Which features are present
in this polar graph?

The correct equation is [tex]x\cdot6=3x-4[/tex].

Let the number be [tex]x[/tex].

According to the question,

Number multiplied by [tex]6[/tex] [tex]=6x[/tex].

[tex]4[/tex] less than thrice the number  [tex]=3x-4[/tex].

Hence, the correct equation will be [tex]x\cdot6=3x-4[/tex].

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a = amount invested at 5%

b = amount invested at 2%

now, we know the total invested by Mr Wilson was 20000, so whatever "a" and "b" might be, we know that a + b = 20000.

[tex]a + b = 20000\implies b = 20000-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{5\% of a}}{\left( \cfrac{5}{100} \right)a}\implies 0.05a~\hfill \stackrel{\textit{2\% of b}}{\left( \cfrac{2}{100} \right)a}\implies \begin{array}{llll} 0.02b\\\\ \stackrel{substituting}{0.02(20000-a)} \end{array}[/tex]

now, we know the total of earned interest is 550 bucks, so then

[tex]0.05a~~ + ~~0.02(20000-a)~~ = ~~550\implies 0.05a+400-0.02a=550 \\\\\\ 0.03a+400=550\implies 0.03a=150\implies a=\cfrac{150}{0.03}\implies a=5000 \\\\\\ ~\hspace{24em}\stackrel{20000~~ - ~~5000}{b=15000}[/tex]

Answer:

m=8

Step-by-step explanation:

-5m=-40

divide both side by -5

-5m=-40

-5=-5 answer is m=8

Answer:

3

Step-by-step explanation:

First we look at our problem 1/2 + 5/2. We can see our denominator is the same so we can add our numerators. 1/2 + 5/2 equals 6/2 = 3.

Answer:

If you add this fraction in fraction strip instead of equivalent fraction method

Step-by-step explanation:

firstly draw 5 1/2 fraction strip

then draw 12 1/4 fraction strip

we taking 1/4 bcoz 1/4 is multiple of 1/2, under 1/2 there is 2 1/4.

The end product will be 12/4

cancel out it 12/4 by 2 ans = 6/2 still we can cancel so cancel out 6/2 by 2 at the end ans will be 3/1 = 3

if you think it wrong then use the equivalent fraction method to see the answer..

1/2 + 5/2

denominators are same so we will take only one denominator and will directly add the numerators

1 + 5 = 6 so

6/2 cancel it the ans will be 3/1 and it's equal to 3.

The least miles per gallon this trip is 25 miles per gallon

The given parameters are:

Distance = 450 miles

Tank size = 18 gallons

The least miles per gallon this trip is calculated as:

Miles per gallon = Distance/Tank size

This gives

Miles per gallon = 450/18

Evaluate the quotient

Miles per gallon =25

Represent as an inequality

x >= 25

Hence, the least miles per gallon this trip is 25 miles per gallon

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The graph of an exponential function shows a geometric increase or decrease using a curve

Exponential functions are inverse of logarithmic functions. The standard exponential function is expressed as:

y = ab^x

where

a is the base

x is the exponent

The graph of an exponential function shows a geometric increase or decrease using a curve. According to the function given there will a decrease rate due to the value of the rate value given which is less than 1. The graph of the function given is attached below;

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Answer:4 1/12.

Step-by-step explanation: First, you add 3 and a half with a quarter. A half equals two quarters so it equals 3 and 3/4.  Then, you add 3 3/4 with 1/3. A common denominator here is 12. 3/4 times 3/3 = 9/12. 1/3 times 4/4 = 4/12. 9+4 = 13. The answer is more than one so we carry and get 4 and 1/12.

Answer:

addition property

Step-by-step explanation:

See attached image.

The upper quartile for the given data is 51 .

Given data: {51,49,52,46,50,38,38,45,34,52,46}

Data in arranged form: {34,38,38,45,46,46,49,50,51,52,52}

Find the median first, then the upper quartile. There are eleven data points, thus look at term six to determine the median as there are five data points on any side. The median is 46 because the sixth term is 46.

The upper extreme, 52, and the median are then used to determine the upper quartile; make sure not to include the median data point when dividing the groups. The upper quartile is the third term (between the median and upper extreme) because there would be two data points on each side if there were only five data points from the median to the upper extreme. The third term, which is 51, falls into the upper quartile.

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Answer:

choice C. Yes, this image proves the pythagorean theorem is true because 9 + 16 = 25

Step-by-step explanation:

The coordinates of the center is at (1, 0) and the length of the radius is 4 units.

An equation is an expression that shows the relationship between two or more variables and numbers.

