Draw and label the following figure.


Isosceles obtuse triangle with the obtuse vertex is angle T.

[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \begin{array}{llll} \textit{\small "z" varies directly with }x^2\\ \textit{\small and inversely with }y^2 \end{array}}{ z=\cfrac{kx^2}{y^2}}\qquad \textit{we know that} \begin{cases} z=76\\ x=5\\ y=2 \end{cases} \implies 76=\cfrac{k(5)^2}{(2)^2} \\\\\\ 76=\cfrac{25k}{4}\implies \cfrac{4}{25}\cdot 76=k\implies \cfrac{304}{25}=k~\hfill \boxed{z=\cfrac{304x^2}{25y^2}} \\\\\\ when \begin{cases} x=9\\ y=9 \end{cases}\implies z=\cfrac{304(9)^2}{25(9)^2}\implies z=\cfrac{304}{25}\implies z= 12.16[/tex]

Step-by-step explanation:

annual salary (that means the income for a whole year) is

$36,000

1 year = 12 months.

twice a month = 2 times in a month

so, he gets 12×2 = 24 paychecks in a year.

so, the gross income per paycheck is

36,000 / 24 = $1,500

100% = $1,500

1% = 100%/100 = 1500/100 = $15

so, $15 will be withheld from each paycheck for Medicare taxes.

6% = 1%×6 = 15×6 = $90

so, $90 will be withheld from each paycheck for social security taxes.

and then there is the federal income tax of $287.95

so, he will actually get for each paycheck

1500 - 15 - 90 - 287.95 = $1,107.05

The expressions (4×2⁵) / (2³ × 1/16) written as the power of 2 is 2⁸

Given: (4×2⁵) / (2³ × 1/16)

In order to write this expression as the power of 2, we need to use some in indices law:

Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base":   5⁴ x 5³ = 5⁴⁺³ = 5⁷ and  P⁴ x P⁶ = P¹⁰

Division law: To divide two variables or numbers with the same base, we need to subtract their powers and raise them to that base":   5¹⁰ ÷ 5³ = 5¹⁰⁻³ = 5⁷ and  P⁸  ÷  P² = P⁸⁻² = P⁶

Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:

8⁻² = 1/8²   and b⁻⁶ = 1/b⁶  

Let's use the laws to create the given expressions as the power of 2:

(4×2⁵) / (2³ × 1/16) = (2²×2⁵) / (2³× 1/2⁴)       Note: 4 = 2² and 16 = 2⁴    

                            = (2²⁺⁵) /(2³⁺⁽⁻⁴⁾)               Note: 1/2⁴ = 2⁻⁴ (reciprocal law)

                            = 2⁷ / 2⁻¹

                            = 2⁷⁻⁽⁻¹⁾                            Division law

                            = 2⁸

Therefore, the expressions as the power of 2 is 2⁸

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Answer:

To find y-intercept: set x = 0 and solve for y. The point will be (0, y). To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).

Step-by-step explanation:

The value of 3xy³ + 2xy³z + xyz + xz = 0

To find the value of a given equation or expression replaces each variable with the given value.

For example, a = 1 and b = 3 then find 3a + 2b.

=>  3(1) + 2(3) = 3 + 6 = 9

Therefore, the value of 3a + 2b = 9

Multiplying any number with zero will give zero i.e 3 × 0 = 0. No matter how large the number is when we multiply it by zero the result will be zero.

Here we have

x = 0, y = 3 and z = 5

We need to find the value of 3xy³ + 2xy³z + xyz + xz

Substitute given values in the given expression

=> 3(0)(y)³ + 2(0)y³z + (0)yz + (0)z     [ x × 0 = 0  ]

=> 0 + 0 + 0 + 0

=> 0

Therefore,

The value of 3xy³ + 2xy³z + xyz + xz = 0

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Answer:

78kg

Step-by-step explanation:

Let total mass be M.

mean=M÷5=76

M=380kg

mass of 4men is 72+74+75+81=302kg

mass of 5th man=380-302=78kg

The statement that is true for the function, h is h(2) = 16

It is given that there is a function h

The range of function, h is [tex]1\leq h(x)\leq 25[/tex]

The domain of the function, h is [tex]-3 \leq x\leq 11[/tex]

And it is also given that h(8) = 19 and h(-2) = 2

Now,

The 1st option is h(-3) = -1

But the range of h is between 1 to 25, hence, this option is not true.

The 2nd option is h(8) = 21

But it is already given that h08) = 19, thus this option is not true.

The 3rd option is h(13) = 18

But the domain of h is between -3 and 11, So, this option is not true as well.

The fourth option is h(2) = 16

In this the values of range and domain are correct.

Thus, h(2) = 16.

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Answer:

The associative property of multiplication states that the product of three or more numbers remains the same regardless of how the numbers are grouped. For example, 3 × (5 × 6) = (3 × 5) × 6.

