the probability of rolling a 6 on a biased dice is 1/5

The age of the oldest of the five friends is 19 years and the youngest is 12 years.

The given information is in a group there are five friends, the sums of the ages of each group of four of them are 58, 59, 61, 62 and 64.

The range of a data set is the difference between smaller values and a larger value in the set.

To find the age of the oldest person

Range=oldest age -the youngest age

[tex]oldest=\frac{Range-youngest age}{4}[/tex]

R=(64-58/4)+(64-59/4)+(64-61/4)+64-62/4)

R=1.5+1.241+0.75+0.5

R=3.991.

64/4=16.

O=16+3.991

Oldest=19 years.

Youngest=16-3.9=12 years.

Hence, the age of the oldest of the five friends is 19 years.

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The length of side AC rounded to 1 decimal place is 17.3 cm.

The figure on the image is a right triangle.

From the image;

using the trigonometric ratio, we determine the length of side AC.

Tangent = Opposite / Adjacent

tan( 68 ) = AC / 7

AC = tan( 68 ) × 7

AC = 17.3 cm

Therefore, side AC has a length of 17.3 cm.

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The possible values for theta, where 0 degrees is less than theta and 360 degrees is greater than theta, would correspond to an angle measure in the range 0 < theta < 360 degrees.

This range includes all angles greater than 0 degrees and less than 360 degrees, which correspond to a full revolution around a circle.

It's important to note that angle measures are typically represented in either degrees or radians, with 360 degrees corresponding to 2π radians. So, if you need the values of theta in radians, the range would be 0 < theta < 2π.

In general, the possible values for theta are dependent on the context in which they are used and the specific system of measurement being employed. For example, in some cases, the range of possible values for theta may be restricted to between 0 and 180 degrees, or between -180 and 180 degrees, depending on the application.

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the value of x will be either 1 or 3 for the condition f (x) = g (x).

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equations: f (x) = -x^2 + 3x - 2 and g (x) = -x + 1

To find the value of x for the  f (x) = g (x)

So,

-x^2 + 3x - 2 =  -x + 1

-x² + 4x -3 = 0

multiply by -1 in the equation

x² - 4x +3 = 0

x² - 3x - x +3 = 0

take (x-3 ) common

x(x -3)-1(x- 3) = 0

Thus,

x = 1 or 3

Therefore, the value of x will be either 1 or 3 for the condition f (x) = g (x).

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Answer:

YB = 11.2

Step-by-step explanation:

Δ AYZ and Δ ABCare similar by the AA postulate

then the ratios of corresponding sides are in proportion , that is

[tex]\frac{AY}{AB}[/tex] = [tex]\frac{AZ}{AC}[/tex] ( substitute values )

[tex]\frac{7}{7+YB}[/tex] = [tex]\frac{15}{15+24}[/tex] = [tex]\frac{15}{39}[/tex] ( cross- multiply )

15(7 + YB) = 7 × 39 = 273 ( divide both sides by 15 )

7 + YB = 18.2 ( subtract 7 from both sides )

YB = 11.2

The length of YB would be; 11.2

We know that proportion is a fraction of a total amount, and the measures are related using a rule of three.

Since Δ AYZ and Δ ABC are similar by the AA postulate

Then the ratios of corresponding sides are in proportion , that is

AY/AB = AZ/AC

cross- multiply ;

15(7 + YB) = 7 × 39 = 273

7 + YB = 18.2

Hence, YB = 11.2

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The number of bacteria that is left is 38

The half-life is the time it takes for half of the bacteria to reduce

The time is given as 1.5 hours

After 1.5 hours:

The number will have gone through 6 / 1.5 = 4 half-lives.

So, the number of bacteria cells after 6 hours will be 600 * (1/2)^4

Evaluate

600 * (1/2)^4 = 600 / 16 = 37.5

Approximate

600 * (1/2)^4 = 600 / 16 = 378

Since the number of bacteria cells is 37.

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Answer:

232 and 58

Step-by-step explanation:

bro just use a calc

Answer:

Part A: C, 129 & Part B: A, 58

Step-by-step explanation:

Part A:

36+ 51 + 42= 129

Part B:

152- 49 - 45= 58

To double check part B:

58 + 49 + 45 = 152

The simplification of the given fraction above would be = 9⅘

A fraction is defined as the part of a whole value which is represented in the form of a numerator and a denominator.

The given fraction that requires simplification is as follows:

= 4/5 × 12

= 48/5

= 9⅘

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Answer: Thirty-five divided by three equals 11.67.

Step-by-step explanation:

Division is the mathematical operation that finds the number of times one quantity is contained within another. In this case, 35 is being divided by 3 to find the result.

To perform the division, we divide 35 by 3, which gives us a quotient of 11 with a remainder of 2. If we want to express this result as a decimal, we can add the remainder divided by the divisor, so the answer would be 11 + 2/3 = 11.67.

In summary, 35 divided by 3 equals 11.67, meaning that 3 goes into 35 a total of 11 times with a remainder of 2.

Answer:

Step-by-step explanation:

If 2 angles are complementary, they are equal to 90 degrees. So, lets say that the measure of the first angle is x, and the measure of the second angle is y.

Since x measures 4.2 degrees more than its complementary angle (y), we can say that x - 4.2 = y

And, since they are complementary angles, x+y = 90.

We can now use a system of equations to solve. Since we know y = x-4.2, we can substitute y with x-4.2, making the equation x + x - 4.2 =90.

Simplify:

x+x-4.2=90

2x -4.2 =90

2x = 94.2

x= 47.1

Since y=x-4.2, we can now find y.

y = x-4.2

y= (47.1)-4.2

y=42.9

So, the measure of the angles is 47.1° and 42.9°.

Hope this helps!

Before reading this article, my opinion of selfies is that they were easy and not very dangerous photographs to capture. When I read the article my perspective changed to be more careful when taking a selfie.

A selfie is a term that refers to a photograph that is taken autonomously of oneself. Now most devices include a front camera to take photos of yourself, the famous selfies.

My perspective before reading the article was that selfies were ordinary photos like any other. However, after reading the article I see that they have a high risk of accidents, so it is necessary to be careful not to be in a risky situation because of a photo.

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Gwen's walked 18.81 meters in her living room.

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

We have to given that;

Gwen's living room is rectangular and measures 6 meters by 5 meters.

Now, Beginning in one corner, Gwen walks the length of her living room and then turns and walks the width.

Hence, Distance cover by him = 6 + 5

                                               = 11 meters

And, Finally, Gwen walks back to the corner she started in.

Hence, The distance cover to back to the corner she started in is,

⇒ d² = 6² + 5²

⇒ d² = 36 + 25

⇒ d = 61

⇒ d = 7.81 meters

Thus, The total distance cover by her by walking = 7.81 + 11

                                                                            = 18.81 meters

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The probability that the number on the red die is smaller than the number on the white die is, 5/12

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

There are 36 possible ways of throwing a dice twice. If the first throw is 1, then there are five possibilities for a greater throw in the second; if the first throw is 2, then there are four, and so on.

Thus the total number where the second throw is greater than the first is 5 + 4 + 3 + 2 + 1 + 0 = 15, so the probability is 15 / 36 = 5 / 12

There is a 5/6 chance that the dice are different.

There is a 1/2 chance that the first will be bigger for two different dice.

Hence, The probability is 5/6 x 1/2 = 5/12

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Answer:

see below

Step-by-step explanation:

4/7*224 = 128

224 miles / 7 gallons = 32 miles per gallon

so given either factors, you'll be able to solve the other.

the problem will become how many gallons used to drive xxx miles.

All three expressions are correct based on the properties of arithmetic operations.

Yolanda wrote 16 ÷ 8 = 2, which means she is finding how many times 8 fits into 16. The answer is 2, meaning 16 is divided into 8 equal parts and each part has a value of 2.

Riku wrote 16 ÷ 2 = 8, which means he is finding how many times 2 fits into 16. The answer is 8, meaning 16 is divided into 2 equal parts and each part has a value of 8.

Mariana wrote 8 x 2 = 16, which means she is finding the product of 8 and 2. The answer is 16, meaning 8 multiplied by 2 gives a total of 16.

All three expressions are correct.

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Answer:

51998

Step-by-step explanation:

To solve the problem, we need to subtract the number of people who watched the first two games from the total number of people who watched all three games:

156330 - (54342 + 49990) = 156330 - 104332 = 51998 people watched the third game.

Therefore, 51998 people watched the third game.

The probability of drawing a white marble is 2/15

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

4 white, 10 blue, and 16 red marbles

This means that

Total = 4 + 10 + 16

Total = 30

So, the probability of drawing a white marble is

P = White/Total

Substitute the known values in the above equation, so, we have the following representation

P =  4 / 30 = 2/15.

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Complete question

a jar contains 4 white, 10 blue, and 16 red marbles. if one marble is drawn at random from the jar, find the probability that a white marble is selected

Answer:

15=19

Step-by-step explanation:

5×3=6+13

15=19

so 15=19

(C) The difference between an actual and expected value for the response variable y is known as a residual. If it is positive, the observed value is greater than the expected value.

The discrepancy between a response variable's observed value and its expected value as predicted by the regression line.

A residual is a discrepancy between an observed and expected value for the response variable y.

In the event that it is positive, the observed value exceeds the expected value.

The information that was ignored throughout the (first) cycle of the modeling is contained in the residuals, which serve as a significant source of information.

They must thus divulge something to us.

