The area of the region under the curve of the function f(x)=5x+7 on the interval [1,b] is 88 square units, where b>1. What is the value of b.

Answer:

The range of T is a subspace of W.

Step-by-step explanation:

we have T:V→W

This is a linear transformation from V to W

we are required to prove that the range of T is a subspace of W

0 is a vector in range , u and v are two vectors in range T

T = T(V) = {T(v)║v∈V}

{w∈W≡v∈V such that T(w) = V}

T(0) = T(0ⁿ)

0 is  Zero in V

0ⁿ  is zero vector in W

T(V) is not an empty subset of W

w₁, w₂   ∈ T(v)

(v₁, v₂ ∈V)

from here we have that

T(v₁) = w₁

T(v₂) = w₂

t(v₁) + t(v₂) = w₁+w₂

v₁,v₂∈V

v₁+v₂∈V

with a scalar ∝

T(∝v) = ∝T(v)

such that

T(∝v) ∈T(v)

so we have that T(v) is a subspace of W. The range of T is a subspace of W.

Answer:

Step-by-step explanation:

Hello,

We can write three equations thanks to Pythagoras

   [tex]AB^2+AC^2=(7+3)^2\\x^2+7^2=AB^2\\x^2+3^2=BC^2\\[/tex]

So it comes

[tex]x^2+7^2+x^2+3^2=(7+3)^2\\\\2x^2=100-49-9=42\\\\x^2 = 42/2=21\\\\x = \sqrt{\boxed{21}}\\[/tex]

Hope this helps

Answer:

x = [tex]\sqrt{21}[/tex]

Step-by-step explanation:

Δ BCD and Δ ABD are similar thus the ratios of corresponding sides are equal, that is

[tex]\frac{BD}{AD}[/tex] = [tex]\frac{CD}{BD}[/tex] , substitute values

[tex]\frac{x}{7}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )

x² = 21 ( take the square root of both sides )

x = [tex]\sqrt{21}[/tex]

Answer:

(0,-2)

Step-by-step explanation:

The y-intercept is simply when the function touches or crosses the y-axis.

We're told that the graph crosses the y-axis at -2. In other words, the y-intercept is at -2.

The ordered pair would be (0,-2)

Answer:

Your answer is B

Step-by-step explanation:

rotating about/around the origin taking a shape and rotating it with the same values but around the point (0,0). so rotating your shape ABC around (0,0) with the same value would give you the shape A'B'C'

Answer:

The formula that represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A) is [tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex] .

Step-by-step explanation:

We are given the area of an Equilateral triangle which is A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex] . And we have to represent the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).

So, the area of an equilateral triangle =  [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]

where, s = side of an equilateral triangle

A  =  [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]

Cross multiplying the fractions we get;

[tex]4 \times A = \sqrt{3} \times \text{s}^{2}[/tex]

[tex]\sqrt{3} \times \text{s}^{2}= 4\text{A}[/tex]

Now. moving [tex]\sqrt{3}[/tex] to the right side of the equation;

[tex]\text{s}^{2}= \frac{4 \text{A}}{\sqrt{3} }[/tex]

Taking square root both sides we get;

[tex]\sqrt{\text{s}^{2}} = \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]

[tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]

Hence, this formula represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).

Answer:

Step-by-step explanation:

This is a permutation problem. Given the 10 cards with numbers 2, 3, 4,5,5,7,7,7,7,7 on it, if Salvador is going to make a row call, the number of ways he can order a row is as shown below;

Total number of cards = 10!

number of times the digit 5 was repeated = 2times

number of times the digit 7 was repeated = 5times

The number of ways he can make a row call = 10!/2!5!

= 10*9*8*7*6*5!/2*5!

=  10*9*8*7*6/2

=  10*9*8*7*3

= 15,120 different ways

Hence, the number of ways he can order the row is 15,120 number of ways.

Answer:

~820.8$

Step-by-step explanation:

The total money (M) after 18 years could be calculated by:

M = principal x (1 + rate)^time

with

principal = 400$

rate = 4% compounded monthly = 0.04/12

time = 18 years = 18 x 12 = 216 months (because of compounded monthly rate)

=> M = 400 x (1 + 0.04/12)^216 = ~820.8$

Answer:

2/3

Step-by-step explanation:

The equation for direct variation is: y = kx, where k is a constant.

Here, we see that y varies directly with x when y = 6 and x = 72, so let's plug these values into the formula to find k:

y = kx

6 = k * 72

k = 6/72 = 1/12

So, k = 1/12. Now our formula is y = (1/12)x. Plug in 8 for x to find y:

y = (1/12)x

y = (1/12) * 8 = 8/12 = 2/3

Thus, y = 2/3.

~ an aesthetics lover

Answer:

Step-by-step explanation: I hope i'm right

[tex]y \alpha x\\y=kx....(1)\\6=72k\\\frac{6}{72} =\frac{72k}{72} \\\\1/12 =k\\y = 1/12x=relationship-between;x-and;y\\x =8 , y =?\\y = \frac{8}{12} \\Cross-Multiply\\12y =8\\12y/12 = 8/12\\\\y = 2/3[/tex]

Answer:

C

Step-by-step explanation:

The critical value we are asked to state in this question is the value of the z statistic

Mathematically;

z-score = (x- mean)/SD/√n

From the question

x = 11.58

mean = 12

SD = 1.93

n = 80

Substituting this value, we have

z= (11.58-12)/1.93/√80 = -1.946

Answer:

I think that is the C

Step-by-step explanation:

Answer:

Option B is the correct answer.

Step-by-step explanation:

here, arc RT =162°

as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.

so, its value must be 81°only.

hope it helps..

Answer:

The conditional probability is given by

P(F|E) = P(E and F)/P(E)

P(F|E) = 0.2/0.4

P(F|E) = 0.5

P(F|E) = 50%

Step-by-step explanation:

Recall that the conditional probability is given by

∵ P(B | A) = P(A and B)/P(A)

For the given case,

P(F|E) = P(E and F)/P(E)

Where P(F|E) is the probability of event F occurring given that event E has occurred.

The probability of event E and F is given as

P(E and F) = 0.2

The probability of event E is given as

P(E) = 0.4

So, the conditional probability is

P(F|E) = P(E and F)/P(E)

P(F|E) = 0.2/0.4

P(F|E) = 0.5

P(F|E) = 50%

Answer: 6 cm, V=48π or V=150.8 cm³

It appears the question is asking for the radius, but below I have shown how to find the volume.

Step-by-step explanation:

The radius is half of the diameter. The diameter of the cone of 12 cm. Half of 12 is 6. Therefore, the radius is 6 cm.

The formula to find the volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]. Now that we have the radius from above, we can use that to plug into the equation along with the given height.

[tex]V=\pi (6^2)\frac{4}{3}[/tex]                    [expand the exponent]

[tex]V=36\pi \frac{4}{3}[/tex]                       [combine like terms]

[tex]V=48\pi[/tex] or [tex]V=150.8 cm^3[/tex]            

Answer:

false

Step-by-step explanation:

When solving the distance formula it is the distance from one point to another. If you had a rectangle and used the distance formula from each point then you would have a perimeter

Answer:

1/2

Step-by-step explanation:

i think sin 5 pi/6

[tex]sin \frac{5 \pi}{6} =sin (\frac{\pi}{2} +\frac{\pi}{3} )=cos \frac{\pi}{3} =\frac{1}{2} \\or\\sin\frac{5 \pi}{6} =sin (\pi-\frac{\pi}{6} )=sin \frac{\pi}{6} =\frac{1}{2}[/tex]

The exact Value of sin 5x/6 is 1/2.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin 5x/6

We can Split it as

sin (5π / 6) = sin (π/2 + π/3)

                  = cos π/3

                  = 1/2

Also, sin (5π / 6) = sin (π - π/6)

                  = sin π/6

                  = 1/2

Hence, the exact value is 1/2.

Learn more about Trigonometry here:

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Hi there! :)

Answer:

Length = 10.5 m, width = 7 m.

Step-by-step explanation:

Given:

Perimeter, or P = 35 m

Ratio of l to w = 3 : 2

Since the ratio is 3 : 2, let l = 3x, and w = 2x.

We know that the formula for the perimeter of a rectangle is P = 2l + 2w. Therefore:

35 = 2(3x) + 2(2x)

35 = 6x + 4x

35 = 10x

x = 3.5

Plug this value of "x" into each expression to solve for the dimensions:

2(3.5) = w

w = 7 m

3(3.5) = l

l = 10.5 m

Therefore, the dimensions are:

Length = 10.5 m, width = 7 m.

Answer:

1, 2

Step-by-step explanation:

The integers, x, that satisfy 1 <= x <= 8 are

1, 2, 3, 4, 5, 6, 7, 8

Now we solve the inequality for x.

-x + 4 >= 2

-x >= -2

x <= 2

Now we see which of the eight integers above make the inequality true.

Only 1 and 2 satisfy the inequality.

Answer:

The centroid

Step-by-step explanation:

Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

Answer:

Step-by-step explanation:

Margin of error is expressed as M.E = [tex]z * \sqrt{\frac{\sigma}{n} }[/tex] where;

z is the z score at 95% confidence

[tex]\sigma[/tex] is the standard deviation

n is the sample size

Given n = 349, [tex]\sigma = 42[/tex] and z score at 95% confidence = 1.645

Substituting this values into the formula above we will have;

M.E = [tex]1.645*\sqrt{\frac{42}{349} }[/tex]

[tex]M.E = 1.645*\sqrt{0.1203} \\\\M.E = 1.645*0.3468\\\\M.E = 0.5705 (to\ four\ dp)[/tex]

Hey there! I'm happy to help!

We see that light travels 186,000 miles per second. How many miles is this per minute. Well, there are 60 seconds a minute, so we multiply by 60!

186,000×60=11160000

And there are 60 minutes in an hour, so we multiply by sixty again!

11160000×60=669600000

Now, we need to write this in scientific notation. To do this, we move the decimal back enough places to have a one digit number, and we multiply that one digit number by 10 to the power of how many places you moved the decimal back.

In the number 669600000 we can move the decimal point back 8 times which gives us 6.696 (we don't need the zeroes after a decimal) multiplied by 10 to the 8th power because we moved the decimal back eight places.

This can be written as 6.696×10^8, which is closest to the answer option 6.7×10^8 miles.

Have a wonderful day! :D

Answer:

The sample size is [tex]n = 2401[/tex]

Step-by-step explanation:

From the question we are told that

    The margin of error is  [tex]E = 0.02[/tex]

Given that the confidence level is  95% then the level of significance can be mathematically evaluated as  

            [tex]\alpha = 100 - 95[/tex]

            [tex]\alpha = 5\%[/tex]

            [tex]\alpha = 0.05[/tex]

Next we would obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the values is  

     [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 1.96[/tex]

The reason we are obtaining critical value of   [tex]\frac{\alpha }{2}[/tex]  instead of     [tex]\alpha[/tex] is  because  

[tex]\alpha[/tex]  represents the area under the normal curve where the confidence level interval (   [tex]1-\alpha[/tex]  ) did not cover which include both the left and right tail while

 [tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the  sample  size

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)      

   Generally the sample size is mathematically evaluated as

          [tex]n = [ \frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p)[/tex]

Where [tex]\r p[/tex] is the proportion of sample taken which we will assume to be [tex]\r p = 0.5[/tex]            

        substituting values  

                 [tex]n = [\frac{ 1.96}{0.02} ]^2 *( 0.5 (1- 0.5)[/tex]

                [tex]n = 2401[/tex]

Answer:

B.

Step-by-step explanation:

The function above the x-axis looks like a parabola, so it must have an x^2 term. It also has an open circle, so it must have a > symbol.

The function below the x-axis has a closed circle, so it must have a <= symbol. It is also a 3rd degree polynomial.

Answer: B.

Answer:

2

Step-by-step explanation:

Answer:

D) [tex]x+5\leq -4[/tex]

Step-by-step explanation:

We solve each of the inequalities

Option A

[tex]x+6<-8\\x<-8-6\\x<-14[/tex]

Option B

[tex]x+4\geq -6[/tex]

[tex]x\geq -6-4\\x\geq-10[/tex]

Option C

[tex]x-3>-10\\x>-10+3\\x>-7[/tex]

Option D

[tex]x+5\leq -4[/tex]

[tex]x\leq -4-5\\x\leq -9[/tex]

Therefore, only option D has -12 in its solution set.

Answer:

The new price is 8.80

Step-by-step explanation:

First find the increase

8 * 10%

8 * .10

.80

Add this to the original price

8 + .80

8.80

The new price is 8.80

Answer:

the answer is $8.80 :))

Answer:

[tex]y(x)=100+0.1x[/tex]

Step-by-step explanation:

Let y represent the total fee (in dollars) of a trip where they climbed x vertical meters.

We know that there is an initial fee of $100, so we know that if we climb x=0 meters, we have a fee of y(0)=100.

[tex]y(0)=100[/tex]

As there is a constant fee (lets called it m) for each vertical meter climbed, we have a linear relationship as:

[tex]y(x)-y(0)=m(x-0)\\\\\\y(x)-100=mx\\\\\\y(x)=100+mx[/tex]

We know that for x=3000, we have a fee of $400, so if we replace this in the linear equation, we have:

[tex]y(3000)=100+m(3000)=400\\\\\\100+3000m=400\\\\3000m=400-100=300\\\\m=300/3000=0.1[/tex]

Then, we have the equation for the total fee in function of the vertical distance:

[tex]y(x)=100+0.1x[/tex]

Answer:

(C) The area of the cylinder's base is [tex]\dfrac{1}{4} \pi x^2[/tex] square units.

(E)The height of the cylinder is 4x units.

Step-by-step explanation:

If the Base Diameter = x

Therefore: Base radius = x/2

Area of the Base

[tex]=\pi (x/2)^2\\=\dfrac{ \pi x^2}{4} $ square units[/tex]

Next, we know that:

The volume of a cylinder = Base Area X Height

[tex]\pi x^3=\dfrac{ \pi x^2}{4} \times Height\\Height =\pi x^3 \div \dfrac{ \pi x^2}{4}\\=\pi x^3 \times \dfrac{ 4}{\pi x^2}\\\\Height=4x$ units[/tex]

Therefore, the correct options are: C and E.

Learn more:  https://brainly.com/question/16856757

Answer:

Nx = λx

Nx = 0, with x≠0

if N is nilpotent matrix, then the system Nx = 0 has non-trivial solutions

Step-by-step explanation:

given that

let N be a square matrix in order of n

note: N is nilpotent matrix with [tex]N^{k} = 0[/tex], k ∈ N

let λ be eigenvalue of N and let x be eigenvector corresponding to eigenvalue λ

Nx = λx (x≠0)

N²x =  λNx = λ²x

∴[tex]N^{k}x[/tex] =  (λ^k)x

[tex]N^{k}[/tex] = 0, (λ^k)x = [tex]0_{n}[/tex], where n is dimensional vector

where x = 0, (λ^k) = 0

λ = 0

therefore, Nx = λx

Nx = 0, with x≠0

note: if N is nilpotent matrix, then the system Nx = 0 has non-trivial solution

Answer:

60°C

Step-by-step explanation:

This is a great example of a problem that looks really complicated, but can be broken down and easily understood!

First, we want to know the temperature the instant it is removed from the heat source. In that case, the time that has elapsed after it has been removed is 0, so we're looking for:

[tex]T(0)=55e^{-0.1(0))}+15=55e^{0}+15[/tex]

Now, any number raised to to the power of zero is 1, so this becomes:

[tex]T(0)=55(1)+15=60[/tex]

For more information on why any number raised to the zero power is 1, I highly recommend researching if it interests you. One of the most intuitive ways is to think of the pattern of exponents:

[tex]3^{3}=3*3*3=27[/tex]

[tex]3^{2}=3*3=9[/tex]

[tex]3^{1}=3[/tex]

You might notice that with each decrease in power, it can be read as dividing the expression by three, so following that pattern gives:

[tex]3^{0}=\frac{3}{3}=1[/tex]

And if we follow the division pattern, we do end up going into negative exponents correctly:

[tex]3^{-1}=\frac{1}{3^{1}}[/tex]

[tex]3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}[/tex]

[tex]3^{-3}=\frac{1}{3^3}=\frac{1}{27}[/tex]

Answer:

Step-by-step explanation:

Given that:

If C(x) =  the cost of producing x units of a commodity

Then;

then the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

We are to consider a given function:

[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]

And the objectives are to determine the following:

a) the total cost at a production level of 1000 units.

So;

If C(1000) = the cost of producing 1000 units of a commodity

[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]

[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]

[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]

[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]

[tex]C(1000) = $310491.1064[/tex]

[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]

(b) Find the average cost at a production level of 1000 units.

Recall that :

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

SO;

[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]

Using the law of indices

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]

c(1000) =$ 310.49 per unit

(c) Find the marginal cost at a production level of 1000 units.

The marginal cost  is C'(x)

Differentiating  C(x) = 54,000 + 130x + 4x^{3/2} to get  C'(x) ; we Have:

[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]

[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]

[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 319.7366596[/tex]

[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]

(d)  Find the production level that will minimize the average cost.

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

the production level that will minimize the average cost is c'(x)

differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]

Also

[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]

[tex]x^2 = 27000\sqrt{x}[/tex]

[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]

x= 0;  or  [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900

Since  production cost can never be zero; then the production cost = 900 units

(e) What is the minimum average cost?

the minimum average cost of c(900) is

[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]

c(900) = 60 + 130 + 4(30)

c(900) = 60 +130 + 120

c(900) = $310 per unit

Answer:

d 13

Step-by-step explanation: