Triangles ABD and BCD are right-angled triangles.
A
5 cm
B
x cm
Work out the value of x.
Give your answer correct to 2 decimal places.
10 cm
D
4 cm
C

The 68.26% confidence interval for the mean of the population, using the z-distribution, is given as follows:

(15.88 ounces, 16.12 ounces).

The bounds of a z-distribution confidence interval are presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which the parameters are given by:

The confidence level is of 68.26%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.6826}{2} = 0.8413[/tex], so the critical value is z = 1.

The values of the remaining parameters are given as follows:

[tex]\overline{x} = 16, \sigma = 1.4, n = 144[/tex]

Hence the lower bound of the interval is obtained as follows:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 16 - \frac{1.4}{\sqrt{144}} = 15.88[/tex]

The upper bound of the interval is obtained as follows:

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 16 + \frac{1.4}{\sqrt{144}} = 16.12[/tex]

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The speed of the humming bird when converted to miles per minute is; 0.67 miles per minute

In scientific problems, sometimes, it is necessary to change units from one to another as specifically needed.

The procedure for unit conversion is;

1. Identify the unit you have.

2. Identify the unit you desire or require.

3. Identify appropriate unit conversion factor(s).

4. Cancel units and carry out the math calculations.

5. Evaluate the result.

We are given the speed as 40 miles per hour. Now, the unit of conversion factor from mph to miles per minute is;

1 mile per hour = 1/60 miles per minute

Thus;

40 miles per hour = 40 * 1/60 = 0.67 miles per minute

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Answer:

option 1

Step-by-step explanation:

for every 10 students 4 like mathematics , then

80 ÷ 10 = 8

so 8 × 4 = 32

it is predicted that out of 80 students 32 like mathematics

Answer:

slope = 4

Step-by-step explanation:

There are two points plotted at: ( -1 , 0) and ( 0 , 4)

slope = change in rise / change in run

slope = change in y / change in x

slope = (0 - 4) / (-1 - 0)

slope = -4/-1

slope = 4

Step-by-step explanation:

Its is 8 inches as 72÷9 is 8

The domain is the set of all real numbers and the range is:

R: (-∞, 4]

For any function, we define the domain as the set of possible inputs, the ones in the horizontal axis, and the range as the set of the output, the ones in the vertical axis.

We can see that we have a parabola that in the bottom part has two arrows, so it extends in the wole domain (the set of all real numbers).

Instead for the range we can see that there is a maximum at y  = 4, so the range is:

R: (-∞, 4]

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Answer:

2.8 x 10º

Step-by-step explanation:

Because if you travel 10 spaces in the number 280,000,00.

The next number in the number sequence using inductive reasoning 100,90,92,82,84,74,76,… is 66.

What is number series?

 A series is a way of speaking casually of numbers. It is the total of a sequence's terms. A series of numbers is called a number series. We must identify the laws that lead to the production of a number series in order to answer the questions about number series. The questions that might arise from these topics are as varied as these series themselves.

Here the given number series,

=> 100,90,92,82,84,74,76,….

Here , first term = 100

Second term = 100-10=90

Third term= 90+2=92

Fourth term = 92-10=82

Fifth term = 82+2=84

Sixth term = 84-10=74

seventh term = 74+2=76

Eighth term= 76-10 = 66.

Therefore next term of the number Series is 66.

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10 kilograms of the 50% fat-content chocolate and 20 kilograms of the 20%, fat-content chocolate are used to make the required 30 kilograms.

Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation.

The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero. Since we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.

Suppose the amount of 50% fat content chocolate is x and the amount of 20% fat content chocolate is y,

Since the candy company wants to produce 30 kilograms,

x+y=30 -----(1)

If a candy manufacturer wishes to meet the dietary requirements of its customers, it may make 30 kg of special chocolate with a 30% fat content. A specific melting procedure is used to blend local chocolate with 20% fat content with foreign chocolate with 50% fat content to create this. The resultant equation reads,

50x + 20y = 30(30)

5x+2y=90 -------(2)

After solving the equation 1 and 2 we get,

x=10

y=20

Thus, 10 kilograms of the 50% fat-content chocolate and 20 kilograms of the 20%, fat-content chocolate are used to make the required 30 kilograms.

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Answer:

105 Children and 3 cooks

Step-by-step explanation:

I took the test :)

a) The total number of children watching the movie is 105 children

b) The total number of cooks that worked at the event is 3 cooks

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

a)

Let the number of children be = a

Let the number of adults be = b

Let the total number of people in the theater be = 140

Now , the equation will be

a + b = 140   equation (1)

And , the number of children present is 3 times the number of adults

So ,

a = 3b

Divide by 3 on both sides of the equation , we get

b = a/3

Substituting the value of b in equation (1) , we get

a + b = 140

a + a/3 = 140

( 4a ) / 3 = 140

Multiply by 3 on both sides of the equation , we get

4a = 420

Divide by 4 on both sides of the equation , we get

a = 105

Therefore , the value of a is 105 and the number of children watching the movie is 105 children

b)

Let the number of cooks be = x

Let the number of waiters be = y

Let the amount for each cook be = $ 85

Let the amount for each waiter be = $ 45

The total number of workers = 10

Now , the equation will be

x + y = 10   be equation (1)

The total amount paid to the employees be = $ 570

Now , the equation will be

85x + 45y = 570   be equation (2)

On simplifying equation (1) and equation (2) , we get

Multiply equation (1) by 45 , we get

45x + 45y = 450   be equation (3)

Subtract equation (3) from equation (2) , we get

40x = 120

Divide by 3 on both sides of the equation , we get

x = 3

Therefore , the value of x is 3 and the number of cooks that worked in the event is 3 cooks

Hence ,

a) The total number of children watching the movie is 105 children

b) The total number of cooks that worked at the event is 3 cooks

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The purpose of post hoc tests following an Analysis of Variance is to address the question of which groups differ from one another. Option A is correct.

Let us understand the post hoc tests:

Post hoc tests are an essential component of ANOVA. When at least three group means are tested for equality using ANOVA, statistically significant findings suggest that not all of the group means are equal. ANOVA results, on the other hand, do not specify which differences between pairs of means are significant. Use post hoc tests to investigate variations between various group averages while keeping the experiment-wise error rate under control.

There are a lot of post hoc tests that you can be used but the main purpose of the post hoc tests is always the same.

Thus, the purpose of post hoc tests following an Analysis of Variance is to address the question of which groups differ from one another. Option A is correct.

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The thing that can be conluded about the diagram is that the ponds are the same length. This is according to the SAS theorem.

According to the SAS theorem, if two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent.

If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. If two triangles meet one of the following criteria, they are congruent. All three corresponding side pairs are equal. Two corresponding side pairs and their corresponding angles are equal.

In this case, the triangle for the frog pond and duck pond are the same.

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The number of tapes Melanie must sell to break even is 360 tapes.

To find the number of tapes Melanie must sell to break even, we must follow these steps.

We must identify how much she earns for each tape that she sells, for this we must subtract the sale price of each tape, by the value that she pays to make each tape.

Now we must divide the total cost of the mother tape by the profit she makes on each tape she sells.

Based on the above, we can infer that she must sell 360 tapes to cover the value of the mother tape and each of the tapes that she needs to sell. Next it is checked:

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The balance on the Bad Debt Expense account for the year, based on the accounts receivable balance and the rates of uncollectibility is $6, 800.

First, find the uncollected receivables estimate for the year using the rates of uncollectibility.

= ∑ (Age of receivable x Rate of uncollectibility)

= (50, 000 x 1%) + ( 20,000 x 3%) + (11, 000 x 5%) + (19, 000 x 25%)

= 500 + 600 + 550 + 4, 750

= $6, 400

The Bad Debts Expense for the year would then be:

= Uncollected receivables estimate + Debit balance on Allowance for doubtful accounts

= 6, 400 + 400

= $6, 800

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Step-by-step explanation:

Slope = (y2 - y1) / (x2 - x1)

Slope = 5/2

x1 = -6

y1 = y

x2 = 4

y2 = 8

5/2 = (8-y) / (4 - (-6))

5/2 = (8-y) / (4+6)

5/2 = (8-y) / 10

5 x 10 = 2 x (8-y)

50 = 16 - 2y

2y = 16 - 50

2y = -34

y = -17

The measure of  the angle AEG = 92°

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles. These are formed in the matching corners or corresponding corners with the transversal.

∠CFH + ∠EFC = 180( angles on a straight line)

making ∠EFC subject and substituting ∠CFH = 2x + 20, we have

∠EFC = 180 - ( 2x + 20)

∠EFC = 180 - 2x -20

∠EFC = 160 - 2x

but ∠EFC = ∠BEF ( alternate angles are equal)

substituting their values

160 - 2x = 3x - 10

collect like terms

-2x - 3x = -10 - 160

-5x = -170

x = -170/-5

x = 34

Also ∠EFC = ∠AEG = 160 -2x ( corresponding angles are equal)

∠AEG = 160 -2X, but x = 34

∠AEG = 160 - 2(34)

∠AEG =160 - 68 = 92°

In conclusion, The value of the ∠AEG = 92°

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A direct variation with nonzero numbers is if y varies directly as x, and y = 6 when x = 2,

The relationship between two variables in which the variables have a constant ratio, k, where k is not equal to 0.

