T= 2pi times the sqrt of l/g (l=2.0m; g= 10m/s^2

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

[tex]2x - 40y = 73...(i)[/tex]

[tex]7x + 65y = 332...(ii)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\pink{To\:find }}{\pink{:}}}}}[/tex]

The values of [tex]x[/tex] and [tex]y[/tex].

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

[tex]x=43.96 [/tex] and [tex]y = 0.373 [/tex].

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

Let us solve this by substitution method.

From [tex]eqn.\:(i),\:we\:have [/tex]

↬[tex]2x - 40y = 73[/tex]

↬[tex]2x = 73 + 40y[/tex]

↬[tex]x = \frac{73 + 40y}{2}...(iii) \\ [/tex]

Substituting the value of [tex]x[/tex] in [tex]eqn.\:(ii)[/tex] gives us

↬[tex]7( \frac{73 + 40y}{2} ) + 65y = 332 \\ [/tex]

↬[tex] \frac{511 + 280y}{2} + \frac{65y \times 2}{1 \times 2} = 332 \\ [/tex]

↬[tex] \frac{511 + 280y + 130y}{2} = 332 \\ [/tex]

↬[tex]410y + 511 = 332 \times 2[/tex]

↬[tex]410y = 664 - 511[/tex]

↬[tex]y = \frac{153}{410} \\ [/tex]

↬[tex]y = 0.373[/tex]

Now, plug the value of [tex]y[/tex] in [tex]eqn.\:(i)[/tex]

↬[tex]2x - 40 \times 0.373 = 73 \\ [/tex]

↬[tex]2x - 14.92= 73 [/tex]

↬[tex]2x = 73 +14.92[/tex]

↬[tex]x = \frac{87.92}{2} \\ [/tex]

↬[tex]x = 43 .96[/tex]

Therefore, the values of [tex]x[/tex] and [tex]y[/tex] are [tex]\boxed{ 43.96 }[/tex] and [tex]\boxed{ 0.373 }[/tex] respectively.

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

9514 1404 393

Answer:

  $442.80

Step-by-step explanation:

The formula for the amount of an ordinary annuity is ...

  A = P(12/r)((1 +r/12)^(12t) -1)

where payment P is made n times per year and interest is accrued at annual rate r.

Filling in the given values, we want ...

  50,000 = P(12/0.04)(1 +0.04/12)^(12·8) -1) = 112.91854P

  P = 50,000/112.91854 ≈ 442.80

You would need to deposit $442.80 each month for 8 years.

Answer:

17

Step-by-step explanation:

We are adding the previous two terms

1+5 = 6

5+6 = 11

6+11 = 17

11+17 = 28

The missing term is 17

Answer:

V = 1071.79 yd^3

Step-by-step explanation:

The volume of a cone is

V = 1/3 pi r^2 h  where r is the radius and h is the height

We are given a diameter of 16 so the radius is 1/2 of the diameter or 8

The height is 16

V = 1/3 ( 3.14) (8)^2 ( 16)

V = 1071.78666 yd^3

Rounding to the nearest hundredth

V = 1071.79 yd^3

[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: of \: Cone \: = \: \pi \: {r}^{2} \: \frac{h}{3} }}}}}\end{gathered}[/tex]

[tex] \bf{\red{ \longrightarrow}} \tt \: r \: = \: \frac{Diameter}{2} \\ [/tex]

[tex]\bf{\red{ \longrightarrow}} \tt \: r \: = \: \frac{16 \: yd}{2} \\ [/tex]

[tex]\bf{\red{ \longrightarrow}} \tt \: r \: = \: \frac{ \cancel{16 \: yd} \: \: ^{8} }{ \cancel{2}} \\ [/tex]

[tex]\bf{\red{ \longrightarrow}} \tt \: \large{\bf{{{\color{navy}{r \: = \: 8 \: yd}}}}}[/tex]

[tex]\bf{\red{ \longrightarrow}} \tt \: \: \large{\bf{{{\color{navy}{h \: = \: 16 \: yd}}}}}[/tex]

[tex] \bf \large \longrightarrow \: \: 3.14 \: \times \: {8}^{2} \: \times \: \frac{16}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \:3.14 \: \times \: 64 \: \times \: \frac{16}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \:3.14 \: \times \: 64 \: \times \: \frac{ \cancel{16} \: \: ^{5.33} }{ \cancel{3}} \\ [/tex]

[tex]\bf \large \longrightarrow \: \:3.14 \: \times \: 64 \: \times \: 5.33[/tex]

[tex]\bf \large \longrightarrow \: \:200.96 \: \times \: 5.3[/tex]

[tex]\bf \large \longrightarrow \: \:1071.79[/tex]

Option (A) is the correct answer

Answer:

x = 11/10

Step-by-step explanation:

5(2x - 1) = 6

Distribute

10x -5 = 6

Add 5 to each side

10x-5+5 = 6+5

10x = 11

Divide each side by 10

10x/10 = 11/10

x = 11/10

9514 1404 393

Answer:

   10·2^-8 grams

Step-by-step explanation:

The each day, the initial amount for that day is multiplied by 1/2. After 8 days, the initial amount has been multiplied by (1/2)^8, where the exponent of 8 signifies that (1/2) is a factor 8 times in the product.

After n days, the quantity remaining is ...

  q(n) = 10·(1/2)^n = 10·2^(-n)

after 8 days the remaining amount is ...

  q(8) = 10·2^-8 . . . grams

Answer:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

Solutions: x = 6, y = 5   or   x = -2, y = 5

Step-by-step explanation:

Use a graph.

Plot point (-2, 5). That will be a point on a circle with radius 5.

From point (-2, 5), go right 4 and down 3 to point (2, 2). (2, 2) is the center of the circle.

You now need the equation of a circle with center (2, 2) and radius 5.

Use the standard equation of a circle:

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

where (h, k) is the center and 5 is the radius.

The circle has equation:

[tex] (x - 2)^2 + (y - 2)^2 = 25 [/tex]

To have a single solution, you need the equation of the line tangent to the circle at (-2, 5), but since you want more than one solution, you need the equation of a secant to the circle. For example, use the equation of the horizontal line through point (2, 5) which is y = 5.

System:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

To solve, let y = 5 in the equation of the circle.

(x - 2)^2 + (5 - 2)^2 = 25

(x - 2)^2 + 9 = 25

(x - 2)^2 = 16

x - 2 = 4  or x - 2 = -4

x = 6 or x = -2

Solutions: x = 6, y = 5   or   x = -2, y = 5

An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, This system by starting with the equation of a circle centered at the origin with radius sqrt(29), which is,

⇒ x² + y² = 29.

Then, Added a linear equation that intersects the circle at (-2,5) to create a system with two solutions.

The entire solution set for this system is: (-2, 5) and (7/5, -19/10)

Thus, An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

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9514 1404 393

Answer:

  11. (-1.5, 3)

  12. √29, identical lengths, true they are congruent

Step-by-step explanation:

11. The midpoint is halfway between the end points. On a graph, you can count the grid squares between the ends of the segment and locate the point that is half that number from either end.

Points C and D differ by 2 in the y-direction, so the midpoint will be 1 unit vertically different from either C or D. That is, it will lie on the line y = 3. The segment CD intersects y=3 at x = -1.5, so the midpoint of CD is (-1.5, 3).

If you like, you can calculate the midpoint as the average of the end points:

  midpoint CD = (C +D)/2 = ((-4, 4) +(1, 2))/2 = (-3, 6)/2 = (-1.5, 3)

__

12. The exact length can be found using the Pythagorean theorem. The segment is the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.

In the previous problem, we observed that the y-coordinates of C and D differed by 2. The x-coordinates differ by 5. Looking at segment AB, we see the same differences: x-coordinates differ by 5 and y-coordinates differ by 2. Then the lengths of each of these segments is ...

  AB = CD = √(2² +5²) = √29

a) The exact lengths of segments AB and CD are √29 units.

b) The lengths of the segments are identical

c) It is TRUE that the segments are congruent.

Answer:

ok as we know 15 is a whole number by itself and 3/8 is the decimal part

so we know it is 15. something

that something is 3/8 to find decimal you do 3/8

3/8 is = .375

so 15.375 is the answer

hope it helps

brainliest give me pls

Answer:

A

Step-by-step explanation:

(f+g)(x)=f(x) + g(x)=(x/2)-3+3x^2+x-6=3x^2+(3/2)x-9

Answer:

174 cm²

Step-by-step explanation:

The figure given is a prism with isosceles trapezoid as base.

Its surface area can be calculating the area of each face that makes up the prism, and summing all together.

There are 6 faces. Their dimensions and areas can be calculated as follows:

2 isosceles trapezium:

It has 2 parallel bases, (a and b), of 4cm and 6cm,

Height (h) = 2.8cm

Area = ½(a+b)*h

Area = ½(4+6)*2.8

Area = ½(10)*2.8 = 5*2.8 = 14 cm²

4 rectangles of different dimensions:

Rectangle 1 (down face): l = 10cm, b = 4cm

Area = 10*4 = 40 cm²

Rectangle 2 and 3 (side faces): l = 10cm, b = 3cm

Area = 2(l*b) = 2(10*3) = 60cm²

Rectangle 4 (top face) = l = 10cm, b = 6cm

Area = 10*6 = 60cm²

Surface area of the figure = 14 + 40 + 60 + 60 = 174 cm²

Answer:

A) Reject H0 if F > 5.417

B) we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms

Step-by-step explanation:

A) From the table, we can see that we have df1 = 3 and df2 = 15. And we are given a significance level of α = 0.01

We are also given f-value of 1.75

Thus,from the f-distribution table attached at significance level of α = 0.01 and df1 = 3 and df2 = 15, we have;

F-critical = 5.417

Normally, we reject H0 if F > 5.417

But in this case, F is 1.75 < 5.417 and so we conclude that we do not reject H0 at the 0.01 level of significance

B) for 0.05 level of significance, df1 = 3 and df2 = 15, from the 2nd table attached, we have;

F-critical = 3.2874

Again the f-value is less than this critical one.

Thus, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms

Answer:

Step-by-step explanation:

If the larger of 2 consecutive integers is 324, then 324-(2-1) = 323 is the smaller.

If the largest of 89 consecutive integers is 324, then 324 - (89-1) = 236 is the smallest.

Hence, the smallest consecutive integer is [tex]237[/tex].

What is the smallest consecutive integer?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Here given that,

The largest of [tex]89[/tex] consecutive integers is [tex]324[/tex]

So, it is of the form

[tex]324-89=237[/tex]

Hence, the smallest consecutive integer is [tex]237[/tex].

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Answer:

  C = (18, 6)

Step-by-step explanation:

You have ...

  AB : BC = 1 : 1/3 = 3 : 1

  (B -A) / (C -B) = 3/1 . . . . . another way to write the distance relation

  B -A = 3(C -B) . . . . . . . . . multiply by (C-B)

  4B -A = 3C . . . . . . . . . . . add 3B

  C = (4B -A)/3 . . . . . . . . . divide by 3 to get an expression for C

  C = (4(14, 4) -(2, -2))/3 = (54, 18)/3

  C = (18, 6)

Answer:

15 dollars

Step-by-step explanation:

12 inches = 1 ft

so 12 inch by 12 inches  is 1 ft * 1 ft

1 ft* 1 ft

1 ft^2

This is smaller than 3 ft^2 so they will get charged for 3 ft^2

3 ft^2 = 3 ft^2 * $5 / ft^2 = 15 dollars

Answer:

federal loans = $29,000

private loans = $14,000

Step-by-step explanation:

x + y = 43000

.045x + .02y = 1585

x = 29,000

y = 14,000

Answer:

Amount of loan from federal : $ 29,000

Amount of loan from private bank : $ 14,000

Step-by-step explanation:

We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.

If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -

x + y = 43,000

At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -

0.045x + 0.02y = 1585

Let's solve the following system for x and y, the amount of each loan,

[tex]\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}[/tex] ( Substitute x = 43000 - y )

[tex]0.045\left(43000-y\right)+0.02y=1585[/tex] ( Simplify )

[tex]1935-0.025y=1585[/tex],

[tex]1935000-25y=1585000[/tex],

[tex]-25y=-350000[/tex],

[tex]y=14000[/tex],

[tex]x=29000[/tex]

Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.

Answer:

please mark my answer brainliest

Step-by-step explanation:

question is unclear to give u correct answer

Answer:

Standard deviation = 2.2360679774998

Step-by-step explanation:

We are asked to find the Standard deviation of a samples of speeches as an awards.

The formula for sample standard deviation is given as:

√[(x - μ)²/N - 1 ]

Step 1

We find the mean (μ)

The mean of the sample =>

= Sum of term/ Number of terms

= (3 + 7 + 5 + 4 + 1)/5

= 20/5

= 4

Step 2

Find the Standard deviation of the sample

√[(x - μ)²/N - 1 ]

N = number of samples or terms = 5

= √[(3 - 4) ² + (7 - 4)² + (5 - 4)² +(4 - 4)² +(1 - 4)²/ 4]

= √ (1 ² + 3² + -1² + 0² + -3²/4)

= √( 1 + 9 + 1 + 0 + 9/4)

= √20/5 - 1

= √5

= 2.2360679774998

The standard deviation of the sample = 2.2360679774998

Answer:

C(x)=1.2x+8,000.

Step-by-step explanation:

C(x)=cost per unit⋅x+fixed costs.

The manufacturer has fixed costs of $8000 no matter how many drinks it produces. In addition to the fixed costs, the manufacturer also spends $1.20 to produce each drink. If we substitute these values into the general cost function, we find that the cost function when x drinks are manufactured is given by

In order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.

Given is that the manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2.

Suppose that you have to sell [x] number of bars to make profits. So, we can write -

{2x} - {1.20x} > {8000}

0.8x > 8000

8x > 80000

x > 10000

Therefore, in order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.

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Let [tex]\mu[/tex] be the average number of televisions per household in the United States .

As per given ,

[tex]H_0:\mu =2.3\\\\ H_a:\mu\neq2.3[/tex]

Since [tex]H_a[/tex] is two-tailed and population standard deviation is unknown, so the test is two-tailed t-test.

For sample : Sample size : n= 73, sample mean: [tex]\overline{x}[/tex] = 2.1, sample standard deviation : s= 0.84.

[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]

[tex]t=\dfrac{2.1-2.3}{\dfrac{0.84}{\sqrt{73}}}\\\\ t=-2.034[/tex]

T-critical value for degree of freedom n-1 = 73-1=72 and 0.01 significance level is 2.646 . [By students' t-distribution table]

Since, [tex]|2.034|<2.646[/tex] i.e. [tex]|T_{cal}|<|T_{crit}|[/tex]

This means we cannot reject null hypothesis.

We conclude that the average number of televisions per household in the United States is 2.3 at the 0.01 significance level.

Answer:

The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Step-by-step explanation:

The complete question is:

Salaries of 42 college graduates who took a statistics course in college have a​ mean, [tex]\bar x[/tex] of, $64, 100. Assuming a standard​ deviation, σ of ​$10​,016 construct a ​99% confidence interval for estimating the population mean μ.

Solution:

The (1 - α)% confidence interval for estimating the population mean μ is:

[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

The critical value of z for 99% confidence interval is:

[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57[/tex]

Compute the 99% confidence interval for estimating the population mean μ as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)[/tex]

Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Parameterize this surface (call it S) by

[tex]\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+u^2\,\mathbf k[/tex]

with [tex]0\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex].

The normal vector to S is

[tex]\mathbf n=\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}=-2u^2\cos v\,\mathbf i-2u^2\sin v\,\mathbf j+u\,\mathbf k[/tex]

Compute the curl of F :

[tex]\nabla\times\mathbf F=-2\,\mathbf i+3\,\mathbf j+5\,\mathbf k[/tex]

So the flux of curl(F) is

[tex]\displaystyle\iint_S(\nabla\times\mathbf F)\cdot\mathrm d\mathbf S=\int_0^{2\pi}\int_0^2(\nabla\times\mathbf F)\cdot\mathbf n\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle\int_0^{2\pi}\int_0^2(5u+4u^2\cos v-6u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{20\pi}[/tex]

Alternatively, you can apply Stokes' theorem, which reduces the surface integral of the curl of F to the line integral of F along the intersection of the paraboloid with the plane z = 4. Parameterize this curve (call it C) by

[tex]\mathbf r(t)=2\cos t\,\mathbf i+2\sin t\,\mathbf j+3\,\mathbf k[/tex]

with [tex]0\le t\le2\pi[/tex]. Then

[tex]\displaystyle\iint_S(\nabla\times\mathbf F)\cdot\mathrm d\mathbf S=\int_0^{2\pi}\mathbf F\cdot\mathrm d\mathbf r[/tex]

[tex]=\displaystyle\int_0^{2\pi}(20\cos^2t-24\sin t)\,\mathrm dt=\boxed{20\pi}[/tex]

Answer:

plz complete question

so I can help you.

Answer:

Y=Srt(12xs^2/z^2)

Step-by-step explanation:

Firstly

We multiply both sides with 1/x^2

We get

Y^2=12/z^2*1/x^2

Y^2=12x^2/z^2

Next: introduce a srt root

We have

Y=srt(12x^2/z^2)

Answer:

800×200= 8 × 200 hundreds= 1600 Hundreds = 160000

Answer:

Step-by-step explanation:

The sequence of the problem above is an arithmetic sequence

For an nth term in an arithmetic sequence

F(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

To find the equation first find the common difference

0.65 - 0.5 = 0.15 or 0.80 - 0.65 = 0.15

The first term is 0.5

Substitute the values into the above formula

That's

f(n) = 0.5 + (n - 1)0.15

f(n) = 0.5 + 0.15n - 0.15

The final answer is

Hope this helps you

Answer:

Step-by-step explanation:

Took the math test on edge

Answer:

C and E

Step-by-step explanation:

C and E are the correct answer

Answer:

Quantitative

Step-by-step explanation: Quantitative or numerical variable are statistical or measured variables which involves numbers. Numerical variables allows for mathematical operations such as addition, subtraction and so on to be performed in them. Quantitative variables include height, age, weight, population and other measured variable with have numerical attributes. They can be measured on either ordinal, ratio or interval scales. Hence, since Julien is trying to determine height, the variable is a quantitative or numeric variable.