100 Points! Find all the zeros of g(x)=x^4-3x^3-5x^2+3x+4. Photo attached. Please show as much work as possible. Thank you!

Step-by-step explanation:

\( \frac{5984}{33} \)

\( \frac{5984}{3 \times 11} \)

\( \frac{544}{3} \)

= 181.33

The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ1

Answer:

X = 5

Step-by-step explanation:

28 = 7x + 3 - 2x

28 = 5x + 3

28 - 3 = 5x + 3 - 3

25 = 5x

25/5 = 5x/5

X = 5

Answer:

X = 5

Step-by-step explanation:

1. Combine like terms.

2. Subtract 3 from both sides.

3. Simplify.

4. Divide both sides of the equation by the same term.

5. Simplify.

Hope this helps!

\(\text{L.H.S}\\\\=1+ \cos^4 x - \sin^4 x\\\\=1+ (\cos^2 x)^2 - (\sin^2 x)^2\\\\=1+(\cos^2 x + \sin^2 x)(\cos^2 x- \sin^2 x)\\\\=1+1\cdot(\cos 2x)\\\\=1+\cos 2x\\\\=2\cos^2 x\\\\=\text{R.H.S}\\\\\text{Proved.}\)

Two factors that need to be controlled to keep this test fair are the temperature and the sample volume.

The control variables are those variables that should be kept constant in order to avoid interfering with the free flow of the experiment.

For the provided test, it is important that the temperature of the environment where the test sample is kept is controlled throughout the duration of the experiment so that some results are not affected by this. Also, the sample volume should be controlled for fair outcomes.

Learn more about control variables here:

https://brainly.com/question/28077766

#SPJ1

Answer:

61.8

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 172.6, \sigma = 42.4\)

What percentage of women have weights between the ejection seat’s weight limits (that is, 133.8 to 208.0 lb)?

We have to find the pvalue of Z when X = 208 subtracted by the pvalue of Z when X = 133.8 for the proportion. Then we multiply by 100 to find the percentage.

X = 208

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{208 - 172.6}{42.4}\)

\(Z = 0.835\)

\(Z = 0.835\) has a pvalue of 0.798

X = 133.8

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{133.8 - 172.6}{42.4}\)

\(Z = -0.915\)

\(Z = -0.915\) has a pvalue of 0.180

0.798 - 0.18 = 0.618

0.618*100 = 61.8%

Without the %, the answer is 61.8.

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

Step-by-step explanation:

The union of the sets is { 22, 33, 44, 55, 66 }

The union of sets can be defined as the sum of the elements of two or more sets without repetition of those elements.

It is also known as the combination of the all the elements of two or more sets.

It is denoted using the symbol , ' ∪ '

Given the sets;

The union of the sets is:

{ 22, 33, 44, 55, 66 }

Thus, the union of the sets is { 22, 33, 44, 55, 66 }

Learn more about sets here:

https://brainly.com/question/13458417

#SPJ1

Answer:

$1,094.93

Step-by-step explanation:

The income is how much money you make. You lose the money you spend. To find how much money you have left, just subtract the income with everything you spent.

This means the final answer is: 2725.98 - (1250.00 + 325.78 + 55.27) = $1,094.93

Function graph that has y- intercept of 3 is g(x) = 3\((\frac{1}{4}) ^{x}\).

y- intercept will be 3 when we will put value of x = 0 and y will be 3 that graph will have y intercept 3

A) h(x) = 5\((2)^{x}\)

when x = 0

Any number with zero power is always 1

h(x) = 5

B) h(x) = 5\((0.5)^{x}\) + 0.5

when x = 0

h(x) = 5 + 0.5

h(x) = 5.5

C) g(x) = 3\((\frac{1}{4}) ^{x}\)

when x = 0

g(x) = 3

Here we get y intercept as 3.

To know more about y- intercept click here :

https://brainly.com/question/14180189

#SPJ1

The angle measure that belongs in the green box is given as follows:

70.67º.

We consider a triangle with side lengths and angles related as follows, as is the case for this problem:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(x)/12  = sin(76º)/12.34

Applying cross multiplication, the missing angle measure is given as follows:

sin(x) = 12 x sine of 76 degrees/12.34

sin(x) = 0.9436.

x = arcsin(0.9436)

x = 70.67º.

More can be learned about the law of sines at https://brainly.com/question/4372174

#SPJ1

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

for such more question on temperature

https://brainly.com/question/14820864

#SPJ8

Answer: 49/50

Step-by-step explanation:

81 + 17 + 2 = 10

98/100 = 49/50

The probability as a fraction in simplest form is 49/50.

What is indian number system and international number system?

International number system is a representation of a number that is divided into periods and arranged according to the value. The periods of international number system are one, thousands, millions, billions, and so on.

Indian number system is used to represent the numbers in the Indian subcontinent. The terms Lakh and Crore are the most commonly used terms to describe a large number in indian number system.

we need to add 16 ounces of the 10% alcohol solution to the 8 ounces of the 15% alcohol solution to obtain 24 ounces of an 11% alcohol solution.

To solve this problem, we need to use the concept of mixtures. A mixture is a combination of two or more substances that are physically combined but not chemically bonded. In this problem, we have two alcohol solutions with different concentrations, and we need to mix them to obtain a new solution with a specific concentration.

Let x be the number of ounces of the 10% alcohol solution we need to add to the 8 ounces of the 15% alcohol solution to get the desired 11% alcohol solution.

We can start by expressing the amount of alcohol in each solution in terms of their concentrations. For example, the 8 ounces of the 15% alcohol solution contains 0.15 x 8 = 1.2 ounces of alcohol. Similarly, the x ounces of the 10% alcohol solution contains 0.10 x ounces of alcohol.

When we mix the two solutions together, the total amount of alcohol in the mixture will be the sum of the amount of alcohol in each solution. Therefore, we can set up an equation based on the amount of alcohol in the mixture:

0.15 x 8 + 0.10 x = (8 + x) * 0.11

The left-hand side of the equation represents the amount of alcohol we have before mixing, and the right-hand side represents the amount of alcohol we have after mixing. We know that the final concentration of alcohol in the mixture should be 11%, so we multiply the total volume of the mixture (8 + x ounces) by 0.11 to get the amount of alcohol in the mixture.

Now we can solve for x:

0.15 x 8 + 0.10 x = (8 + x) * 0.11
1.2 + 0.10 x = 0.88 + 0.11 x
0.02 x = 0.32
x = 16

Therefore, we need to add 16 ounces of the 10% alcohol solution to the 8 ounces of the 15% alcohol solution to obtain 24 ounces of an 11% alcohol solution.
To know more about ounces go through:-
https://brainly.com/question/2853335
#SPJ9

Answer:

1.25

Step-by-step explanation:

Answer:

1.25 cm

Step-by-step explanation:

The blow up snow flake  is 15 cm

The blow up ratio is 12 to 1

Divide the 15 cm by 12 to determine the size in real life

15/12 =1.25 cm

Answer:

X intercept: x = 4 or in point form (4,0)

Zero for the function at (4, 0)

Y intercept : y = 160  or in point form (0,160)

slope = -40  mph

Step-by-step explanation:

The y-intercept, x-intercept are directly obtained from the graph by noticing the points on the axes where the line crosses them.

The slope is calculated using the points (0, 160) and (4, 0) and the formula for the slope of the segment that joins them:

slope = (y2 - y1)/(x2 - x1) = (160 - 0) / (0 - 4) = -160/4 = -40

and the units of the slope are miles over hour (that is miles per hour or mph)

Approximately 7 employees took a break longer than 49 minutes.

We have,

In a box-and-whisker plot, the box represents the interquartile range (IQR), which includes the middle 50% of the data.

The line within the box represents the median.

The "whiskers" extend to the minimum and maximum values, excluding any outliers.

Given the information provided:

Median = 41

Q1 = 37

Q3 = 49

Largest = 55

Smallest = 35

Since Q3 represents the upper quartile and corresponds to the boundary for the upper 25% of the data, we can conclude that 25% of the employees took a break longer than 49 minutes.

Now,

The number of employees who took a break longer than 49 minutes can be estimated by calculating 25% of the total number of employees:

25% of 27 employees

= (25/100) x 27

= 6.75

Since we cannot have a fractional number of employees, we round up to the nearest whole number.

Therefore,

Approximately 7 employees took a break longer than 49 minutes.

Learn more about the interquartile range here:

https://brainly.com/question/29204101

#SPJ1

Answer:

146 and 1

Step-by-step explanation:

146+1=147

Answer:

53÷(13-8) × 2

53÷5×2

53÷10

5.6

Answer:

21.2

Step-by-step explanation:

Always must do the parenthesis first. This will give you 5 and now you must take 53 and 5 and divide them, leaving you with 10.6. Multiply that by 2 and you have 21.2.

Please check out my latest song on Sound cloud. I will post the link below

ANSWER:9

Step-by-step explanation:

Answer:

\(x=13,\:y=0\)

Step-by-step explanation:

Isolate x for 2x-3y=26: \(x=\frac{26+3y}{2}\)

\(\mathrm{Substitute\:}x=\frac{26+3y}{2}\)

\(\begin{bmatrix}3\cdot \frac{26+3y}{2}-4.6y=39\end{bmatrix}\)

\(Simplify\)

\(\begin{bmatrix}39-0.1y=39\end{bmatrix}\)

Isolate y for 39-0.1y=39: y=0

\(\mathrm{For\:}x=\frac{26+3y}{2}\)

\(\mathrm{Substitute\:}y=0\)

\(x=\frac{26+3\cdot \:0}{2}\)

\(\frac{26+3*0}{2}=13\)

\(x=13\)

\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)

\(x=13,\:y=0\)

The area and perimeter of 2D shape of Rectangle is 6.8448cm and 11.04cm repectively. The area and perimeter of 2D shape of circle is 5.0761cm and 8.0028cm respectively.

2D shape of Rectangle with dimensions of Length is3.72 cm and Width is 1.84 cm. we can find the area of rectangle with formula Area = length x width and the formula of perimeter is Perimeter = 2(length + width).

Area = length x width = 3.72 cm x 1.84 cm = 6.8448 square cm (rounded to four decimal places)

Perimeter = 2(length + width) = 2(3.72 cm + 1.84 cm) = 11.04 cm

2D shape of Circle with dimension of diameter of 2.54 cm. we can find the area with formula Area = πr^2 and circumference with formula Circumference = 2πr

Radius = diameter / 2 = 2.54 cm / 2 = 1.27 cm

Area = πr^2 = π(1.27 cm)^2 = 5.0761 square cm (rounded to four decimal places)

Circumference = 2πr = 2π(1.27 cm) = 8.0028 cm (rounded to four decimal places)

To know more about 2D shapes.

https://brainly.com/question/18719120

#SPJ4

____The given question is incomplete, the complete question is given below:

Calculating area and circumference or perimeter of a 2D shape. Use your measurements to calculate the area and circumference of the circle and to calculate the area and perimeter of the rectangle. Rectangle Length: 3.72 cm Width: 1.84 cm  Circle : 2.54 cm Diameter of circle

Answer:

\(\displaystyle y = -3x + 9\)

Step-by-step explanation:

First, find the rate of change of the line:

\(\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-6 + 3}{-1 + 2} = m \hookrightarrow \frac{-3}{1} = m \\ \\ \boxed{-3 = m}\)

_______________________________________________

Now plug all the information into the Slope-Intercept Formula. It does not matter which ordered pair is chosen:

\(\displaystyle 3 = -3[2] + b \hookrightarrow 3 = -6 + b; 9 = b \\ \\ \boxed{\boxed{y = -3x + 9}} \\ \\ OR \\ \\ 6 = -3[1] + b \hookrightarrow 6 = -3 + b; 9 = b \\ \\ \boxed{\boxed{y = -3x + 9}}\)

I am joyous to assist you at any time.

Answer:

to much math

Step-by-step explanation:

Answer:

word form: three hundred twelve and fifty-four thousandths

3=hundreds place

1=tens place

2=ones place

0=tenths place

5=hundredths place

4=thousandths place

hope this helps

Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

Read more on function here: brainly.com/question/10687170

#SPJ1