The standard form of a circle is:

(x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle and r is the radius.

The coordinates of the center is at (1, 0) and the length of the radius is 4 units.

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Your answers seem to be on the right track. These online homework apps can be picky about the answer they accept, though.

Given [tex]f(x) = x^4 - 2x^2 + 3[/tex], we have derivative

[tex]f'(x) = 4x^3 - 4x = 4x (x^2 - 1) = 4x (x - 1) (x + 1)[/tex]

with critical points when [tex]f'(x) = 0[/tex]; this happens when [tex]x=0[/tex] or [tex]x=\pm1[/tex].

We also have second derivative

[tex]f''(x) = 12x^2 - 4 = 12 \left(x^2-\dfrac13\right) = 12 \left(x - \dfrac1{\sqrt3}\right) \left(x + \dfrac1{\sqrt3}\right)[/tex]

with (possible) inflection points when [tex]x=\pm\frac1{\sqrt3}=\pm\frac{\sqrt3}3[/tex].

Intercept

If "intercept" specifically means [tex]y[/tex]-intercept, what you have is correct. Setting [tex]x=0[/tex] gives [tex]f(0) = 3[/tex], so the intercept is the point (0, 3).

They could also be expecting the [tex]x[/tex]-intercepts, in which case we set [tex]f(x)=0[/tex] and solve for [tex]x[/tex]. However, we have

[tex]x^4 - 2x^2 + 3 = \left(x^2 - 1\right)^2 + 2[/tex]

and

[tex]x^2-1\ge-1 \implies (x^2-1)^2 \ge (-1)^2 = 1 \implies x^4-2x^2+3 \ge 2[/tex]

so there are no [tex]x[/tex]-intercepts to worry about.

Relative minima/maxima

Check the sign of the second derivative at each critical point.

[tex]f''(-1) = 8 > 0 \implies \text{rel. min.}[/tex]

[tex]f''(0) = -4 < 0 \implies \text{rel. max.}[/tex]

[tex]f''(1) = 8 > 0 \implies \text{rel. min.}[/tex]

So we have two relative minima at the points (-1, 2) and (1, 2), and a relative maximum at (0, 3).

Inflection points

Simply evaluate [tex]f[/tex] at each of the candidate inflection points found earlier.

[tex]f\left(-\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]

[tex]f\left(\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]

Using the Central Limit Theorem, the standard error of the distribution of differences in sample means is of 1.97.

According to the Central Limit Theorem, it is given by the standard deviation of the sample divided by the square root of the sample size, hence:

It is given by the square root of the sum of the standard errors of each sample squared, hence:

s = sqrt(1.1² + 1.63²) = 1.97.

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Given that the length ratio between the radii of the two circles is (2 · x) / (5 · y). The ratio of the areas of the two circles is (4 · x²) / (25 · y²).

According to the statement we know that the radius ratio between two circles. Given that the area of the circle is directly proportional to the square of its radius, then the area ratio is shown below:

A ∝ r²

A = k · r²

A' · r² = A · r'²

A' / A = r'² / r²

A' / A = (r' / r)²

A' / A = [(2 · x) / (5 · y)]²

A' / A = (4 · x²) / (25 · y²)

Given that the length ratio between the radii of the two circles is (2 · x) / (5 · y). The ratio of the areas of the two circles is (4 · x²) / (25 · y²).

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Sim wants to increase his waist size to 32.4 inches.

Sim wants the increase to be 8% of 30 inches.

The amount of increase Sim wants in his waist size exists

8% × 30 inches.

= 0.08 × 30 inches.

= 2.4 inches.

Adding the wanted increase to his present size would create Sim's waist size to be

30 in + 2.4 in = 32.4 inches.

Sim wants to increase his waist size to 32.4 inches.

Therefore, the correct answer is 32.4 inches.

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Answer:

Step-by-step explanation:

The radius of the base is the distance between the center of the circle and the edge of the base, therefore in this case it is equal to 3 in.

The volume of a cone is given by:

V = π * r² * h / 3

V = π * (3)² * 10 / 3

V = 94. 25 in³

Therefore, The volume of is 94. 25 in³.

Step-by-step explanation:

6.25 points

Find the GCF for the list.

