Solve the inequality.
-2x + 8 < 14
and -3x - 9 ≥ -12
x>?
and
x≤

Speedy cage is 2 inches taller than fluffy cage.

The volume of rectangular prism = lwh

where

Therefore,

height of fluffy cage can be calculate as follows:

4340 = 20 × 14 × h

4340 = 280h

h = 4340 / 280

h = 15.5 inches

height of Kenneth cage can be calculate as follows:

5250 = 20 × 15 × h

5250 = 300h

h = 5250 / 300

h = 17.5 inches

height difference = 17.5  - 15.5 = 2.0 inches

Hence, speedy cage is 2 inches taller than fluffy cage.

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[0.3105, 0.3695] expect to buy a new car next year.

These are the answer choices -

A) [0.3074, 0.3726]

B) [0.3105, 0.3695]

C) [0.3140, 0.3660]

D) [0.3392, 0.3408]

It is given that a sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year.

For large random samples, a confidence interval for a population proportion is given by

[tex]sample proportion[/tex] ± [tex]z * \frac{\sqrt{sample proportion (1 - sample proportion)} }{n}[/tex]

where z* is a multiplier number that comes from the normal curve and determines the level of confidence (see Table 9.1 for some common multiplier numbers).

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The largest possible volume of the given box is; 96.28 ft³

Let b be the length and the width of the base (length and width are the same since the base is square).

Let h be the height of the box.

The surface area of the box is;

S = b² + 4bh

We are given S = 100 ft². Thus;

b² + 4bh = 100

h = (100 - b²)/4b

Volume of the box in terms of b will be;

V(b) = b²h = b² * (100 - b²)/4b

V(b) = 25b - b³/4

The volume is maximum when dV/db = 0. Thus;

dV/db = 25 - 3b²/4

25 - 3b²/4 = 0

√(100/3) = b

b = 5.77 ft

Thus;

h = (100 - (√(100/3)²)/4(5.77)

h = 2.8885 ft

Thus;

Largest volume = [√(100/3)]² * 2.8885

Largest Volume = 96.28 ft³

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The degree of the polynomial is 2

The root of the polynomial is given as:

Root = x - 3i

The above expression is a complex root.

This means that the conjugate is also a root of the polynomial

So, we have

Roots = x - 3i and x + 3i

Multiply the roots

f(x) = (x - 3i)(x + 3i)

This gives

f(x) = x^2 + 9

The degree of the above equation is 2 i.e. the highest power

Hence, the degree of the polynomial is 2

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The cost of electricity consumed by the TV per month is $4.968.

In the question, we are given that a TV set consumes 120W of electric power when switched on. It is kept on for a daily average of 6 hours per day. The number of days in the month is given to be 30 days. The cost per unit of electricity is 23 cents per kWh.

We are asked to find the cost of electricity the TV consumes in the month.

The daily energy consumed by the TV = Power*Daily time = 120*6 Wh = 720 Wh.

The monthly energy consumed by the TV = Daily energy*Number of days in the month = 720*30 Wh = 21600 Wh = 21600/1000 kWh = 21.6 kWh.

Hence, the total cost of electricity the TV consumes = Monthly energy*Per unit cost = 21.6*23 cents = 496.8 cents = $496.8/100 = $4.968.

Therefore, the cost of electricity consumed by the TV per month is $4.968.

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Step-by-step explanation:

x² + (2x)² = (√180)²

x² + 4x² = 180

5x² = 180

x² = 180/5

x² = 36

x = √36 (and no - √36 because x ≥ 0)

x = 6

We have to assume that the sample mean is given , distribution is normal and sample size is also given.

Given confidence level 99%.

We have to answer the assumptions that are needed to make a valid 99% confidence interval.

Confidence interval can be made by formula of margin of error.

Margin of error is the difference between actual values and the calculated values.

Upper level of confidence interval=Mean+ margin of error

Lower level of confidence interval= Mean - margin of error.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the corresponding z value for the confidence level given ,

σ is population mean and n is sample size.

Hence to calculate the confidence interval we need population mean, sample size.

