The angle measurements in the diagram are represented by the following expressions.
Solve for X then find the measurement of ∠A:

Answer:

[tex]y=Ae^{-2x}[/tex]

Step-by-step explanation:

Given that the functions f(x) that have the property that the tangent lines to the graphs of f(x)pass through the point (x+2,0).

Let (x,y) be any arbitrary point of contract

The tangent line passes through two points (x,y) and (x+2,0)

Slope of tangent line = f'(x) = change in y/change in x= [tex]\frac{-y}{2}[/tex]

i.e. we have

[tex]\frac{dy}{dx} =\frac{-y}{2}[/tex]

Separate the variables

[tex]\frac{dy}{y} =-2x\\lny =-2x+c[/tex]

Raise to power e

[tex]y=Ae^{-2x}[/tex]

Thus the functions would have the above form for various values of A

The inclination angle is 10°

Step-by-step explanation:

The given scenario forms a right angled triangle where the length of ramp is hypotenuse and the rise of ramp is the perpendicular

Given

H = 4.2m

P = 0.7m

We have to use the trigonometric ratios to find the angle. The ratio that has to be used should involve both perpendicular and hypotenuse

Let x be the angle

then

[tex]sin\ x = \frac{P}{H}\\sin\ x = \frac{0.7}{4.2}\\sin\ x = 0.1666\\x = sin^{-1} (1.666)\\x = 9.59 => 10[/tex]

Hence,

The inclination angle is 10°

Keywords: Trigonometric ratios, Right angled triangle

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The angle of inclination of the wheelchair ramp to the nearest degree is 9 degrees.

[tex]\[ \theta = \arctan\left(\frac{\text{rise}}{\text{run}}\right) \][/tex]

Given the rise of the ramp is 0.7 m and the run (length) is 4.2 m, we can plug these values into the formula:

[tex]\[ \theta = \arctan\left(\frac{0.7}{4.2}\right) \][/tex]

Now, we calculate the value of θ:

[tex]\[ \theta = \arctan\left(\frac{1}{6}\right) \][/tex]

Using a calculator, we find:

[tex]\[ \theta \approx \arctan(0.1667) \] \[ \theta \approx 9.4623 \text{ degrees} \][/tex]

Rounding to the nearest degree, we get:

[tex]\[ \theta \approx 9 \text{ degrees} \][/tex]

Therefore, the angle of inclination of the wheelchair ramp is approximately 9 degrees to the nearest degree.

Answer:

[tex]p(x)= -\frac{1}{10}x + 685[/tex]

Step-by-step explanation:

Since, Function of demand is the linear function of quantity.

Let x represents the quantity and p represents the price of each unit.

∵ Manufacture has been selling 1450 television sets a week at $540 each,

i.e. [tex](x_1, p_1) = (1450, 540)[/tex]

Also, for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.

i.e. [tex](x_2, p_2) = (1580, 527)[/tex]

Thus, the linear equation of the price,

[tex]p-p_1 = \frac{p_2-p_1}{x_2-x_1}(x-x_1)[/tex]

[tex]p-540 = \frac{527 - 540}{1580-1450}(x-1450)[/tex]

[tex]p-540 = -\frac{13}{130}(x-1450)[/tex]

[tex]p-540 = -\frac{1}{10}(x-1450)[/tex]

[tex]p = -\frac{1}{10}x + 145 + 540[/tex]

[tex]\implies p = -\frac{1}{10}x + 685[/tex]

Hence, the function representing price as a function of the demand is,

[tex]p(x)= -\frac{1}{10}x + 685[/tex]

Answer:  54 mph

Step-by-step explanation:

Speed x Time = Distance

So, Speed = Distance/Time

Speed = 324 miles/6hrs = 54 mph

To calculate the area between the birth rate and death rate curves for a given time interval, find the net growth rate function by subtracting the death rate from the birth rate, and then integrate this function over the time interval. The result reflects the population surge due to the rates of births and deaths.

The student's question involves calculating the area between two exponential growth curves, birth rate and death rate, over a given time interval. To find the area between the curves b(t) = 2300e0.024t and d(t) = 1450e0.019t from t = 0 to t = 10, we need to integrate the difference between them with respect to time over the given interval.Step-by-step Solution:

Subtract the death rate from the birth rate to get the net growth rate function: g(t) = b(t) - d(t) = 2300e0.024t - 1450e0.019t.

Integrate the net growth rate function with respect to t from 0 to 10 to find the total area.

