Find the best fit line for the scatter plot.

Using a system of equations, it is found that £52 was originally shared.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Angela and Michelle shared some money in the ratio 4: 9, hence, considering t as the total:

Angela gave Daniel half her share.Michelle gave Daniel a third of her share. Daniel was given a total of £20, hence:

[tex]\frac{x}{2} + \frac{y}{3} = 20[/tex]

[tex]\frac{4t}{26} + \frac{9t}{39} = 20[/tex]

[tex]\frac{12t + 18t}{78} = 20[/tex]

30t = 20 x 78

t = 20 x 78/30

t = £52.

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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]

[tex]\angle EHF=90^{\circ}[/tex] (an angle inscribed in a semicircle is a right angle)

[tex]\angle HEF=38^{\circ}[/tex] (alternate segment theorem)

[tex]a=52^{\circ}[/tex] (angles in a triangle add to 180 degrees)

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

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

[tex]\displaystyle\lim_{t\to \infty}(20+100(0.3)^{0.2t})=20+100\lim_{t\to \infty}0.3^{0.2t}=20+100\cdot 0=20[/tex]

Answer: 6

Step-by-step explanation:

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

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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Answer:

Hypotenuse = 8.94

Step-by-step explanation:

The rule for the reflection of the pre-image M(-5, 4), L(-4, 2), N(-2, 3), to form the image M'(-5, -4), L'(-4, -2), N'(-2, -3) is the option;

The given pre-image points are;

Possible third point; N(-2, 3)

The image points are;

The difference (change) between the pre-image and the image is a change in the sign of the y-value, which is equivalent to a reflection across the x-axis.

Therefore;

The rule for the reflection is therefore;

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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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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

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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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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The rational number, 5/7 converted to a decimal is 0.714.

A rational number is a number that can be expressed as a fraction of two integers.

A decimal is a non-integer in which the integers are separated from the non integers by a point. In order to convert the fraction to a decimal, divide the numerator by the denominator.

5/7 = 0.714

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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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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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Answer:

a

Step-by-step explanation:

go it right on a mastery test

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 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 value on the table above will be $30.6. Then the correct option is D.

The quantity of anything is stated as though it were a fraction of a hundred.

Raj was friends with his waitress, so he left her a 90 percent tip.

If his tip was $27.54.

Then the value in the table above will be

⇒ $27.54 / 0.90

⇒ $30.6

Then the correct option is D.

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I think the answer is D

☆...hope this helps...☆

_♡_mashi_♡_

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.

[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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Answer:

First, do 15/12 then take that and divide by 500!

Step-by-step explanation:

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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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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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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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

By using trigonometric relations, we will see that:

x = √3

In the image, we can see a right triangle, where the hypotenuse measures √6, and the two legs have the same measure.

Then this is a 45°, 45°, 90° right triangle.

Then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse).

Where a = 45°, adjacent cathetus = x, hypotenuse = √6

Replacing that, we get:

cos(45°) = x/√6

Remember that cos(45°) = 1/√2

Replacing that we get:

1/√2= x/√6

√6/√2 = x

√(6/2) = x

√3 = x

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