Please help me out please

Answer:

1. [tex]\boxed{y=x^2+16\to138sq.\:units}[/tex]

2. [tex]\boxed{y=-x^2+7x\to42sq. \:units}[/tex]

3. [tex]\boxed{y=4x+26\to 204sq.\:units}[/tex]

4.[tex]\boxed{y=-0.5x+13\to72sq.\:units}[/tex]

Step-by-step explanation:

1. The first curve is [tex]y=x^2+16[/tex]

The area under this curve on the interval [-1, 5] is given by:

[tex]\int\limits^5_{-1} {x^2+16} \, dx[/tex]

We integrate to obtain:

[tex]\frac{1}{3}x^3+16x|_{-1}^5[/tex]

We evaluate to obtain:

[tex]\frac{1}{3}(5)^3+16(5)-(\frac{1}{3}(-1)^3+16(-1))=138sq.\:units[/tex]

[tex]\boxed{y=x^2+16\to138sq.\:units}[/tex]

2. The second curve is [tex]y=-x^2+7x[/tex].

The area under this curve on the interval [-1, 5] is given by:

[tex]\int\limits^5_{-1} {-x^2+7x} \, dx[/tex]

We integrate this function to obtain:

[tex]-\frac{1}{3}x^3+\frac{7}{2}x^2|_{-1}^5[/tex]

This evaluates to

[tex]-\frac{1}{3}(5)^3+\frac{7}{2}(5)^2-(-\frac{1}{3}(-1)^3+\frac{7}{2}(-1)^2)=42[/tex] square units.

[tex]\boxed{y=-x^2+7x\to42sq. \:units}[/tex]

3.  The third curve is [tex]y=4x+26[/tex]

The area under this curve on the interval [-1, 5] is given by:

[tex]\int\limits^5_{-1} {4x+26} \, dx[/tex]

We integrate this function to obtain:

[tex]2x^2+26x|_{-1}^5[/tex]

We evaluate the limits of integration to obtain:

[tex]2(5)^2+26(5)-(2(5)^2+26(5))=204sq.\:units[/tex]

[tex]\boxed{y=4x+26\to 204sq.\:units}[/tex]

4. The fourth curve is [tex]y=-0.5x+13[/tex]

The area under this curve on the interval [-1, 5] is given by:

[tex]\int\limits^5_{-1} {-0,5x+13} \, dx[/tex]

We integrate this function to obtain:

[tex]-0.25x^2+13x|_{-1}^5[/tex]

We evaluate the limits of integration to obtain:

[tex]-0.25(5)^2+13(5)-(-0.25(-15)^2+13(-1))=72sq.\:units[/tex]

[tex]\boxed{y=-0.5x+13\to72sq.\:units}[/tex]

Answer: OPTION D

Step-by-step explanation:

You need to remember this property:

[tex]\frac{\sqrt{x} }{\sqrt{y} }=\sqrt{\frac{x}{y} }[/tex]

And remember that:

[tex]\frac{a}{a}=1[/tex]

Then, the first step is rewrite the expression:

[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^2}}[/tex] [tex]=\sqrt{\frac{30(x-1)}{5(x-1)^2}} }[/tex]

Now, to find the corresponding equivalent expression, you need to simplify the expression.

Therefore, the equivalent expression is the following:

[tex]\sqrt{\frac{6}{(x-1)}} }[/tex]

Finally, you can observe that this matches with the option D.

Answer:

Choice D

Step-by-step explanation:

The division of the two radicals can be re-written in the following format;

[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^{2} } }[/tex]

Using the properties of radicals division, the expression can further be written as;

[tex]\sqrt{\frac{30(x-1)}{5(x-1)^{2} } }[/tex]

We simplify the terms under the radical sign to obtain;

[tex]\sqrt{\frac{6}{x-1} }[/tex]

Choice D is thus the correct solution

Answer:

D

Step-by-step explanation:

The formula for volume of cone is  [tex]V=\frac{1}{3}\pi r^2 h[/tex]

Where

V is the volume

r is the radius of the circular base

h is the height of the cone

In the diagram shown, we can clearly see that height is 12, radius is 9. We can simply plug them into the formula and get our exact answer (leaving pi as pi):

[tex]V=\frac{1}{3}\pi (9)^2(12)\\=324 \pi[/tex]

correct answer is D

The situation that can be modeled by the given inequality is required.

Option D. is correct.

Let [tex]x[/tex] be the number of T shirts bought

The initial amount of money is $50

The savings should be at least $8 so more than or equal to $8.

The required inequality is [tex]50-12x\geq 8[/tex]

The inequalities of the other options that are not correct are

C. [tex]50-12x<8[/tex]

Here, [tex]x[/tex] is number of weeks

B. [tex]50-12x\geq 8[/tex]

Here [tex]x[/tex] is the number of packages bought.

So, [tex]12x[/tex] will be the total number of pretezels[/tex]

A. [tex]50-8x<12[/tex]

Here [tex]x[/tex] is the number of weeks.

So, option D. is correct.

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Answer:

Step-by-step explanation:

We know a maximum point on the height vs. time curve is at t=16 seconds. Then the height function can be written by filling in the known values in ...

  h(t) = (center height) + (wheel radius)·cos((frequency)·2π·(t -(time at max height)))

Since t is in seconds, we want the frequency in revolutions per second. That will be ...

  (3.2 rev/min)·(1 min)/(60 sec) = 3.2/60 rev/sec = 4/75 rev/sec

Then our height function is ...

  h(t) = 59 + 45·cos(8π/75·(t -16))

9 minutes is 9·60 sec = 540 sec, so we want to find the value of h(540).

  h(540) = 59 + 45·cos(8π/75·(540 -16))

  = 59 +45·cos(4192π/75)

  ≈ 59 + 45·0.944376 . . . . . calculator in radians mode

 ≈ 101.496937 . . . . feet

_____

The cosine function is a maximum when its argument is zero. We used the process of function translation to translate the maximum point to t=16 from t=0. That is, we replaced t in the usual cosine function with (t-16).

We can also evaluate the cosine function by subtracting multiples of 2π from the argument. When we do that, we find that Shirley's height at 9 minutes is the same as it is after 15 seconds. Some calculators evaluate smaller cosine arguments more accurately than they do larger argument values.

Answer:

the final answer is 50/11

Step-by-step explanation:

Here let's regard the first number of this geometric series as 0.54, holding the 4 to include later.  The next is 0.0054, the next 0.000054, and so on.

Thus, the common ratio is 1/100.  Then the sum of the infinite series, not including that 4, is

   a          0.54        0.54

-------- = ------------ = ------------

 1 - r       1 - 1/100     99/100

                                                                                      54

Multiplying both 0.54 and 99/100 by 100 results in ------- and this

                                                                                        99     0.545454....

Now add the 4 back in, obtaining 4  54/99, or (396 + 54) / 99.

This is the same as 450 / 99.  You can readily check with a calculator to see whether this is equivalent to the given   4.54545454545...

Note that 450/99 is in the form p/q (not pq), where p and q are positive integers.  But also note that 450/99 can be reduced to 150/33, or

50/11.  A calculator will show you that 50/11 is equivalent to the given   4.54545454545...

Hence, the final answer is 50/11 (in the form p/q, NOT pq).

The number 4.54545454545... can be expressed as a rational number in the form of p/q as 50/11.

To express the given number 4.54545454545... as a rational number in the form p/q, we need to use the concept of repeating decimals.

Let x = 4.54545... We can then write 100x = 454.54545... Subtracting the first equation from the second, we get 99x = 450. Solving for x gives us x = 450/99.

This fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor. In this case, 450 and 99 share a common factor of 9. Dividing both numbers by 9 gives us 50/11, which is the simplest form of this fraction.

Therefore, 4.54545454545... as a rational number in the form p/q is 50/11.

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Answer:

C) y = -cos(x) +2

Step-by-step explanation:

The centerline is 2, so 2 is added. That leaves out choices A and B.

There is a minimum (not a maximum) at x=0, so the multiplier is negative, eliminating choice D.

The correct equation is that of C: y = -cos(x) +2.

Answer:

Option a - $9,314.45

Step-by-step explanation:

Cost of the house = $268,500

Time of repayment = 30 years

Repayment is done monthly, so number of repayments = 30 X 12 = 360

Monthly Payment = $1595.85

Rate of interest per payment period = [tex]\frac{.0625}{12}[/tex]

So, Present value of monthly payments = 1595.85 X  [tex]\frac{(1+\frac{.0625}{12})^{360}-1}{(1+\frac{.0625}{12})^{360}*(\frac{.0625}{12})}[/tex]

= $259,185.55

So, Vanessa's down payment = $268,500 - $259,185.55 = $9,314.45

Hope it helps.

Thank you !!

Answer:

Option a - $9,314.45

Step-by-step explanation:

e d g e

Answer:

C

Step-by-step explanation:

Since EF and GH are parallel lines then

∠EGF = ∠GFH = 60° ( Alternate angles )

Answer: 20,000

Step-by-step explanation:

every 30 years 10,000 adds to the population

30 years=10,000 people        

60 years=20,000 people

Answer:

The height of the cone is [tex]48\ in[/tex]

Step-by-step explanation:

step 1

Find the radius of the base of cone

we know that

The volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]V=12,288\pi\ in^{3}[/tex]

[tex]tan(30\°)=\frac{r}{h}[/tex]  ---> remember that the vertex angle of the vertical cross section is 60 degrees

so

[tex]r=(h)tan(30\°)[/tex]

[tex]r=(h)\frac{\sqrt{3}}{3}[/tex]

substitute the values and solve for h

[tex]12,288\pi=\frac{1}{3}\pi ((h)\frac{\sqrt{3}}{3})^{2} h[/tex]

[tex]36,864=\frac{h^{3}}{3}[/tex]

[tex]h^{3}=110,592[/tex]

[tex]h=48\ in[/tex]

Your Right It Is Irrational

Answer:

B) 10.6 cubic inches

Step-by-step explanation:

Vol = (1/3) base area × hight = (1/3)π×1.5²×4.5

ANSWER

x coordinates of the intersection points

EXPLANATION

The given system of equations is:

[tex]y = 4 {x}^{2} - 3x + 6[/tex]

[tex]y = 2 {x}^{4} - 9 {x}^{3} + 2x[/tex]

We want to use the graph of these functions to solve

[tex] 4 {x}^{2} - 3x + 6 = 2 {x}^{4} - 9 {x}^{3} + 2x [/tex]

The point of the intersection of the graph gives the solution to the simultaneous equation above.

Hence the x-coordinates of the intersection points gives the solution set of

[tex]4 {x}^{2} - 3x + 6 = 2 {x}^{4} - 9 {x}^{3} + 2x [/tex]

The last choice is correct.

Answer: It's D

Step-by-step explanation:

Answer:

3.9230231e+12

Step-by-step explanation:

15! is 15 times 14 times 13 times 12 times 11 times 10 times 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 then times 3 because 3 shades of blue.

The number of different ways to purchase 3 shades of blue from 15 options is 455 different ways.

The question is asking about the number of combinations of 3 shades of blue that can be chosen from a total of 15 different shades. To calculate this, we use the formula for combinations without repetition, which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items to choose from, and k is the number of items to choose. In this case, n is 15 and k is 3.

First, we calculate the factorial of n, which is 15! (15 factorial), then the factorial of k, which is 3!, and finally the factorial of n - k, which is 12!. Putting these into the formula gives us:

C(15, 3) = 15! / (3! * 12!) = (15 * 14 * 13) / (3 * 2 * 1) = 455

Therefore, there are 455 different ways to choose 3 shades of blue from 15 different shades.

