8x + y = 23 plus -10x -y = -27

Answer:

x = 1053.07 ft

Step-by-step explanation:

So if you look at the diagram I drew it might become a bit more apparent what you have to do. For this problem you'll need to use one of the six trigonometric functions. In this case you know the angle and the opposite side of the angle, and you need the adjacent side. The trigonometric function tan is defined as [tex]\frac{oppposite}{adjacent}[/tex]. So let's plug in the known values:

[tex]tan(8) = \frac{148}{x}[/tex]

multiply both sides by x

[tex]tan(8) * x = 148[/tex]

Divide both sides by tan(8)

[tex]x=\frac{148}{tan(8)}[/tex]

Calculating tan of 8 degrees using a calculator

[tex]x=\frac{148}{0.141}[/tex]

Simplify

x = 1053.07 ft

The description of graph of the data about relationship of UFO sightings in late 1930s and early 1940s will be :A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).

Given:

Year of incidence                    percent

1936                                         0.9

1937                                         0.8

1938                                          0.8

1939                                          1.3

1940                                           1.4

1941                                            1.2

1942                                            1.7

1943                                             1.8

1944                                              1.6

1945                                              1.5

1946                                              1.5

We have been given the percentages of different years. The points will be (1936,0.9) , (1937,0.8) , (1938,0.8) , (1939,1.3) , (1940,1.4) , (1941,1.2) , (1942,1.7), (1943,1.8) , (1944,1.6) , (1945,1.5) , (1946,1.5).

We have to just plot the points on the graph to find scatter plot. It is called scatter plot as the points are not in line but they are scattered.

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Answer:

343

Step-by-step explanation:

How many three-letter ”words” can be made from 7 letters FGHIJKL” if repetition of letters (a) is allowed? (b) is not allowed? Solution: (a) If repetition is allowed each letter can be any of the 7. So number ways is 7 × 7 × 7=73 = 343

Answer: See below

Step-by-step explanation:

Given:

The letters FGHIJKL

To find:

The number of three letter words can be formed if repetition is allowed (or) if repetition is not allowed

[tex]$$(a) If repetition is allowed:Total no of three letter words can be made$$=7_{C 1} x 7_{C 1} x 7_{C 1}=7^{3}=343$$(b) If repetitions is not allowed :Total no of three letter words can be made without repetition is $$\begin{gathered}=7_{C 1} \times 6_{C 1} \times 5_{C 1} \\=7 x 6 \times 5=210\end{gathered}$$[/tex]

Answer: 10

Step-by-step explanation:

I just took the test!! :)

Using proportions, it is found that the consultant's salary in dollars per month is of $9,681.67.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

A business based in South Africa pays a consultant in the U.S. 1,570,000 rand per year. Considering the conversion rate, his salary in dollars per year is given as follows:

S = 1570000 x 0.074 = $116,180.

Since a year has 12 months, his salary in dollars per month is given by:

Sm = $116,180/12 = $9,681.67.

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The augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]

The system of equations is given as:

-2x + 2y - z = 13

-3x - y + z = 7

-x + 3y - 2z = 0

Remove the variables x, y and z

-2      2    -1  13

-3    -1        1    7

-1     3      -2     0

Express as matrix

[tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]

Hence, the augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]

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Complete question

Write the augmented matrix of the system of equations given below. (10 points)

-2x + 2y - z = 13

-3x - y + z = 7

-x + 3y - 2z = 0

A mean is an arithmetic average of a set of observations. The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

The score earned by Taylor in her first 10 test are 78, 92, 98, 87, 86, 72, 92, 81, 86, 92. Also, she wants the average to be 87, therefore, we can write,

(78 + 92 + 98 + 87 + 86 + 72 + 92 + 81 + 86 + 92 + x)/11 = 87

864 + x = 957

x = 93

Hence, The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.

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Answer:

Step-by-step explanation:

1250x0.05x1.5=93.75

93.75 is the interest

1343.75 is the total ammount.

Answer:

Did you mean " f(x)=8+4^{x-8} ? " The function you entered was linear, meaning there would be no asymptote.

D: (-∞, +∞)

R: (8, +∞)

Horizontal asymptote at y=8

No vertical asymptote

Answer:

The method of matrixes that would be used for this question is Gaussian Elimination.

