log 5 +3 log 2-log4÷log10
​

Answer:

4.5 m

Step-by-step explanation:

The diameter is twice the radius

d = 2r

Divide each side by 2

d/2 = r

9/2 = r

4.5 = r

Answer:

4.5 meters

Step-by-step explanation:

radius is half of the diameter

Answer:

4÷(6+3)

Step-by-step explanation:

6+3 is the sum of a number and 3, and you divide 4 by that.

The algebraic expression represents the statement The quotient of four and the sum of a number and three is 4÷(x + 3).

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Given:

The quotient of four and the sum of a number and three,

The above statement can be written as,

4÷(x + 3)

Here, x is the number

To know more about the expression:

https://brainly.com/question/13947055

#SPJ2

Answer: 11/12

Step-by-step explanation:

Addition of fractions

#1 Change to the same denominator

- LCM (Least common multiple) of 4 and 6 is 12

- 9/12+2/12

#2 Add the numerator as usual

 9/12+2/12

=(9+2)/12

=11/12

-------------------------------------------------

p=3/4+1/6

p=11/12

Answer:

x = 5, -3

Step-by-step explanation:

2x² - 4x - 5 = 25

add 5 to each side

2x² - 4x = 30

factor out the 2

2(x² - 2x) = 30

divide both sides by 2

x² - 2x = 15

divide b by 2, square it -- (b/2)², and add it to both sides

-2/2 = -1 → -1² = 1

x² - 2x + 1 = 15 + 1

factor the expression on the left -- this will be [x - (b/2)]²

(x - 1)² = 16

find the square root of both sides

x - 1 = ±4

add 1 to both sides

x = 4 + 1

x = -4 + 1

solve

x = 5, -3

Answer:

The error was made in step 4, [tex]\pi[/tex] should have also been cancelled making the correct answer as 9 cm.

Step-by-step explanation:

Given that:

Volume of cylinder, [tex]V = 576 \pi\ cm^3[/tex]

Radius of cylinder, r = 8 cm

To find:

The error in calculating the height of cylinder by Sandra ?

Solution:

We know that volume of a cylinder is given as:

[tex]V = B h[/tex]

Where B is the area of circular base and

h is the height of cylinder.

Area of a circle is given as, [tex]B = \pi r^2[/tex]

Let us put it in the formula of volume:

[tex]V = \pi r^2 h[/tex]

Step 1:

Putting the values of V and r:

[tex]576\pi = \pi 8^2 h[/tex]

So, it is correct.

Step 2:

Solving square of 8:

[tex]576\pi = \pi \times 64\times h[/tex]

So, step 2 is also correct.

Step 3:

[tex]h=\dfrac{576\pi}{64 \pi} = \dfrac{64 \pi \times 9}{64\pi}[/tex]

Step 4:

Cancelling 64 [tex]\times \pi[/tex],

h = 9 cm

So, the error was made in step 4, [tex]\pi[/tex] should have also been cancelled making the correct answer as 9 cm.

Answer:

(C) In step 4, the pi should have canceled, making the correct answer 9 cm.

Answer:

Area shaded blue = 294.5 m^2  (to the nearest tenth)

Step-by-step explanation:

Refer to the attached figure.

Consider sector patterned in orange

radius = 11.1 m

angle of sector = 360-130 = 230 degrees

area of sector  =  (angle / 360) * area of complete circle

A1 = (230/360)*pi * 11.1^2

= 78.7175 pi

= 247.298 m^2

Area of right triangle with hypotenuse, L, and one of the angles, x,  known

= (Lsin(x))*L(cos(x)/2

= L^2 sin(2x)/4

A2 = 2* (11.1^2 sin(130/2)/4)

= 11.1^2 * sin(65) / 2

= 47.192 m^2

Area shaded blue

= A1+A2

= 247.298 + 47.192

= 294.49 m^2

Answer:

A

Step-by-step explanation:

Since m∠JOK is 1/5th of the measure of the full circle (we know this because 72° is 1/5th of 360° and 360° is the measure of the whole circle), we know that the measure of minor arc JK will be 1/5th of the circumference of the circle. C = 2πr and we know that r = 5 so the circumference is 10π. 1/5th of that is 2π.

Answer:

[tex]4+3i[/tex]

Step-by-step explanation:

=[tex]\frac{(10+20i)}{4+2i} \\\\\frac{10+20 i}{4+2i}[/tex]x   [tex]\frac{(4-2i)}{(4-2i)}[/tex]

=[tex]\frac{(10+20i)(4-2i)}{(4^{2}-2i^{2}) } \\\frac{40-20i+80i+40}{16+4}\\ \frac{80+60i}{20}\\ 4+3i[/tex](Taking 20 common from both numerator and deniminator)

Answer:   6π

Step-by-step explanation:

Area of a circle is π r².

Area of a section of a circle is π r² × the section of the circle.

[tex]A=\pi r^2\bigg(\dfrac{\theta}{360^o}\bigg)[/tex]

Given: r = 6, Ф = 60°

[tex]A=\pi (6)^2\bigg(\dfrac{60^o}{360^o}\bigg)\\\\\\.\quad =\pi (6)^2\bigg(\dfrac{1}{6}\bigg)\\\\\\.\quad =6\pi[/tex]

Answer:

Hey there!

8 is the correct answer.

It is 16 times greater than the digit to it's right.

Let me know if this helps :)

Answer:

12x

Step-by-step explanation:

This is b/2^2, so basically you take the square root of 36 and multiply that value by 2.

so [tex]\sqrt{36}[/tex] = 6(2)=12

Hope this makes sense!

Step-by-step explanation:

First, let's look at some examples of what a perfect square trinomial looks like.  [tex]x^2 + 16x + 64[/tex]

This trinomial is made from:

[tex](x+8)^2[/tex]

So for your second question (x^2 + ___x + 36), we need to work backwards, starting with the last number of the trinomial, 36. Think of two identical numbers that would make 36 if they got multiplied together. Or: √36. Either way, we get 6. So we can put this as a squared binomial.

[tex](x+6)^2[/tex]

Then, we could solve the binomial to get our middle number. (Use FOIL: Multiply the First terms, then Outer terms, then Inner terms, and Last terms)

[tex](x+6)(x+6)[/tex]

[tex]x^2+6x+6x+36\\x^2+12x+36[/tex]

As you can see, our middle number is 12x, and that is what goes into the blank.

Answer: 12x

Answer:

Step-by-step explanation:

D = {x | x is a whole number}

D = {0, 1, 2, 3, 4,......}

E = {x | x is a perfect square between 49 and 100}

E = {64, 81}

F = {x | x is an even number between 10 and 20}

F = {12, 14, 16, 18}

D∪F = {x | x is whole number}

D∩F = {x | x is an even number between 10 and 20}

D∩E = {x | x is a perfect square between 49 and 100}

E∩F = {null set}

D∩(E∪F) = {12, 14, 16, 18, 64, 81}

Answer:

  f(777) = 390

Step-by-step explanation:

f(1) = 2 . . . . given

f(2) = f(f(1)) = 3 . . . . given

f(3) = f(f(f(1))) = 1+4 = 5

f(5) = f(f(3)) = f(f(f(2))) = 2+2 = 4

f(4) = f(f(5)) = f(f(f(3))) = 3+4 = 7

f(7) = f(f(4)) = f(f(f(5))) = 5+4 = 9

Then the sequence of sequential function values is ...

  2, 3, 5, 4, 7, 9, 6, 11, 13, ... (pattern repeats in groups of 3)

__

Each odd number of the form 4n+1 is the function value f(4n-1) = 4n+1.

Similarly, the next function value is f(4n+1) = (4n+1+3)/2.

Since 777 is 4(194) +1, we have ...

  f(777) = (777+3)/2

  f(777) = 390

This question is incomplete, the complete question is;

Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that women have a higher mean resting heart rate than men?

A.t

B.F

C.Normal

D. Chi-square

Answer:

A) t  test

Step-by-step explanation:

A t-test uses sample information to assess how plausible it is for the population means μ1​ and μ2​ to be equal.

The formula for a t-statistic for two population means (with two independent samples), with unknown population variances shows us how to calculate t-test with mean and standard deviation and it depends on the assumption of having an equal variance or not.

If the variances are assumed to be not equal,

he formula is:

t =  (bar X₁ - bar X₂) / √( s₁²/n₁ + s₂²/n₂ )

If the variances are assumed to be equal, the formula is:

t =  (bar X₁ - bar X₂) / √ (((n₁ - 1)s₁² + (n₂ - 1)s₂²) / (n₁ + n₂ - 2)) ( 1/n₁ + 1/n₂)

it called t-test for independent samples because the samples are not related to each other, in a way that the outcomes from one sample are unrelated from the other sample.

hence option A is correct. t test

Answer:

5/37+30/37*i

Step-by-step explanation:

we multiply by 1+6i

so 5*(1+6i)/(1^1-36i^2)=(5+30i)/37=

5/37+30/37*i

Answer:

x=30

Step-by-step explanation:

[tex]\frac{4}{5}=\frac{20}{x-5} \\\\4(x-5)=20*5\\\\4x-20=20(5)\\\\4x=20(5)+20(1)\\\\4x=20(5+1)\\\\4x=20(6)\\\\x=\frac{20(6)}{4} \\\\x=5*6\\\\x=30[/tex]

[tex] \frac{4}{5} = \frac{20}{(x - 5)} [/tex]

By Cross-multiplication

[tex] \implies4 \times (x - 5) = 20 \times 5[/tex]

[tex] \implies4x - 20 = 100[/tex]

[tex] \implies4x = 100 + 20[/tex]

[tex] \implies4x = 120[/tex]

[tex] \implies \: x = \cancel \frac{120}{4} [/tex]

[tex] \implies \: x = 30[/tex]

Answer: C. x>70

Step-by-step explanation:

       x/10>7

x/10 × 10>7 × 10

           x>70

Hope this helps!! :)

Answer: Area = [tex]\int\limits^5_0 {(5x - x^2)} \, dx[/tex]

Step-by-step explanation:

Thiis is quite straightforward, so I will be gudiding you through the process.

we have that;

y1 = x² -5x

and y² = 0

Taking Limits:

y1 = x² -5x, y2 = 0

x² - 5x = 0;

so x(x - 5) = 0

this gives x = 0 and x = 5

∴ 0≤x≤5

This is to say that the graph intersets at x = 0 and x = 5 and y2  is the upper most function.

Let us take the formula:

Area = ∫b-a (upper curve - lower curve)

where a here represents 0 and b represents 5

the upper curve y2 = 0

whereas the lower curve y1 = x² - 5x

Area = ∫5-0 [ 0 - (x² - 5x) ] dx

This becomes the Area.

Area = [tex]\int\limits^5_0 {(5x - x^2)} \, dx[/tex]

cheers i hope this helped !!!

Answer:

Step-by-step explanation:

GIven that:

The set is :  {l, 2, 3, 4.5.6}

To Prove that:

If four numbers are to be chosen , at least one pair of the selected numbers must add up to 7

From the data set given, this set has three pairs of number which can add up to 7. These are:

{1, 6}  i.e 1 + 6 = 7

{2,5}  i.e  2+ 5 = 7

{3,4}  i.e  3 + 4 = 7

So, if four number are chosen from the set that contains six numbers, then that the possibility for such to occur is either by selecting two pairs out of the three pairs or one pair and two numbers.

Thus, in both cases, at least one pair of the selected numbers must add up to 7.

Answer:

17°

Step-by-step explanation:

Using trigonometrical ratios we have a triangle with opposite of A° as 7cm and adjacent A° as 24cm as drawn in the above diagram.

Using trigonometry the value to be used is Tangent due to the availability of only the opposite and adjacent sides.

tan = opp/adj

tan x(x is the angle) = 7/24

tan x = 0.2917 ~= 0.3

tan x = 0.3

x = tan^-1 0.3

x = 16.7 ~= 17°.

Answer:

With the information given in the question, the blank spaces are filled thus:

Step-by-step explanation:

1. The intercept is the estimated amount of a purchase, if time spent viewing the online catalog was zero minutes.

2. The slope coefficient is the estimate of amount that a purchase charges/changes, for one extra minute spent viewing the online catalog.

3. The proportion of total variation in purchases that can be explained by variation in the minutes spent viewing an online catalog is equal to the coefficient of determination.

4. The p-value is the probability value

5. Reject the null hypothesis if there is sufficient evidence to support the claim that the regression slope coefficient is not equal to zero.

NOTE: In the case of number 5, the assumption is that;

Null Hypothesis: The regression slope coefficient = 0

Alternative Hypothesis: The regression slope coefficient ≠ 0

Other answers require numerical information and full data, in order to be computed or calculated.

Complete  Question

One consequence of the popularity of the internet is that it is throughout to reduce television watching. Suppose that a random sample of 55 individuals who consider themselves to be avid Internet users results in a mean time of 2.10 hours watching television on a weekday. The  standard deviation  is  [tex]\sigma = 1.93[/tex]

Required:

Determine the likelihood of obtaining a sample mean of 2.10 hours or less from a population whose mean is presumed to be 2.45 hours.

Answer:

The  likelihood is  [tex]P(X \le 2.10 ) = 0.08931[/tex]

Step-by-step explanation:

From the question we are told that  

    The sample size is  [tex]n = 55[/tex]

    The population mean is  [tex]\mu = 2.45 \ hours[/tex]

    The random mean considered [tex]\= x = 2.10 \ hours[/tex]

Generally the standard error of  mean is mathematically represented as

              [tex]\sigma _{\= x } = \frac{\sigma }{ \sqrt{n} }[/tex]

=>           [tex]\sigma _{\= x } = \frac{1.93 }{ \sqrt{55} }[/tex]

=>           [tex]\sigma _{\= x } = 0.2602[/tex]

The  likelihood of obtaining a sample mean of 2.10 hours or less from a population whose mean is presumed to be 2.45 hours is mathematically represented as

               [tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 1 - P( \frac{X - \mu }{\sigma_{\= x }} > \frac{ 2.10 - 2.45}{ 0.2602} )[/tex]

Generally    [tex]\frac{X - \mu }{\sigma_{\= x }} = Z(The \ standardized \ value \ of \ X )[/tex]

               [tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 1 - P( Z > -1.345 )[/tex]

From the z-table the value of

           [tex]P( Z > -1.345 ) = 0.91069[/tex]

  So

        [tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 1 - 0.91069[/tex]

         [tex]P(X \le 2.10 ) = 1 - P(X > 2.10 ) = 0.08931[/tex]

        [tex]P(X \le 2.10 ) = 0.08931[/tex]

This question is based on the point of intersection.Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:

[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]

Given:

Equations: r = 1 + cos θ                                                                      ...(1)

                  r = 1 − sin  θ                                                                      ...(2)                                                                

Where, r ≥ 0, 0 ≤ θ < 2π

We need to determined the point of intersection of the graphs of the equations.

To obtain the points of intersection, Equate the two equations above as follows;

r = 1 + cos θ = 1 - sin θ

=> 1 + cos θ = 1 - sin θ

Solve further for θ. We get,

1 + cos θ = 1 - sinθ

cos θ  = - sinθ

Now dividing both sides by - cos θ and solve it further,

[tex]\dfrac{cos\;\theta}{-cos\;\theta} =\dfrac{-sin\;\theta}{-cos\;\theta}\\\\tan\;\theta=-1\\\\\theta=tan^{-1}(1)\\\\\theta=45^{0}=\dfrac{-\pi }{4}[/tex]

To get the 2nd quadrant value of θ, add π ( = 180°) to the value of θ. i.e

[tex]\dfrac{-\pi }{4} +\pi =\dfrac{3\pi }{4} \\[/tex]

Similarly, to get the fourth quadrant value of θ, add 2π ( = 360° ) to the value of θ. i.e

[tex]\dfrac{-\pi }{4} +2\pi =\dfrac{7\pi }{4} \\[/tex]

Therefore, the values of θ are 3π / 4 and 7π / 4.

Now substitute these values into equations (i) and (ii) as follows;

[tex]When \;\theta=\dfrac{3\pi }{4},[/tex]

[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{3\pi }{4} =1+\dfrac{-\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]

[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{3\pi }{4} =1-\dfrac{\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]

[tex]When\; \theta=\dfrac{7\pi }{4}[/tex]

[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{7\pi }{4} =1+\dfrac{\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]

[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{7\pi }{4} =1-\dfrac{-\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]

Represent the results  above in polar coordinates of the form (r, θ). i.e

[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]

Therefore, at the pole where r = 0, is also one of the points of intersection.  

Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:

[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]

For further details, please prefer this link:

https://brainly.com/question/13373561

Question:

The digit 8 in which number represents a value of 8 thousandths?

Answer:

See Explanation

Step-by-step explanation:

The question requires options and the options are missing.

However, the following explanation will guide you

Start by representing 8 thousandths as a digit

[tex]\frac{8}{1000} = 0.008[/tex]

i.e.

8 thousandths implies 0.008

Next;

Replace the 0s with dashes

_ . _ _8

Note that there are two dashes after the decimal point and before 8

PS: The dashes are used to represent digits

This implies that thousandths is the 3rd digit after the decimal point

Typical examples to back up this explanation are:

17.008, 1.1489, 0.008 and so on...

Answer:

1/380

Step-by-step explanation:

Probability of Bob's name drawn first is:

And probability of Laquisha's name drawn second is:

Probability of the two events happening is:

Answer:

Hey there!

1/19 (1/20)=1/380, so the probability is 1/380

Let me know if this helps :)

The tens place has a 0 in that digit. One spot to the right is 5. Since this is 5 or larger, we round up to the nearest ten.

The 0 bumps up to 1. The 5 is replaced with 0

4205 becomes 4210

Answer:

[tex]\mathbf{\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1)}[/tex]

[tex]\mathbf{\dfrac{\partial f}{\partial y}= cos ( -7y^2 -6y-1)}[/tex]

Step-by-step explanation:

Given that :

[tex]f(x,y) = \int ^x_y cos (-7t^2 -6t-1) dt[/tex]

Using the Leibnitz rule of differentiation,

[tex]\dfrac{d}{dt} \int ^{b(t)}_{a(t)} f(x,t) dt= f(b(t),t) *b'(t) -f(a(t),t) * a' (t) + \int^{b(t)}_{a(t)} \dfrac{\partial f}{\partial t} \ dt[/tex]

To find: fx(x,y)

[tex]\dfrac{\partial f}{\partial x}= \dfrac{\partial }{\partial x} [ \int ^x_y cos (-7t^2 -6t -1 ) \ dt][/tex]

[tex]\dfrac{\partial f}{\partial x}= \dfrac{\partial x}{\partial x} cos (-7x^2 -6x -1 ) - \dfrac{\partial y}{\partial x} * cos (-7y^2 -6y-1) + \int ^x_y [\dfrac{\partial }{\partial x} \ \{cos (-7t^2-6t-1)\}] \ dt[/tex]

[tex]\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1) -0+0[/tex]

[tex]\mathbf{\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1)}[/tex]

To find: fy(x,y)

[tex]\dfrac{\partial f}{\partial y}= \dfrac{\partial }{\partial y} [ \int ^x_y cos (-7t^2 -6t -1 ) \ dt][/tex]

[tex]\dfrac{\partial f}{\partial y}= \dfrac{\partial x}{\partial y} cos (-7x^2 -6x -1 ) - \dfrac{\partial y}{\partial y} * cos (-7y^2 -6y-1) + \int ^x_y [\dfrac{\partial }{\partial y} \ \{cos (-7t^2-6t-1)\}] \ dt[/tex]

[tex]\dfrac{\partial f}{\partial y}= 0 - cos ( -7y^2 -6y-1)+0[/tex]

[tex]\mathbf{\dfrac{\partial f}{\partial y}= cos ( -7y^2 -6y-1)}[/tex]

Answer:

11.04hrs

Step-by-step explanation:

Since Steven traveled 530 miles (number of hrs times mph) we would just divide 530 and 48 which is 11.04 hrs