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Probabilities that can be estimated from long-run relative frequencies of events are called objective probabilities.

In contrast to intuition or guessing, objective probability refers to the chances or odds that an event will occur based on the examination of certain measurements. Each metric is based on factual observation, a documented observation, or a long history of data collection.

Instead of being dependent on anecdotes, firsthand knowledge, or hunches, the objective probability is based on statistics, experiments, and mathematical measures. Using objective probability is crucial in the realm of finance to prevent making irrational investment decisions.

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Answer:

The function can have its own inverse, that is, [tex]$f^{-1}(x)=f(x)$[/tex] and this type of function is called an involution. Example f(x)=6-x.

Step-by-step explanation:

A statement that a function can be its own inverse is given.

It is required to explain whether a function has its own inverse. Then explain whether the given statement satisfies the condition.

Step 1 of 3

Consider a function is f(x)=6-x.

This function is a continuous function for all values of x. This function is also a linear function. So, every continuous linear function is a one-to-one function.

So, this function is one-to-one.

Step 2 of 3

Consider f(x) as y and rewrite the equation.

The equation becomes [tex]$y=6-x$[/tex]

Solve the rewritten equation.

Add -6 on both sides of the equation.

[tex]$$\begin{aligned}&y=6-x \\&y-6=6-x-6 \\&y-6=-x\end{aligned}$$[/tex]

Step 3 of 3

Multiply by -1 on both sides.

[tex]$$\begin{aligned}&y-6=-x \\&(-1)(y-6)=(-x)(-1) \\&-y+6=x \\&x=6-y\end{aligned}$$[/tex]

Interchange x and y in solved equation.

[tex]$$\begin{aligned}&x=6-y \\&y=6-x\end{aligned}$$[/tex]

So, the inverse of the given function is [tex]$f^{-1}(x)=6-x$[/tex].

The function and inverse of the function are the same, that is, [tex]$f^{-1}(x)=f(x)$[/tex]

So, a function can have its own inverse. This type of function is called an involution.

The product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a²

The product of two factors of an expression results in a quadratic or polynomial expression depending on the degree to which their power is being raised.

From the information given, we have:

= (t - sa) (9t +6sa)

= 9t² + 6tsa - 9tsa - 6(sa)²

= 9t² - 3tsa - 6s²a²

Therefore, we can conclude that the product of the two factors (t - sa) (9t + 6sa) is 9t² - 3tsa - 6s²a².

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Answer:

(a) 1416

(b) 2 × 2 × 2 × 3 × 59

Step-by-step explanation:

The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357

The square numbers between 0 and 10 are  1, 4, 9 and in descending order 9,4.1so n = 941

m - n = 2357 - 941 = 1416

Unique prime factors of 1416 are 2,3,59

1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59

Answer:

b = 1

Step-by-step explanation:

since the point (1, 4 ) lies on the line then it satisfies the equation , that is

3(1) + b = 4

3 + b = 4 ( subtract 3 from both sides )

b = 1

Answer:

Width = 3y - 3

Step-by-step explanation:

P = 2l + 2w

12x - 4y - 4 = 2(6x - 5y + 1) + 2w

12x - 4y - 4 = (12x - 10y + 2) + 2w

6y - 6 = 2w

w = 3y - 3

The equation connecting L, m, A is L = [tex]\frac{1.8m}{A}[/tex]

Variation is a mathematical relationship that shows how a certain variable behaves when other variables depending on it increase or decrease.

The types of variation are: Direct, indirect, joint and partial.

Analysis:

L ∝ [tex]\frac{m}{A}[/tex]

introducing a constant K to replace the proportionality sign,

L = [tex]\frac{Km}{A}[/tex]

when L = 18, m = 0.4, A = 0.4

18 = [tex]\frac{K(4)}{0.4}[/tex]

4K = 0.4 x 18

k = 1.8

Therefore the equation connecting the three variables is,

L = [tex]\frac{1.8m}{A}[/tex]

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There are three solutions of the equation ||2x-3|-m|=m have if m>0.

We have to estimate the number of solutions of the equation ||2x - 3| - m| = m where m > 0.