Step-by-step explanation:

Gaussian Elimination is a method of solving linear equations by transforming them into upper triangular form. In this case, we want to solve for the original amount of money placed in each account, which can be represented by variables x, y, and z. We can set up the equations as follows:

4x + 5.5y + 6z = 1,300

x + y + z = 24,500

4x = y

We can then use Gaussian Elimination to solve for x, y, and z.

Answer:

y>2/3+3

Step-by-step explanation:

Answer:

y<2/3x+3

Step-by-step explanation:

1. Find the slope, the slope is 2/3

2. Find the y-intercept, the y intercept is 3

3. Make an linear equation out of it, y=2/3x+3

4. Dotted or solid? Its dotted which means the answer has to be greater or less than, not equal or less than or equal or greater than

5. Test you have 2 answer choices y<2/3x+3 or y>2/3x+3, input the origin (0,0)

0<2/3(0)+3, 0<3 which is true

0>2/3(0)+3 0>3 which is false

So y<2/3x+3 is the right answer. :)

The area of triangle is 16 square inches.

Area of triangle is half times the product of base and height.

i.e., A-= 1/2 *b *h

Given:

b= 8 inches, h= 4 inches

Now, Area of triangle

= 1/2*b*h

= 1/2 * 8 *4

=1/2*32

=16.

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Answer:

x = 4.08

Step-by-step explanation:

As we now, from Trigonometric Identities

So for our Problem , [tex]\alpha =27[/tex]  , [tex]Opposite=x[/tex]  ,  [tex]Adjacent = 8[/tex]

by substituting , then  [tex]tan(27)=\frac{x}{8}[/tex]

by multiplying both sides by 8 , then [tex]x=8tan(27)=4.0762=4.08[/tex]

Answer:

true

Step-by-step explanation:

6(6(13x-2)

36(13x-2)

468x-72

please mark brainliest :D

Answer:

True

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=3x-7\\g(x)=13x-2\\h(x)=6x\end{cases}[/tex]

[tex]h(h(g(x)))[/tex] is a composite function.  

Composite functions are when the output of one function is used as the input of another.

Therefore, the given composite function means to substitute the function g(x) in place of the x in function h(x), then substitute this in place of the x in function h(x).

Step 1

Substitute the function g(x) in place of the x in function h(x):

[tex]\begin{aligned}h(x) & = 6x\\\implies h(g(x)) & =6(g(x))\\& = 6(13x-2)\\ & = 78x-12\\\end{aligned}[/tex]

Step 2

Now substitute the above in place of the x in function h(x):

[tex]\begin{aligned}h(x) & = 6x\\\implies h \left(h(g(x))\right) & =6(h(g(x)))\\& = 6(78x-12)\\& = 468x-72\end{aligned}[/tex]

Therefore, the statement is true.

To carry out the composite function in one step:

[tex]\begin{aligned}h(x) &=6x\\\implies h(h(g(x))) & = 6\:(h(g(x)))\\& = 6(6(g(x)))\\& = 6( 6(13x-2))\\& = 6(78x-12)\\& = 468x-72\end{aligned}[/tex]

The approximate 95 % confidence interval for p is found by the formula

p^ ±  Z∝/2 √p^q^/n

The sample size n can be found by the

The formula

n= (Z∝/2)² p^q^/e²

The approximate 95 % confidence interval for p is 0.165; 0.243

This indicates 95 % confidence interval level.

A sample of 6239 nonprofits should be surveyed

Solution

Part a:

Sample Proportion p^= 84/412= 0.2038 ≅ 0.204

q^ = 1-p^= 1.0 -0.204= 0.796

The degree of confidence is 95% so  z∝/2= 1.96

Putting the values

p^ ±  Z∝/2 √p^q^/n

0.204 ±  1.96 √0.204(0.796)/ 412

0.204 ± 0.0389

0.1650 ; 0.2429

0.165; 0.243

The approximate 95 % confidence interval for p is 0.165; 0.243

Part B

This indicates 95 % confidence interval level.

Part C

With ± 0.01 of 0.95  Confidence interval gives range  0.94 to 0.96

For 0.96  interval Z∝/2 = 2.054

For 0.94  interval Z∝/2 = 1.8808

and error  e= 0.01

For solving n  the formula is

n= (Z∝/2)² p^q^/e²

and e= 0.01

Putting the values

n= 1.96²(0.204)(0.796)/ 0.01²

n= 6238.1437≅ 6238.14

A sample of 6239 nonprofits should be surveyed.