Use a calculator or computer software to perform the integration and round the final answer to the nearest integer.

This computation will give the total number of people added to the population over the 10-year period, which reflects the population surge resulting from the different rates of increase in births and deaths.

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m=16t can be used to determine the distance in miles Han has gone after t hours.

Step-by-step explanation:

Speed of Han = 16 miles per hour

Let,

m be the distance covered by Han in miles;

t be the number of hours Han has been biking,

According to formula,

Distance = Speed*Time

[tex]m=16*t\\m=16t[/tex]

m=16t can be used to determine the distance in miles Han has gone after t hours.

Keywords: distance, speed

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Answer:

y = mx + b ( y = 16t + 0

Step-by-step explanation:

Answer:

(a) The ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7  \times (-1)^{n-1}\\[/tex].

Step-by-step explanation:

Here, the given sequence is 7, -7, 7, -7, ...

The first term = 7, Second term = -7, Third term =-7 and so on..

Now check the given sequence for each given formula, we get:

(1)  [tex]a_n = 7  \times (-1)^{n-1}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (-1)^{1-1}\\[/tex]

                                       [tex]= 7 \times (-1)^0 =  7 \times 1 = 7 \implies a_1 = 7[/tex]

Similarly, for, n = 2:  [tex]a_2 = 7  \times (-1)^{2-1}\\[/tex]

                                       [tex]= 7 \times (-1)^1 =  7 \times (-1) = -7 \implies a_2 = -7[/tex]

Hence, the given formula satisfies the given sequence.

(2)  [tex]a_n = 7  \times (-1)^{n}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (-1)^{1}\\[/tex]

                                       [tex]= 7 \times (-1)^1 =  7 \times (-1) = -7 \implies a_1 = -7[/tex]

But, First term = 7

Hence, the given formula DO NOT satisfy the given sequence.

(3)  [tex]a_n = 7  \times (1)^{n-1}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (1)^{1-1}\\[/tex]

                                       [tex]= 7 \times (1)^0 =  7 \times 1 = 7 \implies a_1 = 7[/tex]

Similarly, for, n = 2:  [tex]a_2 = 7  \times (1)^{2-1}\\[/tex]

                                       [tex]= 7 \times (1)^1 =  7 \times (1) = 7 \implies a_2 = 7[/tex]

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

(4) [tex]a_n = 7  \times (1)^{n+1}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (1)^{1+1}\\[/tex]

                                       [tex]= 7 \times (1)^2 =  7 \times 1 = 7 \implies a_1 = 7[/tex]

Similarly, for, n = 2:  [tex]a_2 = 7  \times (1)^{2+1}\\[/tex]

                                       [tex]= 7 \times (1)^3 =  7 \times (1) = 7 \implies a_2 = 7[/tex]

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

So, the ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7  \times (-1)^{n-1}\\[/tex].

Answer:

an=7•(-1)^n-1

Step-by-step explanation:

Answer:

I will forward the challenge to the ISCAP.

Step-by-step explanation:

If the classifying agency does not provide a full response within 120 days, then as per my responsibility, I will forward the challenge to the ISCAP.

ISCAP is the Inter agency security classification appeals panel.

ISCAP is a deciding panel that decides on certain classification or declassification issues to its users, with a forum for further review.

Answer:

test statistic (Z) is 2.5767 and p-value of the test is .009975

Step-by-step explanation:

[tex]H_{0}[/tex]: percentage of students who smoke did not change

[tex]H_{a}[/tex]: percentage of students who smoke has changed

z-statistic for the sample proportion can be calculated as follows:

z=[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where

Then, z=[tex]\frac{0.25-0.18}{\sqrt{\frac{0.18*0.82}{200} } }[/tex] ≈ 2.5767

What is being surveyed is if the percentage of students who smoke has changed over the last five years, therefore we need to seek two tailed p-value, which is .009975.

This p value is significant at 99% confidence level. Since .009975 <α/2=0.005, there is significant evidence that the percentage of students who smoke has changed over the last five years

Answer:

5^20

Step-by-step explanation:

For each comic book, there are five different choices for which kid will receive that comic book. 20 decisions are made, one for each comic book with five different possibilities for each choice. The number of ways to distribute the comic books to the five kids is 5^20.

Final answer:

The formula for distributing 20 comic books among five kids with no restrictions is C(24, 5) = 42,504 ways.

Explanation:

To distribute the 20 comic books to five kids with no restrictions on how many each kid receives, we can use the concept of distributing identical items among distinct groups.

The number of ways to distribute the comic books in this scenario is represented by the formula: C(n+r-1, r) where n is the number of items (in this case, 20 comic books) and r is the number of groups (5 kids).

Therefore, the number of ways to distribute the comic books to the five kids is: C(20+5-1, 5) = C(24, 5) = 42,504 ways.

Answer:

x = 7.8

Step-by-step explanation:

If AE is parallel to BD, then you can use the theorem called ratio of sides of parallel line.

AC/AB = EC/ED

x+11/x = 12/5

x=7.8

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of the unknown sides will be equal to 7.857 units.

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

For the two similar triangles, ΔAEC and ΔBDC, the ratio of the sides will be,

11/7 = (11+x)/(5+7)

11/7 = (11+x)/12

(11×12)/7 = 11+x

18.857 - 11 = x

x = 7.857

Hence, the length of the unknown sides will be equal to 7.857 units.

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Answer:

y-intercept: when x = 0

For Line A:

y = 0 + 7 = 7

For line B:

when x = 0, the value is -5

7 > -5, so y-intercept of line A is greater than line B's.

Answer:

15.5 yards

They will be picked up at an elevation of 15.5 yards

Step-by-step explanation:

Here we are going to make the ski slope of the mountain as the hypotenuse of a right-angled triangle where the top of the slope and bottom of the slope are two ends of the hypotenuse.

We first have to find the height of the top of the mountain with respect to the bottom.

Here we have been given heights with respect to sea level above and below.

Clearly, sum of the distances above and below sea level will be total elevation with respect to the bottom.

h1 - Height of summit above sea level

h2 - Height of bottom below sea level

Hb - Elevation of top w.r.t bottom

Hb = h1 + h2

Hb = [tex]17\frac{3}{4}+13\frac{1}{4}[/tex]

Hb = 31 yards

Now, the ski lift is picking them up in the middle of the slope (hypotenuse of the triangle).

By midpoint theorem line segment parallel to base joins the midpoints of the other 2 sides.

Thus the elevation will clearly be half of total elevation.

Height at which they are picked up is Hb/2

Therefore,

They will be picked up at an elevation of 15.5 yards

Answer:

Option C.

Step-by-step explanation:

Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes.

              Pumpkin bread           zucchini bread                Total

Eggs               2                                     3                           15        

Flour(cups)     3                                     4                           16

Selling price    $5                                  $4

Susan wants to maximize the money raised at the bake sale.

Objective function :

[tex]P=5x+4y[/tex]

Subject to constraints:

[tex]2x+3y\leq 15[/tex]

[tex]3x+4y\leq 16[/tex]

[tex]x,y \geq 0[/tex]

Since the objective function is P = 5x + 4y, therefore the correct option is C.

Answer:

c

Step-by-step explanation:

i got it correct on edgenunity

Answer: The inner diameter of the ring is 16 mm.

Step-by-step explanation:

As we know that ,

Circumference of a circle = [tex]\pi d[/tex] , where d = diameter of the circle .

We are given that ,

The circumference of the outside of a ring is 66 mm and it has an outer diameter of 21 mm .

Now , if circumference of the inside the ring is 50 mm, then we have

[tex]50 = \pi d[/tex] , where d= diameter of the inner circle .

Then , [tex]d=\dfrac{50}{\pi}=\dfrac{50}{\dfrac{22}{7}}=\dfrac{50\times7}{22}\approx15.909090909\approx16\text{ mm}[/tex]

Hence , the inner diameter of the ring is 16 mm.

The diameter of the inner ring is 15.92mm

The formula for calculating the circumference of a circle is expressed as:

C = πd

d is the diameter

Given the following parameters

C = 50mm

The diameter of the inner ring is given as:

d = C/π

d = 50/3.14
d = 15.92mm

Hence the diameter of the inner ring is 15.92mm

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Answer:

b) 9

Step-by-step explanation:

Given: Three machines  operating independently, simultaneously, and at the same constant rate can fill a certain production order in [tex]36[/tex] hours.

To Find: If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled.

Solution:

Let  the time taken by one machine to fill a certain production alone be[tex]=\text{x}[/tex]

Time taken when three machine operate independently and simultaneously

[tex]\frac{1}{\text{x}}+\frac{1}{\text{x}}+\frac{1}{\text{x}}=\frac{1}{36}[/tex]

[tex]\frac{3}{\text{x}}=\frac{1}{36}[/tex]

[tex]\text{x}=108[/tex] [tex]\text{hours}[/tex]

Let time taken when one additional machine is used [tex]=\text{y}[/tex]

Time when when one additional machine is used

[tex]\frac{1}{108}+\frac{1}{108}+\frac{1}{108}+\frac{1}{108}=\frac{1}{\text{y}}[/tex]

[tex]\frac{4}{108}=\frac{1}{\text{y}}[/tex]

[tex]\text{y}=27[/tex] [tex]\text{hours}[/tex]

it takes [tex]27[/tex] [tex]\text{hours}[/tex] when one additional machine is used

Now,

fewer hours taken when one additional  machine is used

[tex]=\text{number of hours taken when three machines are used}-[/tex][tex]\text{number of hours taken when one additional machine is used}[/tex]

[tex]36-27[/tex]

[tex]9[/tex] [tex]\text{hours}[/tex]

in [tex]9[/tex] fewer hours of simultaneous operation the production order can be filled if one additional machine is used

Hence option b) is correct.

Answer:

Step-by-step explanation:

The function goes up to the right until it gets to the vertex at x=0. Then it goes down to the right. That is, it is ...

  increasing from -∞ to 0 (not including 0)

  decreasing from 0 to +∞ (not including 0)

_____

At x=0, the function is neither increasing nor decreasing, so x=0 is not part of either interval.

Answer:

Step-by-step explanation:

Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. This means that

1 gallon of gas would be used to drive 392/14 = 28 miles

a) The number of miles traveled varies directly with the number of gallons of gas used.

Let x =number of gallons of gas you use.

Let y = the number of miles travelled.

Since y varies directly with x, we will introduce a constant of proportionality, k. Therefore,

y = kx

If 28 miles will require 1 gallon of gas, it means

28 = 1×k

k = 28

So y = 28x

b) we want to determine how far you can drive with 3.7 gallons of gas.

x = 3.7

y = 28x = 28×3.7

y = 103.6 miles

Answer:

You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.

Step-by-step explanation:

Calculation

M = 0.96

Z = 1.96

sM = √(0.96)^2/25) = 0.19

μ = M ± Z(sM)

μ = 0.96 ± 1.96*0.19

μ = 0.96 ± 0.3763

Result

M = 0.96, 95% CI [0.5837, 1.3363].

You can be 95% confident that the population mean (μ) falls between 0.5837 and 1.3363.

Answer:

C

Step-by-step explanation:

Rearranging x - y ≤ 2

- y ≤ 2 - x ( multiply through by - 1 )

y ≥ - 2 + x ← change direction of inequality symbol

This region is above the yellow line

y ≥ 0 is above the x- axis

x ≥ 0 is to the right of the y- axis

Thus the solution is the indicated blue region

The inequalities from C satisfy the given graph

Answer:

$9.50

Step-by-step explanation:

Solution is in the attachment . You can see it.

Answer:

Step-by-step explanation:

There are at least a couple of ways you could go at this. Here, we'll use an area formula to find m∠A, then use the law of cosines to find BC. Using BC, we can use the law of sines to find another angle.

  Area = (1/2)·AB·AC·sin(∠A)

  65·2/(12·17) = sin(∠A) ≈ 65/102

  ∠A = arccos(65/102) ≈ 39.587°

From the law of cosines, ...

  BC² = AB² +AC² -2·AB·AC·cos(∠A)

  BC² = 12² +17² -2·12·17·cos(39.587°) ≈ 118.5735

  BC ≈ √118.5735 ≈ 10.889

Then ∠C can be found from the law of sines:

  sin(∠C)/AB = sin(∠A)/BC

  ∠C = arcsin(AB/BC·sin(∠A)) ≈ 44.609°

The measure of ∠B will be the angle that makes the total be 180°:

  39.587° +∠B +44.609° = 180°

  ∠B = 95.804°

_____

There is actually another solution, in which ∠A is obtuse. We thought the diagram showed an acute triangle, so we didn't investigate the other alternative. The above calculations show the triangle is obtuse in any event.

See the second attachment for the other solution.

Answer:

3. [tex]\displaystyle 1\frac{1}{3} = x[/tex]

2C. [tex]\displaystyle III.[/tex]

2B. [tex]\displaystyle I.[/tex]

2A. [tex]\displaystyle II.[/tex]

1. [tex]\displaystyle Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]

Step-by-step explanation:

3. See above.

2C. The keyword is ratio, which signifies division, so you would choose "III.".

