solve 2cos^2x+3sinx=0

Answer:

x=2√2 is the answer

Step-by-step explanation:

x²=8

TAKING SQUARE ROOT ON BOTH SIDES

√x²=√8

x=√2×2×2

x=√2²×√2

x=2√2

i hope this will help you

Answer:

The value of x is -2.828 or 2.828

Step-by-step explanation:

In order to eliminate of square of x, you have to square root both sides :

[tex] {x}^{2} = 8[/tex]

[tex] \sqrt{ {x}^{2} } = ± \sqrt{8} [/tex]

[tex]x = \sqrt{8} \\ x = 2 \sqrt{2} \: or \: 2.828[/tex]

[tex]x = - \sqrt{8} \\ x = - 2 \sqrt{2} \: or \: - 2.828[/tex]

Answer:

  4.25

Step-by-step explanation:

The growth factor is 1 more than the growth rate. The growth rate is the rate of increase in a given time period.

  1 +325% = 1 +3.25 = 4.25

The growth factor is 4.25.

_____

The "increase" amount is what is added to the original. The growth factor is the multiplier of the original.

  x + 325%·x = x(1 +3.25) = 4.25x

Answer:

  B.  x > -5

Step-by-step explanation:

It seems you have a number x such that ...

 [tex]\dfrac{2}{5}(x-1)<\dfrac{3}{5}(x+1)\\\\2x-2<3x+3\qquad\text{multiply by 5, eliminate parentheses}\\\\-5<x\qquad\text{subtract $2x+3$}[/tex]

This matches choice B: x > -5.

Answer:

3.784

Step-by-step explanation:

Answer:

Step-by-step explanation:

The chi-square test is majorly used to test relationship/association between two categorical variables. The use of the chi square test is to ask the question: if there is a significant relationship between company A and B.

But this study only aims to compare company A and B cell phone service and not to establish a relationship between the two company's cell phone service

Answer:

Domain is x and Range is y

Step-by-step explanation:

Domain-(16,-15,22,-1,-6)

Range-(5,-17,-16,-4,-14)

Answer:

196x^2y

Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.

Answer:

There. You didn't ask for and explanation!

Step-by-step explanation:

The solution of expression is,

⇒ 343

We have to given that;

The expression is,

⇒ [tex]49^{\frac{3}{2} }[/tex]

Now, We can simplify with rational exponents as,

⇒ [tex]49^{\frac{3}{2} }[/tex]

⇒ [tex](7^2 )^{\frac{3}{2} }[/tex]

Apply rule of exponent as,

⇒ [tex]7^2^* ^{\frac{3}{2} }[/tex]

⇒ 7³

⇒ 7 × 7 × 7

⇒ 343

Thus, The solution of expression is,

⇒ 343

Learn more about the equation visit:

brainly.com/question/28871326

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Answer:

The length AD is approximately 48.3 m

Step-by-step explanation:

Notice that in triangle CBD, angle B can be found by subtracting [tex]96^o[/tex] and [tex]38^o[/tex] from [tex]180^o[/tex] (addition of all internal angles of a triangle must be [tex]180^o[/tex]):

[tex]180^o-96^o-38^o=46^o[/tex]

So we complete the value in the attached image

We go now into finding the length of the bottom side CD in the triangle CBD, by using the law of sines in that triangle:

[tex]\frac{CD}{sin(46^o)} =\frac{27.3}{sin(38^o)} \\CD=\frac{27.3\,*\,sin(46^o)}{sin(38^o)} \\CD=31.9\,\,m[/tex]

Now we use this value in the law of cosines for the larger triangle ADC, since we know two sides and the angle in between:

[tex]AD^2=AC^2+CD^2-2\,AC * CD * cos (96^o)\\AD^2=(5.8+27.3)^2+31.9^2-2*33.1*31.9*cos(98^o)\\AD^2=2334\\AD=48.3 \,\,m[/tex]

Answer:

[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]    

[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]    

So on this case the 95% confidence interval would be given by (155.301;159.299)    

