7-1 Additional Practice
1. A random selection will be made from a bug containing different
colored disks. Of the 25 disks in the bag, 5 are yellow,
30 P(yellow)
a. The probability that a yellow disk will be selected is Ois 2


How come the answer is 2?

Okay, let's analyze the two functions based on the options:

Function A:

X f(x)

0 5

1 10

2 20

3 40

4 80

Options:

Neither function A nor function B has an x-intercept. - False, function A has an x-intercept at x=0.

Neither function A nor function B has a y-intercept. - False, function A has a y-intercept at f(x)=5.

The domain and range of both functions contain only positive numbers. - False, function A has values that include 0.

The domain and range of both functions contain only positive numbers and zero. - True, the domain and range of both functions contain only non-negative numbers including 0.

Therefore, the correct choice is:

O The domain and range of both functions contain only positive numbers and zero.

Let me know if you have any other questions!

The values closest to these middle elements are 60 and 61 inches.

To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:

3 | 2

4 | 0 9 9

5 | 0 0 0 4 4 9

6 | 1 2 3

7 | 0 0 3 0

8 | 0 8

9 | 0

To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:

We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.

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The values closest to these middle elements are 60 and 61 inches.

To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:

3 | 2

4 | 0 9 9

5 | 0 0 0 4 4 9

6 | 1 2 3

7 | 0 0 3 0

8 | 0 8

9 | 0

To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:

We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.

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Answer:

The mean of a binomial distribution is μ = np, where n is the sample size and p is the probability of success (having blue eyes).

μ = 20 x 0.08

μ = 1.6

Rounded to one decimal place, μ is 1.6.

Answer:

12%

Step-by-step explanation:

Let the rate of interest be R%
r = R% as decimal =R/100

Simple interest earned for 3 years at rate r on ₹15,000 = ₹5,400

The formula for interest earned is given by
I = Prt
where P is the principal amount (15,000)

r = annual interest rate as a decimal (to be determined)

t = number of years

Plugging in known values we get

5400 = 15000 x r x 3

         = 45000 x r

r = 5400/45000

r = 0.12

Rate of interest as a percentage = r x 100 = 0.12 x 100 = 12%

Answer:

[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]

[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]

Choice C: The ratio is the same for both triangles

Step-by-step explanation:

[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]

[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]

So both ratios are the same. This is also because the ratios represent the tan of the angle that the adjacent side makes with the hypotenuse and this angle of 22° is same in both triangles

The length of the two unknown sides of the triangle are: 12√2

There are different methods of finding the missing sides of triangles such as:

Pythagoras Theorem

Law of sines or sine rule

Law of cosines or cosine rule

Now, we are given an Isosceles triangle with a base length and two equal base angles.

Thus, the two unknown sides will have equal side lengths.

∠D = 90°

Thus, using sine rule:

12/sin 90 = QR/sin 45

QR = 12 * 1/√2

Rationalizing the denominator gives:

QR = 12√2

Since the two unknown sides of the triangle are equal, then we say that:

PQ = 12√2

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your aanswer is 9 ⚡

The value of numbers are,

⇒ 9 and 16

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The product of two numbers is 1296.

And, one number is 16 times the other,

Let first number = x

Hence, Second number is, 16x

So, We get;

⇒ 16x × x = 1296

⇒ 16x² = 1296

⇒ x² = 81

⇒ x = 9

Hence, first number = 9

And, Second number is,

= 16x

= 16 x 9

= 144

Thus, The value of numbers are,

⇒ 9 and 16

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The exponential growth functions are,

[tex]y=\frac{9}{11}(4)^t[/tex]

[tex]V=0.8(9)^t[/tex]

[tex]P=0.9(8.3)^t[/tex]

[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]

The exponential decay functions are,

[tex]A= (0.97)^t[/tex]

[tex]y= 3.7 (0.2)^t[/tex]

The function which is neither exponential growth nor exponential decay is,

g(x)=2.1(x).

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

If the base is larger than 1, it will be an exponential growth.

