If f(x) = [tex]x^{2} -2^x,[/tex] what is the value of f(3) ?

PLEASE HELP! WILL PUT BRAINLIESTT!

Answer:

k=9

Step-by-step explanation:

First find r=22/20=1.1

The sum of the first k terms formula is a1•(1-r^k)/(1-r)

a1=20 and the sum is 271.59

Now plug in these values in the formula and find k.

271.59=20(1-1.1^k)/(1-1.1)

When you simplify this equation, you will get k=ln(2.358)/ln(1.1)

k=9

Check the picture below.

Answer:

[tex]\frac{2.5}{100}=0.025\:or\:2.5\%[/tex]

Step-by-step explanation:

In step 4.

Weston made a mistake when he divided 2.5 by 100. He wrote it as he had multiplied 2.5 by 10 instead of moving the point back two decimals places to the left.

In the Step 4:

[tex]\frac{2.5}{100}= 0.025\:or\:2.5\:\%[/tex]

This can be verified by dividing 1 over 40, that'll  give us 0.025

Answer:

m∠A = 39.5°

Step-by-step explanation:

* Lets revise how to find the measure of an angle by using the cosine rule

- In any triangle ABC

# ∠A is opposite to side a

# ∠B is opposite to side b

# ∠C is opposite to side c

- The cosine rule is:

# a² = b² + c² - 2bc × cos(A)

# b² = a² + c² - 2ac × cos(B)

# c² = a² + b² - 2ab × cos(C)

- To find the angles use this rule

# m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

# m∠B = [tex]cos^{-1}\frac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]

# m∠C = [tex]cos^{-1}\frac{a^{2}+b^{2}-c^{2}}{2ab}[/tex]

* Lets solve the problem

∵ a = 14 , b = 17 , c = 22

∵ m∠A = [tex]cos^{-1}\frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

∴ m∠A = [tex]cos^{-1}\frac{17^{2}+22^{2}-14^{2}}{2(17)(22)}[/tex]

∴ m∠A = [tex]cos^{-1}\frac{289+484-196}{748}[/tex]

∴ m∠A = [tex]cos^{-1}\frac{577}{748}[/tex]

∴ m∠A = 39.5°

Answer:

∠A = 39.52°

Step-by-step explanation:

In Δ ABC,

a = 14, b = 17 and c = 22 then we have to find the measure of ∠A.

Since a² = b² + c² - 2.b.c.cosA [ From cosine law]

(14)² = (17)²+ (22)² - 2(17)(22)cosA

196 = 289 + 484 - (748)cosA

196 = 773 - (748)cosA

748(cosA) = 773 - 196 = 577

cosA = [tex]\frac{577}{748}=0.7714[/tex]

A = [tex]cos^{-1}(0.7714)[/tex]

A = 39.52°

Answer:

1408 min.

Step-by-step explanation:

8 × 176 = 1408.

Answer:

1408

Step-by-step explanation:

Final Answer:

The probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.

Explanation:

To find the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F, we can use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is sufficiently large. In this case, we can assume a sample size of 19 is large enough.

Given:
- Population mean (μ) = 98.20°F
- Population standard deviation (σ) = 0.62°F
- Sample size (n) = 19
- Target sample mean (X) = 98.50°F

We need to do the following steps:

1. Calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the sample mean.
  SEM = σ / √n

2. Calculate the Z-score for the sample mean of 98.50°F. The Z-score represents how many standard errors the value is away from the population mean.
  Z = (X - μ) / SEM

3. Use the Z-score to find the area to the left of it on the standard normal distribution, which represents the probability that the sample mean is less than 98.50°F.

Let's calculate each step:

1. Calculate SEM:
  SEM = σ / √n
      = 0.62 / √19
      ≈ 0.62 / 4.3589
      ≈ 0.1422

2. Calculate Z-score:
  Z = (X - μ) / SEM
    = (98.50 - 98.20) / 0.1422
    ≈ 0.30 / 0.1422
    ≈ 2.1095

3. Lastly, to find the probability that the sample mean is less than 98.50°F, we look up the Z-score in the standard normal distribution table (Z-table), use statistical software, or a calculator that provides the cumulative distribution function (CDF) for the normal distribution.

A Z-score of 2.1095 corresponds to a probability of about 0.9826 (using Z-table or a calculator).

Therefore, the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.

Among the options given, the closest to 0.9826 is 0.9826 itself. Hence, that is the correct answer.