Step-by-step explanation:

Answer:

42 or 21.15?

not 100% sure but hope this helps

---------------------------------------------

Answer:

7

Step-by-step explanation:

the proper answer is 6.50384501660364

however, this isn't an integer.

to get it to become an integer, we round it up;

6.5 rounded up is 7

and therefore, the answer would be 7

hope this helps

Answer:

0.007 pounds a day

Step-by-step explanation:

if he loses 18.5 pounds in 4 weeks then each week has 7 days so you divide 18.5 by 7 four times. HOPE THIS HELPS :)

The amount of gallons of water is 160 and  gallons of the premium antifreeze solution that must be mixed is 80.

Let y represent the volume of water

Hence,

Total volume equation :

x +y = 240 equation 1

Pure antifreeze volume:

0.60 = .20 × 240  gallons equation 2

Hence,

Equation 2

x =  .20 × 240 /.60

x = 48 /.60

x = 80 (Pure antifreeze)

So,

y = 240 -80

y = 160 gallons of water

Therefore the volume of water is 160 gallons.

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The probability that the first card is a heart and the second one is not a heart is P = 0.19

A standard deck has 52 cards divided in 4 sets, such that each set has 13 cards.

The probability of randomly drawing a heart is equal to the quotient between the number of cards of the set heart (13) and the total number of cards (52), so we get:

p = 13/52

Now, the probability of not getting a heart is equal to the number of cards that are not hearts (3*13 = 39) and the total number of cards (now is 51 because we already took one).

q = 39/51

The joint probability is equal to the product between the two individual probabilities:

P = q*p = (13/52)*(39/51) = 0.19

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Step-by-step explanation:

if they are proportional, then they must keep the original ratio of 6/1 of sugar to cinnamon.

X 4.5/0.75 = 6 = 6/1

X 9/1.5 = 6 = 6/1

X 12/2 = 6 = 6/1

15/3 = 5 and that is NOT 6/1 (not proportional)

Based on the information, f(t) is increasing on [0,1) and decreasing on (1,4].

It should be noted that to find where the function is increasing and decreasing, we need to find the intervals where the derivative is positive or negative, respectively.

a. h'(x) = 3 > 0 for all x, so h(x) is increasing on (-∞, ∞).

b. h'(x) = 4x + 1 > 0 when x > -1/4, so h(x) is increasing on (-1/4, ∞). h'(x) = 4x + 1 < 0 when x < -1/4, so h(x) is decreasing on (-∞, -1/4).

c. f'(x) = 6x > 0 when x > 0, so f(x) is increasing on (0, ∞). f'(x) = 6x < 0 when x < 0, so f(x) is decreasing on (-∞, 0).

a. f(t) = 20t - 40√t + 50, f'(t) = 20 - 20/√t.

f'(t) > 0 when √t < 1, or t < 1. f'(t) < 0 when √t > 1, or t > 1.

Therefore, f(t) is increasing on [0,1) and decreasing on (1,4].

This means that during the first hour (from 6am to 7am), the average speed of the vehicle is increasing, while during the remaining 3 hours (from 7am to 10am), the average speed is decreasing.

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The value of x in the given triangle is 110°.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given triangle,

∠A=65°,  ∠B=90°,  ∠C=80°, and ∠D=50°

To find the value of ∠E,

Use triangle ∠ABC, in which eqaute the sum of the angle of a triangle to 180°.

65+90+y=180

y=25

The remaining ∠C =80-25 = 55°

Use exterior angle theorem,

According to this, the sum of two interior angles is equal to an exterior angle.

x=50+55

x=105°

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Answer:

9 and 10

Step-by-step explanation:

To three decimal places

[tex]7 \sqrt{2} = 9.899[/tex]

So 7√2 is between 9 and 10 (closer to 10).

The equation of parabola is y = (x - 2)² - 1.

We know that the standard form of the parabola is y=ax²+bx+c. Thus, the vertex form of a parabola is y = a(x-h)² + k.

Given:

Vertex (2, -1) and point (5, 8)

As, we know the vertex form of a parabola can be written as following

y = a(x - h)² + k ......(1)

Now, We are given that vertex is at (2,-1) and there is a point (5,8) on the curve.

i.e. h = 2 and k = -1,

x = 5 and y = 8

So, to find the value of a

y = a(x - h)² + k

8= a( 5- 2)² - 1

8= 9a - 1

9a= 9

a=1

Now, the equation of Parabola is

y = a(x - h)² + k

y = (x - 2)² - 1

Hence, the equation of parabola is y = (x - 2)² - 1.

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The probability of rolling a number less than 12 is 91.6%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

each case in the set is mutually exclusive with the others in the set, the probability that any one of its components will occur is equal to the sum of its component probabilities.

We can have the number 12, the probality will be 1/12

So the probability of rolling a number less than 12 is = (1 -  probability of 12)

=1-1/12

=11/12

=0.916

Hence the probability of rolling a number less than 12 is 91.6%.

