Question: The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Which equation can be used to find the length of the remaining side?

Negative Integers are :

Answer:

3 ( a ) : x = 3.6,

3 ( b ) : x = 5

Step-by-step explanation:

For 3a, we can calculate the value of x through Pythagorean Theorem, which seemingly was your approach. However, the right triangle with x present as the leg, did not have respective lengths 9.6 and 12. The right angle divides 9.6 into two congruent parts, making one of the legs of this right triangle 9.6 / 2 = 4.8. The hypotenuse will be 12 / 2 as well - as this hypotenuse is the radius, half of the diameter. Note that 12 / 2 = 6.

( 4.8 )² + x² = ( 6 )²,

23.04 + x² = 36,

x² = 36 - 23.04 = 12.96,

x = √12.96, x = 3.6

Now as you can see for part b, x is present as the radius. Length 3 forms a right angle with length 8, dividing 8 into two congruent parts, each of length 4. We can form a right triangle with the legs being 4 and 3, the hypotenuse the radius. Remember that all radii are congruent, and therefore x will be the value of this hypotenuse / radius.

( 4 )² + ( 3 )² = ( x )²,

16 + 9 = x² = 25,

x = √25, x = 5

Answer:

0.4

Step-by-step explanation:

we are required to find the probability that the ring is within 12 meters from nthe car.

we start by defining a random variable x to be the distance from the car. the car is the starting point.

x follows a normal distribution (0,30)

[tex]f(x)=\frac{1}{30}[/tex]

[tex]0<x<30[/tex]

probabilty of x ≤ 12

= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]

a = 12

b = 0

[tex]\frac{1}{30} *(12-0)[/tex]

[tex]\frac{12}{30} = 0.4[/tex]

therefore 0.4 is the probability that the ring is within 12 feet of your car.

Answer:

Step-by-step explanation:

-6x²+26x+20

=-2(3x²-13x-10)

=-2(3x²-15x+2x-10)

=-2[3x(x-5)+2(x-5)]

=-2(x-5)(3x+2)

Answer:

Step-by-step explanation:

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

To solve it first of all cross multiply

That's

x + 4 = 6

Move 4 to the right side of the equation

The sign changes to negative

That's

x = 6 - 4

We have the final answer as

Hope this helps you

Answer:

number of nickel = 60

number of dimes  = 20

Step-by-step explanation:

1 nickel = 5 cents

1 dimes = 10 cents

$1 = 100 cents

we will use these value to solve the questions

_______________________________

Total no of coins = 80

let the number of nickels be x

let the number of dimes be y

thus,

x+y = 80

y = 80-x   equation 2

value of x nickels = 5x

value of y dimes = 10y

Total value of x nickels and y dimes = 5x+10y

The total value of the coins is $5.00

total value of the coins in cents = 5*100 = 500

thus

5x+10y = 500

using y = 80-x   from equation 2

5x + 10(80 - x) = 500

5x + 800 - 10x = 500

-5x = 500 - 800 = -300

x = -300/-5 = 60

Thus,

number of nickel = 60

number of dimes = 80-60 = 20

Answer:

Step-by-step explanation:

This problem can be solved using the compound interest formula

[tex]A= P(1+r)^t[/tex]

Given data

A, final amount =?

P, principal = $586

rate, r= 6.6% = 0.066

Time, t= 13 years

Substituting our values into the expression we have

[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]

To the nearest cent the in 13 years the CD will be worth $1344.9

Answer:

False

Step-by-step explanation:

Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.

Step-by-step explanation:

Hey, there!!

Look this figure, simply we find that;

In triangle ABC,

angle CBD is an exterior angle of a triangle.

and its measure is 90°

Then,

angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.

or, 90°= y + 48°

Shifting, 48° in left side,

90°-48°= y

Therefore, the value of y is 42°.

Hope it helps...

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

Answer:

27 ft^3 (Answer d)

Step-by-step explanation:

Here the volume of the pyramid is (1/3) the volume of the cube:

Letting s represent the length of one side of the base,

(1/3)(s)^2(s) = 9 ft^3, equivalent to  s^3 = 27.

Solving for s, we get s = 3 ft.

Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)

Answer:

1. Make a list of activities and the number of students:

Watching TV: 32

Talking on the phone: 41

Video games: 24

Reading: 15

2. Then combine the data in a bar graph as shown in the picture

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]

Cheers.

Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

The composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.

In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.

Solving a composite function means finding the composition of two functions.

The expression of the composite function (q∘p)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].

The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:

s(t)= q[p(t)]

4t -21= 4[p(t)]³ – 1

Solving:

4t -21 +1= 4[p(t)]³

4t -20 = 4[p(t)]³

(4t -20)÷ 4 = [p(t)]³

4t÷4 -20÷ 4 = [p(t)]³

t -5 = [p(t)]³

[tex]\sqrt[3]{t-5}=p(t)[/tex]

Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

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Answer:

C

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Sequence a

30 - 10 = 20

90 - 30 = 60

270 - 90 = 180

This sequence is not arithmetic

Sequence b

200 - 100 = 100

300 - 200 = 100

400 - 300 = 100

This sequence is arithmetic but is finite, that is last term is 400

Sequence c

300 - 150 = 150

450 - 300 = 150

600 - 450 = 150

This sequence is arithmetic and infinite, indicated by ........ within set

Sequence d

2 - 1 = 1

4 - 2 = 2

8 - 4 = 4

This sequence is not arithmetic

Thus the infinite arithmetic sequence is sequence c

Answer:  see proof below

Step-by-step explanation:

Use the Quotient rule for derivatives:

[tex]\text{If}\ y=\dfrac{a}{b}\quad \text{then}\ y'=\dfrac{a'b-ab'}{b^2}[/tex]

Given: [tex]y=\dfrac{2\sqrtx}{1-x}[/tex]

[tex]\sqrtx[/tex][tex]a=2\sqrt x\qquad \rightarrow \qquad a'=\dfrac{1}{\sqrt x}\\\\b=1-x\qquad \rightarrow \qquad b'=-1[/tex]        

[tex]y'=\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)}{(1-x)^2}\\\\\\.\quad =\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)\bigg(\dfrac{\sqrt x}{\sqrt x}\bigg)}{(1-x)^2}\\\\\\.\quad =\dfrac{1-x+2x}{\sqrt x(1-x)^2}\\\\\\.\quad =\dfrac{x+1}{\sqrt x(1-x)^2}[/tex]

LHS = RHS:  [tex]\dfrac{x+1}{\sqrt x(1-x)^2}=\dfrac{x+1}{\sqrt x(1-x)^2}\qquad \checkmark[/tex]

Answer:

Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = $48,722

Alternative hypothesis;Ha; μ > $48,722

Now, let's find the test statistic for the z-score. Formula is;

z = (x' - μ)/(σ/√n)

We are given;

x' = 48,722

μ = 49,870

σ = 3900

n = 50

Thus;

z = (49870- 48722)/(3900/√50)

z = 2.08

So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526

This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722

Answer:

[tex]\huge\boxed{x = k \frac{\sqrt{y} }{\sqrt[3]{z} }}[/tex]

Step-by-step explanation:

Given that:

1) x ∝ √y

2) x ∝ [tex]\frac{1}{\sqrt[3]{z} }[/tex]

Combining the proportionality

=> x ∝ [tex]\frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]

=> [tex]x = k \frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]

Where k is the constant of proportionality.

Answer:

5

----------

( n+1)(n+2)

Step-by-step explanation:

5

----------

n ( n+1)

Replace n with n+1

5

----------

(n+1) ( n+1+1)

5

----------

( n+1)(n+2)

We replace every 'n' with n+1 and simplify

[tex]\frac{5}{(n+1)(n+1+1)} = \frac{5}{(n+1)(n+2)}[/tex]

Answer:

Find a common denominator on the right side of the equation

Step-by-step explanation:

The equation before the problem is

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²

X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²

The right side of the equation now has a common denominator

The next step is to factorize the left side of the equation.

(X+b/2a)²= ( b²-4ac)/4a²

Squaring both sides

X+b/2a= √(b²-4ac)/√4a²

Final equation

X=( -b+√(b²-4ac))/2a

Or

X=( -b-√(b²-4ac))/2a

Answer:

The critical value for two tailed test at alpha=0.1 is ± 1.645

The calculated  z= 9.406

Step-by-step explanation:

Formulate the hypotheses as

H0: p1= p2 there is no difference between the population scrap rates between the old and new cutting methods

Ha : p1≠ p2

Choose the significance level ∝= 0.1

The critical value for two tailed test at alpha=0.1 is ± 1.645

The test statistic is

Z = [tex]\frac{p_1- p_2}\sqrt pq(\frac{1}{n_1} + \frac{1}{n_2})[/tex]

p1= scrap rate of old method = 62/200=0.31

p2= scrap rate of new method = 36/400= 0.09

p = an estimate of the common scrap rate on the assumption that the two rates are same.

p = n1p1+ n2p2/ n1 + n2

p =200 (0.31) + 400 (0.09) / 600

p= 62+ 36/600= 98/600 =0.1633

now q = 1-p= 1- 0.1633= 0.8367

Thus

z= 0.31- 0.09/ √0.1633*0.8367( 1/200 + 1/400)

z= 0.301/√ 0.13663( 3/400)

z= 0.301/0.0320

z= 9.406

The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that the 10% significance level that the scrap rate of the new method is different from the old method.

