A piece of conduit 39.0 ft long cuts across the corner of a room, as shown in the illustration. Find length x and Angle A. Round each answer to the appropriate number of significant digits

Answer:

4 and -9

Step-by-step explanation:

Answer:

An alphabetical dice has 6 sides labeled with the letters A, B, C, D, E, and F. Of these, A, E, and I are vowels and the remaining letters are consonants.

The probability of landing on a vowel on any given roll is therefore 3/6 = 1/2.

The probability of NOT landing on a vowel on any given roll is therefore 1 - 1/2 = 1/2.

Therefore, the probability of NOT landing on a vowel when an alphabetical dice is rolled is 1/2 or 0.5.

Step-by-step explanation:

Step-by-step explanation:

let the numbers be x and y

The system of equations is:

x+y=10

x-y=6

By elimination method,we can:

1. Add both equations to eliminate y and simplify

OR

2.Subtract both equations to eliminate x and simplify.

Going by the first approach

x+x+y+(-y)=10+6

2x+0=16

x=16/2=8

Plug x=8 into any equation,say equation 2

x-y=6

8-y=6

8-6=y

y=2

Answer

Step-by-step explanation:

The probability of being dealt in a queen is 1/13.

To find the probability:

Therefore, the probability of being dealt in a queen is 1/13.

Know more about probability here:

https://brainly.com/question/24756209

#SPJ4

Identifying Eigenvalues and Eigenvectors, A should be a n x n matrix. By resolving the det(λI−A)=0 problem, first determine the eigenvalues of A. Find the fundamental solutions to (λI−A)X=0 to determine the fundamental eigenvectors X≠0 for each.

In linear algebra, a nonzero vector is said to have an eigenvector, or characteristic vector, when a linear transformation is applied to it; this characteristic vector only changes by a scalar amount. The scaling factor for the eigenvector is known as the associated eigenvalue, frequently represented by the symbol. Linear transformations are made intelligible by the usage of eigenvectors. Eigenvectors can be thought of as a non-directional stretching or compressing of an X-Y line chart. In mathematics, eigenvalues are regarded as the factor by which a transformation is stretched, whereas eigenvectors are the real non-zero eigenvalues that point in the direction stretched by the transformation. The direction of the transformation is negative if the eigenvalue is negative.

To know more about Eigenvectors here

https://brainly.com/question/15423383

#SPJ4

Answer:

To calculate George's weighted score, we need to first find the weighted value of each topic.

Content: 87% x 0.50 = 43.5%

Appearance: 90% x 0.25 = 22.5%

Delivery: 85% x 0.25 = 21.25%

Now we can find his total weighted score by adding the weighted values together:

43.5% + 22.5% + 21.25% = 87.25%

So George's weighted score, rounded to the nearest percent, is 87%.

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

From the question we are given the first term 8,second term 11 and we are to find the third term.

Using the formula:Tn=a+(n-1)d

Where a=first term=8

n=number of terms =3

d= difference between terms( second term -first term)=11-8=3

T3=8+(3-1)3

=8+2(3)

=8+6

The next term =14

Answer:

only the third answer is right.

Step-by-step explanation:

to solve it, we need to bring everything to the same denominator (the expression below the division line) or eliminate it completely.

how do we do it ? by multiplying everything with the same expression, so that we can eliminate the denominator for every term.

when looking for the best option I see that

(x² + 5x + 6) = (x + 2)×(x + 3)

that is great, because this covers all 3 denominators in our main expression.

so, we multiply everything by ((x+2)×(x+3)) and eliminate the denominators and the corresponding part of our multiplier.

that leaves us with

x×(x+3) + 2 = 5×(x+2)

now we simply simplify the expression

x² + 3x + 2 = 5x + 10

x² - 8x - 8 = 0

a squared equation has typically 2 solutions. and they are defined as

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case

a = 1

b = -8

c = -8

x = (8 ± sqrt(64 + 32)) / 2 = (8 ± sqrt(96))/2 =

= (8 ± sqrt(16×6))/2 = (8 ± 4×sqrt(6))/2 = 4 ± 2×sqrt(6)

x1 = 4 + 2×sqrt(6)

x2 = 4 - 2×sqrt(6)

both solutions are different from -2 or -3, therefore -2 and -3 are not solutions at all, and they cannot be extraneous solutions either for that reason.

and since we have 2 perfectly fine solutions, the answer options work no or only one solutions are wrong too.