It is possible to describe the residual plot to the students as a kind of magnifier for the modeling procedure.

Therefore, (C) the difference between an actual and expected value for the response variable y is known as a residual. If it is positive, the observed value is greater than the expected value.

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Answer:

16/4 = 4

1 block = 4 minutes

4 blocks = 16 minutes

to put this into a ratio it would be 1:4

Answer: (x+6)(x+4)

Step-by-step explanation: Search math w ay on the internet :)

The value of x is 10

Similar figures are enlargements of each other using a scale factor. All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio.

This shows that x-3/21 = x-1/27

21(x-1) = 27(x-3)

divide through by 3

= 7(x-1) = 9 ( x-3)

7x -7 = 9x-27

collect like terms

9x -7x = 27-10

2x = 20

divide both sides by 2

x = 20/2

x = 10

therefore the value of x is 10

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The total distance between Dylan and Mackenzie is reduced by x feet each time Dylan travels x feet, since Mackenzie travels 2x feet during that time. Therefore, their combined distance of travel is x + 2x = 3x feet.

Since their starting distance apart was 230 feet, and their combined distance of travel is 3x feet, we can write an equation to represent the situation:

230 = 3x

To find the distance each person travels, we can solve for x by dividing both sides of the equation by 3:

230 / 3 = 3x / 3

x = 230 / 3 = 76.67 feet

So, Dylan travels x = 76.67 feet and Mackenzie travels 2x = 2 * 76.67 = 153.33 feet.

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The ratio of c:d:e is 1:3:2.

To find the ratio, you can multiply the first ratio by the second ratio: 1 * 2 = 2 and 3 * 3 = 9, so the ratio becomes 2:9:6, which can be simplified to 1:3:2.

A ratio is a comparison between two values. To calculate a ratio, divide the first value by the second value. For example, if you have three apples and seven bananas, the ratio of apples to bananas would be 3/7.

You can also simplify a ratio by dividing both values by their greatest common divisor. For example, if the ratio of apples to bananas is 6/14, you could simplify it to 3/7.

It's also possible to express a ratio as a fraction, decimal, or percentage. To convert a ratio to a fraction, simply divide the two values. To convert a ratio to a decimal, divide the numerator by the denominator. To convert a ratio to a percentage, multiply the ratio by 100.

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Answer:

x = 20

Step-by-step explanation:

3x + 80 + 2x = 180

5x + 80 = 180

5x = 100

x = 20

There are 265 bottles in the first group, 285 in the second group, 505 in the third group, and 515 in the fourth group in both the ways.

Solution Method 1: With the aid of a diagram

We can make an outline to monitor the quantity of jugs in each gathering. We should dole out a variable to address the quantity of containers in the principal bunch, x.

Bunch 1: x containers

Bunch 2: x + 20 containers

Bunch 3: 2(x + 20) = 2x + 40 containers

Bunch 4: 2x + 50 containers

The complete number of containers is x + (x + 20) + (2x + 40) + (2x + 50) = 1700

Along these lines, 6x + 110 = 1700

Taking away 110 from the two sides: 6x = 1590

Separating the two sides by 6: x = 265

In this way, there are 265 jugs in the principal bunch, 285 in the subsequent gathering, 505 in the third gathering, and 515 in the fourth gathering.

Solution Method 2: With Algebraic Equations

We can address the quantity of containers in each gathering with factors:

Bunch 1: x containers

Bunch 2: y bottles

Bunch 3: z bottles

Bunch 4: w bottles

Considering that:

y = x + 20

z = 2y = 2(x + 20) = 2x + 40

w = z + 10 = 2x + 50

Also, the all out number of jugs is x + y + z + w = 1700

Subbing the upsides of y, z, and w:

x + (x + 20) + (2x + 40) + (2x + 50) = 1700

Working on the articulation:

6x + 110 = 1700

Taking away 110 from the two sides:

6x = 1590

Separating the two sides by 6:

x = 265

Thus, there are 265 containers in the principal bunch, 285 in the subsequent gathering, 505 in the third gathering, and 515 in the fourth gathering.

Connection between the two techniques:

The two techniques utilize similar conditions to address the quantity of jugs in each gathering, and they show up at a similar arrangement. The thing that matters is that the principal technique presents the arrangement in a diagram, which can be simpler for certain individuals to comprehend, while the subsequent strategy utilizes mathematical conditions, which can be more proficient for taking care of the issue. Notwithstanding, the two strategies depend on similar ideas and standards of polynomial math.

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The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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"Stratified Sampling" is the process of dividing the population into non-overlapping groups and taking a simple random sample out of each category.

Differentiated stratified sampling. By employing a characteristic to divide the population, we can then obtain a proportional randomized sample of each group.

Thus, "Stratified Sampling" is the process of dividing the population into non-overlapping groups and taking a simple random sample out of each category.

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