Answer:

The common ratio is -3

Step-by-step explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant called the common ratio

In this problem we have

-2,6,-18,54...

Let

a1=-2, a2=6,a3=-18,a4=54

a2/a1=6/-2=-3

a3/a2=-18/6=-3

a4/a3=54/-18=-3

Each term (except the first term) is found by multiplying the previous term by -3

therefore

we have a geometric sequence and the common ratio is -3

Answer:

No real solutions.

Step-by-step explanation:

[tex]y=x^2-3x-4[/tex]

[tex]x=y+8[/tex]

I'm going to subtract the second expression for y and plug it into the first equation.

So solving x=y+8 for y by subtracting 8 on both sides gives us y=x-8.

I'm going to insert this for the first y like so:

[tex]x-8=x^2-3x-4[/tex]

Now I'm going to move everything to one side.

I'm going to subtract x on both sides and add 8 on both sides.

[tex]0=x^2-3x-x-4+8[/tex]

Simplifying:

[tex]0=x^2-3x+4[/tex]

Now our job since the coefficient of x^2 is 1 is to find two numbers that multiply to be 4 and at the same time add up to be -3. I can't think of any such numbers.

Let's check the discriminant.

Compare [tex]x^2-3x+4[/tex] to [tex]ax^2+bx+c[/tex].

So [tex]a=1,b=-3,c=4[/tex].

The discriminant is [tex]b^2-4ac[/tex].

So plugging in our numbers we get [tex](-3)^2-4(1)(4)[/tex].

Time to simplify:

[tex](-3)^2-4(1)(4)[/tex]

[tex]9-16[/tex]

[tex]-7[/tex]

So since the discriminant is negative, then the solutions will not be real.

Answer:

5

Step-by-step explanation:

The inverse of [tex]f(x)=2^x[/tex] is [tex]g(x)=\log_2(x)[/tex].

[tex]g(32)=\log_2(32)[/tex]

[tex]\log_2(32)=5[/tex] since [tex]2^5=32[/tex].

[tex]g(32)=\log_2(32)=5[/tex]

Note: In general, the inverse of [tex]f(x)=a^x[/tex] is [tex]g(x)=\log_a(x)[/tex].

Answer:

7c^2d-7c+4d-10

Step-by-step explanation:

Start off with the term that has c^2 in it. 5c^2d + 2C = 7c^2d, then since you have multiple choice, the d value differs between the two answer choices that have 7c^2d so you can do +3d +d to get +4d to get the fourth answer choice.

To check your work, you can add/subtract each term to see if you get 7c^2d-7c+4d-10

Answer:

[tex]\large\boxed{V=(157.5+27.648\pi)\ yd^3}[/tex]

Step-by-step explanation:

We have the rectangular prism and the cone.

The formula of a volume of

1) a rectangular prism

[tex]V=lwh[/tex]

l - length

w - width

h - height

2) a cone

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have:

1)

l = 7yd, w = 5yd, h = 4.5yd

Substitute:

[tex]V_R=(7)(5)(4.5)=157.5\ yd^3[/tex]

2)

r = 4.8yd, l = 6yd

l - slant height

Use the Pythagorean theorem to calculate H :

[tex]H^2+r^2=l^2[/tex]

Substitute:

[tex]H^2+4.8^2=6^2[/tex]

[tex]H^2+23.04=36[/tex]           subtract 23.04 from both sides

[tex]H^2=12.96\to H=\sqrt{12.96}\\\\H=3.6\ yd[/tex]

Calculate the volume:

[tex]V_C=\dfrac{1}{3}\pi(4.8)^2(3.6)=\dfrac{82.944}{3}\pi=27.648\pi\ yd^3[/tex]

The volume of the composite solid:

[tex]V=V_R+V_C[/tex]

Substitute:

[tex]V=(157.5+27.648\pi)\ yd^3[/tex]

Answer:

[tex]y=-4x+2[/tex]

Step-by-step explanation:

Since, the slope intercept form of a line is,

[tex]y=mx+c[/tex]

Here, the given equation is,

[tex]4x=2-y[/tex]

[tex]4x+y=2[/tex]    ( Additive property of equality )

[tex]y=-4x+2[/tex]   ( Subtraction property of equality )

Hence, the equation that represents the equivalent equation of the given equation in slope-intercept form is,

[tex]y=-4x+2[/tex]

First option is correct.

Answer:

Step-by-step explanation:

[tex]21[/tex]

Answer:

y = 6x

Step-by-step explanation:

Find slope

Formula

0 - (-3) = 3

0 - (-1/2) = 1/2

Simplify

3/(1/2) = 6

y = 6x

y-intercept

The line crosses the origin, so the y-intercept is 0.

Answer

y = 6x

Answer:

x = -4

Step-by-step explanation:

Notice that the two points given, share the same x-value even when the y-value changes. This is because the equation is going to be a vertical line at -4 on the x-axis. Being a vertical line, you cannot take its slope using the slope formula of: m = (y2 - y1) / (x2 - x1) because the denominator will result in a 0 and you cannot divide by 0 in mathematics.

[tex]A\cap B=\{x:x\in A \wedge x\in B\}[/tex]

[tex]A\cap B=\{2,4\}[/tex]

For this case we have the following sets:

A = {1,2,3,4,5}

B = {2,4}

We must find the intersection of both sets, the symbol ∩ denotes intersection. That is, the numbers in common of both.

We have to:

A∩B = {2,4}

Answer:

The insterseccion of both sets is:

A∩B = {2,4}

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation in the standard form:

[tex]6x+3y=12[/tex]

Convert to the slope intercept form:

[tex]6x+3y=12[/tex]              subtract 6x from both sides

[tex]3y=-6x+12[/tex]           divide both sides by 3

[tex]y=-2x+4[/tex]

slope: m = -2

y-intercept: b = 4

Answer:

no solution

Step-by-step explanation:

If you divide the first equation by 2 you get:

2x+2y=4  (first equation after dividing both sides by 2)

2x+2y=-4  (second equation)

This is setup for elimination.

Subtract the equations:

2x+2y=4

2x+2y=-4

--------------Subtracting!

0+0=8

    0=8

0=8 is a false equation which implies the system has no solution.

Answer:

a) No Solutions

Step-by-step explanation:

It might be helpful to first get the equations in terms of y = mx + b.

The first equation (4x + 4y = -8) can be rewritten like this:

4x + 4y = -8 (original equation)

4y = 4x - 8 (subtract 4x from both sides)

y = x - 4 (divide everything by 4 to get y on its own)

and now you have an equation in terms of y = mx = b, where m is 1 and b is -4.

The second equation can be written like this:

2x + 2y = -4 (original equation)

2y = 2x - 4 (subtract 2x from both sides)

y = x - 2 (divide everything by 2 to get y on its own)

and once again we have an equation with m being 1 and b being -2.

So hopefully you should see that the equations will never touch because they have the same slope. Because the equations never touch, they have no solutions. Have a look at the graph.

Answer:

264 unit^2.

Step-by-step explanation:

The lateral area  is the sum of the 2 sides of area 5*11 and the 2 sides of area 7^11.

That would be 2 * 5 * 11 + 2*7*11

=  264 unit^2.

For this case we have that by definition, the lateral area of a prism is given by:

[tex]LA = 2ac + 2bc[/tex]

Where:

a: It is the height

b: It is the width

c: It's the long

According to the figure we have:

[tex]a = 5 \ units\\b = 7 \ units\\c = 11 \ units[/tex]

Substituting:

[tex]LA = 2 * 5 * 11 + 2 * 7 * 11\\LA = 110 + 154\\LA = 264[/tex]

Finally, the lateral area of the prism is [tex]264 \ units ^ 2[/tex]

ANswer:

Option B

Answer:

A. By SAS only

Step-by-step explanation:

Side Side Side postulate (SSS) states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

In triangles ABC and AED:

So, SAS postulate can be applied.

SSS postulate cannot be applied, because it is not given that sides AB and AE are conruent.

Answer:

ΔABC and ΔAED are congruent to each other by SAS rule.

Step-by-step explanation:

We are given a figure in the question.

The figure shows that:

AC = AD, BC = ED, ∠BAC = ∠EAD

We are also given that triangle BCA is congruent to triangle EDA.

Now, we need to prove that triangle ABC is congruent to triangle AED.

We will use SAS criterion of congruence.

In ΔABC and ΔAED,

AC = AD, ∠BAC = ∠EAD, , BC = ED( all given in the figure)

Hence, the two triangles are congruent to each other by SAS rule.

Answer:

Height and base are both 12 in

Step-by-step explanation:

Formula area triangle: area = (height * base) /2

Since for the first triangle height and base are the same we will call is x.

