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The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)

The function is positive when g(x) > 0.

Then we need to solve:

∛(x - 3) > 0

We can directly remove the cubic root, because it does not affect the sign of the argument, then:

x - 3 > 0

x > 3

The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)

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The interval which the function is positive is (3, ∝)

The equation of the function is given as:

g(x) =∛x - 3

Set the radical greater than 0

x - 3 > 0

Add 3 to both sides of the inequality

x > 3

Express as an interval notation

(3, ∝)

Hence, the interval which the function is positive is (3, ∝)

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Step-by-step explanation:

Answer:

1 13/30

Step-by-step explanation:

10/12 + 6/10 =

= 5/6 + 3/5

= 25/30 + 18/30

= 43/30

= 30/30 + 13/30

= 1 13/30

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

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

[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]

[tex]\huge\textsf{Solving:}[/tex]

[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]

[tex]\mathsf{= \dfrac{10\div2}{12\div2} + \dfrac{6\div2}{10\div2}}[/tex]

[tex]\mathsf{= \dfrac{5}{6} + \dfrac{3}{5}}[/tex]

[tex]\mathsf{= \dfrac{5\times5}{6\times5} + \dfrac{3\times6}{5\times6}}[/tex]

[tex]\mathsf{= \dfrac{25}{30} + \dfrac{18}{30}}[/tex]

[tex]\mathsf{= \dfrac{25 + 18}{30-0}}[/tex]

[tex]\mathsf{= \dfrac{25 + 18}{30}}[/tex]

[tex]\mathsf{= \dfrac{43}{30}}[/tex]

[tex]\approx\mathsf{1\dfrac{13}{30}}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{1\dfrac{13}{30}}}\huge\checkmark[/tex]

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

~[tex]\frak{Amphitrite1040:)}[/tex]

Step-by-step explanation:

let the younger person be x and older be y

4x + 9 = 24

4x = 15

x = 3.75

y = 24 - 3.75

y = 20.25

The histogram that correctly shows the data in the table is the histogram number four.

This a type of graph that allows people to visually represent data by using bars and gathering the data they have in different categories.

This data can be represented using ranges of temperature and the number o elements or substances in these ranges.

This data matches the fourth graph

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Answer:

Percent increase is 70%.

Step-by-step explanation:

The original price was $110. That will go on the bottom (denominator) in our calculation. On the top (numerator) we put the change in the dollar amount. The new price is $187. So we'll subtract:

187 - 110

= 77

The change in price was $77.

change/original

= 77/110

= 0.7

Change the decimal answer to a percent by multiplying by 100.

0.7 × 100

= 70%

The percent increase is 70%.

The number of years it would take sales to reach $1,750,000 is 14.65 years.

The formula that can be used to determine the number of years it would take for the sales to reach $1,750,000 is:

Number of years : In (FV / PV) / r

Where:

Number of years : In ($1,750,000 / 850,000) / 0.04931998

Number of years : In (2.06) / 0.04931998

Number of years : 14.65 years

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Answer:

-1/3

5

Step-by-step explanation:

We need to complete

y = mx + b

with a slope, m, and with the y-intercept, b.

From the graph, we see that the line intersects the y-axis at y = 5, so the y-intercept, b, is 5.

We now have y = mx + 5.

Now we need the slope.

We pick two points that are easy to read, (0, 5) and (3, 4).

m = slope = rise/run

To go from (3, 4) to (0, 5), we go up vertically 1 unit. The rise is 1.

Then we go left horizontally 3 units. The run is -3.

m = slope = rise/run = 1/(-3) = -1/3

Now we have the slope, so we can finish.

y = -1/3 x + 5

Answer:

-1/3

5

The volume of the cone illustrated will be 117.2 unit³.

From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.

It should be noted that the volume of a cone is calculated as:

= 1/3 πr²h.

where,

π = 3.142

r = radius = 4cm

h = height = 7cm

In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:

= 1/3πr²h

= 1/3 × 3.14 × 4² × 7

= 117.2 unit³

Therefore, the volume of the shape is 117.2 unit³.

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Complete question:

A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.

The letter for the graphed function is y = √(x) - 5

The parent function is given as:

y = √x

From the graph, we can see that the function is shifted downwards by 5 unts

This is represented as:

y = √(x) - h

Where h = 5

Substitute the known values in the above equation

y = √(x) - 5

This means that the letter for the graphed function is y = √(x) - 5

Hence, the letter for the graphed function is y = √(x) - 5

So, the complete functions are

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Triangle 1, triangle 3 and triangle 4 are congruent triangles bases on side-side-side and side-angle-side congruency.

Triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, equilateral and scalene triangle.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other. Also, their corresponding angles are congruent.

Triangle 1, triangle 3 and triangle 4 are congruent triangles bases on side-side-side and side-angle-side congruency.

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The inequalities are matched with the respective graphs as shown in the attached image.

In mathematics, inequality is the relationship between two non-equal expressions, denoted by a sign such as 'not equal to,' > 'greater than,' or 'less than.'

Roads feature speed limits, some movies have age limitations, and the time it takes to go to the park are all instances of inequalities in the real world.

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Answer:

40

Step-by-step explanation:

P=2(l+w)

2·(10+10)

          =40

Step-by-step explanation:

Notice that the main vertices (-15,4) and (5,4) both have the same y coordinate. This means that the focal axis is horizontal so we have a horizontal ellispe.

Equation of a horizontal ellipse is

[tex] \frac{(x - h) {}^{2} }{ {a}^{2} } + \frac{(y - k) {}^{2} }{ {b}^{2} } = 1[/tex]

I'll explain the variables.

Step 1: Find the center.

The center (h,k) is the midpoint of either the main or co vertices. It doesn't matter because of the definition of an ellipse.

So using the midpoint formula, let find the midpoint of the main vertices.

[tex]( \frac{ - 15 + 5}{2} ) = - 5[/tex]

[tex] \frac{4 + 4}{2} = 4[/tex]

So our center is (-5,4) so as of right now we have

[tex] \frac{(x + 5) {}^{2} }{ {a}^{2} } + \frac{(y - 4) {}^{2} }{ {b}^{2} } = 1[/tex]

Step 2: The variable a represents the semi major axis. This

basically means what is the distance from the center to either main vertex.

Here, let use (5,4). Using (5,4), our main vertex and (-5,4), our center.

Use the distance formula

[tex]a= \sqrt{(5 - ( - 5) {}^{2} + (4 - 4) {}^{2} } [/tex]

[tex]a = \sqrt{100} [/tex]

[tex]a= 10[/tex]

So our distance is 10, this means a=10

Step 3: The variable b represent the semi minor axis. This basically the distance from the center to either co vertex.

Using the distance formula,

[tex]b = \sqrt{ (- 5 - ( - 5) {}^{2} + (4 - 11) {}^{2} } [/tex]

[tex]b = \sqrt{49} [/tex]

[tex]b = 7[/tex]

So b=7, so finally we plug a=10, b=7

[tex] \frac{(x + 5) {}^{2} }{100} + \frac{(y - 4) {}^{2} }{49} = 1[/tex]

Answer:

Step-by-step explanation:

7/9 * 15/8 = 105/72 = 35/24

[tex](\stackrel{x_1}{-1.2}~,~\stackrel{y_1}{2.9})\qquad (\stackrel{x_2}{2.9}~,~\stackrel{y_2}{9.46}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9.46}-\stackrel{y1}{2.9}}}{\underset{run} {\underset{x_2}{2.9}-\underset{x_1}{(-1.2)}}}\implies \cfrac{6.56}{2.9+1.2}\implies \cfrac{6.56}{4.1}\implies 1.6[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2.9}=\stackrel{m}{1.6}(x-\stackrel{x_1}{(-1.2)}) \\\\\\ y-2.9=1.6(x+1.2)\implies y-2.9=1.6x+1.92\implies \boxed{y=1.6x+4.82} \\\\\\ \textit{when x = 115, what is "y"?}\qquad y=1.6(115)+4.82\implies y=188.82[/tex]

The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.

An odds ratio is a measure of the strength of an association with the exposure and outcome.

The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).

                             Flies      Does not fly     Total

Long beak               11               7                     19

Not a long beak      3              13                     15

Total                       14             20                    34

Probability of long beaks flying = 0.79 (1/14)

Probability of not having long beaks flying = 0.21 (3/14)

Odds ratio = 3.76 (0.79/0.21)

Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.

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Complete question

Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.

Long beakNot a long beakTotalFlies11719Does not fly31315Total142034

Using the normal distribution, there is a 0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion estimate and the sample size are given as follows:

p = 0.45, n = 437.

Hence the mean and the standard error are:

The probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3% is 2 multiplied by the p-value of Z when X = 0.45 - 0.03 = 0.42.

Hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (0.42 - 0.45)/0.0238

Z = -1.26

Z = -1.26 has a p-value of 0.1038.

2 x 0.1038 = 0.2076.

0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

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Answer:30%

Step-by-step explanation:

10% of 50 is 50/10 so 10% is 5
15/5=3 so its three lots of 10%

3*10%=30%

The pounds of alloy that contains 26% copper that would be used is  23.42 pounds.

The pounds of alloy that contains 69% copper that would be used is 29.58 pounds.

0.26a + 0.69b = (53 x 0.5)

0.26a + 0.69b = 26.50 equation 1

a + b = 53 equation 2

Where:

Multiply equation 2 by 0.26

0.26a + 0.26b = 13.78 equation 3

Subtract equation 3 from equation 2

12.72 = 0.43b

b = 12.72 / 0.43

b = 29.58 pounds

a = 53 - 29.58 = 23.42 pounds

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Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

At the null hypothesis, it is tested if the mean is not different to 16 ounces, that is:

[tex]H_0: \mu = 16[/tex]

At the alternative hypothesis, it is tested if the mean is different, hence:

[tex]H_1: \mu \neq 16[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are:

[tex]\overline{x} = 15.75, \mu = 16, \sigma = 1.46, n = 150[/tex].

Hence:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{15.75 - 16}{\frac{1.46}{\sqrt{150}}}[/tex]

z = -2.1

Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different of a value, with z = -2.1, the p-value is of 0.0357.

Since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

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Step-by-step explanation:

1/4×48

=12

So if 12people are out of state

48-12=36,is the number of people living in the state

The common ratio of the given sequence is -1/4. In a geometric sequence, the common ratio is the value that is in between each number in the sequence.

The ratio of the value of a term in the sequence to the value of the previous term in the sequence is said to be the common ratio. I.e.,

C.R = (nth term)/(n - 1)th term

The given sequence is 64, -16, 4, -1, ...

Taking the ratio of the second term to the first term, we get

-16/64 = -1/4

Similarly, the ratio of the third term to the second term,

4/16 = -1/4

Since the ratios are equal, then the common ratio of the sequence is -1/4.

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By the fundamental theorem of calculus,

[tex]\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}[/tex]

In general,

[tex]\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}[/tex]

The correct option is B) 67.4%

A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.

Given here, P(probability that a worker is a college graduate) = 32%

                                                                                                      = 0.32

q (probability that a worker is not a college graduate) is 1-0.32 = 0.68  

now μ(mean) = n×p

                      = 50×0.32

                      = 16

Again standard deviation σ = [tex]\sqrt{npq\\}[/tex]

                                           σ = [tex]\sqrt{50\cdot 0.32\cdot 0.68}[/tex]

                                           σ = 3.2985

now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)

                      = P(z<0.45)  

                      = 0.674 [using z table]

                      = 67.4%

Hence option 2 is the correct answer

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Equation of directrix is : y = 1, so we can say that it's a parabola of form : -

[tex]\qquad \sf  \dashrightarrow \: (x - h) {}^{2} = 4a(y - k)[/tex]

and since the focus is above the directrix, it's a parabola with upward opening.

[tex]\qquad \sf  \dashrightarrow \: (x - ( - 4)) {}^{2} = 4(2)(y - 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (x + 4) {}^{2} = 8(y - 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 8x + 16 = 8y - 40[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8y = {x}^{2} + 8x + 56[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \cfrac{1}{8} {x}^{2} + x + 7[/tex]

Directrix

Focus

Focus lies in Q3 and above y=1

Then

Perpendicular distance

Find a for the equation

Now the equation is

[tex]\\ \rm\dashrightarrow 4a(y-k)=(x-h)^2[/tex]

[tex]\\ \rm\dashrightarrow 4(2)(y-5)=(x+4)^2[/tex]

[tex]\\ \rm\dashrightarrow 8(y-5)=x^2+8x+16[/tex]

[tex]\\ \rm\dashrightarrow 8y-40=x^2+8x+16[/tex]

[tex]\\ \rm\dashrightarrow 8y=x^2+8x+16+40[/tex]

[tex]\\ \rm\dashrightarrow 8y=x^2+8x+56[/tex]

[tex]\\ \rm\dashrightarrow y=\dfrac{x^2}{8}+x+7[/tex]

Answer:

160

Step-by-step explanation:

22+18=40, and this was 25% of the cars.

So, 40(4)=160 cars were sold that week.

The number of cars Captain's Autos sold in total that week is 160.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Number of used car on monday= 22

Number of cars on tuesday= 18

Now,

Let's call the total number of cars sold during the week "x".

We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:

22 + 18 = 0.25x

Simplifying, we get:

40 = 0.25x

Dividing both sides by 0.25, we get:

x = 160

Therefore, by the unitary method the answer will be 160.

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