10m4, 40m⁹

10m5

40m4

10m4

6.25 points

list

The given number of balloons, green = 10, purple = 4, red = 5, tie-dye = 2, black = 3, gives;

a. 5/138

b. 25/276

c. 5/1012

d. 35/46

Given parameters;

Number of balls;

Green = 10

Purple = 4

Red = 5

Tie-dye = 2

Black = 3

Mode of selection = Without replacement

Number of balloons = 10+4+5+2+3 = 24

a. Probability of popping a red balloon = 5/24

Probability of popping a second red balloon = 4/23

Therefore;

Probability of popping two reds consecutively = 5/24 × 4/23 = 5/138

b. Probability of popping a red balloon = 5/24

Probability of popping a green balloon next = 10/23

Therefore;

Probability of popping a red and then a green balloon = 5/24 × 10/23 = 25/276

c. Probability that the first balloon that pops is a red = 5/24

Next balloon is a black = 3/23

Third balloon is red = 4/22

The probability, P, is therefore;

d. The probability that the first balloon is a tie-dye = 2/24 = 1/12

Therefore;

Probability that the first balloon is not a tie-dye = 1 - 1/12 = 11/12

Probability that the second balloon is not a tie-dye = 21/23

Similarly;

Probability that the third balloon is not a tie-dye = 20/22 = 10/11

Which gives;

The probability, P, of popping anything but a tie-dye on three consecutive throws is therefore;

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The five-number summary is:

Minimum: 4

Quartile Q1: 11.25

Median: 12.5

Quartile Q3: 16.5

Maximum: 20

The box plot is attached below.

The five-number summary of a data that is displayed on a box plot include: minimum and maximum values, lower and upper quartiles, and the median.

Given the data, 10, 13, 15, 12, 12, 4, 12, 17, 12, 13, 15, 18, 10, 11, 20, 19, the five-number summary is:

Minimum: 4

Quartile Q1: 11.25

Median: 12.5

Quartile Q3: 16.5

Maximum: 20

There are no outliers. Thus, the box plot that represents the five-number summary is shown in the image attached below.

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Answer: it is correct i got it from edmentum

Step-by-step explanation:

Answer:

A = 8000

B = 4000

C = 12000

Step-by-step explanation:

$24000 = A,B and C

A = 2B

B = 1/3C

solve for the letter that gets described the most

that letter is B

A =2B

B = 1/3C -> C = 3B

24000 = A + B + C

24000 = 2B + B + 3B

24000 = 6B

B = 4000

A =2B = 8000

C = 3B = 12000

Based on the stem and leaf plots given, the correct stem and leaf plot for the first table on per capita income is the third stem and leaf diagram.

For the table on the basketball tornament, the correct stem and leaf plot would be the last one.

First look at the key to the bottom right of the plot to see how to interpret the data.

The key on the third stem and lead plot says 1 I 2 = 12,000. This means that every steam and lead pairing is in thousands.

Based on the income per capita being in thousands, this is the most likely stem and lead plot for the first table on income per capita.

The second table about basketball tornament appearances is on single and double digits. Only a small stem and leaf key will do.

Look at the number of appearances. The minimum is 1. On a stem and leaf, this is shown as 0 I 1. Options A and B don't have this so we go to Options C and D.

As established, Option C is for data in their thousands so it is out. The correct stem and leaf plot is therefore Option D.

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Using the combination formula, it is found that 436,270,780 different selections are possible.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 7 numbers are taken from a set of 61, hence the number of different selections is given by:

C(61,7) = 61!/(7! x 54!) = 436,270,780

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The fraction of the area of polygon H of polygon G's area would be: 1/16.

When a polygon is formed by enlarging or reducing an original polygon by a scale factor, the new polygon formed is similar to the original polygon.

The scale factor = new dimension/original dimension

Given that polygon H is the new polygon formed when polygon G is reduced by a scale factor of 1/4, thus, we would have the following:

Area of polygon H/Area of polygon G = square of the side of polygon H/square of the side of polygon G = square of the scale factor of dilation

Area of polygon H/Area of polygon G = 1²/4² = 1/16

This implies that the area of polygon G is 16 units² while the area of polygon H is 1 units².

Thus, the fraction of the area of polygon H of polygon G's area would be: 1/16.

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Expanding the desired form, we have

[tex]A \sin(\omega t + \phi) = A \bigg(\sin(\omega t) \cos(\phi) + \cos(\omega t) \sin(\phi)\bigg)[/tex]

and matching it up with the given expression, we see that

[tex]\begin{cases} A \sin(\omega t) \cos(\phi) = 2 \sin(4\pi t) \\ A \cos(\omega t) \sin(\phi) = 5 \cos(4\pi t) \end{cases}[/tex]

A natural choice for one of the symbols is [tex]\omega = 4\pi[/tex]. Then

[tex]\begin{cases} A \cos(\phi) = 2 \\ A \sin(\phi) = 5 \end{cases}[/tex]

Use the Pythagorean identity to eliminate [tex]\phi[/tex].

[tex](A\cos(\phi))^2 + (A\sin(\phi))^2 = A^2 \cos^2(\phi) + A^2 \sin^2(\phi) = A^2 (\cos^2(\phi) + \sin^2(\phi)) = A^2[/tex]

so that

[tex]A^2 = 2^2 + 5^2 = 29 \implies A = \pm\sqrt{29}[/tex]

Use the definition of tangent to eliminate [tex]A[/tex].

[tex]\tan(\phi) = \dfrac{\sin(\phi)}{\cos(\phi)} = \dfrac{A\sin(\phi)}{\cos(\phi)}[/tex]

so that

[tex]\tan(\phi) = \dfrac52 \implies \phi = \tan^{-1}\left(\dfrac52\right)[/tex]

We end up with

[tex]y(t) = 2 \sin(4\pi t) + 5 \cos(4\pi t) = \boxed{\pm\sqrt{29} \sin\left(4\pi t + \tan^{-1}\left(\dfrac52\right)\right)}[/tex]

where

• amplitude:

[tex]|A| = \boxed{\sqrt{29}}[/tex]

• angular frequency:

[tex]\boxed{4\pi}[/tex]

• phase shift:

[tex]4\pi t + \tan^{-1}\left(\dfrac 52\right) = 4\pi \left(t + \boxed{\frac1{4\pi} \tan^{-1}\left(\frac52\right)}\,\right)[/tex]

Probability has to do with the possibility that an event may or may not happen.

The term probability has to do with the possibility that an event may or may not happen. The value of probability always ranges from zero to one.

Now;

Total number of fishes = 32 + 14 + 10 + 3 = 59

a) probability of catching a bass and then a carp = 32/59 * 10/59 = 320/3481

b) probability of catching two consecutive bull sharks= 3/59 * 3/59 = 9/3481

c) probability of catching  a fluke and then any different type of fish 14/59 * (32/59 + 10/59 + 3/59) = 14/59 * 45/59 = 630/3481

d) probability of catching  a bass, another bass, and a bull shark =  32/59 * 32/59 * 3/59 = 3072/205379

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1. To determine the better option between a 10% off coupon versus a $10 off coupon, it is necessary to determine the coupon price.

2. On the other hand, the $10 off coupon becomes better when the coupon price is less than $100.

3. The 10% off coupon and the $10 off coupon do not give the same amount of discount unless the coupon or list price is $100 in both situations.

A discount is a monetary reduction in the cost of a good or service offered to customers to increase trade.

Offering discounts enhances sales but not profitability.  So, there is a trade-off that must be considered properly.

Ordinarily, if the coupon price is more than $100, the 10% off coupon becomes better than the $10 off coupon.

For instance, if the coupon price is $110, the 10% off coupon will yield a discount amount of $11 ($110 x 10%), which is more than $10.

For instance, if the coupon price is $99, the discount amount will be $9.90, which is less than $10.

Thus, a 10% off coupon and a $10 off coupon do not offer the same discount amount unless the list price is $100, no more, no less.

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Compare the discounts you would receive with a 10% off coupon versus a $10 off coupon.

Answer: -2

Step-by-step explanation:

The graph passes through (-2, 3) and (4, -9).

So, the average rate of change is [tex]\frac{-9-3}{4-(-2)}=\boxed{-2}[/tex]

Answer: u - 8 = -9

Step-by-step explanation:

Given equation

-7u - 5 = 2

Add 5 on both sides

-7u - 5 + 5 = 2 + 5

-7u = 7

Divide -7 on both sides

-7u / (-7) = 7 / (-7)

u = -1

Substitute values into the goal expression

u - 8 = (-1) - 8 = [tex]\Large\boxed{-9}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The answer is -9.

First, let's find the value of u.

Now, substitute in the expression.

In order to calculate the confidence Interval, what we need is the t distribution. The population mean number of visits is 11.667 and 19.9928 visits. 95 percent contains true mean while the other 5 does not.

We have n = 12

df = n- 1 = 11

a. To compute the confidence interval use a t distribution.

The mean = fx/n

= 15.83

level of significance = 0.05

standard deviation = 6.555

t α/2, df = 2.20

standard error  = 6.555 / √ 12 = 1.8922

margin of error , = 2.2 * 1.8922 = 4.1628

barx - E = 15.83 - 4.1628 = 11.6672

barx + E = 15.83 + 4.1628 = 19.9928

With 95% confidence the population mean number of visits  is between 11.667 and 19.9928 visits.

c. About 95 percent of these confidence intervals will contain true mean.

about __5__percent will not contain the true population

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