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Answer:

Step-by-step explanation:

these seem complicated,  but just think about what they are asking.  they are giving you a point and a slope to a line.  

That gives you the hint to use the "point-slope"  formula

if you don't have it memorized you might as well start trying to now.  You'll need this over and over and over...

y-y1=m(x-x1)

so plug in the given info

y-4= (-1/4)(x-(-2))

y-4 = -1/4 (x +2)

y-4 = (-1/4)x  -1/2

y = (-1/4)x + 7/2   this is the slope intercept formula. y = mx +b

we can now graph this line with the slope intercept formula.

note the graph does pass through (-2,4)  and has a  -1/4 slope   :)

Hot Chocolate Sales and Outside Temperatures:

(A) The scatter plot  is shown below.
(B) The anomaly is located at (189, 16°F).
(C) A negative correlation exists.
(D) Sales are the dependent variable, and temperature is the independent variable.

What is Temperature?

The physical concept of temperature indicates in numerical form how hot or cold something is. A thermometer is used to determine temperature. Thermometers are calibrated using a variety of temperature scales, which historically defined various reference points and thermometric substances.

The following information is provided for hot chocolate sales and outside temperatures:

(Y) Sales    Temperature (X)
100                       92
213                       88
830                      54
679                      62
209                      85
189                       16
1110                       52
456                      65
422                      68
235                      89
199                      91

(A)
Attached below is the scatter plot.

(B)
A cluster is a group of points or values gathered in one location.
A cluster of three values between the temperatures of 80°F and 100°F may be seen on the scatter plot.
A value that differs significantly from the other values in a data set is referred to as an outlier. Either it's too little or it's too big.
In the given data collection, there is an outlier.
The anomalous value is (189, 16°F).

(C)
The scatter plot's points have a decreasing slope.
This suggests that the variables temperature and sales have a bad relationship.
There is a bad association as a result.

(D)
Dependent variables are variables that are being studied, or being kept an eye on for any changes while the other variables in the model are altered.
The variables that are changed to cause the dependent variable to vary proportionately are known as independent variables.
According to the outside temperature, the data in this case shows the sales of hot chocolate.
Sales are therefore the dependent variable, and temperature is the independent variable.
This is due to an increase in hot chocolate sales as the temperature drops.

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The largest number of boxes that can fit into the crate is 27.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

From the given data in the question,

The dimension of the crate is: 28 × 18 × 15

Volume of crate = 6480 cm³

And the dimensions of packs = 8 × 6 × 5

the volume of packs = 240 cm³

Then, the number of boxes that fit into the crate = 6480/240

= 27

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Answer:

24:23

Step-by-step explanation:

Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

According to question,

slope = (-1/2-3/4)/(5/6-(-2/3))

slope = (-5/4)/(9/6)

slope = -30/36

slope = -5/6

Answer: 3/10

Step-by-step explanation:

4/5 is equal to 8/10 and 1/2 is equal to 5/10

then we have 8/10-5/10 which is 3/10

this is the answer since expressions can be a number

Check the picture below.

The ratios of the given values 12/22,18/33 form a proportion  because they all equals to 6/11.

The concept that will be used is the concept of proportion. To know that the values whether they form a proportion, then, we will need to express them, in their lowest term.

12/22 can be expressed in its lowest term by dividing the denominator and the numerator by the factor of 2 givings us 6/11.

18/33 can be expressed in its lowest term by dividing the denominator and the numerator by the factor of 3 givings us 6/11.

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Answer:

i also need help with this because 2,3

Step-by-step explanation: help wich always equals 5,3

Andrew's score on the midterms this week, based on his scores last week and the absolute change, is 95%.

The Midterm score for this week increased by 23 percentage points over the midterm score for the last week. This increase in the midterm score was an absolute change and not a relative change.

As a result of this being an absolute change, the midterm score for Andrew this week would then be:

= Midterm score last week + absolute change in the score

= 72% + 23 percentage points

= 95%

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Step-by-step explanation:

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Question

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The length of a room is

3

4

times its breadth. The total area of the four walls of this room is

15

28

times the area of the floor of the room. What is the ratio of the height of the room to the length of the room?

Medium

Solution

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Correct option is D)

Let breadth =x units

Then length =

3

4

x units

⇒ Area of floor = x×

3

4

x=

3

4

x

2

square units

Let the height of the room =y units. Then

Area of four walls = 2[xy+

3

4

xy]=

3

14

xy

Now,

3

14

xy=

15

28

(

3

4

x

2

)⇒xy=

15

2

×4x

2

y=

15

8

x ⇒

x

y

=

15

8

⇒ y:x=8:15

Answer:

6 [tex]\frac{2}{3}[/tex] Hours

Step-by-step explanation:

Distance = rate times time

Let t = time

1 = .15t   Divide both sides by .15

6.666... = t  The 6 is repeating so as a fraction it would be

6 [tex]\frac{2}{3}[/tex]