As we know in the modulus function

|x|= x if x>0

     -x if x<0

      0 if x=0

here given m > 0

if |2x-3|-m>0 then the modulus value will be ||2x-3|-m|=  |2x-3|-m

Then, |2x - 3| - m = m

⇒|2x - 3| = m+m= 2m

⇒2x - 3 = 2m    or      -(2x-3)=2m

⇒2x - 3 = 2m    or      2x-3=-2m

⇒2x = 3 ± 2m

⇒x = (3 ± 2m)/2

⇒x= (3 + 2m)/2  or   (3 - 2m)/2

If  |2x-3|-m<0 then then the modulus value will be | |2x-3|-m| = -(|2x-3|-m)

-(|2x-3|-m)=m

⇒m-|2x-3|=m

⇒-|2x-3|= m-m

⇒ |2x - 3| = 0

⇒2x = 3

⇒x = 3/2

Therefore The solution of the equation will be (3 + 2m)/2, (3 - 2m)/2, and 3/2.

Therefore there are three solutions of the equation ||2x-3|-m|=m have if m>0.

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The probability shows that when one name is drawn from the jar, the country that has the best chance of having a name drawn is Great Britain.

It should be noted that Great Britain has won 6 golds in the 1500 meters Olympics and the next placed country is Kenya. In this case, the country that has the best chance of having a name drawn is Great Britain.

Note that New Zealand has 3 gold medals while Australia has 2 gold medals. Also, the Olympics has taken place 29 times.

The probability that the winners will be from either New Zealand or Australia will be:

= 3/29 + 2/29

= 5/29

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Answer

A. Great Britain

B. 3/29+2/29=5/29

please give me the brainliest.

The vertex U' is located at (-4, -5)

The vertices are given as:

U = (-4, 5)

V = (-6, 2)

The rule of transformation is given as:

Reflection across the x-axis

This is represented as:

(x, y) => (x, -y)

So, we have:

U' = (-4, -5)

Hence, the vertex U' is located at (-4, -5)

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Complete question

Quadrilateral UVWX is reflected over the x-axis to form quadrilateral U′V′W′X′. If vertex U is located at (-4, 5) and vertex V is located at (-6, 2), then vertex U′ is located at

Answer:

The cost of 30 gallons of gas is $74.7.

Step-by-step explanation:

Step 1 of 3

Here we need to find the cost of 30  gallons.

Given that the price that Tyler pays for gas varies directly with the number of gallons he buys.

The cost of 24  gallons is $59.76  to him.

Let, x  be the number of gallons and y  be the cost or price for gas.

Use the formula for direct variation which is given by y=kx.

Step 2 of 3

Now substitute the value y=$59.76 and x=24.

Put value in y=kx, we get

[tex]$$\begin{aligned}&59.76=k \times 24 \\&k=2.49\end{aligned}$$[/tex]

Substitute value of k is y=kx, we get y=2.49x

Step 3 of 3

Now we need to find the value of y that is the cost for 30 gallons.

Again use direct variation formula y=kx and value of k and x, we get [tex]$y=2.49 \times 30$[/tex]

[tex]$$y=74.7$$[/tex]

Image vertices are  mathematically given as:

Generally, Multiplying the vertices by a scale factor of four is required in order for us to locate the picture vertices for dilation with center (0, 0).

In conclusion,, the image vertices are :

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Step-by-step explanation:

the ans is 19 a6 x5 y3

93-12-62×a2xy×a2x×a2x3y2

ans. 19 a6 x5 y3 add all the spuare and cube

Answer:

[tex]31a^2x(3y-4-2x^2y^2)[/tex]

Step-by-step explanation:

So the given equation is : 93a²xy - 124a²x - 62a²x³y². In this form you'll notice they all have a, and specifically a^2, and they also have x, but we only factor out x^1 since the first variable only has a degree of 1. So this gives us the equation: [tex]a^2x(93y-124-62x^2y^2)[/tex]. Now if we look at the coefficients you'll notice that they have a GCF of 31. So we can factor that out to. This gives you the equation: [tex]31a^2x(3y-4-2x^2y^2)[/tex] Which is your completely factored equation. You could also technically group 2xy^2 and 3y to get: [tex]31a^2x(y(3-2xy)-4)[/tex], although I'm not sure if that's considered "simplifying it"

Answer: 6

Step-by-step explanation:

This is a direct application of the exponent rule [tex](a^b)^c=a^{bc}[/tex].

Answer:

Hypotenuse = 8.94

Step-by-step explanation:

I think the answer is D

☆...hope this helps...☆

_♡_mashi_♡_

Answer:

a

Step-by-step explanation:

go it right on a mastery test

Answer:

x = 3

Step-by-step explanation:

1) Divide both sides by -2.

[tex]6^x=\frac{-432}{-2}[/tex]

2) Two negatives make a positive.

[tex]6^x=\frac{432}{2}[/tex]

3) Simplify [tex]\frac{432}{2}[/tex] to 216.

[tex]6^x=216[/tex]

4) Convert both sides to the same base.

[tex]6^x=6^3[/tex]

5)  Cancel the base of 6 on both sides.

x = 3

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{-2(6)^x = -432}[/tex]

[tex]\huge\textbf{DIVIDE -2 to BOTH SIDES:}[/tex]

[tex]\mathbf{\dfrac{-2(6^x)}{-2} = \dfrac{-432}{-2}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{6^x = 216}[/tex]

[tex]\huge\textbf{Solve for the current exponent:}[/tex]

[tex]\mathbf{6^x = 216}[/tex]

[tex]\huge\textbf{Log them:}[/tex]

[tex]\mathbf{Log \ 6^x = log = 216}[/tex]

[tex]\huge\textbf{Take the log to both of the sides:}[/tex]

[tex]\mathbf{x \times log (6) = log(216)}[/tex]

[tex]\huge\textbf{Convert it:}[/tex]

[tex]\mathbf{x = \dfrac{log(216)}{log(6)}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{x = 3}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\mathsf{x = 3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Mean: 29.5;    Median: 26;    Modes: 25, 26

Step-by-step explanation:

Add 10+12+25+25+26+26+30+31+33+34+47+55 = 354

Then divide it by 12      354/12 = 29.5

Mode are numbers that appear most often which in this case are 2 numbers, 25 and 26.

The points used in plotting the graph of the absolute function as given are; (-2,3), (-1,2), (0,1), (1,0) and (2,1).

The absolute function given is; y = | x − 1 |

Hence, by consider x-values; -2,-1,0,1,2....it follows that the corresponding y-values which are all positive by virtue of the absolute value symbol are; 3, 2, 1, 0, 1.

Hence, the points are; (-2,3), (-1,2), (0,1), (1,0) and (2,1).

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Using the median concept, it is found that the interquartile range of Sara's daily miles is of 21 miles.

The ordered data-set is given as follows:

65, 72, 86, 88, 91, 93, 97

There are 7 elements, hence the median is the 4th element, of 88. Then:

Since the quartiles are the medians of each half, the have that:

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Answer:

50

Step-by-step explanation:

[tex]\sqrt{-64}[/tex] and [tex]\sqrt{-16}[/tex] can be expressed in complex form, with [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-64}[/tex] = [tex]\sqrt{64(-1)}[/tex] = [tex]\sqrt{64}[/tex] × [tex]\sqrt{-1}[/tex] = 8i

[tex]\sqrt{-16}[/tex] = [tex]\sqrt{16(-1)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{-1}[/tex] = 4i

the factors can then be expressed as

(6 + 8i)(3 - 4i) ← expand using FOIL

= 18 - 24i + 24i - 32i² [ i² = ([tex]\sqrt{-1}[/tex] )² = - 1 ]

= 18 - 24i + 24i + 32 ← collect like terms

= 18 + 32 + 0

= 50

The x intercept of the given line is (10, 0)

The x intercept of a line is the point where the line crosses the x-axis

It is the point where the value of y is zero

Given the equation of a line -2x+5y = -20

Substitute y = 0 into the equation

-2x +5(0) = -20

-2x = -20

x = 10

Hence the x intercept of the given line is (10, 0)

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