Find the probability that
event A or B takes place.
A
B
10
19
19

Answer:

16 liters of the 10% acid solution should be in the mixture.

Step-by-step explanation:

Let x represent the volume of the 10% acid solution to be added.

The volume of pure acid added would be (90 - x).

The equation to solve is: 0.1x + (90 - x) = 0.84(90)

Simplifying, we get: 0.1x + 90 - x = 75.6

Combining like terms, we have: -0.9x + 90 = 75.6

Subtracting 90 from both sides: -0.9x = -14.4

Dividing by -0.9: x = 16

Therefore, 16 liters of the 10% acid solution should be in the mixture.

Answer:

The inequality |x – 4| > –3 represents an absolute value inequality.

The absolute value of any real number is always non-negative, meaning it is greater than or equal to zero. Therefore, the left side of the inequality, |x – 4|, will always be greater than or equal to zero.

Since the right side of the inequality, -3, is also greater than or equal to zero, this means that the inequality |x – 4| > –3 holds true for all real numbers x. In other words, there are no restrictions on the value of x.

The solution set for this inequality is the set of all real numbers, often represented as (-∞, +∞).

Answer:

(−∞,∞)

Step-by-step explanation:

|x – 4| > – 3

Since |x – 4| is always positive and - 3 is negative, |x – 4| is always greater than - 3, so the inequality is always true for any value of x.

All real numbers

The result can be shown in multiple forms.

All real numbers

So, the answer is (−∞,∞)

Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

When selecting 2 letters from the set {A, B, C, D}, considering that the order matters, we can use the concept of permutations to calculate the number of possible arrangements.

The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:

P(n, r) = n! / (n - r)!

Where n is the total number of items (in this case, 4) and r is the number of items being selected (in this case, 2).

Using this formula, the number of ways to arrange 2 letters from A, B, C, D is:

P(4, 2) = 4! / (4 - 2)!

= 4! / 2!

= (4 x 3 x 2 x 1) / (2 x 1)

= 24 / 2

= 12

Therefore, there are 12 possible ways to arrange 2 letters selected from A, B, C, D when considering that the order matters.

~~~Harsha~~~

Answer:

Step-by-step explanation:

When selecting 2 letters from the set {A, B, C, D} and considering that the order matters, we can determine the number of possible arrangements using the concept of permutations.

The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:

P(n, r) = n! / (n - r)!

where P(n, r) represents the number of permutations of r objects chosen from a set of n objects.

In this case, we have n = 4 (the total number of letters) and r = 2 (the number of letters to be selected).

Using the formula, we can calculate:

P(4, 2) = 4! / (4 - 2)!

       = 4! / 2!

       = (4 × 3 × 2 × 1) / (2 × 1)

       = 24 / 2

       = 12

Therefore, there are 12 different ways to arrange 2 letters chosen from the set {A, B, C, D} when the order matters.

The probability of winning the jackpot with one ticket is P ( A ) = 1/34

Given data ,

To calculate the probability of winning the jackpot in the lottery, we need to determine the total number of possible outcomes (the sample space) and the number of favorable outcomes (winning outcomes).

Total number of possible outcomes:

For the white balls, there are 43 numbers to choose from, and we need to select 5 distinct numbers in any order. This can be calculated using the combination formula:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of options and r is the number of selections. In this case, we have 43 white balls and need to choose 5, so the number of possible outcomes for the white balls is:

C(43, 5) = 43! / (5! * (43 - 5)!) = 43! / (5! * 38!) = 43 * 42 * 41 * 40 * 39

For the gold ball, there are 34 numbers to choose from, and we need to select 1 number. So the number of possible outcomes for the gold ball is simply 34.

Therefore, the total number of possible outcomes is:

Total outcomes = (43 * 42 * 41 * 40 * 39) * 34

Number of favorable outcomes (winning outcomes):

To win the jackpot, we need to match all 5 distinct numbers from the white balls and the number on the gold ball. Since order doesn't matter for the white balls, we can use the combination formula again:

C(n, r) = n! / (r! * (n - r)!)

In this case, we have 43 white balls and need to choose 5, so the number of favorable outcomes for the white balls is:

C(43, 5) = 43! / (5! * (43 - 5)!) = 43 * 42 * 41 * 40 * 39

For the gold ball, there is only 1 winning number.

Therefore, the number of favorable outcomes is:

Favorable outcomes = (43 * 42 * 41 * 40 * 39) * 1

Probability of winning the jackpot:

The probability of winning the jackpot is the ratio of the number of favorable outcomes to the total number of possible outcomes:

Probability = Favorable outcomes / Total outcomes

Plugging in the values, we get:

Probability = [(43 * 42 * 41 * 40 * 39) * 1] / [(43 * 42 * 41 * 40 * 39) * 34]

Simplifying, we find:

Probability = 1 / 34

Hence , the probability of winning the jackpot with one ticket in this lottery is 1 in 34.

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The possible price for the items if the store sells $600 is (c) $40

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

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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Answer:

670

We can use the pythagorus theorum which says

The square of hypotenuse is equal to the square of perpendicular added to sq of base

Step-by-step explanation:

Use h2=p2+b2

H=6.708

Rounding to the hundredth place the answer is 670.8

Using Pythagoras Theorem (since the triangle is a right angled triangle)

[tex]( {hyp}^{2}) = ( {base}^{2} ) + ( {per}^{2} )[/tex]

[tex]( {hyp}^{2} ) = ( {3}^{2} ) + ( {6}^{2}) [/tex]

[tex]( {hyp}^{2} ) = 9 + 36[/tex]

[tex] {hyp}^{2} = 45[/tex]

Taking under root on both sides

[tex]hyp = 6.7[/tex]

Hence the missing side is 671

Answer:
-328

Step-by-step explanation:

Simply use BODMAS or BIDMAS; this is the order of your operations. It is an acronym that tells you what to do in what order

Brackets: there are no brackets, move on to indices/order

Indices/Order: for the first step, do 5^2, which is 25, and √49, which is 7. The equation is no 12-5*9(7)-25

Division/Multiplication: For this step, multiply 5, 9 and 7 to get 315. The equation is now 12-315-25

Addition/subtraction: For the final step, just solve 12-315-25 in the traditional left to right way, which is -328.

I have grouped addition and subtraction as well as division and multiplication together because they are done at the same time; if a question has either both addition and subtraction or division and multiplication, just solve these parts from left to right. Division is not superior to multiplication and, likewise, addition is not above subtraction.

Answer: 10 cheeseburgers

Step-by-step explanation: 25/2.5=10

Answer:

10

Step-by-step explanation:

To determine the number of cheeseburgers you can get with $25, you can divide the total amount of money by the cost of each cheeseburger.

$25 ÷ $2.50 = 10

Therefore, with $25, you can get 10 cheeseburgers if each cheeseburger costs $2.50.

The rate of growth of the plant is 2 centimeters per week.

Calculate the change in height divided by the change in time (weeks) to find the plant's growth rate.

To calculate the rate of growth of the plant, we need to determine the change in height per week.

Given:

Initial height = 4 cm

Final height = 12 cm

Weeks = 4

To find the rate of growth, we can use the formula:

Rate of growth = (Final height - Initial height) / Weeks

Substituting the given values into the formula:

Rate of growth = (12 cm - 4 cm) / 4 weeks

Rate of growth = 8 cm / 4 weeks

Rate of growth = 2 cm/week

Therefore, the rate of growth of the plant is 2 centimeters per week.

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The job A is the best job based on pay scale

Given data ,

a) Job A:

Hours per week: 40

Hourly rate: $15

On simplifying the equation , we get

Gross pay per week: 40 hours * $15/hour = $600

b) Job B:

Hours per week: 30

Hourly rate: $5

On simplifying the equation , we get

Gross pay per week: 30 hours * $5/hour = $150

In addition to the base pay, Job B also offers tips averaging $350 per week.

Considering the total compensation for each job:

Total compensation for Job A: $600 per week (base pay)

Total compensation for Job B: $150 per week (base pay) + $350 per week (tips) = $500 per week

Based on the total compensation, Job A offers a higher gross pay of $600 per week, while Job B offers a total compensation of $500 per week.

Hence , if the decision is solely based on pay, Job A would be the better choice.

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Answer:

[tex]\{0.559,0.641\}[/tex]

Step-by-step explanation:

[tex]\displaystyle CI_{95\%}=\frac{336}{560}\pm1.96\sqrt{\frac{\frac{336}{560}(1-\frac{336}{560})}{560}}\approx\{0.559,0.641\}[/tex]

The horizontal distance from the base of the skyscraper out to the ship is 1140 m

Under the horizontal line, the angle of depression is measured, typically in degrees. It aids in figuring out how steep or incline the line of sight is in relation to the horizontal plane. The line of sight is steeply directed downward and increases with the angle of depression.

In many different disciplines, such as surveying, navigation, engineering, and physics, the angle of depression is frequently utilized.

We know that;

Tan 45 = x/1140

x = 1140 Tan 45

= 1140 m

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The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.

The mean of the data is 9 students because there are 45 students total and 5 meetings.

When 15 students attend the next meeting, the mean increases to 10.5 students because there are now 60 students total and 6 meetings.

Mean of the first 5 meetings:

There are 45 students total.

There are 5 meetings.

Therefore, the mean is:

= 45 / 5

= 9 students.

There are 60 students total.

There are 6 meetings.

Therefore, the mean is:

= 60/6

= 10 students.

The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.

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Answer:

[tex]A =[/tex] 95.45

Step-by-step explanation:

[tex]A=s(s﹣a)(s﹣b)(s﹣c)[/tex]

[tex]s=a+b+c[/tex]

Solving for A

A=1

4﹣[tex]a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=1[/tex]

4-[tex]124+2·(12·16)2+2·(12·21)2﹣164+2·(16·21)2﹣214≈95.45123[/tex]  

≈ 95.45123

Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two: , the raw score is relatively lower than the mean.

If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.

A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.

Question Two:

If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.

To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.

In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.

By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.

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The function is a good model for the data.

The retail sales in the U.S. in 2016 is estimated to be 282.24 billion dollars.

The year that corresponds to retail sales of $241 billion is 2020.

The function F(t)= 9.44 t +84.182 is a linear model for the data. This means that the graph of the function is a straight line.

The scatter plot shows that the data points are close to a straight line. This means that the function is a good model for the data.