Answer:

Lori will pay $12 more if she makes monthly payments

Step-by-step explanation:

to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72

subtracting the amount she would pay as a down payment

$72 - $60 is $12

Lori will pay $12 more if she makes monthly payments

Answer:

2·5·5·5·5

Step-by-step explanation:

2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.

Answer:

The first table on the list:

x 1   2  3  4    5

y 5 10 15 20 25

Step-by-step explanation:

A linear equation is when the slope is the exact same between each point.  The way we find slope is by finding the change in "y" over the change in "x".

x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5

x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5

x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5

x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5

The slope for each change in points is 5, which means that this table represents a linear function.

The only table that represents a linear function is; Table 1

A linear function is one that has the same slope for every coordinate point.

Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;

Slope = 5/1 = 5

Slope = 10/2 = 5

Slope = 15/3 = 5

Slope = 20/4 = 5

slope = 25/5 = 5

In conclusion, only table 1 represents a linear function.

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Answer:

D: 450 miles

Step-by-step explanation:

So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):

[tex]0.4D=180[/tex]

This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:

[tex]0.4D=180\\D=450[/tex]

So the answer is D or 450 miles.

Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.

Answer:

sine and tangent

will be positive.

Answer:

Step-by-step explanation:

12x - 9 = 8x + 7

4x - 9 = 7

4x = 16

x = 4

solution is C

The solution is Option C.

The value of x is given from the equation x = 4

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as CD

Let the second line be represented as XY

Now , CD is the perpendicular bisector of XY

So , the point F is the midpoint of the line segment XY

The measure of line segment XF = 12x - 9

The measure of line segment FY = 8x + 7

From the perpendicular bisector theorem ,

The measure of line segment XF = The measure of line segment FY

Substituting the values in the equation , we get

12x - 9 = 8x + 7

Subtracting 8x on both sides of the equation , we get

4x - 9 = 7

Adding 9 on both sides of the equation , we get

4x = 16

Divide by 4 on both sides of the equation , we get

x = 4

Therefore , the value of x = 4

Hence , the value of the equation is x = 4

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Answer:

a)2/7

b)1/2

c)9/14

d)6/7

Step-by-step explanation:

The jar contains 4 red marbles, numbered 1 to 4 which means

Red marbles = (R1) , (R2) , (R3) , (R4)

It also contains 10 blue marbles numbered 1 to 10 which means

Blue marbles = (B1) , (B2) , (B3) , (B4) , (B5) , (B6) , (B7) , (B8) , (B9) , (B10) .

We can calculate total marbles = 4red +10 blues

=14marbled

Therefore, total marbles= 14

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10) =7

Total number of Blue marbles = 10

Blue and even marbles = 5

(a) The marble is red

P(The marble is red)=total number of red marbles/Total number of marbles

=4/14

=2/7

(b) The marble is odd-numbered

Blue marbles with odd number= (B1) , (B3) , (B5) , (B7) , (B9) ,

Red marbles with odd number = (R1) , (R3)

Number of odd numbered =(5+2)=7

P(marble is odd-numbered )= Number of odd numbered/ Total number of marbles

P(marble is odd-numbered )=7/14

=1/2

(C) The marble is red or odd-numbered?

Total number of red marbles = 14

Number of red and odd marbles = 2

The marbles that has odd number = (R1) , (R3) ,(B1) , (B3) , (B5) , (B7) , (B9) =7

n(red or even )= n(red) + n(odd)- n(red and odd)

=4+7-2

=9

P(red or odd numbered)= (number of red or odd)/(total number of the marble)

= 9/14

(d) The marble is blue or even-numbered?

Number of Blue and even marbles = 5

Total number of Blue marbles = 10

Number of blue that are even= 5

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10)

=7

n(Blue or even )= n(Blue) + n(even)- n(Blue and even)

= 10+7-5 =12

Now , the probability the marble is blue or even numbered can be calculated as

P(blue or even numbered)= (number of Blue or even)/(total number of the marble)

= 12/14

= 6/7

Answer:

1 box of 20 and 1 box of 14

They will cost $410

Step-by-step explanation:

1. Find how many boxes of 20 DVD movies can be bought

415 - 240 = 175

1 box of 20 DVD movies can be sold

2. Find how many boxes of 14 DVD movies can be bought from $175

175 - 170 = 5

1 box of 14 DVD movies can be bought

3. Find the cost

240 + 170 = 410

Answer:

The Variable has a coefficient.

Step-by-step explanation: