How many solutions does the nonlinear system of equations graphed below
have?
A. One
B. Four
C. Two
D. Zero

Answer:

Step-by-step explanation:

From the picture attached,

m∠COB = 90° - m∠BOS

              = 90° - 40°

              = 50°

tan(30°) = [tex]\frac{AC}{OC}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{AC}{OC}[/tex]

AC = [tex]\frac{OC}{\sqrt{3}}[/tex]  ------(1)

Similarly, tan(50°) = [tex]\frac{BC}{OC}[/tex]

BC = OC[tan(50°)] -------(2)

Now AC + BC = 30 cm

By substituting the values of AC and BC from equation (1) and (2),

[tex]\frac{OC}{\sqrt{3}}+OC(\text{tan}50)=30[/tex]

(1.769)OC = 30

OC = 16.96

1). cos(30°) = [tex]\frac{OC}{AO}[/tex]

[tex]\frac{\sqrt{3}}{2}= \frac{16.96}{OA}[/tex]

[tex]OA=19.58[/tex] cm

Therefore, distance between the ship and town A is 19.58 cm.

2). cos(50°) = [tex]\frac{OC}{OB}[/tex]

0.6428 = [tex]\frac{16.96}{OB}[/tex]

OB = 26.38 cm

Therefore, distance between the ship and town B is 26.38 cm.

Answer:

ya the equation divides y as a function of x

Answer:

[tex]14x cos(\frac{1}{15}x^{2})=14 \sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]

Step-by-step explanation:

In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:

[tex]cos(x)=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{2k}}{(2k)!}[/tex]

So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: [tex]\frac{1}{15}x^{2}[/tex] so for

[tex]cos(\frac{1}{15}x^{2})[/tex]

the modified series will look like this:

[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15}x^{2})^{2k}}{(2k)!}[/tex]

So we can use some algebra to simplify the series:

[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15^{2k}}x^{4k})}{(2k)!}[/tex]

which can be rewritten like this:

[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]

So finally, we can multiply a 14x to the series so we get:

[tex]14xcos(\frac{1}{15}x^{2})=14x\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]

We can input the x into the series by using power rules so we get:

[tex]14xcos(\frac{1}{15}x^{2})=14\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]

And that will be our answer.

Answer:

[tex] \large{ \tt{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]

[tex] \large{ \tt{⇢m \: \angle \: GHI= m \: \angle \: GHQ + m \: \angle \: QHI}}[/tex]

[tex] \large{ \tt{➝14x + 6 = 3x - 3 + 130 \degree}}[/tex]

[tex] \large{ \tt{➝14x + 6 = 3x + 127}}[/tex]

[tex] \large{ \tt{➝ \: 14x - 3x = 127 - 6}}[/tex]

[tex] \large{ \tt{➝ \: 11x = 121}}[/tex]

[tex] \large{ \tt{➝ \: x = \frac{121}{11} }}[/tex]

[tex] \large{ \tt{➝ \: x = 11}}[/tex]

[tex] \large{ \tt{✣ \: REPLACING \: VALUE}} : [/tex]

[tex] \large{ \tt{✺ \: m \: \angle \: GHI = 14x + 6 = 14 \times 11 + 6 = \boxed{ \tt{160 \degree}}}}[/tex]

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

The cost of 16 onions is $ 1.20.

Step-by-step explanation:

To determine what is the cost, in dollars, of 16 onions if 3 onions weigh 1.5 lb and the price of onions is 33 cents per kilogram, the following calculation must be performed:

1.5 pounds = 0.68 kilos

0.68 / 3 = 0.22666 kilos each onion

16 x 0.22666 = 3.626 kilos

0.33 x 3.626 = 1.20

Therefore, the cost of 16 onions is $ 1.20.

Answer:

8 pairs of large glasses and 12 pairs of small ones

Step-by-step explanation:

Let's say the number of large frames she buys is l, and the number of small frames is s. She buys 20 frames of assorted sizes, but they can only be small or large. Therefore, s + l = 20.