K is known as the constant. Assume the variables are x and y, and that y varies directly with x. We can say that the y/x ratio is equal to k, where k is not equal to zero.

This formula can also be written as y = kx where k is not equal to 0.

It's critical to understand that we can use these two ratios interchangeably depending on the problem at hand.

In the example given, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.

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Answer:1 hour and 15 minutes

Step-by-step explanation:

so it takes her 34 minutes for 4 problems so for 2 problems its 17 minutes

and then you do the 34 times 2 because its 4 problems so you add that and that = 68 minutes and then you add 17 for the 2 problems and thats 85 minutes or 1 hour and 15 minutes

Answer:

1 hour & 25 minutes (85 minutes)

Step-by-step explanation:

Time taken for 1 problem,

→ 34 ÷ 4

→ 8.5 minutes

Now time taken for 10 problems,

→ 8.5 × 10

→ 85 minutes

Hence, answer is 85 minutes.

The value of the car depreciates according to the scatter plot model that is attached , from the model we can infer that the model is exponential in nature.

So from the data that is plotted in the scatter plot we can see that

The graph is exponential.

We know that the depreciation is calculated by the formula as

A = A₀(1-r)ⁿ

So it is an exponential form of equation. therefore the scatter plot model will also predict an exponential equation.

A scatter plot is a type of plot or mathematical diagram that displays values for a group of data using two or more variables and Cartesian coordinates. A scatter graph, scatter chart, scattergram, or scatter diagram are other names for it.

If the points are somehow coded according to colour, shape, or size, another variable can be seen. A series of points is used to represent the data, with each point's position on the y line determined by the value of one variable and its position on the vertical axis by the value of the other.

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Check step-by-step explanation.

In order to form the table, we must take several values of x (any values you want to evaluate) and find it's correspondent y value. This is how you  do it:

[tex]y=3x+12[/tex]

[tex]x=0, \\y=3(0)+12\\y=12[/tex]

As you may notice, we are just substituting the x value for the x variable into the equation and calculating y. Do this with several values and form a table (check attached image 1).

[tex]x=1, \\y=3(1)+12\\y=15[/tex]

[tex]x=2, \\y=3(2)+12\\y=18[/tex]

Using the calculated points, draw them in the cartesian plane. Remember that "x" means how many spaces you move horizontally, and "y" means vertical spaces.

Check attached image 2.

Let's take point (2, 18) as an example. This point is generated when you substitute the x value of 2, meaning 2 hotdogs and the souvenir hat. Then, the functions gives a result of 18, which would be the cost of those 2 hotdogs in addition to the souvenir hat. Point (0, 12), on the other hand, means that you didn't buy any hotdogs but you still have to pay $12 for the souvenir hat.

In order to hit the UFO, the Anti Aircraft gun should be set an an angle of elevation of approximately 63.435° above the horizontal in the direction of the UFO

An angle of elevation is an angle that the line of sight makes with the horizontal.

The location of the UFO are;

The angle, θ, to which the anti aircraft gun needs to be set is found from the trigonometric ratio for tangent as follows.

[tex]tan(\theta) = \dfrac{Length \, of \, the \, side \, opposite \, to \, angle \, \theta}{Length \, of \, the \, side \, adjacent \, to \, \theta}[/tex]

The length of the side opposite to the angle θ to which the gun should be directed is the length of the height of the UFO from the observer, therefore;

Length of the side opposite to θ = 100 feet

Length of the side adjacent to θ is the length of the horizontal distance from the observer;

Length of the adjacent side to θ = 50 feet

Therefore;

[tex]tan(\theta) = \dfrac{100\, feet}{50\, feet} = 2[/tex]

tan(θ) = 2

θ is found using the inverse tangent function (arctangent) as follows;

θ = arctan(2) ≈ 63.435°

The direction the anti aircraft un should be set is at angle of elevation of approximately 63.435° above the horizontal

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The equation (in slope-intercept form) of the line passing through the points (5,3) and (4,1) is y = 2x -7

The equation of a line in slope intercept form can be represented as follows:

y = mx + c

where

let's find the slope as follows:

(5, 3)(4, 1)

m = 1 - 3 / 4 - 5

m = - 2 / -1

m = 2

Therefore, let's find the y-intercept using (4, 1)

y = 2x + c

1 = 2(4) + c

c = 1 - 8

c = -7

Therefore, the equation of the line is y = 2x -7

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The time taken for the 5 feet of snow to accumulate is 20 hours.

In this case, Smsnow was falling at the rate of 3 inches per hour and if the snow keeps acclimating, we want to know how long will 5 feet of snow to accumulate.

Since 1 foot = 12 inches

5 feet = 5 × 12

= 60 inches

Therefore the time taken will be the division and this will be:

= 60 / 3

= 20

It'll take 20 hours.