2B. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".

2A. The keyword is total, which signifies addition, so you would choose "II.".

1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:

[tex]\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)[/tex]

I am joyous to assist you anytime.

We found the domain restrictions of a rational expression by checking the values that make the denominator zero. A formula was suggested to calculate Sara's future percentage score. To solve the third equation, a common denominator was found and used to simplify the expression.

1. The domain restrictions for the rational expression 14x-2x/x^2-7x are all real numbers except for the numbers which make the denominator zero. Solving the equation x^2-7x=0, we get x=0 or x=7. Therefore, the domain restrictions are x≠0 and x≠7.

2. There is no picture provided but generally, to calculate the future percentage score given the current percentage score, total points possible, and future total points, you would use the formula (current score/current total points) * 100% + (future score/future total points) * 100%.

3. To solve for x in the equation 3 / (x+2) - 1 / x = 1 / (5x), we first need to find a common denominator. In this case, it would be 5x^2 + 10x. Multiplying each term by the common denominator and simplifying would then give the value of x.

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Answer:

the answer is 17.7

Step-by-step explanation:

Apply tanθ =  

opposite

adjacent

tanθ =  

7

22

θ = tan−1(

7

22

)

θ = 17.7°

The angle the ladder that will make with the wall is 17.7°.

What is tangent of an angle?

Tangent of the angle is the ratio between the opposite side and adjacent side of the angle in the right angle triangle.

So according to the asked question,

the distance between lader foot and the wall  is 7feet.

the height of the wall is 22feet.

So in triangle ΔABC ,

the height of the wall =AB=22feet

the distance between lader foot and the wall=BC=7feet

∠ABC=90°

the angle between the ladder and the wall= ∠BAC=θ

So in ΔABC,

tan ∠BAC=tan θ=BC/AB

⇒tan θ=7/22

⇒θ=tan⁻¹(7/22)

⇒θ=17.7⁰

Therefore the angle the ladder that will make with the wall is 17.7°.

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they use 12 oranges

4•4=16-4=12 which is 3 of the 4/4

The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges.

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

In another word, the fraction is the division of the two numbers but the division is not wholly complete.

As per the given,

They make orange juice using 3/4 of the oranges.

3/4 of 16

(3/4)16 = 3 x 4 = 12 oranges

Hence "The fraction 3/4 of 16 will be the number of oranges and it will be the 12 oranges".

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Answer:

c. probably understates the percent of people who favor a system of national health insurance.

Answer:

Cube.

Step-by-step explanation:

We are asked to find the solid figure, which has congruent squares on all six sides.

We know that a solid, whose length, width, and height are equal in measure is known as cube.

Upon looking at our attached file, we can see that length, width, and height for the solid are equal to x units, which makes its each face a square.

We know that a cube is a three dimensional figure, which contains six equal squares of all six sides.

Therefore, cube has congruent squares on all six sides.

Answer:

120 calories and 9 grams of fiber.

Step-by-step explanation:

We are told that 1/3 cup serving contains 80 calories and 6 grams of fiber.

Let's multiply everything by 3. So,

1 cup serving has 3*80 = 240 calories and 3*6 = 18 grams of fiber.  

But, we want to really know about 1/2 cup. So, now we multiply everything by 1/2.  

1/2 cup has (1/2) (240) = 40 calories and (1/2) (18 grams) = 9 grams of fiber.

Answer:

240 calories and 9 grams of fiber

Step-by-step explanation:

Answer:

0.0421

Step-by-step explanation:

Mean(μ) = 12.00 oz

Standard deviation (σ) = 0.11 oz

Z = (x - μ)/σ

Z = (12.19 - 12.00) / 0.11

Z= 0.19/0.11

Z = 1.727

From the normal distribution table, Z = 1.727 = 0.4579

Φ(Z) = 0.4579

Recall that if Z is positive

Pr(x>a) = 0.5 - Φ(Z)

Pr(x > 12.19) = 0.5 - 0.4579

= 0.0421

Answer:

1 : -1

2:2

3:-5

4: 1/2

5: -3

6: -3/2

7: 1/2

8: -1/2

9: 1

10: 1/3

Step-by-step explanation:

well all u have to do is do rise over run, rise/run. find 2 points and go up according to how much it goes up and go left or right based on the graph. AND sometimes the slope will be negative like number 1.