Use the form  

a

cos

(

b

x

−

c

)

+

d

acos(bx-c)+d

to find the variables used to find the amplitude, period, phase shift, and vertical shift.

a

=

4

a=4

b

=

3

b=3

c

=

π

4

c=π4

d

=

0

d=0

Find the amplitude  

|

a

|

|a|

.

Amplitude:  

4

4

Find the period using the formula  

2

π

|

b

|

2π|b|

.

Tap for more steps...

Period:  

2

π

3

2π3

Find the phase shift using the formula  

c

b

cb

.

Tap for more steps...

Phase Shift:  

π

12

π12

Find the vertical shift  

d

d

.

Vertical Shift:  

0

0

List the properties of the trigonometric function.

Amplitude:  

4

4

Period:  

2

π

3

2π3

Phase Shift:  

π

12

π12

(

π

12

π12

to the right)

Vertical Shift:  

0

0

i think ;-;

Answer:

[tex]\frac{\pi }{4}[/tex]

Step-by-step explanation:

The standard form of the cosine function is

y = a cos(bx + c)

where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and

phase shift = - [tex]\frac{c}{b}[/tex]

here b = 3 and c = - [tex]\frac{3\pi }{4}[/tex], hence

phase shift = - [tex]\frac{-\frac{3\pi }{4} }{3}[/tex] = [tex]\frac{\pi }{4}[/tex]

Answer: The true statements are:

The "(7 + 2x)" in the first term is a factor.

The "9" in the second term is a coefficient.

The "3y" in the first term is a factor.

Step-by-step explanation:

Answer:

Option 1 and 2.

Step-by-step explanation:

Given : Expression  [tex]3y(7 + 2x) + 9xy - 10[/tex]

To find : Observe the expression below and select the true statement(s)?

Solution :

Using definition mentioned below :

We can say that statements which are true are

1) The "(7 + 2x)" in the first term is a factor.  

2) The "9" in the second term is a coefficient.  

Rest are false.

Therefore, option 1 and 2 is correct.

Answer:

Option D

y = x^2 − 6

y = x − 4

Step-by-step explanation:

we know that

The y-intercept of the quadratic equation is the point (0,-6) (see the graph)

Could be option A or option D

The y-intercept of the linear equation is the point (0,-4) and the x-intercept is the point (4,0)

Could be option D

therefore

The system of equations is the option D

Verify

[tex]y=x^{2}-6[/tex]

[tex]y=x-4[/tex]

using a graphing tool

see the attached figure

The system of equations is the option D

Answer:

5

Step-by-step explanation:

.

.

.

Answer:

57°

Step-by-step explanation:

Angle 3 is supplementary to angle TKL.  That means they add up to 180°.  Therefore, 180° - 123° = 57°

Answer:

57°

Step-by-step explanation:

You can notice that by putting ∠3 and ∠TKL together you have a flat angle.

A flat angle has 180 degrees.

so, you can say that m∠3 and m∠TKL add 180 degrees, then they are supplementary angles.

Remember: Two angles are supplementary if they add 180 degrees.

Then, as you know m∠3=123°:

m∠3 + m∠TKL=180°

123 + m∠TKL=180°

m∠TKL=180° - 123°

m∠TKL=57°

The numbers you are multiplying are called the factors the result is called the product.

Answer: Product?

Step-by-step explanation:

Adding: Sum

Subtracting: Difference

Dividing: Quotient

Multiplying: Product

Hope this helps

Answer:

A) 2x³+11x²+8x-16

Step-by-step explanation:

When you multiply s(x) by t(x) you get something like this:

[tex]s(x) \times t(x) = (2 {x}^{2} + 3x - 4) \times (x + 4) \\ = 2 {x}^{3} + 3 {x}^{2} - 4x + 8 {x}^{2} + 12x - 16 \\ = 2 {x}^{3} + 11 {x}^{2} + 8x - 16[/tex]

Answer:  A) 2x³ + 11x² + 8x - 16

Step-by-step explanation:

s(x) · t(x) = (x + 4)(2x² + 3x - 4)

             = x(2x² + 3x - 4) + 4(2x² + 3x - 4)

             =   2x³ + 3x² - 4x  + 8x² + 12x - 16

             =   2x³  + (3x² + 8x²) + (- 4x + 12x) - 16

             =  2x³          + 11x²              + 8x      - 16

Answer:

[tex]\boxed{365}[/tex]

Step-by-step explanation:

Let g = number of girls  

and b = number of boys  

We have conditions (1) and (2):  

[tex]\begin{array}{lrcll}(1) &\frac{2}{7}g & = & \frac{3}{5}b & \\(2) & g - b & = & 165 &\\(3) & 10g & = & 21b & \text{Multiplied each side of (1) by lcm of denominators}\\(4)& g & = & 165 + b &\text{Added b to each side of (2)}\\ & 10(165 + b) & = & 21b & \text{Substituted 4 into (3)} \\\end{array}[/tex]

[tex]\begin{array}{lrcll} & 1650 + 10b & = & 21b & \text{Distributed the 10} \\ & 1650 & = & 11b & \text{Subtracted 10b from each side} \\ (5) & b & = & 150 &\text{Divided each side by 11} \\ & g - 150 & = & 165 & \text{Substituted (5) into (2)} \\ & g & = & 215 &\text{Added 150 to each side} \\\\ & g + b & = & 365 &\text{Added girls and boys} \\\end{array}[/tex]

[tex]\text{The number of children at the festival was \boxed{\textbf{365}}}[/tex]

Check:

[tex]\begin{array}{rlcrl}\frac{2}{7}\times315& = \frac{3}{5} \times150 & \qquad & 315 - 160 & =165\\90 & = 90& \qquad & 165 & = 165\end{array}[/tex]

The Answer will be 3.28 h

hope this will Help:)

Answer:

3.28

Step-by-step explanation:

z score is:

z = (x - μ) / σ

For z = -1.2, μ = 4.6, and σ = 1.1:

-1.2 = (x - 4.6) / 1.1

x = 3.28

Answer:

-3

Step-by-step explanation:

[tex]f(x) = 3 - x[/tex]

[tex]g(x) = 4x + 1[/tex]

[tex]h(x) = (g \bullet f) (x) = g(f(x)) \\ = 4(3 - x) + 1 \\ = 13 - 4x[/tex]

then

[tex]h(4) = 13 - 4 \times 4 = - 3[/tex]

If he bought 4 hats for $5 each and he spent a total of $44, he spent $44 - $20 in shirts.

44 - 20 = 24

2 shirts for $24 is 1 for 12

$12 for each shirt

Hope it helps :)

Answer:

1 shirt= $12

Step-by-step explanation

we can make an equation where S= shirts, and H for hats. this would look like 2S+4H=44. now we get the info H=5(dollars). we plug it in to get 2S+4 x 5=44. now we simplify to get 2S+20=44. we subtract 20 from both sides to simplify further to get 2S=24. now we can divide this by 2 on each side to get S=11, and since S is the shirts, it says one shirt is =to 11, or 1 shirt= $12

(a) ≈ 0.202, (b) ≈ 0.878, (c) ≈ 0.376, calculated using binomial probability formula with 56% chance for baseball fans.

To solve this problem, we can use the binomial probability formula since we have a fixed number of trials (selecting 10 men) and each trial (man) has two possible outcomes (considering themselves a baseball fan or not).

The binomial probability formula is:

[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]

Where:

- [tex]\( P(X = k) \)[/tex] is the probability of getting exactly \( k \) successes,

- [tex]\( n \)[/tex] is the number of trials (in this case, 10 men),

- [tex]\( k \)[/tex] is the number of successes we are interested in (number of men considering themselves baseball fans),

- [tex]\( p \)[/tex] is the probability of success on each trial (in this case, 56% or 0.56),

- [tex]\( \binom{n}{k} \)[/tex] is the binomial coefficient, representing the number of ways to choose [tex]\( k \)[/tex] successes from [tex]\( n \)[/tex] trials.

Let's solve each part of the problem:

(a) Finding the probability of exactly five men considering themselves baseball fans:

[tex]\[ P(X = 5) = \binom{10}{5} \times (0.56)^5 \times (1 - 0.56)^{10 - 5} \][/tex]

(b) Finding the probability of at least six men considering themselves baseball fans. This is the sum of probabilities of having 6, 7, 8, 9, or 10 successes:

[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]

(c) Finding the probability of less than four men considering themselves baseball fans. This is the sum of probabilities of having 0, 1, 2, or 3 successes:

[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]

Let's calculate each part:

(a)

[tex]$\begin{aligned} & P(X=5)=\left(\begin{array}{c}10 \\ 5\end{array}\right) \times(0.56)^5 \times(1-0.56)^{10-5} \\ & =\left(\begin{array}{c}10 \\ 5\end{array}\right) \times(0.56)^5 \times(0.44)^5 \\ & \approx 0.202\end{aligned}$[/tex]

(b)

[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \]\[ = \sum_{k=6}^{10} \binom{10}{k} \times (0.56)^k \times (0.44)^{10 - k} \]\[ \approx 0.878 \][/tex]

(c)

[tex]$\begin{aligned} & P(X < 4)=P(X=0)+P(X=1)+P(X=2)+P(X=3) \\ & =\sum_{k=0}^3\left(\begin{array}{c}10 \\ k\end{array}\right) \times(0.56)^k \times(0.44)^{10-k} \\ & \approx 0.006+0.034+0.111+0.225 \\ & \approx 0.376\end{aligned}$[/tex]

So, the probabilities are:

(a) [tex]\( \approx 0.202 \)[/tex]

(b) [tex]\( \approx 0.878 \)[/tex]

(c) [tex]\( \approx 0.376 \)[/tex]

Answer:

101.956 cm²

Step-by-step explanation:

The area (A) of a parallelogram is calculated using the formula

A = bh ( b is the base and h the perpendicular height )

here b = 14.2 and h = 7.18, hence

A = 14.2 × 7.18 = 101.956 cm²

By DeMoivre's theorem,

[tex](\sqrt2(\cos10^\circ+i\sin10^\circ))^6=(\sqrt2)^6(\cos60^\circ+i\sin60^\circ)[/tex]

[tex]=8(\cos60^\circ+i\sin60^\circ)[/tex]

The answer is 8(cos60° +isin 60°)

Demoivre's theorem:, De Moivre's formula (also known as de Moivre's theorem and de Moivre's identity) states that for any real number x and integer n it holds that (cosx + i sinx)^n= cosnx + i sinnx.

where i is the imaginary unit (i2 = −1).

By DeMoivre's theorem:

[sqrt(2)(cos(10)+isin(10)]^6

(√2 (cos 1o° + isin 10°))^6 = (√2)^6(cos 60° + isin 60°)

=8(cos60° +isin 60°)

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A would be the very first step in solving the equation for x

You have to distribute 2 to x and 7.

2(x + 7) + 3x = 12

2x + 14 +3x = 12

Answer:

A) 2x + 14 + 3x = 12

Step-by-step explanation:

The first step is to distribute the 2

2(x + 7) + 3x = 12

2x+14 +3x =12

Then we combine like terms

5x+14 =12

Subtract 14 from each side

5x+14-14=12-14

5x = -2

Then divide each side by 5

5x/4 = -2/5

x = -2/5

Answer:

  74°

Step-by-step explanation:

The given congruence relations mean ...

  3x -7 = 6x -88

  81 = 3x . . . . . . . add 88-3x

  (3x -7)° = (81 -7)° = 74°

The measure of angle XMZ is 74°.