The area for the first triangle is

area = (x^2) /2 = 0.5x^2

The new triangle area is

first triangle - 36 = ((x/2) * x)/2

0,5x^2 - 36 = (0,5x * x)/2

0,5x^2 - 36 = (0,5x^2)/2

0,5x^2 - 36 = 0,25x^2

0,25x^2 = 36

x^2 = 144

X = square root (144) = 12 in

The little red lines on each side of the triangle mean that the sides are all equal.

A triangle that has all 3 sides the same is an equilateral triangle.

Because all the sides are identical all 3 inside angles are also identical.

180 / 3 = 60 degrees

The outside angle which is DEF would equal 180 - the inside angle.

DEF = 180 - 60 = 120.

The answer is D.

Answer:

120°

Step-by-step explanation:

It is an equilateral triangle, so all its sides and internal angles measure the same.

The sum of the internal angles of a triangle must be 180°, so each internal angle measures 60°.

The DEF angle is an external angle of that triangle, we can use the next property:

An external angle of a triangle is the sum of the internal angles opposed to it.

The two opposite angles to DEF are DCE and CDE:

DEF = DCE + CDE = 60 ° + 60 ° = 120°

Another way to find this same result is to notice that DEF + DEC total 180° since they form a straight line, and we know that DEC measures 60°

So:

DEF + DEC = 180 °

DEF = 180 ° - DEC

DEF = 180 ° -60 °

DEF = 120 °

Answer:

total cost= 16v+24p

Step-by-step explanation:

One set 4v+6p

Multiply the. expression by 4 because we are buying 4 sets

4v+6p

*4. *4

16v+24p

Answer:

(4v + 6p)4 = n

Step-by-step explanation:

If 1 set is

4v + 6p,

Then multiply it by 4 to get the total cost of 4 sets. Since there is so price for 1 set, we could use n for the missing total cost.

Final answer:

To find the mean absolute deviation (MAD) for the data set, calculate the mean, subtract it from each data value to find deviations, take the absolute values, and then find their mean. The MAD for the data set 12, 17, 16, 9, 18, 10, 9 is approximately 3.43.

Explanation:

To find the mean absolute deviation (MAD) for a given data set, we follow these steps:

Calculate the mean (average) of the data set.

Subtract the mean from each data value to find the deviations.

Take the absolute value of each deviation.

Find the average of these absolute values to determine the MAD.

The data set provided is: 12, 17, 16, 9, 18, 10, 9. First, let's calculate the mean:

(12 + 17 + 16 + 9 + 18 + 10 + 9) / 7 = 91 / 7 = 13

Next, we'll find the absolute deviations from the mean:

|12 - 13| = 1

|17 - 13| = 4

|16 - 13| = 3

|9 - 13| = 4

|18 - 13| = 5

|10 - 13| = 3

|9 - 13| = 4

Lastly, we calculate the mean of these absolute values:

(1 + 4 + 3 + 4 + 5 + 3 + 4) / 7 = 24 / 7 ≈ 3.43

The mean absolute deviation of the data set is approximately 3.43.

Final answer:

The mean absolute deviation of the data set is calculated by finding the mean, determining the absolute deviation of each value from the mean, and then taking the mean of those deviations. For this set, the mean absolute deviation is 3.43.

Explanation:

To find the mean absolute deviation, we follow these steps:

First, we calculate the mean of the data set: (12 + 17 + 16 + 9 + 18 + 10 + 9) ÷ 7 = 91 ÷ 7 = 13.

Next, we find the absolute deviation of each data point from the mean:

Add these absolute deviations: 1 + 4 + 3 + 4 + 5 + 3 + 4 = 24.

Finally, we find the mean of these absolute deviations: 24 ÷ 7 = 3.43 (rounded to the nearest hundredth).

The mean absolute deviation for the data set is 3.43.

Answer:

<-6,-4>

Step-by-step explanation:

To find u+v, all you have to do is add the corresponding components of each.

That is for example on this problem, you would do

<-3,-5>+<-3,1>

=<-3+-3,-5+1>

=<-6,-4>.

Answer:

Total overripe fruit = 48

Step-by-step explanation:

Step 1: Assume the value of oranges

Let oranges be x

Oranges = x

Apples = 32 + x

Overripe oranges = 3/5 of oranges

                              = 3x/5

Overripe apples = 1/3 of apples

                           = 1/3 (32 + x)

Step 2: Find x (oranges)

Number of overripe apples and number or overripe oranges are equal.

3x/5 = 1/3 (32 + x)

3 (3x) = 5(32 + x)

9x = 160 + 5x

4x = 160

x = 40

Step 3: Find the total number of overripe fruit.

Total overripe fruit = Overripe apples + Overripe oranges

Total overripe fruit = 1/3 (32 + x) + 3x/5

Total overripe fruit = 1/3 (32 + 40) + 3(40)/5

Total overripe fruit = 24 + 24

Total overripe fruit = 48

!!

Answer:

multiplicity of 1

Step-by-step explanation:

Given the roots of an equation are

x = - 4 ← multiplicity 1

(x + 4)² = 0

x + 4 = 0 or x + 4 = 0 , hence

x = - 4 or x = - 4 , that is

x = - 4 ← with multiplicity 2

(x + 4)³ = 0

has roots x = - 4 with multiplicity 3

The multiplicity is determined by the exponent the factor is raised to

Answer:

f(x) = 4(1.02)^(7x); spreads at a rate of approximately 2% daily

Step-by-step explanation:

The weekly number of people infected is:

f(x) = 4(1.15)^x

So the daily number of people infected is:

f(x) = 4(1+r)^(7x)

To find the value of the daily rate r, we set this equal to the first equation.

4(1.15)^x = 4(1+r)^(7x)

(1.15)^x = (1+r)^(7x)

(1.15)^x = ((1+r)^7)^x

1.15 = (1+r)^7

1.02 = 1+r

r = 0.02

So the equation is f(x) = 4(1.02)^(7x), and the daily rate is approximately 2%.

Using exponential functions, it is found the daily function for the spread is:

[tex]f(x) = 4\left(\frac{1.15}{7}\rigth)^{x}[/tex], and it spreads at a rate of approximately 2% daily.

An exponential function has the following format:

[tex]y = ab^x[/tex]

In which:

In this problem, the function for the weekly spread is:

[tex]f(x) = 4(1.15)^x[/tex]

A week has 7 days, thus, to find the daily spread, we divide the rate of change by 7, that is:

[tex]f(x) = 4\left(\frac{1.15}{7}\right)^x[/tex]

[tex]\frac{15}{7} \approx 2.1[/tex], thus, it spreads at a rate of approximately 2% daily.

A similar problem is given at https://brainly.com/question/23416643

Answer:

1) 0.0008306

2) 0.00008306

3) 0.000008306

4) 0.0000008306

Step-by-step explanation:

Please mark me the brainliest... . I am sure the answers are correct.

Answer:

0.0008306

0.00008306

0.000008306

0.0000008306

Step-by-step explanation:

0.008306 ÷ 10 = 0.0008306

0.008306 ÷ 100 = 0.00008306

0.008306 ÷ 1000 = 0.000008306

0.008306 ÷ 10000 = 0.0000008306

Step-by-step answer:

Referring to the attached diagram, the resultant of two forces each with magnitude F and inclined to each other at 2a equals

Ra = 2Fcos(a) ..............................(1)

Similarly, the resultant of two forces each with magnitude F and inclined to each other at 2b equals

Rb = 2Fcos(b)..............................(2)

We are given that

Ra = 2Rb  ....................................(3)

Substitute (1) & (2) in (3) gives

2Fcos(a) = 2(2Fcos(b))

Expand

2Fcos(a) = 4Fcos(b)

Simplify

cos(a) = 2 cos(b)   QED

Note: Please note that you might have a faster response if you posted this question in the physics or the (new) Engineering section.

Have a nice day!

Answer:

51 and 255

Step-by-step explanation:

Let the number of programs sold by Jay be x.

Then programs sold by Hanna is 5x.

Also, the difference between them is 204.

5x - x =204

4x = 204

x = 204/4

x = 51

Therefore, Jay sold 51 programs and Hanna sold 5 x 51 = 255 programs.

Please mark Brainliest if this helps!

Jay sold 51 programs and Hanna sold 255 programs.

To determine how many programs Jay and Hanna sold, let's start by defining some variables.

Let [tex]J[/tex] be the number of programs Jay sold.

Since Hanna sells 5 times more programs than Jay, we can express her sales as [tex]5J[/tex].

We know the difference in their sales is 204 programs.

Therefore, we can write the equation:

[tex]5J - J = 204[/tex]

Simplify the equation:

[tex]4J = 204[/tex]

Next, solve for [tex]J[/tex] by dividing both sides by 4:

[tex]J = \frac{204}{4}[/tex]

[tex]J = 51[/tex]

So, Jay sold 51 programs.

Since Hanna sells 5 times more programs than Jay, we can calculate Hanna's sales as:

[tex]5 \times 51 = 255[/tex]