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Using the given linear function, we have that:

The linear function for the number of acres left to mow after x hours is given as follows:

y  = 1350 - 1.2x.

After 20 hours, the number acres is given as follows:

y  = 1350 - 1.2(20) = 1326.

After 100 hours, the number acres is given as follows:

y  = 1350 - 1.2(100) = 1230.

The time it takes to mow all the lawns is given by:

1350 - 1.2x = 0.

1.2x = 1350

x = 1350/1.2

x = 1125 hours

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The equation in slope intercept form is y = - 1 / 4 x + 1

Using slope intercept form,

y = mx + b

where

Therefore,

m = - 1 / 4

it passes through (8, -1)

Hen e,

-1 = - 1 / 4 (8) + b

-1  = - 2 + b

b = -1 + 2

b = 1

Therefore,

y = - 1 / 4 x + 1

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Answer:

Proof below

Step-by-step explanation:

If [tex]p[/tex] is prime such that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex], then [tex]p[/tex] divided by 6 has remainder of 1 or 5.

Case 1: p/6 has remainder 0, 2, or 4.

Then there exists some natural number [tex]n[/tex] such that either [tex]p=6n[/tex], [tex]p=6n+2[/tex], or [tex]p=6n+4[/tex].  However,

By definition of divisibility, [tex]p[/tex] is divisible by 2.  Since [tex]p \neq2[/tex], [tex]p[/tex] cannot be prime.  This contradiction implies [tex]p[/tex] cannot have a remainder of 0, 2, or 4 when divided by 6.

Case 2: p/6 has remainder 3.

Then there exists some natural number [tex]n[/tex] such that [tex]p=6n+3[/tex].  However, if [tex]p=6n+3[/tex], then [tex]p=3*(2n+1)[/tex], so [tex]p[/tex] is divisible by 3.  Since [tex]p \neq 3[/tex], [tex]p[/tex] is not prime.  This contradiction implies [tex]p[/tex] cannot have a remainder of 3 when divided by 6.

Therefore, if [tex]p[/tex] is a prime number such that  [tex]p \neq2[/tex] and [tex]p \neq 3[/tex], then when divided by 6, [tex]p[/tex] must have a remainder of 1 or 5.

Check p=2

Consider [tex]p=2[/tex].  Then [tex]q=2+70=72[/tex].  However, [tex]72=2*36[/tex], so [tex]q[/tex] is not prime.  Hence, [tex]p \neq2[/tex].

Check p=3

Consider [tex]p=3[/tex].  Then [tex]q=3+70=73[/tex], and [tex]r=73+70=143[/tex].  However, [tex]143=11*13[/tex], so [tex]r[/tex] is not prime.  Hence, [tex]p \neq 3[/tex].

So, thus far, we've proven that if there is a prime trio with a common difference of 70, that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex].

Proof of the rest of primes by contradiction

By way of contradiction, assume that there does exist some prime trio [tex]\{ p,q,r \}[/tex] such that [tex]q-p=r-q=70[/tex], and [tex]p \neq2[/tex] and [tex]p \neq 3[/tex].

Then, by the Lemma proven earlier, when [tex]p[/tex] is divided by 6, it must have a remainder of 1 or 5.

Case 1: p/6 has remainder 5

Assume that [tex]p[/tex] has remainder 5 when divided by 6.  Then, there exists some natural number [tex]n[/tex], such that [tex]p=6n+5[/tex].  

[tex]q=p+70\\q=(6n+5)+70\\q=6n+75\\q=3*(2n+25)[/tex]

Since [tex]n[/tex] was a natural number, and the natural numbers are closed over multiplication and addition (meaning, multiplying and adding more natural numbers results in another natural number), then [tex]q[/tex] is divisible by 3.

Since [tex]p[/tex] is prime, [tex]0 < p[/tex], which implies [tex]0+70 < p+70[/tex]

Since [tex]q=p+70[/tex], [tex]70 < q[/tex], so [tex]q[/tex] cannot equal 3.  Since [tex]q[/tex] is divisible by 3, but [tex]q \neq 3[/tex], [tex]q[/tex] is not prime, which is a contradiction to the existence of this prime trio.

Therefore, either [tex]p[/tex] cannot have a remainder of 5 when divided by 6, or the prime trio does not exist.

Case 2: p/6 has remainder 1

Assume that [tex]p[/tex] has remainder 1 when divided by 6.  Then, there exists some natural number [tex]n[/tex], such that [tex]p=6n+1[/tex].  

[tex]q=p+70\\q=(6n+1)+70\\r=q+70\\r=((6n+1)+70)+70\\r=6n+141\\r=3*(2n+47)[/tex]

Since [tex]n[/tex] was a natural number, and the natural numbers are closed over multiplication and addition (meaning, multiplying and adding more natural numbers results in another natural number), [tex]r[/tex] is divisible by 3.

Since [tex]q[/tex] is prime, [tex]0 < q[/tex], implying [tex]0 +70 < q+70[/tex].

Since [tex]r=q+70[/tex], then [tex]70 < r[/tex].  Therefore, [tex]r\neq 3[/tex].

Since [tex]r[/tex] is divisible by 3, but [tex]r\neq 3[/tex], [tex]r[/tex] is not prime, which is a contradiction to the existence of this prime trio (with a common difference of 70).  Therefore, either [tex]p[/tex] cannot have a remainder of 1 when divided by 6, or the prime trio does not exist.

Since [tex]p[/tex] was prime, by our lemma [tex]p[/tex] must have either a remainder of 1 or 5.  Since both remainder possibilities resulted in a contradiction, our contradiction assumption is false, so there cannot exist a prime trio such that their common difference is 70.

Answer:

x=13

y=11

Step-by-step explanation:

3y+5+52=90

3y=90-57

3y=33

y=33/3=11

4x=52

x=52/4=13

3y+5 and 52 are complementary

Apply angle sum property

The table that matches the graph shown is the second table.

It should be noted that in the graph, there's a quadratic equation. The form is given as ax² + bx + c.

When x = 0, y = 2. When x = 1, y is a number between 3 and 4. In the second table x we have y(1) = 7/2. This is in the range.

The graph is attached.

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Answer:

11/12

Step-by-step explanation:

2 3/4 ÷ 3

11/4 ÷ 3

11/4 × 1/3

11/12

Answer:

Hello! The answer is 11/12.

Step-by-step explanation:

Convert improper fractions:

[tex]2\frac{3}{4} \\= \frac{11}{4}[/tex]

Change 3 to its reciprocal:

[tex]\frac{1}{3}[/tex]

Multiply:

[tex]\frac{11}{4} * \frac{1}{3} \\= 11/12[/tex]

Step-by-step explanation:

If the cost of 5m cloth is Rs.375

Then cost of 80m cloth is (80m× Rs 375)÷ 5m

then the cost of  is 6000 Rs. you can use the criss cross method

5m = 375 Rs

80m = ?

80 × 375 = (30,000) ÷5

?= 6000

Answer:

11 3/13% per annum

Step-by-step explanation:

to find rate= 100×simple interest ÷ (principal ×time)

simple interest=total amount - principal

=1,500,000-1,300,000

=200,000

=200,000 ×100÷ 1,300,000×4

=3 11/13% per annum

Answer:

p = 7.3

Step-by-step explanation:

Equation: p - 2.5 = 4.8

add 2.5 to both sides:

P - 2.5 + 2.5 = 4.8 + 2.5

simplify

P = 7.3

hope that helps! :)

The inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3

The function is given as:

f(x) = 5x/3 + 5

Rewrite as:

y = 5x/3 + 5

Swap x and y

x = 5y/3 + 5

Subtract 5 from both sides

x - 5 = 5y/3

Multiply through by 3

3x - 15 = 5y

Divide through by 5

y = 3x/5 - 3

Express as inverse function

f-1(x) = 3x/5 - 3

Hence, the inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3

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Answer:

C

Step-by-step explanation:

(5r + 8 - 6r)(4 + 2r - 7) ← collect like terms inside each parenthesis

= (8 - r)(2r - 3)

each term in the second factor is multiplied by each term in the first factor.

8(2r - 3) - r(2r - 3) ← distribute parenthesis

= 16r - 24 - 2r² + 3r ← collect like terms

= - 2r² + 19r - 24

The NPV is positive, therefore, this order can be placed.

The calculation of probability of default will be:

= 1 / 200 = 0.005

We use NPV formula to find out whether the order should be filled or not

NPV = -Variable cost per unit +[(1-π)(price of equipment/1+percentage of return)]

= -$1.6 million +[(1-0.005)($1.725m/1.018)]

= -$1.6m + $1.6860

= 0.0860 million

As NPV is positive this order can be placed.

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