To estimate the retail sales in the U.S. in 2016, we need to find the value of F(11). F(11) = 9.44 * 11 + 84.182

= 282.24.

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Answer:

see explanation

Step-by-step explanation:

a

the sum of the interior angles of a polygon is calculated as

sum = 180° (n - 2) ← n is the number of sides

here n = 73 , then

sum = 180° × (73 - 2) = 180° × 71 = 12,780°

b

here sum of interior angles = 2700° , then

180° (n - 2) = 2700° ( divide both sides by 180° )

n - 2 = 15 ( add 2 to both sides )

n = 17

number of sides is 17

c

the sum of the exterior angles of a polygon = 360°

given the polygon is regular then each exterior angle is congruent , so

number of sides = 360° ÷ 7.2° = 50

Answer:

a)  12870°

b)  17

c)  50

Step-by-step explanation:

The Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.

The number of sides of a 73-gon is n = 73. Therefore, the sum of its interior angles is:

[tex]\begin{aligned}\textsf{Sum of the interior angles of a 73-agon}&=(73-2) \cdot 180^{\circ}\\&=71 \cdot 180^{\circ}\\&=12870^{\circ}\end{aligned}[/tex]

Therefore, the sum of the interior angles of a 73-gon is 12870°.

[tex]\hrulefill[/tex]

The Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.

Given the sum of the interior angles of a regular polygon is 2700°, then:

[tex]\begin{aligned} \textsf{Sum of the interior angles}&=2700^{\circ}\\\\\implies (n-2) \cdot 180^{\circ}&=2700^{\circ}\\n-2&=15\\n&=17\end{aligned}[/tex]

Therefore, the number of sides of the regular polygon is 17.

[tex]\hrulefill[/tex]

According the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.

Therefore, to find the number of sides of a regular polygon given its exterior angle is 7.2°, divide 360° by the exterior angle.

[tex]\begin{aligned}\textsf{Number of sides}&=\dfrac{360^{\circ}}{\sf Exterior\;angle}\\\\&=\dfrac{360^{\circ}}{7.2^{\circ}}\\\\&=50\end{aligned}[/tex]

Therefore, the number of sides of the regular polygon is 50.

The mean number of text messages that Julianna sent per day is 7.

To calculate the mean number of text messages that Julianna sent per day, we need to sum up the number of text messages she sent each day and divide it by the total number of days.

Total number of text messages sent:

13 + 0 + 4 + 4 + 5 + 6 + 17 = 49

Total number of days: 7

Mean = Sum of all observations/number of observations

Mean =Total number of text messages sent/Total number of days

Mean number of text messages per day: 49 / 7

= 7

Therefore, 7 is the  mean number of text messages that Julianna sent per day.

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Use julianna’s text message data to answer the questions.

Text messages sent:

Sun: 13 Mon: 0 tues: 4 wed: 4 thurs: 5 fri: 6 sat: 17

1. What was the mean number of text messages that julianna sent per day ?

A. 4

B.6

C.8

D.7

The calculated values of A and p that satisfy the equation y = Ax - 2p are A = -2.6 and p = -0.626

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

Points = (-0.68, 3.02) and (1.07,-1.53)

The equation is of the form

y = Ax - 2p

Using the given points, we have

3.02 = -0.68A - 2p

-1.53 = 1.07A - 2p

Subtract the eqations

-0.68A - 1.07A = 3.02 + 1.53

So, we have

-1.75A = 4.55

This gives

A = -2.6

Recall that

3.02 = -0.68A - 2p

So, we have

3.02 = 0.68 * 2.6 - 2p

Evaluate

2p = -1.252

Divide by 2

p = -0.626

Hence, the values of A and p are A = -2.6 and p = -0.626

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Question

The variables x and y satisfy the equation y = Ax - 2p, where A and p are constants. The graph of In y against In x is a straight line passing through the points (-0.68, 3.02) and (1.07,-1.53).

Find the values of A and p.​

Answer:

a = 4

b=2

x=18

QR =16+1=17

Angle QRS =59

Step-by-step explanation:

4a+1 = 2a + 9

2a = 8

a = 4

6b = 11b-10

-5b=-10

-b= -2

b=2

6x+13 = 7x - 5 (opposite angles are equal)

-x=-18

x=18

QR =16+1=17

Angle QRS = 180 - 18•6+13 =59 (PQR + QRS = 180)

Answer:

The volume of the shipping box is 3434.6 in³ (to the nearest tenth).

The length of the longest item that will fit inside the shipping box is 26.8 inches (to the nearest tenth).

Step-by-step explanation:

The shipping box can be modelled as a cuboid.

A cuboid is a three-dimensional geometric shape with six rectangular faces and right angles between adjacent faces.

The volume of a cuboid can be calculated by multiplying its length (L), width (W), and height (H) together.

From the given diagram, the width of the cuboid is 16 inches and its height is 12 inches. Therefore, we need to find the measure of its length in order to calculate its volume.