Answer:

24

Step-by-step explanation:

15 =4

15x 6=90

4x6=24

Answer:

15 foot tree = 4 foot shadow

90 foot telephone pole

Setting up a proportion:

15 / 4 = 90 / x

15x = 360

x = 24 feet (telephone pole shadow)

Step-by-step explanation:

The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is \(\frac{x^2}{10} + \frac{y^2}{15} = 1\)

The given parameters are:

The foci of a hyperbola are represented as:

Foci = (k ± c, h)

The center is:

Center = (h,k)

And the directrix is:

Directrix, x = h ± a²/c

By comparison, we have:

k ± c = ±5

h = 0

h ± a²/c = ±2

Substitute h = 0 in h ± a²/c = ±2

0 ± a²/c = ±2

This gives

a²/c = 2

Multiply both sides by c

a² = 2c

k ± c = ±5 means that:

k ± c = 0 ± 5

By comparison, we have:

k = 0 and c = 5

Substitute c = 5 in a² = 2c

a² = 2 * 5

a² = 10

Next, we calculate b using:

b² = c² - a²

This gives

b² = 5² - 10

Evaluate

b² = 15

The hyperbola is represented as:

\(\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1\)

So, we have:

\(\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1\)

Evaluate

\(\frac{x^2}{10} + \frac{y^2}{15} = 1\)

Hence, the equation of the hyperbola is \(\frac{x^2}{10} + \frac{y^2}{15} = 1\)

Read more about hyperbola at:

https://brainly.com/question/3405939

#SPJ1

Answer:

(12 - 2 √22) ft

Step-by-step explanation:

by Pythagoras' Theorem:

in right-angled triangle, the square of the hypotenuse will equal the sum of the squares of the other two sides.

call the ladder L, call the distance of bottom of ladder from bottom of wall G, call the vertical height of the wall where the top of ladder meets it H.

we have L² = G² + H²

H² = L² - G²

   = 13² - 5²

   = 169 - 25

   = 144

H = √144 = 12.

the ladder is opposite the right-angle, ie it's the hypotenuse.

the ladder is 5ft from the wall.

if bottom of ladder is pulled out 4ft more, this reduces the height H.

the length of ladder L remains the same (can't compress a ladder)

G, the floor distance, is now 5 + 4 = 9ft

H² = L² - G²

    = 169 - 9²

    = 169 - 81

    = 88

H = √88

   = √(4 X 22)

   = √4 X √22

   = 2√22

The vertical height, H, was 12 ft.  it's now 2 √22

so it has moved down the wall (12 - 2 √22) ft.

The probability of one event given the known outcome of a (possibly) related event is known as unconditional probability.

Given an incomplete sentence related to probability.

We are required to fill the sentence by the appropriate terms given as options.

Probability is basically the chance of happening an event among all the events possible.  It cannot be negative.

Marginal probability is basically the probability of an event irrespective of the outcome of another variable.

Conditional probability is basically probability of one event occuring in the presence of a second event.

Unconditional probability is basically the chance that a single outcome results among several possible outcomes.

Joint probability is a basically a statistical measure that calculates the likelihood of two events occurring together and at the same point in time.

From the above definitions and the sentence given we can say that the appropriate term is unconditional.

Hence the appropriate term which can be filled in the sentence is unconditional.

Learn more about probability at https://brainly.com/question/24756209

#SPJ4

Finn has 3 hamsters and 8 fish at home, the ratio of fish to total number of pets is -  8 : 11

The ratio refers to the number that may be used to represent one quantity as a percentage of another, to put it simply. Only when the ratio's two numbers use the same unit can they be compared. To compare two objects, we utilize ratios. When the second integer in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. A percentage seems to be an equation in which two proportions are made equal to one another. Ratio, which is comfortably pronounced as the ratio, was directly derived from the Latin term. Everything from "reason," "calculation," and "proportion" were all included in the Latin word ratio.

Given that,

Hamsters: 3

Fish: 8

Thus, total = 3 + 8 = 11

Now, ratio of fish total number of pets:

= 8 : 11

To know more about ratio refer to:

https://brainly.com/question/12024093

#SPJ1

Step-by-step explanation:

Hey there!!

Here,

\(5(1 - b) = 8(b + 2)\)

\( \: \: \: \: \: 5 - 5b = 8b + 16\)

\( \: \: \: \: \: \: \: 8b + 5b = 5 - 16\)

\( \: \: \: \: \: \: \: 13b = - 11\)

\( \: \: \: \: \: \: \: b = \frac{ - 11}{13} \)

Therefore the value of b is -11/13.

Hope it helps...

