Add: 5/7 + 9/11 + 21/77

Answer:

60

Step-by-step explanation:

60 + y + y = 180

2y = 120

y = 60

The intersection of the two intervals in the number line will be = 4, 5,  6,.......+∞ = (-∞,6).

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-∞),9)

The given intervals are;

First interval  = (-∞, 6)

Second interval  = (-∞, 9)

Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞

The second interval includes, 4, 5,.....,+∞

Which gives the intersection as 4, 5, 6,7, 8,9......+∞

The union is the interval that combines the two sets of intervals which is given as follows;

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞

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Answer: 44

Step-by-step explanation: Since 11 members are equal to 25% of the club, 11 members is 1/4 of the club because 25% = 1/4. There are four-fourths in a whole so 11x4 = 44 members. The ski club has 44 members.

Answer:

shift left 3

Step-by-step explanation:

(x+3)²

x = -3

therefore translation by (-3,0)

The negative number shows it move to the left

C

1, -9 , 81 , -729 .....

ratio :-

R1 = -9/1 = -9

R2 = 81/-9 = -9

R3 = -729 / 81 =-9

so ,. R1= R2= R3

Step-by-step explanation:

With this question ,

The length of the rectangle is 3m longer than it's width=3 +w

then the width =w

therefore perimeter= 2L +2w

34= 2(3+w) +2w

34= 6+2w +2w

34-6 = 4w

28=4w

7= w

Area= Length x breadth

Area = (7+3) x7

Area= 10 x7

Area= 70cm square

The slopes of OA, OB and OC are integer values.

According to the statement

we have given that the some points on the graph and we have to find that the slopes of these points have integer value or not.

So, For this we know that the

If a line passing through two points then the slope of the line is

So, [tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

Then

The slope of line OA is 4 because 8/2 = 4.

And

The slope of line OB is 3 because 9/3 = 3.

And

The slope of line OC is 2 because 8/4 is 2.

And

The slope of line OD is 8/5 because it is 8/5.

And

The slope of line OE is 7/6 because it is 7/6.

And

The slope of line OE is 6/7 because it is 6/7.

From all this it is clear that

So,The slopes of OA, OB and OC are integer values.

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The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let x represent the amount of money invested in stocks, y represent bonds and z represent CDs, hence:

x + y + z = 215000     (1)

Also:

0.0225z + 0.02y + 0.092x = 8087.5    (2)

And:

y = 15000 + z    (3)

The solution of the equation is:

x = 50000, y = 90000 and z = 75000

The amount of money invested in stocks was $50000, $90000 was invested in bonds and $75000 was invested in CDs

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1. The formula expressing the dependence of the variable s on t is: s = 60 - 12t

2. the distance travelled at time t = 3.5 h is 18 Km

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

From the question given, bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km.

Thus, we shall determine the distance travel in time t as follow

Speed = distance / time

12 = distance / t

Cross multiply

Distance = 12 × t

Distance in time t = 12t

But the total distance travelled is 60 Km. Thus, the remaining distance (s) from the bicyclist to the station at time (t) will be given as:

s = 60 - 12t

Thus, the formula expressing the dependence of the variable s on t is: s = 60 - 12t

The distance at t = 3.5 hours can be obtained as illustrated below:

s = 60 - 12t

s = 60 - (12 × 3.5)

s = 60 - 42

s = 18 Km

Thus, the distance travelled at t = 3.5 hours is 18 km

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The critical value z_α/2 that corresponds to the confidence level 84​% is; 1.41

We want to find the two tail critical values.

This means that at an 84% confidence level, we want to get the probability of not rejecting the null value to be equal to a = 100% - 84% = 16%.

Now, z - scores refers to a numerical measurement that describes a value's relationship to the mean of a group of values and is gotten from normal distribution. Z-score is measured in terms of standard deviations from the mean.

However, under a normal distribution, we want a/2% = 16%/2 = 8% to be located right in the higher tail and lower tail.

From the above, it denotes that the critical value closest to 0.92 will give you the two tail 84% confidence interval. Utilizing a normal distribution table figure online to find the z score gives;

z = 1.41

Thus, we can conclude from this calculation that he critical value z_α/2 that corresponds to the confidence level 84​% is; 1.41

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The number of ways that the dancers can line up is; 518400 ways

The fundamental counting theorem is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

N = n1 * n2 * n3.....*nₙ

Total = 12

Dancers on Green = 6

Dancers on blue = 6

Number of ways for those wearing green = 6!

Dancers wearing green must be in the first position and so 6 places are left for the blue dancers.

