Write an equation to model this proportional relationship, where x represents the length of the rectangle and y represents the width of the rectangle.

Answer:

x > -5

Step-by-step explanation:

[tex] \frac{2}{5} (x - 1) < \frac{3}{5} (x + 1)[/tex]

[tex]2(x - 1) < 3(x + 1)[/tex]

[tex]2x - 2 < 3x + 3[/tex]

[tex] - 5 < x[/tex]

[tex]x > - 5[/tex]

The area of the screw head is 93.5m².

The area of the hexagon can be illustrated based on the formula:

A = 3✓3/2 × a²

Base = 12.

Height = 3.

Area of each triangle = 0.5 × 12 × 3 = 18

Area of the rectangle = 12 × 6 = 72

Therefore the area of the screw head will be:

= 3√3/2 × 72

= 93.5m²

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Answer:

√2

Step-by-step explanation:

Angle ( θ ) = 45

Hypotenuse side = 2

Opposite side = x

Formula : -

sin θ = Opposite side / Hypotenuse side

Note :

The value of sin 45 = 1/√2

sin 45 = x/2

1/√2 = x/2

Cross multiply,

x*√2 = 2*1

x√2 = 2

2 can be simplified as √2 * √2

x√2 = √2*√2

Divide √2 on both sides,

x = √2

The quantity of liters of the 2% and 66% solutions should you mix together is 4.75 and 11.25 liters.

let

x + y = 16

0.02x + 0.66y = 0.47 × 16

from (1)

x = 16 - y

Substitute into (2)

0.02x + 0.66y = 0.47 × 16

0.02(16 - y) + 0.66y = 7.52

0.32 - 0.02y + 0.66y = 7.52

- 0.02y + 0.66y = 7.52 - 0.32

0.64y = 7.20

y = 7.20/0.64

y = 11.25 liters

Substitute y = 11.25 liters into (1)

x + y = 16

x + 11.25 = 16

x = 16 - 11.25

x = 4.75 liters

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: 9w² - 13w + 10[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + (20 {w}^{2} - 15w + 10) + 2w[/tex]

[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + 20 {w}^{2} - 15w + 10+ 2w[/tex]

[tex]\qquad \tt \rightarrow \: 9 {w}^{2} + 20 {w}^{2} - 15w +2w + 10[/tex]

[tex]\qquad \tt \rightarrow \: 29 {w}^{2} - 13w + 10[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

23%

Step-by-step explanation:

There are 7 Freshman total

There are 30 students total

The probability of picking a Freshman is 7/30 or 23%

Answer:

y = - 3x + 11

Step-by-step explanation:

the altitude is a line from the vertex A drawn perpendicular to the opposite side BC

calculate the slope of BC using the slope formula

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

with (x₁, y₁ ) = B (- 7, 3 ) and (x₂, y₂ ) = C (- 1, 5 )

[tex]m_{BC}[/tex] = [tex]\frac{5-3}{-1-(-7)}[/tex] = [tex]\frac{2}{-1+7}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then

y = - 3x + c ← is the partial equation

to find c substitute A (4, - 1 ) into the partial equation

- 1 = - 12 + c ⇒ c = - 1 + 12 = 11

y = - 3x + 11 ← equation of altitude from A

The function that  will give the area, f(x), of the quilt in square feet is

Area = f(x) = 10x²+31 + 15

Generally, the equation for Area of Rectangle is  mathematically given as

A = Length *Width

Therefore

A= (5x+3)(2x+5) square feet.

inconclusion, Area

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

f(x)=10x+25+ 6+15

(fx) 10x^2 +31x+15

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Answer:

f(x)=10x^2 + 31x + 15

Step-by-step explanation:

Did it and got it right

the other people put so much things for no reason lol

Answer:

the answer is 24500

Step-by-step explanation:

7800+7900+8800

=24500

Answer:

Increasing: [tex](\infty, -1) \cup (2, \infty)[/tex]

Decreasing: [tex](-1, 2)[/tex]

Step-by-step explanation:

So when an equation has and odd degree, it will go in the opposite direction on both ends, so if y went towards infinity as x went towards infinity, then y would go towards negative infinity as x goes towards negative infinity. In this case, by looking at the graph it has an odd degree, due to opposite end behaviors, although on both ends it's increasing because even though it appears that it's going down on the left side, that's only if you start from the right and go towards the left. So it's really increasing from negative infinity to -1, and then it decreases from -1 to 2, until it once again starts increasing from 2 to infinity. This can be represented as (-infinity, -1) U (2, infinity) for increasing and (-1, 2) as decreasing

[tex]\large\boxed{\frac{1}{16}}[/tex]

The answer is equal to the probability of drawing a heart multiplied by the probability of drawing a spade.

The probability of a given suit being drawn is [tex]\frac{13}{54}[/tex], which simplifies to [tex]\frac{1}{4}[/tex]. This is because there are 13 outcomes we would like out of 54 possible outcomes in total.

Multiply [tex]\frac{1}{4}[/tex] by itself (square it) to get the final answer of [tex]\frac{1}{16}[/tex].

Answer corrected. Originally said [tex]\frac{1}{8}[/tex] as the final answer. Thank you, sangers1959!

The linear function with the same y-intercept with the graphed function is: table A.

The equation that models a linear function is, y = mx + b, where m is the slope and b is the y-intercept.

Slope of the graphed function = rise/run = - 2/1 = -2

Using one of the points on the line (x, y) = (5, 0) and the slope, m = -2, find the y-intercept (b) by substituting the values into y = mx + b:

0 = -2(5) + b

0 = -10 + b

10 = b

b = 10

The slope (m) of the graphed function is -2, and the y-intercept (b) is: 10.

Slope (m) of table A = change in y/change in x = (14 - 8)/(3 - 1) = 3

Substitute a point (x, y) = (1, 8) and slope (m) = 3 into y = mx + b to find the y-intercept (b):

8 = 3(1) + b

8 - 3 = b

5 = b

b = 5

Therefore the table with the same y-intercept as the graphed function is table A.

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Answer:

[tex]737\frac{4}{5}[/tex]cents

Step-by-step explanation:

1 Gallon of Gas = 368.9 cents (Note: 9/10 = 0.9)

1/2 Gallon of gas = [tex]\frac{368.9}{\frac{1}{2} }cents\\ =368.9 * 2\\= 737.8 cents[/tex]

or [tex]737\frac{4}{5}[/tex] cents (Reduced to simplest form)

Answer:

x^4-9x^2+26x-24

Step-by-step explanation:

Answer:

[tex] {x}^{3} - 9 {x}^{2} + 26x - 24[/tex]

Step-by-step explanation:

[tex](x - 3)( {x}^{2} - 6x + 8)[/tex]

[tex] {x}^{3} - 6 {x}^{2} + 8x - 3 {x}^{2} + 18x - 24[/tex]

[tex] {x}^{3} - 9 {x}^{2} + 26x - 24[/tex]

The population in the year 2000 is 21

The function is given as:

P(t) = 21e^0.01823t

The year 2000 is 0 years after 2000.

This means that

t = 0

So, we have:

P(0) = 21e^(0.01823 *0)

Evaluate the product

P(0) = 21e^0

Evaluate the expression

P(0) = 21

Hence, the population in the year 2000 is 21

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The value of x = 93 degree and value of angle A and B is 72 , 108 degree

The pair of triangles that are supplementary and they add to form 180 degree angle are called Linear Pairs.

It is given that

∠ A = x -21

∠ B = x+15

also it is given that

angle  A and B form a linear pair

∠ A + ∠ B = 180 degree

To find the value of x

x -21 + x+15 = 180

2x - 6 = 180

2x = 186

x = 93 degree

so

∠ A = x -21 = 93 -21 = 72 degree

∠ B = x+15 = 93+21 = 108 degree

Therefore the value of x = 93 degree and value of angle A and B is 72 , 108 degree.

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Answer:

(C) BE

Step-by-step explanation:

AE = 4

AG = 6

-> AE/AG = 2/3

DF = 2

We need a segment that is 3/2 the length of DF, which is 2.

The only option that works is (C) BE

c = 4 times h

Linear equation: 1.5c + 2h = 360

Hello!

Your answer should be..

c=4h     ( as there are 4 hours )

1.5c+2h=360

c is 1.50 and h is 2.00 so you must add them to reach 360

Hope this helps! :)

Using a significance level of 0.05, the null hypothesis would be rejected for p-values less than 0.05.

Depends on if the p-value is less or more than the significance level:

Hence, the null hypothesis would be rejected for p-values less than 0.05.

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The true statement about this function which models the given situation is: A. the function is linear and is growing by equal differences over equal intervals.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

By critically observing the graph which models the given situation, we can infer and logically deduce that the true statement about this function is that the function is linear and is growing by equal differences over equal intervals.

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The measure of m ∠A0B is 20. Option C

m ∠BOC = 27

m ∠AOC = 47

m∠A0B = unknown

But note that the sum of m ∠BOC + m ∠A0B = m ∠AOC  

We have,

27 +  m ∠A0B = 47

m ∠A0B = 47 - 27

m ∠A0B = 20

Therefore, the measure of m ∠A0B is 20. Option C

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In the research of Professor Nwamabi  the use of air conditioning represents independent variable.

Given 100 participants are randomly selected in a research in which effects of air conditioning on sleep habits is studied.

Dependent variable is the variable whose value is dependent on the other variables like increase in profit and production.

Independent variable is the variable whose value is not dependent on the other variables.

In the research of Professor Nwamabi in which he is examining the effects of air conditioning on sleep habits, use of air conditioning represents independent variable. In this study the effect is on sleep habits means the value of sleep habits will change due to use of air conditioning. It shows that the use of air conditioning is not depending on other variable in the research.

Hence the use of air conditioning represents the independent variable.

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The car start decelerating in section c of the graph.

The graph is a demonstration of curves  which gives the relationship between x and y axis.

Here, section A show the rise in speed of car over time. Meanwhile The curve is increasing curve.
B and D shows maintain level of speed means the curve is straight line and for every value of x there is only one y.

But at section C the speed of car reducing. Meanwhile, the car decelerating and the curve is of decreasing order over the time.

Thus, for section C, car is decelerating and the curve is of decreasing nature over time upto D.

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Answer:

the car is traveling at a constant speed (answer is D)

Step-by-step explanation:

im just smart like dat

The length of xy  in the triangle XYZ is 9 units if xyz is dilated to create triangle x prime, y prime and z prime.

Given triangle xyz is dilated to create x prime, y prime and z prime.The length of oz is 2, the length of Zz Prime is 4,the length of x prime y prime is 9 and the length of side y prime z prime is 12.

Dilation is basically technique of creating similar shapes. Each point is streched outwards from the center point by multiplying the scale.

After dilation the side of the shape used to reduce according to factor. It is reduced by number of times of factor.

The line xy is equal to 9 units after dilation by a factor of 3. So the length of xy is 9/3.

=3 units.

Hence the length of side xy is 3 units if xyz is dilated to create x prime, y prime and z prime.

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Answer: 3

Step-by-step explanation: just did it on edge

Answer:

B. 2

w=2

Step-by-step explanation:

hope this helps!

The expected waiting time is 1.2 minute

According the statement

We know that the kingman formula is

[tex]{ E(W) = \left ( \frac{p}{1-p} \right )\cdot \left ( \frac{ C_{a}^{2}+ C_{s}^{2} }{2} \right ) \cdot \mu_{s} }[/tex]

According to statement the mean value μs is 6 min.

Here the value of P is 6/36 = 1/6

And the value of ca and cs is 1

Substitute the values in formula then

[tex]{ E(W) = \left ( \frac{0.17}{1-0.17} \right )\cdot \left ( \frac{ 1^{2}+ 1^{2} }{2} \right ) \cdot \m6} }[/tex]

[tex]{ E(W) = \left ( \frac{0.17}{0.83} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]

[tex]{ E(W) = \left ( 0.20} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]

[tex]{ E(W) = 1.22[/tex]

So, the expected waiting time is 1.2 minute

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When a newspaper poll produces a statistic that is biased, it mean that

(b) Repeated polls would give, results that are very different from each other.

Statistical bias is anything that leads to a systematic difference between the true parameters of a population and the statistics used to estimate those parameters when people say that the newspaper poll is biased, they mean that:

(b) Responding was voluntary, and only these with access and interest would answer.

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Complete question:

When a newspaper poll produces a statistic that is biased, it means that

(a) Repeated polls would give the truth, about the population, in the same direction.

(b) Repeated polls would give results that are very different from each other.

(c) Repeated polls would give results that would not yield a normal distribution.

(d) Repeated polls would give results that are very similar to each other.

Answer:

I think you would have to do 2 times 7

Answer:

h = 2.5cm or 5/2 cm

Step-by-step explanation:

Vol = Basearea•h

In your question, the base is the triangle shape. The rectangles go around the sides of the 3-d shape and on top is another triangle that we can't really see. In your image it is kind of laying on its side. So if we stand it up properly, the triangles are on the top and bottom. The triangle is the base.

Volume was given; it is 35. Also given is one side of the rectangles, that is 7.

So we can fill in 35 and 7 into the volume formula and calculate the Basearea.

V = B • h

35 = B • 7

35 = 7B

Divide by 7.

5 = B.

We have calculated the Basearea. This is the area of the triangle shaped bottom. The area formula for a triangle is:

A = 1/2bh

We just found that A=5 and we were given that the base of the triangle is 4.

A = 1/2bh

5 = 1/2•4•h

5 = 2h

Divide by 2.

5/2 = h

This is the height of the triangle, h in the picture. (The h in the volume formula and h in the triangle are different)

This is what the question is asking for, h = 5/2 or in decimals, h = 2.5cm