For example, [tex]3^2=9[/tex]

If the base is smaller than 1, it will be an exponential decay.

For example, [tex]0.5^2=0.25[/tex]

If the function does not have an exponent, that means there will be no exponential growth or decay.

Therefore the exponential growth functions are,

[tex]y=\frac{9}{11}(4)^t[/tex]

[tex]V=0.8(9)^t[/tex]

[tex]P=0.9(8.3)^t[/tex]

[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]

The exponential decay functions are,

[tex]A= (0.97)^t[/tex]

[tex]y= 3.7 (0.2)^t[/tex]

The function which is neither exponential growth nor exponential decay is,

g(x)=2.1(x).

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The price of the wheelbarrow is $86, and Pedro will need to pay an additional 30% of the price for shipping and handling.

To calculate the shipping and handling cost, we can first find 30% of the price of the wheelbarrow:

30% of $86 = 0.3 x $86 = $25.80

Therefore, Pedro will need to pay $25.80 for shipping and handling.

Thus, the dimensions of the rectangle are - length 22 inches and width 13 inches.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). The opposite sides of a rectangular are equal and parallel. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.

Let the length of rectangle be 'l'

Let the width be 'w'.

Then,

Perimeter = 2(l + w)

70 = 2(l + w)

35 = l + w

l = 35 - w ...eq 1

Now,

Area = length * width

286 = l*w ...eq 2

Put eq 1 in eq 2

286 = (35 - w)*w

286 = 35w - w²

w² - 35w + 286 = 0

Solving the quadratic equation:

w² - 22w - 13w + 22*13 = 0

w(w - 22) - 13(w - 22)= 0

(w - 22)(w - 13) = 0

w = 22 and w = 13

As, length is greater than width-

width w = 13 inch

Length l = 35 - 13 = 22 inches.

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Answer:

38.part A) 3p = 25.47

partB) $8.49

Step-by-step explanation:

38) to get the price of a game ,$25.47 will be divided by

 25.47÷3=$8.49

the price of 1 game =&8.49

 to get the price of 1 game , the equation will be

 3p=25.47

 p=25.47÷3

 p=$8.49

If 100 different students were chosen from this population, we would expect approximately 27 of them to read more than 94 words per minute. Therefore, the correct choice is (A).

The probability that a randomly selected student in the city will read more than 94 words per minute is 0.2743.

z-score = (x - μ) / σ = (94 - 88) / 10 = 0.6

Therefore, the probability of a z-score being greater than 0.6 is:

P(Z > 0.6) = 1 - P(Z < 0.6) = 1 - 0.7257 = 0.2743

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Answer: yes, the hex of the number 1,000,000 would be 40.

1. If the gross domestic product of a country is significantly higher in one year than in another, the factor that might account for the difference is d. all of these.

2. The Lorenz Curve for the United States indicates that the richest 20 percent of households have d. 46.8 percent of the nation's income.

3. The economic condition most likely to be caused by a war affecting oil production in the Mid East would be a. demand-pull inflation.

The gross domestic product or GDP refers to the total monetary value of goods produced and services provided in a country during one specific period.

The Lorenz Curve, developed by Max Lorenz measures income inequality or wealth inequality using a graphical representation.

When there is a shortage in supply, pressure is mounted on the available quantity of an item, causing its price to increase.

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The relative maximum and minimum point as well as the absolute maximum and minimum points based on labeled points on the graph are;

Points 1, 3, and 5 are relative maximum points

Points 2 and 4 are relative minimum points

Point 5 is an absolute maximum point

Point 2 is an absolute minimum point

A relative maximum is a point in which the maximum with regards to the immediate surrounding points.

Therefore, the relative maximum points are;

The points 1, 3, and 5

The relative minimum points are points that are the minimum points, when compared with the surrounding points

The relative minimum are the points 2 and 4

The absolute maximum is the point which is at the highest point on the graph

The absolute maximum on the graph is therefore, the [oint 5

The absolute minimum on the graph is the point which is the minimum point compared to all other points

Therefore, the absolute minimum point is the point 2

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Interest charge for the month = 51.69 rounded to the nearest penny.

Here, we have,

The particular month in question is 30 days long.

Your balance at the start of the month is 3,000.

Annual interest rate = 21%.

Payment = 150.00.

When the payment is made in the month, it reflects on the tax amount you pay on both the average day balance.

YOU SEND THE PAYMENT IN ON THE FIRST DAY OF THE MONTH.

YOUR ACCOUNT IS CREDITED ON THE 11TH DAY OF THE MONTH.

Average daily balance is 3000 from day 1 until day 10 (10 days)

Average daily balance is 2850 from day 11 until day 30 (20 days)

Average daily balance for the month = 10 * 3000 + 20 * 2850

                                                            = 87000 / 30

                                                            = 2900

Interest charge for the month = 0.21 * 2900 * 30 / 365

Interest charge for the month = 50.05 rounded to the nearest penny

YOU SEND THE PAYMENT IN ON THE TWENTIETH DAY OF THE MONTH.

YOUR ACCOUNT IS CREDITED ON THE 30TH DAY OF THE MONTH.

Average daily balance is 3000 from day 1 until day 29 (29 days)

Average daily balance is 2850 from day 30 until day 30 (1 day)

Average daily balance for the month = 3000 * 29 + 1 * 2850

                                                            = 89850 / 30

                                                            = 2995

Interest charge for the month = 0.21 * 2995 * 30 / 365

Interest charge for the month = 51.69 rounded to the nearest penny

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Complete Question:

Calculate the monthly finance charge for the following credit card transaction. Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. Round your answer to the nearest cent.

3,000 balance, 21% rate, 150 payment, average daily method

Answer:

12[tex]x^{2}[/tex]+4x

Step-by-step explanation:

area = width * height

substitution: area = (3x+1)*4x

distributive property: area = (4x*3x)+(4x*1)

simplify: area = 12[tex]x^{2}[/tex]+4x

Where the above conditions existing, the probability that a randomly selected site will have a    snow depth between 2.25 and 2.7 inches is 68.3 %.

t the value The value one standard deviation below the mean is 2.25 inches.

The  value one standard deviation above the  mean is 2.75 in.

To find the probability , calculate the z-scores for these values

z1 = (2.25  - 2.5 ) /0.25 = -1

z2= ( 2.7 -2.5 )   / 0.25 = 0.8

Using a standard normal distribution table ....

we can see that the probability of a z-  score between -1 and 0.8 is approximately 0.683, or 68.3%.

Hence,  the probability that a randomly chosen location will have a snow depth between 2.25 and 2.7 inches is 68.3%.

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The missing sides of the triangle are

10). ∠ ABD = 60 degrees

11). ∠ ADB = 90 degrees

12). ∠ BAD = 30 degrees

13). ∠ CAD = 30 degrees

14. BD is half of the length = BC / 2 = 6/2 = 3

15. AD is the height this is solved using Pythagoras theorem as below

AD^2 = AB^2 - BD^2

AD^2 = 6^2 - 3^2

AD^2 = 36 - 9

AD = sqrt (27)

16. Area of Δ ABC

= 1/2 * base * height

= 1/2 * 6 * sqrt (27)

= 9 sqrt (3)

= 15.59 square units

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Answer: if the first angle is 61° then the angle x is 119°

               but if the first angle is 67 then the angle x is 113°

Step-by-step explanation:

Line is 180° that means our formula will look like that 67 or 61 + x = 180 in that case we have to calculate x ⇒ 180 - 61 or 67 = x

The maximum pressure differential in a stairwell is 58,860 Pa.

The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.

The difference in static water pressure between consecutive floors is 29,430 Pa.

We have,

Assuming a standard atmospheric pressure of 101.3 kPa.

Maximum pressure differential in a stairwell:

Since each stairwell is no more than 20 stories high and each story is approximately 3 m high, the maximum height difference between two floors in a stairwell is:

= 20 x 3

= 60 m

Using the formula for hydrostatic pressure, the maximum pressure differential in a stairwell is:

ΔP = ρgh

= (1000 kg/m³)(9.81 m/s²)(60 m)

= 58,860 Pa

The atmospheric pressure difference between the top of the building and street level:

The atmospheric pressure decreases with increasing altitude.

Using the formula for hydrostatic pressure, the pressure difference between the top of the building and the street level is:

ΔP = ρgh

= (1000 kg/m³)(9.81 m/s²)(300 m)

= 2,943,000 Pa

The difference in static water pressure between consecutive floors:

Assuming a standard density of water of 1000 kg/m³, the difference in static water pressure between consecutive floors is:

ΔP = ρgh = (1000 kg/m³)(9.81 m/s²)(3 m) = 29,430 Pa

Therefore,

The maximum pressure differential in a stairwell is 58,860 Pa.

The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.

The difference in static water pressure between consecutive floors is 29,430 Pa.

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The missing sides of the triangle have been identified here.

Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.

1) Sin x = 5/14

x = Sin-1 (5/14)

x = 21°

2) Tan x = 8/5

x = Tan-1 (8/5)

x = 58°

3) Cos x = 9/13

x = Cos-1 (9/13)

x = 46°

4) Cos x = 3/5.8

x = Cos-(3/5.8)

x = 59°

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The missing sides of the triangle have been identified here.

Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.

1) Sin x = 5/14

x = Sin-1 (5/14)

x = 21°

2) Tan x = 8/5

x = Tan-1 (8/5)

x = 58°

3) Cos x = 9/13

x = Cos-1 (9/13)

x = 46°

4) Cos x = 3/5.8

x = Cos-(3/5.8)

x = 59°

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The measure of the smaller angle of the  co-interior angles is 69°

Co-interior angles are simply angles that occur in between two parallel lines when they are intersected by a transversal.

The two angles add up to 180º as they occur on the same side of the transversal always.

From the image, the two co-interior angles are:

x + 114

x + 72

Since the two angles add up to 180º.

x + 114 + x + 72 = 180

Solve for x

2x + 186 = 180

2x = 180 - 186

2x = -6

x = -6/2

x = -3

Hence, the measure of the two angles are:

x + 114 = -3 + 114 = 111°

x + 72 = -3 + 72 = 69°

Therefore, the smallest angle is 69 degree.

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This method can be used to quickly obtain the product of two polynomials.A-6k²+25k²-16k-15.

Expression in math is a combination of numbers, symbols and operators that represent a mathematical quantity or operation. It can be a single number, a single variable, or a combination of numbers, variables and symbols combined together to form a mathematical statement. An expression can also include functions, such as polynomials, exponential functions, or logarithmic functions.


The vertical method involves writing the terms of the two factors side by side and multiplying them together to get the product.

(3k+5)  (2k²-5k-3)

6k³  +   0k²  +   0k   +  -15
0k³  +  10k²  + -15k   +   0
0k³  +   5k²   + -15k   +   0
0k³ +   0k²  +  15k   +   0

Adding the terms in each column yields the product:

A-6k³+25k²-16k-15

Therefore, the correct answer is A-6k³+25k²-16k-15.

In conclusion, using the vertical method can simplify algebraic multiplication problems by breaking them down into columns and adding the terms in each column. This method can be used to quickly obtain the product of two polynomials.

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To solve this equation by combining terms, the answer will be: (c) -4a + 22b.

To solve the equation, we need to combine like terms together. This means that the figures with the suffix, a will come together, while those with the suffix, b will also align themselves. Going by this rule, we will have:

12a -16a + 26b -4b.

= -4a + 22b

When a higher number is to be subtracted from a smaller number, the result will be a negative number as is the case with the terms that have the 'a' initials.

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The number line where we plotting -2 1/6 and 11/6 is attached

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

-2 1/6 and 11/6

To start with, we convert both numbers to the same form

i.e. decimal or fraction

When converted to fractions, we have

-13/6 and 11/6

This means that we can plot -13/6 at -13 and 11/6 at point 11 where the difference in each interval is 1/6

Using the above as a guide, we have the following:

The number line is attached

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