And the best option would be:

B. (155.3, 159,3)

Step-by-step explanation:

Information given

[tex]\bar X=157.3[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma =15.6[/tex] represent the population standard deviation

n=234 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The Confidence level is is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]z_{\alpha/2}=1.96[/tex]

And replacing we got:

[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]    

[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]    

So on this case the 95% confidence interval would be given by (155.301;159.299)    

And the best option would be:

B. (155.3, 159,3)

Answer:

x=-4

Step-by-step explanation:

[tex]2x^2+8x=x^2-16[/tex]

Move everything to one side:

[tex]x^2+8x+16=0[/tex]

Factor:

[tex](x+4)^2=0[/tex]

By the zero product rule, x=-4. Hope this helps!

Answer:

x=-4

Step-by-step explanation:

Move everything to one side and combine like-terms

x²+8x+16

Factor

(x+4)²

x=-4

Answer:

13 students

Step-by-step explanation:

At least 30 and fewer than 67 makes it 30-66

So,

30-66 => 13 students

Answer:

16

Step-by-step explanation:

There are two columns in the diagram.

The column headed stem represents tens while the column headed leaf represents units. e.g. 2 3 = 23

So we just have to count how many of the numbers are less than 8 in the 6th Stem column and all the numbers below it, which are:

20, 23, 28, 31, 31, 34, 38, 40, 44, 50, 51, 53, 54, 65, 65, 66

Answer:

12,000

Step-by-step explanation:

The machine fills the containers at a rate of 50+5t milliliters (mL) per second.

Therefore, the rate of change of the number of containers, N is:

[tex]\dfrac{dN}{dt}=50+5t, 0\leq t\leq 60[/tex]

[tex]dN=(50+5t)dt\\$Taking integrals of both sides\\\int dN=\int (50+5t)dt\\N(t)=50t+\frac{5t^2}{2}+C $(C a constant of integration)\\\\When t=0, , No containers are filled, therefore:$ N(t)=0\\0=50(0)+\frac{5(0)^2}{2}+C\\C=0\\$Therefore, N(t)=50t+2.5t^2[/tex]

When t=60 seconds

[tex]N(60)=50(60)+2.5(60)^2\\N(60)=12000$ mL[/tex]

Therefore, 12,000 milliliters of acid solution are put into a container in 60 seconds.

Answer:

[tex]\boxed{\sf \ \ 9x^2-18x-7 \ \ divided \ by \ (3x+1) \ is \ (3x-7) \ }[/tex]

Step-by-step explanation:

Hello,

let's find a and b reals so that

[tex]9x^2-18x-7=(3x+1)(ax+b)[/tex]

[tex](3x+1)(ax+b)=3ax^2+(3b+a)x+b[/tex]

we identify the terms in [tex]x^2[/tex]

   9 = 3a

we identify the terms in x

   -18 = 3b + a

we identify the constant terms

   -7 = b

so ti goes with a = 9/3 = 3, b = -7

so we can write

[tex]9x^2-18x-7=(3x+1)(3x-7)[/tex]

so [tex]9x^2-18x-7 \ divided \ by \ (3x+1) \ is \ (3x-7)[/tex]

hope this helps

Answer:

Step-by-step explanation:

Hello!

Given the independent variable X and the dependent variable Y (see data in attachment)

The regression equation is

^Y= b₀ + bX

Where

b₀= estimation of the y-intercept

b= estimation of the slope

The formulas to manually calculate both estimations are:

[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]

[tex]b_0= \frac{}{y} - b*\frac{}{x}[/tex]

n=7

∑X= 42

∑X²= 292

∑Y= 49

∑Y²= 403

∑XY= 249

[tex]\frac{}{y} = \frac{sumY}{n} = \frac{49}{7} = 7[/tex]

[tex]\frac{}{x} = \frac{sumX}{n} = \frac{42}{7} = 6[/tex]

[tex]b= \frac{249-\frac{42*49}{7} }{292-\frac{42^2}{7} }= -1.13[/tex]

[tex]b_0= 7- (-1.13)*6= 13.75[/tex]

^Y= 13.75 - 1.13X

Using the raw data you can calculate the coefficient of determination as:

[tex]R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]}[/tex]

[tex]R^2= \frac{(-1.13)^2[292-\frac{(42)^2}{7} ]}{[403-\frac{(49)^2}{7} ]}= 0.84[/tex]

This means that 84% of the variability of the dependent variable Y is explained by the response variable X under the model ^Y= 13.75 - 1.13X

I hope this helps!

Answer:

a) Percentage of standardized test takers that scored 550 or less = 76.4%

b) Percentage of standardized test takers that scored 524 = 0.782%

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 514

Standard deviation = σ = 50

a) Percentage of standardized test takers scored 550 or less = P(x ≤ 550)

We first normalize or standardize 550

The standardized score for any is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (550 - 514)/50 = 0.72

To determine the required probability

P(x ≤ 550) = P(z ≤ 0.72)

We'll use data from the normal distribution table for these probabilities

P(x ≤ 550) = P(z ≤ 0.72) = 0.76424 = 76.424%

The normal curve for this question and the b part are sketched in the first attached image to this solution.

b) Percentage of standardized test takers that scored 524 = P(x = 524)

On standardizing,

z = (x - μ)/σ = (524 - 514)/50 = 0.20

For this part, since it's an exact probability, we will use the normal distribution formula

P(z = Z) = [1/(σ√2π)] × e^(-z²/2)

Since z = (x - μ)/σ

It can be written properly as presented in the second attached image to this question.

Putting x = 524 or z = 0.20 in this expression, we get

P(x = 524) = P(z = 0.20) = 0.0078208539 = 0.782%

Hope this Helps!!!

Answer:

Step-by-step explanation:

The required estimate is

90 woods saved by 10 new stoves adopted

Hence the required estimate is 9 woods saved per new stove adopted.

Data from the pilot study will enable this project to qualify for carbon credits if we are 90% confident that the data values from the pilot study fall within [8.1 - 9.9] woods saved per new stove adopted.

The lower and upper limits are derived from the margin of error, which is 10%.

9-0.9 = 8.1

9+0.9 = 9.9

On the other hand, if less than 90% of the values from the pilot study fall within this range, then the data from the study will no enable the project to qualify for carbon credits.

Answer:

[tex]\frac{x}{5} - 4[/tex]

Step-by-step explanation:

You are dividing x by 5 and then subtracting 4.

Answer:

x/5 - 4

Step-by-step explanation:

The quotient of a number x and 5 refers to division of both terms.

x/5

Four less than the quotient refers to subtraction.

x/5 - 4

Answer:

Step-by-step explanation:

According to the condition, your terms are arranged as

5, 7 , -7 ,-5, 5, 7, -7, 5, -5,...................

So one loop will have 4 terms: 5, 7, -7. -5

[tex]255 \div 4 = 63 R 3[/tex]

Hence after 63 loops, the new loop has only 3 terms. That means the last loop will be 5, 7 ,-7. In other words, the 255th term will  be -7

Answer:

(x-1) ( x -i) (x+i)

Step-by-step explanation:

x^3 -2x^2 +x-2

Factor by grouping

x^3 -2x^2      +x-2

x^2(x-2)      +1(x-2)

Factor out (x-2)

(x-2) (x^2+1)

Rewriting

(x-1) ( x^2 - (-1)^2)

(x-1) ( x -i) (x+i)

Answer:

Should be b

Step-by-step explanation:

Since it's a multiple choice question you know that -2 or 2 has to be a root for the cubic.

You can test both -2 and 2 and see that replacing x for 2 has the expression evaluate to 0.

Then, since you know the imaginary roots have to be conjugates, you get B.

