Solve. |7x-20|=|2x+20|

Using the z-score values given, the area under the standard normal distribution curve is 0.123 squared units

The total area under the standard normal distribution curve is 1. Therefore, if we have a z-score, i.e., how far a value is above or below the mean, we can determine the probability of a value less than or greater than that.

The points are

A = z₂ - z₁

z₂ = 0.6230

z₁ = 0.5000

A = 0.6230 - 0.5000

A = 0.123 squared units

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Answer:

Step-by-step explanation:

The exact solutions for the equation 2sec²x - tan²x = -1 in radians are:

x = π/4 + πk, where k is an integer

x = 3π/4 + πk, where k is an integer

These solutions represent all the values of x that satisfy the given equation.

The area of the given figure is 27.5 square centimeter which has a rectangle and triangles

The given figure has a rectangle and triangles

The area of rectangle is length times width

Area of rectangle =5×4

=20 square centimeter

Area of triangle =1/2×base×height

=1/2×2.5×3

=7.5/2

=3.75 square centimeter

As there are two triangle = 2(3.75)

=7.5 square centimeter

Total area = 7.5+ 20

=27.5 square centimeter

Hence, the area of the given figure is 27.5 square centimeter

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The decreasing interval of function is (-∞ , 0) .

The decreasing interval in the function is said to be when the value of the derivative f' (x) ≤ 0 .

Decreasing interval is when f(x) is decreasing as x is increasing.

Here the graph is of a parabola the equation of a upper parabola is

f(x) = x²

Now doing derivation of the parabola equation, we get

f'(x) = 2x

As for decreasing interval we will put

f'(x) ≤ 0

Putting the value of f'(x) in the equation

2x ≤ 0

x ≤ 0

Decreasing interval (-∞ , 0)

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The values are given as:

a. Mean = 19

Median = 20

Mode = 22

Standard deviation = 7.2

Range  = 24

b. Mean = 75

Median  =  80

Mode  = 90

Standard deviation  = 16

Range = 100

The three measures of central tendency include;

The measures of dispersions are;

From the information given, if 4 is added to all the measures, we get;

Mean = 15 + 4 = 19

Median = 16 + 4 = 20

Mode = 18 + 4 = 22

Standard deviation = 3.2 + 4 = 7.2

Range = 20 + 4 = 24

If the values are multiplied by 5

Mean = 15(5) = 75

Median = 16(5) =  80

Mode = 18(5) = 90

Standard deviation = 3.2(5) = 16

Range = 20(5) = 100

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a ) The given expression from Sofia and Ella represents two different values.

b.) The fact about the surface area of prism that Ella's expression shows that is not in Sofia's expression is that the expression is according to the formula.

To determine the surface area of a rectangle prism, the formula that should be used would be given below:

That is;

Surface area of rectangular prism;

= 2(wl+hl+hw)

when the formula is multiplied out the following is gotten;

= 2wl + 2hl + 2hw

From Ella's expression,

2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm). This follows the order of the formula. And it's final answer = 94cm²

From Sofia's expression,

(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm). This doesn't follow the order of the formula and therefore is not correct and not the same final value with Ella's expression.

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Answer:

2.

Quarterly:

Monthly:

Continuously:

3.

Twice a year:

Eight times a year:

Continuously:

Step-by-step explanation:

The formula for compound interest is:

A = P(1+r/n)^nt

The formula for compounded continuously is:
A = Pe^rt

Where:

A = the future value of the investment

P = the principal balance

r = the annual interest rate (decimal)

n = number of times interest is compounded per year

t = the time in years

Using that we can plug the formula in for each question:

2.

Quarterly:

Monthly:

Continuously:

3.

Twice a year:

Eight times a year:

Continuously:

Nancy's bag was 0.2kg over the weight limit.

Let's denote the weight limit as x.