Step-by-step explanation:

first open up the brackets according to BODMAS to get

5-5b=8b+16

then collect like terms together and make sure to change the sighns eg - becomes +

5-16=8b+5b

you get

-11=13b

then divide both sides with 13 to get b

-11/13=b ( you can leave as a negative decimal according to the question)

The gross tax is €2000. Income tax at standard rate is €4680. No tax was paid at higher rate. Excess income cannot be calculated due to limited information. Gross income for the year is €11200.

(i) Calculate her gross tax for the year:

Gross tax = Total tax paid - Tax credit

Gross tax = €6600 - €4600

Gross tax = €2000

(ii) How much income tax did she pay at the standard rate:

Standard rate income = Standard rate cut-off point - Tax credit

Standard rate income = €28000 - €4600

Standard rate income = €23400

Income tax at the standard rate = Standard rate income * Standard rate

Income tax at the standard rate = €23400 * 20%

Income tax at the standard rate = €4680

(iii) How much income tax did she pay at the higher rate:

Income tax at the higher rate = Gross tax - Income tax at the standard rate

Income tax at the higher rate = €2000 - €4680

Income tax at the higher rate = -€2680 (negative value indicates no tax paid at the higher rate)

(iv) How much income did she earn in excess of €28,000:

Income in excess of €28000 = Gross income - Standard rate cut-off point

Income in excess of €28000 = Gross income - €28000

Since we don't have the gross income, we can't calculate the exact amount of income earned in excess of €28000.

(v) What was the woman's gross income for the year:

Gross income = Gross tax + Tax credit

Gross income = €6600 + €4600

Gross income = €11200

Therefore, the woman's gross income for the year was €11200.

Learn more about gross tax here:

https://brainly.com/question/30689717

#SPJ1

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

The given figure is that of a Parallelogram ~ therefore its obvious that it's opposite sides are parallel to each other.

And here, two adjacent angles are made between the transversal and the opposite parallel sides respectively.

Hence they can be said to be a pair of co - interior angles.

\(\qquad \sf  \dashrightarrow \: 110 + 3x + 7 = 180\)

[ sum of two co - interior angles = 180° , note : the values above are in degree ]

\(\qquad \sf  \dashrightarrow \: 3x + 117 = 180\)

\(\qquad \sf  \dashrightarrow \: 3x = 180 - 117\)

\(\qquad \sf  \dashrightarrow \: 3x = 63\)

\(\qquad \sf  \dashrightarrow \: x = 63 \div 3\)

\(\qquad \sf  \dashrightarrow \: x = 21 \degree\)

Therefore, the value of x = 21°

Answer:

2.3333333333333333333333333333333 sec

The number of student tickets are 4 and number of adult tickets are 8 in number.

Two or more expressions with an Equal sign is called as Equation.

Let s be the number of student tickets and a be the number of adult tickets

Estimate that 150 students and 50 adults will buy tickets.

They hope to make $1000 in ticket sales

150s+50a=1000

The adult ticket price to be double the student ticket price.

a=2s

Now 150s+50(2s)=1000

150s+100s=1000

250s=1000

s=4

Substitute 4 in equation.

Now a=2(4)=8

Hence, the number of student tickets are 4 and number of adult tickets are 8 in number.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ9

Answer:

\( \huge{x = \frac{7}{2} }\)

Step-by-step explanation:

5(x - 9) + 3(x + 4) = 2(x - 6)

First expand the terms in the bracket

That's

5x - 45 + 3x + 12 = 2x - 12

Simplify

8x - 33 = 2x - 12

8x - 2x = 33 - 12

6x = 21

Divide both sides by 6

\( \frac{6x}{6} = \frac{21}{6} \\ x = \frac{21}{6} \)

Simplify

We have the final answer as

\(x = \frac{7}{2} \\ \)

Hope this helps you

Answer:

x=3.5

Step-by-step explanation:

5(x-9)+3(x+4)=2(x-6)

5x-45+3x+12=2x-12

8x-33=2x-12

8x-2x=-12+33

6x=21

x=21÷6

=3.5

Hope it helps!!!

First, let's calculate the z-score for the value 2.025 liters using the formula:

z = (x - μ) / σ

Where:

x = the value we want to calculate the probability for (2.025 liters)

μ = the mean of the process (2.050 liters)

σ = the standard deviation of the process (0.020 liters)

Plugging in the values:

z = (2.025 - 2.050) / 0.020

Simplifying:

z= -0.025 / 0.020

z = -1.25

Now, we can look up the probability corresponding to a z-score of -1.25 in the standard normal distribution table or use a calculator.

Using a standard normal distribution table, the probability is approximately 0.1056. This means that the probability of randomly selecting an output from the process that is less than 2.025 liters is approximately 0.1056 or 10.56%.

Alternatively, you can use a calculator or statistical software to find the probability directly by looking up the cumulative distribution function (CDF) of the standard normal distribution at -1.25. The result will also be approximately 0.1056 or 10.56%.

Learn more about Cumulative Distribution Function here:

https://brainly.com/question/30402457

#SPJ11

The factored quadratic expression of 2x²+7x+3 as the the product of two linear binomials is (2x+1)(x+3)

To factor trinomials with a leading coefficient greater than 1, follow these steps

Multiply the coefficient of the leading term by the constant term.

Find two factors of the product from step 1 that add up to the coefficient of the middle term.

Rewrite the middle term using the two factors found in step 2.

Factor by grouping the first two terms and the last two terms.

Factor out the common factor.

Let's use the example 2x²+7x+3 to demonstrate these steps

2 x 3 = 6

Find two factors of 6 that add up to 7: 6 and 1

Rewrite the middle term as 6x + 1x

Factor by grouping

2x² + 6x + 1x + 3

2x(x + 3) + 1(x + 3)

Factor out the common factor

(2x + 1)(x + 3)

Therefore, 2x²+7x+3 can be factored as (2x + 1)(x + 3).

Learn mnore about Trinomial here

brainly.com/question/9702142

#SPJ4

The solution to the equation 3x2 - 30x - 72 = 0 is x = -4 and x = -12.

3x2 - 30x - 72 = 0

3x2 - 30x = 72

3x2 - 24x = 90

3x2 - 24x + 18x = 90 + 18x

3x(x - 8) = 108

x(x - 8) = 36

x = 36 or x = 8

x = -12 or x = -4

The equation 3x2 - 30x - 72 = 0is a second-degree polynomial equation with two solutions. To solve this equation, first use the distributive property to factor out 3x from the first two terms. This yields 3x(x - 8) = 108. Then divide both sides of the equation by 3 to get x(x - 8) = 36. From here, use the quadratic formula to solve for x. This yields x = 36 or x = 8. Since the equation was given in terms of x2, the two solutions are x = -12 and x = -4. To confirm this, substitute these values into the original equation and check that it is true.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

To solve the equation sin(cos(0)) - sin(0) = 0, we first observe that cos(0) = 1. Substituting this value, we get sin(1) - sin(0) = 0. Since sin(0) = 0, we have sin(1) = 0.

The solutions to sin(x) = 0 are x = nπ, where n is an integer. Therefore, the only solution to the given equation in the interval [0,360°] is 0°.

However, if we consider all possible values of x, then the solutions are given by x = 180°n, where n is any integer. This is because sin(x) = sin(180° - x), and so sin(180°n + x) = sin(x) for all integers n and all angles x. Therefore, the answer is (C) {180°n, where n is any integer}.

Learn more about  equation from

https://brainly.com/question/17145398

#SPJ11

Answer:

12−pack of 1.8 ounce bars has the better price per bar

Step-by-step explanation:

a) 10−pack of 2.5 ounce bars $ 19.50

10 pack = $19.50

1 pack = x

10 packs × x = $19.50 × 1

x = $19.50 × 1/10 packs

x = $1.950

12−pack of 1.8 ounce bars 18.75

12 pack = 18.75

1 pack= x

12 packs × x = 1 pack × 18.75

x = 18.75/12

x =$ 1.5625

From the calculation above:

12−pack of 1.8 ounce bars has the better price per because it cost $1.5625

The first transformation is a translation one unit up.

The second transformation is a translation of four units left.

The scale factor is 2.5.

According to the transformations above, the circles are similar, they are related with a scale factor of 2.5.

The equation of the preimage is

The equation of the image is

Answer:

61.538

Step-by-step explanation:

Hey there! I'm happy to help!

If you raise a fraction to an exponent, you apply that exponent to the numerator and the denominator. This would give us \(\frac{y^4}{x^4}\).

Have a wonderful day! :D

Since the exponent is outside the fraction, you apply the exponent to both the numerator and denominator.

(y/x)^4 = y^4/x^4

Best of Luck!

For point 4. Since -4 is less than zero, that is

then to find f(-4) replace x = -4 into x², like this

For point 5. Since 3 is in the interval

then

Finally, for point 6. Since 12 is greater than 3, that is

then to find f(12) replace x = 12 into 4-x, like this