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The significant numbers in 420 are 4 and 2.

Significant numbers are digits that is nonzero or, when zero, followed either by a nonzero digit or by further zeros and then a nonzero digit.

Significant numbers are digits 1 to 9

All zeros between integers are significant.

Zero’s preceding the first integers are insignificant.

Zero’s after the decimal point are significant.

Zeroes used for spacing the decimal point are not significant.

Therefore, it can be concluded that there are 2 significant numbers in 420 which are 4 and 2.

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If the biased dice is rolled 150 times, we can expect to get approximately 45 ones

If the chance of getting a 1 on a biased dice is 0.3, it means that the probability of rolling a 1 on any given roll is 0.3 or 30%.

To determine how many ones you would get if rolled 150 times, we can multiply the probability of rolling a 1 (0.3) by the total number of rolls (150).

Number of ones = Probability of getting a 1 * Total number of rolls

Number of ones = 0.3 * 150 = 45

Therefore, on average, we would expect around 45 instances of rolling a one when using this biased dice over 150 rolls.

It's important to note that the actual number of ones obtained may vary due to the inherent randomness of dice rolls. However, if a biased dice has a 0.3 chance of getting a 1, when rolled 150 times, you would expect to get approximately 45 ones.

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a) The constant of proportionality is given as follows: 0.5.

b) The equation is given as follows: y = 0.5x.

c) The graph would be the graph of a linear function with slope of 0.5 and intercept of 0.

d) 9 points are awarded for 18 minutes of play.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

For every 1 minute of play, the game awards one half point, hence the constant k is given as follows:

k = 0.5.

Thus the equation is given as follows:

y = 0.5x.

Then the number of points for 18 minutes of play is given as follows:

y = 0.5(18)

y = 9.

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The probability that six or fewer individuals will cover their mouth when sneezing is approximately 0.597.

To calculate the probabilities, we can use the binomial probability formula:

P(X = k) = [tex]C(n, k) * p^k * (1 - p)^{(n - k)}[/tex]

Given:

p = 0.29 (probability of an individual covering their mouth)

n = 10 (number of individuals observed)

(a) The probability that five individuals will cover their mouth when sneezing:

P(X = 5) = C(10, 5) * 0.29^5 * (1 - 0.29)^(10 - 5)

Calculating:

P(X = 5) = 0.0001677

Therefore, the probability that five individuals will cover their mouth when sneezing is approximately 0.0002.

(b) The probability that six or fewer individuals will cover their mouth when sneezing:

P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

Calculating each individual probability and summing them up:

P(X ≤ 6) = 0.0075 + 0.043 + 0.1133 + 0.1954 + 0.2383 + 0.0002 + 0.000007

P(X ≤ 6) = 0.597

Therefore, the probability that six or fewer individuals will cover their mouth when sneezing is approximately 0.597.

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Hello!

The sum of an interior angle and its adjacent exterior angle is 180°

The answer is:

C) 180°

Work/explanation:

The sum of an interior angle and its adjacent exterior angle is [tex]\sf{180^o}[/tex], which means that an interior angles and its adjacent exterior angle form a linear pair.

This also means that the angles are supplementary, because they add up to [tex]\sf{180^o}[/tex].

The slope of the graph is equal to 1 for all x between x= 0 and x=3.

Starting at x=3 the function value y increases as x increases.

The slope of the graph is equal to 3 for x between x=3 and x=5

For x between x=0 and x=4, the function value of y is ≤ 0.

For x between x=4 and x=8 the function of value y is ≥ 0.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (0 - 3)/(3 - 0)

Slope (m) = -3/3

Slope (m) = -1.

For x between x=3 and x=5, the slope is given by;

Slope (m) = (3 + 3)/(5 - 3)

Slope (m) = 6/2

Slope (m) = 3.

By critically observing the graph of this function, we can logically deduce that the function value of y is less than or equal to 0 for x between x=0 and x=4 and greater than or equal to 0 for x between x=4 and x=8.

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The expression that does NOT represent 9+9+9+9+9+9+9 is 9 x 7.

The given expression 9+9+9+9+9+9+9 can be simplified by adding all the numbers together:

9+9+9+9+9+9+9 = 63

Therefore, the expression 63 represents 9+9+9+9+9+9+9.

However, if we multiply 9 by 7, we get:

9 x 7 = 63

Therefore, 9 x 7 represents the product of 9 and 7, not the sum of seven nines.

Answer:

Step-by-step explanation:

101.50 x 28 = 2,842.00

Price of TV = 2,499.00

2,842.00 - 2,499.00 = 343.00

$343.00 was paid in finance charges

Answer:

Step-by-step explanation:

The reflection of the point (–4, 6) across both axes is (b) (4, -6)

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

Point = (-4, 6)

The rule of reflections across both axes is

(x, y) = (-x, -y)

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

Image = (4, -6)

Hence, the reflection of the point (–4, 6) across both axes is (b) (4, -6)

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Answer:

To find the monthly payment for a 3-year auto loan at 4% annual interest compounding monthly, we can use the formula for **monthly payment for a loan**:

```

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

```

where:

- M is the monthly payment

- P is the principal or amount borrowed

- i is the monthly interest rate

- n is the number of months

In this case, the principal or amount borrowed is $18,000 and the down payment is $2,000. Therefore, the principal amount that needs to be financed is $16,000.

The monthly interest rate can be calculated by dividing the annual interest rate by 12. In this case, the annual interest rate is 4%, so the monthly interest rate is 4% / 12 = 0.00333333.

The number of months can be calculated by multiplying the number of years by 12. In this case, the number of months is 3 years x 12 months/year = 36 months.

Now we can substitute these values into the formula:

```

M = $16,000 [ 0.00333333(1 + 0.00333333)^36 ] / [ (1 + 0.00333333)^36 – 1]

```

Simplifying this expression gives us:

```

M = $468.43

```

Therefore, Carmen's monthly payment will be **$468.43** .

Alright, let's solve this system of equations whimsically, shall we?

First, imagine these lines as threads of destiny. Each equation is like a thread weaving through the vast fabric of the cosmos, plotted on the 2D plane of our imagination.

So let's embark on this mathematical journey together!

Our first traveler is Line 1, or as we'll call him, "Sir L1." He struts along with the equation y = 3x + 1. His path is clear: for every step he takes in the x direction, he ascends 3 steps in the y. He's quite the climber!

Next, we meet Lady L2 with the equation y = 2x - 3. A bit more relaxed than Sir L1, she ascends 2 steps in the y direction for every step in the x. They clearly don't cross paths—they're too different in their inclinations. This means that Sir L1 and Lady L2 are consistent and independent.

Our third traveler is the mysterious Master L3. His equation is slightly different, written as 3y + x = 6. Let's write this in y = mx + c form to match our other travelers. With a little rearranging, we get y = -1/3x + 2. He's a bit of a downer, descending 1 step in y for every 3 steps in x. Observing him from afar, it's clear he never intersects with Lady L2 or Sir L1. They're all leading their independent lives.

Lastly, we have the young Miss L4, with her equation y = 1/3x - 1. She's a gentle traveler, ascending only a third of a step in y for every step in x. However, like the others, she doesn't cross paths with any of our other travelers.

So, in this whimsical world of equations, it appears that none of our travelers cross paths. Each one treads their own unique path. This means our system of equations is indeed consistent, but each line is independent, meaning they don't intersect, and each has a unique solution. There are no shared points of intersection. It seems our travelers are lone wolves in this cosmos of coordinates!

Picture it like this! Imagine you're running an extraordinary and magical Soup Express, a unique train that only serves delicious soup. Now, this peculiar train only has 144 seats available for each journey, and the moment has come when a bustling crowd of 1990 hungry passengers are waiting eagerly at the platform to board the Soup Express.

So, how many trips must your Soup Express make to serve all the soup-loving travelers?

To find that out, you'll divide the total number of passengers by the number of seats available on your train. That's 1990 passengers divided by 144 seats, which gives you about 13.82 trips. But, oh, the Soup Express can't very well make .82 of a trip, now can it? Your train must make full trips! So, you'll need to round up because even if there is just one passenger left, your train must still make the journey.

So, it turns out your Soup Express will need to make 14 full trips!

Now, let's find out how many passengers will be riding the final journey of the Soup Express. It's like having the leftovers after a grand feast! You've already served 13 full train journeys, each carrying 144 passengers. That's 13 journeys times 144 passengers, which equals 1872 satisfied soup enthusiasts!

