

Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.

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The original price of the bracelet was £1400.

Percentage is a way of expressing a proportion or a fraction as a part of 100. It is denoted using the symbol "%". For example, 50% means 50 out of 100, or half, while 25% means 25 out of 100, or one-quarter.

We can start by using the information given to set up an equation that relates the original price of the bracelet with the sale price and the percentage reduction:

original price x (100% - 70%) = sale price

Simplifying the percentage reduction:

original price x 30% = sale price

Substituting the given sale price (£420):

original price x 30% = £420

To solve for the original price, we need to isolate it on one side of the equation. We can do this by dividing both sides by 30% (which is the same as multiplying by 100/30 or 10/3):

original price = sale price / 30% = £420 / 30% = £1400

Therefore, the original price of the bracelet was £1400.

Complete question - A jewelry shop is having a sale. A bracelet is now reduced to £420. This is 70% of the original price. Work out the original price of the bracelet.

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Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

the answer is ssmsmsmsmsmememememeememekekeke

Answer:

Step-by-step explanation:

tan(43) = 1347/x

Multiply by x to bring it to the other side.

x*tan(43) = 1347

Divide by tan(43) to get x by itself.

x = 1347/tan(43)

Use the tan and cot relationship.

x = 1347 * cot(43)

Multiply.

x ≈ 1444.5

The counting process was an essential component in evaluating the results and drawing conclusions based on the data gathered.

Hi! Bob and Aniyah's apples were counted by a designated individual, likely a teacher, supervisor, or event organizer, who was responsible for ensuring the accuracy and fairness of the counting process.

This person utilized their organizational skills and attention to detail to effectively tally the number of apples collected by both Bob and Aniyah.

By doing so, they were able to determine the final count, which was then used to either compare the performance of the two individuals or contribute to a larger total for a specific event or purpose.

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Answer: A 95% lower confidence bound for the mean capacity of this type of battery = 175.85

Step-by-step explanation:

Given: The capacities were measured for a sample : n= 120 batteries.

\(\overline{x}=178\) and  \(\sigma=12\)

lower confidence bound= \(\overline{x}-z^c\times\dfrac{\sigma}{\sqrt{n}}\)

Critical z value for 9%% confidence = 1.96

So,  a 95% lower confidence bound for the mean capacity of this type of battery will be :

\(178-(1.96)\dfrac{12}{\sqrt{120}}\\\\=178-(1.96)(1.0954451)\\\\=(1.96)(1.0954451)\approx175.85\)

Hence, a 95% lower confidence bound for the mean capacity of this type of battery = 175.85

For the function, the x-intercept of g(x) is at (5,0).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = ln(x)

and g(x) = -f(x - 4)

the function is

g(x) = -ln(x - 4)

when x = 5

g(x) = -ln(5 - 4)

g(x) = -ln1

g(x) = 0

the coordinates are (5, 0)

Hence the x-intercept is (5, 0).

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