The total cost for the first airline can be expressed as:

Cost1 = 20x + 5

The total cost for the second airline is given by:

Cost2 = 25x + 4

As fees were same with both airlines, we will set up equation to find the weight difference:

20x + 5 = 25x + 4

20x-25x = 4-5

-5x = -1

x = -1/-5

x = 0.2kg

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Answer:

[tex]\dfrac{-1}{2}[/tex]

Step-by-step explanation:

          (-2 , 3) ⇒ x₁ = -2 & y₁ = 3

          (0 , 2) ⇒  x₂ = 0 & y₂ = 2

[tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

            [tex]\sf = \dfrac{2-3}{0-[-2]}\\\\\\=\dfrac{-1}{0+2}\\\\=\dfrac{-1}{2}[/tex]

Answer:

Jurek is 8. His brother is 14

Step-by-step explanation:

let's call Jurek J, and let's call his brother B.

his brother is 6 years older than Jurek.

So, B = J + 6.

B + J = 22

(J + 6) + J = 22

2J + 6 = 22

2J = 16

J = 8

so Jurek is 8

B + J = 22, B = 22 - J = 22 - 8 = 14.

Brother is 14

Answer:

5/4 = h/44, so h = 55

The height of the tree is 55 feet.

D is correct.

Movie B has approximately 25% more frames than Movie A.

For Movie A the duration is 100 minutes

Frame rate: 24 frames per second

Total frames in Movie A:

Total frames in Movie A = 100×60×24

Movie B:

Duration: 100 minutes

Frame rate: 30 frames per second

Total frames in Movie B:

Total frames in Movie B = 100 × 60 × 30

To find the percent more frames in Movie B compared to Movie A, we can use the following formula:

Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100

Total frames in Movie A = 100 × 60× 24

Total frames in Movie B = 100 ×60 × 30

Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100

Percent more frames = ((100 × 60× 30) - (100 × 60×24)) / (100 × 60× 24)×100

Percent more frames = (180,000 - 144,000) / 144,000 * 100

Percent more frames = 36,000 / 144,000 * 100

Percent more frames = 25%

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John will need 36 feet of fence to enclose his 9-foot square garden.

A sqaure is simply a polygon made up of four equal sides, with all the interior angles measuring 90 degrees.

The perimeter of a square is expressed as:

Perimeter = 4 × side length

Given that, the side length of the square garden is 9 ft.

To calculate the amount of fence John will need to enclose his 9-foot square garden, we need to determine the perimeter of the square.

Perimeter = 4 × side length

Plug in the side length

Perimeter = 4 × 9 ft

Perimeter = 36 feet

Therefore, the perimeter of the garden is 6 feet.

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Answer: Blue

Step-by-step explanation:

Half of the entire freaking bag is blue,it states it in the question.If there is so many,unless by pure blind luck you will get that.

I hope it helps!

Answer:

the probability that either event will occur is 0.92

Step-by-step explanation:

the probability that either event will occur is 0.92

What is the probability that either event will occur?

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

Event A = 18

Event B = 15

Other Events = 3

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

Total = A + B + C

So, we have

Total = 18 + 15 + 3

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 15/36

For either events, we have

P(A or B) = 33/36 = 0.91666

Hence, the probability that either event will occur is 0.92 (rounded to nearest hundreth)

The solution is:  the measure of angles 2, 3, and 4 are:

m∠2 = 95°

m∠3 = 85°

m∠4 = 95°

Vertical Angle Theorem:

When two straight lines intersect, the opposite vertical angles formed are always equal (congruent) to each other.

Therefore,

m∠3 = 85°

m∠2 = m∠4

Linear pair:

Two adjacent angles which, when combined, form a line, so the sum of a linear pair is 180°.

Therefore,

85° + m∠2 = 180°

m∠3 + m∠4 = 180°

If  85° + m∠2 = 180°

⇒ m∠2 = 180° - 85°

⇒ m∠2 = 95°

As  m∠2 = m∠4  then  m∠4 = 95°

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complete question:

Find the measure of angles 2, 3, and 4. input the measures then click done. i-ready

please help i missed a day of class i cant figure this out

The proportion is solved and the variables are a/b = c/d

Given data ,

Let the proportion be represented as A

Now , the value of A is

a / b = c / d

On simplifying the equation , we get

( a + b ) / b = ( c + d ) / d

On dividing the numerator of the fraction by the denominator , we get

( a / b ) + ( b / b ) = ( c / d ) + ( d / d )

On further simplification , we get

( a / b ) + 1 = ( c / d ) + 1

Subtracting 1 on both sides , we get

( a / b ) = ( c / d )

Hence , the proportion is ( a / b ) = ( c / d )

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The missing sides of the triangle are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 30º, we have that:

Hence the hypotenuse RS is obtained as follows:

sin(30º) = 6/RS

1/2 = 6/RS

RS = 6 x 2

RS = 12.

Applying the cosine, we have that:

cos(30º) = 6/SX

[tex]\frac{\sqrt{3}}{2} = \frac{6}{SX}[/tex]

[tex]SX = \frac{12}{\sqrt{3}}[/tex]

[tex]SX = 4\sqrt{3}[/tex]

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Answer:

Step-by-step explanation:

No explanation is needed because there is no question.

Answer:

you got it

Step-by-step explanation:

no explanation needed

Given statement solution is :- Regardless of the values of T, Q, and S, the whole Valid Statements & Implications is always true.

Let's analyze the two given statements:

¬{[Q → (¬S ∧ R)] ∨ ¬P} → (¬P ↔ P) ∴ ¬(Q ∧ P) ∨ (T ∧ R)

To prove this statement, we can use logical equivalences and deductions:

¬{[Q → (¬S ∧ R)] ∨ ¬P} → (¬P ↔ P) (Given)

¬{[¬Q ∨ (¬S ∧ R)] ∨ ¬P} → (¬P ↔ P) (Implication equivalence)

¬{[(¬Q ∨ ¬S) ∧ (¬Q ∨ R)] ∨ ¬P} → (¬P ↔ P) (Implication equivalence)

¬{(¬Q ∨ ¬S ∨ ¬P) ∧ (¬Q ∨ R ∨ ¬P)} → (¬P ↔ P) (De Morgan's Law)

(Q ∧ S ∧ P) ∨ (¬Q ∧ P) → (¬P ↔ P) (De Morgan's Law)

At this point, the formula ¬P ↔ P is a contradiction. The left side (¬P) states that P is false, while the right side (P) states that P is true. Therefore, the whole statement is always true, regardless of the values of Q, S, and P.

Since the statement is always true, we can conclude ¬(Q ∧ P) ∨ (T ∧ R) is true as well, making the second part of the question valid.

[(T ∨ Q) → (T ∨ S)] ∨ [(T ∨ Q) → (T ∨ S)]

In this statement, we have two identical sub-statements connected by a logical OR operator.

If we assume that (T ∨ Q) → (T ∨ S) is true, then the whole statement is true, regardless of the values of T, Q, and S.

If we assume that (T ∨ Q) → (T ∨ S) is false, then we need to check the other part of the statement.

Assuming (T ∨ Q) → (T ∨ S) is false means that (T ∨ Q) is true, but (T ∨ S) is false. In this case, the second part of the statement [(T ∨ Q) → (T ∨ S)] is true.

Therefore, regardless of the values of T, Q, and S, the whole Valid Statements & Implications is always true.

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Based on the given data, we can estimate that approximately 36 out of the next 100 books that come down the chute will be nonfiction.

To estimate the number of nonfiction books out of the next 100, we can use the ratio of nonfiction to the total number of books that came down the chute so far today.

The total number of books that came down the chute so far is:

41 (fiction) + 23 (nonfiction) = 64

The ratio of nonfiction books to the total number of books in library is:

[tex]23/64[/tex]

To estimate the number of nonfiction books out of the next 100, we can multiply the ratio by 100:

[tex](23/64)*100=35.9375[/tex]

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The surface area for each of the cylinders is given as follows:

13. 126 yd².

14. 490 m².

15. 283 mm².

16. 297 cm².

The surface area of a cylinder of radius r and height h is given by the equation presented as follows, which combines the base area with the lateral area:

S = 2πrh + 2πr²

S = 2πr(h + r)

Item 13:

r = 2 yd and h = 8 yd, hence the surface area is given as follows:

S = 2π x 2(2 + 8)

S = 126 yd².

Item 14:

r = 6 m and h = 7 m, hence the surface area is given as follows:

S = 2π x 6(6 + 7)

S = 490 m².

Item 15:

r = 3 mm and h = 12 mm, hence the surface area is given as follows:

S = 2π x 3(3 + 12)

S = 283 mm².

Item 16:

r = 3.5 mm and h = 10 mm, hence the surface area is given as follows:

S = 2π x 3.5(3.5 + 10)

S = 297 cm².

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Answer

The order of the number from greatest to least is 1.62, 15/20, 16.2%

Step-by-step explanation

Given: 1.62 16.2% 15/20​

To order these data in descending order (i.e. from highest to least), follow the steps below

1. Convert all numbers to decimals

1.62

16.2% = 16.2/100

16.2% = 0.162

15/20 = 0.75

So, the number are 1.62, 0.162, 0.75

2. Compare the three decimals and arrange in descending order

1.62 > 0.75 > 0.162

This means that 1.62 is greater than 0.75 and 0.75 is greater than 0.162

By substituting 16.2% for 0.162 and 15/20 for 0.75, the order of the number from greatest to least is

1.62, 15/20, 16.2%

Answer:

2x and 180 - 5x are complementary angles.

2x + 180 - 5x = 90

-3x + 180 = 90

-3x = -90

x = 30

The mathemematical sum of the three numbers 1+1+1 would give 3

Addition of numbers can involve 2 or more values using the additive sign '+'. For any given sum of values, the result obtained would be greater than any of the individual value in the sum.

Here, 1 + 1 + 1 means that we are adding 1 in three places. The value obtained would be 3.

Therefore, the sum of the 1+1+1 is 3

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The roots of the cubic function:

f(x)=  x³ + 3x² - x - 3

are x = 1, x= -1, x = -3

We want to find the roots of the function:

f(x)=  x³ + 3x² - x - 3

We know that x = 1 is a root, because f(1) = 0.

Then we can write that function as:

(x - 1)*(x - a)*(x - b)

Where a and b are the other two roots, then we need to solve:

x³ + 3x² - x - 3 = (x - 1)*(x - a)*(x - b)

Expanding the right side, we will get:

x³ + 3x² - x - 3 = x³ + (-a - b - 1)x² + (a + b + ab)x + (-ab)

Comparing like terms, we can see that:

(-a - b - 1) = 3

(a + b + ab) = -1

(-ab) = -3

The third equation gives:

ab = 3

Replacing that in the second one we get:

a + b + 3 = -1

a + b = - 1 - 3 = -4

a + b = -4

a = -4 - b

Replacing that in the relation above:

ab = 3

(-4 - b)*b = 3

-4b - b² = 3

b² + 4b + 3  = 0

The zeros of that function are:

[tex]b = \frac{-4 \pm \sqrt{4^2 -4*3*1} }{2*1} \\\\b = \frac{-4 \pm 2}{2}[/tex]

Then if b is the value when we take the positive sign:

b = (-4 + 2)/2 = -1

the value of a is:

a = -4 - b = -4 + 1 = -3

These are the other two roots.

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The equation for g (x) is,

⇒ g(x) = x² -3

Since, The function is,

⇒ f (x) = x²

when x = 0, f(x) = 0

hence it has vertex at (0,0)

Since, g(x) is shifter version of f(x) and has vertex at (-1, 4),

Then, g(x) must be shifted along y axis.

So, We get;

g(x)= x²+c

when x = - 1, g(x)= 4

4 = (-1)² + c

4 = 1 + c

c = 3

Thus, The equation for g (x) is,

g(x) = x² -3

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Answer:

To find Salina Grant's gross pay, we need to calculate the pay for each range and add them together.

For the first 25 chairs, Salina will be paid $10 for each chair, so her pay for this range is:

25 chairs x $10 per chair = $250

For the next 15 chairs (26-40), Salina will be paid $13 for each chair, so her pay for this range is:

15 chairs x $13 per chair = $195

For the remaining 7 chairs (over 40), Salina will be paid $17.50 for each chair, so her pay for this range is:

7 chairs x $17.50 per chair = $122.50

Adding up all three ranges, Salina's gross pay is:

$250 + $195 + $122.50 = $567.50

Therefore, Salina Grant's gross pay for assembling 47 chairs in one week is $567.50.

Step-by-step explanation: