50 + x + 10 + 8x + 2x =650​
what is the value of x?

[tex]\huge\bold{Given:}[/tex]

Length of the perpendicular = 7

Length of the base = 10

[tex]\huge\bold{To\:find:}[/tex]

The length of the missing side (hypotenuse).

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\longrightarrow{\purple{x\:=\: 12.21}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

Let the length of the missing side be [tex]x[/tex].

Using Pythagoras theorem, we have

(Hypotenuse)² = (Perpendicular)² + (Base)²

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = (7)² + (10)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 49 + 100

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 149

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]\sqrt{149}[/tex]

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = 12.206

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = 12.21.

Therefore, the length of the missing side [tex]x[/tex] is [tex]12.21[/tex].

[tex]\huge\bold{To\:verify :}[/tex]

[tex]\longrightarrow{\green{}}[/tex] (12.21)² = (7)² + (10)²

[tex]\longrightarrow{\green{}}[/tex] 149 = 49 + 100

[tex]\longrightarrow{\green{}}[/tex] 149 = 149

[tex]\longrightarrow{\green{}}[/tex] L.H.S. = R. H. S.

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]

Answer:

a) A(x) =  360*x  -  3*x²

b) The Domain of the function is ( 0 : ∞ )

c) x  =  60 yards

   y  =  180 yards

c) A(max) = 10800 yd²

Step-by-step explanation:

Two rectangular corrals, with sides y and x  ( y is the side parallel to the river) having a river as one side of the corrals means:

L  length to be fenced

L = y + 3*x         360  =  y  +  3*x       y   =  360  -  3*x

The total areaof the two corrals as a function of x is

A(t)  =  x*y         as     y  =  360  -  3*x   by substitution we get

A(x)  =  x * ( 360  - 3*x)

A(x) =  360*x  -  3*x²

Tacking derivatives on both sides of the equation we get:

A´(x)  =  360  - 6*x          A´(x)  =  0     360   -  6*x  =  0

x  =  60 yards

and   y  =  360  -  3*x      y  =  360  -  180     y  =  180 yards

A(max) =  60*180  =  10800 yd²

To find out if the value x  =  60 is the x value for a maximum of A we go to the second derivative

A´´(x) =  - 6      A´´(x)  < 0  then there is a maximum value for function A in x = 60

The Domain of the function is ( 0 : ∞ )

Sample variance = 228.408

Standard deviation = 15.113

The well formatted frequency table has been attached to this response.

To calculate the sample variance and standard deviation of the given grouped data, follow these steps:

i. Find the midpoint (m) of the class interval.

This is done by adding the lower bounds and upper bounds of the class intervals and dividing the result by 2. i.e

For class 0 - 9, we have

m = (0 + 9) / 2 = 4.5

For class 10 - 19, we have

m = (10 + 19) / 2 = 14.5

For class 20 - 29, we have

m = (20 + 29) / 2 = 24.5

For class 30 - 39, we have

m = (30 + 39) / 2 = 34.5

For class 40 - 49, we have

m = (40 + 49) / 2 = 44.5

This is shown in the third column of the attached table.

ii. Find the product of each of the frequencies of the class intervals and their corresponding midpoints. i.e

For class 0 - 9, we have

frequency (f) = 13

midpoint (m) = 4.5

=> f x m = 13 x 4.5 = 58.5

For class 10 - 19, we have

frequency (f) = 7

midpoint (m) = 14.5

=> f x m = 7 x 14.5 = 101.5

For class 20 - 29, we have

frequency (f) = 10

midpoint (m) = 24.5

=> f x m = 10 x 24.5 = 245

For class 30 - 39, we have

frequency (f) = 9

midpoint (m) = 34.5

=> f x m = 9 x 34.5 = 310.5

For class 40 - 49, we have

frequency (f) = 11

midpoint (m) = 44.5

=> f x m = 11 x 44.5 = 489.5

This is shown in the fourth column of the attached table.

iii. Calculate the mean (x) of the distribution i.e

This is done by finding the sum of all the results in (ii) above and dividing the outcome by the sum of the frequencies. i.e

x = ∑(f x m) ÷ ∑f

Where;

∑(f x m) = 58.5 + 101.5 + 245 + 310.5 + 489.5 = 1205

∑f = 13 + 7 + 10 + 9 + 11 = 50

=> x = 1205 ÷ 50

=> x = 24.1

Therefore, the mean is 24.1

This is shown on the fifth column of the attached table.

iv. Calculate the deviation of the midpoints from the mean.

This is done by finding the difference between the midpoints and the mean. i.e m - x where x = mean = 24.1 and m = midpoint

For class 0 - 9, we have

midpoint (m) = 4.5

=> m - x = 4.5 - 24.1 = -19.6

For class 10 - 19, we have

midpoint (m) = 14.5

=> m - x = 14.5 - 24.1 = -9.6

For class 20 - 29, we have

midpoint (m) = 24.5

=> m - x = 24.5 - 24.1 = 0.4

For class 30 - 39, we have

midpoint (m) = 34.5

=> m - x = 34.5 - 24.1 = 10.4

For class 40 - 49, we have

midpoint (m) = 44.5

=> m - x = 44.5 - 24.1 = 20.4

This is shown on the sixth column of the attached table.

v. Find the square of each of the results in (iv) above.

This is done by finding (m-x)²

For class 0 - 9, we have

=> (m - x)² = (-19.6)² = 384.16

For class 10 - 19, we have

=> (m - x)² = (-9.6)² = 92.16

For class 20 - 29, we have

=> (m - x)² = (0.4)² = 0.16

For class 30 - 39, we have

=> (m - x)² = (10.4)² = 108.16

For class 40 - 49, we have

=> (m - x)² = (20.4)² = 416.16

This is shown on the seventh column of the attached table.

vi. Multiply each of the results in (v) above by their corresponding frequencies.

This is done by finding f(m-x)²

For class 0 - 9, we have

=> f(m - x)² = 13 x 384.16 =  4994.08

For class 10 - 19, we have

=> f(m - x)² = 7 x 92.16 = 645.12

For class 20 - 29, we have

=> f(m - x)² = 10 x 0.16 = 1.6

For class 30 - 39, we have

=> f(m - x)² = 9 x 108.16 = 973.44

For class 40 - 49, we have

=> f(m - x)² = 11 x 416.16 = 4577.76

This is shown on the eighth column of the attached table.

vi. Calculate the sample variance.

Variance σ², is calculated by using the following relation;

σ² = ∑f(m-x)² ÷ (∑f - 1)

This means the variance is found by finding the sum of the results in (vi) above and then dividing the result by one less than the sum of all the frequencies.

∑f(m-x)² = sum of the results in (vi)

∑f(m-x)² = 4994.08 + 645.12 + 1.6 + 973.44 + 4577.76 = 11192

∑f - 1 = 50 - 1 = 49         {Remember that ∑f was calculated in (iii) above}

∴ σ² = 11192 ÷ 49 = 228.408

Therefore, the variance is 228.408

vii. Calculate the standard deviation

Standard deviation σ, is calculated by using the following relation;

σ =√ [ ∑f(m-x)² ÷ (∑f - 1) ]

This is done by taking the square root of the variance calculated above.

σ = [tex]\sqrt{228.408}[/tex]

σ = 15.113

Therefore, the standard deviation is 15.113

Answer:

H0 : μ ≥ 350

H1 : μ < 350

Step-by-step explanation:

It is claimed that the mean is atleast 350 psi ;

10 such pipes were experimentally sampled ;

Here, the null hypothesis is the claim ; this means that the alternative hypothesis will be the opposite of the claim.

The hypothesis

H0 : μ ≥ 350

H1 : μ < 350

Answer:  r = 5

Step-by-step explanation:

Answer:

1: x intercept:2 y intercept:5

2: x intercept:-7 y intercept:1

3: x intercept:2 y intercept:-2

4: x intercept: 1 y intercept: -2

Step-by-step explanation:

The y intercept is whenever the x unit is at 0, and the x intercept is whenever the y intercept is at 0.  

(-5/2;5)           (1/7;1)            (1;-2)           (2;-2)

Answer:

168cm^3

Step-by-step explanation:

Q to P is going to be 3cm. it is identical to the length T to U.

R to T , W to Q, S to U is going to be identical to P to V. P to V has been identified as 12 cm.

in the middle of the shape, there are 4 identical triangles. the height time length will give us the area of that one shape:

e.g for shape P to V to W to Q and back to P is one rectangle. the length is 12 cm and the width is 3 cm.

12 x 3= 36

36cm^3 is one rectangles surface area, we have 4 identical triangles that means we need to times 36 by 4.

so 36x4=144.

now on the left and right side, we have two squares. on the right, we have T to U to V to W back to T this has the height of 3 width of 4 then we do 3 X 4 which is 12, we times it by 2 because we have two identical squares.

12 X 2=24

finally we add 24 and 144 = 168cm^3.

hope this helps :)

Answer:

7=x

Step-by-step explanation:

6(x-3)=8(x-4)

Distribute

6x -18 = 8x-32

Subtract 6x from each side

6x-18 -6x = 8x-32-8x

-18 = 2x-32

Add 32 to each side

-18+32 = 2x-32+32

14 = 2x

Divide by 2

14/2 =2x/2

7=x

[tex]\sf\purple{x= 7}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

[tex]➺\:6(x - 3) = 8(x - 4)[/tex]

[tex]➺ \: 6x - 18 = 8x - 32[/tex]

[tex]➺ \: 6x - 8x = - 32 + 18[/tex]

[tex]➺ \: - 2x = - 14[/tex]

[tex]➺ \: x = \frac{ - 14}{ - 2} [/tex]

[tex]➺ \: x = 7[/tex]

Therefore, the value of [tex]x[/tex] is 7.

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]

[tex]➺ \: 6(x - 3) = 8(x - 4)[/tex]

[tex]➺ \: 6(7 - 3) = 8(7 - 4)[/tex]

[tex]➺ \: 6 \times 4 = 8 \times 3[/tex]

[tex]➺ \: 24 = 24[/tex]

➺ L. H. S. = R. H. S.

Hence verified.

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]

Answer:

[tex]{ \tt{ {a}^{8} - {12a}^{4} + 36}} \\ = { \tt{ {a}^{4} ( {a}^{2} - 12) + 36 }} \\ = ( {a}^{2} - 12)( {a}^{4} + 36) \\ [/tex]

Answer: [tex]14\ ft[/tex]

Step-by-step explanation:

Given

Length of rectangle is [tex]6\ ft[/tex]

Perimeter must be greater than 40 ft

Suppose l and w be the length and width of the rectangle

[tex]\Rightarrow \text{Perimeter P=}2(l+w)\\\Rightarrow P\geq 40\\\Rightarrow 2(l+w)\geq40\\\Rightarrow l+w\geq20\\\Rightarrow w\geq20-6\\\Rightarrow w\geq14\ ft[/tex]

So, the smallest width can be [tex]14\ ft[/tex]

Answer:

379

Step-by-step explanation:

a23 = 27 + (23-1)(16)

= 27 + (22)(16)

= 27 + 352

= 379

Answer:

Step-by-step explanation:

Answer:

She has 90.96 miles of the trail to hike.

Step-by-step explanation:

Length of the trail:

The length of the trail is of 113.7 miles.

On the first day she hiked of 1/10 the distance of the trail.

Thus:

[tex]\frac{1}{10(113.7) = 11.37[/tex]

On the first day she hiked 11.37 miles.

On the second day she hiked the same distance as the first day.

Also 11.37 miles on the second day, and thus, 2*11.37 = 22.74 miles on the first two days.

How much of the trail does she have left to hike?

113.7 - 22.74 = 90.96

She has 90.96 miles of the trail to hike.

Answer:

Kindly check explanation

Step-by-step explanation:

Using the compound interest formula :

A = P(1 + r/n)^nt

A = final amount ; r = rate ; n = number of compounding times per period ; t = period ; P = principal

P = 2500 ; r = 4% = 0.04 ; t = 5 years

Daily compounding, n = 365

Yearly compounding, n = 1

Quarterly compounding, n = 4

Daily compounding :

A = 2500(1 + 0.04/365)^(5*365)

A = 2500(1.0001095)^1825

A = $3053.4734

Yearly :

A = 2500(1 + 0.04/1)^(5*1)

A = 2500(1.04)^5

A = $3041.6323

Quarterly:

A = 2500(1 + 0.04/4)^(5*4)

A = 2500(1.01)^20

A = $3050.4751

Answer:

x = 2.8

Step-by-step explanation:

sin = opp/hyp

hyp = opp/sin

x = 2.4/sin60

x = 2.771281292110204

rounded

x = 2.8

9514 1404 393

Answer:

Step-by-step explanation:

I find the easiest way to answer these questions is to use a graphing calculator. It can show you the extreme values and the intercepts. The graph below shows the maximum height is 26.5 ft. The time in air is about 2.5 seconds.

__

If you prefer to solve this algebraically, you can use the equation of the axis of symmetry to find the time of the maximum height:

  t = -b/(2a) = -(40)/(2×-16) = 5/4

Then the maximum height is ...

  h(5/4) = -16(5/4)² +40(5/4) +1.5 = -25 +50 +1.5 = 26.5 . . . feet

__

Now that we know the vertex of the function, we can write it in vertex form:

  h(t) = -16(t -5/4)² +26.5

Solving for the value of t that makes this zero, we get ...

  0 = -16(t -5/4)² +26.5

  16(t -5/4)² = 26.5

  (t -5/4)² = 26.5/16 = 1.65625

Then ...

  t = 1.25 +√1.65625 ≈ 2.536954

The cannon ball is in the air about 2.5 seconds.

Answer:

[tex]radius=6.68cm[/tex]

Step-by-step explanation:

Formula to find radius:

[tex]r=\frac{C}{2\pi }[/tex]

[tex]r=42/2\pi[/tex]

[tex]r=42/2(3.14)[/tex]

[tex]r=6.68cm[/tex]

hope this helps......

Answer:

a) The mean is of [tex]\mu = 0.16[/tex]

b) The standard deviation is of [tex]s = 0.008[/tex]

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Question a:

Exactly 16% of all applications were from minority members

This means [tex]p = 0.16[/tex], and thus, the mean is of [tex]\mu = p = 0.16[/tex]

b. Find the standard deviation of p.

2100 open positions, thus [tex]n = 2100[/tex].

[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

[tex]s = \sqrt{\frac{0.16*0.84}{2100}}[/tex]

[tex]s = 0.008[/tex]

The standard deviation is of [tex]s = 0.008[/tex]

Answer:

I thimk it is B

Step-by-step explanation:

Answer:

a) Independent variable - Design of the course

Dependent variable - Final score of the students

b)  H0 - Final score >24.7

Alternate hypothesis - Final score is less than or equal to 24.7

Step-by-step explanation:

a) Independent variable - Design of the course

Dependent variable - Final score of the students

b) Null Hypothesis : Performance of student taking course with the new design is better as compared to the population of student taking the course with the old design.

H0 - Final score >24.7

Alternate hypothesis - Final score is less than or equal to 24.7

Answer:

1060

Step-by-step explanation:

Answer:

,here is the answer

Step-by-step explanation:

here is your answer

A

A

B

C

A

D

B

C

May choices po yan saamen

Step-by-step explanation:

Love you

Answer:

[tex]{ \bf{(a).}} \\ { \tt{ {n}^{th} = a + (n - 1)d }} \\ { \tt{ {n}^{th} = 6 + (n - 1) \times - 4 }} \\ {n}^{th} = 10 - 4n \\ \\ { \bf{(b).}} \\ { \tt{ {n}^{th} = - 8 + (n- 1) \times - 7 }} \\ { \tt{ {n}^{th} = -1 - 7n}}[/tex]

Answer:

the input x is 3

Step-by-step explanation:

2x+5=11

   2x=6

     x=3

Answer:

(x+y) ³

= x³+3x²y+3xy²+y³

=x³+y³+3xy(x+y)

Brainliest please~

(x+y)3= x^3+3x^2y+3xy^2+y^3

Answer:

5

Step-by-step explanation:

WHen we raise a power to a power, we multiply them, in this case 5 is the base so we can just ignore it for now and replace it with x.

(X^1/3)^3

Multiply 1/3 by 3 and we get 1

So:

X^1

Which does nothing, so we can simplify to just:\

X

Remember x is 5 so the answer is:

5