Answer:

50,000

Step-by-step explanation:

ten thousand  thousand  hundreds   tens ones

4                            7                 5            9       2

When rounding to the ten thousands, we look at the thousands place

If it is 5 or higher we round the ten thousands place up

7 is five or higher so we round the 4 up one place  4 becomes 5 and the rest becomes 0

5 0 0 0 0

Answer:

$50,000

Step-by-step explanation:

=> $47,592

While rounding off to the nearest thousand, we check the thousands place. If the digit in the thousands place is greater than 5, 1 will be added to the T. Th. place while if its less than 5, there will be no change and The digits except the ten thousands place will all become zero.

So,

=> $50,000

Answer:

[tex] = \frac{3}{2} [/tex]

Step-by-step explanation:

[tex]y = mx + c[/tex]

Here,

In this equation ,

[tex]2y - 3x = 8[/tex]

to find the value of m or the value of slope we have to solve for y

Let's solve,

[tex]2y - 3x = 8 \\ 2y = 8 + 3x \\ \frac{2y}{2} = \frac{8 + 3x}{2} \\ y = 4 + \frac{3x}{2} \\ y = \frac{3x}{2} + 4[/tex]

So, the slope is,

[tex] = \frac{3}{2}[/tex]

Answer:

To find it's percentage divide $5.60 by

$17.50 and multiply it by 100%

That is

5.60/ 17.50 × 100%

= 32%

Hope this helps you

Answer:

The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]

Step-by-step explanation:

A nth order polynomial f(x) has roots [tex]x_{1}, x_{2}, ..., x_{n}[/tex] such that [tex]f(x) = (x - x_{1})*(x - x_{2})*...*(x - x_{n}}[/tex],

Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2?

So

[tex]x_{1} = x_{2} = \sqrt{3}[/tex]

[tex]x_{3} = -2[/tex]

Then

[tex](x - \sqrt{3})^{2}*(x - (-2)) = (x - \sqrt{3})^{2}*(x + 2) = (x^{2} -2x\sqrt{3} + 3)*(x + 2) = x^{3} + 2x^{2} - 2x^{2}\sqrt{3} - 4x\sqrt{3} + 3x + 6[/tex]

Since [tex]\sqrt{3} = 1.73[/tex]

[tex]x^{3} + 2x^{2} - 3.46x^{2} - 6.93x + 3x + 6 = x^{3} - 1.46x^{2} - 3.93x + 6[/tex]

The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]

Answer: 150

Step-by-step explanation:

How many months are in a year? 12.

The average rate per month is therefore 1800/12 = 150.

Hope that helped,

-sirswagger21

Answer:

  $96,000

Step-by-step explanation:

40% of $240,000 is ...

  0.40 × $240,000 = $96,000

The assessed value is $96,000.

Answer:

[tex]\boxed{\sf \ \ \ m = -\dfrac{tn}{t-s} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let s assume that m+n is different from 0

we have this equation and we need to find m as a function of t, s, and n

[tex]t=\dfrac{ms}{m+n}[/tex]

<=>

[tex](m+n)*t=ms\\\\<=> tm+tn=sm\\<=> (t-s)m = -tn\\<=> m = -\dfrac{tn}{t-s}[/tex]

for t-s different from 0, so t different from s

hope this helps

Answer: f(1/3)=1

Step-by-step explanation:

For this problem, all we have to do in plug in 1/3 into n.

f(1/3)=3(1/3)

f(1/3)=1

Answer:

Read below

Step-by-step explanation:

To copy a segment, you have to open your compass to the length of the given segment. The instructions say to have an endpoint at R, so, with the compass open to the length of the given line segment, place one end of the compass at R and draw an arc that intersects the line that R lies on. This new segment is congruent to the given segment.

I hope this helps!

Answer:

7x+ 4y +8

Step-by-step explanation:

12x -5x +4y +15-7

= 7x + 4y + 8

Answer:

Step-by-step explanation:

15 + 12x - 5x +4y - 7

= 15 - 7 + 12x - 5x + 4y

= 8 + 7x + 4y

= 7x + 4y + 8 ( rearranging the terms )

Hope this helps

Plz mark it as brainliest!!!!