As all sides of a cuboid have interior angles of 90°, and we have been given the face diagonal of the base (24 inches), we can use Pythagoras Theorem to calculate the length (L).

[tex]\begin{aligned}L^2+16^2&=24^2\\L^2+256&=576\\L^2&=320\\L&=\sqrt{320}\\L&=8\sqrt{5}\; \sf in\end{aligned}[/tex]

Substitute L = 8√5, W = 16 and H = 12 into the formula for the volume of a cuboid to calculate the volume of the shipping box:

[tex]\begin{aligned}\sf Volume&=\sf L \cdot W \cdot H\\&=8\sqrt{5} \cdot 16 \cdot 12\\&=128\sqrt{5} \cdot 12\\&=1526\sqrt{5}\\&=3434.60041...\\&=3434.6\; \sf in^3\end{aligned}[/tex]

Therefore, the volume of the shipping box is 3434.6 in³ to the nearest tenth.

[tex]\hrulefill[/tex]

In a cuboid, there are two types of diagonals: face diagonals and body diagonals.

The body diagonal of a cuboid is the longest line that can be drawn inside the cuboid. Therefore, to find the length of the longest item that will fit inside the shipping box, we need to calculate the body diagonal of the cuboid.

The formula for the body diagonal of a cuboid is:

[tex]\sf Body \;diagonal=\sqrt{L^2+W^2+H^2}[/tex]

Substitute L = 8√5, W = 16 and H = 12 into the formula to find the body diagonal of the cuboid (marked as a red dashed line on the given diagram):

[tex]\begin{aligned}\sf Body \;diagonal&=\sf \sqrt{L^2+W^2+H^2}\\&=\sqrt{(8\sqrt{5})^2+16^2+12^2\\&=\sqrt{320+256+144}\\&=\sqrt{720}\\&=26.8328157...\\&=26.8\; \sf in\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the length of the longest item that will fit inside the shipping box is 26.8 inches, to the nearest tenth.

We play total of 4.5 hours of video games on Friday and Saturday.

An expression in math is a statement having minimum of two numbers or variables or both and an operator connecting them.

To get total hours played on Friday and Saturday, we will subtract the sum of hours played from the mean of 1.5 hours per day for the five days given.

The total hours played on Friday and Saturday will be:

= (Mean hours per day * 7) - (Sum of hours played on Sunday to Thursday)

= (1.5 * 7) - (1.75 + 1 + 0.5 + 1.5 + 1.25)

= 10.5 - 6

= 4.5 hours.

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The solution of the equation for B over the interval [0,2π] is undefined

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

-√3tan(β) = tan(β)sin(β)

Divide both sides of the equation by tan(β)

so, we have the following representation

-√3 = sin(β)

Rewrite as

sin(β) = -√3

Take the arc sin of both sides

β = undefined

Hence, the solution of the equation for B over the interval [0,2π] is undefined

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For the given function:

Vertex is at (-2, -4) and range is −4 ≤ y < ∞

Hence, Option b is correct.

The given function is

y = |3x + 6| − 4

We can see that it is consist of absolute value function or mod function.

Since we know that,

An absolute value function is an algebraic function in which the variable is contained inside the absolute value bars.

The absolute value function is also known as the modulus function, and its most frequent form is f(x) = |x|,

where x is a real integer. In general, the absolute value function may be represented as f(x) = a |x - h| + k,

where a denotes how far the graph extends vertically, h represents the horizontal shift, and k represents the vertical displacement from the graph of f(x) = |x|.

If the value of 'a' is negative, the graph opens downwards; otherwise, it opens upwards.

The appropriate method of finding range and vertex both is to plot its graph:

Therefore after plotting graph we get,

Vertex is at (-2, -4)

And range is (-4 , ∞) ⇒ −4 ≤ y < ∞

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The expression that shows the result of that transformation are:

3f(x) = 3.4ˣ

f(3x)=4³ˣ

f(x+3)=4ˣ⁺³

f(x)+3=4ˣ+3.

The given function is f(x) =4ˣ.

We have to find the transformations applied to the function f(x).

Graph transformation involves modifying an existing graph or graphed equation to create a different version of the original graph.

f(x) =4ˣ

We have to find 3f(x), f(3x), f(x+3) and f(x)+3.

3f(x) = 3.4ˣ

f(3x)=4³ˣ

f(x+3)=4ˣ⁺³

f(x)+3=4ˣ+3.

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The volume of the cylinder with a height of 12 cm and a diameter of 8 cm is approximately 602.19 cm³.

To calculate the volume of a cylinder, you can use the formula:

Volume = π * (radius²) * height

Given that the diameter of the cylinder is 8 cm, the radius (r) can be calculated by dividing the diameter by 2:

radius (r) = 8 cm / 2 = 4 cm

The height (h) of the cylinder is 12 cm.

substitute these values into the formula:

Volume = π * (4 cm)² * 12 cm

Volume = π * 16 cm² * 12 cm

Volume ≈ 602.19 cm³ (rounded to two decimal places)

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