Next, the total cost of large frames is 12 dollars for each frame. Therefore, the total cost for the large frames is equal to 12 * l. Similarly, the total cost for the small frames is equal to 5 * s. The total cost of all frames is equal to 156, so

12* l + 5 * s = 156

s + l = 20

In the second equation, we can subtract l from both sides to get

s = 20 - l

We can then plug that into the first equation to get

12 * l + 5 * (20-l) = 156

12 * l + 100 - 5*l = 156

subtract both sides by 100 to isolate the variable and its coefficient

12 * l  -  5 * l = 56

7 * l = 56

divide both sides by 7 to isolate the l

l = 8

The woman buys 8 pairs of large glasses. The number of small glasses is equal to 20-l=20-8=12

Answer:

y - 4 = ¼(x + 2)

Step-by-step explanation:

Point-slope form equation is given as y - b = m(x - a). Where,

(a, b) = a point on the line = (-2, 4)

m = slope = ¼ (sleep of the line perpendicular to y = -4x - 1 is the negative reciprocal of its slope value, -4 which is ¼)

✔️To write the equation, substitute (a, b) = (-2, 4), and m = ¼ into the point-slope equation, y - b = m(x - a).

y - 4 = ¼(x - (-2))

y - 4 = ¼(x + 2)

None of the options are correct

Answer:

Anything to the power of zero (with the exception of zero itself) is equal to one.

So 3⁰ = 1

Answer:

4+4+8+8+422+33+65520222222+222= 65,520,222,923

Answer:

-x-3y

Step-by-step explanation:

-5x+6y-9y+4x

-5x+4x+6y-9y

-x-3y

Answer:

Outlier therefore could only be values below  - 12.75

or could only be values above + 121.125

Step-by-step explanation:

0, 4, 6, 14, 17

inner quartile range of 0 - 17 is 1/2 of 17 subtracted from the higher number = 17 - 1/2 of 8.5 =  8.5 - 4.25 = 4.25 - 4.25 x 3

= 4.25 to 12.75 for inner quartile

inner quartile range is 12.75-4.25 = 8.5

We then 1.5 x 8.5 to show the outlier

= 12.75 meaning there is no outlier if is below.

Lower quartile fences  = 4.25 - 1.5 = 2.75

or -1.5 x 8.5 (the range) =   -12.75

Upper quartile fence = 12.75 + 1.5 = 14.25 x 8.5 =   121.125  this would be an outlier if it is 12.75 higher than 121.125 or 12.75 lower than 5.50.

Outlier therefore could only be values below  - 12.75

or could only be values above + 121.125

An observation is considered an outlier if it exceeds a distance of 1.5 times the interquartile range (IQR) below the lower quartile or above the upper quartile. The values of the lower quartile - 1.5 x IQR and upper quartile + 1.5 x IQR are known as the inner fences.

An observation is an outlier if it falls more than above the upper quartile or more than below the lower quartile. The minimum value is so there are no outliers in the low end of the distribution. The maximum value is so there are no outliers in the high end of the distribution.

Answer:

32

Step-by-step explanation:

18 : 6 = 3

therefore, x : 3 has to equal 3.

X : 3 = 3

X = 3 × 3

X = 9

To verify:

18 : 6 = 9 : 3

3 = 3

It's true that X = 9, so now just replace the X with 9 in the next equation

5 + 3(9) = 32

Answer:

32

Step-by-step explanation:

18 :  6 = x : 3

Product of means  =  Product of extremes

6 * x = 3*18

     x = [tex]\frac{3*18}{6}[/tex]

     x = 3*3

x = 9

Now plugin x = 9 in the expression

5 + 3x = 5 + 3*9

          = 5 + 27

          = 32

Answer:

Your answer is C. X = 29/8c

Step-by-step explanation:

2/3(cx + 1/2) - 1/4 = 5/2

2cx/3+1/3-1/4=5/2

2cx3+1/12=5/2

2cx/3=5/2-1/12

2cx/3=29/12

(3)2cx/3=29/12(3)

2cx= 31/4

(2c)2cx=29/4(2c)

X=29/8c

Your answer is C. X = 29/8c

Answer:

See below

Step-by-step explanation:

Given :-

To Prove :-

Proof :-

Here we are required to prove that ,

[tex]\rm\implies m\angle 5 + m\angle 6 + m\angle 2 = 180^o [/tex]

And here it's given that , y || z . Therefore ,

Now we know that the measure of a straight line is 180°. Therefore ,

[tex]\rm\implies m\angle 1 + m\angle 2 + m\angle 3 = 180^o \\\\\implies\boxed{\rm m\angle 5 + m\angle 6 + m\angle 2 = 180^o} [/tex]

Hence Proved !

Answer:

Step-by-step explanation:

012345678910

'yl\f[pt;]p;d[k;ell-=;q'[;

Answer:

see explanation

Step-by-step explanation:

Assuming you mean

secθ × [tex]\sqrt{1-cos^20}[/tex]

= [tex]\frac{1}{cos0}[/tex] × sinθ [ sin²θ + cos²θ = 1 , so sinθ = [tex]\sqrt{1-cos^20}[/tex] ]

= [tex]\frac{sin0}{cos0}[/tex]

= tanθ

= right side , thus verified

Answer:

4/3

Step-by-step explanation:

Substitute in 4.

(1/3)4

Multiply

4/3

I hope this helps!

Answer:

There is no conversion necessary. It's a 1 to 1 ratio.

ml = [tex]cm^{3}[/tex]

so, 9ml is 9[tex]cm^{3}[/tex]

Answer:

9ml = 9cm³

Step-by-step explanation:

1ml = 1cm³

Therefore,

9ml = 9cm³

Answer:

Step-by-step explanation:

Answer:

(110.295, 122.093).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 12 - 1 = 11

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7959

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.7959\frac{11.3781}{\sqrt{12}} = 5.899[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 116.194 - 5.899 = 110.295

The upper end of the interval is the sample mean added to M. So it is 116.194 + 5.899 = 122.093

So

(110.295, 122.093).

Answer:

See attachment showing the rise and run

Slope = 1

Step-by-step explanation:

In the diagram attached below, the rise is represented by the blue line, while the run is represented by the red line.

Rise = 4 units

Run = 4 units

It's a positive slope because the line slopes upwards from left to right

Slope = rise/run = 4/4

Slope = 1

9514 1404 393

Answer:

Step-by-step explanation:

The graph shows the function value is zero for x=5 and x=7. These are the elements of the solution set.

  x ∈ {5, 7}

__

The graph is below the x-axis between these points, so that is the region where f(x) < 0

  5 < x < 7 . . . . . for f(x) < 0

In interval notation: (5, 7).

Answer:

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.

This means that [tex]\mu = 192723, \sigma = 42000[/tex]

Sample of 75:

This means that [tex]n = 75, s = \frac{42000}{\sqrt{75}}[/tex]

What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?

1 subtracted by the p-value of Z when X = 190000. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{190000 - 192723}{\frac{42000}{\sqrt{75}}}[/tex]

[tex]Z = -0.56[/tex]

[tex]Z = -0.56[/tex] has a p-value of 0.2877

1 - 0.2877 = 0.7123

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

Answer:

[tex]6x+3+69=180[/tex]

[tex]6x=180-72[/tex]

[tex]6x=108[/tex]

[tex]x=18[/tex]

--------------------------

hope it helps..

have a great day!!

Answer:

Option A, 4rad5

Step-by-step explanation:

x² = 5*(5+11)

x² = 5*16

x² = 80

x = 4√5

Answered by GAUTHMATH

Well formatted distribution table is attached below :

Answer:

7%

Step-by-step explanation:

The probability that a customer ordered a small Given that he or she ordered a hot drink ;

This is a conditional probability and will be represented as :

Let :

P(small drink) = P(S)

P(hot drink) = P(H)

Hence, the conditional probability is written as :

P(S|H) = P(SnH) / P(H) = 5 / (5+48+22) = 5/75 = 0.0666 = 0.0666 * 100% = 6.67%

Answer:

y - 1 = -6(x - 1)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 1)

Slope m = -6

Step 2: Find Equation

Answer:

0.001831055

Step-by-step explanation:

Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 14

As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 14)

P(x =14) = 16C14 * 0.5^14 *(1-0.5)^2

               = 120 * 0.5^14 *(1-0.5)^2

= 0.001831055