But remember, you started with 1990 hungry passengers. So, to find out how many are left for the final trip, subtract the number of passengers already served from the total. That's 1990 minus 1872, which equals 118 passengers.

So, there you have it! The Soup Express will make 14 marvelous soup-serving trips, and the final journey will have 118 content passengers sipping on their favorite soup as they ride off into the sunset!

The new function g(x) after shifting upward 66 units and shifting 19 units to the right is g(x) = (x - 19)^2 + 66.

After performing the described transformations on the function f(x) = x^2, the new function g(x) can be determined.

Shift upward 66 units:

To shift the graph of f(x) upward by 66 units, we add 66 to the original function:

f(x) + 66 = x^2 + 66

Shift 19 units to the right:

To shift the graph of f(x) 19 units to the right, we replace x with (x - 19):

f(x - 19) = (x - 19)^2

Combining both transformations, the new function g(x) is:

g(x) = (x - 19)^2 + 66

As a result, the new function g(x) is now g(x) = (x - 19)2 + 66 after being shifted up 66 units and 19 units to the right.

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Answer:

26

Step-by-step explanation:

Since 2 teachers have 40 students together, we have to divide 40 by 2:

40÷2=20

Now the new information is "Ms. fielder has 6 more students than Mr. Pearce." So we minus 6 from one side and add it to 5 the other:

20-6=14

20+6=26

So Ms. Felder has 26 students in all.

I hope this helps...

Please mark me brainliest.

Have a nice day!

Answer: 127

Step-by-step explanation:

Vertical Angles mean that those 2 angles are equal.

Thus,

You set the two equations equal to each other and solve for the value of x.

5x+12 = 6x-11

x = 23

Next

Once you find the value of x you need to plug in 23 back into any equation to get the value of your angle.

5(23) + 12 = 127

The line passing through p₁ and q₁ is parallel to the line passing through p₂ and q₂.

(a) To find the center and radius of a circle with the equation x² + y² + 2x + 8y = 8, we need to rewrite the equation in the standard form of a circle, which is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.

We start by completing the square for both x and y terms:

x² + 2x + y² + 8y = 8

(x² + 2x) + (y² + 8y) = 8

To complete the square for x terms, we add (2/2)² = 1 to both sides inside the parentheses:

(x² + 2x + 1) + (y² + 8y) = 8 + 1

(x + 1)² + (y² + 8y) = 9

To complete the square for y terms, we add (8/2)² = 16 to both sides inside the parentheses:

(x + 1)² + (y² + 8y + 16) = 9 + 16

(x + 1)² + (y + 4)² = 25

Now the equation is in the standard form. We can see that the center of the circle is (-1, -4) and the radius is the square root of 25, which is 5. Therefore, the center of the circle is (-1, -4) and the radius is 5.

(b) To show that the line through p₁(3, -4) and q₁(-2, 6) is parallel to the line through p₂(-3, 6) and q₂(9, -18), we need to demonstrate that the slopes of the two lines are equal.

The slope of the line passing through p₁ and q₁ is given by:

m₁ = (y₂ - y₁) / (x₂ - x₁)

  = (6 - (-4)) / (-2 - 3)

  = 10 / -5

  = -2

The slope of the line passing through p₂ and q₂ is given by:

m₂ = (y₂ - y₁) / (x₂ - x₁)

  = (-18 - 6) / (9 - (-3))

  = -24 / 12

  = -2

We can see that both slopes are equal to -2. Therefore, the line passing through p₁ and q₁ is parallel to the line passing through p₂ and q₂.

By demonstrating that the slopes of the two lines are equal, we have shown that the line through p₁(3, -4) and q₁(-2, 6) is parallel to the line through p₂(-3, 6) and q₂(9, -18).

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The total cost of Beatrice dishwasher for the new house including tax is written as D + 0.02D.

Let

price of the dishwasher = D

Tax percentage = 2%

Amount of tax = 2% of D

= 2/100 × D

= 0.02D

Beatrice total cost for the dishwasher = price of the dishwasher + Amount of tax

= D + 0.02D

Hence, the expression which represents the total cost of Beatrice dishwasher is D + 0.02D

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Rounded to the nearest square kilometer, the area of the forest after 8 years will be approximately 2773 km².

To find the area of the forest after 8 years, we need to calculate the successive decreases in area over each year.

Let's denote the initial area of the forest as A₀ = 5000 km².

Each year, the area decreases by 7.5%, which means it remains at 92.5% of the previous year's area.

After 1 year, the area will be:

A₁ = A₀ - 0.075 * A₀ = 0.925 * A₀

After 2 years, the area will be:

A₂ = 0.925 * A₁ = 0.925 * (0.925 * A₀) = (0.925)² * A₀

Similarly, we can continue this process for 8 years:

A₈ = (0.925)⁸ * A₀

Now, let's calculate the final area after 8 years:

A₈ = (0.925)⁸ * A₀

≈ 0.55465 * A₀ (rounded to 5 decimal places)

To find the area in square kilometers, we multiply this value by the initial area A₀:

A₈ ≈ 0.55465 * 5000 km²

≈ 2773.25 km²

Rounded to the nearest square kilometer, the area of the forest after 8 years will be approximately 2773 km².

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Answer: (1,-2)

Step-by-step explanation:

To check which of the given ordered pairs satisfy the given system of nonlinear inequalities, we will substitute the values of x and y from each ordered pair and then check if the inequalities hold true or not. Let's check one by one.

For the ordered pair (1,-2):

7 - 2(x-1)² ≤ 25 - y

7 - 2(1-1)² ≤ 25 - (-2)

7 ≤ 25 + 2

7 ≤ 27 (This is true)

2 ≤ -y

2 ≤ -(-2)

2 ≤ 2 (This is true)

Therefore, (1,-2) satisfies the given system of nonlinear inequalities.

For the ordered pair (1,-3):

7 - 2(x-1)² ≤ 25 - y

7 - 2(1-1)² ≤ 25 - (-3)

7 ≤ 28 (This is true)

2 ≤ -y

2 ≤ -(-3)

2 ≤ 3 (This is true)

Therefore, (1,-3) does not satisfy the given system of nonlinear inequalities.

For the ordered pair (1,0):

7 - 2(x-1)² ≤ 25 - y

7 - 2(1-1)² ≤ 25 - (0)

7 ≤ 25 (This is true)

2 ≤ -y

2 ≤ -(0)

2 ≤ 0 (This is not true)

Therefore, (1,0) does not satisfy the given system of nonlinear inequalities.

For the ordered pair (0,0):

We do not have the value of x for this ordered pair, so we cannot check whether it satisfies the given system of nonlinear inequalities.

Hence, the ordered pair that satisfies the given system of nonlinear inequalities is (1,-2).

Answer:

For the second question=7

Step-by-step explanation:

29-8

=21

x+x+x=3x

3x=21

x=21/3

x=7

The dimension of the product of the matrices are

The dimensions of a matrix are the number of rows and columns it has.

Given the matrix A is 5 × 3, Matrix B is 5 × 5 and Matrix C is 3 × 4, to find the dimensions of their products, we proceed as follows.

To find the dimension of the products of a matrix A' with dimension a × b and B' with dimension c x d, to have a product,

So, the dimension of AB are 5 × 3 and 5 × 5. Since the number of columns in A is not equal to the number of rows in B, the product does not exist

The dimension of BA are 5 × 5 and 5 × 3. Since the number of columns in B is equal to the number of rows in A, the product exists and the dimension is 5 × 3

The dimensions of AC are 5 × 3 and 3 × 4. Since the number of columns in A is equal to the number of rows in C, the product exists and the dimension is 5 × 4

So,

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The congruence theorems or postulates that are taken to be reasons why ABV≈ XYZ are SSS and SAS. That is option A and C.

The congruence theorem of triangle consist of various theorem that shows how two triangles are similar. They include the following:

Side side side theorem(SSS): This states that triangles are congruent if the three sides of one are equal to the three sides of another one.

Side angle side theorem(SAS): This states that triangles are congruent if two sides and one angle (between the sides) of one triangle are equal to two sides and one angle of another triangle.