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The value of q after solving the inequality, 3q-9 ≤ 8q+10, is q ≤ -19/5.

According to the question,

We have the following information:

3q-9 ≤ 8q+10

Adding 9 to both sides of the inequality:

3q ≤8q+10+9

3q ≤ 8q+19

Subtracting 8q from both sides of the expression:

3q-8q ≤ 19

-5q ≤ 19

Dividing both sides by -5:

q ≤ -19/5

(More to know: inequalities can solved like an equation but the only difference is that the sign of equal has to be replaced by the signs of inequality.)

Hence, the value of q after solving the inequality, 3q-9 ≤ 8q+10, is q ≤ -19/5.

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Altogether, Abby and Annie have 2,400 coins, using the Lowest Common Multiple of 75 and 80.

The lowest common multiple (LCM) of two or more numbers is the common multiple shared by the numbers.

LCM of 75 and 80 can be obtained by multiplying common prime factors of 75 and 80, and then raising them to their respective highest power, i.e. 2^4 × 3^1 × 5^2, which gives 1200.

For instance, 1,200 can be divided by both 75 and 80 evenly without a remainder.  And there is no other number less than 2,000 that 75 and 80 can divide evenly without a remainder.

Abby's coins = 1,200

Annie's coins = 1,200

Total coins = 2,400

Abby's 80 coins will have 15 groups (1,200/80)

Annie's 75 coins will have 16 groups (1,200/75)

Thus, using the LCM of 80 and 75, the total number of coins held by Abby and Annie is 2,400.

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Step-by-step explanation:

domain: x is any value, ⇒ x∈(-∝;+∝);

range: y is not greater, than 4, ⇒ y∈(-∝;4].

The addition using Least multiple, [tex]\frac{2}{8}+\frac{1}{2}[/tex] is equal to [tex]\frac{3}{4}[/tex].

When two or more fractions are there, the least common denominator is the lowest number among all the common multiples of the denominators.

To find the LCD of numbers, factorization method can be used and if the numbers are co-prime then the LCD is just the multiplication of those numbers.

The denominator of given fractions is 8 and 2.

Now, finding the lowest common multiple of 8 and 2,

LCD is 8,

Now, renaming the fraction by multiplying 4 on numerator and denominator of [tex]\frac{1}{2}[/tex],

[tex]\frac{1 \times4}{2 \times4} =\frac{4}{8}[/tex]

Now, denominator is same, so adding the fractions,

[tex]\frac{2}{8}+\frac{4}{8} =\frac{2+4}{8} \\\\=\frac{6}{8}[/tex]

Dividing the numerator and denominator by 2,

[tex]\frac{6}{8} =\frac{6/2}{8/2}\\ =\frac{3}{4}[/tex]

Therefore, by adding the given fractions we get [tex]\frac{3}{4}[/tex].

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The estimates for the number of transistors per IC, using Moore's Law, are given as follows:

Moore's Law states that the number of transistors per IC is expected to double every two years.

From the chart shown by the image at the end of the answer, the reference number is given as follows:

4000 transistors per IC in 1972.

The number of years between 1972 and 2012 is of:

2012 - 1972 = 40.

Hence the number of doubling periods is of:

40/2 = 20 doubling periods.

Thus the estimate for the number of transistors per IC in 2012 = 20 doubling periods is of:

4000 x 2^20 = 4,194,304,000 transistors per IC.

The number of years between 1972 and 2040 is of:

2040 - 1972 = 68.

Hence the number of doubling periods is of:

68/2 = 34 doubling periods.

Thus the estimate for the number of transistors per IC in 2012 = 20 doubling periods is of:

4000 x 2^34 = 6.87 x 10¹³ transistors per IC.

The chart is given by the image at the end of the answer.

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A is the Point of representation of the colder midnight temperature in degrees Celsius.

The temperature in Quebec City was 5°C at 4 pm. By midnight, the temperature dropped 15 degrees.

To find out which point is a representation of the colder midnight temperature in degrees Celsius:

We know that the temperature dropped 15 degrees, and that it was initially of 5°C. So, by midnight, the temperature will be of -10°C (5-15=-10).

We also know that the distance between points is of 5°C. So, the point that we have to mark is point A, which represents -10°C.

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The type of variable that C is can be said to be the binomial variable.

A binomial random variable counts the number of times a specific event occurs in a given number of tries or trials. To be a binomial random variable, a variable must be There is a set number of trials.

It should be noted that the features of the binomial variable include:

1: The number of observations, n, is constant.

2: Each observation is distinct.

3: Each observation denotes one of two possible outcomes ("success" or "failure").

4: The "success" probability p is the same for each outcome.

In this case, the number of coupons the family wins illustrate a binomial.

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