Number of ways to arrange those wearing blue = 6!

Thus;

Number of ways that the dancers can line up = 6! * 6! = 518400 ways

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The target cost for Model J20 is $2000.

The required cost reduction is $30.

The total saving will be $30.3.

The target cost will be:

= Sales price - (100% × Target cost)

= 400 - (100% × Y)

Y + Y = 400

2Y = 400

Y = 400/2 = 200

Target cost = $200

Therefore, the target cost is $200.

The required cost reduction will be:

= $230 - $200

= $30

The required cost reduction is $30.

The three engineering improvements together will be:

Direct labor reduction = 7.5

Additional inspection = 17

Injection molding = 5.8

Total savings = 30.3

The total savings is $30.3.

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Answer:

X = 81

Step-by-step explanation:

600 × 0.45 = 270

270 × 0.3 = 81

X = 81

Answer:

A

Step-by-step explanation:

Triangle side length rule says any two sides added together must be greater than third side .... '6' is the only side length that will work

[tex]s = c(1 + in) \\ s = 4000(1 + 0.03 \times 1) [/tex]

[tex]s = 4120.00[/tex]

Using the cosine double angle formula,

[tex]\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}[/tex]

(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)

Using the Pythagorean identity,

[tex]\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}[/tex]

(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)

Answer:

  76/165

Step-by-step explanation:

The difference of fractions can be found using the formula ...

  a/b -c/d = (ad -bc)/(bd)

Using the given values in the formula, we have ...

  [tex]\dfrac{8}{11}-\dfrac{4}{15}=\dfrac{8(15)-11(4)}{11\cdot15}=\dfrac{120-44}{165}=\boxed{\dfrac{76}{165}}[/tex]

Here, the difference fraction does not need to be reduced. Many calculators and spreadsheets can do this arithmetic for you.

The above formula can also be used for sums of fractions. In that case, the sign changes from minus to plus.

Answer:

Step-by-step explanation:

76/165 is the answer

The linear equation that represent the left balance of sanjaya’s y after visiting x number of days is:

y = 10x + 500.

A linear function is modeled by:

y = mx + b

In which:

From the data given, we have that:

Hence the balance is given as follows:

y = 10x + 500.

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Answer:

Step-by-step explanation:

The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.

The given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...

  [tex]\dfrac{3x^2+x-4}{x-1}=\dfrac{(x-1)(3x+4)}{(x-1)}=3x+4\quad x\ne 1[/tex]

The simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...

  x ≠ 1

In interval notation, this is ...

  (-∞, 1) ∪ (1, ∞)

The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...

  y ≠ 7

In interval notation, this is ...

  (-∞, 7) ∪ (7, ∞)

Answer: u - 8 = -9

Step-by-step explanation:

Given equation

-7u - 5 = 2

Add 5 on both sides

-7u - 5 + 5 = 2 + 5

-7u = 7

Divide -7 on both sides

-7u / (-7) = 7 / (-7)

u = -1

Substitute values into the goal expression

u - 8 = (-1) - 8 = [tex]\Large\boxed{-9}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is -9.

First, let's find the value of u.

Now, substitute in the expression.

This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.

The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.

It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.

The yearly interest rate must be divided by 12.

Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).

Additionally, you'll add 12 to the number of years remaining on your loan term.

The total amount of interest that is paid for the term loan is $383,385.54

Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.

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See below for the values of the probabilities

The probabilities of the whole events

For event A, the probability of the whole event is calculated using

P(A) = n(A)/Total

Using the table of values, we have:

P(F) = 130/200 = 0.65

P(M) = 70/200 = 0.35

P(L) = 60/200 = 0.30

P(S) = 40/200 = 0.20

The probabilities of the intersection events

For events A and B, the probability of the intersection events is calculated using

P(A n B) = n(A n B)/Total

Using the table of values, we have:

P(F n E) = P(E n F) = 60/200 = 0.30

P(F n L) = P(L n F) = 40/200 = 0.20

P(F n S) = P(S n F) = 30/200 = 0.15

P(M n E) = P(E n M) = 40/200 = 0.20

P(M n L) = P(L n M) = 20/200 = 0.10

P(M n S) = P(S n M) = 10/200 = 0.05

The probabilities of the Union (OR) disjoint events

For events A and B, the probability of the union (OR) disjoint events is calculated using

P(A u B) = P(A) + P(B)

Using the table of values, we have:

