Evaluate the function for the given value.
h(a) = 3a + 3
Find h(7).

Answer:

that means it traveled 50 miles in a one hour or 50 mph

Hope This Helps!!!

Answer:

ure def not in high school but elemantarty. Its 50 mph bc 20 divided by 4= 5

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Speed is given by Distance/ Time taken

The Velocity is 7.27m/s in the direction of the runner

Answer:

403909578

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

use a calculator and u will get this answer:)

Answer:

c = 8

Step-by-step explanation:

36/c = 45/10

36 * 10 = 45 * c

360 = 45c

c = 360/45

c = 8

The area of the region enclosed by one loop of the curve r = sin(10θ) is π/40.

We have to find the area of the region enclosed by one loop of the curve.

The given curve is:

r = sin(10θ)

Consider the region r = sin(10θ)

The area of region bounded by the curve r = f(θ) in the sector a ≤ θ ≤ b is

A = \(\int^{b}_{a}\frac{1}{2}r^2d\theta\)

Now to find the area of the region enclosed by one loop of the curve, we have to find the limit by setting r=0.

sin(10θ) = 0

sin(10θ) = sin0   or    sin(10θ) = sinπ

So θ = 0             or      θ = π/10

Hence, the limit of θ is 0 ≤ θ ≤ π/10.

Now the area of the required region is

A = \(\int^{\pi/10}_{0}\frac{1}{2}(\sin10\theta)^2d\theta\)

A = \(\frac{1}{2}\int^{\pi/10}_{0}\sin^{2}10\theta d\theta\)

A = \(\frac{1}{2}\int^{\pi/10}_{0}\frac{(1-\cos20\theta)}{2}d\theta\)

A = \(\frac{1}{4}\int^{\pi/10}_{0}(1-\cos20\theta)d\theta\)

A = \(\frac{1}{4}\left[(\theta-\frac{1}{20}\sin20\theta)\right]^{\pi/10}_{0}\)

A = \(\frac{1}{4}\left[(\frac{\pi}{10}-\frac{1}{20}\sin20\frac{\pi}{10})-(0-\frac{1}{20}\sin20\cdot0)\right]\)

A = \(\frac{1}{4}\left[(\frac{\pi}{10}-\frac{1}{20}\sin2\pi)-(0-\sin0)\right]\)

A = 1/4[(π/10-0)-(0-0)]

A = 1/4(π/10)

A = π/40

Hence, the area of the region enclosed by one loop of the curve r = sin(10θ) is π/40.

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They may require more advanced techniques from dynamical systems theory to fully understand the behavior of the system.

If both eigenvalues of a critical point of a linear system of differential equations in two dimensions are real and equal, the critical point is a degenerate node.

The behavior of the solutions near a degenerate node depends on the higher-order terms in the Taylor series expansion of the vector field around the critical point. Specifically, the critical point is asymptotically stable if the higher-order terms in the Taylor series expansion satisfy certain conditions, and unstable otherwise.

If the higher-order terms in the Taylor series expansion satisfy the so-called "center manifold" conditions, then the critical point is a center, and the solutions near the critical point exhibit periodic behavior.

In general, the classification of a critical point with real and equal eigenvalues can be more complicated than the case where the eigenvalues have different signs, and may require more advanced techniques from dynamical systems theory to fully understand the behavior of the system.

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Answer:

54%

Step-by-step explanation:

2750 is nothing but 54100 if you multiply the numerator and denominator by 2. Now that we have a value over 100, we just have to multiply the entire by 100. The denominator will be canceled, and we're left with 54%

Answer:

54%

Step-by-step explanation:

to find a percentage you must have the denominator (bottom number) that is 100

to get the denominator to 100 you must multiply it by 2

that means you multiply the top and bottom by 2

27 * 2 / 50 * 2

54 / 100

a percentage is a number over 100 and this percentage is 54%

Answer:

7912.8x

Step-by-step explanation:

First do what in the parenthesis (41+3x)=44x

Then what to the left of the ()

2+2.2*46-13=180.2

then multiply what you got in the () to what we just got

180.2*44x=7928.8x

finally we subtract it to the -16x

7928.8x-16x=7912.8x

Based on the information given the gain or loss percent on the whole transaction​ is 2%.

First step is to calculate the profit on the whole transaction

Profit=(8%×8,000)-(4%×8,000)

Profit=640-320

Profit=320

Now let calculate the profit percentage on the whole transaction

Profit percentage=320/(8000+8000)×100

Profit percentage=320/16000×100

Profit percentage=2%

Inconclusion the gain or loss percent on the whole transaction​ is 2%.

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The number of meters of wrapping paper that Alexa bought in all would be 140 meters.

To calculate the total number of meters of wrapping paper that Alexa bought, we need to find the sum of the lengths of the rolls of orange and brown wrapping paper.

For the orange wrapping paper:

Length of orange wrapping paper = 4 rolls x 14 meters/roll

= 56 meters

For the brown wrapping paper:

Length of brown wrapping paper = 6 rolls x 14 meters/roll

= 84 meters

Total length of wrapping paper = Length of orange wrapping paper + Length of brown wrapping paper

= 56 meters + 84 meters

= 140 meters

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Answer:

Hi there!

The correct answer should be: $2.99 per kilogram!

Step-by-step explanation:

17.94 ÷ 6 = 2.99

Answer:

32 cm

Step-by-step explanation:

The volume of the container is:

V= area of the base * the heigth

Since the container has a rectangular base the area of it is:

A = length * width

Let L be the missing length

A = L * 10

V = 10* 25 * L

The container can hold 8 Liters when it's completely full to its brim.

8 liters is 8000 cm^3 ( multiply by 1000)

8000 = 10*25*L

8000 = 250 *L

L = 8000/250

L = 32 cm

v=8litres which is 8 × 1000

l=?

b=10

h=25

since, v=lbh (volume of cuboid)

8000=l × 10 × 25

l=8000/250

l=32

therefore the length is 32cm

Answer:

Step-by-step explanation:

Answer:

given that BC=BD

so LCDB =LCBD=62°=w

now, LCDA=90° because angles made on the circumference of a circle from the end points of the diameter are all 90°

therefore,

x+w=90°

x=90°-w

=90°-62°

=28°

therefore, x=28°

again, we know that the median of a isosceles triangle bisect the angle equally.

therefore, LDCB=2z

now, LDCB =180°-(w+62°)=180°-124°=56°

therefore, LDCB=56°

therefore, 2z=56°

z=28°

now in triangle ADC,

y+(x+w)+z=180°

=>y+90°+28°=180°

=>y=180°-118°

therefore, y=62°

therefore, w=62°,x=28°, y=62° and z=28°

The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.

We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.

If angles QRP and PSQ are supplementary, their sum is 180°:

(2x + 20)° + 30° = 180°

Now, we can solve for x:

2x + 50 = 180

Subtract 50 from both sides:

2x = 130

Divide by 2:

x = 65

Answer:

We need 1.6 liters of the 10 % concentration level and saline solution  and 0.4 liters of the 35 % concentration level and saline solution.

Step-by-step explanation:

Let V₁ be the volume of the 10% concentration saline solution required and V₂ be the volume of 35% concentration saline solution required.

Since mass = concentration × volume, the total mass of the 10% and 35% volume saline solution equal the mass of the 2 liter 15% volume solution.

So, 0.1V₁ + 0.35V₂ = 2 × 0.15

0.1V₁ + 0.35V₂ = 0.3 (1)

Also, the total volume of the 15 % solution must equal 2 liters. So,

V₁ + V₂ = 2 (2)

V₁ = 2 - V₂  (3)

putting equation (3) into equation (1), we have

0.1(2 - V₂) + 0.35V₂ = 0.3

0.2 - 0.1V₂ + 0.35V₂ = 0.3

we now collect terms, so

- 0.1V₂ + 0.35V₂ = 0.3 - 0.2

0.25V₂ = 0.1

we now divide through by 0.25, so

V₂ = 0.1/0.25

V₂ = 0.4   liters  

we now put V₂ into (3), we have,

V₁ = 2 - 0.4  

V₁ = 1.6 liters

So, we need 1.6 liters of the 10 % concentration level and saline solution  and 0.4 liters of the 35 % concentration level and saline solution.

Based on the concept of the slope intercept form, the value of r is 66.

Slope intercept form:

The general formula to calculate the slope intercept form equation is written as,

y = mx + c

where

(x, y) represents the point

m represents  the slope

c represents  the y-intercept.

Given,

Here we know the pair of points (12, 10), (−2, r) and the value of slope which is m = -4.

And we need to find the value of r.

We know that the formula for of the slope intercept form is

y = mx + c

So, we have to use the slope and the point (12, 10), to find the intercept of the line,

When we apply the value on the formula, then we get,

=> 10 = -4(12) + c

=> 10 = -48 + c

=> c = 58

Therefore, the slope intercept form equation is written as

=> y = -4x + 58

Now, we have to find the value of r, by apply the point (-2,r) on the equation, then we get,

=> r = -4(-2) + 58

=> r = 8 + 58

=>r = 66

Therefore, the value of r for the given pair of points is 66.

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Answer:

\(\sqrt{11i}\)

Step-by-step explanation:

x^2-9+20 = 0

x^2+11 = 0

x^2 = -11

x = \(\sqrt{-11} \\\sqrt{11i} \\\)

Answer:

x = 7/5 or x = (-7)/5

Step-by-step explanation:

Solve for x over the real numbers:

49 - 25 x^2 = 0

Multiply both sides by -1:

25 x^2 - 49 = 0

x = (0 ± sqrt(0^2 - 4×25 (-49)))/(2×25) = ( ± sqrt(4900))/50:

x = sqrt(4900)/50 or x = (-sqrt(4900))/50

sqrt(4900) = sqrt(4×25×49) = sqrt(2^2×5^2×7^2) = 2×5×7 = 70:

x = 70/50 or x = (-70)/50

70/50 = 7/5:

x = 7/5 or x = (-70)/50

(-70)/50 = -7/5:

Answer:x = 7/5 or x = (-7)/5

Answer:

(7-5x) (7+5x)

Step-by-step explanation:

49-25x^2

This is the difference of squares

7^2 - (5x)^2

The difference of squares is (a^2 - b^2 = (a-b)(a+b)

(7-5x) (7+5x)

Answer:

-5

Step-by-step explanation:

Answer: f(x)=(x+5)(x-1)

Step-by-step explanation:

got it right on edge

Answer: 82

Step-by-step explanation:

The constant of proportionality between earnings and time in hours is equal to 21.1.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

y = kx

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 274.30/13 = 337.60/16 = 464.20/22

Constant of proportionality (k) = 21.1

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a) Since the coefficient of x2 is negative, MU2 will always be non-negative as long as x2 ≤ 25.

Graphically, if we plot the utility function u(x1, x2) as a three-dimensional surface, it would be challenging to visualize without specific values for x1 and x2. However, we can analyze the partial derivatives at specific points to determine the slope in different directions.

b) The utility value of (22, 10) is higher than (21, 02), so (22, 10) is ranked higher.

c) Given prices P1 = 2, P2 = 1, and income m = -8, the problem becomes:

Maximize: -x1² + 150x1 - 2x2² + 100x2 + x1²²

Subject to: 2x1 + x2 ≤ -8

d) d. To solve the problem, we can use optimization techniques to find the optimal values of x1 and x2 that maximize the utility function while satisfying the budget constraint.

a. To determine if preferences are monotonic, we need to check if the marginal utility of each good is non-negative. The marginal utility of x1 (MU1) is given by the partial derivative of the utility function with respect to x1, and the marginal utility of x2 (MU2) is given by the partial derivative of the utility function with respect to x2.

MU1 = ∂u/∂x1 = -2x1 + 150 + 2x1^2 + 1

MU2 = ∂u/∂x2 = -4x2 + 100

To check for monotonicity, we need to verify if MU1 ≥ 0 and MU2 ≥ 0.

Setting MU1 ≥ 0:

-2x1 + 150 + 2x1^2 + 1 ≥ 0

2x1^2 - 2x1 + 151 ≥ 0

To find the roots of this quadratic equation, we can use the quadratic formula:

x1 = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 2, b = -2, and c = 151. Substituting these values into the quadratic formula, we get:

x1 = (-(-2) ± √((-2)^2 - 4(2)(151))) / (2(2))

x1 = (2 ± √(4 - 1208)) / 4

x1 = (2 ± √(-1204)) / 4

Since the discriminant (√(-1204)) is negative, the roots are complex, which means the quadratic equation does not have real solutions. Therefore, MU1 is not always non-negative.

Setting MU2 ≥ 0:

-4x2 + 100 ≥ 0

-4x2 ≥ -100

x2 ≤ 25

b. To find a bundle that is ranked higher than (21, 02) = (100, 100), we need to find a bundle (x1, x2) that results in a higher utility value than the given bundle.

Substituting (21, 02) into the utility function:

u(21, 02) = -(21^2) + 150(21) - 2(02^2) + 100(02) + (21^2)

= -441 + 3150 - 0 + 0 + 441

= 3150

To find a higher-ranked bundle, we need to increase the utility value. Let's consider the bundle (22, 10):

u(22, 10) = -(22^2) + 150(22) - 2(10^2) + 100(10) + (22^2)

= -484 + 3300 - 200 + 1000 + 484

= 3100

The utility value of (22, 10) is higher than (21, 02), so (22, 10) is ranked higher.

c. The consumer's utility maximization problem can be set up as follows:

Maximize: u(x1, x2) = -x1² + 150x1 - 2x2² + 100x2 + x1²²

Subject to: P1x1 + P2x2 ≤ m

where P1 and P2 are the prices of goods x1 and x2, respectively, and m is the consumer's income.

d. To solve the problem, we can use optimization techniques to find the optimal values of x1 and x2 that maximize the utility function while satisfying the budget constraint.

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Answer:

165

Step-by-step explanation:

First, m<UTS=m<UTV+m<VTS by Angle Addition Postulate.  Then, you substitute all the values that you provided for the angles.  15x+15=x+15+140.  You then solve for x.

15x+15=x+155

14x=140

x=10

You then plug back in 10 for X in the value of m<UTS.  15(10)+15=165

Answer:

Axioms or postulates are universal truths. They cannot be proved. Theorem are statements which can be proved.

The total savings at the end of the third year will be approximately \(\$417,060.15\).

To calculate the total amount saved at the end of the third year, we need to determine the savings accumulated during each period and then sum them.

In the first 15 years, with a monthly savings of \(\$300\)and an annual interest rate of \(3.5\%\), we can use the future value of an ordinary annuity formula:

\(\[A = P \times \left(\frac{(1 + r)^n - 1}{r}\right)\]\)

where:

- \(A\)is the accumulated savings

- \(P\) is the monthly savings amount

- \(r\) is the monthly interest rate (\(3.5\% / 12\))

- \(n\) is the total number of months (15 years x 12 months/year)

Calculating the first 15-year savings:

\(\[A_1 = 300 \times \left(\frac{(1 + \frac{0.035}{12})^{15 \times 12} - 1}{\frac{0.035}{12}}\right)\]\)

In the next 15 years, with a monthly savings of \(\$650\) and an annual interest rate of \(6.5\%\), we can use the same formula:

Calculating the next 15-year savings:

\(\[A_2 = 650 \times \left(\frac{(1 + \frac{0.065}{12})^{15 \times 12} - 1}{\frac{0.065}{12}}\right)\]\)

Finally, to find the total savings at the end of the third year, we sum the accumulated savings from the first and second periods:

\(\[A_{\text{total}} = A_1 + A_2\]\)

To calculate the total savings at the end of the third year, we first need to find the accumulated savings for the two periods.

Calculating the accumulated savings for the first 15 years:

\(\(A_1 = 300 \times \left(\frac{{(1 + \frac{{0.035}}{{12}})^{{15 \times 12}} - 1}}{{\frac{{0.035}}{{12}}}}\right) \approx 68,081.80\)\)

Calculating the accumulated savings for the next 15 years:

\(\(A_2 = 650 \times \left(\frac{{(1 + \frac{{0.065}}{{12}})^{{15 \times 12}} - 1}}{{\frac{{0.065}}{{12}}}}\right) \approx 348,978.35\)\)

Now, we can find the total savings at the end of the third year:

\(\(A_{\text{{total}}} = A_1 + A_2 \approx 68,081.80 + 348,978.35 = 417,060.15\)\)

Therefore, the total savings at the end of the third year will be approximately \(\$417,060.15\).

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If you Saving $300/month for 15 years at 3.5%, then $650/month for another 15 years at 6.5%, will yield approximately $21,628.59 after three years.

To calculate the total amount you will have at the end of the third year, we can follow these steps:

1. Calculate the future value of the first saving period:

Using the formula for compound interest:

\(\[ \text{Future Value} = P \times \frac{{(1 + r)^t - 1}}{r} \]\)

Where:

\(\( P \)\) = Monthly savings amount

\(\( r \)\) = Annual interest rate (as a decimal)

\(\( t \)\) = Time period in years

For the first saving period:

\(\( P = \$300.00 \)\)

\(\( r = 0.035 \)\) (3.5% annual interest rate)

\(\( t = 15 \)\) (years)

Future Value of the first saving period:

\(\[ \text{Future Value} = \$300.00 \times \frac{{(1 + 0.035)^{15} - 1}}{0.035} \]\)

2. Calculate the future value of the second saving period:

For the second saving period:

\(\( P = \$650.00 \)\)

\(\( r = 0.065 \)\) (6.5% annual interest rate)

\(\( t = 15 - 3 = 12 \)\) (remaining years after the first saving period)

Future Value of the second saving period:

\(\[ \text{Future Value} = \$650.00 \times \frac{{(1 + 0.065)^{12} - 1}}{0.065} \]\)

3. Calculate the total future value at the end of the third year:

Total Future Value = Future Value of the first saving period + Future Value of the second saving period

The calculations for the total amount you will have at the end of the third year are as follows:

Future Value of the first saving period:

\(\[ \text{Future Value of the first saving period}\) = \(\$300.00 \times \frac{{(1 + 0.035)^{15} - 1}}{{0.035}} \approx \$7,648.63\)

Future Value of the second saving period:

\(\[ \text{Future Value of the second saving period}\) = \(\$650.00 \times \frac{{(1 + 0.065)^{12} - 1}}{{0.065}} \approx \$13,979.96\)

Total Future Value at the end of the third year:

\(\[ \text{Total Future Value}\) = \(\text{Future Value of the first saving period} + \text{Future Value of the second saving period}\)

\(\[ \approx \$7,648.63 + \$13,979.96 \approx \$21,628.59 \]\)

Therefore, If you Saving $300/month for 15 years at 3.5%, then $650/month for another 15 years at 6.5%, will yield approximately $21,628.59 after three years.

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0.8133 is the probability  that a randomly chosen test taker will score between 560 and 640.

Probability is the possibility that something will happen, to put it simply. We can talk about the chance or likelihood of various outcomes when we don't know how an event will turn out. Events that follow a probability distribution are the subject of statistics.

Probability is a branch of mathematics that deals with numerical representations of how likely it is for an event to occur or for a proposition to be true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates that the event is impossible and 1 indicates certainty.

P(540< x 640)

=  P ( \(\frac{560 - 560}{90}\) < \(\frac{x - mu}{sigma}\) < \(\frac{640-560}{90}\) )

By resolving this, we will obtain a probability ranging from zero to triple zero. Therefore, the likelihood will be zero. Less than zero 89 minutes our chance of being zero is zero. The values are now zero 8133 -0.5 triple zero when utilizing the table. And if we take it out, we get 0.31 33. Therefore, our likelihood of facts here ranges from 5 to 6 40. Its double three at 0.31. Therefore, this is the response to your query.

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Answer

Step by step explanation

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Given:

A jet flies 175 miles in 7 minutes.

To find:

How far will the jet fly in 85 minutes?

Solution:

According to the given information,

Distance covered by the jet in 7 minutes = 175 miles

Using this, we get

Distance covered by the jet in 1 minutes = \(\dfrac{175}{7}\) miles

Distance covered by the jet in 1 minutes = \(25\) miles

Now,

Distance covered by the jet in 85 minutes = \(85\times 25\) miles

Distance covered by the jet in 85 minutes = \(2125\) miles

Therefore, the jet flies 2125 miles in 85 minutes.