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Step-by-step explanation:

To calculate your monthly take-home pay, you can use the following formula:

```

Monthly take-home pay = (Regular hourly rate x 40 hours x 5 days) + (Regular hourly rate x 8 hours x 2 Saturdays x 4 weeks) x 2 - Deductions

```

Where:

- Regular hourly rate = $15.20

- Deductions = 29% of gross pay

First, let's calculate the gross pay for one month:

```

Gross pay = (Regular hourly rate x 40 hours x 5 days) + (Regular hourly rate x 8 hours x 2 Saturdays x 4 weeks) x 2

= ($15.20 x 40 x 5) + ($15.20 x 8 x 2 x 4) x 2

= $3,424

```

Next, let's calculate the deductions:

```

Deductions = Gross pay x 29%

= $3,424 x 0.29

= $992.96

```

Finally, let's calculate the monthly take-home pay:

```

Monthly take-home pay = Gross pay - Deductions

= $3,424 - $992.96

= $2,431.04

```

Therefore, your monthly take-home pay is **$2,431.04**.

Answer:375<52m

Step-by-step explanation:

jennifer will want at least 375 so you could get more and 52 is about per month m so 375<52m

Answer:

4. 375 < 52m

Step-by-step explanation:

In this inequality, "m" represents the number of months Jennifer will need to save in order to afford the party. The left side of the inequality, 375, represents the cost of the party, which Jennifer wants to be able to afford. The right side of the inequality, 52m, represents the amount of money Jennifer saves per month multiplied by the number of months, which should be more than or equal to the cost of the party for her to afford it!

Hope this helps, thank you.

The sin(14°) = opp/1opp = sin(14°)The exact value of x in M194° is therefore x = sin(14°) or approximately 0.2419 (rounded to four decimal places).

To solve for x in M194°, we first need to understand the concept of reference angles.A reference angle is the acute angle formed between the terminal side of an angle and the x-axis in standard position.

To find the reference angle of M194°, we subtract 180° from 194°:

Reference angle = 194° - 180° = 14°We can use this reference angle to determine the quadrant in which M194° lies and find the exact value of x using trigonometric ratios.

The angle M194° is in the third quadrant since it is greater than 180° but less than 270°.

In the third quadrant, sine and cosecant are positive. Therefore, we can use the sine ratio to solve for x.sin(14°) = opp/hypwhere opp is the opposite side and hyp is the hypotenuse. Since the hypotenuse is not given, we can assume it to be 1.

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Answer: 8

Step-by-step explanation:

From the circle.

CF . BF = EF . DF

9.6 = 3. (10+x)

54= 30+3x

3x = 24

x = 8

The required expression is

[tex]( 10x^{6}) \sqrt7[/tex]

Radical expressions are algebraic expressions involving radicals. The radical expressions consist of the root of an algebraic expression (number, variables, or combination of both).

The root can be a square root, cube root, or in general, nth root.

Simplifying radical expressions implies reducing the algebraic expressions to the simplest form and, if possible, completely eliminating the radicals from the expressions.

Given the radical expression

[tex]13x^{2} \sqrt7x^{8}-3\sqrt7x^{12}[/tex]

Take the square root of x⁸ and x¹²

[tex]13x^{2} \sqrt7x^{4}-3\sqrt7x^{6}[/tex]

Factor out √7 which is common to both terms

[tex]\sqrt7(13x^{6} -3x^{6})[/tex]

Simplify the terms in the bracket

[tex] \sqrt7( 10x^{6} )[/tex]

Rewrite the expression

[tex]( 10x^{6}) \sqrt7[/tex]

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Answer: The correct answer is B

Step-by-step explanation:

The point (2, -2) satisfies the blue inequality but not the red inequality. Explanation: To solve this system of inequalities, we need to check if the point (2, -2) is a solution to both of the inequalities. The blue inequality is y > 2x - 6. Plugging in the values of x = 2 and y = -2 gives:-2 > 2(2) - 6 => -2 > -2This is true, so the point (2, -2) satisfies the blue inequality. The red inequality is y < 1/2x + 1. Plugging in the values of x = 2 and y = -2 gives: -2 < 1/2(2) + 1 => -2 < 2This is false, so the point (2, -2) does not satisfy the red inequality. Therefore, the correct answer is B. The point (2, -2) satisfies the blue inequality but not the red inequality.