P(E u S) = P(E) + P(S) = 100/200 + 40/200 = 0.70

P(E u L) = P(E) + P(L) = 100/200 + 60/200 = 0.80

P(E u L u S) = P(E) + P(L) + P(S) = 100/200 + 60/200 + 40/100 = 1

P(F u M) = P(F) + P(M) = 130/200 + 70/200 = 1

The probabilities of the Union (OR) joint events

For events A and B, the probability of the union (OR) joint events is calculated using

P(A u B) = P(A) + P(B) - P(A n B)

Using the table of values, we have:

P(E u F) = P(E) + P(F) - P(E n F) = 100/200 + 130/200 - 60/100 = 0.85

P(L u M) = P(L) + P(M) - P(L n M) = 60/200 + 70/200 - 20/100 = 0.55

The probabilities of the conditional probabilities

For events A and B, the conditional probability is calculated using

P(A/B) = P(A n B)/P(B)

Using the table of values, we have:

P(F/S) = P(F n S)/P(S) = 0.15/0.20 = 0.75

P(F/E) = P(F n E)/P(E) = 0.30/0.50 = 0.60

P(M/S) = P(M n S)/P(S) = 0.05/0.20 = 0.25

P(M/L) = P(M n L)/P(L) = 0.10/0.30 = 0.33

P(S/F) = P(F n S)/P(F) = 0.15/0.65 = 0.23

P(E/F) = P(F n E)/P(F) = 0.30/0.65 = 0.46

P(S/M) = P(M n S)/P(M) = 0.05/0.35 = 0.14

P(L/M) = P(M n L)/P(M) = 0.10/0.35 = 0.29

The multiplication of dependent events

For events A and B, the conditional probability is calculated using

P(A n B) = P(A) * P(B/A)

Using the table of values, we have:

P(F n L) = P(F) * P(L/F)

This gives

P(F n L) = 0.65 * (0.20/0.30)

Evaluate

P(F n L) = 0.43

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Answer:

[tex]\textsf{Option 3}: \quad -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]

Step-by-step explanation:

Given expression:

[tex]-2x^{-3}y(5yx^5+8xy-4y^2x^2)[/tex]

Distribute:

[tex]\implies -2x^{-3}y(5yx^5) -2x^{-3}y(8xy)-2x^{-3}y(-4y^2x^2)[/tex]

Multiply the constants and collect like terms:

[tex]\implies -10 x^{-3}x^5yy-16x^{-3}xyy+8x^{-3}x^2yy^2[/tex]

Remember that a = a¹.

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies -10 x^{(-3+5)}y^{(1+1)}-16x^{(-3+1)}y^{(1+1)}+8x^{(-3+2)}y^{(1+2)}[/tex]

[tex]\implies -10 x^2y^2-16x^{-2}y^2+8x^{-1}y^3[/tex]

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Answer:

Răspuns: 88=>rezultatul

Explicație pas cu pas:

a+2b =18/×3

b+3c=17/×2

3a+6b =54 ^

2b+6c=34 | +

3a+(6b+2b)+6c=54+34

3a+8b+6c=88

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The red dotted line we see is the asymptote, which is a line that the functions will never cross.

The asymptotes we see currently is:

x = -3

and

x = 2

We can find the vertical asymptotes using the denominator of the function since the x value that makes the denominator 0 is the asymptote. Since -3 and 2 is the asymptote, the denominator of the function will be:

(x-2) (x+3)

If we look at the answer choices, we can see that C is the only option with a denominator of (x-2)(x+3), so that is our answer.

Answer:

C

Step-by-step explanation:

there are 2 vertical asymptotes at x = - 3 and x = 2

then the factors on the denominator will be (x + 3) and (x - 2)

then

f(x) = [tex]\frac{1}{(x-2)(x+3)}[/tex]

The Lateral area of the cube = 900 in.²

The Surface area of the cube = 1,350 in.².

A cube's lateral area is the area covered by the lateral surfaces of the cube shape. The formula for the lateral area of a cube is given as: LA = 4a², where:

a = edge length of cube.

The surface area of a cube is the total area of all its 6 surfaces. The formula for finding the surface area of a cube is: 6a², where:

a = edge length of cube.

Edge length of cube (a) = 15 in.

Lateral area = 4a² = 4(15²)

Lateral area = 4(225)

Lateral area of the cube = 900 in.²

Surface area = 6a² = 6(15²)

Surface area = 6(225)

Surface area of the cube = 1,350 in.².

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Check the picture below.

Answer: 28 [tex]units^{2}[/tex]

Step-by-step explanation:

Answer:

87 adults

174 children

70 students

Step-by-step explanation: