Solve the system of equations x + y = 8; y = x ^ 2 - 4

Answer:

\(\frac{6}{10}\)

Step-by-step explanation:÷

convert 0.7 to a fraction so \(\frac{7}{10}\)

and convert the mixed number to a fraction \(\frac{7}{6\\}\)

now divide them

\(\frac{7}{10}\) ÷  \(\frac{7}{6\\}\)

\(\frac{7}{10}\) x \(\frac{6}{7}\)

so 7 and 7 cancel out so 1 over 10 and 6 over 1 now multiply and you get

6 over 10

:)

Answer:

19 feet

Step-by-step explanation:

The dolphin goes from 15 feet below then he goes above the ocean by 4. So add 15 + 4 to get 19 feet.

Answer:

i think 6 not sure tho sorry if its worng

Answer:

There is not enough evidence to suggest that mean starting salary of a graduate with a bachelor in economics is different from $48,500.

Step-by-step explanation:

In this case we need to test whether the mean starting salary of a graduate with a bachelor in economics is $48,500.

The information provided are:

\(\bar x=\$43350\\s=\$15000\\n=50\\\alpha =0.01\)

The hypothesis for the test can be defined as follows:

H₀: The mean starting salary of a graduate with a bachelor in economics is $48,500, i.e. μ = 48500.

Hₐ: The mean starting salary of a graduate with a bachelor in economics is different from $48,500, i.e. μ ≠ 48500.

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

 \(t=\frac{\bar x-\mu}{s/\sqrt{n}}\)

   \(=\frac{43350-48500}{15000/\sqrt{50}}\\\\=-2.42773\\\\\approx -2.43\)

Thus, the test statistic value is -2.43.

Compute the p-value of the test as follows:

 \(p-value=2\times P(t_{49}>-2.43)=0.0188\)

*Use a t-table.

Thus, the p-value of the test is 0.0188.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.0188 > α = 0.01

The null hypothesis will not be rejected at 1% level of significance.

Thus, concluding that there is not enough evidence to suggest that mean starting salary of a graduate with a bachelor in economics is different from $48,500.

Based on the information, it can be inferred that the baby weighed 7.06 pounds at birth.

To calculate how much the baby weighed at birth we must take into account the information we have available

Current Weight: 6.8 lbs.

% lost: 3.7%

According to the above, we must calculate what percentage the current weight is equal to:

100% - 3.7% = 96.3%

Now we must make a rule of three to find the weight of the baby at birth:

96.3 - 6.8

100 - ?

100% * 6.8 pounds / 96.3% = 7.06 pounds

According to the above, the baby was born thinking 7.06 pounds, that is, she lost 0.26 pounds.

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Answer:

Moshde must do 59 cuts & styles per month

Step-by-step explanation:

she has to earn $1140+$1188=$2328

since she get $40 for a haircut and style

then she need to \(\frac{2328}{40}=58,2\) roundup it 59

Moshde must do 59 cuts & styles per month

Step-by-step explanation:

the two numbers are 0.25 or -0.25

The magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree 5.4<cos335°<, sin335°

What is direction ?

Direction is characterized as the course that anything follows, the route that must be taken to go to a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you turn right instead of left, that is an illustration of direction.

The basis of the x, y, and z directions of a line or unit vector is identified by the number triplet known as the direction number. They are easily identified as a percentage of a unit vector.

u = 7cos300°i + 7sin300j

v = 4cos70i + 4sin70 j

u = 7*0.5i + 7*(-√3/2)j

  = 3.5i - 6.062j

v = 1.368i + 3.758j

u + v =(3.5+1.368)i +(-6.062+3.758)j

        = 4.868i +(-2.304)j

Magnitude of (u+v) = √(4.868)² +(2.304)²

                               = 5.385 ≈ 5.4

For direction

tanФ = y/x

        = -2.304/4.868

    Ф = -25.327

∴(u+v) is in 4th Quandrant

∴ Ф = 360 - 25.327

     = 334.672

    ≈ 335°

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The value of ∂x/∂s is  4s^2 * t^6.

To find ∂x/∂s, we need to differentiate x with respect to s while treating t as a constant. Let's begin by substituting the given expressions for x, y, and z into the function f(x, y, z):

f(x, y, z) = (x^2)(y^3) + z^3

Substituting x, y, and z:

f(s, t) = ((s^2)(t^3))^2 * (s*t)^3 + ((s^2)*t)^3

Expanding the expression:

f(s, t) = (s^4 * t^6) * (s^3 * t^3) + (s^6 * t^3)

Now, let's differentiate x with respect to s:

∂x/∂s = ∂/∂s [(s^2)(t^3)]^2

Using the chain rule, we can differentiate each term separately:

∂x/∂s = 2 * (s^2 * t^3)^1 * ∂/∂s [(s^2)(t^3)]

Differentiating (s^2)(t^3) with respect to s:

∂/∂s [(s^2)(t^3)] = 2s * t^3

Substituting back into the expression for ∂x/∂s:

∂x/∂s = 2 * (s^2 * t^3)^1 * 2s * t^3

Simplifying:

∂x/∂s = 4s^2 * t^6

Therefore, ∂x/∂s = 4s^2 * t^6.

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Step-by-step explanation:

70 ÷ 3 = 23  1/3

The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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A. (0.6, -2.8)

Hope this helps! :)

Answer:

x=31/2

Step-by-step explanation:

don't have steps but its right.

Answer:

x = 31/2 = 15 1/2 = 15.5

Step-by-step explanation:

(x- 4.5)/2=5.5

Multiply both sides by 2.

x−4.5=5.5×2

Multiply 5.5 and 2 to get 11.

x−4.5=11

Add 4.5 to both sides.

x=11+4.5

Add 11 and 4.5 to get 15.5.

x=15.5

Answer:

Step-by-step explanation:

The ODE is separable.

\(\dfrac{dy}{dx} = xy \iff \dfrac{dy}y = x\,dx\)

Integrate both sides to get

\(\displaystyle \int\frac{dy}y = \int x\,dx\)

\(\boxed{\ln|y| = \dfrac12 x^2 + C}\)

But notice that replacing the constant \(C\) with \(-C\) doesn't affect the solution, since its derivative would recover the same ODE as before.

\(\ln|y| = \dfrac12 x^2 - C \implies \dfrac1y \dfrac{dy}{dx} = x \implies \dfrac{dy}{dx} = xy\)

so either of the first two answers are technically correct.

Answer:

0.24510

Step-by-step explanation:

True.

Here's an example statement in Python that reads an integer variables from standard input and stores it in an existing integer variable called datum:

datum = int(input("Enter an integer value: "))

This statement first prompts the user to enter an integer value by printing the string "Enter an integer value: " to the console. The input() function then reads the user's input from the console as a string. Finally, the int() function converts the string to an integer and assigns the result to the datum variable.

Note that the specific syntax and function calls may vary depending on the programming language being used, but the general concept of reading an integer value from standard input into an existing variable is applicable to most programming languages.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

Skewed to the left

Step-by-step explanation:

In pearson mode skewdness, the mean, mode and median are used to determine if we have a positive or negative skewed distribution.

Now, If the mean is greater than the median, it means that the distribution is positively skewed and therefore skewed to the right. However, If the mean is less than the median, it means that the distribution is negatively skewed and therefore skewed to the left.

In our question, the median is 85 and mean is 78. Thus, it means median is greater than the mean and as such, the distribution isnegatively skewed and therefore skewed to the left.

Answer:

-----------------------

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

Answer:

√43

Step-by-step explanation:

Implement the Pythagorean formula to solve for sides of a right triangle: a^2 + b^2 = c^2, where "a" and "b" are the legs and "c" is the hypotenuse.

a = √6 and c = 49

√6^2 + b^2 = 49

6 + b^2 = 49

b^2 = 43

b = √43

Answer:

The square root of 43

Step-by-step explanation:

 I did this in class the other day

The number of coffee shops per capita in the city is approximately 0.000124.

To calculate the number of coffee shops per capita in the given city, we divide the total number of coffee shops by the total population and round the result to six decimal places.

Number of coffee shops: 99

Population: 801,100

Coffee shops per capita = Number of coffee shops / Population

Coffee shops per capita = 99 / 801,100

Coffee shops per capita = 0.000123719

Rounding the result to six decimal places, the number of coffee shops per capita in the city is approximately 0.000124.

This means that for every person in the city, there are approximately 0.000124 coffee shops available. Another way to interpret this is that, on average, each person in the city can expect to have access to 0.000124 coffee shops.

Please note that this calculation assumes an equal distribution of coffee shops throughout the city and does not take into account factors such as location, density, or other variables that may affect coffee shop accessibility.

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The firm should produce good  x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .

What is Lagrange multipliers ?

Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.

To minimize the cost C = x₁² + x₂²

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:

L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)

Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:

∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0

∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0

∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0

Solving these equations simultaneously, we get:

x₁ = 4

x₂ = 8

λ = 1/20

Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.

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Answer:

B

Step-by-step explanation:

The area of the shaded region = 30.903 in²

From the attached figure we can observe that the radius of the circle R is r = 6 in.

Using the forula for the area of circle, the area of circle R would be,

A₁ = πr²

A₁ = π × 6²

A₁ = 36π

A₁ = 113.097 in²

So, the diameter would be d = 6 × 2 = 12 in.

The circle R is inscribed in a square.

So, the side length of square is equal to the diameter of the circle.

This means the side length 'a' os square = 12 in.

Using the formula of the area of square,

A₂ = side²

A₂ = a²

A₂ = 12²

A₂ = 144 in²

so, the area of the shaded region would be,

A = A₂ - A₁

A = 144 -113.097

A = 30.903 in²

This is the required area.

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From the data, we can see that all points are spread out evenly.

So, we have cases with both less time watching and lower scores, less time watching and greater grades, and we have more time watching and lowers scores and more time watching and greater grades.

So, there is no tendency on the data, it is close to random.

So, there is no relationship, in this case, for time watching TV and scores.

So, the correct alternative is the fourth alternative.

The area of the composite shapes are:

1) A = 22 cm²

2) A = 91.5cm²

1) The formula for area of a trapezium is:

A = ¹/₂(sum of parallel sides) * height

Area of rectangle = Length * width

Thus:

Total Area of composite shape is:

A = (7 * 2) + ¹/₂(6 + 2)*2

A = 14 + 8

A = 22 cm²

2) Area of square = side * side

Area of semi circle = ¹/₂π(r²)

Total area of composite shape is:

A = (5 * 5) + (21 * 3) + ¹/₂π(1.5²)

A = 91.5cm²

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