1) Ruth works a job where she gets paid $750 per week. Next year her pay will be
increasing by 12% (of what it currently is).
help

Answer:

6 13/14

Step-by-step explanation:

Add the whole numbers first.

6 + 2/7 + 9/14

Find the Least Common Denominator (LCD) of 2/7, 9/14. In other words, find the Least Common Multiple (LCM) of 7,14.

LCD: 14

Make the denominators the same as the LCD.

6 + 2 × 2/7 × 2 + 9/14

Simplify. Denominators are now the same.

6 + 4/14 + 9/14

Join the denominators.

6 + 4 + 9/14

Simplify

6 13/14

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- ElizabethKate

The solution is 97/14 of the given exprsseion.

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

Given expression as :

⇒ \(4\dfrac{2}{7} + 2\dfrac{9}{14}\)

⇒ (28 + 2)/7 + (28 + 9)/14

⇒ 30/7 + 37/14

⇒ (60 + 37)/14

⇒ 97/14

Hence, the solution is 97/14 of the given expression.

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Answer: $7.80

Step-by-step explanation:

Based on the information given in the question, the expected profit that the farmer makes will be:

= (Probability of edible stocks × Profit) - (Probability of inedible stocks × Loss)

= (95% × $8) - (5% × $4)

= (0.95 × $8) - (0.05 × $4)

= $7.60 + $0.20

= $7.80

Therefore, the expected profit that the farmer makes is $7.80.

Answer:

$7.40/bushel

Step-by-step explanation:

i took the test and got it right

The directional derivative of the function in the direction of the given vector is positive, indicating that the function is increasing in that direction.

The directional derivative is a measure of the rate of change of a function in a particular direction. To calculate the directional derivative, we need to take the dot product of the gradient of the function with the unit vector in the given direction. The sign of the directional derivative tells us whether the function is increasing or decreasing in that direction.
In this case, we are given that the angle between the vector and a unit vector is 99 degrees. Since the dot product of two vectors is equal to the product of their magnitudes times the cosine of the angle between them, we can write:
cos(99) = (u . v) / (|u| |v|)
where u is the given vector and v is the unit vector. We know that the magnitude of the unit vector is 1, so we can

simplify:
cos(99) = u . v / |u|
Multiplying both sides by |u|, we get:
cos(99) |u| = u . v
This tells us the magnitude of the projection of the vector u onto the unit vector v. If u and v point in the same direction, the projection is positive; if they point in opposite directions, the projection is negative.
Since u is nonzero and the angle between u and v is less than 180 degrees (i.e., they point in the same direction), the sign of the projection is positive.

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Answer: 61 Biscuits

Step-by-step explanation: 13g of butter per biscuit, 25g sugar per biscuit, 32.5g flour per biscuit, 21.25g rice per biscuit

By taking the amount of flour per biscuit (the largest ingredient) and dividing 2000 by it you get 61 which is the most amount of biscuits he can make with his ingredients.

Answer:

x=\frac{94}{\sin 10}=541.3244\approx 541.3\text{ feet}

x=

sin10

94

​

=541.3244≈541.3 feet

Step-by-step explanation:

There are no local maxima or local minima, but there is a saddle point at (x₁, x₂, x₃) = (0, 0, 0).

To find all local maxima, local minima, and saddle points for the given function `f(x₁, x2, x3) = x1X2 + X2X3 +X1X3`, we need to find its critical points and classify them as maxima, minima or saddle points using the Hessian matrix test.

Let's begin: Calculation of partial derivatives: ∂f/∂x₁ = x₂ + x₃

∂f/∂x₂ = x₁ + x₃

∂f/∂x₃ = x₁ + x₂

Calculation of second-order partial derivatives: ∂²f/∂x₁² = 0∂

²f/∂x₂² = 0

∂²f/∂x₃² = 0

∂²f/∂x₁∂x₂ = 1

∂²f/∂x₁∂x₃ = 1

∂²f/∂x₂∂x₁ = 1

∂²f/∂x₂∂x₃ = 1

∂²f/∂x₃∂x₁ = 1

∂²f/∂x₃∂x₂ = 1

The Hessian matrix H of the second-order partial derivatives is:

H = |0 1 1|     |1 0 1|     |1 1 0|

The determinant of H is given by: det(H) = -2

The trace of H is given by: tr(H) = 0Since `det(H) < 0` and `tr(H) = 0`, we can conclude that the given function `f(x₁, x2, x3) = x1X2 + X2X3 +X1X3` has a saddle point at (x₁, x₂, x₃) = (0, 0, 0).

Therefore, there are no local maxima or local minima of the given function.

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Answer:

-1

Step-by-step explanation:

number explanation

1. 20 + 4x = 16

  -20           -20

2. 4x = -4

    4       4

3. -4 divided by 4 = -1

word explanation

1.rewrite the problem

2. subtract 20 from 20 and subtract 20 from 16

all of the numbers subtract 20 except the number with the variable

3. 20 - 20 = 0

16 - 20 = -4 because you take the sign of the bigger number

4. you bring down 4x divided by 4 it gets crossed out then you do -4 divided by 4 and your answer is

negative 1

-1

Each guest receive 352 gm veal roast.

The pound is a unit of measurement used in the U. S. customary system and the British imperial system to measure weight. One familiar use of pounds is measuring how much a person weights.

We know that,

1 pound = 453.592 gm

12.4 pound = ? gm

12.4 pound = 12.4×453.592

                   = 5624.541 gm

Total number of guest = 16

Then,

Each guest receive veal roast = \(\frac{5624.541 gm}{16}\)

                                                 = 352 gm

Hence, Each guest receive veal roast is 352 gm.

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Answer:

50 minutes

Step-by-step explanation:

This indicates that after accounting for the inflation rate of 7%, the purchasing power of the $1,000 investment decreased by approximately 1.92%.

The real rate of return represents the rate of return adjusted for inflation, which reflects the purchasing power of the investment. To calculate the real rate of return, we subtract the inflation rate from the nominal interest rate.

In this case, the nominal rate of interest is 5 percent, but prices have actually risen by 7 percent, indicating an inflation rate of 7 percent. Therefore, the real rate of return can be calculated as follows:

Real rate of return = Nominal interest rate - Inflation rate

Real rate of return = 5% - 7%

Real rate of return = -2%

The negative sign indicates that the purchasing power of the investment has decreased. To express the real rate of return as a positive value, we take the absolute value, resulting in approximately 2%. Therefore, Gladys earned a real rate of return of approximately -2% or -1.92% (rounded to two decimal places).

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Answer:

The maximum height it reaches is 20 meters

The time taken by it to reach the height is 2 seconds

Step-by-step explanation:

The formula of the height of the stone is h = u t - \(\frac{1}{2}\) g t², where

∵ A stone is thrown vertically upwards with an initial velocity of 20 m/s

∴ u = 20 m/s

∵ g = 10 m/s²

→ Substitute them in the equation above

∴ h(t) = 20t - \(\frac{1}{2}\) (10) t²

∴ h(t) = 20t - 5t²

→ Arrange the terms of the right side according to the greatest power of t

∴ h(t) = -5t² + 20t

To find the maximum height and the time of it find the vertex of the quadratic function (m, k), where m = \(\frac{-b}{2a}\) and k is the value of h at t = m, a is the coefficient of t² and b is the coefficient of t

∵ The coefficient of t² is -5

∴ a = -5

∵ The coefficient of t is 20

∴ b = 20

→ Use them to find h

∵ m = \(\frac{-20}{2(-5)}\) = \(\frac{-20}{-10}\) = h

∴ m = 2

→ Substitute it in the equation above to find k

∵ h(m) = k

∵ k = -5(2)² + 20(2)

∴ k = -5(4) + 40

∴ k = -20 + 40

∴ k = 20

∴ The coordinate of the vertex of the function are (2, 20)

→ m represents the time of the maximum height and k represents

  the maximum height

∴ The maximum height it reaches is 20 meters

∴ The time taken by it to reach the height is 2 seconds

Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Answer:

I think the 3rd one

Step-by-step explanation:

Hope its right

Answer:

A

Step-by-step explanation:

IT IS A

The closed-form solution for the given recurrence relation t(n) = t(n-1) * 3 with the base case t(0) = 1 is:

t(n) = 3^n


1. Start with the given recurrence relation: t(n) = t(n-1) * 3
2. Notice that the base case is t(0) = 1
3. We can rewrite the relation for a few terms to recognize the pattern:

  t(1) = t(0) * 3 = 3^1
  t(2) = t(1) * 3 = (3^1) * 3 = 3^2
  t(3) = t(2) * 3 = (3^2) * 3 = 3^3

4. Based on this pattern, we can generalize the closed-form solution as t(n) = 3^n


The closed-form solution for the given recurrence relation t(n) = t(n-1) * 3 with the base case t(0) = 1 is t(n) = 3^n.

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a) The expression for the magnitude of the electric field at the upper right corner of the square is E = (k_e * 4) / (a^2 * 2) + (k_e * 5) / a^2

b)The expression for the total electric force exerted on the charge q is given by:

F = q * [(k_e * 4) / (a^2 * 2) + (k_e * 5) / a^2]

(a) To find the expression for the magnitude of the electric field at the upper right corner of the square, we need to consider the contributions from charges A and C.

The electric field due to a point charge is given by the equation:

E = k_e * (q / r^2)

where E is the electric field, k_e is the electrostatic constant, q is the charge, and r is the distance from the charge.

For the upper right corner, the distance from charge A is a√2, and the distance from charge C is a.

Therefore, the expression for the magnitude of the electric field at the upper right corner is:

E = (k_e * A) / (a√2)^2 + (k_e * C) / a^2

Substituting the given values A = 4 and C = 5, we have:

E = (k_e * 4) / (a^2 * 2) + (k_e * 5) / a^2

(b) The expression for the total electric force exerted on the charge q is given by:

F = q * E

where F is the force and q is the charge. Substituting the expression for the electric field from part (a), we have:

F = q * [(k_e * 4) / (a^2 * 2) + (k_e * 5) / a^2]

(c) If each of the four charges were negative with the same magnitude, the answers to parts (a) and (b) would change as follows:

The force would be the same magnitude but opposite direction as the force in part (b).

The electric field would be the same magnitude but opposite direction as the field in part (a).

In other words, the signs of both the electric field and force would be reversed. The magnitudes, however, would remain the same.

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If a dilation was performed so that the scale factor from AMY to MEG is 1/3, then the perimeter of MEG will be 5 units

Given the sides of the triangle AMY given as:

If the scale factor from AMY to MEG is 1/3, then the sides of triangle MEG will be:

ME = 5/3

EG = 7/3

MG = 3/3

The perimeter of MEG = ME + G + MG

The perimeter of MEG = 5/3 + 7/3 +3/3

The perimeter of MEG = 15/3

The perimeter of MEG = 5 units

Hence the perimeter of MEG is 5 units

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______________________________

_______________________________

Answer:

c

Step-by-step explanation:

Answer:

n= 6

Step-by-step explanation:

7^9/7^6 is the same as 7^9 - 7^6/ 7^9-6 but it gives you 7^3

Answer:

The answer is 9.

Answer:

3/4 ×12 = 9

Multiple 3/4 by 12

And it Equal to 9

Answer:

y=2x-7

Step-by-step explanation:

The equation we are looking for would be y=mx+b.

Currently, you are trying to find "m" and "b"

m is the slope, and you can find this slope by finding (11-(-5))/9-1), which is equal to 16/8, or 2. So, we now know m, or the slope.

To find b, we need to plug in one of our points to the equation. Let's use (9,11).

11 is the y value, so we input it to the y place. 9 is the x value, so we input into the x place.

11=2(9)+b

If we solve this, we get -7=b

So, your equation is y=2x-7

The percent increase between the total without Daya's employer contribution and the total with is A. 94%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, Daya contributes a set percentage of her gross pay towards a 401k account and will have a total of $172,486.00 by retirement and her employer also contributes a set percentage, which will increase her total by $161,531.00.

Therefore, the percentage increase will be:

= Increase in amount / Original amount × 100

= 161,531/172486 × 100

= 94%

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The sum of digits in 343 is 10, an even number, while in 124 it is 7, an odd number. There are 450 three-digit numbers with an even sum of digits.


To determine the number of 3-digit numbers from 100 to 999 (inclusive) where the sum of the digits is even, we need to consider the possible combinations of digits.

There are 9 choices for the hundreds digit (1 to 9), 10 choices for the tens digit (0 to 9), and 10 choices for the units digit (0 to 9).

If the hundreds digit is fixed, there are two possibilities for the sum of the tens and units digits: even or odd.

For odd sums, half of the options will be even and the other half will be odd.

Therefore, half of the total combinations will have an even sum of digits.

Hence, there are 450 three-digit numbers from 100 to 999 (inclusive) with an even sum of digits.


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If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

Let's solve the problem step by step:

1. Identify the given information:

  - The triangle is isosceles, meaning it has two equal sides.

  - The two equal sides, labeled "a," are longer than the base, labeled "b."

  - The perimeter of the triangle is 15.7 centimeters.

  - One of the longer sides is 6.3 centimeters.

2. Set up the equation based on the given information:

  Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:

  2a + b = 15.7

3. Substitute the known value into the equation:

  One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:

  2(6.3) + b = 15.7

4. Simplify and solve the equation:

  12.6 + b = 15.7

  Subtract 12.6 from both sides:

  b = 15.7 - 12.6

  b = 3.1

5. Interpret the result:

  The length of the base, labeled "b," is found to be 3.1 centimeters.

Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.

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Answer:

24

**Solving Steps**

2 x (2 x X - 6) = 84

4x-12=84

84+12=96

96/4 = 24

Hope it helps.

(a)  The remainder of 7k+3 when divided by 4 is 3.

(b)  The remainder of 2r+3s when divided by 11 is either 8 or 7, depending on the value of s.

(a) Let k be an integer with k≡3 (mod4). We know that k leaves a remainder of 3 when divided by 4. Now, we need to compute the remainder of 7k+3 when divided by 4.

Using the distributive property, we can rewrite the expression as 7k+3 = 4k + 3k + 3. Since 4k is a multiple of 4, it leaves a remainder of 0 when divided by 4.

The expression now becomes 3k + 3. We can factor out a 3, which leaves us with 3(k+1). Since k leaves a remainder of 3 when divided by 4, k+1 leaves a remainder of 0 when divided by 4. Therefore, the remainder of 7k+3 when divided by 4 is 3.

(b) Let r and s be integers with r≡3 (mod11) and s≡−7 (mod11). We know that r leaves a remainder of 3 when divided by 11 and s leaves a remainder of -7 or 4 when divided by 11 (since -7 is equivalent to 4 mod 11). Now, we need to compute the remainder of 2r+3s when divided by 11.

Using the distributive property, we can rewrite the expression as 2r+3s = 2r + 3(-7) or 2r + 3(4). In either case, we can simplify the expression by multiplying the coefficients by their respective remainders.

For the first expression, we get 2(3) + 3(-7) = -19 or 8 when reduced modulo 11. For the second expression, we get 2(3) + 3(4) = 18 or 7 when reduced modulo 11. Therefore, the remainder of 2r+3s when divided by 11 is either 8 or 7, depending on the value of s.

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Answer:

3.73737373737

Step-by-step explanation:

hope this helps

In the 2012 Gallup survey, a random sample of 474,195 U.S. adults was interviewed by phone to gather information about their work status, height, and weight.

The objective was to determine the prevalence of obesity (defined as having a body mass index greater than 30) among different work status groups. The survey found that 24.9% of the participants who were employed (either full-time or part-time by choice) were classified as obese. In contrast, 28.6% of the participants who were unemployed and actively seeking work were also found to be obese. This indicates that there may be a relationship between employment status and obesity rates in the U.S. adult population.

However, it is important to note that correlation does not necessarily imply causation, and various factors could contribute to these findings. Further research may be necessary to determine the underlying causes behind the differences in obesity rates among employed and unemployed individuals.

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