1) what is the initial value?

2) what is the rate of change?

3) when it is 90 degrees out, how much water is consumed on average

Answer:

(4, -8) or x=4 y=-8

Step-by-step explanation:

Answer: x=4 and y=−8

Step-by-step explanation: 7x+2y=12, −3x−2y=4

7x+2y+−2y=12+−2y

7x /7 = −2y+12 /7

x= −2 /7 y+ 12 /7

−3( −2 /7 y+ 12 /7 )−2y=4

−8 /7 y+ −36 /7 + 36 /7 =4+ 36 /7

−8 /7 y / /−8/7 = 64 /7 /−8 /7

y=−8

x= −2 /7 y+ 12 /7

x= −2 /7 (−8)+ 12 /7

x=4

x=4 and y=−8

P(2) is true, P(k) is 2k is less than (k+1)!, The given statement "P(n) inequality holds for all integers n≥2." is proved by using mathematical induction.

To write P(2), we substitute n = 2 into the property P(n):

2n < (n+1)!

2(2) < (2+1)!

4 < 6

P(2) is true.

To write P(k), we use the same property P(n):

2n < (n+1)!

2k < (k+1)!

P(k) is the property that 2k is less than (k+1)!.

To write P(k+1), we again use the property P(n):

2n < (n+1)!

2(k+1) < (k+2)!

P(k+1) is the property that 2(k+1) is less than (k+2)!.

To prove the inequality holds for all integers n ≥ 2 using mathematical induction, we need to show two things:

Base case: P(2) is true. We have already shown this in part (a).

Inductive step: Assume P(k) is true for some arbitrary integer k ≥ 2. We need to show that P(k+1) is also true.

From part (c), we have:

2(k+1) < (k+2)!    

Divide both sides by 2:

k+1 < (k+2)! / 2

Since (k+2)! / 2 = (k+2)(k+1)! / 2, we can write:

k+1 < (k+2)(k+1)! / 2  

We know from the inductive hypothesis that 2k < (k+1)!, so we can substitute this into the inequality above:

k+1 < (k+2)(2k) / 2

k+1 < (k+2)k

k+1 < k^2 + 2k

k^2 + k + 1 < k^2 + 3k + 2

(k+1)(k+1) < (k+2)(k+1)

Since k ≥ 2, we know that k+1 > 1, so we can divide both sides by (k+1):

k+1 < k+2

Therefore, P(k+1) is true.

By mathematical induction, we have shown that P(n) is true for all integers n ≥ 2.

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y = -6

The line is horizontal, meaning it is zero slope, and the line is located on -6, making the equation y = -6

Answer:

B: Subtraction property of equality

Answer:

y=x^2+3x-10

Step-by-step explanation:

.........

To stretch the spring from its natural length to 0.6 feet beyond its natural length, the work done is 0.2 foot-pounds.

The work done in stretching a spring is given by the formula:

Work = (1/2)k(x2^2 - x1^2),

where k is the spring constant, x2 is the final displacement, and x1 is the initial displacement.

Given that a force of 2 pounds is required to hold the spring stretched 0.5 feet beyond its natural length, we can calculate the spring constant using Hooke's Law:

F = kx,

where F is the force applied, k is the spring constant, and x is the displacement.

2 pounds = k * 0.5 feet,

k = 2 pounds / 0.5 feet = 4 pounds/feet.

Now we can calculate the work done:

Work = (1/2) * (4 pounds/feet) * ((0.6 feet)^2 - (0.5 feet)^2),

Work = (1/2) * (4 pounds/feet) * (0.36 - 0.25),

Work = (1/2) * (4 pounds/feet) * 0.11,

Work = 0.2 foot-pounds.

The work done in stretching the spring from its natural length to 0.6 feet beyond its natural length is 0.2 foot-pounds. This calculation is based on the given force required to hold the spring stretched 0.5 feet beyond its natural length and the spring constant.

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Answer:

\(x = \frac{2(A_T) }{(AB) + (AC) + (BC)} \)

Answer:

y = tan x

Step-by-step explanation:

y = tan x has a period of pi, not 2pi.

To solve triangle DEF, use Pythagorean theorem and right triangle trigonometry: find third side using \($c^2 = a^2 + b^2$\), and find all angles using \($\tan C = \frac{b}{a}$\), \($\sin C = \frac{b}{c}$\), \($\cos C = \frac{a}{c}$\).

To solve for all angles and sides of triangle DEF using right triangle trigonometry and the Pythagorean theorem, we need to know the lengths of all sides of the triangle. Let's assume that we have the lengths of two sides of the triangle and call them a and b.

If we know a and b, we can use the Pythagorean theorem to find the length of the third side c:

\($c^2 = a^2 + b^2$\)

Once we have the length of all sides, we can use right triangle trigonometry to find all angles. For example, if we have the lengths of sides a and b, we can use the tangent function to find angle C:

\($\tan C = \frac{b}{a}$\)

Similarly, we can use the sine and cosine functions to find the other angles:

\($\sin C = \frac{b}{c}$\)

\($\cos C = \frac{a}{c}$\)

So, if we know two sides of the triangle, we can use the Pythagorean theorem to find the third side and then use right triangle trigonometry to find all angles.

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The probability of a bill exceeding $300 is 0.0091.

A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

For normal distribution z score = (X-μ)/σ

here mean= μ = 196

std deviation  = σ = 44.0000

probability of a bill exceeding

$300  = P(X>300)

          =P(Z>(300-196)/44)  

          =P(Z>2.36)

          =0.0091

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Answer:

D

Step-by-step explanation:

I just took the USA test prep

D) −5/2x-3≤-13 inequality represents the number line .

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

Here, we have,

from the given number line ,

we get,

D) −5/2x-3≤-13 inequality represents the number line .

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The x/2√14 is equivalent to the quotient shown here when x > 0 √14x.Read more on simplification of radicals.

To find the equivalent expression of the quotient shown here when x > 0 √14x,

we need to rationalize the denominator as we can’t have a radical in the denominator. When we rationalize the denominator of √14x, we can get the following equivalent choice shown below:

√14x/√14x × √14x/√14x

= √14x²/14x

= √14(x*x)/14x

= x√14/√(14²)√14/14

= x/2√14

The equivalent choice to the quotient shown here when x > 0 √14x is x/2√14.

Therefore, x/2√14 is equivalent to the quotient shown here when x > 0 √14x.Read more on simplification of radicals.

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Answer:

B

Step-by-step explanation:

Now, the total amount of discount eligible by Jamie to be applied will be the percentage on the hardcover books plus the percentage on the fiction books

Mathematically, that would be 20% + 15% = 35%

So what this means is that , Jamie is entitled to a total of 35% off

So applying this to the price of the book, we have;

32.99 -(35/100 * 32.99)

= 32.99-(0.35 * 32.99)

= 32.99-(11.5465) = $21.4435

So if she is paying 21.4435 for the book, the amount saved will be 32-21.4435 = $11.5465 which is approximately $11.55

Answer:

A. $10.56

Step-by-step explanation:

20% of $32.99 equals $6.60

$32.99-$6.60 = $26.39

$26.39 x 15%= $3.96

$6.60 +$3.96 = $10.56

Answer:

yes

Step-by-step explanation:

Answer:

15 miles

Step-by-step explanation

After setting up a ration you multiply the 2.5 by 6 to get 15.

Answer:

534.37500

Step-by-step explanation:

1/42.75 = 12.5/x

x= 534.37500

you setup a ratio of litre/cost = litre/cost

you can also multiply 42.75 by 12.5, which is way easier.

Answer:

-3

Step-by-step explanation:

Slope going down.

From point (-2,3) to (-1,0): Down 3, Over 1 (-3/1)

Answer:

Brainliest pls

Step-by-step explanation:

-20

Answer:

The answer is -20.

Step-by-step explanation:

REMEMBER THIS:

Please excuse my dear aunt sally…

PLEASE = PARENTHESIS

EXCUSE= EQUATION

MY = MULTIPLICATION

DEAR = DIVISION

AUNT = ADDITION

SALLY = SUBTRACTION

^In that order^

Remember to use this statement to remember how to simplify the expression. PEMDAS.

When a point is reflected, it must be reflected across a line

The coordinate of D' is: (-2,-1)

The coordinates of D are given as:

\(\mathbf{D =(-2,1)}\)

The line of reflection is the x-axis

The rule of reflection, across the x-axis is:

\(\mathbf{(x,y) \to (x,-y)}\)

So, we have:

\(\mathbf{(-2,1) \to (-2,-1)}\)

This means that; the coordinates of D' are:

\(\mathbf{D' = (-2,-1)}\)

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Answer:

-2 -1

Step-by-step explanation: khan

Answer:

3

Step-by-step explanation:

In a linear grammar, for all productions, there is at most one variable on the left side of any production. This means that each production consists of a single nonterminal symbol and a string of terminal symbols.

For instance, consider the following linear grammar:
S → aSb | ε
This grammar is linear because each production has only one nonterminal symbol on the left-hand side. The first production has S on the left-hand side, and it generates a string of terminal symbols (a and b) by concatenating them with another instance of S.

The second production has ε (the empty string) on the left-hand side, indicating that S can also generate the empty string.A linear grammar is a type of formal grammar that generates a language consisting of a set of strings that can be generated by a finite set of production rules. In a linear grammar, all productions have at most one nonterminal symbol on the left-hand side.

This makes the grammar easier to analyze and manipulate than other types of grammars, such as context-free or context-sensitive grammars.

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Mark can solve math problems at a rate of 6 problems in 10 minutes. In 2 hours, he will be able to solve approximately 72 math problems.

To determine how many problems Mark can solve in 2 hours, we need to convert the time units to be consistent. Since there are 60 minutes in an hour, 2 hours would be equivalent to 2 x 60 = 120 minutes.

Next, we can set up a proportion to find the number of problems Mark can solve in 120 minutes:

6 problems / 10 minutes = x problems / 120 minutes

Cross-multiplying, we get:

10x = 6 * 120

Simplifying further:

10x = 720

Dividing both sides by 10:

x = 72

Therefore, Mark can solve approximately 72 math problems in 2 hours.

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The complete question is:

Mark can solve 6 math problems in 10 minutes. If he continues at this rate, how many math problems can Mark solve in 2 hours?

Answer:

1. To adjust the recipe to serve 30 cupcakes instead of 10, you will need to multiply the amount of each ingredient by 3.

2. This number was determined by dividing the desired number of servings (30) by the original number of servings (10). 30/10 = 3.

3. For 30 cupcakes, you will need 3 times the amount of vegetable oil listed in the original recipe. The original recipe calls for 1/2 cup of vegetable oil, so for 30 cupcakes, you will need 3 * (1/2) = **1 and 1/2 cups** of vegetable oil.

4. For 30 cupcakes, you will need 3 times the amount of flour listed in the original recipe. The original recipe calls for 1 and 1/2 cups of all-purpose flour, so for 30 cupcakes, you will need 3 * (1 and 1/2) = **4 and 1/2 cups** of all-purpose flour.

5. The difference in the amount of vanilla extract you would need for 30 cupcakes is calculated by subtracting the amount needed for 10 cupcakes from the amount needed for 30 cupcakes. The original recipe calls for 1 teaspoon of vanilla extract, so for 30 cupcakes, you will need 3 * (1) = **3 teaspoons** of vanilla extract. The difference is therefore 3 - 1 = **2 teaspoons**.

6. The difference in the amount of salt you would need for 30 cupcakes is calculated by subtracting the amount needed for 10 cupcakes from the amount needed for 30 cupcakes. The original recipe calls for 1/8 teaspoon of salt, so for 30 cupcakes, you will need 3 * (1/8) = **3/8 teaspoon** of salt. The difference is therefore (3/8) - (1/8) = **2/8 or 1/4 teaspoon**.

In the real world, it would make more sense to round the amount of an ingredient like salt or nutmeg rather than coming up with the exact amount because these ingredients are used in such small quantities that a slight variation in their amounts is unlikely to have a significant impact on the final product.

Answer:

there is no slope its undefined

Step-by-step explanation:

The z-values for the given situations are approximate:

a. The area to the left of z is 0.1827. z = -0.90

b. The area between −z and z is 0.9830. z = 2.17

c. The area between −z and z is 0.2148. z = 0.85

d. The area to the left of z is 0.9997. z = 3.49

e. The area to the right of z is 0.6847. z= -0.48

a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.

b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.

c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.

d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.

e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.

In summary, the z-values for the given situations are approximate:

a. -0.90

b. 2.17

c. 0.85

d. 3.49

e. -0.48

These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.

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Answer: nothing here?

Step-by-step explanation:

Answer:

0.3 lbs

0.1 + 0.2 =0.3

you're welcome

Answer:

Carter got 0.3 pounds of snacks