Giselle works as a carpenter and as a blacksmith.
She earns \$20$20dollar sign, 20 per hour as a carpenter and \$25$25dollar sign, 25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 303030 hours, and earned a total of \$690$690dollar sign, 690.
How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?

Answer:

5/1hour

Step-by-step explanation:

hope this helps

Answer:

5 animals in one hour

Step-by-step explanation:

Ratios are fractions set equal to each other, like this:

\(\frac{x}{y} =\frac{x}{y}\)

We have one side of the ratio:

\(\frac{35}{7}\)

If we set 7 hours equal to 1 hour, we'll end up with:

\(\frac{35}{7}=\frac{?}{1}\)

If we cross multiply we end up with:

35*1 = ?*7

or

35 = 7x

When we divide both sides:

5 = x

So the vet cared for 5 animals in one hour.

Answer:

See below

Step-by-step explanation:

For seg FG to be tangent to the circle with center E, the side lengths 6, 10, 12 must follow the rule of Pythagorean triplets.

So,

\( {10}^{2} + {6}^{2} = 100 + 36 = 136 \\ \\ {12}^{2} = 144 \\ \\ \because \: {10}^{2} + {6}^{2} \neq \: {12}^{2} \\ \)

From above it is obvious that given segment lengths doesn't follow the Pythagorean triplet rule. Therefore, seg FG is not tangent to the circle with center E.

Answer:

17+15=32.............

The volume of the rectangular pyramid with a base of 16m by 12m and a height of 7 m is 448 m³.

A rectangular pyramid is a three-dimentional object with a rectangular shaped base and triangular shaped faces that correspond to each side of the base.

The volume of rectangular pyramid is expressed as;

Volume V = (1/3) × l × w × h

Where l is the base length, w is the base width and h is the height of the pyramid.

From the diagram:

Length l = 16 meters

Width w = 12 meters

Height h = 7 meters

Volume V = ?

Plug these values into the above formula and solve for volume:

Volume V = (1/3) × l × w × h

Volume V = (1/3) × 16 × 12 × 7

Volume V = 448 m³

Therefore, the volume of the pyramid is 448 m³.

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Answer:

If in triangles ABC and DEF, angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse), then triangle ABC is congruent to triangle DEF.

D

Step-by-step explanation: im smart

Answer:

60%

Step-by-step explanation:

33/55 = 0.6 which is 60%

The solution to the initial value problem dy/dx = (x - 4)(y - 5) with the initial condition y(0) = 7 is y = e^((1/2)x^2 - 4x + ln(2)) + 5.

To solve the initial value problem dy/dx = (x - 4)(y - 5) with the initial condition y(0) = 7, we can separate the variables and integrate.

First, let's rewrite the differential equation as:

1 / (y - 5) dy = (x - 4) dx.

Now, we integrate both sides with respect to their respective variables:

∫(1 / (y - 5)) dy = ∫(x - 4) dx.

Integrating the left side with respect to y gives:

ln|y - 5| = ∫(x - 4) dx = (1/2)x^2 - 4x + C1,

where C1 is the constant of integration.

To simplify, we can exponentiate both sides:

|y - 5| = e^((1/2)x^2 - 4x + C1).

Next, we consider the absolute value. Since we have an initial condition y(0) = 7, we know that y - 5 is positive when x = 0. Therefore, we can remove the absolute value sign:

y - 5 = e^((1/2)x^2 - 4x + C1).

Now, we solve for y:

y = e^((1/2)x^2 - 4x + C1) + 5.

To determine the constant of integration C1, we substitute the initial condition y(0) = 7 into the equation:

7 = e^((1/2)(0)^2 - 4(0) + C1) + 5.

Simplifying, we find:

7 = e^(C1) + 5.

e^(C1) = 7 - 5 = 2.

Taking the natural logarithm of both sides, we get:

C1 = ln(2).

Finally, we substitute the value of C1 back into the equation to obtain the solution to the initial value problem:

y = e^((1/2)x^2 - 4x + ln(2)) + 5.

Therefore, the solution to the initial value problem is y = e^((1/2)x^2 - 4x + ln(2)) + 5.

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Answer:

This function is defined! Look at 1st and 2nd portions. It is clearly defined at both f(0) and f(2)!  

Check the correct answer by putting:

\(f(0)=(x+2)^2 -1=(0+2)^2-1=4-1=3\)

and:

\(f(2)=-2+1=-1\)

Therefore: \(f(0)>f(2)\). (Option 2)

Answer:

A. Auto Loans

Step-by-step explanation:

Answer:

A. Auto Loans

Step-by-step explanation:

According to the information, we can conclude that the value of c is 13 kg/s.

In the given problem, the damping constant is given as 13. In the notation used in the text, the damping constant (c) represents the coefficient of the velocity term in the differential equation that governs the motion of the mass-spring system.

To find the position of the mass after time t, we need to solve the differential equation that describes the motion of the system. The equation is given by:

where,

In this case, the mass (m) is 5 kg. We are not given the spring constant (k) directly, but we can calculate it using the given information. The force required to hold the spring stretched by 0.5 meters beyond its natural length is 1.5 N. This force is equal to the spring constant multiplied by the displacement:

Now we have all the values needed to solve the differential equation. Substituting the values, we have:

Solving this differential equation, we find that the general solution is of the form:

where,

c and d = constants

a and b = the roots of the characteristic equation:

ms² + cs + k = 0.

For the given values, we have:

Plugging these values into the characteristic equation, we can solve for the roots a and b.

The final form of the position function will depend on the specific values of a and b. Without further information, we cannot determine the exact form of the position function.

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Answer:

h(8) = - \(\frac{3}{7}\)

Step-by-step explanation:

Substitute x = 8 into h(x)

h(8) = \(\frac{8^2-11(8)+18}{8+6}\) = \(\frac{64-88+18}{14}\) = \(\frac{-6}{14}\) = - \(\frac{3}{7}\)

The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.

The function being used is;

f(x) = (x - 3)⁻²

If we separate this function according to x, we obtain;

f'(x) = -2/(x - 3)³

Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.

This suggests that;

0.06 - 0.25 = -2/(c - 3)³ x 6

-0.19 =  -12/(c - 3)³

(c - 3)³ = 63.157

c = 6.98

If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).

But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.

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The complete question is-

Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?

A particular solution is y_p(x) = x^2 - 2x.

To find the general solution to the differential equation xy" + (x + 1)y' + y = x², we can use the method of variation of parameters. Let's denote the general solution as y(x) = u(x)y₁(x) + v(x)y₂(x), where y₁(x) = e^x and y₂(x) = x + 1 are two linearly independent solutions of the homogeneous equation xy" + (x + 1)y' + y = 0.

First, let's find the Wronskian W(x) = y₁(x)y₂'(x) - y₁'(x)y₂(x) of the two solutions y₁(x) and y₂(x):

W(x) = (e^x)(1) - (e^x)(1) = 0.

Since the Wronskian is identically zero on the interval I = (0, ∞), we can use the modified variation of parameters formula:

u(x) = - ∫(y₂(x)f(x))/W(x) dx

v(x) = ∫(y₁(x)f(x))/W(x) dx,

where f(x) = x².

Calculating the integrals:

u(x) = - ∫((x + 1)(x²))/0 dx = undefined

v(x) = ∫((e^x)(x²))/0 dx = undefined.

Unfortunately, the integrals for u(x) and v(x) are undefined, which means we cannot use the variation of parameters method to find the particular solution in this case.

However, we can find a particular solution by using the method of undetermined coefficients. We assume a particular solution of the form y_p(x) = Ax^2 + Bx + C, where A, B, and C are constants. Substituting this into the original equation, we get:

x(Ax + 2A) + (x + 1)(2Ax + B) + Ax^2 + Bx + C = x².

Simplifying and comparing coefficients, we find:

A = 1, B = -2, C = 0.

Therefore, a particular solution is y_p(x) = x^2 - 2x.

The general solution to the differential equation is the sum of the particular solution and the homogeneous solution:

y(x) = y_p(x) + c₁y₁(x) + c₂y₂(x),

where c₁ and c₂ are arbitrary constants. Since y₁(x) = e^x and y₂(x) = x + 1 are linearly independent, this general solution represents all solutions to the differential equation on the interval I = (0, ∞).

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Answer:

Step-by-step explanation: 92 gallons bc if u calc the rate on 3 gallons per minute, times 4 which gives 12, add that to the 80 gallons alr filled then boom. 92.

Aloioi

Step-by-step explanation:

Answer:

C (-6, -1)

Step-by-step explanation:

The 95% confidence interval is (0.56, 0.62). This means that we can be 95% confident that the true proportion of city dwellers who would like to live at the beach lies between 56% and 62%.

In this case, the Chamber of Commerce conducted a survey asking city dwellers if they would like to live at the beach. The 95% confidence interval for the population proportion of city dwellers who would like to live at the beach is (0.56, 0.62).

To break this down:
1. Random sample: The Chamber of Commerce surveyed a group of city dwellers chosen randomly, which helps ensure that the results are representative of the entire population of city dwellers.
2. Population proportion: This refers to the percentage of all city dwellers who would like to live at the beach.
3. 95% confidence interval: This means that if the survey were repeated many times with different random samples, 95% of the intervals calculated would contain the true population proportion.

In this case, the 95% confidence interval is (0.56, 0.62). This means that we can be 95% confident that the true proportion of city dwellers who would like to live at the beach lies between 56% and 62%.

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The mean score for this set of scores is 7.

In statistics, the mean refers to the measure of central tendency or average of a set of numbers. The mean is used to describe the typical value in a set of data. It is calculated by adding up all the values in the set and dividing the sum by the total number of values.

So, for the given set of scores, we have:

7 + 8 + 3 + 9 + 10 + 6 + 8 + 5 = 56

There are 8 scores in the set, so we divide by 8 to get the mean:

Mean = 56 / 8 = 7

Therefore, the mean score is 7.

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Answer:

A

Step-by-step explanation:

The rest of the steps are right

If Solomon bought a $65 000 corporate bond. The value of Solomon's investment after a total of 8 years is $95,280.2.

To solve this problem, we can use the formula for compound interest:

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

where:

A = the future value of the investment

P = the initial principal

r = the interest rate

n = the number of times the interest is compounded per year

t = the number of years

We can break down the problem into two parts: the first 3 years when the interest is compounded monthly, and the remaining 5 years when the interest is compounded semi-annually.

For the first 3 years, we have:

P = $65,000

r = 4.2% = 0.042

n = 12 (compounded monthly)

t = 3

So the future value of Solomon's investment after 3 years is:

A1 = $65,000(1 + 0.042/12)^(12*3)

= $73,712.12

Now we can use this amount as the new principal for the remaining 5 years, where the interest is compounded semi-annually:

P = $73,372.27

r = 5.2% = 0.052

n = 2 (compounded semi-annually)

t = 5

So the future value of Solomon's investment after a total of 8 years is:

A2 = $73,712.12 (1 + 0.052/2)^(2*5)

= $95,280.29

Therefore, the value of Solomon's investment after a total of 8 years is approximately $95,280.29.

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The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Answer:

y= 6.5x+3 is the equation

If Peter needs 2 3/7 feet of ribbon to make a bow, and he has 17 feet of ribbon, then the number of  bows Peter  can make is 7 bows.

Using this formula to determine the number of bows

Number of bows = Number of ribbon in feet ÷ Number of ribbons in feet needed

Where:

Number of ribbon in feet =17

Number of ribbons in feet needed  =2 3/7 or 2.43

Let plug in the formula

Number of bows = 17 / 2.43

Number of bows = 6.99

Number of bows =  7 bows (Approximately)

Therefore he can make 7 bows.

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Answer: the answer is 7

Step-by-step explanation: I have my ways ;>

Answer:

- 1 1/4

Step-by-step explanation:

-9 1/4 + 8 = -1 1/4

The derivative of a function represents the rate of change of the function at a specific point. In this case, f'(0) = 1 indicates that at x = 0,

To find f'(0), we need to calculate the derivative of f(x) with respect to x and then evaluate it at x = 0.

Using the product rule and chain rule, we can differentiate f(x) = (x-1)^2 sin(x) as follows:

f'(x) = 2(x-1) sin(x) + (x-1)^2 cos(x)

Now, let's substitute x = 0 into the derivative expression:

f'(0) = 2(0-1) sin(0) + (0-1)^2 cos(0)

= -2(0) + 1^2 (1)

= 0 + 1

= 1

Therefore, f'(0) = 1.

the function f(x) = (x-1)^2 sin(x) is increasing with a rate of 1. It means that as we move along the x-axis from negative values towards x = 0, the function is getting steeper and the slope at x = 0 is positive.

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The function that represents h(x) is h(x) = 10x² +29x - 21

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

f(x) = 5x - 3

g(x) = 2x + 7

Also, we have

The function h(x) = f(x) • g(x)

This means that

h(x) = f(x) • g(x)

Substitute the known values in the above equation, so, we have the following representation

h(x) = (5x - 3) * (2x + 7)

Expand

h(x) = 10x² +29x - 21

Hence, the function that represents h(x) is h(x) = 10x² +29x - 21

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Answer:

option 4

Step-by-step explanation:

b) It will take approximately 24.6 years to save $3,000 for your vacation by saving $100 each month with a 3% nominal interest rate compounded monthly.

c) equivalent effective interest rates are:

i. Semi-annually: 5.06%

ii. Quarterly: 5.11%

iii. Daily: 5.13%

iv. Continuously: 5.13%

EXPLANATION:

To calculate the time it will take for you to save $3,000 for your vacation, we can use the future value formula for monthly compounding:

\(Future Value = Principal * (1 + rate/n)^(n*time)\)

Where:

- Principal is the amount you save each month ($100)

- Rate is the nominal interest rate (3% or 0.03)

- n is the number of compounding periods per year (12 for monthly compounding)

- Time is the number of years we want to calculate

We need to solve for time. Let's substitute the given values into the formula:

\($3,000 = $100 * (1 + 0.03/12)^(12*time)Dividing both sides of the equation by $100:30 = (1.0025)^(12*time)\)

Taking the natural logarithm (ln) of both sides:

\(ln(30) = ln((1.0025)^(12*time))Using logarithmic properties (ln(a^b) = b * ln(a)):ln(30) = 12*time * ln(1.0025)\)

Solving for time:

\(time = ln(30) / (12 * ln(1.0025))\)

Using a calculator:

time ≈ 24.6

c)To calculate the equivalent effective interest rate for a nominal rate of 5% compounded at different intervals:

i. Semi-annually:

The effective interest rate for semi-annual compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

For semi-annual compounding:

\(Effective Interest Rate = (1 + (0.05 / 2))^2 - 1\)

Calculating:

Effective Interest Rate ≈ 0.050625 or 5.06%

ii. Quarterly:

The effective interest rate for quarterly compounding is calculated similarly:

\(Effective Interest Rate = (1 + (0.05 / 4))^4 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051136 or 5.11%

iii. Daily:

The effective interest rate for daily compounding is calculated using the formula:

Effective Interest Rate = (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1

Since there are approximately 365 days in a year:

\(Effective Interest Rate = (1 + (0.05 / 365))^365 - 1\)

Calculating:

Effective Interest Rate ≈ 0.051267 or 5.13%

iv. Continuously:

The effective interest rate for continuous compounding is calculated using the formula:

\(Effective Interest Rate = e^(nominal rate) - 1\)

For a nominal rate of 5%:

\(Effective Interest Rate = e^(0.05) - 1\)

Calculating:

Effective Interest Rate ≈ 0.05127 or 5.13%

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The exact value of tan 20 cannot be found. Note: By using the Pythagorean Theorem, we can also find the missing side opposite to the angle 20 degrees, which is 6.16 approximately.

Given information: Cot 0 = 14.0 lies in quadrant III. Illustration: We can draw a triangle to solve the given problem. For that, we have to find the hypotenuse, adjacent and opposite side of the angle first. We know that cot = adjacent/opposite. So, the hypotenuse will be = opposite/cotangent of the angle. Hypotenuse, opposite, and adjacent sides in the III quadrant. Hence, the adjacent side and hypotenuse are negative. Here, we can take opposite as 14 and cot as 0.

So, the adjacent side and hypotenuse can be found by Hypotenuse = opposite/cotangent of the angle.

= 14/0 = infinity (since cot 0 = adjacent/opposite = 0/14 = 0, which means that the adjacent side is zero.

Then we can say that the angle 0 degrees is not defined for the cotangent function.)

Adjacent side = (cot) x (opposite)= 14 x 0 = 0

Now, we can apply the Pythagorean Theorem to find the missing side of the triangle.

Hypotenuse² = Opposite² + Adjacent²Hypotenuse²

= 14² + 0² = 196

Hypotenuse = sqrt(196)

= 14

So, the triangle is shown as follows:Trianlge-III quadrantNow we can find sin, cos and tan of the angle 20 degrees.

Solution:a. sin 20° = opposite/hypotenuse=14/14=1b.

cos 20° = adjacent/hypotenuse=0/14=0c.

tan 20° = opposite/adjacent=14/0= undefined (since adjacent side is zero).

Hence, the exact value of tan 20 cannot be found. Note: By using the Pythagorean Theorem, we can also find the missing side opposite to the angle 20 degrees, which is 6.16 approximately.

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